LMFDB - Embedded newform 441.2.h.h.373.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.6
Character	$\chi$	$=$	441.373
Dual form			441.2.h.h.214.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.10281 q^{2} +(1.22001 + 1.22947i) q^{3} -0.783802 q^{4} +(0.0527330 + 0.0913363i) q^{5} +(-1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-0.0231690 + 2.99991i) q^{9} +O(q^{10})$	\(q-1.10281 q^{2} +(1.22001 + 1.22947i) q^{3} -0.783802 q^{4} +(0.0527330 + 0.0913363i) q^{5} +(-1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-0.0231690 + 2.99991i) q^{9} +(-0.0581547 - 0.100727i) q^{10} +(-1.66866 + 2.89020i) q^{11} +(-0.956244 - 0.963657i) q^{12} +(1.23997 - 2.14770i) q^{13} +(-0.0479602 + 0.176264i) q^{15} -1.81805 q^{16} +(0.806594 + 1.39706i) q^{17} +(0.0255511 - 3.30834i) q^{18} +(-3.84133 + 6.65338i) q^{19} +(-0.0413323 - 0.0715896i) q^{20} +(1.84022 - 3.18735i) q^{22} +(0.948593 + 1.64301i) q^{23} +(3.74544 + 3.77448i) q^{24} +(2.49444 - 4.32049i) q^{25} +(-1.36746 + 2.36851i) q^{26} +(-3.71655 + 3.63142i) q^{27} +(4.64521 + 8.04574i) q^{29} +(0.0528911 - 0.194387i) q^{30} -9.26162 q^{31} -4.13506 q^{32} +(-5.58917 + 1.47451i) q^{33} +(-0.889523 - 1.54070i) q^{34} +(0.0181599 - 2.35134i) q^{36} +(0.991268 - 1.71693i) q^{37} +(4.23627 - 7.33744i) q^{38} +(4.15329 - 1.09570i) q^{39} +(0.161891 + 0.280404i) q^{40} +(-3.74268 + 6.48252i) q^{41} +(-3.77388 - 6.53655i) q^{43} +(1.30790 - 2.26534i) q^{44} +(-0.275223 + 0.156078i) q^{45} +(-1.04612 - 1.81194i) q^{46} +3.19560 q^{47} +(-2.21803 - 2.23523i) q^{48} +(-2.75090 + 4.76470i) q^{50} +(-0.733589 + 2.69610i) q^{51} +(-0.971894 + 1.68337i) q^{52} +(4.98839 + 8.64015i) q^{53} +(4.09866 - 4.00478i) q^{54} -0.351974 q^{55} +(-12.8665 + 3.39438i) q^{57} +(-5.12280 - 8.87296i) q^{58} -4.45986 q^{59} +(0.0375913 - 0.138156i) q^{60} +5.67100 q^{61} +10.2138 q^{62} +8.19630 q^{64} +0.261550 q^{65} +(6.16381 - 1.62610i) q^{66} +9.97141 q^{67} +(-0.632210 - 1.09502i) q^{68} +(-0.862736 + 3.17075i) q^{69} +3.29042 q^{71} +(-0.0711292 + 9.20977i) q^{72} +(-2.36189 - 4.09091i) q^{73} +(-1.09318 + 1.89345i) q^{74} +(8.35513 - 2.20421i) q^{75} +(3.01084 - 5.21493i) q^{76} +(-4.58031 + 1.20835i) q^{78} +7.69409 q^{79} +(-0.0958713 - 0.166054i) q^{80} +(-8.99893 - 0.139010i) q^{81} +(4.12748 - 7.14901i) q^{82} +(0.584428 + 1.01226i) q^{83} +(-0.0850683 + 0.147343i) q^{85} +(4.16189 + 7.20860i) q^{86} +(-4.22477 + 15.5270i) q^{87} +(-5.12280 + 8.87296i) q^{88} +(3.01477 - 5.22173i) q^{89} +(0.303519 - 0.172125i) q^{90} +(-0.743509 - 1.28780i) q^{92} +(-11.2992 - 11.3868i) q^{93} -3.52415 q^{94} -0.810260 q^{95} +(-5.04480 - 5.08391i) q^{96} +(1.90127 + 3.29310i) q^{97} +(-8.63168 - 5.07279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} + 64 q^{51} + 32 q^{53} - 12 q^{57} + 32 q^{60} + 96 q^{64} - 120 q^{65} + 24 q^{67} - 112 q^{71} + 68 q^{74} - 60 q^{78} - 24 q^{79} - 40 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 32 q^{93} - 128 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9 + 20 * q^11 + 4 * q^15 + 24 * q^16 - 32 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 - 84 * q^30 - 96 * q^32 - 4 * q^36 - 12 * q^37 + 8 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 + 64 * q^51 + 32 * q^53 - 12 * q^57 + 32 * q^60 + 96 * q^64 - 120 * q^65 + 24 * q^67 - 112 * q^71 + 68 * q^74 - 60 * q^78 - 24 * q^79 - 40 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 32 * q^93 - 128 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.10281			−0.779807			−0.389903	−	0.920856i	$-0.627492\pi$
$2$	−1.10281			−0.779807			−0.389903	+	0.920856i	$0.627492\pi$
$3$	1.22001	+	1.22947i	0.704371	+	0.709832i
$3$	1.22001	+	1.22947i	0.704371	+	0.709832i
$4$	−0.783802			−0.391901
$5$	0.0527330	+	0.0913363i	0.0235829	+	0.0408468i	0.877576	−	0.479438i	$-0.159159\pi$
$5$	0.0527330	+	0.0913363i	0.0235829	+	0.0408468i	−0.853993	+	0.520284i	$0.825826\pi$
$6$	−1.34544	−	1.35587i	−0.549273	−	0.553532i
$7$		0			0
$7$		0			0
$8$	3.07001			1.08541
$9$	−0.0231690	+	2.99991i	−0.00772300	+	0.999970i
$10$	−0.0581547	−	0.100727i	−0.0183901	−	0.0318527i
$11$	−1.66866	+	2.89020i	−0.503119	+	0.871428i	0.496874	+	0.867822i	$0.334481\pi$
$11$	−1.66866	+	2.89020i	−0.503119	+	0.871428i	−0.999994	+	0.00360543i	$0.998852\pi$
$12$	−0.956244	−	0.963657i	−0.276044	−	0.278184i
$13$	1.23997	−	2.14770i	0.343907	−	0.595664i	−0.641248	−	0.767334i	$-0.721583\pi$
$13$	1.23997	−	2.14770i	0.343907	−	0.595664i	0.985155	+	0.171670i	$0.0549162\pi$
$14$		0			0
$15$	−0.0479602	+	0.176264i	−0.0123833	+	0.0455113i
$16$	−1.81805			−0.454512
$17$	0.806594	+	1.39706i	0.195628	+	0.338837i	0.947106	−	0.320921i	$-0.103992\pi$
$17$	0.806594	+	1.39706i	0.195628	+	0.338837i	−0.751478	+	0.659758i	$0.770659\pi$
$18$	0.0255511	−	3.30834i	0.00602245	−	0.779784i
$19$	−3.84133	+	6.65338i	−0.881262	+	1.52639i	−0.0313221	+	0.999509i	$0.509972\pi$
$19$	−3.84133	+	6.65338i	−0.881262	+	1.52639i	−0.849939	+	0.526880i	$0.823362\pi$
$20$	−0.0413323	−	0.0715896i	−0.00924218	−	0.0160079i
$21$		0			0
$22$	1.84022	−	3.18735i	0.392336	−	0.679546i
$23$	0.948593	+	1.64301i	0.197795	+	0.342592i	0.947813	−	0.318826i	$-0.103289\pi$
$23$	0.948593	+	1.64301i	0.197795	+	0.342592i	−0.750018	+	0.661417i	$0.769955\pi$
$24$	3.74544	+	3.77448i	0.764534	+	0.770462i
$25$	2.49444	−	4.32049i	0.498888	−	0.864099i
$26$	−1.36746	+	2.36851i	−0.268181	+	0.464503i
$27$	−3.71655	+	3.63142i	−0.715251	+	0.698868i
$28$		0			0
$29$	4.64521	+	8.04574i	0.862594	+	1.49406i	0.869416	+	0.494080i	$0.164495\pi$
$29$	4.64521	+	8.04574i	0.862594	+	1.49406i	−0.00682200	+	0.999977i	$0.502172\pi$
$30$	0.0528911	−	0.194387i	0.00965655	−	0.0354900i
$31$	−9.26162			−1.66344			−0.831718	−	0.555199i	$-0.812642\pi$
$31$	−9.26162			−1.66344			−0.831718	+	0.555199i	$0.812642\pi$
$32$	−4.13506			−0.730982
$33$	−5.58917	+	1.47451i	−0.972950	+	0.256678i
$34$	−0.889523	−	1.54070i	−0.152552	−	0.264228i
$35$		0			0
$36$	0.0181599	−	2.35134i	0.00302665	−	0.391889i
$37$	0.991268	−	1.71693i	0.162963	−	0.282261i	−0.772967	−	0.634447i	$-0.781228\pi$
$37$	0.991268	−	1.71693i	0.162963	−	0.282261i	0.935930	+	0.352186i	$0.114561\pi$
$38$	4.23627	−	7.33744i	0.687214	−	1.19029i
$39$	4.15329	−	1.09570i	0.665059	−	0.175452i
$40$	0.161891	+	0.280404i	0.0255973	+	0.0443357i
$41$	−3.74268	+	6.48252i	−0.584509	+	1.01240i	0.410427	+	0.911893i	$0.365379\pi$
$41$	−3.74268	+	6.48252i	−0.584509	+	1.01240i	−0.994936	+	0.100506i	$0.967954\pi$
$42$		0			0
$43$	−3.77388	−	6.53655i	−0.575512	−	0.996815i	−0.995986	−	0.0895108i	$-0.971470\pi$
$43$	−3.77388	−	6.53655i	−0.575512	−	0.996815i	0.420474	−	0.907304i	$-0.361864\pi$
$44$	1.30790	−	2.26534i	0.197173	−	0.341514i
$45$	−0.275223	+	0.156078i	−0.0410278	+	0.0232668i
$46$	−1.04612	−	1.81194i	−0.154242	−	0.267155i
$47$	3.19560			0.466127			0.233063	−	0.972462i	$-0.425125\pi$
$47$	3.19560			0.466127			0.233063	+	0.972462i	$0.425125\pi$
$48$	−2.21803	−	2.23523i	−0.320145	−	0.322627i
$49$		0			0
$50$	−2.75090	+	4.76470i	−0.389036	+	0.673830i
$51$	−0.733589	+	2.69610i	−0.102723	+	0.377530i
$52$	−0.971894	+	1.68337i	−0.134777	+	0.233441i
$53$	4.98839	+	8.64015i	0.685209	+	1.18682i	0.973371	+	0.229234i	$0.0736223\pi$
$53$	4.98839	+	8.64015i	0.685209	+	1.18682i	−0.288163	+	0.957581i	$0.593044\pi$
$54$	4.09866	−	4.00478i	0.557757	−	0.544982i
$55$	−0.351974			−0.0474601
$56$		0			0
$57$	−12.8665	+	3.39438i	−1.70422	+	0.449597i
$58$	−5.12280	−	8.87296i	−0.672657	−	1.16508i
$59$	−4.45986			−0.580625			−0.290312	−	0.956932i	$-0.593759\pi$
$59$	−4.45986			−0.580625			−0.290312	+	0.956932i	$0.593759\pi$
$60$	0.0375913	−	0.138156i	0.00485301	−	0.0178359i
$61$	5.67100			0.726097			0.363048	−	0.931770i	$-0.381736\pi$
$61$	5.67100			0.726097			0.363048	+	0.931770i	$0.381736\pi$
$62$	10.2138			1.29716
$63$		0			0
$64$	8.19630			1.02454
$65$	0.261550			0.0324413
$66$	6.16381	−	1.62610i	0.758713	−	0.200160i
$67$	9.97141			1.21820			0.609101	−	0.793093i	$-0.291530\pi$
$67$	9.97141			1.21820			0.609101	+	0.793093i	$0.291530\pi$
$68$	−0.632210	−	1.09502i	−0.0766667	−	0.132791i
$69$	−0.862736	+	3.17075i	−0.103861	+	0.381713i
$70$		0			0
$71$	3.29042			0.390502			0.195251	−	0.980753i	$-0.437448\pi$
$71$	3.29042			0.390502			0.195251	+	0.980753i	$0.437448\pi$
$72$	−0.0711292	+	9.20977i	−0.00838265	+	1.08538i
$73$	−2.36189	−	4.09091i	−0.276438	−	0.478805i	0.694059	−	0.719919i	$-0.255821\pi$
$73$	−2.36189	−	4.09091i	−0.276438	−	0.478805i	−0.970497	+	0.241113i	$0.922488\pi$
$74$	−1.09318	+	1.89345i	−0.127080	+	0.220109i
$75$	8.35513	−	2.20421i	0.964767	−	0.254520i
$76$	3.01084	−	5.21493i	0.345367	−	0.598194i
$77$		0			0
$78$	−4.58031	+	1.20835i	−0.518618	+	0.136819i
$79$	7.69409			0.865653			0.432827	−	0.901477i	$-0.357516\pi$
$79$	7.69409			0.865653			0.432827	+	0.901477i	$0.357516\pi$
$80$	−0.0958713	−	0.166054i	−0.0107187	−	0.0185654i
$81$	−8.99893	−	0.139010i	−0.999881	−	0.0154455i
$82$	4.12748	−	7.14901i	0.455804	−	0.789476i
$83$	0.584428	+	1.01226i	0.0641493	+	0.111110i	0.896316	−	0.443415i	$-0.146233\pi$
$83$	0.584428	+	1.01226i	0.0641493	+	0.111110i	−0.832167	+	0.554525i	$0.812900\pi$
$84$		0			0
$85$	−0.0850683	+	0.147343i	−0.00922695	+	0.0159815i
$86$	4.16189	+	7.20860i	0.448788	+	0.777323i
$87$	−4.22477	+	15.5270i	−0.452943	+	1.66467i
$88$	−5.12280	+	8.87296i	−0.546093	+	0.945860i
$89$	3.01477	−	5.22173i	0.319565	−	0.553503i	−0.660832	−	0.750534i	$-0.729797\pi$
$89$	3.01477	−	5.22173i	0.319565	−	0.553503i	0.980397	+	0.197031i	$0.0631299\pi$
$90$	0.303519	−	0.172125i	0.0319937	−	0.0181436i
$91$		0			0
$92$	−0.743509	−	1.28780i	−0.0775162	−	0.134262i
$93$	−11.2992	−	11.3868i	−1.17168	−	1.18076i
$94$	−3.52415			−0.363489
$95$	−0.810260			−0.0831309
$96$	−5.04480	−	5.08391i	−0.514883	−	0.518875i
$97$	1.90127	+	3.29310i	0.193045	+	0.334364i	0.946258	−	0.323413i	$-0.104830\pi$
$97$	1.90127	+	3.29310i	0.193045	+	0.334364i	−0.753213	+	0.657777i	$0.771497\pi$
$98$		0			0
$99$	−8.63168	−	5.07279i	−0.867516	−	0.509834i
$100$	−1.95515	+	3.38641i	−0.195515	+	0.338641i
$101$	8.73512	−	15.1297i	0.869177	−	1.50546i	0.00633771	−	0.999980i	$-0.497983\pi$
$101$	8.73512	−	15.1297i	0.869177	−	1.50546i	0.862839	−	0.505479i	$-0.168684\pi$
$102$	0.809012	−	2.97330i	0.0801041	−	0.294400i
$103$	−4.36602	−	7.56217i	−0.430197	−	0.745123i	0.566693	−	0.823929i	$-0.308223\pi$
$103$	−4.36602	−	7.56217i	−0.430197	−	0.745123i	−0.996890	+	0.0788062i	$0.974889\pi$
$104$	3.80674	−	6.59346i	0.373281	−	0.646542i
$105$		0			0
$106$	−5.50127	−	9.52848i	−0.534330	−	0.925487i
$107$	9.07316	−	15.7152i	0.877135	−	1.51924i	0.0226645	−	0.999743i	$-0.492785\pi$
$107$	9.07316	−	15.7152i	0.877135	−	1.51924i	0.854471	−	0.519500i	$-0.173882\pi$
$108$	2.91304	−	2.84632i	0.280308	−	0.273887i
$109$	2.11124	+	3.65678i	0.202220	+	0.350256i	0.949243	−	0.314542i	$-0.101851\pi$
$109$	2.11124	+	3.65678i	0.202220	+	0.350256i	−0.747023	+	0.664798i	$0.768518\pi$
$110$	0.388161			0.0370097
$111$	3.32025	−	0.875932i	0.315145	−	0.0831398i
$112$		0			0
$113$	1.02824	−	1.78096i	0.0967285	−	0.167539i	−0.813600	−	0.581425i	$-0.802495\pi$
$113$	1.02824	−	1.78096i	0.0967285	−	0.167539i	0.910329	+	0.413886i	$0.135829\pi$
$114$	14.1894	−	3.74337i	1.32896	−	0.350599i
$115$	−0.100044	+	0.173282i	−0.00932919	+	0.0161586i
$116$	−3.64093	−	6.30627i	−0.338052	−	0.585523i
$117$	6.41417	+	3.76957i	0.592990	+	0.348497i
$118$	4.91840			0.452775
$119$		0			0
$120$	−0.147238	+	0.541134i	−0.0134410	+	0.0493986i
$121$	−0.0688352	−	0.119226i	−0.00625774	−	0.0108387i
$122$	−6.25405			−0.566215
$123$	−12.5361	+	3.30721i	−1.13034	+	0.298201i
$124$	7.25928			0.651902
$125$	1.05349			0.0942268
$126$		0			0
$127$	0.317159			0.0281433			0.0140717	−	0.999901i	$-0.495521\pi$
$127$	0.317159			0.0281433			0.0140717	+	0.999901i	$0.495521\pi$
$128$	−0.768871			−0.0679592
$129$	3.43231	−	12.6145i	0.302198	−	1.11064i
$130$	−0.288441			−0.0252980
$131$	−7.47816	−	12.9525i	−0.653370	−	1.13167i	−0.982300	−	0.187315i	$-0.940021\pi$
$131$	−7.47816	−	12.9525i	−0.653370	−	1.13167i	0.328930	−	0.944354i	$-0.393312\pi$
$132$	4.38081	−	1.15572i	0.381300	−	0.100593i
$133$		0			0
$134$	−10.9966			−0.949962
$135$	−0.527666	−	0.147960i	−0.0454143	−	0.0127344i
$136$	2.47625	+	4.28900i	0.212337	+	0.367779i
$137$	7.62367	−	13.2046i	0.651334	−	1.12814i	−0.331466	−	0.943467i	$-0.607543\pi$
$137$	7.62367	−	13.2046i	0.651334	−	1.12814i	0.982799	−	0.184676i	$-0.0591235\pi$
$138$	0.951437	−	3.49674i	0.0809917	−	0.297663i
$139$	4.05943	−	7.03114i	0.344316	−	0.596374i	−0.640913	−	0.767614i	$-0.721444\pi$
$139$	4.05943	−	7.03114i	0.344316	−	0.596374i	0.985229	+	0.171240i	$0.0547774\pi$
$140$		0			0
$141$	3.89866	+	3.92888i	0.328326	+	0.330872i
$142$	−3.62872			−0.304516
$143$	4.13818	+	7.16754i	0.346052	+	0.599380i
$144$	0.0421224	−	5.45399i	0.00351020	−	0.454499i
$145$	−0.489912	+	0.848553i	−0.0406850	+	0.0704685i
$146$	2.60473	+	4.51152i	0.215569	+	0.373376i
$147$		0			0
$148$	−0.776958	+	1.34573i	−0.0638656	+	0.110618i
$149$	5.57430	+	9.65497i	0.456664	+	0.790966i	0.998782	−	0.0493365i	$-0.0157107\pi$
$149$	5.57430	+	9.65497i	0.456664	+	0.790966i	−0.542118	+	0.840303i	$0.682377\pi$
$150$	−9.21415	+	2.43083i	−0.752332	+	0.198476i
$151$	5.63676	−	9.76315i	0.458713	−	0.794514i	−0.540180	−	0.841549i	$-0.681644\pi$
$151$	5.63676	−	9.76315i	0.458713	−	0.794514i	0.998893	+	0.0470354i	$0.0149774\pi$
$152$	−11.7929	+	20.4260i	−0.956534	+	1.65677i
$153$	−4.20975	+	2.38734i	−0.340338	+	0.193005i
$154$		0			0
$155$	−0.488393	−	0.845922i	−0.0392287	−	0.0679461i
$156$	−3.25536	+	0.858812i	−0.260637	+	0.0687600i
$157$	12.2064			0.974173			0.487087	−	0.873354i	$-0.338060\pi$
$157$	12.2064			0.974173			0.487087	+	0.873354i	$0.338060\pi$
$158$	−8.48515			−0.675042
$159$	−4.53689	+	16.6741i	−0.359799	+	1.32234i
$160$	−0.218054	−	0.377681i	−0.0172387	−	0.0298583i
$161$		0			0
$162$	9.92414	+	0.153302i	0.779714	+	0.0120445i
$163$	−4.48132	+	7.76187i	−0.351004	+	0.607957i	−0.986426	−	0.164209i	$-0.947493\pi$
$163$	−4.48132	+	7.76187i	−0.351004	+	0.607957i	0.635422	+	0.772165i	$0.280826\pi$
$164$	2.93352	−	5.08101i	0.229070	−	0.396760i
$165$	−0.429410	−	0.432739i	−0.0334295	−	0.0336887i
$166$	−0.644515	−	1.11633i	−0.0500240	−	0.0866442i
$167$	−8.70833	+	15.0833i	−0.673871	+	1.16718i	0.302927	+	0.953014i	$0.402036\pi$
$167$	−8.70833	+	15.0833i	−0.673871	+	1.16718i	−0.976798	+	0.214165i	$0.931297\pi$
$168$		0			0
$169$	3.42493	+	5.93216i	0.263456	+	0.456320i
$170$	0.0938145	−	0.162491i	0.00719524	−	0.0124625i
$171$	−19.8705	−	11.6778i	−1.51954	−	0.893024i
$172$	2.95798	+	5.12337i	0.225544	+	0.390653i
$173$	2.82933			0.215110			0.107555	−	0.994199i	$-0.465698\pi$
$173$	2.82933			0.215110			0.107555	+	0.994199i	$0.465698\pi$
$174$	4.65914	−	17.1234i	0.353208	−	1.29812i
$175$		0			0
$176$	3.03370	−	5.25453i	0.228674	−	0.396075i
$177$	−5.44106	−	5.48325i	−0.408975	−	0.412146i
$178$	−3.32473	+	5.75860i	−0.249199	+	0.431625i
$179$	5.08135	+	8.80115i	0.379798	+	0.657829i	0.991033	−	0.133620i	$-0.0426603\pi$
$179$	5.08135	+	8.80115i	0.379798	+	0.657829i	−0.611235	+	0.791449i	$0.709327\pi$
$180$	0.215720	−	0.122334i	0.0160788	−	0.00911827i
$181$	−17.0870			−1.27006			−0.635032	−	0.772486i	$-0.719013\pi$
$181$	−17.0870			−1.27006			−0.635032	+	0.772486i	$0.719013\pi$
$182$		0			0
$183$	6.91865	+	6.97229i	0.511441	+	0.515407i
$184$	2.91220	+	5.04407i	0.214690	+	0.371854i
$185$	0.209090			0.0153726
$186$	12.4609	+	12.5576i	0.913681	+	0.920765i
$187$	−5.38371			−0.393696
$188$	−2.50472			−0.182676
$189$		0			0
$190$	0.893566			0.0648261
$191$	−22.4000			−1.62081			−0.810404	−	0.585872i	$-0.800752\pi$
$191$	−22.4000			−1.62081			−0.810404	+	0.585872i	$0.800752\pi$
$192$	9.99954	+	10.0771i	0.721654	+	0.727249i
$193$	−0.256786			−0.0184839			−0.00924194	−	0.999957i	$-0.502942\pi$
$193$	−0.256786			−0.0184839			−0.00924194	+	0.999957i	$0.502942\pi$
$194$	−2.09675	−	3.63168i	−0.150538	−	0.260739i
$195$	0.319093	+	0.321567i	0.0228507	+	0.0230279i
$196$		0			0
$197$	−0.763370			−0.0543878			−0.0271939	−	0.999630i	$-0.508657\pi$
$197$	−0.763370			−0.0543878			−0.0271939	+	0.999630i	$0.508657\pi$
$198$	9.51913	+	5.59434i	0.676495	+	0.397572i
$199$	2.51561	+	4.35716i	0.178327	+	0.308871i	0.941307	−	0.337550i	$-0.109598\pi$
$199$	2.51561	+	4.35716i	0.178327	+	0.308871i	−0.762981	+	0.646421i	$0.776265\pi$
$200$	7.65796	−	13.2640i	0.541500	−	0.937905i
$201$	12.1652	+	12.2595i	0.858066	+	0.864719i
$202$	−9.63321	+	16.6852i	−0.677790	+	1.17397i
$203$		0			0
$204$	0.574988	−	2.11321i	0.0402572	−	0.147954i
$205$	−0.789452			−0.0551377
$206$	4.81491	+	8.33966i	0.335470	+	0.581052i
$207$	−4.95087	+	2.80763i	−0.344109	+	0.195144i
$208$	−2.25433	+	3.90462i	−0.156310	+	0.270737i
$209$	−12.8197	−	22.2044i	−0.886759	−	1.53591i
$210$		0			0
$211$	−3.60537	+	6.24468i	−0.248204	+	0.429901i	−0.963027	−	0.269403i	$-0.913174\pi$
$211$	−3.60537	+	6.24468i	−0.248204	+	0.429901i	0.714824	+	0.699305i	$0.246507\pi$
$212$	−3.90991	−	6.77217i	−0.268534	−	0.465114i
$213$	4.01434	+	4.04546i	0.275058	+	0.277190i
$214$	−10.0060	+	17.3309i	−0.683996	+	1.18472i
$215$	0.398017	−	0.689385i	0.0271445	−	0.0470157i
$216$	−11.4099	+	11.1485i	−0.776343	+	0.758561i
$217$		0			0
$218$	−2.32831	−	4.03274i	−0.157693	−	0.273132i
$219$	2.14812	−	7.89480i	0.145156	−	0.533481i
$220$	0.275878			0.0185997
$221$	4.00062			0.269111
$222$	−3.66162	+	0.965990i	−0.245752	+	0.0648330i
$223$	5.59106	+	9.68400i	0.374405	+	0.648488i	0.990238	−	0.139388i	$-0.0445137\pi$
$223$	5.59106	+	9.68400i	0.374405	+	0.648488i	−0.615833	+	0.787877i	$0.711180\pi$
$224$		0			0
$225$	12.9033	+	7.58319i	0.860220	+	0.505546i
$226$	−1.13395	+	1.96407i	−0.0754295	+	0.130648i
$227$	−11.8853	+	20.5860i	−0.788857	+	1.36634i	0.137811	+	0.990459i	$0.455993\pi$
$227$	−11.8853	+	20.5860i	−0.788857	+	1.36634i	−0.926668	+	0.375881i	$0.877340\pi$
$228$	10.0848	−	2.66052i	0.667884	−	0.176198i
$229$	0.952737	+	1.65019i	0.0629586	+	0.109048i	0.895787	−	0.444484i	$-0.146613\pi$
$229$	0.952737	+	1.65019i	0.0629586	+	0.109048i	−0.832828	+	0.553532i	$0.813280\pi$
$230$	0.110330	−	0.191098i	0.00727497	−	0.0126006i
$231$		0			0
$232$	14.2609	+	24.7006i	0.936272	+	1.62167i
$233$	−3.27092	+	5.66540i	−0.214285	+	0.371153i	−0.953051	−	0.302809i	$-0.902075\pi$
$233$	−3.27092	+	5.66540i	−0.214285	+	0.371153i	0.738766	+	0.673962i	$0.235409\pi$
$234$	−7.07363	−	4.15713i	−0.462418	−	0.271760i
$235$	0.168514	+	0.291875i	0.0109926	+	0.0190398i
$236$	3.49565			0.227547
$237$	9.38684	+	9.45962i	0.609741	+	0.614468i
$238$		0			0
$239$	10.6735	−	18.4870i	0.690409	−	1.19582i	−0.281295	−	0.959621i	$-0.590764\pi$
$239$	10.6735	−	18.4870i	0.690409	−	1.19582i	0.971704	−	0.236202i	$-0.0759028\pi$
$240$	0.0871940	−	0.320457i	0.00562835	−	0.0206854i
$241$	10.0331	−	17.3778i	0.646288	−	1.11940i	−0.337715	−	0.941248i	$-0.609654\pi$
$241$	10.0331	−	17.3778i	0.646288	−	1.11940i	0.984003	−	0.178155i	$-0.0570127\pi$
$242$	0.0759124	+	0.131484i	0.00487983	+	0.00845212i
$243$	−10.8078	−	11.2335i	−0.693323	−	0.720627i
$244$	−4.44494			−0.284558
$245$		0			0
$246$	13.8250	−	3.64724i	0.881451	−	0.232540i
$247$	9.52629	+	16.5000i	0.606144	+	1.04987i
$248$	−28.4333			−1.80552
$249$	−0.531531	+	1.95349i	−0.0336844	+	0.123798i
$250$	−1.16180			−0.0734787
$251$	−6.81467			−0.430138			−0.215069	−	0.976599i	$-0.568998\pi$
$251$	−6.81467			−0.430138			−0.215069	+	0.976599i	$0.568998\pi$
$252$		0			0
$253$	−6.33151			−0.398059
$254$	−0.349767			−0.0219464
$255$	−0.284936	+	0.0751704i	−0.0178434	+	0.00470735i
$256$	−15.5447			−0.971542
$257$	7.19415	+	12.4606i	0.448759	+	0.777273i	0.998306	−	0.0581897i	$-0.0185328\pi$
$257$	7.19415	+	12.4606i	0.448759	+	0.777273i	−0.549546	+	0.835463i	$0.685199\pi$
$258$	−3.78519	+	13.9114i	−0.235656	+	0.866088i
$259$		0			0
$260$	−0.205004			−0.0127138
$261$	−24.2441	+	13.7488i	−1.50067	+	0.851030i
$262$	8.24701	+	14.2842i	0.509502	+	0.882484i
$263$	0.769503	−	1.33282i	0.0474496	−	0.0821851i	−0.841325	−	0.540529i	$-0.818224\pi$
$263$	0.769503	−	1.33282i	0.0474496	−	0.0821851i	0.888775	+	0.458344i	$0.151557\pi$
$264$	−17.1588	+	4.52675i	−1.05605	+	0.278602i
$265$	−0.526106	+	0.911243i	−0.0323185	+	0.0559772i
$266$		0			0
$267$	10.0980	−	2.66399i	0.617986	−	0.163034i
$268$	−7.81562			−0.477415
$269$	13.1285	+	22.7393i	0.800461	+	1.38644i	0.919313	+	0.393527i	$0.128745\pi$
$269$	13.1285	+	22.7393i	0.800461	+	1.38644i	−0.118852	+	0.992912i	$0.537921\pi$
$270$	0.581917	+	0.163172i	0.0354144	+	0.00993035i
$271$	−8.96673	+	15.5308i	−0.544690	+	0.943431i	0.453936	+	0.891034i	$0.350019\pi$
$271$	−8.96673	+	15.5308i	−0.544690	+	0.943431i	−0.998626	+	0.0523969i	$0.983314\pi$
$272$	−1.46643	−	2.53993i	−0.0889152	−	0.154006i
$273$		0			0
$274$	−8.40748	+	14.5622i	−0.507915	+	0.879734i
$275$	8.32473	+	14.4188i	0.502000	+	0.869489i
$276$	0.676214	−	2.48524i	0.0407033	−	0.149594i
$277$	9.43563	−	16.3430i	0.566932	−	0.981955i	−0.429935	−	0.902860i	$-0.641463\pi$
$277$	9.43563	−	16.3430i	0.566932	−	0.981955i	0.996867	−	0.0790954i	$-0.0252032\pi$
$278$	−4.47680	+	7.75404i	−0.268500	+	0.465056i
$279$	0.214582	−	27.7840i	0.0128467	−	1.66339i
$280$		0			0
$281$	−2.49578	−	4.32283i	−0.148886	−	0.257878i	0.781930	−	0.623366i	$-0.214235\pi$
$281$	−2.49578	−	4.32283i	−0.148886	−	0.257878i	−0.930816	+	0.365488i	$0.880902\pi$
$282$	−4.29949	−	4.33282i	−0.256031	−	0.258016i
$283$	15.3927			0.915000			0.457500	−	0.889210i	$-0.348745\pi$
$283$	15.3927			0.915000			0.457500	+	0.889210i	$0.348745\pi$
$284$	−2.57904			−0.153038
$285$	−0.988522	−	0.996187i	−0.0585550	−	0.0590090i
$286$	−4.56364	−	7.90446i	−0.269854	−	0.467401i
$287$		0			0
$288$	0.0958052	−	12.4048i	0.00564537	−	0.730960i
$289$	7.19881	−	12.4687i	0.423460	−	0.733454i
$290$	0.540282	−	0.935796i	0.0317265	−	0.0549518i
$291$	−1.72919	+	6.35516i	−0.101367	+	0.372546i
$292$	1.85126	+	3.20647i	0.108337	+	0.187644i
$293$	12.9013	−	22.3456i	0.753700	−	1.30545i	−0.192318	−	0.981333i	$-0.561601\pi$
$293$	12.9013	−	22.3456i	0.753700	−	1.30545i	0.946018	−	0.324114i	$-0.105066\pi$
$294$		0			0
$295$	−0.235182	−	0.407347i	−0.0136928	−	0.0237167i
$296$	3.04321	−	5.27099i	0.176883	−	0.306370i
$297$	−4.29389	−	16.8012i	−0.249157	−	0.974903i
$298$	−6.14741	−	10.6476i	−0.356110	−	0.616801i
$299$	4.70492			0.272093
$300$	−6.54877	+	1.72766i	−0.378093	+	0.0997465i
$301$		0			0
$302$	−6.21629	+	10.7669i	−0.357707	+	0.619567i
$303$	29.2583	−	7.71877i	1.68085	−	0.443432i
$304$	6.98373	−	12.0962i	0.400544	−	0.693763i
$305$	0.299049	+	0.517968i	0.0171235	+	0.0296588i
$306$	4.64257	−	2.63279i	0.265398	−	0.150507i
$307$	22.2914			1.27224			0.636120	−	0.771590i	$-0.280538\pi$
$307$	22.2914			1.27224			0.636120	+	0.771590i	$0.280538\pi$
$308$		0			0
$309$	3.97085	−	14.5938i	0.225894	−	0.830210i
$310$	0.538607	+	0.932894i	0.0305908	+	0.0529848i
$311$	1.30986			0.0742755			0.0371377	−	0.999310i	$-0.488176\pi$
$311$	1.30986			0.0742755			0.0371377	+	0.999310i	$0.488176\pi$
$312$	12.7507	−	3.36382i	0.721865	−	0.190439i
$313$	−21.5770			−1.21960			−0.609802	−	0.792554i	$-0.708751\pi$
$313$	−21.5770			−1.21960			−0.609802	+	0.792554i	$0.708751\pi$
$314$	−13.4613			−0.759667
$315$		0			0
$316$	−6.03065			−0.339250
$317$	−24.7819			−1.39189			−0.695946	−	0.718094i	$-0.745015\pi$
$317$	−24.7819			−1.39189			−0.695946	+	0.718094i	$0.745015\pi$
$318$	5.00335	−	18.3884i	0.280574	−	1.03117i
$319$	−31.0051			−1.73595
$320$	0.432216	+	0.748620i	0.0241616	+	0.0418491i
$321$	30.3906	−	8.01748i	1.69624	−	0.447492i
$322$		0			0
$323$	−12.3936			−0.689597
$324$	7.05338	+	0.108956i	0.391854	+	0.00605312i
$325$	−6.18608	−	10.7146i	−0.343142	−	0.594339i
$326$	4.94206	−	8.55990i	0.273715	−	0.474089i
$327$	−1.92015	+	7.05699i	−0.106185	+	0.390252i
$328$	−11.4901	+	19.9014i	−0.634434	+	1.09887i
$329$		0			0
$330$	0.473559	+	0.477231i	0.0260686	+	0.0262707i
$331$	13.8451			0.760996			0.380498	−	0.924782i	$-0.375753\pi$
$331$	13.8451			0.760996			0.380498	+	0.924782i	$0.375753\pi$
$332$	−0.458076	−	0.793410i	−0.0251402	−	0.0435440i
$333$	5.12766	+	3.01349i	0.280994	+	0.165139i
$334$	9.60367	−	16.6340i	0.525489	−	0.910174i
$335$	0.525823	+	0.910752i	0.0287288	+	0.0497597i
$336$		0			0
$337$	1.69444	−	2.93485i	0.0923018	−	0.159871i	−0.816178	−	0.577801i	$-0.803911\pi$
$337$	1.69444	−	2.93485i	0.0923018	−	0.159871i	0.908479	+	0.417930i	$0.137244\pi$
$338$	−3.77706	−	6.54206i	−0.205445	−	0.355841i
$339$	3.44408	−	0.908600i	0.187057	−	0.0493484i
$340$	0.0666767	−	0.115487i	0.00361605	−	0.00626319i
$341$	15.4545	−	26.7679i	0.836906	−	1.44956i
$342$	21.9135	+	12.8784i	1.18495	+	0.696386i
$343$		0			0
$344$	−11.5859	−	20.0673i	−0.624668	−	1.08196i
$345$	−0.335099	+	0.0884040i	−0.0180411	+	0.00475951i
$346$	−3.12022			−0.167744
$347$	−14.5148			−0.779195			−0.389597	−	0.920985i	$-0.627386\pi$
$347$	−14.5148			−0.779195			−0.389597	+	0.920985i	$0.627386\pi$
$348$	3.31139	−	12.1701i	0.177509	−	0.652385i
$349$	−7.86412	−	13.6211i	−0.420957	−	0.729119i	0.575076	−	0.818100i	$-0.304972\pi$
$349$	−7.86412	−	13.6211i	−0.420957	−	0.729119i	−0.996033	+	0.0889810i	$0.971639\pi$
$350$		0			0
$351$	3.19077	+	12.4849i	0.170311	+	0.666395i
$352$	6.90000	−	11.9511i	0.367771	−	0.636998i
$353$	−2.07211	+	3.58900i	−0.110287	+	0.191023i	−0.915886	−	0.401438i	$-0.868510\pi$
$353$	−2.07211	+	3.58900i	−0.110287	+	0.191023i	0.805599	+	0.592462i	$0.201844\pi$
$354$	6.00048	+	6.04700i	0.318922	+	0.321394i
$355$	0.173514	+	0.300535i	0.00920917	+	0.0159508i
$356$	−2.36298	+	4.09281i	−0.125238	+	0.216918i
$357$		0			0
$358$	−5.60378	−	9.70603i	−0.296169	−	0.512979i
$359$	−3.96994	+	6.87614i	−0.209525	+	0.362909i	−0.951565	−	0.307447i	$-0.900525\pi$
$359$	−3.96994	+	6.87614i	−0.209525	+	0.362909i	0.742040	+	0.670356i	$0.233859\pi$
$360$	−0.844937	+	0.479163i	−0.0445321	+	0.0252541i
$361$	−20.0116	−	34.6612i	−1.05324	−	1.82427i
$362$	18.8437			0.990405
$363$	0.0626049	−	0.230087i	0.00328590	−	0.0120764i
$364$		0			0
$365$	0.249099	−	0.431453i	0.0130385	−	0.0225833i
$366$	−7.62998	−	7.68914i	−0.398826	−	0.401918i
$367$	−6.57455	+	11.3875i	−0.343189	+	0.594420i	−0.985023	−	0.172423i	$-0.944840\pi$
$367$	−6.57455	+	11.3875i	−0.343189	+	0.594420i	0.641834	+	0.766843i	$0.278174\pi$
$368$	−1.72459	−	2.98708i	−0.0899004	−	0.155712i
$369$	−19.3603	−	11.3779i	−1.00785	−	0.592310i
$370$	−0.230588			−0.0119877
$371$		0			0
$372$	8.85636	+	8.92503i	0.459181	+	0.462741i
$373$	−3.90543	−	6.76441i	−0.202216	−	0.350248i	0.747026	−	0.664794i	$-0.231481\pi$
$373$	−3.90543	−	6.76441i	−0.202216	−	0.350248i	−0.949242	+	0.314547i	$0.898147\pi$
$374$	5.93723			0.307007
$375$	1.28526	+	1.29523i	0.0663706	+	0.0668852i
$376$	9.81055			0.505940
$377$	23.0398			1.18661
$378$		0			0
$379$	−31.6147			−1.62394			−0.811968	−	0.583702i	$-0.801604\pi$
$379$	−31.6147			−1.62394			−0.811968	+	0.583702i	$0.801604\pi$
$380$	0.635084			0.0325791
$381$	0.386936	+	0.389936i	0.0198233	+	0.0199770i
$382$	24.7030			1.26392
$383$	−5.36593	−	9.29407i	−0.274186	−	0.474905i	0.695743	−	0.718291i	$-0.255075\pi$
$383$	−5.36593	−	9.29407i	−0.274186	−	0.474905i	−0.969930	+	0.243386i	$0.921742\pi$
$384$	−0.938027	−	0.945300i	−0.0478685	−	0.0482396i
$385$		0			0
$386$	0.283187			0.0144139
$387$	19.6965	−	11.1699i	1.00123	−	0.567796i
$388$	−1.49022	−	2.58114i	−0.0756546	−	0.131038i
$389$	−12.0734	+	20.9118i	−0.612147	+	1.06027i	0.378731	+	0.925507i	$0.376361\pi$
$389$	−12.0734	+	20.9118i	−0.612147	+	1.06027i	−0.990878	+	0.134763i	$0.956973\pi$
$390$	−0.351900	−	0.354628i	−0.0178192	−	0.0179573i
$391$	−1.53026	+	2.65049i	−0.0773885	+	0.134041i
$392$		0			0
$393$	6.80131	−	24.9963i	0.343081	−	1.26090i
$394$	0.841854			0.0424120
$395$	0.405733	+	0.702750i	0.0204146	+	0.0353592i
$396$	6.76553	+	3.97606i	0.339981	+	0.199805i
$397$	12.0285	−	20.8339i	0.603691	−	1.04562i	−0.388566	−	0.921421i	$-0.627029\pi$
$397$	12.0285	−	20.8339i	0.603691	−	1.04562i	0.992257	−	0.124203i	$-0.0396373\pi$
$398$	−2.77424	−	4.80513i	−0.139060	−	0.240860i
$399$		0			0
$400$	−4.53501	+	7.85487i	−0.226751	+	0.392744i
$401$	0.781158	+	1.35301i	0.0390092	+	0.0675659i	0.884871	−	0.465836i	$-0.154247\pi$
$401$	0.781158	+	1.35301i	0.0390092	+	0.0675659i	−0.845862	+	0.533402i	$0.820913\pi$
$402$	−13.4159	−	13.5199i	−0.669126	−	0.674314i
$403$	−11.4842	+	19.8911i	−0.572067	+	0.990849i
$404$	−6.84661	+	11.8587i	−0.340631	+	0.589991i
$405$	−0.461844	−	0.829259i	−0.0229492	−	0.0412062i
$406$		0			0
$407$	3.30817	+	5.72992i	0.163980	+	0.284022i
$408$	−2.25213	+	8.27708i	−0.111497	+	0.409776i
$409$	22.3456			1.10492			0.552460	−	0.833539i	$-0.313689\pi$
$409$	22.3456			1.10492			0.552460	+	0.833539i	$0.313689\pi$
$410$	0.870619			0.0429968
$411$	25.5355	−	6.73664i	1.25957	−	0.332294i
$412$	3.42210	+	5.92725i	0.168595	+	0.292014i
$413$		0			0
$414$	5.45988	−	3.09629i	0.268339	−	0.152174i
$415$	−0.0616373	+	0.106759i	−0.00302566	+	0.00524059i
$416$	−5.12736	+	8.88086i	−0.251390	+	0.435420i
$417$	13.5971	−	3.58711i	0.665852	−	0.175661i
$418$	14.1378	+	24.4873i	0.691501	+	1.19771i
$419$	−2.98648	+	5.17273i	−0.145899	+	0.252704i	−0.929708	−	0.368298i	$-0.879941\pi$
$419$	−2.98648	+	5.17273i	−0.145899	+	0.252704i	0.783809	+	0.621002i	$0.213274\pi$
$420$		0			0
$421$	7.31594	+	12.6716i	0.356557	+	0.617575i	0.987383	−	0.158349i	$-0.0506172\pi$
$421$	7.31594	+	12.6716i	0.356557	+	0.617575i	−0.630826	+	0.775924i	$0.717284\pi$
$422$	3.97605	−	6.88672i	0.193551	−	0.335240i
$423$	−0.0740389	+	9.58652i	−0.00359989	+	0.466113i
$424$	15.3144	+	26.5254i	0.743735	+	1.28819i
$425$	8.04799			0.390385
$426$	−4.42707	−	4.46139i	−0.214492	−	0.216155i
$427$		0			0
$428$	−7.11156	+	12.3176i	−0.343750	+	0.595393i
$429$	−3.76363	+	13.8322i	−0.181710	+	0.667825i
$430$	−0.438938	+	0.760263i	−0.0211675	+	0.0366631i
$431$	9.70169	+	16.8038i	0.467314	+	0.809411i	0.999303	−	0.0373401i	$-0.0118885\pi$
$431$	9.70169	+	16.8038i	0.467314	+	0.809411i	−0.531989	+	0.846751i	$0.678555\pi$
$432$	6.75688	−	6.60211i	0.325090	−	0.317644i
$433$	−1.35217			−0.0649810			−0.0324905	−	0.999472i	$-0.510344\pi$
$433$	−1.35217			−0.0649810			−0.0324905	+	0.999472i	$0.510344\pi$
$434$		0			0
$435$	−1.64096	+	0.432910i	−0.0786781	+	0.0207564i
$436$	−1.65480	−	2.86619i	−0.0792503	−	0.137266i
$437$	−14.5754			−0.697238
$438$	−2.36897	+	8.70650i	−0.113194	+	0.416013i
$439$	−17.3412			−0.827650			−0.413825	−	0.910356i	$-0.635807\pi$
$439$	−17.3412			−0.827650			−0.413825	+	0.910356i	$0.635807\pi$
$440$	−1.08056			−0.0515139
$441$		0			0
$442$	−4.41194			−0.209854
$443$	19.6100			0.931698			0.465849	−	0.884864i	$-0.345749\pi$
$443$	19.6100			0.931698			0.465849	+	0.884864i	$0.345749\pi$
$444$	−2.60242	+	0.686557i	−0.123506	+	0.0325826i
$445$	0.635912			0.0301451
$446$	−6.16590	−	10.6796i	−0.291964	−	0.505696i
$447$	−5.06977	+	18.6325i	−0.239792	+	0.881289i
$448$		0			0
$449$	−17.7345			−0.836942			−0.418471	−	0.908230i	$-0.637434\pi$
$449$	−17.7345			−0.836942			−0.418471	+	0.908230i	$0.637434\pi$
$450$	−14.2299	−	8.36285i	−0.670806	−	0.394228i
$451$	−12.4905	−	21.6342i	−0.588155	−	1.01871i
$452$	−0.805935	+	1.39592i	−0.0379080	+	0.0656586i
$453$	18.8803	−	4.98091i	0.887075	−	0.234023i
$454$	13.1073	−	22.7025i	0.615156	−	1.06548i
$455$		0			0
$456$	−39.5005	+	10.4208i	−1.84978	+	0.487999i
$457$	0.485451			0.0227084			0.0113542	−	0.999936i	$-0.496386\pi$
$457$	0.485451			0.0227084			0.0113542	+	0.999936i	$0.496386\pi$
$458$	−1.05069	−	1.81985i	−0.0490956	−	0.0850361i
$459$	−8.07107	−	2.26317i	−0.376725	−	0.105636i
$460$	0.0784150	−	0.135819i	0.00365612	−	0.00633259i
$461$	−3.99687	−	6.92279i	−0.186153	−	0.322426i	0.757811	−	0.652474i	$-0.226269\pi$
$461$	−3.99687	−	6.92279i	−0.186153	−	0.322426i	−0.943964	+	0.330047i	$0.892935\pi$
$462$		0			0
$463$	5.24280	−	9.08080i	0.243654	−	0.422021i	−0.718098	−	0.695942i	$-0.754987\pi$
$463$	5.24280	−	9.08080i	0.243654	−	0.422021i	0.961752	+	0.273921i	$0.0883206\pi$
$464$	−8.44523	−	14.6276i	−0.392060	−	0.679068i
$465$	0.444189	−	1.63249i	0.0205988	−	0.0757050i
$466$	3.60721	−	6.24788i	0.167101	−	0.289427i
$467$	10.9489	−	18.9640i	0.506653	−	0.877549i	−0.493317	−	0.869849i	$-0.664216\pi$
$467$	10.9489	−	18.9640i	0.506653	−	0.877549i	0.999970	−	0.00769944i	$-0.00245083\pi$
$468$	−5.02744	−	2.95460i	−0.232394	−	0.136576i
$469$		0			0
$470$	−0.185839	−	0.321883i	−0.00857213	−	0.0148474i
$471$	14.8918	+	15.0073i	0.686179	+	0.691499i
$472$	−13.6918			−0.630218
$473$	25.1893			1.15820
$474$	−10.3519	−	10.4322i	−0.475480	−	0.479167i
$475$	19.1639	+	33.1929i	0.879301	+	1.52299i
$476$		0			0
$477$	−26.0353	+	14.7645i	−1.19207	+	0.676022i
$478$	−11.7708	+	20.3877i	−0.538386	+	0.932512i
$479$	2.00085	−	3.46557i	0.0914210	−	0.158346i	−0.816688	−	0.577079i	$-0.804192\pi$
$479$	2.00085	−	3.46557i	0.0914210	−	0.158346i	0.908109	+	0.418733i	$0.137526\pi$
$480$	0.198318	−	0.728864i	0.00905194	−	0.0332679i
$481$	−2.45829	−	4.25789i	−0.112088	−	0.194143i
$482$	−11.0646	+	19.1645i	−0.503980	+	0.872918i
$483$		0			0
$484$	0.0539532	+	0.0934496i	0.00245242	+	0.00424771i
$485$	−0.200520	+	0.347311i	−0.00910514	+	0.0157706i
$486$	11.9190	+	12.3884i	0.540658	+	0.561950i
$487$	13.2377	+	22.9284i	0.599859	+	1.03899i	0.992841	+	0.119440i	$0.0381100\pi$
$487$	13.2377	+	22.9284i	0.599859	+	1.03899i	−0.392982	+	0.919546i	$0.628557\pi$
$488$	17.4100			0.788116
$489$	−15.0102	+	3.95991i	−0.678784	+	0.179073i
$490$		0			0
$491$	14.2149	−	24.6210i	0.641511	−	1.11113i	−0.343584	−	0.939122i	$-0.611641\pi$
$491$	14.2149	−	24.6210i	0.641511	−	1.11113i	0.985096	−	0.172008i	$-0.0550255\pi$
$492$	9.82584	−	2.59220i	0.442983	−	0.116865i
$493$	−7.49360	+	12.9793i	−0.337495	+	0.584558i
$494$	−10.5057	−	18.1965i	−0.472675	−	0.818697i
$495$	0.00815487	−	1.05589i	0.000366534	−	0.0474587i
$496$	16.8381			0.756052
$497$		0			0
$498$	0.586179	−	2.15434i	0.0262673	−	0.0965383i
$499$	3.71559	+	6.43559i	0.166333	+	0.288097i	0.937128	−	0.348986i	$-0.113474\pi$
$499$	3.71559	+	6.43559i	0.166333	+	0.288097i	−0.770795	+	0.637083i	$0.780141\pi$
$500$	−0.825726			−0.0369276
$501$	−29.1686	+	7.69510i	−1.30316	+	0.343792i
$502$	7.51531			0.335425
$503$	10.1610			0.453057			0.226529	−	0.974004i	$-0.427262\pi$
$503$	10.1610			0.453057			0.226529	+	0.974004i	$0.427262\pi$
$504$		0			0
$505$	1.84252			0.0819910
$506$	6.98247			0.310409
$507$	−3.11494	+	11.4481i	−0.138339	+	0.508428i
$508$	−0.248590			−0.0110294
$509$	14.4532	+	25.0336i	0.640625	+	1.10960i	0.985293	+	0.170871i	$0.0546581\pi$
$509$	14.4532	+	25.0336i	0.640625	+	1.10960i	−0.344668	+	0.938725i	$0.612009\pi$
$510$	0.314232	−	0.0828990i	0.0139144	−	0.00367083i
$511$		0			0
$512$	18.6806			0.825575
$513$	−9.88474	−	38.6771i	−0.436422	−	1.70764i
$514$	−7.93381	−	13.7418i	−0.349945	−	0.606123i
$515$	0.460467	−	0.797553i	0.0202906	−	0.0351444i
$516$	−2.69025	+	9.88727i	−0.118432	+	0.435263i
$517$	−5.33237	+	9.23593i	−0.234517	+	0.406196i
$518$		0			0
$519$	3.45180	+	3.47856i	0.151517	+	0.152692i
$520$	0.802963			0.0352123
$521$	−16.8995	−	29.2708i	−0.740381	−	1.28238i	−0.952322	−	0.305095i	$-0.901312\pi$
$521$	−16.8995	−	29.2708i	−0.740381	−	1.28238i	0.211941	−	0.977283i	$-0.432022\pi$
$522$	26.7368	−	15.1624i	1.17024	−	0.663639i
$523$	7.18895	−	12.4516i	0.314351	−	0.544471i	−0.664949	−	0.746889i	$-0.731547\pi$
$523$	7.18895	−	12.4516i	0.314351	−	0.544471i	0.979299	+	0.202418i	$0.0648799\pi$
$524$	5.86140	+	10.1522i	0.256056	+	0.443502i
$525$		0			0
$526$	−0.848618	+	1.46985i	−0.0370015	+	0.0640885i
$527$	−7.47036	−	12.9390i	−0.325414	−	0.563634i
$528$	10.1614	−	2.68072i	0.442218	−	0.116664i
$529$	9.70034	−	16.8015i	0.421754	−	0.730499i
$530$	0.580197	−	1.00493i	0.0252022	−	0.0436514i
$531$	0.103331	−	13.3792i	0.00448416	−	0.580607i
$532$		0			0
$533$	9.28166	+	16.0763i	0.402033	+	0.696342i
$534$	−11.1362	+	2.93789i	−0.481910	+	0.127135i
$535$	1.91382			0.0827417
$536$	30.6124			1.32225
$537$	−4.62143	+	16.9848i	−0.199429	+	0.732948i
$538$	−14.4783	−	25.0772i	−0.624205	−	1.08116i
$539$		0			0
$540$	0.413586	+	0.115971i	0.0177979	+	0.00499062i
$541$	12.5882	−	21.8034i	0.541210	−	0.937403i	−0.457625	−	0.889145i	$-0.651300\pi$
$541$	12.5882	−	21.8034i	0.541210	−	0.937403i	0.998835	−	0.0482577i	$-0.0153669\pi$
$542$	9.88863	−	17.1276i	0.424753	−	0.735694i
$543$	−20.8462	−	21.0078i	−0.894596	−	0.901532i
$544$	−3.33531	−	5.77693i	−0.143000	−	0.247684i
$545$	−0.222664	+	0.385666i	−0.00953789	+	0.0165201i
$546$		0			0
$547$	1.59011	+	2.75416i	0.0679883	+	0.117759i	0.898016	−	0.439963i	$-0.145009\pi$
$547$	1.59011	+	2.75416i	0.0679883	+	0.117759i	−0.830027	+	0.557723i	$0.811675\pi$
$548$	−5.97545	+	10.3498i	−0.255258	+	0.442121i
$549$	−0.131391	+	17.0125i	−0.00560764	+	0.726075i
$550$	−9.18062	−	15.9013i	−0.391463	−	0.678034i
$551$	−71.3752			−3.04068
$552$	−2.64861	+	9.73424i	−0.112732	+	0.414317i
$553$		0			0
$554$	−10.4057	+	18.0233i	−0.442098	+	0.765736i
$555$	0.255092	+	0.257069i	0.0108280	+	0.0109120i
$556$	−3.18179	+	5.51102i	−0.134938	+	0.233719i
$557$	−10.0229	−	17.3602i	−0.424686	−	0.735577i	0.571705	−	0.820459i	$-0.306282\pi$
$557$	−10.0229	−	17.3602i	−0.424686	−	0.735577i	−0.996391	+	0.0848820i	$0.972949\pi$
$558$	−0.236644	+	30.6406i	−0.0100180	+	1.29712i
$559$	−18.7181			−0.791689
$560$		0			0
$561$	−6.56817	−	6.61909i	−0.277308	−	0.279458i
$562$	2.75238	+	4.76727i	0.116102	+	0.201095i
$563$	39.8013			1.67743			0.838713	−	0.544574i	$-0.183309\pi$
$563$	39.8013			1.67743			0.838713	+	0.544574i	$0.183309\pi$
$564$	−3.05578	−	3.07947i	−0.128671	−	0.129669i
$565$	0.216888			0.00912457
$566$	−16.9753			−0.713523
$567$		0			0
$568$	10.1017			0.423856
$569$	13.8159			0.579194			0.289597	−	0.957149i	$-0.406479\pi$
$569$	13.8159			0.579194			0.289597	+	0.957149i	$0.406479\pi$
$570$	1.09016	+	1.09861i	0.0456616	+	0.0460156i
$571$	10.4387			0.436846			0.218423	−	0.975854i	$-0.429909\pi$
$571$	10.4387			0.436846			0.218423	+	0.975854i	$0.429909\pi$
$572$	−3.24352	−	5.61793i	−0.135618	−	0.234898i
$573$	−27.3281	−	27.5400i	−1.14165	−	1.15050i
$574$		0			0
$575$	9.46483			0.394711
$576$	−0.189900	+	24.5882i	−0.00791250	+	1.02451i
$577$	12.7461	+	22.0769i	0.530628	+	0.919075i	0.999361	+	0.0357353i	$0.0113773\pi$
$577$	12.7461	+	22.0769i	0.530628	+	0.919075i	−0.468733	+	0.883340i	$0.655289\pi$
$578$	−7.93895	+	13.7507i	−0.330217	+	0.571952i
$579$	−0.313281	−	0.315710i	−0.0130195	−	0.0131204i
$580$	0.383994	−	0.665098i	0.0159445	−	0.0276167i
$581$		0			0
$582$	1.90697	−	7.00855i	0.0790466	−	0.290514i
$583$	−33.2957			−1.37897
$584$	−7.25104	−	12.5592i	−0.300050	−	0.519702i
$585$	−0.00605986	+	0.784628i	−0.000250544	+	0.0324404i
$586$	−14.2277	+	24.6431i	−0.587740	+	1.01800i
$587$	17.5168	+	30.3401i	0.722998	+	1.25227i	0.959793	+	0.280709i	$0.0905697\pi$
$587$	17.5168	+	30.3401i	0.722998	+	1.25227i	−0.236795	+	0.971560i	$0.576097\pi$
$588$		0			0
$589$	35.5769	−	61.6210i	1.46592	−	2.53905i
$590$	0.259362	+	0.449228i	0.0106778	+	0.0184944i
$591$	−0.931316	−	0.938536i	−0.0383092	−	0.0386062i
$592$	−1.80217	+	3.12146i	−0.0740689	+	0.128291i
$593$	−18.0646	+	31.2888i	−0.741824	+	1.28488i	0.209840	+	0.977736i	$0.432706\pi$
$593$	−18.0646	+	31.2888i	−0.741824	+	1.28488i	−0.951664	+	0.307141i	$0.900628\pi$
$594$	4.73536	+	18.5286i	0.194294	+	0.760236i
$595$		0			0
$596$	−4.36915	−	7.56759i	−0.178967	−	0.309980i
$597$	−2.28792	+	8.40861i	−0.0936383	+	0.344142i
$598$	−5.18865			−0.212180
$599$	−40.9484			−1.67310			−0.836552	−	0.547887i	$-0.815432\pi$
$599$	−40.9484			−1.67310			−0.836552	+	0.547887i	$0.815432\pi$
$600$	25.6504	−	6.76694i	1.04717	−	0.276259i
$601$	−12.8547	−	22.2650i	−0.524354	−	0.908207i	−0.999598	−	0.0283533i	$-0.990974\pi$
$601$	−12.8547	−	22.2650i	−0.524354	−	0.908207i	0.475244	−	0.879854i	$-0.342360\pi$
$602$		0			0
$603$	−0.231028	+	29.9133i	−0.00940817	+	1.21817i
$604$	−4.41810	+	7.65238i	−0.179770	+	0.311371i
$605$	0.00725978	−	0.0125743i	0.000295152	−	0.000511218i
$606$	−32.2665	+	8.51236i	−1.31074	+	0.345791i
$607$	3.42258	+	5.92808i	0.138918	+	0.240613i	0.927087	−	0.374845i	$-0.122304\pi$
$607$	3.42258	+	5.92808i	0.138918	+	0.240613i	−0.788169	+	0.615459i	$0.788971\pi$
$608$	15.8841	−	27.5121i	0.644187	−	1.11576i
$609$		0			0
$610$	−0.329795	−	0.571222i	−0.0133530	−	0.0231281i
$611$	3.96246	−	6.86319i	0.160304	−	0.277655i
$612$	3.29961	−	1.87120i	0.133379	−	0.0756389i
$613$	14.5648	+	25.2271i	0.588269	+	1.01891i	0.994459	+	0.105123i	$0.0335235\pi$
$613$	14.5648	+	25.2271i	0.588269	+	1.01891i	−0.406191	+	0.913788i	$0.633143\pi$
$614$	−24.5833			−0.992101
$615$	−0.963137	−	0.970604i	−0.0388374	−	0.0391385i
$616$		0			0
$617$	−10.3395	+	17.9085i	−0.416252	+	0.720969i	−0.995559	−	0.0941404i	$-0.969990\pi$
$617$	−10.3395	+	17.9085i	−0.416252	+	0.720969i	0.579307	+	0.815109i	$0.303323\pi$
$618$	−4.37911	+	16.0942i	−0.176154	+	0.647404i
$619$	−4.43178	+	7.67606i	−0.178128	+	0.308527i	−0.941239	−	0.337740i	$-0.890337\pi$
$619$	−4.43178	+	7.67606i	−0.178128	+	0.308527i	0.763111	+	0.646267i	$0.223671\pi$
$620$	0.382804	+	0.663035i	0.0153738	+	0.0266281i
$621$	−9.49197	−	2.66159i	−0.380900	−	0.106806i
$622$	−1.44453			−0.0579205
$623$		0			0
$624$	−7.55090	+	1.99204i	−0.302278	+	0.0797453i
$625$	−12.4166	−	21.5062i	−0.496666	−	0.860250i
$626$	23.7954			0.951055
$627$	11.6594	−	42.8509i	0.465632	−	1.71130i
$628$	−9.56737			−0.381779
$629$	3.19820			0.127521
$630$		0			0
$631$	26.4661			1.05360			0.526799	−	0.849990i	$-0.323392\pi$
$631$	26.4661			1.05360			0.526799	+	0.849990i	$0.323392\pi$
$632$	23.6210			0.939592
$633$	−12.0762	+	3.18588i	−0.479985	+	0.126627i
$634$	27.3299			1.08541
$635$	0.0167248	+	0.0289681i	0.000663702	+	0.00114957i
$636$	3.55603	−	13.0692i	0.141006	−	0.518227i
$637$		0			0
$638$	34.1928			1.35371
$639$	−0.0762358	+	9.87098i	−0.00301584	+	0.390490i
$640$	−0.0405449	−	0.0702258i	−0.00160268	−	0.00277592i
$641$	8.26595	−	14.3171i	0.326486	−	0.565489i	−0.655326	−	0.755346i	$-0.727469\pi$
$641$	8.26595	−	14.3171i	0.326486	−	0.565489i	0.981812	+	0.189856i	$0.0608022\pi$
$642$	−33.5151	+	8.84178i	−1.32274	+	0.348957i
$643$	15.4460	−	26.7532i	0.609130	−	1.05504i	−0.382254	−	0.924057i	$-0.624852\pi$
$643$	15.4460	−	26.7532i	0.609130	−	1.05504i	0.991384	−	0.130987i	$-0.0418147\pi$
$644$		0			0
$645$	1.33316	−	0.351706i	0.0524930	−	0.0138484i
$646$	13.6678			0.537752
$647$	−0.649903	−	1.12567i	−0.0255503	−	0.0442545i	0.852968	−	0.521964i	$-0.174800\pi$
$647$	−0.649903	−	1.12567i	−0.0255503	−	0.0442545i	−0.878518	+	0.477710i	$0.841467\pi$
$648$	−27.6268	−	0.426762i	−1.08528	−	0.0167648i
$649$	7.44198	−	12.8899i	0.292123	−	0.505972i
$650$	6.82209	+	11.8162i	0.267584	+	0.463470i
$651$		0			0
$652$	3.51247	−	6.08377i	0.137559	−	0.238259i
$653$	22.4435	+	38.8733i	0.878281	+	1.52123i	0.853226	+	0.521542i	$0.174643\pi$
$653$	22.4435	+	38.8733i	0.878281	+	1.52123i	0.0250558	+	0.999686i	$0.492024\pi$
$654$	2.11757	−	7.78254i	0.0828035	−	0.304321i
$655$	0.788692	−	1.36605i	0.0308167	−	0.0533762i
$656$	6.80438	−	11.7855i	0.265667	−	0.460148i
$657$	12.3271	−	6.99068i	0.480926	−	0.272732i
$658$		0			0
$659$	8.96167	+	15.5221i	0.349097	+	0.604654i	0.986089	−	0.166216i	$-0.0531549\pi$
$659$	8.96167	+	15.5221i	0.349097	+	0.604654i	−0.636992	+	0.770870i	$0.719822\pi$
$660$	0.336572	+	0.339182i	0.0131011	+	0.0132026i
$661$	−33.0256			−1.28455			−0.642274	−	0.766475i	$-0.722009\pi$
$661$	−33.0256			−1.28455			−0.642274	+	0.766475i	$0.722009\pi$
$662$	−15.2686			−0.593430
$663$	4.88078	+	4.91862i	0.189554	+	0.191023i
$664$	1.79420	+	3.10765i	0.0696285	+	0.120600i
$665$		0			0
$666$	−5.65485	−	3.32332i	−0.219121	−	0.128776i
$667$	−8.81283	+	15.2643i	−0.341234	+	0.591035i
$668$	6.82561	−	11.8223i	0.264091	−	0.457419i
$669$	−5.08501	+	18.6885i	−0.196598	+	0.722541i
$670$	−0.579885	−	1.00439i	−0.0224029	−	0.0388030i
$671$	−9.46295	+	16.3903i	−0.365313	+	0.632741i
$672$		0			0
$673$	−10.6758	−	18.4909i	−0.411520	−	0.712774i	0.583536	−	0.812087i	$-0.301669\pi$
$673$	−10.6758	−	18.4909i	−0.411520	−	0.712774i	−0.995056	+	0.0993135i	$0.968335\pi$
$674$	−1.86865	+	3.23659i	−0.0719776	+	0.124669i
$675$	6.41884	+	25.1157i	0.247061	+	0.966704i
$676$	−2.68447	−	4.64964i	−0.103249	−	0.178832i
$677$	−8.30167			−0.319059			−0.159530	−	0.987193i	$-0.550998\pi$
$677$	−8.30167			−0.319059			−0.159530	+	0.987193i	$0.550998\pi$
$678$	−3.79818	+	1.00202i	−0.145868	+	0.0384822i
$679$		0			0
$680$	−0.261161	+	0.452344i	−0.0100151	+	0.0173466i
$681$	−39.8099	+	10.5024i	−1.52552	+	0.402454i
$682$	−17.0434	+	29.5200i	−0.652625	+	1.13038i
$683$	−1.24728	−	2.16036i	−0.0477259	−	0.0826637i	0.841176	−	0.540762i	$-0.181864\pi$
$683$	−1.24728	−	2.16036i	−0.0477259	−	0.0826637i	−0.888902	+	0.458098i	$0.848531\pi$
$684$	15.5746	+	9.15308i	0.595509	+	0.349977i
$685$	1.60808			0.0614414
$686$		0			0
$687$	−0.866505	+	3.18460i	−0.0330592	+	0.121500i
$688$	6.86110	+	11.8838i	0.261577	+	0.453065i
$689$	24.7419			0.942591
$690$	0.369552	−	0.0974932i	0.0140686	−	0.00371150i
$691$	16.8691			0.641731			0.320865	−	0.947125i	$-0.396026\pi$
$691$	16.8691			0.641731			0.320865	+	0.947125i	$0.396026\pi$
$692$	−2.21763			−0.0843017
$693$		0			0
$694$	16.0071			0.607621
$695$	0.856265			0.0324800
$696$	−12.9701	+	47.6681i	−0.491631	+	1.80685i
$697$	−12.0753			−0.457385
$698$	8.67266	+	15.0215i	0.328265	+	0.568572i
$699$	−10.9559	+	2.89034i	−0.414392	+	0.109323i
$700$		0			0
$701$	16.4806			0.622465			0.311232	−	0.950334i	$-0.399258\pi$
$701$	16.4806			0.622465			0.311232	+	0.950334i	$0.399258\pi$
$702$	−3.51883	−	13.7685i	−0.132810	−	0.519659i
$703$	7.61558	+	13.1906i	0.287227	+	0.497492i
$704$	−13.6768	+	23.6889i	−0.515464	+	0.892811i
$705$	−0.153262	+	0.563271i	−0.00577217	+	0.0212140i
$706$	2.28515	−	3.95800i	0.0860029	−	0.148961i
$707$		0			0
$708$	4.26472	+	4.29778i	0.160278	+	0.161520i
$709$	−29.4925			−1.10761			−0.553807	−	0.832645i	$-0.686825\pi$
$709$	−29.4925			−1.10761			−0.553807	+	0.832645i	$0.686825\pi$
$710$	−0.191354	−	0.331434i	−0.00718138	−	0.0124385i
$711$	−0.178264	+	23.0816i	−0.00668544	+	0.865627i
$712$	9.25539	−	16.0308i	0.346860	−	0.600780i
$713$	−8.78551	−	15.2169i	−0.329020	−	0.569879i
$714$		0			0
$715$	−0.436438	+	0.755933i	−0.0163219	+	0.0282703i
$716$	−3.98277	−	6.89836i	−0.148843	−	0.257804i
$717$	35.7508	−	9.43158i	1.33514	−	0.352229i
$718$	4.37810	−	7.58310i	0.163389	−	0.282999i
$719$	−0.217311	+	0.376394i	−0.00810433	+	0.0140371i	−0.870049	−	0.492965i	$-0.835913\pi$
$719$	−0.217311	+	0.376394i	−0.00810433	+	0.0140371i	0.861945	+	0.507002i	$0.169246\pi$
$720$	0.500368	−	0.283758i	0.0186476	−	0.0105750i
$721$		0			0
$722$	22.0691	+	38.2248i	0.821327	+	1.42258i
$723$	33.6058	−	8.86571i	1.24981	−	0.329719i
$724$	13.3928			0.497740
$725$	46.3488			1.72135
$726$	−0.0690415	+	0.253743i	−0.00256237	+	0.00941729i
$727$	−13.5839	−	23.5280i	−0.503799	−	0.872605i	−0.999990	−	0.00439187i	$-0.998602\pi$
$727$	−13.5839	−	23.5280i	−0.503799	−	0.872605i	0.496192	−	0.868213i	$-0.334731\pi$
$728$		0			0
$729$	0.625513	−	26.9928i	0.0231672	−	0.999732i
$730$	−0.274710	+	0.475812i	−0.0101675	+	0.0176106i
$731$	6.08798	−	10.5447i	0.225172	−	0.390009i
$732$	−5.42285	−	5.46490i	−0.200434	−	0.201988i
$733$	−2.83307	−	4.90702i	−0.104642	−	0.181245i	0.808950	−	0.587878i	$-0.200036\pi$
$733$	−2.83307	−	4.90702i	−0.104642	−	0.181245i	−0.913592	+	0.406632i	$0.866703\pi$
$734$	7.25050	−	12.5582i	0.267621	−	0.463533i
$735$		0			0
$736$	−3.92249	−	6.79395i	−0.144585	−	0.250428i
$737$	−16.6389	+	28.8194i	−0.612901	+	1.06158i
$738$	21.3508	+	12.5477i	0.785932	+	0.461888i
$739$	6.80540	+	11.7873i	0.250341	+	0.433603i	0.963620	−	0.267278i	$-0.0861241\pi$
$739$	6.80540	+	11.7873i	0.250341	+	0.433603i	−0.713279	+	0.700880i	$0.752791\pi$
$740$	−0.163885			−0.00602455
$741$	−8.66407	+	31.8424i	−0.318282	+	1.16976i
$742$		0			0
$743$	−6.33421	+	10.9712i	−0.232380	+	0.402493i	−0.958508	−	0.285066i	$-0.907985\pi$
$743$	−6.33421	+	10.9712i	−0.232380	+	0.402493i	0.726128	+	0.687559i	$0.241318\pi$
$744$	−34.6888	−	34.9578i	−1.27175	−	1.28161i
$745$	−0.587900	+	1.01827i	−0.0215390	+	0.0373066i
$746$	4.30696	+	7.45988i	0.157689	+	0.273126i
$747$	−3.05022	+	1.72978i	−0.111602	+	0.0632892i
$748$	4.21977			0.154290
$749$		0			0
$750$	−1.41740	−	1.42839i	−0.0517563	−	0.0521576i
$751$	3.57269	+	6.18808i	0.130369	+	0.225806i	0.923819	−	0.382830i	$-0.125050\pi$
$751$	3.57269	+	6.18808i	0.130369	+	0.225806i	−0.793450	+	0.608636i	$0.791717\pi$
$752$	−5.80977			−0.211860
$753$	−8.31394	−	8.37840i	−0.302977	−	0.305326i
$754$	−25.4086			−0.925325
$755$	1.18897			0.0432712
$756$		0			0
$757$	37.6446			1.36822			0.684108	−	0.729381i	$-0.260192\pi$
$757$	37.6446			1.36822			0.684108	+	0.729381i	$0.260192\pi$
$758$	34.8651			1.26636
$759$	−7.72448	−	7.78437i	−0.280381	−	0.282555i
$760$	−2.48751			−0.0902315
$761$	5.02358	+	8.70109i	0.182104	+	0.315414i	0.942597	−	0.333933i	$-0.108376\pi$
$761$	5.02358	+	8.70109i	0.182104	+	0.315414i	−0.760493	+	0.649347i	$0.775042\pi$
$762$	−0.426718	−	0.430027i	−0.0154584	−	0.0155782i
$763$		0			0
$764$	17.5572			0.635196
$765$	−0.440044	−	0.258611i	−0.0159098	−	0.00935010i
$766$	5.91762	+	10.2496i	0.213812	+	0.370334i
$767$	−5.53011	+	9.57843i	−0.199681	+	0.345857i
$768$	−18.9646	−	19.1116i	−0.684326	−	0.689632i
$769$	−16.1463	+	27.9663i	−0.582252	+	1.00849i	0.412960	+	0.910749i	$0.364495\pi$
$769$	−16.1463	+	27.9663i	−0.582252	+	1.00849i	−0.995212	+	0.0977407i	$0.968838\pi$
$770$		0			0
$771$	−6.54301	+	24.0470i	−0.235641	+	0.866032i
$772$	0.201270			0.00724385
$773$	−24.2939	−	42.0783i	−0.873792	−	1.51345i	−0.858044	−	0.513576i	$-0.828321\pi$
$773$	−24.2939	−	42.0783i	−0.873792	−	1.51345i	−0.0157473	−	0.999876i	$-0.505013\pi$
$774$	−21.7216	+	12.3183i	−0.780766	+	0.442771i
$775$	−23.1025	+	40.0148i	−0.829867	+	1.43737i
$776$	5.83694	+	10.1099i	0.209534	+	0.362923i
$777$		0			0
$778$	13.3147	−	23.0618i	0.477356	−	0.826806i
$779$	−28.7538	−	49.8030i	−1.03021	−	1.78438i
$780$	−0.250106	−	0.252045i	−0.00895522	−	0.00902466i
$781$	−5.49059	+	9.50998i	−0.196469	+	0.340294i
$782$	1.68759	−	2.92299i	0.0603481	−	0.104526i
$783$	−46.4817	−	13.0337i	−1.66112	−	0.465786i
$784$		0			0
$785$	0.643678	+	1.11488i	0.0229739	+	0.0397919i
$786$	−7.50057	+	27.5663i	−0.267537	+	0.983257i
$787$	−48.9551			−1.74506			−0.872531	−	0.488560i	$-0.837522\pi$
$787$	−48.9551			−1.74506			−0.872531	+	0.488560i	$0.837522\pi$
$788$	0.598331			0.0213147
$789$	2.57745	−	0.679970i	0.0917597	−	0.0242076i
$790$	−0.447448	−	0.775003i	−0.0159195	−	0.0275734i
$791$		0			0
$792$	−26.4994	−	15.5735i	−0.941615	−	0.553381i
$793$	7.03188	−	12.1796i	0.249710	−	0.432510i
$794$	−13.2652	+	22.9759i	−0.470763	+	0.815385i
$795$	−1.76219	+	0.464893i	−0.0624986	+	0.0164880i
$796$	−1.97174	−	3.41515i	−0.0698864	−	0.121047i
$797$	−1.44417	+	2.50137i	−0.0511550	+	0.0886030i	−0.890469	−	0.455044i	$-0.849624\pi$
$797$	−1.44417	+	2.50137i	−0.0511550	+	0.0886030i	0.839314	+	0.543647i	$0.182957\pi$
$798$		0			0
$799$	2.57755	+	4.46445i	0.0911873	+	0.157941i
$800$	−10.3147	+	17.8655i	−0.364678	+	0.631641i
$801$	15.5949	+	9.16502i	0.551018	+	0.323830i
$802$	−0.861472	−	1.49211i	−0.0304196	−	0.0526883i
$803$	15.7647			0.556326
$804$	−9.53510	−	9.60903i	−0.336277	−	0.338884i
$805$		0			0
$806$	12.6649	−	21.9362i	0.446102	−	0.772671i
$807$	−11.9403	+	43.8832i	−0.420317	+	1.54476i
$808$	26.8169	−	46.4483i	0.943417	−	1.63405i
$809$	−5.84869	−	10.1302i	−0.205629	−	0.356160i	0.744704	−	0.667395i	$-0.232591\pi$
$809$	−5.84869	−	10.1302i	−0.205629	−	0.356160i	−0.950333	+	0.311235i	$0.899257\pi$
$810$	0.509328	+	0.914518i	0.0178960	+	0.0321329i
$811$	17.1780			0.603199			0.301600	−	0.953435i	$-0.402479\pi$
$811$	17.1780			0.603199			0.301600	+	0.953435i	$0.402479\pi$
$812$		0			0
$813$	−30.0341	+	7.92343i	−1.05334	+	0.277887i
$814$	−3.64830	−	6.31904i	−0.127873	−	0.221482i
$815$	−0.945254			−0.0331108
$816$	1.33370	−	4.90165i	0.0466889	−	0.171592i
$817$	57.9869			2.02870
$818$	−24.6431			−0.861624
$819$		0			0
$820$	0.618775			0.0216085
$821$	34.0137			1.18709			0.593543	−	0.804803i	$-0.297729\pi$
$821$	34.0137			1.18709			0.593543	+	0.804803i	$0.297729\pi$
$822$	−28.1609	+	7.42925i	−0.982224	+	0.259125i
$823$	43.3780			1.51206			0.756031	−	0.654536i	$-0.227136\pi$
$823$	43.3780			1.51206			0.756031	+	0.654536i	$0.227136\pi$
$824$	−13.4037	−	23.2160i	−0.466942	−	0.808767i
$825$	−7.57125	+	27.8260i	−0.263597	+	0.968779i
$826$		0			0
$827$	−34.0909			−1.18546			−0.592728	−	0.805403i	$-0.701949\pi$
$827$	−34.0909			−1.18546			−0.592728	+	0.805403i	$0.701949\pi$
$828$	3.88050	−	2.20062i	0.134857	−	0.0764770i
$829$	−8.45833	−	14.6503i	−0.293770	−	0.508824i	0.680928	−	0.732350i	$-0.261577\pi$
$829$	−8.45833	−	14.6503i	−0.293770	−	0.508824i	−0.974698	+	0.223526i	$0.928243\pi$
$830$	0.0679744	−	0.117735i	0.00235943	−	0.00408665i
$831$	31.6047	−	8.33778i	1.09635	−	0.289234i
$832$	10.1632	−	17.6032i	0.352345	−	0.610280i
$833$		0			0
$834$	−14.9950	+	3.95591i	−0.519236	+	0.136982i
$835$	−1.83687			−0.0635674
$836$	10.0481	+	17.4039i	0.347522	+	0.601926i
$837$	34.4213	−	33.6329i	1.18977	−	1.16252i
$838$	3.29353	−	5.70456i	0.113773	−	0.197061i
$839$	8.16244	+	14.1378i	0.281799	+	0.488089i	0.971828	−	0.235692i	$-0.0757357\pi$
$839$	8.16244	+	14.1378i	0.281799	+	0.488089i	−0.690029	+	0.723782i	$0.742402\pi$
$840$		0			0
$841$	−28.6560	+	49.6336i	−0.988138	+	1.71150i
$842$	−8.06812	−	13.9744i	−0.278046	−	0.481589i
$843$	2.26989	−	8.34235i	0.0781792	−	0.287326i
$844$	2.82590	−	4.89459i	0.0972713	−	0.168479i
$845$	−0.361214	+	0.625641i	−0.0124261	+	0.0215227i
$846$	0.0816511	−	10.5721i	0.00280722	−	0.363478i
$847$		0			0
$848$	−9.06915	−	15.7082i	−0.311436	−	0.539423i
$849$	18.7792	+	18.9248i	0.644499	+	0.649496i
$850$	−8.87544			−0.304425
$851$	3.76124			0.128934
$852$	−3.14645	−	3.17084i	−0.107796	−	0.108631i
$853$	14.4524	+	25.0323i	0.494841	+	0.857089i	0.999982	−	0.00594733i	$-0.00189311\pi$
$853$	14.4524	+	25.0323i	0.494841	+	0.857089i	−0.505142	+	0.863036i	$0.668560\pi$
$854$		0			0
$855$	0.0187729	−	2.43071i	0.000642020	−	0.0831285i
$856$	27.8547	−	48.2458i	0.952055	−	1.64901i
$857$	−14.5284	+	25.1639i	−0.496280	+	0.859582i	−0.999991	−	0.00429061i	$-0.998634\pi$
$857$	−14.5284	+	25.1639i	−0.496280	+	0.859582i	0.503711	+	0.863872i	$0.331968\pi$
$858$	4.15059	−	15.2543i	0.141699	−	0.520774i
$859$	−6.29820	−	10.9088i	−0.214892	−	0.372203i	0.738347	−	0.674421i	$-0.235607\pi$
$859$	−6.29820	−	10.9088i	−0.214892	−	0.372203i	−0.953239	+	0.302217i	$0.902273\pi$
$860$	−0.311966	+	0.540341i	−0.0106380	+	0.0184255i
$861$		0			0
$862$	−10.6992	−	18.5315i	−0.364415	−	0.631185i
$863$	7.33309	−	12.7013i	0.249621	−	0.432357i	−0.713799	−	0.700350i	$-0.753027\pi$
$863$	7.33309	−	12.7013i	0.249621	−	0.432357i	0.963421	+	0.267993i	$0.0863605\pi$
$864$	15.3682	−	15.0162i	0.522836	−	0.510860i
$865$	0.149199	+	0.258420i	0.00507292	+	0.00878655i
$866$	1.49119			0.0506726
$867$	24.1124	−	6.36122i	0.818901	−	0.216038i
$868$		0			0
$869$	−12.8388	+	22.2375i	−0.435527	+	0.754354i
$870$	1.80968	−	0.477419i	0.0613538	−	0.0161860i
$871$	12.3643	−	21.4156i	0.418948	−	0.725639i
$872$	6.48154	+	11.2264i	0.219493	+	0.380172i
$873$	−9.92307	+	5.62736i	−0.335845	+	0.190457i
$874$	16.0740			0.543711
$875$		0			0
$876$	−1.68370	+	6.18797i	−0.0568869	+	0.209072i
$877$	−16.5951	−	28.7435i	−0.560376	−	0.970600i	−0.997463	−	0.0711811i	$-0.977323\pi$
$877$	−16.5951	−	28.7435i	−0.560376	−	0.970600i	0.437087	−	0.899419i	$-0.356010\pi$
$878$	19.1241			0.645407
$879$	43.2128	−	11.4002i	1.45753	−	0.384518i
$880$	0.639905			0.0215712
$881$	31.7179			1.06860			0.534301	−	0.845294i	$-0.320575\pi$
$881$	31.7179			1.06860			0.534301	+	0.845294i	$0.320575\pi$
$882$		0			0
$883$	−39.5231			−1.33006			−0.665029	−	0.746818i	$-0.731581\pi$
$883$	−39.5231			−1.33006			−0.665029	+	0.746818i	$0.731581\pi$
$884$	−3.13569			−0.105465
$885$	0.213896	−	0.786115i	0.00719003	−	0.0264250i
$886$	−21.6262			−0.726545
$887$	24.9513	+	43.2169i	0.837782	+	1.45108i	0.891745	+	0.452538i	$0.149481\pi$
$887$	24.9513	+	43.2169i	0.837782	+	1.45108i	−0.0539627	+	0.998543i	$0.517185\pi$
$888$	10.1932	−	2.68912i	0.342062	−	0.0902411i
$889$		0			0
$890$	−0.701292			−0.0235074
$891$	15.4179	−	25.7767i	0.516519	−	0.863553i
$892$	−4.38228	−	7.59034i	−0.146730	−	0.254143i
$893$	−12.2754	+	21.2616i	−0.410779	+	0.711491i
$894$	5.59101	−	20.5482i	0.186991	−	0.687235i
$895$	−0.535910	+	0.928223i	−0.0179135	+	0.0310271i
$896$		0			0
$897$	5.74003	+	5.78454i	0.191654	+	0.193140i
$898$	19.5578			0.652653
$899$	−43.0222	−	74.5166i	−1.43487	−	2.48527i
$900$	−10.1136	−	5.94372i	−0.337121	−	0.198124i
$901$	−8.04721	+	13.9382i	−0.268092	+	0.464348i
$902$	13.7747	+	23.8585i	0.458648	+	0.794401i
$903$		0			0
$904$	3.15671	−	5.46757i	0.104990	−	0.181849i
$905$	−0.901048	−	1.56066i	−0.0299518	−	0.0518781i
$906$	−20.8215	+	5.49301i	−0.691747	+	0.182493i
$907$	6.96080	−	12.0565i	0.231129	−	0.400328i	−0.727011	−	0.686625i	$-0.759091\pi$
$907$	6.96080	−	12.0565i	0.231129	−	0.400328i	0.958141	+	0.286298i	$0.0924246\pi$
$908$	9.31574	−	16.1353i	0.309154	−	0.535470i
$909$	45.1853	+	26.5551i	1.49870	+	0.880778i
$910$		0			0
$911$	2.70428	+	4.68394i	0.0895967	+	0.155186i	0.907341	−	0.420396i	$-0.138109\pi$
$911$	2.70428	+	4.68394i	0.0895967	+	0.155186i	−0.817744	+	0.575582i	$0.804776\pi$
$912$	23.3920	−	6.17116i	0.774587	−	0.204347i
$913$	−3.90084			−0.129099
$914$	−0.535362			−0.0177082
$915$	−0.271982	+	0.999594i	−0.00899144	+	0.0330456i
$916$	−0.746758	−	1.29342i	−0.0246736	−	0.0427359i
$917$		0			0
$918$	8.90089	+	2.49585i	0.293773	+	0.0823754i
$919$	−17.0142	+	29.4694i	−0.561245	+	0.972105i	0.436143	+	0.899877i	$0.356344\pi$
$919$	−17.0142	+	29.4694i	−0.561245	+	0.972105i	−0.997388	+	0.0722280i	$0.976989\pi$
$920$	−0.307138	+	0.531978i	−0.0101260	+	0.0175388i
$921$	27.1957	+	27.4065i	0.896129	+	0.903076i
$922$	4.40781	+	7.63455i	0.145163	+	0.251430i
$923$	4.08004	−	7.06683i	0.134296	−	0.232608i
$924$		0			0
$925$	−4.94531	−	8.56554i	−0.162601	−	0.281633i
$926$	−5.78184	+	10.0144i	−0.190003	+	0.329095i
$927$	22.7870	−	12.9225i	0.748423	−	0.424429i
$928$	−19.2082	−	33.2696i	−0.630541	−	1.09213i
$929$	−10.6329			−0.348855			−0.174427	−	0.984670i	$-0.555807\pi$
$929$	−10.6329			−0.348855			−0.174427	+	0.984670i	$0.555807\pi$
$930$	−0.489857	+	1.80033i	−0.0160631	+	0.0590353i
$931$		0			0
$932$	2.56375	−	4.44055i	0.0839785	−	0.145455i
$933$	1.59804	+	1.61043i	0.0523175	+	0.0527231i
$934$	−12.0746	+	20.9137i	−0.395092	+	0.684319i
$935$	−0.283900	−	0.491729i	−0.00928451	−	0.0160812i
$936$	19.6916	+	11.5726i	0.643640	+	0.378263i
$937$	−52.6692			−1.72063			−0.860314	−	0.509765i	$-0.829732\pi$
$937$	−52.6692			−1.72063			−0.860314	+	0.509765i	$0.829732\pi$
$938$		0			0
$939$	−26.3241	−	26.5282i	−0.859053	−	0.865714i
$940$	−0.132082	−	0.228772i	−0.00430802	−	0.00746172i
$941$	34.3656			1.12029			0.560143	−	0.828396i	$-0.310746\pi$
$941$	34.3656			1.12029			0.560143	+	0.828396i	$0.310746\pi$
$942$	−16.4229	−	16.5502i	−0.535087	−	0.539236i
$943$	−14.2011			−0.462453
$944$	8.10825			0.263901
$945$		0			0
$946$	−27.7791			−0.903175
$947$	−40.5840			−1.31880			−0.659401	−	0.751791i	$-0.729190\pi$
$947$	−40.5840			−1.31880			−0.659401	+	0.751791i	$0.729190\pi$
$948$	−7.35743	−	7.41447i	−0.238958	−	0.240811i
$949$	−11.7147			−0.380276
$950$	−21.1342	−	36.6056i	−0.685685	−	1.18764i
$951$	−30.2341	−	30.4685i	−0.980408	−	0.988009i
$952$		0			0
$953$	−22.6904			−0.735013			−0.367507	−	0.930021i	$-0.619789\pi$
$953$	−22.6904			−0.735013			−0.367507	+	0.930021i	$0.619789\pi$
$954$	28.7120	−	16.2825i	0.929586	−	0.527167i
$955$	−1.18122	−	2.04593i	−0.0382234	−	0.0662049i
$956$	−8.36589	+	14.4901i	−0.270572	+	0.468645i
$957$	−37.8264	−	38.1197i	−1.22275	−	1.23223i
$958$	−2.20656	+	3.82187i	−0.0712907	+	0.123479i
$959$		0			0
$960$	−0.393096	+	1.44472i	−0.0126871	+	0.0466280i
$961$	54.7775			1.76702
$962$	2.71104	+	4.69566i	0.0874074	+	0.151394i
$963$	46.9339	+	27.5828i	1.51242	+	0.888842i
$964$	−7.86395	+	13.6208i	−0.253281	+	0.438695i
$965$	−0.0135411	−	0.0234539i	−0.000435904	−	0.000755008i
$966$		0			0
$967$	−12.1388	+	21.0250i	−0.390357	+	0.676118i	−0.992497	−	0.122273i	$-0.960982\pi$
$967$	−12.1388	+	21.0250i	−0.390357	+	0.676118i	0.602139	+	0.798391i	$0.294315\pi$
$968$	−0.211325	−	0.366026i	−0.00679224	−	0.0117645i
$969$	−15.1202	−	15.2375i	−0.485732	−	0.489498i
$970$	0.221136	−	0.383019i	0.00710025	−	0.0122980i
$971$	22.7886	−	39.4709i	0.731319	−	1.26668i	−0.225000	−	0.974359i	$-0.572238\pi$
$971$	22.7886	−	39.4709i	0.731319	−	1.26668i	0.956319	−	0.292324i	$-0.0944285\pi$
$972$	8.47121	+	8.80481i	0.271714	+	0.282414i
$973$		0			0
$974$	−14.5988	−	25.2858i	−0.467774	−	0.810209i
$975$	5.62617	−	20.6774i	0.180182	−	0.662208i
$976$	−10.3102			−0.330020
$977$	−14.6896			−0.469963			−0.234981	−	0.972000i	$-0.575503\pi$
$977$	−14.6896			−0.469963			−0.234981	+	0.972000i	$0.575503\pi$
$978$	16.5534	−	4.36704i	0.529321	−	0.139643i
$979$	10.0612	+	17.4266i	0.321558	+	0.556956i
$980$		0			0
$981$	−11.0189	+	6.24881i	−0.351807	+	0.199509i
$982$	−15.6764	+	27.1524i	−0.500255	+	0.866467i
$983$	−22.2955	+	38.6169i	−0.711115	+	1.23169i	0.253324	+	0.967381i	$0.418476\pi$
$983$	−22.2955	+	38.6169i	−0.711115	+	1.23169i	−0.964439	+	0.264305i	$0.914857\pi$
$984$	−38.4861	+	10.1532i	−1.22689	+	0.323672i
$985$	−0.0402548	−	0.0697234i	−0.00128262	−	0.00222157i
$986$	8.26404	−	14.3137i	0.263181	−	0.455842i
$987$		0			0
$988$	−7.46673	−	12.9328i	−0.237548	−	0.411446i
$989$	7.15976	−	12.4011i	0.227667	−	0.394331i
$990$	−0.00899330	+	1.16445i	−0.000285826	+	0.0370086i
$991$	−12.0915	−	20.9430i	−0.384098	−	0.665277i	0.607546	−	0.794285i	$-0.292154\pi$
$991$	−12.0915	−	20.9430i	−0.384098	−	0.665277i	−0.991644	+	0.129007i	$0.958821\pi$
$992$	38.2973			1.21594
$993$	16.8911	+	17.0221i	0.536024	+	0.540179i
$994$		0			0
$995$	−0.265311	+	0.459532i	−0.00841093	+	0.0145682i
$996$	0.416615	−	1.53115i	0.0132010	−	0.0485165i
$997$	−5.43262	+	9.40957i	−0.172053	+	0.298004i	−0.939137	−	0.343542i	$-0.888373\pi$
$997$	−5.43262	+	9.40957i	−0.172053	+	0.298004i	0.767085	+	0.641546i	$0.221707\pi$
$998$	−4.09760	−	7.09726i	−0.129707	−	0.224660i
$999$	2.55079	+	9.98076i	0.0807034	+	0.315777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.h.373.6		24
3.2	odd	2		1323.2.h.h.226.7		24
7.2	even	3		441.2.f.h.148.7	✓	24
7.3	odd	6		441.2.g.h.67.7		24
7.4	even	3		441.2.g.h.67.8		24
7.5	odd	6		441.2.f.h.148.8	yes	24
7.6	odd	2	inner	441.2.h.h.373.5		24
9.2	odd	6		1323.2.g.h.667.6		24
9.7	even	3		441.2.g.h.79.8		24
21.2	odd	6		1323.2.f.h.442.6		24
21.5	even	6		1323.2.f.h.442.5		24
21.11	odd	6		1323.2.g.h.361.6		24
21.17	even	6		1323.2.g.h.361.5		24
21.20	even	2		1323.2.h.h.226.8		24
63.2	odd	6		1323.2.f.h.883.6		24
63.5	even	6		3969.2.a.bi.1.7		12
63.11	odd	6		1323.2.h.h.802.7		24
63.16	even	3		441.2.f.h.295.7	yes	24
63.20	even	6		1323.2.g.h.667.5		24
63.23	odd	6		3969.2.a.bi.1.8		12
63.25	even	3	inner	441.2.h.h.214.6		24
63.34	odd	6		441.2.g.h.79.7		24
63.38	even	6		1323.2.h.h.802.8		24
63.40	odd	6		3969.2.a.bh.1.6		12
63.47	even	6		1323.2.f.h.883.5		24
63.52	odd	6	inner	441.2.h.h.214.5		24
63.58	even	3		3969.2.a.bh.1.5		12
63.61	odd	6		441.2.f.h.295.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.7	✓	24	7.2	even	3
441.2.f.h.148.8	yes	24	7.5	odd	6
441.2.f.h.295.7	yes	24	63.16	even	3
441.2.f.h.295.8	yes	24	63.61	odd	6
441.2.g.h.67.7		24	7.3	odd	6
441.2.g.h.67.8		24	7.4	even	3
441.2.g.h.79.7		24	63.34	odd	6
441.2.g.h.79.8		24	9.7	even	3
441.2.h.h.214.5		24	63.52	odd	6	inner
441.2.h.h.214.6		24	63.25	even	3	inner
441.2.h.h.373.5		24	7.6	odd	2	inner
441.2.h.h.373.6		24	1.1	even	1	trivial
1323.2.f.h.442.5		24	21.5	even	6
1323.2.f.h.442.6		24	21.2	odd	6
1323.2.f.h.883.5		24	63.47	even	6
1323.2.f.h.883.6		24	63.2	odd	6
1323.2.g.h.361.5		24	21.17	even	6
1323.2.g.h.361.6		24	21.11	odd	6
1323.2.g.h.667.5		24	63.20	even	6
1323.2.g.h.667.6		24	9.2	odd	6
1323.2.h.h.226.7		24	3.2	odd	2
1323.2.h.h.226.8		24	21.20	even	2
1323.2.h.h.802.7		24	63.11	odd	6
1323.2.h.h.802.8		24	63.38	even	6
3969.2.a.bh.1.5		12	63.58	even	3
3969.2.a.bh.1.6		12	63.40	odd	6
3969.2.a.bi.1.7		12	63.5	even	6
3969.2.a.bi.1.8		12	63.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.10281 q^{2} +(1.22001 + 1.22947i) q^{3} -0.783802 q^{4} +(0.0527330 + 0.0913363i) q^{5} +(-1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-0.0231690 + 2.99991i) q^{9} +O(q^{10})\)	\(q-1.10281 q^{2} +(1.22001 + 1.22947i) q^{3} -0.783802 q^{4} +(0.0527330 + 0.0913363i) q^{5} +(-1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-0.0231690 + 2.99991i) q^{9} +(-0.0581547 - 0.100727i) q^{10} +(-1.66866 + 2.89020i) q^{11} +(-0.956244 - 0.963657i) q^{12} +(1.23997 - 2.14770i) q^{13} +(-0.0479602 + 0.176264i) q^{15} -1.81805 q^{16} +(0.806594 + 1.39706i) q^{17} +(0.0255511 - 3.30834i) q^{18} +(-3.84133 + 6.65338i) q^{19} +(-0.0413323 - 0.0715896i) q^{20} +(1.84022 - 3.18735i) q^{22} +(0.948593 + 1.64301i) q^{23} +(3.74544 + 3.77448i) q^{24} +(2.49444 - 4.32049i) q^{25} +(-1.36746 + 2.36851i) q^{26} +(-3.71655 + 3.63142i) q^{27} +(4.64521 + 8.04574i) q^{29} +(0.0528911 - 0.194387i) q^{30} -9.26162 q^{31} -4.13506 q^{32} +(-5.58917 + 1.47451i) q^{33} +(-0.889523 - 1.54070i) q^{34} +(0.0181599 - 2.35134i) q^{36} +(0.991268 - 1.71693i) q^{37} +(4.23627 - 7.33744i) q^{38} +(4.15329 - 1.09570i) q^{39} +(0.161891 + 0.280404i) q^{40} +(-3.74268 + 6.48252i) q^{41} +(-3.77388 - 6.53655i) q^{43} +(1.30790 - 2.26534i) q^{44} +(-0.275223 + 0.156078i) q^{45} +(-1.04612 - 1.81194i) q^{46} +3.19560 q^{47} +(-2.21803 - 2.23523i) q^{48} +(-2.75090 + 4.76470i) q^{50} +(-0.733589 + 2.69610i) q^{51} +(-0.971894 + 1.68337i) q^{52} +(4.98839 + 8.64015i) q^{53} +(4.09866 - 4.00478i) q^{54} -0.351974 q^{55} +(-12.8665 + 3.39438i) q^{57} +(-5.12280 - 8.87296i) q^{58} -4.45986 q^{59} +(0.0375913 - 0.138156i) q^{60} +5.67100 q^{61} +10.2138 q^{62} +8.19630 q^{64} +0.261550 q^{65} +(6.16381 - 1.62610i) q^{66} +9.97141 q^{67} +(-0.632210 - 1.09502i) q^{68} +(-0.862736 + 3.17075i) q^{69} +3.29042 q^{71} +(-0.0711292 + 9.20977i) q^{72} +(-2.36189 - 4.09091i) q^{73} +(-1.09318 + 1.89345i) q^{74} +(8.35513 - 2.20421i) q^{75} +(3.01084 - 5.21493i) q^{76} +(-4.58031 + 1.20835i) q^{78} +7.69409 q^{79} +(-0.0958713 - 0.166054i) q^{80} +(-8.99893 - 0.139010i) q^{81} +(4.12748 - 7.14901i) q^{82} +(0.584428 + 1.01226i) q^{83} +(-0.0850683 + 0.147343i) q^{85} +(4.16189 + 7.20860i) q^{86} +(-4.22477 + 15.5270i) q^{87} +(-5.12280 + 8.87296i) q^{88} +(3.01477 - 5.22173i) q^{89} +(0.303519 - 0.172125i) q^{90} +(-0.743509 - 1.28780i) q^{92} +(-11.2992 - 11.3868i) q^{93} -3.52415 q^{94} -0.810260 q^{95} +(-5.04480 - 5.08391i) q^{96} +(1.90127 + 3.29310i) q^{97} +(-8.63168 - 5.07279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} + 64 q^{51} + 32 q^{53} - 12 q^{57} + 32 q^{60} + 96 q^{64} - 120 q^{65} + 24 q^{67} - 112 q^{71} + 68 q^{74} - 60 q^{78} - 24 q^{79} - 40 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 32 q^{93} - 128 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9 + 20 * q^11 + 4 * q^15 + 24 * q^16 - 32 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 - 84 * q^30 - 96 * q^32 - 4 * q^36 - 12 * q^37 + 8 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 + 64 * q^51 + 32 * q^53 - 12 * q^57 + 32 * q^60 + 96 * q^64 - 120 * q^65 + 24 * q^67 - 112 * q^71 + 68 * q^74 - 60 * q^78 - 24 * q^79 - 40 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 32 * q^93 - 128 * q^95 + 20 * q^99

Introduction

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