LMFDB - Embedded newform 441.2.h.h.214.5

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			214.5
Character	$\chi$	$=$	441.214
Dual form			441.2.h.h.373.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.10281 q^{2} +(-1.22001 + 1.22947i) q^{3} -0.783802 q^{4} +(-0.0527330 + 0.0913363i) q^{5} +(1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-0.0231690 - 2.99991i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	$-0.840841\pi$
$5$	−0.0527330	+	0.0913363i	−0.0235829	+	0.0408468i	0.853993	+	0.520284i	$0.174174\pi$
$6$	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	−0.999994	−	0.00360543i	$-0.998852\pi$
$11$	−1.66866	−	2.89020i	−0.503119	−	0.871428i	0.496874	−	0.867822i	$-0.334481\pi$
$12$	0.956244	−	0.963657i	0.276044	−	0.278184i
$13$	−1.23997	−	2.14770i	−0.343907	−	0.595664i	0.641248	−	0.767334i	$-0.278417\pi$
$13$	−1.23997	−	2.14770i	−0.343907	−	0.595664i	−0.985155	+	0.171670i	$0.945084\pi$
$14$		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	$-0.896008\pi$
$17$	−0.806594	+	1.39706i	−0.195628	+	0.338837i	0.751478	+	0.659758i	$0.229341\pi$
$18$	0.0255511	+	3.30834i	0.00602245	+	0.779784i
$19$	3.84133	+	6.65338i	0.881262	+	1.52639i	0.849939	+	0.526880i	$0.176638\pi$
$19$	3.84133	+	6.65338i	0.881262	+	1.52639i	0.0313221	+	0.999509i	$0.490028\pi$
$20$	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	−0.750018	−	0.661417i	$-0.769955\pi$
$23$	0.948593	−	1.64301i	0.197795	−	0.342592i	0.947813	+	0.318826i	$0.103289\pi$
$24$	−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	−0.00682200	−	0.999977i	$-0.502172\pi$
$29$	4.64521	−	8.04574i	0.862594	−	1.49406i	0.869416	−	0.494080i	$-0.164495\pi$
$30$	0.0528911	+	0.194387i	0.00965655	+	0.0354900i
$31$	9.26162			1.66344			0.831718	−	0.555199i	$-0.187358\pi$
$31$	9.26162			1.66344			0.831718	+	0.555199i	$0.187358\pi$
$32$	−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	0.935930	−	0.352186i	$-0.114561\pi$
$37$	0.991268	+	1.71693i	0.162963	+	0.282261i	−0.772967	+	0.634447i	$0.781228\pi$
$38$	−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	0.994936	+	0.100506i	$0.0320462\pi$
$41$	3.74268	+	6.48252i	0.584509	+	1.01240i	−0.410427	+	0.911893i	$0.634621\pi$
$42$		0			0
$43$	−3.77388	+	6.53655i	−0.575512	+	0.996815i	0.420474	+	0.907304i	$0.361864\pi$
$43$	−3.77388	+	6.53655i	−0.575512	+	0.996815i	−0.995986	+	0.0895108i	$0.971470\pi$
$44$	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	$-0.574875\pi$
$47$	−3.19560			−0.466127			−0.233063	+	0.972462i	$0.574875\pi$
$48$	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	−0.288163	−	0.957581i	$-0.593044\pi$
$53$	4.98839	−	8.64015i	0.685209	−	1.18682i	0.973371	−	0.229234i	$-0.0736223\pi$
$54$	−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	$-0.406241\pi$
$59$	4.45986			0.580625			0.290312	+	0.956932i	$0.406241\pi$
$60$	0.0375913	+	0.138156i	0.00485301	+	0.0178359i
$61$	−5.67100			−0.726097			−0.363048	−	0.931770i	$-0.618264\pi$
$61$	−5.67100			−0.726097			−0.363048	+	0.931770i	$0.618264\pi$
$62$	−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	$-0.744179\pi$
$73$	2.36189	−	4.09091i	0.276438	−	0.478805i	0.970497	+	0.241113i	$0.0775125\pi$
$74$	−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	$-0.853767\pi$
$83$	−0.584428	+	1.01226i	−0.0641493	+	0.111110i	0.832167	+	0.554525i	$0.187100\pi$
$84$		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	$-0.270203\pi$
$89$	−3.01477	−	5.22173i	−0.319565	−	0.553503i	−0.980397	+	0.197031i	$0.936870\pi$
$90$	−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	$-0.895170\pi$
$97$	−1.90127	+	3.29310i	−0.193045	+	0.334364i	0.753213	+	0.657777i	$0.228503\pi$
$98$		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	−0.862839	−	0.505479i	$-0.831316\pi$
$101$	−8.73512	−	15.1297i	−0.869177	−	1.50546i	−0.00633771	−	0.999980i	$-0.502017\pi$
$102$	0.809012	+	2.97330i	0.0801041	+	0.294400i
$103$	4.36602	−	7.56217i	0.430197	−	0.745123i	−0.566693	−	0.823929i	$-0.691777\pi$
$103$	4.36602	−	7.56217i	0.430197	−	0.745123i	0.996890	+	0.0788062i	$0.0251108\pi$
$104$	−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	0.854471	+	0.519500i	$0.173882\pi$
$107$	9.07316	+	15.7152i	0.877135	+	1.51924i	0.0226645	+	0.999743i	$0.492785\pi$
$108$	−2.91304	−	2.84632i	−0.280308	−	0.273887i
$109$	2.11124	−	3.65678i	0.202220	−	0.350256i	−0.747023	−	0.664798i	$-0.768518\pi$
$109$	2.11124	−	3.65678i	0.202220	−	0.350256i	0.949243	+	0.314542i	$0.101851\pi$
$110$	−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	0.910329	−	0.413886i	$-0.135829\pi$
$113$	1.02824	+	1.78096i	0.0967285	+	0.167539i	−0.813600	+	0.581425i	$0.802495\pi$
$114$	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	−0.328930	−	0.944354i	$-0.606688\pi$
$131$	7.47816	−	12.9525i	0.653370	−	1.13167i	0.982300	−	0.187315i	$-0.0599786\pi$
$132$	−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	0.982799	+	0.184676i	$0.0591235\pi$
$137$	7.62367	+	13.2046i	0.651334	+	1.12814i	−0.331466	+	0.943467i	$0.607543\pi$
$138$	−0.951437	−	3.49674i	−0.0809917	−	0.297663i
$139$	−4.05943	−	7.03114i	−0.344316	−	0.596374i	0.640913	−	0.767614i	$-0.278556\pi$
$139$	−4.05943	−	7.03114i	−0.344316	−	0.596374i	−0.985229	+	0.171240i	$0.945223\pi$
$140$		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	−0.542118	−	0.840303i	$-0.682377\pi$
$149$	5.57430	−	9.65497i	0.456664	−	0.790966i	0.998782	+	0.0493365i	$0.0157107\pi$
$150$	9.21415	+	2.43083i	0.752332	+	0.198476i
$151$	5.63676	+	9.76315i	0.458713	+	0.794514i	0.998893	−	0.0470354i	$-0.0149774\pi$
$151$	5.63676	+	9.76315i	0.458713	+	0.794514i	−0.540180	+	0.841549i	$0.681644\pi$
$152$	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	$-0.661940\pi$
$157$	−12.2064			−0.974173			−0.487087	+	0.873354i	$0.661940\pi$
$158$	−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	0.635422	−	0.772165i	$-0.280826\pi$
$163$	−4.48132	−	7.76187i	−0.351004	−	0.607957i	−0.986426	+	0.164209i	$0.947493\pi$
$164$	−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	0.976798	+	0.214165i	$0.0687030\pi$
$167$	8.70833	+	15.0833i	0.673871	+	1.16718i	−0.302927	+	0.953014i	$0.597964\pi$
$168$		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	$-0.534302\pi$
$173$	−2.82933			−0.215110			−0.107555	+	0.994199i	$0.534302\pi$
$174$	−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	−0.611235	−	0.791449i	$-0.709327\pi$
$179$	5.08135	−	8.80115i	0.379798	−	0.657829i	0.991033	+	0.133620i	$0.0426603\pi$
$180$	−0.215720	−	0.122334i	−0.0160788	−	0.00911827i
$181$	17.0870			1.27006			0.635032	−	0.772486i	$-0.280987\pi$
$181$	17.0870			1.27006			0.635032	+	0.772486i	$0.280987\pi$
$182$		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	$-0.890402\pi$
$199$	−2.51561	+	4.35716i	−0.178327	+	0.308871i	0.762981	+	0.646421i	$0.223735\pi$
$200$	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	0.714824	−	0.699305i	$-0.246507\pi$
$211$	−3.60537	−	6.24468i	−0.248204	−	0.429901i	−0.963027	+	0.269403i	$0.913174\pi$
$212$	−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	$-0.955486\pi$
$223$	−5.59106	+	9.68400i	−0.374405	+	0.648488i	0.615833	+	0.787877i	$0.288820\pi$
$224$		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	0.926668	+	0.375881i	$0.122660\pi$
$227$	11.8853	+	20.5860i	0.788857	+	1.36634i	−0.137811	+	0.990459i	$0.544007\pi$
$228$	10.0848	+	2.66052i	0.667884	+	0.176198i
$229$	−0.952737	+	1.65019i	−0.0629586	+	0.109048i	−0.895787	−	0.444484i	$-0.853387\pi$
$229$	−0.952737	+	1.65019i	−0.0629586	+	0.109048i	0.832828	+	0.553532i	$0.186720\pi$
$230$	−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	0.738766	−	0.673962i	$-0.235409\pi$
$233$	−3.27092	−	5.66540i	−0.214285	−	0.371153i	−0.953051	+	0.302809i	$0.902075\pi$
$234$	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	0.971704	+	0.236202i	$0.0759028\pi$
$239$	10.6735	+	18.4870i	0.690409	+	1.19582i	−0.281295	+	0.959621i	$0.590764\pi$
$240$	0.0871940	+	0.320457i	0.00562835	+	0.0206854i
$241$	−10.0331	−	17.3778i	−0.646288	−	1.11940i	−0.984003	−	0.178155i	$-0.942987\pi$
$241$	−10.0331	−	17.3778i	−0.646288	−	1.11940i	0.337715	−	0.941248i	$-0.390346\pi$
$242$	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	$-0.431002\pi$
$251$	6.81467			0.430138			0.215069	+	0.976599i	$0.431002\pi$
$252$		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	$-0.981467\pi$
$257$	−7.19415	+	12.4606i	−0.448759	+	0.777273i	0.549546	+	0.835463i	$0.314801\pi$
$258$	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	0.888775	−	0.458344i	$-0.151557\pi$
$263$	0.769503	+	1.33282i	0.0474496	+	0.0821851i	−0.841325	+	0.540529i	$0.818224\pi$
$264$	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	0.118852	+	0.992912i	$0.462079\pi$
$269$	−13.1285	+	22.7393i	−0.800461	+	1.38644i	−0.919313	+	0.393527i	$0.871255\pi$
$270$	0.581917	−	0.163172i	0.0354144	−	0.00993035i
$271$	8.96673	+	15.5308i	0.544690	+	0.943431i	0.998626	+	0.0523969i	$0.0166861\pi$
$271$	8.96673	+	15.5308i	0.544690	+	0.943431i	−0.453936	+	0.891034i	$0.649981\pi$
$272$	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	0.996867	+	0.0790954i	$0.0252032\pi$
$277$	9.43563	+	16.3430i	0.566932	+	0.981955i	−0.429935	+	0.902860i	$0.641463\pi$
$278$	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	−0.930816	−	0.365488i	$-0.880902\pi$
$281$	−2.49578	+	4.32283i	−0.148886	+	0.257878i	0.781930	+	0.623366i	$0.214235\pi$
$282$	−4.29949	+	4.33282i	−0.256031	+	0.258016i
$283$	−15.3927			−0.915000			−0.457500	−	0.889210i	$-0.651255\pi$
$283$	−15.3927			−0.915000			−0.457500	+	0.889210i	$0.651255\pi$
$284$	−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	−0.946018	−	0.324114i	$-0.894934\pi$
$293$	−12.9013	−	22.3456i	−0.753700	−	1.30545i	0.192318	−	0.981333i	$-0.438399\pi$
$294$		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	$-0.719462\pi$
$307$	−22.2914			−1.27224			−0.636120	+	0.771590i	$0.719462\pi$
$308$		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	$-0.511824\pi$
$311$	−1.30986			−0.0742755			−0.0371377	+	0.999310i	$0.511824\pi$
$312$	12.7507	+	3.36382i	0.721865	+	0.190439i
$313$	21.5770			1.21960			0.609802	−	0.792554i	$-0.291249\pi$
$313$	21.5770			1.21960			0.609802	+	0.792554i	$0.291249\pi$
$314$	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	0.908479	−	0.417930i	$-0.137244\pi$
$337$	1.69444	+	2.93485i	0.0923018	+	0.159871i	−0.816178	+	0.577801i	$0.803911\pi$
$338$	−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	$-0.695028\pi$
$349$	7.86412	−	13.6211i	0.420957	−	0.729119i	0.996033	+	0.0889810i	$0.0283610\pi$
$350$		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	$-0.131490\pi$
$353$	2.07211	+	3.58900i	0.110287	+	0.191023i	−0.805599	+	0.592462i	$0.798156\pi$
$354$	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	0.742040	−	0.670356i	$-0.233859\pi$
$359$	−3.96994	−	6.87614i	−0.209525	−	0.362909i	−0.951565	+	0.307447i	$0.900525\pi$
$360$	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	$-0.0551596\pi$
$367$	6.57455	+	11.3875i	0.343189	+	0.594420i	−0.641834	+	0.766843i	$0.721826\pi$
$368$	−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	−0.949242	−	0.314547i	$-0.898147\pi$
$373$	−3.90543	+	6.76441i	−0.202216	+	0.350248i	0.747026	+	0.664794i	$0.231481\pi$
$374$	−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	$-0.744925\pi$
$383$	5.36593	−	9.29407i	0.274186	−	0.474905i	0.969930	+	0.243386i	$0.0782582\pi$
$384$	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	−0.990878	−	0.134763i	$-0.956973\pi$
$389$	−12.0734	−	20.9118i	−0.612147	−	1.06027i	0.378731	−	0.925507i	$-0.376361\pi$
$390$	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	−0.992257	−	0.124203i	$-0.960363\pi$
$397$	−12.0285	−	20.8339i	−0.603691	−	1.04562i	0.388566	−	0.921421i	$-0.372971\pi$
$398$	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	−0.845862	−	0.533402i	$-0.820913\pi$
$401$	0.781158	−	1.35301i	0.0390092	−	0.0675659i	0.884871	+	0.465836i	$0.154247\pi$
$402$	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	$-0.686311\pi$
$409$	−22.3456			−1.10492			−0.552460	+	0.833539i	$0.686311\pi$
$410$	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	$-0.120059\pi$
$419$	2.98648	+	5.17273i	0.145899	+	0.252704i	−0.783809	+	0.621002i	$0.786726\pi$
$420$		0			0
$421$	7.31594	−	12.6716i	0.356557	−	0.617575i	−0.630826	−	0.775924i	$-0.717284\pi$
$421$	7.31594	−	12.6716i	0.356557	−	0.617575i	0.987383	+	0.158349i	$0.0506172\pi$
$422$	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	−0.531989	−	0.846751i	$-0.678555\pi$
$431$	9.70169	−	16.8038i	0.467314	−	0.809411i	0.999303	+	0.0373401i	$0.0118885\pi$
$432$	−6.75688	−	6.60211i	−0.325090	−	0.317644i
$433$	1.35217			0.0649810			0.0324905	−	0.999472i	$-0.489656\pi$
$433$	1.35217			0.0649810			0.0324905	+	0.999472i	$0.489656\pi$
$434$		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	$-0.364193\pi$
$439$	17.3412			0.827650			0.413825	+	0.910356i	$0.364193\pi$
$440$	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	$-0.773731\pi$
$461$	3.99687	−	6.92279i	0.186153	−	0.322426i	0.943964	+	0.330047i	$0.107065\pi$
$462$		0			0
$463$	5.24280	+	9.08080i	0.243654	+	0.422021i	0.961752	−	0.273921i	$-0.0883206\pi$
$463$	5.24280	+	9.08080i	0.243654	+	0.422021i	−0.718098	+	0.695942i	$0.754987\pi$
$464$	−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	−0.999970	−	0.00769944i	$-0.997549\pi$
$467$	−10.9489	−	18.9640i	−0.506653	−	0.877549i	0.493317	−	0.869849i	$-0.335784\pi$
$468$	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	$-0.195808\pi$
$479$	−2.00085	−	3.46557i	−0.0914210	−	0.158346i	−0.908109	+	0.418733i	$0.862474\pi$
$480$	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	−0.392982	−	0.919546i	$-0.628557\pi$
$487$	13.2377	−	22.9284i	0.599859	−	1.03899i	0.992841	−	0.119440i	$-0.0381100\pi$
$488$	−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	0.985096	+	0.172008i	$0.0550255\pi$
$491$	14.2149	+	24.6210i	0.641511	+	1.11113i	−0.343584	+	0.939122i	$0.611641\pi$
$492$	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	−0.770795	−	0.637083i	$-0.780141\pi$
$499$	3.71559	−	6.43559i	0.166333	−	0.288097i	0.937128	+	0.348986i	$0.113474\pi$
$500$	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	$-0.572738\pi$
$503$	−10.1610			−0.453057			−0.226529	+	0.974004i	$0.572738\pi$
$504$		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	0.344668	+	0.938725i	$0.387991\pi$
$509$	−14.4532	+	25.0336i	−0.640625	+	1.10960i	−0.985293	+	0.170871i	$0.945342\pi$
$510$	−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	−0.211941	−	0.977283i	$-0.567978\pi$
$521$	16.8995	−	29.2708i	0.740381	−	1.28238i	0.952322	−	0.305095i	$-0.0986883\pi$
$522$	26.7368	+	15.1624i	1.17024	+	0.663639i
$523$	−7.18895	−	12.4516i	−0.314351	−	0.544471i	0.664949	−	0.746889i	$-0.268453\pi$
$523$	−7.18895	−	12.4516i	−0.314351	−	0.544471i	−0.979299	+	0.202418i	$0.935120\pi$
$524$	−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	0.998835	+	0.0482577i	$0.0153669\pi$
$541$	12.5882	+	21.8034i	0.541210	+	0.937403i	−0.457625	+	0.889145i	$0.651300\pi$
$542$	−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	−0.830027	−	0.557723i	$-0.811675\pi$
$547$	1.59011	−	2.75416i	0.0679883	−	0.117759i	0.898016	+	0.439963i	$0.145009\pi$
$548$	−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	−0.996391	−	0.0848820i	$-0.972949\pi$
$557$	−10.0229	+	17.3602i	−0.424686	+	0.735577i	0.571705	+	0.820459i	$0.306282\pi$
$558$	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	$-0.816691\pi$
$563$	−39.8013			−1.67743			−0.838713	+	0.544574i	$0.816691\pi$
$564$	−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	0.468733	+	0.883340i	$0.344711\pi$
$577$	−12.7461	+	22.0769i	−0.530628	+	0.919075i	−0.999361	+	0.0357353i	$0.988623\pi$
$578$	−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	0.236795	+	0.971560i	$0.423903\pi$
$587$	−17.5168	+	30.3401i	−0.722998	+	1.25227i	−0.959793	+	0.280709i	$0.909430\pi$
$588$		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	0.951664	+	0.307141i	$0.0993724\pi$
$593$	18.0646	+	31.2888i	0.741824	+	1.28488i	−0.209840	+	0.977736i	$0.567294\pi$
$594$	−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	−0.475244	−	0.879854i	$-0.657640\pi$
$601$	12.8547	−	22.2650i	0.524354	−	0.908207i	0.999598	−	0.0283533i	$-0.00902635\pi$
$602$		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	$-0.877696\pi$
$607$	−3.42258	+	5.92808i	−0.138918	+	0.240613i	0.788169	+	0.615459i	$0.211029\pi$
$608$	−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	−0.406191	−	0.913788i	$-0.633143\pi$
$613$	14.5648	−	25.2271i	0.588269	−	1.01891i	0.994459	−	0.105123i	$-0.0335235\pi$
$614$	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	0.579307	−	0.815109i	$-0.303323\pi$
$617$	−10.3395	−	17.9085i	−0.416252	−	0.720969i	−0.995559	+	0.0941404i	$0.969990\pi$
$618$	−4.37911	−	16.0942i	−0.176154	−	0.647404i
$619$	4.43178	+	7.67606i	0.178128	+	0.308527i	0.941239	−	0.337740i	$-0.109663\pi$
$619$	4.43178	+	7.67606i	0.178128	+	0.308527i	−0.763111	+	0.646267i	$0.776329\pi$
$620$	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	0.981812	−	0.189856i	$-0.0608022\pi$
$641$	8.26595	+	14.3171i	0.326486	+	0.565489i	−0.655326	+	0.755346i	$0.727469\pi$
$642$	33.5151	+	8.84178i	1.32274	+	0.348957i
$643$	−15.4460	−	26.7532i	−0.609130	−	1.05504i	−0.991384	−	0.130987i	$-0.958185\pi$
$643$	−15.4460	−	26.7532i	−0.609130	−	1.05504i	0.382254	−	0.924057i	$-0.375148\pi$
$644$		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	$-0.825200\pi$
$647$	0.649903	−	1.12567i	0.0255503	−	0.0442545i	0.878518	+	0.477710i	$0.158533\pi$
$648$	−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	0.0250558	−	0.999686i	$-0.492024\pi$
$653$	22.4435	−	38.8733i	0.878281	−	1.52123i	0.853226	−	0.521542i	$-0.174643\pi$
$654$	−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	−0.636992	−	0.770870i	$-0.719822\pi$
$659$	8.96167	−	15.5221i	0.349097	−	0.604654i	0.986089	+	0.166216i	$0.0531549\pi$
$660$	0.336572	−	0.339182i	0.0131011	−	0.0132026i
$661$	33.0256			1.28455			0.642274	−	0.766475i	$-0.277991\pi$
$661$	33.0256			1.28455			0.642274	+	0.766475i	$0.277991\pi$
$662$	−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	−0.995056	−	0.0993135i	$-0.968335\pi$
$673$	−10.6758	+	18.4909i	−0.411520	+	0.712774i	0.583536	+	0.812087i	$0.301669\pi$
$674$	−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	$-0.449002\pi$
$677$	8.30167			0.319059			0.159530	+	0.987193i	$0.449002\pi$
$678$	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	−0.888902	−	0.458098i	$-0.848531\pi$
$683$	−1.24728	+	2.16036i	−0.0477259	+	0.0826637i	0.841176	+	0.540762i	$0.181864\pi$
$684$	−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	$-0.603974\pi$
$691$	−16.8691			−0.641731			−0.320865	+	0.947125i	$0.603974\pi$
$692$	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	$-0.164087\pi$
$719$	0.217311	+	0.376394i	0.00810433	+	0.0140371i	−0.861945	+	0.507002i	$0.830754\pi$
$720$	−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	−0.496192	−	0.868213i	$-0.665269\pi$
$727$	13.5839	−	23.5280i	0.503799	−	0.872605i	0.999990	−	0.00439187i	$-0.00139798\pi$
$728$		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	$-0.799964\pi$
$733$	2.83307	−	4.90702i	0.104642	−	0.181245i	0.913592	+	0.406632i	$0.133297\pi$
$734$	−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	−0.713279	−	0.700880i	$-0.752791\pi$
$739$	6.80540	−	11.7873i	0.250341	−	0.433603i	0.963620	+	0.267278i	$0.0861241\pi$
$740$	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	0.726128	−	0.687559i	$-0.241318\pi$
$743$	−6.33421	−	10.9712i	−0.232380	−	0.402493i	−0.958508	+	0.285066i	$0.907985\pi$
$744$	−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	−0.793450	−	0.608636i	$-0.791717\pi$
$751$	3.57269	−	6.18808i	0.130369	−	0.225806i	0.923819	+	0.382830i	$0.125050\pi$
$752$	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	$-0.891624\pi$
$761$	−5.02358	+	8.70109i	−0.182104	+	0.315414i	0.760493	+	0.649347i	$0.224958\pi$
$762$	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	0.995212	+	0.0977407i	$0.0311616\pi$
$769$	16.1463	+	27.9663i	0.582252	+	1.00849i	−0.412960	+	0.910749i	$0.635505\pi$
$770$		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	0.0157473	−	0.999876i	$-0.494987\pi$
$773$	24.2939	−	42.0783i	0.873792	−	1.51345i	0.858044	−	0.513576i	$-0.171679\pi$
$774$	−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	$-0.162478\pi$
$787$	48.9551			1.74506			0.872531	+	0.488560i	$0.162478\pi$
$788$	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	$-0.150376\pi$
$797$	1.44417	+	2.50137i	0.0511550	+	0.0886030i	−0.839314	+	0.543647i	$0.817043\pi$
$798$		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	−0.950333	−	0.311235i	$-0.899257\pi$
$809$	−5.84869	+	10.1302i	−0.205629	+	0.356160i	0.744704	+	0.667395i	$0.232591\pi$
$810$	−0.509328	+	0.914518i	−0.0178960	+	0.0321329i
$811$	−17.1780			−0.603199			−0.301600	−	0.953435i	$-0.597521\pi$
$811$	−17.1780			−0.603199			−0.301600	+	0.953435i	$0.597521\pi$
$812$		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	$-0.738423\pi$
$829$	8.45833	−	14.6503i	0.293770	−	0.508824i	0.974698	+	0.223526i	$0.0717567\pi$
$830$	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	$-0.924264\pi$
$839$	−8.16244	+	14.1378i	−0.281799	+	0.488089i	0.690029	+	0.723782i	$0.257598\pi$
$840$		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	$-0.998107\pi$
$853$	−14.4524	+	25.0323i	−0.494841	+	0.857089i	0.505142	+	0.863036i	$0.331440\pi$
$854$		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	$-0.00136575\pi$
$857$	14.5284	+	25.1639i	0.496280	+	0.859582i	−0.503711	+	0.863872i	$0.668032\pi$
$858$	4.15059	+	15.2543i	0.141699	+	0.520774i
$859$	6.29820	−	10.9088i	0.214892	−	0.372203i	−0.738347	−	0.674421i	$-0.764393\pi$
$859$	6.29820	−	10.9088i	0.214892	−	0.372203i	0.953239	+	0.302217i	$0.0977268\pi$
$860$	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	0.963421	−	0.267993i	$-0.0863605\pi$
$863$	7.33309	+	12.7013i	0.249621	+	0.432357i	−0.713799	+	0.700350i	$0.753027\pi$
$864$	−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	0.437087	+	0.899419i	$0.356010\pi$
$877$	−16.5951	+	28.7435i	−0.560376	+	0.970600i	−0.997463	+	0.0711811i	$0.977323\pi$
$878$	−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	$-0.679425\pi$
$881$	−31.7179			−1.06860			−0.534301	+	0.845294i	$0.679425\pi$
$882$		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	0.0539627	+	0.998543i	$0.482815\pi$
$887$	−24.9513	+	43.2169i	−0.837782	+	1.45108i	−0.891745	+	0.452538i	$0.850519\pi$
$888$	−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	0.958141	−	0.286298i	$-0.0924246\pi$
$907$	6.96080	+	12.0565i	0.231129	+	0.400328i	−0.727011	+	0.686625i	$0.759091\pi$
$908$	−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	−0.817744	−	0.575582i	$-0.804776\pi$
$911$	2.70428	−	4.68394i	0.0895967	−	0.155186i	0.907341	+	0.420396i	$0.138109\pi$
$912$	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	−0.997388	−	0.0722280i	$-0.976989\pi$
$919$	−17.0142	−	29.4694i	−0.561245	−	0.972105i	0.436143	−	0.899877i	$-0.356344\pi$
$920$	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	$-0.444193\pi$
$929$	10.6329			0.348855			0.174427	+	0.984670i	$0.444193\pi$
$930$	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	$-0.170268\pi$
$937$	52.6692			1.72063			0.860314	+	0.509765i	$0.170268\pi$
$938$		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	$-0.689254\pi$
$941$	−34.3656			−1.12029			−0.560143	+	0.828396i	$0.689254\pi$
$942$	−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	0.602139	−	0.798391i	$-0.294315\pi$
$967$	−12.1388	−	21.0250i	−0.390357	−	0.676118i	−0.992497	+	0.122273i	$0.960982\pi$
$968$	−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	−0.956319	−	0.292324i	$-0.905572\pi$
$971$	−22.7886	−	39.4709i	−0.731319	−	1.26668i	0.225000	−	0.974359i	$-0.427762\pi$
$972$	−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	0.964439	+	0.264305i	$0.0851427\pi$
$983$	22.2955	+	38.6169i	0.711115	+	1.23169i	−0.253324	+	0.967381i	$0.581524\pi$
$984$	−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	−0.991644	−	0.129007i	$-0.958821\pi$
$991$	−12.0915	+	20.9430i	−0.384098	+	0.665277i	0.607546	+	0.794285i	$0.292154\pi$
$992$	−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	$-0.111627\pi$
$997$	5.43262	+	9.40957i	0.172053	+	0.298004i	−0.767085	+	0.641546i	$0.778293\pi$
$998$	−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.214.5		24
3.2	odd	2		1323.2.h.h.802.8		24
7.2	even	3		441.2.g.h.79.7		24
7.3	odd	6		441.2.f.h.295.7	yes	24
7.4	even	3		441.2.f.h.295.8	yes	24
7.5	odd	6		441.2.g.h.79.8		24
7.6	odd	2	inner	441.2.h.h.214.6		24
9.4	even	3		441.2.g.h.67.7		24
9.5	odd	6		1323.2.g.h.361.5		24
21.2	odd	6		1323.2.g.h.667.5		24
21.5	even	6		1323.2.g.h.667.6		24
21.11	odd	6		1323.2.f.h.883.5		24
21.17	even	6		1323.2.f.h.883.6		24
21.20	even	2		1323.2.h.h.802.7		24
63.4	even	3		441.2.f.h.148.8	yes	24
63.5	even	6		1323.2.h.h.226.7		24
63.11	odd	6		3969.2.a.bi.1.7		12
63.13	odd	6		441.2.g.h.67.8		24
63.23	odd	6		1323.2.h.h.226.8		24
63.25	even	3		3969.2.a.bh.1.6		12
63.31	odd	6		441.2.f.h.148.7	✓	24
63.32	odd	6		1323.2.f.h.442.5		24
63.38	even	6		3969.2.a.bi.1.8		12
63.40	odd	6	inner	441.2.h.h.373.6		24
63.41	even	6		1323.2.g.h.361.6		24
63.52	odd	6		3969.2.a.bh.1.5		12
63.58	even	3	inner	441.2.h.h.373.5		24
63.59	even	6		1323.2.f.h.442.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.7	✓	24	63.31	odd	6
441.2.f.h.148.8	yes	24	63.4	even	3
441.2.f.h.295.7	yes	24	7.3	odd	6
441.2.f.h.295.8	yes	24	7.4	even	3
441.2.g.h.67.7		24	9.4	even	3
441.2.g.h.67.8		24	63.13	odd	6
441.2.g.h.79.7		24	7.2	even	3
441.2.g.h.79.8		24	7.5	odd	6
441.2.h.h.214.5		24	1.1	even	1	trivial
441.2.h.h.214.6		24	7.6	odd	2	inner
441.2.h.h.373.5		24	63.58	even	3	inner
441.2.h.h.373.6		24	63.40	odd	6	inner
1323.2.f.h.442.5		24	63.32	odd	6
1323.2.f.h.442.6		24	63.59	even	6
1323.2.f.h.883.5		24	21.11	odd	6
1323.2.f.h.883.6		24	21.17	even	6
1323.2.g.h.361.5		24	9.5	odd	6
1323.2.g.h.361.6		24	63.41	even	6
1323.2.g.h.667.5		24	21.2	odd	6
1323.2.g.h.667.6		24	21.5	even	6
1323.2.h.h.226.7		24	63.5	even	6
1323.2.h.h.226.8		24	63.23	odd	6
1323.2.h.h.802.7		24	21.20	even	2
1323.2.h.h.802.8		24	3.2	odd	2
3969.2.a.bh.1.5		12	63.52	odd	6
3969.2.a.bh.1.6		12	63.25	even	3
3969.2.a.bi.1.7		12	63.11	odd	6
3969.2.a.bi.1.8		12	63.38	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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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