LMFDB - Embedded newform 441.2.f.h.148.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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([2, 0]))

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

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, degree $2$, 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			148.8
Character	$\chi$	$=$	441.148
Dual form			441.2.f.h.295.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.551407 + 0.955065i) q^{2} +(1.67475 - 0.441824i) q^{3} +(0.391901 - 0.678793i) q^{4} +(-0.0527330 + 0.0913363i) q^{5} +(1.34544 + 1.35587i) q^{6} +3.07001 q^{8} +(2.60958 - 1.47989i) q^{9} +O(q^{10})$	\(q+(0.551407 + 0.955065i) q^{2} +(1.67475 - 0.441824i) q^{3} +(0.391901 - 0.678793i) q^{4} +(-0.0527330 + 0.0913363i) q^{5} +(1.34544 + 1.35587i) q^{6} +3.07001 q^{8} +(2.60958 - 1.47989i) q^{9} -0.116309 q^{10} +(-1.66866 - 2.89020i) q^{11} +(0.356430 - 1.30996i) q^{12} +(-1.23997 + 2.14770i) q^{13} +(-0.0479602 + 0.176264i) q^{15} +(0.909025 + 1.57448i) q^{16} +1.61319 q^{17} +(2.85233 + 1.67630i) q^{18} -7.68266 q^{19} +(0.0413323 + 0.0715896i) q^{20} +(1.84022 - 3.18735i) q^{22} +(0.948593 - 1.64301i) q^{23} +(5.14151 - 1.35641i) q^{24} +(2.49444 + 4.32049i) q^{25} -2.73492 q^{26} +(3.71655 - 3.63142i) q^{27} +(4.64521 + 8.04574i) q^{29} +(-0.194789 + 0.0513883i) q^{30} +(-4.63081 + 8.02080i) q^{31} +(2.06753 - 3.58107i) q^{32} +(-4.07155 - 4.10311i) q^{33} +(0.889523 + 1.54070i) q^{34} +(0.0181599 - 2.35134i) q^{36} -1.98254 q^{37} +(-4.23627 - 7.33744i) q^{38} +(-1.12774 + 4.14471i) q^{39} +(-0.161891 + 0.280404i) q^{40} +(3.74268 - 6.48252i) q^{41} +(-3.77388 - 6.53655i) q^{43} -2.61579 q^{44} +(-0.00244354 + 0.316389i) q^{45} +2.09224 q^{46} +(1.59780 + 2.76747i) q^{47} +(2.21803 + 2.23523i) q^{48} +(-2.75090 + 4.76470i) q^{50} +(2.70169 - 0.712745i) q^{51} +(0.971894 + 1.68337i) q^{52} -9.97679 q^{53} +(5.51758 + 1.54715i) q^{54} +0.351974 q^{55} +(-12.8665 + 3.39438i) q^{57} +(-5.12280 + 8.87296i) q^{58} +(-2.22993 + 3.86235i) q^{59} +(0.100851 + 0.101633i) q^{60} +(2.83550 + 4.91123i) q^{61} -10.2138 q^{62} +8.19630 q^{64} +(-0.130775 - 0.226509i) q^{65} +(1.67366 - 6.15107i) q^{66} +(-4.98571 + 8.63550i) q^{67} +(0.632210 - 1.09502i) q^{68} +(0.862736 - 3.17075i) q^{69} +3.29042 q^{71} +(8.01146 - 4.54329i) q^{72} -4.72378 q^{73} +(-1.09318 - 1.89345i) q^{74} +(6.08646 + 6.13365i) q^{75} +(-3.01084 + 5.21493i) q^{76} +(-4.58031 + 1.20835i) q^{78} +(-3.84705 - 6.66328i) q^{79} -0.191743 q^{80} +(4.61985 - 7.72379i) q^{81} +8.25496 q^{82} +(-0.584428 - 1.01226i) q^{83} +(-0.0850683 + 0.147343i) q^{85} +(4.16189 - 7.20860i) q^{86} +(11.3344 + 11.4223i) q^{87} +(-5.12280 - 8.87296i) q^{88} +6.02954 q^{89} +(-0.303519 + 0.172125i) q^{90} +(-0.743509 - 1.28780i) q^{92} +(-4.21167 + 15.4788i) q^{93} +(-1.76208 + 3.05201i) q^{94} +(0.405130 - 0.701706i) q^{95} +(1.88040 - 6.91088i) q^{96} +(-1.90127 - 3.29310i) q^{97} +(-8.63168 - 5.07279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9} + 20 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} + 48 q^{32} - 4 q^{36} + 24 q^{37} + 32 q^{39} - 112 q^{44} - 48 q^{46} - 4 q^{50} - 56 q^{51} - 64 q^{53} - 12 q^{57} - 88 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} + 168 q^{72} + 68 q^{74} - 60 q^{78} + 12 q^{79} + 80 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 80 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9 + 20 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 + 48 * q^32 - 4 * q^36 + 24 * q^37 + 32 * q^39 - 112 * q^44 - 48 * q^46 - 4 * q^50 - 56 * q^51 - 64 * q^53 - 12 * q^57 - 88 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 + 168 * q^72 + 68 * q^74 - 60 * q^78 + 12 * q^79 + 80 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 80 * q^93 + 64 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.551407	+	0.955065i	0.389903	+	0.675333i	0.992436	−	0.122762i	$-0.0391750\pi$
$2$	0.551407	+	0.955065i	0.389903	+	0.675333i	−0.602533	+	0.798094i	$0.705842\pi$
$3$	1.67475	−	0.441824i	0.966918	−	0.255087i
$3$	1.67475	−	0.441824i	0.966918	−	0.255087i
$4$	0.391901	−	0.678793i	0.195951	−	0.339396i
$5$	−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
$9$	2.60958	−	1.47989i	0.869861	−	0.493297i
$10$	−0.116309			−0.0367803
$11$	−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	$-0.334481\pi$
$12$	0.356430	−	1.30996i	0.102892	−	0.378153i
$13$	−1.23997	+	2.14770i	−0.343907	+	0.595664i	−0.985155	−	0.171670i	$-0.945084\pi$
$13$	−1.23997	+	2.14770i	−0.343907	+	0.595664i	0.641248	+	0.767334i	$0.278417\pi$
$14$		0			0
$15$	−0.0479602	+	0.176264i	−0.0123833	+	0.0455113i
$16$	0.909025	+	1.57448i	0.227256	+	0.393619i
$17$	1.61319			0.391255			0.195628	−	0.980678i	$-0.437326\pi$
$17$	1.61319			0.391255			0.195628	+	0.980678i	$0.437326\pi$
$18$	2.85233	+	1.67630i	0.672301	+	0.395107i
$19$	−7.68266			−1.76252			−0.881262	−	0.472629i	$-0.843305\pi$
$19$	−7.68266			−1.76252			−0.881262	+	0.472629i	$0.843305\pi$
$20$	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	$0.103289\pi$
$24$	5.14151	−	1.35641i	1.04951	−	0.276875i
$25$	2.49444	+	4.32049i	0.498888	+	0.864099i
$26$	−2.73492			−0.536362
$27$	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	$0.502172\pi$
$30$	−0.194789	+	0.0513883i	−0.0355635	+	0.00938218i
$31$	−4.63081	+	8.02080i	−0.831718	+	1.44058i	0.0649574	+	0.997888i	$0.479309\pi$
$31$	−4.63081	+	8.02080i	−0.831718	+	1.44058i	−0.896675	+	0.442689i	$0.854024\pi$
$32$	2.06753	−	3.58107i	0.365491	−	0.633049i
$33$	−4.07155	−	4.10311i	−0.708765	−	0.714260i
$34$	0.889523	+	1.54070i	0.152552	+	0.264228i
$35$		0			0
$36$	0.0181599	−	2.35134i	0.00302665	−	0.391889i
$37$	−1.98254			−0.325927			−0.162963	−	0.986632i	$-0.552105\pi$
$37$	−1.98254			−0.325927			−0.162963	+	0.986632i	$0.552105\pi$
$38$	−4.23627	−	7.33744i	−0.687214	−	1.19029i
$39$	−1.12774	+	4.14471i	−0.180583	+	0.663684i
$40$	−0.161891	+	0.280404i	−0.0255973	+	0.0443357i
$41$	3.74268	−	6.48252i	0.584509	−	1.01240i	−0.410427	−	0.911893i	$-0.634621\pi$
$41$	3.74268	−	6.48252i	0.584509	−	1.01240i	0.994936	−	0.100506i	$-0.0320462\pi$
$42$		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	$-0.361864\pi$
$44$	−2.61579			−0.394346
$45$	−0.00244354	+	0.316389i	−0.000364262	+	0.0471645i
$46$	2.09224			0.308484
$47$	1.59780	+	2.76747i	0.233063	+	0.403677i	0.958708	−	0.284392i	$-0.0917917\pi$
$47$	1.59780	+	2.76747i	0.233063	+	0.403677i	−0.725645	+	0.688070i	$0.758458\pi$
$48$	2.21803	+	2.23523i	0.320145	+	0.322627i
$49$		0			0
$50$	−2.75090	+	4.76470i	−0.389036	+	0.673830i
$51$	2.70169	−	0.712745i	0.378312	−	0.0998042i
$52$	0.971894	+	1.68337i	0.134777	+	0.233441i
$53$	−9.97679			−1.37042			−0.685209	−	0.728347i	$-0.740289\pi$
$53$	−9.97679			−1.37042			−0.685209	+	0.728347i	$0.740289\pi$
$54$	5.51758	+	1.54715i	0.750847	+	0.210541i
$55$	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
$59$	−2.22993	+	3.86235i	−0.290312	+	0.502836i	−0.973884	−	0.227048i	$-0.927093\pi$
$59$	−2.22993	+	3.86235i	−0.290312	+	0.502836i	0.683571	+	0.729884i	$0.260426\pi$
$60$	0.100851	+	0.101633i	0.0130198	+	0.0131208i
$61$	2.83550	+	4.91123i	0.363048	+	0.628818i	0.988461	−	0.151476i	$-0.0484027\pi$
$61$	2.83550	+	4.91123i	0.363048	+	0.628818i	−0.625413	+	0.780294i	$0.715069\pi$
$62$	−10.2138			−1.29716
$63$		0			0
$64$	8.19630			1.02454
$65$	−0.130775	−	0.226509i	−0.0162207	−	0.0280950i
$66$	1.67366	−	6.15107i	0.206013	−	0.757145i
$67$	−4.98571	+	8.63550i	−0.609101	+	1.05499i	0.382288	+	0.924043i	$0.375136\pi$
$67$	−4.98571	+	8.63550i	−0.609101	+	1.05499i	−0.991389	+	0.130951i	$0.958197\pi$
$68$	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	$0.437448\pi$
$72$	8.01146	−	4.54329i	0.944160	−	0.535431i
$73$	−4.72378			−0.552877			−0.276438	−	0.961032i	$-0.589154\pi$
$73$	−4.72378			−0.552877			−0.276438	+	0.961032i	$0.589154\pi$
$74$	−1.09318	−	1.89345i	−0.127080	−	0.220109i
$75$	6.08646	+	6.13365i	0.702804	+	0.708253i
$76$	−3.01084	+	5.21493i	−0.345367	+	0.598194i
$77$		0			0
$78$	−4.58031	+	1.20835i	−0.518618	+	0.136819i
$79$	−3.84705	−	6.66328i	−0.432827	−	0.749678i	0.564289	−	0.825577i	$-0.309150\pi$
$79$	−3.84705	−	6.66328i	−0.432827	−	0.749678i	−0.997115	+	0.0758997i	$0.975817\pi$
$80$	−0.191743			−0.0214375
$81$	4.61985	−	7.72379i	0.513317	−	0.858199i
$82$	8.25496			0.911608
$83$	−0.584428	−	1.01226i	−0.0641493	−	0.111110i	0.832167	−	0.554525i	$-0.187100\pi$
$83$	−0.584428	−	1.01226i	−0.0641493	−	0.111110i	−0.896316	+	0.443415i	$0.853767\pi$
$84$		0			0
$85$	−0.0850683	+	0.147343i	−0.00922695	+	0.0159815i
$86$	4.16189	−	7.20860i	0.448788	−	0.777323i
$87$	11.3344	+	11.4223i	1.21517	+	1.22459i
$88$	−5.12280	−	8.87296i	−0.546093	−	0.945860i
$89$	6.02954			0.639130			0.319565	−	0.947564i	$-0.396463\pi$
$89$	6.02954			0.639130			0.319565	+	0.947564i	$0.396463\pi$
$90$	−0.303519	+	0.172125i	−0.0319937	+	0.0181436i
$91$		0			0
$92$	−0.743509	−	1.28780i	−0.0775162	−	0.134262i
$93$	−4.21167	+	15.4788i	−0.436730	+	1.60508i
$94$	−1.76208	+	3.05201i	−0.181744	+	0.314791i
$95$	0.405130	−	0.701706i	0.0415655	−	0.0719935i
$96$	1.88040	−	6.91088i	0.191917	−	0.705339i
$97$	−1.90127	−	3.29310i	−0.193045	−	0.334364i	0.753213	−	0.657777i	$-0.228503\pi$
$97$	−1.90127	−	3.29310i	−0.193045	−	0.334364i	−0.946258	+	0.323413i	$0.895170\pi$
$98$		0			0
$99$	−8.63168	−	5.07279i	−0.867516	−	0.509834i
$100$	3.91029			0.391029
$101$	−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	$-0.502017\pi$
$102$	2.17045	+	2.18727i	0.214906	+	0.216572i
$103$	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
$107$	−18.1463			−1.75427			−0.877135	−	0.480244i	$-0.840548\pi$
$107$	−18.1463			−1.75427			−0.877135	+	0.480244i	$0.840548\pi$
$108$	−1.00846	−	3.94593i	−0.0970394	−	0.379697i
$109$	−4.22248			−0.404440			−0.202220	−	0.979340i	$-0.564816\pi$
$109$	−4.22248			−0.404440			−0.202220	+	0.979340i	$0.564816\pi$
$110$	0.194081	+	0.336157i	0.0185049	+	0.0320514i
$111$	−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	$0.135829\pi$
$114$	−10.3366	−	10.4167i	−0.968107	−	0.975613i
$115$	0.100044	+	0.173282i	0.00932919	+	0.0161586i
$116$	7.28186			0.676103
$117$	−0.0574579	+	7.43962i	−0.00531198	+	0.687793i
$118$	−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
$122$	−3.12703	+	5.41617i	−0.283108	+	0.490357i
$123$	3.40393	−	12.5102i	0.306922	−	1.12801i
$124$	3.62964	+	6.28672i	0.325951	+	0.564564i
$125$	−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	$0.495521\pi$
$128$	0.384435	+	0.665862i	0.0339796	+	0.0588544i
$129$	−9.20832	−	9.27971i	−0.810747	−	0.817033i
$130$	0.144221	−	0.249797i	0.0126490	−	0.0219087i
$131$	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
$135$	0.135696	+	0.530952i	0.0116788	+	0.0456971i
$136$	4.95251			0.424674
$137$	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	$0.607543\pi$
$138$	3.50399	−	0.924403i	0.298279	−	0.0786904i
$139$	−4.05943	+	7.03114i	−0.344316	+	0.596374i	−0.985229	−	0.171240i	$-0.945223\pi$
$139$	−4.05943	+	7.03114i	−0.344316	+	0.596374i	0.640913	+	0.767614i	$0.278556\pi$
$140$		0			0
$141$	3.89866	+	3.92888i	0.328326	+	0.330872i
$142$	1.81436	+	3.14257i	0.152258	+	0.263718i
$143$	8.27636			0.692104
$144$	4.70223	+	2.76347i	0.391852	+	0.230289i
$145$	−0.979825			−0.0813700
$146$	−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	$0.0157107\pi$
$150$	−2.50192	+	9.19510i	−0.204281	+	0.750777i
$151$	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	$0.681644\pi$
$152$	−23.5859			−1.91307
$153$	4.20975	−	2.38734i	0.340338	−	0.193005i
$154$		0			0
$155$	−0.488393	−	0.845922i	−0.0392287	−	0.0679461i
$156$	2.37143	+	2.38982i	0.189867	+	0.191339i
$157$	6.10318	−	10.5710i	0.487087	−	0.843659i	−0.512803	−	0.858506i	$-0.671393\pi$
$157$	6.10318	−	10.5710i	0.487087	−	0.843659i	0.999890	+	0.0148476i	$0.00472630\pi$
$158$	4.24258	−	7.34836i	0.337521	−	0.584604i
$159$	−16.7086	+	4.40798i	−1.32508	+	0.349576i
$160$	0.218054	+	0.377681i	0.0172387	+	0.0298583i
$161$		0			0
$162$	9.92414	+	0.153302i	0.779714	+	0.0120445i
$163$	8.96264			0.702008			0.351004	−	0.936374i	$-0.385840\pi$
$163$	8.96264			0.702008			0.351004	+	0.936374i	$0.385840\pi$
$164$	−2.93352	−	5.08101i	−0.229070	−	0.396760i
$165$	0.589468	−	0.155510i	0.0458900	−	0.0121065i
$166$	0.644515	−	1.11633i	0.0500240	−	0.0866442i
$167$	8.70833	−	15.0833i	0.673871	−	1.16718i	−0.302927	−	0.953014i	$-0.597964\pi$
$167$	8.70833	−	15.0833i	0.673871	−	1.16718i	0.976798	−	0.214165i	$-0.0687030\pi$
$168$		0			0
$169$	3.42493	+	5.93216i	0.263456	+	0.456320i
$170$	−0.187629			−0.0143905
$171$	−20.0485	+	11.3695i	−1.53315	+	0.869447i
$172$	−5.91595			−0.451087
$173$	1.41466	+	2.45027i	0.107555	+	0.186291i	0.914779	−	0.403954i	$-0.132365\pi$
$173$	1.41466	+	2.45027i	0.107555	+	0.186291i	−0.807224	+	0.590245i	$0.799031\pi$
$174$	−4.65914	+	17.1234i	−0.353208	+	1.29812i
$175$		0			0
$176$	3.03370	−	5.25453i	0.228674	−	0.396075i
$177$	−2.02810	+	7.45372i	−0.152441	+	0.560256i
$178$	3.32473	+	5.75860i	0.249199	+	0.431625i
$179$	−10.1627			−0.759595			−0.379798	−	0.925070i	$-0.624006\pi$
$179$	−10.1627			−0.759595			−0.379798	+	0.925070i	$0.624006\pi$
$180$	0.213805	+	0.125652i	0.0159361	+	0.00936553i
$181$	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
$185$	0.104545	−	0.181078i	0.00768631	−	0.0133131i
$186$	−17.1056	+	4.51272i	−1.25425	+	0.330888i
$187$	−2.69186	−	4.66243i	−0.196848	−	0.340951i
$188$	2.50472			0.182676
$189$		0			0
$190$	0.893566			0.0648261
$191$	11.2000	+	19.3990i	0.810404	+	1.40366i	0.912582	+	0.408894i	$0.134086\pi$
$191$	11.2000	+	19.3990i	0.810404	+	1.40366i	−0.102178	+	0.994766i	$0.532581\pi$
$192$	13.7268	−	3.62132i	0.990644	−	0.261346i
$193$	0.128393	−	0.222383i	0.00924194	−	0.0160075i	−0.861367	−	0.507982i	$-0.830391\pi$
$193$	0.128393	−	0.222383i	0.00924194	−	0.0160075i	0.870609	+	0.491975i	$0.163725\pi$
$194$	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	$0.508657\pi$
$198$	0.0852720	−	11.0410i	0.00606002	−	0.784648i
$199$	5.03121			0.356653			0.178327	−	0.983971i	$-0.442932\pi$
$199$	5.03121			0.356653			0.178327	+	0.983971i	$0.442932\pi$
$200$	7.65796	+	13.2640i	0.541500	+	0.937905i
$201$	−4.53445	+	16.6651i	−0.319835	+	1.17547i
$202$	9.63321	−	16.6852i	0.677790	−	1.17397i
$203$		0			0
$204$	0.574988	−	2.11321i	0.0402572	−	0.147954i
$205$	0.394726	+	0.683686i	0.0275689	+	0.0477507i
$206$	9.62981			0.670941
$207$	0.0439559	−	5.69139i	0.00305515	−	0.395579i
$208$	−4.50867			−0.312620
$209$	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
$213$	5.51064	−	1.45379i	0.377583	−	0.0996119i
$214$	−10.0060	−	17.3309i	−0.683996	−	1.18472i
$215$	0.796033			0.0542890
$216$	11.4099	−	11.1485i	0.776343	−	0.758561i
$217$		0			0
$218$	−2.32831	−	4.03274i	−0.157693	−	0.273132i
$219$	−7.91116	+	2.08708i	−0.534587	+	0.141032i
$220$	0.137939	−	0.238917i	0.00929983	−	0.0161078i
$221$	−2.00031	+	3.46464i	−0.134555	+	0.233057i
$222$	−2.66738	−	2.68806i	−0.179023	−	0.180411i
$223$	−5.59106	−	9.68400i	−0.374405	−	0.648488i	0.615833	−	0.787877i	$-0.288820\pi$
$223$	−5.59106	−	9.68400i	−0.374405	−	0.648488i	−0.990238	+	0.139388i	$0.955486\pi$
$224$		0			0
$225$	12.9033	+	7.58319i	0.860220	+	0.505546i
$226$	2.26791			0.150859
$227$	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	$0.544007\pi$
$228$	−2.73833	+	10.0640i	−0.181350	+	0.666503i
$229$	−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
$233$	6.54184			0.428570			0.214285	−	0.976771i	$-0.431258\pi$
$233$	6.54184			0.428570			0.214285	+	0.976771i	$0.431258\pi$
$234$	−7.13700	+	4.04738i	−0.466560	+	0.264586i
$235$	−0.337028			−0.0219853
$236$	1.74782	+	3.02732i	0.113774	+	0.197062i
$237$	−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	$-0.0759028\pi$
$240$	−0.321121	+	0.0847165i	−0.0207283	+	0.00546842i
$241$	−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	$-0.390346\pi$
$242$	−0.151825			−0.00975967
$243$	4.32454	−	14.9766i	0.277419	−	0.960749i
$244$	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
$248$	−14.2167	+	24.6240i	−0.902758	+	1.56362i
$249$	−1.42601	−	1.43707i	−0.0903698	−	0.0910704i
$250$	−0.580900	−	1.00615i	−0.0367394	−	0.0636344i
$251$	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
$254$	0.174884	+	0.302907i	0.0109732	+	0.0190061i
$255$	−0.0773687	+	0.284347i	−0.00484502	+	0.0178065i
$256$	7.77234	−	13.4621i	0.485771	−	0.841380i
$257$	−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
$261$	24.0289	+	14.1216i	1.48735	+	0.874107i
$262$	16.4940			1.01900
$263$	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	$0.818224\pi$
$264$	−12.4997	−	12.5966i	−0.769304	−	0.775268i
$265$	0.526106	−	0.911243i	0.0323185	−	0.0559772i
$266$		0			0
$267$	10.0980	−	2.66399i	0.617986	−	0.163034i
$268$	3.90781	+	6.76852i	0.238707	+	0.413453i
$269$	26.2571			1.60092			0.800461	−	0.599385i	$-0.204588\pi$
$269$	26.2571			1.60092			0.800461	+	0.599385i	$0.204588\pi$
$270$	−0.432270	+	0.422369i	−0.0263071	+	0.0257046i
$271$	−17.9335			−1.08938			−0.544690	−	0.838637i	$-0.683353\pi$
$271$	−17.9335			−1.08938			−0.544690	+	0.838637i	$0.683353\pi$
$272$	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
$276$	−1.81417	−	1.82824i	−0.109200	−	0.110047i
$277$	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	$0.641463\pi$
$278$	−8.95359			−0.537001
$279$	−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	$0.880902\pi$
$282$	−1.60259	+	5.88988i	−0.0954329	+	0.350737i
$283$	7.69634	−	13.3304i	0.457500	−	0.792413i	−0.541328	−	0.840811i	$-0.682078\pi$
$283$	7.69634	−	13.3304i	0.457500	−	0.792413i	0.998828	+	0.0483984i	$0.0154117\pi$
$284$	1.28952	−	2.23352i	0.0765190	−	0.132535i
$285$	0.368462	−	1.35418i	0.0218258	−	0.0802146i
$286$	4.56364	+	7.90446i	0.269854	+	0.467401i
$287$		0			0
$288$	0.0958052	−	12.4048i	0.00564537	−	0.730960i
$289$	−14.3976			−0.846919
$290$	−0.540282	−	0.935796i	−0.0317265	−	0.0549518i
$291$	−4.63913	−	4.67510i	−0.271951	−	0.274059i
$292$	−1.85126	+	3.20647i	−0.108337	+	0.187644i
$293$	−12.9013	+	22.3456i	−0.753700	+	1.30545i	0.192318	+	0.981333i	$0.438399\pi$
$293$	−12.9013	+	22.3456i	−0.753700	+	1.30545i	−0.946018	+	0.324114i	$0.894934\pi$
$294$		0			0
$295$	−0.235182	−	0.407347i	−0.0136928	−	0.0237167i
$296$	−6.08642			−0.353766
$297$	−16.6972	−	4.68197i	−0.968869	−	0.271676i
$298$	12.2948			0.712220
$299$	2.35246	+	4.07458i	0.136046	+	0.235639i
$300$	6.54877	−	1.72766i	0.378093	−	0.0997465i
$301$		0			0
$302$	−6.21629	+	10.7669i	−0.357707	+	0.619567i
$303$	−21.3138	−	21.4790i	−1.22445	−	1.23394i
$304$	−6.98373	−	12.0962i	−0.400544	−	0.693763i
$305$	−0.598098			−0.0342470
$306$	4.60135	+	2.70418i	0.263042	+	0.154588i
$307$	−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
$311$	0.654931	−	1.13437i	0.0371377	−	0.0643245i	−0.846859	−	0.531817i	$-0.821509\pi$
$311$	0.654931	−	1.13437i	0.0371377	−	0.0643245i	0.883997	+	0.467493i	$0.154843\pi$
$312$	−3.46219	+	12.7243i	−0.196008	+	0.720373i
$313$	−10.7885	−	18.6862i	−0.609802	−	1.05621i	−0.991273	−	0.131827i	$-0.957916\pi$
$313$	−10.7885	−	18.6862i	−0.609802	−	1.05621i	0.381471	−	0.924381i	$-0.375418\pi$
$314$	13.4613			0.759667
$315$		0			0
$316$	−6.03065			−0.339250
$317$	12.3910	+	21.4618i	0.695946	+	1.20541i	0.969861	+	0.243660i	$0.0783480\pi$
$317$	12.3910	+	21.4618i	0.695946	+	1.20541i	−0.273915	+	0.961754i	$0.588319\pi$
$318$	−13.4232	−	13.5272i	−0.752734	−	0.758570i
$319$	15.5025	−	26.8512i	0.867975	−	1.50338i
$320$	−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
$324$	−3.43233	−	6.16288i	−0.190685	−	0.342382i
$325$	−12.3722			−0.686283
$326$	4.94206	+	8.55990i	0.273715	+	0.474089i
$327$	−7.07161	+	1.86559i	−0.391061	+	0.103168i
$328$	11.4901	−	19.9014i	0.634434	−	1.09887i
$329$		0			0
$330$	0.473559	+	0.477231i	0.0260686	+	0.0262707i
$331$	−6.92256	−	11.9902i	−0.380498	−	0.659042i	0.610635	−	0.791912i	$-0.290914\pi$
$331$	−6.92256	−	11.9902i	−0.380498	−	0.659042i	−0.991133	+	0.132870i	$0.957581\pi$
$332$	−0.916151			−0.0502803
$333$	−5.17359	+	2.93394i	−0.283511	+	0.160779i
$334$	19.2073			1.05098
$335$	−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
$339$	0.935172	−	3.43697i	0.0507916	−	0.186670i
$340$	0.0666767	+	0.115487i	0.00361605	+	0.00626319i
$341$	30.9089			1.67381
$342$	−21.9135	−	12.8784i	−1.18495	−	0.696386i
$343$		0			0
$344$	−11.5859	−	20.0673i	−0.624668	−	1.08196i
$345$	0.244110	+	0.246002i	0.0131424	+	0.0132443i
$346$	−1.56011	+	2.70219i	−0.0838720	+	0.145271i
$347$	7.25739	−	12.5702i	0.389597	−	0.674802i	−0.602798	−	0.797894i	$-0.705948\pi$
$347$	7.25739	−	12.5702i	0.389597	−	0.674802i	0.992395	+	0.123091i	$0.0392809\pi$
$348$	12.1953	−	3.21730i	0.653736	−	0.172465i
$349$	7.86412	+	13.6211i	0.420957	+	0.729119i	0.996033	−	0.0889810i	$-0.0283610\pi$
$349$	7.86412	+	13.6211i	0.420957	+	0.729119i	−0.575076	+	0.818100i	$0.695028\pi$
$350$		0			0
$351$	3.19077	+	12.4849i	0.170311	+	0.666395i
$352$	−13.8000			−0.735542
$353$	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	$0.798156\pi$
$354$	−8.23709	+	2.17307i	−0.437796	+	0.115497i
$355$	−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
$359$	7.93988			0.419051			0.209525	−	0.977803i	$-0.432808\pi$
$359$	7.93988			0.419051			0.209525	+	0.977803i	$0.432808\pi$
$360$	−0.00750171	+	0.971318i	−0.000395375	+	0.0511930i
$361$	40.0233			2.10649
$362$	9.42187	+	16.3192i	0.495202	+	0.857716i
$363$	−0.0626049	+	0.230087i	−0.00328590	+	0.0120764i
$364$		0			0
$365$	0.249099	−	0.431453i	0.0130385	−	0.0225833i
$366$	−2.84400	+	10.4523i	−0.148658	+	0.546352i
$367$	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	$0.721826\pi$
$368$	3.44918			0.179801
$369$	0.173428	−	22.4554i	0.00902832	−	1.16898i
$370$	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	$0.231481\pi$
$374$	2.96862	−	5.14180i	0.153504	−	0.265876i
$375$	−1.76433	+	0.465456i	−0.0911096	+	0.0240361i
$376$	4.90527	+	8.49618i	0.252970	+	0.438157i
$377$	−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	$0.801604\pi$
$380$	−0.317542	−	0.549999i	−0.0162896	−	0.0282143i
$381$	0.531163	−	0.140128i	0.0272123	−	0.00717900i
$382$	−12.3515	+	21.3934i	−0.631958	+	1.09458i
$383$	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
$387$	−19.5216	−	11.4728i	−0.992341	−	0.583193i
$388$	−2.98045			−0.151309
$389$	−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	$-0.376361\pi$
$390$	0.131167	−	0.482069i	0.00664191	−	0.0244105i
$391$	1.53026	−	2.65049i	0.0773885	−	0.134041i
$392$		0			0
$393$	6.80131	−	24.9963i	0.343081	−	1.26090i
$394$	−0.420927	−	0.729067i	−0.0212060	−	0.0367299i
$395$	0.811466			0.0408293
$396$	−6.82613	+	3.87109i	−0.343026	+	0.194530i
$397$	24.0569			1.20738			0.603691	−	0.797218i	$-0.293696\pi$
$397$	24.0569			1.20738			0.603691	+	0.797218i	$0.293696\pi$
$398$	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	$0.154247\pi$
$402$	−18.4166	+	4.85857i	−0.918536	+	0.242323i
$403$	−11.4842	−	19.8911i	−0.572067	−	0.990849i
$404$	−13.6932			−0.681263
$405$	0.461844	+	0.829259i	0.0229492	+	0.0412062i
$406$		0			0
$407$	3.30817	+	5.72992i	0.163980	+	0.284022i
$408$	8.29422	−	2.18814i	0.410625	−	0.108329i
$409$	11.1728	−	19.3519i	0.552460	−	0.956889i	−0.445636	−	0.895214i	$-0.647023\pi$
$409$	11.1728	−	19.3519i	0.552460	−	0.956889i	0.998096	−	0.0616748i	$-0.0196442\pi$
$410$	−0.435309	+	0.753978i	−0.0214984	+	0.0372363i
$411$	18.6018	+	18.7461i	0.917561	+	0.924675i
$412$	−3.42210	−	5.92725i	−0.168595	−	0.292014i
$413$		0			0
$414$	5.45988	−	3.09629i	0.268339	−	0.152174i
$415$	0.123275			0.00605131
$416$	5.12736	+	8.88086i	0.251390	+	0.435420i
$417$	−3.69201	+	13.5690i	−0.180799	+	0.664475i
$418$	−14.1378	+	24.4873i	−0.691501	+	1.19771i
$419$	2.98648	−	5.17273i	0.145899	−	0.252704i	−0.783809	−	0.621002i	$-0.786726\pi$
$419$	2.98648	−	5.17273i	0.145899	−	0.252704i	0.929708	+	0.368298i	$0.120059\pi$
$420$		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	$0.717284\pi$
$422$	−7.95210			−0.387102
$423$	8.26515	+	4.85738i	0.401865	+	0.236174i
$424$	−30.6289			−1.48747
$425$	4.02400	+	6.96977i	0.195193	+	0.338083i
$426$	4.42707	+	4.46139i	0.214492	+	0.216155i
$427$		0			0
$428$	−7.11156	+	12.3176i	−0.343750	+	0.595393i
$429$	13.8609	−	3.65670i	0.669208	−	0.176547i
$430$	0.438938	+	0.760263i	0.0211675	+	0.0366631i
$431$	−19.4034			−0.934628			−0.467314	−	0.884091i	$-0.654778\pi$
$431$	−19.4034			−0.934628			−0.467314	+	0.884091i	$0.654778\pi$
$432$	9.09603	+	2.55057i	0.437633	+	0.122714i
$433$	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
$437$	−7.28772	+	12.6227i	−0.348619	+	0.603826i
$438$	−6.35556	−	6.40484i	−0.303681	−	0.306035i
$439$	−8.67059	−	15.0179i	−0.413825	−	0.716766i	0.581479	−	0.813561i	$-0.302474\pi$
$439$	−8.67059	−	15.0179i	−0.413825	−	0.716766i	−0.995304	+	0.0967954i	$0.969141\pi$
$440$	1.08056			0.0515139
$441$		0			0
$442$	−4.41194			−0.209854
$443$	−9.80499	−	16.9827i	−0.465849	−	0.806874i	0.533390	−	0.845869i	$-0.320918\pi$
$443$	−9.80499	−	16.9827i	−0.465849	−	0.806874i	−0.999239	+	0.0389949i	$0.987584\pi$
$444$	−0.706635	+	2.59704i	−0.0335354	+	0.123250i
$445$	−0.317956	+	0.550716i	−0.0150726	+	0.0261064i
$446$	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	$0.637434\pi$
$450$	−0.127471	+	16.5049i	−0.00600905	+	0.778049i
$451$	−24.9810			−1.17631
$452$	−0.805935	−	1.39592i	−0.0379080	−	0.0656586i
$453$	13.7538	+	13.8604i	0.646208	+	0.651218i
$454$	−13.1073	+	22.7025i	−0.615156	+	1.06548i
$455$		0			0
$456$	−39.5005	+	10.4208i	−1.84978	+	0.487999i
$457$	−0.242725	−	0.420413i	−0.0113542	−	0.0196661i	0.860292	−	0.509801i	$-0.170281\pi$
$457$	−0.242725	−	0.420413i	−0.0113542	−	0.0196661i	−0.871647	+	0.490135i	$0.836948\pi$
$458$	−2.10138			−0.0981912
$459$	5.99549	−	5.85817i	0.279846	−	0.273436i
$460$	0.156830			0.00731224
$461$	3.99687	+	6.92279i	0.186153	+	0.322426i	0.943964	−	0.330047i	$-0.107065\pi$
$461$	3.99687	+	6.92279i	0.186153	+	0.322426i	−0.757811	+	0.652474i	$0.773731\pi$
$462$		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
$465$	−1.19169	−	1.20092i	−0.0552631	−	0.0556916i
$466$	3.60721	+	6.24788i	0.167101	+	0.289427i
$467$	21.8977			1.01331			0.506653	−	0.862150i	$-0.330883\pi$
$467$	21.8977			1.01331			0.506653	+	0.862150i	$0.330883\pi$
$468$	5.02744	+	2.95460i	0.232394	+	0.136576i
$469$		0			0
$470$	−0.185839	−	0.321883i	−0.00857213	−	0.0148474i
$471$	5.55078	−	20.4003i	0.255766	−	0.939998i
$472$	−6.84592	+	11.8575i	−0.315109	+	0.545785i
$473$	−12.5946	+	21.8145i	−0.579102	+	1.00303i
$474$	3.85858	−	14.1811i	0.177230	−	0.651361i
$475$	−19.1639	−	33.1929i	−0.879301	−	1.52299i
$476$		0			0
$477$	−26.0353	+	14.7645i	−1.19207	+	0.676022i
$478$	23.5417			1.07677
$479$	−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	$0.862474\pi$
$480$	0.532055	+	0.536180i	0.0242849	+	0.0244732i
$481$	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
$485$	0.401040			0.0182103
$486$	16.6882	−	4.12798i	0.756992	−	0.187249i
$487$	−26.4755			−1.19972			−0.599859	−	0.800106i	$-0.704777\pi$
$487$	−26.4755			−1.19972			−0.599859	+	0.800106i	$0.704777\pi$
$488$	8.70502	+	15.0775i	0.394058	+	0.682528i
$489$	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	$-0.0550255\pi$
$492$	−7.15783	−	7.21333i	−0.322700	−	0.325202i
$493$	7.49360	+	12.9793i	0.337495	+	0.584558i
$494$	21.0115			0.945350
$495$	0.918504	−	0.520882i	0.0412837	−	0.0234119i
$496$	−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	$0.113474\pi$
$500$	−0.412863	+	0.715100i	−0.0184638	+	0.0319802i
$501$	7.92014	−	29.1083i	0.353846	−	1.30046i
$502$	3.75765	+	6.50845i	0.167712	+	0.290486i
$503$	−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
$506$	−3.49124	−	6.04700i	−0.155204	−	0.268822i
$507$	8.35688	+	8.42167i	0.371142	+	0.374019i
$508$	0.124295	−	0.215285i	0.00551470	−	0.00955174i
$509$	−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
$513$	−28.5530	+	27.8990i	−1.26065	+	1.23177i
$514$	−15.8676			−0.699891
$515$	0.460467	+	0.797553i	0.0202906	+	0.0351444i
$516$	−9.90775	+	2.61381i	−0.436164	+	0.115067i
$517$	5.33237	−	9.23593i	0.234517	−	0.406196i
$518$		0			0
$519$	3.45180	+	3.47856i	0.151517	+	0.152692i
$520$	−0.401482	−	0.695387i	−0.0176061	−	0.0304947i
$521$	−33.7990			−1.48076			−0.740381	−	0.672187i	$-0.765355\pi$
$521$	−33.7990			−1.48076			−0.740381	+	0.672187i	$0.765355\pi$
$522$	−0.237380	+	30.7359i	−0.0103899	+	1.34527i
$523$	14.3779			0.628701			0.314351	−	0.949307i	$-0.398213\pi$
$523$	14.3779			0.628701			0.314351	+	0.949307i	$0.398213\pi$
$524$	−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
$528$	2.75912	−	10.1404i	0.120075	−	0.441304i
$529$	9.70034	+	16.8015i	0.421754	+	0.730499i
$530$	1.16039			0.0504043
$531$	−0.103331	+	13.3792i	−0.00448416	+	0.580607i
$532$		0			0
$533$	9.28166	+	16.0763i	0.402033	+	0.696342i
$534$	8.11238	+	8.17528i	0.351057	+	0.353779i
$535$	0.956910	−	1.65742i	0.0413708	−	0.0716564i
$536$	−15.3062	+	26.5111i	−0.661127	+	1.14511i
$537$	−17.0200	+	4.49012i	−0.734466	+	0.193763i
$538$	14.4783	+	25.0772i	0.624205	+	1.08116i
$539$		0			0
$540$	0.413586	+	0.115971i	0.0177979	+	0.00499062i
$541$	−25.1764			−1.08242			−0.541210	−	0.840888i	$-0.682034\pi$
$541$	−25.1764			−1.08242			−0.541210	+	0.840888i	$0.682034\pi$
$542$	−9.88863	−	17.1276i	−0.424753	−	0.735694i
$543$	28.6164	−	7.54943i	1.22805	−	0.323977i
$544$	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	$0.811675\pi$
$548$	11.9509			0.510517
$549$	14.6675	+	8.62003i	0.625996	+	0.367894i
$550$	18.3612			0.782926
$551$	−35.6876	−	61.8127i	−1.52034	−	2.63331i
$552$	2.64861	−	9.73424i	0.112732	−	0.414317i
$553$		0			0
$554$	−10.4057	+	18.0233i	−0.442098	+	0.765736i
$555$	0.0950828	−	0.349450i	0.00403604	−	0.0148333i
$556$	3.18179	+	5.51102i	0.134938	+	0.233719i
$557$	20.0459			0.849371			0.424686	−	0.905341i	$-0.360385\pi$
$557$	20.0459			0.849371			0.424686	+	0.905341i	$0.360385\pi$
$558$	−26.6539	+	15.1154i	−1.12835	+	0.639884i
$559$	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
$563$	19.9007	−	34.4690i	0.838713	−	1.45269i	−0.0522584	−	0.998634i	$-0.516642\pi$
$563$	19.9007	−	34.4690i	0.838713	−	1.45269i	0.890971	−	0.454060i	$-0.150025\pi$
$564$	4.19478	−	1.10665i	0.176632	−	0.0465982i
$565$	0.108444	+	0.187831i	0.00456228	+	0.00790211i
$566$	16.9753			0.713523
$567$		0			0
$568$	10.1017			0.423856
$569$	−6.90797	−	11.9649i	−0.289597	−	0.501597i	0.684117	−	0.729373i	$-0.260188\pi$
$569$	−6.90797	−	11.9649i	−0.289597	−	0.501597i	−0.973714	+	0.227776i	$0.926855\pi$
$570$	1.49650	−	0.394799i	0.0626815	−	0.0165363i
$571$	−5.21935	+	9.04019i	−0.218423	+	0.378320i	−0.954326	−	0.298767i	$-0.903425\pi$
$571$	−5.21935	+	9.04019i	−0.218423	+	0.378320i	0.735903	+	0.677087i	$0.236758\pi$
$572$	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
$576$	21.3889	−	12.1296i	0.891205	−	0.505401i
$577$	25.4923			1.06126			0.530628	−	0.847605i	$-0.321956\pi$
$577$	25.4923			1.06126			0.530628	+	0.847605i	$0.321956\pi$
$578$	−7.93895	−	13.7507i	−0.330217	−	0.571952i
$579$	0.116772	−	0.429164i	0.00485289	−	0.0178354i
$580$	−0.383994	+	0.665098i	−0.0159445	+	0.0276167i
$581$		0			0
$582$	1.90697	−	7.00855i	0.0790466	−	0.290514i
$583$	16.6478	+	28.8349i	0.689483	+	1.19422i
$584$	−14.5021			−0.600100
$585$	−0.676477	−	0.397562i	−0.0279689	−	0.0164372i
$586$	−28.4554			−1.17548
$587$	−17.5168	−	30.3401i	−0.722998	−	1.25227i	−0.959793	−	0.280709i	$-0.909430\pi$
$587$	−17.5168	−	30.3401i	−0.722998	−	1.25227i	0.236795	−	0.971560i	$-0.423903\pi$
$588$		0			0
$589$	35.5769	−	61.6210i	1.46592	−	2.53905i
$590$	0.259362	−	0.449228i	0.0106778	−	0.0184944i
$591$	−1.27845	+	0.337275i	−0.0525886	+	0.0138736i
$592$	−1.80217	−	3.12146i	−0.0740689	−	0.128291i
$593$	−36.1292			−1.48365			−0.741824	−	0.670594i	$-0.766039\pi$
$593$	−36.1292			−1.48365			−0.741824	+	0.670594i	$0.766039\pi$
$594$	−4.73536	−	18.5286i	−0.194294	−	0.760236i
$595$		0			0
$596$	−4.36915	−	7.56759i	−0.178967	−	0.309980i
$597$	8.42603	−	2.22291i	0.344854	−	0.0909777i
$598$	−2.59433	+	4.49350i	−0.106090	+	0.183753i
$599$	20.4742	−	35.4623i	0.836552	−	1.44895i	−0.0562080	−	0.998419i	$-0.517901\pi$
$599$	20.4742	−	35.4623i	0.836552	−	1.44895i	0.892760	−	0.450532i	$-0.148766\pi$
$600$	18.6855	+	18.8304i	0.762833	+	0.768748i
$601$	12.8547	+	22.2650i	0.524354	+	0.908207i	0.999598	+	0.0283533i	$0.00902635\pi$
$601$	12.8547	+	22.2650i	0.524354	+	0.908207i	−0.475244	+	0.879854i	$0.657640\pi$
$602$		0			0
$603$	−0.231028	+	29.9133i	−0.00940817	+	1.21817i
$604$	8.83620			0.359540
$605$	−0.00725978	−	0.0125743i	−0.000295152	−	0.000511218i
$606$	8.76130	−	32.1998i	0.355904	−	1.30803i
$607$	−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
$611$	−7.92493			−0.320608
$612$	0.0292953	−	3.79315i	0.00118419	−	0.153329i
$613$	−29.1297			−1.17654			−0.588269	−	0.808666i	$-0.700190\pi$
$613$	−29.1297			−1.17654			−0.588269	+	0.808666i	$0.700190\pi$
$614$	−12.2917	−	21.2898i	−0.496051	−	0.859185i
$615$	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	$0.303323\pi$
$618$	16.1275	−	4.25468i	0.648745	−	0.171148i
$619$	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	$0.776329\pi$
$620$	−0.765607			−0.0307475
$621$	−2.44098	−	9.55108i	−0.0979530	−	0.383272i
$622$	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
$626$	11.8977	−	20.6074i	0.475528	−	0.823638i
$627$	31.2803	+	31.5228i	1.24921	+	1.25890i
$628$	−4.78368	−	8.28558i	−0.190890	−	0.330631i
$629$	−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	$0.323392\pi$
$632$	−11.8105	−	20.4564i	−0.469796	−	0.813711i
$633$	−3.27904	+	12.0512i	−0.130330	+	0.478993i
$634$	−13.6649	+	23.6683i	−0.542704	+	0.939990i
$635$	−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
$639$	8.58664	−	4.86947i	0.339682	−	0.192633i
$640$	−0.0810898			−0.00320536
$641$	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	$0.727469\pi$
$642$	−24.4148	−	24.6041i	−0.963574	−	0.971045i
$643$	−15.4460	+	26.7532i	−0.609130	+	1.05504i	0.382254	+	0.924057i	$0.375148\pi$
$643$	−15.4460	+	26.7532i	−0.609130	+	1.05504i	−0.991384	+	0.130987i	$0.958185\pi$
$644$		0			0
$645$	1.33316	−	0.351706i	0.0524930	−	0.0138484i
$646$	−6.83390	−	11.8367i	−0.268876	−	0.465707i
$647$	−1.29981			−0.0511007			−0.0255503	−	0.999674i	$-0.508134\pi$
$647$	−1.29981			−0.0511007			−0.0255503	+	0.999674i	$0.508134\pi$
$648$	14.1830	−	23.7122i	0.557161	−	0.931502i
$649$	14.8840			0.584247
$650$	−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	$-0.174643\pi$
$654$	−5.68109	−	5.72514i	−0.222148	−	0.223871i
$655$	0.788692	+	1.36605i	0.0308167	+	0.0533762i
$656$	13.6088			0.531333
$657$	−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	$0.719822\pi$
$660$	0.125454	−	0.461071i	0.00488329	−	0.0179472i
$661$	−16.5128	+	28.6010i	−0.642274	+	1.11245i	0.342649	+	0.939463i	$0.388676\pi$
$661$	−16.5128	+	28.6010i	−0.642274	+	1.11245i	−0.984924	+	0.172989i	$0.944658\pi$
$662$	7.63429	−	13.2230i	0.296715	−	0.513925i
$663$	−1.81926	+	6.68619i	−0.0706542	+	0.259670i
$664$	−1.79420	−	3.10765i	−0.0696285	−	0.120600i
$665$		0			0
$666$	−5.65485	−	3.32332i	−0.219121	−	0.128776i
$667$	17.6257			0.682469
$668$	−6.82561	−	11.8223i	−0.264091	−	0.457419i
$669$	−13.6423	−	13.7480i	−0.527440	−	0.531529i
$670$	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	$0.968335\pi$
$674$	3.73729			0.143955
$675$	24.9603	+	6.99898i	0.960721	+	0.269391i
$676$	5.36894			0.206498
$677$	−4.15084	−	7.18946i	−0.159530	−	0.276313i	0.775170	−	0.631753i	$-0.217664\pi$
$677$	−4.15084	−	7.18946i	−0.159530	−	0.276313i	−0.934699	+	0.355440i	$0.884331\pi$
$678$	3.79818	−	1.00202i	0.145868	−	0.0384822i
$679$		0			0
$680$	−0.261161	+	0.452344i	−0.0100151	+	0.0173466i
$681$	29.0003	+	29.2252i	1.11130	+	1.11991i
$682$	17.0434	+	29.5200i	0.652625	+	1.13038i
$683$	2.49456			0.0954518			0.0477259	−	0.998860i	$-0.484803\pi$
$683$	2.49456			0.0954518			0.0477259	+	0.998860i	$0.484803\pi$
$684$	−0.139516	+	18.0645i	−0.00533454	+	0.690714i
$685$	−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
$689$	12.3710	−	21.4271i	0.471296	−	0.816308i
$690$	−0.100344	+	0.368788i	−0.00382004	+	0.0140395i
$691$	8.43455	+	14.6091i	0.320865	+	0.555755i	0.980667	−	0.195685i	$-0.0626930\pi$
$691$	8.43455	+	14.6091i	0.320865	+	0.555755i	−0.659801	+	0.751440i	$0.729360\pi$
$692$	2.21763			0.0843017
$693$		0			0
$694$	16.0071			0.607621
$695$	−0.428132	−	0.741547i	−0.0162400	−	0.0281285i
$696$	34.7967	+	35.0665i	1.31897	+	1.32919i
$697$	6.03765	−	10.4575i	0.228692	−	0.396107i
$698$	−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	$0.399258\pi$
$702$	−10.1645	+	9.93165i	−0.383633	+	0.374846i
$703$	15.2312			0.574454
$704$	−13.6768	−	23.6889i	−0.515464	−	0.892811i
$705$	−0.564438	+	0.148907i	−0.0212580	+	0.00560816i
$706$	−2.28515	+	3.95800i	−0.0860029	+	0.148961i
$707$		0			0
$708$	4.26472	+	4.29778i	0.160278	+	0.161520i
$709$	14.7462	+	25.5412i	0.553807	+	0.959222i	0.997995	+	0.0632882i	$0.0201587\pi$
$709$	14.7462	+	25.5412i	0.553807	+	0.959222i	−0.444188	+	0.895933i	$0.646508\pi$
$710$	−0.382707			−0.0143628
$711$	−19.9001	−	11.6952i	−0.746313	−	0.438604i
$712$	18.5108			0.693721
$713$	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
$717$	9.70741	−	35.6769i	0.362530	−	1.33238i
$718$	4.37810	+	7.58310i	0.163389	+	0.282999i
$719$	−0.434622			−0.0162087			−0.00810433	−	0.999967i	$-0.502580\pi$
$719$	−0.434622			−0.0162087			−0.00810433	+	0.999967i	$0.502580\pi$
$720$	−0.500368	+	0.283758i	−0.0186476	+	0.0105750i
$721$		0			0
$722$	22.0691	+	38.2248i	0.821327	+	1.42258i
$723$	−24.4808	−	24.6707i	−0.910453	−	0.917511i
$724$	6.69640	−	11.5985i	0.248870	−	0.431055i
$725$	−23.1744	+	40.1392i	−0.860675	+	1.49073i
$726$	−0.254269	+	0.0670798i	−0.00943680	+	0.00248957i
$727$	13.5839	+	23.5280i	0.503799	+	0.872605i	0.999990	+	0.00439187i	$0.00139798\pi$
$727$	13.5839	+	23.5280i	0.503799	+	0.872605i	−0.496192	+	0.868213i	$0.665269\pi$
$728$		0			0
$729$	0.625513	−	26.9928i	0.0231672	−	0.999732i
$730$	0.549420			0.0203350
$731$	−6.08798	−	10.5447i	−0.225172	−	0.390009i
$732$	7.44417	−	1.96388i	0.275144	−	0.0725871i
$733$	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
$737$	33.2777			1.22580
$738$	21.5420	−	12.2164i	0.792973	−	0.449693i
$739$	−13.6108			−0.500681			−0.250341	−	0.968158i	$-0.580543\pi$
$739$	−13.6108			−0.500681			−0.250341	+	0.968158i	$0.580543\pi$
$740$	−0.0819427	−	0.141929i	−0.00301227	−	0.00521741i
$741$	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	$0.241318\pi$
$744$	−12.9299	+	47.5203i	−0.474033	+	1.74218i
$745$	0.587900	+	1.01827i	0.0215390	+	0.0373066i
$746$	−8.61393			−0.315378
$747$	−3.02314	−	1.77668i	−0.110611	−	0.0650055i
$748$	−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	$0.125050\pi$
$752$	−2.90488	+	5.03140i	−0.105930	+	0.183476i
$753$	11.4129	−	3.01088i	0.415908	−	0.109723i
$754$	−12.7043	−	22.0045i	−0.462663	−	0.801355i
$755$	−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	$0.260192\pi$
$758$	−17.4325	−	30.1940i	−0.633178	−	1.09670i
$759$	−10.6037	+	2.79741i	−0.384890	+	0.101540i
$760$	1.24376	−	2.15425i	0.0451157	−	0.0781428i
$761$	−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
$765$	−0.00394189	+	0.510395i	−0.000142519	+	0.0184534i
$766$	11.8352			0.427625
$767$	−5.53011	−	9.57843i	−0.199681	−	0.345857i
$768$	7.06886	−	25.9797i	0.255076	−	0.937460i
$769$	16.1463	−	27.9663i	0.582252	−	1.00849i	−0.412960	−	0.910749i	$-0.635505\pi$
$769$	16.1463	−	27.9663i	0.582252	−	1.00849i	0.995212	−	0.0977407i	$-0.0311616\pi$
$770$		0			0
$771$	−6.54301	+	24.0470i	−0.235641	+	0.866032i
$772$	−0.100635	−	0.174305i	−0.00362192	−	0.00627336i
$773$	−48.5878			−1.74758			−0.873792	−	0.486300i	$-0.838346\pi$
$773$	−48.5878			−1.74758			−0.873792	+	0.486300i	$0.838346\pi$
$774$	0.192853	−	24.9706i	0.00693198	−	0.897549i
$775$	−46.2051			−1.65973
$776$	−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
$780$	−0.343330	+	0.0905755i	−0.0122932	+	0.00324312i
$781$	−5.49059	−	9.50998i	−0.196469	−	0.340294i
$782$	3.37518			0.120696
$783$	46.4817	+	13.0337i	1.66112	+	0.465786i
$784$		0			0
$785$	0.643678	+	1.11488i	0.0229739	+	0.0397919i
$786$	27.6234	−	7.28746i	0.985294	−	0.259935i
$787$	−24.4776	+	42.3964i	−0.872531	+	1.51127i	−0.0131602	+	0.999913i	$0.504189\pi$
$787$	−24.4776	+	42.3964i	−0.872531	+	1.51127i	−0.859370	+	0.511354i	$0.829144\pi$
$788$	−0.299165	+	0.518170i	−0.0106573	+	0.0184590i
$789$	1.87760	+	1.89215i	0.0668442	+	0.0673625i
$790$	0.447448	+	0.775003i	0.0159195	+	0.0275734i
$791$		0			0
$792$	−26.4994	−	15.5735i	−0.941615	−	0.553381i
$793$	−14.0638			−0.499419
$794$	13.2652	+	22.9759i	0.470763	+	0.815385i
$795$	0.478488	−	1.75855i	0.0169702	−	0.0623694i
$796$	1.97174	−	3.41515i	0.0698864	−	0.121047i
$797$	1.44417	−	2.50137i	0.0511550	−	0.0886030i	−0.839314	−	0.543647i	$-0.817043\pi$
$797$	1.44417	−	2.50137i	0.0511550	−	0.0886030i	0.890469	+	0.455044i	$0.150376\pi$
$798$		0			0
$799$	2.57755	+	4.46445i	0.0911873	+	0.157941i
$800$	20.6293			0.729356
$801$	15.7346	−	8.92306i	0.555954	−	0.315281i
$802$	1.72294			0.0608393
$803$	7.88237	+	13.6527i	0.278163	+	0.481792i
$804$	9.53510	+	9.60903i	0.336277	+	0.338884i
$805$		0			0
$806$	12.6649	−	21.9362i	0.446102	−	0.772671i
$807$	43.9741	−	11.6010i	1.54796	−	0.408375i
$808$	−26.8169	−	46.4483i	−0.943417	−	1.63405i
$809$	11.6974			0.411258			0.205629	−	0.978630i	$-0.434076\pi$
$809$	11.6974			0.411258			0.205629	+	0.978630i	$0.434076\pi$
$810$	−0.537332	+	0.898350i	−0.0188799	+	0.0315648i
$811$	−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
$815$	−0.472627	+	0.818614i	−0.0165554	+	0.0286748i
$816$	3.57810	+	3.60584i	0.125259	+	0.126230i
$817$	28.9934	+	50.2181i	1.01435	+	1.75691i
$818$	24.6431			0.861624
$819$		0			0
$820$	0.618775			0.0216085
$821$	−17.0068	−	29.4567i	−0.593543	−	1.02805i	−0.993751	−	0.111622i	$-0.964396\pi$
$821$	−17.0068	−	29.4567i	−0.593543	−	1.02805i	0.400208	−	0.916424i	$-0.368938\pi$
$822$	−7.64652	+	28.1027i	−0.266703	+	0.980193i
$823$	−21.6890	+	37.5664i	−0.756031	+	1.30948i	0.188829	+	0.982010i	$0.439531\pi$
$823$	−21.6890	+	37.5664i	−0.756031	+	1.30948i	−0.944860	+	0.327474i	$0.893803\pi$
$824$	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	$0.701949\pi$
$828$	−3.84605	−	2.26030i	−0.133659	−	0.0785508i
$829$	−16.9167			−0.587540			−0.293770	−	0.955876i	$-0.594910\pi$
$829$	−16.9167			−0.587540			−0.293770	+	0.955876i	$0.594910\pi$
$830$	0.0679744	+	0.117735i	0.00235943	+	0.00408665i
$831$	23.0231	+	23.2016i	0.798661	+	0.804853i
$832$	−10.1632	+	17.6032i	−0.352345	+	0.610280i
$833$		0			0
$834$	−14.9950	+	3.95591i	−0.519236	+	0.136982i
$835$	0.918434	+	1.59077i	0.0317837	+	0.0550510i
$836$	20.0963			0.695044
$837$	11.9163	+	46.6261i	0.411887	+	1.61163i
$838$	6.58705			0.227546
$839$	−8.16244	−	14.1378i	−0.281799	−	0.488089i	0.690029	−	0.723782i	$-0.257598\pi$
$839$	−8.16244	−	14.1378i	−0.281799	−	0.488089i	−0.971828	+	0.235692i	$0.924264\pi$
$840$		0			0
$841$	−28.6560	+	49.6336i	−0.988138	+	1.71150i
$842$	−8.06812	+	13.9744i	−0.278046	+	0.481589i
$843$	−6.08975	−	6.13696i	−0.209742	−	0.211368i
$844$	2.82590	+	4.89459i	0.0972713	+	0.168479i
$845$	−0.722428			−0.0248523
$846$	−0.0816511	+	10.5721i	−0.00280722	+	0.363478i
$847$		0			0
$848$	−9.06915	−	15.7082i	−0.311436	−	0.539423i
$849$	6.99974	−	25.7256i	0.240230	−	0.882901i
$850$	−4.43772	+	7.68635i	−0.152212	+	0.263640i
$851$	−1.88062	+	3.25733i	−0.0644668	+	0.111660i
$852$	1.17281	−	4.31032i	0.0401797	−	0.147669i
$853$	−14.4524	−	25.0323i	−0.494841	−	0.857089i	0.505142	−	0.863036i	$-0.331440\pi$
$853$	−14.4524	−	25.0323i	−0.494841	−	0.857089i	−0.999982	+	0.00594733i	$0.998107\pi$
$854$		0			0
$855$	0.0187729	−	2.43071i	0.000642020	−	0.0831285i
$856$	−55.7095			−1.90411
$857$	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	$0.668032\pi$
$858$	11.1353	+	11.2217i	0.380154	+	0.383102i
$859$	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
$863$	−14.6662			−0.499243			−0.249621	−	0.968344i	$-0.580306\pi$
$863$	−14.6662			−0.499243			−0.249621	+	0.968344i	$0.580306\pi$
$864$	−5.32029	−	20.8173i	−0.181000	−	0.708219i
$865$	−0.298398			−0.0101458
$866$	0.745594	+	1.29141i	0.0253363	+	0.0438838i
$867$	−24.1124	+	6.36122i	−0.818901	+	0.216038i
$868$		0			0
$869$	−12.8388	+	22.2375i	−0.435527	+	0.754354i
$870$	−1.31829	−	1.32852i	−0.0446944	−	0.0450409i
$871$	−12.3643	−	21.4156i	−0.418948	−	0.725639i
$872$	−12.9631			−0.438985
$873$	−9.83497	−	5.77995i	−0.332863	−	0.195622i
$874$	−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	$0.977323\pi$
$878$	9.56205	−	16.5620i	0.322704	−	0.558939i
$879$	−11.7336	+	43.1235i	−0.395763	+	1.45452i
$880$	0.319953	+	0.554174i	0.0107856	+	0.0186812i
$881$	−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	$0.731581\pi$
$884$	1.56785	+	2.71559i	0.0527324	+	0.0913352i
$885$	−0.573847	−	0.578296i	−0.0192897	−	0.0194392i
$886$	10.8131	−	18.7288i	0.363272	−	0.629206i
$887$	−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
$891$	−30.0323	−	0.463920i	−1.00612	−	0.0155419i
$892$	−8.76457			−0.293459
$893$	−12.2754	−	21.2616i	−0.410779	−	0.711491i
$894$	20.5908	−	5.43215i	0.688659	−	0.181678i
$895$	0.535910	−	0.928223i	0.0179135	−	0.0310271i
$896$		0			0
$897$	5.74003	+	5.78454i	0.191654	+	0.193140i
$898$	−9.77891	−	16.9376i	−0.326326	−	0.565214i
$899$	−86.0443			−2.86974
$900$	10.2042	−	5.78680i	0.340141	−	0.192893i
$901$	−16.0944			−0.536183
$902$	−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
$906$	−5.65365	+	20.7784i	−0.187830	+	0.690317i
$907$	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	$0.759091\pi$
$908$	18.6315			0.618308
$909$	−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	$0.804776\pi$
$912$	−17.0404	−	17.1725i	−0.564264	−	0.568638i
$913$	−1.95042	+	3.37822i	−0.0645494	+	0.111803i
$914$	0.267681	−	0.463637i	0.00885409	−	0.0153357i
$915$	−1.00166	+	0.264254i	−0.0331140	+	0.00873596i
$916$	0.746758	+	1.29342i	0.0246736	+	0.0427359i
$917$		0			0
$918$	8.90089	+	2.49585i	0.293773	+	0.0823754i
$919$	34.0283			1.12249			0.561245	−	0.827649i	$-0.310322\pi$
$919$	34.0283			1.12249			0.561245	+	0.827649i	$0.310322\pi$
$920$	0.307138	+	0.531978i	0.0101260	+	0.0175388i
$921$	−37.3326	+	9.84889i	−1.23015	+	0.324532i
$922$	−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
$926$	11.5637			0.380006
$927$	0.202313	−	26.1953i	0.00664482	−	0.860368i
$928$	38.4165			1.26108
$929$	−5.31646	−	9.20837i	−0.174427	−	0.302117i	0.765536	−	0.643393i	$-0.222474\pi$
$929$	−5.31646	−	9.20837i	−0.174427	−	0.302117i	−0.939963	+	0.341277i	$0.889141\pi$
$930$	0.489857	−	1.80033i	0.0160631	−	0.0590353i
$931$		0			0
$932$	2.56375	−	4.44055i	0.0839785	−	0.145455i
$933$	0.595653	−	2.18916i	0.0195008	−	0.0716698i
$934$	12.0746	+	20.9137i	0.395092	+	0.684319i
$935$	0.567799			0.0185690
$936$	−0.176397	+	22.8397i	−0.00576570	+	0.746540i
$937$	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
$941$	17.1828	−	29.7615i	0.560143	−	0.970197i	−0.437340	−	0.899296i	$-0.644079\pi$
$941$	17.1828	−	29.7615i	0.560143	−	0.970197i	0.997483	−	0.0709006i	$-0.0225873\pi$
$942$	22.5444	−	5.94754i	0.734536	−	0.193781i
$943$	−7.10057	−	12.2985i	−0.231226	−	0.400496i
$944$	−8.10825			−0.263901
$945$		0			0
$946$	−27.7791			−0.903175
$947$	20.2920	+	35.1468i	0.659401	+	1.14212i	0.980771	+	0.195162i	$0.0625234\pi$
$947$	20.2920	+	35.1468i	0.659401	+	1.14212i	−0.321370	+	0.946954i	$0.604143\pi$
$948$	−10.0998	+	2.66448i	−0.328027	+	0.0865384i
$949$	5.85736	−	10.1453i	0.190138	−	0.329329i
$950$	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	$0.619789\pi$
$954$	−28.4571	−	16.7241i	−0.921333	−	0.541462i
$955$	−2.36244			−0.0764468
$956$	−8.36589	−	14.4901i	−0.270572	−	0.468645i
$957$	14.0994	−	51.8184i	0.455769	−	1.67505i
$958$	2.20656	−	3.82187i	0.0712907	−	0.123479i
$959$		0			0
$960$	−0.393096	+	1.44472i	−0.0126871	+	0.0466280i
$961$	−27.3888	−	47.4387i	−0.883509	−	1.53028i
$962$	5.42208			0.174815
$963$	−47.3543	+	26.8546i	−1.52597	+	0.865376i
$964$	−15.7279			−0.506562
$965$	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
$969$	−20.7561	+	5.47578i	−0.666784	+	0.175907i
$970$	0.221136	+	0.383019i	0.00710025	+	0.0122980i
$971$	45.5771			1.46264			0.731319	−	0.682035i	$-0.238905\pi$
$971$	45.5771			1.46264			0.731319	+	0.682035i	$0.238905\pi$
$972$	−8.47121	−	8.80481i	−0.271714	−	0.282414i
$973$		0			0
$974$	−14.5988	−	25.2858i	−0.467774	−	0.810209i
$975$	−20.7203	+	5.46631i	−0.663580	+	0.175062i
$976$	−5.15508	+	8.92885i	−0.165010	+	0.285806i
$977$	7.34481	−	12.7216i	0.234981	−	0.407000i	−0.724286	−	0.689500i	$-0.757830\pi$
$977$	7.34481	−	12.7216i	0.234981	−	0.407000i	0.959267	+	0.282500i	$0.0911637\pi$
$978$	12.0587	+	12.1522i	0.385594	+	0.388584i
$979$	−10.0612	−	17.4266i	−0.321558	−	0.556956i
$980$		0			0
$981$	−11.0189	+	6.24881i	−0.351807	+	0.199509i
$982$	31.3528			1.00051
$983$	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	$0.581524\pi$
$984$	10.4501	−	38.4065i	0.333138	−	1.22436i
$985$	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
$989$	−14.3195			−0.455334
$990$	1.00395	+	0.590013i	0.0319075	+	0.0187518i
$991$	24.1829			0.768196			0.384098	−	0.923292i	$-0.374512\pi$
$991$	24.1829			0.768196			0.384098	+	0.923292i	$0.374512\pi$
$992$	19.1487	+	33.1665i	0.607971	+	1.05304i
$993$	−16.8911	−	17.0221i	−0.536024	−	0.540179i
$994$		0			0
$995$	−0.265311	+	0.459532i	−0.00841093	+	0.0145682i
$996$	−1.53433	+	0.404778i	−0.0486170	+	0.0128259i
$997$	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	$0.778293\pi$
$998$	8.19521			0.259415
$999$	−7.36820	+	7.19943i	−0.233119	+	0.227780i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.7	✓	24	7.6	odd	2	inner
441.2.f.h.148.8	yes	24	1.1	even	1	trivial
441.2.f.h.295.7	yes	24	63.34	odd	6	inner
441.2.f.h.295.8	yes	24	9.7	even	3	inner
441.2.g.h.67.7		24	7.2	even	3
441.2.g.h.67.8		24	7.5	odd	6
441.2.g.h.79.7		24	63.25	even	3
441.2.g.h.79.8		24	63.52	odd	6
441.2.h.h.214.5		24	63.16	even	3
441.2.h.h.214.6		24	63.61	odd	6
441.2.h.h.373.5		24	7.4	even	3
441.2.h.h.373.6		24	7.3	odd	6
1323.2.f.h.442.5		24	3.2	odd	2
1323.2.f.h.442.6		24	21.20	even	2
1323.2.f.h.883.5		24	9.2	odd	6
1323.2.f.h.883.6		24	63.20	even	6
1323.2.g.h.361.5		24	21.2	odd	6
1323.2.g.h.361.6		24	21.5	even	6
1323.2.g.h.667.5		24	63.11	odd	6
1323.2.g.h.667.6		24	63.38	even	6
1323.2.h.h.226.7		24	21.17	even	6
1323.2.h.h.226.8		24	21.11	odd	6
1323.2.h.h.802.7		24	63.47	even	6
1323.2.h.h.802.8		24	63.2	odd	6
3969.2.a.bh.1.5		12	63.13	odd	6
3969.2.a.bh.1.6		12	9.4	even	3
3969.2.a.bi.1.7		12	9.5	odd	6
3969.2.a.bi.1.8		12	63.41	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.551407 + 0.955065i) q^{2} +(1.67475 - 0.441824i) q^{3} +(0.391901 - 0.678793i) q^{4} +(-0.0527330 + 0.0913363i) q^{5} +(1.34544 + 1.35587i) q^{6} +3.07001 q^{8} +(2.60958 - 1.47989i) q^{9} +O(q^{10})\)	\(q+(0.551407 + 0.955065i) q^{2} +(1.67475 - 0.441824i) q^{3} +(0.391901 - 0.678793i) q^{4} +(-0.0527330 + 0.0913363i) q^{5} +(1.34544 + 1.35587i) q^{6} +3.07001 q^{8} +(2.60958 - 1.47989i) q^{9} -0.116309 q^{10} +(-1.66866 - 2.89020i) q^{11} +(0.356430 - 1.30996i) q^{12} +(-1.23997 + 2.14770i) q^{13} +(-0.0479602 + 0.176264i) q^{15} +(0.909025 + 1.57448i) q^{16} +1.61319 q^{17} +(2.85233 + 1.67630i) q^{18} -7.68266 q^{19} +(0.0413323 + 0.0715896i) q^{20} +(1.84022 - 3.18735i) q^{22} +(0.948593 - 1.64301i) q^{23} +(5.14151 - 1.35641i) q^{24} +(2.49444 + 4.32049i) q^{25} -2.73492 q^{26} +(3.71655 - 3.63142i) q^{27} +(4.64521 + 8.04574i) q^{29} +(-0.194789 + 0.0513883i) q^{30} +(-4.63081 + 8.02080i) q^{31} +(2.06753 - 3.58107i) q^{32} +(-4.07155 - 4.10311i) q^{33} +(0.889523 + 1.54070i) q^{34} +(0.0181599 - 2.35134i) q^{36} -1.98254 q^{37} +(-4.23627 - 7.33744i) q^{38} +(-1.12774 + 4.14471i) q^{39} +(-0.161891 + 0.280404i) q^{40} +(3.74268 - 6.48252i) q^{41} +(-3.77388 - 6.53655i) q^{43} -2.61579 q^{44} +(-0.00244354 + 0.316389i) q^{45} +2.09224 q^{46} +(1.59780 + 2.76747i) q^{47} +(2.21803 + 2.23523i) q^{48} +(-2.75090 + 4.76470i) q^{50} +(2.70169 - 0.712745i) q^{51} +(0.971894 + 1.68337i) q^{52} -9.97679 q^{53} +(5.51758 + 1.54715i) q^{54} +0.351974 q^{55} +(-12.8665 + 3.39438i) q^{57} +(-5.12280 + 8.87296i) q^{58} +(-2.22993 + 3.86235i) q^{59} +(0.100851 + 0.101633i) q^{60} +(2.83550 + 4.91123i) q^{61} -10.2138 q^{62} +8.19630 q^{64} +(-0.130775 - 0.226509i) q^{65} +(1.67366 - 6.15107i) q^{66} +(-4.98571 + 8.63550i) q^{67} +(0.632210 - 1.09502i) q^{68} +(0.862736 - 3.17075i) q^{69} +3.29042 q^{71} +(8.01146 - 4.54329i) q^{72} -4.72378 q^{73} +(-1.09318 - 1.89345i) q^{74} +(6.08646 + 6.13365i) q^{75} +(-3.01084 + 5.21493i) q^{76} +(-4.58031 + 1.20835i) q^{78} +(-3.84705 - 6.66328i) q^{79} -0.191743 q^{80} +(4.61985 - 7.72379i) q^{81} +8.25496 q^{82} +(-0.584428 - 1.01226i) q^{83} +(-0.0850683 + 0.147343i) q^{85} +(4.16189 - 7.20860i) q^{86} +(11.3344 + 11.4223i) q^{87} +(-5.12280 - 8.87296i) q^{88} +6.02954 q^{89} +(-0.303519 + 0.172125i) q^{90} +(-0.743509 - 1.28780i) q^{92} +(-4.21167 + 15.4788i) q^{93} +(-1.76208 + 3.05201i) q^{94} +(0.405130 - 0.701706i) q^{95} +(1.88040 - 6.91088i) q^{96} +(-1.90127 - 3.29310i) q^{97} +(-8.63168 - 5.07279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9} + 20 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} + 48 q^{32} - 4 q^{36} + 24 q^{37} + 32 q^{39} - 112 q^{44} - 48 q^{46} - 4 q^{50} - 56 q^{51} - 64 q^{53} - 12 q^{57} - 88 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} + 168 q^{72} + 68 q^{74} - 60 q^{78} + 12 q^{79} + 80 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 80 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9 + 20 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 + 48 * q^32 - 4 * q^36 + 24 * q^37 + 32 * q^39 - 112 * q^44 - 48 * q^46 - 4 * q^50 - 56 * q^51 - 64 * q^53 - 12 * q^57 - 88 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 + 168 * q^72 + 68 * q^74 - 60 * q^78 + 12 * q^79 + 80 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 80 * q^93 + 64 * q^95 + 20 * q^99

Introduction

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