LMFDB - Embedded newform 441.2.f.f.148.2

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			148.2
Root			$-0.335166 - 0.580525i$ of defining polynomial
Character	$\chi$	$=$	441.148
Dual form			441.2.f.f.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.335166 - 0.580525i) q^{2} +(1.27533 - 1.17198i) q^{3} +(0.775327 - 1.34291i) q^{4} +(0.712469 - 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(0.252918 - 2.98932i) q^{9} +O(q^{10})$	\(q+(-0.335166 - 0.580525i) q^{2} +(1.27533 - 1.17198i) q^{3} +(0.775327 - 1.34291i) q^{4} +(0.712469 - 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(0.252918 - 2.98932i) q^{9} -0.955182 q^{10} +(2.46539 + 4.27018i) q^{11} +(-0.585065 - 2.62131i) q^{12} +(1.37730 - 2.38556i) q^{13} +(-0.537632 - 2.40879i) q^{15} +(-0.752918 - 1.30409i) q^{16} +1.11968 q^{17} +(-1.82014 + 0.855094i) q^{18} -4.01505 q^{19} +(-1.10479 - 1.91356i) q^{20} +(1.65263 - 2.86244i) q^{22} +(-2.71830 + 4.70824i) q^{23} +(-3.03543 + 2.78946i) q^{24} +(1.48478 + 2.57171i) q^{25} -1.84650 q^{26} +(-3.18087 - 4.10878i) q^{27} +(3.40555 + 5.89858i) q^{29} +(-1.21817 + 1.11946i) q^{30} +(1.25292 - 2.17012i) q^{31} +(-2.88483 + 4.99666i) q^{32} +(8.14874 + 2.55648i) q^{33} +(-0.375279 - 0.650002i) q^{34} +(-3.81828 - 2.65735i) q^{36} -1.41957 q^{37} +(1.34571 + 2.33083i) q^{38} +(-1.03932 - 4.65654i) q^{39} +(-1.69576 + 2.93714i) q^{40} +(-0.124384 + 0.215440i) q^{41} +(-0.498313 - 0.863104i) q^{43} +7.64592 q^{44} +(-3.50872 - 2.44191i) q^{45} +3.64434 q^{46} +(-4.73790 - 8.20628i) q^{47} +(-2.48859 - 0.780738i) q^{48} +(0.995294 - 1.72390i) q^{50} +(1.42796 - 1.31224i) q^{51} +(-2.13572 - 3.69917i) q^{52} +0.820458 q^{53} +(-1.31913 + 3.22370i) q^{54} +7.02604 q^{55} +(-5.12050 + 4.70556i) q^{57} +(2.28285 - 3.95401i) q^{58} +(-3.29204 + 5.70197i) q^{59} +(-3.65163 - 1.14561i) q^{60} +(0.0376322 + 0.0651809i) q^{61} -1.67974 q^{62} +0.855913 q^{64} +(-1.96257 - 3.39927i) q^{65} +(-1.24708 - 5.58740i) q^{66} +(6.29385 - 10.9013i) q^{67} +(0.868117 - 1.50362i) q^{68} +(2.05125 + 9.19035i) q^{69} +0.0804951 q^{71} +(-0.601975 + 7.11494i) q^{72} +10.6910 q^{73} +(0.475793 + 0.824098i) q^{74} +(4.90757 + 1.53964i) q^{75} +(-3.11297 + 5.39183i) q^{76} +(-2.35489 + 2.16407i) q^{78} +(0.922457 + 1.59774i) q^{79} -2.14572 q^{80} +(-8.87206 - 1.51211i) q^{81} +0.166758 q^{82} +(7.23583 + 12.5328i) q^{83} +(0.797736 - 1.38172i) q^{85} +(-0.334036 + 0.578567i) q^{86} +(11.2562 + 3.53138i) q^{87} +(-5.86792 - 10.1635i) q^{88} +13.5258 q^{89} +(-0.241583 + 2.85534i) q^{90} +(4.21515 + 7.30085i) q^{92} +(-0.945458 - 4.23601i) q^{93} +(-3.17597 + 5.50094i) q^{94} +(-2.86059 + 4.95469i) q^{95} +(2.17690 + 9.75334i) q^{96} +(-2.70160 - 4.67930i) q^{97} +(13.3885 - 6.28982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9	$ 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9} - 14 q^{10} + 4 q^{11} + 2 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} + 24 q^{17} - 2 q^{18} + 2 q^{19} - 5 q^{20} - q^{22} + 3 q^{23} + 9 q^{24} - q^{25} + 22 q^{26} + 7 q^{27} + 7 q^{29} + 10 q^{30} + 3 q^{31} - 2 q^{32} + 13 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} - 22 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} + 20 q^{44} - 17 q^{45} - 6 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} - 15 q^{51} + 10 q^{52} + 42 q^{53} - 52 q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} - 30 q^{59} + 31 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} - 22 q^{66} - 2 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 12 q^{72} + 30 q^{73} - 36 q^{74} + 17 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} + 40 q^{80} - 31 q^{81} - 10 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} + 34 q^{87} - 18 q^{88} + 56 q^{89} - 28 q^{90} + 27 q^{92} + 18 q^{93} + 3 q^{94} - 14 q^{95} + 58 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9 - 14 * q^10 + 4 * q^11 + 2 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 + 24 * q^17 - 2 * q^18 + 2 * q^19 - 5 * q^20 - q^22 + 3 * q^23 + 9 * q^24 - q^25 + 22 * q^26 + 7 * q^27 + 7 * q^29 + 10 * q^30 + 3 * q^31 - 2 * q^32 + 13 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 - 22 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 + 20 * q^44 - 17 * q^45 - 6 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 - 15 * q^51 + 10 * q^52 + 42 * q^53 - 52 * q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 - 30 * q^59 + 31 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 - 22 * q^66 - 2 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 12 * q^72 + 30 * q^73 - 36 * q^74 + 17 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 + 40 * q^80 - 31 * q^81 - 10 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 + 34 * q^87 - 18 * q^88 + 56 * q^89 - 28 * q^90 + 27 * q^92 + 18 * q^93 + 3 * q^94 - 14 * q^95 + 58 * q^96 + 12 * q^97 + 35 * 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 $

$2$	−0.335166	−	0.580525i	−0.236998	−	0.410493i	0.722853	−	0.691002i	$-0.242830\pi$
$2$	−0.335166	−	0.580525i	−0.236998	−	0.410493i	−0.959852	+	0.280508i	$0.909497\pi$
$3$	1.27533	−	1.17198i	0.736310	−	0.676644i
$3$	1.27533	−	1.17198i	0.736310	−	0.676644i
$4$	0.775327	−	1.34291i	0.387664	−	0.671453i
$5$	0.712469	−	1.23403i	0.318626	−	0.551876i	−0.661576	−	0.749878i	$-0.730112\pi$
$5$	0.712469	−	1.23403i	0.318626	−	0.551876i	0.980202	+	0.198002i	$0.0634454\pi$
$6$	−1.10781	−	0.347551i	−0.452262	−	0.141887i
$7$		0			0
$7$		0			0
$8$	−2.38012			−0.841499
$9$	0.252918	−	2.98932i	0.0843060	−	0.996440i
$10$	−0.955182			−0.302055
$11$	2.46539	+	4.27018i	0.743342	+	1.28751i	0.950965	+	0.309297i	$0.100094\pi$
$11$	2.46539	+	4.27018i	0.743342	+	1.28751i	−0.207623	+	0.978209i	$0.566573\pi$
$12$	−0.585065	−	2.62131i	−0.168894	−	0.756708i
$13$	1.37730	−	2.38556i	0.381995	−	0.661635i	−0.609352	−	0.792900i	$-0.708571\pi$
$13$	1.37730	−	2.38556i	0.381995	−	0.661635i	0.991347	+	0.131265i	$0.0419038\pi$
$14$		0			0
$15$	−0.537632	−	2.40879i	−0.138816	−	0.621948i
$16$	−0.752918	−	1.30409i	−0.188230	−	0.326023i
$17$	1.11968			0.271562			0.135781	−	0.990739i	$-0.456646\pi$
$17$	1.11968			0.271562			0.135781	+	0.990739i	$0.456646\pi$
$18$	−1.82014	+	0.855094i	−0.429012	+	0.201548i
$19$	−4.01505			−0.921115			−0.460557	−	0.887630i	$-0.652350\pi$
$19$	−4.01505			−0.921115			−0.460557	+	0.887630i	$0.652350\pi$
$20$	−1.10479	−	1.91356i	−0.247039	−	0.427884i
$21$		0			0
$22$	1.65263	−	2.86244i	0.352342	−	0.610274i
$23$	−2.71830	+	4.70824i	−0.566806	+	0.981736i	0.430073	+	0.902794i	$0.358488\pi$
$23$	−2.71830	+	4.70824i	−0.566806	+	0.981736i	−0.996879	+	0.0789424i	$0.974846\pi$
$24$	−3.03543	+	2.78946i	−0.619605	+	0.569395i
$25$	1.48478	+	2.57171i	0.296955	+	0.514342i
$26$	−1.84650			−0.362129
$27$	−3.18087	−	4.10878i	−0.612160	−	0.790734i
$28$		0			0
$29$	3.40555	+	5.89858i	0.632394	+	1.09534i	0.987061	+	0.160346i	$0.0512611\pi$
$29$	3.40555	+	5.89858i	0.632394	+	1.09534i	−0.354667	+	0.934993i	$0.615406\pi$
$30$	−1.21817	+	1.11946i	−0.222406	+	0.204384i
$31$	1.25292	−	2.17012i	0.225031	−	0.389765i	−0.731298	−	0.682058i	$-0.761085\pi$
$31$	1.25292	−	2.17012i	0.225031	−	0.389765i	0.956329	+	0.292294i	$0.0944184\pi$
$32$	−2.88483	+	4.99666i	−0.509970	+	0.883294i
$33$	8.14874	+	2.55648i	1.41851	+	0.445026i
$34$	−0.375279	−	0.650002i	−0.0643597	−	0.111474i
$35$		0			0
$36$	−3.81828	−	2.65735i	−0.636380	−	0.442891i
$37$	−1.41957			−0.233376			−0.116688	−	0.993169i	$-0.537228\pi$
$37$	−1.41957			−0.233376			−0.116688	+	0.993169i	$0.537228\pi$
$38$	1.34571	+	2.33083i	0.218303	+	0.378111i
$39$	−1.03932	−	4.65654i	−0.166424	−	0.745643i
$40$	−1.69576	+	2.93714i	−0.268123	+	0.464403i
$41$	−0.124384	+	0.215440i	−0.0194256	+	0.0336460i	−0.875575	−	0.483083i	$-0.839517\pi$
$41$	−0.124384	+	0.215440i	−0.0194256	+	0.0336460i	0.856149	+	0.516729i	$0.172850\pi$
$42$		0			0
$43$	−0.498313	−	0.863104i	−0.0759921	−	0.131622i	0.825525	−	0.564365i	$-0.190879\pi$
$43$	−0.498313	−	0.863104i	−0.0759921	−	0.131622i	−0.901517	+	0.432743i	$0.857546\pi$
$44$	7.64592			1.15267
$45$	−3.50872	−	2.44191i	−0.523049	−	0.364018i
$46$	3.64434			0.537328
$47$	−4.73790	−	8.20628i	−0.691093	−	1.19701i	−0.971480	−	0.237122i	$-0.923796\pi$
$47$	−4.73790	−	8.20628i	−0.691093	−	1.19701i	0.280387	−	0.959887i	$-0.409537\pi$
$48$	−2.48859	−	0.780738i	−0.359197	−	0.112690i
$49$		0			0
$50$	0.995294	−	1.72390i	0.140756	−	0.243796i
$51$	1.42796	−	1.31224i	0.199954	−	0.183751i
$52$	−2.13572	−	3.69917i	−0.296171	−	0.512983i
$53$	0.820458			0.112699			0.0563493	−	0.998411i	$-0.482054\pi$
$53$	0.820458			0.112699			0.0563493	+	0.998411i	$0.482054\pi$
$54$	−1.31913	+	3.22370i	−0.179510	+	0.438690i
$55$	7.02604			0.947392
$56$		0			0
$57$	−5.12050	+	4.70556i	−0.678226	+	0.623267i
$58$	2.28285	−	3.95401i	0.299753	−	0.519187i
$59$	−3.29204	+	5.70197i	−0.428586	+	0.742334i	−0.996748	−	0.0805836i	$-0.974322\pi$
$59$	−3.29204	+	5.70197i	−0.428586	+	0.742334i	0.568161	+	0.822917i	$0.307655\pi$
$60$	−3.65163	−	1.14561i	−0.471423	−	0.147898i
$61$	0.0376322	+	0.0651809i	0.00481831	+	0.00834556i	0.868425	−	0.495821i	$-0.165133\pi$
$61$	0.0376322	+	0.0651809i	0.00481831	+	0.00834556i	−0.863606	+	0.504167i	$0.831800\pi$
$62$	−1.67974			−0.213328
$63$		0			0
$64$	0.855913			0.106989
$65$	−1.96257	−	3.39927i	−0.243427	−	0.421628i
$66$	−1.24708	−	5.58740i	−0.153505	−	0.687761i
$67$	6.29385	−	10.9013i	0.768916	−	1.33180i	−0.169235	−	0.985576i	$-0.554130\pi$
$67$	6.29385	−	10.9013i	0.768916	−	1.33180i	0.938151	−	0.346226i	$-0.112537\pi$
$68$	0.868117	−	1.50362i	0.105275	−	0.182341i
$69$	2.05125	+	9.19035i	0.246941	+	1.10639i
$70$		0			0
$71$	0.0804951			0.00955301			0.00477651	−	0.999989i	$-0.498480\pi$
$71$	0.0804951			0.00955301			0.00477651	+	0.999989i	$0.498480\pi$
$72$	−0.601975	+	7.11494i	−0.0709435	+	0.838504i
$73$	10.6910			1.25129			0.625644	−	0.780109i	$-0.284836\pi$
$73$	10.6910			1.25129			0.625644	+	0.780109i	$0.284836\pi$
$74$	0.475793	+	0.824098i	0.0553098	+	0.0957995i
$75$	4.90757	+	1.53964i	0.566678	+	0.177782i
$76$	−3.11297	+	5.39183i	−0.357083	+	0.618485i
$77$		0			0
$78$	−2.35489	+	2.16407i	−0.266639	+	0.245032i
$79$	0.922457	+	1.59774i	0.103785	+	0.179760i	0.913241	−	0.407420i	$-0.133571\pi$
$79$	0.922457	+	1.59774i	0.103785	+	0.179760i	−0.809456	+	0.587180i	$0.800238\pi$
$80$	−2.14572			−0.239899
$81$	−8.87206	−	1.51211i	−0.985785	−	0.168012i
$82$	0.166758			0.0184153
$83$	7.23583	+	12.5328i	0.794236	+	1.37566i	0.923323	+	0.384023i	$0.125462\pi$
$83$	7.23583	+	12.5328i	0.794236	+	1.37566i	−0.129088	+	0.991633i	$0.541205\pi$
$84$		0			0
$85$	0.797736	−	1.38172i	0.0865266	−	0.149868i
$86$	−0.334036	+	0.578567i	−0.0360200	+	0.0623885i
$87$	11.2562	+	3.53138i	1.20679	+	0.378604i
$88$	−5.86792	−	10.1635i	−0.625522	−	1.08344i
$89$	13.5258			1.43374			0.716868	−	0.697209i	$-0.245575\pi$
$89$	13.5258			1.43374			0.716868	+	0.697209i	$0.245575\pi$
$90$	−0.241583	+	2.85534i	−0.0254651	+	0.300980i
$91$		0			0
$92$	4.21515	+	7.30085i	0.439460	+	0.761167i
$93$	−0.945458	−	4.23601i	−0.0980394	−	0.439253i
$94$	−3.17597	+	5.50094i	−0.327576	+	0.567378i
$95$	−2.86059	+	4.95469i	−0.293491	+	0.508341i
$96$	2.17690	+	9.75334i	0.222179	+	0.995446i
$97$	−2.70160	−	4.67930i	−0.274306	−	0.475111i	0.695654	−	0.718377i	$-0.255115\pi$
$97$	−2.70160	−	4.67930i	−0.274306	−	0.475111i	−0.969960	+	0.243266i	$0.921781\pi$
$98$		0			0
$99$	13.3885	−	6.28982i	1.34559	−	0.632151i
$100$	4.60475			0.460475
$101$	−2.56770	−	4.44739i	−0.255496	−	0.442531i	0.709534	−	0.704671i	$-0.248905\pi$
$101$	−2.56770	−	4.44739i	−0.255496	−	0.442531i	−0.965030	+	0.262139i	$0.915572\pi$
$102$	−1.24039	−	0.389145i	−0.122817	−	0.0385311i
$103$	−7.10561	+	12.3073i	−0.700137	+	1.21267i	0.268282	+	0.963341i	$0.413544\pi$
$103$	−7.10561	+	12.3073i	−0.700137	+	1.21267i	−0.968418	+	0.249332i	$0.919789\pi$
$104$	−3.27814	+	5.67791i	−0.321448	+	0.556765i
$105$		0			0
$106$	−0.274990	−	0.476296i	−0.0267094	−	0.0462620i
$107$	−7.66030			−0.740549			−0.370274	−	0.928922i	$-0.620736\pi$
$107$	−7.66030			−0.740549			−0.370274	+	0.928922i	$0.620736\pi$
$108$	−7.98392	+	1.08597i	−0.768253	+	0.104498i
$109$	1.69879			0.162714			0.0813572	−	0.996685i	$-0.474075\pi$
$109$	1.69879			0.162714			0.0813572	+	0.996685i	$0.474075\pi$
$110$	−2.35489	−	4.07880i	−0.224530	−	0.388898i
$111$	−1.81042	+	1.66371i	−0.171838	+	0.157913i
$112$		0			0
$113$	−0.300351	+	0.520224i	−0.0282547	+	0.0489385i	−0.879807	−	0.475331i	$-0.842328\pi$
$113$	−0.300351	+	0.520224i	−0.0282547	+	0.0489385i	0.851552	+	0.524270i	$0.175662\pi$
$114$	4.44791	+	1.39543i	0.416585	+	0.130694i
$115$	3.87341	+	6.70895i	0.361198	+	0.625613i
$116$	10.5617			0.980625
$117$	−6.78285	−	4.72055i	−0.627075	−	0.436415i
$118$	4.41352			0.406297
$119$		0			0
$120$	1.27963	+	5.73322i	0.116814	+	0.523369i
$121$	−6.65626	+	11.5290i	−0.605115	+	1.04809i
$122$	0.0252261	−	0.0436929i	0.00228386	−	0.00395577i
$123$	0.0938609	+	0.420532i	0.00846316	+	0.0379181i
$124$	−1.94284	−	3.36510i	−0.174472	−	0.302195i
$125$	11.3561			1.01572
$126$		0			0
$127$	7.25977			0.644200			0.322100	−	0.946706i	$-0.395611\pi$
$127$	7.25977			0.644200			0.322100	+	0.946706i	$0.395611\pi$
$128$	5.48278	+	9.49645i	0.484614	+	0.839375i
$129$	−1.64705	−	0.516726i	−0.145015	−	0.0454952i
$130$	−1.31557	+	2.27864i	−0.115384	+	0.199850i
$131$	−10.2265	+	17.7128i	−0.893492	+	1.54757i	−0.0578326	+	0.998326i	$0.518419\pi$
$131$	−10.2265	+	17.7128i	−0.893492	+	1.54757i	−0.835660	+	0.549248i	$0.814914\pi$
$132$	9.75105	−	8.96088i	0.848720	−	0.779945i
$133$		0			0
$134$	−8.43794			−0.728927
$135$	−7.33663	+	0.997927i	−0.631437	+	0.0858879i
$136$	−2.66497			−0.228519
$137$	−6.10581	−	10.5756i	−0.521655	−	0.903532i	−0.999683	−	0.0251879i	$-0.991982\pi$
$137$	−6.10581	−	10.5756i	−0.521655	−	0.903532i	0.478028	−	0.878345i	$-0.341352\pi$
$138$	4.64772	−	4.27110i	0.395640	−	0.363580i
$139$	1.24092	−	2.14933i	0.105253	−	0.182304i	−0.808588	−	0.588375i	$-0.799768\pi$
$139$	1.24092	−	2.14933i	0.105253	−	0.182304i	0.913842	+	0.406071i	$0.133101\pi$
$140$		0			0
$141$	−15.6600	−	4.91296i	−1.31881	−	0.413746i
$142$	−0.0269793	−	0.0467294i	−0.00226405	−	0.00392145i
$143$	13.5823			1.13581
$144$	−4.08878	+	1.92088i	−0.340731	+	0.160074i
$145$	9.70538			0.805988
$146$	−3.58327	−	6.20640i	−0.296553	−	0.513645i
$147$		0			0
$148$	−1.10063	+	1.90635i	−0.0904715	+	0.156701i
$149$	4.27797	−	7.40966i	0.350465	−	0.607023i	−0.635866	−	0.771799i	$-0.719357\pi$
$149$	4.27797	−	7.40966i	0.350465	−	0.607023i	0.986331	+	0.164777i	$0.0526903\pi$
$150$	−0.751054	−	3.36500i	−0.0613233	−	0.274751i
$151$	8.82962	+	15.2933i	0.718544	+	1.24455i	0.961577	+	0.274537i	$0.0885244\pi$
$151$	8.82962	+	15.2933i	0.718544	+	1.24455i	−0.243033	+	0.970018i	$0.578142\pi$
$152$	9.55629			0.775117
$153$	0.283187	−	3.34708i	0.0228943	−	0.270595i
$154$		0			0
$155$	−1.78533	−	3.09228i	−0.143401	−	0.248378i
$156$	−7.05911	−	2.21463i	−0.565181	−	0.177313i
$157$	3.16074	−	5.47457i	0.252255	−	0.436918i	−0.711891	−	0.702289i	$-0.752161\pi$
$157$	3.16074	−	5.47457i	0.252255	−	0.436918i	0.964146	+	0.265371i	$0.0854946\pi$
$158$	0.618353	−	1.07102i	0.0491936	−	0.0852057i
$159$	1.04635	−	0.961562i	0.0829811	−	0.0762568i
$160$	4.11070	+	7.11993i	0.324979	+	0.562880i
$161$		0			0
$162$	2.09580	+	5.65726i	0.164662	+	0.444477i
$163$	8.02267			0.628384			0.314192	−	0.949359i	$-0.398266\pi$
$163$	8.02267			0.628384			0.314192	+	0.949359i	$0.398266\pi$
$164$	0.192877	+	0.334073i	0.0150612	+	0.0260867i
$165$	8.96050	−	8.23439i	0.697574	−	0.641047i
$166$	4.85041	−	8.40116i	0.376465	−	0.652057i
$167$	−1.06038	+	1.83663i	−0.0820545	+	0.142123i	−0.904132	−	0.427253i	$-0.859482\pi$
$167$	−1.06038	+	1.83663i	−0.0820545	+	0.142123i	0.822078	+	0.569375i	$0.192815\pi$
$168$		0			0
$169$	2.70608	+	4.68706i	0.208160	+	0.360543i
$170$	−1.06950			−0.0820267
$171$	−1.01548	+	12.0023i	−0.0776555	+	0.917835i
$172$	−1.54542			−0.117837
$173$	−9.14404	−	15.8379i	−0.695208	−	1.20414i	−0.970110	−	0.242664i	$-0.921979\pi$
$173$	−9.14404	−	15.8379i	−0.695208	−	1.20414i	0.274902	−	0.961472i	$-0.411354\pi$
$174$	−1.72265	−	7.71812i	−0.130594	−	0.585109i
$175$		0			0
$176$	3.71247	−	6.43018i	0.279838	−	0.484693i
$177$	2.48419	+	11.1301i	0.186723	+	0.836588i
$178$	−4.53341	−	7.85209i	−0.339793	−	0.588539i
$179$	−7.62551			−0.569958			−0.284979	−	0.958534i	$-0.591987\pi$
$179$	−7.62551			−0.569958			−0.284979	+	0.958534i	$0.591987\pi$
$180$	−5.99965	+	2.81860i	−0.447188	+	0.210086i
$181$	−15.5305			−1.15438			−0.577188	−	0.816611i	$-0.695850\pi$
$181$	−15.5305			−1.15438			−0.577188	+	0.816611i	$0.695850\pi$
$182$		0			0
$183$	0.124384	+	0.0390227i	0.00919475	+	0.00288464i
$184$	6.46989	−	11.2062i	0.476967	−	0.826130i
$185$	−1.01140	+	1.75180i	−0.0743597	+	0.128795i
$186$	−2.14222	+	1.96863i	−0.157075	+	0.144347i
$187$	2.76044	+	4.78122i	0.201863	+	0.349638i
$188$	−14.6937			−1.07165
$189$		0			0
$190$	3.83510			0.278227
$191$	−7.41624	−	12.8453i	−0.536620	−	0.929454i	−0.999083	−	0.0428150i	$-0.986367\pi$
$191$	−7.41624	−	12.8453i	−0.536620	−	0.929454i	0.462463	−	0.886639i	$-0.346966\pi$
$192$	1.09157	−	1.00311i	0.0787772	−	0.0723935i
$193$	−8.28387	+	14.3481i	−0.596286	+	1.03280i	0.397078	+	0.917785i	$0.370024\pi$
$193$	−8.28387	+	14.3481i	−0.596286	+	1.03280i	−0.993364	+	0.115013i	$0.963309\pi$
$194$	−1.81097	+	3.13669i	−0.130020	+	0.225201i
$195$	−6.48680	−	2.03509i	−0.464529	−	0.145736i
$196$		0			0
$197$	−4.03740			−0.287653			−0.143826	−	0.989603i	$-0.545941\pi$
$197$	−4.03740			−0.287653			−0.143826	+	0.989603i	$0.545941\pi$
$198$	−8.13876	−	5.66420i	−0.578397	−	0.402537i
$199$	−25.2814			−1.79215			−0.896076	−	0.443901i	$-0.853594\pi$
$199$	−25.2814			−1.79215			−0.896076	+	0.443901i	$0.853594\pi$
$200$	−3.53395	−	6.12097i	−0.249888	−	0.432818i
$201$	−4.74937	−	21.2790i	−0.334995	−	1.50090i
$202$	−1.72121	+	2.98123i	−0.121104	+	0.209758i
$203$		0			0
$204$	−0.655085	−	2.93503i	−0.0458651	−	0.205493i
$205$	0.177240	+	0.306988i	0.0123790	+	0.0214410i
$206$	9.52625			0.663725
$207$	13.3869	+	9.31668i	0.930456	+	0.647554i
$208$	−4.14798			−0.287611
$209$	−9.89864	−	17.1449i	−0.684703	−	1.18594i
$210$		0			0
$211$	−3.76246	+	6.51678i	−0.259019	+	0.448634i	−0.965979	−	0.258619i	$-0.916732\pi$
$211$	−3.76246	+	6.51678i	−0.259019	+	0.448634i	0.706961	+	0.707253i	$0.250066\pi$
$212$	0.636123	−	1.10180i	0.0436891	−	0.0756718i
$213$	0.102658	−	0.0943388i	0.00703398	−	0.00646399i
$214$	2.56747	+	4.44699i	0.175509	+	0.303990i
$215$	−1.42013			−0.0968521
$216$	7.57086	+	9.77938i	0.515132	+	0.665402i
$217$		0			0
$218$	−0.569377	−	0.986190i	−0.0385631	−	0.0667932i
$219$	13.6345	−	12.5297i	0.921337	−	0.846677i
$220$	5.44748	−	9.43531i	0.367269	−	0.636129i
$221$	1.54214	−	2.67106i	0.103735	−	0.179675i
$222$	1.57262	+	0.493374i	0.105547	+	0.0331131i
$223$	−6.49230	−	11.2450i	−0.434757	−	0.753020i	0.562519	−	0.826784i	$-0.309832\pi$
$223$	−6.49230	−	11.2450i	−0.434757	−	0.753020i	−0.997276	+	0.0737638i	$0.976499\pi$
$224$		0			0
$225$	8.06319	−	3.78804i	0.537546	−	0.252536i
$226$	0.402671			0.0267852
$227$	−14.4832	−	25.0857i	−0.961286	−	1.66500i	−0.719277	−	0.694723i	$-0.755527\pi$
$227$	−14.4832	−	25.0857i	−0.961286	−	1.66500i	−0.242009	−	0.970274i	$-0.577806\pi$
$228$	2.34906	+	10.5247i	0.155571	+	0.697015i
$229$	7.71790	−	13.3678i	0.510013	−	0.883369i	−0.489919	−	0.871768i	$-0.662974\pi$
$229$	7.71790	−	13.3678i	0.510013	−	0.883369i	0.999933	−	0.0116012i	$-0.00369285\pi$
$230$	2.59648	−	4.49723i	0.171207	−	0.296538i
$231$		0			0
$232$	−8.10561	−	14.0393i	−0.532159	−	0.921727i
$233$	4.94648			0.324055			0.162027	−	0.986786i	$-0.448197\pi$
$233$	4.94648			0.324055			0.162027	+	0.986786i	$0.448197\pi$
$234$	−0.467014	+	5.51978i	−0.0305296	+	0.360840i
$235$	−13.5024			−0.880800
$236$	5.10481	+	8.84179i	0.332295	+	0.575551i
$237$	3.04896	+	0.956542i	0.198051	+	0.0621341i
$238$		0			0
$239$	6.51732	−	11.2883i	0.421571	−	0.730182i	−0.574523	−	0.818489i	$-0.694812\pi$
$239$	6.51732	−	11.2883i	0.421571	−	0.730182i	0.996093	+	0.0883069i	$0.0281456\pi$
$240$	−2.73650	+	2.51475i	−0.176640	+	0.162326i
$241$	7.29123	+	12.6288i	0.469670	+	0.813492i	0.999399	−	0.0346754i	$-0.0110397\pi$
$241$	7.29123	+	12.6288i	0.469670	+	0.813492i	−0.529729	+	0.848167i	$0.677706\pi$
$242$	8.92382			0.573645
$243$	−13.0869	+	8.46947i	−0.839528	+	0.543317i
$244$	0.116709			0.00747154
$245$		0			0
$246$	0.212671	−	0.195437i	0.0135594	−	0.0124606i
$247$	−5.52993	+	9.57812i	−0.351861	+	0.609441i
$248$	−2.98209	+	5.16514i	−0.189363	+	0.327987i
$249$	23.9163	+	7.50319i	1.51563	+	0.475495i
$250$	−3.80619	−	6.59251i	−0.240724	−	0.416947i
$251$	14.0715			0.888187			0.444094	−	0.895980i	$-0.353526\pi$
$251$	14.0715			0.888187			0.444094	+	0.895980i	$0.353526\pi$
$252$		0			0
$253$	−26.8067			−1.68532
$254$	−2.43323	−	4.21448i	−0.152674	−	0.264440i
$255$	−0.601975	−	2.69708i	−0.0376972	−	0.168897i
$256$	4.53120	−	7.84826i	0.283200	−	0.490517i
$257$	−4.18108	+	7.24184i	−0.260808	+	0.451733i	−0.966457	−	0.256829i	$-0.917322\pi$
$257$	−4.18108	+	7.24184i	−0.260808	+	0.451733i	0.705649	+	0.708562i	$0.250656\pi$
$258$	0.252065	+	1.12935i	0.0156929	+	0.0703100i
$259$		0			0
$260$	−6.08653			−0.377471
$261$	18.4941	−	8.68841i	1.14475	−	0.537799i
$262$	13.7103			0.847025
$263$	−1.63533	−	2.83247i	−0.100839	−	0.174658i	0.811192	−	0.584780i	$-0.198819\pi$
$263$	−1.63533	−	2.83247i	−0.100839	−	0.174658i	−0.912030	+	0.410122i	$0.865486\pi$
$264$	−19.3950	−	6.08473i	−1.19368	−	0.374489i
$265$	0.584551	−	1.01247i	0.0359087	−	0.0621956i
$266$		0			0
$267$	17.2499	−	15.8520i	1.05568	−	0.970129i
$268$	−9.75958	−	16.9041i	−0.596161	−	1.03258i
$269$	−15.3870			−0.938161			−0.469081	−	0.883155i	$-0.655415\pi$
$269$	−15.3870			−0.938161			−0.469081	+	0.883155i	$0.655415\pi$
$270$	3.03831	+	3.92463i	0.184906	+	0.238845i
$271$	8.12617			0.493630			0.246815	−	0.969063i	$-0.420616\pi$
$271$	8.12617			0.493630			0.246815	+	0.969063i	$0.420616\pi$
$272$	−0.843026	−	1.46016i	−0.0511160	−	0.0885355i
$273$		0			0
$274$	−4.09293	+	7.08915i	−0.247263	+	0.428271i
$275$	−7.32110	+	12.6805i	−0.441479	+	0.764664i
$276$	13.9322	+	4.37090i	0.838618	+	0.263097i
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	0.605982	−	0.795478i	$-0.292780\pi$
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	−0.991895	+	0.127057i	$0.959447\pi$
$278$	−1.66365			−0.0997793
$279$	−6.17029	−	4.29423i	−0.369406	−	0.257089i
$280$		0			0
$281$	−0.724081	−	1.25415i	−0.0431951	−	0.0748161i	0.843620	−	0.536941i	$-0.180420\pi$
$281$	−0.724081	−	1.25415i	−0.0431951	−	0.0748161i	−0.886815	+	0.462125i	$0.847087\pi$
$282$	2.39660	+	10.7377i	0.142715	+	0.639419i
$283$	−8.71926	+	15.1022i	−0.518306	+	0.897732i	0.481468	+	0.876464i	$0.340104\pi$
$283$	−8.71926	+	15.1022i	−0.518306	+	0.897732i	−0.999774	+	0.0212686i	$0.993229\pi$
$284$	0.0624100	−	0.108097i	0.00370335	−	0.00641440i
$285$	2.15862	+	9.67142i	0.127865	+	0.572885i
$286$	−4.55234	−	7.88489i	−0.269186	−	0.466243i
$287$		0			0
$288$	14.2070	+	9.88741i	0.837156	+	0.582621i
$289$	−15.7463			−0.926254
$290$	−3.25292	−	5.63422i	−0.191018	−	0.330853i
$291$	−8.92948	−	2.80142i	−0.523455	−	0.164222i
$292$	8.28903	−	14.3570i	0.485079	−	0.840181i
$293$	0.900048	−	1.55893i	0.0525814	−	0.0910736i	−0.838537	−	0.544845i	$-0.816588\pi$
$293$	0.900048	−	1.55893i	0.0525814	−	0.0910736i	0.891118	+	0.453772i	$0.149922\pi$
$294$		0			0
$295$	4.69094	+	8.12495i	0.273117	+	0.473053i
$296$	3.37875			0.196386
$297$	9.70311	−	23.7126i	0.563031	−	1.37595i
$298$	−5.73532			−0.332238
$299$	7.48786	+	12.9693i	0.433034	+	0.750037i
$300$	5.87256	−	5.39668i	0.339053	−	0.311578i
$301$		0			0
$302$	5.91878	−	10.2516i	0.340588	−	0.589915i
$303$	−8.48691	−	2.66257i	−0.487560	−	0.152961i
$304$	3.02300	+	5.23599i	0.173381	+	0.300305i
$305$	0.107247			0.00614095
$306$	−2.03798	+	0.957431i	−0.116503	+	0.0547327i
$307$	−1.06478			−0.0607699			−0.0303850	−	0.999538i	$-0.509673\pi$
$307$	−1.06478			−0.0607699			−0.0303850	+	0.999538i	$0.509673\pi$
$308$		0			0
$309$	5.36193	+	24.0234i	0.305029	+	1.36665i
$310$	−1.19676	+	2.07286i	−0.0679717	+	0.117730i
$311$	−8.46463	+	14.6612i	−0.479985	+	0.831359i	−0.999736	−	0.0229591i	$-0.992691\pi$
$311$	−8.46463	+	14.6612i	−0.479985	+	0.831359i	0.519751	+	0.854318i	$0.326025\pi$
$312$	2.47370	+	11.0831i	0.140046	+	0.627458i
$313$	−4.13928	−	7.16944i	−0.233966	−	0.405241i	0.725006	−	0.688743i	$-0.241837\pi$
$313$	−4.13928	−	7.16944i	−0.233966	−	0.405241i	−0.958972	+	0.283502i	$0.908504\pi$
$314$	−4.23750			−0.239136
$315$		0			0
$316$	2.86082			0.160934
$317$	−3.27371	−	5.67023i	−0.183870	−	0.318472i	0.759325	−	0.650711i	$-0.225529\pi$
$317$	−3.27371	−	5.67023i	−0.183870	−	0.318472i	−0.943195	+	0.332239i	$0.892196\pi$
$318$	−0.908913	−	0.285151i	−0.0509693	−	0.0159905i
$319$	−16.7920	+	29.0846i	−0.940171	+	1.62842i
$320$	0.609811	−	1.05622i	0.0340895	−	0.0590447i
$321$	−9.76938	+	8.97773i	−0.545274	+	0.501088i
$322$		0			0
$323$	−4.49556			−0.250140
$324$	−8.90937	+	10.7420i	−0.494965	+	0.596776i
$325$	8.17995			0.453742
$326$	−2.68893	−	4.65736i	−0.148926	−	0.257947i
$327$	2.16651	−	1.99095i	0.119808	−	0.110100i
$328$	0.296049	−	0.512773i	0.0163466	−	0.0283131i
$329$		0			0
$330$	−7.78353	−	2.44191i	−0.428469	−	0.134422i
$331$	13.3629	+	23.1453i	0.734493	+	1.27218i	0.954946	+	0.296781i	$0.0959131\pi$
$331$	13.3629	+	23.1453i	0.734493	+	1.27218i	−0.220453	+	0.975398i	$0.570754\pi$
$332$	22.4405			1.23158
$333$	−0.359036	+	4.24356i	−0.0196750	+	0.232546i
$334$	1.42161			0.0777872
$335$	−8.96834	−	15.5336i	−0.489993	−	0.848692i
$336$		0			0
$337$	−4.76164	+	8.24740i	−0.259383	+	0.449264i	−0.966077	−	0.258255i	$-0.916853\pi$
$337$	−4.76164	+	8.24740i	−0.259383	+	0.449264i	0.706694	+	0.707520i	$0.250186\pi$
$338$	1.81397	−	3.14189i	0.0986670	−	0.170896i
$339$	0.226647	+	1.01546i	0.0123097	+	0.0551523i
$340$	−1.23701	−	2.14257i	−0.0670864	−	0.116197i
$341$	12.3557			0.669099
$342$	7.30796	−	3.43324i	0.395169	−	0.185648i
$343$		0			0
$344$	1.18605	+	2.05429i	0.0639473	+	0.110760i
$345$	12.8026	+	4.01654i	0.689271	+	0.216243i
$346$	−6.12955	+	10.6167i	−0.329526	+	0.570757i
$347$	9.35156	−	16.1974i	0.502018	−	0.869521i	−0.497979	−	0.867189i	$-0.665924\pi$
$347$	9.35156	−	16.1974i	0.502018	−	0.869521i	0.999997	−	0.00233189i	$-0.000742265\pi$
$348$	13.4696	−	12.3781i	0.722044	−	0.663534i
$349$	15.0542	+	26.0747i	0.805834	+	1.39574i	0.915727	+	0.401801i	$0.131616\pi$
$349$	15.0542	+	26.0747i	0.805834	+	1.39574i	−0.109893	+	0.993943i	$0.535051\pi$
$350$		0			0
$351$	−14.1827	+	1.92913i	−0.757019	+	0.102970i
$352$	−28.4488			−1.51633
$353$	3.12966	+	5.42074i	0.166575	+	0.288517i	0.937214	−	0.348756i	$-0.113396\pi$
$353$	3.12966	+	5.42074i	0.166575	+	0.288517i	−0.770638	+	0.637273i	$0.780062\pi$
$354$	5.62868	−	5.17256i	0.299161	−	0.274919i
$355$	0.0573502	−	0.0993335i	0.00304383	−	0.00527208i
$356$	10.4870	−	18.1639i	0.555807	−	0.962686i
$357$		0			0
$358$	2.55582	+	4.42680i	0.135079	+	0.233964i
$359$	10.1951			0.538077			0.269038	−	0.963129i	$-0.413294\pi$
$359$	10.1951			0.538077			0.269038	+	0.963129i	$0.413294\pi$
$360$	8.35117	+	5.81203i	0.440145	+	0.306321i
$361$	−2.87941			−0.151548
$362$	5.20532	+	9.01587i	0.273585	+	0.473864i
$363$	5.02285	+	22.5042i	0.263631	+	1.18117i
$364$		0			0
$365$	7.61701	−	13.1931i	0.398693	−	0.690556i
$366$	−0.0190357	−	0.0852873i	−0.000995014	−	0.00445804i
$367$	−14.3278	−	24.8165i	−0.747906	−	1.29541i	−0.948824	−	0.315804i	$-0.897726\pi$
$367$	−14.3278	−	24.8165i	−0.747906	−	1.29541i	0.200918	−	0.979608i	$-0.435608\pi$
$368$	8.18664			0.426758
$369$	0.612560	+	0.426313i	0.0318886	+	0.0221930i
$370$	1.35595			0.0704926
$371$		0			0
$372$	−6.42160	−	2.01463i	−0.332944	−	0.104454i
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	−0.579421	−	0.815028i	$-0.696721\pi$
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	0.995546	+	0.0942796i	$0.0300548\pi$
$374$	1.85041	−	3.20501i	0.0956826	−	0.165727i
$375$	14.4828	−	13.3092i	0.747887	−	0.687282i
$376$	11.2768	+	19.5319i	0.581555	+	1.00728i
$377$	18.7619			0.966286
$378$		0			0
$379$	−1.01893			−0.0523388			−0.0261694	−	0.999658i	$-0.508331\pi$
$379$	−1.01893			−0.0523388			−0.0261694	+	0.999658i	$0.508331\pi$
$380$	4.43579	+	7.68302i	0.227551	+	0.394130i
$381$	9.25858	−	8.50831i	0.474331	−	0.435894i
$382$	−4.97135	+	8.61063i	−0.254356	+	0.440558i
$383$	−5.79327	+	10.0342i	−0.296022	+	0.512725i	−0.975222	−	0.221228i	$-0.928994\pi$
$383$	−5.79327	+	10.0342i	−0.296022	+	0.512725i	0.679200	+	0.733953i	$0.262327\pi$
$384$	18.1220	+	5.68536i	0.924784	+	0.290130i
$385$		0			0
$386$	11.1059			0.565275
$387$	−2.70613	+	1.27132i	−0.137560	+	0.0646250i
$388$	−8.37848			−0.425353
$389$	−8.90675	−	15.4270i	−0.451590	−	0.782178i	0.546895	−	0.837201i	$-0.315810\pi$
$389$	−8.90675	−	15.4270i	−0.451590	−	0.782178i	−0.998485	+	0.0550239i	$0.982476\pi$
$390$	0.992739	+	4.44784i	0.0502693	+	0.225225i
$391$	−3.04363	+	5.27172i	−0.153923	+	0.266602i
$392$		0			0
$393$	7.71695	+	34.5749i	0.389269	+	1.74407i
$394$	1.35320	+	2.34381i	0.0681732	+	0.118079i
$395$	2.62889			0.132274
$396$	1.93379	−	22.8561i	0.0971767	−	1.14856i
$397$	−13.0846			−0.656696			−0.328348	−	0.944557i	$-0.606492\pi$
$397$	−13.0846			−0.656696			−0.328348	+	0.944557i	$0.606492\pi$
$398$	8.47348	+	14.6765i	0.424737	+	0.735666i
$399$		0			0
$400$	2.23583	−	3.87257i	0.111792	−	0.193629i
$401$	−7.05165	+	12.2138i	−0.352143	+	0.609929i	−0.986625	−	0.163009i	$-0.947880\pi$
$401$	−7.05165	+	12.2138i	−0.352143	+	0.609929i	0.634482	+	0.772938i	$0.281213\pi$
$402$	−10.7611	+	9.88912i	−0.536717	+	0.493224i
$403$	−3.45129	−	5.97782i	−0.171921	−	0.297776i
$404$	−7.96323			−0.396185
$405$	−8.18706	+	9.87108i	−0.406818	+	0.490498i
$406$		0			0
$407$	−3.49980	−	6.06183i	−0.173479	−	0.300474i
$408$	−3.39871	+	3.12329i	−0.168261	+	0.154626i
$409$	−1.32300	+	2.29150i	−0.0654179	+	0.113307i	−0.896879	−	0.442275i	$-0.854171\pi$
$409$	−1.32300	+	2.29150i	−0.0654179	+	0.113307i	0.831461	+	0.555583i	$0.187505\pi$
$410$	0.118810	−	0.205784i	0.00586759	−	0.0101630i
$411$	−20.1813	−	6.33142i	−0.995470	−	0.312306i
$412$	11.0183	+	19.0843i	0.542835	+	0.940217i
$413$		0			0
$414$	0.921719	−	10.8941i	0.0453000	−	0.535415i
$415$	20.6212			1.01226
$416$	7.94655	+	13.7638i	0.389612	+	0.674827i
$417$	−0.936401	−	4.19543i	−0.0458557	−	0.205451i
$418$	−6.63538	+	11.4928i	−0.324547	+	0.562132i
$419$	−16.7567	+	29.0235i	−0.818619	+	1.41789i	0.0880816	+	0.996113i	$0.471926\pi$
$419$	−16.7567	+	29.0235i	−0.818619	+	1.41789i	−0.906700	+	0.421776i	$0.861407\pi$
$420$		0			0
$421$	−2.41950	−	4.19071i	−0.117919	−	0.204242i	0.801024	−	0.598633i	$-0.204289\pi$
$421$	−2.41950	−	4.19071i	−0.117919	−	0.204242i	−0.918943	+	0.394390i	$0.870956\pi$
$422$	5.04421			0.245548
$423$	−25.7295	+	12.0876i	−1.25101	+	0.587718i
$424$	−1.95279			−0.0948358
$425$	1.66247	+	2.87949i	0.0806418	+	0.139676i
$426$	−0.0891734	−	0.0279761i	−0.00432047	−	0.00135545i
$427$		0			0
$428$	−5.93923	+	10.2871i	−0.287084	+	0.497244i
$429$	17.3219	−	15.9182i	0.836310	−	0.768540i
$430$	0.475980	+	0.824422i	0.0229538	+	0.0397571i
$431$	−35.3285			−1.70172			−0.850858	−	0.525396i	$-0.823917\pi$
$431$	−35.3285			−1.70172			−0.850858	+	0.525396i	$0.823917\pi$
$432$	−2.96329	+	7.24173i	−0.142571	+	0.348418i
$433$	−5.47404			−0.263066			−0.131533	−	0.991312i	$-0.541990\pi$
$433$	−5.47404			−0.263066			−0.131533	+	0.991312i	$0.541990\pi$
$434$		0			0
$435$	12.3775	−	11.3745i	0.593458	−	0.545367i
$436$	1.31712	−	2.28131i	0.0630785	−	0.109255i
$437$	10.9141	−	18.9038i	0.522093	−	0.904292i
$438$	−11.8436	−	3.71567i	−0.565910	−	0.177541i
$439$	3.19906	+	5.54093i	0.152683	+	0.264454i	0.932213	−	0.361911i	$-0.117875\pi$
$439$	3.19906	+	5.54093i	0.152683	+	0.264454i	−0.779530	+	0.626365i	$0.784542\pi$
$440$	−16.7228			−0.797229
$441$		0			0
$442$	−2.06749			−0.0983404
$443$	3.19341	+	5.53115i	0.151723	+	0.262793i	0.931861	−	0.362815i	$-0.118184\pi$
$443$	3.19341	+	5.53115i	0.151723	+	0.262793i	−0.780138	+	0.625608i	$0.784851\pi$
$444$	0.830543	+	3.72115i	0.0394158	+	0.176598i
$445$	9.63674	−	16.6913i	0.456825	−	0.791245i
$446$	−4.35200	+	7.53789i	−0.206073	+	0.356929i
$447$	−3.22817	−	14.4634i	−0.152687	−	0.684097i
$448$		0			0
$449$	−11.7460			−0.554327			−0.277163	−	0.960823i	$-0.589394\pi$
$449$	−11.7460			−0.554327			−0.277163	+	0.960823i	$0.589394\pi$
$450$	−4.90156	−	3.41126i	−0.231062	−	0.160808i
$451$	−1.22662			−0.0577593
$452$	0.465741	+	0.806687i	0.0219066	+	0.0379434i
$453$	29.1842	+	9.15587i	1.37119	+	0.430180i
$454$	−9.70859	+	16.8158i	−0.455647	+	0.789203i
$455$		0			0
$456$	12.1874	−	11.1998i	0.570727	−	0.524478i
$457$	−5.26120	−	9.11266i	−0.246108	−	0.426272i	0.716334	−	0.697757i	$-0.245819\pi$
$457$	−5.26120	−	9.11266i	−0.246108	−	0.426272i	−0.962443	+	0.271485i	$0.912485\pi$
$458$	−10.3471			−0.483489
$459$	−3.56156	−	4.60051i	−0.166239	−	0.214733i
$460$	12.0127			0.560093
$461$	3.54278	+	6.13627i	0.165004	+	0.285794i	0.936657	−	0.350249i	$-0.113903\pi$
$461$	3.54278	+	6.13627i	0.165004	+	0.285794i	−0.771653	+	0.636044i	$0.780570\pi$
$462$		0			0
$463$	16.3760	−	28.3641i	0.761059	−	1.31819i	−0.181246	−	0.983438i	$-0.558013\pi$
$463$	16.3760	−	28.3641i	0.761059	−	1.31819i	0.942305	−	0.334755i	$-0.108654\pi$
$464$	5.12820	−	8.88230i	0.238071	−	0.412350i
$465$	−5.90098	−	1.85130i	−0.273651	−	0.0858518i
$466$	−1.65789	−	2.87156i	−0.0768004	−	0.133022i
$467$	3.92431			0.181596			0.0907978	−	0.995869i	$-0.471058\pi$
$467$	3.92431			0.181596			0.0907978	+	0.995869i	$0.471058\pi$
$468$	−11.5982	+	5.44876i	−0.536126	+	0.251869i
$469$		0			0
$470$	4.52555	+	7.83849i	0.208748	+	0.361563i
$471$	−2.38511	−	10.6862i	−0.109900	−	0.492394i
$472$	7.83544	−	13.5714i	0.360655	−	0.624673i
$473$	2.45707	−	4.25577i	0.112976	−	0.195681i
$474$	−0.466612	−	2.09060i	−0.0214322	−	0.0960244i
$475$	−5.96145	−	10.3255i	−0.273530	−	0.473768i
$476$		0			0
$477$	0.207509	−	2.45261i	0.00950117	−	0.112297i
$478$	−8.73755			−0.399646
$479$	8.04324	+	13.9313i	0.367505	+	0.636537i	0.989175	−	0.146742i	$-0.0468787\pi$
$479$	8.04324	+	13.9313i	0.367505	+	0.636537i	−0.621670	+	0.783279i	$0.713545\pi$
$480$	13.5869	+	4.26258i	0.620155	+	0.194559i
$481$	−1.95518	+	3.38647i	−0.0891486	+	0.154410i
$482$	4.88755	−	8.46549i	0.222622	−	0.385592i
$483$		0			0
$484$	10.3216	+	17.8775i	0.469162	+	0.812612i
$485$	−7.69921			−0.349603
$486$	9.30304	+	4.75862i	0.421995	+	0.215855i
$487$	3.50344			0.158756			0.0793781	−	0.996845i	$-0.474707\pi$
$487$	3.50344			0.158756			0.0793781	+	0.996845i	$0.474707\pi$
$488$	−0.0895692	−	0.155138i	−0.00405461	−	0.00702279i
$489$	10.2315	−	9.40242i	0.462686	−	0.425192i
$490$		0			0
$491$	−20.5546	+	35.6017i	−0.927618	+	1.60668i	−0.140321	+	0.990106i	$0.544814\pi$
$491$	−20.5546	+	35.6017i	−0.927618	+	1.60668i	−0.787296	+	0.616575i	$0.788520\pi$
$492$	0.637508	+	0.200004i	0.0287411	+	0.00901686i
$493$	3.81312	+	6.60452i	0.171734	+	0.297452i
$494$	7.41379			0.333562
$495$	1.77701	−	21.0031i	0.0798708	−	0.944019i
$496$	−3.77338			−0.169430
$497$		0			0
$498$	−3.66015	−	16.3988i	−0.164015	−	0.734849i
$499$	−5.91486	+	10.2448i	−0.264785	+	0.458622i	−0.967507	−	0.252843i	$-0.918634\pi$
$499$	−5.91486	+	10.2448i	−0.264785	+	0.458622i	0.702722	+	0.711465i	$0.251968\pi$
$500$	8.80470	−	15.2502i	0.393758	−	0.682009i
$501$	0.800166	+	3.58505i	0.0357488	+	0.160168i
$502$	−4.71631	−	8.16888i	−0.210499	−	0.364595i
$503$	−21.8595			−0.974665			−0.487332	−	0.873217i	$-0.662030\pi$
$503$	−21.8595			−0.974665			−0.487332	+	0.873217i	$0.662030\pi$
$504$		0			0
$505$	−7.31762			−0.325630
$506$	8.98470	+	15.5620i	0.399419	+	0.691813i
$507$	8.94428	+	2.80606i	0.397230	+	0.124622i
$508$	5.62869	−	9.74918i	0.249733	−	0.432550i
$509$	8.44831	−	14.6329i	0.374465	−	0.648592i	−0.615782	−	0.787917i	$-0.711160\pi$
$509$	8.44831	−	14.6329i	0.374465	−	0.648592i	0.990247	+	0.139324i	$0.0444931\pi$
$510$	−1.36396	+	1.25343i	−0.0603971	+	0.0555029i
$511$		0			0
$512$	15.8563			0.700756
$513$	12.7714	+	16.4969i	0.563869	+	0.728357i
$514$	5.60542			0.247245
$515$	10.1250	+	17.5371i	0.446163	+	0.772777i
$516$	−1.97092	+	1.81121i	−0.0867649	+	0.0797340i
$517$	23.3615	−	40.4633i	1.02744	−	1.77957i
$518$		0			0
$519$	−30.2234	−	9.48190i	−1.32666	−	0.416209i
$520$	4.67115	+	8.09067i	0.204843	+	0.354799i
$521$	−34.4932			−1.51117			−0.755587	−	0.655048i	$-0.772648\pi$
$521$	−34.4932			−1.51117			−0.755587	+	0.655048i	$0.772648\pi$
$522$	−11.2424	−	7.82421i	−0.492068	−	0.342456i
$523$	1.99123			0.0870704			0.0435352	−	0.999052i	$-0.486138\pi$
$523$	1.99123			0.0870704			0.0435352	+	0.999052i	$0.486138\pi$
$524$	15.8577	+	27.4664i	0.692749	+	1.19988i
$525$		0			0
$526$	−1.09622	+	1.89870i	−0.0477972	+	0.0827873i
$527$	1.40287	−	2.42983i	0.0611098	−	0.105845i
$528$	−2.80145	−	12.5515i	−0.121917	−	0.546235i
$529$	−3.27836	−	5.67829i	−0.142538	−	0.246882i
$530$	−0.783687			−0.0340412
$531$	16.2124	+	11.2831i	0.703558	+	0.489644i
$532$		0			0
$533$	0.342629	+	0.593452i	0.0148409	+	0.0257052i
$534$	−14.9841	−	4.70091i	−0.648425	−	0.203428i
$535$	−5.45772	+	9.45305i	−0.235958	+	0.408691i
$536$	−14.9801	+	25.9463i	−0.647042	+	1.12071i
$537$	−9.72503	+	8.93696i	−0.419666	+	0.385658i
$538$	5.15720	+	8.93253i	0.222343	+	0.385109i
$539$		0			0
$540$	−4.34817	+	10.6261i	−0.187115	+	0.457276i
$541$	30.1363			1.29566			0.647830	−	0.761785i	$-0.275677\pi$
$541$	30.1363			1.29566			0.647830	+	0.761785i	$0.275677\pi$
$542$	−2.72362	−	4.71745i	−0.116989	−	0.202632i
$543$	−19.8065	+	18.2015i	−0.849979	+	0.781102i
$544$	−3.23008	+	5.59466i	−0.138488	+	0.239869i
$545$	1.21033	−	2.09636i	0.0518450	−	0.0897982i
$546$		0			0
$547$	7.68070	+	13.3034i	0.328403	+	0.568810i	0.982195	−	0.187864i	$-0.0601563\pi$
$547$	7.68070	+	13.3034i	0.328403	+	0.568810i	−0.653792	+	0.756674i	$0.726823\pi$
$548$	−18.9360			−0.808906
$549$	0.204365	−	0.0960093i	0.00872206	−	0.00409758i
$550$	9.81514			0.418519
$551$	−13.6734	−	23.6831i	−0.582508	−	1.00893i
$552$	−4.88221	−	21.8741i	−0.207801	−	0.931025i
$553$		0			0
$554$	−4.30546	+	7.45728i	−0.182921	+	0.316829i
$555$	0.763209	+	3.41946i	0.0323964	+	0.145148i
$556$	−1.92423	−	3.33287i	−0.0816056	−	0.141345i
$557$	23.2823			0.986504			0.493252	−	0.869886i	$-0.335808\pi$
$557$	23.2823			0.986504			0.493252	+	0.869886i	$0.335808\pi$
$558$	−0.424838	+	5.02129i	−0.0179848	+	0.212568i
$559$	−2.74531			−0.116114
$560$		0			0
$561$	9.12397	+	2.86244i	0.385214	+	0.120852i
$562$	−0.485375	+	0.840695i	−0.0204743	+	0.0354626i
$563$	2.27942	−	3.94808i	0.0960663	−	0.166392i	−0.813987	−	0.580883i	$-0.802707\pi$
$563$	2.27942	−	3.94808i	0.0960663	−	0.166392i	0.910053	+	0.414492i	$0.136041\pi$
$564$	−18.7392	+	17.2207i	−0.789065	+	0.725123i
$565$	0.427982	+	0.741286i	0.0180053	+	0.0311861i
$566$	11.6896			0.491351
$567$		0			0
$568$	−0.191588			−0.00803885
$569$	−9.09976	−	15.7612i	−0.381482	−	0.660746i	0.609793	−	0.792561i	$-0.291253\pi$
$569$	−9.09976	−	15.7612i	−0.381482	−	0.660746i	−0.991274	+	0.131815i	$0.957919\pi$
$570$	4.89101	−	4.49467i	0.204862	−	0.188261i
$571$	8.52275	−	14.7618i	0.356666	−	0.617763i	−0.630736	−	0.775998i	$-0.717247\pi$
$571$	8.52275	−	14.7618i	0.356666	−	0.617763i	0.987402	+	0.158234i	$0.0505801\pi$
$572$	10.5307	−	18.2398i	0.440313	−	0.762644i
$573$	−24.5126	−	7.69027i	−1.02403	−	0.321266i
$574$		0			0
$575$	−16.1443			−0.673264
$576$	0.216476	−	2.55860i	0.00901983	−	0.106608i
$577$	−11.4095			−0.474982			−0.237491	−	0.971390i	$-0.576325\pi$
$577$	−11.4095			−0.474982			−0.237491	+	0.971390i	$0.576325\pi$
$578$	5.27764	+	9.14113i	0.219521	+	0.380221i
$579$	6.25105	+	28.0070i	0.259785	+	1.16393i
$580$	7.52485	−	13.0334i	0.312452	−	0.541183i
$581$		0			0
$582$	1.36657	+	6.12273i	0.0566460	+	0.253795i
$583$	2.02275	+	3.50350i	0.0837736	+	0.145100i
$584$	−25.4459			−1.05296
$585$	−10.6579	+	5.00701i	−0.440649	+	0.207014i
$586$	−1.20666			−0.0498468
$587$	−2.52544	−	4.37420i	−0.104236	−	0.180543i	0.809190	−	0.587548i	$-0.199906\pi$
$587$	−2.52544	−	4.37420i	−0.104236	−	0.180543i	−0.913426	+	0.407005i	$0.866573\pi$
$588$		0			0
$589$	−5.03052	+	8.71312i	−0.207279	+	0.359018i
$590$	3.14449	−	5.44642i	0.129457	−	0.224226i
$591$	−5.14900	+	4.73176i	−0.211802	+	0.194638i
$592$	1.06882	+	1.85126i	0.0439283	+	0.0760861i
$593$	−19.9778			−0.820391			−0.410196	−	0.911998i	$-0.634540\pi$
$593$	−19.9778			−0.820391			−0.410196	+	0.911998i	$0.634540\pi$
$594$	−17.0179	+	2.31477i	−0.698254	+	0.0949763i
$595$		0			0
$596$	−6.63365	−	11.4898i	−0.271725	−	0.470641i
$597$	−32.2421	+	29.6293i	−1.31958	+	1.21265i
$598$	5.01935	−	8.69378i	0.205257	−	0.355515i
$599$	−2.19660	+	3.80463i	−0.0897508	+	0.155453i	−0.907406	−	0.420256i	$-0.861940\pi$
$599$	−2.19660	+	3.80463i	−0.0897508	+	0.155453i	0.817655	+	0.575709i	$0.195274\pi$
$600$	−11.6806	−	3.66452i	−0.476859	−	0.149604i
$601$	−12.1778	−	21.0926i	−0.496743	−	0.860385i	0.503250	−	0.864141i	$-0.332138\pi$
$601$	−12.1778	−	21.0926i	−0.496743	−	0.860385i	−0.999993	+	0.00375637i	$0.998804\pi$
$602$		0			0
$603$	−30.9955	−	21.5715i	−1.26224	−	0.878457i
$604$	27.3834			1.11421
$605$	9.48476	+	16.4281i	0.385610	+	0.667897i
$606$	1.29884	+	5.81927i	0.0527616	+	0.236392i
$607$	6.56281	−	11.3671i	0.266376	−	0.461377i	−0.701547	−	0.712623i	$-0.747507\pi$
$607$	6.56281	−	11.3671i	0.266376	−	0.461377i	0.967923	+	0.251246i	$0.0808403\pi$
$608$	11.5827	−	20.0618i	0.469741	−	0.813615i
$609$		0			0
$610$	−0.0359456	−	0.0622597i	−0.00145540	−	0.00252082i
$611$	−26.1021			−1.05598
$612$	−4.27525	−	2.97537i	−0.172817	−	0.120272i
$613$	46.4806			1.87733			0.938667	−	0.344825i	$-0.112062\pi$
$613$	46.4806			1.87733			0.938667	+	0.344825i	$0.112062\pi$
$614$	0.356877	+	0.618129i	0.0144024	+	0.0249456i
$615$	0.585823	+	0.183789i	0.0236227	+	0.00741108i
$616$		0			0
$617$	14.1948	−	24.5862i	0.571463	−	0.989803i	−0.424953	−	0.905215i	$-0.639709\pi$
$617$	14.1948	−	24.5862i	0.571463	−	0.989803i	0.996416	−	0.0845873i	$-0.0269572\pi$
$618$	12.1491	−	11.1646i	0.488708	−	0.449105i
$619$	15.9606	+	27.6446i	0.641511	+	1.11113i	0.985096	+	0.172008i	$0.0550254\pi$
$619$	15.9606	+	27.6446i	0.641511	+	1.11113i	−0.343585	+	0.939122i	$0.611641\pi$
$620$	−5.53686			−0.222366
$621$	27.9917	−	3.80742i	1.12327	−	0.152787i
$622$	11.3482			0.455023
$623$		0			0
$624$	−5.29004	+	4.86136i	−0.211771	+	0.194610i
$625$	0.666993	−	1.15527i	0.0266797	−	0.0462106i
$626$	−2.77469	+	4.80591i	−0.110899	+	0.192083i
$627$	−32.7176	−	10.2644i	−1.30661	−	0.409920i
$628$	−4.90122	−	8.48916i	−0.195580	−	0.338754i
$629$	−1.58947			−0.0633762
$630$		0			0
$631$	38.7184			1.54135			0.770677	−	0.637226i	$-0.219918\pi$
$631$	38.7184			1.54135			0.770677	+	0.637226i	$0.219918\pi$
$632$	−2.19556	−	3.80282i	−0.0873346	−	0.151268i
$633$	2.83917	+	12.7206i	0.112847	+	0.505597i
$634$	−2.19447	+	3.80094i	−0.0871537	+	0.150955i
$635$	5.17236	−	8.95878i	0.205259	−	0.355519i
$636$	−0.480022	−	2.15068i	−0.0190341	−	0.0852799i
$637$		0			0
$638$	22.5124			0.891276
$639$	0.0203587	−	0.240626i	0.000805377	−	0.00951900i
$640$	15.6252			0.617641
$641$	20.2001	+	34.9875i	0.797854	+	1.38192i	0.921011	+	0.389537i	$0.127365\pi$
$641$	20.2001	+	34.9875i	0.797854	+	1.38192i	−0.123157	+	0.992387i	$0.539302\pi$
$642$	8.48616	+	2.66234i	0.334922	+	0.105074i
$643$	−6.27355	+	10.8661i	−0.247405	+	0.428517i	−0.962805	−	0.270198i	$-0.912911\pi$
$643$	−6.27355	+	10.8661i	−0.247405	+	0.428517i	0.715400	+	0.698715i	$0.246244\pi$
$644$		0			0
$645$	−1.81113	+	1.66437i	−0.0713132	+	0.0655344i
$646$	1.50676	+	2.60979i	0.0592827	+	0.102681i
$647$	34.5548			1.35849			0.679245	−	0.733912i	$-0.262308\pi$
$647$	34.5548			1.35849			0.679245	+	0.733912i	$0.262308\pi$
$648$	21.1166	+	3.59899i	0.829537	+	0.141382i
$649$	−32.4646			−1.27435
$650$	−2.74164	−	4.74866i	−0.107536	−	0.186258i
$651$		0			0
$652$	6.22019	−	10.7737i	0.243602	−	0.421930i
$653$	11.1472	−	19.3075i	0.436223	−	0.755560i	−0.561172	−	0.827699i	$-0.689649\pi$
$653$	11.1472	−	19.3075i	0.436223	−	0.755560i	0.997395	+	0.0721392i	$0.0229826\pi$
$654$	−1.88194	−	0.590415i	−0.0735896	−	0.0230871i
$655$	14.5721	+	25.2396i	0.569379	+	0.986194i
$656$	0.374605			0.0146259
$657$	2.70395	−	31.9589i	0.105491	−	1.24683i
$658$		0			0
$659$	3.57493	+	6.19196i	0.139259	+	0.241204i	0.927217	−	0.374526i	$-0.122194\pi$
$659$	3.57493	+	6.19196i	0.139259	+	0.241204i	−0.787957	+	0.615730i	$0.788861\pi$
$660$	−4.11070	−	18.4175i	−0.160009	−	0.716899i
$661$	21.4530	−	37.1577i	0.834425	−	1.44527i	−0.0600736	−	0.998194i	$-0.519134\pi$
$661$	21.4530	−	37.1577i	0.834425	−	1.44527i	0.894498	−	0.447072i	$-0.147533\pi$
$662$	8.95760	−	15.5150i	0.348147	−	0.603008i
$663$	−1.16370	−	5.21383i	−0.0451945	−	0.202488i
$664$	−17.2221	−	29.8296i	−0.668349	−	1.15761i
$665$		0			0
$666$	2.58383	−	1.21387i	0.100121	−	0.0470365i
$667$	−37.0293			−1.43378
$668$	1.64428	+	2.84798i	0.0636191	+	0.110192i
$669$	−21.4587	−	6.73219i	−0.829642	−	0.260281i
$670$	−6.01177	+	10.4127i	−0.232255	+	0.402277i
$671$	−0.185556	+	0.321392i	−0.00716331	+	0.0124072i
$672$		0			0
$673$	−18.8270	−	32.6094i	−0.725729	−	1.25700i	−0.958673	−	0.284510i	$-0.908169\pi$
$673$	−18.8270	−	32.6094i	−0.725729	−	1.25700i	0.232944	−	0.972490i	$-0.425164\pi$
$674$	6.38376			0.245893
$675$	5.84369	−	14.2809i	0.224924	−	0.549672i
$676$	8.39238			0.322784
$677$	−13.1808	−	22.8298i	−0.506580	−	0.877422i	−0.999971	−	0.00761453i	$-0.997576\pi$
$677$	−13.1808	−	22.8298i	−0.506580	−	0.877422i	0.493391	−	0.869808i	$-0.335757\pi$
$678$	0.513537	−	0.471923i	0.0197223	−	0.0181241i
$679$		0			0
$680$	−1.89871	+	3.28866i	−0.0728121	+	0.126114i
$681$	−47.8709	−	15.0184i	−1.83442	−	0.575506i
$682$	−4.14122	−	7.17280i	−0.158575	−	0.274661i
$683$	−3.93175			−0.150444			−0.0752222	−	0.997167i	$-0.523967\pi$
$683$	−3.93175			−0.150444			−0.0752222	+	0.997167i	$0.523967\pi$
$684$	15.3306	+	10.6694i	0.586179	+	0.407953i
$685$	−17.4008			−0.664850
$686$		0			0
$687$	−5.82396	−	26.0936i	−0.222198	−	0.995531i
$688$	−0.750378	+	1.29969i	−0.0286079	+	0.0495503i
$689$	1.13002	−	1.95725i	0.0430503	−	0.0745653i
$690$	−1.95931	−	8.77846i	−0.0745898	−	0.334190i
$691$	9.95052	+	17.2348i	0.378536	+	0.655643i	0.990849	−	0.134972i	$-0.0430944\pi$
$691$	9.95052	+	17.2348i	0.378536	+	0.655643i	−0.612314	+	0.790615i	$0.709761\pi$
$692$	−28.3585			−1.07803
$693$		0			0
$694$	−12.5373			−0.475910
$695$	−1.76823	−	3.06266i	−0.0670727	−	0.116173i
$696$	−26.7911	−	8.40511i	−1.01552	−	0.318595i
$697$	−0.139270	+	0.241223i	−0.00527524	+	0.00913699i
$698$	10.0913	−	17.4787i	0.381963	−	0.661579i
$699$	6.30838	−	5.79718i	0.238605	−	0.219270i
$700$		0			0
$701$	43.7908			1.65396			0.826979	−	0.562234i	$-0.190058\pi$
$701$	43.7908			1.65396			0.826979	+	0.562234i	$0.190058\pi$
$702$	5.87349	+	7.58686i	0.221681	+	0.286348i
$703$	5.69965			0.214966
$704$	2.11016	+	3.65490i	0.0795295	+	0.137749i
$705$	−17.2200	+	15.8246i	−0.648542	+	0.595988i
$706$	2.09792	−	3.63370i	0.0789561	−	0.136756i
$707$		0			0
$708$	16.8727	+	5.29343i	0.634115	+	0.198939i
$709$	−22.3172	−	38.6545i	−0.838139	−	1.45170i	−0.891449	−	0.453121i	$-0.850310\pi$
$709$	−22.3172	−	38.6545i	−0.838139	−	1.45170i	0.0533097	−	0.998578i	$-0.483023\pi$
$710$	−0.0768875			−0.00288554
$711$	5.00947	−	2.35342i	0.187870	−	0.0882602i
$712$	−32.1931			−1.20649
$713$	6.81163	+	11.7981i	0.255097	+	0.441842i
$714$		0			0
$715$	9.67699	−	16.7610i	0.361899	−	0.626827i
$716$	−5.91227	+	10.2403i	−0.220952	+	0.382700i
$717$	−4.91800	−	22.0345i	−0.183666	−	0.822894i
$718$	−3.41705	−	5.91851i	−0.127523	−	0.220877i
$719$	−39.0192			−1.45517			−0.727586	−	0.686016i	$-0.759358\pi$
$719$	−39.0192			−1.45517			−0.727586	+	0.686016i	$0.759358\pi$
$720$	−0.542692	+	6.41425i	−0.0202249	+	0.239045i
$721$		0			0
$722$	0.965081	+	1.67157i	0.0359166	+	0.0622094i
$723$	24.0994	+	7.56064i	0.896267	+	0.281183i
$724$	−12.0413	+	20.8561i	−0.447510	+	0.775109i
$725$	−10.1130	+	17.5162i	−0.375586	+	0.650534i
$726$	11.3808	−	10.4586i	0.422381	−	0.388153i
$727$	11.2554	+	19.4949i	0.417439	+	0.723025i	0.995681	−	0.0928402i	$-0.0295946\pi$
$727$	11.2554	+	19.4949i	0.417439	+	0.723025i	−0.578242	+	0.815865i	$0.696261\pi$
$728$		0			0
$729$	−6.76407	+	26.1390i	−0.250521	+	0.968111i
$730$	−10.2119			−0.377958
$731$	−0.557951	−	0.966399i	−0.0206366	−	0.0357436i
$732$	0.148842	−	0.136781i	0.00550137	−	0.00505557i
$733$	−0.448519	+	0.776858i	−0.0165664	+	0.0286939i	−0.874190	−	0.485584i	$-0.838607\pi$
$733$	−0.448519	+	0.776858i	−0.0165664	+	0.0286939i	0.857623	+	0.514278i	$0.171940\pi$
$734$	−9.60441	+	16.6353i	−0.354505	+	0.614021i
$735$		0			0
$736$	−15.6837	−	27.1649i	−0.578108	−	1.00131i
$737$	62.0671			2.28627
$738$	0.0421760	−	0.498492i	0.00155252	−	0.0183497i
$739$	−3.58063			−0.131716			−0.0658578	−	0.997829i	$-0.520978\pi$
$739$	−3.58063			−0.131716			−0.0658578	+	0.997829i	$0.520978\pi$
$740$	1.56833	+	2.71643i	0.0576531	+	0.0998581i
$741$	4.17291	+	18.6962i	0.153296	+	0.686823i
$742$		0			0
$743$	−24.7964	+	42.9486i	−0.909691	+	1.57563i	−0.0951977	+	0.995458i	$0.530348\pi$
$743$	−24.7964	+	42.9486i	−0.909691	+	1.57563i	−0.814493	+	0.580173i	$0.802985\pi$
$744$	2.25030	+	10.0822i	0.0825001	+	0.369631i
$745$	−6.09583	−	10.5583i	−0.223334	−	0.386826i
$746$	−10.7745			−0.394483
$747$	39.2947	−	18.4604i	1.43772	−	0.675432i
$748$	8.56098			0.313020
$749$		0			0
$750$	−12.5804	−	3.94682i	−0.459373	−	0.144118i
$751$	21.4515	−	37.1551i	0.782776	−	1.35581i	−0.147543	−	0.989056i	$-0.547136\pi$
$751$	21.4515	−	37.1551i	0.782776	−	1.35581i	0.930319	−	0.366752i	$-0.119530\pi$
$752$	−7.13450	+	12.3573i	−0.260168	+	0.450625i
$753$	17.9458	−	16.4916i	0.653982	−	0.600987i
$754$	−6.28835	−	10.8917i	−0.229008	−	0.396654i
$755$	25.1633			0.915786
$756$		0			0
$757$	13.8029			0.501677			0.250838	−	0.968029i	$-0.419294\pi$
$757$	13.8029			0.501677			0.250838	+	0.968029i	$0.419294\pi$
$758$	0.341510	+	0.591513i	0.0124042	+	0.0214847i
$759$	−34.1873	+	31.4170i	−1.24092	+	1.14036i
$760$	6.80856	−	11.7928i	0.246972	−	0.427769i
$761$	20.3599	−	35.2643i	0.738044	−	1.27833i	−0.215330	−	0.976541i	$-0.569083\pi$
$761$	20.3599	−	35.2643i	0.738044	−	1.27833i	0.953375	−	0.301789i	$-0.0975839\pi$
$762$	−8.04245	−	2.52314i	−0.291347	−	0.0914036i
$763$		0			0
$764$	−23.0001			−0.832113
$765$	−3.92864	−	2.73415i	−0.142040	−	0.0988534i
$766$	7.76683			0.280627
$767$	9.06826	+	15.7067i	0.327436	+	0.567135i
$768$	−3.41926	−	15.3196i	−0.123382	−	0.552798i
$769$	−5.57381	+	9.65413i	−0.200997	+	0.348137i	−0.948850	−	0.315728i	$-0.897751\pi$
$769$	−5.57381	+	9.65413i	−0.200997	+	0.348137i	0.747853	+	0.663864i	$0.231085\pi$
$770$		0			0
$771$	3.15506	+	14.1359i	0.113627	+	0.509090i
$772$	12.8454	+	22.2489i	0.462317	+	0.800756i
$773$	−0.925662			−0.0332937			−0.0166469	−	0.999861i	$-0.505299\pi$
$773$	−0.925662			−0.0332937			−0.0166469	+	0.999861i	$0.505299\pi$
$774$	1.64504	+	1.14487i	0.0591297	+	0.0411515i
$775$	7.44121			0.267296
$776$	6.43012	+	11.1373i	0.230828	+	0.399806i
$777$		0			0
$778$	−5.97049	+	10.3412i	−0.214052	+	0.370750i
$779$	0.499408	−	0.865001i	0.0178932	−	0.0309919i
$780$	−7.76232	+	7.13331i	−0.277936	+	0.255413i
$781$	0.198452	+	0.343728i	0.00710116	+	0.0122996i
$782$	4.08049			0.145918
$783$	13.4033	−	32.7553i	0.478996	−	1.17058i
$784$		0			0
$785$	−4.50386	−	7.80092i	−0.160750	−	0.278427i
$786$	17.4851	−	16.0682i	0.623673	−	0.573134i
$787$	11.5120	−	19.9393i	0.410358	−	0.710761i	−0.584571	−	0.811343i	$-0.698737\pi$
$787$	11.5120	−	19.9393i	0.410358	−	0.710761i	0.994929	+	0.100582i	$0.0320704\pi$
$788$	−3.13030	+	5.42184i	−0.111512	+	0.193145i
$789$	−5.40519	−	1.69575i	−0.192430	−	0.0603705i
$790$	−0.881115	−	1.52614i	−0.0313487	−	0.0542975i
$791$		0			0
$792$	−31.8661	+	14.9705i	−1.13231	+	0.531955i
$793$	0.207324			0.00736228
$794$	4.38551	+	7.59592i	0.155636	+	0.269569i
$795$	−0.441105	−	1.97631i	−0.0156444	−	0.0700927i
$796$	−19.6014	+	33.9505i	−0.694752	+	1.20335i
$797$	−11.3925	+	19.7325i	−0.403544	+	0.698960i	−0.994151	−	0.108000i	$-0.965555\pi$
$797$	−11.3925	+	19.7325i	−0.403544	+	0.698960i	0.590606	+	0.806960i	$0.298889\pi$
$798$		0			0
$799$	−5.30492	−	9.18839i	−0.187675	−	0.325062i
$800$	−17.1333			−0.605753
$801$	3.42093	−	40.4331i	0.120873	−	1.42863i
$802$	9.45390			0.333829
$803$	26.3575	+	45.6525i	0.930135	+	1.61104i
$804$	−32.2579	−	10.1202i	−1.13765	−	0.356912i
$805$		0			0
$806$	−2.31352	+	4.00713i	−0.0814901	+	0.141145i
$807$	−19.6234	+	18.0333i	−0.690778	+	0.634801i
$808$	6.11143	+	10.5853i	0.214999	+	0.372390i
$809$	−13.4751			−0.473758			−0.236879	−	0.971539i	$-0.576124\pi$
$809$	−13.4751			−0.473758			−0.236879	+	0.971539i	$0.576124\pi$
$810$	8.47444	+	1.44434i	0.297761	+	0.0507488i
$811$	30.7348			1.07924			0.539622	−	0.841907i	$-0.318567\pi$
$811$	30.7348			1.07924			0.539622	+	0.841907i	$0.318567\pi$
$812$		0			0
$813$	10.3635	−	9.52372i	0.363465	−	0.334011i
$814$	−2.34603	+	4.06344i	−0.0822283	+	0.142424i
$815$	5.71590	−	9.90023i	0.200219	−	0.346790i
$816$	−2.78642	−	0.874176i	−0.0975442	−	0.0306023i
$817$	2.00075	+	3.46540i	0.0699974	+	0.121239i
$818$	1.77369			0.0620158
$819$		0			0
$820$	0.549675			0.0191955
$821$	8.49319	+	14.7106i	0.296414	+	0.513405i	0.975313	−	0.220827i	$-0.0708757\pi$
$821$	8.49319	+	14.7106i	0.296414	+	0.513405i	−0.678899	+	0.734232i	$0.737542\pi$
$822$	3.08854	+	13.8378i	0.107725	+	0.482650i
$823$	9.29157	−	16.0935i	0.323884	−	0.560983i	−0.657402	−	0.753540i	$-0.728345\pi$
$823$	9.29157	−	16.0935i	0.323884	−	0.560983i	0.981286	+	0.192557i	$0.0616780\pi$
$824$	16.9122	−	29.2928i	0.589164	−	1.02046i
$825$	5.52453	+	24.7520i	0.192340	+	0.861754i
$826$		0			0
$827$	14.5419			0.505670			0.252835	−	0.967509i	$-0.418637\pi$
$827$	14.5419			0.505670			0.252835	+	0.967509i	$0.418637\pi$
$828$	22.8907	−	10.7539i	0.795506	−	0.373724i
$829$	9.57433			0.332530			0.166265	−	0.986081i	$-0.446829\pi$
$829$	9.57433			0.332530			0.166265	+	0.986081i	$0.446829\pi$
$830$	−6.91154	−	11.9711i	−0.239903	−	0.415524i
$831$	−21.2293	−	6.66019i	−0.736435	−	0.231040i
$832$	1.17885	−	2.04183i	0.0408693	−	0.0707877i
$833$		0			0
$834$	−2.12170	+	1.94977i	−0.0734685	+	0.0675150i
$835$	1.51097	+	2.61708i	0.0522894	+	0.0905678i
$836$	−30.6987			−1.06174
$837$	−12.9019	+	1.75491i	−0.445955	+	0.0606587i
$838$	22.4651			0.776045
$839$	−21.2303	−	36.7720i	−0.732952	−	1.26951i	−0.955616	−	0.294615i	$-0.904809\pi$
$839$	−21.2303	−	36.7720i	−0.732952	−	1.26951i	0.222664	−	0.974895i	$-0.428525\pi$
$840$		0			0
$841$	−8.69551	+	15.0611i	−0.299845	+	0.519347i
$842$	−1.62187	+	2.80917i	−0.0558934	+	0.0968103i
$843$	−2.39328	−	0.750836i	−0.0824288	−	0.0258602i
$844$	5.83428	+	10.1053i	0.200824	+	0.347838i
$845$	7.71198			0.265300
$846$	15.6408	+	10.8853i	0.537742	+	0.374243i
$847$		0			0
$848$	−0.617738	−	1.06995i	−0.0212132	−	0.0367423i
$849$	6.57959	+	29.4791i	0.225811	+	1.01172i
$850$	1.11441	−	1.93021i	0.0382239	−	0.0662058i
$851$	3.85883	−	6.68370i	0.132279	−	0.229114i
$852$	−0.0470949	−	0.211003i	−0.00161344	−	0.00722884i
$853$	−7.14039	−	12.3675i	−0.244482	−	0.423456i	0.717504	−	0.696555i	$-0.245285\pi$
$853$	−7.14039	−	12.3675i	−0.244482	−	0.423456i	−0.961986	+	0.273099i	$0.911951\pi$
$854$		0			0
$855$	14.0877	+	9.80436i	0.481788	+	0.335302i
$856$	18.2324			0.623171
$857$	17.3895	+	30.1195i	0.594013	+	1.02886i	0.993685	+	0.112203i	$0.0357907\pi$
$857$	17.3895	+	30.1195i	0.594013	+	1.02886i	−0.399672	+	0.916658i	$0.630876\pi$
$858$	−15.0467	−	4.72055i	−0.513685	−	0.161157i
$859$	−6.32429	+	10.9540i	−0.215782	+	0.373745i	−0.953514	−	0.301348i	$-0.902563\pi$
$859$	−6.32429	+	10.9540i	−0.215782	+	0.373745i	0.737732	+	0.675093i	$0.235897\pi$
$860$	−1.10107	+	1.90710i	−0.0375460	+	0.0650316i
$861$		0			0
$862$	11.8409	+	20.5091i	0.403304	+	0.698543i
$863$	−26.4797			−0.901379			−0.450690	−	0.892681i	$-0.648822\pi$
$863$	−26.4797			−0.901379			−0.450690	+	0.892681i	$0.648822\pi$
$864$	29.7064	−	4.04066i	1.01063	−	0.137466i
$865$	−26.0594			−0.886045
$866$	1.83471	+	3.17782i	0.0623461	+	0.107987i
$867$	−20.0817	+	18.4544i	−0.682011	+	0.626744i
$868$		0			0
$869$	−4.54843	+	7.87811i	−0.154295	+	0.267247i
$870$	−10.7517	−	3.37311i	−0.364518	−	0.114359i
$871$	−17.3371	−	30.0287i	−0.587444	−	1.01748i
$872$	−4.04332			−0.136924
$873$	−14.6712	+	6.89246i	−0.496545	+	0.233274i
$874$	−14.6322			−0.494941
$875$		0			0
$876$	−6.25494	−	28.0245i	−0.211335	−	0.946860i
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	−0.999747	−	0.0224835i	$-0.992843\pi$
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	0.519345	+	0.854565i	$0.326176\pi$
$878$	2.14443	−	3.71427i	0.0723711	−	0.125350i
$879$	−0.679181	−	3.04299i	−0.0229082	−	0.102637i
$880$	−5.29004	−	9.16261i	−0.178327	−	0.308872i
$881$	20.3637			0.686071			0.343036	−	0.939322i	$-0.388545\pi$
$881$	20.3637			0.686071			0.343036	+	0.939322i	$0.388545\pi$
$882$		0			0
$883$	49.1950			1.65554			0.827772	−	0.561065i	$-0.189608\pi$
$883$	49.1950			1.65554			0.827772	+	0.561065i	$0.189608\pi$
$884$	−2.39132	−	4.14189i	−0.0804288	−	0.139307i
$885$	15.5048	+	4.86427i	0.521188	+	0.163511i
$886$	2.14065	−	3.70771i	0.0719164	−	0.124563i
$887$	−2.10846	+	3.65196i	−0.0707952	+	0.122621i	−0.899250	−	0.437435i	$-0.855887\pi$
$887$	−2.10846	+	3.65196i	−0.0707952	+	0.122621i	0.828455	+	0.560056i	$0.189220\pi$
$888$	4.30902	−	3.95984i	0.144601	−	0.132883i
$889$		0			0
$890$	−12.9196			−0.433067
$891$	−15.4161	−	41.6132i	−0.516459	−	1.39409i
$892$	−20.1346			−0.674157
$893$	19.0229	+	32.9486i	0.636576	+	1.10258i
$894$	−7.31441	+	6.72169i	−0.244630	+	0.224807i
$895$	−5.43294	+	9.41013i	−0.181603	+	0.314546i
$896$		0			0
$897$	24.7493	+	7.76453i	0.826355	+	0.259250i
$898$	3.93685	+	6.81883i	0.131375	+	0.227547i
$899$	17.0675			0.569233
$900$	1.16462	−	13.7651i	0.0388208	−	0.458836i
$901$	0.918649			0.0306046
$902$	0.411122	+	0.712084i	0.0136889	+	0.0237098i
$903$		0			0
$904$	0.714872	−	1.23819i	0.0237763	−	0.0411817i
$905$	−11.0650	+	19.1652i	−0.367814	+	0.637072i
$906$	−4.46634	−	20.0109i	−0.148384	−	0.664817i
$907$	−23.9925	−	41.5563i	−0.796659	−	1.37985i	−0.921780	−	0.387713i	$-0.873265\pi$
$907$	−23.9925	−	41.5563i	−0.796659	−	1.37985i	0.125121	−	0.992142i	$-0.460068\pi$
$908$	−44.9170			−1.49062
$909$	−13.9441	+	6.55085i	−0.462496	+	0.217278i
$910$		0			0
$911$	−12.8667	−	22.2858i	−0.426294	−	0.738362i	0.570247	−	0.821474i	$-0.306848\pi$
$911$	−12.8667	−	22.2858i	−0.426294	−	0.738362i	−0.996540	+	0.0831113i	$0.973514\pi$
$912$	9.99180	+	3.13470i	0.330862	+	0.103800i
$913$	−35.6782	+	61.7965i	−1.18078	+	2.04517i
$914$	−3.52675	+	6.10852i	−0.116655	+	0.202052i
$915$	0.136775	−	0.125692i	0.00452165	−	0.00415524i
$916$	−11.9678	−	20.7288i	−0.395427	−	0.684900i
$917$		0			0
$918$	−1.47700	+	3.60951i	−0.0487482	+	0.119132i
$919$	−2.26957			−0.0748661			−0.0374330	−	0.999299i	$-0.511918\pi$
$919$	−2.26957			−0.0748661			−0.0374330	+	0.999299i	$0.511918\pi$
$920$	−9.21919	−	15.9681i	−0.303948	−	0.526453i
$921$	−1.35794	+	1.24790i	−0.0447455	+	0.0411196i
$922$	2.37484	−	4.11334i	0.0782111	−	0.135466i
$923$	0.110866	−	0.192026i	0.00364920	−	0.00632060i
$924$		0			0
$925$	−2.10775	−	3.65073i	−0.0693024	−	0.120035i
$926$	−21.9548			−0.721479
$927$	34.9933	+	24.3537i	1.14933	+	0.799880i
$928$	−39.2976			−1.29001
$929$	22.9248	+	39.7069i	0.752138	+	1.30274i	0.946785	+	0.321868i	$0.104311\pi$
$929$	22.9248	+	39.7069i	0.752138	+	1.30274i	−0.194647	+	0.980873i	$0.562356\pi$
$930$	0.903084	+	4.04616i	0.0296133	+	0.132679i
$931$		0			0
$932$	3.83514	−	6.64266i	0.125624	−	0.217587i
$933$	6.38745	+	28.6182i	0.209116	+	0.936917i
$934$	−1.31530	−	2.27816i	−0.0430379	−	0.0745438i
$935$	7.86691			0.257275
$936$	16.1440	+	11.2355i	0.527683	+	0.367243i
$937$	56.2075			1.83622			0.918110	−	0.396325i	$-0.129715\pi$
$937$	56.2075			1.83622			0.918110	+	0.396325i	$0.129715\pi$
$938$		0			0
$939$	−13.6814	−	4.29222i	−0.446475	−	0.140071i
$940$	−10.4688	+	18.1325i	−0.341454	+	0.591416i
$941$	−17.6402	+	30.5536i	−0.575053	+	0.996020i	0.420983	+	0.907068i	$0.361685\pi$
$941$	−17.6402	+	30.5536i	−0.575053	+	0.996020i	−0.996036	+	0.0889519i	$0.971648\pi$
$942$	−5.40420	+	4.96627i	−0.176078	+	0.161810i
$943$	−0.676229	−	1.17126i	−0.0220210	−	0.0381415i
$944$	9.91453			0.322691
$945$		0			0
$946$	−3.29411			−0.107101
$947$	25.3565	+	43.9188i	0.823976	+	1.42717i	0.902699	+	0.430272i	$0.141582\pi$
$947$	25.3565	+	43.9188i	0.823976	+	1.42717i	−0.0787236	+	0.996896i	$0.525084\pi$
$948$	3.64849	−	3.35283i	0.118497	−	0.108895i
$949$	14.7248	−	25.5040i	0.477986	−	0.827896i
$950$	−3.99615	+	6.92154i	−0.129652	+	0.224564i
$951$	−10.8204	−	3.39467i	−0.350877	−	0.110080i
$952$		0			0
$953$	25.9988			0.842184			0.421092	−	0.907018i	$-0.361647\pi$
$953$	25.9988			0.842184			0.421092	+	0.907018i	$0.361647\pi$
$954$	−1.49335	+	0.701569i	−0.0483491	+	0.0227141i
$955$	−21.1354			−0.683924
$956$	−10.1061	−	17.5043i	−0.326855	−	0.566130i
$957$	12.6713	+	56.7722i	0.409605	+	1.83519i
$958$	5.39165	−	9.33861i	0.174196	−	0.301717i
$959$		0			0
$960$	−0.460166	−	2.06172i	−0.0148518	−	0.0665417i
$961$	12.3604	+	21.4088i	0.398722	+	0.690607i
$962$	2.62125			0.0845123
$963$	−1.93743	+	22.8991i	−0.0624327	+	0.737912i
$964$	22.6124			0.728295
$965$	11.8040	+	20.4451i	0.379984	+	0.658152i
$966$		0			0
$967$	−12.9810	+	22.4838i	−0.417442	+	0.723031i	−0.995681	−	0.0928360i	$-0.970407\pi$
$967$	−12.9810	+	22.4838i	−0.417442	+	0.723031i	0.578239	+	0.815867i	$0.303740\pi$
$968$	15.8427	−	27.4404i	0.509204	−	0.881967i
$969$	−5.73331	+	5.26871i	−0.184180	+	0.169255i
$970$	2.58052	+	4.46959i	0.0828554	+	0.143510i
$971$	−7.94412			−0.254939			−0.127469	−	0.991843i	$-0.540685\pi$
$971$	−7.94412			−0.254939			−0.127469	+	0.991843i	$0.540685\pi$
$972$	1.22703	+	24.1411i	0.0393572	+	0.774327i
$973$		0			0
$974$	−1.17424	−	2.03384i	−0.0376249	−	0.0651683i
$975$	10.4321	−	9.58675i	0.334095	−	0.307022i
$976$	0.0566680	−	0.0981518i	0.00181390	−	0.00314176i
$977$	26.1274	−	45.2540i	0.835889	−	1.44780i	−0.0574149	−	0.998350i	$-0.518286\pi$
$977$	26.1274	−	45.2540i	0.835889	−	1.44780i	0.893304	−	0.449452i	$-0.148381\pi$
$978$	−8.88761	−	2.78828i	−0.284194	−	0.0891595i
$979$	33.3464	+	57.7577i	1.06576	+	1.84594i
$980$		0			0
$981$	0.429654	−	5.07822i	0.0137178	−	0.162135i
$982$	27.5569			0.879376
$983$	−19.4190	−	33.6346i	−0.619369	−	1.07278i	−0.989601	−	0.143839i	$-0.954055\pi$
$983$	−19.4190	−	33.6346i	−0.619369	−	1.07278i	0.370232	−	0.928939i	$-0.379278\pi$
$984$	−0.223400	−	1.00092i	−0.00712174	−	0.0319081i
$985$	−2.87652	+	4.98228i	−0.0916535	+	0.158749i
$986$	2.55606	−	4.42722i	0.0814015	−	0.140991i
$987$		0			0
$988$	8.57501	+	14.8524i	0.272807	+	0.472516i
$989$	5.41827			0.172291
$990$	−12.7884	+	6.00793i	−0.406443	+	0.190944i
$991$	30.9378			0.982771			0.491385	−	0.870942i	$-0.336491\pi$
$991$	30.9378			0.982771			0.491385	+	0.870942i	$0.336491\pi$
$992$	7.22890	+	12.5208i	0.229518	+	0.397536i
$993$	44.1679	+	13.8567i	1.40163	+	0.439728i
$994$		0			0
$995$	−18.0122	+	31.1981i	−0.571025	+	0.989045i
$996$	28.6190	−	26.2999i	0.906829	−	0.833344i
$997$	23.5335	+	40.7612i	0.745313	+	1.29092i	0.950048	+	0.312103i	$0.101033\pi$
$997$	23.5335	+	40.7612i	0.745313	+	1.29092i	−0.204735	+	0.978817i	$0.565633\pi$
$998$	7.92985			0.251015
$999$	4.51549	+	5.83271i	0.142864	+	0.184539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.f.148.2		10
3.2	odd	2		1323.2.f.f.442.4		10
7.2	even	3		441.2.g.f.67.2		10
7.3	odd	6		63.2.h.b.58.4	yes	10
7.4	even	3		441.2.h.f.373.4		10
7.5	odd	6		63.2.g.b.4.2	✓	10
7.6	odd	2		441.2.f.e.148.2		10
9.2	odd	6		1323.2.f.f.883.4		10
9.4	even	3		3969.2.a.ba.1.4		5
9.5	odd	6		3969.2.a.bb.1.2		5
9.7	even	3	inner	441.2.f.f.295.2		10
21.2	odd	6		1323.2.g.f.361.4		10
21.5	even	6		189.2.g.b.172.4		10
21.11	odd	6		1323.2.h.f.226.2		10
21.17	even	6		189.2.h.b.37.2		10
21.20	even	2		1323.2.f.e.442.4		10
28.3	even	6		1008.2.q.i.625.1		10
28.19	even	6		1008.2.t.i.193.4		10
63.2	odd	6		1323.2.h.f.802.2		10
63.5	even	6		567.2.e.e.487.4		10
63.11	odd	6		1323.2.g.f.667.4		10
63.13	odd	6		3969.2.a.z.1.4		5
63.16	even	3		441.2.h.f.214.4		10
63.20	even	6		1323.2.f.e.883.4		10
63.25	even	3		441.2.g.f.79.2		10
63.31	odd	6		567.2.e.f.163.2		10
63.34	odd	6		441.2.f.e.295.2		10
63.38	even	6		189.2.g.b.100.4		10
63.40	odd	6		567.2.e.f.487.2		10
63.41	even	6		3969.2.a.bc.1.2		5
63.47	even	6		189.2.h.b.46.2		10
63.52	odd	6		63.2.g.b.16.2	yes	10
63.59	even	6		567.2.e.e.163.4		10
63.61	odd	6		63.2.h.b.25.4	yes	10
84.47	odd	6		3024.2.t.i.1873.1		10
84.59	odd	6		3024.2.q.i.2305.5		10
252.47	odd	6		3024.2.q.i.2881.5		10
252.115	even	6		1008.2.t.i.961.4		10
252.187	even	6		1008.2.q.i.529.1		10
252.227	odd	6		3024.2.t.i.289.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	7.5	odd	6
63.2.g.b.16.2	yes	10	63.52	odd	6
63.2.h.b.25.4	yes	10	63.61	odd	6
63.2.h.b.58.4	yes	10	7.3	odd	6
189.2.g.b.100.4		10	63.38	even	6
189.2.g.b.172.4		10	21.5	even	6
189.2.h.b.37.2		10	21.17	even	6
189.2.h.b.46.2		10	63.47	even	6
441.2.f.e.148.2		10	7.6	odd	2
441.2.f.e.295.2		10	63.34	odd	6
441.2.f.f.148.2		10	1.1	even	1	trivial
441.2.f.f.295.2		10	9.7	even	3	inner
441.2.g.f.67.2		10	7.2	even	3
441.2.g.f.79.2		10	63.25	even	3
441.2.h.f.214.4		10	63.16	even	3
441.2.h.f.373.4		10	7.4	even	3
567.2.e.e.163.4		10	63.59	even	6
567.2.e.e.487.4		10	63.5	even	6
567.2.e.f.163.2		10	63.31	odd	6
567.2.e.f.487.2		10	63.40	odd	6
1008.2.q.i.529.1		10	252.187	even	6
1008.2.q.i.625.1		10	28.3	even	6
1008.2.t.i.193.4		10	28.19	even	6
1008.2.t.i.961.4		10	252.115	even	6
1323.2.f.e.442.4		10	21.20	even	2
1323.2.f.e.883.4		10	63.20	even	6
1323.2.f.f.442.4		10	3.2	odd	2
1323.2.f.f.883.4		10	9.2	odd	6
1323.2.g.f.361.4		10	21.2	odd	6
1323.2.g.f.667.4		10	63.11	odd	6
1323.2.h.f.226.2		10	21.11	odd	6
1323.2.h.f.802.2		10	63.2	odd	6
3024.2.q.i.2305.5		10	84.59	odd	6
3024.2.q.i.2881.5		10	252.47	odd	6
3024.2.t.i.289.1		10	252.227	odd	6
3024.2.t.i.1873.1		10	84.47	odd	6
3969.2.a.z.1.4		5	63.13	odd	6
3969.2.a.ba.1.4		5	9.4	even	3
3969.2.a.bb.1.2		5	9.5	odd	6
3969.2.a.bc.1.2		5	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)

\(f(q)\)	\(=\)	\(q+(-0.335166 - 0.580525i) q^{2} +(1.27533 - 1.17198i) q^{3} +(0.775327 - 1.34291i) q^{4} +(0.712469 - 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(0.252918 - 2.98932i) q^{9} +O(q^{10})\)	\(q+(-0.335166 - 0.580525i) q^{2} +(1.27533 - 1.17198i) q^{3} +(0.775327 - 1.34291i) q^{4} +(0.712469 - 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(0.252918 - 2.98932i) q^{9} -0.955182 q^{10} +(2.46539 + 4.27018i) q^{11} +(-0.585065 - 2.62131i) q^{12} +(1.37730 - 2.38556i) q^{13} +(-0.537632 - 2.40879i) q^{15} +(-0.752918 - 1.30409i) q^{16} +1.11968 q^{17} +(-1.82014 + 0.855094i) q^{18} -4.01505 q^{19} +(-1.10479 - 1.91356i) q^{20} +(1.65263 - 2.86244i) q^{22} +(-2.71830 + 4.70824i) q^{23} +(-3.03543 + 2.78946i) q^{24} +(1.48478 + 2.57171i) q^{25} -1.84650 q^{26} +(-3.18087 - 4.10878i) q^{27} +(3.40555 + 5.89858i) q^{29} +(-1.21817 + 1.11946i) q^{30} +(1.25292 - 2.17012i) q^{31} +(-2.88483 + 4.99666i) q^{32} +(8.14874 + 2.55648i) q^{33} +(-0.375279 - 0.650002i) q^{34} +(-3.81828 - 2.65735i) q^{36} -1.41957 q^{37} +(1.34571 + 2.33083i) q^{38} +(-1.03932 - 4.65654i) q^{39} +(-1.69576 + 2.93714i) q^{40} +(-0.124384 + 0.215440i) q^{41} +(-0.498313 - 0.863104i) q^{43} +7.64592 q^{44} +(-3.50872 - 2.44191i) q^{45} +3.64434 q^{46} +(-4.73790 - 8.20628i) q^{47} +(-2.48859 - 0.780738i) q^{48} +(0.995294 - 1.72390i) q^{50} +(1.42796 - 1.31224i) q^{51} +(-2.13572 - 3.69917i) q^{52} +0.820458 q^{53} +(-1.31913 + 3.22370i) q^{54} +7.02604 q^{55} +(-5.12050 + 4.70556i) q^{57} +(2.28285 - 3.95401i) q^{58} +(-3.29204 + 5.70197i) q^{59} +(-3.65163 - 1.14561i) q^{60} +(0.0376322 + 0.0651809i) q^{61} -1.67974 q^{62} +0.855913 q^{64} +(-1.96257 - 3.39927i) q^{65} +(-1.24708 - 5.58740i) q^{66} +(6.29385 - 10.9013i) q^{67} +(0.868117 - 1.50362i) q^{68} +(2.05125 + 9.19035i) q^{69} +0.0804951 q^{71} +(-0.601975 + 7.11494i) q^{72} +10.6910 q^{73} +(0.475793 + 0.824098i) q^{74} +(4.90757 + 1.53964i) q^{75} +(-3.11297 + 5.39183i) q^{76} +(-2.35489 + 2.16407i) q^{78} +(0.922457 + 1.59774i) q^{79} -2.14572 q^{80} +(-8.87206 - 1.51211i) q^{81} +0.166758 q^{82} +(7.23583 + 12.5328i) q^{83} +(0.797736 - 1.38172i) q^{85} +(-0.334036 + 0.578567i) q^{86} +(11.2562 + 3.53138i) q^{87} +(-5.86792 - 10.1635i) q^{88} +13.5258 q^{89} +(-0.241583 + 2.85534i) q^{90} +(4.21515 + 7.30085i) q^{92} +(-0.945458 - 4.23601i) q^{93} +(-3.17597 + 5.50094i) q^{94} +(-2.86059 + 4.95469i) q^{95} +(2.17690 + 9.75334i) q^{96} +(-2.70160 - 4.67930i) q^{97} +(13.3885 - 6.28982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9	\( 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9} - 14 q^{10} + 4 q^{11} + 2 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} + 24 q^{17} - 2 q^{18} + 2 q^{19} - 5 q^{20} - q^{22} + 3 q^{23} + 9 q^{24} - q^{25} + 22 q^{26} + 7 q^{27} + 7 q^{29} + 10 q^{30} + 3 q^{31} - 2 q^{32} + 13 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} - 22 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} + 20 q^{44} - 17 q^{45} - 6 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} - 15 q^{51} + 10 q^{52} + 42 q^{53} - 52 q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} - 30 q^{59} + 31 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} - 22 q^{66} - 2 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 12 q^{72} + 30 q^{73} - 36 q^{74} + 17 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} + 40 q^{80} - 31 q^{81} - 10 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} + 34 q^{87} - 18 q^{88} + 56 q^{89} - 28 q^{90} + 27 q^{92} + 18 q^{93} + 3 q^{94} - 14 q^{95} + 58 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9 - 14 * q^10 + 4 * q^11 + 2 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 + 24 * q^17 - 2 * q^18 + 2 * q^19 - 5 * q^20 - q^22 + 3 * q^23 + 9 * q^24 - q^25 + 22 * q^26 + 7 * q^27 + 7 * q^29 + 10 * q^30 + 3 * q^31 - 2 * q^32 + 13 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 - 22 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 + 20 * q^44 - 17 * q^45 - 6 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 - 15 * q^51 + 10 * q^52 + 42 * q^53 - 52 * q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 - 30 * q^59 + 31 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 - 22 * q^66 - 2 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 12 * q^72 + 30 * q^73 - 36 * q^74 + 17 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 + 40 * q^80 - 31 * q^81 - 10 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 + 34 * q^87 - 18 * q^88 + 56 * q^89 - 28 * q^90 + 27 * q^92 + 18 * q^93 + 3 * q^94 - 14 * q^95 + 58 * q^96 + 12 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

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