LMFDB - Embedded newform 441.2.h.f.214.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$10$
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			214.5
Root			$-1.02682 + 1.77851i$ of defining polynomial
Character	$\chi$	$=$	441.214
Dual form			441.2.h.f.373.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.05365 q^{2} +(1.70867 + 0.283604i) q^{3} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(3.50901 + 0.582422i) q^{6} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +O(q^{10})$	\(q+2.05365 q^{2} +(1.70867 + 0.283604i) q^{3} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(3.50901 + 0.582422i) q^{6} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +(-0.150168 + 0.260099i) q^{10} +(-0.832020 - 1.44110i) q^{11} +(3.78891 + 0.628880i) q^{12} +(-0.0999454 - 0.173111i) q^{13} +(-0.160862 + 0.195670i) q^{15} -3.51780 q^{16} +(-3.13555 + 5.43093i) q^{17} +(5.83058 + 1.99034i) q^{18} +(-3.45879 - 5.99080i) q^{19} +(-0.162147 + 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(3.09092 - 5.35363i) q^{23} +(0.763064 + 0.126652i) q^{24} +(2.48931 + 4.31160i) q^{25} +(-0.205252 - 0.355508i) q^{26} +(4.57630 + 2.46119i) q^{27} +(-2.46757 + 4.27396i) q^{29} +(-0.330354 + 0.401837i) q^{30} +2.51780 q^{31} -8.11747 q^{32} +(-1.01295 - 2.69834i) q^{33} +(-6.43931 + 11.1532i) q^{34} +(6.29567 + 2.14910i) q^{36} +(-3.50023 - 6.06257i) q^{37} +(-7.10312 - 12.3030i) q^{38} +(-0.121679 - 0.324134i) q^{39} +(-0.0326554 + 0.0565608i) q^{40} +(-1.15895 - 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} +(-1.84497 - 3.19558i) q^{44} +(-0.330354 + 0.288715i) q^{45} +(6.34765 - 10.9944i) q^{46} +1.81177 q^{47} +(-6.01077 - 0.997660i) q^{48} +(5.11215 + 8.85451i) q^{50} +(-6.89787 + 8.39045i) q^{51} +(-0.221625 - 0.383865i) q^{52} +(-2.67307 + 4.62989i) q^{53} +(9.39810 + 5.05442i) q^{54} +0.243359 q^{55} +(-4.21093 - 11.2172i) q^{57} +(-5.06752 + 8.77720i) q^{58} +4.57099 q^{59} +(-0.356705 + 0.433890i) q^{60} +0.678276 q^{61} +5.17066 q^{62} -9.63481 q^{64} +0.0292332 q^{65} +(-2.08024 - 5.54143i) q^{66} -6.18684 q^{67} +(-6.95296 + 12.0429i) q^{68} +(6.79968 - 8.27101i) q^{69} +1.27749 q^{71} +(1.26791 + 0.432816i) q^{72} +(0.778603 - 1.34858i) q^{73} +(-7.18823 - 12.4504i) q^{74} +(3.03063 + 8.07311i) q^{75} +(-7.66972 - 13.2843i) q^{76} +(-0.249886 - 0.665657i) q^{78} +12.7957 q^{79} +(0.257231 - 0.445537i) q^{80} +(7.12141 + 5.50323i) q^{81} +(-2.38008 - 4.12241i) q^{82} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-1.93247 + 3.34713i) q^{86} +(-5.42839 + 6.60299i) q^{87} +(-0.371566 - 0.643571i) q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.678430 + 0.592918i) q^{90} +(6.85398 - 11.8714i) q^{92} +(4.30209 + 0.714056i) q^{93} +3.72074 q^{94} +1.01167 q^{95} +(-13.8701 - 2.30214i) q^{96} +(3.98514 - 6.90246i) q^{97} +(-0.965543 - 4.89786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9} + 7 q^{10} + 4 q^{11} + 20 q^{12} + 8 q^{13} - 19 q^{15} - 4 q^{16} - 12 q^{17} + 4 q^{18} - q^{19} - 5 q^{20} - q^{22} + 3 q^{23} - 6 q^{24} - q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} + 16 q^{30} - 6 q^{31} + 4 q^{32} - 14 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} + 2 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + 16 q^{45} + 3 q^{46} + 54 q^{47} + 5 q^{48} + 19 q^{50} - 9 q^{51} + 10 q^{52} - 21 q^{53} - q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} + 60 q^{59} + 10 q^{60} - 28 q^{61} + 12 q^{62} - 50 q^{64} + 22 q^{65} - 19 q^{66} + 4 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 36 q^{72} - 15 q^{73} - 36 q^{74} + 14 q^{75} - 5 q^{76} - 20 q^{78} + 8 q^{79} - 20 q^{80} + 23 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} - 2 q^{87} - 18 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 6 q^{93} - 6 q^{94} + 28 q^{95} - 59 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9 + 7 * q^10 + 4 * q^11 + 20 * q^12 + 8 * q^13 - 19 * q^15 - 4 * q^16 - 12 * q^17 + 4 * q^18 - q^19 - 5 * q^20 - q^22 + 3 * q^23 - 6 * q^24 - q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 + 16 * q^30 - 6 * q^31 + 4 * q^32 - 14 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 + 2 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + 16 * q^45 + 3 * q^46 + 54 * q^47 + 5 * q^48 + 19 * q^50 - 9 * q^51 + 10 * q^52 - 21 * q^53 - q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 + 60 * q^59 + 10 * q^60 - 28 * q^61 + 12 * q^62 - 50 * q^64 + 22 * q^65 - 19 * q^66 + 4 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 36 * q^72 - 15 * q^73 - 36 * q^74 + 14 * q^75 - 5 * q^76 - 20 * q^78 + 8 * q^79 - 20 * q^80 + 23 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 - 2 * q^87 - 18 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 6 * q^93 - 6 * q^94 + 28 * q^95 - 59 * q^96 + 12 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.05365			1.45215			0.726073	−	0.687617i	$-0.241343\pi$
$2$	2.05365			1.45215			0.726073	+	0.687617i	$0.241343\pi$
$3$	1.70867	+	0.283604i	0.986504	+	0.163739i
$3$	1.70867	+	0.283604i	0.986504	+	0.163739i
$4$	2.21746			1.10873
$5$	−0.0731228	+	0.126652i	−0.0327015	+	0.0566407i	−0.881913	−	0.471412i	$-0.843744\pi$
$5$	−0.0731228	+	0.126652i	−0.0327015	+	0.0566407i	0.849211	+	0.528053i	$0.177078\pi$
$6$	3.50901	+	0.582422i	1.43255	+	0.237773i
$7$		0			0
$7$		0			0
$8$	0.446582			0.157891
$9$	2.83914	+	0.969173i	0.946379	+	0.323058i
$10$	−0.150168	+	0.260099i	−0.0474874	+	0.0822506i
$11$	−0.832020	−	1.44110i	−0.250864	−	0.434508i	0.712900	−	0.701265i	$-0.247381\pi$
$11$	−0.832020	−	1.44110i	−0.250864	−	0.434508i	−0.963764	+	0.266757i	$0.914048\pi$
$12$	3.78891	+	0.628880i	1.09377	+	0.181542i
$13$	−0.0999454	−	0.173111i	−0.0277199	−	0.0480122i	0.851833	−	0.523814i	$-0.175491\pi$
$13$	−0.0999454	−	0.173111i	−0.0277199	−	0.0480122i	−0.879553	+	0.475802i	$0.842158\pi$
$14$		0			0
$15$	−0.160862	+	0.195670i	−0.0415345	+	0.0505218i
$16$	−3.51780			−0.879449
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	0.182119	+	0.983277i	$0.441704\pi$
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	−0.942602	+	0.333919i	$0.891629\pi$
$18$	5.83058	+	1.99034i	1.37428	+	0.469127i
$19$	−3.45879	−	5.99080i	−0.793500	−	1.37438i	−0.923787	−	0.382907i	$-0.874923\pi$
$19$	−3.45879	−	5.99080i	−0.793500	−	1.37438i	0.130287	−	0.991476i	$-0.458410\pi$
$20$	−0.162147	+	0.280847i	−0.0362571	+	0.0627992i
$21$		0			0
$22$	−1.70867	−	2.95951i	−0.364291	−	0.630970i
$23$	3.09092	−	5.35363i	0.644501	−	1.11631i	−0.339916	−	0.940456i	$-0.610399\pi$
$23$	3.09092	−	5.35363i	0.644501	−	1.11631i	0.984417	−	0.175852i	$-0.0562682\pi$
$24$	0.763064	+	0.126652i	0.155760	+	0.0258528i
$25$	2.48931	+	4.31160i	0.497861	+	0.862321i
$26$	−0.205252	−	0.355508i	−0.0402533	−	0.0697208i
$27$	4.57630	+	2.46119i	0.880710	+	0.473657i
$28$		0			0
$29$	−2.46757	+	4.27396i	−0.458217	+	0.793655i	−0.998867	−	0.0475930i	$-0.984845\pi$
$29$	−2.46757	+	4.27396i	−0.458217	+	0.793655i	0.540650	+	0.841248i	$0.318178\pi$
$30$	−0.330354	+	0.401837i	−0.0603141	+	0.0733650i
$31$	2.51780			0.452209			0.226105	−	0.974103i	$-0.427401\pi$
$31$	2.51780			0.452209			0.226105	+	0.974103i	$0.427401\pi$
$32$	−8.11747			−1.43498
$33$	−1.01295	−	2.69834i	−0.176332	−	0.469720i
$34$	−6.43931	+	11.1532i	−1.10433	+	1.91276i
$35$		0			0
$36$	6.29567	+	2.14910i	1.04928	+	0.358184i
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	−0.995994	−	0.0894162i	$-0.971500\pi$
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	0.420560	−	0.907264i	$-0.361833\pi$
$38$	−7.10312	−	12.3030i	−1.15228	−	1.99581i
$39$	−0.121679	−	0.324134i	−0.0194843	−	0.0519030i
$40$	−0.0326554	+	0.0565608i	−0.00516327	+	0.00894304i
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	0.761223	−	0.648491i	$-0.224599\pi$
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	−0.942221	+	0.334993i	$0.891266\pi$
$42$		0			0
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	−0.928812	−	0.370550i	$-0.879169\pi$
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	0.785312	+	0.619100i	$0.212502\pi$
$44$	−1.84497	−	3.19558i	−0.278140	−	0.481752i
$45$	−0.330354	+	0.288715i	−0.0492463	+	0.0430391i
$46$	6.34765	−	10.9944i	0.935910	−	1.62104i
$47$	1.81177			0.264275			0.132137	−	0.991231i	$-0.457816\pi$
$47$	1.81177			0.264275			0.132137	+	0.991231i	$0.457816\pi$
$48$	−6.01077	−	0.997660i	−0.867579	−	0.144000i
$49$		0			0
$50$	5.11215	+	8.85451i	0.722967	+	1.25222i
$51$	−6.89787	+	8.39045i	−0.965895	+	1.17490i
$52$	−0.221625	−	0.383865i	−0.0307338	−	0.0532325i
$53$	−2.67307	+	4.62989i	−0.367174	+	0.635964i	−0.989123	−	0.147094i	$-0.953008\pi$
$53$	−2.67307	+	4.62989i	−0.367174	+	0.635964i	0.621948	+	0.783058i	$0.286341\pi$
$54$	9.39810	+	5.05442i	1.27892	+	0.687819i
$55$	0.243359			0.0328145
$56$		0			0
$57$	−4.21093	−	11.2172i	−0.557751	−	1.48576i
$58$	−5.06752	+	8.77720i	−0.665398	+	1.15250i
$59$	4.57099			0.595092			0.297546	−	0.954708i	$-0.403832\pi$
$59$	4.57099			0.595092			0.297546	+	0.954708i	$0.403832\pi$
$60$	−0.356705	+	0.433890i	−0.0460505	+	0.0560149i
$61$	0.678276			0.0868443			0.0434221	−	0.999057i	$-0.486174\pi$
$61$	0.678276			0.0868443			0.0434221	+	0.999057i	$0.486174\pi$
$62$	5.17066			0.656674
$63$		0			0
$64$	−9.63481			−1.20435
$65$	0.0292332			0.00362593
$66$	−2.08024	−	5.54143i	−0.256060	−	0.682103i
$67$	−6.18684			−0.755842			−0.377921	−	0.925838i	$-0.623361\pi$
$67$	−6.18684			−0.755842			−0.377921	+	0.925838i	$0.623361\pi$
$68$	−6.95296	+	12.0429i	−0.843170	+	1.46041i
$69$	6.79968	−	8.27101i	0.818586	−	0.995713i
$70$		0			0
$71$	1.27749			0.151611			0.0758053	−	0.997123i	$-0.475847\pi$
$71$	1.27749			0.151611			0.0758053	+	0.997123i	$0.475847\pi$
$72$	1.26791	+	0.432816i	0.149424	+	0.0510078i
$73$	0.778603	−	1.34858i	0.0911286	−	0.157839i	−0.816858	−	0.576839i	$-0.804286\pi$
$73$	0.778603	−	1.34858i	0.0911286	−	0.157839i	0.907986	+	0.419000i	$0.137619\pi$
$74$	−7.18823	−	12.4504i	−0.835614	−	1.44733i
$75$	3.03063	+	8.07311i	0.349947	+	0.932202i
$76$	−7.66972	−	13.2843i	−0.879777	−	1.52382i
$77$		0			0
$78$	−0.249886	−	0.665657i	−0.0282940	−	0.0753708i
$79$	12.7957			1.43963			0.719817	−	0.694164i	$-0.244226\pi$
$79$	12.7957			1.43963			0.719817	+	0.694164i	$0.244226\pi$
$80$	0.257231	−	0.445537i	0.0287593	−	0.0498126i
$81$	7.12141	+	5.50323i	0.791267	+	0.611470i
$82$	−2.38008	−	4.12241i	−0.262835	−	0.455244i
$83$	−3.75687	+	6.50709i	−0.412370	+	0.714246i	−0.995148	−	0.0983854i	$-0.968632\pi$
$83$	−3.75687	+	6.50709i	−0.412370	+	0.714246i	0.582778	+	0.812631i	$0.301966\pi$
$84$		0			0
$85$	−0.458561	−	0.794251i	−0.0497379	−	0.0861486i
$86$	−1.93247	+	3.34713i	−0.208383	+	0.360930i
$87$	−5.42839	+	6.60299i	−0.581984	+	0.707915i
$88$	−0.371566	−	0.643571i	−0.0396090	−	0.0686048i
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	0.519155	−	0.854680i	$-0.326247\pi$
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	−0.999752	+	0.0222619i	$0.992913\pi$
$90$	−0.678430	+	0.592918i	−0.0715128	+	0.0624991i
$91$		0			0
$92$	6.85398	−	11.8714i	0.714577	−	1.23768i
$93$	4.30209	+	0.714056i	0.446106	+	0.0740442i
$94$	3.72074			0.383765
$95$	1.01167			0.103795
$96$	−13.8701	−	2.30214i	−1.41561	−	0.234962i
$97$	3.98514	−	6.90246i	0.404630	−	0.700839i	−0.589649	−	0.807660i	$-0.700734\pi$
$97$	3.98514	−	6.90246i	0.404630	−	0.700839i	0.994278	+	0.106821i	$0.0340671\pi$
$98$		0			0
$99$	−0.965543	−	4.89786i	−0.0970408	−	0.492253i
$100$	5.51993	+	9.56080i	0.551993	+	0.956080i
$101$	7.42150	+	12.8544i	0.738467	+	1.27906i	0.953186	+	0.302386i	$0.0977832\pi$
$101$	7.42150	+	12.8544i	0.738467	+	1.27906i	−0.214719	+	0.976676i	$0.568883\pi$
$102$	−14.1658	+	17.2310i	−1.40262	+	1.70612i
$103$	−0.101974	+	0.176624i	−0.0100478	+	0.0174033i	−0.871006	−	0.491273i	$-0.836532\pi$
$103$	−0.101974	+	0.176624i	−0.0100478	+	0.0174033i	0.860958	+	0.508676i	$0.169865\pi$
$104$	−0.0446339	−	0.0773081i	−0.00437671	−	0.00758068i
$105$		0			0
$106$	−5.48953	+	9.50815i	−0.533191	+	0.923513i
$107$	3.48444	+	6.03524i	0.336854	+	0.583448i	0.983839	−	0.179054i	$-0.0573038\pi$
$107$	3.48444	+	6.03524i	0.336854	+	0.583448i	−0.646985	+	0.762503i	$0.723970\pi$
$108$	10.1478	+	5.45759i	0.976468	+	0.525157i
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	−0.661270	−	0.750148i	$-0.729982\pi$
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	0.980282	+	0.197603i	$0.0633157\pi$
$110$	0.499772			0.0476514
$111$	−4.26138	−	11.3516i	−0.404472	−	1.07745i
$112$		0			0
$113$	−0.0193234	−	0.0334691i	−0.00181779	−	0.00314851i	0.865115	−	0.501573i	$-0.167245\pi$
$113$	−0.0193234	−	0.0334691i	−0.00181779	−	0.00314851i	−0.866933	+	0.498425i	$0.833912\pi$
$114$	−8.64776	−	23.0362i	−0.809937	−	2.15754i
$115$	0.452033	+	0.782945i	0.0421523	+	0.0730100i
$116$	−5.47174	+	9.47733i	−0.508038	+	0.879948i
$117$	−0.115985	−	0.588349i	−0.0107228	−	0.0543929i
$118$	9.38718			0.864160
$119$		0			0
$120$	−0.0718382	+	0.0873827i	−0.00655790	+	0.00797692i
$121$	4.11548	−	7.12823i	0.374135	−	0.648021i
$122$	1.39294			0.126111
$123$	−1.41098	−	3.75862i	−0.127223	−	0.338903i
$124$	5.58311			0.501378
$125$	−1.45933			−0.130526
$126$		0			0
$127$	13.4788			1.19605			0.598027	−	0.801476i	$-0.295952\pi$
$127$	13.4788			1.19605			0.598027	+	0.801476i	$0.295952\pi$
$128$	−3.55154			−0.313915
$129$	−2.07008	+	2.51801i	−0.182261	+	0.221698i
$130$	0.0600345			0.00526538
$131$	−9.91665	+	17.1761i	−0.866422	+	1.50069i	−0.000793988		1.00000i	$0.500253\pi$
$131$	−9.91665	+	17.1761i	−0.866422	+	1.50069i	−0.865628	+	0.500687i	$0.833081\pi$
$132$	−2.24617	−	5.98345i	−0.195504	−	0.520793i
$133$		0			0
$134$	−12.7056			−1.09759
$135$	−0.646348	+	0.399630i	−0.0556288	+	0.0343947i
$136$	−1.40028	+	2.42536i	−0.120073	+	0.207973i
$137$	3.22255	+	5.58162i	0.275321	+	0.476870i	0.970216	−	0.242241i	$-0.0778826\pi$
$137$	3.22255	+	5.58162i	0.275321	+	0.476870i	−0.694895	+	0.719111i	$0.744549\pi$
$138$	13.9641	−	16.9857i	1.18871	−	1.44592i
$139$	−6.26527	−	10.8518i	−0.531413	−	0.920435i	−0.999328	−	0.0366611i	$-0.988328\pi$
$139$	−6.26527	−	10.8518i	−0.531413	−	0.920435i	0.467914	−	0.883774i	$-0.345006\pi$
$140$		0			0
$141$	3.09573	+	0.513826i	0.260708	+	0.0432720i
$142$	2.62352			0.220161
$143$	−0.166313	+	0.288063i	−0.0139078	+	0.0240890i
$144$	−9.98750	−	3.40935i	−0.832292	−	0.284113i
$145$	−0.360872	−	0.625048i	−0.0299688	−	0.0519074i
$146$	1.59897	−	2.76950i	0.132332	−	0.229206i
$147$		0			0
$148$	−7.76161	−	13.4435i	−0.638000	−	1.10505i
$149$	−8.88364	+	15.3869i	−0.727776	+	1.26054i	0.230045	+	0.973180i	$0.426113\pi$
$149$	−8.88364	+	15.3869i	−0.727776	+	1.26054i	−0.957821	+	0.287365i	$0.907221\pi$
$150$	6.22383	+	16.5793i	0.508174	+	1.35369i
$151$	−4.23300	−	7.33177i	−0.344476	−	0.596651i	0.640782	−	0.767723i	$-0.278610\pi$
$151$	−4.23300	−	7.33177i	−0.344476	−	0.596651i	−0.985259	+	0.171072i	$0.945277\pi$
$152$	−1.54463	−	2.67538i	−0.125286	−	0.217002i
$153$	−14.1658	+	12.3803i	−1.14524	+	1.00089i
$154$		0			0
$155$	−0.184108	+	0.318885i	−0.0147879	+	0.0256135i
$156$	−0.269819	−	0.718755i	−0.0216028	−	0.0575464i
$157$	−5.69935			−0.454858			−0.227429	−	0.973795i	$-0.573032\pi$
$157$	−5.69935			−0.454858			−0.227429	+	0.973795i	$0.573032\pi$
$158$	26.2779			2.09056
$159$	−5.88046	+	7.15288i	−0.466351	+	0.567261i
$160$	0.593572	−	1.02810i	0.0469260	−	0.0812782i
$161$		0			0
$162$	14.6248	+	11.3017i	1.14904	+	0.887944i
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	0.821403	−	0.570349i	$-0.193192\pi$
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	−0.904638	+	0.426181i	$0.859859\pi$
$164$	−2.56993	−	4.45125i	−0.200678	−	0.347584i
$165$	0.415821	+	0.0690175i	0.0323716	+	0.00537300i
$166$	−7.71528	+	13.3632i	−0.598821	+	1.03719i
$167$	5.78723	+	10.0238i	0.447829	+	0.775663i	0.998244	−	0.0592278i	$-0.0188638\pi$
$167$	5.78723	+	10.0238i	0.447829	+	0.775663i	−0.550415	+	0.834891i	$0.685530\pi$
$168$		0			0
$169$	6.48002	−	11.2237i	0.498463	−	0.863364i
$170$	−0.941721	−	1.63111i	−0.0722267	−	0.125100i
$171$	−4.01386	−	20.3609i	−0.306947	−	1.55703i
$172$	−2.08661	+	3.61412i	−0.159103	+	0.275574i
$173$	15.9109			1.20968			0.604842	−	0.796345i	$-0.293236\pi$
$173$	15.9109			1.20968			0.604842	+	0.796345i	$0.293236\pi$
$174$	−11.1480	+	13.5602i	−0.845127	+	1.02800i
$175$		0			0
$176$	2.92688	+	5.06950i	0.220622	+	0.382128i
$177$	7.81033	+	1.29635i	0.587060	+	0.0974395i
$178$	−9.31110	−	16.1273i	−0.697897	−	1.20879i
$179$	3.87665	−	6.71456i	0.289755	−	0.501870i	−0.683996	−	0.729485i	$-0.739760\pi$
$179$	3.87665	−	6.71456i	0.289755	−	0.501870i	0.973751	+	0.227615i	$0.0730929\pi$
$180$	−0.732546	+	0.640214i	−0.0546008	+	0.0477187i
$181$	12.1618			0.903982			0.451991	−	0.892022i	$-0.350714\pi$
$181$	12.1618			0.903982			0.451991	+	0.892022i	$0.350714\pi$
$182$		0			0
$183$	1.15895	+	0.192362i	0.0856722	+	0.0142198i
$184$	1.38035	−	2.39084i	0.101761	−	0.176255i
$185$	1.02379			0.0752703
$186$	8.83497	+	1.46642i	0.647812	+	0.107523i
$187$	10.4354			0.763110
$188$	4.01754			0.293009
$189$		0			0
$190$	2.07760			0.150725
$191$	−4.96765			−0.359447			−0.179723	−	0.983717i	$-0.557520\pi$
$191$	−4.96765			−0.359447			−0.179723	+	0.983717i	$0.557520\pi$
$192$	−16.4628	−	2.73247i	−1.18810	−	0.197199i
$193$	−14.9044			−1.07284			−0.536422	−	0.843950i	$-0.680224\pi$
$193$	−14.9044			−1.07284			−0.536422	+	0.843950i	$0.680224\pi$
$194$	8.18406	−	14.1752i	0.587581	−	1.01772i
$195$	0.0499500	+	0.00829064i	0.00357699	+	0.000593705i
$196$		0			0
$197$	−21.2608			−1.51477			−0.757386	−	0.652968i	$-0.773524\pi$
$197$	−21.2608			−1.51477			−0.757386	+	0.652968i	$0.773524\pi$
$198$	−1.98288	−	10.0585i	−0.140917	−	0.714824i
$199$	9.97208	−	17.2722i	0.706902	−	1.22439i	−0.259098	−	0.965851i	$-0.583425\pi$
$199$	9.97208	−	17.2722i	0.706902	−	1.22439i	0.966001	−	0.258540i	$-0.0832413\pi$
$200$	1.11168	+	1.92549i	0.0786077	+	0.136152i
$201$	−10.5713	−	1.75461i	−0.745641	−	0.123761i
$202$	15.2411	+	26.3984i	1.07236	+	1.85739i
$203$		0			0
$204$	−15.2957	+	18.6055i	−1.07092	+	1.30264i
$205$	0.338983			0.0236756
$206$	−0.209419	+	0.362724i	−0.0145909	+	0.0252722i
$207$	13.9641	−	12.2040i	0.970574	−	0.848240i
$208$	0.351587	+	0.608967i	0.0243782	+	0.0422243i
$209$	−5.75556	+	9.96893i	−0.398121	+	0.689565i
$210$		0			0
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	0.913293	+	0.407303i	$0.133531\pi$
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	−0.103912	+	0.994587i	$0.533136\pi$
$212$	−5.92742	+	10.2666i	−0.407097	+	0.705112i
$213$	2.18282	+	0.362302i	0.149564	+	0.0248245i
$214$	7.15581	+	12.3942i	0.489161	+	0.847252i
$215$	−0.137616	−	0.238358i	−0.00938535	−	0.0162559i
$216$	2.04370	+	1.09912i	0.139056	+	0.0747860i
$217$		0			0
$218$	6.83983	−	11.8469i	0.463252	−	0.802376i
$219$	1.71284	−	2.08347i	0.115743	−	0.140788i
$220$	0.539638			0.0363824
$221$	1.25354			0.0843220
$222$	−8.75137	−	23.3122i	−0.587353	−	1.56462i
$223$	−2.03052	+	3.51696i	−0.135974	+	0.235513i	−0.925969	−	0.377600i	$-0.876750\pi$
$223$	−2.03052	+	3.51696i	−0.135974	+	0.235513i	0.789995	+	0.613113i	$0.210083\pi$
$224$		0			0
$225$	2.88879	+	14.6538i	0.192586	+	0.976921i
$226$	−0.0396834	−	0.0687336i	−0.00263970	−	0.00457209i
$227$	−1.92643	−	3.33667i	−0.127861	−	0.221462i	0.794986	−	0.606627i	$-0.207478\pi$
$227$	−1.92643	−	3.33667i	−0.127861	−	0.221462i	−0.922848	+	0.385165i	$0.874145\pi$
$228$	−9.33756	−	24.8738i	−0.618395	−	1.64731i
$229$	6.55812	−	11.3590i	0.433373	−	0.750624i	−0.563788	−	0.825919i	$-0.690657\pi$
$229$	6.55812	−	11.3590i	0.433373	−	0.750624i	0.997161	+	0.0752952i	$0.0239899\pi$
$230$	0.928316	+	1.60789i	0.0612113	+	0.106021i
$231$		0			0
$232$	−1.10197	+	1.90868i	−0.0723481	+	0.125311i
$233$	−8.75115	−	15.1574i	−0.573307	−	0.992997i	−0.996223	−	0.0868284i	$-0.972327\pi$
$233$	−8.75115	−	15.1574i	−0.573307	−	0.992997i	0.422916	−	0.906169i	$-0.361007\pi$
$234$	−0.238191	−	1.20826i	−0.0155711	−	0.0789864i
$235$	−0.132482	+	0.229466i	−0.00864218	+	0.0149687i
$236$	10.1360			0.659795
$237$	21.8638	+	3.62892i	1.42020	+	0.235724i
$238$		0			0
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	0.959752	−	0.280849i	$-0.0906161\pi$
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	−0.723099	+	0.690745i	$0.757283\pi$
$240$	0.565880	−	0.688327i	0.0365274	−	0.0444313i
$241$	3.11553	+	5.39626i	0.200689	+	0.347604i	0.948751	−	0.316026i	$-0.102349\pi$
$241$	3.11553	+	5.39626i	0.200689	+	0.347604i	−0.748062	+	0.663629i	$0.769015\pi$
$242$	8.45174	−	14.6389i	0.543299	−	0.941021i
$243$	10.6074	+	11.4229i	0.680467	+	0.732779i
$244$	1.50405			0.0962868
$245$		0			0
$246$	−2.89764	−	7.71886i	−0.184747	−	0.492137i
$247$	−0.691380	+	1.19751i	−0.0439915	+	0.0761954i
$248$	1.12440			0.0713997
$249$	−8.26470	+	10.0530i	−0.523754	+	0.637085i
$250$	−2.99694			−0.189543
$251$	−5.65283			−0.356803			−0.178402	−	0.983958i	$-0.557093\pi$
$251$	−5.65283			−0.356803			−0.178402	+	0.983958i	$0.557093\pi$
$252$		0			0
$253$	−10.2868			−0.646727
$254$	27.6808			1.73684
$255$	−0.558279	−	1.48717i	−0.0349608	−	0.0931299i
$256$	11.9760			0.748501
$257$	5.90082	−	10.2205i	0.368083	−	0.637539i	−0.621183	−	0.783666i	$-0.713347\pi$
$257$	5.90082	−	10.2205i	0.368083	−	0.637539i	0.989266	+	0.146127i	$0.0466808\pi$
$258$	−4.25121	+	5.17110i	−0.264669	+	0.321939i
$259$		0			0
$260$	0.0648233			0.00402017
$261$	−11.1480	+	9.74286i	−0.690043	+	0.603068i
$262$	−20.3653	+	35.2737i	−1.25817	+	2.17922i
$263$	11.1200	+	19.2605i	0.685691	+	1.18765i	0.973219	+	0.229879i	$0.0738331\pi$
$263$	11.1200	+	19.2605i	0.685691	+	1.18765i	−0.287528	+	0.957772i	$0.592834\pi$
$264$	−0.452366	−	1.20503i	−0.0278412	−	0.0741645i
$265$	−0.390925	−	0.677101i	−0.0240143	−	0.0415940i
$266$		0			0
$267$	−5.51988	−	14.7041i	−0.337811	−	0.899876i
$268$	−13.7191			−0.838024
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	−0.827313	−	0.561741i	$-0.810132\pi$
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	0.900138	+	0.435604i	$0.143465\pi$
$270$	−1.32737	+	0.820699i	−0.0807811	+	0.0499462i
$271$	11.6129	+	20.1142i	0.705435	+	1.22185i	0.966534	+	0.256537i	$0.0825815\pi$
$271$	11.6129	+	20.1142i	0.705435	+	1.22185i	−0.261100	+	0.965312i	$0.584085\pi$
$272$	11.0302	−	19.1049i	0.668806	−	1.15841i
$273$		0			0
$274$	6.61797	+	11.4627i	0.399806	+	0.692484i
$275$	4.14231	−	7.17469i	0.249790	−	0.432650i
$276$	15.0780	−	18.3406i	0.907590	−	1.10398i
$277$	2.30900	+	3.99931i	0.138734	+	0.240295i	0.927018	−	0.375017i	$-0.122363\pi$
$277$	2.30900	+	3.99931i	0.138734	+	0.240295i	−0.788283	+	0.615312i	$0.789030\pi$
$278$	−12.8666	−	22.2857i	−0.771690	−	1.33661i
$279$	7.14837	+	2.44018i	0.427962	+	0.146090i
$280$		0			0
$281$	5.90841	−	10.2337i	0.352466	−	0.610489i	−0.634215	−	0.773157i	$-0.718676\pi$
$281$	5.90841	−	10.2337i	0.352466	−	0.610489i	0.986681	+	0.162668i	$0.0520098\pi$
$282$	6.35754	+	1.05522i	0.378586	+	0.0628372i
$283$	−15.8497			−0.942165			−0.471082	−	0.882089i	$-0.656137\pi$
$283$	−15.8497			−0.942165			−0.471082	+	0.882089i	$0.656137\pi$
$284$	2.83279			0.168095
$285$	1.72861	+	0.286912i	0.102394	+	0.0169952i
$286$	−0.341548	+	0.591579i	−0.0201962	+	0.0349808i
$287$		0			0
$288$	−23.0466	−	7.86723i	−1.35803	−	0.463581i
$289$	−11.1634	−	19.3355i	−0.656669	−	1.13738i
$290$	−0.741102	−	1.28363i	−0.0435190	−	0.0753772i
$291$	8.76687	−	10.6639i	0.513923	−	0.625127i
$292$	1.72652	−	2.99042i	0.101037	−	0.175001i
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	0.583330	−	0.812235i	$-0.301749\pi$
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	−0.995081	+	0.0990615i	$0.968416\pi$
$294$		0			0
$295$	−0.334243	+	0.578927i	−0.0194604	+	0.0337064i
$296$	−1.56314	−	2.70744i	−0.0908557	−	0.157367i
$297$	−0.260748	−	8.64268i	−0.0151302	−	0.501499i
$298$	−18.2438	+	31.5993i	−1.05684	+	1.83050i
$299$	−1.23569			−0.0714619
$300$	6.72029	+	17.9018i	0.387996	+	1.03356i
$301$		0			0
$302$	−8.69307	−	15.0568i	−0.500230	−	0.866424i
$303$	9.03537	+	24.0688i	0.519068	+	1.38272i
$304$	12.1673	+	21.0744i	0.697843	+	1.20870i
$305$	−0.0495974	+	0.0859053i	−0.00283994	+	0.00491892i
$306$	−29.0915	+	25.4247i	−1.66305	+	1.45343i
$307$	−27.3916			−1.56332			−0.781660	−	0.623704i	$-0.785627\pi$
$307$	−27.3916			−1.56332			−0.781660	+	0.623704i	$0.785627\pi$
$308$		0			0
$309$	−0.224332	+	0.272873i	−0.0127618	+	0.0155232i
$310$	−0.378093	+	0.654877i	−0.0214742	+	0.0371945i
$311$	14.0557			0.797026			0.398513	−	0.917163i	$-0.369526\pi$
$311$	14.0557			0.797026			0.398513	+	0.917163i	$0.369526\pi$
$312$	−0.0543399	−	0.144753i	−0.00307639	−	0.00819501i
$313$	−21.7446			−1.22908			−0.614540	−	0.788886i	$-0.710658\pi$
$313$	−21.7446			−1.22908			−0.614540	+	0.788886i	$0.710658\pi$
$314$	−11.7045			−0.660520
$315$		0			0
$316$	28.3740			1.59616
$317$	8.56297			0.480944			0.240472	−	0.970656i	$-0.422698\pi$
$317$	8.56297			0.480944			0.240472	+	0.970656i	$0.422698\pi$
$318$	−12.0764	+	14.6895i	−0.677209	+	0.823745i
$319$	8.21228			0.459799
$320$	0.704524	−	1.22027i	0.0393841	−	0.0682153i
$321$	4.24217	+	11.3005i	0.236775	+	0.630730i
$322$		0			0
$323$	43.3808			2.41377
$324$	15.7914	+	12.2032i	0.877301	+	0.677955i
$325$	0.497589	−	0.861850i	0.0276013	−	0.0478068i
$326$	−2.18235	−	3.77995i	−0.120869	−	0.209352i
$327$	7.32692	−	8.91233i	0.405179	−	0.492853i
$328$	−0.517568	−	0.896453i	−0.0285779	−	0.0494984i
$329$		0			0
$330$	0.853949	+	0.141737i	0.0470083	+	0.00780239i
$331$	10.8472			0.596216			0.298108	−	0.954532i	$-0.403644\pi$
$331$	10.8472			0.596216			0.298108	+	0.954532i	$0.403644\pi$
$332$	−8.33070	+	14.4292i	−0.457207	+	0.791905i
$333$	−4.06195	−	20.6048i	−0.222593	−	1.12914i
$334$	11.8849	+	20.5853i	0.650314	+	1.12638i
$335$	0.452399	−	0.783578i	0.0247172	−	0.0428114i
$336$		0			0
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	0.908014	−	0.418940i	$-0.137598\pi$
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	−0.816819	+	0.576893i	$0.804265\pi$
$338$	13.3077	−	23.0496i	0.723842	−	1.25373i
$339$	−0.0235254	−	0.0626679i	−0.00127772	−	0.00340365i
$340$	−1.01684	−	1.76122i	−0.0551459	−	0.0955154i
$341$	−2.09486	−	3.62840i	−0.113443	−	0.196489i
$342$	−8.24304	−	41.8140i	−0.445732	−	2.26104i
$343$		0			0
$344$	−0.420231	+	0.727861i	−0.0226573	+	0.0392437i
$345$	0.550332	+	1.46600i	0.0296289	+	0.0789266i
$346$	32.6754			1.75664
$347$	−11.5330			−0.619126			−0.309563	−	0.950879i	$-0.600183\pi$
$347$	−11.5330			−0.619126			−0.309563	+	0.950879i	$0.600183\pi$
$348$	−12.0372	+	14.6419i	−0.645263	+	0.784886i
$349$	4.44917	−	7.70619i	0.238159	−	0.412503i	−0.722027	−	0.691865i	$-0.756789\pi$
$349$	4.44917	−	7.70619i	0.238159	−	0.412503i	0.960186	+	0.279362i	$0.0901228\pi$
$350$		0			0
$351$	−0.0313221	−	1.03819i	−0.00167185	−	0.0554145i
$352$	6.75390	+	11.6981i	0.359984	+	0.623511i
$353$	−1.32349	−	2.29236i	−0.0704424	−	0.122010i	0.828653	−	0.559763i	$-0.189108\pi$
$353$	−1.32349	−	2.29236i	−0.0704424	−	0.122010i	−0.899095	+	0.437753i	$0.855774\pi$
$354$	16.0396	+	2.66224i	0.852497	+	0.141496i
$355$	−0.0934139	+	0.161798i	−0.00495790	+	0.00858733i
$356$	−10.0538	−	17.4137i	−0.532852	−	0.922926i
$357$		0			0
$358$	7.96127	−	13.7893i	0.420766	−	0.728789i
$359$	−12.9835	−	22.4882i	−0.685245	−	1.18688i	−0.973360	−	0.229284i	$-0.926362\pi$
$359$	−12.9835	−	22.4882i	−0.685245	−	1.18688i	0.288114	−	0.957596i	$-0.406972\pi$
$360$	−0.147530	+	0.128935i	−0.00777553	+	0.00679547i
$361$	−14.4264	+	24.9873i	−0.759286	+	1.31512i
$362$	24.9761			1.31271
$363$	9.05362	−	11.0127i	0.475192	−	0.578014i
$364$		0			0
$365$	0.113867	+	0.197224i	0.00596009	+	0.0103232i
$366$	2.38008	+	0.395042i	0.124409	+	0.0206492i
$367$	8.79371	+	15.2312i	0.459028	+	0.795060i	0.998910	−	0.0466808i	$-0.0148644\pi$
$367$	8.79371	+	15.2312i	0.459028	+	0.795060i	−0.539882	+	0.841741i	$0.681531\pi$
$368$	−10.8732	+	18.8330i	−0.566806	+	0.981736i
$369$	−1.34494	−	6.82241i	−0.0700148	−	0.355160i
$370$	2.10249			0.109303
$371$		0			0
$372$	9.53971	+	1.58339i	0.494611	+	0.0820950i
$373$	−0.407538	+	0.705876i	−0.0211015	+	0.0365489i	−0.876383	−	0.481614i	$-0.840051\pi$
$373$	−0.407538	+	0.705876i	−0.0211015	+	0.0365489i	0.855282	+	0.518163i	$0.173384\pi$
$374$	21.4306			1.10815
$375$	−2.49352	−	0.413871i	−0.128765	−	0.0213722i
$376$	0.809107			0.0417265
$377$	0.986490			0.0508068
$378$		0			0
$379$	−20.4312			−1.04948			−0.524741	−	0.851262i	$-0.675838\pi$
$379$	−20.4312			−1.04948			−0.524741	+	0.851262i	$0.675838\pi$
$380$	2.24333			0.115080
$381$	23.0310	+	3.82265i	1.17991	+	0.195840i
$382$	−10.2018			−0.521969
$383$	8.94638	−	15.4956i	0.457139	−	0.791788i	−0.541670	−	0.840591i	$-0.682208\pi$
$383$	8.94638	−	15.4956i	0.457139	−	0.791788i	0.998808	+	0.0488039i	$0.0155409\pi$
$384$	−6.06843	−	1.00723i	−0.309678	−	0.0514000i
$385$		0			0
$386$	−30.6084			−1.55793
$387$	−4.25121	+	3.71538i	−0.216101	+	0.188863i
$388$	8.83688	−	15.3059i	0.448625	−	0.777041i
$389$	−7.81392	−	13.5341i	−0.396181	−	0.686206i	0.597070	−	0.802189i	$-0.296331\pi$
$389$	−7.81392	−	13.5341i	−0.396181	−	0.686206i	−0.993251	+	0.115983i	$0.962998\pi$
$390$	0.102580	+	0.0170260i	0.00519431	+	0.000862146i
$391$	19.3835	+	33.5731i	0.980264	+	1.69787i
$392$		0			0
$393$	−21.8156	+	26.5360i	−1.10045	+	1.33857i
$394$	−43.6622			−2.19967
$395$	−0.935661	+	1.62061i	−0.0470782	+	0.0815419i
$396$	−2.14105	−	10.8608i	−0.107592	−	0.545776i
$397$	−9.63064	−	16.6808i	−0.483348	−	0.837183i	0.516469	−	0.856306i	$-0.327246\pi$
$397$	−9.63064	−	16.6808i	−0.483348	−	0.837183i	−0.999817	+	0.0191225i	$0.993913\pi$
$398$	20.4791	−	35.4709i	1.02653	−	1.77799i
$399$		0			0
$400$	−8.75687	−	15.1673i	−0.437843	−	0.758367i
$401$	−7.15064	+	12.3853i	−0.357086	+	0.618491i	−0.987473	−	0.157790i	$-0.949563\pi$
$401$	−7.15064	+	12.3853i	−0.357086	+	0.618491i	0.630387	+	0.776281i	$0.282896\pi$
$402$	−21.7097	−	3.60335i	−1.08278	−	0.179719i
$403$	−0.251642	−	0.435857i	−0.0125352	−	0.0217116i
$404$	16.4569	+	28.5041i	0.818760	+	1.41813i
$405$	−1.21774	+	0.499532i	−0.0605098	+	0.0248219i
$406$		0			0
$407$	−5.82452	+	10.0884i	−0.288711	+	0.500062i
$408$	−3.08047	+	3.74703i	−0.152506	+	0.185505i
$409$	−31.8610			−1.57542			−0.787712	−	0.616044i	$-0.788734\pi$
$409$	−31.8610			−1.57542			−0.787712	+	0.616044i	$0.788734\pi$
$410$	0.696152			0.0343805
$411$	3.92332	+	10.4511i	0.193523	+	0.515514i
$412$	−0.226124	+	0.391657i	−0.0111403	+	0.0192956i
$413$		0			0
$414$	28.6774	−	25.0628i	1.40942	−	1.23177i
$415$	−0.549426	−	0.951633i	−0.0269702	−	0.0467138i
$416$	0.811304	+	1.40522i	0.0397774	+	0.0688965i
$417$	−7.62771	−	20.3190i	−0.373530	−	0.995025i
$418$	−11.8199	+	20.4726i	−0.578130	+	1.00135i
$419$	−11.9480	−	20.6945i	−0.583697	−	1.01099i	−0.995036	−	0.0995110i	$-0.968272\pi$
$419$	−11.9480	−	20.6945i	−0.583697	−	1.01099i	0.411339	−	0.911482i	$-0.365061\pi$
$420$		0			0
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	−0.894278	−	0.447513i	$-0.852310\pi$
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	0.834696	+	0.550711i	$0.185643\pi$
$422$	24.1446	+	41.8197i	1.17534	+	2.03575i
$423$	5.14388	+	1.75592i	0.250104	+	0.0853759i
$424$	−1.19375	+	2.06763i	−0.0579734	+	0.100413i
$425$	−31.2214			−1.51446
$426$	4.48274	+	0.744039i	0.217189	+	0.0360488i
$427$		0			0
$428$	7.72661	+	13.3829i	0.373480	+	0.646886i
$429$	−0.365871	+	0.445039i	−0.0176644	+	0.0214867i
$430$	−0.282615	−	0.489503i	−0.0136289	−	0.0236059i
$431$	2.46382	−	4.26746i	0.118678	−	0.205556i	−0.800566	−	0.599244i	$-0.795468\pi$
$431$	2.46382	−	4.26746i	0.118678	−	0.205556i	0.919244	+	0.393688i	$0.128801\pi$
$432$	−16.0985	−	8.65797i	−0.774539	−	0.416557i
$433$	−30.8539			−1.48274			−0.741371	−	0.671095i	$-0.765824\pi$
$433$	−30.8539			−1.48274			−0.741371	+	0.671095i	$0.765824\pi$
$434$		0			0
$435$	−0.439346	−	1.17035i	−0.0210650	−	0.0561139i
$436$	7.38543	−	12.7919i	0.353698	−	0.612622i
$437$	−42.7633			−2.04565
$438$	3.51757	−	4.27871i	0.168076	−	0.204444i
$439$	−2.44822			−0.116847			−0.0584235	−	0.998292i	$-0.518607\pi$
$439$	−2.44822			−0.116847			−0.0584235	+	0.998292i	$0.518607\pi$
$440$	0.108680			0.00518110
$441$		0			0
$442$	2.57432			0.122448
$443$	−26.2950			−1.24931			−0.624657	−	0.780899i	$-0.714761\pi$
$443$	−26.2950			−1.24931			−0.624657	+	0.780899i	$0.714761\pi$
$444$	−9.44944	−	25.1718i	−0.448450	−	1.19460i
$445$	1.32614			0.0628650
$446$	−4.16996	+	7.22259i	−0.197453	+	0.341999i
$447$	−19.5430	+	23.7718i	−0.924354	+	1.12437i
$448$		0			0
$449$	−38.7077			−1.82673			−0.913365	−	0.407141i	$-0.866526\pi$
$449$	−38.7077			−1.82673			−0.913365	+	0.407141i	$0.866526\pi$
$450$	5.93255	+	30.0937i	0.279663	+	1.41863i
$451$	−1.92854	+	3.34034i	−0.0908116	+	0.157290i
$452$	−0.0428488	−	0.0742163i	−0.00201544	−	0.00349084i
$453$	−5.15350	−	13.7281i	−0.242132	−	0.645002i
$454$	−3.95620	−	6.85233i	−0.185673	−	0.321596i
$455$		0			0
$456$	−1.88053	−	5.00943i	−0.0880638	−	0.234588i
$457$	−9.15511			−0.428258			−0.214129	−	0.976805i	$-0.568691\pi$
$457$	−9.15511			−0.428258			−0.214129	+	0.976805i	$0.568691\pi$
$458$	13.4681	−	23.3274i	0.629321	−	1.09002i
$459$	−27.7158	+	17.1364i	−1.29366	+	0.799859i
$460$	1.00237	+	1.73615i	0.0467355	+	0.0809483i
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	0.294070	+	0.955784i	$0.404990\pi$
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	−0.974768	+	0.223220i	$0.928343\pi$
$462$		0			0
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	0.609721	−	0.792616i	$-0.291282\pi$
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	−0.991286	+	0.131726i	$0.957948\pi$
$464$	8.68041	−	15.0349i	0.402978	−	0.697978i
$465$	−0.405018	+	0.492657i	−0.0187823	+	0.0228464i
$466$	−17.9718	−	31.1280i	−0.832526	−	1.44198i
$467$	−7.68632	−	13.3131i	−0.355680	−	0.616057i	0.631554	−	0.775332i	$-0.282418\pi$
$467$	−7.68632	−	13.3131i	−0.355680	−	0.616057i	−0.987234	+	0.159276i	$0.949084\pi$
$468$	−0.257191	−	1.30464i	−0.0118887	−	0.0603070i
$469$		0			0
$470$	−0.272071	+	0.471241i	−0.0125497	+	0.0217367i
$471$	−9.73834	−	1.61636i	−0.448719	−	0.0744779i
$472$	2.04132			0.0939594
$473$	3.13170			0.143996
$474$	44.9004	+	7.45252i	2.06234	+	0.342305i
$475$	17.2200	−	29.8259i	0.790106	−	1.36850i
$476$		0			0
$477$	−12.0764	+	10.5542i	−0.552939	+	0.483245i
$478$	7.51341	+	13.0136i	0.343655	+	0.595228i
$479$	−18.9646	−	32.8476i	−0.866513	−	1.50084i	−0.865537	−	0.500844i	$-0.833023\pi$
$479$	−18.9646	−	32.8476i	−0.866513	−	1.50084i	−0.000975329	−	1.00000i	$-0.500310\pi$
$480$	1.30579	−	1.58834i	0.0596011	−	0.0724977i
$481$	−0.699663	+	1.21185i	−0.0319019	+	0.0552557i
$482$	6.39820	+	11.0820i	0.291430	+	0.504772i
$483$		0			0
$484$	9.12591	−	15.8065i	0.414814	−	0.718479i
$485$	0.582809	+	1.00946i	0.0264640	+	0.0458370i
$486$	21.7839	+	23.4586i	0.988137	+	1.06410i
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	−0.809131	−	0.587628i	$-0.800062\pi$
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	0.913466	+	0.406914i	$0.133395\pi$
$488$	0.302906			0.0137119
$489$	−1.29376	−	3.44637i	−0.0585058	−	0.155850i
$490$		0			0
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	−0.973309	−	0.229497i	$-0.926292\pi$
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	0.287904	−	0.957659i	$-0.407042\pi$
$492$	−3.12878	−	8.33457i	−0.141056	−	0.375752i
$493$	−15.4744	−	26.8024i	−0.696932	−	1.20712i
$494$	−1.41985	+	2.45925i	−0.0638820	+	0.110647i
$495$	0.690929	+	0.235857i	0.0310549	+	0.0106010i
$496$	−8.85709			−0.397695
$497$		0			0
$498$	−16.9728	+	20.6454i	−0.760568	+	0.925141i
$499$	−4.63436	+	8.02694i	−0.207462	+	0.359335i	−0.950914	−	0.309454i	$-0.899854\pi$
$499$	−4.63436	+	8.02694i	−0.207462	+	0.359335i	0.743452	+	0.668789i	$0.233187\pi$
$500$	−3.23600			−0.144718
$501$	7.04571	+	18.7687i	0.314779	+	0.838522i
$502$	−11.6089			−0.518131
$503$	22.4230			0.999791			0.499896	−	0.866086i	$-0.333372\pi$
$503$	22.4230			0.999791			0.499896	+	0.866086i	$0.333372\pi$
$504$		0			0
$505$	−2.17072			−0.0965960
$506$	−21.1255			−0.939143
$507$	14.2553	−	17.3399i	0.633102	−	0.770094i
$508$	29.8888			1.32610
$509$	−18.8207	+	32.5984i	−0.834213	+	1.44490i	0.0604572	+	0.998171i	$0.480744\pi$
$509$	−18.8207	+	32.5984i	−0.834213	+	1.44490i	−0.894670	+	0.446728i	$0.852589\pi$
$510$	−1.14651	−	3.05411i	−0.0507682	−	0.135238i
$511$		0			0
$512$	31.6976			1.40085
$513$	−1.08396	−	35.9284i	−0.0478578	−	1.58628i
$514$	12.1182	−	20.9893i	0.534511	−	0.925800i
$515$	−0.0149133	−	0.0258306i	−0.000657158	−	0.00113823i
$516$	−4.59032	+	5.58358i	−0.202078	+	0.245804i
$517$	−1.50743	−	2.61095i	−0.0662969	−	0.114830i
$518$		0			0
$519$	27.1866	+	4.51240i	1.19336	+	0.198072i
$520$	0.0130550			0.000572500
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	0.175067	+	0.984556i	$0.443986\pi$
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	−0.940185	+	0.340666i	$0.889348\pi$
$522$	−22.8940	+	20.0084i	−1.00204	+	0.875743i
$523$	11.8735	+	20.5656i	0.519194	+	0.899270i	0.999751	+	0.0223069i	$0.00710109\pi$
$523$	11.8735	+	20.5656i	0.519194	+	0.899270i	−0.480557	+	0.876963i	$0.659566\pi$
$524$	−21.9898	+	38.0874i	−0.960628	+	1.66386i
$525$		0			0
$526$	22.8366	+	39.5542i	0.995723	+	1.72464i
$527$	−7.89468	+	13.6740i	−0.343898	+	0.595648i
$528$	3.56335	+	9.49220i	0.155075	+	0.413095i
$529$	−7.60755	−	13.1767i	−0.330763	−	0.572898i
$530$	−0.802820	−	1.39053i	−0.0348723	−	0.0604006i
$531$	12.9777	+	4.43008i	0.563182	+	0.192249i
$532$		0			0
$533$	−0.231664	+	0.401254i	−0.0100345	+	0.0173802i
$534$	−11.3359	−	30.1970i	−0.490552	−	1.30675i
$535$	−1.01917			−0.0440626
$536$	−2.76293			−0.119340
$537$	8.52822	−	10.3736i	0.368020	−	0.447652i
$538$	2.45292	−	4.24857i	0.105753	−	0.183169i
$539$		0			0
$540$	−1.43325	+	0.886164i	−0.0616773	+	0.0381344i
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	0.989428	−	0.145028i	$-0.0463271\pi$
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	−0.620311	+	0.784356i	$0.712994\pi$
$542$	23.8488	+	41.3074i	1.02439	+	1.77430i
$543$	20.7806	+	3.44914i	0.891782	+	0.148017i
$544$	25.4527	−	44.0854i	1.09128	−	1.89015i
$545$	0.487083	+	0.843653i	0.0208643	+	0.0361381i
$546$		0			0
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	−0.996674	−	0.0814901i	$-0.974032\pi$
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	0.568910	+	0.822400i	$0.307365\pi$
$548$	7.14586	+	12.3770i	0.305256	+	0.528719i
$549$	1.92572	+	0.657366i	0.0821876	+	0.0280557i
$550$	8.50683	−	14.7343i	0.362732	−	0.628271i
$551$	34.1392			1.45438
$552$	3.03662	−	3.69369i	0.129247	−	0.157214i
$553$		0			0
$554$	4.74187	+	8.21316i	0.201463	+	0.348944i
$555$	1.74932	+	0.290350i	0.0742544	+	0.0123247i
$556$	−13.8930	−	24.0633i	−0.589193	−	1.02051i
$557$	−0.122740	+	0.212593i	−0.00520068	+	0.00900784i	−0.868614	−	0.495489i	$-0.834989\pi$
$557$	−0.122740	+	0.212593i	−0.00520068	+	0.00900784i	0.863413	+	0.504497i	$0.168322\pi$
$558$	14.6802	+	5.01126i	0.621463	+	0.212144i
$559$	0.376192			0.0159112
$560$		0			0
$561$	17.8307	+	2.95951i	0.752811	+	0.124951i
$562$	12.1338	−	21.0163i	0.511833	−	0.886520i
$563$	44.2509			1.86495			0.932477	−	0.361230i	$-0.117643\pi$
$563$	44.2509			1.86495			0.932477	+	0.361230i	$0.117643\pi$
$564$	6.86466	+	1.13939i	0.289054	+	0.0479769i
$565$	0.00565192			0.000237778
$566$	−32.5496			−1.36816
$567$		0			0
$568$	0.570506			0.0239379
$569$	−5.53533			−0.232053			−0.116027	−	0.993246i	$-0.537016\pi$
$569$	−5.53533			−0.232053			−0.116027	+	0.993246i	$0.537016\pi$
$570$	3.54995	+	0.589216i	0.148691	+	0.0246795i
$571$	−4.10381			−0.171739			−0.0858696	−	0.996306i	$-0.527367\pi$
$571$	−4.10381			−0.171739			−0.0858696	+	0.996306i	$0.527367\pi$
$572$	−0.368793	+	0.638768i	−0.0154200	+	0.0267082i
$573$	−8.48810	−	1.40884i	−0.354595	−	0.0588553i
$574$		0			0
$575$	30.7770			1.28349
$576$	−27.3545	−	9.33780i	−1.13977	−	0.389075i
$577$	2.82275	−	4.88915i	0.117513	−	0.203538i	−0.801269	−	0.598305i	$-0.795841\pi$
$577$	2.82275	−	4.88915i	0.117513	−	0.203538i	0.918781	+	0.394767i	$0.129175\pi$
$578$	−22.9256	−	39.7083i	−0.953579	−	1.65165i
$579$	−25.4668	−	4.22695i	−1.05836	−	0.175666i
$580$	−0.800218	−	1.38602i	−0.0332272	−	0.0575513i
$581$		0			0
$582$	18.0040	−	21.8998i	0.746292	−	0.907776i
$583$	8.89619			0.368442
$584$	0.347710	−	0.602252i	0.0143884	−	0.0249214i
$585$	0.0829970	+	0.0283320i	0.00343150	+	0.00117138i
$586$	−14.4742	−	25.0700i	−0.597923	−	1.03563i
$587$	−9.36644	+	16.2232i	−0.386595	+	0.669601i	−0.991989	−	0.126324i	$-0.959682\pi$
$587$	−9.36644	+	16.2232i	−0.386595	+	0.669601i	0.605394	+	0.795926i	$0.293015\pi$
$588$		0			0
$589$	−8.70852	−	15.0836i	−0.358828	−	0.621509i
$590$	−0.686417	+	1.18891i	−0.0282594	+	0.0489466i
$591$	−36.3278	−	6.02965i	−1.49433	−	0.248027i
$592$	12.3131	+	21.3269i	0.506065	+	0.876530i
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	0.992107	−	0.125398i	$-0.0400207\pi$
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	−0.604651	+	0.796491i	$0.706687\pi$
$594$	−0.535484	−	17.7490i	−0.0219712	−	0.728250i
$595$		0			0
$596$	−19.6991	+	34.1198i	−0.806906	+	1.39760i
$597$	21.9375	−	26.6844i	0.897842	−	1.09212i
$598$	−2.53767			−0.103773
$599$	2.67451			0.109278			0.0546388	−	0.998506i	$-0.482599\pi$
$599$	2.67451			0.109278			0.0546388	+	0.998506i	$0.482599\pi$
$600$	1.35342	+	3.60531i	0.0552533	+	0.147186i
$601$	6.60716	−	11.4439i	0.269511	−	0.466808i	−0.699224	−	0.714902i	$-0.746471\pi$
$601$	6.60716	−	11.4439i	0.269511	−	0.466808i	0.968736	+	0.248095i	$0.0798044\pi$
$602$		0			0
$603$	−17.5653	−	5.99612i	−0.715313	−	0.244181i
$604$	−9.38650	−	16.2579i	−0.381931	−	0.661524i
$605$	0.601872	+	1.04247i	0.0244696	+	0.0423825i
$606$	18.5554	+	49.4287i	0.753763	+	2.00790i
$607$	12.9026	−	22.3480i	0.523701	−	0.907076i	−0.475919	−	0.879489i	$-0.657884\pi$
$607$	12.9026	−	22.3480i	0.523701	−	0.907076i	0.999619	−	0.0275869i	$-0.00878231\pi$
$608$	28.0766	+	48.6301i	1.13866	+	1.97221i
$609$		0			0
$610$	−0.101856	+	0.176419i	−0.00412401	+	0.00714299i
$611$	−0.181079	−	0.313637i	−0.00732565	−	0.0126884i
$612$	−31.4120	+	27.4528i	−1.26976	+	1.10971i
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	−0.454333	−	0.890832i	$-0.650122\pi$
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	0.998650	−	0.0519519i	$-0.0165443\pi$
$614$	−56.2526			−2.27017
$615$	0.579212	+	0.0961370i	0.0233561	+	0.00387662i
$616$		0			0
$617$	−4.76588	−	8.25474i	−0.191867	−	0.332323i	0.754002	−	0.656872i	$-0.228121\pi$
$617$	−4.76588	−	8.25474i	−0.191867	−	0.332323i	−0.945869	+	0.324549i	$0.894788\pi$
$618$	−0.460698	+	0.560385i	−0.0185320	+	0.0225420i
$619$	17.3536	+	30.0573i	0.697499	+	1.20810i	0.969331	+	0.245759i	$0.0790371\pi$
$619$	17.3536	+	30.0573i	0.697499	+	1.20810i	−0.271832	+	0.962345i	$0.587630\pi$
$620$	−0.408253	+	0.707114i	−0.0163958	+	0.0283984i
$621$	27.3213	−	16.8925i	1.09637	−	0.677871i
$622$	28.8654			1.15740
$623$		0			0
$624$	0.428043	+	1.14024i	0.0171354	+	0.0456461i
$625$	−12.3398	+	21.3732i	−0.493593	+	0.854928i
$626$	−44.6558			−1.78480
$627$	−12.6616	+	15.4014i	−0.505656	+	0.615071i
$628$	−12.6381			−0.504314
$629$	43.9006			1.75043
$630$		0			0
$631$	−36.7963			−1.46484			−0.732419	−	0.680854i	$-0.761609\pi$
$631$	−36.7963			−1.46484			−0.732419	+	0.680854i	$0.761609\pi$
$632$	5.71435			0.227305
$633$	14.3136	+	38.1291i	0.568914	+	1.51550i
$634$	17.5853			0.698401
$635$	−0.985611	+	1.70713i	−0.0391128	+	0.0677453i
$636$	−13.0397	+	15.8612i	−0.517057	+	0.628938i
$637$		0			0
$638$	16.8651			0.667696
$639$	3.62698	+	1.23811i	0.143481	+	0.0489790i
$640$	0.259699	−	0.449811i	0.0102655	−	0.0177804i
$641$	22.0922	+	38.2648i	0.872590	+	1.51137i	0.859308	+	0.511458i	$0.170894\pi$
$641$	22.0922	+	38.2648i	0.872590	+	1.51137i	0.0132813	+	0.999912i	$0.495772\pi$
$642$	8.71191	+	23.2071i	0.343831	+	0.915912i
$643$	−7.24065	−	12.5412i	−0.285543	−	0.494575i	0.687197	−	0.726471i	$-0.258841\pi$
$643$	−7.24065	−	12.5412i	−0.285543	−	0.494575i	−0.972741	+	0.231895i	$0.925507\pi$
$644$		0			0
$645$	−0.167542	−	0.446305i	−0.00659696	−	0.0175732i
$646$	89.0889			3.50515
$647$	16.6536	−	28.8448i	0.654719	−	1.13401i	−0.327245	−	0.944940i	$-0.606120\pi$
$647$	16.6536	−	28.8448i	0.654719	−	1.13401i	0.981964	−	0.189068i	$-0.0605465\pi$
$648$	3.18029	+	2.45765i	0.124934	+	0.0965455i
$649$	−3.80315	−	6.58725i	−0.149287	−	0.258572i
$650$	1.02187	−	1.76993i	0.0400811	−	0.0694225i
$651$		0			0
$652$	−2.35643	−	4.08146i	−0.0922850	−	0.159842i
$653$	4.53322	−	7.85176i	0.177398	−	0.307263i	−0.763590	−	0.645701i	$-0.776565\pi$
$653$	4.53322	−	7.85176i	0.177398	−	0.307263i	0.940989	+	0.338438i	$0.109899\pi$
$654$	15.0469	−	18.3028i	0.588380	−	0.715694i
$655$	−1.45027	−	2.51194i	−0.0566666	−	0.0981495i
$656$	4.07696	+	7.06150i	0.159178	+	0.275705i
$657$	3.51757	−	3.07420i	0.137233	−	0.119936i
$658$		0			0
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	−0.357184	−	0.934034i	$-0.616263\pi$
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	0.987489	−	0.157686i	$-0.0504035\pi$
$660$	0.922066	+	0.153043i	0.0358914	+	0.00595720i
$661$	8.65915			0.336802			0.168401	−	0.985719i	$-0.446140\pi$
$661$	8.65915			0.336802			0.168401	+	0.985719i	$0.446140\pi$
$662$	22.2763			0.865794
$663$	2.14189	+	0.355508i	0.0831839	+	0.0138068i
$664$	−1.67775	+	2.90595i	−0.0651094	+	0.112773i
$665$		0			0
$666$	−8.34179	−	42.3150i	−0.323238	−	1.63967i
$667$	15.2541	+	26.4209i	0.590642	+	1.02302i
$668$	12.8329	+	22.2273i	0.496522	+	0.860001i
$669$	−4.46692	+	5.43348i	−0.172701	+	0.210070i
$670$	0.929067	−	1.60919i	0.0358930	−	0.0621685i
$671$	−0.564339	−	0.977464i	−0.0217861	−	0.0377346i
$672$		0			0
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	−0.691831	−	0.722059i	$-0.743196\pi$
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	0.971237	+	0.238114i	$0.0765291\pi$
$674$	3.43803	+	5.95484i	0.132428	+	0.229372i
$675$	0.780128	+	25.8579i	0.0300271	+	0.995270i
$676$	14.3692	−	24.8881i	0.552661	−	0.957236i
$677$	−38.3315			−1.47320			−0.736600	−	0.676329i	$-0.763570\pi$
$677$	−38.3315			−1.47320			−0.736600	+	0.676329i	$0.763570\pi$
$678$	−0.0483128	−	0.128698i	−0.00185544	−	0.00494260i
$679$		0			0
$680$	−0.204785	−	0.354698i	−0.00785315	−	0.0136021i
$681$	−2.34534	−	6.24762i	−0.0898738	−	0.239409i
$682$	−4.30209	−	7.45144i	−0.164736	−	0.285330i
$683$	−3.31659	+	5.74450i	−0.126906	+	0.219807i	−0.922476	−	0.386054i	$-0.873838\pi$
$683$	−3.31659	+	5.74450i	−0.126906	+	0.219807i	0.795570	+	0.605861i	$0.207171\pi$
$684$	−8.90056	−	45.1494i	−0.340321	−	1.72633i
$685$	−0.942567			−0.0360136
$686$		0			0
$687$	14.4272	−	17.5489i	0.550430	−	0.669534i
$688$	3.31022	−	5.73347i	0.126201	−	0.218587i
$689$	1.06864			0.0407121
$690$	1.13019	+	3.01064i	0.0430255	+	0.114613i
$691$	23.3875			0.889704			0.444852	−	0.895604i	$-0.353256\pi$
$691$	23.3875			0.889704			0.444852	+	0.895604i	$0.353256\pi$
$692$	35.2818			1.34121
$693$		0			0
$694$	−23.6848			−0.899061
$695$	1.83254			0.0695121
$696$	−2.42422	+	2.94878i	−0.0918899	+	0.111773i
$697$	14.5358			0.550583
$698$	9.13702	−	15.8258i	0.345841	−	0.599015i
$699$	−10.6542	−	28.3810i	−0.402978	−	1.07347i
$700$		0			0
$701$	9.26736			0.350023			0.175012	−	0.984566i	$-0.444004\pi$
$701$	9.26736			0.350023			0.175012	+	0.984566i	$0.444004\pi$
$702$	−0.0643244	−	2.13208i	−0.00242777	−	0.0804700i
$703$	−24.2131	+	41.9383i	−0.913214	+	1.58173i
$704$	8.01636	+	13.8847i	0.302128	+	0.523301i
$705$	−0.291446	+	0.354510i	−0.0109765	+	0.0133516i
$706$	−2.71799	−	4.70769i	−0.102293	−	0.177176i
$707$		0			0
$708$	17.3191	+	2.87460i	0.650891	+	0.108034i
$709$	14.2355			0.534626			0.267313	−	0.963610i	$-0.413864\pi$
$709$	14.2355			0.534626			0.267313	+	0.963610i	$0.413864\pi$
$710$	−0.191839	+	0.332275i	−0.00719959	+	0.0124701i
$711$	36.3289	+	12.4013i	1.36244	+	0.465085i
$712$	−2.02478	−	3.50702i	−0.0758817	−	0.131431i
$713$	7.78230	−	13.4793i	0.291449	−	0.504805i
$714$		0			0
$715$	−0.0243226	−	0.0421280i	−0.000909613	−	0.00157550i
$716$	8.59632	−	14.8893i	0.321260	−	0.556438i
$717$	4.45416	+	11.8652i	0.166344	+	0.443113i
$718$	−26.6636	−	46.1827i	−0.995077	−	1.72352i
$719$	−6.92848	−	12.0005i	−0.258389	−	0.447542i	0.707422	−	0.706792i	$-0.249858\pi$
$719$	−6.92848	−	12.0005i	−0.258389	−	0.447542i	−0.965810	+	0.259249i	$0.916525\pi$
$720$	1.16212	−	1.01564i	0.0433096	−	0.0378507i
$721$		0			0
$722$	−29.6268	+	51.3151i	−1.10259	+	1.90975i
$723$	3.79303	+	10.1040i	0.141064	+	0.375773i
$724$	26.9684			1.00227
$725$	−24.5702			−0.912513
$726$	18.5929	−	22.6161i	0.690048	−	0.839362i
$727$	−15.7000	+	27.1932i	−0.582280	+	1.00854i	0.412928	+	0.910764i	$0.364506\pi$
$727$	−15.7000	+	27.1932i	−0.582280	+	1.00854i	−0.995208	+	0.0977755i	$0.968827\pi$
$728$		0			0
$729$	14.8851	+	22.5263i	0.551299	+	0.834308i
$730$	0.233843	+	0.405028i	0.00865492	+	0.0149908i
$731$	−5.90107	−	10.2209i	−0.218259	−	0.378035i
$732$	2.56993	+	0.426554i	0.0949873	+	0.0157659i
$733$	−13.3003	+	23.0368i	−0.491257	+	0.850883i	−0.999949	−	0.0100658i	$-0.996796\pi$
$733$	−13.3003	+	23.0368i	−0.491257	+	0.850883i	0.508692	+	0.860949i	$0.330129\pi$
$734$	18.0592	+	31.2794i	0.666576	+	1.15454i
$735$		0			0
$736$	−25.0904	+	43.4579i	−0.924845	+	1.60188i
$737$	5.14757	+	8.91586i	0.189613	+	0.328420i
$738$	−2.76203	−	14.0108i	−0.101672	−	0.515745i
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	−0.384693	−	0.923045i	$-0.625693\pi$
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	0.991727	−	0.128368i	$-0.0409740\pi$
$740$	2.27020			0.0834543
$741$	−1.52096	+	1.85007i	−0.0558739	+	0.0679640i
$742$		0			0
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	0.965570	+	0.260144i	$0.0837701\pi$
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	−0.257493	+	0.966280i	$0.582897\pi$
$744$	1.92124	+	0.318885i	0.0704360	+	0.0116909i
$745$	−1.29919	−	2.25027i	−0.0475988	−	0.0824435i
$746$	−0.836938	+	1.44962i	−0.0306425	+	0.0530743i
$747$	−16.9728	+	14.8335i	−0.621001	+	0.542728i
$748$	23.1400			0.846082
$749$		0			0
$750$	−5.12080	−	0.849945i	−0.186985	−	0.0310356i
$751$	18.9498	−	32.8220i	0.691487	−	1.19769i	−0.279863	−	0.960040i	$-0.590289\pi$
$751$	18.9498	−	32.8220i	0.691487	−	1.19769i	0.971351	−	0.237651i	$-0.0763776\pi$
$752$	−6.37345			−0.232416
$753$	−9.65885	−	1.60316i	−0.351988	−	0.0584226i
$754$	2.02590			0.0737789
$755$	1.23811			0.0450596
$756$		0			0
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$	−41.9585			−1.52400
$759$	−17.5768	−	2.91738i	−0.637999	−	0.105894i
$760$	0.451792			0.0163882
$761$	13.8735	−	24.0296i	0.502913	−	0.871072i	−0.497081	−	0.867704i	$-0.665595\pi$
$761$	13.8735	−	24.0296i	0.502913	−	0.871072i	0.999994	−	0.00336738i	$-0.00107187\pi$
$762$	47.2974	+	7.85037i	1.71340	+	0.284389i
$763$		0			0
$764$	−11.0156			−0.398529
$765$	−0.532151	−	2.69941i	−0.0192400	−	0.0975974i
$766$	18.3727	−	31.8224i	0.663832	−	1.14979i
$767$	−0.456849	−	0.791286i	−0.0164959	−	0.0285717i
$768$	20.4631	+	3.39644i	0.738399	+	0.122559i
$769$	6.07668	+	10.5251i	0.219131	+	0.379546i	0.954542	−	0.298075i	$-0.0963445\pi$
$769$	6.07668	+	10.5251i	0.219131	+	0.379546i	−0.735412	+	0.677621i	$0.763011\pi$
$770$		0			0
$771$	12.9812	−	15.7901i	0.467505	−	0.568665i
$772$	−33.0499			−1.18949
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	−0.201682	−	0.979451i	$-0.564641\pi$
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	0.949071	−	0.315063i	$-0.102026\pi$
$774$	−8.73049	+	7.63007i	−0.313811	+	0.274257i
$775$	6.26756	+	10.8557i	0.225137	+	0.389950i
$776$	1.77969	−	3.08252i	0.0638873	−	0.110656i
$777$		0			0
$778$	−16.0470	−	27.7942i	−0.575313	−	0.996472i
$779$	−8.01714	+	13.8861i	−0.287244	+	0.497521i
$780$	0.110762	+	0.0183841i	0.00396591	+	0.000658258i
$781$	−1.06290	−	1.84100i	−0.0380336	−	0.0658761i
$782$	39.8068	+	68.9473i	1.42349	+	2.46555i
$783$	−21.8114	+	13.4858i	−0.779476	+	0.481942i
$784$		0			0
$785$	0.416753	−	0.721837i	0.0148746	−	0.0257635i
$786$	−44.8014	+	54.4956i	−1.59801	+	1.94379i
$787$	20.8969			0.744893			0.372446	−	0.928054i	$-0.378519\pi$
$787$	20.8969			0.744893			0.372446	+	0.928054i	$0.378519\pi$
$788$	−47.1450			−1.67947
$789$	13.5382	+	36.0636i	0.481972	+	1.28390i
$790$	−1.92152	+	3.32816i	−0.0683645	+	0.118411i
$791$		0			0
$792$	−0.431195	−	2.18730i	−0.0153218	−	0.0777222i
$793$	−0.0677905	−	0.117417i	−0.00240731	−	0.00416959i
$794$	−19.7779	−	34.2564i	−0.701892	−	1.21571i
$795$	−0.475934	−	1.26781i	−0.0168797	−	0.0449647i
$796$	22.1127	−	38.3003i	0.783763	−	1.35752i
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	0.871627	−	0.490171i	$-0.163066\pi$
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	−0.860313	+	0.509765i	$0.829732\pi$
$798$		0			0
$799$	−5.68091	+	9.83963i	−0.200976	+	0.348101i
$800$	−20.2069	−	34.9993i	−0.714420	−	1.23741i
$801$	−5.26155	−	26.6900i	−0.185908	−	0.943043i
$802$	−14.6849	+	25.4350i	−0.518541	+	0.898139i
$803$	−2.59125			−0.0914433
$804$	−23.4414	−	3.89078i	−0.826714	−	0.137217i
$805$		0			0
$806$	−0.516783	−	0.895095i	−0.0182029	−	0.0315284i
$807$	2.62759	−	3.19616i	0.0924957	−	0.112510i
$808$	3.31431	+	5.74055i	0.116597	+	0.201952i
$809$	25.2796	−	43.7856i	0.888783	−	1.53942i	0.0474686	−	0.998873i	$-0.484885\pi$
$809$	25.2796	−	43.7856i	0.888783	−	1.53942i	0.841315	−	0.540545i	$-0.181782\pi$
$810$	−2.50080	+	1.02586i	−0.0878690	+	0.0360451i
$811$	0.784071			0.0275325			0.0137662	−	0.999905i	$-0.495618\pi$
$811$	0.784071			0.0275325			0.0137662	+	0.999905i	$0.495618\pi$
$812$		0			0
$813$	14.1382	+	37.6620i	0.495850	+	1.32087i
$814$	−11.9615	+	20.7179i	−0.419250	+	0.726163i
$815$	0.310823			0.0108876
$816$	24.2653	−	29.5159i	0.849455	−	1.03326i
$817$	13.0188			0.455470
$818$	−65.4311			−2.28775
$819$		0			0
$820$	0.751682			0.0262499
$821$	43.4413			1.51611			0.758056	−	0.652189i	$-0.226149\pi$
$821$	43.4413			1.51611			0.758056	+	0.652189i	$0.226149\pi$
$822$	8.05710	+	21.4628i	0.281024	+	0.748602i
$823$	3.96546			0.138227			0.0691136	−	0.997609i	$-0.477983\pi$
$823$	3.96546			0.138227			0.0691136	+	0.997609i	$0.477983\pi$
$824$	−0.0455399	+	0.0788774i	−0.00158646	+	0.00274782i
$825$	9.11262	−	11.0844i	0.317261	−	0.385910i
$826$		0			0
$827$	29.3159			1.01941			0.509707	−	0.860348i	$-0.329754\pi$
$827$	29.3159			1.01941			0.509707	+	0.860348i	$0.329754\pi$
$828$	30.9649	−	27.0620i	1.07610	−	0.940469i
$829$	17.5213	−	30.3478i	0.608541	−	1.05402i	−0.382940	−	0.923773i	$-0.625088\pi$
$829$	17.5213	−	30.3478i	0.608541	−	1.05402i	0.991481	−	0.130251i	$-0.0415782\pi$
$830$	−1.12833	−	1.95432i	−0.0391648	−	0.0678353i
$831$	2.81111	+	7.48836i	0.0975165	+	0.259768i
$832$	0.962955	+	1.66789i	0.0333844	+	0.0578236i
$833$		0			0
$834$	−15.6646	−	41.7280i	−0.542421	−	1.44492i
$835$	−1.69272			−0.0585788
$836$	−12.7627	+	22.1057i	−0.441408	+	0.764541i
$837$	11.5222	+	6.19678i	0.398265	+	0.214192i
$838$	−24.5369	−	42.4992i	−0.847614	−	1.46811i
$839$	18.7921	−	32.5489i	0.648777	−	1.12371i	−0.334639	−	0.942347i	$-0.608614\pi$
$839$	18.7921	−	32.5489i	0.648777	−	1.12371i	0.983415	−	0.181368i	$-0.0580524\pi$
$840$		0			0
$841$	2.32218	+	4.02213i	0.0800750	+	0.138694i
$842$	−2.51060	+	4.34848i	−0.0865208	+	0.149858i
$843$	12.9979	−	15.8104i	0.447670	−	0.544538i
$844$	26.0705	+	45.1555i	0.897385	+	1.55432i
$845$	0.947675	+	1.64142i	0.0326010	+	0.0564666i
$846$	10.5637	+	3.60604i	0.363188	+	0.123978i
$847$		0			0
$848$	9.40331	−	16.2870i	0.322911	−	0.559298i
$849$	−27.0819	−	4.49503i	−0.929449	−	0.154269i
$850$	−64.1177			−2.19922
$851$	−43.2757			−1.48347
$852$	4.84031	+	0.803389i	0.165826	+	0.0275237i
$853$	−16.3849	+	28.3795i	−0.561009	+	0.971696i	0.436400	+	0.899753i	$0.356253\pi$
$853$	−16.3849	+	28.3795i	−0.561009	+	0.971696i	−0.997409	+	0.0719434i	$0.977080\pi$
$854$		0			0
$855$	2.87226	+	0.980479i	0.0982291	+	0.0335317i
$856$	1.55609	+	2.69523i	0.0531861	+	0.0921211i
$857$	13.7673	+	23.8457i	0.470283	+	0.814554i	0.999422	−	0.0339808i	$-0.0108185\pi$
$857$	13.7673	+	23.8457i	0.470283	+	0.814554i	−0.529139	+	0.848535i	$0.677485\pi$
$858$	−0.751369	+	0.913952i	−0.0256513	+	0.0312018i
$859$	−23.2550	+	40.2789i	−0.793451	+	1.37430i	0.130366	+	0.991466i	$0.458385\pi$
$859$	−23.2550	+	40.2789i	−0.793451	+	1.37430i	−0.923818	+	0.382832i	$0.874949\pi$
$860$	−0.305158	−	0.528549i	−0.0104058	−	0.0180234i
$861$		0			0
$862$	5.05981	−	8.76384i	0.172338	−	0.298498i
$863$	2.44007	+	4.22633i	0.0830610	+	0.143866i	0.904563	−	0.426339i	$-0.140197\pi$
$863$	2.44007	+	4.22633i	0.0830610	+	0.143866i	−0.821502	+	0.570205i	$0.806864\pi$
$864$	−37.1480	−	19.9786i	−1.26380	−	0.679687i
$865$	−1.16345	+	2.01516i	−0.0395585	+	0.0685174i
$866$	−63.3629			−2.15316
$867$	−13.5909	−	36.2041i	−0.461572	−	1.22956i
$868$		0			0
$869$	−10.6463	−	18.4400i	−0.361152	−	0.625533i
$870$	−0.902261	−	2.40348i	−0.0305895	−	0.0814856i
$871$	0.618346	+	1.07101i	0.0209518	+	0.0362897i
$872$	1.48738	−	2.57622i	0.0503690	−	0.0872417i
$873$	18.0040	−	15.7348i	0.609345	−	0.532541i
$874$	−87.8207			−2.97058
$875$		0			0
$876$	3.79815	−	4.62001i	0.128328	−	0.156096i
$877$	−19.6446	+	34.0255i	−0.663352	+	1.14896i	0.316378	+	0.948633i	$0.397533\pi$
$877$	−19.6446	+	34.0255i	−0.663352	+	1.14896i	−0.979729	+	0.200326i	$0.935800\pi$
$878$	−5.02777			−0.169679
$879$	−8.58070	−	22.8576i	−0.289420	−	0.770968i
$880$	−0.856086			−0.0288587
$881$	−47.3713			−1.59598			−0.797990	−	0.602670i	$-0.794103\pi$
$881$	−47.3713			−1.59598			−0.797990	+	0.602670i	$0.794103\pi$
$882$		0			0
$883$	−2.67206			−0.0899221			−0.0449610	−	0.998989i	$-0.514316\pi$
$883$	−2.67206			−0.0899221			−0.0449610	+	0.998989i	$0.514316\pi$
$884$	2.77966			0.0934902
$885$	−0.735299	+	0.894404i	−0.0247168	+	0.0300651i
$886$	−54.0007			−1.81419
$887$	−11.4800	+	19.8840i	−0.385461	+	0.667638i	−0.991833	−	0.127543i	$-0.959291\pi$
$887$	−11.4800	+	19.8840i	−0.385461	+	0.667638i	0.606372	+	0.795181i	$0.292624\pi$
$888$	−1.90306	−	5.06944i	−0.0638624	−	0.170119i
$889$		0			0
$890$	2.72342			0.0912891
$891$	2.00556	−	14.8415i	0.0671889	−	0.497208i
$892$	−4.50259	+	7.79871i	−0.150758	+	0.261120i
$893$	−6.26655	−	10.8540i	−0.209702	−	0.363214i
$894$	−40.1345	+	48.8188i	−1.34230	+	1.63275i
$895$	0.566944	+	0.981976i	0.0189508	+	0.0328238i
$896$		0			0
$897$	−2.11140	−	0.350447i	−0.0704975	−	0.0117011i
$898$	−79.4920			−2.65268
$899$	−6.21284	+	10.7610i	−0.207210	+	0.358898i
$900$	6.40577	+	32.4942i	0.213526	+	1.08314i
$901$	−16.7631	−	29.0345i	−0.558459	−	0.967280i
$902$	−3.96054	+	6.85986i	−0.131872	+	0.228408i
$903$		0			0
$904$	−0.00862948	−	0.0149467i	−0.000287012	−	0.000497120i
$905$	−0.889308	+	1.54033i	−0.0295616	+	0.0512022i
$906$	−10.5835	−	28.1926i	−0.351612	−	0.936638i
$907$	13.9491	+	24.1606i	0.463173	+	0.802238i	0.999117	−	0.0420148i	$-0.0133777\pi$
$907$	13.9491	+	24.1606i	0.463173	+	0.802238i	−0.535944	+	0.844253i	$0.680044\pi$
$908$	−4.27177	−	7.39892i	−0.141764	−	0.245542i
$909$	8.61250	+	43.6882i	0.285659	+	1.44905i
$910$		0			0
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	0.368513	+	0.929623i	$0.379867\pi$
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	−0.989333	+	0.145670i	$0.953466\pi$
$912$	14.8132	+	39.4600i	0.490514	+	1.30665i
$913$	12.5032			0.413794
$914$	−18.8014			−0.621894
$915$	−0.109109	+	0.132718i	−0.00360703	+	0.00438753i
$916$	14.5424	−	25.1881i	0.480493	−	0.832239i
$917$		0			0
$918$	−56.9184	+	35.1921i	−1.87859	+	1.16151i
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	0.501653	−	0.865069i	$-0.332726\pi$
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	−0.999998	+	0.00190951i	$0.999392\pi$
$920$	0.201870	+	0.349649i	0.00665546	+	0.0115276i
$921$	−46.8033	−	7.76836i	−1.54222	−	0.255976i
$922$	−30.0145	+	51.9866i	−0.988474	+	1.71209i
$923$	−0.127680	−	0.221147i	−0.00420262	−	0.00727916i
$924$		0			0
$925$	17.4263	−	30.1832i	0.572972	−	0.992417i
$926$	−16.8611	−	29.2042i	−0.554089	−	0.959710i
$927$	−0.460698	+	0.402631i	−0.0151313	+	0.0132241i
$928$	20.0304	−	34.6937i	0.657531	−	1.13888i
$929$	45.9351			1.50708			0.753540	−	0.657402i	$-0.228344\pi$
$929$	45.9351			1.50708			0.753540	+	0.657402i	$0.228344\pi$
$930$	−0.831764	+	1.01174i	−0.0272746	+	0.0331763i
$931$		0			0
$932$	−19.4053	−	33.6110i	−0.635642	−	1.10096i
$933$	24.0166	+	3.98625i	0.786269	+	0.130504i
$934$	−15.7850	−	27.3404i	−0.516500	−	0.894604i
$935$	−0.763064	+	1.32167i	−0.0249549	+	0.0432231i
$936$	−0.0517967	−	0.262746i	−0.00169303	−	0.00858813i
$937$	45.3797			1.48249			0.741245	−	0.671235i	$-0.234236\pi$
$937$	45.3797			1.48249			0.741245	+	0.671235i	$0.234236\pi$
$938$		0			0
$939$	−37.1545	−	6.16686i	−1.21249	−	0.201248i
$940$	−0.293774	+	0.508831i	−0.00958184	+	0.0165962i
$941$	−49.4003			−1.61040			−0.805202	−	0.593000i	$-0.797943\pi$
$941$	−49.4003			−1.61040			−0.805202	+	0.593000i	$0.797943\pi$
$942$	−19.9991	−	3.31943i	−0.651606	−	0.108153i
$943$	−14.3289			−0.466613
$944$	−16.0798			−0.523353
$945$		0			0
$946$	6.43141			0.209103
$947$	31.6505			1.02850			0.514252	−	0.857639i	$-0.328070\pi$
$947$	31.6505			1.02850			0.514252	+	0.857639i	$0.328070\pi$
$948$	48.4820	+	8.04698i	1.57462	+	0.261354i
$949$	−0.311271			−0.0101043
$950$	35.3637	−	61.2517i	1.14735	−	1.98727i
$951$	14.6313	+	2.42849i	0.474453	+	0.0787492i
$952$		0			0
$953$	−19.1237			−0.619477			−0.309739	−	0.950822i	$-0.600242\pi$
$953$	−19.1237			−0.619477			−0.309739	+	0.950822i	$0.600242\pi$
$954$	−24.8006	+	21.6746i	−0.802949	+	0.701742i
$955$	0.363249	−	0.629165i	0.0117545	−	0.0203593i
$956$	8.11273	+	14.0517i	0.262384	+	0.454463i
$957$	14.0321	+	2.32903i	0.453594	+	0.0752870i
$958$	−38.9465	−	67.4573i	−1.25830	−	2.17945i
$959$		0			0
$960$	1.54988	−	1.88524i	0.0500221	−	0.0608459i
$961$	−24.6607			−0.795507
$962$	−1.43686	+	2.48871i	−0.0463262	+	0.0802394i
$963$	4.04363	+	20.5119i	0.130304	+	0.660987i
$964$	6.90857	+	11.9660i	0.222510	+	0.385399i
$965$	1.08985	−	1.88768i	0.0350836	−	0.0607666i
$966$		0			0
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	0.934982	−	0.354696i	$-0.115416\pi$
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	−0.774667	+	0.632370i	$0.782082\pi$
$968$	1.83790	−	3.18334i	0.0590724	−	0.102316i
$969$	74.1237	+	12.3030i	2.38120	+	0.395228i
$970$	1.19688	+	2.07306i	0.0384296	+	0.0665621i
$971$	−0.522554	−	0.905090i	−0.0167695	−	0.0290457i	0.857519	−	0.514453i	$-0.172005\pi$
$971$	−0.522554	−	0.905090i	−0.0167695	−	0.0290457i	−0.874288	+	0.485407i	$0.838671\pi$
$972$	23.5215	+	25.3298i	0.754453	+	0.812453i
$973$		0			0
$974$	4.72847	−	8.18994i	0.151510	−	0.262423i
$975$	1.09464	−	1.33150i	0.0350566	−	0.0426422i
$976$	−2.38603			−0.0763751
$977$	−18.8862			−0.604222			−0.302111	−	0.953273i	$-0.597691\pi$
$977$	−18.8862			−0.604222			−0.302111	+	0.953273i	$0.597691\pi$
$978$	−2.65692	−	7.07762i	−0.0849590	−	0.226317i
$979$	−7.54466	+	13.0677i	−0.241128	+	0.417647i
$980$		0			0
$981$	15.0469	−	13.1503i	0.480410	−	0.419858i
$982$	−31.1899	−	54.0224i	−0.995309	−	1.72393i
$983$	1.14446	+	1.98226i	0.0365025	+	0.0632242i	0.883700	−	0.468055i	$-0.155045\pi$
$983$	1.14446	+	1.98226i	0.0365025	+	0.0632242i	−0.847197	+	0.531279i	$0.821712\pi$
$984$	−0.630117	−	1.67853i	−0.0200874	−	0.0535096i
$985$	1.55465	−	2.69274i	0.0495353	−	0.0857977i
$986$	−31.7789	−	55.0427i	−1.01205	−	1.75292i
$987$		0			0
$988$	−1.53311	+	2.65542i	−0.0487746	+	0.0844801i
$989$	5.81707	+	10.0755i	0.184972	+	0.320381i
$990$	1.41892	+	0.484366i	0.0450963	+	0.0153942i
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	−0.976789	−	0.214206i	$-0.931284\pi$
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	0.673902	+	0.738821i	$0.264617\pi$
$992$	−20.4381			−0.648911
$993$	18.5343	+	3.07631i	0.588170	+	0.0976237i
$994$		0			0
$995$	1.45837	+	2.52598i	0.0462336	+	0.0800789i
$996$	−18.3266	+	22.2922i	−0.580702	+	0.706355i
$997$	18.5075	+	32.0560i	0.586139	+	1.01522i	0.994732	+	0.102507i	$0.0326863\pi$
$997$	18.5075	+	32.0560i	0.586139	+	1.01522i	−0.408593	+	0.912717i	$0.633980\pi$
$998$	−9.51732	+	16.4845i	−0.301266	+	0.521807i
$999$	−1.09694	−	36.3589i	−0.0347057	−	1.15034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.f.214.5		10
3.2	odd	2		1323.2.h.f.802.1		10
7.2	even	3		441.2.g.f.79.1		10
7.3	odd	6		441.2.f.e.295.1		10
7.4	even	3		441.2.f.f.295.1		10
7.5	odd	6		63.2.g.b.16.1	yes	10
7.6	odd	2		63.2.h.b.25.5	yes	10
9.4	even	3		441.2.g.f.67.1		10
9.5	odd	6		1323.2.g.f.361.5		10
21.2	odd	6		1323.2.g.f.667.5		10
21.5	even	6		189.2.g.b.100.5		10
21.11	odd	6		1323.2.f.f.883.5		10
21.17	even	6		1323.2.f.e.883.5		10
21.20	even	2		189.2.h.b.46.1		10
28.19	even	6		1008.2.t.i.961.2		10
28.27	even	2		1008.2.q.i.529.5		10
63.4	even	3		441.2.f.f.148.1		10
63.5	even	6		189.2.h.b.37.1		10
63.11	odd	6		3969.2.a.bb.1.1		5
63.13	odd	6		63.2.g.b.4.1	✓	10
63.20	even	6		567.2.e.e.487.5		10
63.23	odd	6		1323.2.h.f.226.1		10
63.25	even	3		3969.2.a.ba.1.5		5
63.31	odd	6		441.2.f.e.148.1		10
63.32	odd	6		1323.2.f.f.442.5		10
63.34	odd	6		567.2.e.f.487.1		10
63.38	even	6		3969.2.a.bc.1.1		5
63.40	odd	6		63.2.h.b.58.5	yes	10
63.41	even	6		189.2.g.b.172.5		10
63.47	even	6		567.2.e.e.163.5		10
63.52	odd	6		3969.2.a.z.1.5		5
63.58	even	3	inner	441.2.h.f.373.5		10
63.59	even	6		1323.2.f.e.442.5		10
63.61	odd	6		567.2.e.f.163.1		10
84.47	odd	6		3024.2.t.i.289.3		10
84.83	odd	2		3024.2.q.i.2881.3		10
252.103	even	6		1008.2.q.i.625.5		10
252.131	odd	6		3024.2.q.i.2305.3		10
252.139	even	6		1008.2.t.i.193.2		10
252.167	odd	6		3024.2.t.i.1873.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	63.13	odd	6
63.2.g.b.16.1	yes	10	7.5	odd	6
63.2.h.b.25.5	yes	10	7.6	odd	2
63.2.h.b.58.5	yes	10	63.40	odd	6
189.2.g.b.100.5		10	21.5	even	6
189.2.g.b.172.5		10	63.41	even	6
189.2.h.b.37.1		10	63.5	even	6
189.2.h.b.46.1		10	21.20	even	2
441.2.f.e.148.1		10	63.31	odd	6
441.2.f.e.295.1		10	7.3	odd	6
441.2.f.f.148.1		10	63.4	even	3
441.2.f.f.295.1		10	7.4	even	3
441.2.g.f.67.1		10	9.4	even	3
441.2.g.f.79.1		10	7.2	even	3
441.2.h.f.214.5		10	1.1	even	1	trivial
441.2.h.f.373.5		10	63.58	even	3	inner
567.2.e.e.163.5		10	63.47	even	6
567.2.e.e.487.5		10	63.20	even	6
567.2.e.f.163.1		10	63.61	odd	6
567.2.e.f.487.1		10	63.34	odd	6
1008.2.q.i.529.5		10	28.27	even	2
1008.2.q.i.625.5		10	252.103	even	6
1008.2.t.i.193.2		10	252.139	even	6
1008.2.t.i.961.2		10	28.19	even	6
1323.2.f.e.442.5		10	63.59	even	6
1323.2.f.e.883.5		10	21.17	even	6
1323.2.f.f.442.5		10	63.32	odd	6
1323.2.f.f.883.5		10	21.11	odd	6
1323.2.g.f.361.5		10	9.5	odd	6
1323.2.g.f.667.5		10	21.2	odd	6
1323.2.h.f.226.1		10	63.23	odd	6
1323.2.h.f.802.1		10	3.2	odd	2
3024.2.q.i.2305.3		10	252.131	odd	6
3024.2.q.i.2881.3		10	84.83	odd	2
3024.2.t.i.289.3		10	84.47	odd	6
3024.2.t.i.1873.3		10	252.167	odd	6
3969.2.a.z.1.5		5	63.52	odd	6
3969.2.a.ba.1.5		5	63.25	even	3
3969.2.a.bb.1.1		5	63.11	odd	6
3969.2.a.bc.1.1		5	63.38	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.05365 q^{2} +(1.70867 + 0.283604i) q^{3} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(3.50901 + 0.582422i) q^{6} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +O(q^{10})\)	\(q+2.05365 q^{2} +(1.70867 + 0.283604i) q^{3} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(3.50901 + 0.582422i) q^{6} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +(-0.150168 + 0.260099i) q^{10} +(-0.832020 - 1.44110i) q^{11} +(3.78891 + 0.628880i) q^{12} +(-0.0999454 - 0.173111i) q^{13} +(-0.160862 + 0.195670i) q^{15} -3.51780 q^{16} +(-3.13555 + 5.43093i) q^{17} +(5.83058 + 1.99034i) q^{18} +(-3.45879 - 5.99080i) q^{19} +(-0.162147 + 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(3.09092 - 5.35363i) q^{23} +(0.763064 + 0.126652i) q^{24} +(2.48931 + 4.31160i) q^{25} +(-0.205252 - 0.355508i) q^{26} +(4.57630 + 2.46119i) q^{27} +(-2.46757 + 4.27396i) q^{29} +(-0.330354 + 0.401837i) q^{30} +2.51780 q^{31} -8.11747 q^{32} +(-1.01295 - 2.69834i) q^{33} +(-6.43931 + 11.1532i) q^{34} +(6.29567 + 2.14910i) q^{36} +(-3.50023 - 6.06257i) q^{37} +(-7.10312 - 12.3030i) q^{38} +(-0.121679 - 0.324134i) q^{39} +(-0.0326554 + 0.0565608i) q^{40} +(-1.15895 - 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} +(-1.84497 - 3.19558i) q^{44} +(-0.330354 + 0.288715i) q^{45} +(6.34765 - 10.9944i) q^{46} +1.81177 q^{47} +(-6.01077 - 0.997660i) q^{48} +(5.11215 + 8.85451i) q^{50} +(-6.89787 + 8.39045i) q^{51} +(-0.221625 - 0.383865i) q^{52} +(-2.67307 + 4.62989i) q^{53} +(9.39810 + 5.05442i) q^{54} +0.243359 q^{55} +(-4.21093 - 11.2172i) q^{57} +(-5.06752 + 8.77720i) q^{58} +4.57099 q^{59} +(-0.356705 + 0.433890i) q^{60} +0.678276 q^{61} +5.17066 q^{62} -9.63481 q^{64} +0.0292332 q^{65} +(-2.08024 - 5.54143i) q^{66} -6.18684 q^{67} +(-6.95296 + 12.0429i) q^{68} +(6.79968 - 8.27101i) q^{69} +1.27749 q^{71} +(1.26791 + 0.432816i) q^{72} +(0.778603 - 1.34858i) q^{73} +(-7.18823 - 12.4504i) q^{74} +(3.03063 + 8.07311i) q^{75} +(-7.66972 - 13.2843i) q^{76} +(-0.249886 - 0.665657i) q^{78} +12.7957 q^{79} +(0.257231 - 0.445537i) q^{80} +(7.12141 + 5.50323i) q^{81} +(-2.38008 - 4.12241i) q^{82} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-1.93247 + 3.34713i) q^{86} +(-5.42839 + 6.60299i) q^{87} +(-0.371566 - 0.643571i) q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.678430 + 0.592918i) q^{90} +(6.85398 - 11.8714i) q^{92} +(4.30209 + 0.714056i) q^{93} +3.72074 q^{94} +1.01167 q^{95} +(-13.8701 - 2.30214i) q^{96} +(3.98514 - 6.90246i) q^{97} +(-0.965543 - 4.89786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9} + 7 q^{10} + 4 q^{11} + 20 q^{12} + 8 q^{13} - 19 q^{15} - 4 q^{16} - 12 q^{17} + 4 q^{18} - q^{19} - 5 q^{20} - q^{22} + 3 q^{23} - 6 q^{24} - q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} + 16 q^{30} - 6 q^{31} + 4 q^{32} - 14 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} + 2 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + 16 q^{45} + 3 q^{46} + 54 q^{47} + 5 q^{48} + 19 q^{50} - 9 q^{51} + 10 q^{52} - 21 q^{53} - q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} + 60 q^{59} + 10 q^{60} - 28 q^{61} + 12 q^{62} - 50 q^{64} + 22 q^{65} - 19 q^{66} + 4 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 36 q^{72} - 15 q^{73} - 36 q^{74} + 14 q^{75} - 5 q^{76} - 20 q^{78} + 8 q^{79} - 20 q^{80} + 23 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} - 2 q^{87} - 18 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 6 q^{93} - 6 q^{94} + 28 q^{95} - 59 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9 + 7 * q^10 + 4 * q^11 + 20 * q^12 + 8 * q^13 - 19 * q^15 - 4 * q^16 - 12 * q^17 + 4 * q^18 - q^19 - 5 * q^20 - q^22 + 3 * q^23 - 6 * q^24 - q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 + 16 * q^30 - 6 * q^31 + 4 * q^32 - 14 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 + 2 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + 16 * q^45 + 3 * q^46 + 54 * q^47 + 5 * q^48 + 19 * q^50 - 9 * q^51 + 10 * q^52 - 21 * q^53 - q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 + 60 * q^59 + 10 * q^60 - 28 * q^61 + 12 * q^62 - 50 * q^64 + 22 * q^65 - 19 * q^66 + 4 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 36 * q^72 - 15 * q^73 - 36 * q^74 + 14 * q^75 - 5 * q^76 - 20 * q^78 + 8 * q^79 - 20 * q^80 + 23 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 - 2 * q^87 - 18 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 6 * q^93 - 6 * q^94 + 28 * q^95 - 59 * q^96 + 12 * q^97 + 35 * q^99

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