LMFDB - Embedded newform 441.2.h.f.373.4

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			373.4
Root			$-0.335166 - 0.580525i$ of defining polynomial
Character	$\chi$	$=$	441.373
Dual form			441.2.h.f.214.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.670333 q^{2} +(-1.65263 - 0.518475i) q^{3} -1.55065 q^{4} +(0.712469 + 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(2.46237 + 1.71369i) q^{9} +O(q^{10})$	\(q+0.670333 q^{2} +(-1.65263 - 0.518475i) q^{3} -1.55065 q^{4} +(0.712469 + 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(2.46237 + 1.71369i) q^{9} +(0.477591 + 0.827212i) q^{10} +(2.46539 - 4.27018i) q^{11} +(2.56266 + 0.803975i) q^{12} +(1.37730 - 2.38556i) q^{13} +(-0.537632 - 2.40879i) q^{15} +1.50584 q^{16} +(-0.559839 - 0.969670i) q^{17} +(1.65061 + 1.14874i) q^{18} +(2.00752 - 3.47713i) q^{19} +(-1.10479 - 1.91356i) q^{20} +(1.65263 - 2.86244i) q^{22} +(-2.71830 - 4.70824i) q^{23} +(3.93346 + 1.23403i) q^{24} +(1.48478 - 2.57171i) q^{25} +(0.923251 - 1.59912i) q^{26} +(-3.18087 - 4.10878i) q^{27} +(3.40555 + 5.89858i) q^{29} +(-0.360392 - 1.61469i) q^{30} -2.50584 q^{31} +5.76965 q^{32} +(-6.28835 + 5.77878i) q^{33} +(-0.375279 - 0.650002i) q^{34} +(-3.81828 - 2.65735i) q^{36} +(0.709787 - 1.22939i) q^{37} +(1.34571 - 2.33083i) q^{38} +(-3.51302 + 3.22835i) q^{39} +(-1.69576 - 2.93714i) q^{40} +(-0.124384 + 0.215440i) q^{41} +(-0.498313 - 0.863104i) q^{43} +(-3.82296 + 6.62156i) q^{44} +(-0.360392 + 4.25959i) q^{45} +(-1.82217 - 3.15609i) q^{46} +9.47579 q^{47} +(-2.48859 - 0.780738i) q^{48} +(0.995294 - 1.72390i) q^{50} +(0.422457 + 1.89277i) q^{51} +(-2.13572 + 3.69917i) q^{52} +(-0.410229 - 0.710537i) q^{53} +(-2.13224 - 2.75425i) q^{54} +7.02604 q^{55} +(-5.12050 + 4.70556i) q^{57} +(2.28285 + 3.95401i) q^{58} +6.58407 q^{59} +(0.833682 + 3.73521i) q^{60} -0.0752645 q^{61} -1.67974 q^{62} +0.855913 q^{64} +3.92514 q^{65} +(-4.21529 + 3.87370i) q^{66} -12.5877 q^{67} +(0.868117 + 1.50362i) q^{68} +(2.05125 + 9.19035i) q^{69} +0.0804951 q^{71} +(-5.86073 - 4.07880i) q^{72} +(-5.34551 - 9.25869i) q^{73} +(0.475793 - 0.824098i) q^{74} +(-3.78715 + 3.48026i) q^{75} +(-3.11297 + 5.39183i) q^{76} +(-2.35489 + 2.16407i) q^{78} -1.84491 q^{79} +(1.07286 + 1.85825i) q^{80} +(3.12651 + 8.43949i) q^{81} +(-0.0833788 + 0.144416i) q^{82} +(7.23583 + 12.5328i) q^{83} +(0.797736 - 1.38172i) q^{85} +(-0.334036 - 0.578567i) q^{86} +(-2.56984 - 11.5139i) q^{87} +(-5.86792 + 10.1635i) q^{88} +(-6.76292 + 11.7137i) q^{89} +(-0.241583 + 2.85534i) q^{90} +(4.21515 + 7.30085i) q^{92} +(4.14122 + 1.29921i) q^{93} +6.35193 q^{94} +5.72119 q^{95} +(-9.53509 - 2.99142i) q^{96} +(-2.70160 - 4.67930i) q^{97} +(13.3885 - 6.28982i) 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.670333			0.473997			0.236998	−	0.971510i	$-0.423836\pi$
$2$	0.670333			0.473997			0.236998	+	0.971510i	$0.423836\pi$
$3$	−1.65263	−	0.518475i	−0.954146	−	0.299342i
$3$	−1.65263	−	0.518475i	−0.954146	−	0.299342i
$4$	−1.55065			−0.775327
$5$	0.712469	+	1.23403i	0.318626	+	0.551876i	0.980202	−	0.198002i	$-0.0634454\pi$
$5$	0.712469	+	1.23403i	0.318626	+	0.551876i	−0.661576	+	0.749878i	$0.730112\pi$
$6$	−1.10781	−	0.347551i	−0.452262	−	0.141887i
$7$		0			0
$7$		0			0
$8$	−2.38012			−0.841499
$9$	2.46237	+	1.71369i	0.820789	+	0.571231i
$10$	0.477591	+	0.827212i	0.151028	+	0.261587i
$11$	2.46539	−	4.27018i	0.743342	−	1.28751i	−0.207623	−	0.978209i	$-0.566573\pi$
$11$	2.46539	−	4.27018i	0.743342	−	1.28751i	0.950965	−	0.309297i	$-0.100094\pi$
$12$	2.56266	+	0.803975i	0.739775	+	0.232088i
$13$	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
$16$	1.50584			0.376459
$17$	−0.559839	−	0.969670i	−0.135781	−	0.235180i	0.790115	−	0.612959i	$-0.210021\pi$
$17$	−0.559839	−	0.969670i	−0.135781	−	0.235180i	−0.925896	+	0.377780i	$0.876688\pi$
$18$	1.65061	+	1.14874i	0.389051	+	0.270762i
$19$	2.00752	−	3.47713i	0.460557	−	0.797709i	−0.538431	−	0.842669i	$-0.680983\pi$
$19$	2.00752	−	3.47713i	0.460557	−	0.797709i	0.998989	+	0.0449606i	$0.0143162\pi$
$20$	−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	−0.996879	−	0.0789424i	$-0.974846\pi$
$23$	−2.71830	−	4.70824i	−0.566806	−	0.981736i	0.430073	−	0.902794i	$-0.358488\pi$
$24$	3.93346	+	1.23403i	0.802913	+	0.251896i
$25$	1.48478	−	2.57171i	0.296955	−	0.514342i
$26$	0.923251	−	1.59912i	0.181064	−	0.313613i
$27$	−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	$0.615406\pi$
$30$	−0.360392	−	1.61469i	−0.0657984	−	0.294801i
$31$	−2.50584			−0.450061			−0.225031	−	0.974352i	$-0.572248\pi$
$31$	−2.50584			−0.450061			−0.225031	+	0.974352i	$0.572248\pi$
$32$	5.76965			1.01994
$33$	−6.28835	+	5.77878i	−1.09466	+	1.00596i
$34$	−0.375279	−	0.650002i	−0.0643597	−	0.111474i
$35$		0			0
$36$	−3.81828	−	2.65735i	−0.636380	−	0.442891i
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	−0.801765	−	0.597639i	$-0.796106\pi$
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	0.918453	+	0.395529i	$0.129439\pi$
$38$	1.34571	−	2.33083i	0.218303	−	0.378111i
$39$	−3.51302	+	3.22835i	−0.562534	+	0.516949i
$40$	−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	$0.857546\pi$
$44$	−3.82296	+	6.62156i	−0.576333	+	0.998238i
$45$	−0.360392	+	4.25959i	−0.0537241	+	0.634983i
$46$	−1.82217	−	3.15609i	−0.268664	−	0.465340i
$47$	9.47579			1.38219			0.691093	−	0.722766i	$-0.257129\pi$
$47$	9.47579			1.38219			0.691093	+	0.722766i	$0.257129\pi$
$48$	−2.48859	−	0.780738i	−0.359197	−	0.112690i
$49$		0			0
$50$	0.995294	−	1.72390i	0.140756	−	0.243796i
$51$	0.422457	+	1.89277i	0.0591559	+	0.265041i
$52$	−2.13572	+	3.69917i	−0.296171	+	0.512983i
$53$	−0.410229	−	0.710537i	−0.0563493	−	0.0975998i	0.836475	−	0.548005i	$-0.184613\pi$
$53$	−0.410229	−	0.710537i	−0.0563493	−	0.0975998i	−0.892824	+	0.450406i	$0.851279\pi$
$54$	−2.13224	−	2.75425i	−0.290162	−	0.374805i
$55$	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
$59$	6.58407			0.857173			0.428586	−	0.903501i	$-0.359012\pi$
$59$	6.58407			0.857173			0.428586	+	0.903501i	$0.359012\pi$
$60$	0.833682	+	3.73521i	0.107628	+	0.482213i
$61$	−0.0752645			−0.00963663			−0.00481831	−	0.999988i	$-0.501534\pi$
$61$	−0.0752645			−0.00963663			−0.00481831	+	0.999988i	$0.501534\pi$
$62$	−1.67974			−0.213328
$63$		0			0
$64$	0.855913			0.106989
$65$	3.92514			0.486854
$66$	−4.21529	+	3.87370i	−0.518866	+	0.476820i
$67$	−12.5877			−1.53783			−0.768916	−	0.639350i	$-0.779204\pi$
$67$	−12.5877			−1.53783			−0.768916	+	0.639350i	$0.779204\pi$
$68$	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	$0.498480\pi$
$72$	−5.86073	−	4.07880i	−0.690694	−	0.480691i
$73$	−5.34551	−	9.25869i	−0.625644	−	1.08365i	−0.988416	−	0.151769i	$-0.951503\pi$
$73$	−5.34551	−	9.25869i	−0.625644	−	1.08365i	0.362772	−	0.931878i	$-0.381830\pi$
$74$	0.475793	−	0.824098i	0.0553098	−	0.0957995i
$75$	−3.78715	+	3.48026i	−0.437303	+	0.401866i
$76$	−3.11297	+	5.39183i	−0.357083	+	0.618485i
$77$		0			0
$78$	−2.35489	+	2.16407i	−0.266639	+	0.245032i
$79$	−1.84491			−0.207569			−0.103785	−	0.994600i	$-0.533095\pi$
$79$	−1.84491			−0.207569			−0.103785	+	0.994600i	$0.533095\pi$
$80$	1.07286	+	1.85825i	0.119950	+	0.207759i
$81$	3.12651	+	8.43949i	0.347390	+	0.937721i
$82$	−0.0833788	+	0.144416i	−0.00920765	+	0.0159481i
$83$	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
$87$	−2.56984	−	11.5139i	−0.275516	−	1.23442i
$88$	−5.86792	+	10.1635i	−0.625522	+	1.08344i
$89$	−6.76292	+	11.7137i	−0.716868	+	1.24165i	0.245366	+	0.969430i	$0.421092\pi$
$89$	−6.76292	+	11.7137i	−0.716868	+	1.24165i	−0.962235	+	0.272222i	$0.912242\pi$
$90$	−0.241583	+	2.85534i	−0.0254651	+	0.300980i
$91$		0			0
$92$	4.21515	+	7.30085i	0.439460	+	0.761167i
$93$	4.14122	+	1.29921i	0.429424	+	0.134722i
$94$	6.35193			0.655152
$95$	5.72119			0.586982
$96$	−9.53509	−	2.99142i	−0.973171	−	0.305310i
$97$	−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
$100$	−2.30238	+	3.98783i	−0.230238	+	0.398783i
$101$	−2.56770	+	4.44739i	−0.255496	+	0.442531i	−0.965030	−	0.262139i	$-0.915572\pi$
$101$	−2.56770	+	4.44739i	−0.255496	+	0.442531i	0.709534	+	0.704671i	$0.248905\pi$
$102$	0.283187	+	1.26878i	0.0280397	+	0.125628i
$103$	−7.10561	−	12.3073i	−0.700137	−	1.21267i	−0.968418	−	0.249332i	$-0.919789\pi$
$103$	−7.10561	−	12.3073i	−0.700137	−	1.21267i	0.268282	−	0.963341i	$-0.413544\pi$
$104$	−3.27814	+	5.67791i	−0.321448	+	0.556765i
$105$		0			0
$106$	−0.274990	−	0.476296i	−0.0267094	−	0.0462620i
$107$	3.83015	−	6.63401i	0.370274	−	0.641334i	−0.619333	−	0.785128i	$-0.712597\pi$
$107$	3.83015	−	6.63401i	0.370274	−	0.641334i	0.989608	+	0.143794i	$0.0459303\pi$
$108$	4.93244	+	6.37129i	0.474624	+	0.613078i
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	0.822476	−	0.568800i	$-0.192592\pi$
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	−0.903833	+	0.427885i	$0.859259\pi$
$110$	4.70979			0.449061
$111$	−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	$0.175662\pi$
$114$	−3.43244	+	3.15429i	−0.321477	+	0.295426i
$115$	3.87341	−	6.70895i	0.361198	−	0.625613i
$116$	−5.28083	−	9.14666i	−0.490312	−	0.849246i
$117$	7.47954	−	3.51385i	0.691484	−	0.324855i
$118$	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
$122$	−0.0504522			−0.00456773
$123$	0.317261	−	0.291552i	0.0286065	−	0.0262884i
$124$	3.88569			0.348945
$125$	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	$0.395611\pi$
$128$	−10.9656			−0.969227
$129$	0.376030	+	1.68475i	0.0331076	+	0.148334i
$130$	2.63115			0.230767
$131$	−10.2265	−	17.7128i	−0.893492	−	1.54757i	−0.835660	−	0.549248i	$-0.814914\pi$
$131$	−10.2265	−	17.7128i	−0.893492	−	1.54757i	−0.0578326	−	0.998326i	$-0.518419\pi$
$132$	9.75105	−	8.96088i	0.848720	−	0.779945i
$133$		0			0
$134$	−8.43794			−0.728927
$135$	2.80409	−	6.85267i	0.241337	−	0.589784i
$136$	1.33248	+	2.30793i	0.114260	+	0.197903i
$137$	−6.10581	+	10.5756i	−0.521655	+	0.903532i	0.478028	+	0.878345i	$0.341352\pi$
$137$	−6.10581	+	10.5756i	−0.521655	+	0.903532i	−0.999683	+	0.0251879i	$0.991982\pi$
$138$	1.37502	+	6.16059i	0.117049	+	0.524425i
$139$	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
$142$	0.0539585			0.00452810
$143$	−6.79117	−	11.7626i	−0.567906	−	0.983642i
$144$	3.70792	+	2.58054i	0.308994	+	0.215045i
$145$	−4.85269	+	8.40511i	−0.402994	+	0.698006i
$146$	−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	0.986331	−	0.164777i	$-0.0526903\pi$
$149$	4.27797	+	7.40966i	0.350465	+	0.607023i	−0.635866	+	0.771799i	$0.719357\pi$
$150$	−2.53865	+	2.33293i	−0.207280	+	0.190483i
$151$	8.82962	−	15.2933i	0.718544	−	1.24455i	−0.243033	−	0.970018i	$-0.578142\pi$
$151$	8.82962	−	15.2933i	0.718544	−	1.24455i	0.961577	−	0.274537i	$-0.0885244\pi$
$152$	−4.77814	+	8.27599i	−0.387559	+	0.671271i
$153$	0.283187	−	3.34708i	0.0228943	−	0.270595i
$154$		0			0
$155$	−1.78533	−	3.09228i	−0.143401	−	0.248378i
$156$	5.44748	−	5.00605i	0.436148	−	0.400805i
$157$	−6.32149			−0.504510			−0.252255	−	0.967661i	$-0.581172\pi$
$157$	−6.32149			−0.504510			−0.252255	+	0.967661i	$0.581172\pi$
$158$	−1.23671			−0.0983871
$159$	0.309561	+	1.38695i	0.0245498	+	0.109992i
$160$	4.11070	+	7.11993i	0.324979	+	0.562880i
$161$		0			0
$162$	2.09580	+	5.65726i	0.164662	+	0.444477i
$163$	−4.01134	+	6.94784i	−0.314192	+	0.544197i	−0.979265	−	0.202581i	$-0.935067\pi$
$163$	−4.01134	+	6.94784i	−0.314192	+	0.544197i	0.665073	+	0.746778i	$0.268400\pi$
$164$	0.192877	−	0.334073i	0.0150612	−	0.0260867i
$165$	−11.6114	−	3.64283i	−0.903950	−	0.283594i
$166$	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
$170$	0.534749	−	0.926212i	0.0410133	−	0.0710372i
$171$	10.9020	−	5.12170i	0.833697	−	0.391666i
$172$	0.772712	+	1.33838i	0.0589187	+	0.102050i
$173$	18.2881			1.39042			0.695208	−	0.718808i	$-0.255312\pi$
$173$	18.2881			1.39042			0.695208	+	0.718808i	$0.255312\pi$
$174$	−1.72265	−	7.71812i	−0.130594	−	0.585109i
$175$		0			0
$176$	3.71247	−	6.43018i	0.279838	−	0.484693i
$177$	−10.8810	−	3.41367i	−0.817868	−	0.256587i
$178$	−4.53341	+	7.85209i	−0.339793	+	0.588539i
$179$	3.81276	+	6.60389i	0.284979	+	0.493598i	0.972604	−	0.232468i	$-0.0746801\pi$
$179$	3.81276	+	6.60389i	0.284979	+	0.493598i	−0.687625	+	0.726066i	$0.741347\pi$
$180$	0.558844	−	6.60516i	0.0416538	−	0.492319i
$181$	−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
$185$	2.02280			0.148719
$186$	2.77599	+	0.870905i	0.203546	+	0.0638578i
$187$	−5.52088			−0.403727
$188$	−14.6937			−1.07165
$189$		0			0
$190$	3.83510			0.278227
$191$	14.8325			1.07324			0.536620	−	0.843824i	$-0.319701\pi$
$191$	14.8325			1.07324			0.536620	+	0.843824i	$0.319701\pi$
$192$	−1.41451	−	0.443769i	−0.102083	−	0.0320263i
$193$	16.5677			1.19257			0.596286	−	0.802772i	$-0.296642\pi$
$193$	16.5677			1.19257			0.596286	+	0.802772i	$0.296642\pi$
$194$	−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	$0.545941\pi$
$198$	8.97472	−	4.21628i	0.637806	−	0.299638i
$199$	12.6407	+	21.8943i	0.896076	+	1.55205i	0.832468	+	0.554074i	$0.186927\pi$
$199$	12.6407	+	21.8943i	0.896076	+	1.55205i	0.0636081	+	0.997975i	$0.479739\pi$
$200$	−3.53395	+	6.12097i	−0.249888	+	0.432818i
$201$	20.8028	+	6.52640i	1.46732	+	0.460337i
$202$	−1.72121	+	2.98123i	−0.121104	+	0.209758i
$203$		0			0
$204$	−0.655085	−	2.93503i	−0.0458651	−	0.205493i
$205$	−0.354480			−0.0247579
$206$	−4.76312	−	8.24997i	−0.331862	−	0.574803i
$207$	1.37502	−	16.2518i	0.0955703	−	1.12958i
$208$	2.07399	−	3.59226i	0.143805	−	0.249078i
$209$	−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
$213$	−0.133029	−	0.0417347i	−0.00911497	−	0.00285961i
$214$	2.56747	−	4.44699i	0.175509	−	0.303990i
$215$	0.710065	−	1.22987i	0.0484261	−	0.0838764i
$216$	7.57086	+	9.77938i	0.515132	+	0.665402i
$217$		0			0
$218$	−0.569377	−	0.986190i	−0.0385631	−	0.0667932i
$219$	4.03374	+	18.0727i	0.272575	+	1.22124i
$220$	−10.8950			−0.734538
$221$	−3.08427			−0.207471
$222$	−1.21358	+	1.11524i	−0.0814504	+	0.0748501i
$223$	−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
$226$	−0.201335	+	0.348723i	−0.0133926	+	0.0231967i
$227$	−14.4832	+	25.0857i	−0.961286	+	1.66500i	−0.242009	+	0.970274i	$0.577806\pi$
$227$	−14.4832	+	25.0857i	−0.961286	+	1.66500i	−0.719277	+	0.694723i	$0.755527\pi$
$228$	7.94012	−	7.29670i	0.525847	−	0.483235i
$229$	7.71790	+	13.3678i	0.510013	+	0.883369i	0.999933	+	0.0116012i	$0.00369285\pi$
$229$	7.71790	+	13.3678i	0.510013	+	0.883369i	−0.489919	+	0.871768i	$0.662974\pi$
$230$	2.59648	−	4.49723i	0.171207	−	0.296538i
$231$		0			0
$232$	−8.10561	−	14.0393i	−0.532159	−	0.921727i
$233$	−2.47324	+	4.28378i	−0.162027	+	0.280640i	−0.935596	−	0.353073i	$-0.885137\pi$
$233$	−2.47324	+	4.28378i	−0.162027	+	0.280640i	0.773568	+	0.633713i	$0.218470\pi$
$234$	5.01378	−	2.35545i	0.327761	−	0.153980i
$235$	6.75121	+	11.6934i	0.440400	+	0.762795i
$236$	−10.2096			−0.664589
$237$	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	$0.0281456\pi$
$240$	−0.809586	−	3.62725i	−0.0522586	−	0.234138i
$241$	7.29123	−	12.6288i	0.469670	−	0.813492i	−0.529729	−	0.848167i	$-0.677706\pi$
$241$	7.29123	−	12.6288i	0.469670	−	0.813492i	0.999399	+	0.0346754i	$0.0110397\pi$
$242$	−4.46191	−	7.72826i	−0.286823	−	0.496791i
$243$	−0.791301	−	15.5684i	−0.0507620	−	0.998711i
$244$	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
$248$	5.96419			0.378726
$249$	−5.46019	−	24.4637i	−0.346026	−	1.55032i
$250$	7.61238			0.481449
$251$	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
$254$	4.86646			0.305349
$255$	−2.03475	+	1.86986i	−0.127421	+	0.117095i
$256$	−9.06240			−0.566400
$257$	−4.18108	−	7.24184i	−0.260808	−	0.451733i	0.705649	−	0.708562i	$-0.250656\pi$
$257$	−4.18108	−	7.24184i	−0.260808	−	0.451733i	−0.966457	+	0.256829i	$0.917322\pi$
$258$	0.252065	+	1.12935i	0.0156929	+	0.0703100i
$259$		0			0
$260$	−6.08653			−0.377471
$261$	−1.72265	+	20.3605i	−0.106629	+	1.26029i
$262$	−6.85515	−	11.8735i	−0.423512	−	0.733545i
$263$	−1.63533	+	2.83247i	−0.100839	+	0.174658i	−0.912030	−	0.410122i	$-0.865486\pi$
$263$	−1.63533	+	2.83247i	−0.100839	+	0.174658i	0.811192	+	0.584780i	$0.198819\pi$
$264$	14.9670	−	13.7542i	0.921157	−	0.846511i
$265$	0.584551	−	1.01247i	0.0359087	−	0.0621956i
$266$		0			0
$267$	17.2499	−	15.8520i	1.05568	−	0.970129i
$268$	19.5192			1.19232
$269$	7.69349	+	13.3255i	0.469081	+	0.812471i	0.999375	−	0.0353420i	$-0.0112521\pi$
$269$	7.69349	+	13.3255i	0.469081	+	0.812471i	−0.530295	+	0.847813i	$0.677919\pi$
$270$	1.87967	−	4.59357i	0.114393	−	0.279556i
$271$	−4.06308	+	7.03747i	−0.246815	+	0.427496i	−0.962640	−	0.270783i	$-0.912717\pi$
$271$	−4.06308	+	7.03747i	−0.246815	+	0.427496i	0.715825	+	0.698279i	$0.246051\pi$
$272$	−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
$276$	−3.18077	−	14.2511i	−0.191460	−	0.857813i
$277$	−6.42287	+	11.1247i	−0.385913	+	0.668421i	−0.991895	−	0.127057i	$-0.959447\pi$
$277$	−6.42287	+	11.1247i	−0.385913	+	0.668421i	0.605982	+	0.795478i	$0.292780\pi$
$278$	0.831826	−	1.44077i	0.0498896	−	0.0864114i
$279$	−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	$0.847087\pi$
$282$	−10.4974	−	3.29332i	−0.625111	−	0.196114i
$283$	17.4385			1.03661			0.518306	−	0.855195i	$-0.326563\pi$
$283$	17.4385			1.03661			0.518306	+	0.855195i	$0.326563\pi$
$284$	−0.124820			−0.00740671
$285$	−9.45500	−	2.96629i	−0.560066	−	0.175708i
$286$	−4.55234	−	7.88489i	−0.269186	−	0.466243i
$287$		0			0
$288$	14.2070	+	9.88741i	0.837156	+	0.582621i
$289$	7.87316	−	13.6367i	0.463127	−	0.802160i
$290$	−3.25292	+	5.63422i	−0.191018	+	0.330853i
$291$	2.03864	+	9.13386i	0.119507	+	0.535437i
$292$	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
$296$	−1.68938	+	2.92609i	−0.0981931	+	0.170075i
$297$	−25.3873	+	3.45317i	−1.47312	+	0.200373i
$298$	2.86766	+	4.96693i	0.166119	+	0.287727i
$299$	−14.9757			−0.866068
$300$	5.87256	−	5.39668i	0.339053	−	0.311578i
$301$		0			0
$302$	5.91878	−	10.2516i	0.340588	−	0.589915i
$303$	6.54931	−	6.01859i	0.376248	−	0.345759i
$304$	3.02300	−	5.23599i	0.173381	−	0.300305i
$305$	−0.0536236	−	0.0928787i	−0.00307048	−	0.00531822i
$306$	0.189830	−	2.24366i	0.0108518	−	0.128261i
$307$	−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
$311$	16.9293			0.959970			0.479985	−	0.877277i	$-0.340642\pi$
$311$	16.9293			0.959970			0.479985	+	0.877277i	$0.340642\pi$
$312$	8.36141	−	7.68385i	0.473372	−	0.435012i
$313$	8.27856			0.467932			0.233966	−	0.972245i	$-0.424830\pi$
$313$	8.27856			0.467932			0.233966	+	0.972245i	$0.424830\pi$
$314$	−4.23750			−0.239136
$315$		0			0
$316$	2.86082			0.160934
$317$	6.54741			0.367739			0.183870	−	0.982951i	$-0.441138\pi$
$317$	6.54741			0.367739			0.183870	+	0.982951i	$0.441138\pi$
$318$	0.207509	+	0.929717i	0.0116365	+	0.0521359i
$319$	33.5840			1.88034
$320$	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
$324$	−4.84814	−	13.0867i	−0.269341	−	0.727040i
$325$	−4.08997	−	7.08404i	−0.226871	−	0.392952i
$326$	−2.68893	+	4.65736i	−0.148926	+	0.257947i
$327$	0.640957	+	2.87173i	0.0354450	+	0.158807i
$328$	0.296049	−	0.512773i	0.0163466	−	0.0283131i
$329$		0			0
$330$	−7.78353	−	2.44191i	−0.428469	−	0.134422i
$331$	−26.7258			−1.46899			−0.734493	−	0.678617i	$-0.762580\pi$
$331$	−26.7258			−1.46899			−0.734493	+	0.678617i	$0.762580\pi$
$332$	−11.2203	−	19.4341i	−0.615792	−	1.06658i
$333$	3.85455	−	1.81085i	0.211228	−	0.0992337i
$334$	−0.710806	+	1.23115i	−0.0388936	+	0.0673657i
$335$	−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
$339$	0.766092	−	0.704012i	0.0416084	−	0.0382367i
$340$	−1.23701	+	2.14257i	−0.0670864	+	0.116197i
$341$	−6.17786	+	10.7004i	−0.334550	+	0.579457i
$342$	7.30796	−	3.43324i	0.395169	−	0.185648i
$343$		0			0
$344$	1.18605	+	2.05429i	0.0639473	+	0.110760i
$345$	−9.87974	+	9.07914i	−0.531907	+	0.488805i
$346$	12.2591			0.659053
$347$	−18.7031			−1.00404			−0.502018	−	0.864857i	$-0.667409\pi$
$347$	−18.7031			−1.00404			−0.502018	+	0.864857i	$0.667409\pi$
$348$	3.98494	+	17.8540i	0.213615	+	0.957076i
$349$	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
$352$	14.2244	−	24.6374i	0.758164	−	1.31318i
$353$	3.12966	−	5.42074i	0.166575	−	0.288517i	−0.770638	−	0.637273i	$-0.780062\pi$
$353$	3.12966	−	5.42074i	0.166575	−	0.288517i	0.937214	+	0.348756i	$0.113396\pi$
$354$	−7.29391	−	2.28830i	−0.387667	−	0.121622i
$355$	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
$359$	−5.09755	+	8.82921i	−0.269038	+	0.465988i	−0.968614	−	0.248571i	$-0.920039\pi$
$359$	−5.09755	+	8.82921i	−0.269038	+	0.465988i	0.699575	+	0.714559i	$0.253372\pi$
$360$	0.857777	−	10.1383i	0.0452088	−	0.534338i
$361$	1.43970	+	2.49364i	0.0757739	+	0.131244i
$362$	−10.4106			−0.547171
$363$	5.02285	+	22.5042i	0.263631	+	1.18117i
$364$		0			0
$365$	7.61701	−	13.1931i	0.398693	−	0.690556i
$366$	0.0833788	+	0.0261582i	0.00435828	+	0.00136731i
$367$	−14.3278	+	24.8165i	−0.747906	+	1.29541i	0.200918	+	0.979608i	$0.435608\pi$
$367$	−14.3278	+	24.8165i	−0.747906	+	1.29541i	−0.948824	+	0.315804i	$0.897726\pi$
$368$	−4.09332	−	7.08984i	−0.213379	−	0.369584i
$369$	−0.675478	+	0.317336i	−0.0351640	+	0.0165198i
$370$	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	0.995546	−	0.0942796i	$-0.0300548\pi$
$373$	8.03670	+	13.9200i	0.416124	+	0.720749i	−0.579421	+	0.815028i	$0.696721\pi$
$374$	−3.70083			−0.191365
$375$	−18.7674	−	5.88786i	−0.969147	−	0.304048i
$376$	−22.5535			−1.16311
$377$	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	$0.508331\pi$
$380$	−8.87158			−0.455103
$381$	−11.9977	−	3.76401i	−0.614661	−	0.192836i
$382$	9.94270			0.508713
$383$	−5.79327	−	10.0342i	−0.296022	−	0.512725i	0.679200	−	0.733953i	$-0.262327\pi$
$383$	−5.79327	−	10.0342i	−0.296022	−	0.512725i	−0.975222	+	0.221228i	$0.928994\pi$
$384$	18.1220	+	5.68536i	0.924784	+	0.290130i
$385$		0			0
$386$	11.1059			0.565275
$387$	0.252065	−	2.97924i	0.0128132	−	0.151443i
$388$	4.18924	+	7.25598i	0.212677	+	0.368367i
$389$	−8.90675	+	15.4270i	−0.451590	+	0.782178i	−0.998485	−	0.0550239i	$-0.982476\pi$
$389$	−8.90675	+	15.4270i	−0.451590	+	0.782178i	0.546895	+	0.837201i	$0.315810\pi$
$390$	−4.34831	−	1.36418i	−0.220185	−	0.0690782i
$391$	−3.04363	+	5.27172i	−0.153923	+	0.266602i
$392$		0			0
$393$	7.71695	+	34.5749i	0.389269	+	1.74407i
$394$	−2.70640			−0.136346
$395$	−1.31444	−	2.27668i	−0.0661369	−	0.114552i
$396$	−20.7609	+	9.75334i	−1.04327	+	0.490124i
$397$	6.54229	−	11.3316i	0.328348	−	0.568715i	−0.653836	−	0.756636i	$-0.726841\pi$
$397$	6.54229	−	11.3316i	0.328348	−	0.568715i	0.982184	+	0.187921i	$0.0601748\pi$
$398$	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	0.634482	−	0.772938i	$-0.281213\pi$
$401$	−7.05165	−	12.2138i	−0.352143	−	0.609929i	−0.986625	+	0.163009i	$0.947880\pi$
$402$	13.9448	+	4.37486i	0.695503	+	0.218198i
$403$	−3.45129	+	5.97782i	−0.171921	+	0.297776i
$404$	3.98161	−	6.89636i	0.198093	−	0.343107i
$405$	−8.18706	+	9.87108i	−0.406818	+	0.490498i
$406$		0			0
$407$	−3.49980	−	6.06183i	−0.173479	−	0.300474i
$408$	−1.00550	−	4.50501i	−0.0497796	−	0.223031i
$409$	2.64599			0.130836			0.0654179	−	0.997858i	$-0.479162\pi$
$409$	2.64599			0.130836			0.0654179	+	0.997858i	$0.479162\pi$
$410$	−0.237619			−0.0117352
$411$	15.5738	−	14.3118i	0.768200	−	0.705949i
$412$	11.0183	+	19.0843i	0.542835	+	0.940217i
$413$		0			0
$414$	0.921719	−	10.8941i	0.0453000	−	0.535415i
$415$	−10.3106	+	17.8585i	−0.506128	+	0.876639i
$416$	7.94655	−	13.7638i	0.389612	−	0.674827i
$417$	−3.16515	+	2.90866i	−0.154998	+	0.142438i
$418$	−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	$0.870956\pi$
$422$	−2.52210	+	4.36841i	−0.122774	+	0.212651i
$423$	23.3329	+	16.2386i	1.13448	+	0.789548i
$424$	0.976394	+	1.69116i	0.0474179	+	0.0821302i
$425$	−3.32495			−0.161284
$426$	−0.0891734	−	0.0279761i	−0.00432047	−	0.00135545i
$427$		0			0
$428$	−5.93923	+	10.2871i	−0.287084	+	0.497244i
$429$	5.12465	+	22.9603i	0.247420	+	1.10854i
$430$	0.475980	−	0.824422i	0.0229538	−	0.0397571i
$431$	17.6643	+	30.5954i	0.850858	+	1.47373i	0.880435	+	0.474166i	$0.157251\pi$
$431$	17.6643	+	30.5954i	0.850858	+	1.47373i	−0.0295774	+	0.999562i	$0.509416\pi$
$432$	−4.78988	−	6.18714i	−0.230453	−	0.297679i
$433$	−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
$437$	−21.8282			−1.04419
$438$	2.70395	+	12.1147i	0.129200	+	0.578864i
$439$	−6.39812			−0.305365			−0.152683	−	0.988275i	$-0.548791\pi$
$439$	−6.39812			−0.305365			−0.152683	+	0.988275i	$0.548791\pi$
$440$	−16.7228			−0.797229
$441$		0			0
$442$	−2.06749			−0.0983404
$443$	−6.38682			−0.303447			−0.151723	−	0.988423i	$-0.548482\pi$
$443$	−6.38682			−0.303447			−0.151723	+	0.988423i	$0.548482\pi$
$444$	2.80734	−	2.57985i	0.133230	−	0.122434i
$445$	−19.2735			−0.913650
$446$	−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	$0.589394\pi$
$450$	5.40502	−	2.53925i	0.254795	−	0.119701i
$451$	0.613311	+	1.06229i	0.0288797	+	0.0500210i
$452$	0.465741	−	0.806687i	0.0219066	−	0.0379434i
$453$	−22.5213	+	20.6963i	−1.05814	+	0.972397i
$454$	−9.70859	+	16.8158i	−0.455647	+	0.789203i
$455$		0			0
$456$	12.1874	−	11.1998i	0.570727	−	0.524478i
$457$	10.5224			0.492217			0.246108	−	0.969242i	$-0.420848\pi$
$457$	10.5224			0.492217			0.246108	+	0.969242i	$0.420848\pi$
$458$	5.17356	+	8.96087i	0.241745	+	0.418714i
$459$	−2.20338	+	5.38465i	−0.102845	+	0.251334i
$460$	−6.00633	+	10.4033i	−0.280046	+	0.485055i
$461$	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
$465$	1.34722	+	6.03604i	0.0624758	+	0.279915i
$466$	−1.65789	+	2.87156i	−0.0768004	+	0.133022i
$467$	−1.96216	+	3.39856i	−0.0907978	+	0.157266i	−0.907847	−	0.419301i	$-0.862275\pi$
$467$	−1.96216	+	3.39856i	−0.0907978	+	0.157266i	0.817049	+	0.576568i	$0.195608\pi$
$468$	−11.5982	+	5.44876i	−0.536126	+	0.251869i
$469$		0			0
$470$	4.52555	+	7.83849i	0.208748	+	0.361563i
$471$	10.4471	+	3.27753i	0.481376	+	0.151021i
$472$	−15.6709			−0.721310
$473$	−4.91414			−0.225952
$474$	2.04382	+	0.641201i	0.0938757	+	0.0294513i
$475$	−5.96145	−	10.3255i	−0.273530	−	0.473768i
$476$		0			0
$477$	0.207509	−	2.45261i	0.00950117	−	0.112297i
$478$	4.36878	−	7.56694i	0.199823	−	0.346104i
$479$	8.04324	−	13.9313i	0.367505	−	0.636537i	−0.621670	−	0.783279i	$-0.713545\pi$
$479$	8.04324	−	13.9313i	0.367505	−	0.636537i	0.989175	+	0.146742i	$0.0468787\pi$
$480$	−3.10195	−	13.8979i	−0.141584	−	0.634350i
$481$	−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
$485$	3.84961	−	6.66771i	0.174802	−	0.302765i
$486$	−0.530435	−	10.4360i	−0.0240610	−	0.473386i
$487$	−1.75172	−	3.03407i	−0.0793781	−	0.137487i	0.823604	−	0.567166i	$-0.191960\pi$
$487$	−1.75172	−	3.03407i	−0.0793781	−	0.137487i	−0.902982	+	0.429679i	$0.858627\pi$
$488$	0.179138			0.00810921
$489$	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	$0.788520\pi$
$492$	−0.491962	+	0.452096i	−0.0221794	+	0.0203821i
$493$	3.81312	−	6.60452i	0.171734	−	0.297452i
$494$	−3.70689	−	6.42053i	−0.166781	−	0.288873i
$495$	17.3007	+	12.0405i	0.777609	+	0.541180i
$496$	−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	0.702722	−	0.711465i	$-0.251968\pi$
$499$	−5.91486	−	10.2448i	−0.264785	−	0.458622i	−0.967507	+	0.252843i	$0.918634\pi$
$500$	−17.6094			−0.787517
$501$	2.70466	−	2.48549i	0.120835	−	0.111043i
$502$	9.43261			0.420998
$503$	−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
$506$	−17.9694			−0.798837
$507$	−2.04202	−	9.14901i	−0.0906892	−	0.406322i
$508$	−11.2574			−0.499466
$509$	8.44831	+	14.6329i	0.374465	+	0.648592i	0.990247	−	0.139324i	$-0.0444931\pi$
$509$	8.44831	+	14.6329i	0.374465	+	0.648592i	−0.615782	+	0.787917i	$0.711160\pi$
$510$	−1.36396	+	1.25343i	−0.0603971	+	0.0555029i
$511$		0			0
$512$	15.8563			0.700756
$513$	−20.6724	+	2.81186i	−0.912710	+	0.124147i
$514$	−2.80271	−	4.85444i	−0.123622	−	0.214120i
$515$	10.1250	−	17.5371i	0.446163	−	0.772777i
$516$	−0.583092	−	2.61247i	−0.0256692	−	0.115008i
$517$	23.3615	−	40.4633i	1.02744	−	1.77957i
$518$		0			0
$519$	−30.2234	−	9.48190i	−1.32666	−	0.416209i
$520$	−9.34230			−0.409687
$521$	17.2466	+	29.8720i	0.755587	+	1.30872i	0.945082	+	0.326834i	$0.105982\pi$
$521$	17.2466	+	29.8720i	0.755587	+	1.30872i	−0.189495	+	0.981882i	$0.560685\pi$
$522$	−1.15475	+	13.6483i	−0.0505420	+	0.597371i
$523$	−0.995615	+	1.72445i	−0.0435352	+	0.0754051i	−0.886972	−	0.461823i	$-0.847195\pi$
$523$	−0.995615	+	1.72445i	−0.0435352	+	0.0754051i	0.843437	+	0.537229i	$0.180529\pi$
$524$	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
$528$	−9.46922	+	8.70189i	−0.412095	+	0.378701i
$529$	−3.27836	+	5.67829i	−0.142538	+	0.246882i
$530$	0.391843	−	0.678693i	0.0170206	−	0.0294805i
$531$	16.2124	+	11.2831i	0.703558	+	0.489644i
$532$		0			0
$533$	0.342629	+	0.593452i	0.0148409	+	0.0257052i
$534$	11.5632	−	10.6261i	0.500387	−	0.459838i
$535$	10.9154			0.471916
$536$	29.9602			1.29408
$537$	−2.87712	−	12.8906i	−0.124157	−	0.556270i
$538$	5.15720	+	8.93253i	0.222343	+	0.385109i
$539$		0			0
$540$	−4.34817	+	10.6261i	−0.187115	+	0.457276i
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	0.335810	+	0.941930i	$0.390990\pi$
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	−0.983640	+	0.180145i	$0.942343\pi$
$542$	−2.72362	+	4.71745i	−0.116989	+	0.202632i
$543$	25.6662	+	8.05220i	1.10144	+	0.345553i
$544$	−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	$0.726823\pi$
$548$	9.46800	−	16.3991i	0.404453	−	0.700533i
$549$	−0.185329	−	0.128980i	−0.00790964	−	0.00550474i
$550$	−4.90757	−	8.50016i	−0.209260	−	0.362448i
$551$	27.3469			1.16502
$552$	−4.88221	−	21.8741i	−0.207801	−	0.931025i
$553$		0			0
$554$	−4.30546	+	7.45728i	−0.182921	+	0.316829i
$555$	−3.34294	−	1.04877i	−0.141900	−	0.0445179i
$556$	−1.92423	+	3.33287i	−0.0816056	+	0.141345i
$557$	−11.6412	−	20.1631i	−0.493252	−	0.854338i	0.506718	−	0.862112i	$-0.330859\pi$
$557$	−11.6412	−	20.1631i	−0.493252	−	0.854338i	−0.999970	+	0.00777438i	$0.997525\pi$
$558$	−4.13615	−	2.87857i	−0.175097	−	0.121859i
$559$	−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
$563$	−4.55885			−0.192133			−0.0960663	−	0.995375i	$-0.530626\pi$
$563$	−4.55885			−0.192133			−0.0960663	+	0.995375i	$0.530626\pi$
$564$	24.2832	+	7.61830i	1.02251	+	0.320788i
$565$	−0.855964			−0.0360107
$566$	11.6896			0.491351
$567$		0			0
$568$	−0.191588			−0.00803885
$569$	18.1995			0.762963			0.381482	−	0.924376i	$-0.375414\pi$
$569$	18.1995			0.762963			0.381482	+	0.924376i	$0.375414\pi$
$570$	−6.33800	−	1.98840i	−0.265470	−	0.0832850i
$571$	−17.0455			−0.713332			−0.356666	−	0.934232i	$-0.616087\pi$
$571$	−17.0455			−0.713332			−0.356666	+	0.934232i	$0.616087\pi$
$572$	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
$576$	2.10757	+	1.46677i	0.0878155	+	0.0611155i
$577$	5.70473	+	9.88088i	0.237491	+	0.411346i	0.959994	−	0.280022i	$-0.0903417\pi$
$577$	5.70473	+	9.88088i	0.237491	+	0.411346i	−0.722503	+	0.691368i	$0.757008\pi$
$578$	5.27764	−	9.14113i	0.219521	−	0.380221i
$579$	−27.3803	−	8.58995i	−1.13789	−	0.356986i
$580$	7.52485	−	13.0334i	0.312452	−	0.541183i
$581$		0			0
$582$	1.36657	+	6.12273i	0.0566460	+	0.253795i
$583$	−4.04549			−0.167547
$584$	12.7229	+	22.0368i	0.526479	+	0.911889i
$585$	9.66514	+	6.72649i	0.399604	+	0.278106i
$586$	0.603332	−	1.04500i	0.0249234	−	0.0431686i
$587$	−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
$591$	6.67232	+	2.09329i	0.274463	+	0.0861064i
$592$	1.06882	−	1.85126i	0.0439283	−	0.0760861i
$593$	9.98892	−	17.3013i	0.410196	−	0.710480i	−0.584715	−	0.811239i	$-0.698794\pi$
$593$	9.98892	−	17.3013i	0.410196	−	0.710480i	0.994911	+	0.100759i	$0.0321271\pi$
$594$	−17.0179	+	2.31477i	−0.698254	+	0.0949763i
$595$		0			0
$596$	−6.63365	−	11.4898i	−0.271725	−	0.470641i
$597$	−9.53873	−	42.7371i	−0.390394	−	1.74911i
$598$	−10.0387			−0.410513
$599$	4.39321			0.179502			0.0897508	−	0.995964i	$-0.471393\pi$
$599$	4.39321			0.179502			0.0897508	+	0.995964i	$0.471393\pi$
$600$	9.01387	−	8.28344i	0.367990	−	0.338170i
$601$	−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
$604$	−13.6917	+	23.7147i	−0.557107	+	0.964937i
$605$	9.48476	−	16.4281i	0.385610	−	0.667897i
$606$	4.39022	−	4.03446i	0.178340	−	0.163889i
$607$	6.56281	+	11.3671i	0.266376	+	0.461377i	0.967923	−	0.251246i	$-0.0808403\pi$
$607$	6.56281	+	11.3671i	0.266376	+	0.461377i	−0.701547	+	0.712623i	$0.747507\pi$
$608$	11.5827	−	20.0618i	0.469741	−	0.813615i
$609$		0			0
$610$	−0.0359456	−	0.0622597i	−0.00145540	−	0.00252082i
$611$	13.0510	−	22.6051i	0.527988	−	0.914502i
$612$	−0.439125	+	5.19016i	−0.0177506	+	0.209800i
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.767960	−	0.640497i	$-0.778728\pi$
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.170707	−	0.985322i	$-0.554605\pi$
$614$	−0.713754			−0.0288048
$615$	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	$-0.0269572\pi$
$618$	3.59427	+	16.1037i	0.144583	+	0.647786i
$619$	15.9606	−	27.6446i	0.641511	−	1.11113i	−0.343585	−	0.939122i	$-0.611641\pi$
$619$	15.9606	−	27.6446i	0.641511	−	1.11113i	0.985096	−	0.172008i	$-0.0550254\pi$
$620$	2.76843	+	4.79506i	0.111183	+	0.192574i
$621$	−10.6985	+	26.1452i	−0.429317	+	1.04917i
$622$	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
$626$	5.54939			0.221798
$627$	7.46956	+	33.4664i	0.298306	+	1.33652i
$628$	9.80244			0.391160
$629$	−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	$0.219918\pi$
$632$	4.39112			0.174669
$633$	9.59675	−	8.81908i	0.381436	−	0.350527i
$634$	4.38895			0.174307
$635$	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
$639$	0.198209	+	0.137944i	0.00784101	+	0.00545698i
$640$	−7.81261	−	13.5318i	−0.308821	−	0.534893i
$641$	20.2001	−	34.9875i	0.797854	−	1.38192i	−0.123157	−	0.992387i	$-0.539302\pi$
$641$	20.2001	−	34.9875i	0.797854	−	1.38192i	0.921011	−	0.389537i	$-0.127365\pi$
$642$	−6.54874	+	6.01806i	−0.258458	+	0.237514i
$643$	−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
$646$	−3.01352			−0.118565
$647$	−17.2774	−	29.9253i	−0.679245	−	1.17649i	−0.975209	−	0.221287i	$-0.928974\pi$
$647$	−17.2774	−	29.9253i	−0.679245	−	1.17649i	0.295964	−	0.955199i	$-0.404359\pi$
$648$	−7.44147	−	20.0870i	−0.292328	−	0.789091i
$649$	16.2323	−	28.1151i	0.637173	−	1.10362i
$650$	−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	0.997395	−	0.0721392i	$-0.0229826\pi$
$653$	11.1472	+	19.3075i	0.436223	+	0.755560i	−0.561172	+	0.827699i	$0.689649\pi$
$654$	0.429654	+	1.92501i	0.0168008	+	0.0752740i
$655$	14.5721	−	25.2396i	0.569379	−	0.986194i
$656$	−0.187302	+	0.324417i	−0.00731293	+	0.0126664i
$657$	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	$0.788861\pi$
$660$	18.0053	+	5.64876i	0.700857	+	0.219878i
$661$	−42.9060			−1.66885			−0.834425	−	0.551122i	$-0.814200\pi$
$661$	−42.9060			−1.66885			−0.834425	+	0.551122i	$0.814200\pi$
$662$	−17.9152			−0.696294
$663$	5.09716	+	1.59912i	0.197957	+	0.0621046i
$664$	−17.2221	−	29.8296i	−0.668349	−	1.15761i
$665$		0			0
$666$	2.58383	−	1.21387i	0.100121	−	0.0470365i
$667$	18.5146	−	32.0683i	0.716889	−	1.24169i
$668$	1.64428	−	2.84798i	0.0636191	−	0.110192i
$669$	4.89912	+	21.9499i	0.189411	+	0.848632i
$670$	−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	$-0.425164\pi$
$674$	−3.19188	+	5.52850i	−0.122947	+	0.212950i
$675$	−15.2895	+	2.07967i	−0.588492	+	0.0800465i
$676$	−4.19619	−	7.26801i	−0.161392	−	0.279539i
$677$	26.3616			1.01316			0.506580	−	0.862193i	$-0.330910\pi$
$677$	26.3616			1.01316			0.506580	+	0.862193i	$0.330910\pi$
$678$	0.513537	−	0.471923i	0.0197223	−	0.0181241i
$679$		0			0
$680$	−1.89871	+	3.28866i	−0.0728121	+	0.126114i
$681$	36.9417	−	33.9482i	1.41561	−	1.30090i
$682$	−4.14122	+	7.17280i	−0.158575	+	0.274661i
$683$	1.96588	+	3.40500i	0.0752222	+	0.130289i	0.901183	−	0.433439i	$-0.142700\pi$
$683$	1.96588	+	3.40500i	0.0752222	+	0.130289i	−0.825961	+	0.563728i	$0.809367\pi$
$684$	−16.9052	+	7.94198i	−0.646387	+	0.303669i
$685$	−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
$689$	−2.26004			−0.0861006
$690$	−6.62271	+	6.08604i	−0.252122	+	0.231692i
$691$	−19.9010			−0.757072			−0.378536	−	0.925587i	$-0.623572\pi$
$691$	−19.9010			−0.757072			−0.378536	+	0.925587i	$0.623572\pi$
$692$	−28.3585			−1.07803
$693$		0			0
$694$	−12.5373			−0.475910
$695$	3.53645			0.134145
$696$	6.11653	+	27.4044i	0.231847	+	1.03876i
$697$	0.278541			0.0105505
$698$	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	$0.190058\pi$
$702$	−9.50716	+	1.29316i	−0.358825	+	0.0488072i
$703$	−2.84983	−	4.93604i	−0.107483	−	0.186166i
$704$	2.11016	−	3.65490i	0.0795295	−	0.137749i
$705$	−5.09449	−	22.8252i	−0.191870	−	0.859648i
$706$	2.09792	−	3.63370i	0.0789561	−	0.136756i
$707$		0			0
$708$	16.8727	+	5.29343i	0.634115	+	0.198939i
$709$	44.6344			1.67628			0.838139	−	0.545457i	$-0.183644\pi$
$709$	44.6344			1.67628			0.838139	+	0.545457i	$0.183644\pi$
$710$	0.0384437	+	0.0665865i	0.00144277	+	0.00249895i
$711$	−4.54286	−	3.16162i	−0.170371	−	0.118570i
$712$	16.0966	−	27.8801i	0.603244	−	1.04485i
$713$	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
$717$	−16.6234	+	15.2764i	−0.620814	+	0.570506i
$718$	−3.41705	+	5.91851i	−0.127523	+	0.220877i
$719$	19.5096	−	33.7917i	0.727586	−	1.26022i	−0.230315	−	0.973116i	$-0.573976\pi$
$719$	19.5096	−	33.7917i	0.727586	−	1.26022i	0.957901	−	0.287100i	$-0.0926912\pi$
$720$	−0.542692	+	6.41425i	−0.0202249	+	0.239045i
$721$		0			0
$722$	0.965081	+	1.67157i	0.0359166	+	0.0622094i
$723$	−18.5974	+	17.0904i	−0.691645	+	0.635598i
$724$	24.0825			0.895019
$725$	20.2259			0.751171
$726$	3.36698	+	15.0853i	0.124960	+	0.559869i
$727$	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
$730$	5.10593	−	8.84373i	0.188979	−	0.327321i
$731$	−0.557951	+	0.966399i	−0.0206366	+	0.0357436i
$732$	−0.192877	−	0.0605107i	−0.00712894	−	0.00223654i
$733$	−0.448519	−	0.776858i	−0.0165664	−	0.0286939i	0.857623	−	0.514278i	$-0.171940\pi$
$733$	−0.448519	−	0.776858i	−0.0165664	−	0.0286939i	−0.874190	+	0.485584i	$0.838607\pi$
$734$	−9.60441	+	16.6353i	−0.354505	+	0.614021i
$735$		0			0
$736$	−15.6837	−	27.1649i	−0.578108	−	1.00131i
$737$	−31.0335	+	53.7517i	−1.14314	+	1.97997i
$738$	−0.452795	+	0.212720i	−0.0166676	+	0.00783035i
$739$	1.79032	+	3.10092i	0.0658578	+	0.114069i	0.897074	−	0.441880i	$-0.145688\pi$
$739$	1.79032	+	3.10092i	0.0658578	+	0.114069i	−0.831216	+	0.555949i	$0.812355\pi$
$740$	−3.13667			−0.115306
$741$	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	$0.802985\pi$
$744$	−9.85660	−	3.09228i	−0.361360	−	0.113369i
$745$	−6.09583	+	10.5583i	−0.223334	+	0.386826i
$746$	5.38726	+	9.33101i	0.197242	+	0.341633i
$747$	−3.66015	+	43.2604i	−0.133918	+	1.58282i
$748$	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	0.930319	+	0.366752i	$0.119530\pi$
$751$	21.4515	+	37.1551i	0.782776	+	1.35581i	−0.147543	+	0.989056i	$0.547136\pi$
$752$	14.2690			0.520337
$753$	−23.2550	−	7.29574i	−0.847461	−	0.265871i
$754$	12.5767			0.458016
$755$	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	$0.419294\pi$
$758$	−0.683021			−0.0248084
$759$	44.3015	+	13.8986i	1.60804	+	0.504487i
$760$	−13.6171			−0.493945
$761$	20.3599	+	35.2643i	0.738044	+	1.27833i	0.953375	+	0.301789i	$0.0975839\pi$
$761$	20.3599	+	35.2643i	0.738044	+	1.27833i	−0.215330	+	0.976541i	$0.569083\pi$
$762$	−8.04245	−	2.52314i	−0.291347	−	0.0914036i
$763$		0			0
$764$	−23.0001			−0.832113
$765$	4.33216	−	2.03523i	0.156630	−	0.0735838i
$766$	−3.88342	−	6.72627i	−0.140313	−	0.243030i
$767$	9.06826	−	15.7067i	0.327436	−	0.567135i
$768$	14.9768	+	4.69862i	0.540428	+	0.169547i
$769$	−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
$772$	−25.6908			−0.924633
$773$	0.462831	+	0.801647i	0.0166469	+	0.0288332i	0.874229	−	0.485514i	$-0.161368\pi$
$773$	0.462831	+	0.801647i	0.0166469	+	0.0288332i	−0.857582	+	0.514347i	$0.828034\pi$
$774$	0.168967	−	1.99708i	0.00607341	−	0.0717835i
$775$	−3.72061	+	6.44428i	−0.133648	+	0.231485i
$776$	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
$780$	10.0588	+	3.15571i	0.360162	+	0.112993i
$781$	0.198452	−	0.343728i	0.00710116	−	0.0122996i
$782$	−2.04024	+	3.53381i	−0.0729590	+	0.126369i
$783$	13.4033	−	32.7553i	0.478996	−	1.17058i
$784$		0			0
$785$	−4.50386	−	7.80092i	−0.160750	−	0.278427i
$786$	5.17293	+	23.1767i	0.184512	+	0.826684i
$787$	−23.0240			−0.820716			−0.410358	−	0.911925i	$-0.634596\pi$
$787$	−23.0240			−0.820716			−0.410358	+	0.911925i	$0.634596\pi$
$788$	6.26061			0.223025
$789$	4.17116	−	3.83315i	0.148497	−	0.136464i
$790$	−0.881115	−	1.52614i	−0.0313487	−	0.0542975i
$791$		0			0
$792$	−31.8661	+	14.9705i	−1.13231	+	0.531955i
$793$	−0.103662	+	0.179548i	−0.00368114	+	0.00637593i
$794$	4.38551	−	7.59592i	0.155636	−	0.269569i
$795$	−1.49099	+	1.37017i	−0.0528798	+	0.0485947i
$796$	−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
$800$	8.56664	−	14.8379i	0.302877	−	0.524598i
$801$	−36.7265	+	17.2539i	−1.29767	+	0.609637i
$802$	−4.72695	−	8.18732i	−0.166914	−	0.289104i
$803$	−52.7150			−1.86027
$804$	−32.2579	−	10.1202i	−1.13765	−	0.356912i
$805$		0			0
$806$	−2.31352	+	4.00713i	−0.0814901	+	0.141145i
$807$	−5.80555	−	26.0110i	−0.204365	−	0.915632i
$808$	6.11143	−	10.5853i	0.214999	−	0.372390i
$809$	6.73753	+	11.6697i	0.236879	+	0.410286i	0.959817	−	0.280627i	$-0.0905422\pi$
$809$	6.73753	+	11.6697i	0.236879	+	0.410286i	−0.722938	+	0.690913i	$0.757209\pi$
$810$	−5.48805	+	6.61691i	−0.192830	+	0.232495i
$811$	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
$815$	−11.4318			−0.400439
$816$	0.636152	+	2.85020i	0.0222698	+	0.0997769i
$817$	−4.00150			−0.139995
$818$	1.77369			0.0620158
$819$		0			0
$820$	0.549675			0.0191955
$821$	−16.9864			−0.592829			−0.296414	−	0.955059i	$-0.595791\pi$
$821$	−16.9864			−0.592829			−0.296414	+	0.955059i	$0.595791\pi$
$822$	10.4396	−	9.59367i	0.364124	−	0.334618i
$823$	−18.5831			−0.647768			−0.323884	−	0.946097i	$-0.604989\pi$
$823$	−18.5831			−0.647768			−0.323884	+	0.946097i	$0.604989\pi$
$824$	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	$0.418637\pi$
$828$	−2.13218	+	25.2009i	−0.0740982	+	0.875791i
$829$	−4.78717	−	8.29161i	−0.166265	−	0.287980i	0.770839	−	0.637030i	$-0.219837\pi$
$829$	−4.78717	−	8.29161i	−0.166265	−	0.287980i	−0.937104	+	0.349051i	$0.886504\pi$
$830$	−6.91154	+	11.9711i	−0.239903	+	0.415524i
$831$	16.3825	−	15.0550i	0.568303	−	0.522251i
$832$	1.17885	−	2.04183i	0.0408693	−	0.0707877i
$833$		0			0
$834$	−2.12170	+	1.94977i	−0.0734685	+	0.0675150i
$835$	−3.02195			−0.104579
$836$	15.3494	+	26.5859i	0.530869	+	0.919492i
$837$	7.97075	+	10.2959i	0.275509	+	0.355879i
$838$	−11.2326	+	19.4554i	−0.388023	+	0.672075i
$839$	−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
$843$	0.546395	+	2.44806i	0.0188189	+	0.0843155i
$844$	5.83428	−	10.1053i	0.200824	−	0.347838i
$845$	−3.85599	+	6.67877i	−0.132650	+	0.229757i
$846$	15.6408	+	10.8853i	0.537742	+	0.374243i
$847$		0			0
$848$	−0.617738	−	1.06995i	−0.0212132	−	0.0367423i
$849$	−28.8194	−	9.04143i	−0.989079	−	0.310301i
$850$	−2.22882			−0.0764479
$851$	−7.71767			−0.264558
$852$	0.206281	+	0.0647161i	0.00706708	+	0.00221714i
$853$	−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
$856$	−9.11621	+	15.7897i	−0.311586	+	0.539682i
$857$	17.3895	−	30.1195i	0.594013	−	1.02886i	−0.399672	−	0.916658i	$-0.630876\pi$
$857$	17.3895	−	30.1195i	0.594013	−	1.02886i	0.993685	−	0.112203i	$-0.0357907\pi$
$858$	3.43522	+	15.3911i	0.117276	+	0.525442i
$859$	−6.32429	−	10.9540i	−0.215782	−	0.373745i	0.737732	−	0.675093i	$-0.235897\pi$
$859$	−6.32429	−	10.9540i	−0.215782	−	0.373745i	−0.953514	+	0.301348i	$0.902563\pi$
$860$	−1.10107	+	1.90710i	−0.0375460	+	0.0650316i
$861$		0			0
$862$	11.8409	+	20.5091i	0.403304	+	0.698543i
$863$	13.2398	−	22.9321i	0.450690	−	0.780617i	−0.547739	−	0.836649i	$-0.684511\pi$
$863$	13.2398	−	22.9321i	0.450690	−	0.780617i	0.998429	+	0.0560318i	$0.0178448\pi$
$864$	−18.3525	−	23.7062i	−0.624366	−	0.806501i
$865$	13.0297	+	22.5681i	0.443022	+	0.767337i
$866$	−3.66943			−0.124692
$867$	−20.0817	+	18.4544i	−0.682011	+	0.626744i
$868$		0			0
$869$	−4.54843	+	7.87811i	−0.154295	+	0.267247i
$870$	8.29707	−	7.62472i	0.281297	−	0.258502i
$871$	−17.3371	+	30.0287i	−0.587444	+	1.01748i
$872$	2.02166	+	3.50162i	0.0684621	+	0.118580i
$873$	1.36657	−	16.1519i	0.0462512	−	0.546658i
$874$	−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	0.519345	−	0.854565i	$-0.326176\pi$
$877$	−14.2267	−	24.6414i	−0.480402	−	0.832081i	−0.999747	+	0.0224835i	$0.992843\pi$
$878$	−4.28887			−0.144742
$879$	−2.29571	+	2.10968i	−0.0774325	+	0.0711578i
$880$	10.5801			0.356654
$881$	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	$0.189608\pi$
$884$	4.78264			0.160858
$885$	−3.53981	−	15.8597i	−0.118989	−	0.533117i
$886$	−4.28129			−0.143833
$887$	−2.10846	−	3.65196i	−0.0707952	−	0.122621i	0.828455	−	0.560056i	$-0.189220\pi$
$887$	−2.10846	−	3.65196i	−0.0707952	−	0.122621i	−0.899250	+	0.437435i	$0.855887\pi$
$888$	4.30902	−	3.95984i	0.144601	−	0.132883i
$889$		0			0
$890$	−12.9196			−0.433067
$891$	43.7461	+	7.45585i	1.46555	+	0.249780i
$892$	10.0673	+	17.4371i	0.337078	+	0.583837i
$893$	19.0229	−	32.9486i	0.636576	−	1.10258i
$894$	−2.16395	−	9.69531i	−0.0723733	−	0.324260i
$895$	−5.43294	+	9.41013i	−0.181603	+	0.314546i
$896$		0			0
$897$	24.7493	+	7.76453i	0.826355	+	0.259250i
$898$	−7.87371			−0.262749
$899$	−8.53374	−	14.7809i	−0.284616	−	0.492970i
$900$	−12.5032	+	5.87394i	−0.416774	+	0.195798i
$901$	−0.459325	+	0.795574i	−0.0153023	+	0.0265044i
$902$	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
$906$	−15.0968	+	13.8734i	−0.501556	+	0.460913i
$907$	−23.9925	+	41.5563i	−0.796659	+	1.37985i	0.125121	+	0.992142i	$0.460068\pi$
$907$	−23.9925	+	41.5563i	−0.796659	+	1.37985i	−0.921780	+	0.387713i	$0.873265\pi$
$908$	22.4585	−	38.8993i	0.745311	−	1.29092i
$909$	−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	$0.973514\pi$
$912$	−7.71063	+	7.08580i	−0.255324	+	0.234634i
$913$	71.3565			2.36155
$914$	7.05351			0.233309
$915$	0.0404646	+	0.181297i	0.00133772	+	0.00599348i
$916$	−11.9678	−	20.7288i	−0.395427	−	0.684900i
$917$		0			0
$918$	−1.47700	+	3.60951i	−0.0487482	+	0.119132i
$919$	1.13478	−	1.96550i	0.0374330	−	0.0648359i	−0.846702	−	0.532068i	$-0.821415\pi$
$919$	1.13478	−	1.96550i	0.0374330	−	0.0648359i	0.884135	+	0.467232i	$0.154749\pi$
$920$	−9.21919	+	15.9681i	−0.303948	+	0.526453i
$921$	1.75968	+	0.552059i	0.0579834	+	0.0181910i
$922$	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
$926$	10.9774	−	19.0134i	0.360740	−	0.624819i
$927$	3.59427	−	42.4819i	0.118051	−	1.39529i
$928$	19.6488	+	34.0328i	0.645004	+	1.11718i
$929$	−45.8496			−1.50428			−0.752138	−	0.659006i	$-0.770977\pi$
$929$	−45.8496			−1.50428			−0.752138	+	0.659006i	$0.770977\pi$
$930$	0.903084	+	4.04616i	0.0296133	+	0.132679i
$931$		0			0
$932$	3.83514	−	6.64266i	0.125624	−	0.217587i
$933$	−27.9778	−	8.77739i	−0.915952	−	0.287359i
$934$	−1.31530	+	2.27816i	−0.0430379	+	0.0745438i
$935$	−3.93346	−	6.81294i	−0.128638	−	0.222807i
$936$	−17.8022	+	8.36337i	−0.581883	+	0.273365i
$937$	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
$941$	35.2803			1.15011			0.575053	−	0.818116i	$-0.304982\pi$
$941$	35.2803			1.15011			0.575053	+	0.818116i	$0.304982\pi$
$942$	7.00302	+	2.19704i	0.228171	+	0.0715833i
$943$	1.35246			0.0440421
$944$	9.91453			0.322691
$945$		0			0
$946$	−3.29411			−0.107101
$947$	−50.7130			−1.64795			−0.823976	−	0.566625i	$-0.808249\pi$
$947$	−50.7130			−1.64795			−0.823976	+	0.566625i	$0.808249\pi$
$948$	−4.72788	−	1.48327i	−0.153554	−	0.0481742i
$949$	−29.4495			−0.955972
$950$	−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	$0.361647\pi$
$954$	0.139100	−	1.64407i	0.00450352	−	0.0532286i
$955$	10.5677	+	18.3038i	0.341962	+	0.592296i
$956$	−10.1061	+	17.5043i	−0.326855	+	0.566130i
$957$	−55.5019	−	17.4124i	−1.79412	−	0.562864i
$958$	5.39165	−	9.33861i	0.174196	−	0.301717i
$959$		0			0
$960$	−0.460166	−	2.06172i	−0.0148518	−	0.0665417i
$961$	−24.7208			−0.797445
$962$	−1.31062	−	2.27006i	−0.0422562	−	0.0731898i
$963$	20.7999	−	9.77167i	0.670267	−	0.314888i
$964$	−11.3062	+	19.5829i	−0.364148	+	0.630722i
$965$	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
$969$	7.42950	+	2.33083i	0.238670	+	0.0748772i
$970$	2.58052	−	4.46959i	0.0828554	−	0.143510i
$971$	3.97206	−	6.87981i	0.127469	−	0.220783i	−0.795226	−	0.606313i	$-0.792648\pi$
$971$	3.97206	−	6.87981i	0.127469	−	0.220783i	0.922696	+	0.385530i	$0.125981\pi$
$972$	1.22703	+	24.1411i	0.0393572	+	0.774327i
$973$		0			0
$974$	−1.17424	−	2.03384i	−0.0376249	−	0.0651683i
$975$	3.08631	+	13.8278i	0.0988411	+	0.442845i
$976$	−0.113336			−0.00362779
$977$	−52.2548			−1.67178			−0.835889	−	0.548898i	$-0.815048\pi$
$977$	−52.2548			−1.67178			−0.835889	+	0.548898i	$0.815048\pi$
$978$	6.85853	−	6.30275i	0.219312	−	0.201540i
$979$	33.3464	+	57.7577i	1.06576	+	1.84594i
$980$		0			0
$981$	0.429654	−	5.07822i	0.0137178	−	0.162135i
$982$	−13.7784	+	23.8650i	−0.439688	+	0.761562i
$983$	−19.4190	+	33.6346i	−0.619369	+	1.07278i	0.370232	+	0.928939i	$0.379278\pi$
$983$	−19.4190	+	33.6346i	−0.619369	+	1.07278i	−0.989601	+	0.143839i	$0.954055\pi$
$984$	−0.755120	+	0.693929i	−0.0240723	+	0.0221216i
$985$	−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
$989$	−2.70914	+	4.69236i	−0.0861455	+	0.149208i
$990$	11.5972	+	8.07113i	0.368584	+	0.256517i
$991$	−15.4689	−	26.7929i	−0.491385	−	0.851104i	0.508565	−	0.861023i	$-0.330176\pi$
$991$	−15.4689	−	26.7929i	−0.491385	−	0.851104i	−0.999951	+	0.00991892i	$0.996843\pi$
$992$	−14.4578			−0.459036
$993$	44.1679	+	13.8567i	1.40163	+	0.439728i
$994$		0			0
$995$	−18.0122	+	31.1981i	−0.571025	+	0.989045i
$996$	8.46687	+	37.9348i	0.268283	+	1.20201i
$997$	23.5335	−	40.7612i	0.745313	−	1.29092i	−0.204735	−	0.978817i	$-0.565633\pi$
$997$	23.5335	−	40.7612i	0.745313	−	1.29092i	0.950048	−	0.312103i	$-0.101033\pi$
$998$	−3.96492	−	6.86745i	−0.125507	−	0.217385i
$999$	−7.30902	+	0.994170i	−0.231247	+	0.0314542i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	7.3	odd	6
63.2.g.b.16.2	yes	10	63.34	odd	6
63.2.h.b.25.4	yes	10	63.52	odd	6
63.2.h.b.58.4	yes	10	7.6	odd	2
189.2.g.b.100.4		10	63.20	even	6
189.2.g.b.172.4		10	21.17	even	6
189.2.h.b.37.2		10	21.20	even	2
189.2.h.b.46.2		10	63.38	even	6
441.2.f.e.148.2		10	7.5	odd	6
441.2.f.e.295.2		10	63.61	odd	6
441.2.f.f.148.2		10	7.2	even	3
441.2.f.f.295.2		10	63.16	even	3
441.2.g.f.67.2		10	7.4	even	3
441.2.g.f.79.2		10	9.7	even	3
441.2.h.f.214.4		10	63.25	even	3	inner
441.2.h.f.373.4		10	1.1	even	1	trivial
567.2.e.e.163.4		10	63.41	even	6
567.2.e.e.487.4		10	63.59	even	6
567.2.e.f.163.2		10	63.13	odd	6
567.2.e.f.487.2		10	63.31	odd	6
1008.2.q.i.529.1		10	252.115	even	6
1008.2.q.i.625.1		10	28.27	even	2
1008.2.t.i.193.4		10	28.3	even	6
1008.2.t.i.961.4		10	252.223	even	6
1323.2.f.e.442.4		10	21.5	even	6
1323.2.f.e.883.4		10	63.47	even	6
1323.2.f.f.442.4		10	21.2	odd	6
1323.2.f.f.883.4		10	63.2	odd	6
1323.2.g.f.361.4		10	21.11	odd	6
1323.2.g.f.667.4		10	9.2	odd	6
1323.2.h.f.226.2		10	3.2	odd	2
1323.2.h.f.802.2		10	63.11	odd	6
3024.2.q.i.2305.5		10	84.83	odd	2
3024.2.q.i.2881.5		10	252.227	odd	6
3024.2.t.i.289.1		10	252.83	odd	6
3024.2.t.i.1873.1		10	84.59	odd	6
3969.2.a.z.1.4		5	63.40	odd	6
3969.2.a.ba.1.4		5	63.58	even	3
3969.2.a.bb.1.2		5	63.23	odd	6
3969.2.a.bc.1.2		5	63.5	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)

\(f(q)\)	\(=\)	\(q+0.670333 q^{2} +(-1.65263 - 0.518475i) q^{3} -1.55065 q^{4} +(0.712469 + 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(2.46237 + 1.71369i) q^{9} +O(q^{10})\)	\(q+0.670333 q^{2} +(-1.65263 - 0.518475i) q^{3} -1.55065 q^{4} +(0.712469 + 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(2.46237 + 1.71369i) q^{9} +(0.477591 + 0.827212i) q^{10} +(2.46539 - 4.27018i) q^{11} +(2.56266 + 0.803975i) q^{12} +(1.37730 - 2.38556i) q^{13} +(-0.537632 - 2.40879i) q^{15} +1.50584 q^{16} +(-0.559839 - 0.969670i) q^{17} +(1.65061 + 1.14874i) q^{18} +(2.00752 - 3.47713i) q^{19} +(-1.10479 - 1.91356i) q^{20} +(1.65263 - 2.86244i) q^{22} +(-2.71830 - 4.70824i) q^{23} +(3.93346 + 1.23403i) q^{24} +(1.48478 - 2.57171i) q^{25} +(0.923251 - 1.59912i) q^{26} +(-3.18087 - 4.10878i) q^{27} +(3.40555 + 5.89858i) q^{29} +(-0.360392 - 1.61469i) q^{30} -2.50584 q^{31} +5.76965 q^{32} +(-6.28835 + 5.77878i) q^{33} +(-0.375279 - 0.650002i) q^{34} +(-3.81828 - 2.65735i) q^{36} +(0.709787 - 1.22939i) q^{37} +(1.34571 - 2.33083i) q^{38} +(-3.51302 + 3.22835i) q^{39} +(-1.69576 - 2.93714i) q^{40} +(-0.124384 + 0.215440i) q^{41} +(-0.498313 - 0.863104i) q^{43} +(-3.82296 + 6.62156i) q^{44} +(-0.360392 + 4.25959i) q^{45} +(-1.82217 - 3.15609i) q^{46} +9.47579 q^{47} +(-2.48859 - 0.780738i) q^{48} +(0.995294 - 1.72390i) q^{50} +(0.422457 + 1.89277i) q^{51} +(-2.13572 + 3.69917i) q^{52} +(-0.410229 - 0.710537i) q^{53} +(-2.13224 - 2.75425i) q^{54} +7.02604 q^{55} +(-5.12050 + 4.70556i) q^{57} +(2.28285 + 3.95401i) q^{58} +6.58407 q^{59} +(0.833682 + 3.73521i) q^{60} -0.0752645 q^{61} -1.67974 q^{62} +0.855913 q^{64} +3.92514 q^{65} +(-4.21529 + 3.87370i) q^{66} -12.5877 q^{67} +(0.868117 + 1.50362i) q^{68} +(2.05125 + 9.19035i) q^{69} +0.0804951 q^{71} +(-5.86073 - 4.07880i) q^{72} +(-5.34551 - 9.25869i) q^{73} +(0.475793 - 0.824098i) q^{74} +(-3.78715 + 3.48026i) q^{75} +(-3.11297 + 5.39183i) q^{76} +(-2.35489 + 2.16407i) q^{78} -1.84491 q^{79} +(1.07286 + 1.85825i) q^{80} +(3.12651 + 8.43949i) q^{81} +(-0.0833788 + 0.144416i) q^{82} +(7.23583 + 12.5328i) q^{83} +(0.797736 - 1.38172i) q^{85} +(-0.334036 - 0.578567i) q^{86} +(-2.56984 - 11.5139i) q^{87} +(-5.86792 + 10.1635i) q^{88} +(-6.76292 + 11.7137i) q^{89} +(-0.241583 + 2.85534i) q^{90} +(4.21515 + 7.30085i) q^{92} +(4.14122 + 1.29921i) q^{93} +6.35193 q^{94} +5.72119 q^{95} +(-9.53509 - 2.99142i) q^{96} +(-2.70160 - 4.67930i) q^{97} +(13.3885 - 6.28982i) 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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