LMFDB - Embedded newform 405.4.e.t.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (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:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.95327307.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 85x^{2} - 68x + 16 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 85x^2 - 68*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.1
Root			$0.500000 + 2.36807i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.t.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22969 - 3.86194i) q^{2} +(-5.94305 + 10.2937i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-2.54062 - 4.40048i) q^{7} +17.3296 q^{8} +O(q^{10})$	\(q+(-2.22969 - 3.86194i) q^{2} +(-5.94305 + 10.2937i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-2.54062 - 4.40048i) q^{7} +17.3296 q^{8} +22.2969 q^{10} +(-29.1503 - 50.4899i) q^{11} +(-10.6060 + 18.3701i) q^{13} +(-11.3296 + 19.6234i) q^{14} +(8.90475 + 15.4235i) q^{16} -68.8451 q^{17} -40.8133 q^{19} +(-29.7152 - 51.4683i) q^{20} +(-129.993 + 225.154i) q^{22} +(72.1592 - 124.983i) q^{23} +(-12.5000 - 21.6506i) q^{25} +94.5921 q^{26} +60.3960 q^{28} +(110.029 + 190.576i) q^{29} +(-145.773 + 252.486i) q^{31} +(109.028 - 188.842i) q^{32} +(153.503 + 265.875i) q^{34} +25.4062 q^{35} +260.637 q^{37} +(91.0010 + 157.618i) q^{38} +(-43.3240 + 75.0393i) q^{40} +(84.8832 - 147.022i) q^{41} +(219.298 + 379.835i) q^{43} +692.967 q^{44} -643.571 q^{46} +(127.740 + 221.253i) q^{47} +(158.591 - 274.687i) q^{49} +(-55.7423 + 96.5485i) q^{50} +(-126.063 - 218.348i) q^{52} +214.714 q^{53} +291.503 q^{55} +(-44.0278 - 76.2585i) q^{56} +(490.661 - 849.850i) q^{58} +(-165.762 + 287.108i) q^{59} +(-27.4823 - 47.6008i) q^{61} +1300.11 q^{62} -829.920 q^{64} +(-53.0298 - 91.8503i) q^{65} +(-379.090 + 656.603i) q^{67} +(409.149 - 708.668i) q^{68} +(-56.6479 - 98.1171i) q^{70} -904.348 q^{71} +866.622 q^{73} +(-581.139 - 1006.56i) q^{74} +(242.555 - 420.118i) q^{76} +(-148.120 + 256.551i) q^{77} +(-103.480 - 179.233i) q^{79} -89.0475 q^{80} -757.054 q^{82} +(231.699 + 401.314i) q^{83} +(172.113 - 298.108i) q^{85} +(977.933 - 1693.83i) q^{86} +(-505.163 - 874.968i) q^{88} +601.736 q^{89} +107.783 q^{91} +(857.691 + 1485.56i) q^{92} +(569.643 - 986.651i) q^{94} +(102.033 - 176.727i) q^{95} +(-114.682 - 198.634i) q^{97} -1414.43 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8}+O(q^{10}) $ 6 * q + q^2 - 23 * q^4 - 15 * q^5 - 44 * q^7 - 72 * q^8	$ 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8} - 10 q^{10} - 38 q^{11} - 28 q^{13} + 108 q^{14} - 191 q^{16} - 38 q^{17} + 374 q^{19} - 115 q^{20} - 122 q^{22} + 81 q^{23} - 75 q^{25} + 832 q^{26} + 820 q^{28} - 160 q^{29} - 227 q^{31} + 569 q^{32} - 17 q^{34} + 440 q^{35} + 156 q^{37} + 757 q^{38} + 180 q^{40} + 338 q^{41} - 22 q^{43} + 3272 q^{44} - 2850 q^{46} + 472 q^{47} + 197 q^{49} + 25 q^{50} + 1566 q^{52} + 1042 q^{53} + 380 q^{55} + 1254 q^{56} + 2096 q^{58} - 140 q^{59} - 595 q^{61} + 2814 q^{62} - 1836 q^{64} - 140 q^{65} - 878 q^{67} + 3053 q^{68} + 540 q^{70} - 1204 q^{71} + 2588 q^{73} - 2878 q^{74} - 525 q^{76} - 288 q^{77} - 629 q^{79} + 1910 q^{80} - 3364 q^{82} + 1287 q^{83} + 95 q^{85} + 3730 q^{86} + 858 q^{88} + 4308 q^{89} - 880 q^{91} - 1959 q^{92} + 1108 q^{94} - 935 q^{95} - 1392 q^{97} - 5386 q^{98}+O(q^{100}) $ 6 * q + q^2 - 23 * q^4 - 15 * q^5 - 44 * q^7 - 72 * q^8 - 10 * q^10 - 38 * q^11 - 28 * q^13 + 108 * q^14 - 191 * q^16 - 38 * q^17 + 374 * q^19 - 115 * q^20 - 122 * q^22 + 81 * q^23 - 75 * q^25 + 832 * q^26 + 820 * q^28 - 160 * q^29 - 227 * q^31 + 569 * q^32 - 17 * q^34 + 440 * q^35 + 156 * q^37 + 757 * q^38 + 180 * q^40 + 338 * q^41 - 22 * q^43 + 3272 * q^44 - 2850 * q^46 + 472 * q^47 + 197 * q^49 + 25 * q^50 + 1566 * q^52 + 1042 * q^53 + 380 * q^55 + 1254 * q^56 + 2096 * q^58 - 140 * q^59 - 595 * q^61 + 2814 * q^62 - 1836 * q^64 - 140 * q^65 - 878 * q^67 + 3053 * q^68 + 540 * q^70 - 1204 * q^71 + 2588 * q^73 - 2878 * q^74 - 525 * q^76 - 288 * q^77 - 629 * q^79 + 1910 * q^80 - 3364 * q^82 + 1287 * q^83 + 95 * q^85 + 3730 * q^86 + 858 * q^88 + 4308 * q^89 - 880 * q^91 - 1959 * q^92 + 1108 * q^94 - 935 * q^95 - 1392 * q^97 - 5386 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.22969	−	3.86194i	−0.788315	−	1.36540i	−0.926999	−	0.375065i	$-0.877620\pi$
$2$	−2.22969	−	3.86194i	−0.788315	−	1.36540i	0.138684	−	0.990337i	$-0.455713\pi$
$3$		0			0
$3$		0			0
$4$	−5.94305	+	10.2937i	−0.742881	+	1.28671i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−2.54062	−	4.40048i	−0.137180	−	0.237603i	0.789248	−	0.614075i	$-0.210471\pi$
$7$	−2.54062	−	4.40048i	−0.137180	−	0.237603i	−0.926428	+	0.376471i	$0.877137\pi$
$8$	17.3296			0.765867
$9$		0			0
$10$	22.2969			0.705090
$11$	−29.1503	−	50.4899i	−0.799014	−	1.38393i	−0.920259	−	0.391311i	$-0.872022\pi$
$11$	−29.1503	−	50.4899i	−0.799014	−	1.38393i	0.121244	−	0.992623i	$-0.461312\pi$
$12$		0			0
$13$	−10.6060	+	18.3701i	−0.226274	+	0.391918i	−0.956701	−	0.291073i	$-0.905988\pi$
$13$	−10.6060	+	18.3701i	−0.226274	+	0.391918i	0.730427	+	0.682991i	$0.239321\pi$
$14$	−11.3296	+	19.6234i	−0.216283	+	0.374613i
$15$		0			0
$16$	8.90475	+	15.4235i	0.139137	+	0.240992i
$17$	−68.8451			−0.982199			−0.491099	−	0.871104i	$-0.663405\pi$
$17$	−68.8451			−0.982199			−0.491099	+	0.871104i	$0.663405\pi$
$18$		0			0
$19$	−40.8133			−0.492800			−0.246400	−	0.969168i	$-0.579248\pi$
$19$	−40.8133			−0.492800			−0.246400	+	0.969168i	$0.579248\pi$
$20$	−29.7152	−	51.4683i	−0.332226	−	0.575433i
$21$		0			0
$22$	−129.993	+	225.154i	−1.25975	+	2.18195i
$23$	72.1592	−	124.983i	0.654184	−	1.13308i	−0.327914	−	0.944708i	$-0.606346\pi$
$23$	72.1592	−	124.983i	0.654184	−	1.13308i	0.982098	−	0.188372i	$-0.0603210\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	94.5921			0.713501
$27$		0			0
$28$	60.3960			0.407635
$29$	110.029	+	190.576i	0.704547	+	1.22031i	0.966855	+	0.255327i	$0.0821831\pi$
$29$	110.029	+	190.576i	0.704547	+	1.22031i	−0.262308	+	0.964984i	$0.584484\pi$
$30$		0			0
$31$	−145.773	+	252.486i	−0.844566	+	1.46283i	0.0414319	+	0.999141i	$0.486808\pi$
$31$	−145.773	+	252.486i	−0.844566	+	1.46283i	−0.885998	+	0.463690i	$0.846525\pi$
$32$	109.028	−	188.842i	0.602301	−	1.04322i
$33$		0			0
$34$	153.503	+	265.875i	0.774282	+	1.34110i
$35$	25.4062			0.122698
$36$		0			0
$37$	260.637			1.15807			0.579033	−	0.815304i	$-0.303430\pi$
$37$	260.637			1.15807			0.579033	+	0.815304i	$0.303430\pi$
$38$	91.0010	+	157.618i	0.388482	+	0.672870i
$39$		0			0
$40$	−43.3240	+	75.0393i	−0.171253	+	0.296619i
$41$	84.8832	−	147.022i	0.323330	−	0.560024i	−0.657843	−	0.753155i	$-0.728531\pi$
$41$	84.8832	−	147.022i	0.323330	−	0.560024i	0.981173	+	0.193131i	$0.0618643\pi$
$42$		0			0
$43$	219.298	+	379.835i	0.777735	+	1.34708i	0.933244	+	0.359242i	$0.116965\pi$
$43$	219.298	+	379.835i	0.777735	+	1.34708i	−0.155509	+	0.987834i	$0.549702\pi$
$44$	692.967			2.37429
$45$		0			0
$46$	−643.571			−2.06281
$47$	127.740	+	221.253i	0.396444	+	0.686661i	0.993284	−	0.115699i	$-0.0369109\pi$
$47$	127.740	+	221.253i	0.396444	+	0.686661i	−0.596841	+	0.802360i	$0.703578\pi$
$48$		0			0
$49$	158.591	−	274.687i	0.462363	−	0.800836i
$50$	−55.7423	+	96.5485i	−0.157663	+	0.273080i
$51$		0			0
$52$	−126.063	−	218.348i	−0.336189	−	0.582297i
$53$	214.714			0.556477			0.278239	−	0.960512i	$-0.410249\pi$
$53$	214.714			0.556477			0.278239	+	0.960512i	$0.410249\pi$
$54$		0			0
$55$	291.503			0.714660
$56$	−44.0278	−	76.2585i	−0.105062	−	0.181973i
$57$		0			0
$58$	490.661	−	849.850i	1.11081	−	1.92398i
$59$	−165.762	+	287.108i	−0.365769	+	0.633530i	−0.988899	−	0.148588i	$-0.952527\pi$
$59$	−165.762	+	287.108i	−0.365769	+	0.633530i	0.623131	+	0.782118i	$0.285861\pi$
$60$		0			0
$61$	−27.4823	−	47.6008i	−0.0576845	−	0.0999124i	0.835741	−	0.549124i	$-0.185038\pi$
$61$	−27.4823	−	47.6008i	−0.0576845	−	0.0999124i	−0.893426	+	0.449211i	$0.851705\pi$
$62$	1300.11			2.66314
$63$		0			0
$64$	−829.920			−1.62094
$65$	−53.0298	−	91.8503i	−0.101193	−	0.175271i
$66$		0			0
$67$	−379.090	+	656.603i	−0.691241	+	1.19727i	0.280190	+	0.959945i	$0.409603\pi$
$67$	−379.090	+	656.603i	−0.691241	+	1.19727i	−0.971431	+	0.237321i	$0.923731\pi$
$68$	409.149	−	708.668i	0.729657	−	1.26380i
$69$		0			0
$70$	−56.6479	−	98.1171i	−0.0967246	−	0.167532i
$71$	−904.348			−1.51164			−0.755819	−	0.654780i	$-0.772761\pi$
$71$	−904.348			−1.51164			−0.755819	+	0.654780i	$0.772761\pi$
$72$		0			0
$73$	866.622			1.38946			0.694729	−	0.719271i	$-0.255524\pi$
$73$	866.622			1.38946			0.694729	+	0.719271i	$0.255524\pi$
$74$	−581.139	−	1006.56i	−0.912920	−	1.58122i
$75$		0			0
$76$	242.555	−	420.118i	0.366092	−	0.634090i
$77$	−148.120	+	256.551i	−0.219218	+	0.379697i
$78$		0			0
$79$	−103.480	−	179.233i	−0.147373	−	0.255257i	0.782883	−	0.622169i	$-0.213748\pi$
$79$	−103.480	−	179.233i	−0.147373	−	0.255257i	−0.930256	+	0.366912i	$0.880415\pi$
$80$	−89.0475			−0.124448
$81$		0			0
$82$	−757.054			−1.01954
$83$	231.699	+	401.314i	0.306412	+	0.530722i	0.977575	−	0.210589i	$-0.0675380\pi$
$83$	231.699	+	401.314i	0.306412	+	0.530722i	−0.671162	+	0.741310i	$0.734205\pi$
$84$		0			0
$85$	172.113	−	298.108i	0.219626	−	0.380404i
$86$	977.933	−	1693.83i	1.22620	−	2.12384i
$87$		0			0
$88$	−505.163	−	874.968i	−0.611938	−	1.05991i
$89$	601.736			0.716673			0.358337	−	0.933592i	$-0.383344\pi$
$89$	601.736			0.716673			0.358337	+	0.933592i	$0.383344\pi$
$90$		0			0
$91$	107.783			0.124162
$92$	857.691	+	1485.56i	0.971961	+	1.68349i
$93$		0			0
$94$	569.643	−	986.651i	0.625045	−	1.08261i
$95$	102.033	−	176.727i	0.110194	−	0.190861i
$96$		0			0
$97$	−114.682	−	198.634i	−0.120043	−	0.207920i	0.799741	−	0.600345i	$-0.204970\pi$
$97$	−114.682	−	198.634i	−0.120043	−	0.207920i	−0.919784	+	0.392424i	$0.871637\pi$
$98$	−1414.43			−1.45795
$99$		0			0
$100$	297.152			0.297152
$101$	−672.831	−	1165.38i	−0.662863	−	1.14811i	−0.979860	−	0.199686i	$-0.936008\pi$
$101$	−672.831	−	1165.38i	−0.662863	−	1.14811i	0.316997	−	0.948427i	$-0.397326\pi$
$102$		0			0
$103$	798.149	−	1382.44i	0.763534	−	1.32248i	−0.177484	−	0.984124i	$-0.556796\pi$
$103$	798.149	−	1382.44i	0.763534	−	1.32248i	0.941018	−	0.338356i	$-0.109871\pi$
$104$	−183.797	+	318.345i	−0.173296	+	0.300157i
$105$		0			0
$106$	−478.747	−	829.214i	−0.438679	−	0.759815i
$107$	958.786			0.866256			0.433128	−	0.901333i	$-0.357410\pi$
$107$	958.786			0.866256			0.433128	+	0.901333i	$0.357410\pi$
$108$		0			0
$109$	1690.23			1.48527			0.742635	−	0.669696i	$-0.233576\pi$
$109$	1690.23			1.48527			0.742635	+	0.669696i	$0.233576\pi$
$110$	−649.963	−	1125.77i	−0.563377	−	0.975798i
$111$		0			0
$112$	45.2471	−	78.3703i	0.0381737	−	0.0661188i
$113$	5.81057	−	10.0642i	0.00483728	−	0.00837842i	−0.863597	−	0.504183i	$-0.831794\pi$
$113$	5.81057	−	10.0642i	0.00483728	−	0.00837842i	0.868434	+	0.495805i	$0.165127\pi$
$114$		0			0
$115$	360.796	+	624.917i	0.292560	+	0.506729i
$116$	−2615.63			−2.09358
$117$		0			0
$118$	1478.39			1.15336
$119$	174.909	+	302.951i	0.134738	+	0.233374i
$120$		0			0
$121$	−1033.98	+	1790.91i	−0.776848	+	1.34554i
$122$	−122.554	+	212.270i	−0.0909471	+	0.157525i
$123$		0			0
$124$	−1732.67	−	3001.07i	−1.25482	−	2.17342i
$125$	125.000			0.0894427
$126$		0			0
$127$	309.141			0.215999			0.107999	−	0.994151i	$-0.465556\pi$
$127$	309.141			0.215999			0.107999	+	0.994151i	$0.465556\pi$
$128$	978.240	+	1694.36i	0.675508	+	1.17001i
$129$		0			0
$130$	−236.480	+	409.596i	−0.159544	+	0.276338i
$131$	−1392.51	+	2411.90i	−0.928736	+	1.60862i	−0.143296	+	0.989680i	$0.545770\pi$
$131$	−1392.51	+	2411.90i	−0.928736	+	1.60862i	−0.785440	+	0.618938i	$0.787563\pi$
$132$		0			0
$133$	103.691	+	179.598i	0.0676026	+	0.117091i
$134$	3381.01			2.17966
$135$		0			0
$136$	−1193.06			−0.752233
$137$	1244.71	+	2155.89i	0.776222	+	1.34446i	0.934105	+	0.356998i	$0.116200\pi$
$137$	1244.71	+	2155.89i	0.776222	+	1.34446i	−0.157884	+	0.987458i	$0.550467\pi$
$138$		0			0
$139$	−893.026	+	1546.77i	−0.544931	+	0.943849i	0.453680	+	0.891165i	$0.350111\pi$
$139$	−893.026	+	1546.77i	−0.544931	+	0.943849i	−0.998611	+	0.0526839i	$0.983222\pi$
$140$	−150.990	+	261.523i	−0.0911499	+	0.157876i
$141$		0			0
$142$	2016.42	+	3492.54i	1.19165	+	2.06399i
$143$	1236.67			0.723185
$144$		0			0
$145$	−1100.29			−0.630166
$146$	−1932.30	−	3346.84i	−1.09533	−	1.89717i
$147$		0			0
$148$	−1548.98	+	2682.91i	−0.860304	+	1.49009i
$149$	−784.416	+	1358.65i	−0.431288	+	0.747012i	−0.996984	−	0.0776011i	$-0.975274\pi$
$149$	−784.416	+	1358.65i	−0.431288	+	0.747012i	0.565697	+	0.824613i	$0.308607\pi$
$150$		0			0
$151$	219.163	+	379.602i	0.118114	+	0.204580i	0.919020	−	0.394210i	$-0.128982\pi$
$151$	219.163	+	379.602i	0.118114	+	0.204580i	−0.800906	+	0.598790i	$0.795648\pi$
$152$	−707.277			−0.377419
$153$		0			0
$154$	1321.04			0.691252
$155$	−728.863	−	1262.43i	−0.377701	−	0.654198i
$156$		0			0
$157$	22.3739	−	38.7528i	0.0113735	−	0.0196994i	−0.860283	−	0.509817i	$-0.829713\pi$
$157$	22.3739	−	38.7528i	0.0113735	−	0.0196994i	0.871656	+	0.490118i	$0.163046\pi$
$158$	−461.458	+	799.270i	−0.232352	+	0.402446i
$159$		0			0
$160$	545.140	+	944.211i	0.269357	+	0.466540i
$161$	−733.315			−0.358965
$162$		0			0
$163$	−2611.84			−1.25506			−0.627531	−	0.778591i	$-0.715935\pi$
$163$	−2611.84			−1.25506			−0.627531	+	0.778591i	$0.715935\pi$
$164$	1008.93	+	1747.52i	0.480391	+	0.832062i
$165$		0			0
$166$	1033.23	−	1789.61i	0.483099	−	0.836752i
$167$	94.4733	−	163.633i	0.0437758	−	0.0758220i	−0.843307	−	0.537432i	$-0.819395\pi$
$167$	94.4733	−	163.633i	0.0437758	−	0.0758220i	0.887083	+	0.461610i	$0.152728\pi$
$168$		0			0
$169$	873.527	+	1512.99i	0.397600	+	0.688663i
$170$	−1535.03			−0.692539
$171$		0			0
$172$	−5213.19			−2.31106
$173$	752.510	+	1303.38i	0.330707	+	0.572801i	0.982651	−	0.185466i	$-0.0593796\pi$
$173$	752.510	+	1303.38i	0.330707	+	0.572801i	−0.651944	+	0.758267i	$0.726046\pi$
$174$		0			0
$175$	−63.5154	+	110.012i	−0.0274361	+	0.0475207i
$176$	519.153	−	899.200i	0.222345	−	0.385112i
$177$		0			0
$178$	−1341.69	−	2323.87i	−0.564964	−	0.978547i
$179$	−3136.62			−1.30973			−0.654865	−	0.755746i	$-0.727275\pi$
$179$	−3136.62			−1.30973			−0.654865	+	0.755746i	$0.727275\pi$
$180$		0			0
$181$	4512.67			1.85317			0.926586	−	0.376084i	$-0.122730\pi$
$181$	4512.67			1.85317			0.926586	+	0.376084i	$0.122730\pi$
$182$	−240.322	−	416.250i	−0.0978784	−	0.169530i
$183$		0			0
$184$	1250.49	−	2165.91i	0.501018	−	0.867788i
$185$	−651.592	+	1128.59i	−0.258951	+	0.448517i
$186$		0			0
$187$	2006.86	+	3475.98i	0.784791	+	1.35930i
$188$	−3036.67			−1.17804
$189$		0			0
$190$	−910.010			−0.347469
$191$	−603.717	−	1045.67i	−0.228709	−	0.396136i	0.728717	−	0.684815i	$-0.240117\pi$
$191$	−603.717	−	1045.67i	−0.228709	−	0.396136i	−0.957426	+	0.288680i	$0.906784\pi$
$192$		0			0
$193$	−461.582	+	799.483i	−0.172152	+	0.298177i	−0.939172	−	0.343447i	$-0.888405\pi$
$193$	−461.582	+	799.483i	−0.172152	+	0.298177i	0.767020	+	0.641623i	$0.221739\pi$
$194$	−511.409	+	885.787i	−0.189263	+	0.327813i
$195$		0			0
$196$	1885.02	+	3264.95i	0.686961	+	1.18985i
$197$	−1180.87			−0.427075			−0.213537	−	0.976935i	$-0.568499\pi$
$197$	−1180.87			−0.427075			−0.213537	+	0.976935i	$0.568499\pi$
$198$		0			0
$199$	−839.805			−0.299157			−0.149578	−	0.988750i	$-0.547792\pi$
$199$	−839.805			−0.299157			−0.149578	+	0.988750i	$0.547792\pi$
$200$	−216.620	−	375.197i	−0.0765867	−	0.132652i
$201$		0			0
$202$	−3000.41	+	5196.87i	−1.04509	+	1.81015i
$203$	559.083	−	968.360i	0.193300	−	0.334806i
$204$		0			0
$205$	424.416	+	735.110i	0.144598	+	0.250450i
$206$	−7118.51			−2.40762
$207$		0			0
$208$	−377.774			−0.125932
$209$	1189.72	+	2060.66i	0.393755	+	0.682003i
$210$		0			0
$211$	1294.82	−	2242.70i	0.422461	−	0.731725i	−0.573718	−	0.819053i	$-0.694499\pi$
$211$	1294.82	−	2242.70i	0.422461	−	0.731725i	0.996180	+	0.0873280i	$0.0278328\pi$
$212$	−1276.06	+	2210.20i	−0.413396	+	0.716023i
$213$		0			0
$214$	−2137.80	−	3702.77i	−0.682882	−	1.18279i
$215$	−2192.98			−0.695627
$216$		0			0
$217$	1481.41			0.463432
$218$	−3768.69	−	6527.56i	−1.17086	−	2.02799i
$219$		0			0
$220$	−1732.42	+	3000.64i	−0.530907	+	0.919559i
$221$	730.168	−	1264.69i	0.222246	−	0.384942i
$222$		0			0
$223$	2090.38	+	3620.64i	0.627722	+	1.08725i	0.988008	+	0.154405i	$0.0493459\pi$
$223$	2090.38	+	3620.64i	0.627722	+	1.08725i	−0.360285	+	0.932842i	$0.617321\pi$
$224$	−1107.99			−0.330495
$225$		0			0
$226$	−51.8232			−0.0152532
$227$	1301.34	+	2253.98i	0.380497	+	0.659039i	0.991133	−	0.132872i	$-0.0424198\pi$
$227$	1301.34	+	2253.98i	0.380497	+	0.659039i	−0.610637	+	0.791911i	$0.709086\pi$
$228$		0			0
$229$	922.676	−	1598.12i	0.266254	−	0.461165i	−0.701638	−	0.712534i	$-0.747547\pi$
$229$	922.676	−	1598.12i	0.266254	−	0.461165i	0.967891	+	0.251369i	$0.0808807\pi$
$230$	1608.93	−	2786.74i	0.461259	−	0.798923i
$231$		0			0
$232$	1906.76	+	3302.60i	0.539589	+	0.934596i
$233$	240.637			0.0676594			0.0338297	−	0.999428i	$-0.489230\pi$
$233$	240.637			0.0676594			0.0338297	+	0.999428i	$0.489230\pi$
$234$		0			0
$235$	−1277.40			−0.354590
$236$	−1970.26	−	3412.59i	−0.543445	−	0.941275i
$237$		0			0
$238$	779.986	−	1350.98i	0.212433	−	0.367944i
$239$	−1283.82	+	2223.64i	−0.347462	+	0.601822i	−0.985798	−	0.167936i	$-0.946290\pi$
$239$	−1283.82	+	2223.64i	−0.347462	+	0.601822i	0.638336	+	0.769758i	$0.279623\pi$
$240$		0			0
$241$	−1994.00	−	3453.70i	−0.532965	−	0.923122i	−0.999259	−	0.0384925i	$-0.987744\pi$
$241$	−1994.00	−	3453.70i	−0.532965	−	0.923122i	0.466294	−	0.884630i	$-0.345589\pi$
$242$	9221.86			2.44960
$243$		0			0
$244$	653.315			0.171411
$245$	792.953	+	1373.43i	0.206775	+	0.358145i
$246$		0			0
$247$	432.864	−	749.742i	0.111508	−	0.193137i
$248$	−2526.18	+	4375.47i	−0.646825	+	1.12033i
$249$		0			0
$250$	−278.711	−	482.742i	−0.0705090	−	0.122125i
$251$	967.393			0.243272			0.121636	−	0.992575i	$-0.461186\pi$
$251$	967.393			0.243272			0.121636	+	0.992575i	$0.461186\pi$
$252$		0			0
$253$	−8413.86			−2.09081
$254$	−689.289	−	1193.88i	−0.170275	−	0.294925i
$255$		0			0
$256$	1042.67	−	1805.96i	0.254558	−	0.440907i
$257$	−1871.52	+	3241.56i	−0.454249	+	0.786783i	−0.998645	−	0.0520460i	$-0.983426\pi$
$257$	−1871.52	+	3241.56i	−0.454249	+	0.786783i	0.544396	+	0.838829i	$0.316759\pi$
$258$		0			0
$259$	−662.178	−	1146.93i	−0.158864	−	0.275160i
$260$	1260.63			0.300697
$261$		0			0
$262$	12419.5			2.92855
$263$	1248.74	+	2162.88i	0.292777	+	0.507105i	0.974465	−	0.224538i	$-0.0720872\pi$
$263$	1248.74	+	2162.88i	0.292777	+	0.507105i	−0.681688	+	0.731643i	$0.738754\pi$
$264$		0			0
$265$	−536.786	+	929.741i	−0.124432	+	0.215523i
$266$	462.397	−	800.896i	0.106584	−	0.184609i
$267$		0			0
$268$	−4505.90	−	7804.44i	−1.02702	−	1.77885i
$269$	−2142.91			−0.485709			−0.242855	−	0.970063i	$-0.578084\pi$
$269$	−2142.91			−0.485709			−0.242855	+	0.970063i	$0.578084\pi$
$270$		0			0
$271$	1540.64			0.345341			0.172671	−	0.984980i	$-0.444760\pi$
$271$	1540.64			0.345341			0.172671	+	0.984980i	$0.444760\pi$
$272$	−613.048	−	1061.83i	−0.136660	−	0.236702i
$273$		0			0
$274$	5550.62	−	9613.95i	1.22381	−	2.11971i
$275$	−728.758	+	1262.25i	−0.159803	+	0.276787i
$276$		0			0
$277$	−3388.90	−	5869.75i	−0.735088	−	1.27321i	−0.954685	−	0.297619i	$-0.903808\pi$
$277$	−3388.90	−	5869.75i	−0.735088	−	1.27321i	0.219597	−	0.975591i	$-0.429526\pi$
$278$	7964.69			1.71831
$279$		0			0
$280$	440.278			0.0939702
$281$	−413.827	−	716.769i	−0.0878535	−	0.152167i	0.818750	−	0.574150i	$-0.194667\pi$
$281$	−413.827	−	716.769i	−0.0878535	−	0.152167i	−0.906604	+	0.421983i	$0.861334\pi$
$282$		0			0
$283$	1585.99	−	2747.01i	0.333135	−	0.577007i	−0.649990	−	0.759943i	$-0.725227\pi$
$283$	1585.99	−	2747.01i	0.333135	−	0.577007i	0.983125	+	0.182936i	$0.0585602\pi$
$284$	5374.58	−	9309.05i	1.12297	−	1.94504i
$285$		0			0
$286$	−2757.39	−	4775.94i	−0.570098	−	0.987438i
$287$	−862.623			−0.177418
$288$		0			0
$289$	−173.358			−0.0352856
$290$	2453.31	+	4249.25i	0.496769	+	0.860430i
$291$		0			0
$292$	−5150.38	+	8920.71i	−1.03220	+	1.78783i
$293$	−688.012	+	1191.67i	−0.137181	+	0.237605i	−0.926429	−	0.376471i	$-0.877138\pi$
$293$	−688.012	+	1191.67i	−0.137181	+	0.237605i	0.789247	+	0.614075i	$0.210471\pi$
$294$		0			0
$295$	−828.809	−	1435.54i	−0.163577	−	0.283323i
$296$	4516.73			0.886923
$297$		0			0
$298$	6996.02			1.35996
$299$	1530.63	+	2651.14i	0.296050	+	0.512773i
$300$		0			0
$301$	1114.30	−	1930.03i	0.213380	−	0.369585i
$302$	977.333	−	1692.79i	0.186223	−	0.322547i
$303$		0			0
$304$	−363.432	−	629.483i	−0.0685666	−	0.118761i
$305$	274.823			0.0515946
$306$		0			0
$307$	−119.504			−0.0222165			−0.0111083	−	0.999938i	$-0.503536\pi$
$307$	−119.504			−0.0222165			−0.0111083	+	0.999938i	$0.503536\pi$
$308$	−1760.56	−	3049.39i	−0.325706	−	0.564140i
$309$		0			0
$310$	−3250.28	+	5629.65i	−0.595495	+	1.03143i
$311$	−1069.68	+	1852.73i	−0.195035	+	0.337810i	−0.946912	−	0.321493i	$-0.895815\pi$
$311$	−1069.68	+	1852.73i	−0.195035	+	0.337810i	0.751877	+	0.659303i	$0.229149\pi$
$312$		0			0
$313$	−2581.75	−	4471.72i	−0.466227	−	0.807529i	0.533029	−	0.846097i	$-0.321054\pi$
$313$	−2581.75	−	4471.72i	−0.466227	−	0.807529i	−0.999256	+	0.0385677i	$0.987720\pi$
$314$	−199.548			−0.0358635
$315$		0			0
$316$	2459.95			0.437922
$317$	4315.85	+	7475.26i	0.764675	+	1.32446i	0.940418	+	0.340020i	$0.110434\pi$
$317$	4315.85	+	7475.26i	0.764675	+	1.32446i	−0.175743	+	0.984436i	$0.556233\pi$
$318$		0			0
$319$	6414.76	−	11110.7i	1.12589	−	1.95009i
$320$	2074.80	−	3593.66i	0.362452	−	0.627786i
$321$		0			0
$322$	1635.07	+	2832.02i	0.282977	+	0.490131i
$323$	2809.79			0.484028
$324$		0			0
$325$	530.298			0.0905097
$326$	5823.60	+	10086.8i	0.989385	+	1.71366i
$327$		0			0
$328$	1470.99	−	2547.83i	0.247628	−	0.428904i
$329$	649.079	−	1124.24i	0.108769	−	0.188393i
$330$		0			0
$331$	1471.17	+	2548.14i	0.244298	+	0.423137i	0.961934	−	0.273281i	$-0.0881090\pi$
$331$	1471.17	+	2548.14i	0.244298	+	0.423137i	−0.717636	+	0.696419i	$0.754776\pi$
$332$	−5507.98			−0.910512
$333$		0			0
$334$	−842.585			−0.138037
$335$	−1895.45	−	3283.01i	−0.309133	−	0.535433i
$336$		0			0
$337$	−4948.73	+	8571.45i	−0.799924	+	1.38551i	0.119740	+	0.992805i	$0.461794\pi$
$337$	−4948.73	+	8571.45i	−0.799924	+	1.38551i	−0.919665	+	0.392704i	$0.871540\pi$
$338$	3895.39	−	6747.02i	0.626868	−	1.08577i
$339$		0			0
$340$	2045.75	+	3543.34i	0.326312	+	0.565190i
$341$	16997.3			2.69928
$342$		0			0
$343$	−3354.53			−0.528070
$344$	3800.34	+	6582.38i	0.595641	+	1.03168i
$345$		0			0
$346$	3355.73	−	5812.29i	0.521402	−	0.903095i
$347$	6007.87	−	10405.9i	0.929451	−	1.60986i	0.145208	−	0.989401i	$-0.453615\pi$
$347$	6007.87	−	10405.9i	0.929451	−	1.60986i	0.784242	−	0.620454i	$-0.213052\pi$
$348$		0			0
$349$	−3947.31	−	6836.94i	−0.605428	−	1.04863i	−0.991984	−	0.126367i	$-0.959668\pi$
$349$	−3947.31	−	6836.94i	−0.605428	−	1.04863i	0.386555	−	0.922266i	$-0.373665\pi$
$350$	566.479			0.0865131
$351$		0			0
$352$	−12712.8			−1.92499
$353$	−370.577	−	641.858i	−0.0558748	−	0.0967781i	0.836735	−	0.547608i	$-0.184461\pi$
$353$	−370.577	−	641.858i	−0.0558748	−	0.0967781i	−0.892610	+	0.450830i	$0.851128\pi$
$354$		0			0
$355$	2260.87	−	3915.94i	0.338013	−	0.585455i
$356$	−3576.15	+	6194.07i	−0.532403	+	0.922149i
$357$		0			0
$358$	6993.68	+	12113.4i	1.03248	+	1.78831i
$359$	−11564.4			−1.70012			−0.850060	−	0.526685i	$-0.823435\pi$
$359$	−11564.4			−1.70012			−0.850060	+	0.526685i	$0.823435\pi$
$360$		0			0
$361$	−5193.28			−0.757148
$362$	−10061.9	−	17427.6i	−1.46088	−	2.53032i
$363$		0			0
$364$	−640.558	+	1109.48i	−0.0922372	+	0.159760i
$365$	−2166.56	+	3752.58i	−0.310692	+	0.538135i
$366$		0			0
$367$	574.284	+	994.690i	0.0816823	+	0.141478i	0.903973	−	0.427590i	$-0.140637\pi$
$367$	574.284	+	994.690i	0.0816823	+	0.141478i	−0.822290	+	0.569068i	$0.807304\pi$
$368$	2570.24			0.364084
$369$		0			0
$370$	5811.39			0.816540
$371$	−545.507	−	944.846i	−0.0763378	−	0.132221i
$372$		0			0
$373$	2301.49	−	3986.29i	0.319481	−	0.553358i	−0.660899	−	0.750475i	$-0.729825\pi$
$373$	2301.49	−	3986.29i	0.319481	−	0.553358i	0.980380	+	0.197117i	$0.0631580\pi$
$374$	8949.34	−	15500.7i	1.23732	−	2.14311i
$375$		0			0
$376$	2213.69	+	3834.22i	0.303623	+	0.525890i
$377$	−4667.85			−0.637683
$378$		0			0
$379$	−3988.46			−0.540563			−0.270282	−	0.962781i	$-0.587117\pi$
$379$	−3988.46			−0.540563			−0.270282	+	0.962781i	$0.587117\pi$
$380$	1212.78	+	2100.59i	0.163721	+	0.283574i
$381$		0			0
$382$	−2692.21	+	4663.04i	−0.360590	+	0.624559i
$383$	−3894.10	+	6744.78i	−0.519528	+	0.899849i	0.480215	+	0.877151i	$0.340559\pi$
$383$	−3894.10	+	6744.78i	−0.519528	+	0.899849i	−0.999742	+	0.0226975i	$0.992775\pi$
$384$		0			0
$385$	−740.599	−	1282.75i	−0.0980374	−	0.169806i
$386$	4116.74			0.542841
$387$		0			0
$388$	2726.23			0.356710
$389$	−4262.43	−	7382.75i	−0.555563	−	0.962263i	−0.997859	−	0.0653944i	$-0.979169\pi$
$389$	−4262.43	−	7382.75i	−0.555563	−	0.962263i	0.442297	−	0.896869i	$-0.354164\pi$
$390$		0			0
$391$	−4967.80	+	8604.49i	−0.642538	+	1.11291i
$392$	2748.31	−	4760.21i	0.354108	−	0.613334i
$393$		0			0
$394$	2632.98	+	4560.46i	0.336669	+	0.583129i
$395$	1034.80			0.131814
$396$		0			0
$397$	−155.729			−0.0196872			−0.00984361	−	0.999952i	$-0.503133\pi$
$397$	−155.729			−0.0196872			−0.00984361	+	0.999952i	$0.503133\pi$
$398$	1872.51	+	3243.27i	0.235830	+	0.408469i
$399$		0			0
$400$	222.619	−	385.587i	0.0278274	−	0.0481984i
$401$	−2966.98	+	5138.96i	−0.369486	+	0.639968i	−0.989485	−	0.144634i	$-0.953799\pi$
$401$	−2966.98	+	5138.96i	−0.369486	+	0.639968i	0.619999	+	0.784602i	$0.287133\pi$
$402$		0			0
$403$	−3092.12	−	5355.70i	−0.382207	−	0.662002i
$404$	15994.7			1.96971
$405$		0			0
$406$	−4986.33			−0.609526
$407$	−7597.65	−	13159.5i	−0.925311	−	1.60268i
$408$		0			0
$409$	−7080.71	+	12264.1i	−0.856035	+	1.48270i	0.0196459	+	0.999807i	$0.493746\pi$
$409$	−7080.71	+	12264.1i	−0.856035	+	1.48270i	−0.875681	+	0.482890i	$0.839587\pi$
$410$	1892.63	−	3278.14i	0.227977	−	0.394868i
$411$		0			0
$412$	9486.88	+	16431.8i	1.13443	+	1.96489i
$413$	1684.55			0.200705
$414$		0			0
$415$	−2316.99			−0.274064
$416$	2312.69	+	4005.70i	0.272570	+	0.472105i
$417$		0			0
$418$	5305.42	−	9189.26i	0.620805	−	1.07527i
$419$	−4812.12	+	8334.84i	−0.561068	+	0.971798i	0.436336	+	0.899784i	$0.356276\pi$
$419$	−4812.12	+	8334.84i	−0.561068	+	0.971798i	−0.997404	+	0.0720142i	$0.977057\pi$
$420$		0			0
$421$	768.128	+	1330.44i	0.0889223	+	0.154018i	0.907056	−	0.421010i	$-0.138324\pi$
$421$	768.128	+	1330.44i	0.0889223	+	0.154018i	−0.818134	+	0.575028i	$0.804991\pi$
$422$	−11548.2			−1.33213
$423$		0			0
$424$	3720.91			0.426187
$425$	860.563	+	1490.54i	0.0982199	+	0.170122i
$426$		0			0
$427$	−139.644	+	241.871i	−0.0158264	+	0.0274121i
$428$	−5698.11	+	9869.42i	−0.643525	+	1.11462i
$429$		0			0
$430$	4889.67	+	8469.15i	0.548373	+	0.949811i
$431$	11582.2			1.29441			0.647207	−	0.762314i	$-0.275937\pi$
$431$	11582.2			1.29441			0.647207	+	0.762314i	$0.275937\pi$
$432$		0			0
$433$	14892.6			1.65287			0.826437	−	0.563029i	$-0.190364\pi$
$433$	14892.6			1.65287			0.826437	+	0.563029i	$0.190364\pi$
$434$	−3303.09	−	5721.11i	−0.365330	−	0.632770i
$435$		0			0
$436$	−10045.1	+	17398.6i	−1.10338	+	1.91111i
$437$	−2945.05	+	5100.98i	−0.322382	+	0.558382i
$438$		0			0
$439$	821.253	+	1422.45i	0.0892853	+	0.154647i	0.907209	−	0.420680i	$-0.138208\pi$
$439$	821.253	+	1422.45i	0.0892853	+	0.154647i	−0.817924	+	0.575326i	$0.804875\pi$
$440$	5051.63			0.547334
$441$		0			0
$442$	−6512.20			−0.700800
$443$	−1958.15	−	3391.62i	−0.210011	−	0.363749i	0.741707	−	0.670724i	$-0.234017\pi$
$443$	−1958.15	−	3391.62i	−0.210011	−	0.363749i	−0.951718	+	0.306975i	$0.900683\pi$
$444$		0			0
$445$	−1504.34	+	2605.59i	−0.160253	+	0.277566i
$446$	9321.79	−	16145.8i	0.989686	−	1.71419i
$447$		0			0
$448$	2108.51	+	3652.04i	0.222361	+	0.385140i
$449$	−3985.25			−0.418876			−0.209438	−	0.977822i	$-0.567163\pi$
$449$	−3985.25			−0.418876			−0.209438	+	0.977822i	$0.567163\pi$
$450$		0			0
$451$	−9897.50			−1.03338
$452$	69.0650	+	119.624i	0.00718705	+	0.0124483i
$453$		0			0
$454$	5803.16	−	10051.4i	0.599902	−	1.03906i
$455$	−269.457	+	466.713i	−0.0277634	+	0.0480876i
$456$		0			0
$457$	7088.89	+	12278.3i	0.725611	+	1.25680i	0.958722	+	0.284345i	$0.0917763\pi$
$457$	7088.89	+	12278.3i	0.725611	+	1.25680i	−0.233111	+	0.972450i	$0.574890\pi$
$458$	−8229.13			−0.839567
$459$		0			0
$460$	−8576.91			−0.869349
$461$	8197.14	+	14197.9i	0.828154	+	1.43441i	0.899485	+	0.436952i	$0.143942\pi$
$461$	8197.14	+	14197.9i	0.828154	+	1.43441i	−0.0713305	+	0.997453i	$0.522725\pi$
$462$		0			0
$463$	−1659.80	+	2874.86i	−0.166603	+	0.288566i	−0.937224	−	0.348729i	$-0.886613\pi$
$463$	−1659.80	+	2874.86i	−0.166603	+	0.288566i	0.770620	+	0.637295i	$0.219947\pi$
$464$	−1959.56	+	3394.06i	−0.196057	+	0.339580i
$465$		0			0
$466$	−536.546	−	929.324i	−0.0533369	−	0.0923822i
$467$	−2529.79			−0.250674			−0.125337	−	0.992114i	$-0.540001\pi$
$467$	−2529.79			−0.250674			−0.125337	+	0.992114i	$0.540001\pi$
$468$		0			0
$469$	3852.49			0.379299
$470$	2848.22	+	4933.26i	0.279529	+	0.484158i
$471$		0			0
$472$	−2872.58	+	4975.46i	−0.280130	+	0.485199i
$473$	12785.2	−	22144.6i	1.24284	−	2.15267i
$474$		0			0
$475$	510.166	+	883.633i	0.0492800	+	0.0853555i
$476$	−4157.97			−0.400379
$477$		0			0
$478$	11450.1			1.09564
$479$	4323.38	+	7488.31i	0.412401	+	0.714300i	0.995152	−	0.0983514i	$-0.0313569\pi$
$479$	4323.38	+	7488.31i	0.412401	+	0.714300i	−0.582751	+	0.812651i	$0.698024\pi$
$480$		0			0
$481$	−2764.30	+	4787.91i	−0.262040	+	0.453867i
$482$	−8891.99	+	15401.4i	−0.840288	+	1.45542i
$483$		0			0
$484$	−12290.0	−	21287.0i	−1.15421	−	1.99915i
$485$	1146.82			0.107370
$486$		0			0
$487$	−15251.7			−1.41914			−0.709569	−	0.704636i	$-0.751110\pi$
$487$	−15251.7			−1.41914			−0.709569	+	0.704636i	$0.751110\pi$
$488$	−476.257	−	824.902i	−0.0441786	−	0.0765196i
$489$		0			0
$490$	3536.08	−	6124.67i	0.326008	−	0.564662i
$491$	883.434	−	1530.15i	0.0811992	−	0.140641i	−0.822566	−	0.568670i	$-0.807458\pi$
$491$	883.434	−	1530.15i	0.0811992	−	0.140641i	0.903765	+	0.428028i	$0.140792\pi$
$492$		0			0
$493$	−7574.95	−	13120.2i	−0.692005	−	1.19859i
$494$	−3860.61			−0.351614
$495$		0			0
$496$	−5192.28			−0.470041
$497$	2297.60	+	3979.56i	0.207367	+	0.359171i
$498$		0			0
$499$	−5866.92	+	10161.8i	−0.526332	+	0.911633i	0.473198	+	0.880956i	$0.343100\pi$
$499$	−5866.92	+	10161.8i	−0.526332	+	0.911633i	−0.999529	+	0.0306768i	$0.990234\pi$
$500$	−742.881	+	1286.71i	−0.0664453	+	0.115087i
$501$		0			0
$502$	−2156.99	−	3736.01i	−0.191775	−	0.332164i
$503$	−977.608			−0.0866589			−0.0433294	−	0.999061i	$-0.513797\pi$
$503$	−977.608			−0.0866589			−0.0433294	+	0.999061i	$0.513797\pi$
$504$		0			0
$505$	6728.31			0.592883
$506$	18760.3	+	32493.8i	1.64822	+	2.85479i
$507$		0			0
$508$	−1837.24	+	3182.19i	−0.160461	+	0.277927i
$509$	−4837.36	+	8378.55i	−0.421242	+	0.729613i	−0.996061	−	0.0886678i	$-0.971739\pi$
$509$	−4837.36	+	8378.55i	−0.421242	+	0.729613i	0.574819	+	0.818280i	$0.305072\pi$
$510$		0			0
$511$	−2201.76	−	3813.55i	−0.190607	−	0.330140i
$512$	6352.52			0.548329
$513$		0			0
$514$	16691.6			1.43237
$515$	3990.75	+	6912.18i	0.341463	+	0.591431i
$516$		0			0
$517$	7447.35	−	12899.2i	0.633528	−	1.09730i
$518$	−2952.91	+	5114.58i	−0.250470	+	0.433826i
$519$		0			0
$520$	−918.984	−	1591.73i	−0.0775002	−	0.134234i
$521$	5178.95			0.435497			0.217748	−	0.976005i	$-0.430129\pi$
$521$	5178.95			0.435497			0.217748	+	0.976005i	$0.430129\pi$
$522$		0			0
$523$	14280.7			1.19398			0.596992	−	0.802248i	$-0.296363\pi$
$523$	14280.7			1.19398			0.596992	+	0.802248i	$0.296363\pi$
$524$	−16551.5	−	28668.1i	−1.37988	−	2.39002i
$525$		0			0
$526$	5568.60	−	9645.09i	0.461601	−	0.799517i
$527$	10035.7	−	17382.4i	0.829532	−	1.43679i
$528$		0			0
$529$	−4330.39	−	7500.46i	−0.355913	−	0.616459i
$530$	4787.47			0.392367
$531$		0			0
$532$	−2464.96			−0.200883
$533$	1800.54	+	3118.62i	0.146322	+	0.253438i
$534$		0			0
$535$	−2396.97	+	4151.67i	−0.193701	+	0.335499i
$536$	−6569.47	+	11378.7i	−0.529399	+	0.916946i
$537$		0			0
$538$	4778.04	+	8275.80i	0.382892	+	0.663188i
$539$	−18491.9			−1.47774
$540$		0			0
$541$	12923.8			1.02706			0.513529	−	0.858072i	$-0.328338\pi$
$541$	12923.8			1.02706			0.513529	+	0.858072i	$0.328338\pi$
$542$	−3435.16	−	5949.87i	−0.272238	−	0.471529i
$543$		0			0
$544$	−7506.04	+	13000.8i	−0.591579	+	1.02464i
$545$	−4225.57	+	7318.90i	−0.332117	+	0.575243i
$546$		0			0
$547$	−6826.66	−	11824.1i	−0.533614	−	0.924246i	−0.999229	−	0.0392591i	$-0.987500\pi$
$547$	−6826.66	−	11824.1i	−0.533614	−	0.924246i	0.465615	−	0.884987i	$-0.345833\pi$
$548$	−29589.4			−2.30656
$549$		0			0
$550$	6499.63			0.503900
$551$	−4490.64	−	7778.02i	−0.347201	−	0.601370i
$552$		0			0
$553$	−525.808	+	910.726i	−0.0404333	+	0.0700326i
$554$	−15112.4	+	26175.5i	−1.15896	+	2.00738i
$555$		0			0
$556$	−10614.6	−	18385.0i	−0.809638	−	1.40233i
$557$	−9313.63			−0.708494			−0.354247	−	0.935152i	$-0.615263\pi$
$557$	−9313.63			−0.708494			−0.354247	+	0.935152i	$0.615263\pi$
$558$		0			0
$559$	−9303.46			−0.703925
$560$	226.236	+	391.852i	0.0170718	+	0.0295692i
$561$		0			0
$562$	−1845.41	+	3196.35i	−0.138512	+	0.239911i
$563$	5312.70	−	9201.86i	0.397697	−	0.688831i	−0.595744	−	0.803174i	$-0.703143\pi$
$563$	5312.70	−	9201.86i	0.397697	−	0.688831i	0.993441	+	0.114343i	$0.0364762\pi$
$564$		0			0
$565$	29.0529	+	50.3211i	0.00216330	+	0.00374694i
$566$	−14145.1			−1.05046
$567$		0			0
$568$	−15672.0			−1.15771
$569$	−4530.25	−	7846.62i	−0.333775	−	0.578115i	0.649474	−	0.760384i	$-0.274989\pi$
$569$	−4530.25	−	7846.62i	−0.333775	−	0.578115i	−0.983249	+	0.182269i	$0.941656\pi$
$570$		0			0
$571$	10689.6	−	18514.9i	0.783440	−	1.35696i	−0.146486	−	0.989213i	$-0.546796\pi$
$571$	10689.6	−	18514.9i	0.783440	−	1.35696i	0.929926	−	0.367746i	$-0.119870\pi$
$572$	−7349.58	+	12729.9i	−0.537240	+	0.930528i
$573$		0			0
$574$	1923.38	+	3331.40i	0.139861	+	0.242247i
$575$	−3607.96			−0.261674
$576$		0			0
$577$	6347.76			0.457991			0.228996	−	0.973427i	$-0.426456\pi$
$577$	6347.76			0.457991			0.228996	+	0.973427i	$0.426456\pi$
$578$	386.535	+	669.499i	0.0278162	+	0.0481791i
$579$		0			0
$580$	6539.07	−	11326.0i	0.468138	−	0.810839i
$581$	1177.32	−	2039.17i	0.0840676	−	0.145609i
$582$		0			0
$583$	−6259.00	−	10840.9i	−0.444633	−	0.770127i
$584$	15018.2			1.06414
$585$		0			0
$586$	6136.22			0.432568
$587$	−7386.86	−	12794.4i	−0.519401	−	0.899628i	−0.999746	−	0.0225488i	$-0.992822\pi$
$587$	−7386.86	−	12794.4i	−0.519401	−	0.899628i	0.480345	−	0.877080i	$-0.340511\pi$
$588$		0			0
$589$	5949.46	−	10304.8i	0.416202	−	0.720884i
$590$	−3695.98	+	6401.62i	−0.257900	+	0.446696i
$591$		0			0
$592$	2320.91	+	4019.93i	0.161129	+	0.279084i
$593$	26868.1			1.86061			0.930304	−	0.366790i	$-0.119543\pi$
$593$	26868.1			1.86061			0.930304	+	0.366790i	$0.119543\pi$
$594$		0			0
$595$	−1749.09			−0.120514
$596$	−9323.64	−	16149.0i	−0.640791	−	1.10988i
$597$		0			0
$598$	6825.68	−	11822.4i	0.466761	−	0.808454i
$599$	874.913	−	1515.39i	0.0596794	−	0.103368i	−0.834642	−	0.550793i	$-0.814325\pi$
$599$	874.913	−	1515.39i	0.0596794	−	0.103368i	0.894322	+	0.447425i	$0.147659\pi$
$600$		0			0
$601$	8981.99	+	15557.3i	0.609622	+	1.05590i	0.991303	+	0.131602i	$0.0420122\pi$
$601$	8981.99	+	15557.3i	0.609622	+	1.05590i	−0.381680	+	0.924294i	$0.624654\pi$
$602$	−9938.21			−0.672843
$603$		0			0
$604$	−5209.99			−0.350979
$605$	−5169.92	−	8954.57i	−0.347417	−	0.601744i
$606$		0			0
$607$	2209.11	−	3826.29i	0.147718	−	0.255856i	−0.782666	−	0.622443i	$-0.786140\pi$
$607$	2209.11	−	3826.29i	0.147718	−	0.255856i	0.930384	+	0.366587i	$0.119474\pi$
$608$	−4449.79	+	7707.26i	−0.296814	+	0.514097i
$609$		0			0
$610$	−612.771	−	1061.35i	−0.0406728	−	0.0704473i
$611$	−5419.24			−0.358820
$612$		0			0
$613$	−20179.7			−1.32961			−0.664804	−	0.747018i	$-0.731485\pi$
$613$	−20179.7			−1.32961			−0.664804	+	0.747018i	$0.731485\pi$
$614$	266.458	+	461.518i	0.0175136	+	0.0303345i
$615$		0			0
$616$	−2566.85	+	4445.92i	−0.167892	+	0.290797i
$617$	2336.51	−	4046.95i	0.152454	−	0.264058i	−0.779675	−	0.626184i	$-0.784616\pi$
$617$	2336.51	−	4046.95i	0.152454	−	0.264058i	0.932129	+	0.362126i	$0.117949\pi$
$618$		0			0
$619$	9988.40	+	17300.4i	0.648574	+	1.12336i	0.983464	+	0.181106i	$0.0579678\pi$
$619$	9988.40	+	17300.4i	0.648574	+	1.12336i	−0.334889	+	0.942258i	$0.608699\pi$
$620$	17326.7			1.12235
$621$		0			0
$622$	9540.19			0.614994
$623$	−1528.78	−	2647.93i	−0.0983136	−	0.170284i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−11513.0	+	19941.1i	−0.735068	+	1.27318i
$627$		0			0
$628$	265.939	+	460.619i	0.0168983	+	0.0292686i
$629$	−17943.5			−1.13745
$630$		0			0
$631$	10457.5			0.659757			0.329879	−	0.944023i	$-0.392992\pi$
$631$	10457.5			0.659757			0.329879	+	0.944023i	$0.392992\pi$
$632$	−1793.27	−	3106.04i	−0.112868	−	0.195493i
$633$		0			0
$634$	19246.0	−	33335.1i	1.20561	−	2.08818i
$635$	−772.852	+	1338.62i	−0.0482988	+	0.0836559i
$636$		0			0
$637$	3364.01	+	5826.63i	0.209242	+	0.362417i
$638$	−57211.8			−3.55021
$639$		0			0
$640$	−9782.40			−0.604193
$641$	−2197.93	−	3806.92i	−0.135434	−	0.234578i	0.790329	−	0.612682i	$-0.209909\pi$
$641$	−2197.93	−	3806.92i	−0.135434	−	0.234578i	−0.925763	+	0.378104i	$0.876576\pi$
$642$		0			0
$643$	−2893.18	+	5011.13i	−0.177443	+	0.307340i	−0.941004	−	0.338395i	$-0.890116\pi$
$643$	−2893.18	+	5011.13i	−0.177443	+	0.307340i	0.763561	+	0.645736i	$0.223449\pi$
$644$	4358.13	−	7548.50i	0.266668	−	0.461883i
$645$		0			0
$646$	−6264.97	−	10851.2i	−0.381566	−	0.660892i
$647$	−25367.7			−1.54143			−0.770717	−	0.637178i	$-0.780102\pi$
$647$	−25367.7			−1.54143			−0.770717	+	0.637178i	$0.780102\pi$
$648$		0			0
$649$	19328.1			1.16902
$650$	−1182.40	−	2047.98i	−0.0713501	−	0.123582i
$651$		0			0
$652$	15522.3	−	26885.4i	0.932362	−	1.61490i
$653$	10816.6	−	18734.9i	0.648218	−	1.12275i	−0.335330	−	0.942101i	$-0.608848\pi$
$653$	10816.6	−	18734.9i	0.648218	−	1.12275i	0.983548	−	0.180646i	$-0.0578190\pi$
$654$		0			0
$655$	−6962.56	−	12059.5i	−0.415343	−	0.719396i
$656$	3023.46			0.179948
$657$		0			0
$658$	−5788.98			−0.342976
$659$	−9156.22	−	15859.0i	−0.541238	−	0.937451i	−0.998833	−	0.0482907i	$-0.984623\pi$
$659$	−9156.22	−	15859.0i	−0.541238	−	0.937451i	0.457596	−	0.889160i	$-0.348711\pi$
$660$		0			0
$661$	2763.04	−	4785.73i	0.162587	−	0.281609i	−0.773209	−	0.634151i	$-0.781350\pi$
$661$	2763.04	−	4785.73i	0.162587	−	0.281609i	0.935796	+	0.352543i	$0.114683\pi$
$662$	6560.51	−	11363.1i	0.385168	−	0.667131i
$663$		0			0
$664$	4015.24	+	6954.60i	0.234671	+	0.406462i
$665$	−1036.91			−0.0604656
$666$		0			0
$667$	31758.4			1.84361
$668$	1122.92	+	1944.95i	0.0650404	+	0.112653i
$669$		0			0
$670$	−8452.53	+	14640.2i	−0.487388	+	0.844180i
$671$	−1602.24	+	2775.16i	−0.0921814	+	0.159663i
$672$		0			0
$673$	−718.621	−	1244.69i	−0.0411602	−	0.0712916i	0.844711	−	0.535222i	$-0.179772\pi$
$673$	−718.621	−	1244.69i	−0.0411602	−	0.0712916i	−0.885872	+	0.463931i	$0.846439\pi$
$674$	44136.6			2.52237
$675$		0			0
$676$	−20765.7			−1.18148
$677$	11702.9	+	20270.1i	0.664373	+	1.15073i	0.979455	+	0.201663i	$0.0646346\pi$
$677$	11702.9	+	20270.1i	0.664373	+	1.15073i	−0.315082	+	0.949064i	$0.602032\pi$
$678$		0			0
$679$	−582.724	+	1009.31i	−0.0329351	+	0.0570452i
$680$	2982.64	−	5166.08i	0.168204	−	0.291339i
$681$		0			0
$682$	−37898.7	−	65642.5i	−2.12788	−	3.68560i
$683$	19227.4			1.07719			0.538593	−	0.842566i	$-0.318956\pi$
$683$	19227.4			1.07719			0.538593	+	0.842566i	$0.318956\pi$
$684$		0			0
$685$	−12447.1			−0.694274
$686$	7479.58	+	12955.0i	0.416285	+	0.721027i
$687$		0			0
$688$	−3905.59	+	6764.67i	−0.216423	+	0.374856i
$689$	−2277.25	+	3944.32i	−0.125916	+	0.218094i
$690$		0			0
$691$	17642.4	+	30557.5i	0.971271	+	1.68229i	0.691728	+	0.722158i	$0.256850\pi$
$691$	17642.4	+	30557.5i	0.971271	+	1.68229i	0.279544	+	0.960133i	$0.409817\pi$
$692$	−17888.8			−0.982703
$693$		0			0
$694$	−53582.8			−2.93080
$695$	−4465.13	−	7733.83i	−0.243701	−	0.422102i
$696$		0			0
$697$	−5843.79	+	10121.7i	−0.317574	+	0.550055i
$698$	−17602.6	+	30488.5i	−0.954537	+	1.65331i
$699$		0			0
$700$	−754.950	−	1307.61i	−0.0407635	−	0.0706044i
$701$	9173.00			0.494236			0.247118	−	0.968985i	$-0.420516\pi$
$701$	9173.00			0.494236			0.247118	+	0.968985i	$0.420516\pi$
$702$		0			0
$703$	−10637.4			−0.570695
$704$	24192.4	+	41902.5i	1.29515	+	2.24327i
$705$		0			0
$706$	−1652.54	+	2862.29i	−0.0880940	+	0.152583i
$707$	−3418.81	+	5921.56i	−0.181864	+	0.314997i
$708$		0			0
$709$	16975.8	+	29403.0i	0.899210	+	1.55748i	0.828506	+	0.559981i	$0.189191\pi$
$709$	16975.8	+	29403.0i	0.899210	+	1.55748i	0.0707045	+	0.997497i	$0.477475\pi$
$710$	−20164.2			−1.06584
$711$		0			0
$712$	10427.8			0.548876
$713$	21037.7	+	36438.3i	1.10500	+	1.91392i
$714$		0			0
$715$	−3091.67	+	5354.93i	−0.161709	+	0.280088i
$716$	18641.1	−	32287.3i	0.972973	−	1.68524i
$717$		0			0
$718$	25784.9	+	44660.8i	1.34023	+	2.32135i
$719$	−6727.90			−0.348968			−0.174484	−	0.984660i	$-0.555826\pi$
$719$	−6727.90			−0.348968			−0.174484	+	0.984660i	$0.555826\pi$
$720$		0			0
$721$	−8111.17			−0.418968
$722$	11579.4	+	20056.1i	0.596871	+	1.03381i
$723$		0			0
$724$	−26819.0	+	46451.9i	−1.37669	+	2.38449i
$725$	2750.72	−	4764.39i	0.140909	−	0.244062i
$726$		0			0
$727$	18363.1	+	31805.8i	0.936793	+	1.62257i	0.771406	+	0.636344i	$0.219554\pi$
$727$	18363.1	+	31805.8i	0.936793	+	1.62257i	0.165387	+	0.986229i	$0.447113\pi$
$728$	1867.83			0.0950912
$729$		0			0
$730$	19323.0			0.979694
$731$	−15097.6	−	26149.8i	−0.763890	−	1.32310i
$732$		0			0
$733$	−13345.7	+	23115.4i	−0.672489	+	1.16478i	0.304708	+	0.952446i	$0.401441\pi$
$733$	−13345.7	+	23115.4i	−0.672489	+	1.16478i	−0.977196	+	0.212338i	$0.931892\pi$
$734$	2560.95	−	4435.70i	0.128783	−	0.223058i
$735$		0			0
$736$	−15734.7	−	27253.4i	−0.788030	−	1.36491i
$737$	44202.4			2.20925
$738$		0			0
$739$	12207.0			0.607634			0.303817	−	0.952730i	$-0.401739\pi$
$739$	12207.0			0.607634			0.303817	+	0.952730i	$0.401739\pi$
$740$	−7744.88	−	13414.5i	−0.384740	−	0.666389i
$741$		0			0
$742$	−2432.62	+	4213.43i	−0.120356	+	0.208463i
$743$	6236.64	−	10802.2i	0.307941	−	0.533370i	−0.669971	−	0.742388i	$-0.733693\pi$
$743$	6236.64	−	10802.2i	0.307941	−	0.533370i	0.977912	+	0.209018i	$0.0670267\pi$
$744$		0			0
$745$	−3922.08	−	6793.24i	−0.192878	−	0.334074i
$746$	−20526.4			−1.00741
$747$		0			0
$748$	−47707.4			−2.33202
$749$	−2435.91	−	4219.12i	−0.118833	−	0.205825i
$750$		0			0
$751$	7551.32	−	13079.3i	0.366913	−	0.635511i	−0.622168	−	0.782883i	$-0.713748\pi$
$751$	7551.32	−	13079.3i	0.366913	−	0.635511i	0.989081	+	0.147372i	$0.0470814\pi$
$752$	−2274.99	+	3940.40i	−0.110320	+	0.191079i
$753$		0			0
$754$	10407.9	+	18027.0i	0.502695	+	0.870693i
$755$	−2191.63			−0.105645
$756$		0			0
$757$	−3418.34			−0.164124			−0.0820618	−	0.996627i	$-0.526150\pi$
$757$	−3418.34			−0.164124			−0.0820618	+	0.996627i	$0.526150\pi$
$758$	8893.04	+	15403.2i	0.426134	+	0.738086i
$759$		0			0
$760$	1768.19	−	3062.60i	0.0843935	−	0.146174i
$761$	6342.27	−	10985.1i	0.302112	−	0.523273i	−0.674502	−	0.738273i	$-0.735642\pi$
$761$	6342.27	−	10985.1i	0.302112	−	0.523273i	0.976614	+	0.215000i	$0.0689750\pi$
$762$		0			0
$763$	−4294.22	−	7437.81i	−0.203750	−	0.352906i
$764$	14351.7			0.679614
$765$		0			0
$766$	34730.6			1.63821
$767$	−3516.13	−	6090.11i	−0.165528	−	0.286703i
$768$		0			0
$769$	13790.1	−	23885.2i	0.646663	−	1.12005i	−0.337252	−	0.941415i	$-0.609497\pi$
$769$	13790.1	−	23885.2i	0.646663	−	1.12005i	0.983915	−	0.178639i	$-0.0571693\pi$
$770$	−3302.61	+	5720.29i	−0.154569	+	0.267721i
$771$		0			0
$772$	−5486.41	−	9502.74i	−0.255777	−	0.443019i
$773$	17386.0			0.808966			0.404483	−	0.914546i	$-0.367452\pi$
$773$	17386.0			0.808966			0.404483	+	0.914546i	$0.367452\pi$
$774$		0			0
$775$	7288.63			0.337826
$776$	−1987.39	−	3442.25i	−0.0919368	−	0.159239i
$777$		0			0
$778$	−19007.8	+	32922.5i	−0.875917	+	1.51713i
$779$	−3464.36	+	6000.45i	−0.159337	+	0.275980i
$780$		0			0
$781$	26362.0	+	45660.4i	1.20782	+	2.09201i
$782$	44306.7			2.02609
$783$		0			0
$784$	5648.84			0.257327
$785$	111.870	+	193.764i	0.00508637	+	0.00880985i
$786$		0			0
$787$	−2340.15	+	4053.25i	−0.105994	+	0.183587i	−0.914144	−	0.405390i	$-0.867136\pi$
$787$	−2340.15	+	4053.25i	−0.105994	+	0.183587i	0.808150	+	0.588977i	$0.200469\pi$
$788$	7017.99	−	12155.5i	0.317266	−	0.549520i
$789$		0			0
$790$	−2307.29	−	3996.35i	−0.103911	−	0.179979i
$791$	−59.0498			−0.00265432
$792$		0			0
$793$	1165.91			0.0522100
$794$	347.228	+	601.417i	0.0155197	+	0.0268810i
$795$		0			0
$796$	4991.00	−	8644.66i	0.222238	−	0.384927i
$797$	−3639.31	+	6303.47i	−0.161745	+	0.280151i	−0.935495	−	0.353341i	$-0.885046\pi$
$797$	−3639.31	+	6303.47i	−0.161745	+	0.280151i	0.773749	+	0.633492i	$0.218379\pi$
$798$		0			0
$799$	−8794.30	−	15232.2i	−0.389386	−	0.674437i
$800$	−5451.40			−0.240920
$801$		0			0
$802$	26461.8			1.16508
$803$	−25262.3	−	43755.6i	−1.11020	−	1.92292i
$804$		0			0
$805$	1833.29	−	3175.35i	0.0802670	−	0.139026i
$806$	−13788.9	+	23883.1i	−0.602599	+	1.04373i
$807$		0			0
$808$	−11659.9	−	20195.5i	−0.507665	−	0.879301i
$809$	29212.5			1.26954			0.634770	−	0.772701i	$-0.281095\pi$
$809$	29212.5			1.26954			0.634770	+	0.772701i	$0.281095\pi$
$810$		0			0
$811$	41992.4			1.81819			0.909094	−	0.416590i	$-0.136775\pi$
$811$	41992.4			1.81819			0.909094	+	0.416590i	$0.136775\pi$
$812$	6645.31	+	11510.0i	0.287198	+	0.497441i
$813$		0			0
$814$	−33880.8	+	58683.3i	−1.45887	+	2.52684i
$815$	6529.61	−	11309.6i	0.280641	−	0.486084i
$816$		0			0
$817$	−8950.26	−	15502.3i	−0.383268	−	0.663840i
$818$	63151.2			2.69930
$819$		0			0
$820$	−10089.3			−0.429675
$821$	4361.49	+	7554.33i	0.185405	+	0.321130i	0.943713	−	0.330766i	$-0.107307\pi$
$821$	4361.49	+	7554.33i	0.185405	+	0.321130i	−0.758308	+	0.651896i	$0.773974\pi$
$822$		0			0
$823$	−6792.41	+	11764.8i	−0.287690	+	0.498293i	−0.973258	−	0.229715i	$-0.926220\pi$
$823$	−6792.41	+	11764.8i	−0.287690	+	0.498293i	0.685568	+	0.728008i	$0.259554\pi$
$824$	13831.6	−	23957.0i	0.584765	−	1.01284i
$825$		0			0
$826$	−3756.03	−	6505.63i	−0.158219	−	0.274043i
$827$	26573.6			1.11736			0.558679	−	0.829384i	$-0.311308\pi$
$827$	26573.6			1.11736			0.558679	+	0.829384i	$0.311308\pi$
$828$		0			0
$829$	−43238.4			−1.81150			−0.905748	−	0.423816i	$-0.860690\pi$
$829$	−43238.4			−1.81150			−0.905748	+	0.423816i	$0.860690\pi$
$830$	5166.16	+	8948.06i	0.216048	+	0.374207i
$831$		0			0
$832$	8802.09	−	15245.7i	0.366776	−	0.635275i
$833$	−10918.2	+	18910.8i	−0.454132	+	0.786580i
$834$		0			0
$835$	472.366	+	818.163i	0.0195771	+	0.0339086i
$836$	−28282.3			−1.17005
$837$		0			0
$838$	42918.2			1.76919
$839$	2046.61	+	3544.83i	0.0842154	+	0.145865i	0.905057	−	0.425291i	$-0.139828\pi$
$839$	2046.61	+	3544.83i	0.0842154	+	0.145865i	−0.820841	+	0.571156i	$0.806495\pi$
$840$		0			0
$841$	−12018.2	+	20816.2i	−0.492773	+	0.853508i
$842$	3425.38	−	5932.93i	0.140197	−	0.242829i
$843$		0			0
$844$	15390.4	+	26657.0i	0.627677	+	1.08717i
$845$	−8735.27			−0.355624
$846$		0			0
$847$	10507.8			0.426273
$848$	1911.98	+	3311.64i	0.0774264	+	0.134107i
$849$		0			0
$850$	3837.58	−	6646.88i	0.154856	−	0.268219i
$851$	18807.3	−	32575.2i	0.757587	−	1.31218i
$852$		0			0
$853$	10100.7	+	17495.0i	0.405443	+	0.702248i	0.994373	−	0.105936i	$-0.0337839\pi$
$853$	10100.7	+	17495.0i	0.405443	+	0.702248i	−0.588930	+	0.808184i	$0.700451\pi$
$854$	1245.45			0.0499046
$855$		0			0
$856$	16615.4			0.663436
$857$	−2275.83	−	3941.85i	−0.0907126	−	0.157119i	0.817099	−	0.576498i	$-0.195581\pi$
$857$	−2275.83	−	3941.85i	−0.0907126	−	0.157119i	−0.907811	+	0.419379i	$0.862248\pi$
$858$		0			0
$859$	−5981.28	+	10359.9i	−0.237577	+	0.411496i	−0.960019	−	0.279937i	$-0.909687\pi$
$859$	−5981.28	+	10359.9i	−0.237577	+	0.411496i	0.722441	+	0.691432i	$0.243020\pi$
$860$	13033.0	−	22573.8i	0.516768	−	0.895069i
$861$		0			0
$862$	−25824.6	−	44729.6i	−1.02041	−	1.76740i
$863$	−7164.61			−0.282603			−0.141301	−	0.989967i	$-0.545129\pi$
$863$	−7164.61			−0.282603			−0.141301	+	0.989967i	$0.545129\pi$
$864$		0			0
$865$	−7525.10			−0.295793
$866$	−33206.0	−	57514.5i	−1.30299	−	2.25684i
$867$		0			0
$868$	−8804.09	+	15249.1i	−0.344275	+	0.596301i
$869$	−6032.97	+	10449.4i	−0.235506	+	0.407908i
$870$		0			0
$871$	−8041.22	−	13927.8i	−0.312820	−	0.541820i
$872$	29291.0			1.13752
$873$		0			0
$874$	26266.2			1.01655
$875$	−317.577	−	550.060i	−0.0122698	−	0.0212519i
$876$		0			0
$877$	9609.34	−	16643.9i	0.369994	−	0.640848i	−0.619570	−	0.784941i	$-0.712693\pi$
$877$	9609.34	−	16643.9i	0.369994	−	0.640848i	0.989564	+	0.144093i	$0.0460265\pi$
$878$	3662.28	−	6343.26i	0.140770	−	0.243821i
$879$		0			0
$880$	2595.77	+	4496.00i	0.0994355	+	0.172227i
$881$	−45914.5			−1.75585			−0.877923	−	0.478802i	$-0.841071\pi$
$881$	−45914.5			−1.75585			−0.877923	+	0.478802i	$0.841071\pi$
$882$		0			0
$883$	−44656.7			−1.70194			−0.850972	−	0.525211i	$-0.823986\pi$
$883$	−44656.7			−1.70194			−0.850972	+	0.525211i	$0.823986\pi$
$884$	8678.84	+	15032.2i	0.330205	+	0.571932i
$885$		0			0
$886$	−8732.16	+	15124.5i	−0.331109	+	0.573498i
$887$	−7487.58	+	12968.9i	−0.283437	+	0.490926i	−0.972229	−	0.234032i	$-0.924808\pi$
$887$	−7487.58	+	12968.9i	−0.283437	+	0.490926i	0.688792	+	0.724959i	$0.258141\pi$
$888$		0			0
$889$	−785.409	−	1360.37i	−0.0296308	−	0.0513220i
$890$	13416.9			0.505319
$891$		0			0
$892$	−49692.9			−1.86529
$893$	−5213.50	−	9030.05i	−0.195368	−	0.338387i
$894$		0			0
$895$	7841.54	−	13581.9i	0.292865	−	0.507256i
$896$	4970.67	−	8609.45i	0.185333	−	0.321006i
$897$		0			0
$898$	8885.87	+	15390.8i	0.330206	+	0.571934i
$899$	−64156.8			−2.38015
$900$		0			0
$901$	−14782.0			−0.546571
$902$	22068.4	+	38223.5i	0.814630	+	1.41098i
$903$		0			0
$904$	100.695	−	174.409i	0.00370471	−	0.00641675i
$905$	−11281.7	+	19540.4i	−0.414382	+	0.717730i
$906$		0			0
$907$	7409.07	+	12832.9i	0.271240	+	0.469801i	0.969180	−	0.246356i	$-0.0792331\pi$
$907$	7409.07	+	12832.9i	0.271240	+	0.469801i	−0.697940	+	0.716156i	$0.745900\pi$
$908$	−30935.6			−1.13065
$909$		0			0
$910$	2403.22			0.0875451
$911$	−10923.2	−	18919.6i	−0.397259	−	0.688073i	0.596128	−	0.802890i	$-0.296705\pi$
$911$	−10923.2	−	18919.6i	−0.397259	−	0.688073i	−0.993387	+	0.114817i	$0.963372\pi$
$912$		0			0
$913$	13508.2	−	23396.9i	0.489656	−	0.848109i
$914$	31612.1	−	54753.7i	1.14402	−	1.98150i
$915$		0			0
$916$	10967.0	+	18995.4i	0.395590	+	0.685182i
$917$	14151.4			0.509618
$918$		0			0
$919$	28878.9			1.03659			0.518296	−	0.855201i	$-0.326566\pi$
$919$	28878.9			1.03659			0.518296	+	0.855201i	$0.326566\pi$
$920$	6252.44	+	10829.5i	0.224062	+	0.388087i
$921$		0			0
$922$	36554.2	−	63313.7i	1.30569	−	2.26153i
$923$	9591.47	−	16612.9i	0.342045	−	0.592439i
$924$		0			0
$925$	−3257.96	−	5642.95i	−0.115807	−	0.200583i
$926$	14803.4			0.525344
$927$		0			0
$928$	47985.0			1.69740
$929$	−2304.39	−	3991.33i	−0.0813829	−	0.140959i	0.822461	−	0.568821i	$-0.192600\pi$
$929$	−2304.39	−	3991.33i	−0.0813829	−	0.140959i	−0.903844	+	0.427862i	$0.859267\pi$
$930$		0			0
$931$	−6472.60	+	11210.9i	−0.227853	+	0.394652i
$932$	−1430.12	+	2477.03i	−0.0502629	+	0.0870578i
$933$		0			0
$934$	5640.65	+	9769.89i	0.197610	+	0.342270i
$935$	−20068.6			−0.701938
$936$		0			0
$937$	−21063.8			−0.734391			−0.367195	−	0.930144i	$-0.619682\pi$
$937$	−21063.8			−0.734391			−0.367195	+	0.930144i	$0.619682\pi$
$938$	−8589.86	−	14878.1i	−0.299007	−	0.517896i
$939$		0			0
$940$	7591.67	−	13149.2i	0.263418	−	0.456254i
$941$	10122.4	−	17532.5i	0.350670	−	0.607378i	−0.635697	−	0.771938i	$-0.719287\pi$
$941$	10122.4	−	17532.5i	0.350670	−	0.607378i	0.986367	+	0.164561i	$0.0526206\pi$
$942$		0			0
$943$	−12250.2	−	21218.0i	−0.423035	−	0.732717i
$944$	−5904.27			−0.203567
$945$		0			0
$946$	−114028.			−3.91901
$947$	14989.2	+	25962.0i	0.514342	+	0.890867i	0.999862	+	0.0166412i	$0.00529732\pi$
$947$	14989.2	+	25962.0i	0.514342	+	0.890867i	−0.485519	+	0.874226i	$0.661369\pi$
$948$		0			0
$949$	−9191.36	+	15919.9i	−0.314398	+	0.544554i
$950$	2275.02	−	3940.46i	0.0776964	−	0.134574i
$951$		0			0
$952$	3031.10	+	5250.02i	0.103192	+	0.178733i
$953$	5782.65			0.196556			0.0982782	−	0.995159i	$-0.468666\pi$
$953$	5782.65			0.196556			0.0982782	+	0.995159i	$0.468666\pi$
$954$		0			0
$955$	6037.17			0.204564
$956$	−15259.6	−	26430.4i	−0.516246	−	0.894164i
$957$		0			0
$958$	19279.6	−	33393.2i	0.650204	−	1.12619i
$959$	6324.64	−	10954.6i	0.212965	−	0.368866i
$960$		0			0
$961$	−27603.8	−	47811.2i	−0.926583	−	1.60489i
$962$	24654.2			0.826281
$963$		0			0
$964$	47401.6			1.58372
$965$	−2307.91	−	3997.42i	−0.0769889	−	0.133349i
$966$		0			0
$967$	13059.6	−	22619.9i	0.434300	−	0.752229i	−0.562938	−	0.826499i	$-0.690329\pi$
$967$	13059.6	−	22619.9i	0.434300	−	0.752229i	0.997238	+	0.0742695i	$0.0236625\pi$
$968$	−17918.5	+	31035.8i	−0.594962	+	1.03050i
$969$		0			0
$970$	−2557.05	−	4428.94i	−0.0846411	−	0.146603i
$971$	5101.93			0.168619			0.0843093	−	0.996440i	$-0.473132\pi$
$971$	5101.93			0.168619			0.0843093	+	0.996440i	$0.473132\pi$
$972$		0			0
$973$	9075.34			0.299016
$974$	34006.6	+	58901.1i	1.11873	+	1.93769i
$975$		0			0
$976$	489.447	−	847.747i	0.0160521	−	0.0278030i
$977$	22951.2	−	39752.6i	0.751559	−	1.30174i	−0.195508	−	0.980702i	$-0.562635\pi$
$977$	22951.2	−	39752.6i	0.751559	−	1.30174i	0.947067	−	0.321037i	$-0.104031\pi$
$978$		0			0
$979$	−17540.8	−	30381.6i	−0.572632	−	0.991828i
$980$	−18850.2			−0.614437
$981$		0			0
$982$	−7879.14			−0.256042
$983$	−6708.27	−	11619.1i	−0.217661	−	0.376999i	0.736432	−	0.676512i	$-0.236509\pi$
$983$	−6708.27	−	11619.1i	−0.217661	−	0.376999i	−0.954092	+	0.299513i	$0.903176\pi$
$984$		0			0
$985$	2952.18	−	5113.33i	0.0954968	−	0.165405i
$986$	−33779.6	+	58508.0i	−1.09104	+	1.88973i
$987$		0			0
$988$	5145.06	+	8911.51i	0.165674	+	0.286956i
$989$	63297.4			2.03513
$990$		0			0
$991$	3806.66			0.122021			0.0610104	−	0.998137i	$-0.480568\pi$
$991$	3806.66			0.122021			0.0610104	+	0.998137i	$0.480568\pi$
$992$	31786.6	+	55056.0i	1.01736	+	1.76213i
$993$		0			0
$994$	10245.9	−	17746.4i	0.326941	−	0.566279i
$995$	2099.51	−	3636.46i	0.0668935	−	0.115863i
$996$		0			0
$997$	11261.9	+	19506.2i	0.357742	+	0.619627i	0.987583	−	0.157097i	$-0.0502135\pi$
$997$	11261.9	+	19506.2i	0.357742	+	0.619627i	−0.629841	+	0.776724i	$0.716880\pi$
$998$	52325.7			1.65966
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.t.271.1		6
3.2	odd	2		405.4.e.r.271.3		6
9.2	odd	6		405.4.e.r.136.3		6
9.4	even	3		135.4.a.f.1.3	✓	3
9.5	odd	6		135.4.a.g.1.1	yes	3
9.7	even	3	inner	405.4.e.t.136.1		6
36.23	even	6		2160.4.a.be.1.3		3
36.31	odd	6		2160.4.a.bm.1.3		3
45.4	even	6		675.4.a.r.1.1		3
45.13	odd	12		675.4.b.l.649.2		6
45.14	odd	6		675.4.a.q.1.3		3
45.22	odd	12		675.4.b.l.649.5		6
45.23	even	12		675.4.b.k.649.5		6
45.32	even	12		675.4.b.k.649.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.a.f.1.3	✓	3	9.4	even	3
135.4.a.g.1.1	yes	3	9.5	odd	6
405.4.e.r.136.3		6	9.2	odd	6
405.4.e.r.271.3		6	3.2	odd	2
405.4.e.t.136.1		6	9.7	even	3	inner
405.4.e.t.271.1		6	1.1	even	1	trivial
675.4.a.q.1.3		3	45.14	odd	6
675.4.a.r.1.1		3	45.4	even	6
675.4.b.k.649.2		6	45.32	even	12
675.4.b.k.649.5		6	45.23	even	12
675.4.b.l.649.2		6	45.13	odd	12
675.4.b.l.649.5		6	45.22	odd	12
2160.4.a.be.1.3		3	36.23	even	6
2160.4.a.bm.1.3		3	36.31	odd	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.22969 - 3.86194i) q^{2} +(-5.94305 + 10.2937i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-2.54062 - 4.40048i) q^{7} +17.3296 q^{8} +O(q^{10})\)	\(q+(-2.22969 - 3.86194i) q^{2} +(-5.94305 + 10.2937i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-2.54062 - 4.40048i) q^{7} +17.3296 q^{8} +22.2969 q^{10} +(-29.1503 - 50.4899i) q^{11} +(-10.6060 + 18.3701i) q^{13} +(-11.3296 + 19.6234i) q^{14} +(8.90475 + 15.4235i) q^{16} -68.8451 q^{17} -40.8133 q^{19} +(-29.7152 - 51.4683i) q^{20} +(-129.993 + 225.154i) q^{22} +(72.1592 - 124.983i) q^{23} +(-12.5000 - 21.6506i) q^{25} +94.5921 q^{26} +60.3960 q^{28} +(110.029 + 190.576i) q^{29} +(-145.773 + 252.486i) q^{31} +(109.028 - 188.842i) q^{32} +(153.503 + 265.875i) q^{34} +25.4062 q^{35} +260.637 q^{37} +(91.0010 + 157.618i) q^{38} +(-43.3240 + 75.0393i) q^{40} +(84.8832 - 147.022i) q^{41} +(219.298 + 379.835i) q^{43} +692.967 q^{44} -643.571 q^{46} +(127.740 + 221.253i) q^{47} +(158.591 - 274.687i) q^{49} +(-55.7423 + 96.5485i) q^{50} +(-126.063 - 218.348i) q^{52} +214.714 q^{53} +291.503 q^{55} +(-44.0278 - 76.2585i) q^{56} +(490.661 - 849.850i) q^{58} +(-165.762 + 287.108i) q^{59} +(-27.4823 - 47.6008i) q^{61} +1300.11 q^{62} -829.920 q^{64} +(-53.0298 - 91.8503i) q^{65} +(-379.090 + 656.603i) q^{67} +(409.149 - 708.668i) q^{68} +(-56.6479 - 98.1171i) q^{70} -904.348 q^{71} +866.622 q^{73} +(-581.139 - 1006.56i) q^{74} +(242.555 - 420.118i) q^{76} +(-148.120 + 256.551i) q^{77} +(-103.480 - 179.233i) q^{79} -89.0475 q^{80} -757.054 q^{82} +(231.699 + 401.314i) q^{83} +(172.113 - 298.108i) q^{85} +(977.933 - 1693.83i) q^{86} +(-505.163 - 874.968i) q^{88} +601.736 q^{89} +107.783 q^{91} +(857.691 + 1485.56i) q^{92} +(569.643 - 986.651i) q^{94} +(102.033 - 176.727i) q^{95} +(-114.682 - 198.634i) q^{97} -1414.43 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8}+O(q^{10}) \) 6 * q + q^2 - 23 * q^4 - 15 * q^5 - 44 * q^7 - 72 * q^8	\( 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8} - 10 q^{10} - 38 q^{11} - 28 q^{13} + 108 q^{14} - 191 q^{16} - 38 q^{17} + 374 q^{19} - 115 q^{20} - 122 q^{22} + 81 q^{23} - 75 q^{25} + 832 q^{26} + 820 q^{28} - 160 q^{29} - 227 q^{31} + 569 q^{32} - 17 q^{34} + 440 q^{35} + 156 q^{37} + 757 q^{38} + 180 q^{40} + 338 q^{41} - 22 q^{43} + 3272 q^{44} - 2850 q^{46} + 472 q^{47} + 197 q^{49} + 25 q^{50} + 1566 q^{52} + 1042 q^{53} + 380 q^{55} + 1254 q^{56} + 2096 q^{58} - 140 q^{59} - 595 q^{61} + 2814 q^{62} - 1836 q^{64} - 140 q^{65} - 878 q^{67} + 3053 q^{68} + 540 q^{70} - 1204 q^{71} + 2588 q^{73} - 2878 q^{74} - 525 q^{76} - 288 q^{77} - 629 q^{79} + 1910 q^{80} - 3364 q^{82} + 1287 q^{83} + 95 q^{85} + 3730 q^{86} + 858 q^{88} + 4308 q^{89} - 880 q^{91} - 1959 q^{92} + 1108 q^{94} - 935 q^{95} - 1392 q^{97} - 5386 q^{98}+O(q^{100}) \) 6 * q + q^2 - 23 * q^4 - 15 * q^5 - 44 * q^7 - 72 * q^8 - 10 * q^10 - 38 * q^11 - 28 * q^13 + 108 * q^14 - 191 * q^16 - 38 * q^17 + 374 * q^19 - 115 * q^20 - 122 * q^22 + 81 * q^23 - 75 * q^25 + 832 * q^26 + 820 * q^28 - 160 * q^29 - 227 * q^31 + 569 * q^32 - 17 * q^34 + 440 * q^35 + 156 * q^37 + 757 * q^38 + 180 * q^40 + 338 * q^41 - 22 * q^43 + 3272 * q^44 - 2850 * q^46 + 472 * q^47 + 197 * q^49 + 25 * q^50 + 1566 * q^52 + 1042 * q^53 + 380 * q^55 + 1254 * q^56 + 2096 * q^58 - 140 * q^59 - 595 * q^61 + 2814 * q^62 - 1836 * q^64 - 140 * q^65 - 878 * q^67 + 3053 * q^68 + 540 * q^70 - 1204 * q^71 + 2588 * q^73 - 2878 * q^74 - 525 * q^76 - 288 * q^77 - 629 * q^79 + 1910 * q^80 - 3364 * q^82 + 1287 * q^83 + 95 * q^85 + 3730 * q^86 + 858 * q^88 + 4308 * q^89 - 880 * q^91 - 1959 * q^92 + 1108 * q^94 - 935 * q^95 - 1392 * q^97 - 5386 * q^98

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