LMFDB - Embedded newform 245.4.e.k.116.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 11x^{2} + 121 $ x^4 + 11*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.2
Root			$1.65831 + 2.87228i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.k.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15831 + 2.00626i) q^{2} +(2.50000 - 4.33013i) q^{3} +(1.31662 - 2.28046i) q^{4} +(2.50000 + 4.33013i) q^{5} +11.5831 q^{6} +24.6332 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(1.15831 + 2.00626i) q^{2} +(2.50000 - 4.33013i) q^{3} +(1.31662 - 2.28046i) q^{4} +(2.50000 + 4.33013i) q^{5} +11.5831 q^{6} +24.6332 q^{8} +(1.00000 + 1.73205i) q^{9} +(-5.79156 + 10.0313i) q^{10} +(-23.1332 + 40.0680i) q^{11} +(-6.58312 - 11.4023i) q^{12} +61.3325 q^{13} +25.0000 q^{15} +(18.0000 + 31.1769i) q^{16} +(50.6662 - 87.7565i) q^{17} +(-2.31662 + 4.01251i) q^{18} +(1.83375 + 3.17615i) q^{19} +13.1662 q^{20} -107.182 q^{22} +(-42.4327 - 73.4957i) q^{23} +(61.5831 - 106.665i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(71.0422 + 123.049i) q^{26} +145.000 q^{27} +30.1980 q^{29} +(28.9578 + 50.1564i) q^{30} +(94.4987 - 163.677i) q^{31} +(56.8338 - 98.4389i) q^{32} +(115.666 + 200.340i) q^{33} +234.749 q^{34} +5.26650 q^{36} +(-9.03425 - 15.6478i) q^{37} +(-4.24812 + 7.35795i) q^{38} +(153.331 - 265.577i) q^{39} +(61.5831 + 106.665i) q^{40} -481.662 q^{41} -97.7995 q^{43} +(60.9156 + 105.509i) q^{44} +(-5.00000 + 8.66025i) q^{45} +(98.3008 - 170.262i) q^{46} +(58.8325 + 101.901i) q^{47} +180.000 q^{48} -57.9156 q^{50} +(-253.331 - 438.783i) q^{51} +(80.7519 - 139.866i) q^{52} +(-333.997 + 578.501i) q^{53} +(167.955 + 290.907i) q^{54} -231.332 q^{55} +18.3375 q^{57} +(34.9787 + 60.5849i) q^{58} +(28.6675 - 49.6536i) q^{59} +(32.9156 - 57.0115i) q^{60} +(369.499 + 639.991i) q^{61} +437.836 q^{62} +551.325 q^{64} +(153.331 + 265.577i) q^{65} +(-267.955 + 464.112i) q^{66} +(-276.198 + 478.389i) q^{67} +(-133.417 - 231.085i) q^{68} -424.327 q^{69} -740.264 q^{71} +(24.6332 + 42.6660i) q^{72} +(116.662 - 202.065i) q^{73} +(20.9290 - 36.2501i) q^{74} +(62.5000 + 108.253i) q^{75} +9.65745 q^{76} +710.422 q^{78} +(537.593 + 931.138i) q^{79} +(-90.0000 + 155.885i) q^{80} +(335.500 - 581.103i) q^{81} +(-557.916 - 966.338i) q^{82} -683.325 q^{83} +506.662 q^{85} +(-113.282 - 196.211i) q^{86} +(75.4950 - 130.761i) q^{87} +(-569.847 + 987.004i) q^{88} +(-690.159 - 1195.39i) q^{89} -23.1662 q^{90} -223.472 q^{92} +(-472.494 - 818.383i) q^{93} +(-136.293 + 236.066i) q^{94} +(-9.16876 + 15.8808i) q^{95} +(-284.169 - 492.195i) q^{96} -218.008 q^{97} -92.5330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 10 * q^3 - 8 * q^4 + 10 * q^5 - 20 * q^6 + 72 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9} + 10 q^{10} - 66 q^{11} + 40 q^{12} - 20 q^{13} + 100 q^{15} + 72 q^{16} + 70 q^{17} + 4 q^{18} + 140 q^{19} - 80 q^{20} - 44 q^{22} + 16 q^{23} + 180 q^{24} - 50 q^{25} + 450 q^{26} + 580 q^{27} - 516 q^{29} - 50 q^{30} - 20 q^{31} + 360 q^{32} + 330 q^{33} + 740 q^{34} - 32 q^{36} - 328 q^{37} + 580 q^{38} - 50 q^{39} + 180 q^{40} - 600 q^{41} - 232 q^{43} - 88 q^{44} - 20 q^{45} + 632 q^{46} - 30 q^{47} + 720 q^{48} + 100 q^{50} - 350 q^{51} + 920 q^{52} - 540 q^{53} - 290 q^{54} - 660 q^{55} + 1400 q^{57} + 1314 q^{58} + 380 q^{59} - 200 q^{60} + 1080 q^{61} + 2680 q^{62} - 448 q^{64} - 50 q^{65} - 110 q^{66} - 468 q^{67} - 600 q^{68} + 160 q^{69} - 2112 q^{71} + 72 q^{72} - 860 q^{73} - 1296 q^{74} + 250 q^{75} - 2880 q^{76} + 4500 q^{78} - 158 q^{79} - 360 q^{80} + 1342 q^{81} - 1900 q^{82} - 80 q^{83} + 700 q^{85} - 148 q^{86} - 1290 q^{87} - 1364 q^{88} - 240 q^{89} + 40 q^{90} - 2592 q^{92} + 100 q^{93} - 910 q^{94} - 700 q^{95} - 1800 q^{96} - 3260 q^{97} - 264 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 10 * q^3 - 8 * q^4 + 10 * q^5 - 20 * q^6 + 72 * q^8 + 4 * q^9 + 10 * q^10 - 66 * q^11 + 40 * q^12 - 20 * q^13 + 100 * q^15 + 72 * q^16 + 70 * q^17 + 4 * q^18 + 140 * q^19 - 80 * q^20 - 44 * q^22 + 16 * q^23 + 180 * q^24 - 50 * q^25 + 450 * q^26 + 580 * q^27 - 516 * q^29 - 50 * q^30 - 20 * q^31 + 360 * q^32 + 330 * q^33 + 740 * q^34 - 32 * q^36 - 328 * q^37 + 580 * q^38 - 50 * q^39 + 180 * q^40 - 600 * q^41 - 232 * q^43 - 88 * q^44 - 20 * q^45 + 632 * q^46 - 30 * q^47 + 720 * q^48 + 100 * q^50 - 350 * q^51 + 920 * q^52 - 540 * q^53 - 290 * q^54 - 660 * q^55 + 1400 * q^57 + 1314 * q^58 + 380 * q^59 - 200 * q^60 + 1080 * q^61 + 2680 * q^62 - 448 * q^64 - 50 * q^65 - 110 * q^66 - 468 * q^67 - 600 * q^68 + 160 * q^69 - 2112 * q^71 + 72 * q^72 - 860 * q^73 - 1296 * q^74 + 250 * q^75 - 2880 * q^76 + 4500 * q^78 - 158 * q^79 - 360 * q^80 + 1342 * q^81 - 1900 * q^82 - 80 * q^83 + 700 * q^85 - 148 * q^86 - 1290 * q^87 - 1364 * q^88 - 240 * q^89 + 40 * q^90 - 2592 * q^92 + 100 * q^93 - 910 * q^94 - 700 * q^95 - 1800 * q^96 - 3260 * q^97 - 264 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.15831	+	2.00626i	0.409525	+	0.709319i	0.994837	−	0.101490i	$-0.0323610\pi$
$2$	1.15831	+	2.00626i	0.409525	+	0.709319i	−0.585311	+	0.810809i	$0.699028\pi$
$3$	2.50000	−	4.33013i	0.481125	−	0.833333i	−0.518640	−	0.854993i	$-0.673562\pi$
$3$	2.50000	−	4.33013i	0.481125	−	0.833333i	0.999765	+	0.0216593i	$0.00689490\pi$
$4$	1.31662	−	2.28046i	0.164578	−	0.285058i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	11.5831			0.788132
$7$		0			0
$7$		0			0
$8$	24.6332			1.08865
$9$	1.00000	+	1.73205i	0.0370370	+	0.0641500i
$10$	−5.79156	+	10.0313i	−0.183145	+	0.317217i
$11$	−23.1332	+	40.0680i	−0.634085	+	1.09827i	0.352623	+	0.935765i	$0.385290\pi$
$11$	−23.1332	+	40.0680i	−0.634085	+	1.09827i	−0.986708	+	0.162502i	$0.948044\pi$
$12$	−6.58312	−	11.4023i	−0.158365	−	0.274297i
$13$	61.3325			1.30851			0.654253	−	0.756276i	$-0.272983\pi$
$13$	61.3325			1.30851			0.654253	+	0.756276i	$0.272983\pi$
$14$		0			0
$15$	25.0000			0.430331
$16$	18.0000	+	31.1769i	0.281250	+	0.487139i
$17$	50.6662	−	87.7565i	0.722845	−	1.25200i	−0.237009	−	0.971507i	$-0.576167\pi$
$17$	50.6662	−	87.7565i	0.722845	−	1.25200i	0.959855	−	0.280497i	$-0.0904994\pi$
$18$	−2.31662	+	4.01251i	−0.0303352	+	0.0525421i
$19$	1.83375	+	3.17615i	0.0221417	+	0.0383505i	0.876884	−	0.480702i	$-0.159618\pi$
$19$	1.83375	+	3.17615i	0.0221417	+	0.0383505i	−0.854742	+	0.519053i	$0.826285\pi$
$20$	13.1662			0.147203
$21$		0			0
$22$	−107.182			−1.03870
$23$	−42.4327	−	73.4957i	−0.384689	−	0.666300i	0.607037	−	0.794673i	$-0.292358\pi$
$23$	−42.4327	−	73.4957i	−0.384689	−	0.666300i	−0.991726	+	0.128373i	$0.959025\pi$
$24$	61.5831	−	106.665i	0.523775	−	0.907205i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	71.0422	+	123.049i	0.535866	+	0.928147i
$27$	145.000			1.03353
$28$		0			0
$29$	30.1980			0.193366			0.0966832	−	0.995315i	$-0.469177\pi$
$29$	30.1980			0.193366			0.0966832	+	0.995315i	$0.469177\pi$
$30$	28.9578	+	50.1564i	0.176232	+	0.305242i
$31$	94.4987	−	163.677i	0.547499	−	0.948296i	−0.450946	−	0.892551i	$-0.648913\pi$
$31$	94.4987	−	163.677i	0.547499	−	0.948296i	0.998445	−	0.0557451i	$-0.0177534\pi$
$32$	56.8338	−	98.4389i	0.313965	−	0.543803i
$33$	115.666	+	200.340i	0.610149	+	1.05681i
$34$	234.749			1.18409
$35$		0			0
$36$	5.26650			0.0243819
$37$	−9.03425	−	15.6478i	−0.0401411	−	0.0695265i	0.845257	−	0.534360i	$-0.179447\pi$
$37$	−9.03425	−	15.6478i	−0.0401411	−	0.0695265i	−0.885398	+	0.464834i	$0.846114\pi$
$38$	−4.24812	+	7.35795i	−0.0181351	+	0.0314110i
$39$	153.331	−	265.577i	0.629555	−	1.09042i
$40$	61.5831	+	106.665i	0.243429	+	0.421631i
$41$	−481.662			−1.83471			−0.917354	−	0.398072i	$-0.869679\pi$
$41$	−481.662			−1.83471			−0.917354	+	0.398072i	$0.869679\pi$
$42$		0			0
$43$	−97.7995			−0.346844			−0.173422	−	0.984848i	$-0.555482\pi$
$43$	−97.7995			−0.346844			−0.173422	+	0.984848i	$0.555482\pi$
$44$	60.9156	+	105.509i	0.208713	+	0.361502i
$45$	−5.00000	+	8.66025i	−0.0165635	+	0.0286888i
$46$	98.3008	−	170.262i	0.315079	−	0.545734i
$47$	58.8325	+	101.901i	0.182587	+	0.316250i	0.942761	−	0.333470i	$-0.108219\pi$
$47$	58.8325	+	101.901i	0.182587	+	0.316250i	−0.760174	+	0.649720i	$0.774886\pi$
$48$	180.000			0.541266
$49$		0			0
$50$	−57.9156			−0.163810
$51$	−253.331	−	438.783i	−0.695558	−	1.20474i
$52$	80.7519	−	139.866i	0.215351	−	0.373000i
$53$	−333.997	+	578.501i	−0.865624	+	1.49931i	0.000801827		1.00000i	$0.499745\pi$
$53$	−333.997	+	578.501i	−0.865624	+	1.49931i	−0.866426	+	0.499305i	$0.833589\pi$
$54$	167.955	+	290.907i	0.423256	+	0.733101i
$55$	−231.332			−0.567143
$56$		0			0
$57$	18.3375			0.0426116
$58$	34.9787	+	60.5849i	0.0791884	+	0.137158i
$59$	28.6675	−	49.6536i	0.0632575	−	0.109565i	−0.832662	−	0.553781i	$-0.813184\pi$
$59$	28.6675	−	49.6536i	0.0632575	−	0.109565i	0.895920	+	0.444216i	$0.146518\pi$
$60$	32.9156	−	57.0115i	0.0708231	−	0.122669i
$61$	369.499	+	639.991i	0.775565	+	1.34332i	0.934476	+	0.356025i	$0.115868\pi$
$61$	369.499	+	639.991i	0.775565	+	1.34332i	−0.158911	+	0.987293i	$0.550798\pi$
$62$	437.836			0.896859
$63$		0			0
$64$	551.325			1.07681
$65$	153.331	+	265.577i	0.292591	+	0.506782i
$66$	−267.955	+	464.112i	−0.499743	+	0.865580i
$67$	−276.198	+	478.389i	−0.503626	+	0.872306i	0.496365	+	0.868114i	$0.334668\pi$
$67$	−276.198	+	478.389i	−0.503626	+	0.872306i	−0.999991	+	0.00419224i	$0.998666\pi$
$68$	−133.417	−	231.085i	−0.237929	−	0.412105i
$69$	−424.327			−0.740334
$70$		0			0
$71$	−740.264			−1.23737			−0.618684	−	0.785640i	$-0.712334\pi$
$71$	−740.264			−1.23737			−0.618684	+	0.785640i	$0.712334\pi$
$72$	24.6332	+	42.6660i	0.0403202	+	0.0698367i
$73$	116.662	−	202.065i	0.187045	−	0.323972i	−0.757218	−	0.653162i	$-0.773442\pi$
$73$	116.662	−	202.065i	0.187045	−	0.323972i	0.944264	+	0.329190i	$0.106776\pi$
$74$	20.9290	−	36.2501i	0.0328776	−	0.0569457i
$75$	62.5000	+	108.253i	0.0962250	+	0.166667i
$76$	9.65745			0.0145761
$77$		0			0
$78$	710.422			1.03127
$79$	537.593	+	931.138i	0.765619	+	1.32609i	0.939919	+	0.341398i	$0.110901\pi$
$79$	537.593	+	931.138i	0.765619	+	1.32609i	−0.174300	+	0.984693i	$0.555766\pi$
$80$	−90.0000	+	155.885i	−0.125779	+	0.217855i
$81$	335.500	−	581.103i	0.460219	−	0.797124i
$82$	−557.916	−	966.338i	−0.751359	−	1.30139i
$83$	−683.325			−0.903671			−0.451835	−	0.892101i	$-0.649231\pi$
$83$	−683.325			−0.903671			−0.451835	+	0.892101i	$0.649231\pi$
$84$		0			0
$85$	506.662			0.646532
$86$	−113.282	−	196.211i	−0.142041	−	0.246023i
$87$	75.4950	−	130.761i	0.0930335	−	0.161139i
$88$	−569.847	+	987.004i	−0.690294	+	1.19562i
$89$	−690.159	−	1195.39i	−0.821985	−	1.42372i	−0.904202	−	0.427106i	$-0.859533\pi$
$89$	−690.159	−	1195.39i	−0.821985	−	1.42372i	0.0822166	−	0.996614i	$-0.473800\pi$
$90$	−23.1662			−0.0271326
$91$		0			0
$92$	−223.472			−0.253245
$93$	−472.494	−	818.383i	−0.526831	−	0.912499i
$94$	−136.293	+	236.066i	−0.149548	+	0.259025i
$95$	−9.16876	+	15.8808i	−0.00990205	+	0.0171509i
$96$	−284.169	−	492.195i	−0.302113	−	0.523275i
$97$	−218.008			−0.228199			−0.114100	−	0.993469i	$-0.536398\pi$
$97$	−218.008			−0.228199			−0.114100	+	0.993469i	$0.536398\pi$
$98$		0			0
$99$	−92.5330			−0.0939385
$100$	32.9156	+	57.0115i	0.0329156	+	0.0570115i
$101$	−737.164	+	1276.81i	−0.726243	+	1.25789i	0.232217	+	0.972664i	$0.425402\pi$
$101$	−737.164	+	1276.81i	−0.726243	+	1.25789i	−0.958460	+	0.285226i	$0.907931\pi$
$102$	586.873	−	1016.49i	0.569697	−	0.986745i
$103$	−405.495	−	702.338i	−0.387909	−	0.671878i	0.604259	−	0.796788i	$-0.293469\pi$
$103$	−405.495	−	702.338i	−0.387909	−	0.671878i	−0.992168	+	0.124910i	$0.960136\pi$
$104$	1510.82			1.42450
$105$		0			0
$106$	−1547.49			−1.41798
$107$	−220.330	−	381.623i	−0.199066	−	0.344793i	0.749160	−	0.662390i	$-0.230458\pi$
$107$	−220.330	−	381.623i	−0.199066	−	0.344793i	−0.948226	+	0.317596i	$0.897124\pi$
$108$	190.911	−	330.667i	0.170096	−	0.294615i
$109$	953.094	−	1650.81i	0.837522	−	1.45063i	−0.0544393	−	0.998517i	$-0.517337\pi$
$109$	953.094	−	1650.81i	0.837522	−	1.45063i	0.891961	−	0.452113i	$-0.149330\pi$
$110$	−267.955	−	464.112i	−0.232259	−	0.402285i
$111$	−90.3425			−0.0772517
$112$		0			0
$113$	962.470			0.801252			0.400626	−	0.916242i	$-0.368793\pi$
$113$	962.470			0.801252			0.400626	+	0.916242i	$0.368793\pi$
$114$	21.2406	+	36.7898i	0.0174505	+	0.0302252i
$115$	212.164	−	367.478i	0.172038	−	0.297979i
$116$	39.7594	−	68.8653i	0.0318239	−	0.0551206i
$117$	61.3325	+	106.231i	0.0484632	+	0.0839407i
$118$	132.824			0.103622
$119$		0			0
$120$	615.831			0.468479
$121$	−404.794	−	701.125i	−0.304128	−	0.526765i
$122$	−855.990	+	1482.62i	−0.635227	+	1.10025i
$123$	−1204.16	+	2085.66i	−0.882724	+	1.52892i
$124$	−248.839	−	431.001i	−0.180213	−	0.312138i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−1621.74			−1.13312			−0.566558	−	0.824022i	$-0.691725\pi$
$127$	−1621.74			−1.13312			−0.566558	+	0.824022i	$0.691725\pi$
$128$	183.937	+	318.587i	0.127014	+	0.219995i
$129$	−244.499	+	423.484i	−0.166875	+	0.289037i
$130$	−355.211	+	615.243i	−0.239647	+	0.415080i
$131$	−690.159	−	1195.39i	−0.460301	−	0.797265i	0.538675	−	0.842514i	$-0.318925\pi$
$131$	−690.159	−	1195.39i	−0.460301	−	0.797265i	−0.998976	+	0.0452490i	$0.985592\pi$
$132$	609.156			0.401668
$133$		0			0
$134$	−1279.69			−0.824991
$135$	362.500	+	627.868i	0.231104	+	0.400284i
$136$	1248.07	−	2161.73i	0.786923	−	1.36299i
$137$	974.829	−	1688.45i	0.607921	−	1.05295i	−0.383661	−	0.923474i	$-0.625337\pi$
$137$	974.829	−	1688.45i	0.607921	−	1.05295i	0.991582	−	0.129477i	$-0.0413298\pi$
$138$	−491.504	−	851.309i	−0.303185	−	0.525132i
$139$	−2800.00			−1.70858			−0.854291	−	0.519795i	$-0.826008\pi$
$139$	−2800.00			−1.70858			−0.854291	+	0.519795i	$0.826008\pi$
$140$		0			0
$141$	588.325			0.351389
$142$	−857.457	−	1485.16i	−0.506734	−	0.877689i
$143$	−1418.82	+	2457.47i	−0.829704	+	1.43709i
$144$	−36.0000	+	62.3538i	−0.0208333	+	0.0360844i
$145$	75.4950	+	130.761i	0.0432380	+	0.0748905i
$146$	540.526			0.306399
$147$		0			0
$148$	−47.5789			−0.0264254
$149$	717.058	+	1241.98i	0.394253	+	0.682866i	0.993006	−	0.118068i	$-0.0376700\pi$
$149$	717.058	+	1241.98i	0.394253	+	0.682866i	−0.598752	+	0.800934i	$0.704337\pi$
$150$	−144.789	+	250.782i	−0.0788132	+	0.136508i
$151$	992.791	−	1719.56i	0.535047	−	0.926729i	−0.464114	−	0.885776i	$-0.653627\pi$
$151$	992.791	−	1719.56i	0.535047	−	0.926729i	0.999161	−	0.0409537i	$-0.0130396\pi$
$152$	45.1713	+	78.2389i	0.0241044	+	0.0417501i
$153$	202.665			0.107088
$154$		0			0
$155$	944.987			0.489698
$156$	−403.759	−	699.332i	−0.207222	−	0.358919i
$157$	20.3300	−	35.2126i	0.0103345	−	0.0178998i	−0.860812	−	0.508923i	$-0.830044\pi$
$157$	20.3300	−	35.2126i	0.0103345	−	0.0178998i	0.871146	+	0.491023i	$0.163377\pi$
$158$	−1245.40	+	2157.10i	−0.627081	+	1.08614i
$159$	1669.99	+	2892.50i	0.832947	+	1.44271i
$160$	568.338			0.280819
$161$		0			0
$162$	1554.46			0.753886
$163$	1976.99	+	3424.25i	0.950000	+	1.64545i	0.745416	+	0.666599i	$0.232251\pi$
$163$	1976.99	+	3424.25i	0.950000	+	1.64545i	0.204584	+	0.978849i	$0.434416\pi$
$164$	−634.169	+	1098.41i	−0.301953	+	0.522998i
$165$	−578.331	+	1001.70i	−0.272867	+	0.472619i
$166$	−791.504	−	1370.92i	−0.370076	−	0.640990i
$167$	−3380.30			−1.56632			−0.783161	−	0.621819i	$-0.786394\pi$
$167$	−3380.30			−1.56632			−0.783161	+	0.621819i	$0.786394\pi$
$168$		0			0
$169$	1564.68			0.712187
$170$	586.873	+	1016.49i	0.264771	+	0.458598i
$171$	−3.66750	+	6.35230i	−0.00164012	+	0.00284078i
$172$	−128.765	+	223.028i	−0.0570829	+	0.0988705i
$173$	1603.33	+	2777.05i	0.704619	+	1.22044i	0.966829	+	0.255424i	$0.0822152\pi$
$173$	1603.33	+	2777.05i	0.704619	+	1.22044i	−0.262210	+	0.965011i	$0.584451\pi$
$174$	349.787			0.152398
$175$		0			0
$176$	−1665.59			−0.713346
$177$	−143.338	−	248.268i	−0.0608695	−	0.105429i
$178$	1598.84	−	2769.27i	0.673247	−	1.16610i
$179$	−721.325	+	1249.37i	−0.301198	+	0.521689i	−0.976407	−	0.215936i	$-0.930720\pi$
$179$	−721.325	+	1249.37i	−0.301198	+	0.521689i	0.675210	+	0.737626i	$0.264053\pi$
$180$	13.1662	+	22.8046i	0.00545197	+	0.00944308i
$181$	908.680			0.373158			0.186579	−	0.982440i	$-0.440260\pi$
$181$	908.680			0.373158			0.186579	+	0.982440i	$0.440260\pi$
$182$		0			0
$183$	3694.99			1.49258
$184$	−1045.26	−	1810.44i	−0.418790	−	0.725365i
$185$	45.1713	−	78.2389i	0.0179517	−	0.0310932i
$186$	1094.59	−	1895.89i	0.431502	−	0.747383i
$187$	2344.15	+	4060.19i	0.916691	+	1.58776i
$188$	309.841			0.120199
$189$		0			0
$190$	−42.4812			−0.0162206
$191$	−1237.32	−	2143.10i	−0.468739	−	0.811881i	0.530622	−	0.847609i	$-0.321958\pi$
$191$	−1237.32	−	2143.10i	−0.468739	−	0.811881i	−0.999362	+	0.0357280i	$0.988625\pi$
$192$	1378.31	−	2387.31i	0.518079	−	0.897339i
$193$	−1766.76	+	3060.12i	−0.658934	+	1.14131i	0.321958	+	0.946754i	$0.395659\pi$
$193$	−1766.76	+	3060.12i	−0.658934	+	1.14131i	−0.980892	+	0.194553i	$0.937674\pi$
$194$	−252.521	−	437.379i	−0.0934533	−	0.161866i
$195$	1533.31			0.563091
$196$		0			0
$197$	−1952.57			−0.706165			−0.353083	−	0.935592i	$-0.614867\pi$
$197$	−1952.57			−0.706165			−0.353083	+	0.935592i	$0.614867\pi$
$198$	−107.182	−	185.645i	−0.0384702	−	0.0666324i
$199$	2032.34	−	3520.11i	0.723962	−	1.25394i	−0.235438	−	0.971889i	$-0.575652\pi$
$199$	2032.34	−	3520.11i	0.723962	−	1.25394i	0.959400	−	0.282049i	$-0.0910142\pi$
$200$	−307.916	+	533.325i	−0.108865	+	0.188559i
$201$	1380.99	+	2391.94i	0.484615	+	0.839377i
$202$	−3415.46			−1.18966
$203$		0			0
$204$	−1334.17			−0.457895
$205$	−1204.16	−	2085.66i	−0.410253	−	0.710579i
$206$	939.380	−	1627.05i	0.317717	−	0.550302i
$207$	84.8655	−	146.991i	0.0284955	−	0.0493556i
$208$	1103.98	+	1912.16i	0.368017	+	0.637425i
$209$	−169.683			−0.0561588
$210$		0			0
$211$	−4325.34			−1.41123			−0.705613	−	0.708598i	$-0.749328\pi$
$211$	−4325.34			−1.41123			−0.705613	+	0.708598i	$0.749328\pi$
$212$	879.499	+	1523.34i	0.284926	+	0.493506i
$213$	−1850.66	+	3205.44i	−0.595329	+	1.03114i
$214$	510.422	−	884.077i	0.163045	−	0.282403i
$215$	−244.499	−	423.484i	−0.0775566	−	0.134332i
$216$	3571.82			1.12515
$217$		0			0
$218$	4415.92			1.37194
$219$	−583.312	−	1010.33i	−0.179984	−	0.311742i
$220$	−304.578	+	527.545i	−0.0933393	+	0.161668i
$221$	3107.49	−	5382.33i	0.945847	−	1.63826i
$222$	−104.645	−	181.250i	−0.0316365	−	0.0547960i
$223$	982.970			0.295177			0.147589	−	0.989049i	$-0.452849\pi$
$223$	982.970			0.295177			0.147589	+	0.989049i	$0.452849\pi$
$224$		0			0
$225$	−50.0000			−0.0148148
$226$	1114.84	+	1930.96i	0.328133	+	0.568343i
$227$	−830.482	+	1438.44i	−0.242824	+	0.420584i	−0.961518	−	0.274743i	$-0.911407\pi$
$227$	−830.482	+	1438.44i	−0.242824	+	0.420584i	0.718694	+	0.695327i	$0.244740\pi$
$228$	24.1436	−	41.8180i	0.00701294	−	0.0121468i
$229$	−287.164	−	497.382i	−0.0828660	−	0.143528i	0.821614	−	0.570044i	$-0.193074\pi$
$229$	−287.164	−	497.382i	−0.0828660	−	0.143528i	−0.904480	+	0.426516i	$0.859741\pi$
$230$	983.008			0.281816
$231$		0			0
$232$	743.875			0.210508
$233$	1158.24	+	2006.13i	0.325660	+	0.564059i	0.981646	−	0.190714i	$-0.0610802\pi$
$233$	1158.24	+	2006.13i	0.325660	+	0.564059i	−0.655986	+	0.754773i	$0.727747\pi$
$234$	−142.084	+	246.097i	−0.0396938	+	0.0687517i
$235$	−294.162	+	509.504i	−0.0816555	+	0.141431i
$236$	−75.4887	−	130.750i	−0.0208216	−	0.0360641i
$237$	5375.93			1.47343
$238$		0			0
$239$	−3659.31			−0.990382			−0.495191	−	0.868784i	$-0.664902\pi$
$239$	−3659.31			−0.990382			−0.495191	+	0.868784i	$0.664902\pi$
$240$	450.000	+	779.423i	0.121031	+	0.209631i
$241$	1223.17	−	2118.59i	0.326934	−	0.566266i	−0.654968	−	0.755657i	$-0.727318\pi$
$241$	1223.17	−	2118.59i	0.326934	−	0.566266i	0.981902	+	0.189391i	$0.0606512\pi$
$242$	937.757	−	1624.24i	0.249096	−	0.431447i
$243$	280.000	+	484.974i	0.0739177	+	0.128029i
$244$	1945.96			0.510564
$245$		0			0
$246$	−5579.16			−1.44599
$247$	112.469	+	194.801i	0.0289725	+	0.0501818i
$248$	2327.81	−	4031.89i	0.596033	−	1.03236i
$249$	−1708.31	+	2958.88i	−0.434779	+	0.753059i
$250$	−144.789	−	250.782i	−0.0366291	−	0.0634434i
$251$	2909.29			0.731605			0.365802	−	0.930693i	$-0.380795\pi$
$251$	2909.29			0.731605			0.365802	+	0.930693i	$0.380795\pi$
$252$		0			0
$253$	3926.43			0.975702
$254$	−1878.48	−	3253.62i	−0.464040	−	0.803741i
$255$	1266.66	−	2193.91i	0.311063	−	0.538777i
$256$	1779.19	−	3081.64i	0.434372	−	0.752354i
$257$	84.3400	+	146.081i	0.0204708	+	0.0354564i	0.876079	−	0.482167i	$-0.160150\pi$
$257$	84.3400	+	146.081i	0.0204708	+	0.0354564i	−0.855609	+	0.517623i	$0.826817\pi$
$258$	−1132.82			−0.273359
$259$		0			0
$260$	807.519			0.192616
$261$	30.1980	+	52.3045i	0.00716172	+	0.0124045i
$262$	1598.84	−	2769.27i	0.377010	−	0.653000i
$263$	1622.24	−	2809.80i	0.380347	−	0.658781i	−0.610764	−	0.791812i	$-0.709138\pi$
$263$	1622.24	−	2809.80i	0.380347	−	0.658781i	0.991112	+	0.133031i	$0.0424711\pi$
$264$	2849.24	+	4935.02i	0.664236	+	1.15049i
$265$	−3339.97			−0.774238
$266$		0			0
$267$	−6901.59			−1.58191
$268$	727.298	+	1259.72i	0.165772	+	0.287125i
$269$	−1424.33	+	2467.01i	−0.322836	+	0.559168i	−0.981072	−	0.193644i	$-0.937969\pi$
$269$	−1424.33	+	2467.01i	−0.322836	+	0.559168i	0.658236	+	0.752811i	$0.271303\pi$
$270$	−839.776	+	1454.54i	−0.189286	+	0.327853i
$271$	−1425.49	−	2469.02i	−0.319529	−	0.553440i	0.660861	−	0.750508i	$-0.270191\pi$
$271$	−1425.49	−	2469.02i	−0.319529	−	0.553440i	−0.980390	+	0.197068i	$0.936858\pi$
$272$	3647.97			0.813201
$273$		0			0
$274$	4516.62			0.995837
$275$	−578.331	−	1001.70i	−0.126817	−	0.219654i
$276$	−558.680	+	967.662i	−0.121843	+	0.211038i
$277$	−1149.31	+	1990.67i	−0.249298	+	0.431797i	−0.963331	−	0.268315i	$-0.913533\pi$
$277$	−1149.31	+	1990.67i	−0.249298	+	0.431797i	0.714033	+	0.700112i	$0.246867\pi$
$278$	−3243.27	−	5617.52i	−0.699708	−	1.21193i
$279$	377.995			0.0811110
$280$		0			0
$281$	6109.20			1.29695			0.648477	−	0.761234i	$-0.275406\pi$
$281$	6109.20			1.29695			0.648477	+	0.761234i	$0.275406\pi$
$282$	681.464	+	1180.33i	0.143903	+	0.249247i
$283$	2927.47	−	5070.54i	0.614913	−	1.06506i	−0.375487	−	0.926828i	$-0.622525\pi$
$283$	2927.47	−	5070.54i	0.614913	−	1.06506i	0.990400	−	0.138233i	$-0.0441421\pi$
$284$	−974.650	+	1688.14i	−0.203644	+	0.352721i
$285$	45.8438	+	79.4038i	0.00952825	+	0.0165034i
$286$	−6573.75			−1.35914
$287$		0			0
$288$	227.335			0.0465133
$289$	−2677.64	−	4637.80i	−0.545011	−	0.943986i
$290$	−174.894	+	302.924i	−0.0354141	+	0.0613391i
$291$	−545.019	+	944.000i	−0.109792	+	0.190166i
$292$	−307.201	−	532.088i	−0.0615671	−	0.106637i
$293$	5135.34			1.02392			0.511962	−	0.859008i	$-0.328919\pi$
$293$	5135.34			1.02392			0.511962	+	0.859008i	$0.328919\pi$
$294$		0			0
$295$	286.675			0.0565792
$296$	−222.543	−	385.456i	−0.0436995	−	0.0756898i
$297$	−3354.32	+	5809.85i	−0.655345	+	1.13509i
$298$	−1661.16	+	2877.21i	−0.322913	+	0.559302i
$299$	−2602.51	−	4507.67i	−0.503367	−	0.871858i
$300$	329.156			0.0633461
$301$		0			0
$302$	4599.85			0.876462
$303$	3685.82	+	6384.03i	0.698828	+	1.21040i
$304$	−66.0151	+	114.341i	−0.0124547	+	0.0215721i
$305$	−1847.49	+	3199.95i	−0.346843	+	0.600750i
$306$	234.749	+	406.598i	0.0438553	+	0.0759596i
$307$	−2102.97			−0.390954			−0.195477	−	0.980708i	$-0.562625\pi$
$307$	−2102.97			−0.390954			−0.195477	+	0.980708i	$0.562625\pi$
$308$		0			0
$309$	−4054.95			−0.746531
$310$	1094.59	+	1895.89i	0.200544	+	0.347352i
$311$	−2882.15	+	4992.03i	−0.525504	+	0.910200i	0.474055	+	0.880495i	$0.342790\pi$
$311$	−2882.15	+	4992.03i	−0.525504	+	0.910200i	−0.999559	+	0.0297045i	$0.990543\pi$
$312$	3777.05	−	6542.04i	0.685363	−	1.18708i
$313$	−680.006	−	1177.81i	−0.122799	−	0.212695i	0.798071	−	0.602563i	$-0.205854\pi$
$313$	−680.006	−	1177.81i	−0.122799	−	0.212695i	−0.920871	+	0.389868i	$0.872521\pi$
$314$	94.1939			0.0169289
$315$		0			0
$316$	2831.23			0.504017
$317$	−2569.47	−	4450.46i	−0.455256	−	0.788526i	0.543447	−	0.839443i	$-0.317119\pi$
$317$	−2569.47	−	4450.46i	−0.455256	−	0.788526i	−0.998703	+	0.0509173i	$0.983785\pi$
$318$	−3868.73	+	6700.84i	−0.682226	+	1.18165i
$319$	−698.578	+	1209.97i	−0.122611	+	0.212368i
$320$	1378.31	+	2387.31i	0.240781	+	0.417045i
$321$	−2203.30			−0.383103
$322$		0			0
$323$	371.637			0.0640200
$324$	−883.455	−	1530.19i	−0.151484	−	0.262378i
$325$	−766.656	+	1327.89i	−0.130851	+	0.226640i
$326$	−4579.95	+	7932.71i	−0.778098	+	1.34771i
$327$	−4765.47	−	8254.04i	−0.805905	−	1.39587i
$328$	−11864.9			−1.99735
$329$		0			0
$330$	−2679.55			−0.446983
$331$	−912.850	−	1581.10i	−0.151585	−	0.262554i	0.780225	−	0.625499i	$-0.215105\pi$
$331$	−912.850	−	1581.10i	−0.151585	−	0.262554i	−0.931810	+	0.362945i	$0.881771\pi$
$332$	−899.683	+	1558.30i	−0.148724	+	0.257598i
$333$	18.0685	−	31.2956i	0.00297342	−	0.00515011i
$334$	−3915.45	−	6781.76i	−0.641449	−	1.11102i
$335$	−2761.98			−0.450457
$336$		0			0
$337$	153.985			0.0248905			0.0124452	−	0.999923i	$-0.496038\pi$
$337$	153.985			0.0248905			0.0124452	+	0.999923i	$0.496038\pi$
$338$	1812.38	+	3139.14i	0.291659	+	0.505168i
$339$	2406.17	−	4167.62i	0.385503	−	0.667710i
$340$	667.084	−	1155.42i	0.106405	−	0.184299i
$341$	4372.13	+	7572.74i	0.694322	+	1.20260i
$342$	−16.9925			−0.00268669
$343$		0			0
$344$	−2409.12			−0.377590
$345$	−1060.82	−	1837.39i	−0.165544	−	0.286730i
$346$	−3714.32	+	6433.39i	−0.577118	+	0.999598i
$347$	−2179.69	+	3775.34i	−0.337211	+	0.584066i	−0.983907	−	0.178682i	$-0.942817\pi$
$347$	−2179.69	+	3775.34i	−0.337211	+	0.584066i	0.646696	+	0.762748i	$0.276150\pi$
$348$	−198.797	−	344.327i	−0.0306225	−	0.0530398i
$349$	−1689.00			−0.259054			−0.129527	−	0.991576i	$-0.541346\pi$
$349$	−1689.00			−0.259054			−0.129527	+	0.991576i	$0.541346\pi$
$350$		0			0
$351$	8893.21			1.35238
$352$	2629.50	+	4554.43i	0.398161	+	0.689635i
$353$	−1960.68	+	3396.00i	−0.295627	+	0.512041i	−0.975131	−	0.221631i	$-0.928862\pi$
$353$	−1960.68	+	3396.00i	−0.295627	+	0.512041i	0.679503	+	0.733672i	$0.262195\pi$
$354$	332.059	−	575.143i	0.0498552	−	0.0863518i
$355$	−1850.66	−	3205.44i	−0.276684	−	0.479231i
$356$	−3634.72			−0.541123
$357$		0			0
$358$	−3342.08			−0.493392
$359$	1433.93	+	2483.64i	0.210808	+	0.365130i	0.951968	−	0.306199i	$-0.0990572\pi$
$359$	1433.93	+	2483.64i	0.210808	+	0.365130i	−0.741160	+	0.671329i	$0.765724\pi$
$360$	−123.166	+	213.330i	−0.0180318	+	0.0312319i
$361$	3422.77	−	5928.42i	0.499019	−	0.864327i
$362$	1052.54	+	1823.04i	0.152818	+	0.264688i
$363$	−4047.94			−0.585295
$364$		0			0
$365$	1166.62			0.167298
$366$	4279.95	+	7413.09i	0.611247	+	1.05871i
$367$	5751.50	−	9961.89i	0.818054	−	1.41691i	−0.0890605	−	0.996026i	$-0.528386\pi$
$367$	5751.50	−	9961.89i	0.818054	−	1.41691i	0.907114	−	0.420884i	$-0.138280\pi$
$368$	1527.58	−	2645.84i	0.216387	−	0.374794i
$369$	−481.662	−	834.264i	−0.0679522	−	0.117697i
$370$	209.290			0.0294066
$371$		0			0
$372$	−2488.39			−0.346820
$373$	−2543.21	−	4404.98i	−0.353037	−	0.611477i	0.633743	−	0.773543i	$-0.281518\pi$
$373$	−2543.21	−	4404.98i	−0.353037	−	0.611477i	−0.986780	+	0.162066i	$0.948184\pi$
$374$	−5430.52	+	9405.93i	−0.750816	+	1.30045i
$375$	−312.500	+	541.266i	−0.0430331	+	0.0745356i
$376$	1449.24	+	2510.15i	0.198773	+	0.344285i
$377$	1852.12			0.253021
$378$		0			0
$379$	954.827			0.129409			0.0647047	−	0.997904i	$-0.479389\pi$
$379$	954.827			0.129409			0.0647047	+	0.997904i	$0.479389\pi$
$380$	24.1436	+	41.8180i	0.00325932	+	0.00564531i
$381$	−4054.34	+	7022.32i	−0.545171	+	0.944264i
$382$	2866.40	−	4964.76i	0.383921	−	0.664971i
$383$	1541.95	+	2670.74i	0.205719	+	0.356315i	0.950361	−	0.311148i	$-0.100714\pi$
$383$	1541.95	+	2670.74i	0.205719	+	0.356315i	−0.744643	+	0.667463i	$0.767380\pi$
$384$	1839.37			0.244439
$385$		0			0
$386$	−8185.84			−1.07940
$387$	−97.7995	−	169.394i	−0.0128461	−	0.0222500i
$388$	−287.034	+	497.158i	−0.0375566	+	0.0650499i
$389$	3165.57	−	5482.93i	0.412599	−	0.714642i	−0.582574	−	0.812777i	$-0.697954\pi$
$389$	3165.57	−	5482.93i	0.412599	−	0.714642i	0.995173	+	0.0981353i	$0.0312878\pi$
$390$	1776.05	+	3076.22i	0.230600	+	0.399411i
$391$	−8599.63			−1.11228
$392$		0			0
$393$	−6901.59			−0.885850
$394$	−2261.68	−	3917.35i	−0.289193	−	0.500896i
$395$	−2687.96	+	4655.69i	−0.342395	+	0.593046i
$396$	−121.831	+	211.018i	−0.0154602	+	0.0267779i
$397$	−6066.62	−	10507.7i	−0.766939	−	1.32838i	−0.939215	−	0.343329i	$-0.888445\pi$
$397$	−6066.62	−	10507.7i	−0.766939	−	1.32838i	0.172276	−	0.985049i	$-0.444888\pi$
$398$	9416.32			1.18592
$399$		0			0
$400$	−900.000			−0.112500
$401$	135.335	+	234.407i	0.0168536	+	0.0291913i	0.874329	−	0.485333i	$-0.161302\pi$
$401$	135.335	+	234.407i	0.0168536	+	0.0291913i	−0.857476	+	0.514525i	$0.827968\pi$
$402$	−3199.24	+	5541.24i	−0.396924	+	0.687492i
$403$	5795.84	−	10038.7i	0.716406	−	1.24085i
$404$	1941.14	+	3362.15i	0.239047	+	0.414042i
$405$	3355.00			0.411633
$406$		0			0
$407$	835.967			0.101812
$408$	−6240.37	−	10808.6i	−0.757217	−	1.31154i
$409$	2009.96	−	3481.36i	0.242998	−	0.420885i	−0.718569	−	0.695456i	$-0.755202\pi$
$409$	2009.96	−	3481.36i	0.242998	−	0.420885i	0.961567	+	0.274571i	$0.0885358\pi$
$410$	2789.58	−	4831.69i	0.336018	−	0.582001i
$411$	−4874.14	−	8442.26i	−0.584973	−	1.01320i
$412$	−2135.54			−0.255365
$413$		0			0
$414$	393.203			0.0466784
$415$	−1708.31	−	2958.88i	−0.202067	−	0.349990i
$416$	3485.76	−	6037.51i	0.410825	−	0.711570i
$417$	−7000.00	+	12124.4i	−0.822042	+	1.42382i
$418$	−196.545	−	340.427i	−0.0229984	−	0.0398345i
$419$	−2437.28			−0.284175			−0.142087	−	0.989854i	$-0.545381\pi$
$419$	−2437.28			−0.284175			−0.142087	+	0.989854i	$0.545381\pi$
$420$		0			0
$421$	−4751.36			−0.550041			−0.275020	−	0.961438i	$-0.588685\pi$
$421$	−4751.36			−0.550041			−0.275020	+	0.961438i	$0.588685\pi$
$422$	−5010.09	−	8677.73i	−0.577932	−	1.00101i
$423$	−117.665	+	203.802i	−0.0135250	+	0.0234260i
$424$	−8227.44	+	14250.4i	−0.942358	+	1.63221i
$425$	1266.66	+	2193.91i	0.144569	+	0.250401i
$426$	−8574.57			−0.975210
$427$		0			0
$428$	−1160.37			−0.131048
$429$	7094.10	+	12287.3i	0.798383	+	1.38284i
$430$	566.412	−	981.054i	0.0635228	−	0.110025i
$431$	−3962.59	+	6863.41i	−0.442857	+	0.767051i	−0.997900	−	0.0647706i	$-0.979368\pi$
$431$	−3962.59	+	6863.41i	−0.442857	+	0.767051i	0.555043	+	0.831822i	$0.312702\pi$
$432$	2610.00	+	4520.65i	0.290680	+	0.503472i
$433$	11487.3			1.27492			0.637462	−	0.770481i	$-0.279984\pi$
$433$	11487.3			1.27492			0.637462	+	0.770481i	$0.279984\pi$
$434$		0			0
$435$	754.950			0.0832117
$436$	−2509.73	−	4346.99i	−0.275675	−	0.477484i
$437$	155.622	−	269.546i	0.0170353	−	0.0295060i
$438$	1351.32	−	2340.55i	0.147416	−	0.255333i
$439$	−4573.96	−	7922.33i	−0.497274	−	0.861303i	0.502721	−	0.864449i	$-0.332332\pi$
$439$	−4573.96	−	7922.33i	−0.497274	−	0.861303i	−0.999995	+	0.00314511i	$0.998999\pi$
$440$	−5698.47			−0.617418
$441$		0			0
$442$	14397.8			1.54939
$443$	−932.176	−	1614.58i	−0.0999752	−	0.173162i	0.811699	−	0.584076i	$-0.198543\pi$
$443$	−932.176	−	1614.58i	−0.0999752	−	0.173162i	−0.911674	+	0.410914i	$0.865210\pi$
$444$	−118.947	+	206.023i	−0.0127139	+	0.0220212i
$445$	3450.79	−	5976.95i	0.367603	−	0.636707i
$446$	1138.59	+	1972.09i	0.120883	+	0.209375i
$447$	7170.58			0.758741
$448$		0			0
$449$	4490.88			0.472022			0.236011	−	0.971750i	$-0.424160\pi$
$449$	4490.88			0.472022			0.236011	+	0.971750i	$0.424160\pi$
$450$	−57.9156	−	100.313i	−0.00606704	−	0.0105084i
$451$	11142.4	−	19299.2i	1.16336	−	2.01500i
$452$	1267.21	−	2194.87i	0.131869	−	0.228403i
$453$	−4963.95	−	8597.82i	−0.514850	−	0.891746i
$454$	−3847.83			−0.397770
$455$		0			0
$456$	451.713			0.0463890
$457$	7171.91	+	12422.1i	0.734109	+	1.27151i	0.955113	+	0.296241i	$0.0957330\pi$
$457$	7171.91	+	12422.1i	0.734109	+	1.27151i	−0.221005	+	0.975273i	$0.570934\pi$
$458$	665.251	−	1152.25i	0.0678714	−	0.117557i
$459$	7346.61	−	12724.7i	0.747081	−	1.29398i
$460$	−558.680	−	967.662i	−0.0566274	−	0.0980815i
$461$	14558.7			1.47086			0.735429	−	0.677602i	$-0.236981\pi$
$461$	14558.7			1.47086			0.735429	+	0.677602i	$0.236981\pi$
$462$		0			0
$463$	−1809.56			−0.181636			−0.0908178	−	0.995868i	$-0.528948\pi$
$463$	−1809.56			−0.181636			−0.0908178	+	0.995868i	$0.528948\pi$
$464$	543.564	+	941.480i	0.0543843	+	0.0941964i
$465$	2362.47	−	4091.92i	0.235606	−	0.408082i
$466$	−2683.20	+	4647.45i	−0.266732	+	0.461993i
$467$	2990.82	+	5180.26i	0.296357	+	0.513306i	0.975300	−	0.220886i	$-0.0708947\pi$
$467$	2990.82	+	5180.26i	0.296357	+	0.513306i	−0.678942	+	0.734192i	$0.737561\pi$
$468$	323.008			0.0319039
$469$		0			0
$470$	−1362.93			−0.133760
$471$	−101.650	−	176.063i	−0.00994433	−	0.0172241i
$472$	706.174	−	1223.13i	0.0688650	−	0.119278i
$473$	2262.42	−	3918.63i	0.219929	−	0.380927i
$474$	6227.00	+	10785.5i	0.603409	+	1.04513i
$475$	−91.6876			−0.00885666
$476$		0			0
$477$	−1335.99			−0.128241
$478$	−4238.63	−	7341.52i	−0.405586	−	0.702496i
$479$	5763.75	−	9983.11i	0.549796	−	0.952275i	−0.448492	−	0.893787i	$-0.648039\pi$
$479$	5763.75	−	9983.11i	0.549796	−	0.952275i	0.998288	−	0.0584884i	$-0.0186281\pi$
$480$	1420.84	−	2460.97i	0.135109	−	0.234016i
$481$	−554.093	−	959.718i	−0.0525249	−	0.0909758i
$482$	5667.23			0.535551
$483$		0			0
$484$	−2131.85			−0.200211
$485$	−545.019	−	944.000i	−0.0510269	−	0.0883811i
$486$	−648.655	+	1123.50i	−0.0605424	+	0.104862i
$487$	−7895.74	+	13675.8i	−0.734682	+	1.27251i	0.220180	+	0.975459i	$0.429335\pi$
$487$	−7895.74	+	13675.8i	−0.734682	+	1.27251i	−0.954863	+	0.297048i	$0.903998\pi$
$488$	9101.95	+	15765.0i	0.844316	+	1.46240i
$489$	19769.9			1.82828
$490$		0			0
$491$	13064.9			1.20083			0.600417	−	0.799687i	$-0.295001\pi$
$491$	13064.9			1.20083			0.600417	+	0.799687i	$0.295001\pi$
$492$	3170.84	+	5492.06i	0.290554	+	0.503255i
$493$	1530.02	−	2650.07i	0.139774	−	0.242096i
$494$	−260.548	+	451.282i	−0.0237299	+	0.0411015i
$495$	−231.332	−	400.680i	−0.0210053	−	0.0363822i
$496$	6803.91			0.615937
$497$		0			0
$498$	−7915.04			−0.712211
$499$	10067.9	+	17438.1i	0.903209	+	1.56440i	0.823303	+	0.567602i	$0.192129\pi$
$499$	10067.9	+	17438.1i	0.903209	+	1.56440i	0.0799059	+	0.996802i	$0.474538\pi$
$500$	−164.578	+	285.058i	−0.0147203	+	0.0254963i
$501$	−8450.76	+	14637.1i	−0.753597	+	1.30527i
$502$	3369.87	+	5836.78i	0.299611	+	0.518941i
$503$	−751.675			−0.0666313			−0.0333156	−	0.999445i	$-0.510607\pi$
$503$	−751.675			−0.0666313			−0.0333156	+	0.999445i	$0.510607\pi$
$504$		0			0
$505$	−7371.64			−0.649571
$506$	4548.03	+	7877.42i	0.399574	+	0.692083i
$507$	3911.69	−	6775.24i	0.342651	−	0.593489i
$508$	−2135.22	+	3698.31i	−0.186486	+	0.323004i
$509$	6167.23	+	10682.0i	0.537049	+	0.930196i	0.999061	+	0.0433224i	$0.0137943\pi$
$509$	6167.23	+	10682.0i	0.537049	+	0.930196i	−0.462012	+	0.886874i	$0.652872\pi$
$510$	5868.73			0.509553
$511$		0			0
$512$	11186.4			0.965574
$513$	265.894	+	460.542i	0.0228840	+	0.0396363i
$514$	−195.384	+	338.415i	−0.0167666	+	0.0290406i
$515$	2027.47	−	3511.69i	0.173478	−	0.300473i
$516$	643.826	+	1115.14i	0.0549280	+	0.0951382i
$517$	−5443.95			−0.463104
$518$		0			0
$519$	16033.3			1.35604
$520$	3777.05	+	6542.04i	0.318528	+	0.551706i
$521$	868.216	−	1503.80i	0.0730082	−	0.126454i	−0.827210	−	0.561893i	$-0.810073\pi$
$521$	868.216	−	1503.80i	0.0730082	−	0.126454i	0.900218	+	0.435439i	$0.143407\pi$
$522$	−69.9574	+	121.170i	−0.00586581	+	0.0101599i
$523$	710.710	+	1230.99i	0.0594210	+	0.102920i	0.894206	−	0.447656i	$-0.147741\pi$
$523$	710.710	+	1230.99i	0.0594210	+	0.102920i	−0.834785	+	0.550577i	$0.814408\pi$
$524$	−3634.72			−0.303022
$525$		0			0
$526$	7516.23			0.623048
$527$	−9575.79	−	16585.8i	−0.791514	−	1.37094i
$528$	−4163.98	+	7212.23i	−0.343209	+	0.594455i
$529$	2482.42	−	4299.68i	0.204029	−	0.353389i
$530$	−3868.73	−	6700.84i	−0.317070	−	0.549181i
$531$	114.670			0.00937148
$532$		0			0
$533$	−29541.6			−2.40073
$534$	−7994.19	−	13846.3i	−0.647833	−	1.12208i
$535$	1101.65	−	1908.11i	0.0890252	−	0.154196i
$536$	−6803.65	+	11784.3i	−0.548271	+	0.949633i
$537$	3606.62	+	6246.86i	0.289827	+	0.501996i
$538$	−6599.26			−0.528837
$539$		0			0
$540$	1909.11			0.152139
$541$	−2886.63	−	4999.79i	−0.229401	−	0.397334i	0.728230	−	0.685333i	$-0.240343\pi$
$541$	−2886.63	−	4999.79i	−0.229401	−	0.397334i	−0.957631	+	0.287999i	$0.907010\pi$
$542$	3302.32	−	5719.79i	0.261710	−	0.453295i
$543$	2271.70	−	3934.70i	0.179536	−	0.310965i
$544$	−5759.11	−	9975.06i	−0.453896	−	0.786172i
$545$	9530.94			0.749102
$546$		0			0
$547$	−3941.30			−0.308076			−0.154038	−	0.988065i	$-0.549228\pi$
$547$	−3941.30			−0.308076			−0.154038	+	0.988065i	$0.549228\pi$
$548$	−2566.97	−	4446.12i	−0.200101	−	0.346585i
$549$	−738.997	+	1279.98i	−0.0574493	+	0.0995050i
$550$	1339.78	−	2320.56i	0.103870	−	0.179907i
$551$	55.3756	+	95.9134i	0.00428145	+	0.00741570i
$552$	−10452.6			−0.805961
$553$		0			0
$554$	−5325.06			−0.408376
$555$	−225.856	−	391.195i	−0.0172740	−	0.0299194i
$556$	−3686.55	+	6385.29i	−0.281195	+	0.487044i
$557$	3475.87	−	6020.38i	0.264412	−	0.457974i	−0.702998	−	0.711192i	$-0.748156\pi$
$557$	3475.87	−	6020.38i	0.264412	−	0.457974i	0.967409	+	0.253218i	$0.0814889\pi$
$558$	437.836	+	758.355i	0.0332170	+	0.0575335i
$559$	−5998.29			−0.453847
$560$		0			0
$561$	23441.5			1.76417
$562$	7076.36	+	12256.6i	0.531136	+	0.919954i
$563$	12142.3	−	21031.1i	0.908946	−	1.57434i	0.0934159	−	0.995627i	$-0.470221\pi$
$563$	12142.3	−	21031.1i	0.908946	−	1.57434i	0.815530	−	0.578714i	$-0.196445\pi$
$564$	774.603	−	1341.65i	0.0578310	−	0.100166i
$565$	2406.17	+	4167.62i	0.179165	+	0.310324i
$566$	13563.7			1.00729
$567$		0			0
$568$	−18235.1			−1.34706
$569$	10781.7	+	18674.5i	0.794363	+	1.37588i	0.923243	+	0.384217i	$0.125528\pi$
$569$	10781.7	+	18674.5i	0.794363	+	1.37588i	−0.128880	+	0.991660i	$0.541138\pi$
$570$	−106.203	+	183.949i	−0.00780412	+	0.0135171i
$571$	1844.78	−	3195.25i	0.135204	−	0.234181i	−0.790471	−	0.612499i	$-0.790164\pi$
$571$	1844.78	−	3195.25i	0.135204	−	0.234181i	0.925675	+	0.378319i	$0.123498\pi$
$572$	3736.11	+	6471.13i	0.273102	+	0.473027i
$573$	−12373.2			−0.902090
$574$		0			0
$575$	2121.64			0.153875
$576$	551.325	+	954.923i	0.0398817	+	0.0690772i
$577$	−11092.0	+	19211.8i	−0.800285	+	1.38613i	0.119144	+	0.992877i	$0.461985\pi$
$577$	−11092.0	+	19211.8i	−0.800285	+	1.38613i	−0.919429	+	0.393257i	$0.871348\pi$
$578$	6203.08	−	10744.1i	0.446391	−	0.773172i
$579$	8833.80	+	15300.6i	0.634059	+	1.09822i
$580$	397.594			0.0284641
$581$		0			0
$582$	−2525.21			−0.179851
$583$	−15452.9	−	26765.2i	−1.09776	−	1.90137i
$584$	2873.78	−	4977.53i	0.203626	−	0.352691i
$585$	−306.662	+	531.155i	−0.0216734	+	0.0375394i
$586$	5948.33	+	10302.8i	0.419323	+	0.726289i
$587$	−10605.3			−0.745705			−0.372852	−	0.927891i	$-0.621620\pi$
$587$	−10605.3			−0.745705			−0.372852	+	0.927891i	$0.621620\pi$
$588$		0			0
$589$	693.149			0.0484902
$590$	332.059	+	575.143i	0.0231706	+	0.0401327i
$591$	−4881.42	+	8454.86i	−0.339754	+	0.588471i
$592$	325.233	−	563.320i	0.0225794	−	0.0391087i
$593$	3138.62	+	5436.26i	0.217349	+	0.376459i	0.953997	−	0.299817i	$-0.0969258\pi$
$593$	3138.62	+	5436.26i	0.217349	+	0.376459i	−0.736648	+	0.676277i	$0.763592\pi$
$594$	−15541.4			−1.07352
$595$		0			0
$596$	3776.39			0.259542
$597$	−10161.7	−	17600.5i	−0.696633	−	1.20660i
$598$	6029.03	−	10442.6i	0.412283	−	0.714096i
$599$	4985.36	−	8634.90i	0.340061	−	0.589003i	−0.644383	−	0.764703i	$-0.722886\pi$
$599$	4985.36	−	8634.90i	0.340061	−	0.589003i	0.984444	+	0.175700i	$0.0562190\pi$
$600$	1539.58	+	2666.63i	0.104755	+	0.181441i
$601$	24619.2			1.67094			0.835472	−	0.549533i	$-0.185194\pi$
$601$	24619.2			1.67094			0.835472	+	0.549533i	$0.185194\pi$
$602$		0			0
$603$	−1104.79			−0.0746113
$604$	−2614.27	−	4528.04i	−0.176114	−	0.305039i
$605$	2023.97	−	3505.62i	0.136010	−	0.235577i
$606$	−8538.66	+	14789.4i	−0.572375	+	0.991383i
$607$	5626.47	+	9745.34i	0.376230	+	0.651649i	0.990510	−	0.137439i	$-0.0438870\pi$
$607$	5626.47	+	9745.34i	0.376230	+	0.651649i	−0.614281	+	0.789088i	$0.710554\pi$
$608$	416.876			0.0278068
$609$		0			0
$610$	−8559.90			−0.568164
$611$	3608.34	+	6249.83i	0.238916	+	0.413815i
$612$	266.834	−	462.170i	0.0176244	−	0.0305263i
$613$	7646.61	−	13244.3i	0.503824	−	0.872648i	−0.496167	−	0.868227i	$-0.665260\pi$
$613$	7646.61	−	13244.3i	0.503824	−	0.872648i	0.999990	−	0.00442069i	$-0.00140715\pi$
$614$	−2435.90	−	4219.10i	−0.160105	−	0.277311i
$615$	−12041.6			−0.789533
$616$		0			0
$617$	−17589.4			−1.14769			−0.573843	−	0.818966i	$-0.694548\pi$
$617$	−17589.4			−1.14769			−0.573843	+	0.818966i	$0.694548\pi$
$618$	−4696.90	−	8135.27i	−0.305723	−	0.529528i
$619$	−11733.7	+	20323.3i	−0.761900	+	1.31965i	0.179970	+	0.983672i	$0.442400\pi$
$619$	−11733.7	+	20323.3i	−0.761900	+	1.31965i	−0.941870	+	0.335978i	$0.890933\pi$
$620$	1244.19	−	2155.01i	0.0805936	−	0.139592i
$621$	−6152.75	−	10656.9i	−0.397587	−	0.688640i
$622$	−13353.7			−0.860829
$623$		0			0
$624$	11039.8			0.708249
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	1575.32	−	2728.53i	0.100579	−	0.174208i
$627$	−424.206	+	734.747i	−0.0270194	+	0.0467990i
$628$	−53.5339	−	92.7235i	−0.00340165	−	0.00589183i
$629$	−1830.93			−0.116063
$630$		0			0
$631$	−6040.86			−0.381114			−0.190557	−	0.981676i	$-0.561029\pi$
$631$	−6040.86			−0.381114			−0.190557	+	0.981676i	$0.561029\pi$
$632$	13242.7	+	22937.0i	0.833488	+	1.44364i
$633$	−10813.3	+	18729.3i	−0.678976	+	1.17602i
$634$	5952.51	−	10310.0i	0.372877	−	0.645843i
$635$	−4054.34	−	7022.32i	−0.253373	−	0.438854i
$636$	8794.99			0.548340
$637$		0			0
$638$	−3236.68			−0.200849
$639$	−740.264	−	1282.17i	−0.0458285	−	0.0793772i
$640$	−919.683	+	1592.94i	−0.0568026	+	0.0983849i
$641$	−12555.8	+	21747.3i	−0.773673	+	1.34004i	0.161865	+	0.986813i	$0.448249\pi$
$641$	−12555.8	+	21747.3i	−0.773673	+	1.34004i	−0.935538	+	0.353227i	$0.885084\pi$
$642$	−2552.11	−	4420.38i	−0.156891	−	0.271742i
$643$	−3095.03			−0.189823			−0.0949113	−	0.995486i	$-0.530257\pi$
$643$	−3095.03			−0.189823			−0.0949113	+	0.995486i	$0.530257\pi$
$644$		0			0
$645$	−2444.99			−0.149258
$646$	430.472	+	745.600i	0.0262178	+	0.0454106i
$647$	4589.31	−	7948.93i	0.278863	−	0.483005i	−0.692239	−	0.721668i	$-0.743376\pi$
$647$	4589.31	−	7948.93i	0.278863	−	0.483005i	0.971103	+	0.238663i	$0.0767090\pi$
$648$	8264.46	−	14314.5i	0.501016	−	0.867785i
$649$	1326.35	+	2297.30i	0.0802213	+	0.138947i
$650$	−3552.11			−0.214346
$651$		0			0
$652$	10411.8			0.625397
$653$	7219.19	+	12504.0i	0.432632	+	0.749341i	0.997099	−	0.0761147i	$-0.0242515\pi$
$653$	7219.19	+	12504.0i	0.432632	+	0.749341i	−0.564467	+	0.825456i	$0.690918\pi$
$654$	11039.8	−	19121.5i	0.660077	−	1.14329i
$655$	3450.79	−	5976.95i	0.205853	−	0.356548i
$656$	−8669.92	−	15016.7i	−0.516012	−	0.893759i
$657$	466.650			0.0277104
$658$		0			0
$659$	−2900.64			−0.171461			−0.0857305	−	0.996318i	$-0.527322\pi$
$659$	−2900.64			−0.171461			−0.0857305	+	0.996318i	$0.527322\pi$
$660$	1522.89	+	2637.72i	0.0898158	+	0.155566i
$661$	4988.26	−	8639.92i	0.293526	−	0.508403i	−0.681115	−	0.732177i	$-0.738504\pi$
$661$	4988.26	−	8639.92i	0.293526	−	0.508403i	0.974641	+	0.223774i	$0.0718378\pi$
$662$	2114.73	−	3662.82i	0.124156	−	0.215045i
$663$	−15537.4	−	26911.6i	−0.910142	−	1.57641i
$664$	−16832.5			−0.983777
$665$		0			0
$666$	83.7159			0.00487076
$667$	−1281.38	−	2219.42i	−0.0743859	−	0.128840i
$668$	−4450.59	+	7708.65i	−0.257782	+	0.446492i
$669$	2457.42	−	4256.38i	0.142017	−	0.245981i
$670$	−3199.24	−	5541.24i	−0.184474	−	0.319517i
$671$	−34190.8			−1.96710
$672$		0			0
$673$	20760.8			1.18911			0.594554	−	0.804055i	$-0.297329\pi$
$673$	20760.8			1.18911			0.594554	+	0.804055i	$0.297329\pi$
$674$	178.363	+	308.933i	0.0101933	+	0.0176553i
$675$	−1812.50	+	3139.34i	−0.103353	+	0.179012i
$676$	2060.09	−	3568.18i	0.117210	−	0.203014i
$677$	1604.56	+	2779.19i	0.0910907	+	0.157774i	0.907970	−	0.419034i	$-0.137631\pi$
$677$	1604.56	+	2779.19i	0.0910907	+	0.157774i	−0.816880	+	0.576808i	$0.804298\pi$
$678$	11148.4			0.631492
$679$		0			0
$680$	12480.7			0.703845
$681$	4152.41	+	7192.19i	0.233658	+	0.404707i
$682$	−10128.6	+	17543.2i	−0.568685	+	0.984991i
$683$	−2166.79	+	3752.98i	−0.121391	+	0.210255i	−0.920316	−	0.391175i	$-0.872069\pi$
$683$	−2166.79	+	3752.98i	−0.121391	+	0.210255i	0.798926	+	0.601430i	$0.205402\pi$
$684$	9.65745	+	16.7272i	0.000539857	+	0.000935059i
$685$	9748.29			0.543741
$686$		0			0
$687$	−2871.64			−0.159476
$688$	−1760.39	−	3049.09i	−0.0975498	−	0.168961i
$689$	−20484.9	+	35480.9i	−1.13267	+	1.96185i
$690$	2457.52	−	4256.55i	0.135589	−	0.234846i
$691$	−7222.98	−	12510.6i	−0.397649	−	0.688748i	0.595787	−	0.803143i	$-0.296840\pi$
$691$	−7222.98	−	12510.6i	−0.397649	−	0.688748i	−0.993435	+	0.114395i	$0.963507\pi$
$692$	8443.94			0.463859
$693$		0			0
$694$	−10099.1			−0.552385
$695$	−7000.00	−	12124.4i	−0.382051	−	0.661731i
$696$	1859.69	−	3221.07i	0.101281	−	0.175423i
$697$	−24404.0	+	42269.0i	−1.32621	+	2.29706i
$698$	−1956.39	−	3388.56i	−0.106089	−	0.183752i
$699$	11582.4			0.626733
$700$		0			0
$701$	−859.801			−0.0463256			−0.0231628	−	0.999732i	$-0.507374\pi$
$701$	−859.801			−0.0463256			−0.0231628	+	0.999732i	$0.507374\pi$
$702$	10301.1	+	17842.1i	0.553833	+	0.959267i
$703$	33.1332	−	57.3883i	0.00177758	−	0.00307886i
$704$	−12753.9	+	22090.5i	−0.682787	+	1.18262i
$705$	1470.81	+	2547.52i	0.0785730	+	0.136093i
$706$	−9084.31			−0.484267
$707$		0			0
$708$	−754.887			−0.0400712
$709$	3989.56	+	6910.13i	0.211327	+	0.366030i	0.952130	−	0.305693i	$-0.0988880\pi$
$709$	3989.56	+	6910.13i	0.211327	+	0.366030i	−0.740803	+	0.671723i	$0.765555\pi$
$710$	4287.28	−	7425.80i	0.226618	−	0.392514i
$711$	−1075.19	+	1862.28i	−0.0567125	+	0.0982290i
$712$	−17000.9	−	29446.3i	−0.894851	−	1.54993i
$713$	−16039.4			−0.842467
$714$		0			0
$715$	−14188.2			−0.742110
$716$	1899.43	+	3289.91i	0.0991410	+	0.171717i
$717$	−9148.28	+	15845.3i	−0.476498	+	0.825318i
$718$	−3321.88	+	5753.67i	−0.172662	+	0.299060i
$719$	−16851.6	−	29187.9i	−0.874076	−	1.51394i	−0.857744	−	0.514077i	$-0.828135\pi$
$719$	−16851.6	−	29187.9i	−0.874076	−	1.51394i	−0.0163313	−	0.999867i	$-0.505199\pi$
$720$	−360.000			−0.0186339
$721$		0			0
$722$	15858.6			0.817444
$723$	−6115.83	−	10592.9i	−0.314592	−	0.544890i
$724$	1196.39	−	2072.21i	0.0614137	−	0.106372i
$725$	−377.475	+	653.806i	−0.0193366	+	0.0334920i
$726$	−4688.78	−	8121.21i	−0.239693	−	0.415160i
$727$	30277.0			1.54458			0.772290	−	0.635270i	$-0.219111\pi$
$727$	30277.0			1.54458			0.772290	+	0.635270i	$0.219111\pi$
$728$		0			0
$729$	20917.0			1.06269
$730$	1351.32	+	2340.55i	0.0685129	+	0.118668i
$731$	−4955.13	+	8582.54i	−0.250714	+	0.434250i
$732$	4864.91	−	8426.27i	0.245645	−	0.425470i
$733$	9681.97	+	16769.7i	0.487874	+	0.845023i	0.999903	−	0.0139454i	$-0.00443911\pi$
$733$	9681.97	+	16769.7i	0.487874	+	0.845023i	−0.512028	+	0.858968i	$0.671106\pi$
$734$	26648.1			1.34005
$735$		0			0
$736$	−9646.45			−0.483115
$737$	−12778.7	−	22133.4i	−0.638684	−	1.10623i
$738$	1115.83	−	1932.68i	0.0556563	−	0.0963995i
$739$	−12476.2	+	21609.4i	−0.621035	+	1.07566i	0.368259	+	0.929723i	$0.379954\pi$
$739$	−12476.2	+	21609.4i	−0.621035	+	1.07566i	−0.989293	+	0.145940i	$0.953379\pi$
$740$	−118.947	−	206.023i	−0.00590890	−	0.0102345i
$741$	1124.69			0.0557576
$742$		0			0
$743$	−8154.54			−0.402640			−0.201320	−	0.979526i	$-0.564523\pi$
$743$	−8154.54			−0.402640			−0.201320	+	0.979526i	$0.564523\pi$
$744$	−11639.1	−	20159.4i	−0.573533	−	0.993388i
$745$	−3585.29	+	6209.91i	−0.176315	+	0.305387i
$746$	5891.67	−	10204.7i	0.289155	−	0.500831i
$747$	−683.325	−	1183.55i	−0.0334693	−	0.0579705i
$748$	12345.5			0.603469
$749$		0			0
$750$	−1447.89			−0.0704926
$751$	2155.63	+	3733.66i	0.104740	+	0.181416i	0.913632	−	0.406542i	$-0.133265\pi$
$751$	2155.63	+	3733.66i	0.104740	+	0.181416i	−0.808892	+	0.587958i	$0.799932\pi$
$752$	−2117.97	+	3668.43i	−0.102705	+	0.177891i
$753$	7273.22	−	12597.6i	0.351993	−	0.609670i
$754$	2145.33	+	3715.82i	0.103619	+	0.179473i
$755$	9927.91			0.478561
$756$		0			0
$757$	3624.79			0.174036			0.0870179	−	0.996207i	$-0.472266\pi$
$757$	3624.79			0.174036			0.0870179	+	0.996207i	$0.472266\pi$
$758$	1105.99	+	1915.63i	0.0529964	+	0.0917925i
$759$	9816.07	−	17001.9i	0.469435	−	0.813085i
$760$	−225.856	+	391.195i	−0.0107798	+	0.0186712i
$761$	10288.2	+	17819.7i	0.490075	+	0.848835i	0.999935	−	0.0114227i	$-0.00363604\pi$
$761$	10288.2	+	17819.7i	0.490075	+	0.848835i	−0.509860	+	0.860258i	$0.670303\pi$
$762$	−18784.8			−0.893045
$763$		0			0
$764$	−6516.34			−0.308577
$765$	506.662	+	877.565i	0.0239456	+	0.0414751i
$766$	−3572.13	+	6187.11i	−0.168494	+	0.291840i
$767$	1758.25	−	3045.38i	0.0827728	−	0.143367i
$768$	−8895.94	−	15408.2i	−0.417975	−	0.723953i
$769$	3066.14			0.143781			0.0718907	−	0.997413i	$-0.477097\pi$
$769$	3066.14			0.143781			0.0718907	+	0.997413i	$0.477097\pi$
$770$		0			0
$771$	843.400			0.0393960
$772$	4652.32	+	8058.06i	0.216892	+	0.375668i
$773$	−9693.52	+	16789.7i	−0.451037	+	0.781219i	−0.998451	−	0.0556429i	$-0.982279\pi$
$773$	−9693.52	+	16789.7i	−0.451037	+	0.781219i	0.547413	+	0.836862i	$0.315613\pi$
$774$	226.565	−	392.422i	0.0105216	−	0.0182239i
$775$	2362.47	+	4091.92i	0.109500	+	0.189659i
$776$	−5370.23			−0.248428
$777$		0			0
$778$	14666.9			0.675879
$779$	−883.250	−	1529.83i	−0.0406235	−	0.0703620i
$780$	2018.80	−	3496.66i	0.0926725	−	0.160513i
$781$	17124.7	−	29660.9i	0.784597	−	1.35896i
$782$	−9961.06	−	17253.1i	−0.455507	−	0.788962i
$783$	4378.71			0.199850
$784$		0			0
$785$	203.300			0.00924342
$786$	−7994.19	−	13846.3i	−0.362778	−	0.628350i
$787$	21681.7	−	37553.8i	0.982044	−	1.70095i	0.327645	−	0.944801i	$-0.393745\pi$
$787$	21681.7	−	37553.8i	0.982044	−	1.70095i	0.654399	−	0.756150i	$-0.272922\pi$
$788$	−2570.80	+	4452.75i	−0.116219	+	0.201298i
$789$	−8111.18	−	14049.0i	−0.365990	−	0.633912i
$790$	−12454.0			−0.560878
$791$		0			0
$792$	−2279.39			−0.102266
$793$	22662.3	+	39252.2i	1.01483	+	1.75774i
$794$	14054.1	−	24342.4i	0.628162	−	1.08801i
$795$	−8349.94	+	14462.5i	−0.372505	+	0.645198i
$796$	−5351.65	−	9269.32i	−0.238297	−	0.412742i
$797$	−17132.6			−0.761439			−0.380720	−	0.924691i	$-0.624324\pi$
$797$	−17132.6			−0.761439			−0.380720	+	0.924691i	$0.624324\pi$
$798$		0			0
$799$	11923.3			0.527929
$800$	1420.84	+	2460.97i	0.0627930	+	0.108761i
$801$	1380.32	−	2390.78i	0.0608878	−	0.105461i
$802$	−313.520	+	543.032i	−0.0138039	+	0.0239091i
$803$	5397.56	+	9348.86i	0.237205	+	0.410852i
$804$	7272.98			0.319028
$805$		0			0
$806$	26853.6			1.17355
$807$	7121.64	+	12335.0i	0.310649	+	0.538059i
$808$	−18158.7	+	31451.9i	−0.790622	+	1.36940i
$809$	540.244	−	935.729i	0.0234783	−	0.0406656i	−0.854048	−	0.520195i	$-0.825859\pi$
$809$	540.244	−	935.729i	0.0234783	−	0.0406656i	0.877526	+	0.479529i	$0.159193\pi$
$810$	3886.14	+	6730.99i	0.168574	+	0.291979i
$811$	−19593.9			−0.848378			−0.424189	−	0.905574i	$-0.639441\pi$
$811$	−19593.9			−0.848378			−0.424189	+	0.905574i	$0.639441\pi$
$812$		0			0
$813$	−14254.9			−0.614933
$814$	968.311	+	1677.16i	0.0416944	+	0.0722169i
$815$	−9884.96	+	17121.3i	−0.424853	+	0.735867i
$816$	9119.92	−	15796.2i	0.391251	−	0.677667i
$817$	−179.340	−	310.626i	−0.00767970	−	0.0133016i
$818$	9312.66			0.398056
$819$		0			0
$820$	−6341.69			−0.270075
$821$	−2561.90	−	4437.34i	−0.108905	−	0.188629i	0.806422	−	0.591341i	$-0.201401\pi$
$821$	−2561.90	−	4437.34i	−0.108905	−	0.188629i	−0.915327	+	0.402712i	$0.868068\pi$
$822$	11291.6	−	19557.6i	0.479122	−	0.829864i
$823$	6592.03	−	11417.7i	0.279202	−	0.483593i	−0.691984	−	0.721913i	$-0.743263\pi$
$823$	6592.03	−	11417.7i	0.279202	−	0.483593i	0.971187	+	0.238320i	$0.0765966\pi$
$824$	−9988.66	−	17300.9i	−0.422295	−	0.731437i
$825$	−5783.31			−0.244060
$826$		0			0
$827$	24658.7			1.03684			0.518421	−	0.855126i	$-0.326520\pi$
$827$	24658.7			1.03684			0.518421	+	0.855126i	$0.326520\pi$
$828$	−223.472	−	387.065i	−0.00937946	−	0.0162457i
$829$	−14281.2	+	24735.7i	−0.598318	+	1.03632i	0.394751	+	0.918788i	$0.370831\pi$
$829$	−14281.2	+	24735.7i	−0.598318	+	1.03632i	−0.993069	+	0.117529i	$0.962503\pi$
$830$	3957.52	−	6854.62i	0.165503	−	0.286660i
$831$	5746.57	+	9953.36i	0.239887	+	0.415497i
$832$	33814.1			1.40901
$833$		0			0
$834$	−32432.7			−1.34659
$835$	−8450.76	−	14637.1i	−0.350240	−	0.606634i
$836$	−223.408	+	386.955i	−0.00924251	+	0.0160085i
$837$	13702.3	−	23733.1i	0.565856	−	0.980091i
$838$	−2823.14	−	4889.82i	−0.116377	−	0.201570i
$839$	−31106.0			−1.27997			−0.639987	−	0.768386i	$-0.721060\pi$
$839$	−31106.0			−1.27997			−0.639987	+	0.768386i	$0.721060\pi$
$840$		0			0
$841$	−23477.1			−0.962609
$842$	−5503.56	−	9532.45i	−0.225256	−	0.390154i
$843$	15273.0	−	26453.6i	0.623998	−	1.08080i
$844$	−5694.85	+	9863.76i	−0.232257	+	0.402281i
$845$	3911.69	+	6775.24i	0.159250	+	0.275829i
$846$	−545.171			−0.0221553
$847$		0			0
$848$	−24047.8			−0.973827
$849$	−14637.4	−	25352.7i	−0.591700	−	1.02485i
$850$	−2934.37	+	5082.47i	−0.118409	+	0.205091i
$851$	−766.696	+	1327.96i	−0.0308837	+	0.0534921i
$852$	4873.25	+	8440.72i	0.195956	+	0.339406i
$853$	20567.9			0.825596			0.412798	−	0.910823i	$-0.364552\pi$
$853$	20567.9			0.825596			0.412798	+	0.910823i	$0.364552\pi$
$854$		0			0
$855$	−36.6750			−0.00146697
$856$	−5427.44	−	9400.61i	−0.216713	−	0.375358i
$857$	−3229.72	+	5594.04i	−0.128734	+	0.222974i	−0.923186	−	0.384353i	$-0.874425\pi$
$857$	−3229.72	+	5594.04i	−0.128734	+	0.222974i	0.794452	+	0.607327i	$0.207758\pi$
$858$	−16434.4	+	28465.2i	−0.653916	+	1.13262i
$859$	24107.2	+	41754.9i	0.957541	+	1.65851i	0.728444	+	0.685105i	$0.240244\pi$
$859$	24107.2	+	41754.9i	0.957541	+	1.65851i	0.229096	+	0.973404i	$0.426423\pi$
$860$	−1287.65			−0.0510565
$861$		0			0
$862$	−18359.7			−0.725445
$863$	15854.7	+	27461.2i	0.625378	+	1.08319i	0.988468	+	0.151433i	$0.0483887\pi$
$863$	15854.7	+	27461.2i	0.625378	+	1.08319i	−0.363089	+	0.931754i	$0.618278\pi$
$864$	8240.89	−	14273.6i	0.324492	−	0.562036i
$865$	−8016.66	+	13885.3i	−0.315115	+	0.545795i
$866$	13305.8	+	23046.4i	0.522114	+	0.904328i
$867$	−26776.4			−1.04887
$868$		0			0
$869$	−49745.1			−1.94187
$870$	874.468	+	1514.62i	0.0340773	+	0.0590236i
$871$	−16939.9	+	29340.8i	−0.658998	+	1.14142i
$872$	23477.8	−	40664.7i	0.911765	−	1.57922i
$873$	−218.008	−	377.600i	−0.00845182	−	0.0146390i
$874$	721.037			0.0279055
$875$		0			0
$876$	−3072.01			−0.118486
$877$	−12827.4	−	22217.7i	−0.493900	−	0.855459i	0.506076	−	0.862489i	$-0.331096\pi$
$877$	−12827.4	−	22217.7i	−0.493900	−	0.855459i	−0.999975	+	0.00702998i	$0.997762\pi$
$878$	10596.1	−	18353.1i	0.407292	−	0.705451i
$879$	12838.4	−	22236.7i	0.492636	−	0.853271i
$880$	−4163.98	−	7212.23i	−0.159509	−	0.276278i
$881$	−11470.4			−0.438647			−0.219323	−	0.975652i	$-0.570385\pi$
$881$	−11470.4			−0.438647			−0.219323	+	0.975652i	$0.570385\pi$
$882$		0			0
$883$	39124.0			1.49108			0.745542	−	0.666459i	$-0.232191\pi$
$883$	39124.0			1.49108			0.745542	+	0.666459i	$0.232191\pi$
$884$	−8182.79	−	14173.0i	−0.311331	−	0.539242i
$885$	716.688	−	1241.34i	0.0272217	−	0.0471493i
$886$	2159.50	−	3740.37i	0.0818848	−	0.141829i
$887$	−7792.88	−	13497.7i	−0.294994	−	0.510944i	0.679990	−	0.733222i	$-0.261984\pi$
$887$	−7792.88	−	13497.7i	−0.294994	−	0.510944i	−0.974983	+	0.222278i	$0.928651\pi$
$888$	−2225.43			−0.0840997
$889$		0			0
$890$	15988.4			0.602171
$891$	15522.4	+	26885.6i	0.583637	+	1.01089i
$892$	1294.20	−	2241.62i	0.0485797	−	0.0841425i
$893$	−215.768	+	373.722i	−0.00808557	+	0.0140046i
$894$	8305.78	+	14386.0i	0.310723	+	0.538189i
$895$	−7213.25			−0.269399
$896$		0			0
$897$	−26025.1			−0.968731
$898$	5201.85	+	9009.86i	0.193305	+	0.334814i
$899$	2853.67	−	4942.71i	0.105868	−	0.183369i
$900$	−65.8312	+	114.023i	−0.00243819	+	0.00422308i
$901$	33844.8	+	58620.9i	1.25142	+	2.16753i
$902$	51625.6			1.90570
$903$		0			0
$904$	23708.8			0.872280
$905$	2271.70	+	3934.70i	0.0834407	+	0.144524i
$906$	11499.6	−	19917.9i	0.421688	−	0.730385i
$907$	−13798.1	+	23898.9i	−0.505134	+	0.874918i	0.494848	+	0.868980i	$0.335224\pi$
$907$	−13798.1	+	23898.9i	−0.505134	+	0.874918i	−0.999982	+	0.00593879i	$0.998110\pi$
$908$	2186.87	+	3787.77i	0.0799270	+	0.138438i
$909$	−2948.65			−0.107592
$910$		0			0
$911$	−14396.2			−0.523565			−0.261782	−	0.965127i	$-0.584310\pi$
$911$	−14396.2			−0.523565			−0.261782	+	0.965127i	$0.584310\pi$
$912$	330.075	+	571.707i	0.0119845	+	0.0207578i
$913$	15807.5	−	27379.4i	0.573004	−	0.992472i
$914$	−16614.6	+	28777.4i	−0.601272	+	1.04143i
$915$	9237.47	+	15999.8i	0.333750	+	0.578072i
$916$	−1512.35			−0.0545517
$917$		0			0
$918$	34038.7			1.22379
$919$	−5139.78	−	8902.35i	−0.184489	−	0.319545i	0.758915	−	0.651190i	$-0.225730\pi$
$919$	−5139.78	−	8902.35i	−0.184489	−	0.319545i	−0.943404	+	0.331645i	$0.892396\pi$
$920$	5226.28	−	9052.19i	0.187289	−	0.324393i
$921$	−5257.42	+	9106.13i	−0.188098	+	0.325795i
$922$	16863.5	+	29208.4i	0.602353	+	1.04331i
$923$	−45402.2			−1.61910
$924$		0			0
$925$	451.713			0.0160565
$926$	−2096.03	−	3630.43i	−0.0743843	−	0.128837i
$927$	810.990	−	1404.68i	0.0287340	−	0.0497687i
$928$	1716.27	−	2972.66i	0.0607103	−	0.105153i
$929$	3249.94	+	5629.06i	0.114776	+	0.198798i	0.917690	−	0.397297i	$-0.130052\pi$
$929$	3249.94	+	5629.06i	0.114776	+	0.198798i	−0.802914	+	0.596095i	$0.796718\pi$
$930$	10945.9			0.385947
$931$		0			0
$932$	6099.86			0.214386
$933$	14410.8	+	24960.2i	0.505667	+	0.875840i
$934$	−6928.62	+	12000.7i	−0.242732	+	0.420424i
$935$	−11720.7	+	20300.9i	−0.409957	+	0.710066i
$936$	1510.82	+	2616.81i	0.0527592	+	0.0913817i
$937$	10269.8			0.358056			0.179028	−	0.983844i	$-0.442705\pi$
$937$	10269.8			0.358056			0.179028	+	0.983844i	$0.442705\pi$
$938$		0			0
$939$	−6800.06			−0.236328
$940$	774.603	+	1341.65i	0.0268774	+	0.0465531i
$941$	17198.1	−	29788.0i	0.595794	−	1.03195i	−0.397640	−	0.917541i	$-0.630171\pi$
$941$	17198.1	−	29788.0i	0.595794	−	1.03195i	0.993434	−	0.114404i	$-0.0364959\pi$
$942$	235.485	−	407.871i	0.00814491	−	0.0141074i
$943$	20438.3	+	35400.1i	0.705792	+	1.22247i
$944$	2064.06			0.0711647
$945$		0			0
$946$	10482.4			0.360265
$947$	−13596.1	−	23549.1i	−0.466539	−	0.808070i	0.532730	−	0.846285i	$-0.321166\pi$
$947$	−13596.1	−	23549.1i	−0.466539	−	0.808070i	−0.999270	+	0.0382155i	$0.987833\pi$
$948$	7078.08	−	12259.6i	0.242495	−	0.420014i
$949$	7155.20	−	12393.2i	0.244750	−	0.423919i
$950$	−106.203	−	183.949i	−0.00362703	−	0.00628220i
$951$	−25694.7			−0.876140
$952$		0			0
$953$	49965.2			1.69836			0.849178	−	0.528107i	$-0.177098\pi$
$953$	49965.2			1.69836			0.849178	+	0.528107i	$0.177098\pi$
$954$	−1547.49	−	2680.34i	−0.0525178	−	0.0909635i
$955$	6186.59	−	10715.5i	0.209627	−	0.363084i
$956$	−4817.94	+	8344.92i	−0.162995	+	0.282316i
$957$	3492.89	+	6049.86i	0.117982	+	0.204351i
$958$	26704.9			0.900622
$959$		0			0
$960$	13783.1			0.463384
$961$	−2964.53	−	5134.71i	−0.0995108	−	0.172358i
$962$	1283.63	−	2223.31i	0.0430206	−	0.0745138i
$963$	440.660	−	763.245i	0.0147457	−	0.0255402i
$964$	−3220.90	−	5578.77i	−0.107612	−	0.186390i
$965$	−17667.6			−0.589368
$966$		0			0
$967$	−16755.5			−0.557208			−0.278604	−	0.960406i	$-0.589872\pi$
$967$	−16755.5			−0.557208			−0.278604	+	0.960406i	$0.589872\pi$
$968$	−9971.40	−	17271.0i	−0.331088	−	0.573461i
$969$	929.093	−	1609.24i	0.0308016	−	0.0533500i
$970$	1262.60	−	2186.89i	0.0417936	−	0.0723886i
$971$	−18808.7	−	32577.6i	−0.621626	−	1.07669i	−0.989183	−	0.146687i	$-0.953139\pi$
$971$	−18808.7	−	32577.6i	−0.621626	−	1.07669i	0.367557	−	0.930001i	$-0.380194\pi$
$972$	1474.62			0.0486610
$973$		0			0
$974$	−36583.0			−1.20348
$975$	3833.28	+	6639.44i	0.125911	+	0.218084i
$976$	−13302.0	+	23039.7i	−0.436255	+	0.755616i
$977$	13845.5	−	23981.1i	0.453384	−	0.785284i	−0.545210	−	0.838300i	$-0.683550\pi$
$977$	13845.5	−	23981.1i	0.453384	−	0.785284i	0.998594	+	0.0530160i	$0.0168834\pi$
$978$	22899.7	+	39663.5i	0.748725	+	1.29683i
$979$	63862.5			2.08483
$980$		0			0
$981$	3812.38			0.124077
$982$	15133.2	+	26211.5i	0.491772	+	0.851774i
$983$	−11377.1	+	19705.7i	−0.369149	+	0.639385i	−0.989433	−	0.144992i	$-0.953684\pi$
$983$	−11377.1	+	19705.7i	−0.369149	+	0.639385i	0.620283	+	0.784378i	$0.287018\pi$
$984$	−29662.3	+	51376.6i	−0.960975	+	1.66446i
$985$	−4881.42	−	8454.86i	−0.157903	−	0.273497i
$986$	7088.96			0.228964
$987$		0			0
$988$	592.316			0.0190729
$989$	4149.90	+	7187.84i	0.133427	+	0.231102i
$990$	535.911	−	928.224i	0.0172044	−	0.0297989i
$991$	27735.5	−	48039.2i	0.889047	−	1.53987i	0.0480435	−	0.998845i	$-0.484701\pi$
$991$	27735.5	−	48039.2i	0.889047	−	1.53987i	0.841004	−	0.541030i	$-0.181965\pi$
$992$	−10741.4	−	18604.7i	−0.343791	−	0.595464i
$993$	−9128.50			−0.291726
$994$		0			0
$995$	20323.4			0.647531
$996$	4498.41	+	7791.48i	0.143110	+	0.247874i
$997$	−7590.97	+	13147.9i	−0.241132	+	0.417653i	−0.961037	−	0.276420i	$-0.910852\pi$
$997$	−7590.97	+	13147.9i	−0.241132	+	0.417653i	0.719905	+	0.694072i	$0.244185\pi$
$998$	−23323.6	+	40397.6i	−0.739774	+	1.28133i
$999$	−1309.97	−	2268.93i	−0.0414870	−	0.0718576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.k.116.2		4
7.2	even	3	inner	245.4.e.k.226.2		4
7.3	odd	6		245.4.a.j.1.1	yes	2
7.4	even	3		245.4.a.i.1.1	✓	2
7.5	odd	6		245.4.e.j.226.2		4
7.6	odd	2		245.4.e.j.116.2		4
21.11	odd	6		2205.4.a.x.1.2		2
21.17	even	6		2205.4.a.w.1.2		2
35.4	even	6		1225.4.a.q.1.2		2
35.24	odd	6		1225.4.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.i.1.1	✓	2	7.4	even	3
245.4.a.j.1.1	yes	2	7.3	odd	6
245.4.e.j.116.2		4	7.6	odd	2
245.4.e.j.226.2		4	7.5	odd	6
245.4.e.k.116.2		4	1.1	even	1	trivial
245.4.e.k.226.2		4	7.2	even	3	inner
1225.4.a.p.1.2		2	35.24	odd	6
1225.4.a.q.1.2		2	35.4	even	6
2205.4.a.w.1.2		2	21.17	even	6
2205.4.a.x.1.2		2	21.11	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.15831 + 2.00626i) q^{2} +(2.50000 - 4.33013i) q^{3} +(1.31662 - 2.28046i) q^{4} +(2.50000 + 4.33013i) q^{5} +11.5831 q^{6} +24.6332 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(1.15831 + 2.00626i) q^{2} +(2.50000 - 4.33013i) q^{3} +(1.31662 - 2.28046i) q^{4} +(2.50000 + 4.33013i) q^{5} +11.5831 q^{6} +24.6332 q^{8} +(1.00000 + 1.73205i) q^{9} +(-5.79156 + 10.0313i) q^{10} +(-23.1332 + 40.0680i) q^{11} +(-6.58312 - 11.4023i) q^{12} +61.3325 q^{13} +25.0000 q^{15} +(18.0000 + 31.1769i) q^{16} +(50.6662 - 87.7565i) q^{17} +(-2.31662 + 4.01251i) q^{18} +(1.83375 + 3.17615i) q^{19} +13.1662 q^{20} -107.182 q^{22} +(-42.4327 - 73.4957i) q^{23} +(61.5831 - 106.665i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(71.0422 + 123.049i) q^{26} +145.000 q^{27} +30.1980 q^{29} +(28.9578 + 50.1564i) q^{30} +(94.4987 - 163.677i) q^{31} +(56.8338 - 98.4389i) q^{32} +(115.666 + 200.340i) q^{33} +234.749 q^{34} +5.26650 q^{36} +(-9.03425 - 15.6478i) q^{37} +(-4.24812 + 7.35795i) q^{38} +(153.331 - 265.577i) q^{39} +(61.5831 + 106.665i) q^{40} -481.662 q^{41} -97.7995 q^{43} +(60.9156 + 105.509i) q^{44} +(-5.00000 + 8.66025i) q^{45} +(98.3008 - 170.262i) q^{46} +(58.8325 + 101.901i) q^{47} +180.000 q^{48} -57.9156 q^{50} +(-253.331 - 438.783i) q^{51} +(80.7519 - 139.866i) q^{52} +(-333.997 + 578.501i) q^{53} +(167.955 + 290.907i) q^{54} -231.332 q^{55} +18.3375 q^{57} +(34.9787 + 60.5849i) q^{58} +(28.6675 - 49.6536i) q^{59} +(32.9156 - 57.0115i) q^{60} +(369.499 + 639.991i) q^{61} +437.836 q^{62} +551.325 q^{64} +(153.331 + 265.577i) q^{65} +(-267.955 + 464.112i) q^{66} +(-276.198 + 478.389i) q^{67} +(-133.417 - 231.085i) q^{68} -424.327 q^{69} -740.264 q^{71} +(24.6332 + 42.6660i) q^{72} +(116.662 - 202.065i) q^{73} +(20.9290 - 36.2501i) q^{74} +(62.5000 + 108.253i) q^{75} +9.65745 q^{76} +710.422 q^{78} +(537.593 + 931.138i) q^{79} +(-90.0000 + 155.885i) q^{80} +(335.500 - 581.103i) q^{81} +(-557.916 - 966.338i) q^{82} -683.325 q^{83} +506.662 q^{85} +(-113.282 - 196.211i) q^{86} +(75.4950 - 130.761i) q^{87} +(-569.847 + 987.004i) q^{88} +(-690.159 - 1195.39i) q^{89} -23.1662 q^{90} -223.472 q^{92} +(-472.494 - 818.383i) q^{93} +(-136.293 + 236.066i) q^{94} +(-9.16876 + 15.8808i) q^{95} +(-284.169 - 492.195i) q^{96} -218.008 q^{97} -92.5330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 10 * q^3 - 8 * q^4 + 10 * q^5 - 20 * q^6 + 72 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9} + 10 q^{10} - 66 q^{11} + 40 q^{12} - 20 q^{13} + 100 q^{15} + 72 q^{16} + 70 q^{17} + 4 q^{18} + 140 q^{19} - 80 q^{20} - 44 q^{22} + 16 q^{23} + 180 q^{24} - 50 q^{25} + 450 q^{26} + 580 q^{27} - 516 q^{29} - 50 q^{30} - 20 q^{31} + 360 q^{32} + 330 q^{33} + 740 q^{34} - 32 q^{36} - 328 q^{37} + 580 q^{38} - 50 q^{39} + 180 q^{40} - 600 q^{41} - 232 q^{43} - 88 q^{44} - 20 q^{45} + 632 q^{46} - 30 q^{47} + 720 q^{48} + 100 q^{50} - 350 q^{51} + 920 q^{52} - 540 q^{53} - 290 q^{54} - 660 q^{55} + 1400 q^{57} + 1314 q^{58} + 380 q^{59} - 200 q^{60} + 1080 q^{61} + 2680 q^{62} - 448 q^{64} - 50 q^{65} - 110 q^{66} - 468 q^{67} - 600 q^{68} + 160 q^{69} - 2112 q^{71} + 72 q^{72} - 860 q^{73} - 1296 q^{74} + 250 q^{75} - 2880 q^{76} + 4500 q^{78} - 158 q^{79} - 360 q^{80} + 1342 q^{81} - 1900 q^{82} - 80 q^{83} + 700 q^{85} - 148 q^{86} - 1290 q^{87} - 1364 q^{88} - 240 q^{89} + 40 q^{90} - 2592 q^{92} + 100 q^{93} - 910 q^{94} - 700 q^{95} - 1800 q^{96} - 3260 q^{97} - 264 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 10 * q^3 - 8 * q^4 + 10 * q^5 - 20 * q^6 + 72 * q^8 + 4 * q^9 + 10 * q^10 - 66 * q^11 + 40 * q^12 - 20 * q^13 + 100 * q^15 + 72 * q^16 + 70 * q^17 + 4 * q^18 + 140 * q^19 - 80 * q^20 - 44 * q^22 + 16 * q^23 + 180 * q^24 - 50 * q^25 + 450 * q^26 + 580 * q^27 - 516 * q^29 - 50 * q^30 - 20 * q^31 + 360 * q^32 + 330 * q^33 + 740 * q^34 - 32 * q^36 - 328 * q^37 + 580 * q^38 - 50 * q^39 + 180 * q^40 - 600 * q^41 - 232 * q^43 - 88 * q^44 - 20 * q^45 + 632 * q^46 - 30 * q^47 + 720 * q^48 + 100 * q^50 - 350 * q^51 + 920 * q^52 - 540 * q^53 - 290 * q^54 - 660 * q^55 + 1400 * q^57 + 1314 * q^58 + 380 * q^59 - 200 * q^60 + 1080 * q^61 + 2680 * q^62 - 448 * q^64 - 50 * q^65 - 110 * q^66 - 468 * q^67 - 600 * q^68 + 160 * q^69 - 2112 * q^71 + 72 * q^72 - 860 * q^73 - 1296 * q^74 + 250 * q^75 - 2880 * q^76 + 4500 * q^78 - 158 * q^79 - 360 * q^80 + 1342 * q^81 - 1900 * q^82 - 80 * q^83 + 700 * q^85 - 148 * q^86 - 1290 * q^87 - 1364 * q^88 - 240 * q^89 + 40 * q^90 - 2592 * q^92 + 100 * q^93 - 910 * q^94 - 700 * q^95 - 1800 * q^96 - 3260 * q^97 - 264 * q^99

Introduction

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