LMFDB - Embedded newform 245.4.e.n.226.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,4,Mod(116,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [6,3,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.5567659200.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 17x^{4} - 28x^{3} + 289x^{2} - 238x + 196 $ x^6 + 17x^4 - 28x^3 + 289x^2 - 238x + 196
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$0.430543 + 0.745723i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.4.e.n.116.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.930543 - 1.61175i) q^{2} +(4.76818 + 8.25873i) q^{3} +(2.26818 + 3.92860i) q^{4} +(2.50000 - 4.33013i) q^{5} +17.7480 q^{6} +23.3312 q^{8} +(-31.9711 + 55.3755i) q^{9} +(-4.65272 - 8.05874i) q^{10} +(18.4904 + 32.0262i) q^{11} +(-21.6302 + 37.4645i) q^{12} +22.7931 q^{13} +47.6818 q^{15} +(3.56530 - 6.17529i) q^{16} +(-67.7830 - 117.404i) q^{17} +(59.5009 + 103.059i) q^{18} +(3.11310 - 5.39205i) q^{19} +22.6818 q^{20} +68.8243 q^{22} +(24.3698 - 42.2098i) q^{23} +(111.248 + 192.686i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(21.2100 - 36.7367i) q^{26} -352.293 q^{27} -71.1172 q^{29} +(44.3700 - 76.8510i) q^{30} +(62.4618 + 108.187i) q^{31} +(86.6896 + 150.151i) q^{32} +(-176.331 + 305.414i) q^{33} -252.300 q^{34} -290.064 q^{36} +(-42.4960 + 73.6052i) q^{37} +(-5.79375 - 10.0351i) q^{38} +(108.682 + 188.242i) q^{39} +(58.3281 - 101.027i) q^{40} -92.5942 q^{41} +299.680 q^{43} +(-83.8788 + 145.282i) q^{44} +(159.855 + 276.877i) q^{45} +(-45.3544 - 78.5561i) q^{46} +(-36.4589 + 63.1487i) q^{47} +68.0000 q^{48} -46.5272 q^{50} +(646.403 - 1119.60i) q^{51} +(51.6988 + 89.5450i) q^{52} +(-181.342 - 314.094i) q^{53} +(-327.824 + 567.808i) q^{54} +184.904 q^{55} +59.3753 q^{57} +(-66.1776 + 114.623i) q^{58} +(-187.763 - 325.215i) q^{59} +(108.151 + 187.323i) q^{60} +(344.805 - 597.220i) q^{61} +232.494 q^{62} +379.719 q^{64} +(56.9827 - 98.6970i) q^{65} +(328.166 + 568.401i) q^{66} +(486.295 + 842.288i) q^{67} +(307.488 - 532.585i) q^{68} +464.799 q^{69} +281.900 q^{71} +(-745.924 + 1291.98i) q^{72} +(-371.490 - 643.440i) q^{73} +(79.0887 + 136.986i) q^{74} +(119.204 - 206.468i) q^{75} +28.2443 q^{76} +404.532 q^{78} +(-296.421 + 513.417i) q^{79} +(-17.8265 - 30.8764i) q^{80} +(-816.578 - 1414.35i) q^{81} +(-86.1630 + 149.239i) q^{82} +493.406 q^{83} -677.830 q^{85} +(278.866 - 483.009i) q^{86} +(-339.099 - 587.337i) q^{87} +(431.403 + 747.212i) q^{88} +(481.488 - 833.962i) q^{89} +595.009 q^{90} +221.101 q^{92} +(-595.659 + 1031.71i) q^{93} +(67.8532 + 117.525i) q^{94} +(-15.5655 - 26.9602i) q^{95} +(-826.703 + 1431.89i) q^{96} -740.748 q^{97} -2364.62 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 2 q^{3} - 13 q^{4} + 15 q^{5} - 48 q^{6} - 30 q^{8} - 81 q^{9} - 15 q^{10} + 74 q^{11} - 152 q^{12} - 88 q^{13} + 20 q^{15} + 79 q^{16} - 52 q^{17} + 411 q^{18} + 168 q^{19} - 130 q^{20}+ \cdots - 6976 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 2 * q^3 - 13 * q^4 + 15 * q^5 - 48 * q^6 - 30 * q^8 - 81 * q^9 - 15 * q^10 + 74 * q^11 - 152 * q^12 - 88 * q^13 + 20 * q^15 + 79 * q^16 - 52 * q^17 + 411 * q^18 + 168 * q^19 - 130 * q^20 + 368 * q^22 + 124 * q^23 + 420 * q^24 - 75 * q^25 - 446 * q^26 - 340 * q^27 + 664 * q^29 - 120 * q^30 + 320 * q^31 + 183 * q^32 - 106 * q^33 - 1164 * q^34 + 362 * q^36 + 54 * q^37 - 460 * q^38 + 982 * q^39 - 75 * q^40 - 724 * q^41 - 32 * q^43 + 264 * q^44 + 405 * q^45 + 336 * q^46 - 730 * q^47 + 408 * q^48 - 150 * q^50 + 1178 * q^51 + 1202 * q^52 - 110 * q^53 - 180 * q^54 + 740 * q^55 - 1912 * q^57 - 450 * q^58 - 180 * q^59 + 760 * q^60 + 1222 * q^61 - 928 * q^62 - 782 * q^64 - 220 * q^65 - 532 * q^66 - 204 * q^67 + 918 * q^68 + 1432 * q^69 - 272 * q^71 - 765 * q^72 + 310 * q^73 - 502 * q^74 + 50 * q^75 - 3592 * q^76 + 7576 * q^78 + 1034 * q^79 - 395 * q^80 - 2283 * q^81 - 6 * q^82 + 3320 * q^83 - 520 * q^85 - 764 * q^86 - 1574 * q^87 + 20 * q^88 + 242 * q^89 + 4110 * q^90 + 192 * q^92 - 1376 * q^93 - 1108 * q^94 - 840 * q^95 - 3156 * q^96 - 200 * q^97 - 6976 * q^99

Character values

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

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

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 $

$2$	0.930543	−	1.61175i	0.328997	−	0.569839i	−0.653316	−	0.757085i	$-0.726623\pi$
$2$	0.930543	−	1.61175i	0.328997	−	0.569839i	0.982313	+	0.187246i	$0.0599562\pi$
$3$	4.76818	+	8.25873i	0.917636	+	1.58939i	0.802995	+	0.595986i	$0.203239\pi$
$3$	4.76818	+	8.25873i	0.917636	+	1.58939i	0.114642	+	0.993407i	$0.463428\pi$
$4$	2.26818	+	3.92860i	0.283522	+	0.491075i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	17.7480			1.20760
$7$		0			0
$7$		0			0
$8$	23.3312			1.03111
$9$	−31.9711	+	55.3755i	−1.18411	+	2.05094i
$10$	−4.65272	−	8.05874i	−0.147132	−	0.254840i
$11$	18.4904	+	32.0262i	0.506823	+	0.877843i	0.999969	+	0.00789628i	$0.00251349\pi$
$11$	18.4904	+	32.0262i	0.506823	+	0.877843i	−0.493146	+	0.869947i	$0.664153\pi$
$12$	−21.6302	+	37.4645i	−0.520341	+	0.901257i
$13$	22.7931			0.486282			0.243141	−	0.969991i	$-0.421822\pi$
$13$	22.7931			0.486282			0.243141	+	0.969991i	$0.421822\pi$
$14$		0			0
$15$	47.6818			0.820759
$16$	3.56530	−	6.17529i	0.0557079	−	0.0964888i
$17$	−67.7830	−	117.404i	−0.967047	−	1.67497i	−0.704013	−	0.710187i	$-0.748610\pi$
$17$	−67.7830	−	117.404i	−0.967047	−	1.67497i	−0.263034	−	0.964787i	$-0.584723\pi$
$18$	59.5009	+	103.059i	0.779139	+	1.34951i
$19$	3.11310	−	5.39205i	0.0375892	−	0.0651064i	−0.846619	−	0.532200i	$-0.821366\pi$
$19$	3.11310	−	5.39205i	0.0375892	−	0.0651064i	0.884208	+	0.467093i	$0.154699\pi$
$20$	22.6818			0.253590
$21$		0			0
$22$	68.8243			0.666972
$23$	24.3698	−	42.2098i	0.220933	−	0.382667i	−0.734158	−	0.678978i	$-0.762423\pi$
$23$	24.3698	−	42.2098i	0.220933	−	0.382667i	0.955092	+	0.296311i	$0.0957564\pi$
$24$	111.248	+	192.686i	0.946180	+	1.63883i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	21.2100	−	36.7367i	0.159985	−	0.277103i
$27$	−352.293			−2.51107
$28$		0			0
$29$	−71.1172			−0.455384			−0.227692	−	0.973733i	$-0.573118\pi$
$29$	−71.1172			−0.455384			−0.227692	+	0.973733i	$0.573118\pi$
$30$	44.3700	−	76.8510i	0.270027	−	0.467700i
$31$	62.4618	+	108.187i	0.361886	+	0.626806i	0.988271	−	0.152708i	$-0.0487995\pi$
$31$	62.4618	+	108.187i	0.361886	+	0.626806i	−0.626385	+	0.779514i	$0.715466\pi$
$32$	86.6896	+	150.151i	0.478897	+	0.829474i
$33$	−176.331	+	305.414i	−0.930158	+	1.61108i
$34$	−252.300			−1.27262
$35$		0			0
$36$	−290.064			−1.34289
$37$	−42.4960	+	73.6052i	−0.188819	+	0.327044i	−0.944857	−	0.327484i	$-0.893799\pi$
$37$	−42.4960	+	73.6052i	−0.188819	+	0.327044i	0.756038	+	0.654528i	$0.227133\pi$
$38$	−5.79375	−	10.0351i	−0.0247334	−	0.0428396i
$39$	108.682	+	188.242i	0.446230	+	0.772893i
$40$	58.3281	−	101.027i	0.230562	−	0.399345i
$41$	−92.5942			−0.352702			−0.176351	−	0.984327i	$-0.556429\pi$
$41$	−92.5942			−0.352702			−0.176351	+	0.984327i	$0.556429\pi$
$42$		0			0
$43$	299.680			1.06281			0.531405	−	0.847118i	$-0.321664\pi$
$43$	299.680			1.06281			0.531405	+	0.847118i	$0.321664\pi$
$44$	−83.8788	+	145.282i	−0.287391	+	0.497776i
$45$	159.855	+	276.877i	0.529551	+	0.917210i
$46$	−45.3544	−	78.5561i	−0.145373	−	0.251793i
$47$	−36.4589	+	63.1487i	−0.113151	+	0.195983i	−0.917039	−	0.398798i	$-0.869428\pi$
$47$	−36.4589	+	63.1487i	−0.113151	+	0.195983i	0.803888	+	0.594780i	$0.202761\pi$
$48$	68.0000			0.204478
$49$		0			0
$50$	−46.5272			−0.131599
$51$	646.403	−	1119.60i	1.77479	−	3.07403i
$52$	51.6988	+	89.5450i	0.137872	+	0.238801i
$53$	−181.342	−	314.094i	−0.469987	−	0.814041i	0.529424	−	0.848357i	$-0.322408\pi$
$53$	−181.342	−	314.094i	−0.469987	−	0.814041i	−0.999411	+	0.0343161i	$0.989075\pi$
$54$	−327.824	+	567.808i	−0.826133	+	1.43090i
$55$	184.904			0.453316
$56$		0			0
$57$	59.3753			0.137973
$58$	−66.1776	+	114.623i	−0.149820	+	0.259495i
$59$	−187.763	−	325.215i	−0.414316	−	0.717617i	0.581040	−	0.813875i	$-0.302646\pi$
$59$	−187.763	−	325.215i	−0.414316	−	0.717617i	−0.995356	+	0.0962580i	$0.969313\pi$
$60$	108.151	+	187.323i	0.232703	+	0.403054i
$61$	344.805	−	597.220i	0.723734	−	1.25354i	−0.235759	−	0.971812i	$-0.575757\pi$
$61$	344.805	−	597.220i	0.723734	−	1.25354i	0.959493	−	0.281733i	$-0.0909092\pi$
$62$	232.494			0.476238
$63$		0			0
$64$	379.719			0.741638
$65$	56.9827	−	98.6970i	0.108736	−	0.188336i
$66$	328.166	+	568.401i	0.612038	+	1.06008i
$67$	486.295	+	842.288i	0.886723	+	1.53585i	0.843726	+	0.536774i	$0.180357\pi$
$67$	486.295	+	842.288i	0.886723	+	1.53585i	0.0429971	+	0.999075i	$0.486309\pi$
$68$	307.488	−	532.585i	0.548359	−	0.949785i
$69$	464.799			0.810945
$70$		0			0
$71$	281.900			0.471202			0.235601	−	0.971850i	$-0.424294\pi$
$71$	281.900			0.471202			0.235601	+	0.971850i	$0.424294\pi$
$72$	−745.924	+	1291.98i	−1.22095	+	2.11474i
$73$	−371.490	−	643.440i	−0.595612	−	1.03163i	−0.993460	−	0.114178i	$-0.963576\pi$
$73$	−371.490	−	643.440i	−0.595612	−	1.03163i	0.397849	−	0.917451i	$-0.369757\pi$
$74$	79.0887	+	136.986i	0.124242	+	0.215193i
$75$	119.204	−	206.468i	0.183527	−	0.317879i
$76$	28.2443			0.0426295
$77$		0			0
$78$	404.532			0.587233
$79$	−296.421	+	513.417i	−0.422152	+	0.731189i	−0.996150	−	0.0876682i	$-0.972058\pi$
$79$	−296.421	+	513.417i	−0.422152	+	0.731189i	0.573998	+	0.818857i	$0.305392\pi$
$80$	−17.8265	−	30.8764i	−0.0249133	−	0.0431511i
$81$	−816.578	−	1414.35i	−1.12013	−	1.94013i
$82$	−86.1630	+	149.239i	−0.116038	+	0.200984i
$83$	493.406			0.652510			0.326255	−	0.945282i	$-0.394213\pi$
$83$	493.406			0.652510			0.326255	+	0.945282i	$0.394213\pi$
$84$		0			0
$85$	−677.830			−0.864953
$86$	278.866	−	483.009i	0.349661	−	0.605631i
$87$	−339.099	−	587.337i	−0.417877	−	0.723784i
$88$	431.403	+	747.212i	0.522588	+	0.905148i
$89$	481.488	−	833.962i	0.573457	−	0.993257i	−0.422750	−	0.906246i	$-0.638935\pi$
$89$	481.488	−	833.962i	0.573457	−	0.993257i	0.996207	−	0.0870105i	$-0.0277314\pi$
$90$	595.009			0.696883
$91$		0			0
$92$	221.101			0.250558
$93$	−595.659	+	1031.71i	−0.664160	+	1.15036i
$94$	67.8532	+	117.525i	0.0744524	+	0.128955i
$95$	−15.5655	−	26.9602i	−0.0168104	−	0.0291165i
$96$	−826.703	+	1431.89i	−0.878907	+	1.52231i
$97$	−740.748			−0.775377			−0.387689	−	0.921790i	$-0.626726\pi$
$97$	−740.748			−0.775377			−0.387689	+	0.921790i	$0.626726\pi$
$98$		0			0
$99$	−2364.62			−2.40054
$100$	56.7045	−	98.2150i	0.0567045	−	0.0982150i
$101$	306.897	+	531.562i	0.302351	+	0.523687i	0.976668	−	0.214755i	$-0.0688953\pi$
$101$	306.897	+	531.562i	0.302351	+	0.523687i	−0.674317	+	0.738442i	$0.735562\pi$
$102$	−1203.01	−	2083.68i	−1.16780	−	2.02269i
$103$	402.747	−	697.578i	0.385280	−	0.667324i	−0.606528	−	0.795062i	$-0.707438\pi$
$103$	402.747	−	697.578i	0.385280	−	0.667324i	0.991808	+	0.127738i	$0.0407716\pi$
$104$	531.791			0.501408
$105$		0			0
$106$	−674.988			−0.618497
$107$	965.650	−	1672.55i	0.872457	−	1.51114i	0.0130091	−	0.999915i	$-0.495859\pi$
$107$	965.650	−	1672.55i	0.872457	−	1.51114i	0.859448	−	0.511224i	$-0.170808\pi$
$108$	−799.064	−	1384.02i	−0.711944	−	1.23312i
$109$	−53.2309	−	92.1986i	−0.0467761	−	0.0810186i	0.841689	−	0.539962i	$-0.181561\pi$
$109$	−53.2309	−	92.1986i	−0.0467761	−	0.0810186i	−0.888465	+	0.458943i	$0.848228\pi$
$110$	172.061	−	298.018i	0.149140	−	0.258317i
$111$	−810.514			−0.693068
$112$		0			0
$113$	309.076			0.257305			0.128652	−	0.991690i	$-0.458935\pi$
$113$	309.076			0.257305			0.128652	+	0.991690i	$0.458935\pi$
$114$	55.2513	−	95.6980i	0.0453926	−	0.0786223i
$115$	−121.849	−	211.049i	−0.0988043	−	0.171134i
$116$	−161.306	−	279.391i	−0.129111	−	0.223628i
$117$	−728.719	+	1262.18i	−0.575813	+	0.997337i
$118$	−698.887			−0.545235
$119$		0			0
$120$	1112.48			0.846289
$121$	−18.2862	+	31.6726i	−0.0137387	+	0.0237961i
$122$	−641.712	−	1111.48i	−0.476212	−	0.824824i
$123$	−441.506	−	764.711i	−0.323652	−	0.560582i
$124$	−283.349	+	490.775i	−0.205206	+	0.355427i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−199.470			−0.139371			−0.0696856	−	0.997569i	$-0.522200\pi$
$127$	−199.470			−0.139371			−0.0696856	+	0.997569i	$0.522200\pi$
$128$	−340.172	+	589.196i	−0.234901	+	0.406860i
$129$	1428.93	+	2474.98i	0.975273	+	1.68922i
$130$	−106.050	−	183.684i	−0.0715476	−	0.123924i
$131$	300.861	−	521.106i	0.200659	−	0.347552i	−0.748082	−	0.663606i	$-0.769025\pi$
$131$	300.861	−	521.106i	0.200659	−	0.347552i	0.948741	+	0.316055i	$0.102358\pi$
$132$	−1599.80			−1.05488
$133$		0			0
$134$	1810.08			1.16692
$135$	−880.733	+	1525.47i	−0.561492	+	0.972533i
$136$	−1581.46	−	2739.17i	−0.997127	−	1.72707i
$137$	−1046.10	−	1811.90i	−0.652370	−	1.12994i	−0.982546	−	0.186018i	$-0.940442\pi$
$137$	−1046.10	−	1811.90i	−0.652370	−	1.12994i	0.330177	−	0.943919i	$-0.392892\pi$
$138$	432.516	−	749.139i	0.266798	−	0.462108i
$139$	−834.466			−0.509198			−0.254599	−	0.967047i	$-0.581943\pi$
$139$	−834.466			−0.509198			−0.254599	+	0.967047i	$0.581943\pi$
$140$		0			0
$141$	−695.370			−0.415324
$142$	262.320	−	454.351i	0.155024	−	0.268509i
$143$	421.452	+	729.977i	0.246459	+	0.426879i
$144$	227.973	+	394.861i	0.131929	+	0.228507i
$145$	−177.793	+	307.946i	−0.101827	+	0.176369i
$146$	−1382.75			−0.783817
$147$		0			0
$148$	−385.554			−0.214137
$149$	122.129	−	211.534i	0.0671491	−	0.116306i	−0.830496	−	0.557024i	$-0.811943\pi$
$149$	122.129	−	211.534i	0.0671491	−	0.116306i	0.897645	+	0.440719i	$0.145276\pi$
$150$	−221.850	−	384.255i	−0.120760	−	0.209162i
$151$	401.079	+	694.689i	0.216155	+	0.374391i	0.953629	−	0.300984i	$-0.0973152\pi$
$151$	401.079	+	694.689i	0.216155	+	0.374391i	−0.737475	+	0.675375i	$0.763982\pi$
$152$	72.6325	−	125.803i	0.0387584	−	0.0671315i
$153$	8668.38			4.58037
$154$		0			0
$155$	624.618			0.323681
$156$	−493.018	+	853.933i	−0.253032	+	0.438265i
$157$	1770.69	+	3066.93i	0.900105	+	1.55903i	0.827356	+	0.561677i	$0.189844\pi$
$157$	1770.69	+	3066.93i	0.900105	+	1.55903i	0.0727488	+	0.997350i	$0.476823\pi$
$158$	551.666	+	955.513i	0.277773	+	0.481117i
$159$	1729.35	−	2995.32i	0.862554	−	1.49399i
$160$	866.896			0.428339
$161$		0			0
$162$	−3039.45			−1.47408
$163$	1107.28	−	1917.87i	0.532081	−	0.921591i	−0.467218	−	0.884142i	$-0.654744\pi$
$163$	1107.28	−	1917.87i	0.532081	−	0.921591i	0.999299	−	0.0374489i	$-0.0119232\pi$
$164$	−210.020	−	363.766i	−0.0999990	−	0.173203i
$165$	881.653	+	1527.07i	0.415979	+	0.720497i
$166$	459.135	−	795.246i	0.214674	−	0.371826i
$167$	2617.07			1.21266			0.606332	−	0.795212i	$-0.292640\pi$
$167$	2617.07			1.21266			0.606332	+	0.795212i	$0.292640\pi$
$168$		0			0
$169$	−1677.47			−0.763530
$170$	−630.750	+	1092.49i	−0.284567	+	0.492884i
$171$	199.058	+	344.779i	0.0890197	+	0.154187i
$172$	679.729	+	1177.32i	0.301330	+	0.521920i
$173$	−817.019	+	1415.12i	−0.359057	+	0.621905i	−0.987804	−	0.155706i	$-0.950235\pi$
$173$	−817.019	+	1415.12i	−0.359057	+	0.621905i	0.628747	+	0.777610i	$0.283568\pi$
$174$	−1262.19			−0.549920
$175$		0			0
$176$	263.695			0.112936
$177$	1790.58	−	3101.37i	0.760384	−	1.31702i
$178$	−896.092	−	1552.08i	−0.377331	−	0.653556i
$179$	−484.580	−	839.317i	−0.202342	−	0.350467i	0.746941	−	0.664891i	$-0.231522\pi$
$179$	−484.580	−	839.317i	−0.202342	−	0.350467i	−0.949283	+	0.314424i	$0.898189\pi$
$180$	−725.161	+	1256.02i	−0.300279	+	0.520099i
$181$	−4358.20			−1.78974			−0.894869	−	0.446329i	$-0.852731\pi$
$181$	−4358.20			−1.78974			−0.894869	+	0.446329i	$0.852731\pi$
$182$		0			0
$183$	6576.37			2.65650
$184$	568.579	−	984.807i	0.227805	−	0.394570i
$185$	212.480	+	368.026i	0.0844423	+	0.146258i
$186$	1108.57	+	1920.10i	0.437013	+	0.756929i
$187$	2506.66	−	4341.67i	0.980243	−	1.69783i
$188$	−330.781			−0.128323
$189$		0			0
$190$	−57.9375			−0.0221223
$191$	−1454.99	+	2520.11i	−0.551199	+	0.954705i	0.446989	+	0.894539i	$0.352496\pi$
$191$	−1454.99	+	2520.11i	−0.551199	+	0.954705i	−0.998188	+	0.0601658i	$0.980837\pi$
$192$	1810.57	+	3135.99i	0.680554	+	1.17875i
$193$	1859.62	+	3220.96i	0.693568	+	1.20130i	0.970661	+	0.240452i	$0.0772957\pi$
$193$	1859.62	+	3220.96i	0.693568	+	1.20130i	−0.277093	+	0.960843i	$0.589371\pi$
$194$	−689.298	+	1193.90i	−0.255097	+	0.441840i
$195$	1086.82			0.399120
$196$		0			0
$197$	−1550.03			−0.560582			−0.280291	−	0.959915i	$-0.590431\pi$
$197$	−1550.03			−0.560582			−0.280291	+	0.959915i	$0.590431\pi$
$198$	−2200.38	+	3811.18i	−0.789770	+	1.36792i
$199$	−1802.57	−	3122.14i	−0.642115	−	1.11218i	−0.984960	−	0.172784i	$-0.944724\pi$
$199$	−1802.57	−	3122.14i	−0.642115	−	1.11218i	0.342845	−	0.939392i	$-0.388610\pi$
$200$	−291.641	−	505.136i	−0.103111	−	0.178593i
$201$	−4637.49	+	8032.36i	−1.62738	+	2.81870i
$202$	1142.32			0.397889
$203$		0			0
$204$	5864.63			2.01278
$205$	−231.486	+	400.945i	−0.0788666	+	0.136601i
$206$	−749.546	−	1298.25i	−0.253512	−	0.439095i
$207$	1558.26	+	2698.98i	0.523220	+	0.906243i
$208$	81.2643	−	140.754i	0.0270897	−	0.0469208i
$209$	230.249			0.0762042
$210$		0			0
$211$	−3305.27			−1.07841			−0.539204	−	0.842175i	$-0.681275\pi$
$211$	−3305.27			−1.07841			−0.539204	+	0.842175i	$0.681275\pi$
$212$	822.634	−	1424.84i	0.266504	−	0.461598i
$213$	1344.15	+	2328.13i	0.432392	+	0.748925i
$214$	−1797.16	−	3112.77i	−0.574071	−	0.994320i
$215$	749.201	−	1297.65i	0.237652	−	0.411625i
$216$	−8219.44			−2.58918
$217$		0			0
$218$	−198.135			−0.0615567
$219$	3542.66	−	6136.07i	1.09311	−	1.89332i
$220$	419.394	+	726.412i	0.128525	+	0.222612i
$221$	−1544.98	−	2675.99i	−0.470257	−	0.814510i
$222$	−754.218	+	1306.34i	−0.228017	+	0.394937i
$223$	−3451.37			−1.03642			−0.518209	−	0.855254i	$-0.673401\pi$
$223$	−3451.37			−1.03642			−0.518209	+	0.855254i	$0.673401\pi$
$224$		0			0
$225$	1598.55			0.473645
$226$	287.609	−	498.153i	0.0846525	−	0.146622i
$227$	1023.62	+	1772.96i	0.299296	+	0.518395i	0.975975	−	0.217883i	$-0.0699150\pi$
$227$	1023.62	+	1772.96i	0.299296	+	0.518395i	−0.676679	+	0.736278i	$0.736582\pi$
$228$	134.674	+	233.262i	0.0391184	+	0.0677550i
$229$	−693.708	+	1201.54i	−0.200181	+	0.346724i	−0.948587	−	0.316517i	$-0.897486\pi$
$229$	−693.708	+	1201.54i	−0.200181	+	0.346724i	0.748405	+	0.663241i	$0.230820\pi$
$230$	−453.544			−0.130025
$231$		0			0
$232$	−1659.25			−0.469549
$233$	187.497	−	324.754i	0.0527181	−	0.0913104i	−0.838462	−	0.544960i	$-0.816545\pi$
$233$	187.497	−	324.754i	0.0527181	−	0.0913104i	0.891180	+	0.453650i	$0.149878\pi$
$234$	1356.21	+	2349.02i	0.378881	+	0.656241i
$235$	182.295	+	315.743i	0.0506025	+	0.0876461i
$236$	851.760	−	1475.29i	0.234936	−	0.406921i
$237$	−5653.56			−1.54953
$238$		0			0
$239$	−5560.93			−1.50505			−0.752525	−	0.658564i	$-0.771164\pi$
$239$	−5560.93			−1.50505			−0.752525	+	0.658564i	$0.771164\pi$
$240$	170.000	−	294.449i	0.0457227	−	0.0791941i
$241$	2353.10	+	4075.68i	0.628947	+	1.08937i	0.987763	+	0.155960i	$0.0498472\pi$
$241$	2353.10	+	4075.68i	0.628947	+	1.08937i	−0.358816	+	0.933408i	$0.616819\pi$
$242$	34.0322	+	58.9455i	0.00903997	+	0.0156577i
$243$	3031.22	−	5250.23i	0.800218	−	1.38602i
$244$	3128.32			0.820779
$245$		0			0
$246$	−1643.36			−0.425922
$247$	70.9572	−	122.901i	0.0182789	−	0.0316601i
$248$	1457.31	+	2524.14i	0.373143	+	0.646303i
$249$	2352.65	+	4074.90i	0.598767	+	1.03709i
$250$	−116.318	+	201.469i	−0.0294264	+	0.0509680i
$251$	−589.085			−0.148138			−0.0740692	−	0.997253i	$-0.523599\pi$
$251$	−589.085			−0.148138			−0.0740692	+	0.997253i	$0.523599\pi$
$252$		0			0
$253$	1802.43			0.447896
$254$	−185.616	+	321.496i	−0.0458526	+	0.0794191i
$255$	−3232.01	−	5598.01i	−0.793712	−	1.37475i
$256$	2151.97	+	3727.31i	0.525382	+	0.909989i
$257$	−2333.08	+	4041.01i	−0.566278	+	0.980822i	0.430652	+	0.902518i	$0.358284\pi$
$257$	−2333.08	+	4041.01i	−0.566278	+	0.980822i	−0.996930	+	0.0783038i	$0.975050\pi$
$258$	5318.72			1.28345
$259$		0			0
$260$	516.988			0.123316
$261$	2273.69	−	3938.15i	0.539226	−	0.933967i
$262$	−559.928	−	969.824i	−0.132032	−	0.228687i
$263$	2235.98	+	3872.83i	0.524246	+	0.908020i	0.999602	+	0.0282263i	$0.00898592\pi$
$263$	2235.98	+	3872.83i	0.524246	+	0.908020i	−0.475356	+	0.879794i	$0.657681\pi$
$264$	−4114.01	+	7125.68i	−0.959091	+	1.66119i
$265$	−1813.42			−0.420369
$266$		0			0
$267$	9183.29			2.10490
$268$	−2206.01	+	3820.92i	−0.502812	+	0.870895i
$269$	−2128.56	−	3686.78i	−0.482457	−	0.835640i	0.517340	−	0.855780i	$-0.326922\pi$
$269$	−2128.56	−	3686.78i	−0.482457	−	0.835640i	−0.999797	+	0.0201401i	$0.993589\pi$
$270$	1639.12	+	2839.04i	0.369458	+	0.639920i
$271$	−1934.35	+	3350.39i	−0.433591	+	0.751002i	−0.997179	−	0.0750540i	$-0.976087\pi$
$271$	−1934.35	+	3350.39i	−0.433591	+	0.751002i	0.563588	+	0.826056i	$0.309420\pi$
$272$	−966.668			−0.215488
$273$		0			0
$274$	−3893.78			−0.858510
$275$	462.259	−	800.656i	0.101365	−	0.175569i
$276$	1054.25	+	1826.01i	0.229921	+	0.398235i
$277$	−4103.65	−	7107.73i	−0.890124	−	1.54174i	−0.839726	−	0.543011i	$-0.817284\pi$
$277$	−4103.65	−	7107.73i	−0.890124	−	1.54174i	−0.0503982	−	0.998729i	$-0.516049\pi$
$278$	−776.507	+	1344.95i	−0.167524	+	0.290161i
$279$	−7987.88			−1.71406
$280$		0			0
$281$	6471.27			1.37382			0.686910	−	0.726743i	$-0.258967\pi$
$281$	6471.27			1.37382			0.686910	+	0.726743i	$0.258967\pi$
$282$	−647.072	+	1120.76i	−0.136640	+	0.236668i
$283$	735.401	+	1273.75i	0.154470	+	0.267550i	0.932866	−	0.360224i	$-0.117300\pi$
$283$	735.401	+	1273.75i	0.154470	+	0.267550i	−0.778396	+	0.627774i	$0.783966\pi$
$284$	639.398	+	1107.47i	0.133596	+	0.231395i
$285$	148.438	−	257.103i	0.0308517	−	0.0534366i
$286$	1568.72			0.324337
$287$		0			0
$288$	−11086.2			−2.26827
$289$	−6732.57	+	11661.2i	−1.37036	+	2.37353i
$290$	330.888	+	573.115i	0.0670014	+	0.116050i
$291$	−3532.02	−	6117.64i	−0.711514	−	1.23238i
$292$	1685.21	−	2918.87i	0.337738	−	0.584980i
$293$	5489.18			1.09448			0.547238	−	0.836977i	$-0.315679\pi$
$293$	5489.18			1.09448			0.547238	+	0.836977i	$0.315679\pi$
$294$		0			0
$295$	−1877.63			−0.370576
$296$	−991.484	+	1717.30i	−0.194692	+	0.337216i
$297$	−6514.02	−	11282.6i	−1.27267	−	2.20432i
$298$	−227.293	−	393.683i	−0.0441837	−	0.0765284i
$299$	555.464	−	962.092i	0.107436	−	0.186084i
$300$	1081.51			0.208136
$301$		0			0
$302$	1492.89			0.284457
$303$	−2926.68	+	5069.16i	−0.554896	+	0.961108i
$304$	−22.1983	−	38.4486i	−0.00418803	−	0.00725387i
$305$	−1724.03	−	2986.10i	−0.323664	−	0.560602i
$306$	8066.30	−	13971.2i	1.50693	−	2.61007i
$307$	−1035.35			−0.192477			−0.0962383	−	0.995358i	$-0.530681\pi$
$307$	−1035.35			−0.192477			−0.0962383	+	0.995358i	$0.530681\pi$
$308$		0			0
$309$	7681.47			1.41419
$310$	581.235	−	1006.73i	0.106490	−	0.184446i
$311$	1272.02	+	2203.20i	0.231928	+	0.401711i	0.958376	−	0.285511i	$-0.0921632\pi$
$311$	1272.02	+	2203.20i	0.231928	+	0.401711i	−0.726447	+	0.687222i	$0.758830\pi$
$312$	2535.68	+	4391.92i	0.460110	+	0.796934i
$313$	1299.86	−	2251.43i	0.234737	−	0.406576i	−0.724460	−	0.689317i	$-0.757911\pi$
$313$	1299.86	−	2251.43i	0.234737	−	0.406576i	0.959196	+	0.282742i	$0.0912439\pi$
$314$	6590.82			1.18453
$315$		0			0
$316$	−2689.35			−0.478758
$317$	1362.56	−	2360.03i	0.241417	−	0.418147i	−0.719701	−	0.694284i	$-0.755721\pi$
$317$	1362.56	−	2360.03i	0.241417	−	0.418147i	0.961118	+	0.276137i	$0.0890544\pi$
$318$	−3218.46	−	5574.54i	−0.567555	−	0.983034i
$319$	−1314.98	−	2277.62i	−0.230799	−	0.399755i
$320$	949.297	−	1644.23i	0.165835	−	0.287235i
$321$	18417.6			3.20239
$322$		0			0
$323$	−844.061			−0.145402
$324$	3704.29	−	6416.02i	0.635166	−	1.10014i
$325$	−284.914	−	493.485i	−0.0486282	−	0.0842265i
$326$	−2060.75	−	3569.33i	−0.350106	−	0.606401i
$327$	507.629	−	879.239i	0.0858469	−	0.148691i
$328$	−2160.34			−0.363673
$329$		0			0
$330$	3281.66			0.547423
$331$	2589.06	−	4484.39i	0.429933	−	0.744665i	−0.566934	−	0.823763i	$-0.691871\pi$
$331$	2589.06	−	4484.39i	0.429933	−	0.744665i	0.996867	+	0.0790979i	$0.0252040\pi$
$332$	1119.13	+	1938.39i	0.185001	+	0.320431i
$333$	−2717.28	−	4706.47i	−0.447166	−	0.774513i
$334$	2435.29	−	4218.05i	0.398962	−	0.691023i
$335$	4862.95			0.793109
$336$		0			0
$337$	−3656.07			−0.590975			−0.295488	−	0.955347i	$-0.595482\pi$
$337$	−3656.07			−0.590975			−0.295488	+	0.955347i	$0.595482\pi$
$338$	−1560.96	+	2703.67i	−0.251199	+	0.435089i
$339$	1473.73	+	2552.58i	0.236112	+	0.408959i
$340$	−1537.44	−	2662.92i	−0.245233	−	0.424757i
$341$	−2309.88	+	4000.83i	−0.366825	+	0.635359i
$342$	740.929			0.117149
$343$		0			0
$344$	6991.92			1.09587
$345$	1162.00	−	2012.64i	0.181333	−	0.314078i
$346$	1520.54	+	2633.66i	0.236257	+	0.409209i
$347$	836.575	+	1448.99i	0.129423	+	0.224167i	0.923453	−	0.383711i	$-0.125354\pi$
$347$	836.575	+	1448.99i	0.129423	+	0.224167i	−0.794030	+	0.607878i	$0.792021\pi$
$348$	1538.28	−	2664.37i	0.236955	−	0.410418i
$349$	−777.313			−0.119222			−0.0596112	−	0.998222i	$-0.518986\pi$
$349$	−777.313			−0.119222			−0.0596112	+	0.998222i	$0.518986\pi$
$350$		0			0
$351$	−8029.85			−1.22109
$352$	−3205.84	+	5552.68i	−0.485432	+	0.840793i
$353$	2211.46	+	3830.36i	0.333439	+	0.577534i	0.983184	−	0.182619i	$-0.0584574\pi$
$353$	2211.46	+	3830.36i	0.333439	+	0.577534i	−0.649744	+	0.760153i	$0.725124\pi$
$354$	−3332.42	−	5771.91i	−0.500327	−	0.866592i
$355$	704.749	−	1220.66i	0.105364	−	0.182496i
$356$	4368.41			0.650351
$357$		0			0
$358$	−1803.69			−0.266279
$359$	481.081	−	833.257i	0.0707256	−	0.122500i	−0.828494	−	0.559998i	$-0.810802\pi$
$359$	481.081	−	833.257i	0.0707256	−	0.122500i	0.899220	+	0.437498i	$0.144135\pi$
$360$	3729.62	+	6459.90i	0.546023	+	0.945740i
$361$	3410.12	+	5906.50i	0.497174	+	0.861131i
$362$	−4055.49	+	7024.32i	−0.588818	+	1.01986i
$363$	−348.767			−0.0504285
$364$		0			0
$365$	−3714.90			−0.532731
$366$	6119.60	−	10599.5i	0.873980	−	1.51378i
$367$	−3641.34	−	6306.98i	−0.517919	−	0.897062i	−0.999783	−	0.0208164i	$-0.993373\pi$
$367$	−3641.34	−	6306.98i	−0.517919	−	0.897062i	0.481864	−	0.876246i	$-0.339960\pi$
$368$	−173.772	−	300.981i	−0.0246154	−	0.0426352i
$369$	2960.34	−	5127.45i	0.417639	−	0.723373i
$370$	790.887			0.111125
$371$		0			0
$372$	−5404.24			−0.753217
$373$	574.619	−	995.269i	0.0797658	−	0.138158i	−0.823383	−	0.567486i	$-0.807916\pi$
$373$	574.619	−	995.269i	0.0797658	−	0.138158i	0.903149	+	0.429328i	$0.141249\pi$
$374$	−4665.12	−	8080.22i	−0.644993	−	1.11716i
$375$	−596.022	−	1032.34i	−0.0820759	−	0.142160i
$376$	−850.632	+	1473.34i	−0.116670	+	0.202079i
$377$	−1620.98			−0.221445
$378$		0			0
$379$	−10452.6			−1.41666			−0.708332	−	0.705879i	$-0.750552\pi$
$379$	−10452.6			−1.41666			−0.708332	+	0.705879i	$0.750552\pi$
$380$	70.6107	−	122.301i	0.00953224	−	0.0165103i
$381$	−951.110	−	1647.37i	−0.127892	−	0.221515i
$382$	2707.85	+	4690.14i	0.362686	+	0.628190i
$383$	−6734.64	+	11664.7i	−0.898496	+	1.55624i	−0.0690786	+	0.997611i	$0.522006\pi$
$383$	−6734.64	+	11664.7i	−0.898496	+	1.55624i	−0.829417	+	0.558629i	$0.811327\pi$
$384$	−6488.01			−0.862214
$385$		0			0
$386$	6921.84			0.912727
$387$	−9581.10	+	16595.0i	−1.25849	+	2.17976i
$388$	−1680.15	−	2910.10i	−0.219837	−	0.380768i
$389$	−5317.73	−	9210.58i	−0.693110	−	1.20050i	−0.970814	−	0.239835i	$-0.922907\pi$
$389$	−5317.73	−	9210.58i	−0.693110	−	1.20050i	0.277704	−	0.960667i	$-0.410427\pi$
$390$	1011.33	−	1751.67i	0.131309	−	0.227434i
$391$	−6607.44			−0.854611
$392$		0			0
$393$	5738.23			0.736528
$394$	−1442.37	+	2498.25i	−0.184430	+	0.319442i
$395$	1482.11	+	2567.08i	0.188792	+	0.326998i
$396$	−5363.39	−	9289.66i	−0.680607	−	1.17885i
$397$	515.966	−	893.679i	0.0652282	−	0.112979i	−0.831567	−	0.555424i	$-0.812556\pi$
$397$	515.966	−	893.679i	0.0652282	−	0.112979i	0.896795	+	0.442446i	$0.145889\pi$
$398$	−6709.48			−0.845015
$399$		0			0
$400$	−178.265			−0.0222831
$401$	3234.48	−	5602.28i	0.402798	−	0.697667i	−0.591264	−	0.806478i	$-0.701371\pi$
$401$	3234.48	−	5602.28i	0.402798	−	0.697667i	0.994062	+	0.108811i	$0.0347043\pi$
$402$	8630.76	+	14948.9i	1.07080	+	1.85469i
$403$	1423.70	+	2465.92i	0.175979	+	0.304804i
$404$	−1392.20	+	2411.35i	−0.171446	+	0.296954i
$405$	−8165.78			−1.00188
$406$		0			0
$407$	−3143.06			−0.382791
$408$	15081.4	−	26121.7i	1.83000	−	3.16965i
$409$	−4326.09	−	7493.01i	−0.523011	−	0.905881i	−0.999641	−	0.0267777i	$-0.991475\pi$
$409$	−4326.09	−	7493.01i	−0.523011	−	0.905881i	0.476630	−	0.879104i	$-0.341858\pi$
$410$	430.815	+	746.193i	0.0518937	+	0.0898826i
$411$	9976.02	−	17279.0i	1.19728	−	2.07374i
$412$	3654.01			0.436942
$413$		0			0
$414$	5800.11			0.688550
$415$	1233.51	−	2136.51i	0.145906	−	0.252716i
$416$	1975.93	+	3422.40i	0.232879	+	0.403358i
$417$	−3978.88	−	6891.63i	−0.467258	−	0.809315i
$418$	214.257	−	371.104i	0.0250709	−	0.0434241i
$419$	−7303.41			−0.851539			−0.425770	−	0.904832i	$-0.639997\pi$
$419$	−7303.41			−0.851539			−0.425770	+	0.904832i	$0.639997\pi$
$420$		0			0
$421$	−11599.8			−1.34285			−0.671425	−	0.741072i	$-0.734317\pi$
$421$	−11599.8			−1.34285			−0.671425	+	0.741072i	$0.734317\pi$
$422$	−3075.70	+	5327.26i	−0.354793	+	0.614519i
$423$	−2331.26	−	4037.86i	−0.267966	−	0.464131i
$424$	−4230.95	−	7328.21i	−0.484606	−	0.839362i
$425$	−1694.58	+	2935.09i	−0.193409	+	0.334995i
$426$	5003.15			0.569022
$427$		0			0
$428$	8761.06			0.989444
$429$	−4019.12	+	6961.32i	−0.452319	+	0.783440i
$430$	−1394.33	−	2415.05i	−0.156373	−	0.270846i
$431$	753.434	+	1304.99i	0.0842034	+	0.145845i	0.905051	−	0.425302i	$-0.139832\pi$
$431$	753.434	+	1304.99i	0.0842034	+	0.145845i	−0.820848	+	0.571147i	$0.806499\pi$
$432$	−1256.03	+	2175.51i	−0.139886	+	0.242290i
$433$	−2112.02			−0.234405			−0.117203	−	0.993108i	$-0.537393\pi$
$433$	−2112.02			−0.234405			−0.117203	+	0.993108i	$0.537393\pi$
$434$		0			0
$435$	−3390.99			−0.373760
$436$	241.474	−	418.246i	0.0265241	−	0.0459411i
$437$	−151.732	−	262.807i	−0.0166094	−	0.0287683i
$438$	−6593.20	−	11419.8i	−0.719259	−	1.24579i
$439$	−1746.44	+	3024.92i	−0.189870	+	0.328865i	−0.945207	−	0.326472i	$-0.894140\pi$
$439$	−1746.44	+	3024.92i	−0.189870	+	0.328865i	0.755337	+	0.655337i	$0.227473\pi$
$440$	4314.03			0.467417
$441$		0			0
$442$	−5750.70			−0.618853
$443$	−487.337	+	844.093i	−0.0522666	+	0.0905283i	−0.890975	−	0.454052i	$-0.849978\pi$
$443$	−487.337	+	844.093i	−0.0522666	+	0.0905283i	0.838708	+	0.544581i	$0.183311\pi$
$444$	−1838.39	−	3184.18i	−0.196500	−	0.340348i
$445$	−2407.44	−	4169.81i	−0.256458	−	0.444198i
$446$	−3211.65	+	5562.74i	−0.340978	+	0.590591i
$447$	2329.34			0.246474
$448$		0			0
$449$	6113.63			0.642584			0.321292	−	0.946980i	$-0.395883\pi$
$449$	6113.63			0.642584			0.321292	+	0.946980i	$0.395883\pi$
$450$	1487.52	−	2576.46i	0.155828	−	0.269902i
$451$	−1712.10	−	2965.44i	−0.178758	−	0.309617i
$452$	701.040	+	1214.24i	0.0729517	+	0.126356i
$453$	−3824.83	+	6624.80i	−0.396703	+	0.687109i
$454$	3810.09			0.393869
$455$		0			0
$456$	1385.30			0.142264
$457$	776.754	−	1345.38i	0.0795077	−	0.137711i	−0.823530	−	0.567273i	$-0.807999\pi$
$457$	776.754	−	1345.38i	0.0795077	−	0.137711i	0.903038	+	0.429561i	$0.141332\pi$
$458$	1291.05	+	2236.16i	0.131718	+	0.228142i
$459$	23879.5	+	41360.5i	2.42832	+	4.20597i
$460$	552.751	−	957.394i	0.0560265	−	0.0970407i
$461$	−9419.28			−0.951626			−0.475813	−	0.879546i	$-0.657846\pi$
$461$	−9419.28			−0.951626			−0.475813	+	0.879546i	$0.657846\pi$
$462$		0			0
$463$	−11458.4			−1.15014			−0.575070	−	0.818104i	$-0.695025\pi$
$463$	−11458.4			−1.15014			−0.575070	+	0.818104i	$0.695025\pi$
$464$	−253.554	+	439.169i	−0.0253685	+	0.0439395i
$465$	2978.29	+	5158.55i	0.297022	+	0.514456i
$466$	−348.947	−	604.395i	−0.0346882	−	0.0600816i
$467$	1060.54	−	1836.91i	0.105087	−	0.182017i	−0.808686	−	0.588240i	$-0.799821\pi$
$467$	1060.54	−	1836.91i	0.105087	−	0.182017i	0.913774	+	0.406223i	$0.133154\pi$
$468$	−6611.46			−0.653023
$469$		0			0
$470$	678.532			0.0665922
$471$	−16885.9	+	29247.3i	−1.65194	+	2.86124i
$472$	−4380.75	−	7587.67i	−0.427204	−	0.739939i
$473$	5541.20	+	9597.64i	0.538657	+	0.932980i
$474$	−5260.88	+	9112.11i	−0.509790	+	0.882982i
$475$	−155.655			−0.0150357
$476$		0			0
$477$	23190.8			2.22607
$478$	−5174.69	+	8962.82i	−0.495156	+	0.857636i
$479$	8630.62	+	14948.7i	0.823263	+	1.42593i	0.903239	+	0.429137i	$0.141182\pi$
$479$	8630.62	+	14948.7i	0.823263	+	1.42593i	−0.0799760	+	0.996797i	$0.525484\pi$
$480$	4133.52	+	7159.46i	0.393059	+	0.680798i
$481$	−968.615	+	1677.69i	−0.0918192	+	0.159035i
$482$	8758.63			0.827686
$483$		0			0
$484$	−165.905			−0.0155809
$485$	−1851.87	+	3207.53i	−0.173380	+	0.300302i
$486$	−5641.37	−	9771.14i	−0.526539	−	0.911991i
$487$	9258.38	+	16036.0i	0.861473	+	1.49211i	0.870507	+	0.492155i	$0.163791\pi$
$487$	9258.38	+	16036.0i	0.861473	+	1.49211i	−0.00903482	+	0.999959i	$0.502876\pi$
$488$	8044.74	−	13933.9i	0.746246	−	1.29254i
$489$	21118.9			1.95303
$490$		0			0
$491$	7914.77			0.727472			0.363736	−	0.931502i	$-0.381501\pi$
$491$	7914.77			0.727472			0.363736	+	0.931502i	$0.381501\pi$
$492$	2002.83	−	3469.00i	0.183525	−	0.317875i
$493$	4820.54	+	8349.41i	0.440377	+	0.762756i
$494$	−132.058	−	228.730i	−0.0120274	−	0.0208321i
$495$	−5911.56	+	10239.1i	−0.536778	+	0.929726i
$496$	890.782			0.0806397
$497$		0			0
$498$	8756.96			0.787969
$499$	−1194.46	+	2068.86i	−0.107157	+	0.185601i	−0.914617	−	0.404321i	$-0.867508\pi$
$499$	−1194.46	+	2068.86i	−0.107157	+	0.185601i	0.807461	+	0.589922i	$0.200841\pi$
$500$	−283.522	−	491.075i	−0.0253590	−	0.0439231i
$501$	12478.6	+	21613.6i	1.11278	+	1.92740i
$502$	−548.169	+	949.457i	−0.0487370	+	0.0844150i
$503$	−18073.0			−1.60206			−0.801030	−	0.598624i	$-0.795715\pi$
$503$	−18073.0			−1.60206			−0.801030	+	0.598624i	$0.795715\pi$
$504$		0			0
$505$	3068.97			0.270431
$506$	1677.24	−	2905.06i	0.147356	−	0.255229i
$507$	−7998.50	−	13853.8i	−0.700643	−	1.21355i
$508$	−452.434	−	783.639i	−0.0395148	−	0.0684417i
$509$	9335.85	−	16170.2i	0.812975	−	1.40811i	−0.0977979	−	0.995206i	$-0.531180\pi$
$509$	9335.85	−	16170.2i	0.812975	−	1.40811i	0.910773	−	0.412908i	$-0.135487\pi$
$510$	−12030.1			−1.04451
$511$		0			0
$512$	2567.23			0.221595
$513$	−1096.72	+	1899.58i	−0.0943890	+	0.163487i
$514$	4342.06	+	7520.67i	0.372607	+	0.645374i
$515$	−2013.73	−	3487.89i	−0.172302	−	0.298436i
$516$	−6482.14	+	11227.4i	−0.553024	+	0.957865i
$517$	−2696.55			−0.229389
$518$		0			0
$519$	−15582.8			−1.31793
$520$	1329.48	−	2302.72i	0.112118	−	0.194194i
$521$	−1763.02	−	3053.64i	−0.148252	−	0.256780i	0.782330	−	0.622865i	$-0.214031\pi$
$521$	−1763.02	−	3053.64i	−0.148252	−	0.256780i	−0.930581	+	0.366085i	$0.880698\pi$
$522$	−4231.54	−	7329.24i	−0.354807	−	0.614544i
$523$	−5483.13	+	9497.05i	−0.458433	+	0.794029i	−0.998878	−	0.0473502i	$-0.984922\pi$
$523$	−5483.13	+	9497.05i	−0.458433	+	0.794029i	0.540446	+	0.841379i	$0.318256\pi$
$524$	2729.62			0.227565
$525$		0			0
$526$	8322.71			0.689900
$527$	8467.70	−	14666.5i	0.699922	−	1.21230i
$528$	1257.34	+	2177.78i	0.103634	+	0.179500i
$529$	4895.72	+	8479.64i	0.402377	+	0.696938i
$530$	−1687.47	+	2922.78i	−0.138300	+	0.239543i
$531$	24011.9			1.96239
$532$		0			0
$533$	−2110.51			−0.171513
$534$	8545.45	−	14801.2i	0.692505	−	1.19945i
$535$	−4828.25	−	8362.77i	−0.390174	−	0.675802i
$536$	11345.9	+	19651.6i	0.914305	+	1.58362i
$537$	4621.13	−	8004.03i	0.371353	−	0.643202i
$538$	−7922.88			−0.634907
$539$		0			0
$540$	−7990.64			−0.636782
$541$	−5674.90	+	9829.22i	−0.450985	+	0.781130i	−0.998447	−	0.0557009i	$-0.982261\pi$
$541$	−5674.90	+	9829.22i	−0.450985	+	0.781130i	0.547462	+	0.836830i	$0.315594\pi$
$542$	3599.99	+	6235.36i	0.285300	+	0.494154i
$543$	−20780.7	−	35993.2i	−1.64233	−	2.84460i
$544$	11752.2	−	20355.4i	0.926232	−	1.60428i
$545$	−532.309			−0.0418378
$546$		0			0
$547$	11206.1			0.875940			0.437970	−	0.898989i	$-0.355698\pi$
$547$	11206.1			0.875940			0.437970	+	0.898989i	$0.355698\pi$
$548$	4745.50	−	8219.44i	0.369923	−	0.640725i
$549$	22047.6	+	38187.5i	1.71397	+	2.96868i
$550$	−860.304	−	1490.09i	−0.0666972	−	0.115523i
$551$	−221.395	+	383.467i	−0.0171175	+	0.0296484i
$552$	10844.3			0.836170
$553$		0			0
$554$	−15274.5			−1.17139
$555$	−2026.28	+	3509.63i	−0.154975	+	0.268424i
$556$	−1892.72	−	3278.28i	−0.144369	−	0.250054i
$557$	−6315.49	−	10938.8i	−0.480424	−	0.832118i	0.519324	−	0.854577i	$-0.326184\pi$
$557$	−6315.49	−	10938.8i	−0.480424	−	0.832118i	−0.999748	+	0.0224592i	$0.992850\pi$
$558$	−7433.07	+	12874.5i	−0.563919	+	0.976737i
$559$	6830.65			0.516826
$560$		0			0
$561$	47808.9			3.59803
$562$	6021.79	−	10430.1i	0.451982	−	0.782856i
$563$	3500.34	+	6062.78i	0.262028	+	0.453846i	0.966781	−	0.255607i	$-0.0822753\pi$
$563$	3500.34	+	6062.78i	0.262028	+	0.453846i	−0.704752	+	0.709453i	$0.748942\pi$
$564$	−1577.22	−	2731.83i	−0.117754	−	0.203956i
$565$	772.691	−	1338.34i	0.0575351	−	0.0996538i
$566$	2737.29			0.203281
$567$		0			0
$568$	6577.07			0.485858
$569$	4329.63	−	7499.13i	0.318994	−	0.552513i	−0.661285	−	0.750135i	$-0.729988\pi$
$569$	4329.63	−	7499.13i	0.318994	−	0.552513i	0.980278	+	0.197622i	$0.0633218\pi$
$570$	−276.256	−	478.490i	−0.0203002	−	0.0351610i
$571$	−12815.9	−	22197.9i	−0.939283	−	1.62689i	−0.766813	−	0.641870i	$-0.778159\pi$
$571$	−12815.9	−	22197.9i	−0.939283	−	1.62689i	−0.172469	−	0.985015i	$-0.555175\pi$
$572$	−1911.86	+	3311.44i	−0.139753	+	0.242060i
$573$	−27750.5			−2.02320
$574$		0			0
$575$	−1218.49			−0.0883733
$576$	−12140.0	+	21027.1i	−0.878183	+	1.52106i
$577$	1273.42	+	2205.63i	0.0918775	+	0.159137i	0.908301	−	0.418317i	$-0.137380\pi$
$577$	1273.42	+	2205.63i	0.0918775	+	0.159137i	−0.816424	+	0.577453i	$0.804047\pi$
$578$	12529.9	+	21702.4i	0.901687	+	1.56177i
$579$	−17734.0	+	30716.3i	−1.27289	+	2.20470i
$580$	−1613.06			−0.115481
$581$		0			0
$582$	−13146.8			−0.936344
$583$	6706.17	−	11615.4i	0.476400	−	0.825149i
$584$	−8667.33	−	15012.3i	−0.614138	−	1.06372i
$585$	3643.60	+	6310.89i	0.257511	+	0.446023i
$586$	5107.92	−	8847.18i	0.360079	−	0.623675i
$587$	−17798.8			−1.25150			−0.625752	−	0.780022i	$-0.715208\pi$
$587$	−17798.8			−1.25150			−0.625752	+	0.780022i	$0.715208\pi$
$588$		0			0
$589$	777.800			0.0544121
$590$	−1747.22	+	3026.27i	−0.121918	+	0.211169i
$591$	−7390.80	−	12801.2i	−0.514411	−	0.890986i
$592$	303.022	+	524.849i	0.0210374	+	0.0364378i
$593$	1595.64	−	2763.73i	0.110498	−	0.191388i	−0.805473	−	0.592632i	$-0.798089\pi$
$593$	1595.64	−	2763.73i	0.110498	−	0.191388i	0.915971	+	0.401244i	$0.131422\pi$
$594$	−24246.3			−1.67481
$595$		0			0
$596$	1108.04			0.0761531
$597$	17190.0	−	29773.9i	1.17846	−	2.04115i
$598$	−1033.77	−	1790.54i	−0.0706921	−	0.122442i
$599$	−10255.9	−	17763.7i	−0.699571	−	1.21169i	−0.968615	−	0.248565i	$-0.920041\pi$
$599$	−10255.9	−	17763.7i	−0.699571	−	1.21169i	0.269044	−	0.963128i	$-0.413292\pi$
$600$	2781.19	−	4817.16i	0.189236	−	0.327766i
$601$	−22802.2			−1.54762			−0.773810	−	0.633418i	$-0.781651\pi$
$601$	−22802.2			−1.54762			−0.773810	+	0.633418i	$0.781651\pi$
$602$		0			0
$603$	−62189.5			−4.19992
$604$	−1819.44	+	3151.36i	−0.122569	+	0.212296i
$605$	91.4310	+	158.363i	0.00614413	+	0.0106419i
$606$	5446.81	+	9434.15i	0.365118	+	0.632403i
$607$	1565.07	−	2710.79i	0.104653	−	0.181264i	−0.808943	−	0.587887i	$-0.799960\pi$
$607$	1565.07	−	2710.79i	0.104653	−	0.181264i	0.913596	+	0.406622i	$0.133293\pi$
$608$	1079.49			0.0720054
$609$		0			0
$610$	−6417.12			−0.425937
$611$	−831.011	+	1439.35i	−0.0550231	+	0.0953028i
$612$	19661.4	+	34054.6i	1.29864	+	2.24931i
$613$	6368.05	+	11029.8i	0.419581	+	0.726736i	0.995897	−	0.0904910i	$-0.0288436\pi$
$613$	6368.05	+	11029.8i	0.419581	+	0.726736i	−0.576316	+	0.817227i	$0.695510\pi$
$614$	−963.435	+	1668.72i	−0.0633242	+	0.109681i
$615$	−4415.06			−0.289484
$616$		0			0
$617$	−16662.4			−1.08720			−0.543600	−	0.839345i	$-0.682939\pi$
$617$	−16662.4			−1.08720			−0.543600	+	0.839345i	$0.682939\pi$
$618$	7147.94	−	12380.6i	0.465263	−	0.805859i
$619$	−4983.86	−	8632.31i	−0.323616	−	0.560520i	0.657615	−	0.753354i	$-0.271565\pi$
$619$	−4983.86	−	8632.31i	−0.323616	−	0.560520i	−0.981231	+	0.192834i	$0.938232\pi$
$620$	1416.75	+	2453.88i	0.0917708	+	0.158952i
$621$	−8585.33	+	14870.2i	−0.554778	+	0.960904i
$622$	4734.68			0.305215
$623$		0			0
$624$	1549.93			0.0994341
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−2419.16	−	4190.10i	−0.154455	−	0.267524i
$627$	1097.87	+	1901.57i	0.0699278	+	0.121118i
$628$	−8032.49	+	13912.7i	−0.510400	+	0.884038i
$629$	11522.0			0.730386
$630$		0			0
$631$	−6243.76			−0.393914			−0.196957	−	0.980412i	$-0.563106\pi$
$631$	−6243.76			−0.393914			−0.196957	+	0.980412i	$0.563106\pi$
$632$	−6915.88	+	11978.7i	−0.435283	+	0.753932i
$633$	−15760.1	−	27297.3i	−0.989587	−	1.71401i
$634$	−2535.85	−	4392.22i	−0.158851	−	0.275138i
$635$	−498.676	+	863.732i	−0.0311643	+	0.0539782i
$636$	15689.9			0.978214
$637$		0			0
$638$	−4894.59			−0.303728
$639$	−9012.63	+	15610.3i	−0.557956	+	0.966408i
$640$	1700.86	+	2945.98i	0.105051	+	0.181953i
$641$	12957.9	+	22443.8i	0.798452	+	1.38296i	0.920624	+	0.390450i	$0.127681\pi$
$641$	12957.9	+	22443.8i	0.798452	+	1.38296i	−0.122172	+	0.992509i	$0.538986\pi$
$642$	17138.3	−	29684.5i	1.05358	−	1.82485i
$643$	−11833.7			−0.725778			−0.362889	−	0.931832i	$-0.618210\pi$
$643$	−11833.7			−0.725778			−0.362889	+	0.931832i	$0.618210\pi$
$644$		0			0
$645$	14289.3			0.872311
$646$	−785.436	+	1360.41i	−0.0478368	+	0.0828557i
$647$	3634.27	+	6294.74i	0.220831	+	0.382491i	0.955061	−	0.296411i	$-0.0957897\pi$
$647$	3634.27	+	6294.74i	0.220831	+	0.382491i	−0.734229	+	0.678901i	$0.762456\pi$
$648$	−19051.8	−	32998.7i	−1.15498	−	2.00048i
$649$	6943.61	−	12026.7i	0.419970	−	0.727409i
$650$	−1060.50			−0.0639941
$651$		0			0
$652$	10046.1			0.603427
$653$	15227.9	−	26375.5i	0.912577	−	1.58063i	0.102167	−	0.994767i	$-0.467422\pi$
$653$	15227.9	−	26375.5i	0.912577	−	1.58063i	0.810410	−	0.585863i	$-0.199244\pi$
$654$	−944.741	−	1636.34i	−0.0564867	−	0.0978378i
$655$	−1504.30	−	2605.53i	−0.0897374	−	0.155430i
$656$	−330.127	+	571.796i	−0.0196483	+	0.0340318i
$657$	47507.7			2.82109
$658$		0			0
$659$	16170.2			0.955843			0.477922	−	0.878403i	$-0.341390\pi$
$659$	16170.2			0.955843			0.477922	+	0.878403i	$0.341390\pi$
$660$	−3999.49	+	6927.32i	−0.235879	+	0.408554i
$661$	5165.93	+	8947.65i	0.303981	+	0.526510i	0.977034	−	0.213084i	$-0.0683507\pi$
$661$	5165.93	+	8947.65i	0.303981	+	0.526510i	−0.673053	+	0.739594i	$0.735017\pi$
$662$	−4818.47	−	8345.83i	−0.282893	−	0.489985i
$663$	14733.5	−	25519.2i	0.863051	−	1.49485i
$664$	11511.8			0.672806
$665$		0			0
$666$	−10114.2			−0.588464
$667$	−1733.11	+	3001.84i	−0.100609	+	0.174261i
$668$	5935.98	+	10281.4i	0.343817	+	0.595509i
$669$	−16456.8	−	28504.0i	−0.951054	−	1.64727i
$670$	4525.19	−	7837.86i	0.260930	−	0.451945i
$671$	25502.3			1.46722
$672$		0			0
$673$	18387.1			1.05315			0.526576	−	0.850128i	$-0.323475\pi$
$673$	18387.1			1.05315			0.526576	+	0.850128i	$0.323475\pi$
$674$	−3402.13	+	5892.66i	−0.194429	+	0.336761i
$675$	4403.66	+	7627.37i	0.251107	+	0.434930i
$676$	−3804.81	−	6590.13i	−0.216478	−	0.374950i
$677$	−897.961	+	1555.31i	−0.0509770	+	0.0882948i	−0.890388	−	0.455203i	$-0.849567\pi$
$677$	−897.961	+	1555.31i	−0.0509770	+	0.0882948i	0.839411	+	0.543497i	$0.182900\pi$
$678$	5485.48			0.310721
$679$		0			0
$680$	−15814.6			−0.891857
$681$	−9761.62	+	16907.6i	−0.549289	+	0.951397i
$682$	4298.89	+	7445.90i	0.241368	+	0.418062i
$683$	2601.93	+	4506.67i	0.145769	+	0.252479i	0.929659	−	0.368420i	$-0.120101\pi$
$683$	2601.93	+	4506.67i	0.145769	+	0.252479i	−0.783891	+	0.620899i	$0.786768\pi$
$684$	−902.999	+	1564.04i	−0.0504781	+	0.0874307i
$685$	−10461.0			−0.583497
$686$		0			0
$687$	−13230.9			−0.734774
$688$	1068.45	−	1850.61i	0.0592069	−	0.102549i
$689$	−4133.36	−	7159.18i	−0.228546	−	0.395854i
$690$	−2162.58	−	3745.69i	−0.119316	−	0.206661i
$691$	−4451.78	+	7710.71i	−0.245085	+	0.424500i	−0.962155	−	0.272501i	$-0.912149\pi$
$691$	−4451.78	+	7710.71i	−0.245085	+	0.424500i	0.717071	+	0.697001i	$0.245483\pi$
$692$	−7412.58			−0.407202
$693$		0			0
$694$	3113.88			0.170319
$695$	−2086.16	+	3613.34i	−0.113860	+	0.197211i
$696$	−7911.61	−	13703.3i	−0.430875	−	0.746297i
$697$	6276.32	+	10870.9i	0.341080	+	0.590767i
$698$	−723.324	+	1252.83i	−0.0392238	+	0.0679376i
$699$	3576.07			0.193504
$700$		0			0
$701$	−8343.11			−0.449522			−0.224761	−	0.974414i	$-0.572160\pi$
$701$	−8343.11			−0.449522			−0.224761	+	0.974414i	$0.572160\pi$
$702$	−7472.12	+	12942.1i	−0.401734	+	0.695823i
$703$	264.589	+	458.281i	0.0141951	+	0.0245866i
$704$	7021.13	+	12161.0i	0.375879	+	0.651042i
$705$	−1738.43	+	3011.04i	−0.0928694	+	0.160854i
$706$	8231.43			0.438802
$707$		0			0
$708$	16245.4			0.862343
$709$	14295.0	−	24759.6i	0.757206	−	1.31152i	−0.187064	−	0.982348i	$-0.559897\pi$
$709$	14295.0	−	24759.6i	0.757206	−	1.31152i	0.944270	−	0.329172i	$-0.106769\pi$
$710$	−1311.60	−	2271.76i	−0.0693288	−	0.120081i
$711$	−18953.8	−	32829.0i	−0.999751	−	1.73162i
$712$	11233.7	−	19457.4i	0.591294	−	1.02415i
$713$	6088.74			0.319811
$714$		0			0
$715$	4214.52			0.220439
$716$	2198.23	−	3807.44i	0.114737	−	0.198730i
$717$	−26515.5	−	45926.2i	−1.38109	−	2.39211i
$718$	−895.334	−	1550.76i	−0.0465370	−	0.0806044i
$719$	13365.2	−	23149.2i	0.693237	−	1.20072i	−0.277535	−	0.960716i	$-0.589517\pi$
$719$	13365.2	−	23149.2i	0.693237	−	1.20072i	0.970771	−	0.240006i	$-0.0771493\pi$
$720$	2279.73			0.118001
$721$		0			0
$722$	12693.0			0.654275
$723$	−22440.0	+	38867.2i	−1.15429	+	1.99929i
$724$	−9885.18	−	17121.6i	−0.507431	−	0.878896i
$725$	888.965	+	1539.73i	0.0455384	+	0.0788748i
$726$	−324.543	+	562.125i	−0.0165908	+	0.0287361i
$727$	8903.62			0.454219			0.227109	−	0.973869i	$-0.427073\pi$
$727$	8903.62			0.454219			0.227109	+	0.973869i	$0.427073\pi$
$728$		0			0
$729$	13718.4			0.696969
$730$	−3456.88	+	5987.49i	−0.175267	+	0.303571i
$731$	−20313.2	−	35183.6i	−1.02779	−	1.78018i
$732$	14916.4	+	25835.9i	0.753177	+	1.30454i
$733$	−3011.28	+	5215.69i	−0.151738	+	0.262818i	−0.931867	−	0.362801i	$-0.881820\pi$
$733$	−3011.28	+	5215.69i	−0.151738	+	0.262818i	0.780128	+	0.625620i	$0.215154\pi$
$734$	−13553.7			−0.681575
$735$		0			0
$736$	8450.45			0.423217
$737$	−17983.5	+	31148.4i	−0.898823	+	1.55681i
$738$	−5509.44	−	9542.63i	−0.274804	−	0.475974i
$739$	−7039.27	−	12192.4i	−0.350398	−	0.606906i	0.635921	−	0.771754i	$-0.280620\pi$
$739$	−7039.27	−	12192.4i	−0.350398	−	0.606906i	−0.986319	+	0.164847i	$0.947287\pi$
$740$	−963.885	+	1669.50i	−0.0478826	+	0.0829350i
$741$	1353.35			0.0670937
$742$		0			0
$743$	31431.4			1.55196			0.775980	−	0.630757i	$-0.217256\pi$
$743$	31431.4			1.55196			0.775980	+	0.630757i	$0.217256\pi$
$744$	−13897.5	+	24071.1i	−0.684819	+	1.18614i
$745$	−610.646	−	1057.67i	−0.0300300	−	0.0520135i
$746$	−1069.42	−	1852.28i	−0.0524854	−	0.0909073i
$747$	−15774.7	+	27322.6i	−0.772645	+	1.33826i
$748$	22742.2			1.11168
$749$		0			0
$750$	−2218.50			−0.108011
$751$	1231.56	−	2133.12i	0.0598405	−	0.103647i	−0.834553	−	0.550927i	$-0.814274\pi$
$751$	1231.56	−	2133.12i	0.0598405	−	0.103647i	0.894394	+	0.447281i	$0.147607\pi$
$752$	259.974	+	450.288i	0.0126068	+	0.0218355i
$753$	−2808.86	−	4865.09i	−0.135937	−	0.235450i
$754$	−1508.39	+	2612.61i	−0.0728547	+	0.126188i
$755$	4010.79			0.193335
$756$		0			0
$757$	37987.2			1.82387			0.911935	−	0.410335i	$-0.134588\pi$
$757$	37987.2			1.82387			0.911935	+	0.410335i	$0.134588\pi$
$758$	−9726.63	+	16847.0i	−0.466078	+	0.807271i
$759$	8594.30	+	14885.8i	0.411006	+	0.711882i
$760$	−363.163	−	629.016i	−0.0173333	−	0.0300221i
$761$	9345.97	−	16187.7i	0.445192	−	0.771095i	−0.552874	−	0.833265i	$-0.686469\pi$
$761$	9345.97	−	16187.7i	0.445192	−	0.771095i	0.998066	+	0.0621700i	$0.0198021\pi$
$762$	−3540.20			−0.168304
$763$		0			0
$764$	−13200.7			−0.625109
$765$	21670.9	−	37535.2i	1.02420	−	1.77397i
$766$	12533.7	+	21709.1i	0.591204	+	1.02400i
$767$	−4279.70	−	7412.66i	−0.201475	−	0.348964i
$768$	−20521.9	+	35545.0i	−0.964219	+	1.67008i
$769$	27250.5			1.27786			0.638932	−	0.769263i	$-0.279376\pi$
$769$	27250.5			1.27786			0.638932	+	0.769263i	$0.279376\pi$
$770$		0			0
$771$	−44498.1			−2.07855
$772$	−8435.92	+	14611.4i	−0.393284	+	0.681188i
$773$	−546.335	−	946.281i	−0.0254209	−	0.0440302i	0.853035	−	0.521854i	$-0.174759\pi$
$773$	−546.335	−	946.281i	−0.0254209	−	0.0440302i	−0.878456	+	0.477823i	$0.841426\pi$
$774$	17831.3	+	30884.6i	0.828077	+	1.43427i
$775$	1561.55	−	2704.68i	0.0723773	−	0.125361i
$776$	−17282.6			−0.799495
$777$		0			0
$778$	−19793.5			−0.912124
$779$	−288.255	+	499.273i	−0.0132578	+	0.0229632i
$780$	2465.09	+	4269.66i	0.113160	+	0.195998i
$781$	5212.42	+	9028.18i	0.238816	+	0.413641i
$782$	−6148.51	+	10649.5i	−0.281164	+	0.486991i
$783$	25054.1			1.14350
$784$		0			0
$785$	17706.9			0.805078
$786$	5339.67	−	9248.59i	0.242315	−	0.419702i
$787$	−6319.57	−	10945.8i	−0.286237	−	0.495777i	0.686671	−	0.726968i	$-0.259071\pi$
$787$	−6319.57	−	10945.8i	−0.286237	−	0.495777i	−0.972908	+	0.231191i	$0.925738\pi$
$788$	−3515.73	−	6089.43i	−0.158938	−	0.275288i
$789$	−21323.1	+	36932.7i	−0.962134	+	1.66646i
$790$	5516.66			0.248448
$791$		0			0
$792$	−55169.6			−2.47521
$793$	7859.18	−	13612.5i	0.351939	−	0.609576i
$794$	−960.257	−	1663.21i	−0.0429197	−	0.0743391i
$795$	−8646.73	−	14976.6i	−0.385746	−	0.668132i
$796$	8177.11	−	14163.2i	0.364108	−	0.630653i
$797$	−8666.66			−0.385180			−0.192590	−	0.981279i	$-0.561689\pi$
$797$	−8666.66			−0.385180			−0.192590	+	0.981279i	$0.561689\pi$
$798$		0			0
$799$	9885.18			0.437688
$800$	2167.24	−	3753.77i	0.0957794	−	0.165895i
$801$	30787.4	+	53325.3i	1.35808	+	2.35226i
$802$	−6019.64	−	10426.3i	−0.265038	−	0.459060i
$803$	13738.0	−	23794.9i	0.603739	−	1.04571i
$804$	−42074.6			−1.84559
$805$		0			0
$806$	5299.25			0.231586
$807$	20298.8	−	35158.5i	0.885440	−	1.53363i
$808$	7160.29	+	12402.0i	0.311755	+	0.539976i
$809$	−1777.60	−	3078.89i	−0.0772522	−	0.133805i	0.824811	−	0.565408i	$-0.191281\pi$
$809$	−1777.60	−	3078.89i	−0.0772522	−	0.133805i	−0.902063	+	0.431603i	$0.857948\pi$
$810$	−7598.61	+	13161.2i	−0.329615	+	0.570910i
$811$	−21940.0			−0.949961			−0.474981	−	0.879996i	$-0.657545\pi$
$811$	−21940.0			−0.949961			−0.474981	+	0.879996i	$0.657545\pi$
$812$		0			0
$813$	−36893.2			−1.59152
$814$	−2924.75	+	5065.82i	−0.125937	+	0.218129i
$815$	−5536.42	−	9589.36i	−0.237954	−	0.412148i
$816$	−4609.24	−	7983.45i	−0.197740	−	0.342496i
$817$	932.936	−	1615.89i	0.0399502	−	0.0691957i
$818$	−16102.5			−0.688275
$819$		0			0
$820$	−2100.20			−0.0894418
$821$	14786.4	−	25610.7i	0.628560	−	1.08870i	−0.359281	−	0.933229i	$-0.616978\pi$
$821$	14786.4	−	25610.7i	0.628560	−	1.08870i	0.987841	−	0.155468i	$-0.0496885\pi$
$822$	−18566.2	−	32157.6i	−0.787800	−	1.36451i
$823$	9657.36	+	16727.0i	0.409034	+	0.708467i	0.994782	−	0.102026i	$-0.0325326\pi$
$823$	9657.36	+	16727.0i	0.409034	+	0.708467i	−0.585748	+	0.810493i	$0.699199\pi$
$824$	9396.58	−	16275.4i	0.397264	−	0.688081i
$825$	8816.53			0.372063
$826$		0			0
$827$	21107.8			0.887535			0.443768	−	0.896142i	$-0.353642\pi$
$827$	21107.8			0.887535			0.443768	+	0.896142i	$0.353642\pi$
$828$	−7068.82	+	12243.6i	−0.296689	+	0.513880i
$829$	5399.89	+	9352.88i	0.226231	+	0.391844i	0.956688	−	0.291115i	$-0.0940261\pi$
$829$	5399.89	+	9352.88i	0.226231	+	0.391844i	−0.730457	+	0.682959i	$0.760693\pi$
$830$	−2295.68	−	3976.23i	−0.0960049	−	0.166285i
$831$	39133.9	−	67781.8i	1.63362	−	2.82951i
$832$	8654.96			0.360645
$833$		0			0
$834$	−14810.1			−0.614906
$835$	6542.67	−	11332.2i	0.271160	−	0.469662i
$836$	522.247	+	904.558i	0.0216056	+	0.0374220i
$837$	−22004.9	−	38113.6i	−0.908722	−	1.57395i
$838$	−6796.14	+	11771.3i	−0.280154	+	0.485240i
$839$	11829.3			0.486761			0.243381	−	0.969931i	$-0.421744\pi$
$839$	11829.3			0.486761			0.243381	+	0.969931i	$0.421744\pi$
$840$		0			0
$841$	−19331.3			−0.792626
$842$	−10794.1	+	18696.0i	−0.441793	+	0.765208i
$843$	30856.2	+	53444.4i	1.26067	+	2.18354i
$844$	−7496.94	−	12985.1i	−0.305753	−	0.529579i
$845$	−4193.69	+	7263.68i	−0.170730	+	0.295714i
$846$	−8677.35			−0.352640
$847$		0			0
$848$	−2586.16			−0.104728
$849$	−7013.04	+	12146.9i	−0.283495	+	0.491027i
$850$	3153.75	+	5462.46i	0.127262	+	0.220424i
$851$	2071.24	+	3587.49i	0.0834327	+	0.144510i
$852$	−6097.53	+	10561.2i	−0.245185	+	0.424674i
$853$	3426.91			0.137556			0.0687779	−	0.997632i	$-0.478090\pi$
$853$	3426.91			0.137556			0.0687779	+	0.997632i	$0.478090\pi$
$854$		0			0
$855$	1990.58			0.0796216
$856$	22529.8	−	39022.8i	0.899595	−	1.55814i
$857$	3654.08	+	6329.06i	0.145649	+	0.252271i	0.929615	−	0.368533i	$-0.120140\pi$
$857$	3654.08	+	6329.06i	0.145649	+	0.252271i	−0.783966	+	0.620804i	$0.786806\pi$
$858$	7479.93	+	12955.6i	0.297623	+	0.515498i
$859$	−11269.9	+	19520.0i	−0.447641	+	0.775337i	−0.998232	−	0.0594383i	$-0.981069\pi$
$859$	−11269.9	+	19520.0i	−0.447641	+	0.775337i	0.550591	+	0.834775i	$0.314402\pi$
$860$	6797.29			0.269518
$861$		0			0
$862$	2804.41			0.110811
$863$	−845.475	+	1464.41i	−0.0333491	+	0.0577624i	−0.882218	−	0.470841i	$-0.843951\pi$
$863$	−845.475	+	1464.41i	−0.0333491	+	0.0577624i	0.848869	+	0.528603i	$0.177284\pi$
$864$	−30540.2	−	52897.1i	−1.20254	−	2.08287i
$865$	4085.10	+	7075.59i	0.160575	+	0.278124i
$866$	−1965.33	+	3404.05i	−0.0771185	+	0.133573i
$867$	−128408.			−5.02996
$868$		0			0
$869$	−21923.7			−0.855825
$870$	−3155.47	+	5465.43i	−0.122966	+	0.212983i
$871$	11084.2	+	19198.4i	0.431198	+	0.746856i
$872$	−1241.94	−	2151.11i	−0.0482311	−	0.0835387i
$873$	23682.5	−	41019.3i	0.918134	−	1.59026i
$874$	−564.771			−0.0218577
$875$		0			0
$876$	32141.6			1.23968
$877$	−16510.8	+	28597.5i	−0.635723	+	1.10110i	0.350638	+	0.936511i	$0.385965\pi$
$877$	−16510.8	+	28597.5i	−0.635723	+	1.10110i	−0.986361	+	0.164594i	$0.947369\pi$
$878$	3250.27	+	5629.64i	0.124933	+	0.216391i
$879$	26173.4	+	45333.7i	1.00433	+	1.73955i
$880$	659.237	−	1141.83i	0.0252533	−	0.0437399i
$881$	29413.5			1.12482			0.562410	−	0.826859i	$-0.309874\pi$
$881$	29413.5			1.12482			0.562410	+	0.826859i	$0.309874\pi$
$882$		0			0
$883$	22413.5			0.854218			0.427109	−	0.904200i	$-0.359532\pi$
$883$	22413.5			0.854218			0.427109	+	0.904200i	$0.359532\pi$
$884$	7008.60	−	12139.3i	0.266657	−	0.461863i
$885$	−8952.88	−	15506.8i	−0.340054	−	0.588991i
$886$	906.976	+	1570.93i	0.0343910	+	0.0595670i
$887$	−24534.7	+	42495.4i	−0.928744	+	1.60863i	−0.143317	+	0.989677i	$0.545777\pi$
$887$	−24534.7	+	42495.4i	−0.928744	+	1.60863i	−0.785427	+	0.618954i	$0.787557\pi$
$888$	−18910.3			−0.714626
$889$		0			0
$890$	−8960.92			−0.337495
$891$	30197.6	−	52303.8i	1.13542	−	1.96660i
$892$	−7828.33	−	13559.1i	−0.293847	−	0.508959i
$893$	227.001	+	393.177i	0.00850648	+	0.0147337i
$894$	2167.55	−	3754.30i	0.0810891	−	0.140450i
$895$	−4845.80			−0.180980
$896$		0			0
$897$	10594.2			0.394348
$898$	5689.00	−	9853.64i	0.211408	−	0.366169i
$899$	−4442.11	−	7693.96i	−0.164797	−	0.285437i
$900$	3625.80	+	6280.08i	0.134289	+	0.232595i
$901$	−24583.9	+	42580.5i	−0.908999	+	1.57443i
$902$	−6372.73			−0.235243
$903$		0			0
$904$	7211.13			0.265308
$905$	−10895.5	+	18871.6i	−0.400197	+	0.693162i
$906$	7118.34	+	12329.3i	0.261028	+	0.452113i
$907$	21427.2	+	37113.0i	0.784431	+	1.35867i	0.929339	+	0.369229i	$0.120378\pi$
$907$	21427.2	+	37113.0i	0.784431	+	1.35867i	−0.144908	+	0.989445i	$0.546289\pi$
$908$	−4643.51	+	8042.80i	−0.169714	+	0.293953i
$909$	−39247.3			−1.43207
$910$		0			0
$911$	−48846.7			−1.77647			−0.888234	−	0.459391i	$-0.848068\pi$
$911$	−48846.7			−1.77647			−0.888234	+	0.459391i	$0.848068\pi$
$912$	211.691	−	366.659i	0.00768617	−	0.0133128i
$913$	9123.25	+	15801.9i	0.330707	+	0.572801i
$914$	−1445.61	−	2503.86i	−0.0523155	−	0.0906131i
$915$	16440.9	−	28476.5i	0.594011	−	1.02886i
$916$	−6293.81			−0.227023
$917$		0			0
$918$	88883.6			3.19564
$919$	11200.4	−	19399.7i	0.402033	−	0.696342i	−0.591938	−	0.805984i	$-0.701637\pi$
$919$	11200.4	−	19399.7i	0.402033	−	0.696342i	0.993971	+	0.109641i	$0.0349702\pi$
$920$	−2842.89	−	4924.04i	−0.101878	−	0.176457i
$921$	−4936.72	−	8550.64i	−0.176624	−	0.305921i
$922$	−8765.05	+	15181.5i	−0.313082	+	0.542274i
$923$	6425.36			0.229137
$924$		0			0
$925$	2124.80			0.0755275
$926$	−10662.5	+	18468.0i	−0.378392	+	0.655395i
$927$	25752.5	+	44604.6i	0.912429	+	1.58037i
$928$	−6165.12	−	10678.3i	−0.218082	−	0.377729i
$929$	1149.02	−	1990.17i	0.0405794	−	0.0702855i	−0.845022	−	0.534731i	$-0.820413\pi$
$929$	1149.02	−	1990.17i	0.0405794	−	0.0702855i	0.885602	+	0.464445i	$0.153746\pi$
$930$	11085.7			0.390876
$931$		0			0
$932$	1701.10			0.0597870
$933$	−12130.4	+	21010.5i	−0.425652	+	0.737250i
$934$	−1973.75	−	3418.64i	−0.0691469	−	0.119766i
$935$	−12533.3	−	21708.3i	−0.438378	−	0.759293i
$936$	−17001.9	+	29448.2i	−0.593724	+	1.02836i
$937$	47163.3			1.64435			0.822176	−	0.569233i	$-0.192760\pi$
$937$	47163.3			1.64435			0.822176	+	0.569233i	$0.192760\pi$
$938$		0			0
$939$	24791.9			0.861611
$940$	−826.953	+	1432.33i	−0.0286939	+	0.0496992i
$941$	20228.5	+	35036.8i	0.700776	+	1.21378i	0.968194	+	0.250199i	$0.0804960\pi$
$941$	20228.5	+	35036.8i	0.700776	+	1.21378i	−0.267419	+	0.963580i	$0.586171\pi$
$942$	31426.2	+	54431.8i	1.08696	+	1.88268i
$943$	−2256.51	+	3908.38i	−0.0779236	+	0.134968i
$944$	−2677.73			−0.0923227
$945$		0			0
$946$	20625.3			0.708865
$947$	3181.57	−	5510.64i	0.109173	−	0.189094i	−0.806262	−	0.591558i	$-0.798513\pi$
$947$	3181.57	−	5510.64i	0.109173	−	0.189094i	0.915436	+	0.402465i	$0.131846\pi$
$948$	−12823.3	−	22210.6i	−0.439326	−	0.760935i
$949$	−8467.41	−	14666.0i	−0.289635	−	0.501663i
$950$	−144.844	+	250.877i	−0.00494669	+	0.00856791i
$951$	25987.8			0.886133
$952$		0			0
$953$	−48268.8			−1.64069			−0.820346	−	0.571867i	$-0.806219\pi$
$953$	−48268.8			−1.64069			−0.820346	+	0.571867i	$0.806219\pi$
$954$	21580.1	−	37377.8i	0.732370	−	1.26850i
$955$	7274.93	+	12600.5i	0.246504	+	0.426957i
$956$	−12613.2	−	21846.7i	−0.426715	−	0.739092i
$957$	12540.1	−	21720.2i	0.423579	−	0.733660i
$958$	32124.7			1.08340
$959$		0			0
$960$	18105.7			0.608706
$961$	7092.53	−	12284.6i	0.238076	−	0.412360i
$962$	1802.68	+	3122.33i	0.0604164	+	0.104644i
$963$	61745.7	+	106947.i	2.06617	+	3.57872i
$964$	−10674.5	+	18488.8i	−0.356641	+	0.617721i
$965$	18596.2			0.620346
$966$		0			0
$967$	−26795.3			−0.891084			−0.445542	−	0.895261i	$-0.646989\pi$
$967$	−26795.3			−0.891084			−0.445542	+	0.895261i	$0.646989\pi$
$968$	−426.640	+	738.962i	−0.0141660	+	0.0245363i
$969$	−4024.64	−	6970.87i	−0.133426	−	0.231101i
$970$	3446.49	+	5969.50i	0.114083	+	0.197597i
$971$	10791.9	−	18692.1i	0.356672	−	0.617775i	−0.630730	−	0.776002i	$-0.717245\pi$
$971$	10791.9	−	18692.1i	0.356672	−	0.617775i	0.987403	+	0.158227i	$0.0505779\pi$
$972$	27501.4			0.907519
$973$		0			0
$974$	34461.3			1.13369
$975$	2717.04	−	4706.05i	0.0892460	−	0.154579i
$976$	−2458.67	−	4258.54i	−0.0806354	−	0.139665i
$977$	−25553.1	−	44259.4i	−0.836763	−	1.44932i	−0.892587	−	0.450876i	$-0.851112\pi$
$977$	−25553.1	−	44259.4i	−0.836763	−	1.44932i	0.0558235	−	0.998441i	$-0.482222\pi$
$978$	19652.1	−	34038.4i	0.642540	−	1.11291i
$979$	35611.6			1.16256
$980$		0			0
$981$	6807.39			0.221553
$982$	7365.04	−	12756.6i	0.239336	−	0.414542i
$983$	−20792.8	−	36014.2i	−0.674658	−	1.16854i	−0.976569	−	0.215205i	$-0.930958\pi$
$983$	−20792.8	−	36014.2i	−0.674658	−	1.16854i	0.301911	−	0.953336i	$-0.402375\pi$
$984$	−10300.9	−	17841.7i	−0.333720	−	0.578019i
$985$	−3875.06	+	6711.81i	−0.125350	+	0.217113i
$986$	17942.9			0.579531
$987$		0			0
$988$	643.775			0.0207300
$989$	7303.17	−	12649.5i	0.234810	−	0.406703i
$990$	11001.9	+	19055.9i	0.353196	+	0.611754i
$991$	14541.3	+	25186.2i	0.466114	+	0.807332i	0.999251	−	0.0386963i	$-0.0123205\pi$
$991$	14541.3	+	25186.2i	0.466114	+	0.807332i	−0.533137	+	0.846029i	$0.678987\pi$
$992$	−10829.6	+	18757.4i	−0.346613	+	0.600351i
$993$	49380.4			1.57809
$994$		0			0
$995$	−18025.7			−0.574325
$996$	−10672.4	+	18485.2i	−0.339527	+	0.588079i
$997$	17251.5	+	29880.5i	0.548004	+	0.949171i	0.998411	+	0.0563479i	$0.0179456\pi$
$997$	17251.5	+	29880.5i	0.548004	+	0.949171i	−0.450407	+	0.892823i	$0.648721\pi$
$998$	2222.99	+	3850.33i	0.0705085	+	0.122124i
$999$	14971.0	−	25930.6i	0.474137	−	0.821229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.n.226.2		6
7.2	even	3		245.4.a.l.1.2		3
7.3	odd	6		245.4.e.m.116.2		6
7.4	even	3	inner	245.4.e.n.116.2		6
7.5	odd	6		35.4.a.c.1.2	✓	3
7.6	odd	2		245.4.e.m.226.2		6
21.2	odd	6		2205.4.a.bm.1.2		3
21.5	even	6		315.4.a.p.1.2		3
28.19	even	6		560.4.a.u.1.1		3
35.9	even	6		1225.4.a.y.1.2		3
35.12	even	12		175.4.b.e.99.3		6
35.19	odd	6		175.4.a.f.1.2		3
35.33	even	12		175.4.b.e.99.4		6
56.5	odd	6		2240.4.a.bt.1.1		3
56.19	even	6		2240.4.a.bv.1.3		3
105.89	even	6		1575.4.a.ba.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.c.1.2	✓	3	7.5	odd	6
175.4.a.f.1.2		3	35.19	odd	6
175.4.b.e.99.3		6	35.12	even	12
175.4.b.e.99.4		6	35.33	even	12
245.4.a.l.1.2		3	7.2	even	3
245.4.e.m.116.2		6	7.3	odd	6
245.4.e.m.226.2		6	7.6	odd	2
245.4.e.n.116.2		6	7.4	even	3	inner
245.4.e.n.226.2		6	1.1	even	1	trivial
315.4.a.p.1.2		3	21.5	even	6
560.4.a.u.1.1		3	28.19	even	6
1225.4.a.y.1.2		3	35.9	even	6
1575.4.a.ba.1.2		3	105.89	even	6
2205.4.a.bm.1.2		3	21.2	odd	6
2240.4.a.bt.1.1		3	56.5	odd	6
2240.4.a.bv.1.3		3	56.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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+(0.930543 - 1.61175i) q^{2} +(4.76818 + 8.25873i) q^{3} +(2.26818 + 3.92860i) q^{4} +(2.50000 - 4.33013i) q^{5} +17.7480 q^{6} +23.3312 q^{8} +(-31.9711 + 55.3755i) q^{9} +(-4.65272 - 8.05874i) q^{10} +(18.4904 + 32.0262i) q^{11} +(-21.6302 + 37.4645i) q^{12} +22.7931 q^{13} +47.6818 q^{15} +(3.56530 - 6.17529i) q^{16} +(-67.7830 - 117.404i) q^{17} +(59.5009 + 103.059i) q^{18} +(3.11310 - 5.39205i) q^{19} +22.6818 q^{20} +68.8243 q^{22} +(24.3698 - 42.2098i) q^{23} +(111.248 + 192.686i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(21.2100 - 36.7367i) q^{26} -352.293 q^{27} -71.1172 q^{29} +(44.3700 - 76.8510i) q^{30} +(62.4618 + 108.187i) q^{31} +(86.6896 + 150.151i) q^{32} +(-176.331 + 305.414i) q^{33} -252.300 q^{34} -290.064 q^{36} +(-42.4960 + 73.6052i) q^{37} +(-5.79375 - 10.0351i) q^{38} +(108.682 + 188.242i) q^{39} +(58.3281 - 101.027i) q^{40} -92.5942 q^{41} +299.680 q^{43} +(-83.8788 + 145.282i) q^{44} +(159.855 + 276.877i) q^{45} +(-45.3544 - 78.5561i) q^{46} +(-36.4589 + 63.1487i) q^{47} +68.0000 q^{48} -46.5272 q^{50} +(646.403 - 1119.60i) q^{51} +(51.6988 + 89.5450i) q^{52} +(-181.342 - 314.094i) q^{53} +(-327.824 + 567.808i) q^{54} +184.904 q^{55} +59.3753 q^{57} +(-66.1776 + 114.623i) q^{58} +(-187.763 - 325.215i) q^{59} +(108.151 + 187.323i) q^{60} +(344.805 - 597.220i) q^{61} +232.494 q^{62} +379.719 q^{64} +(56.9827 - 98.6970i) q^{65} +(328.166 + 568.401i) q^{66} +(486.295 + 842.288i) q^{67} +(307.488 - 532.585i) q^{68} +464.799 q^{69} +281.900 q^{71} +(-745.924 + 1291.98i) q^{72} +(-371.490 - 643.440i) q^{73} +(79.0887 + 136.986i) q^{74} +(119.204 - 206.468i) q^{75} +28.2443 q^{76} +404.532 q^{78} +(-296.421 + 513.417i) q^{79} +(-17.8265 - 30.8764i) q^{80} +(-816.578 - 1414.35i) q^{81} +(-86.1630 + 149.239i) q^{82} +493.406 q^{83} -677.830 q^{85} +(278.866 - 483.009i) q^{86} +(-339.099 - 587.337i) q^{87} +(431.403 + 747.212i) q^{88} +(481.488 - 833.962i) q^{89} +595.009 q^{90} +221.101 q^{92} +(-595.659 + 1031.71i) q^{93} +(67.8532 + 117.525i) q^{94} +(-15.5655 - 26.9602i) q^{95} +(-826.703 + 1431.89i) q^{96} -740.748 q^{97} -2364.62 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 2 q^{3} - 13 q^{4} + 15 q^{5} - 48 q^{6} - 30 q^{8} - 81 q^{9} - 15 q^{10} + 74 q^{11} - 152 q^{12} - 88 q^{13} + 20 q^{15} + 79 q^{16} - 52 q^{17} + 411 q^{18} + 168 q^{19} - 130 q^{20}+ \cdots - 6976 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 2 * q^3 - 13 * q^4 + 15 * q^5 - 48 * q^6 - 30 * q^8 - 81 * q^9 - 15 * q^10 + 74 * q^11 - 152 * q^12 - 88 * q^13 + 20 * q^15 + 79 * q^16 - 52 * q^17 + 411 * q^18 + 168 * q^19 - 130 * q^20 + 368 * q^22 + 124 * q^23 + 420 * q^24 - 75 * q^25 - 446 * q^26 - 340 * q^27 + 664 * q^29 - 120 * q^30 + 320 * q^31 + 183 * q^32 - 106 * q^33 - 1164 * q^34 + 362 * q^36 + 54 * q^37 - 460 * q^38 + 982 * q^39 - 75 * q^40 - 724 * q^41 - 32 * q^43 + 264 * q^44 + 405 * q^45 + 336 * q^46 - 730 * q^47 + 408 * q^48 - 150 * q^50 + 1178 * q^51 + 1202 * q^52 - 110 * q^53 - 180 * q^54 + 740 * q^55 - 1912 * q^57 - 450 * q^58 - 180 * q^59 + 760 * q^60 + 1222 * q^61 - 928 * q^62 - 782 * q^64 - 220 * q^65 - 532 * q^66 - 204 * q^67 + 918 * q^68 + 1432 * q^69 - 272 * q^71 - 765 * q^72 + 310 * q^73 - 502 * q^74 + 50 * q^75 - 3592 * q^76 + 7576 * q^78 + 1034 * q^79 - 395 * q^80 - 2283 * q^81 - 6 * q^82 + 3320 * q^83 - 520 * q^85 - 764 * q^86 - 1574 * q^87 + 20 * q^88 + 242 * q^89 + 4110 * q^90 + 192 * q^92 - 1376 * q^93 - 1108 * q^94 - 840 * q^95 - 3156 * q^96 - 200 * q^97 - 6976 * q^99

Introduction

L-functions

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