LMFDB - Embedded newform 261.3.s.a.172.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			172.1
Character	$\chi$	$=$	261.172
Dual form			261.3.s.a.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.293128 + 2.60158i) q^{2} +(-2.78259 - 0.635107i) q^{4} +(1.65260 - 1.31790i) q^{5} +(0.747987 + 3.27715i) q^{7} +(-0.990802 + 2.83155i) q^{8} +O(q^{10})$	\(q+(-0.293128 + 2.60158i) q^{2} +(-2.78259 - 0.635107i) q^{4} +(1.65260 - 1.31790i) q^{5} +(0.747987 + 3.27715i) q^{7} +(-0.990802 + 2.83155i) q^{8} +(2.94421 + 4.68569i) q^{10} +(0.536371 + 1.53286i) q^{11} +(-3.68793 + 7.65807i) q^{13} +(-8.74502 + 0.985327i) q^{14} +(-17.3621 - 8.36113i) q^{16} +(19.7801 + 19.7801i) q^{17} +(-9.28934 + 5.83688i) q^{19} +(-5.43551 + 2.61761i) q^{20} +(-4.14508 + 0.946088i) q^{22} +(-20.8669 + 26.1663i) q^{23} +(-4.56881 + 20.0173i) q^{25} +(-18.8421 - 11.8392i) q^{26} -9.59400i q^{28} +(-12.6644 - 26.0886i) q^{29} +(3.96474 - 35.1880i) q^{31} +(20.4573 - 32.5576i) q^{32} +(-57.2575 + 45.6614i) q^{34} +(5.55509 + 4.43004i) q^{35} +(2.28364 - 6.52628i) q^{37} +(-12.4622 - 25.8779i) q^{38} +(2.09431 + 5.98520i) q^{40} +(22.9886 - 22.9886i) q^{41} +(55.6405 - 6.26918i) q^{43} +(-0.518968 - 4.60597i) q^{44} +(-61.9571 - 61.9571i) q^{46} +(-60.5913 + 21.2018i) q^{47} +(33.9673 - 16.3578i) q^{49} +(-50.7373 - 17.7537i) q^{50} +(15.1257 - 18.9670i) q^{52} +(22.4008 + 28.0897i) q^{53} +(2.90657 + 1.82632i) q^{55} +(-10.0205 - 1.12904i) q^{56} +(71.5838 - 25.3002i) q^{58} +84.6397 q^{59} +(-38.2161 + 60.8206i) q^{61} +(90.3823 + 20.6292i) q^{62} +(18.4397 + 14.7051i) q^{64} +(3.99793 + 17.5161i) q^{65} +(-14.4421 - 29.9894i) q^{67} +(-42.4773 - 67.6022i) q^{68} +(-13.1535 + 13.1535i) q^{70} +(2.14727 - 4.45886i) q^{71} +(8.36674 + 74.2568i) q^{73} +(16.3092 + 7.85411i) q^{74} +(29.5554 - 10.3419i) q^{76} +(-4.62221 + 2.90432i) q^{77} +(28.5672 + 9.99609i) q^{79} +(-39.7117 + 9.06394i) q^{80} +(53.0682 + 66.5454i) q^{82} +(7.54034 - 33.0364i) q^{83} +(58.7568 + 6.62030i) q^{85} +146.591i q^{86} -4.87181 q^{88} +(-7.04081 + 62.4889i) q^{89} +(-27.8552 - 6.35776i) q^{91} +(74.6825 - 59.5573i) q^{92} +(-37.3973 - 163.848i) q^{94} +(-7.65912 + 21.8885i) q^{95} +(-21.4247 - 34.0971i) q^{97} +(32.5993 + 93.1635i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{15}{28}\right)$	$1$

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 $

$2$	−0.293128	+	2.60158i	−0.146564	+	1.30079i	0.678017	+	0.735046i	$0.262840\pi$
$2$	−0.293128	+	2.60158i	−0.146564	+	1.30079i	−0.824581	+	0.565744i	$0.808589\pi$
$3$		0			0
$3$		0			0
$4$	−2.78259	−	0.635107i	−0.695647	−	0.158777i
$5$	1.65260	−	1.31790i	0.330520	−	0.263581i	−0.444142	−	0.895956i	$-0.646491\pi$
$5$	1.65260	−	1.31790i	0.330520	−	0.263581i	0.774662	+	0.632375i	$0.217920\pi$
$6$		0			0
$7$	0.747987	+	3.27715i	0.106855	+	0.468164i	0.999837	+	0.0180702i	$0.00575225\pi$
$7$	0.747987	+	3.27715i	0.106855	+	0.468164i	−0.892981	+	0.450094i	$0.851391\pi$
$8$	−0.990802	+	2.83155i	−0.123850	+	0.353944i
$9$		0			0
$10$	2.94421	+	4.68569i	0.294421	+	0.468569i
$11$	0.536371	+	1.53286i	0.0487610	+	0.139351i	0.965689	−	0.259703i	$-0.0836245\pi$
$11$	0.536371	+	1.53286i	0.0487610	+	0.139351i	−0.916928	+	0.399053i	$0.869339\pi$
$12$		0			0
$13$	−3.68793	+	7.65807i	−0.283687	+	0.589082i	−0.993307	−	0.115502i	$-0.963152\pi$
$13$	−3.68793	+	7.65807i	−0.283687	+	0.589082i	0.709620	+	0.704584i	$0.248867\pi$
$14$	−8.74502	+	0.985327i	−0.624644	+	0.0703805i
$15$		0			0
$16$	−17.3621	−	8.36113i	−1.08513	−	0.522571i
$17$	19.7801	+	19.7801i	1.16353	+	1.16353i	0.983696	+	0.179837i	$0.0575570\pi$
$17$	19.7801	+	19.7801i	1.16353	+	1.16353i	0.179837	+	0.983696i	$0.442443\pi$
$18$		0			0
$19$	−9.28934	+	5.83688i	−0.488913	+	0.307204i	−0.753833	−	0.657066i	$-0.771797\pi$
$19$	−9.28934	+	5.83688i	−0.488913	+	0.307204i	0.264920	+	0.964270i	$0.414654\pi$
$20$	−5.43551	+	2.61761i	−0.271776	+	0.130880i
$21$		0			0
$22$	−4.14508	+	0.946088i	−0.188413	+	0.0430040i
$23$	−20.8669	+	26.1663i	−0.907259	+	1.13767i	0.0827374	+	0.996571i	$0.473634\pi$
$23$	−20.8669	+	26.1663i	−0.907259	+	1.13767i	−0.989996	+	0.141095i	$0.954938\pi$
$24$		0			0
$25$	−4.56881	+	20.0173i	−0.182752	+	0.800690i
$26$	−18.8421	−	11.8392i	−0.724694	−	0.455356i
$27$		0			0
$28$		−	9.59400i		−	0.342643i
$29$	−12.6644	−	26.0886i	−0.436703	−	0.899606i
$29$	−12.6644	−	26.0886i	−0.436703	−	0.899606i
$30$		0			0
$31$	3.96474	−	35.1880i	0.127895	−	1.13510i	−0.751744	−	0.659455i	$-0.770787\pi$
$31$	3.96474	−	35.1880i	0.127895	−	1.13510i	0.879639	−	0.475642i	$-0.157784\pi$
$32$	20.4573	−	32.5576i	0.639290	−	1.01742i
$33$		0			0
$34$	−57.2575	+	45.6614i	−1.68404	+	1.34298i
$35$	5.55509	+	4.43004i	0.158717	+	0.126573i
$36$		0			0
$37$	2.28364	−	6.52628i	0.0617201	−	0.176386i	−0.908894	−	0.417027i	$-0.863072\pi$
$37$	2.28364	−	6.52628i	0.0617201	−	0.176386i	0.970614	+	0.240641i	$0.0773577\pi$
$38$	−12.4622	−	25.8779i	−0.327951	−	0.680998i
$39$		0			0
$40$	2.09431	+	5.98520i	0.0523578	+	0.149630i
$41$	22.9886	−	22.9886i	0.560698	−	0.560698i	−0.368808	−	0.929506i	$-0.620234\pi$
$41$	22.9886	−	22.9886i	0.560698	−	0.560698i	0.929506	+	0.368808i	$0.120234\pi$
$42$		0			0
$43$	55.6405	−	6.26918i	1.29397	−	0.145795i	0.562000	−	0.827137i	$-0.310032\pi$
$43$	55.6405	−	6.26918i	1.29397	−	0.145795i	0.731965	+	0.681342i	$0.238603\pi$
$44$	−0.518968	−	4.60597i	−0.0117947	−	0.104681i
$45$		0			0
$46$	−61.9571	−	61.9571i	−1.34689	−	1.34689i
$47$	−60.5913	+	21.2018i	−1.28918	+	0.451103i	−0.885858	−	0.463957i	$-0.846429\pi$
$47$	−60.5913	+	21.2018i	−1.28918	+	0.451103i	−0.403319	+	0.915059i	$0.632144\pi$
$48$		0			0
$49$	33.9673	−	16.3578i	0.693210	−	0.333832i
$50$	−50.7373	−	17.7537i	−1.01475	−	0.355075i
$51$		0			0
$52$	15.1257	−	18.9670i	0.290879	−	0.364750i
$53$	22.4008	+	28.0897i	0.422656	+	0.529994i	0.946880	−	0.321586i	$-0.104216\pi$
$53$	22.4008	+	28.0897i	0.422656	+	0.529994i	−0.524224	+	0.851580i	$0.675645\pi$
$54$		0			0
$55$	2.90657	+	1.82632i	0.0528467	+	0.0332058i
$56$	−10.0205	−	1.12904i	−0.178938	−	0.0201614i
$57$		0			0
$58$	71.5838	−	25.3002i	1.23420	−	0.436210i
$59$	84.6397			1.43457			0.717286	−	0.696779i	$-0.245384\pi$
$59$	84.6397			1.43457			0.717286	+	0.696779i	$0.245384\pi$
$60$		0			0
$61$	−38.2161	+	60.8206i	−0.626494	+	0.997059i	0.371158	+	0.928570i	$0.378961\pi$
$61$	−38.2161	+	60.8206i	−0.626494	+	0.997059i	−0.997652	+	0.0684897i	$0.978182\pi$
$62$	90.3823	+	20.6292i	1.45778	+	0.332729i
$63$		0			0
$64$	18.4397	+	14.7051i	0.288120	+	0.229768i
$65$	3.99793	+	17.5161i	0.0615066	+	0.269478i
$66$		0			0
$67$	−14.4421	−	29.9894i	−0.215554	−	0.447603i	0.764953	−	0.644086i	$-0.222762\pi$
$67$	−14.4421	−	29.9894i	−0.215554	−	0.447603i	−0.980507	+	0.196483i	$0.937048\pi$
$68$	−42.4773	−	67.6022i	−0.624666	−	0.994150i
$69$		0			0
$70$	−13.1535	+	13.1535i	−0.187906	+	0.187906i
$71$	2.14727	−	4.45886i	0.0302433	−	0.0628008i	−0.885300	−	0.465021i	$-0.846047\pi$
$71$	2.14727	−	4.45886i	0.0302433	−	0.0628008i	0.915543	+	0.402220i	$0.131761\pi$
$72$		0			0
$73$	8.36674	+	74.2568i	0.114613	+	1.01722i	0.910993	+	0.412421i	$0.135317\pi$
$73$	8.36674	+	74.2568i	0.114613	+	1.01722i	−0.796381	+	0.604796i	$0.793255\pi$
$74$	16.3092	+	7.85411i	0.220395	+	0.106137i
$75$		0			0
$76$	29.5554	−	10.3419i	0.388887	−	0.136078i
$77$	−4.62221	+	2.90432i	−0.0600287	+	0.0377185i
$78$		0			0
$79$	28.5672	+	9.99609i	0.361610	+	0.126533i	0.504968	−	0.863138i	$-0.331504\pi$
$79$	28.5672	+	9.99609i	0.361610	+	0.126533i	−0.143358	+	0.989671i	$0.545790\pi$
$80$	−39.7117	+	9.06394i	−0.496396	+	0.113299i
$81$		0			0
$82$	53.0682	+	66.5454i	0.647173	+	0.811529i
$83$	7.54034	−	33.0364i	0.0908475	−	0.398029i	−0.908975	−	0.416850i	$-0.863134\pi$
$83$	7.54034	−	33.0364i	0.0908475	−	0.398029i	0.999823	+	0.0188210i	$0.00599126\pi$
$84$		0			0
$85$	58.7568	+	6.62030i	0.691256	+	0.0778859i
$86$			146.591i			1.70455i
$87$		0			0
$88$	−4.87181			−0.0553614
$89$	−7.04081	+	62.4889i	−0.0791103	+	0.702123i	0.890079	+	0.455806i	$0.150649\pi$
$89$	−7.04081	+	62.4889i	−0.0791103	+	0.702123i	−0.969189	+	0.246317i	$0.920780\pi$
$90$		0			0
$91$	−27.8552	−	6.35776i	−0.306101	−	0.0698655i
$92$	74.6825	−	59.5573i	0.811766	−	0.647362i
$93$		0			0
$94$	−37.3973	−	163.848i	−0.397843	−	1.74306i
$95$	−7.65912	+	21.8885i	−0.0806223	+	0.230405i
$96$		0			0
$97$	−21.4247	−	34.0971i	−0.220873	−	0.351517i	0.717845	−	0.696202i	$-0.245128\pi$
$97$	−21.4247	−	34.0971i	−0.220873	−	0.351517i	−0.938718	+	0.344685i	$0.887986\pi$
$98$	32.5993	+	93.1635i	0.332646	+	0.950648i
$99$		0			0
$100$	25.4262	−	52.7981i	0.254262	−	0.527981i
$101$	66.4243	−	7.48422i	0.657666	−	0.0741011i	0.223176	−	0.974778i	$-0.428357\pi$
$101$	66.4243	−	7.48422i	0.657666	−	0.0741011i	0.434489	+	0.900677i	$0.356929\pi$
$102$		0			0
$103$	107.577	+	51.8063i	1.04444	+	0.502974i	0.875785	−	0.482702i	$-0.160344\pi$
$103$	107.577	+	51.8063i	1.04444	+	0.502974i	0.168651	+	0.985676i	$0.446059\pi$
$104$	−18.0302	−	18.0302i	−0.173367	−	0.173367i
$105$		0			0
$106$	−79.6439	+	50.0436i	−0.751358	+	0.472109i
$107$	111.488	−	53.6896i	1.04194	−	0.501772i	0.166977	−	0.985961i	$-0.446599\pi$
$107$	111.488	−	53.6896i	1.04194	−	0.501772i	0.874964	+	0.484189i	$0.160885\pi$
$108$		0			0
$109$	194.239	−	44.3338i	1.78201	−	0.406732i	0.800685	−	0.599085i	$-0.204469\pi$
$109$	194.239	−	44.3338i	1.78201	−	0.406732i	0.981326	+	0.192353i	$0.0616118\pi$
$110$	−5.60331	+	7.02633i	−0.0509392	+	0.0638757i
$111$		0			0
$112$	14.4140	−	63.1520i	0.128697	−	0.563858i
$113$	−72.7633	−	45.7202i	−0.643923	−	0.404604i	0.170108	−	0.985425i	$-0.445588\pi$
$113$	−72.7633	−	45.7202i	−0.643923	−	0.404604i	−0.814031	+	0.580822i	$0.802731\pi$
$114$		0			0
$115$			70.7431i			0.615158i
$116$	18.6708	+	80.6369i	0.160955	+	0.695146i
$117$		0			0
$118$	−24.8102	+	220.197i	−0.210256	+	1.86608i
$119$	−50.0269	+	79.6174i	−0.420394	+	0.669054i
$120$		0			0
$121$	92.5396	−	73.7979i	0.764790	−	0.609900i
$122$	−147.028	−	117.251i	−1.20514	−	0.961070i
$123$		0			0
$124$	−33.3804	+	95.3957i	−0.269197	+	0.769320i
$125$	41.7585	+	86.7125i	0.334068	+	0.693700i
$126$		0			0
$127$	−63.5926	−	181.737i	−0.500729	−	1.43100i	−0.865973	−	0.500090i	$-0.833300\pi$
$127$	−63.5926	−	181.737i	−0.500729	−	1.43100i	0.365244	−	0.930912i	$-0.380986\pi$
$128$	65.0947	−	65.0947i	0.508552	−	0.508552i
$129$		0			0
$130$	−46.7414	+	5.26649i	−0.359549	+	0.0405115i
$131$	−28.3477	−	251.593i	−0.216395	−	1.92056i	−0.363790	−	0.931481i	$-0.618517\pi$
$131$	−28.3477	−	251.593i	−0.216395	−	1.92056i	0.147395	−	0.989078i	$-0.452911\pi$
$132$		0			0
$133$	−26.0766	−	26.0766i	−0.196065	−	0.196065i
$134$	82.2533	−	28.7817i	0.613831	−	0.214789i
$135$		0			0
$136$	−75.6064	+	36.4101i	−0.555929	+	0.267721i
$137$	108.507	+	37.9681i	0.792019	+	0.277139i	0.695814	−	0.718222i	$-0.255044\pi$
$137$	108.507	+	37.9681i	0.792019	+	0.277139i	0.0962049	+	0.995362i	$0.469330\pi$
$138$		0			0
$139$	−52.1449	+	65.3877i	−0.375143	+	0.470415i	−0.933184	−	0.359399i	$-0.882982\pi$
$139$	−52.1449	+	65.3877i	−0.375143	+	0.470415i	0.558041	+	0.829814i	$0.311553\pi$
$140$	−12.6440	−	15.8550i	−0.0903141	−	0.113250i
$141$		0			0
$142$	10.9707	+	6.89332i	0.0772582	+	0.0485445i
$143$	−13.7168	−	1.54552i	−0.0959220	−	0.0108078i
$144$		0			0
$145$	−55.3114	−	26.4235i	−0.381458	−	0.182231i
$146$	−195.638			−1.33998
$147$		0			0
$148$	−10.4993	+	16.7096i	−0.0709413	+	0.112902i
$149$	0.907472	+	0.207125i	0.00609042	+	0.00139010i	0.225565	−	0.974228i	$-0.427577\pi$
$149$	0.907472	+	0.207125i	0.00609042	+	0.00139010i	−0.219475	+	0.975618i	$0.570434\pi$
$150$		0			0
$151$	−130.951	−	104.430i	−0.867227	−	0.691590i	0.0851980	−	0.996364i	$-0.472848\pi$
$151$	−130.951	−	104.430i	−0.867227	−	0.691590i	−0.952425	+	0.304774i	$0.901419\pi$
$152$	−7.32352	−	32.0864i	−0.0481811	−	0.211095i
$153$		0			0
$154$	−6.20094	−	12.8764i	−0.0402658	−	0.0836129i
$155$	−39.8223	−	63.3769i	−0.256918	−	0.408883i
$156$		0			0
$157$	149.089	−	149.089i	0.949615	−	0.949615i	−0.0491756	−	0.998790i	$-0.515659\pi$
$157$	149.089	−	149.089i	0.949615	−	0.949615i	0.998790	+	0.0491756i	$0.0156594\pi$
$158$	−34.3795	+	71.3897i	−0.217592	+	0.451834i
$159$		0			0
$160$	−9.10008	−	80.7654i	−0.0568755	−	0.504784i
$161$	−101.359	−	48.8120i	−0.629560	−	0.303180i
$162$		0			0
$163$	−233.265	+	81.6231i	−1.43108	+	0.500755i	−0.930934	−	0.365189i	$-0.881005\pi$
$163$	−233.265	+	81.6231i	−1.43108	+	0.500755i	−0.500142	+	0.865943i	$0.666719\pi$
$164$	−78.5681	+	49.3676i	−0.479074	+	0.301022i
$165$		0			0
$166$	83.7365	+	29.3007i	0.504437	+	0.176510i
$167$	−122.972	+	28.0675i	−0.736357	+	0.168069i	−0.574221	−	0.818700i	$-0.694695\pi$
$167$	−122.972	+	28.0675i	−0.736357	+	0.168069i	−0.162135	+	0.986769i	$0.551838\pi$
$168$		0			0
$169$	60.3246	+	75.6446i	0.356950	+	0.447601i
$170$	−34.4465	+	150.920i	−0.202626	+	0.887764i
$171$		0			0
$172$	−158.806	−	17.8932i	−0.923291	−	0.104030i
$173$		−	120.512i		−	0.696603i	−0.937383	−	0.348301i	$-0.886759\pi$
$173$		−	120.512i		−	0.696603i	0.937383	−	0.348301i	$-0.113241\pi$
$174$		0			0
$175$	−69.0169			−0.394382
$176$	3.50393	−	31.0983i	0.0199087	−	0.176695i
$177$		0			0
$178$	−160.506	−	36.6345i	−0.901720	−	0.205812i
$179$	−75.4516	+	60.1706i	−0.421517	+	0.336149i	−0.811167	−	0.584814i	$-0.801167\pi$
$179$	−75.4516	+	60.1706i	−0.421517	+	0.336149i	0.389650	+	0.920963i	$0.372596\pi$
$180$		0			0
$181$	25.1019	+	109.979i	0.138685	+	0.607618i	0.995725	+	0.0923680i	$0.0294436\pi$
$181$	25.1019	+	109.979i	0.138685	+	0.607618i	−0.857040	+	0.515250i	$0.827699\pi$
$182$	24.7053	−	70.6038i	0.135744	−	0.387933i
$183$		0			0
$184$	−53.4163	−	85.0115i	−0.290306	−	0.462019i
$185$	−4.82706	−	13.7949i	−0.0260922	−	0.0745673i
$186$		0			0
$187$	−19.7106	+	40.9295i	−0.105404	+	0.218874i
$188$	182.066	−	20.5139i	0.968437	−	0.109117i
$189$		0			0
$190$	−54.6996	−	26.3419i	−0.287893	−	0.138642i
$191$	−63.9811	−	63.9811i	−0.334980	−	0.334980i	0.519494	−	0.854474i	$-0.326120\pi$
$191$	−63.9811	−	63.9811i	−0.334980	−	0.334980i	−0.854474	+	0.519494i	$0.826120\pi$
$192$		0			0
$193$	−11.0125	+	6.91962i	−0.0570597	+	0.0358530i	−0.560260	−	0.828317i	$-0.689299\pi$
$193$	−11.0125	+	6.91962i	−0.0570597	+	0.0358530i	0.503200	+	0.864170i	$0.332156\pi$
$194$	94.9866	−	45.7432i	0.489622	−	0.235789i
$195$		0			0
$196$	−104.906	+	23.9441i	−0.535234	+	0.122164i
$197$	68.8268	−	86.3061i	0.349375	−	0.438102i	−0.575831	−	0.817569i	$-0.695321\pi$
$197$	68.8268	−	86.3061i	0.349375	−	0.438102i	0.925205	+	0.379467i	$0.123893\pi$
$198$		0			0
$199$	−35.9069	+	157.318i	−0.180437	+	0.790545i	0.800985	+	0.598684i	$0.204309\pi$
$199$	−35.9069	+	157.318i	−0.180437	+	0.790545i	−0.981422	+	0.191861i	$0.938548\pi$
$200$	−52.1531	−	32.7700i	−0.260765	−	0.163850i
$201$		0			0
$202$			175.002i			0.866346i
$203$	76.0232	−	61.0170i	0.374499	−	0.300576i
$204$		0			0
$205$	7.69419	−	68.2878i	0.0375326	−	0.333111i
$206$	−166.312	+	264.684i	−0.807340	+	1.28487i
$207$		0			0
$208$	128.060	−	102.125i	0.615674	−	0.490984i
$209$	−13.9297	−	11.1085i	−0.0666490	−	0.0531508i
$210$		0			0
$211$	−67.7357	+	193.577i	−0.321022	+	0.917429i	0.664411	+	0.747367i	$0.268682\pi$
$211$	−67.7357	+	193.577i	−0.321022	+	0.917429i	−0.985433	+	0.170062i	$0.945603\pi$
$212$	−44.4922	−	92.3889i	−0.209869	−	0.435797i
$213$		0			0
$214$	106.998	+	305.782i	0.499990	+	1.42889i
$215$	83.6893	−	83.6893i	0.389253	−	0.389253i
$216$		0			0
$217$	118.282	−	13.3272i	0.545078	−	0.0614155i
$218$	58.4011	+	518.324i	0.267895	+	2.37763i
$219$		0			0
$220$	−6.92787	−	6.92787i	−0.0314903	−	0.0314903i
$221$	−224.425	+	78.5296i	−1.01550	+	0.355338i
$222$		0			0
$223$	258.623	−	124.546i	1.15974	−	0.558503i	0.247796	−	0.968812i	$-0.420294\pi$
$223$	258.623	−	124.546i	1.15974	−	0.558503i	0.911946	+	0.410310i	$0.134579\pi$
$224$	121.998	+	42.6889i	0.544633	+	0.190575i
$225$		0			0
$226$	140.274	−	175.898i	0.620680	−	0.778309i
$227$	260.334	+	326.448i	1.14684	+	1.43810i	0.880390	+	0.474251i	$0.157281\pi$
$227$	260.334	+	326.448i	1.14684	+	1.43810i	0.266455	+	0.963847i	$0.414148\pi$
$228$		0			0
$229$	−188.462	−	118.419i	−0.822980	−	0.517113i	0.0534903	−	0.998568i	$-0.482965\pi$
$229$	−188.462	−	118.419i	−0.822980	−	0.517113i	−0.876470	+	0.481456i	$0.840108\pi$
$230$	−184.044	−	20.7368i	−0.800191	−	0.0901599i
$231$		0			0
$232$	86.4190	−	10.0113i	0.372496	−	0.0431521i
$233$	278.251			1.19421			0.597106	−	0.802162i	$-0.296317\pi$
$233$	278.251			1.19421			0.597106	+	0.802162i	$0.296317\pi$
$234$		0			0
$235$	−72.1913	+	114.892i	−0.307197	+	0.488901i
$236$	−235.517	−	53.7553i	−0.997955	−	0.227777i
$237$		0			0
$238$	−192.467	−	153.487i	−0.808684	−	0.644904i
$239$	−50.5445	−	221.450i	−0.211483	−	0.926568i	−0.963560	−	0.267493i	$-0.913805\pi$
$239$	−50.5445	−	221.450i	−0.211483	−	0.926568i	0.752077	−	0.659075i	$-0.229052\pi$
$240$		0			0
$241$	−42.8849	−	89.0514i	−0.177946	−	0.369508i	0.792850	−	0.609417i	$-0.208597\pi$
$241$	−42.8849	−	89.0514i	−0.177946	−	0.369508i	−0.970795	+	0.239909i	$0.922882\pi$
$242$	164.865	+	262.382i	0.681261	+	1.08422i
$243$		0			0
$244$	144.967	−	144.967i	0.594128	−	0.594128i
$245$	34.5763	−	71.7985i	0.141128	−	0.293055i
$246$		0			0
$247$	−10.4408	−	92.6645i	−0.0422704	−	0.375160i
$248$	95.7084	+	46.0907i	0.385921	+	0.185850i
$249$		0			0
$250$	−237.830	+	83.2203i	−0.951320	+	0.332881i
$251$	−194.960	+	122.502i	−0.776734	+	0.488055i	−0.861134	−	0.508377i	$-0.830245\pi$
$251$	−194.960	+	122.502i	−0.776734	+	0.488055i	0.0844001	+	0.996432i	$0.473103\pi$
$252$		0			0
$253$	−51.3017	−	17.9512i	−0.202774	−	0.0709535i
$254$	491.445	−	112.169i	1.93482	−	0.441611i
$255$		0			0
$256$	209.089	+	262.189i	0.816753	+	1.02418i
$257$	28.4685	−	124.729i	0.110772	−	0.485325i	−0.888859	−	0.458181i	$-0.848501\pi$
$257$	28.4685	−	124.729i	0.110772	−	0.485325i	0.999632	−	0.0271449i	$-0.00864154\pi$
$258$		0			0
$259$	23.0957	+	2.60226i	0.0891726	+	0.0100473i
$260$		−	51.2791i		−	0.197227i
$261$		0			0
$262$	662.850			2.52996
$263$	−49.1255	+	436.001i	−0.186789	+	1.65780i	0.454685	+	0.890653i	$0.349752\pi$
$263$	−49.1255	+	436.001i	−0.186789	+	1.65780i	−0.641473	+	0.767145i	$0.721677\pi$
$264$		0			0
$265$	74.0391	+	16.8989i	0.279393	+	0.0637696i
$266$	75.4842	−	60.1967i	0.283775	−	0.226303i
$267$		0			0
$268$	21.1400	+	92.6205i	0.0788807	+	0.345599i
$269$	9.97216	−	28.4988i	0.0370712	−	0.105944i	−0.923860	−	0.382730i	$-0.874984\pi$
$269$	9.97216	−	28.4988i	0.0370712	−	0.105944i	0.960931	+	0.276787i	$0.0892696\pi$
$270$		0			0
$271$	−151.857	−	241.680i	−0.560359	−	0.891807i	0.439620	−	0.898184i	$-0.355113\pi$
$271$	−151.857	−	241.680i	−0.560359	−	0.891807i	−0.999980	+	0.00637705i	$0.997970\pi$
$272$	−178.039	−	508.806i	−0.654555	−	1.87061i
$273$		0			0
$274$	−130.583	+	271.159i	−0.476581	+	0.989632i
$275$	−33.1342	+	3.73333i	−0.120488	+	0.0135757i
$276$		0			0
$277$	43.1264	+	20.7686i	0.155691	+	0.0749769i	0.510107	−	0.860111i	$-0.329606\pi$
$277$	43.1264	+	20.7686i	0.155691	+	0.0749769i	−0.354416	+	0.935088i	$0.615320\pi$
$278$	−154.826	−	154.826i	−0.556929	−	0.556929i
$279$		0			0
$280$	−18.0479	+	11.3402i	−0.0644567	+	0.0405008i
$281$	−233.726	+	112.557i	−0.831765	+	0.400557i	−0.800777	−	0.598963i	$-0.795580\pi$
$281$	−233.726	+	112.557i	−0.831765	+	0.400557i	−0.0309882	+	0.999520i	$0.509865\pi$
$282$		0			0
$283$	−291.071	+	66.4350i	−1.02852	+	0.234753i	−0.703305	−	0.710888i	$-0.748293\pi$
$283$	−291.071	+	66.4350i	−1.02852	+	0.234753i	−0.325213	+	0.945641i	$0.605436\pi$
$284$	−8.80683	+	11.0434i	−0.0310100	+	0.0388853i
$285$		0			0
$286$	8.04158	−	35.2324i	0.0281174	−	0.123190i
$287$	92.5323	+	58.1419i	0.322412	+	0.202585i
$288$		0			0
$289$			493.502i			1.70762i
$290$	84.9562	−	136.152i	0.292952	−	0.469489i
$291$		0			0
$292$	23.8799	−	211.940i	0.0817804	−	0.725821i
$293$	−86.6122	+	137.842i	−0.295605	+	0.470452i	−0.961197	−	0.275864i	$-0.911036\pi$
$293$	−86.6122	+	137.842i	−0.295605	+	0.470452i	0.665592	+	0.746316i	$0.268179\pi$
$294$		0			0
$295$	139.876	−	111.547i	0.474155	−	0.378126i
$296$	16.2168	+	12.9325i	0.0547866	+	0.0436909i
$297$		0			0
$298$	−0.804857	+	2.30015i	−0.00270086	+	0.00771862i
$299$	−123.428	−	256.300i	−0.412802	−	0.857191i
$300$		0			0
$301$	62.1634	+	177.653i	0.206523	+	0.590209i
$302$	310.069	−	310.069i	1.02672	−	1.02672i
$303$		0			0
$304$	210.085	−	23.6709i	0.691069	−	0.0778648i
$305$	16.9998	+	150.877i	0.0557371	+	0.494680i
$306$		0			0
$307$	−308.959	−	308.959i	−1.00638	−	1.00638i	−0.999980	−	0.00640010i	$-0.997963\pi$
$307$	−308.959	−	308.959i	−1.00638	−	1.00638i	−0.00640010	−	0.999980i	$-0.502037\pi$
$308$	14.7062	−	5.14594i	0.0477476	−	0.0167076i
$309$		0			0
$310$	176.553	−	85.0235i	0.569526	−	0.274269i
$311$	−138.716	−	48.5389i	−0.446033	−	0.156074i	0.0979112	−	0.995195i	$-0.468784\pi$
$311$	−138.716	−	48.5389i	−0.446033	−	0.156074i	−0.543944	+	0.839122i	$0.683070\pi$
$312$		0			0
$313$	191.897	−	240.631i	0.613089	−	0.768789i	−0.374265	−	0.927322i	$-0.622105\pi$
$313$	191.897	−	240.631i	0.613089	−	0.768789i	0.987354	+	0.158533i	$0.0506763\pi$
$314$	344.166	+	431.571i	1.09607	+	1.37443i
$315$		0			0
$316$	−73.1421	−	45.9582i	−0.231462	−	0.145437i
$317$	304.859	+	34.3493i	0.961699	+	0.108357i	0.578833	−	0.815446i	$-0.303508\pi$
$317$	304.859	+	34.3493i	0.961699	+	0.108357i	0.382866	+	0.923804i	$0.374937\pi$
$318$		0			0
$319$	33.1973	−	33.4059i	0.104067	−	0.104721i
$320$	49.8534			0.155792
$321$		0			0
$322$	156.699	−	249.386i	0.486644	−	0.774490i
$323$	−299.198	−	68.2899i	−0.926309	−	0.211424i
$324$		0			0
$325$	−136.444	−	108.811i	−0.419828	−	0.334802i
$326$	−143.972	−	630.784i	−0.441633	−	1.93492i
$327$		0			0
$328$	42.3163	+	87.8706i	0.129013	+	0.267898i
$329$	−114.803	−	182.708i	−0.348945	−	0.555344i
$330$		0			0
$331$	403.766	−	403.766i	1.21984	−	1.21984i	0.252147	−	0.967689i	$-0.418863\pi$
$331$	403.766	−	403.766i	1.21984	−	1.21984i	0.967689	−	0.252147i	$-0.0811368\pi$
$332$	−41.9633	+	87.1377i	−0.126395	+	0.262463i
$333$		0			0
$334$	−36.9734	−	328.148i	−0.110699	−	0.982478i
$335$	−63.3903	−	30.5272i	−0.189225	−	0.0911258i
$336$		0			0
$337$	−145.066	+	50.7607i	−0.430462	+	0.150625i	−0.536809	−	0.843704i	$-0.680370\pi$
$337$	−145.066	+	50.7607i	−0.430462	+	0.150625i	0.106347	+	0.994329i	$0.466085\pi$
$338$	−214.478	+	134.766i	−0.634551	+	0.398715i
$339$		0			0
$340$	−159.291	−	55.7384i	−0.468504	−	0.163937i
$341$	56.0648	−	12.7964i	0.164413	−	0.0375262i
$342$		0			0
$343$	181.709	+	227.856i	0.529763	+	0.664302i
$344$	−37.3773	+	163.760i	−0.108655	+	0.476048i
$345$		0			0
$346$	313.522	+	35.3255i	0.906134	+	0.102097i
$347$		−	133.826i		−	0.385665i	−0.981232	−	0.192833i	$-0.938233\pi$
$347$		−	133.826i		−	0.385665i	0.981232	−	0.192833i	$-0.0617675\pi$
$348$		0			0
$349$	302.341			0.866306			0.433153	−	0.901320i	$-0.357401\pi$
$349$	302.341			0.866306			0.433153	+	0.901320i	$0.357401\pi$
$350$	20.2308	−	179.553i	0.0578022	−	0.513009i
$351$		0			0
$352$	60.8789	+	13.8952i	0.172951	+	0.0394750i
$353$	228.144	−	181.939i	0.646300	−	0.515407i	−0.244590	−	0.969627i	$-0.578653\pi$
$353$	228.144	−	181.939i	0.646300	−	0.515407i	0.890890	+	0.454220i	$0.150082\pi$
$354$		0			0
$355$	−2.32777	−	10.1986i	−0.00655709	−	0.0287285i
$356$	59.2788	−	169.409i	0.166514	−	0.475869i
$357$		0			0
$358$	−134.422	−	213.931i	−0.375480	−	0.597573i
$359$	91.7727	+	262.271i	0.255634	+	0.730561i	0.998154	+	0.0607363i	$0.0193449\pi$
$359$	91.7727	+	262.271i	0.255634	+	0.730561i	−0.742520	+	0.669824i	$0.766369\pi$
$360$		0			0
$361$	−104.409	+	216.808i	−0.289222	+	0.600577i
$362$	−293.477	+	33.0669i	−0.810709	+	0.0913450i
$363$		0			0
$364$	73.4715	+	35.3820i	0.201845	+	0.0972033i
$365$	111.690	+	111.690i	0.306001	+	0.306001i
$366$		0			0
$367$	−333.384	+	209.479i	−0.908402	+	0.570787i	−0.903210	−	0.429200i	$-0.858796\pi$
$367$	−333.384	+	209.479i	−0.908402	+	0.570787i	−0.00519258	+	0.999987i	$0.501653\pi$
$368$	581.073	−	279.830i	1.57900	−	0.760408i
$369$		0			0
$370$	37.3036	−	8.51431i	0.100821	−	0.0230116i
$371$	−75.2986	+	94.4214i	−0.202961	+	0.254505i
$372$		0			0
$373$	−140.557	+	615.820i	−0.376828	+	1.65099i	0.330278	+	0.943884i	$0.392857\pi$
$373$	−140.557	+	615.820i	−0.376828	+	1.65099i	−0.707106	+	0.707107i	$0.750000\pi$
$374$	−100.704	−	63.2763i	−0.269261	−	0.169188i
$375$		0			0
$376$		−	192.574i		−	0.512166i
$377$	246.494	−	0.772011i	0.653829	−	0.00204778i
$378$		0			0
$379$	15.7228	−	139.543i	0.0414849	−	0.368188i	−0.955768	−	0.294121i	$-0.904973\pi$
$379$	15.7228	−	139.543i	0.0414849	−	0.368188i	0.997253	−	0.0740679i	$-0.0235981\pi$
$380$	35.2137	−	56.0423i	0.0926676	−	0.147480i
$381$		0			0
$382$	185.207	−	147.697i	0.484834	−	0.386642i
$383$	−36.2240	−	28.8877i	−0.0945798	−	0.0754248i	0.575058	−	0.818112i	$-0.304979\pi$
$383$	−36.2240	−	28.8877i	−0.0945798	−	0.0754248i	−0.669638	+	0.742688i	$0.733551\pi$
$384$		0			0
$385$	−3.81104	+	10.8913i	−0.00989880	+	0.0282891i
$386$	−14.7739	−	30.6783i	−0.0382743	−	0.0794774i
$387$		0			0
$388$	37.9606	+	108.485i	0.0978366	+	0.279601i
$389$	26.4083	−	26.4083i	0.0678878	−	0.0678878i	−0.672348	−	0.740235i	$-0.734714\pi$
$389$	26.4083	−	26.4083i	0.0678878	−	0.0678878i	0.740235	+	0.672348i	$0.234714\pi$
$390$		0			0
$391$	−930.321	+	104.822i	−2.37934	+	0.268087i
$392$	12.6630	+	112.387i	0.0323036	+	0.286702i
$393$		0			0
$394$	204.357	+	204.357i	0.518673	+	0.518673i
$395$	60.3840	−	21.1293i	0.152871	−	0.0534919i
$396$		0			0
$397$	117.280	−	56.4792i	0.295416	−	0.142265i	−0.280305	−	0.959911i	$-0.590436\pi$
$397$	117.280	−	56.4792i	0.295416	−	0.142265i	0.575721	+	0.817646i	$0.304721\pi$
$398$	−398.751	−	139.529i	−1.00189	−	0.350576i
$399$		0			0
$400$	246.691	−	309.340i	0.616727	−	0.773351i
$401$	66.7442	+	83.6946i	0.166444	+	0.208715i	0.858058	−	0.513553i	$-0.171671\pi$
$401$	66.7442	+	83.6946i	0.166444	+	0.208715i	−0.691613	+	0.722268i	$0.743100\pi$
$402$		0			0
$403$	254.851	+	160.133i	0.632384	+	0.397353i
$404$	−189.584	−	21.3610i	−0.469269	−	0.0528739i
$405$		0			0
$406$	136.456	+	215.666i	0.336099	+	0.531198i
$407$	11.2287			0.0275890
$408$		0			0
$409$	−50.0176	+	79.6026i	−0.122292	+	0.194627i	−0.902260	−	0.431193i	$-0.858093\pi$
$409$	−50.0176	+	79.6026i	−0.122292	+	0.194627i	0.779967	+	0.625820i	$0.215236\pi$
$410$	175.401	+	40.0341i	0.427807	+	0.0976442i
$411$		0			0
$412$	−266.440	−	212.478i	−0.646698	−	0.515724i
$413$	63.3094	+	277.377i	0.153292	+	0.671615i
$414$		0			0
$415$	−31.0776	−	64.5334i	−0.0748859	−	0.155502i
$416$	173.883	+	276.734i	0.417989	+	0.665225i
$417$		0			0
$418$	32.9829	−	32.9829i	0.0789064	−	0.0789064i
$419$	−231.659	+	481.044i	−0.552885	+	1.14808i	0.417981	+	0.908456i	$0.362738\pi$
$419$	−231.659	+	481.044i	−0.552885	+	1.14808i	−0.970866	+	0.239622i	$0.922977\pi$
$420$		0			0
$421$	34.7595	+	308.499i	0.0825641	+	0.732777i	0.964983	+	0.262312i	$0.0844851\pi$
$421$	34.7595	+	308.499i	0.0825641	+	0.732777i	−0.882419	+	0.470465i	$0.844086\pi$
$422$	−483.752	−	232.963i	−1.14633	−	0.552044i
$423$		0			0
$424$	−101.732	+	35.5976i	−0.239934	+	0.0839566i
$425$	−486.314	+	305.571i	−1.14427	+	0.718991i
$426$		0			0
$427$	−227.903	−	79.7468i	−0.533731	−	0.186761i
$428$	−344.323	+	78.5894i	−0.804492	+	0.183620i
$429$		0			0
$430$	193.193	+	242.256i	0.449286	+	0.563387i
$431$	−115.439	+	505.772i	−0.267840	+	1.17348i	0.644680	+	0.764452i	$0.276991\pi$
$431$	−115.439	+	505.772i	−0.267840	+	1.17348i	−0.912520	+	0.409032i	$0.865867\pi$
$432$		0			0
$433$	−296.513	−	33.4090i	−0.684788	−	0.0771570i	−0.237286	−	0.971440i	$-0.576258\pi$
$433$	−296.513	−	33.4090i	−0.684788	−	0.0771570i	−0.447502	+	0.894283i	$0.647686\pi$
$434$			311.626i			0.718033i
$435$		0			0
$436$	−568.644			−1.30423
$437$	41.1105	−	364.866i	0.0940744	−	0.834933i
$438$		0			0
$439$	−382.182	−	87.2307i	−0.870575	−	0.198703i	−0.236177	−	0.971710i	$-0.575895\pi$
$439$	−382.182	−	87.2307i	−0.870575	−	0.198703i	−0.634398	+	0.773007i	$0.718752\pi$
$440$	−8.05115	+	6.42058i	−0.0182981	+	0.0145922i
$441$		0			0
$442$	−138.516	−	606.878i	−0.313385	−	1.37303i
$443$	96.7899	−	276.610i	0.218487	−	0.624401i	−0.781513	−	0.623890i	$-0.785552\pi$
$443$	96.7899	−	276.610i	0.218487	−	0.624401i	1.00000		0.000511357i	$-0.000162770\pi$
$444$		0			0
$445$	70.7188	+	112.548i	0.158919	+	0.252918i
$446$	248.207	+	709.335i	0.556518	+	1.59044i
$447$		0			0
$448$	−34.3983	+	71.4288i	−0.0767819	+	0.159439i
$449$	250.577	−	28.2332i	0.558078	−	0.0628803i	0.171579	−	0.985170i	$-0.445113\pi$
$449$	250.577	−	28.2332i	0.558078	−	0.0628803i	0.386498	+	0.922290i	$0.373684\pi$
$450$		0			0
$451$	47.5687	+	22.9079i	0.105474	+	0.0507936i
$452$	173.433	+	173.433i	0.383701	+	0.383701i
$453$		0			0
$454$	−925.592	+	581.588i	−2.03875	+	1.28103i
$455$	−54.4123	+	26.2036i	−0.119588	+	0.0575903i
$456$		0			0
$457$	705.200	−	160.957i	1.54311	−	0.352204i	0.635525	−	0.772080i	$-0.280784\pi$
$457$	705.200	−	160.957i	1.54311	−	0.352204i	0.907581	+	0.419876i	$0.137927\pi$
$458$	363.320	−	455.588i	0.793274	−	0.994735i
$459$		0			0
$460$	44.9295	−	196.849i	0.0976728	−	0.427932i
$461$	216.528	+	136.054i	0.469693	+	0.295128i	0.746005	−	0.665940i	$-0.231969\pi$
$461$	216.528	+	136.054i	0.469693	+	0.295128i	−0.276312	+	0.961068i	$0.589112\pi$
$462$		0			0
$463$			184.621i			0.398750i	0.979923	+	0.199375i	$0.0638912\pi$
$463$			184.621i			0.398750i	−0.979923	+	0.199375i	$0.936109\pi$
$464$	1.75027	+	558.840i	0.00377214	+	1.20440i
$465$		0			0
$466$	−81.5632	+	723.893i	−0.175028	+	1.55342i
$467$	−49.4154	+	78.6442i	−0.105815	+	0.168403i	−0.895434	−	0.445193i	$-0.853135\pi$
$467$	−49.4154	+	78.6442i	−0.105815	+	0.168403i	0.789620	+	0.613596i	$0.210278\pi$
$468$		0			0
$469$	87.4772	−	69.7607i	0.186519	−	0.148744i
$470$	−277.739	−	221.489i	−0.590934	−	0.471254i
$471$		0			0
$472$	−83.8612	+	239.662i	−0.177672	+	0.507758i
$473$	39.4537	+	81.9265i	0.0834116	+	0.173206i
$474$		0			0
$475$	−74.3971	−	212.615i	−0.156626	−	0.447610i
$476$	189.770	−	189.770i	0.398676	−	0.398676i
$477$		0			0
$478$	590.935	−	66.5824i	1.23627	−	0.139294i
$479$	−25.3827	−	225.277i	−0.0529910	−	0.470308i	−0.991983	−	0.126370i	$-0.959667\pi$
$479$	−25.3827	−	225.277i	−0.0529910	−	0.470308i	0.938992	−	0.343938i	$-0.111761\pi$
$480$		0			0
$481$	41.5568	+	41.5568i	0.0863966	+	0.0863966i
$482$	244.245	−	85.4651i	0.506733	−	0.177313i
$483$		0			0
$484$	−304.369	+	146.576i	−0.628862	+	0.302844i
$485$	−80.3432	−	28.1133i	−0.165656	−	0.0579656i
$486$		0			0
$487$	−370.896	+	465.089i	−0.761593	+	0.955007i	−0.999869	−	0.0161901i	$-0.994846\pi$
$487$	−370.896	+	465.089i	−0.761593	+	0.955007i	0.238276	+	0.971197i	$0.423418\pi$
$488$	−134.352	−	168.472i	−0.275312	−	0.345230i
$489$		0			0
$490$	176.654	+	110.999i	0.360519	+	0.226529i
$491$	−626.759	−	70.6187i	−1.27649	−	0.143826i	−0.552430	−	0.833559i	$-0.686299\pi$
$491$	−626.759	−	70.6187i	−1.27649	−	0.143826i	−0.724064	+	0.689733i	$0.757728\pi$
$492$		0			0
$493$	265.531	−	766.536i	0.538602	−	1.55484i
$494$	244.135			0.494200
$495$		0			0
$496$	−363.048	+	577.787i	−0.731951	+	1.16489i
$497$	16.2185	+	3.70176i	0.0326327	+	0.00744821i
$498$		0			0
$499$	203.883	+	162.591i	0.408583	+	0.325834i	0.806120	−	0.591752i	$-0.201564\pi$
$499$	203.883	+	162.591i	0.408583	+	0.325834i	−0.397537	+	0.917586i	$0.630135\pi$
$500$	−61.1250	−	267.806i	−0.122250	−	0.535612i
$501$		0			0
$502$	−261.550	−	543.114i	−0.521015	−	1.08190i
$503$	−327.270	−	520.847i	−0.650636	−	1.03548i	−0.995308	−	0.0967578i	$-0.969153\pi$
$503$	−327.270	−	520.847i	−0.650636	−	1.03548i	0.344672	−	0.938723i	$-0.387990\pi$
$504$		0			0
$505$	99.9093	−	99.9093i	0.197840	−	0.197840i
$506$	61.7396	−	128.204i	0.122015	−	0.253367i
$507$		0			0
$508$	61.5293	+	546.088i	0.121121	+	1.07498i
$509$	−548.973	−	264.372i	−1.07853	−	0.519394i	−0.191685	−	0.981456i	$-0.561395\pi$
$509$	−548.973	−	264.372i	−1.07853	−	0.519394i	−0.886847	+	0.462063i	$0.847110\pi$
$510$		0			0
$511$	−237.092	+	82.9622i	−0.463977	+	0.162353i
$512$	−431.605	+	271.195i	−0.842978	+	0.529678i
$513$		0			0
$514$	316.147	+	110.625i	0.615071	+	0.215223i
$515$	246.057	−	56.1610i	0.477782	−	0.109051i
$516$		0			0
$517$	−64.9988	−	81.5060i	−0.125723	−	0.157652i
$518$	−13.5400	+	59.3225i	−0.0261390	+	0.114522i
$519$		0			0
$520$	−53.5588	−	6.03463i	−0.102998	−	0.0116051i
$521$			862.957i			1.65635i	0.560472	+	0.828174i	$0.310620\pi$
$521$			862.957i			1.65635i	−0.560472	+	0.828174i	$0.689380\pi$
$522$		0			0
$523$	−212.873			−0.407023			−0.203512	−	0.979073i	$-0.565235\pi$
$523$	−212.873			−0.407023			−0.203512	+	0.979073i	$0.565235\pi$
$524$	−80.9086	+	718.084i	−0.154406	+	1.37039i
$525$		0			0
$526$	−1119.89	−	255.608i	−2.12907	−	0.485947i
$527$	774.444	−	617.599i	1.46953	−	1.17191i
$528$		0			0
$529$	−131.533	−	576.286i	−0.248646	−	1.08939i
$530$	−65.6669	+	187.665i	−0.123900	+	0.354085i
$531$		0			0
$532$	55.9990	+	89.1219i	0.105261	+	0.167522i
$533$	91.2680	+	260.829i	0.171235	+	0.489360i
$534$		0			0
$535$	113.487	−	235.658i	0.212125	−	0.440481i
$536$	99.2259	−	11.1801i	0.185123	−	0.0208583i
$537$		0			0
$538$	71.2188	+	34.2972i	0.132377	+	0.0637494i
$539$	43.2932	+	43.2932i	0.0803214	+	0.0803214i
$540$		0			0
$541$	485.409	−	305.003i	0.897244	−	0.563776i	−0.00259581	−	0.999997i	$-0.500826\pi$
$541$	485.409	−	305.003i	0.897244	−	0.563776i	0.899840	+	0.436221i	$0.143683\pi$
$542$	673.263	−	324.226i	1.24218	−	0.598203i
$543$		0			0
$544$	1048.64	−	239.345i	1.92764	−	0.439972i
$545$	262.572	−	329.255i	0.481783	−	0.604137i
$546$		0			0
$547$	126.015	−	552.109i	0.230375	−	1.00934i	−0.718954	−	0.695057i	$-0.755379\pi$
$547$	126.015	−	552.109i	0.230375	−	1.00934i	0.949330	−	0.314282i	$-0.101764\pi$
$548$	−277.815	−	174.563i	−0.506962	−	0.318545i
$549$		0			0
$550$		−	87.2957i		−	0.158719i
$551$	269.920	+	168.425i	0.489873	+	0.305672i
$552$		0			0
$553$	−11.3908	+	101.096i	−0.0205981	+	0.182813i
$554$	−66.6727	+	106.109i	−0.120348	+	0.191533i
$555$		0			0
$556$	186.626	−	148.829i	0.335658	−	0.267679i
$557$	−476.901	−	380.316i	−0.856195	−	0.682793i	0.0936187	−	0.995608i	$-0.470157\pi$
$557$	−476.901	−	380.316i	−0.856195	−	0.682793i	−0.949814	+	0.312815i	$0.898728\pi$
$558$		0			0
$559$	−157.189	+	449.219i	−0.281196	+	0.803612i
$560$	−59.4077	−	123.361i	−0.106085	−	0.220288i
$561$		0			0
$562$	−224.313	−	641.050i	−0.399134	−	1.14066i
$563$	166.697	−	166.697i	0.296087	−	0.296087i	−0.543392	−	0.839479i	$-0.682860\pi$
$563$	166.697	−	166.697i	0.296087	−	0.296087i	0.839479	+	0.543392i	$0.182860\pi$
$564$		0			0
$565$	−180.504	+	20.3379i	−0.319475	+	0.0359962i
$566$	−87.5151	−	776.718i	−0.154620	−	1.37229i
$567$		0			0
$568$	10.4980	+	10.4980i	0.0184823	+	0.0184823i
$569$	−398.096	+	139.300i	−0.699641	+	0.244815i	−0.656579	−	0.754258i	$-0.727997\pi$
$569$	−398.096	+	139.300i	−0.699641	+	0.244815i	−0.0430621	+	0.999072i	$0.513711\pi$
$570$		0			0
$571$	436.857	−	210.379i	0.765074	−	0.368440i	−0.0102962	−	0.999947i	$-0.503277\pi$
$571$	436.857	−	210.379i	0.765074	−	0.368440i	0.775370	+	0.631507i	$0.217563\pi$
$572$	37.1867	+	13.0122i	0.0650118	+	0.0227486i
$573$		0			0
$574$	−178.385	+	223.687i	−0.310775	+	0.389699i
$575$	−428.441	−	537.248i	−0.745115	−	0.934344i
$576$		0			0
$577$	−319.262	−	200.606i	−0.553313	−	0.347670i	0.226175	−	0.974087i	$-0.427378\pi$
$577$	−319.262	−	200.606i	−0.553313	−	0.347670i	−0.779488	+	0.626417i	$0.784521\pi$
$578$	−1283.89	−	144.659i	−2.22126	−	0.250275i
$579$		0			0
$580$	137.127	+	108.654i	0.236426	+	0.187335i
$581$	113.905			0.196050
$582$		0			0
$583$	−31.0424	+	49.4037i	−0.0532460	+	0.0847405i
$584$	−218.552	−	49.8830i	−0.374233	−	0.0854161i
$585$		0			0
$586$	−333.220	−	265.734i	−0.568635	−	0.453471i
$587$	99.0689	+	434.049i	0.168772	+	0.739436i	0.986490	+	0.163819i	$0.0523812\pi$
$587$	99.0689	+	434.049i	0.168772	+	0.739436i	−0.817719	+	0.575618i	$0.804762\pi$
$588$		0			0
$589$	168.558	+	350.015i	0.286177	+	0.594254i
$590$	249.197	+	396.595i	0.422368	+	0.672195i
$591$		0			0
$592$	−94.2158	+	94.2158i	−0.159148	+	0.159148i
$593$	86.6242	−	179.877i	0.146078	−	0.303334i	−0.815073	−	0.579359i	$-0.803303\pi$
$593$	86.6242	−	179.877i	0.146078	−	0.303334i	0.961150	+	0.276025i	$0.0890172\pi$
$594$		0			0
$595$	22.2536	+	197.507i	0.0374011	+	0.331944i
$596$	−2.39357	−	1.15268i	−0.00401606	−	0.00193403i
$597$		0			0
$598$	702.966	−	245.978i	1.17553	−	0.411335i
$599$	584.155	−	367.049i	0.975218	−	0.612770i	0.0526531	−	0.998613i	$-0.483232\pi$
$599$	584.155	−	367.049i	0.975218	−	0.612770i	0.922564	+	0.385843i	$0.126089\pi$
$600$		0			0
$601$	770.520	+	269.617i	1.28206	+	0.448614i	0.883459	−	0.468509i	$-0.155209\pi$
$601$	770.520	+	269.617i	1.28206	+	0.448614i	0.398605	+	0.917123i	$0.369494\pi$
$602$	−480.400	+	109.648i	−0.798007	+	0.182140i
$603$		0			0
$604$	298.059	+	373.754i	0.493475	+	0.618798i
$605$	55.6724	−	243.917i	0.0920206	−	0.403168i
$606$		0			0
$607$	−417.041	−	46.9893i	−0.687053	−	0.0774123i	−0.238465	−	0.971151i	$-0.576644\pi$
$607$	−417.041	−	46.9893i	−0.687053	−	0.0774123i	−0.448588	+	0.893739i	$0.648073\pi$
$608$			421.845i			0.693825i
$609$		0			0
$610$	−397.503			−0.651644
$611$	61.0917	−	542.204i	0.0999864	−	0.887404i
$612$		0			0
$613$	−474.629	−	108.331i	−0.774272	−	0.176723i	−0.182911	−	0.983129i	$-0.558552\pi$
$613$	−474.629	−	108.331i	−0.774272	−	0.176723i	−0.591361	+	0.806407i	$0.701409\pi$
$614$	894.345	−	713.216i	1.45659	−	1.16159i
$615$		0			0
$616$	−3.64405	−	15.9656i	−0.00591566	−	0.0259182i
$617$	47.1635	−	134.786i	0.0764400	−	0.218453i	−0.899322	−	0.437287i	$-0.855940\pi$
$617$	47.1635	−	134.786i	0.0764400	−	0.218453i	0.975762	+	0.218834i	$0.0702252\pi$
$618$		0			0
$619$	284.337	+	452.519i	0.459349	+	0.731049i	0.993437	−	0.114379i	$-0.0364880\pi$
$619$	284.337	+	452.519i	0.459349	+	0.731049i	−0.534089	+	0.845429i	$0.679345\pi$
$620$	70.5580	+	201.643i	0.113803	+	0.325231i
$621$		0			0
$622$	166.939	−	346.653i	0.268391	−	0.557320i
$623$	−210.052	+	23.6672i	−0.337162	+	0.0379890i
$624$		0			0
$625$	−279.179	−	134.446i	−0.446687	−	0.215113i
$626$	569.771	+	569.771i	0.910177	+	0.910177i
$627$		0			0
$628$	−509.542	+	320.167i	−0.811373	+	0.509819i
$629$	174.261	−	83.9196i	0.277044	−	0.133417i
$630$		0			0
$631$	−615.560	+	140.498i	−0.975531	+	0.222659i	−0.680435	−	0.732809i	$-0.738209\pi$
$631$	−615.560	+	140.498i	−0.975531	+	0.222659i	−0.295097	+	0.955467i	$0.595352\pi$
$632$	−56.6089	+	70.9853i	−0.0895710	+	0.112318i
$633$		0			0
$634$	−178.725	+	783.046i	−0.281901	+	1.23509i
$635$	−344.606	−	216.530i	−0.542686	−	0.340992i
$636$		0			0
$637$			320.450i			0.503061i
$638$	77.1770	+	96.1576i	0.120967	+	0.150717i
$639$		0			0
$640$	21.7869	−	193.364i	0.0340420	−	0.302132i
$641$	165.562	−	263.490i	0.258287	−	0.411061i	−0.692257	−	0.721651i	$-0.743384\pi$
$641$	165.562	−	263.490i	0.258287	−	0.411061i	0.950544	+	0.310590i	$0.100527\pi$
$642$		0			0
$643$	338.182	−	269.691i	0.525944	−	0.419426i	−0.324191	−	0.945992i	$-0.605092\pi$
$643$	338.182	−	269.691i	0.525944	−	0.419426i	0.850135	+	0.526565i	$0.176520\pi$
$644$	251.040	+	200.197i	0.389813	+	0.310866i
$645$		0			0
$646$	265.365	−	758.369i	0.410782	−	1.17395i
$647$	−363.531	−	754.879i	−0.561871	−	1.16674i	−0.967540	−	0.252717i	$-0.918676\pi$
$647$	−363.531	−	754.879i	−0.561871	−	1.16674i	0.405669	−	0.914020i	$-0.367039\pi$
$648$		0			0
$649$	45.3983	+	129.741i	0.0699511	+	0.199909i
$650$	323.075	−	323.075i	0.497038	−	0.497038i
$651$		0			0
$652$	700.920	−	78.9747i	1.07503	−	0.121127i
$653$	74.8295	+	664.130i	0.114593	+	1.01705i	0.911035	+	0.412329i	$0.135285\pi$
$653$	74.8295	+	664.130i	0.114593	+	1.01705i	−0.796441	+	0.604716i	$0.793287\pi$
$654$		0			0
$655$	−378.423	−	378.423i	−0.577746	−	0.577746i
$656$	−591.341	+	206.919i	−0.901434	+	0.315425i
$657$		0			0
$658$	508.982	−	245.113i	0.773528	−	0.372512i
$659$	214.794	+	75.1598i	0.325940	+	0.114051i	0.488289	−	0.872682i	$-0.337621\pi$
$659$	214.794	+	75.1598i	0.325940	+	0.114051i	−0.162349	+	0.986733i	$0.551907\pi$
$660$		0			0
$661$	806.234	−	1010.99i	1.21972	−	1.52948i	0.447274	−	0.894397i	$-0.352395\pi$
$661$	806.234	−	1010.99i	1.21972	−	1.52948i	0.772445	−	0.635082i	$-0.219034\pi$
$662$	932.074	+	1168.78i	1.40797	+	1.76554i
$663$		0			0
$664$	86.0732	+	54.0834i	0.129628	+	0.0814509i
$665$	−77.4608	−	8.72773i	−0.116482	−	0.0131244i
$666$		0			0
$667$	946.909	+	213.008i	1.41965	+	0.319352i
$668$	360.005			0.538929
$669$		0			0
$670$	98.0003	−	155.967i	0.146269	−	0.232786i
$671$	−113.727	−	25.9576i	−0.169490	−	0.0386849i
$672$		0			0
$673$	680.365	+	542.573i	1.01094	+	0.806201i	0.981129	−	0.193354i	$-0.0619367\pi$
$673$	680.365	+	542.573i	1.01094	+	0.806201i	0.0298152	+	0.999555i	$0.490508\pi$
$674$	−89.5353	−	392.280i	−0.132842	−	0.582018i
$675$		0			0
$676$	−119.816	−	248.800i	−0.177242	−	0.368048i
$677$	96.3077	+	153.273i	0.142257	+	0.226400i	0.910251	−	0.414056i	$-0.135888\pi$
$677$	96.3077	+	153.273i	0.142257	+	0.226400i	−0.767995	+	0.640456i	$0.778745\pi$
$678$		0			0
$679$	95.7160	−	95.7160i	0.140966	−	0.140966i
$680$	−76.9621	+	159.813i	−0.113180	+	0.235020i
$681$		0			0
$682$	16.8568	+	149.608i	0.0247167	+	0.219367i
$683$	92.8083	+	44.6941i	0.135883	+	0.0654380i	0.500590	−	0.865685i	$-0.333116\pi$
$683$	92.8083	+	44.6941i	0.135883	+	0.0654380i	−0.364707	+	0.931122i	$0.618831\pi$
$684$		0			0
$685$	229.356	−	80.2552i	0.334827	−	0.117161i
$686$	−646.049	+	405.939i	−0.941762	+	0.591748i
$687$		0			0
$688$	−1018.45	−	356.372i	−1.48031	−	0.517982i
$689$	−297.725	+	67.9539i	−0.432112	+	0.0986268i
$690$		0			0
$691$	3.30579	+	4.14533i	0.00478407	+	0.00599903i	0.784218	−	0.620486i	$-0.213065\pi$
$691$	3.30579	+	4.14533i	0.00478407	+	0.00599903i	−0.779434	+	0.626485i	$0.784493\pi$
$692$	−76.5382	+	335.336i	−0.110604	+	0.484589i
$693$		0			0
$694$	348.159	+	39.2281i	0.501670	+	0.0565246i
$695$			176.782i			0.254362i
$696$		0			0
$697$	909.433			1.30478
$698$	−88.6245	+	786.564i	−0.126969	+	1.12688i
$699$		0			0
$700$	192.046	+	43.8331i	0.274351	+	0.0626188i
$701$	685.038	−	546.300i	0.977230	−	0.779315i	0.00188473	−	0.999998i	$-0.499400\pi$
$701$	685.038	−	546.300i	0.977230	−	0.779315i	0.975346	+	0.220683i	$0.0708286\pi$
$702$		0			0
$703$	16.8796	+	73.9542i	0.0240107	+	0.105198i
$704$	−12.6504	+	36.1528i	−0.0179693	+	0.0513535i
$705$		0			0
$706$	406.453	+	646.866i	0.575712	+	0.916241i
$707$	74.2114	+	212.084i	0.104967	+	0.299977i
$708$		0			0
$709$	−461.567	+	958.454i	−0.651011	+	1.35184i	0.270210	+	0.962801i	$0.412907\pi$
$709$	−461.567	+	958.454i	−0.651011	+	1.35184i	−0.921222	+	0.389038i	$0.872808\pi$
$710$	27.2149	−	3.06638i	0.0383308	−	0.00431884i
$711$		0			0
$712$	−169.965	−	81.8506i	−0.238714	−	0.114959i
$713$	838.009	+	838.009i	1.17533	+	1.17533i
$714$		0			0
$715$	−24.7053	+	15.5234i	−0.0345529	+	0.0217110i
$716$	248.165	−	119.510i	0.346600	−	0.166914i
$717$		0			0
$718$	−709.221	+	161.875i	−0.987773	+	0.225453i
$719$	−273.918	+	343.482i	−0.380971	+	0.477722i	−0.934935	−	0.354818i	$-0.884543\pi$
$719$	−273.918	+	343.482i	−0.380971	+	0.477722i	0.553965	+	0.832540i	$0.313114\pi$
$720$		0			0
$721$	−89.3107	+	391.296i	−0.123871	+	0.542713i
$722$	−533.439	−	335.182i	−0.738835	−	0.464241i
$723$		0			0
$724$		−	321.968i		−	0.444707i
$725$	580.083	−	134.313i	0.800114	−	0.185259i
$726$		0			0
$727$	110.794	−	983.327i	0.152399	−	1.35258i	−0.651876	−	0.758325i	$-0.726018\pi$
$727$	110.794	−	983.327i	0.152399	−	1.35258i	0.804276	−	0.594256i	$-0.202554\pi$
$728$	45.6013	−	72.5740i	0.0626391	−	0.0996896i
$729$		0			0
$730$	−323.311	+	257.832i	−0.442892	+	0.353194i
$731$	1224.58	+	976.568i	1.67521	+	1.33593i
$732$		0			0
$733$	228.839	−	653.984i	0.312195	−	0.892202i	−0.675714	−	0.737164i	$-0.736164\pi$
$733$	228.839	−	653.984i	0.312195	−	0.892202i	0.987909	−	0.155038i	$-0.0495499\pi$
$734$	−447.252	−	928.728i	−0.609335	−	1.26530i
$735$		0			0
$736$	425.031	+	1214.67i	0.577488	+	1.65037i
$737$	38.2232	−	38.2232i	0.0518633	−	0.0518633i
$738$		0			0
$739$	96.2273	−	10.8422i	0.130213	−	0.0146715i	−0.0466175	−	0.998913i	$-0.514844\pi$
$739$	96.2273	−	10.8422i	0.130213	−	0.0146715i	0.176830	+	0.984241i	$0.443416\pi$
$740$	4.67044	+	41.4513i	0.00631141	+	0.0560153i
$741$		0			0
$742$	−223.573	−	223.573i	−0.301311	−	0.301311i
$743$	374.477	−	131.035i	0.504007	−	0.176360i	−0.0662864	−	0.997801i	$-0.521115\pi$
$743$	374.477	−	131.035i	0.504007	−	0.176360i	0.570294	+	0.821441i	$0.306829\pi$
$744$		0			0
$745$	1.77266	−	0.853668i	0.00237941	−	0.00114586i
$746$	−1560.90	−	546.184i	−2.09236	−	0.732150i
$747$		0			0
$748$	80.8411	−	101.372i	0.108076	−	0.135523i
$749$	259.340	+	325.202i	0.346249	+	0.434182i
$750$		0			0
$751$	121.033	+	76.0501i	0.161163	+	0.101265i	0.610199	−	0.792249i	$-0.291090\pi$
$751$	121.033	+	76.0501i	0.161163	+	0.101265i	−0.449036	+	0.893514i	$0.648233\pi$
$752$	1229.26	+	138.505i	1.63466	+	0.184182i
$753$		0			0
$754$	−70.2456	+	641.499i	−0.0931640	+	0.850794i
$755$	−354.039			−0.468926
$756$		0			0
$757$	−365.032	+	580.945i	−0.482209	+	0.767431i	−0.995892	−	0.0905488i	$-0.971138\pi$
$757$	−365.032	+	580.945i	−0.482209	+	0.767431i	0.513683	+	0.857980i	$0.328281\pi$
$758$	358.425	+	81.8081i	0.472856	+	0.107926i
$759$		0			0
$760$	−54.3897	−	43.3744i	−0.0715654	−	0.0570715i
$761$	−260.780	−	1142.55i	−0.342681	−	1.50138i	−0.793391	−	0.608712i	$-0.791686\pi$
$761$	−260.780	−	1142.55i	−0.342681	−	1.50138i	0.450710	−	0.892670i	$-0.351171\pi$
$762$		0			0
$763$	290.577	+	603.389i	0.380835	+	0.790812i
$764$	137.398	+	218.668i	0.179840	+	0.286214i
$765$		0			0
$766$	85.7720	−	85.7720i	0.111974	−	0.111974i
$767$	−312.146	+	648.177i	−0.406969	+	0.845081i
$768$		0			0
$769$	−127.159	−	1128.57i	−0.165357	−	1.46758i	−0.752764	−	0.658291i	$-0.771280\pi$
$769$	−127.159	−	1128.57i	−0.165357	−	1.46758i	0.587407	−	0.809292i	$-0.300149\pi$
$770$	−27.2175	−	13.1073i	−0.0353474	−	0.0170224i
$771$		0			0
$772$	35.0380	−	12.2603i	0.0453860	−	0.0158812i
$773$	−348.475	+	218.961i	−0.450809	+	0.283262i	−0.738238	−	0.674540i	$-0.764342\pi$
$773$	−348.475	+	218.961i	−0.450809	+	0.283262i	0.287430	+	0.957802i	$0.407199\pi$
$774$		0			0
$775$	686.254	+	240.130i	0.885488	+	0.309846i
$776$	117.775	−	26.8815i	0.151772	−	0.0346411i
$777$		0			0
$778$	60.9624	+	76.4444i	0.0783579	+	0.0982576i
$779$	−79.3674	+	347.731i	−0.101884	+	0.446381i
$780$		0			0
$781$	7.98654	+	0.899867i	0.0102260	+	0.00115220i
$782$		−	2451.03i		−	3.13431i
$783$		0			0
$784$	−726.511			−0.926673
$785$	49.8996	−	442.871i	0.0635663	−	0.564167i
$786$		0			0
$787$	1444.84	+	329.776i	1.83589	+	0.419029i	0.992905	−	0.118913i	$-0.0379410\pi$
$787$	1444.84	+	329.776i	1.83589	+	0.419029i	0.842982	+	0.537942i	$0.180798\pi$
$788$	−246.330	+	196.442i	−0.312602	+	0.249291i
$789$		0			0
$790$	37.2693	+	163.288i	0.0471763	+	0.206693i
$791$	95.4058	−	272.654i	0.120614	−	0.344696i
$792$		0			0
$793$	−324.830	−	516.964i	−0.409622	−	0.651910i
$794$	112.557	+	321.670i	0.141760	+	0.405126i
$795$		0			0
$796$	199.828	−	414.947i	0.251040	−	0.521291i
$797$	−1314.76	+	148.138i	−1.64964	+	0.185870i	−0.887263	−	0.461264i	$-0.847396\pi$
$797$	−1314.76	+	148.138i	−1.64964	+	0.185870i	−0.762377	+	0.647133i	$0.775968\pi$
$798$		0			0
$799$	−1617.87	−	779.127i	−2.02487	−	0.975128i
$800$	558.248	+	558.248i	0.697810	+	0.697810i
$801$		0			0
$802$	−237.303	+	149.107i	−0.295889	+	0.185919i
$803$	−109.338	+	52.6542i	−0.136161	+	0.0655719i
$804$		0			0
$805$	−231.836	+	52.9150i	−0.287995	+	0.0657329i
$806$	−491.303	+	616.075i	−0.609558	+	0.764361i
$807$		0			0
$808$	−44.6214	+	195.499i	−0.0552245	+	0.241954i
$809$	−2.27206	−	1.42763i	−0.00280848	−	0.00176468i	0.530627	−	0.847605i	$-0.321956\pi$
$809$	−2.27206	−	1.42763i	−0.00280848	−	0.00176468i	−0.533436	+	0.845841i	$0.679099\pi$
$810$		0			0
$811$		−	1038.68i		−	1.28074i	−0.768065	−	0.640372i	$-0.778780\pi$
$811$		−	1038.68i		−	1.28074i	0.768065	−	0.640372i	$-0.221220\pi$
$812$	−250.294	+	121.502i	−0.308243	+	0.149633i
$813$		0			0
$814$	−3.29146	+	29.2125i	−0.00404356	+	0.0358876i
$815$	−277.923	+	442.312i	−0.341010	+	0.542714i
$816$		0			0
$817$	−480.271	+	383.004i	−0.587847	+	0.468793i
$818$	−192.431	−	153.459i	−0.235246	−	0.187602i
$819$		0			0
$820$	−64.7798	+	185.130i	−0.0789998	+	0.225768i
$821$	129.540	+	268.992i	0.157783	+	0.327639i	0.964842	−	0.262832i	$-0.0846564\pi$
$821$	129.540	+	268.992i	0.157783	+	0.327639i	−0.807059	+	0.590471i	$0.798942\pi$
$822$		0			0
$823$	−17.8224	−	50.9335i	−0.0216554	−	0.0618876i	0.932548	−	0.361045i	$-0.117580\pi$
$823$	−17.8224	−	50.9335i	−0.0216554	−	0.0618876i	−0.954204	+	0.299158i	$0.903294\pi$
$824$	−253.280	+	253.280i	−0.307378	+	0.307378i
$825$		0			0
$826$	−740.176	+	83.3978i	−0.896097	+	0.100966i
$827$	84.3167	+	748.331i	0.101955	+	0.904874i	0.935717	+	0.352751i	$0.114754\pi$
$827$	84.3167	+	748.331i	0.101955	+	0.904874i	−0.833762	+	0.552123i	$0.813818\pi$
$828$		0			0
$829$	577.896	+	577.896i	0.697100	+	0.697100i	0.963784	−	0.266684i	$-0.0859281\pi$
$829$	577.896	+	577.896i	0.697100	+	0.697100i	−0.266684	+	0.963784i	$0.585928\pi$
$830$	176.999	−	61.9345i	0.213251	−	0.0746198i
$831$		0			0
$832$	−180.617	+	86.9807i	−0.217088	+	0.104544i
$833$	995.433	+	348.317i	1.19500	+	0.418148i
$834$		0			0
$835$	−166.233	+	208.449i	−0.199081	+	0.249640i
$836$	31.7054	+	39.7573i	0.0379251	+	0.0475565i
$837$		0			0
$838$	−1183.57	−	743.687i	−1.41238	−	0.887454i
$839$	−984.677	−	110.946i	−1.17363	−	0.132237i	−0.496459	−	0.868060i	$-0.665367\pi$
$839$	−984.677	−	110.946i	−1.17363	−	0.132237i	−0.677173	+	0.735824i	$0.736795\pi$
$840$		0			0
$841$	−520.226	+	660.792i	−0.618580	+	0.785722i
$842$	−812.774			−0.965290
$843$		0			0
$844$	311.423	−	495.627i	0.368984	−	0.587235i
$845$	199.385	+	45.5083i	0.235958	+	0.0538560i
$846$		0			0
$847$	311.065	+	248.066i	0.367255	+	0.292876i
$848$	−154.062	−	674.991i	−0.181677	−	0.795980i
$849$		0			0
$850$	−652.416	−	1354.76i	−0.767549	−	1.59383i
$851$	123.116	+	195.938i	0.144672	+	0.230244i
$852$		0			0
$853$	−708.359	+	708.359i	−0.830432	+	0.830432i	−0.987576	−	0.157143i	$-0.949772\pi$
$853$	−708.359	+	708.359i	−0.830432	+	0.830432i	0.157143	+	0.987576i	$0.449772\pi$
$854$	274.273	−	569.533i	0.321162	−	0.666900i
$855$		0			0
$856$	41.5627	+	368.879i	0.0485545	+	0.430933i
$857$	−1042.24	−	501.914i	−1.21614	−	0.585665i	−0.287909	−	0.957658i	$-0.592960\pi$
$857$	−1042.24	−	501.914i	−1.21614	−	0.585665i	−0.928235	+	0.371993i	$0.878674\pi$
$858$		0			0
$859$	265.713	−	92.9771i	0.309328	−	0.108239i	−0.171151	−	0.985245i	$-0.554748\pi$
$859$	265.713	−	92.9771i	0.309328	−	0.108239i	0.480479	+	0.877006i	$0.340463\pi$
$860$	−286.025	+	179.721i	−0.332587	+	0.208978i
$861$		0			0
$862$	−1281.97	−	448.580i	−1.48720	−	0.520394i
$863$	679.019	−	154.982i	0.786812	−	0.179585i	0.189806	−	0.981822i	$-0.439214\pi$
$863$	679.019	−	154.982i	0.786812	−	0.179585i	0.597006	+	0.802237i	$0.296357\pi$
$864$		0			0
$865$	−158.824	−	199.159i	−0.183611	−	0.230241i
$866$	173.832	−	761.609i	0.200730	−	0.879457i
$867$		0			0
$868$	−337.594	−	38.0377i	−0.388933	−	0.0438222i
$869$			49.1511i			0.0565605i
$870$		0			0
$871$	282.923			0.324825
$872$	−66.9192	+	593.924i	−0.0767422	+	0.681106i
$873$		0			0
$874$	937.178	+	213.905i	1.07229	+	0.244742i
$875$	−252.935	+	201.709i	−0.289068	+	0.230524i
$876$		0			0
$877$	−109.131	−	478.132i	−0.124436	−	0.545191i	−0.998261	−	0.0589496i	$-0.981225\pi$
$877$	−109.131	−	478.132i	−0.124436	−	0.545191i	0.873825	−	0.486241i	$-0.161632\pi$
$878$	338.966	−	968.709i	0.386066	−	1.10331i
$879$		0			0
$880$	−35.1939	−	56.0108i	−0.0399931	−	0.0636487i
$881$	−533.158	−	1523.68i	−0.605173	−	1.72949i	−0.680919	−	0.732359i	$-0.738419\pi$
$881$	−533.158	−	1523.68i	−0.605173	−	1.72949i	0.0757457	−	0.997127i	$-0.475866\pi$
$882$		0			0
$883$	30.8917	−	64.1473i	0.0349849	−	0.0726470i	−0.882744	−	0.469854i	$-0.844306\pi$
$883$	30.8917	−	64.1473i	0.0349849	−	0.0726470i	0.917729	+	0.397207i	$0.130021\pi$
$884$	674.356	−	75.9817i	0.762846	−	0.0859521i
$885$		0			0
$886$	691.250	+	332.889i	0.780192	+	0.375721i
$887$	−703.431	−	703.431i	−0.793045	−	0.793045i	0.188943	−	0.981988i	$-0.439494\pi$
$887$	−703.431	−	703.431i	−0.793045	−	0.793045i	−0.981988	+	0.188943i	$0.939494\pi$
$888$		0			0
$889$	548.013	−	344.340i	0.616438	−	0.387334i
$890$	−313.533	+	150.990i	−0.352285	+	0.169651i
$891$		0			0
$892$	−798.740	+	182.307i	−0.895448	+	0.204380i
$893$	439.101	−	550.616i	0.491715	−	0.616591i
$894$		0			0
$895$	−45.3921	+	198.876i	−0.0507175	+	0.222208i
$896$	262.015	+	164.635i	0.292427	+	0.183744i
$897$		0			0
$898$			660.172i			0.735158i
$899$	−968.216	+	342.201i	−1.07699	+	0.380646i
$900$		0			0
$901$	−112.527	+	998.705i	−0.124891	+	1.10844i
$902$	−73.5405	+	117.039i	−0.0815305	+	0.129755i
$903$		0			0
$904$	201.553	−	160.733i	0.222957	−	0.177802i
$905$	186.425	+	148.669i	0.205995	+	0.164275i
$906$		0			0
$907$	59.8347	−	170.998i	0.0659699	−	0.188531i	−0.906179	−	0.422893i	$-0.861014\pi$
$907$	59.8347	−	170.998i	0.0659699	−	0.188531i	0.972149	+	0.234362i	$0.0753002\pi$
$908$	−517.072	−	1073.71i	−0.569462	−	1.18250i
$909$		0			0
$910$	−52.2210	−	149.239i	−0.0573857	−	0.163999i
$911$	152.526	−	152.526i	0.167427	−	0.167427i	−0.618420	−	0.785848i	$-0.712227\pi$
$911$	152.526	−	152.526i	0.167427	−	0.167427i	0.785848	+	0.618420i	$0.212227\pi$
$912$		0			0
$913$	54.6846	−	6.16147i	0.0598955	−	0.00674860i
$914$	212.030	+	1881.81i	0.231980	+	2.05888i
$915$		0			0
$916$	449.204	+	449.204i	0.490398	+	0.490398i
$917$	803.304	−	281.088i	0.876013	−	0.306530i
$918$		0			0
$919$	−565.486	+	272.324i	−0.615328	+	0.296326i	−0.715466	−	0.698647i	$-0.753786\pi$
$919$	−565.486	+	272.324i	−0.615328	+	0.296326i	0.100139	+	0.994973i	$0.468071\pi$
$920$	−200.313	−	70.0925i	−0.217731	−	0.0761875i
$921$		0			0
$922$	−417.426	+	523.435i	−0.452739	+	0.567717i
$923$	26.2273	+	32.8880i	0.0284152	+	0.0356316i
$924$		0			0
$925$	120.205	+	75.5296i	0.129951	+	0.0816536i
$926$	−480.307	−	54.1176i	−0.518690	−	0.0584423i
$927$		0			0
$928$	−1108.46	−	121.379i	−1.19446	−	0.130796i
$929$	492.172			0.529787			0.264893	−	0.964278i	$-0.414663\pi$
$929$	492.172			0.529787			0.264893	+	0.964278i	$0.414663\pi$
$930$		0			0
$931$	−220.055	+	350.216i	−0.236364	+	0.376172i
$932$	−774.258	−	176.719i	−0.830749	−	0.189613i
$933$		0			0
$934$	−190.114	−	151.611i	−0.203548	−	0.162324i
$935$	21.3674	+	93.6168i	0.0228529	+	0.100125i
$936$		0			0
$937$	−184.078	−	382.243i	−0.196455	−	0.407943i	0.779349	−	0.626590i	$-0.215550\pi$
$937$	−184.078	−	382.243i	−0.196455	−	0.407943i	−0.975804	+	0.218647i	$0.929836\pi$
$938$	155.846	+	248.028i	0.166147	+	0.264422i
$939$		0			0
$940$	273.847	−	273.847i	0.291327	−	0.291327i
$941$	216.286	−	449.122i	0.229847	−	0.477281i	−0.753866	−	0.657028i	$-0.771813\pi$
$941$	216.286	−	449.122i	0.229847	−	0.477281i	0.983713	+	0.179746i	$0.0575277\pi$
$942$		0			0
$943$	121.825	+	1081.23i	0.129189	+	1.14659i
$944$	−1469.52	−	707.684i	−1.55669	−	0.749665i
$945$		0			0
$946$	−224.703	+	78.6271i	−0.237530	+	0.0831153i
$947$	290.724	−	182.674i	0.306995	−	0.192898i	−0.369719	−	0.929144i	$-0.620546\pi$
$947$	290.724	−	182.674i	0.306995	−	0.192898i	0.676714	+	0.736246i	$0.263403\pi$
$948$		0			0
$949$	−599.520	−	209.781i	−0.631739	−	0.221055i
$950$	574.942	−	131.227i	0.605203	−	0.138134i
$951$		0			0
$952$	−175.874	−	220.539i	−0.184742	−	0.231659i
$953$	−175.056	+	766.968i	−0.183689	+	0.804794i	0.796165	+	0.605079i	$0.206859\pi$
$953$	−175.056	+	766.968i	−0.183689	+	0.804794i	−0.979854	+	0.199714i	$0.935999\pi$
$954$		0			0
$955$	−190.056	−	21.4142i	−0.199012	−	0.0224232i
$956$			648.304i			0.678143i
$957$		0			0
$958$	593.518			0.619539
$959$	−43.2655	+	383.992i	−0.0451152	+	0.400408i
$960$		0			0
$961$	−285.572	−	65.1799i	−0.297161	−	0.0678251i
$962$	−120.295	+	95.9318i	−0.125046	+	0.0997212i
$963$		0			0
$964$	62.7737	+	275.030i	0.0651180	+	0.285301i
$965$	−9.07988	+	25.9488i	−0.00940921	+	0.0268900i
$966$		0			0
$967$	−868.458	−	1382.14i	−0.898096	−	1.42931i	−0.903151	−	0.429324i	$-0.858752\pi$
$967$	−868.458	−	1382.14i	−0.898096	−	1.42931i	0.00505524	−	0.999987i	$-0.498391\pi$
$968$	117.274	+	335.150i	0.121151	+	0.346229i
$969$		0			0
$970$	96.6898	−	200.778i	0.0996802	−	0.206988i
$971$	1256.96	−	141.626i	1.29450	−	0.145856i	0.562296	−	0.826936i	$-0.309918\pi$
$971$	1256.96	−	141.626i	1.29450	−	0.145856i	0.732209	+	0.681080i	$0.238490\pi$
$972$		0			0
$973$	−253.289	−	121.977i	−0.260317	−	0.125362i
$974$	−1101.25	−	1101.25i	−1.13064	−	1.13064i
$975$		0			0
$976$	1172.04	−	736.442i	1.20086	−	0.754551i
$977$	733.846	−	353.401i	0.751121	−	0.361721i	−0.0188307	−	0.999823i	$-0.505994\pi$
$977$	733.846	−	353.401i	0.751121	−	0.361721i	0.769952	+	0.638102i	$0.220280\pi$
$978$		0			0
$979$	−99.5632	+	22.7247i	−0.101699	+	0.0232121i
$980$	−141.811	+	177.826i	−0.144705	+	0.181455i
$981$		0			0
$982$	367.441	−	1609.86i	0.374176	−	1.63937i
$983$	288.111	+	181.032i	0.293094	+	0.184163i	0.670550	−	0.741864i	$-0.266058\pi$
$983$	288.111	+	181.032i	0.293094	+	0.184163i	−0.377456	+	0.926028i	$0.623201\pi$
$984$		0			0
$985$		−	233.337i		−	0.236890i
$986$	1916.37	+	915.493i	1.94358	+	0.928492i
$987$		0			0
$988$	−29.7995	+	264.478i	−0.0301614	+	0.267690i
$989$	−997.006	+	1586.73i	−1.00810	+	1.60437i
$990$		0			0
$991$	1449.02	−	1155.56i	1.46218	−	1.16605i	0.510135	−	0.860094i	$-0.329595\pi$
$991$	1449.02	−	1155.56i	1.46218	−	1.16605i	0.952046	−	0.305956i	$-0.0989760\pi$
$992$	−1064.53	−	848.934i	−1.07311	−	0.855780i
$993$		0			0
$994$	−14.3845	+	41.1086i	−0.0144713	+	0.0413567i
$995$	147.991	+	307.306i	0.148735	+	0.308851i
$996$		0			0
$997$	78.3281	+	223.849i	0.0785638	+	0.224523i	0.976466	−	0.215673i	$-0.0691947\pi$
$997$	78.3281	+	223.849i	0.0785638	+	0.224523i	−0.897902	+	0.440196i	$0.854909\pi$
$998$	−482.757	+	482.757i	−0.483725	+	0.483725i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.172.1		48
3.2	odd	2		29.3.f.a.27.4	yes	48
29.14	odd	28	inner	261.3.s.a.217.1		48
87.14	even	28		29.3.f.a.14.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.14.4	✓	48	87.14	even	28
29.3.f.a.27.4	yes	48	3.2	odd	2
261.3.s.a.172.1		48	1.1	even	1	trivial
261.3.s.a.217.1		48	29.14	odd	28	inner

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.293128 + 2.60158i) q^{2} +(-2.78259 - 0.635107i) q^{4} +(1.65260 - 1.31790i) q^{5} +(0.747987 + 3.27715i) q^{7} +(-0.990802 + 2.83155i) q^{8} +O(q^{10})\)	\(q+(-0.293128 + 2.60158i) q^{2} +(-2.78259 - 0.635107i) q^{4} +(1.65260 - 1.31790i) q^{5} +(0.747987 + 3.27715i) q^{7} +(-0.990802 + 2.83155i) q^{8} +(2.94421 + 4.68569i) q^{10} +(0.536371 + 1.53286i) q^{11} +(-3.68793 + 7.65807i) q^{13} +(-8.74502 + 0.985327i) q^{14} +(-17.3621 - 8.36113i) q^{16} +(19.7801 + 19.7801i) q^{17} +(-9.28934 + 5.83688i) q^{19} +(-5.43551 + 2.61761i) q^{20} +(-4.14508 + 0.946088i) q^{22} +(-20.8669 + 26.1663i) q^{23} +(-4.56881 + 20.0173i) q^{25} +(-18.8421 - 11.8392i) q^{26} -9.59400i q^{28} +(-12.6644 - 26.0886i) q^{29} +(3.96474 - 35.1880i) q^{31} +(20.4573 - 32.5576i) q^{32} +(-57.2575 + 45.6614i) q^{34} +(5.55509 + 4.43004i) q^{35} +(2.28364 - 6.52628i) q^{37} +(-12.4622 - 25.8779i) q^{38} +(2.09431 + 5.98520i) q^{40} +(22.9886 - 22.9886i) q^{41} +(55.6405 - 6.26918i) q^{43} +(-0.518968 - 4.60597i) q^{44} +(-61.9571 - 61.9571i) q^{46} +(-60.5913 + 21.2018i) q^{47} +(33.9673 - 16.3578i) q^{49} +(-50.7373 - 17.7537i) q^{50} +(15.1257 - 18.9670i) q^{52} +(22.4008 + 28.0897i) q^{53} +(2.90657 + 1.82632i) q^{55} +(-10.0205 - 1.12904i) q^{56} +(71.5838 - 25.3002i) q^{58} +84.6397 q^{59} +(-38.2161 + 60.8206i) q^{61} +(90.3823 + 20.6292i) q^{62} +(18.4397 + 14.7051i) q^{64} +(3.99793 + 17.5161i) q^{65} +(-14.4421 - 29.9894i) q^{67} +(-42.4773 - 67.6022i) q^{68} +(-13.1535 + 13.1535i) q^{70} +(2.14727 - 4.45886i) q^{71} +(8.36674 + 74.2568i) q^{73} +(16.3092 + 7.85411i) q^{74} +(29.5554 - 10.3419i) q^{76} +(-4.62221 + 2.90432i) q^{77} +(28.5672 + 9.99609i) q^{79} +(-39.7117 + 9.06394i) q^{80} +(53.0682 + 66.5454i) q^{82} +(7.54034 - 33.0364i) q^{83} +(58.7568 + 6.62030i) q^{85} +146.591i q^{86} -4.87181 q^{88} +(-7.04081 + 62.4889i) q^{89} +(-27.8552 - 6.35776i) q^{91} +(74.6825 - 59.5573i) q^{92} +(-37.3973 - 163.848i) q^{94} +(-7.65912 + 21.8885i) q^{95} +(-21.4247 - 34.0971i) q^{97} +(32.5993 + 93.1635i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

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