LMFDB - Embedded newform 525.3.s.h.124.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(124,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("525.124");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 22x^{14} + 343x^{12} - 2542x^{10} + 13621x^{8} - 35080x^{6} + 64300x^{4} - 28000x^{2} + 10000 $ x^16 - 22x^14 + 343x^12 - 2542x^10 + 13621x^8 - 35080x^6 + 64300x^4 - 28000*x^2 + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.8
Root			$3.04878 - 1.76021i$ of defining polynomial
Character	$\chi$	$=$	525.124
Dual form			525.3.s.h.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.04878 + 1.76021i) q^{2} +(0.866025 + 1.50000i) q^{3} +(4.19671 + 7.26891i) q^{4} +6.09756i q^{6} +(6.99575 + 0.244004i) q^{7} +15.4667i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(3.04878 + 1.76021i) q^{2} +(0.866025 + 1.50000i) q^{3} +(4.19671 + 7.26891i) q^{4} +6.09756i q^{6} +(6.99575 + 0.244004i) q^{7} +15.4667i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-1.29685 - 2.24621i) q^{11} +(-7.26891 + 12.5901i) q^{12} +11.5763 q^{13} +(20.8990 + 13.0579i) q^{14} +(-10.4379 + 18.0789i) q^{16} +(11.6023 + 20.0957i) q^{17} +(-9.14634 + 5.28064i) q^{18} +(-25.9538 - 14.9844i) q^{19} +(5.69249 + 10.7049i) q^{21} -9.13094i q^{22} +(-30.4048 - 17.5542i) q^{23} +(-23.2000 + 13.3945i) q^{24} +(35.2936 + 20.3768i) q^{26} -5.19615 q^{27} +(27.5854 + 51.8754i) q^{28} +24.4905 q^{29} +(-32.4355 + 18.7266i) q^{31} +(-10.0673 + 5.81233i) q^{32} +(2.24621 - 3.89055i) q^{33} +81.6898i q^{34} -25.1802 q^{36} +(-22.2990 - 12.8743i) q^{37} +(-52.7516 - 91.3685i) q^{38} +(10.0254 + 17.3645i) q^{39} +3.71113i q^{41} +(-1.48783 + 42.6570i) q^{42} -74.2225i q^{43} +(10.8850 - 18.8534i) q^{44} +(-61.7983 - 107.038i) q^{46} +(-1.68959 + 2.92646i) q^{47} -36.1578 q^{48} +(48.8809 + 3.41398i) q^{49} +(-20.0957 + 34.8068i) q^{51} +(48.5823 + 84.1471i) q^{52} +(34.6744 - 20.0193i) q^{53} +(-15.8419 - 9.14634i) q^{54} +(-3.77394 + 108.201i) q^{56} -51.9076i q^{57} +(74.6661 + 43.1085i) q^{58} +(42.7180 - 24.6632i) q^{59} +(-0.765094 - 0.441727i) q^{61} -131.852 q^{62} +(-11.1276 + 17.8095i) q^{63} +42.5790 q^{64} +(13.6964 - 7.90763i) q^{66} +(-56.3388 + 32.5272i) q^{67} +(-97.3825 + 168.671i) q^{68} -60.8096i q^{69} +86.0786 q^{71} +(-40.1836 - 23.2000i) q^{72} +(30.7886 + 53.3274i) q^{73} +(-45.3231 - 78.5019i) q^{74} -251.541i q^{76} +(-8.52436 - 16.0304i) q^{77} +70.5872i q^{78} +(13.7718 - 23.8534i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.53239 + 11.3144i) q^{82} -131.445 q^{83} +(-53.9235 + 86.3036i) q^{84} +(130.648 - 226.288i) q^{86} +(21.2094 + 36.7357i) q^{87} +(34.7415 - 20.0580i) q^{88} +(56.5108 + 32.6265i) q^{89} +(80.9849 + 2.82467i) q^{91} -294.679i q^{92} +(-56.1799 - 32.4355i) q^{93} +(-10.3024 + 5.94809i) q^{94} +(-17.4370 - 10.0673i) q^{96} -42.2375 q^{97} +(143.018 + 96.4494i) q^{98} +7.78111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 12 * q^4 - 24 * q^9	$ 16 q + 12 q^{4} - 24 q^{9} + 40 q^{11} + 32 q^{14} - 4 q^{16} + 96 q^{21} - 96 q^{24} + 240 q^{26} + 200 q^{29} - 252 q^{31} - 72 q^{36} + 24 q^{39} + 36 q^{44} - 164 q^{46} - 76 q^{49} + 36 q^{51} - 36 q^{54} + 392 q^{56} + 108 q^{59} - 792 q^{61} + 8 q^{64} + 48 q^{66} + 328 q^{71} + 280 q^{74} + 412 q^{79} - 72 q^{81} - 264 q^{84} + 356 q^{86} - 564 q^{89} - 228 q^{91} - 60 q^{94} - 216 q^{96} - 240 q^{99}+O(q^{100}) $ 16 * q + 12 * q^4 - 24 * q^9 + 40 * q^11 + 32 * q^14 - 4 * q^16 + 96 * q^21 - 96 * q^24 + 240 * q^26 + 200 * q^29 - 252 * q^31 - 72 * q^36 + 24 * q^39 + 36 * q^44 - 164 * q^46 - 76 * q^49 + 36 * q^51 - 36 * q^54 + 392 * q^56 + 108 * q^59 - 792 * q^61 + 8 * q^64 + 48 * q^66 + 328 * q^71 + 280 * q^74 + 412 * q^79 - 72 * q^81 - 264 * q^84 + 356 * q^86 - 564 * q^89 - 228 * q^91 - 60 * q^94 - 216 * q^96 - 240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	3.04878	+	1.76021i	1.52439	+	0.880107i	0.999583	+	0.0288858i	$0.00919591\pi$
$2$	3.04878	+	1.76021i	1.52439	+	0.880107i	0.524807	+	0.851221i	$0.324137\pi$
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	4.19671	+	7.26891i	1.04918	+	1.81723i
$5$		0			0
$5$		0			0
$6$			6.09756i			1.01626i
$7$	6.99575	+	0.244004i	0.999392	+	0.0348577i
$7$	6.99575	+	0.244004i	0.999392	+	0.0348577i
$8$			15.4667i			1.93334i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.29685	−	2.24621i	−0.117896	−	0.204201i	0.801038	−	0.598614i	$-0.204281\pi$
$11$	−1.29685	−	2.24621i	−0.117896	−	0.204201i	−0.918934	+	0.394412i	$0.870948\pi$
$12$	−7.26891	+	12.5901i	−0.605742	+	1.04918i
$13$	11.5763			0.890485			0.445242	−	0.895410i	$-0.353117\pi$
$13$	11.5763			0.890485			0.445242	+	0.895410i	$0.353117\pi$
$14$	20.8990	+	13.0579i	1.49278	+	0.932709i
$15$		0			0
$16$	−10.4379	+	18.0789i	−0.652366	+	1.12993i
$17$	11.6023	+	20.0957i	0.682486	+	1.18210i	0.974220	+	0.225600i	$0.0724343\pi$
$17$	11.6023	+	20.0957i	0.682486	+	1.18210i	−0.291734	+	0.956499i	$0.594232\pi$
$18$	−9.14634	+	5.28064i	−0.508130	+	0.293369i
$19$	−25.9538	−	14.9844i	−1.36599	−	0.788654i	−0.375576	−	0.926791i	$-0.622555\pi$
$19$	−25.9538	−	14.9844i	−1.36599	−	0.788654i	−0.990413	+	0.138137i	$0.955889\pi$
$20$		0			0
$21$	5.69249	+	10.7049i	0.271071	+	0.509759i
$22$		−	9.13094i		−	0.415043i
$23$	−30.4048	−	17.5542i	−1.32195	−	0.763226i	−0.337908	−	0.941179i	$-0.609719\pi$
$23$	−30.4048	−	17.5542i	−1.32195	−	0.763226i	−0.984039	+	0.177953i	$0.943053\pi$
$24$	−23.2000	+	13.3945i	−0.966668	+	0.558106i
$25$		0			0
$26$	35.2936	+	20.3768i	1.35745	+	0.783722i
$27$	−5.19615			−0.192450
$28$	27.5854	+	51.8754i	0.985194	+	1.85269i
$29$	24.4905			0.844499			0.422250	−	0.906480i	$-0.361241\pi$
$29$	24.4905			0.844499			0.422250	+	0.906480i	$0.361241\pi$
$30$		0			0
$31$	−32.4355	+	18.7266i	−1.04631	+	0.604085i	−0.921613	−	0.388110i	$-0.873128\pi$
$31$	−32.4355	+	18.7266i	−1.04631	+	0.604085i	−0.124693	+	0.992195i	$0.539795\pi$
$32$	−10.0673	+	5.81233i	−0.314602	+	0.181635i
$33$	2.24621	−	3.89055i	0.0680670	−	0.117896i
$34$			81.6898i			2.40264i
$35$		0			0
$36$	−25.1802			−0.699451
$37$	−22.2990	−	12.8743i	−0.602675	−	0.347954i	0.167418	−	0.985886i	$-0.446457\pi$
$37$	−22.2990	−	12.8743i	−0.602675	−	0.347954i	−0.770093	+	0.637932i	$0.779790\pi$
$38$	−52.7516	−	91.3685i	−1.38820	−	2.40443i
$39$	10.0254	+	17.3645i	0.257061	+	0.445242i
$40$		0			0
$41$			3.71113i			0.0905155i	0.998975	+	0.0452577i	$0.0144109\pi$
$41$			3.71113i			0.0905155i	−0.998975	+	0.0452577i	$0.985589\pi$
$42$	−1.48783	+	42.6570i	−0.0354245	+	1.01564i
$43$		−	74.2225i		−	1.72611i	−0.505114	−	0.863053i	$-0.668549\pi$
$43$		−	74.2225i		−	1.72611i	0.505114	−	0.863053i	$-0.331451\pi$
$44$	10.8850	−	18.8534i	0.247386	−	0.428486i
$45$		0			0
$46$	−61.7983	−	107.038i	−1.34344	−	2.32691i
$47$	−1.68959	+	2.92646i	−0.0359488	+	0.0622652i	−0.883440	−	0.468544i	$-0.844779\pi$
$47$	−1.68959	+	2.92646i	−0.0359488	+	0.0622652i	0.847491	+	0.530809i	$0.178112\pi$
$48$	−36.1578			−0.753287
$49$	48.8809	+	3.41398i	0.997570	+	0.0696731i
$50$		0			0
$51$	−20.0957	+	34.8068i	−0.394033	+	0.682486i
$52$	48.5823	+	84.1471i	0.934276	+	1.61821i
$53$	34.6744	−	20.0193i	0.654234	−	0.377722i	−0.135843	−	0.990730i	$-0.543374\pi$
$53$	34.6744	−	20.0193i	0.654234	−	0.377722i	0.790076	+	0.613008i	$0.210041\pi$
$54$	−15.8419	−	9.14634i	−0.293369	−	0.169377i
$55$		0			0
$56$	−3.77394	+	108.201i	−0.0673917	+	1.93216i
$57$		−	51.9076i		−	0.910660i
$58$	74.6661	+	43.1085i	1.28735	+	0.743250i
$59$	42.7180	−	24.6632i	0.724033	−	0.418021i	−0.0922022	−	0.995740i	$-0.529391\pi$
$59$	42.7180	−	24.6632i	0.724033	−	0.418021i	0.816235	+	0.577720i	$0.196057\pi$
$60$		0			0
$61$	−0.765094	−	0.441727i	−0.0125425	−	0.00724143i	0.493716	−	0.869623i	$-0.335638\pi$
$61$	−0.765094	−	0.441727i	−0.0125425	−	0.00724143i	−0.506258	+	0.862382i	$0.668972\pi$
$62$	−131.852			−2.12664
$63$	−11.1276	+	17.8095i	−0.176628	+	0.282690i
$64$	42.5790			0.665297
$65$		0			0
$66$	13.6964	−	7.90763i	0.207521	−	0.119813i
$67$	−56.3388	+	32.5272i	−0.840877	+	0.485481i	−0.857562	−	0.514380i	$-0.828022\pi$
$67$	−56.3388	+	32.5272i	−0.840877	+	0.485481i	0.0166850	+	0.999861i	$0.494689\pi$
$68$	−97.3825	+	168.671i	−1.43210	+	2.48046i
$69$		−	60.8096i		−	0.881298i
$70$		0			0
$71$	86.0786			1.21237			0.606187	−	0.795322i	$-0.292698\pi$
$71$	86.0786			1.21237			0.606187	+	0.795322i	$0.292698\pi$
$72$	−40.1836	−	23.2000i	−0.558106	−	0.322223i
$73$	30.7886	+	53.3274i	0.421761	+	0.730512i	0.996112	−	0.0880974i	$-0.0280787\pi$
$73$	30.7886	+	53.3274i	0.421761	+	0.730512i	−0.574350	+	0.818609i	$0.694745\pi$
$74$	−45.3231	−	78.5019i	−0.612474	−	1.06084i
$75$		0			0
$76$		−	251.541i		−	3.30975i
$77$	−8.52436	−	16.0304i	−0.110706	−	0.208187i
$78$			70.5872i			0.904964i
$79$	13.7718	−	23.8534i	0.174326	−	0.301942i	−0.765602	−	0.643315i	$-0.777559\pi$
$79$	13.7718	−	23.8534i	0.174326	−	0.301942i	0.939928	+	0.341373i	$0.110892\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−6.53239	+	11.3144i	−0.0796633	+	0.137981i
$83$	−131.445			−1.58367			−0.791837	−	0.610732i	$-0.790875\pi$
$83$	−131.445			−1.58367			−0.791837	+	0.610732i	$0.790875\pi$
$84$	−53.9235	+	86.3036i	−0.641946	+	1.02742i
$85$		0			0
$86$	130.648	−	226.288i	1.51916	−	2.63126i
$87$	21.2094	+	36.7357i	0.243786	+	0.422250i
$88$	34.7415	−	20.0580i	0.394789	−	0.227932i
$89$	56.5108	+	32.6265i	0.634953	+	0.366590i	0.782668	−	0.622440i	$-0.213858\pi$
$89$	56.5108	+	32.6265i	0.634953	+	0.366590i	−0.147715	+	0.989030i	$0.547192\pi$
$90$		0			0
$91$	80.9849	+	2.82467i	0.889944	+	0.0310403i
$92$		−	294.679i		−	3.20304i
$93$	−56.1799	−	32.4355i	−0.604085	−	0.348769i
$94$	−10.3024	+	5.94809i	−0.109600	+	0.0632776i
$95$		0			0
$96$	−17.4370	−	10.0673i	−0.181635	−	0.104867i
$97$	−42.2375			−0.435438			−0.217719	−	0.976011i	$-0.569862\pi$
$97$	−42.2375			−0.435438			−0.217719	+	0.976011i	$0.569862\pi$
$98$	143.018	+	96.4494i	1.45937	+	0.984177i
$99$	7.78111			0.0785970
$100$		0			0
$101$	−129.874	+	74.9830i	−1.28589	+	0.742406i	−0.977918	−	0.208991i	$-0.932982\pi$
$101$	−129.874	+	74.9830i	−1.28589	+	0.742406i	−0.307968	+	0.951397i	$0.599649\pi$
$102$	−122.535	+	70.7454i	−1.20132	+	0.693583i
$103$	69.8388	−	120.964i	0.678047	−	1.17441i	−0.297521	−	0.954715i	$-0.596160\pi$
$103$	69.8388	−	120.964i	0.678047	−	1.17441i	0.975568	−	0.219697i	$-0.0705067\pi$
$104$			179.047i			1.72161i
$105$		0			0
$106$	140.953			1.32974
$107$	156.958	+	90.6198i	1.46690	+	0.846914i	0.999314	−	0.0370350i	$-0.0117913\pi$
$107$	156.958	+	90.6198i	1.46690	+	0.846914i	0.467584	+	0.883949i	$0.345125\pi$
$108$	−21.8067	−	37.7703i	−0.201914	−	0.349725i
$109$	−36.9049	−	63.9212i	−0.338577	−	0.586433i	0.645588	−	0.763686i	$-0.276612\pi$
$109$	−36.9049	−	63.9212i	−0.338577	−	0.586433i	−0.984165	+	0.177253i	$0.943279\pi$
$110$		0			0
$111$		−	44.5979i		−	0.401783i
$112$	−77.4319	+	123.928i	−0.691356	+	1.10650i
$113$		−	7.38562i		−	0.0653595i	−0.999466	−	0.0326797i	$-0.989596\pi$
$113$		−	7.38562i		−	0.0653595i	0.999466	−	0.0326797i	$-0.0104041\pi$
$114$	91.3685	−	158.255i	0.801478	−	1.38820i
$115$		0			0
$116$	102.779	+	178.019i	0.886029	+	1.53465i
$117$	−17.3645	+	30.0761i	−0.148414	+	0.257061i
$118$	173.650			1.47161
$119$	76.2630	+	143.415i	0.640866	+	1.20517i
$120$		0			0
$121$	57.1364	−	98.9631i	0.472201	−	0.817877i
$122$	−1.55507	−	2.69346i	−0.0127465	−	0.0220775i
$123$	−5.56670	+	3.21394i	−0.0452577	+	0.0261296i
$124$	−272.244	−	157.180i	−2.19552	−	1.26758i
$125$		0			0
$126$	−65.2740	+	34.7103i	−0.518047	+	0.275478i
$127$		−	208.640i		−	1.64283i	−0.570329	−	0.821416i	$-0.693184\pi$
$127$		−	208.640i		−	1.64283i	0.570329	−	0.821416i	$-0.306816\pi$
$128$	170.083	+	98.1975i	1.32877	+	0.767168i
$129$	111.334	−	64.2786i	0.863053	−	0.498284i
$130$		0			0
$131$	94.8997	+	54.7904i	0.724425	+	0.418247i	0.816379	−	0.577516i	$-0.195978\pi$
$131$	94.8997	+	54.7904i	0.724425	+	0.418247i	−0.0919540	+	0.995763i	$0.529311\pi$
$132$	37.7068			0.285657
$133$	−177.910	−	111.160i	−1.33767	−	0.835790i
$134$	−229.019			−1.70910
$135$		0			0
$136$	−310.814	+	179.448i	−2.28540	+	1.31947i
$137$	−153.678	+	88.7262i	−1.12174	+	0.647637i	−0.941844	−	0.336049i	$-0.890909\pi$
$137$	−153.678	+	88.7262i	−1.12174	+	0.647637i	−0.179895	+	0.983686i	$0.557576\pi$
$138$	107.038	−	185.395i	0.775636	−	1.34344i
$139$			169.894i			1.22226i	0.791532	+	0.611128i	$0.209284\pi$
$139$			169.894i			1.22226i	−0.791532	+	0.611128i	$0.790716\pi$
$140$		0			0
$141$	−5.85293			−0.0415101
$142$	262.435	+	151.517i	1.84813	+	1.06702i
$143$	−15.0127	−	26.0028i	−0.104984	−	0.181838i
$144$	−31.3136	−	54.2367i	−0.217455	−	0.376644i
$145$		0			0
$146$			216.778i			1.48478i
$147$	37.2111	+	76.2780i	0.253137	+	0.518898i
$148$		−	216.119i		−	1.46026i
$149$	42.6928	−	73.9461i	0.286529	−	0.496283i	−0.686450	−	0.727177i	$-0.740832\pi$
$149$	42.6928	−	73.9461i	0.286529	−	0.496283i	0.972979	+	0.230894i	$0.0741652\pi$
$150$		0			0
$151$	68.9977	+	119.507i	0.456938	+	0.791440i	0.998797	−	0.0490293i	$-0.0156128\pi$
$151$	68.9977	+	119.507i	0.456938	+	0.791440i	−0.541859	+	0.840469i	$0.682279\pi$
$152$	231.760	−	401.419i	1.52473	−	2.64092i
$153$	−69.6135			−0.454990
$154$	2.22799	−	63.8777i	0.0144675	−	0.414791i
$155$		0			0
$156$	−84.1471	+	145.747i	−0.539404	+	0.934276i
$157$	3.43335	+	5.94674i	0.0218685	+	0.0378773i	0.876753	−	0.480942i	$-0.159705\pi$
$157$	3.43335	+	5.94674i	0.0218685	+	0.0378773i	−0.854884	+	0.518819i	$0.826372\pi$
$158$	83.9742	−	48.4825i	0.531482	−	0.306851i
$159$	60.0578	+	34.6744i	0.377722	+	0.218078i
$160$		0			0
$161$	−208.421	−	130.224i	−1.29454	−	0.808843i
$162$		−	31.6838i		−	0.195579i
$163$	−239.652	−	138.363i	−1.47026	−	0.848854i	−0.470816	−	0.882231i	$-0.656040\pi$
$163$	−239.652	−	138.363i	−1.47026	−	0.848854i	−0.999443	+	0.0333772i	$0.989374\pi$
$164$	−26.9759	+	15.5745i	−0.164487	+	0.0949667i
$165$		0			0
$166$	−400.747	−	231.371i	−2.41414	−	1.39380i
$167$	42.3799			0.253772			0.126886	−	0.991917i	$-0.459502\pi$
$167$	42.3799			0.253772			0.126886	+	0.991917i	$0.459502\pi$
$168$	−165.570	+	88.0439i	−0.985535	+	0.524071i
$169$	−34.9892			−0.207036
$170$		0			0
$171$	77.8614	−	44.9533i	0.455330	−	0.262885i
$172$	539.517	−	311.490i	3.13673	−	1.81099i
$173$	14.7801	−	25.5999i	0.0854342	−	0.147976i	−0.820142	−	0.572160i	$-0.806106\pi$
$173$	14.7801	−	25.5999i	0.0854342	−	0.147976i	0.905576	+	0.424184i	$0.139439\pi$
$174$			149.332i			0.858231i
$175$		0			0
$176$	54.1454			0.307644
$177$	73.9897	+	42.7180i	0.418021	+	0.241344i
$178$	114.859	+	198.942i	0.645277	+	1.11765i
$179$	−74.3408	−	128.762i	−0.415312	−	0.719341i	0.580149	−	0.814510i	$-0.302994\pi$
$179$	−74.3408	−	128.762i	−0.415312	−	0.719341i	−0.995461	+	0.0951690i	$0.969661\pi$
$180$		0			0
$181$			257.302i			1.42156i	0.703414	+	0.710780i	$0.251658\pi$
$181$			257.302i			1.42156i	−0.703414	+	0.710780i	$0.748342\pi$
$182$	241.933	+	151.163i	1.32930	+	0.830563i
$183$		−	1.53019i		−	0.00836168i
$184$	271.505	−	470.261i	1.47557	−	2.55577i
$185$		0			0
$186$	−114.187	−	197.777i	−0.613908	−	1.06332i
$187$	30.0928	−	52.1223i	0.160924	−	0.278729i
$188$	−28.3629			−0.150867
$189$	−36.3510	−	1.26788i	−0.192333	−	0.00670837i
$190$		0			0
$191$	−60.8021	+	105.312i	−0.318336	+	0.551373i	−0.980141	−	0.198302i	$-0.936457\pi$
$191$	−60.8021	+	105.312i	−0.318336	+	0.551373i	0.661805	+	0.749676i	$0.269791\pi$
$192$	36.8745	+	63.8685i	0.192055	+	0.332649i
$193$	−210.039	+	121.266i	−1.08829	+	0.628323i	−0.933120	−	0.359566i	$-0.882925\pi$
$193$	−210.039	+	121.266i	−1.08829	+	0.628323i	−0.155167	+	0.987888i	$0.549592\pi$
$194$	−128.773	−	74.3470i	−0.663777	−	0.383232i
$195$		0			0
$196$	180.323	+	369.638i	0.920015	+	1.88591i
$197$		−	98.9929i		−	0.502502i	−0.967922	−	0.251251i	$-0.919158\pi$
$197$		−	98.9929i		−	0.502502i	0.967922	−	0.251251i	$-0.0808420\pi$
$198$	23.7229	+	13.6964i	0.119813	+	0.0691738i
$199$	−68.2115	+	39.3819i	−0.342772	+	0.197899i	−0.661497	−	0.749948i	$-0.730079\pi$
$199$	−68.2115	+	39.3819i	−0.342772	+	0.197899i	0.318725	+	0.947847i	$0.396745\pi$
$200$		0			0
$201$	−97.5816	−	56.3388i	−0.485481	−	0.280292i
$202$	−527.945			−2.61359
$203$	171.329	+	5.97578i	0.843986	+	0.0294373i
$204$	−337.343			−1.65364
$205$		0			0
$206$	425.846	−	245.863i	2.06722	−	1.19351i
$207$	91.2143	−	52.6626i	0.440649	−	0.254409i
$208$	−120.832	+	209.287i	−0.580922	+	1.00619i
$209$			77.7303i			0.371915i
$210$		0			0
$211$	−107.144			−0.507790			−0.253895	−	0.967232i	$-0.581712\pi$
$211$	−107.144			−0.507790			−0.253895	+	0.967232i	$0.581712\pi$
$212$	291.036	+	168.030i	1.37281	+	0.792594i
$213$	74.5462	+	129.118i	0.349982	+	0.606187i
$214$	319.020	+	552.559i	1.49075	+	2.58205i
$215$		0			0
$216$		−	80.3673i		−	0.372071i
$217$	−231.480	+	123.092i	−1.06673	+	0.567246i
$218$		−	259.842i		−	1.19194i
$219$	−53.3274	+	92.3657i	−0.243504	+	0.421761i
$220$		0			0
$221$	134.311	+	232.634i	0.607743	+	1.05264i
$222$	78.5019	−	135.969i	0.353612	−	0.612474i
$223$	−8.72021			−0.0391041			−0.0195520	−	0.999809i	$-0.506224\pi$
$223$	−8.72021			−0.0391041			−0.0195520	+	0.999809i	$0.506224\pi$
$224$	−71.8462	+	38.2051i	−0.320742	+	0.170559i
$225$		0			0
$226$	13.0003	−	22.5171i	0.0575233	−	0.0996333i
$227$	−126.511	−	219.123i	−0.557316	−	0.965299i	−0.997719	−	0.0674992i	$-0.978498\pi$
$227$	−126.511	−	219.123i	−0.557316	−	0.965299i	0.440404	−	0.897800i	$-0.354835\pi$
$228$	377.312	−	217.841i	1.65488	−	0.955443i
$229$	−125.988	−	72.7394i	−0.550167	−	0.317639i	0.199022	−	0.979995i	$-0.436223\pi$
$229$	−125.988	−	72.7394i	−0.550167	−	0.317639i	−0.749189	+	0.662356i	$0.769557\pi$
$230$		0			0
$231$	16.6632	−	26.6692i	0.0721352	−	0.115451i
$232$			378.787i			1.63270i
$233$	223.015	+	128.758i	0.957146	+	0.552609i	0.895294	−	0.445477i	$-0.146966\pi$
$233$	223.015	+	128.758i	0.957146	+	0.552609i	0.0618526	+	0.998085i	$0.480299\pi$
$234$	−105.881	+	61.1303i	−0.452482	+	0.261241i
$235$		0			0
$236$	358.549	+	207.009i	1.51928	+	0.877155i
$237$	47.7068			0.201295
$238$	−19.9326	+	571.481i	−0.0837506	+	2.40118i
$239$	128.682			0.538418			0.269209	−	0.963082i	$-0.413238\pi$
$239$	128.682			0.538418			0.269209	+	0.963082i	$0.413238\pi$
$240$		0			0
$241$	−8.02227	+	4.63166i	−0.0332874	+	0.0192185i	−0.516551	−	0.856256i	$-0.672784\pi$
$241$	−8.02227	+	4.63166i	−0.0332874	+	0.0192185i	0.483264	+	0.875475i	$0.339451\pi$
$242$	348.392	−	201.144i	1.43964	−	0.831175i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$		−	7.41519i		−	0.0303901i
$245$		0			0
$246$	−22.6289			−0.0919872
$247$	−300.449	−	173.464i	−1.21639	−	0.702285i
$248$	−289.639	−	501.670i	−1.16790	−	2.02286i
$249$	−113.835	−	197.167i	−0.457167	−	0.791837i
$250$		0			0
$251$		−	29.9212i		−	0.119208i	−0.998222	−	0.0596040i	$-0.981016\pi$
$251$		−	29.9212i		−	0.119208i	0.998222	−	0.0596040i	$-0.0189838\pi$
$252$	−176.155	−	6.14408i	−0.699026	−	0.0243813i
$253$			91.0608i			0.359924i
$254$	367.251	−	636.097i	1.44587	−	2.50432i
$255$		0			0
$256$	260.539	+	451.267i	1.01773	+	1.76276i
$257$	−48.3438	+	83.7338i	−0.188108	+	0.325813i	−0.944619	−	0.328168i	$-0.893569\pi$
$257$	−48.3438	+	83.7338i	−0.188108	+	0.325813i	0.756511	+	0.653980i	$0.226902\pi$
$258$	452.576			1.75417
$259$	−152.857	−	95.5065i	−0.590180	−	0.368751i
$260$		0			0
$261$	−36.7357	+	63.6281i	−0.140750	+	0.243786i
$262$	192.886	+	334.088i	0.736204	+	1.27514i
$263$	−55.6388	+	32.1231i	−0.211554	+	0.122141i	−0.602034	−	0.798471i	$-0.705643\pi$
$263$	−55.6388	+	32.1231i	−0.211554	+	0.122141i	0.390479	+	0.920612i	$0.372309\pi$
$264$	60.1740	+	34.7415i	0.227932	+	0.131596i
$265$		0			0
$266$	−346.743	−	652.062i	−1.30354	−	2.45136i
$267$			113.022i			0.423302i
$268$	−472.875	−	273.014i	−1.76446	−	1.01871i
$269$	171.096	−	98.7823i	0.636044	−	0.367220i	−0.147045	−	0.989130i	$-0.546976\pi$
$269$	171.096	−	98.7823i	0.636044	−	0.367220i	0.783089	+	0.621910i	$0.213643\pi$
$270$		0			0
$271$	−133.483	−	77.0667i	−0.492559	−	0.284379i	0.233077	−	0.972458i	$-0.425121\pi$
$271$	−133.483	−	77.0667i	−0.492559	−	0.284379i	−0.725635	+	0.688080i	$0.758454\pi$
$272$	−484.410			−1.78092
$273$	65.8980	+	123.924i	0.241385	+	0.453932i
$274$	−624.708			−2.27996
$275$		0			0
$276$	442.019	−	255.200i	1.60152	−	0.924637i
$277$	293.758	−	169.602i	1.06050	−	0.612280i	0.134929	−	0.990855i	$-0.456919\pi$
$277$	293.758	−	169.602i	1.06050	−	0.612280i	0.925570	+	0.378575i	$0.123586\pi$
$278$	−299.049	+	517.968i	−1.07572	+	1.86320i
$279$		−	112.360i		−	0.402724i
$280$		0			0
$281$	−111.976			−0.398492			−0.199246	−	0.979949i	$-0.563849\pi$
$281$	−111.976			−0.398492			−0.199246	+	0.979949i	$0.563849\pi$
$282$	−17.8443	−	10.3024i	−0.0632776	−	0.0365333i
$283$	32.7042	+	56.6453i	0.115563	+	0.200160i	0.918004	−	0.396570i	$-0.129800\pi$
$283$	32.7042	+	56.6453i	0.115563	+	0.200160i	−0.802442	+	0.596730i	$0.796466\pi$
$284$	361.246	+	625.697i	1.27199	+	2.20316i
$285$		0			0
$286$		−	105.703i		−	0.369589i
$287$	−0.905532	+	25.9622i	−0.00315516	+	0.0904605i
$288$		−	34.8740i		−	0.121090i
$289$	−124.725	+	216.029i	−0.431573	+	0.747507i
$290$		0			0
$291$	−36.5787	−	63.3562i	−0.125700	−	0.217719i
$292$	−258.421	+	447.599i	−0.885004	+	1.53287i
$293$	−100.992			−0.344681			−0.172341	−	0.985037i	$-0.555133\pi$
$293$	−100.992			−0.344681			−0.172341	+	0.985037i	$0.555133\pi$
$294$	−20.8170	+	298.054i	−0.0708060	+	1.01379i
$295$		0			0
$296$	199.123	−	344.891i	0.672713	−	1.16517i
$297$	6.73864	+	11.6717i	0.0226890	+	0.0392985i
$298$	260.322	−	150.297i	0.873564	−	0.504352i
$299$	−351.975	−	203.213i	−1.17717	−	0.679642i
$300$		0			0
$301$	18.1106	−	519.242i	0.0601681	−	1.72506i
$302$			485.802i			1.60862i
$303$	−224.949	−	129.874i	−0.742406	−	0.428628i
$304$	541.804	−	312.811i	1.78225	−	1.02898i
$305$		0			0
$306$	−212.236	−	122.535i	−0.693583	−	0.400440i
$307$	−400.388			−1.30420			−0.652098	−	0.758135i	$-0.726111\pi$
$307$	−400.388			−1.30420			−0.652098	+	0.758135i	$0.726111\pi$
$308$	80.7490	−	129.237i	0.262172	−	0.419602i
$309$	241.929			0.782941
$310$		0			0
$311$	−31.1758	+	17.9993i	−0.100244	+	0.0578757i	−0.549284	−	0.835636i	$-0.685099\pi$
$311$	−31.1758	+	17.9993i	−0.100244	+	0.0578757i	0.449040	+	0.893512i	$0.351766\pi$
$312$	−268.571	+	155.059i	−0.860803	+	0.496985i
$313$	−57.2476	+	99.1558i	−0.182900	+	0.316792i	−0.942867	−	0.333170i	$-0.891882\pi$
$313$	−57.2476	+	99.1558i	−0.182900	+	0.316792i	0.759967	+	0.649962i	$0.225215\pi$
$314$			24.1737i			0.0769864i
$315$		0			0
$316$	231.184			0.731596
$317$	−3.49195	−	2.01608i	−0.0110156	−	0.00635987i	0.494482	−	0.869188i	$-0.335358\pi$
$317$	−3.49195	−	2.01608i	−0.0110156	−	0.00635987i	−0.505498	+	0.862828i	$0.668691\pi$
$318$	122.069	+	211.429i	0.383864	+	0.664872i
$319$	−31.7605	−	55.0108i	−0.0995627	−	0.172448i
$320$		0			0
$321$			313.916i			0.977932i
$322$	−406.208	−	763.888i	−1.26151	−	2.37232i
$323$		−	695.413i		−	2.15298i
$324$	37.7703	−	65.4202i	0.116575	−	0.201914i
$325$		0			0
$326$	−487.098	−	843.678i	−1.49417	−	2.58797i
$327$	63.9212	−	110.715i	0.195478	−	0.338577i
$328$	−57.3989			−0.174997
$329$	−12.5340	+	20.0605i	−0.0380974	+	0.0609742i
$330$		0			0
$331$	−253.691	+	439.406i	−0.766439	+	1.32751i	0.173043	+	0.984914i	$0.444640\pi$
$331$	−253.691	+	439.406i	−0.766439	+	1.32751i	−0.939482	+	0.342598i	$0.888693\pi$
$332$	−551.636	−	955.461i	−1.66155	−	2.87790i
$333$	66.8969	−	38.6229i	0.200892	−	0.115985i
$334$	129.207	+	74.5976i	0.386847	+	0.223346i
$335$		0			0
$336$	−252.951	−	8.82265i	−0.752829	−	0.0262579i
$337$		−	264.279i		−	0.784210i	−0.919921	−	0.392105i	$-0.871747\pi$
$337$		−	264.279i		−	0.784210i	0.919921	−	0.392105i	$-0.128253\pi$
$338$	−106.674	−	61.5884i	−0.315604	−	0.182214i
$339$	11.0784	−	6.39614i	0.0326797	−	0.0188677i
$340$		0			0
$341$	84.1280	+	48.5713i	0.246710	+	0.142438i
$342$	316.510			0.925467
$343$	341.126	+	35.8105i	0.994535	+	0.104404i
$344$	1147.98			3.33714
$345$		0			0
$346$	90.1226	−	52.0323i	0.260470	−	0.150382i
$347$	−203.055	+	117.234i	−0.585172	+	0.337849i	−0.763186	−	0.646179i	$-0.776366\pi$
$347$	−203.055	+	117.234i	−0.585172	+	0.337849i	0.178014	+	0.984028i	$0.443033\pi$
$348$	−178.019	+	308.338i	−0.511549	+	0.886029i
$349$		−	54.2133i		−	0.155339i	−0.996979	−	0.0776695i	$-0.975252\pi$
$349$		−	54.2133i		−	0.155339i	0.996979	−	0.0776695i	$-0.0247479\pi$
$350$		0			0
$351$	−60.1522			−0.171374
$352$	26.1115	+	15.0755i	0.0741803	+	0.0428280i
$353$	260.913	+	451.914i	0.739129	+	1.28021i	0.952888	+	0.303322i	$0.0980959\pi$
$353$	260.913	+	451.914i	0.739129	+	1.28021i	−0.213759	+	0.976886i	$0.568571\pi$
$354$	150.385	+	260.475i	0.424818	+	0.735806i
$355$		0			0
$356$			547.696i			1.53847i
$357$	−149.077	+	238.596i	−0.417584	+	0.668336i
$358$		−	523.423i		−	1.46208i
$359$	−233.973	+	405.253i	−0.651735	+	1.12884i	0.330967	+	0.943642i	$0.392625\pi$
$359$	−233.973	+	405.253i	−0.651735	+	1.12884i	−0.982702	+	0.185196i	$0.940708\pi$
$360$		0			0
$361$	268.566	+	465.171i	0.743951	+	1.28856i
$362$	−452.907	+	784.458i	−1.25112	+	2.16701i
$363$	197.926			0.545251
$364$	319.337	+	600.526i	0.877301	+	1.64980i
$365$		0			0
$366$	2.69346	−	4.66520i	0.00735917	−	0.0127465i
$367$	−86.1123	−	149.151i	−0.234638	−	0.406406i	0.724529	−	0.689244i	$-0.242057\pi$
$367$	−86.1123	−	149.151i	−0.234638	−	0.406406i	−0.959168	+	0.282839i	$0.908724\pi$
$368$	634.721	−	366.456i	1.72479	−	0.995806i
$369$	−9.64181	−	5.56670i	−0.0261296	−	0.0150859i
$370$		0			0
$371$	247.458	−	131.589i	0.667003	−	0.354687i
$372$		−	544.489i		−	1.46368i
$373$	−399.213	−	230.486i	−1.07028	−	0.617924i	−0.142019	−	0.989864i	$-0.545359\pi$
$373$	−399.213	−	230.486i	−1.07028	−	0.617924i	−0.928257	+	0.371940i	$0.878693\pi$
$374$	183.493	−	105.940i	0.490622	−	0.283261i
$375$		0			0
$376$	−45.2627	−	26.1324i	−0.120379	−	0.0695011i
$377$	283.509			0.752014
$378$	−108.594	−	67.8510i	−0.287287	−	0.179500i
$379$	−444.638			−1.17319			−0.586594	−	0.809881i	$-0.699532\pi$
$379$	−444.638			−1.17319			−0.586594	+	0.809881i	$0.699532\pi$
$380$		0			0
$381$	312.960	−	180.687i	0.821416	−	0.474245i
$382$	−370.744	+	214.049i	−0.970535	+	0.560339i
$383$	−264.731	+	458.528i	−0.691205	+	1.19720i	0.280239	+	0.959930i	$0.409586\pi$
$383$	−264.731	+	458.528i	−0.691205	+	1.19720i	−0.971443	+	0.237271i	$0.923747\pi$
$384$			340.166i			0.885849i
$385$		0			0
$386$	−853.818			−2.21196
$387$	192.836	+	111.334i	0.498284	+	0.287684i
$388$	−177.258	−	307.020i	−0.456851	−	0.791290i
$389$	97.7554	+	169.317i	0.251299	+	0.435263i	0.963884	−	0.266323i	$-0.0858089\pi$
$389$	97.7554	+	169.317i	0.251299	+	0.435263i	−0.712585	+	0.701586i	$0.752476\pi$
$390$		0			0
$391$		−	814.674i		−	2.08356i
$392$	−52.8030	+	756.026i	−0.134701	+	1.92864i
$393$			189.799i			0.482950i
$394$	174.249	−	301.808i	0.442256	−	0.766009i
$395$		0			0
$396$	32.6550	+	56.5601i	0.0824622	+	0.142829i
$397$	−14.6276	+	25.3358i	−0.0368454	+	0.0638181i	−0.883860	−	0.467751i	$-0.845064\pi$
$397$	−14.6276	+	25.3358i	−0.0368454	+	0.0638181i	0.847015	+	0.531570i	$0.178398\pi$
$398$	−277.283			−0.696690
$399$	12.6657	−	363.132i	0.0317435	−	0.910106i
$400$		0			0
$401$	−105.396	+	182.551i	−0.262833	+	0.455241i	−0.966994	−	0.254800i	$-0.917990\pi$
$401$	−105.396	+	182.551i	−0.262833	+	0.455241i	0.704160	+	0.710041i	$0.251324\pi$
$402$	−198.337	−	343.529i	−0.493375	−	0.854550i
$403$	−375.483	+	216.785i	−0.931720	+	0.537929i
$404$	−1090.09	−	629.363i	−2.69824	−	1.55783i
$405$		0			0
$406$	511.826	+	319.795i	1.26066	+	0.787672i
$407$			66.7843i			0.164089i
$408$	−538.345	−	310.814i	−1.31947	−	0.761799i
$409$	−281.014	+	162.244i	−0.687077	+	0.396684i	−0.802516	−	0.596631i	$-0.796506\pi$
$409$	−281.014	+	162.244i	−0.687077	+	0.396684i	0.115439	+	0.993315i	$0.463172\pi$
$410$		0			0
$411$	−266.179	−	153.678i	−0.647637	−	0.373913i
$412$	1172.37			2.84556
$413$	304.862	−	162.114i	0.738164	−	0.392529i
$414$	370.790			0.895628
$415$		0			0
$416$	−116.542	+	67.2853i	−0.280148	+	0.161744i
$417$	−254.841	+	147.132i	−0.611128	+	0.352835i
$418$	−136.822	+	236.983i	−0.327325	+	0.566944i
$419$			693.958i			1.65622i	0.560563	+	0.828112i	$0.310585\pi$
$419$			693.958i			1.65622i	−0.560563	+	0.828112i	$0.689415\pi$
$420$		0			0
$421$	−341.554			−0.811292			−0.405646	−	0.914030i	$-0.632953\pi$
$421$	−341.554			−0.811292			−0.405646	+	0.914030i	$0.632953\pi$
$422$	−326.657	−	188.596i	−0.774070	−	0.446909i
$423$	−5.06878	−	8.77939i	−0.0119829	−	0.0207551i
$424$	309.632	+	536.298i	0.730264	+	1.26485i
$425$		0			0
$426$			524.869i			1.23209i
$427$	−5.24462	−	3.27690i	−0.0122825	−	0.00767423i
$428$			1521.22i			3.55425i
$429$	26.0028	−	45.0382i	0.0606127	−	0.104984i
$430$		0			0
$431$	205.726	+	356.328i	0.477323	+	0.826748i	0.999662	−	0.0259902i	$-0.00827387\pi$
$431$	205.726	+	356.328i	0.477323	+	0.826748i	−0.522339	+	0.852738i	$0.674941\pi$
$432$	54.2367	−	93.9407i	0.125548	−	0.217455i
$433$	−443.458			−1.02415			−0.512077	−	0.858940i	$-0.671124\pi$
$433$	−443.458			−1.02415			−0.512077	+	0.858940i	$0.671124\pi$
$434$	−922.400	−	32.1723i	−2.12535	−	0.0741298i
$435$		0			0
$436$	309.758	−	536.517i	0.710454	−	1.23054i
$437$	526.080	+	911.197i	1.20384	+	2.08512i
$438$	−325.167	+	187.735i	−0.742390	+	0.428619i
$439$	268.002	+	154.731i	0.610484	+	0.352463i	0.773155	−	0.634217i	$-0.218678\pi$
$439$	268.002	+	154.731i	0.610484	+	0.352463i	−0.162671	+	0.986680i	$0.552011\pi$
$440$		0			0
$441$	−82.1912	+	121.875i	−0.186375	+	0.276361i
$442$			945.666i			2.13952i
$443$	708.981	+	409.330i	1.60041	+	0.923996i	0.991405	+	0.130829i	$0.0417640\pi$
$443$	708.981	+	409.330i	1.60041	+	0.923996i	0.609004	+	0.793167i	$0.291569\pi$
$444$	324.178	−	187.164i	0.730131	−	0.421541i
$445$		0			0
$446$	−26.5860	−	15.3494i	−0.0596099	−	0.0344158i
$447$	147.892			0.330855
$448$	297.872	+	10.3895i	0.664893	+	0.0231908i
$449$	−315.756			−0.703243			−0.351621	−	0.936142i	$-0.614370\pi$
$449$	−315.756			−0.703243			−0.351621	+	0.936142i	$0.614370\pi$
$450$		0			0
$451$	8.33600	−	4.81279i	0.0184834	−	0.0106714i
$452$	53.6854	−	30.9953i	0.118773	−	0.0685736i
$453$	−119.507	+	206.993i	−0.263813	+	0.456938i
$454$		−	890.743i		−	1.96199i
$455$		0			0
$456$	802.839			1.76061
$457$	162.212	+	93.6533i	0.354950	+	0.204931i	0.666863	−	0.745180i	$-0.267636\pi$
$457$	162.212	+	93.6533i	0.354950	+	0.204931i	−0.311913	+	0.950111i	$0.600970\pi$
$458$	−256.074	−	443.533i	−0.559113	−	0.968412i
$459$	−60.2871	−	104.420i	−0.131344	−	0.227495i
$460$		0			0
$461$		−	8.27599i		−	0.0179523i	−0.999960	−	0.00897613i	$-0.997143\pi$
$461$		−	8.27599i		−	0.0179523i	0.999960	−	0.00897613i	$-0.00285723\pi$
$462$	97.7461	−	51.9778i	0.211572	−	0.112506i
$463$			472.925i			1.02144i	0.859748	+	0.510718i	$0.170620\pi$
$463$			472.925i			1.02144i	−0.859748	+	0.510718i	$0.829380\pi$
$464$	−255.628	+	442.761i	−0.550922	+	0.954226i
$465$		0			0
$466$	453.283	+	785.108i	0.972709	+	1.68478i
$467$	358.456	−	620.865i	0.767573	−	1.32948i	−0.171303	−	0.985218i	$-0.554798\pi$
$467$	358.456	−	620.865i	0.767573	−	1.32948i	0.938876	−	0.344257i	$-0.111869\pi$
$468$	−291.494			−0.622851
$469$	−402.069	+	213.805i	−0.857289	+	0.455875i
$470$		0			0
$471$	−5.94674	+	10.3001i	−0.0126258	+	0.0218685i
$472$	381.458	+	660.705i	0.808174	+	1.39980i
$473$	−166.720	+	96.2556i	−0.352473	+	0.203500i
$474$	145.448	+	83.9742i	0.306851	+	0.177161i
$475$		0			0
$476$	−722.420	+	1156.22i	−1.51769	+	2.42904i
$477$			120.116i			0.251815i
$478$	392.323	+	226.508i	0.820759	+	0.473866i
$479$	−178.320	+	102.953i	−0.372276	+	0.214933i	−0.674452	−	0.738319i	$-0.735620\pi$
$479$	−178.320	+	102.953i	−0.372276	+	0.214933i	0.302177	+	0.953252i	$0.402287\pi$
$480$		0			0
$481$	−258.140	−	149.037i	−0.536673	−	0.309848i
$482$	−32.6108			−0.0676573
$483$	14.8378	−	425.408i	0.0307201	−	0.880762i
$484$	959.138			1.98169
$485$		0			0
$486$	47.5258	−	27.4390i	0.0977897	−	0.0564589i
$487$	279.621	−	161.439i	0.574171	−	0.331498i	−0.184643	−	0.982806i	$-0.559113\pi$
$487$	279.621	−	161.439i	0.574171	−	0.331498i	0.758813	+	0.651308i	$0.225779\pi$
$488$	6.83205	−	11.8335i	0.0140001	−	0.0242489i
$489$		−	479.304i		−	0.980172i
$490$		0			0
$491$	272.380			0.554745			0.277372	−	0.960763i	$-0.410536\pi$
$491$	272.380			0.554745			0.277372	+	0.960763i	$0.410536\pi$
$492$	−46.7236	−	26.9759i	−0.0949667	−	0.0548290i
$493$	284.145	+	492.153i	0.576359	+	0.998282i
$494$	−610.669	−	1057.71i	−1.23617	−	2.14111i
$495$		0			0
$496$		−	781.864i		−	1.57634i
$497$	602.184	+	21.0035i	1.21164	+	0.0422606i
$498$		−	801.494i		−	1.60943i
$499$	264.597	−	458.296i	0.530255	−	0.918429i	−0.469122	−	0.883134i	$-0.655429\pi$
$499$	264.597	−	458.296i	0.530255	−	0.918429i	0.999377	−	0.0352954i	$-0.0112372\pi$
$500$		0			0
$501$	36.7020	+	63.5698i	0.0732576	+	0.126886i
$502$	52.6677	−	91.2231i	0.104916	−	0.181719i
$503$	−204.695			−0.406948			−0.203474	−	0.979080i	$-0.565223\pi$
$503$	−204.695			−0.406948			−0.203474	+	0.979080i	$0.565223\pi$
$504$	−275.454	−	172.106i	−0.546535	−	0.341481i
$505$		0			0
$506$	−160.286	+	277.624i	−0.316772	+	0.548665i
$507$	−30.3015	−	52.4837i	−0.0597663	−	0.103518i
$508$	1516.58	−	875.599i	2.98540	−	1.72362i
$509$	473.892	+	273.602i	0.931026	+	0.537528i	0.887136	−	0.461508i	$-0.152691\pi$
$509$	473.892	+	273.602i	0.931026	+	0.537528i	0.0438903	+	0.999036i	$0.486025\pi$
$510$		0			0
$511$	202.377	+	380.577i	0.396041	+	0.744770i
$512$			1048.84i			2.04851i
$513$	134.860	+	77.8614i	0.262885	+	0.151777i
$514$	−294.779	+	170.191i	−0.573500	+	0.331110i
$515$		0			0
$516$	934.470	+	539.517i	1.81099	+	1.04558i
$517$	8.76461			0.0169528
$518$	−297.914	−	560.238i	−0.575124	−	1.08154i
$519$	51.1998			0.0986509
$520$		0			0
$521$	30.1482	−	17.4061i	0.0578660	−	0.0334090i	−0.470788	−	0.882246i	$-0.656030\pi$
$521$	30.1482	−	17.4061i	0.0578660	−	0.0334090i	0.528654	+	0.848837i	$0.322697\pi$
$522$	−223.998	+	129.325i	−0.429115	+	0.247750i
$523$	415.860	−	720.290i	0.795143	−	1.37723i	−0.127606	−	0.991825i	$-0.540729\pi$
$523$	415.860	−	720.290i	0.795143	−	1.37723i	0.922748	−	0.385403i	$-0.125938\pi$
$524$			919.756i			1.75526i
$525$		0			0
$526$	−226.174			−0.429989
$527$	−752.650	−	434.543i	−1.42818	−	0.824559i
$528$	46.8913	+	81.2180i	0.0888092	+	0.153822i
$529$	351.800	+	609.336i	0.665029	+	1.15186i
$530$		0			0
$531$			147.979i			0.278680i
$532$	61.3770	−	1759.72i	0.115370	−	3.30774i
$533$			42.9612i			0.0806027i
$534$	−198.942	+	344.578i	−0.372551	+	0.645277i
$535$		0			0
$536$	−503.088	−	871.374i	−0.938597	−	1.62570i
$537$	128.762	−	223.022i	0.239780	−	0.415312i
$538$	695.512			1.29277
$539$	−55.7228	−	114.224i	−0.103382	−	0.211919i
$540$		0			0
$541$	112.177	−	194.296i	0.207351	−	0.359143i	−0.743528	−	0.668705i	$-0.766849\pi$
$541$	112.177	−	194.296i	0.207351	−	0.359143i	0.950879	+	0.309562i	$0.100182\pi$
$542$	−271.308	−	469.919i	−0.500568	−	0.867008i
$543$	−385.954	+	222.830i	−0.710780	+	0.410369i
$544$	−233.606	−	134.872i	−0.429422	−	0.247927i
$545$		0			0
$546$	−17.2236	+	493.810i	−0.0315450	+	0.904414i
$547$		−	456.739i		−	0.834989i	−0.908679	−	0.417495i	$-0.862908\pi$
$547$		−	456.739i		−	0.834989i	0.908679	−	0.417495i	$-0.137092\pi$
$548$	−1289.89	−	744.716i	−2.35381	−	1.35897i
$549$	2.29528	−	1.32518i	0.00418084	−	0.00241381i
$550$		0			0
$551$	−635.621	−	366.976i	−1.15358	−	0.666018i
$552$	940.522			1.70384
$553$	102.164	−	163.512i	0.184745	−	0.295682i
$554$	1194.14			2.15549
$555$		0			0
$556$	−1234.94	+	712.994i	−2.22112	+	1.28236i
$557$	−672.945	+	388.525i	−1.20816	+	0.697532i	−0.962357	−	0.271788i	$-0.912385\pi$
$557$	−672.945	+	388.525i	−1.20816	+	0.697532i	−0.245803	+	0.969320i	$0.579052\pi$
$558$	197.777	−	342.561i	0.354440	−	0.613908i
$559$		−	859.223i		−	1.53707i
$560$		0			0
$561$	104.245			0.185819
$562$	−341.391	−	197.102i	−0.607457	−	0.350716i
$563$	41.7094	+	72.2428i	0.0740842	+	0.128318i	0.900688	−	0.434467i	$-0.143063\pi$
$563$	41.7094	+	72.2428i	0.0740842	+	0.128318i	−0.826603	+	0.562785i	$0.809730\pi$
$564$	−24.5630	−	42.5444i	−0.0435514	−	0.0754333i
$565$		0			0
$566$			230.265i			0.406829i
$567$	−29.5790	−	55.6245i	−0.0521676	−	0.0981031i
$568$			1331.35i			2.34393i
$569$	−111.671	+	193.421i	−0.196259	+	0.339931i	−0.947313	−	0.320311i	$-0.896213\pi$
$569$	−111.671	+	193.421i	−0.196259	+	0.339931i	0.751053	+	0.660241i	$0.229546\pi$
$570$		0			0
$571$	−88.3631	−	153.049i	−0.154751	−	0.268037i	0.778217	−	0.627995i	$-0.216124\pi$
$571$	−88.3631	−	153.049i	−0.154751	−	0.268037i	−0.932969	+	0.359958i	$0.882791\pi$
$572$	126.008	−	218.252i	0.220294	−	0.381560i
$573$	−210.625			−0.367582
$574$	−48.4597	+	77.5590i	−0.0844246	+	0.135120i
$575$		0			0
$576$	−63.8685	+	110.624i	−0.110883	+	0.192055i
$577$	450.802	+	780.812i	0.781286	+	1.35323i	0.931193	+	0.364527i	$0.118769\pi$
$577$	450.802	+	780.812i	0.781286	+	1.35323i	−0.149907	+	0.988700i	$0.547897\pi$
$578$	−760.516	+	439.084i	−1.31577	+	0.759661i
$579$	−363.799	−	210.039i	−0.628323	−	0.362762i
$580$		0			0
$581$	−919.556	−	32.0731i	−1.58271	−	0.0552033i
$582$		−	257.546i		−	0.442518i
$583$	−89.9351	−	51.9240i	−0.154263	−	0.0890635i
$584$	−824.798	+	476.197i	−1.41233	+	0.815406i
$585$		0			0
$586$	−307.901	−	177.767i	−0.525429	−	0.303356i
$587$	163.544			0.278610			0.139305	−	0.990250i	$-0.455513\pi$
$587$	163.544			0.278610			0.139305	+	0.990250i	$0.455513\pi$
$588$	−398.293	+	590.601i	−0.677370	+	1.00442i
$589$	1122.43			1.90566
$590$		0			0
$591$	148.489	−	85.7304i	0.251251	−	0.145060i
$592$	465.507	−	268.760i	0.786329	−	0.453987i
$593$	579.932	−	1004.47i	0.977964	−	1.69388i	0.308177	−	0.951329i	$-0.400281\pi$
$593$	579.932	−	1004.47i	0.977964	−	1.69388i	0.669786	−	0.742554i	$-0.266386\pi$
$594$			47.4458i			0.0798750i
$595$		0			0
$596$	716.677			1.20248
$597$	−118.146	−	68.2115i	−0.197899	−	0.114257i
$598$	−715.396	−	1239.10i	−1.19631	−	2.07208i
$599$	16.3990	+	28.4039i	0.0273773	+	0.0474188i	0.879389	−	0.476103i	$-0.157951\pi$
$599$	16.3990	+	28.4039i	0.0273773	+	0.0474188i	−0.852012	+	0.523522i	$0.824618\pi$
$600$		0			0
$601$		−	796.834i		−	1.32585i	−0.748687	−	0.662924i	$-0.769315\pi$
$601$		−	796.834i		−	1.32585i	0.748687	−	0.662924i	$-0.230685\pi$
$602$	969.192	−	1551.18i	1.60995	−	2.57670i
$603$		−	195.163i		−	0.323654i
$604$	−579.126	+	1003.08i	−0.958817	+	1.66072i
$605$		0			0
$606$	−457.214	−	791.917i	−0.754478	−	1.30679i
$607$	262.046	−	453.877i	0.431707	−	0.747739i	−0.565313	−	0.824876i	$-0.691245\pi$
$607$	262.046	−	453.877i	0.431707	−	0.747739i	0.997020	+	0.0771375i	$0.0245780\pi$
$608$	348.378			0.572990
$609$	139.412	+	262.169i	0.228919	+	0.430491i
$610$		0			0
$611$	−19.5593	+	33.8776i	−0.0320119	+	0.0554462i
$612$	−292.147	−	506.014i	−0.477365	−	0.826821i
$613$	219.738	−	126.866i	0.358463	−	0.206959i	−0.309944	−	0.950755i	$-0.600310\pi$
$613$	219.738	−	126.866i	0.358463	−	0.206959i	0.668406	+	0.743796i	$0.266977\pi$
$614$	−1220.69	−	704.769i	−1.98810	−	1.14783i
$615$		0			0
$616$	247.937	−	131.844i	0.402495	−	0.214032i
$617$			620.813i			1.00618i	0.864234	+	0.503090i	$0.167804\pi$
$617$			620.813i			1.00618i	−0.864234	+	0.503090i	$0.832196\pi$
$618$	737.588	+	425.846i	1.19351	+	0.689072i
$619$	−555.643	+	320.801i	−0.897647	+	0.518257i	−0.876436	−	0.481519i	$-0.840085\pi$
$619$	−555.643	+	320.801i	−0.897647	+	0.518257i	−0.0212107	+	0.999775i	$0.506752\pi$
$620$		0			0
$621$	157.988	+	91.2143i	0.254409	+	0.146883i
$622$	−126.731			−0.203747
$623$	387.374	+	242.036i	0.621789	+	0.388501i
$624$	−418.573			−0.670791
$625$		0			0
$626$	−349.071	+	201.536i	−0.557621	+	0.321943i
$627$	−116.595	+	67.3164i	−0.185958	+	0.107363i
$628$	−28.8175	+	49.9134i	−0.0458878	+	0.0794800i
$629$		−	597.484i		−	0.949896i
$630$		0			0
$631$	−166.338			−0.263610			−0.131805	−	0.991276i	$-0.542077\pi$
$631$	−166.338			−0.263610			−0.131805	+	0.991276i	$0.542077\pi$
$632$	368.933	+	213.004i	0.583755	+	0.337031i
$633$	−92.7891	−	160.715i	−0.146586	−	0.253895i
$634$	−7.09746	−	12.2932i	−0.0111947	−	0.0193899i
$635$		0			0
$636$			582.073i			0.915209i
$637$	565.860	+	39.5213i	0.888321	+	0.0620429i
$638$		−	223.621i		−	0.350503i
$639$	−129.118	+	223.639i	−0.202062	+	0.349982i
$640$		0			0
$641$	−68.5302	−	118.698i	−0.106911	−	0.185176i	0.807606	−	0.589722i	$-0.200763\pi$
$641$	−68.5302	−	118.698i	−0.106911	−	0.185176i	−0.914518	+	0.404546i	$0.867429\pi$
$642$	−552.559	+	957.061i	−0.860685	+	1.49075i
$643$	812.010			1.26285			0.631423	−	0.775438i	$-0.282471\pi$
$643$	812.010			1.26285			0.631423	+	0.775438i	$0.282471\pi$
$644$	71.9030	−	2061.50i	0.111651	−	3.20109i
$645$		0			0
$646$	1224.08	−	2120.16i	1.89485	−	3.28198i
$647$	−114.148	−	197.709i	−0.176426	−	0.305579i	0.764228	−	0.644946i	$-0.223120\pi$
$647$	−114.148	−	197.709i	−0.176426	−	0.305579i	−0.940654	+	0.339368i	$0.889787\pi$
$648$	120.551	−	69.6001i	0.186035	−	0.107408i
$649$	−110.798	−	63.9691i	−0.170721	−	0.0985656i
$650$		0			0
$651$	−385.106	−	240.619i	−0.591561	−	0.369614i
$652$		−	2322.68i		−	3.56239i
$653$	−754.406	−	435.557i	−1.15529	−	0.667009i	−0.205122	−	0.978736i	$-0.565759\pi$
$653$	−754.406	−	435.557i	−1.15529	−	0.667009i	−0.950171	+	0.311728i	$0.899092\pi$
$654$	389.763	−	225.030i	0.595968	−	0.344082i
$655$		0			0
$656$	−67.0932	−	38.7363i	−0.102276	−	0.0590492i
$657$	−184.731			−0.281174
$658$	−73.5243	+	39.0975i	−0.111739	+	0.0594187i
$659$	677.945			1.02875			0.514374	−	0.857566i	$-0.328024\pi$
$659$	677.945			1.02875			0.514374	+	0.857566i	$0.328024\pi$
$660$		0			0
$661$	608.681	−	351.422i	0.920849	−	0.531652i	0.0369430	−	0.999317i	$-0.488238\pi$
$661$	608.681	−	351.422i	0.920849	−	0.531652i	0.883906	+	0.467665i	$0.154905\pi$
$662$	−1546.90	+	893.102i	−2.33670	+	1.34910i
$663$	−232.634	+	402.934i	−0.350881	+	0.607743i
$664$		−	2033.02i		−	3.06177i
$665$		0			0
$666$	271.939			0.408316
$667$	−744.628	−	429.911i	−1.11638	−	0.644544i
$668$	177.856	+	308.055i	0.266251	+	0.461161i
$669$	−7.55192	−	13.0803i	−0.0112884	−	0.0195520i
$670$		0			0
$671$			2.29142i			0.00341493i
$672$	−119.528	−	74.6827i	−0.177870	−	0.111135i
$673$		−	612.283i		−	0.909782i	−0.890547	−	0.454891i	$-0.849678\pi$
$673$		−	612.283i		−	0.909782i	0.890547	−	0.454891i	$-0.150322\pi$
$674$	465.187	−	805.727i	0.690188	−	1.19544i
$675$		0			0
$676$	−146.839	−	254.333i	−0.217218	−	0.376232i
$677$	2.89408	−	5.01270i	0.00427487	−	0.00740428i	−0.863880	−	0.503698i	$-0.831973\pi$
$677$	2.89408	−	5.01270i	0.00427487	−	0.00740428i	0.868155	+	0.496293i	$0.165306\pi$
$678$	45.0343			0.0664222
$679$	−295.483	−	10.3061i	−0.435173	−	0.0151784i
$680$		0			0
$681$	219.123	−	379.532i	0.321766	−	0.557316i
$682$	170.992	+	296.167i	0.250721	+	0.434262i
$683$	101.123	−	58.3832i	0.148057	−	0.0854806i	−0.424142	−	0.905596i	$-0.639424\pi$
$683$	101.123	−	58.3832i	0.148057	−	0.0854806i	0.572198	+	0.820115i	$0.306091\pi$
$684$	653.523	+	377.312i	0.955443	+	0.551625i
$685$		0			0
$686$	976.982	+	709.632i	1.42417	+	1.03445i
$687$		−	251.977i		−	0.366778i
$688$	1341.86	+	774.724i	1.95038	+	1.12605i
$689$	401.401	−	231.749i	0.582585	−	0.336356i
$690$		0			0
$691$	820.541	+	473.740i	1.18747	+	0.685585i	0.957730	−	0.287667i	$-0.0928796\pi$
$691$	820.541	+	473.740i	1.18747	+	0.685585i	0.229738	+	0.973252i	$0.426213\pi$
$692$	248.111			0.358542
$693$	54.4346	+	1.89862i	0.0785493	+	0.00273971i
$694$	−825.425			−1.18937
$695$		0			0
$696$	−568.180	+	328.039i	−0.816350	+	0.471320i
$697$	−74.5778	+	43.0575i	−0.106998	+	0.0617755i
$698$	95.4270	−	165.284i	0.136715	−	0.236797i
$699$			446.030i			0.638097i
$700$		0			0
$701$	1168.56			1.66700			0.833498	−	0.552523i	$-0.186335\pi$
$701$	1168.56			1.66700			0.833498	+	0.552523i	$0.186335\pi$
$702$	−183.391	−	105.881i	−0.261241	−	0.150827i
$703$	385.829	+	668.275i	0.548832	+	0.950604i
$704$	−55.2187	−	95.6415i	−0.0784356	−	0.135854i
$705$		0			0
$706$			1837.05i			2.60205i
$707$	−926.865	+	492.872i	−1.31098	+	0.697132i
$708$			717.099i			1.01285i
$709$	334.781	−	579.857i	0.472187	−	0.817852i	−0.527306	−	0.849675i	$-0.676798\pi$
$709$	334.781	−	579.857i	0.472187	−	0.817852i	0.999494	+	0.0318230i	$0.0101313\pi$
$710$		0			0
$711$	41.3153	+	71.5602i	0.0581087	+	0.100647i
$712$	−504.625	+	874.035i	−0.708742	+	1.22758i
$713$	1314.93			1.84422
$714$	−874.484	+	465.018i	−1.22477	+	0.651286i
$715$		0			0
$716$	623.973	−	1080.75i	0.871471	−	1.50943i
$717$	111.442	+	193.023i	0.155428	+	0.269209i
$718$	−1426.66	+	823.685i	−1.98700	+	1.14719i
$719$	805.983	+	465.334i	1.12098	+	0.647196i	0.941650	−	0.336593i	$-0.109275\pi$
$719$	805.983	+	465.334i	1.12098	+	0.647196i	0.179327	+	0.983790i	$0.442608\pi$
$720$		0			0
$721$	518.091	−	829.195i	0.718572	−	1.15006i
$722$			1890.94i			2.61903i
$723$	−13.8950	−	8.02227i	−0.0192185	−	0.0110958i
$724$	−1870.31	+	1079.82i	−2.58330	+	1.49147i
$725$		0			0
$726$	603.433	+	348.392i	0.831175	+	0.479879i
$727$	290.932			0.400182			0.200091	−	0.979777i	$-0.435876\pi$
$727$	290.932			0.400182			0.200091	+	0.979777i	$0.435876\pi$
$728$	−43.6882	+	1252.57i	−0.0600113	+	1.72056i
$729$	27.0000			0.0370370
$730$		0			0
$731$	1491.55	−	861.149i	2.04043	−	1.17804i
$732$	11.1228	−	6.42174i	0.0151951	−	0.00877288i
$733$	−0.482712	+	0.836082i	−0.000658543	+	0.00114063i	−0.866354	−	0.499430i	$-0.833543\pi$
$733$	−0.482712	+	0.836082i	−0.000658543	+	0.00114063i	0.865696	+	0.500570i	$0.166876\pi$
$734$		−	606.304i		−	0.826027i
$735$		0			0
$736$	408.124			0.554516
$737$	146.126	+	84.3659i	0.198271	+	0.114472i
$738$	−19.5972	−	33.9433i	−0.0265544	−	0.0459936i
$739$	−49.9365	−	86.4925i	−0.0675731	−	0.117040i	0.830259	−	0.557377i	$-0.188192\pi$
$739$	−49.9365	−	86.4925i	−0.0675731	−	0.117040i	−0.897832	+	0.440337i	$0.854859\pi$
$740$		0			0
$741$		−	600.898i		−	0.810929i
$742$	986.070	+	34.3931i	1.32894	+	0.0463518i
$743$		−	890.635i		−	1.19870i	−0.800486	−	0.599351i	$-0.795425\pi$
$743$		−	890.635i		−	1.19870i	0.800486	−	0.599351i	$-0.204575\pi$
$744$	501.670	−	868.917i	0.674287	−	1.16790i
$745$		0			0
$746$	−811.408	−	1405.40i	−1.08768	−	1.88391i
$747$	197.167	−	341.504i	0.263946	−	0.457167i
$748$	505.162			0.675351
$749$	1075.93	+	672.251i	1.43648	+	0.897532i
$750$		0			0
$751$	−310.537	+	537.867i	−0.413499	+	0.716200i	−0.995270	−	0.0971521i	$-0.969027\pi$
$751$	−310.537	+	537.867i	−0.413499	+	0.716200i	0.581771	+	0.813353i	$0.302360\pi$
$752$	−35.2715	−	61.0920i	−0.0469035	−	0.0812393i
$753$	44.8818	−	25.9125i	0.0596040	−	0.0344124i
$754$	864.357	+	499.037i	1.14636	+	0.661853i
$755$		0			0
$756$	−143.338	−	269.553i	−0.189601	−	0.356551i
$757$			675.637i			0.892519i	0.894904	+	0.446259i	$0.147244\pi$
$757$			675.637i			0.892519i	−0.894904	+	0.446259i	$0.852756\pi$
$758$	−1355.60	−	782.658i	−1.78840	−	1.03253i
$759$	−136.591	+	78.8609i	−0.179962	+	0.103901i
$760$		0			0
$761$	549.336	+	317.159i	0.721861	+	0.416766i	0.815437	−	0.578846i	$-0.196497\pi$
$761$	549.336	+	317.159i	0.721861	+	0.416766i	−0.0935765	+	0.995612i	$0.529830\pi$
$762$	1272.19			1.66954
$763$	−242.580	−	456.181i	−0.317930	−	0.597878i
$764$	−1020.67			−1.33596
$765$		0			0
$766$	−1614.22	+	931.967i	−2.10733	+	1.21667i
$767$	494.516	−	285.509i	0.644741	−	0.372241i
$768$	−451.267	+	781.618i	−0.587587	+	1.01773i
$769$		−	17.8434i		−	0.0232033i	−0.999933	−	0.0116017i	$-0.996307\pi$
$769$		−	17.8434i		−	0.0232033i	0.999933	−	0.0116017i	$-0.00369301\pi$
$770$		0			0
$771$	−167.468			−0.217208
$772$	−1762.95	−	1017.84i	−2.28361	−	1.31844i
$773$	129.289	+	223.935i	0.167256	+	0.289697i	0.937454	−	0.348108i	$-0.113176\pi$
$773$	129.289	+	223.935i	0.167256	+	0.289697i	−0.770198	+	0.637805i	$0.779843\pi$
$774$	391.943	+	678.865i	0.506386	+	0.877086i
$775$		0			0
$776$		−	653.274i		−	0.841848i
$777$	10.8821	−	311.996i	0.0140053	−	0.401539i
$778$			688.281i			0.884680i
$779$	55.6092	−	96.3180i	0.0713854	−	0.123643i
$780$		0			0
$781$	−111.631	−	193.351i	−0.142934	−	0.247568i
$782$	1434.00	−	2483.76i	1.83376	−	3.17616i
$783$	−127.256			−0.162524
$784$	−571.933	+	848.078i	−0.729506	+	1.08173i
$785$		0			0
$786$	−334.088	+	578.657i	−0.425048	+	0.736204i
$787$	540.685	+	936.494i	0.687020	+	1.18995i	0.972797	+	0.231658i	$0.0744149\pi$
$787$	540.685	+	936.494i	0.687020	+	1.18995i	−0.285777	+	0.958296i	$0.592252\pi$
$788$	719.570	−	415.444i	0.913160	−	0.527213i
$789$	−96.3693	−	55.6388i	−0.122141	−	0.0705182i
$790$		0			0
$791$	1.80212	−	51.6679i	0.00227828	−	0.0653198i
$792$			120.348i			0.151954i
$793$	−8.85696	−	5.11357i	−0.0111689	−	0.00644838i
$794$	−89.1928	+	51.4955i	−0.112333	+	0.0648558i
$795$		0			0
$796$	−572.527	−	330.549i	−0.719256	−	0.415262i
$797$	−145.723			−0.182839			−0.0914195	−	0.995812i	$-0.529140\pi$
$797$	−145.723			−0.182839			−0.0914195	+	0.995812i	$0.529140\pi$
$798$	677.805	−	1084.82i	0.849380	−	1.35942i
$799$	−78.4124			−0.0981382
$800$		0			0
$801$	−169.533	+	97.8796i	−0.211651	+	0.122197i
$802$	−642.659	+	371.040i	−0.801321	+	0.462643i
$803$	79.8564	−	138.315i	0.0994476	−	0.172248i
$804$		−	945.749i		−	1.17630i
$805$		0			0
$806$	−1526.35			−1.89374
$807$	296.347	+	171.096i	0.367220	+	0.212015i
$808$	−1159.74	−	2008.73i	−1.43532	−	2.48605i
$809$	−108.425	−	187.797i	−0.134023	−	0.232134i	0.791201	−	0.611556i	$-0.209456\pi$
$809$	−108.425	−	187.797i	−0.134023	−	0.232134i	−0.925224	+	0.379422i	$0.876123\pi$
$810$		0			0
$811$		−	8.20233i		−	0.0101139i	−0.999987	−	0.00505693i	$-0.998390\pi$
$811$		−	8.20233i		−	0.0101139i	0.999987	−	0.00505693i	$-0.00160968\pi$
$812$	675.581	+	1270.45i	0.831996	+	1.56460i
$813$		−	266.967i		−	0.328372i
$814$	−117.555	+	203.611i	−0.144416	+	0.250136i
$815$		0			0
$816$	−419.512	−	726.616i	−0.514108	−	0.890460i
$817$	−1112.18	+	1926.36i	−1.36130	+	2.35784i
$818$	−1142.33			−1.39650
$819$	−128.816	+	206.168i	−0.157285	+	0.251731i
$820$		0			0
$821$	−786.474	+	1362.21i	−0.957946	+	1.65921i	−0.230469	+	0.973080i	$0.574026\pi$
$821$	−786.474	+	1362.21i	−0.957946	+	1.65921i	−0.727477	+	0.686132i	$0.759307\pi$
$822$	−541.013	−	937.063i	−0.658167	−	1.13998i
$823$	−864.881	+	499.339i	−1.05089	+	0.606731i	−0.922898	−	0.385045i	$-0.874186\pi$
$823$	−864.881	+	499.339i	−1.05089	+	0.606731i	−0.127991	+	0.991775i	$0.540853\pi$
$824$	1870.92	+	1080.18i	2.27053	+	1.31089i
$825$		0			0
$826$	1214.81	+	42.3714i	1.47072	+	0.0512970i
$827$		−	1344.24i		−	1.62544i	−0.582658	−	0.812718i	$-0.697987\pi$
$827$		−	1344.24i		−	1.62544i	0.582658	−	0.812718i	$-0.302013\pi$
$828$	765.599	+	442.019i	0.924637	+	0.533839i
$829$	1312.22	−	757.611i	1.58290	−	0.913885i	0.588462	−	0.808525i	$-0.299734\pi$
$829$	1312.22	−	757.611i	1.58290	−	0.913885i	0.994434	−	0.105360i	$-0.0335996\pi$
$830$		0			0
$831$	508.805	+	293.758i	0.612280	+	0.353500i
$832$	492.908			0.592437
$833$	498.523	+	1021.91i	0.598467	+	1.22678i
$834$	−1035.94			−1.24213
$835$		0			0
$836$	−565.014	+	326.211i	−0.675855	+	0.390205i
$837$	168.540	−	97.3065i	0.201362	−	0.116256i
$838$	−1221.51	+	2115.72i	−1.45765	+	2.52473i
$839$		−	439.769i		−	0.524159i	−0.965046	−	0.262079i	$-0.915592\pi$
$839$		−	439.769i		−	0.524159i	0.965046	−	0.262079i	$-0.0844082\pi$
$840$		0			0
$841$	−241.217			−0.286821
$842$	−1041.32	−	601.208i	−1.23673	−	0.714024i
$843$	−96.9743	−	167.964i	−0.115035	−	0.199246i
$844$	−449.650	−	778.817i	−0.532761	−	0.922769i
$845$		0			0
$846$		−	35.6886i		−	0.0421851i
$847$	423.859	−	678.379i	0.500424	−	0.800920i
$848$			835.833i			0.985652i
$849$	−56.6453	+	98.1126i	−0.0667201	+	0.115563i
$850$		0			0
$851$	451.997	+	782.881i	0.531136	+	0.919955i
$852$	−625.697	+	1083.74i	−0.734386	+	1.27199i
$853$	222.026			0.260288			0.130144	−	0.991495i	$-0.458456\pi$
$853$	222.026			0.260288			0.130144	+	0.991495i	$0.458456\pi$
$854$	−10.2216	−	19.2222i	−0.0119691	−	0.0225084i
$855$		0			0
$856$	−1401.59	+	2427.62i	−1.63737	+	2.83601i
$857$	−521.173	−	902.699i	−0.608137	−	1.05332i	−0.991547	−	0.129746i	$-0.958584\pi$
$857$	−521.173	−	902.699i	−0.608137	−	1.05332i	0.383410	−	0.923578i	$-0.374750\pi$
$858$	158.554	−	91.5411i	0.184795	−	0.106691i
$859$	−132.904	−	76.7321i	−0.154719	−	0.0893272i	0.420642	−	0.907227i	$-0.361805\pi$
$859$	−132.904	−	76.7321i	−0.154719	−	0.0893272i	−0.575361	+	0.817900i	$0.695138\pi$
$860$		0			0
$861$	−39.7274	+	21.1256i	−0.0461410	+	0.0245361i
$862$			1448.49i			1.68038i
$863$	−695.406	−	401.493i	−0.805800	−	0.465229i	0.0396949	−	0.999212i	$-0.487361\pi$
$863$	−695.406	−	401.493i	−0.805800	−	0.465229i	−0.845495	+	0.533983i	$0.820695\pi$
$864$	52.3110	−	30.2018i	0.0605451	−	0.0349557i
$865$		0			0
$866$	−1352.01	−	780.582i	−1.56121	−	0.901365i
$867$	−432.059			−0.498338
$868$	−1866.20	−	1166.02i	−2.15000	−	1.34334i
$869$	−71.4397			−0.0822091
$870$		0			0
$871$	−652.195	+	376.545i	−0.748789	+	0.432313i
$872$	988.649	−	570.797i	1.13377	−	0.654583i
$873$	63.3562	−	109.736i	0.0725730	−	0.125700i
$874$			3704.05i			4.23804i
$875$		0			0
$876$	−895.197			−1.02191
$877$	1164.51	+	672.328i	1.32783	+	0.766622i	0.984963	−	0.172763i	$-0.0552693\pi$
$877$	1164.51	+	672.328i	1.32783	+	0.766622i	0.342865	+	0.939385i	$0.388603\pi$
$878$	544.720	+	943.483i	0.620410	+	1.07458i
$879$	−87.4613	−	151.487i	−0.0995009	−	0.172341i
$880$		0			0
$881$		−	1052.91i		−	1.19513i	−0.801822	−	0.597563i	$-0.796136\pi$
$881$		−	1052.91i		−	1.19513i	0.801822	−	0.597563i	$-0.203864\pi$
$882$	−465.110	+	226.897i	−0.527335	+	0.257253i
$883$		−	1372.84i		−	1.55475i	−0.629037	−	0.777375i	$-0.716551\pi$
$883$		−	1372.84i		−	1.55475i	0.629037	−	0.777375i	$-0.283449\pi$
$884$	−1127.33	+	1952.59i	−1.27526	+	2.20881i
$885$		0			0
$886$	1441.02	+	2495.92i	1.62643	+	2.81706i
$887$	314.555	−	544.825i	0.354628	−	0.614233i	−0.632427	−	0.774620i	$-0.717941\pi$
$887$	314.555	−	544.825i	0.354628	−	0.614233i	0.987054	+	0.160387i	$0.0512743\pi$
$888$	689.782			0.776782
$889$	50.9090	−	1459.59i	0.0572654	−	1.64183i
$890$		0			0
$891$	−11.6717	+	20.2159i	−0.0130995	+	0.0226890i
$892$	−36.5962	−	63.3864i	−0.0410271	−	0.0710610i
$893$	87.7028	−	50.6352i	0.0982114	−	0.0567024i
$894$	450.891	+	260.322i	0.504352	+	0.291188i
$895$		0			0
$896$	1165.90	+	728.466i	1.30122	+	0.813020i
$897$		−	703.950i		−	0.784783i
$898$	−962.671	−	555.798i	−1.07202	−	0.618929i
$899$	−794.361	+	458.624i	−0.883605	+	0.510150i
$900$		0			0
$901$	804.602	+	464.537i	0.893010	+	0.515580i
$902$	33.8862			0.0375678
$903$	794.547	−	422.511i	0.879897	−	0.467897i
$904$	114.231			0.126362
$905$		0			0
$906$	−728.704	+	420.717i	−0.804309	+	0.464368i
$907$	−51.7804	+	29.8954i	−0.0570897	+	0.0329608i	−0.528273	−	0.849074i	$-0.677160\pi$
$907$	−51.7804	+	29.8954i	−0.0570897	+	0.0329608i	0.471183	+	0.882035i	$0.343827\pi$
$908$	1061.86	−	1839.19i	1.16944	−	2.02554i
$909$		−	449.898i		−	0.494938i
$910$		0			0
$911$	−850.964			−0.934099			−0.467050	−	0.884231i	$-0.654683\pi$
$911$	−850.964			−0.934099			−0.467050	+	0.884231i	$0.654683\pi$
$912$	938.432	+	541.804i	1.02898	+	0.594083i
$913$	170.465	+	295.253i	0.186708	+	0.323388i
$914$	329.700	+	571.057i	0.360722	+	0.624788i
$915$		0			0
$916$		−	1221.06i		−	1.33304i
$917$	650.525	+	406.455i	0.709406	+	0.443245i
$918$		−	424.473i		−	0.462389i
$919$	330.505	−	572.452i	0.359636	−	0.622908i	−0.628264	−	0.778000i	$-0.716234\pi$
$919$	330.505	−	572.452i	0.359636	−	0.622908i	0.987900	+	0.155093i	$0.0495676\pi$
$920$		0			0
$921$	−346.746	−	600.582i	−0.376489	−	0.652098i
$922$	14.5675	−	25.2317i	0.0157999	−	0.0273662i
$923$	996.472			1.07960
$924$	263.787	+	9.20061i	0.285484	+	0.00995737i
$925$		0			0
$926$	−832.448	+	1441.84i	−0.898972	+	1.55707i
$927$	209.517	+	362.893i	0.226016	+	0.391471i
$928$	−246.552	+	142.347i	−0.265681	+	0.153391i
$929$	231.638	+	133.736i	0.249341	+	0.143957i	0.619462	−	0.785026i	$-0.287351\pi$
$929$	231.638	+	133.736i	0.249341	+	0.143957i	−0.370122	+	0.928983i	$0.620684\pi$
$930$		0			0
$931$	−1217.49	−	821.059i	−1.30772	−	0.881911i
$932$			2161.43i			2.31914i
$933$	−53.9980	−	31.1758i	−0.0578757	−	0.0334145i
$934$	2185.71	−	1261.92i	2.34016	−	1.35109i
$935$		0			0
$936$	−465.178	−	268.571i	−0.496985	−	0.286934i
$937$	−1625.83			−1.73515			−0.867573	−	0.497309i	$-0.834321\pi$
$937$	−1625.83			−1.73515			−0.867573	+	0.497309i	$0.834321\pi$
$938$	−1602.16	−	55.8817i	−1.70806	−	0.0595754i
$939$	−198.312			−0.211194
$940$		0			0
$941$	−257.993	+	148.952i	−0.274168	+	0.158291i	−0.630780	−	0.775961i	$-0.717265\pi$
$941$	−257.993	+	148.952i	−0.274168	+	0.158291i	0.356612	+	0.934253i	$0.383932\pi$
$942$	−36.2606	+	20.9351i	−0.0384932	+	0.0222241i
$943$	65.1460	−	112.836i	0.0690838	−	0.119657i
$944$			1029.72i			1.09081i
$945$		0			0
$946$	−677.722			−0.716408
$947$	791.333	+	456.876i	0.835621	+	0.482446i	0.855773	−	0.517351i	$-0.173082\pi$
$947$	791.333	+	456.876i	0.835621	+	0.482446i	−0.0201524	+	0.999797i	$0.506415\pi$
$948$	200.211	+	346.776i	0.211193	+	0.365798i
$949$	356.418	+	617.334i	0.375572	+	0.650510i
$950$		0			0
$951$		−	6.98391i		−	0.00734375i
$952$	−2218.16	+	1179.54i	−2.33000	+	1.23901i
$953$			1451.89i			1.52349i	0.647875	+	0.761746i	$0.275658\pi$
$953$			1451.89i			1.52349i	−0.647875	+	0.761746i	$0.724342\pi$
$954$	−211.429	+	366.206i	−0.221624	+	0.383864i
$955$		0			0
$956$	540.040	+	935.377i	0.564896	+	0.978428i
$957$	55.0108	−	95.2815i	0.0574826	−	0.0995627i
$958$	−724.878			−0.756657
$959$	−1096.74	+	583.208i	−1.14363	+	0.608142i
$960$		0			0
$961$	220.874	−	382.566i	0.229838	−	0.398091i
$962$	−524.674	−	908.762i	−0.545399	−	0.944659i
$963$	−470.874	+	271.859i	−0.488966	+	0.282305i
$964$	−67.3342	−	38.8754i	−0.0698487	−	0.0403272i
$965$		0			0
$966$	794.047	−	1270.86i	0.821994	−	1.31559i
$967$			235.985i			0.244039i	0.992528	+	0.122019i	$0.0389370\pi$
$967$			235.985i			0.244039i	−0.992528	+	0.122019i	$0.961063\pi$
$968$	1530.63	+	883.710i	1.58123	+	0.912924i
$969$	1043.12	−	602.245i	1.07649	−	0.621512i
$970$		0			0
$971$	−555.872	−	320.933i	−0.572474	−	0.330518i	0.185663	−	0.982613i	$-0.440557\pi$
$971$	−555.872	−	320.933i	−0.572474	−	0.330518i	−0.758137	+	0.652096i	$0.773890\pi$
$972$	130.840			0.134609
$973$	−41.4548	+	1188.53i	−0.0426051	+	1.22151i
$974$	1136.67			1.16701
$975$		0			0
$976$	15.9719	−	9.22136i	0.0163646	−	0.00944812i
$977$	554.990	−	320.423i	0.568055	−	0.327967i	−0.188317	−	0.982108i	$-0.560303\pi$
$977$	554.990	−	320.423i	0.568055	−	0.327967i	0.756372	+	0.654142i	$0.226970\pi$
$978$	843.678	−	1461.29i	0.862657	−	1.49417i
$979$		−	169.247i		−	0.172878i
$980$		0			0
$981$	221.429			0.225718
$982$	830.425	+	479.446i	0.845647	+	0.488235i
$983$	212.865	+	368.692i	0.216546	+	0.375068i	0.953750	−	0.300602i	$-0.0971876\pi$
$983$	212.865	+	368.692i	0.216546	+	0.375068i	−0.737204	+	0.675670i	$0.763854\pi$
$984$	−49.7089	−	86.0984i	−0.0505172	−	0.0874984i
$985$		0			0
$986$			2000.62i			2.02903i
$987$	−40.9456	−	1.42814i	−0.0414849	−	0.00144695i
$988$		−	2911.92i		−	2.94728i
$989$	−1302.92	+	2256.72i	−1.31741	+	2.28182i
$990$		0			0
$991$	548.625	+	950.247i	0.553608	+	0.958877i	0.998010	+	0.0630498i	$0.0200827\pi$
$991$	548.625	+	950.247i	0.553608	+	0.958877i	−0.444402	+	0.895827i	$0.646584\pi$
$992$	217.691	−	377.052i	0.219447	−	0.380093i
$993$	−878.813			−0.885008
$994$	1798.96	+	1124.01i	1.80981	+	1.13079i
$995$		0			0
$996$	955.461	−	1654.91i	0.959299	−	1.66155i
$997$	−637.487	−	1104.16i	−0.639405	−	1.10748i	−0.985564	−	0.169306i	$-0.945847\pi$
$997$	−637.487	−	1104.16i	−0.639405	−	1.10748i	0.346159	−	0.938176i	$-0.387486\pi$
$998$	1613.40	−	931.496i	1.61663	−	0.933362i
$999$	115.869	+	66.8969i	0.115985	+	0.0669639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.s.h.124.8		16
5.2	odd	4		525.3.o.l.376.1		8
5.3	odd	4		105.3.n.a.61.4	yes	8
5.4	even	2	inner	525.3.s.h.124.1		16
7.3	odd	6	inner	525.3.s.h.199.1		16
15.8	even	4		315.3.w.a.271.1		8
35.3	even	12		105.3.n.a.31.4	✓	8
35.17	even	12		525.3.o.l.451.1		8
35.23	odd	12		735.3.h.a.391.1		8
35.24	odd	6	inner	525.3.s.h.199.8		16
35.33	even	12		735.3.h.a.391.2		8
105.38	odd	12		315.3.w.a.136.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.4	✓	8	35.3	even	12
105.3.n.a.61.4	yes	8	5.3	odd	4
315.3.w.a.136.1		8	105.38	odd	12
315.3.w.a.271.1		8	15.8	even	4
525.3.o.l.376.1		8	5.2	odd	4
525.3.o.l.451.1		8	35.17	even	12
525.3.s.h.124.1		16	5.4	even	2	inner
525.3.s.h.124.8		16	1.1	even	1	trivial
525.3.s.h.199.1		16	7.3	odd	6	inner
525.3.s.h.199.8		16	35.24	odd	6	inner
735.3.h.a.391.1		8	35.23	odd	12
735.3.h.a.391.2		8	35.33	even	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.04878 + 1.76021i) q^{2} +(0.866025 + 1.50000i) q^{3} +(4.19671 + 7.26891i) q^{4} +6.09756i q^{6} +(6.99575 + 0.244004i) q^{7} +15.4667i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(3.04878 + 1.76021i) q^{2} +(0.866025 + 1.50000i) q^{3} +(4.19671 + 7.26891i) q^{4} +6.09756i q^{6} +(6.99575 + 0.244004i) q^{7} +15.4667i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-1.29685 - 2.24621i) q^{11} +(-7.26891 + 12.5901i) q^{12} +11.5763 q^{13} +(20.8990 + 13.0579i) q^{14} +(-10.4379 + 18.0789i) q^{16} +(11.6023 + 20.0957i) q^{17} +(-9.14634 + 5.28064i) q^{18} +(-25.9538 - 14.9844i) q^{19} +(5.69249 + 10.7049i) q^{21} -9.13094i q^{22} +(-30.4048 - 17.5542i) q^{23} +(-23.2000 + 13.3945i) q^{24} +(35.2936 + 20.3768i) q^{26} -5.19615 q^{27} +(27.5854 + 51.8754i) q^{28} +24.4905 q^{29} +(-32.4355 + 18.7266i) q^{31} +(-10.0673 + 5.81233i) q^{32} +(2.24621 - 3.89055i) q^{33} +81.6898i q^{34} -25.1802 q^{36} +(-22.2990 - 12.8743i) q^{37} +(-52.7516 - 91.3685i) q^{38} +(10.0254 + 17.3645i) q^{39} +3.71113i q^{41} +(-1.48783 + 42.6570i) q^{42} -74.2225i q^{43} +(10.8850 - 18.8534i) q^{44} +(-61.7983 - 107.038i) q^{46} +(-1.68959 + 2.92646i) q^{47} -36.1578 q^{48} +(48.8809 + 3.41398i) q^{49} +(-20.0957 + 34.8068i) q^{51} +(48.5823 + 84.1471i) q^{52} +(34.6744 - 20.0193i) q^{53} +(-15.8419 - 9.14634i) q^{54} +(-3.77394 + 108.201i) q^{56} -51.9076i q^{57} +(74.6661 + 43.1085i) q^{58} +(42.7180 - 24.6632i) q^{59} +(-0.765094 - 0.441727i) q^{61} -131.852 q^{62} +(-11.1276 + 17.8095i) q^{63} +42.5790 q^{64} +(13.6964 - 7.90763i) q^{66} +(-56.3388 + 32.5272i) q^{67} +(-97.3825 + 168.671i) q^{68} -60.8096i q^{69} +86.0786 q^{71} +(-40.1836 - 23.2000i) q^{72} +(30.7886 + 53.3274i) q^{73} +(-45.3231 - 78.5019i) q^{74} -251.541i q^{76} +(-8.52436 - 16.0304i) q^{77} +70.5872i q^{78} +(13.7718 - 23.8534i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.53239 + 11.3144i) q^{82} -131.445 q^{83} +(-53.9235 + 86.3036i) q^{84} +(130.648 - 226.288i) q^{86} +(21.2094 + 36.7357i) q^{87} +(34.7415 - 20.0580i) q^{88} +(56.5108 + 32.6265i) q^{89} +(80.9849 + 2.82467i) q^{91} -294.679i q^{92} +(-56.1799 - 32.4355i) q^{93} +(-10.3024 + 5.94809i) q^{94} +(-17.4370 - 10.0673i) q^{96} -42.2375 q^{97} +(143.018 + 96.4494i) q^{98} +7.78111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 12 * q^4 - 24 * q^9	\( 16 q + 12 q^{4} - 24 q^{9} + 40 q^{11} + 32 q^{14} - 4 q^{16} + 96 q^{21} - 96 q^{24} + 240 q^{26} + 200 q^{29} - 252 q^{31} - 72 q^{36} + 24 q^{39} + 36 q^{44} - 164 q^{46} - 76 q^{49} + 36 q^{51} - 36 q^{54} + 392 q^{56} + 108 q^{59} - 792 q^{61} + 8 q^{64} + 48 q^{66} + 328 q^{71} + 280 q^{74} + 412 q^{79} - 72 q^{81} - 264 q^{84} + 356 q^{86} - 564 q^{89} - 228 q^{91} - 60 q^{94} - 216 q^{96} - 240 q^{99}+O(q^{100}) \) 16 * q + 12 * q^4 - 24 * q^9 + 40 * q^11 + 32 * q^14 - 4 * q^16 + 96 * q^21 - 96 * q^24 + 240 * q^26 + 200 * q^29 - 252 * q^31 - 72 * q^36 + 24 * q^39 + 36 * q^44 - 164 * q^46 - 76 * q^49 + 36 * q^51 - 36 * q^54 + 392 * q^56 + 108 * q^59 - 792 * q^61 + 8 * q^64 + 48 * q^66 + 328 * q^71 + 280 * q^74 + 412 * q^79 - 72 * q^81 - 264 * q^84 + 356 * q^86 - 564 * q^89 - 228 * q^91 - 60 * q^94 - 216 * q^96 - 240 * q^99

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