LMFDB - Embedded newform 60.5.c.a.31.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.c (of order $2$, degree $1$, 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:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$16$
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} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 $ x^16 - 4x^15 - 9x^14 + 18x^13 + 263x^12 - 444x^11 - 1732x^10 - 832x^9 + 25296x^8 - 6656x^7 - 110848x^6 - 227328x^5 + 1077248x^4 + 589824x^3 - 2359296x^2 - 8388608*x + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.13
Root			$-2.48191 - 1.35651i$ of defining polynomial
Character	$\chi$	$=$	60.31
Dual form			60.5.c.a.31.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37483 - 3.21872i) q^{2} -5.19615i q^{3} +(-4.72038 - 15.2878i) q^{4} -11.1803 q^{5} +(-16.7250 - 12.3400i) q^{6} -19.2859i q^{7} +(-60.4174 - 21.1124i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(2.37483 - 3.21872i) q^{2} -5.19615i q^{3} +(-4.72038 - 15.2878i) q^{4} -11.1803 q^{5} +(-16.7250 - 12.3400i) q^{6} -19.2859i q^{7} +(-60.4174 - 21.1124i) q^{8} -27.0000 q^{9} +(-26.5514 + 35.9864i) q^{10} -28.1695i q^{11} +(-79.4379 + 24.5278i) q^{12} -28.6347 q^{13} +(-62.0759 - 45.8006i) q^{14} +58.0948i q^{15} +(-211.436 + 144.329i) q^{16} +290.124 q^{17} +(-64.1204 + 86.9056i) q^{18} -459.035i q^{19} +(52.7755 + 170.923i) q^{20} -100.212 q^{21} +(-90.6699 - 66.8978i) q^{22} -63.0305i q^{23} +(-109.703 + 313.938i) q^{24} +125.000 q^{25} +(-68.0024 + 92.1671i) q^{26} +140.296i q^{27} +(-294.839 + 91.0366i) q^{28} +1141.80 q^{29} +(186.991 + 137.965i) q^{30} -1335.53i q^{31} +(-37.5694 + 1023.31i) q^{32} -146.373 q^{33} +(688.996 - 933.831i) q^{34} +215.622i q^{35} +(127.450 + 412.772i) q^{36} +1365.02 q^{37} +(-1477.51 - 1090.13i) q^{38} +148.790i q^{39} +(675.488 + 236.044i) q^{40} +1242.93 q^{41} +(-237.987 + 322.556i) q^{42} -663.357i q^{43} +(-430.651 + 132.971i) q^{44} +301.869 q^{45} +(-202.878 - 149.687i) q^{46} +3936.26i q^{47} +(749.955 + 1098.65i) q^{48} +2029.06 q^{49} +(296.854 - 402.341i) q^{50} -1507.53i q^{51} +(135.166 + 437.762i) q^{52} -4618.99 q^{53} +(451.575 + 333.179i) q^{54} +314.945i q^{55} +(-407.170 + 1165.20i) q^{56} -2385.22 q^{57} +(2711.59 - 3675.15i) q^{58} +2602.83i q^{59} +(888.143 - 274.229i) q^{60} -5396.32 q^{61} +(-4298.69 - 3171.64i) q^{62} +520.718i q^{63} +(3204.53 + 2551.11i) q^{64} +320.145 q^{65} +(-347.611 + 471.135i) q^{66} -6033.14i q^{67} +(-1369.50 - 4435.38i) q^{68} -327.516 q^{69} +(694.029 + 512.066i) q^{70} +955.221i q^{71} +(1631.27 + 570.034i) q^{72} -8814.75 q^{73} +(3241.68 - 4393.61i) q^{74} -649.519i q^{75} +(-7017.65 + 2166.82i) q^{76} -543.273 q^{77} +(478.914 + 353.351i) q^{78} +3717.96i q^{79} +(2363.93 - 1613.65i) q^{80} +729.000 q^{81} +(2951.75 - 4000.66i) q^{82} +5992.78i q^{83} +(473.040 + 1532.03i) q^{84} -3243.69 q^{85} +(-2135.16 - 1575.36i) q^{86} -5932.99i q^{87} +(-594.726 + 1701.93i) q^{88} +10839.6 q^{89} +(716.887 - 971.634i) q^{90} +552.244i q^{91} +(-963.600 + 297.528i) q^{92} -6939.59 q^{93} +(12669.8 + 9347.95i) q^{94} +5132.17i q^{95} +(5317.28 + 195.216i) q^{96} +5581.91 q^{97} +(4818.66 - 6530.97i) q^{98} +760.577i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	$ 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) $ 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 50 * q^10 - 352 * q^13 - 804 * q^14 - 190 * q^16 + 324 * q^18 + 600 * q^20 + 288 * q^21 + 436 * q^22 - 1998 * q^24 + 2000 * q^25 - 852 * q^26 - 1156 * q^28 - 3456 * q^29 + 7668 * q^32 + 4772 * q^34 - 702 * q^36 + 9376 * q^37 - 1320 * q^38 + 550 * q^40 + 1248 * q^41 - 324 * q^42 - 6420 * q^44 - 1112 * q^46 - 4176 * q^48 - 3952 * q^49 - 1500 * q^50 + 12704 * q^52 - 5184 * q^53 - 486 * q^54 - 2604 * q^56 - 11232 * q^57 + 12708 * q^58 + 3150 * q^60 - 3808 * q^61 - 16152 * q^62 - 11902 * q^64 + 2400 * q^65 - 2916 * q^66 - 12312 * q^68 + 9792 * q^69 - 17100 * q^70 + 4860 * q^72 + 11040 * q^73 + 30516 * q^74 - 5160 * q^76 - 27456 * q^77 - 3600 * q^78 + 10800 * q^80 + 11664 * q^81 - 54040 * q^82 - 2052 * q^84 - 11200 * q^85 + 39768 * q^86 - 7220 * q^88 + 7584 * q^89 - 1350 * q^90 + 28848 * q^92 + 19872 * q^93 + 49776 * q^94 + 18882 * q^96 - 14496 * q^97 + 23940 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	2.37483	−	3.21872i	0.593707	−	0.804681i
$2$	2.37483	−	3.21872i	0.593707	−	0.804681i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−4.72038	−	15.2878i	−0.295024	−	0.955490i
$5$	−11.1803			−0.447214
$5$	−11.1803			−0.447214
$6$	−16.7250	−	12.3400i	−0.464583	−	0.342777i
$7$		−	19.2859i		−	0.393589i	−0.980445	−	0.196794i	$-0.936947\pi$
$7$		−	19.2859i		−	0.393589i	0.980445	−	0.196794i	$-0.0630532\pi$
$8$	−60.4174	−	21.1124i	−0.944023	−	0.329881i
$9$	−27.0000			−0.333333
$10$	−26.5514	+	35.9864i	−0.265514	+	0.359864i
$11$		−	28.1695i		−	0.232806i	−0.993202	−	0.116403i	$-0.962864\pi$
$11$		−	28.1695i		−	0.232806i	0.993202	−	0.116403i	$-0.0371364\pi$
$12$	−79.4379	+	24.5278i	−0.551652	+	0.170332i
$13$	−28.6347			−0.169436			−0.0847179	−	0.996405i	$-0.526999\pi$
$13$	−28.6347			−0.169436			−0.0847179	+	0.996405i	$0.526999\pi$
$14$	−62.0759	−	45.8006i	−0.316714	−	0.233677i
$15$			58.0948i			0.258199i
$16$	−211.436	+	144.329i	−0.825922	+	0.563785i
$17$	290.124			1.00389			0.501945	−	0.864899i	$-0.332618\pi$
$17$	290.124			1.00389			0.501945	+	0.864899i	$0.332618\pi$
$18$	−64.1204	+	86.9056i	−0.197902	+	0.268227i
$19$		−	459.035i		−	1.27156i	−0.771868	−	0.635782i	$-0.780678\pi$
$19$		−	459.035i		−	1.27156i	0.771868	−	0.635782i	$-0.219322\pi$
$20$	52.7755	+	170.923i	0.131939	+	0.427308i
$21$	−100.212			−0.227239
$22$	−90.6699	−	66.8978i	−0.187335	−	0.138219i
$23$		−	63.0305i		−	0.119150i	−0.998224	−	0.0595752i	$-0.981025\pi$
$23$		−	63.0305i		−	0.119150i	0.998224	−	0.0595752i	$-0.0189746\pi$
$24$	−109.703	+	313.938i	−0.190457	+	0.545032i
$25$	125.000			0.200000
$26$	−68.0024	+	92.1671i	−0.100595	+	0.136342i
$27$			140.296i			0.192450i
$28$	−294.839	+	91.0366i	−0.376070	+	0.116118i
$29$	1141.80			1.35767			0.678837	−	0.734289i	$-0.262484\pi$
$29$	1141.80			1.35767			0.678837	+	0.734289i	$0.262484\pi$
$30$	186.991	+	137.965i	0.207768	+	0.153295i
$31$		−	1335.53i		−	1.38972i	−0.719143	−	0.694862i	$-0.755465\pi$
$31$		−	1335.53i		−	1.38972i	0.719143	−	0.694862i	$-0.244535\pi$
$32$	−37.5694	+	1023.31i	−0.0366889	+	0.999327i
$33$	−146.373			−0.134411
$34$	688.996	−	933.831i	0.596017	−	0.807812i
$35$			215.622i			0.176018i
$36$	127.450	+	412.772i	0.0983413	+	0.318497i
$37$	1365.02			0.997090			0.498545	−	0.866864i	$-0.333868\pi$
$37$	1365.02			0.997090			0.498545	+	0.866864i	$0.333868\pi$
$38$	−1477.51	−	1090.13i	−1.02320	−	0.754937i
$39$			148.790i			0.0978238i
$40$	675.488	+	236.044i	0.422180	+	0.147527i
$41$	1242.93			0.739401			0.369700	−	0.929151i	$-0.379460\pi$
$41$	1242.93			0.739401			0.369700	+	0.929151i	$0.379460\pi$
$42$	−237.987	+	322.556i	−0.134913	+	0.182855i
$43$		−	663.357i		−	0.358765i	−0.983779	−	0.179383i	$-0.942590\pi$
$43$		−	663.357i		−	0.358765i	0.983779	−	0.179383i	$-0.0574100\pi$
$44$	−430.651	+	132.971i	−0.222444	+	0.0686833i
$45$	301.869			0.149071
$46$	−202.878	−	149.687i	−0.0958780	−	0.0707404i
$47$			3936.26i			1.78192i	0.454080	+	0.890961i	$0.349968\pi$
$47$			3936.26i			1.78192i	−0.454080	+	0.890961i	$0.650032\pi$
$48$	749.955	+	1098.65i	0.325501	+	0.476846i
$49$	2029.06			0.845088
$50$	296.854	−	402.341i	0.118741	−	0.160936i
$51$		−	1507.53i		−	0.579597i
$52$	135.166	+	437.762i	0.0499876	+	0.161894i
$53$	−4618.99			−1.64435			−0.822177	−	0.569232i	$-0.807240\pi$
$53$	−4618.99			−1.64435			−0.822177	+	0.569232i	$0.807240\pi$
$54$	451.575	+	333.179i	0.154861	+	0.114259i
$55$			314.945i			0.104114i
$56$	−407.170	+	1165.20i	−0.129838	+	0.371557i
$57$	−2385.22			−0.734138
$58$	2711.59	−	3675.15i	0.806061	−	1.09250i
$59$			2602.83i			0.747725i	0.927484	+	0.373862i	$0.121967\pi$
$59$			2602.83i			0.747725i	−0.927484	+	0.373862i	$0.878033\pi$
$60$	888.143	−	274.229i	0.246706	−	0.0761748i
$61$	−5396.32			−1.45023			−0.725117	−	0.688626i	$-0.758214\pi$
$61$	−5396.32			−1.45023			−0.725117	+	0.688626i	$0.758214\pi$
$62$	−4298.69	−	3171.64i	−1.11829	−	0.825089i
$63$			520.718i			0.131196i
$64$	3204.53	+	2551.11i	0.782357	+	0.622830i
$65$	320.145			0.0757740
$66$	−347.611	+	471.135i	−0.0798005	+	0.108158i
$67$		−	6033.14i		−	1.34398i	−0.740559	−	0.671991i	$-0.765439\pi$
$67$		−	6033.14i		−	1.34398i	0.740559	−	0.671991i	$-0.234561\pi$
$68$	−1369.50	−	4435.38i	−0.296172	−	0.959208i
$69$	−327.516			−0.0687915
$70$	694.029	+	512.066i	0.141639	+	0.104503i
$71$			955.221i			0.189490i	0.995502	+	0.0947452i	$0.0302036\pi$
$71$			955.221i			0.189490i	−0.995502	+	0.0947452i	$0.969796\pi$
$72$	1631.27	+	570.034i	0.314674	+	0.109960i
$73$	−8814.75			−1.65411			−0.827055	−	0.562121i	$-0.809986\pi$
$73$	−8814.75			−1.65411			−0.827055	+	0.562121i	$0.809986\pi$
$74$	3241.68	−	4393.61i	0.591979	−	0.802340i
$75$		−	649.519i		−	0.115470i
$76$	−7017.65	+	2166.82i	−1.21497	+	0.375142i
$77$	−543.273			−0.0916298
$78$	478.914	+	353.351i	0.0787170	+	0.0580787i
$79$			3717.96i			0.595731i	0.954608	+	0.297866i	$0.0962747\pi$
$79$			3717.96i			0.595731i	−0.954608	+	0.297866i	$0.903725\pi$
$80$	2363.93	−	1613.65i	0.369364	−	0.252132i
$81$	729.000			0.111111
$82$	2951.75	−	4000.66i	0.438988	−	0.594982i
$83$			5992.78i			0.869905i	0.900453	+	0.434953i	$0.143235\pi$
$83$			5992.78i			0.869905i	−0.900453	+	0.434953i	$0.856765\pi$
$84$	473.040	+	1532.03i	0.0670408	+	0.217124i
$85$	−3243.69			−0.448954
$86$	−2135.16	−	1575.36i	−0.288692	−	0.213002i
$87$		−	5932.99i		−	0.783854i
$88$	−594.726	+	1701.93i	−0.0767983	+	0.219774i
$89$	10839.6			1.36847			0.684233	−	0.729263i	$-0.260137\pi$
$89$	10839.6			1.36847			0.684233	+	0.729263i	$0.260137\pi$
$90$	716.887	−	971.634i	0.0885046	−	0.119955i
$91$			552.244i			0.0666881i
$92$	−963.600	+	297.528i	−0.113847	+	0.0351522i
$93$	−6939.59			−0.802358
$94$	12669.8	+	9347.95i	1.43388	+	1.05794i
$95$			5132.17i			0.568661i
$96$	5317.28	+	195.216i	0.576962	+	0.0211823i
$97$	5581.91			0.593253			0.296626	−	0.954994i	$-0.404138\pi$
$97$	5581.91			0.593253			0.296626	+	0.954994i	$0.404138\pi$
$98$	4818.66	−	6530.97i	0.501735	−	0.680026i
$99$			760.577i			0.0776020i
$100$	−590.048	−	1910.98i	−0.0590048	−	0.191098i
$101$	18138.4			1.77810			0.889050	−	0.457809i	$-0.151366\pi$
$101$	18138.4			1.77810			0.889050	+	0.457809i	$0.151366\pi$
$102$	−4852.33	−	3580.13i	−0.466391	−	0.344111i
$103$			15849.0i			1.49392i	0.664869	+	0.746960i	$0.268487\pi$
$103$			15849.0i			1.49392i	−0.664869	+	0.746960i	$0.731513\pi$
$104$	1730.03	+	604.546i	0.159951	+	0.0558937i
$105$	1120.41			0.101624
$106$	−10969.3	+	14867.3i	−0.976264	+	1.32318i
$107$		−	2519.57i		−	0.220069i	−0.993928	−	0.110035i	$-0.964904\pi$
$107$		−	2519.57i		−	0.220069i	0.993928	−	0.110035i	$-0.0350962\pi$
$108$	2144.82	−	662.251i	0.183884	−	0.0567774i
$109$	1083.02			0.0911555			0.0455778	−	0.998961i	$-0.485487\pi$
$109$	1083.02			0.0911555			0.0455778	+	0.998961i	$0.485487\pi$
$110$	1013.72	+	747.940i	0.0837786	+	0.0618132i
$111$		−	7092.83i		−	0.575670i
$112$	2783.51	+	4077.72i	0.221899	+	0.325074i
$113$	−665.859			−0.0521466			−0.0260733	−	0.999660i	$-0.508300\pi$
$113$	−665.859			−0.0521466			−0.0260733	+	0.999660i	$0.508300\pi$
$114$	−5664.48	+	7677.35i	−0.435863	+	0.590747i
$115$			704.703i			0.0532856i
$116$	−5389.75	−	17455.7i	−0.400546	−	1.29724i
$117$	773.136			0.0564786
$118$	8377.79	+	6181.27i	0.601680	+	0.443929i
$119$		−	5595.30i		−	0.395120i
$120$	1226.52	−	3509.94i	0.0851749	−	0.243746i
$121$	13847.5			0.945801
$122$	−12815.3	+	17369.3i	−0.861014	+	1.16698i
$123$		−	6458.47i		−	0.426893i
$124$	−20417.3	+	6304.19i	−1.32787	+	0.410002i
$125$	−1397.54			−0.0894427
$126$	1676.05	+	1236.62i	0.105571	+	0.0778922i
$127$		−	9928.67i		−	0.615579i	−0.951454	−	0.307789i	$-0.900411\pi$
$127$		−	9928.67i		−	0.615579i	0.951454	−	0.307789i	$-0.0995892\pi$
$128$	15821.5	−	4256.06i	0.965671	−	0.259769i
$129$	−3446.90			−0.207133
$130$	760.290	−	1030.46i	0.0449876	−	0.0609739i
$131$		−	25186.1i		−	1.46764i	−0.679346	−	0.733818i	$-0.737736\pi$
$131$		−	25186.1i		−	1.46764i	0.679346	−	0.733818i	$-0.262264\pi$
$132$	690.937	+	2237.73i	0.0396543	+	0.128428i
$133$	−8852.88			−0.500474
$134$	−19419.0	−	14327.7i	−1.08148	−	0.797932i
$135$		−	1568.56i		−	0.0860663i
$136$	−17528.6	−	6125.22i	−0.947696	−	0.331165i
$137$	−3063.11			−0.163200			−0.0816002	−	0.996665i	$-0.526003\pi$
$137$	−3063.11			−0.163200			−0.0816002	+	0.996665i	$0.526003\pi$
$138$	−777.795	+	1054.18i	−0.0408420	+	0.0553552i
$139$		−	23379.5i		−	1.21006i	−0.796204	−	0.605028i	$-0.793162\pi$
$139$		−	23379.5i		−	1.21006i	0.796204	−	0.605028i	$-0.206838\pi$
$140$	3296.40	−	1017.82i	0.168184	−	0.0519296i
$141$	20453.4			1.02879
$142$	3074.59	+	2268.49i	0.152479	+	0.112502i
$143$			806.624i			0.0394457i
$144$	5708.77	−	3896.88i	0.275307	−	0.187928i
$145$	−12765.8			−0.607171
$146$	−20933.5	+	28372.3i	−0.982057	+	1.33103i
$147$		−	10543.3i		−	0.487912i
$148$	−6443.40	−	20868.1i	−0.294165	−	0.952709i
$149$	−14924.8			−0.672257			−0.336129	−	0.941816i	$-0.609118\pi$
$149$	−14924.8			−0.672257			−0.336129	+	0.941816i	$0.609118\pi$
$150$	−2090.62	−	1542.50i	−0.0929166	−	0.0685554i
$151$			5685.42i			0.249350i	0.992198	+	0.124675i	$0.0397888\pi$
$151$			5685.42i			0.249350i	−0.992198	+	0.124675i	$0.960211\pi$
$152$	−9691.32	+	27733.7i	−0.419465	+	1.20039i
$153$	−7833.36			−0.334630
$154$	−1290.18	+	1748.65i	−0.0544013	+	0.0737328i
$155$			14931.6i			0.621504i
$156$	2274.68	−	702.346i	0.0934697	−	0.0288604i
$157$	29681.0			1.20415			0.602073	−	0.798441i	$-0.294341\pi$
$157$	29681.0			1.20415			0.602073	+	0.798441i	$0.294341\pi$
$158$	11967.1	+	8829.51i	0.479374	+	0.353690i
$159$			24001.0i			0.949368i
$160$	420.039	−	11441.0i	0.0164078	−	0.446913i
$161$	−1215.60			−0.0468962
$162$	1731.25	−	2346.45i	0.0659675	−	0.0894090i
$163$			11159.3i			0.420011i	0.977700	+	0.210005i	$0.0673482\pi$
$163$			11159.3i			0.420011i	−0.977700	+	0.210005i	$0.932652\pi$
$164$	−5867.12	−	19001.8i	−0.218141	−	0.706490i
$165$	1636.50			0.0601102
$166$	19289.1	+	14231.8i	0.699996	+	0.516469i
$167$			45348.0i			1.62602i	0.582251	+	0.813009i	$0.302172\pi$
$167$			45348.0i			1.62602i	−0.582251	+	0.813009i	$0.697828\pi$
$168$	6054.57	+	2115.72i	0.214518	+	0.0749617i
$169$	−27741.1			−0.971291
$170$	−7703.21	+	10440.5i	−0.266547	+	0.361265i
$171$			12393.9i			0.423855i
$172$	−10141.3	+	3131.30i	−0.342797	+	0.105844i
$173$	−18639.7			−0.622797			−0.311399	−	0.950279i	$-0.600797\pi$
$173$	−18639.7			−0.622797			−0.311399	+	0.950279i	$0.600797\pi$
$174$	−19096.7	−	14089.8i	−0.630752	−	0.465380i
$175$		−	2410.73i		−	0.0787178i
$176$	4065.67	+	5956.05i	0.131252	+	0.192280i
$177$	13524.7			0.431699
$178$	25742.2	−	34889.8i	0.812468	−	1.10118i
$179$		−	59685.9i		−	1.86280i	−0.364001	−	0.931399i	$-0.618589\pi$
$179$		−	59685.9i		−	1.86280i	0.364001	−	0.931399i	$-0.381411\pi$
$180$	−1424.94	−	4614.93i	−0.0439796	−	0.142436i
$181$	23124.2			0.705845			0.352923	−	0.935653i	$-0.385188\pi$
$181$	23124.2			0.705845			0.352923	+	0.935653i	$0.385188\pi$
$182$	1777.52	+	1311.48i	0.0536626	+	0.0395932i
$183$			28040.1i			0.837293i
$184$	−1330.72	+	3808.14i	−0.0393054	+	0.112481i
$185$	−15261.3			−0.445912
$186$	−16480.3	+	22336.6i	−0.476366	+	0.645642i
$187$		−	8172.67i		−	0.233712i
$188$	60177.0	−	18580.7i	1.70261	−	0.525709i
$189$	2705.73			0.0757462
$190$	16519.0	+	12188.0i	0.457591	+	0.337618i
$191$			4215.25i			0.115547i	0.998330	+	0.0577733i	$0.0184001\pi$
$191$			4215.25i			0.115547i	−0.998330	+	0.0577733i	$0.981600\pi$
$192$	13256.0	−	16651.2i	0.359591	−	0.451694i
$193$	42051.8			1.12894			0.564469	−	0.825454i	$-0.309081\pi$
$193$	42051.8			1.12894			0.564469	+	0.825454i	$0.309081\pi$
$194$	13256.1	−	17966.6i	0.352218	−	0.477379i
$195$		−	1663.52i		−	0.0437481i
$196$	−9577.92	−	31019.9i	−0.249321	−	0.807473i
$197$	−3599.70			−0.0927542			−0.0463771	−	0.998924i	$-0.514768\pi$
$197$	−3599.70			−0.0927542			−0.0463771	+	0.998924i	$0.514768\pi$
$198$	2448.09	+	1806.24i	0.0624449	+	0.0460728i
$199$			13966.2i			0.352673i	0.984330	+	0.176336i	$0.0564246\pi$
$199$			13966.2i			0.352673i	−0.984330	+	0.176336i	$0.943575\pi$
$200$	−7552.18	−	2639.05i	−0.188805	−	0.0659762i
$201$	−31349.1			−0.775949
$202$	43075.6	−	58382.5i	1.05567	−	1.43080i
$203$		−	22020.7i		−	0.534366i
$204$	−23046.9	+	7116.12i	−0.553799	+	0.170995i
$205$	−13896.4			−0.330670
$206$	51013.6	+	37638.6i	1.20213	+	0.886951i
$207$			1701.82i			0.0397168i
$208$	6054.40	−	4132.81i	0.139941	−	0.0955253i
$209$	−12930.8			−0.296028
$210$	2660.77	−	3606.28i	0.0603350	−	0.0817751i
$211$		−	22691.1i		−	0.509673i	−0.966984	−	0.254836i	$-0.917978\pi$
$211$		−	22691.1i		−	0.509673i	0.966984	−	0.254836i	$-0.0820216\pi$
$212$	21803.4	+	70614.3i	0.485123	+	1.57116i
$213$	4963.47			0.109402
$214$	−8109.81	−	5983.55i	−0.177086	−	0.130657i
$215$			7416.56i			0.160445i
$216$	2961.99	−	8476.33i	0.0634856	−	0.181677i
$217$	−25756.8			−0.546980
$218$	2571.98	−	3485.94i	0.0541197	−	0.0733512i
$219$			45802.8i			0.955001i
$220$	4814.82	−	1486.66i	0.0994798	−	0.0307161i
$221$	−8307.61			−0.170095
$222$	−22829.9	−	16844.3i	−0.463231	−	0.341779i
$223$			84540.5i			1.70002i	0.526763	+	0.850012i	$0.323405\pi$
$223$			84540.5i			1.70002i	−0.526763	+	0.850012i	$0.676595\pi$
$224$	19735.4	+	724.558i	0.393324	+	0.0144403i
$225$	−3375.00			−0.0666667
$226$	−1581.30	+	2143.22i	−0.0309598	+	0.0419614i
$227$			739.621i			0.0143535i	0.999974	+	0.00717674i	$0.00228445\pi$
$227$			739.621i			0.0143535i	−0.999974	+	0.00717674i	$0.997716\pi$
$228$	11259.1	+	36464.8i	0.216588	+	0.701462i
$229$	−60378.3			−1.15136			−0.575679	−	0.817676i	$-0.695262\pi$
$229$	−60378.3			−1.15136			−0.575679	+	0.817676i	$0.695262\pi$
$230$	2268.24	+	1673.55i	0.0428780	+	0.0316361i
$231$			2822.93i			0.0529025i
$232$	−68984.9	−	24106.2i	−1.28168	−	0.447871i
$233$	−26943.7			−0.496301			−0.248151	−	0.968721i	$-0.579823\pi$
$233$	−26943.7			−0.496301			−0.248151	+	0.968721i	$0.579823\pi$
$234$	1836.06	−	2488.51i	0.0335318	−	0.0454473i
$235$		−	44008.8i		−	0.796900i
$236$	39791.6	−	12286.3i	0.714443	−	0.220597i
$237$	19319.1			0.343945
$238$	−18009.7	−	13287.9i	−0.317946	−	0.234586i
$239$			35882.1i			0.628177i	0.949394	+	0.314089i	$0.101699\pi$
$239$			35882.1i			0.628177i	−0.949394	+	0.314089i	$0.898301\pi$
$240$	−8384.75	−	12283.3i	−0.145569	−	0.213252i
$241$	47555.3			0.818776			0.409388	−	0.912360i	$-0.365742\pi$
$241$	47555.3			0.818776			0.409388	+	0.912360i	$0.365742\pi$
$242$	32885.4	−	44571.2i	0.561529	−	0.761069i
$243$		−	3788.00i		−	0.0641500i
$244$	25472.7	+	82498.0i	0.427853	+	1.38568i
$245$	−22685.5			−0.377935
$246$	−20788.0	−	15337.8i	−0.343513	−	0.253450i
$247$			13144.3i			0.215449i
$248$	−28196.1	+	80689.0i	−0.458444	+	1.31193i
$249$	31139.4			0.502240
$250$	−3318.92	+	4498.30i	−0.0531028	+	0.0719729i
$251$		−	64104.2i		−	1.01751i	−0.860911	−	0.508756i	$-0.830106\pi$
$251$		−	64104.2i		−	1.01751i	0.860911	−	0.508756i	$-0.169894\pi$
$252$	7960.65	−	2457.99i	0.125357	−	0.0387060i
$253$	−1775.54			−0.0277389
$254$	−31957.7	−	23578.9i	−0.495345	−	0.365474i
$255$			16854.7i			0.259204i
$256$	23874.4	−	61032.6i	0.364294	−	0.931284i
$257$	−38018.5			−0.575611			−0.287806	−	0.957689i	$-0.592926\pi$
$257$	−38018.5			−0.575611			−0.287806	+	0.957689i	$0.592926\pi$
$258$	−8185.81	+	11094.6i	−0.122976	+	0.166676i
$259$		−	26325.5i		−	0.392444i
$260$	−1511.21	−	4894.33i	−0.0223551	−	0.0724013i
$261$	−30828.7			−0.452558
$262$	−81067.2	−	59812.7i	−1.18098	−	0.871346i
$263$		−	101432.i		−	1.46644i	−0.679994	−	0.733218i	$-0.738018\pi$
$263$		−	101432.i		−	1.46644i	0.679994	−	0.733218i	$-0.261982\pi$
$264$	8843.49	+	3090.29i	0.126887	+	0.0443395i
$265$	51641.9			0.735377
$266$	−21024.1	+	28495.0i	−0.297135	+	0.402722i
$267$		−	56324.3i		−	0.790084i
$268$	−92233.6	+	28478.7i	−1.28416	+	0.396507i
$269$	118525.			1.63796			0.818982	−	0.573819i	$-0.194539\pi$
$269$	118525.			1.63796			0.818982	+	0.573819i	$0.194539\pi$
$270$	−5048.76	−	3725.06i	−0.0692559	−	0.0510982i
$271$			48236.2i			0.656802i	0.944538	+	0.328401i	$0.106510\pi$
$271$			48236.2i			0.656802i	−0.944538	+	0.328401i	$0.893490\pi$
$272$	−61342.8	+	41873.3i	−0.829136	+	0.565978i
$273$	2869.54			0.0385024
$274$	−7274.35	+	9859.30i	−0.0968932	+	0.131324i
$275$		−	3521.19i		−	0.0465612i
$276$	1546.00	+	5007.01i	0.0202951	+	0.0657296i
$277$	−17265.4			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$277$	−17265.4			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$278$	−75252.2	−	55522.3i	−0.973709	−	0.718419i
$279$			36059.2i			0.463242i
$280$	4552.30	−	13027.4i	0.0580651	−	0.166165i
$281$	−80910.7			−1.02469			−0.512346	−	0.858779i	$-0.671224\pi$
$281$	−80910.7			−1.02469			−0.512346	+	0.858779i	$0.671224\pi$
$282$	48573.4	−	65834.0i	0.610802	−	0.827850i
$283$			44418.4i			0.554613i	0.960782	+	0.277306i	$0.0894417\pi$
$283$			44418.4i			0.554613i	−0.960782	+	0.277306i	$0.910558\pi$
$284$	14603.3	−	4509.01i	0.181056	−	0.0559042i
$285$	26667.5			0.328317
$286$	2596.30	+	1915.59i	0.0317412	+	0.0234192i
$287$		−	23971.0i		−	0.291020i
$288$	1014.37	−	27629.4i	0.0122296	−	0.333109i
$289$	651.209			0.00779695
$290$	−30316.5	+	41089.5i	−0.360481	+	0.488579i
$291$		−	29004.5i		−	0.342515i
$292$	41609.0	+	134759.i	0.488002	+	1.58049i
$293$	12219.3			0.142335			0.0711677	−	0.997464i	$-0.477327\pi$
$293$	12219.3			0.142335			0.0711677	+	0.997464i	$0.477327\pi$
$294$	−33935.9	−	25038.5i	−0.392613	−	0.289677i
$295$		−	29100.5i		−	0.334393i
$296$	−82470.8	−	28818.7i	−0.941275	−	0.328921i
$297$	3952.07			0.0448035
$298$	−35443.8	+	48038.8i	−0.399124	+	0.540953i
$299$			1804.86i			0.0201883i
$300$	−9929.74	+	3065.98i	−0.110330	+	0.0340664i
$301$	−12793.4			−0.141206
$302$	18299.8	+	13501.9i	0.200647	+	0.148041i
$303$		−	94249.9i		−	1.02659i
$304$	66252.0	+	97056.5i	0.716889	+	1.05021i
$305$	60332.7			0.648564
$306$	−18602.9	+	25213.4i	−0.198672	+	0.269271i
$307$		−	45783.2i		−	0.485768i	−0.970055	−	0.242884i	$-0.921907\pi$
$307$		−	45783.2i		−	0.485768i	0.970055	−	0.242884i	$-0.0780934\pi$
$308$	2564.46	+	8305.47i	0.0270330	+	0.0875514i
$309$	82353.8			0.862515
$310$	48060.8	+	35460.1i	0.500112	+	0.368991i
$311$			93050.8i			0.962054i	0.876706	+	0.481027i	$0.159736\pi$
$311$			93050.8i			0.962054i	−0.876706	+	0.481027i	$0.840264\pi$
$312$	3141.31	−	8989.51i	0.0322702	−	0.0923479i
$313$	153178.			1.56353			0.781767	−	0.623571i	$-0.214319\pi$
$313$	153178.			1.56353			0.781767	+	0.623571i	$0.214319\pi$
$314$	70487.3	−	95535.0i	0.714910	−	0.968954i
$315$		−	5821.81i		−	0.0586728i
$316$	56839.5	−	17550.2i	0.569215	−	0.175755i
$317$	25234.5			0.251117			0.125559	−	0.992086i	$-0.459928\pi$
$317$	25234.5			0.251117			0.125559	+	0.992086i	$0.459928\pi$
$318$	77252.5	+	56998.2i	0.763938	+	0.563646i
$319$		−	32164.1i		−	0.316075i
$320$	−35827.8	−	28522.3i	−0.349881	−	0.278538i
$321$	−13092.1			−0.127057
$322$	−2886.84	+	3912.67i	−0.0278426	+	0.0377365i
$323$		−	133177.i		−	1.27651i
$324$	−3441.16	−	11144.8i	−0.0327804	−	0.106166i
$325$	−3579.33			−0.0338872
$326$	35918.6	+	26501.4i	0.337975	+	0.249363i
$327$		−	5627.53i		−	0.0526287i
$328$	−75094.8	−	26241.3i	−0.698011	−	0.243914i
$329$	75914.2			0.701345
$330$	3886.41	−	5267.45i	0.0356879	−	0.0483696i
$331$			158659.i			1.44813i	0.689730	+	0.724066i	$0.257729\pi$
$331$			158659.i			1.44813i	−0.689730	+	0.724066i	$0.742271\pi$
$332$	91616.6	−	28288.2i	0.831186	−	0.256643i
$333$	−36855.4			−0.332363
$334$	145963.	+	107694.i	1.30843	+	0.965379i
$335$			67452.5i			0.601047i
$336$	21188.5	−	14463.5i	0.187681	−	0.128114i
$337$	−15308.6			−0.134796			−0.0673980	−	0.997726i	$-0.521470\pi$
$337$	−15308.6			−0.134796			−0.0673980	+	0.997726i	$0.521470\pi$
$338$	−65880.2	+	89290.8i	−0.576663	+	0.781580i
$339$			3459.91i			0.0301068i
$340$	15311.5	+	49589.0i	0.132452	+	0.428971i
$341$	−37621.1			−0.323536
$342$	39892.7	+	29433.5i	0.341068	+	0.251646i
$343$		−	85437.4i		−	0.726206i
$344$	−14005.1	+	40078.3i	−0.118350	+	0.338683i
$345$	3661.74			0.0307645
$346$	−44266.1	+	59996.1i	−0.369759	+	0.501153i
$347$			145358.i			1.20720i	0.797288	+	0.603599i	$0.206267\pi$
$347$			145358.i			1.20720i	−0.797288	+	0.603599i	$0.793733\pi$
$348$	−90702.6	+	28006.0i	−0.748964	+	0.231256i
$349$	−91594.6			−0.752002			−0.376001	−	0.926619i	$-0.622701\pi$
$349$	−91594.6			−0.752002			−0.376001	+	0.926619i	$0.622701\pi$
$350$	−7759.48	−	5725.08i	−0.0633427	−	0.0467353i
$351$		−	4017.33i		−	0.0326079i
$352$	28826.2	+	1058.31i	0.232649	+	0.00854139i
$353$	84192.7			0.675655			0.337827	−	0.941208i	$-0.390308\pi$
$353$	84192.7			0.675655			0.337827	+	0.941208i	$0.390308\pi$
$354$	32118.8	−	43532.3i	0.256303	−	0.347380i
$355$		−	10679.7i		−	0.0847426i
$356$	−51167.1	−	165714.i	−0.403730	−	1.30756i
$357$	−29074.0			−0.228123
$358$	−192112.	−	141744.i	−1.49896	−	1.10596i
$359$			53396.4i			0.414308i	0.978308	+	0.207154i	$0.0664201\pi$
$359$			53396.4i			0.414308i	−0.978308	+	0.207154i	$0.933580\pi$
$360$	−18238.2	−	6373.18i	−0.140727	−	0.0491758i
$361$	−80392.1			−0.616877
$362$	54916.0	−	74430.4i	0.419065	−	0.567980i
$363$		−	71953.6i		−	0.546059i
$364$	8442.62	−	2606.80i	0.0637198	−	0.0196746i
$365$	98551.9			0.739741
$366$	90253.3	+	66590.4i	0.673754	+	0.497107i
$367$			141341.i			1.04938i	0.851292	+	0.524692i	$0.175820\pi$
$367$			141341.i			1.04938i	−0.851292	+	0.524692i	$0.824180\pi$
$368$	9097.12	+	13326.9i	0.0671751	+	0.0984089i
$369$	−33559.2			−0.246467
$370$	−36243.1	+	49122.1i	−0.264741	+	0.358817i
$371$			89081.1i			0.647199i
$372$	32757.5	+	106091.i	0.236715	+	0.766645i
$373$	−98354.8			−0.706932			−0.353466	−	0.935447i	$-0.614997\pi$
$373$	−98354.8			−0.706932			−0.353466	+	0.935447i	$0.614997\pi$
$374$	−26305.6	−	19408.7i	−0.188063	−	0.138756i
$375$			7261.84i			0.0516398i
$376$	83103.9	−	237819.i	0.587822	−	1.68217i
$377$	−32695.2			−0.230039
$378$	6425.65	−	8709.00i	0.0449711	−	0.0609516i
$379$		−	233635.i		−	1.62652i	−0.581902	−	0.813259i	$-0.697691\pi$
$379$		−	233635.i		−	1.62652i	0.581902	−	0.813259i	$-0.302309\pi$
$380$	78459.7	−	24225.8i	0.543350	−	0.167769i
$381$	−51590.9			−0.355405
$382$	13567.7	+	10010.5i	0.0929782	+	0.0686008i
$383$			70931.0i			0.483547i	0.970333	+	0.241773i	$0.0777291\pi$
$383$			70931.0i			0.483547i	−0.970333	+	0.241773i	$0.922271\pi$
$384$	−22115.1	−	82211.2i	−0.149978	−	0.557530i
$385$	6073.98			0.0409781
$386$	99865.8	−	135353.i	0.670258	−	0.908435i
$387$			17910.6i			0.119588i
$388$	−26348.8	−	85335.4i	−0.175024	−	0.566847i
$389$	5365.04			0.0354547			0.0177274	−	0.999843i	$-0.494357\pi$
$389$	5365.04			0.0354547			0.0177274	+	0.999843i	$0.494357\pi$
$390$	−5354.42	−	3950.58i	−0.0352033	−	0.0259736i
$391$		−	18286.7i		−	0.119614i
$392$	−122590.	−	42838.2i	−0.797782	−	0.278778i
$393$	−130871.			−0.847340
$394$	−8548.67	+	11586.4i	−0.0550688	+	0.0746376i
$395$		−	41568.0i		−	0.266419i
$396$	11627.6	−	3590.21i	0.0741479	−	0.0228944i
$397$	−228645.			−1.45071			−0.725356	−	0.688374i	$-0.758325\pi$
$397$	−228645.			−1.45071			−0.725356	+	0.688374i	$0.758325\pi$
$398$	44953.3	+	33167.3i	0.283789	+	0.209384i
$399$			46000.9i			0.288949i
$400$	−26429.5	+	18041.1i	−0.165184	+	0.112757i
$401$	−182899.			−1.13743			−0.568714	−	0.822536i	$-0.692559\pi$
$401$	−182899.			−1.13743			−0.568714	+	0.822536i	$0.692559\pi$
$402$	−74448.7	+	100904.i	−0.460686	+	0.624391i
$403$			38242.3i			0.235469i
$404$	−85620.2	−	277297.i	−0.524582	−	1.69896i
$405$	−8150.47			−0.0496904
$406$	−70878.5	−	52295.3i	−0.429994	−	0.317257i
$407$		−	38451.8i		−	0.232128i
$408$	−31827.6	+	91081.2i	−0.191198	+	0.547152i
$409$	−132579.			−0.792552			−0.396276	−	0.918131i	$-0.629698\pi$
$409$	−132579.			−0.792552			−0.396276	+	0.918131i	$0.629698\pi$
$410$	−33001.6	+	44728.7i	−0.196321	+	0.266084i
$411$			15916.4i			0.0942238i
$412$	242297.	−	74813.3i	1.42743	−	0.440742i
$413$	50197.8			0.294296
$414$	5477.70	+	4041.54i	0.0319593	+	0.0235801i
$415$		−	67001.3i		−	0.389033i
$416$	1075.79	−	29302.1i	0.00621641	−	0.169322i
$417$	−121483.			−0.698626
$418$	−30708.4	+	41620.7i	−0.175754	+	0.238208i
$419$			291072.i			1.65795i	0.559283	+	0.828976i	$0.311076\pi$
$419$			291072.i			1.65795i	−0.559283	+	0.828976i	$0.688924\pi$
$420$	−5288.75	−	17128.6i	−0.0299816	−	0.0971009i
$421$	−33411.3			−0.188508			−0.0942540	−	0.995548i	$-0.530047\pi$
$421$	−33411.3			−0.188508			−0.0942540	+	0.995548i	$0.530047\pi$
$422$	−73036.5	−	53887.5i	−0.410124	−	0.302596i
$423$		−	106279.i		−	0.593974i
$424$	279067.	+	97517.9i	1.55231	+	0.542441i
$425$	36265.6			0.200778
$426$	11787.4	−	15976.1i	0.0649529	−	0.0880340i
$427$			104073.i			0.570796i
$428$	−38518.8	+	11893.3i	−0.210274	+	0.0649256i
$429$	4191.34			0.0227740
$430$	23871.9	+	17613.1i	0.129107	+	0.0952572i
$431$		−	91506.5i		−	0.492603i	−0.969193	−	0.246302i	$-0.920785\pi$
$431$		−	91506.5i		−	0.492603i	0.969193	−	0.246302i	$-0.0792154\pi$
$432$	−20248.8	−	29663.7i	−0.108500	−	0.158949i
$433$	301690.			1.60911			0.804553	−	0.593881i	$-0.202405\pi$
$433$	301690.			1.60911			0.804553	+	0.593881i	$0.202405\pi$
$434$	−61167.9	+	82903.9i	−0.324746	+	0.440145i
$435$			66332.8i			0.350550i
$436$	−5112.26	−	16557.0i	−0.0268931	−	0.0870982i
$437$	−28933.2			−0.151507
$438$	147427.	+	108774.i	0.768471	+	0.566991i
$439$		−	176051.i		−	0.913502i	−0.889594	−	0.456751i	$-0.849013\pi$
$439$		−	176051.i		−	0.913502i	0.889594	−	0.456751i	$-0.150987\pi$
$440$	6649.23	−	19028.2i	0.0343452	−	0.0982859i
$441$	−54784.5			−0.281696
$442$	−19729.2	+	26739.9i	−0.100987	+	0.136872i
$443$			189794.i			0.967108i	0.875315	+	0.483554i	$0.160654\pi$
$443$			189794.i			0.967108i	−0.875315	+	0.483554i	$0.839346\pi$
$444$	−108434.	+	33480.9i	−0.550047	+	0.169836i
$445$	−121191.			−0.611997
$446$	272113.	+	200769.i	1.36798	+	1.00932i
$447$			77551.4i			0.388128i
$448$	49200.4	−	61802.2i	0.245139	−	0.307927i
$449$	−55275.5			−0.274183			−0.137091	−	0.990558i	$-0.543775\pi$
$449$	−55275.5			−0.274183			−0.137091	+	0.990558i	$0.543775\pi$
$450$	−8015.05	+	10863.2i	−0.0395805	+	0.0536454i
$451$		−	35012.8i		−	0.172137i
$452$	3143.11	+	10179.6i	0.0153845	+	0.0498255i
$453$	29542.3			0.143962
$454$	2380.64	+	1756.47i	0.0115500	+	0.00852177i
$455$		−	6174.27i		−	0.0298238i
$456$	144109.	+	50357.6i	0.693043	+	0.242178i
$457$	401864.			1.92418			0.962091	−	0.272728i	$-0.0879258\pi$
$457$	401864.			1.92418			0.962091	+	0.272728i	$0.0879258\pi$
$458$	−143388.	+	194341.i	−0.683569	+	0.926476i
$459$			40703.3i			0.193199i
$460$	10773.4	−	3326.46i	0.0509139	−	0.0157205i
$461$	231421.			1.08893			0.544467	−	0.838782i	$-0.316732\pi$
$461$	231421.			1.08893			0.544467	+	0.838782i	$0.316732\pi$
$462$	9086.24	+	6703.98i	0.0425697	+	0.0314086i
$463$		−	34800.1i		−	0.162337i	−0.996700	−	0.0811687i	$-0.974135\pi$
$463$		−	34800.1i		−	0.162337i	0.996700	−	0.0811687i	$-0.0258652\pi$
$464$	−241419.	+	164795.i	−1.12133	+	0.765436i
$465$	77587.0			0.358825
$466$	−63986.7	+	86724.3i	−0.294658	+	0.399364i
$467$		−	182183.i		−	0.835359i	−0.908594	−	0.417679i	$-0.862844\pi$
$467$		−	182183.i		−	0.835359i	0.908594	−	0.417679i	$-0.137156\pi$
$468$	−3649.49	−	11819.6i	−0.0166625	−	0.0539647i
$469$	−116354.			−0.528977
$470$	−141652.	−	104513.i	−0.641250	−	0.473125i
$471$		−	154227.i		−	0.695214i
$472$	54951.9	−	157256.i	0.246660	−	0.705869i
$473$	−18686.4			−0.0835227
$474$	45879.5	−	62182.8i	0.204203	−	0.276766i
$475$		−	57379.4i		−	0.254313i
$476$	−85540.0	+	26411.9i	−0.377533	+	0.116570i
$477$	124713.			0.548118
$478$	115495.	+	85213.8i	0.505482	+	0.372953i
$479$			388419.i			1.69289i	0.532473	+	0.846447i	$0.321263\pi$
$479$			388419.i			1.69289i	−0.532473	+	0.846447i	$0.678737\pi$
$480$	−59449.0	−	2182.59i	−0.258025	−	0.00947303i
$481$	−39086.8			−0.168943
$482$	112936.	−	153068.i	0.486113	−	0.658854i
$483$			6316.43i			0.0270756i
$484$	−65365.4	−	211698.i	−0.279034	−	0.903704i
$485$	−62407.7			−0.265311
$486$	−12192.5	−	8995.84i	−0.0516203	−	0.0380863i
$487$		−	320680.i		−	1.35212i	−0.736849	−	0.676058i	$-0.763687\pi$
$487$		−	320680.i		−	1.35212i	0.736849	−	0.676058i	$-0.236313\pi$
$488$	326032.	+	113929.i	1.36905	+	0.478404i
$489$	57985.3			0.242493
$490$	−53874.2	+	73018.5i	−0.224383	+	0.304117i
$491$			206317.i			0.855800i	0.903826	+	0.427900i	$0.140746\pi$
$491$			206317.i			0.855800i	−0.903826	+	0.427900i	$0.859254\pi$
$492$	−98736.0	+	30486.4i	−0.407892	+	0.125944i
$493$	331265.			1.36296
$494$	42307.9	+	31215.5i	0.173367	+	0.127913i
$495$		−	8503.51i		−	0.0347047i
$496$	192755.	+	282378.i	0.783505	+	1.14780i
$497$	18422.3			0.0745813
$498$	73950.7	−	100229.i	0.298183	−	0.404143i
$499$		−	465187.i		−	1.86821i	−0.356993	−	0.934107i	$-0.616198\pi$
$499$		−	465187.i		−	1.86821i	0.356993	−	0.934107i	$-0.383802\pi$
$500$	6596.93	+	21365.4i	0.0263877	+	0.0854616i
$501$	235635.			0.938782
$502$	−206334.	−	152237.i	−0.818772	−	0.604104i
$503$		−	227645.i		−	0.899750i	−0.893092	−	0.449875i	$-0.851469\pi$
$503$		−	227645.i		−	0.899750i	0.893092	−	0.449875i	$-0.148531\pi$
$504$	10993.6	−	31460.5i	0.0432792	−	0.123852i
$505$	−202794.			−0.795191
$506$	−4216.60	+	5714.97i	−0.0164688	+	0.0223210i
$507$			144147.i			0.560775i
$508$	−151788.	+	46867.1i	−0.588179	+	0.181610i
$509$	9630.55			0.0371720			0.0185860	−	0.999827i	$-0.494084\pi$
$509$	9630.55			0.0371720			0.0185860	+	0.999827i	$0.494084\pi$
$510$	54250.7	+	40027.0i	0.208576	+	0.153891i
$511$			170000.i			0.651039i
$512$	−139750.	−	221787.i	−0.533103	−	0.846050i
$513$	64400.8			0.244713
$514$	−90287.5	+	122371.i	−0.341744	+	0.463183i
$515$		−	177197.i		−	0.668101i
$516$	16270.7	+	52695.7i	0.0611092	+	0.197914i
$517$	110883.			0.414842
$518$	−84734.6	−	62518.6i	−0.315792	−	0.232997i
$519$			96854.7i			0.359572i
$520$	−19342.4	−	6759.03i	−0.0715324	−	0.0249964i
$521$	112120.			0.413053			0.206527	−	0.978441i	$-0.433784\pi$
$521$	112120.			0.413053			0.206527	+	0.978441i	$0.433784\pi$
$522$	−73212.9	+	99229.2i	−0.268687	+	0.364165i
$523$			448729.i			1.64052i	0.571993	+	0.820258i	$0.306170\pi$
$523$			448729.i			1.64052i	−0.571993	+	0.820258i	$0.693830\pi$
$524$	−385041.	+	118888.i	−1.40231	+	0.432988i
$525$	−12526.5			−0.0454477
$526$	−326481.	−	240883.i	−1.18001	−	0.870633i
$527$		−	387469.i		−	1.39513i
$528$	30948.5	−	21125.9i	0.111013	−	0.0757786i
$529$	275868.			0.985803
$530$	122641.	−	166221.i	0.436599	−	0.591744i
$531$		−	70276.4i		−	0.249242i
$532$	41789.0	+	135341.i	0.147652	+	0.478198i
$533$	−35591.0			−0.125281
$534$	−181292.	−	133761.i	−0.635766	−	0.469079i
$535$			28169.7i			0.0984179i
$536$	−127374.	+	364507.i	−0.443354	+	1.26875i
$537$	−310137.			−1.07549
$538$	281476.	−	381499.i	0.972471	−	1.31804i
$539$		−	57157.5i		−	0.196741i
$540$	−23979.9	+	7404.19i	−0.0822355	+	0.0253916i
$541$	−101996.			−0.348487			−0.174244	−	0.984703i	$-0.555748\pi$
$541$	−101996.			−0.348487			−0.174244	+	0.984703i	$0.555748\pi$
$542$	155259.	+	114553.i	0.528516	+	0.389948i
$543$		−	120157.i		−	0.407520i
$544$	−10899.8	+	296887.i	−0.0368316	+	1.00322i
$545$	−12108.5			−0.0407660
$546$	6814.67	−	9236.27i	0.0228591	−	0.0309821i
$547$			368616.i			1.23197i	0.787758	+	0.615984i	$0.211242\pi$
$547$			368616.i			1.23197i	−0.787758	+	0.615984i	$0.788758\pi$
$548$	14459.0	+	46828.3i	0.0481480	+	0.155936i
$549$	145701.			0.483411
$550$	−11333.7	−	8362.22i	−0.0374669	−	0.0276437i
$551$		−	524128.i		−	1.72637i
$552$	19787.7	+	6914.65i	0.0649407	+	0.0226930i
$553$	71704.0			0.234473
$554$	−41002.3	+	55572.5i	−0.133595	+	0.181067i
$555$			79300.3i			0.257448i
$556$	−357422.	+	110360.i	−1.15620	+	0.356995i
$557$	303706.			0.978910			0.489455	−	0.872028i	$-0.337196\pi$
$557$	303706.			0.978910			0.489455	+	0.872028i	$0.337196\pi$
$558$	116065.	+	85634.4i	0.372762	+	0.275030i
$559$			18995.0i			0.0607877i
$560$	−31120.5	−	45590.3i	−0.0992364	−	0.145377i
$561$	−42466.4			−0.134934
$562$	−192149.	+	260429.i	−0.608367	+	0.824551i
$563$			29621.8i			0.0934534i	0.998908	+	0.0467267i	$0.0148790\pi$
$563$			29621.8i			0.0934534i	−0.998908	+	0.0467267i	$0.985121\pi$
$564$	−96548.0	−	312689.i	−0.303518	−	0.983001i
$565$	7444.53			0.0233206
$566$	142971.	+	105486.i	0.446286	+	0.329278i
$567$		−	14059.4i		−	0.0437321i
$568$	20167.0	−	57712.0i	0.0625093	−	0.178883i
$569$	−498051.			−1.53833			−0.769164	−	0.639052i	$-0.779327\pi$
$569$	−498051.			−1.53833			−0.769164	+	0.639052i	$0.779327\pi$
$570$	63330.8	−	85835.4i	0.194924	−	0.264190i
$571$			196843.i			0.603736i	0.953350	+	0.301868i	$0.0976103\pi$
$571$			196843.i			0.603736i	−0.953350	+	0.301868i	$0.902390\pi$
$572$	12331.5	−	3807.57i	0.0376899	−	0.0116374i
$573$	21903.1			0.0667109
$574$	−77156.1	−	56927.1i	−0.234178	−	0.172781i
$575$		−	7878.82i		−	0.0238301i
$576$	−86522.4	−	68880.0i	−0.260786	−	0.207610i
$577$	−135033.			−0.405591			−0.202795	−	0.979221i	$-0.565003\pi$
$577$	−135033.			−0.405591			−0.202795	+	0.979221i	$0.565003\pi$
$578$	1546.51	−	2096.06i	0.00462911	−	0.00627406i
$579$		−	218508.i		−	0.651793i
$580$	60259.3	+	195161.i	0.179130	+	0.580145i
$581$	115576.			0.342385
$582$	−93357.4	−	68880.7i	−0.275615	−	0.203353i
$583$			130115.i			0.382815i
$584$	532565.	+	186100.i	1.56152	+	0.545660i
$585$	−8643.92			−0.0252580
$586$	29018.8	−	39330.7i	0.0845055	−	0.114535i
$587$		−	35351.5i		−	0.102596i	−0.998683	−	0.0512981i	$-0.983664\pi$
$587$		−	35351.5i		−	0.102596i	0.998683	−	0.0512981i	$-0.0163359\pi$
$588$	−161184.	+	49768.3i	−0.466195	+	0.143946i
$589$	−613053.			−1.76713
$590$	−93666.6	−	69108.7i	−0.269079	−	0.198531i
$591$			18704.6i			0.0535517i
$592$	−288614.	+	197011.i	−0.823519	+	0.562144i
$593$	−553805.			−1.57488			−0.787440	−	0.616392i	$-0.788594\pi$
$593$	−553805.			−1.57488			−0.787440	+	0.616392i	$0.788594\pi$
$594$	9385.50	−	12720.6i	0.0266002	−	0.0360526i
$595$			62557.3i			0.176703i
$596$	70450.7	+	228168.i	0.198332	+	0.642335i
$597$	72570.4			0.203616
$598$	5809.34	+	4286.23i	0.0162452	+	0.0119860i
$599$		−	284209.i		−	0.792108i	−0.918227	−	0.396054i	$-0.870379\pi$
$599$		−	284209.i		−	0.792108i	0.918227	−	0.396054i	$-0.129621\pi$
$600$	−13712.9	+	39242.3i	−0.0380914	+	0.109006i
$601$	517703.			1.43328			0.716641	−	0.697442i	$-0.245679\pi$
$601$	517703.			1.43328			0.716641	+	0.697442i	$0.245679\pi$
$602$	−30382.2	+	41178.5i	−0.0838350	+	0.113626i
$603$			162895.i			0.447994i
$604$	86917.8	−	26837.4i	0.238251	−	0.0735641i
$605$	−154820.			−0.422975
$606$	−303365.	−	223827.i	−0.826075	−	0.609492i
$607$			287344.i			0.779876i	0.920841	+	0.389938i	$0.127504\pi$
$607$			287344.i			0.779876i	−0.920841	+	0.389938i	$0.872496\pi$
$608$	469735.	+	17245.7i	1.27071	+	0.0466523i
$609$	−114423.			−0.308516
$610$	143280.	−	194194.i	0.385057	−	0.521887i
$611$		−	112714.i		−	0.301921i
$612$	36976.4	+	119755.i	0.0987239	+	0.319736i
$613$	−467697.			−1.24464			−0.622319	−	0.782763i	$-0.713810\pi$
$613$	−467697.			−1.24464			−0.622319	+	0.782763i	$0.713810\pi$
$614$	−147363.	−	108727.i	−0.390888	−	0.288404i
$615$			72207.9i			0.190912i
$616$	32823.2	+	11469.8i	0.0865006	+	0.0302269i
$617$	−94926.6			−0.249355			−0.124677	−	0.992197i	$-0.539790\pi$
$617$	−94926.6			−0.249355			−0.124677	+	0.992197i	$0.539790\pi$
$618$	195576.	−	265074.i	0.512081	−	0.694050i
$619$			371758.i			0.970238i	0.874448	+	0.485119i	$0.161224\pi$
$619$			371758.i			0.970238i	−0.874448	+	0.485119i	$0.838776\pi$
$620$	228272.	−	70483.0i	0.593841	−	0.183358i
$621$	8842.94			0.0229305
$622$	299505.	+	220980.i	0.774147	+	0.571178i
$623$		−	209051.i		−	0.538613i
$624$	−21474.7	−	31459.6i	−0.0551516	−	0.0807948i
$625$	15625.0			0.0400000
$626$	363771.	−	493037.i	0.928281	−	1.25815i
$627$			67190.4i			0.170912i
$628$	−140106.	−	453758.i	−0.355252	−	1.15055i
$629$	396025.			1.00097
$630$	−18738.8	−	13825.8i	−0.0472129	−	0.0348344i
$631$		−	545789.i		−	1.37078i	−0.728178	−	0.685388i	$-0.759633\pi$
$631$		−	545789.i		−	1.37078i	0.728178	−	0.685388i	$-0.240367\pi$
$632$	78494.9	−	224629.i	0.196520	−	0.562384i
$633$	−117907.			−0.294260
$634$	59927.7	−	81223.0i	0.149090	−	0.202069i
$635$			111006.i			0.275295i
$636$	366923.	−	113294.i	0.907111	−	0.280086i
$637$	−58101.3			−0.143188
$638$	−103527.	−	76384.2i	−0.254339	−	0.187656i
$639$		−	25791.0i		−	0.0631634i
$640$	−176890.	+	47584.2i	−0.431861	+	0.116172i
$641$	176298.			0.429072			0.214536	−	0.976716i	$-0.431176\pi$
$641$	176298.			0.429072			0.214536	+	0.976716i	$0.431176\pi$
$642$	−31091.4	+	42139.8i	−0.0754346	+	0.102240i
$643$			569717.i			1.37796i	0.724779	+	0.688981i	$0.241942\pi$
$643$			569717.i			1.37796i	−0.724779	+	0.688981i	$0.758058\pi$
$644$	5738.08	+	18583.9i	0.0138355	+	0.0448089i
$645$	38537.6			0.0926328
$646$	−428661.	−	316273.i	−1.02719	−	0.757874i
$647$		−	314453.i		−	0.751186i	−0.926785	−	0.375593i	$-0.877439\pi$
$647$		−	314453.i		−	0.751186i	0.926785	−	0.375593i	$-0.122561\pi$
$648$	−44044.3	−	15390.9i	−0.104891	−	0.0366534i
$649$	73320.4			0.174075
$650$	−8500.30	+	11520.9i	−0.0201191	+	0.0272684i
$651$			133836.i			0.315799i
$652$	170601.	−	52676.0i	0.401316	−	0.123913i
$653$	−488553.			−1.14574			−0.572869	−	0.819647i	$-0.694170\pi$
$653$	−488553.			−1.14574			−0.572869	+	0.819647i	$0.694170\pi$
$654$	−18113.5	−	13364.4i	−0.0423493	−	0.0312460i
$655$			281589.i			0.656347i
$656$	−262801.	+	179391.i	−0.610687	+	0.416863i
$657$	237998.			0.551370
$658$	180283.	−	244347.i	0.416393	−	0.564359i
$659$		−	76000.3i		−	0.175003i	−0.996164	−	0.0875013i	$-0.972112\pi$
$659$		−	76000.3i		−	0.175003i	0.996164	−	0.0875013i	$-0.0278882\pi$
$660$	−7724.91	−	25018.6i	−0.0177339	−	0.0574347i
$661$	200869.			0.459738			0.229869	−	0.973222i	$-0.426170\pi$
$661$	200869.			0.459738			0.229869	+	0.973222i	$0.426170\pi$
$662$	510679.	+	376788.i	1.16529	+	0.859767i
$663$			43167.6i			0.0982044i
$664$	126522.	−	362068.i	0.286965	−	0.821210i
$665$	98978.2			0.223819
$666$	−87525.3	+	118628.i	−0.197326	+	0.267447i
$667$		−	71968.5i		−	0.161767i
$668$	693274.	−	214060.i	1.55364	−	0.479714i
$669$	439285.			0.981509
$670$	217111.	+	160188.i	0.483651	+	0.356846i
$671$			152012.i			0.337623i
$672$	3764.91	−	102548.i	0.00833713	−	0.227086i
$673$	−341117.			−0.753135			−0.376568	−	0.926389i	$-0.622896\pi$
$673$	−341117.			−0.753135			−0.376568	+	0.926389i	$0.622896\pi$
$674$	−36355.4	+	49274.3i	−0.0800293	+	0.108468i
$675$			17537.0i			0.0384900i
$676$	130948.	+	424101.i	0.286554	+	0.928059i
$677$	−113833.			−0.248366			−0.124183	−	0.992259i	$-0.539631\pi$
$677$	−113833.			−0.248366			−0.124183	+	0.992259i	$0.539631\pi$
$678$	11136.5	+	8216.68i	0.0242264	+	0.0178746i
$679$		−	107652.i		−	0.233498i
$680$	195975.	+	68482.0i	0.423822	+	0.148101i
$681$	3843.18			0.00828699
$682$	−89343.7	+	121092.i	−0.192086	+	0.260343i
$683$			879589.i			1.88555i	0.333428	+	0.942775i	$0.391794\pi$
$683$			879589.i			1.88555i	−0.333428	+	0.942775i	$0.608206\pi$
$684$	189477.	−	58504.1i	0.404989	−	0.125047i
$685$	34246.6			0.0729854
$686$	−275000.	−	202899.i	−0.584364	−	0.431154i
$687$			313735.i			0.664736i
$688$	95741.6	+	140258.i	0.202266	+	0.296312i
$689$	132263.			0.278612
$690$	8696.01	−	11786.1i	0.0182651	−	0.0247556i
$691$			558055.i			1.16875i	0.811484	+	0.584374i	$0.198660\pi$
$691$			558055.i			1.16875i	−0.811484	+	0.584374i	$0.801340\pi$
$692$	87986.5	+	284961.i	0.183740	+	0.595076i
$693$	14668.4			0.0305433
$694$	467866.	+	345199.i	0.971410	+	0.716722i
$695$			261391.i			0.541154i
$696$	−125260.	+	358456.i	−0.258579	+	0.739976i
$697$	360605.			0.742278
$698$	−217521.	+	294818.i	−0.446469	+	0.605122i
$699$			140004.i			0.286540i
$700$	−36854.9	+	11379.6i	−0.0752140	+	0.0232236i
$701$	−513378.			−1.04472			−0.522362	−	0.852724i	$-0.674949\pi$
$701$	−513378.			−1.04472			−0.522362	+	0.852724i	$0.674949\pi$
$702$	−12930.7	−	9540.47i	−0.0262390	−	0.0193596i
$703$		−	626590.i		−	1.26786i
$704$	71863.6	−	90270.2i	0.144999	−	0.182137i
$705$	−228676.			−0.460090
$706$	199943.	−	270993.i	0.401141	−	0.543687i
$707$		−	349815.i		−	0.699841i
$708$	−63841.7	−	206763.i	−0.127361	−	0.412484i
$709$	440653.			0.876605			0.438302	−	0.898828i	$-0.355580\pi$
$709$	440653.			0.876605			0.438302	+	0.898828i	$0.355580\pi$
$710$	−34375.0	−	25362.4i	−0.0681908	−	0.0503123i
$711$		−	100385.i		−	0.198577i
$712$	−654902.	−	228850.i	−1.29186	−	0.451431i
$713$	−84178.9			−0.165586
$714$	−69045.8	+	93581.3i	−0.135438	+	0.183566i
$715$		−	9018.33i		−	0.0176406i
$716$	−912468.	+	281740.i	−1.77988	+	0.549570i
$717$	186449.			0.362678
$718$	171868.	+	126807.i	0.333386	+	0.245978i
$719$			594526.i			1.15004i	0.818139	+	0.575021i	$0.195006\pi$
$719$			594526.i			1.15004i	−0.818139	+	0.575021i	$0.804994\pi$
$720$	−63826.0	+	43568.4i	−0.123121	+	0.0840440i
$721$	305661.			0.587990
$722$	−190917.	+	258760.i	−0.366244	+	0.496390i
$723$		−	247105.i		−	0.472720i
$724$	−109155.	−	353519.i	−0.208241	−	0.674428i
$725$	142726.			0.271535
$726$	−231599.	−	170877.i	−0.439403	−	0.324199i
$727$			77530.5i			0.146691i	0.997307	+	0.0733455i	$0.0233676\pi$
$727$			77530.5i			0.146691i	−0.997307	+	0.0733455i	$0.976632\pi$
$728$	11659.2	−	33365.2i	0.0219991	−	0.0629550i
$729$	−19683.0			−0.0370370
$730$	234044.	−	317212.i	0.439189	−	0.595255i
$731$		−	192456.i		−	0.360161i
$732$	428672.	−	132360.i	0.800025	−	0.247021i
$733$	−739223.			−1.37584			−0.687920	−	0.725787i	$-0.741476\pi$
$733$	−739223.			−1.37584			−0.687920	+	0.725787i	$0.741476\pi$
$734$	454936.	+	335660.i	0.844420	+	0.623027i
$735$			117877.i			0.218201i
$736$	64499.8	+	2368.02i	0.119070	+	0.00437149i
$737$	−169951.			−0.312887
$738$	−79697.3	+	108018.i	−0.146329	+	0.198327i
$739$		−	730948.i		−	1.33844i	−0.743066	−	0.669218i	$-0.766629\pi$
$739$		−	730948.i		−	1.33844i	0.743066	−	0.669218i	$-0.233371\pi$
$740$	72039.4	+	233313.i	0.131555	+	0.426065i
$741$	68299.8			0.124389
$742$	286728.	+	211552.i	0.520789	+	0.384247i
$743$		−	380418.i		−	0.689102i	−0.938768	−	0.344551i	$-0.888031\pi$
$743$		−	380418.i		−	0.689102i	0.938768	−	0.344551i	$-0.111969\pi$
$744$	419272.	+	146511.i	0.757444	+	0.264683i
$745$	166864.			0.300643
$746$	−233576.	+	316577.i	−0.419711	+	0.568855i
$747$		−	161805.i		−	0.289968i
$748$	−124942.	+	38578.1i	−0.223309	+	0.0689505i
$749$	−48592.1			−0.0866168
$750$	23373.9	+	17245.6i	0.0415536	+	0.0306589i
$751$		−	839595.i		−	1.48864i	−0.667822	−	0.744321i	$-0.732773\pi$
$751$		−	839595.i		−	1.48864i	0.667822	−	0.744321i	$-0.267227\pi$
$752$	−568116.	−	832268.i	−1.00462	−	1.47173i
$753$	−333095.			−0.587461
$754$	−77645.4	+	105237.i	−0.136576	+	0.185108i
$755$		−	63564.9i		−	0.111513i
$756$	−12772.1	−	41364.8i	−0.0223469	−	0.0723748i
$757$	−411596.			−0.718256			−0.359128	−	0.933288i	$-0.616926\pi$
$757$	−411596.			−0.718256			−0.359128	+	0.933288i	$0.616926\pi$
$758$	−752006.	−	554842.i	−1.30883	−	0.965675i
$759$			9225.97i			0.0160151i
$760$	108352.	−	310072.i	0.187591	−	0.536829i
$761$	−152823.			−0.263888			−0.131944	−	0.991257i	$-0.542122\pi$
$761$	−152823.			−0.263888			−0.131944	+	0.991257i	$0.542122\pi$
$762$	−122520.	+	166057.i	−0.211006	+	0.285987i
$763$		−	20887.0i		−	0.0358778i
$764$	64442.1	−	19897.6i	0.110404	−	0.0340890i
$765$	87579.6			0.149651
$766$	228307.	+	168449.i	0.389101	+	0.287085i
$767$		−	74531.1i		−	0.126691i
$768$	−317135.	−	124055.i	−0.537677	−	0.210325i
$769$	888025.			1.50166			0.750832	−	0.660494i	$-0.229653\pi$
$769$	888025.			1.50166			0.750832	+	0.660494i	$0.229653\pi$
$770$	14424.7	−	19550.5i	0.0243290	−	0.0329743i
$771$			197550.i			0.332329i
$772$	−198501.	−	642881.i	−0.333064	−	1.07869i
$773$	84232.3			0.140968			0.0704839	−	0.997513i	$-0.477546\pi$
$773$	84232.3			0.140968			0.0704839	+	0.997513i	$0.477546\pi$
$774$	57649.4	+	42534.7i	0.0962306	+	0.0710005i
$775$		−	166941.i		−	0.277945i
$776$	−337245.	−	117848.i	−0.560044	−	0.195703i
$777$	−136791.			−0.226577
$778$	12741.1	−	17268.6i	0.0210497	−	0.0285297i
$779$		−	570550.i		−	0.940196i
$780$	−25431.7	+	7852.46i	−0.0418009	+	0.0129067i
$781$	26908.1			0.0441145
$782$	−58859.8	−	43427.8i	−0.0962511	−	0.0710156i
$783$			160191.i			0.261285i
$784$	−429015.	+	292851.i	−0.697977	+	0.476447i
$785$	−331844.			−0.538511
$786$	−310796.	+	421237.i	−0.503072	+	0.681839i
$787$		−	971179.i		−	1.56801i	−0.620752	−	0.784007i	$-0.713173\pi$
$787$		−	971179.i		−	1.56801i	0.620752	−	0.784007i	$-0.286827\pi$
$788$	16991.9	+	55031.6i	0.0273647	+	0.0886257i
$789$	−527056.			−0.846647
$790$	−133796.	−	98716.9i	−0.214382	−	0.158175i
$791$			12841.7i			0.0205243i
$792$	16057.6	−	45952.1i	0.0255994	−	0.0732580i
$793$	154522.			0.245721
$794$	−542993.	+	735946.i	−0.861298	+	1.16736i
$795$		−	268339.i		−	0.424570i
$796$	213513.	−	65925.7i	0.336975	−	0.104047i
$797$	274894.			0.432761			0.216381	−	0.976309i	$-0.430575\pi$
$797$	274894.			0.432761			0.216381	+	0.976309i	$0.430575\pi$
$798$	148064.	+	109244.i	0.232512	+	0.171551i
$799$			1.14201e6i			1.78885i
$800$	−4696.18	+	127914.i	−0.00733777	+	0.199865i
$801$	−292670.			−0.456155
$802$	−434355.	+	588703.i	−0.675299	+	0.915267i
$803$			248307.i			0.385087i
$804$	147980.	+	479260.i	0.228923	+	0.741411i
$805$	13590.8			0.0209726
$806$	123091.	+	90818.9i	0.189478	+	0.139800i
$807$		−	615873.i		−	0.945679i
$808$	−1.09588e6	−	382945.i	−1.67857	−	0.586562i
$809$	863110.			1.31877			0.659385	−	0.751805i	$-0.270817\pi$
$809$	863110.			1.31877			0.659385	+	0.751805i	$0.270817\pi$
$810$	−19356.0	+	26234.1i	−0.0295015	+	0.0399849i
$811$		−	391388.i		−	0.595067i	−0.954711	−	0.297534i	$-0.903836\pi$
$811$		−	391388.i		−	0.595067i	0.954711	−	0.297534i	$-0.0961640\pi$
$812$	−336649.	+	103946.i	−0.510581	+	0.157651i
$813$	250643.			0.379205
$814$	−123766.	−	91316.5i	−0.186789	−	0.137816i
$815$		−	124764.i		−	0.187835i
$816$	217580.	+	318746.i	0.326768	+	0.478702i
$817$	−304504.			−0.456193
$818$	−314852.	+	426735.i	−0.470544	+	0.637752i
$819$		−	14910.6i		−	0.0222294i
$820$	65596.4	+	212446.i	0.0975556	+	0.315952i
$821$	420749.			0.624219			0.312109	−	0.950046i	$-0.398964\pi$
$821$	420749.			0.624219			0.312109	+	0.950046i	$0.398964\pi$
$822$	51230.4	+	37798.7i	0.0758201	+	0.0559413i
$823$		−	412920.i		−	0.609630i	−0.952412	−	0.304815i	$-0.901405\pi$
$823$		−	412920.i		−	0.609630i	0.952412	−	0.304815i	$-0.0985946\pi$
$824$	334610.	−	957556.i	0.492816	−	1.41029i
$825$	−18296.6			−0.0268821
$826$	119211.	−	161573.i	0.174726	−	0.236815i
$827$			1.35535e6i			1.98171i	0.134932	+	0.990855i	$0.456918\pi$
$827$			1.35535e6i			1.98171i	−0.134932	+	0.990855i	$0.543082\pi$
$828$	26017.2	−	8033.26i	0.0379490	−	0.0117174i
$829$	−441966.			−0.643102			−0.321551	−	0.946892i	$-0.604204\pi$
$829$	−441966.			−0.643102			−0.321551	+	0.946892i	$0.604204\pi$
$830$	−215659.	−	159117.i	−0.313048	−	0.230972i
$831$			89713.5i			0.129914i
$832$	−91760.7	−	73050.2i	−0.132559	−	0.105530i
$833$	588679.			0.848376
$834$	−288502.	+	391022.i	−0.414779	+	0.562171i
$835$		−	507007.i		−	0.727178i
$836$	61038.3	+	197684.i	0.0873353	+	0.282852i
$837$	187369.			0.267453
$838$	936880.	+	691246.i	1.33412	+	0.984338i
$839$			606640.i			0.861801i	0.902399	+	0.430901i	$0.141804\pi$
$839$			606640.i			0.861801i	−0.902399	+	0.430901i	$0.858196\pi$
$840$	−67692.1	−	23654.5i	−0.0959356	−	0.0335239i
$841$	596436.			0.843281
$842$	−79346.2	+	107542.i	−0.111918	+	0.151689i
$843$			420425.i			0.591606i
$844$	−346898.	+	107111.i	−0.486987	+	0.150366i
$845$	310154.			0.434375
$846$	−342083.	−	252395.i	−0.477960	−	0.352646i
$847$		−	267060.i		−	0.372257i
$848$	976620.	−	666653.i	1.35811	−	0.927061i
$849$	230805.			0.320206
$850$	86124.5	−	116729.i	0.119203	−	0.161562i
$851$		−	86037.7i		−	0.118804i
$852$	−23429.5	−	75880.8i	−0.0322763	−	0.104533i
$853$	167085.			0.229636			0.114818	−	0.993387i	$-0.463372\pi$
$853$	167085.			0.229636			0.114818	+	0.993387i	$0.463372\pi$
$854$	334981.	+	247155.i	0.459309	+	0.338885i
$855$		−	138568.i		−	0.189554i
$856$	−53194.2	+	152226.i	−0.0725966	+	0.207750i
$857$	1.08085e6			1.47164			0.735822	−	0.677175i	$-0.236796\pi$
$857$	1.08085e6			1.47164			0.735822	+	0.677175i	$0.236796\pi$
$858$	9953.72	−	13490.8i	0.0135211	−	0.0183258i
$859$			501417.i			0.679536i	0.940509	+	0.339768i	$0.110349\pi$
$859$			501417.i			0.679536i	−0.940509	+	0.339768i	$0.889651\pi$
$860$	113383.	−	35009.0i	0.153303	−	0.0473350i
$861$	−124557.			−0.168020
$862$	−294534.	−	217312.i	−0.396389	−	0.292462i
$863$			334736.i			0.449449i	0.974422	+	0.224725i	$0.0721483\pi$
$863$			334736.i			0.449449i	−0.974422	+	0.224725i	$0.927852\pi$
$864$	−143566.	−	5270.84i	−0.192321	−	0.00706078i
$865$	208398.			0.278523
$866$	716461.	−	971056.i	0.955337	−	1.29482i
$867$		−	3383.78i		−	0.00450157i
$868$	121582.	+	393765.i	0.161372	+	0.522634i
$869$	104733.			0.138690
$870$	213507.	+	157529.i	0.282081	+	0.208124i
$871$			172757.i			0.227719i
$872$	−65433.2	−	22865.1i	−0.0860529	−	0.0300705i
$873$	−150712.			−0.197751
$874$	−68711.4	+	93128.0i	−0.0899510	+	0.121915i
$875$			26952.8i			0.0352037i
$876$	700226.	−	216207.i	0.912494	−	0.281748i
$877$	−393662.			−0.511829			−0.255914	−	0.966699i	$-0.582377\pi$
$877$	−393662.			−0.511829			−0.255914	+	0.966699i	$0.582377\pi$
$878$	−566660.	−	418091.i	−0.735078	−	0.542353i
$879$		−	63493.6i		−	0.0821773i
$880$	−45455.6	−	66590.7i	−0.0586978	−	0.0859900i
$881$	−354446.			−0.456665			−0.228333	−	0.973583i	$-0.573327\pi$
$881$	−354446.			−0.456665			−0.228333	+	0.973583i	$0.573327\pi$
$882$	−130104.	+	176336.i	−0.167245	+	0.226675i
$883$		−	852839.i		−	1.09382i	−0.837192	−	0.546910i	$-0.815804\pi$
$883$		−	852839.i		−	1.09382i	0.837192	−	0.546910i	$-0.184196\pi$
$884$	39215.1	+	127005.i	0.0501821	+	0.162524i
$885$	−151211.			−0.193062
$886$	610895.	+	450728.i	0.778214	+	0.574179i
$887$			620430.i			0.788579i	0.918986	+	0.394290i	$0.129009\pi$
$887$			620430.i			0.788579i	−0.918986	+	0.394290i	$0.870991\pi$
$888$	−149747.	+	428531.i	−0.189903	+	0.543446i
$889$	−191483.			−0.242285
$890$	−287807.	+	390079.i	−0.363347	+	0.492462i
$891$		−	20535.6i		−	0.0258673i
$892$	1.29244e6	−	399063.i	1.62436	−	0.501547i
$893$	1.80688e6			2.26583
$894$	249617.	+	184171.i	0.312319	+	0.230434i
$895$			667309.i			0.833068i
$896$	−82081.8	−	305132.i	−0.102242	−	0.380077i
$897$	9378.31			0.0116557
$898$	−131270.	+	177917.i	−0.162784	+	0.220630i
$899$		−	1.52491e6i		−	1.88679i
$900$	15931.3	+	51596.5i	0.0196683	+	0.0636993i
$901$	−1.34008e6			−1.65075
$902$	−112697.	−	83149.4i	−0.138515	−	0.102199i
$903$			66476.5i			0.0815254i
$904$	40229.5	+	14057.9i	0.0492275	+	0.0172022i
$905$	−258536.			−0.315663
$906$	70157.9	−	95088.6i	0.0854713	−	0.115844i
$907$			1.05362e6i			1.28077i	0.768054	+	0.640385i	$0.221225\pi$
$907$			1.05362e6i			1.28077i	−0.768054	+	0.640385i	$0.778775\pi$
$908$	11307.2	−	3491.29i	0.0137146	−	0.00423462i
$909$	−489737.			−0.592700
$910$	−19873.3	−	14662.8i	−0.0239987	−	0.0177066i
$911$			1.11079e6i			1.33842i	0.743071	+	0.669212i	$0.233368\pi$
$911$			1.11079e6i			1.33842i	−0.743071	+	0.669212i	$0.766632\pi$
$912$	504320.	−	344255.i	0.606341	−	0.413896i
$913$	168814.			0.202519
$914$	954357.	−	1.29349e6i	1.14240	−	1.54835i
$915$		−	313498.i		−	0.374449i
$916$	285009.	+	923054.i	0.339678	+	1.10011i
$917$	−485736.			−0.577645
$918$	131013.	+	96663.4i	0.155464	+	0.114704i
$919$			1.10097e6i			1.30360i	0.758390	+	0.651801i	$0.225986\pi$
$919$			1.10097e6i			1.30360i	−0.758390	+	0.651801i	$0.774014\pi$
$920$	14878.0	−	42576.3i	0.0175779	−	0.0503028i
$921$	−237896.			−0.280458
$922$	549586.	−	744882.i	0.646508	−	0.876245i
$923$		−	27352.4i		−	0.0321064i
$924$	43156.5	−	13325.3i	0.0505478	−	0.0156075i
$925$	170627.			0.199418
$926$	−112012.	−	82644.2i	−0.130630	−	0.0963808i
$927$		−	427923.i		−	0.497973i
$928$	−42896.9	+	1.16842e6i	−0.0498116	+	1.35676i
$929$	−1.41544e6			−1.64006			−0.820031	−	0.572319i	$-0.806044\pi$
$929$	−1.41544e6			−1.64006			−0.820031	+	0.572319i	$0.806044\pi$
$930$	184256.	−	249731.i	0.213037	−	0.288740i
$931$		−	931407.i		−	1.07458i
$932$	127185.	+	411911.i	0.146421	+	0.474211i
$933$	483506.			0.555442
$934$	−586396.	−	432652.i	−0.672198	−	0.495958i
$935$			91373.2i			0.104519i
$936$	−46710.9	−	16322.7i	−0.0533171	−	0.0186312i
$937$	−250113.			−0.284877			−0.142439	−	0.989804i	$-0.545494\pi$
$937$	−250113.			−0.284877			−0.142439	+	0.989804i	$0.545494\pi$
$938$	−276321.	+	374512.i	−0.314057	+	0.425657i
$939$		−	795935.i		−	0.902706i
$940$	−672799.	+	207738.i	−0.761429	+	0.235104i
$941$	538389.			0.608019			0.304010	−	0.952669i	$-0.401675\pi$
$941$	538389.			0.608019			0.304010	+	0.952669i	$0.401675\pi$
$942$	−496414.	−	366263.i	−0.559426	−	0.412754i
$943$		−	78342.7i		−	0.0880999i
$944$	−375663.	−	550332.i	−0.421556	−	0.617562i
$945$	−30251.0			−0.0338747
$946$	−44377.1	+	60146.5i	−0.0495880	+	0.0672091i
$947$			106656.i			0.118928i	0.998230	+	0.0594640i	$0.0189391\pi$
$947$			106656.i			0.118928i	−0.998230	+	0.0594640i	$0.981061\pi$
$948$	−91193.4	−	295347.i	−0.101472	−	0.328636i
$949$	252407.			0.280266
$950$	−184688.	−	136266.i	−0.204641	−	0.150987i
$951$		−	131122.i		−	0.144983i
$952$	−118130.	+	338054.i	−0.130343	+	0.373002i
$953$	−1.33258e6			−1.46726			−0.733631	−	0.679548i	$-0.762176\pi$
$953$	−1.33258e6			−1.46726			−0.733631	+	0.679548i	$0.762176\pi$
$954$	296171.	−	401416.i	0.325421	−	0.441060i
$955$		−	47128.0i		−	0.0516740i
$956$	548560.	−	169377.i	0.600217	−	0.185327i
$957$	−167129.			−0.182486
$958$	1.25022e6	+	922429.i	1.36224	+	1.00508i
$959$			59074.7i			0.0642339i
$960$	−148206.	+	186167.i	−0.160814	+	0.202004i
$961$	−860107.			−0.931335
$962$	−92824.4	+	125810.i	−0.100303	+	0.135945i
$963$			68028.4i			0.0733564i
$964$	−224479.	−	727018.i	−0.241558	−	0.782332i
$965$	−470154.			−0.504876
$966$	20330.9	+	15000.4i	0.0217872	+	0.0160750i
$967$		−	541951.i		−	0.579571i	−0.957092	−	0.289786i	$-0.906416\pi$
$967$		−	541951.i		−	0.579571i	0.957092	−	0.289786i	$-0.0935840\pi$
$968$	−836629.	−	292353.i	−0.892858	−	0.312002i
$969$	−692009.			−0.736995
$970$	−148208.	+	200873.i	−0.157517	+	0.213491i
$971$			1.19103e6i			1.26323i	0.775281	+	0.631617i	$0.217608\pi$
$971$			1.19103e6i			1.26323i	−0.775281	+	0.631617i	$0.782392\pi$
$972$	−57910.3	+	17880.8i	−0.0612947	+	0.0189258i
$973$	−450894.			−0.476265
$974$	−1.03218e6	−	761560.i	−1.08802	−	0.802761i
$975$			18598.8i			0.0195648i
$976$	1.14098e6	−	778844.i	1.19778	−	0.817619i
$977$	−546137.			−0.572153			−0.286077	−	0.958207i	$-0.592351\pi$
$977$	−546137.			−0.572153			−0.286077	+	0.958207i	$0.592351\pi$
$978$	137705.	−	186639.i	0.143970	−	0.195130i
$979$		−	305347.i		−	0.318587i
$980$	107084.	+	346813.i	0.111500	+	0.361113i
$981$	−29241.5			−0.0303852
$982$	664078.	+	489968.i	0.688646	+	0.508094i
$983$		−	1.29131e6i		−	1.33636i	−0.744001	−	0.668179i	$-0.767074\pi$
$983$		−	1.29131e6i		−	1.33636i	0.744001	−	0.668179i	$-0.232926\pi$
$984$	−136354.	+	390204.i	−0.140824	+	0.402997i
$985$	40245.9			0.0414809
$986$	786698.	−	1.06625e6i	0.809197	−	1.09675i
$987$		−	394462.i		−	0.404921i
$988$	200948.	−	62046.1i	0.205859	−	0.0635625i
$989$	−41811.7			−0.0427470
$990$	−27370.5	−	20194.4i	−0.0279262	−	0.0206044i
$991$			1.36845e6i			1.39342i	0.717353	+	0.696709i	$0.245353\pi$
$991$			1.36845e6i			1.39342i	−0.717353	+	0.696709i	$0.754647\pi$
$992$	1.36666e6	+	50174.9i	1.38879	+	0.0509874i
$993$	824416.			0.836080
$994$	43749.7	−	59296.2i	0.0442794	−	0.0600142i
$995$		−	156147.i		−	0.157720i
$996$	−146990.	−	476054.i	−0.148173	−	0.479885i
$997$	533291.			0.536505			0.268252	−	0.963349i	$-0.413554\pi$
$997$	533291.			0.536505			0.268252	+	0.963349i	$0.413554\pi$
$998$	−1.49731e6	−	1.10474e6i	−1.50332	−	1.10917i
$999$			191506.i			0.191890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.c.a.31.13	✓	16
3.2	odd	2		180.5.c.c.91.4		16
4.3	odd	2	inner	60.5.c.a.31.14	yes	16
5.2	odd	4		300.5.f.b.199.28		32
5.3	odd	4		300.5.f.b.199.5		32
5.4	even	2		300.5.c.d.151.4		16
8.3	odd	2		960.5.e.f.511.7		16
8.5	even	2		960.5.e.f.511.14		16
12.11	even	2		180.5.c.c.91.3		16
20.3	even	4		300.5.f.b.199.27		32
20.7	even	4		300.5.f.b.199.6		32
20.19	odd	2		300.5.c.d.151.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.13	✓	16	1.1	even	1	trivial
60.5.c.a.31.14	yes	16	4.3	odd	2	inner
180.5.c.c.91.3		16	12.11	even	2
180.5.c.c.91.4		16	3.2	odd	2
300.5.c.d.151.3		16	20.19	odd	2
300.5.c.d.151.4		16	5.4	even	2
300.5.f.b.199.5		32	5.3	odd	4
300.5.f.b.199.6		32	20.7	even	4
300.5.f.b.199.27		32	20.3	even	4
300.5.f.b.199.28		32	5.2	odd	4
960.5.e.f.511.7		16	8.3	odd	2
960.5.e.f.511.14		16	8.5	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.37483 - 3.21872i) q^{2} -5.19615i q^{3} +(-4.72038 - 15.2878i) q^{4} -11.1803 q^{5} +(-16.7250 - 12.3400i) q^{6} -19.2859i q^{7} +(-60.4174 - 21.1124i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(2.37483 - 3.21872i) q^{2} -5.19615i q^{3} +(-4.72038 - 15.2878i) q^{4} -11.1803 q^{5} +(-16.7250 - 12.3400i) q^{6} -19.2859i q^{7} +(-60.4174 - 21.1124i) q^{8} -27.0000 q^{9} +(-26.5514 + 35.9864i) q^{10} -28.1695i q^{11} +(-79.4379 + 24.5278i) q^{12} -28.6347 q^{13} +(-62.0759 - 45.8006i) q^{14} +58.0948i q^{15} +(-211.436 + 144.329i) q^{16} +290.124 q^{17} +(-64.1204 + 86.9056i) q^{18} -459.035i q^{19} +(52.7755 + 170.923i) q^{20} -100.212 q^{21} +(-90.6699 - 66.8978i) q^{22} -63.0305i q^{23} +(-109.703 + 313.938i) q^{24} +125.000 q^{25} +(-68.0024 + 92.1671i) q^{26} +140.296i q^{27} +(-294.839 + 91.0366i) q^{28} +1141.80 q^{29} +(186.991 + 137.965i) q^{30} -1335.53i q^{31} +(-37.5694 + 1023.31i) q^{32} -146.373 q^{33} +(688.996 - 933.831i) q^{34} +215.622i q^{35} +(127.450 + 412.772i) q^{36} +1365.02 q^{37} +(-1477.51 - 1090.13i) q^{38} +148.790i q^{39} +(675.488 + 236.044i) q^{40} +1242.93 q^{41} +(-237.987 + 322.556i) q^{42} -663.357i q^{43} +(-430.651 + 132.971i) q^{44} +301.869 q^{45} +(-202.878 - 149.687i) q^{46} +3936.26i q^{47} +(749.955 + 1098.65i) q^{48} +2029.06 q^{49} +(296.854 - 402.341i) q^{50} -1507.53i q^{51} +(135.166 + 437.762i) q^{52} -4618.99 q^{53} +(451.575 + 333.179i) q^{54} +314.945i q^{55} +(-407.170 + 1165.20i) q^{56} -2385.22 q^{57} +(2711.59 - 3675.15i) q^{58} +2602.83i q^{59} +(888.143 - 274.229i) q^{60} -5396.32 q^{61} +(-4298.69 - 3171.64i) q^{62} +520.718i q^{63} +(3204.53 + 2551.11i) q^{64} +320.145 q^{65} +(-347.611 + 471.135i) q^{66} -6033.14i q^{67} +(-1369.50 - 4435.38i) q^{68} -327.516 q^{69} +(694.029 + 512.066i) q^{70} +955.221i q^{71} +(1631.27 + 570.034i) q^{72} -8814.75 q^{73} +(3241.68 - 4393.61i) q^{74} -649.519i q^{75} +(-7017.65 + 2166.82i) q^{76} -543.273 q^{77} +(478.914 + 353.351i) q^{78} +3717.96i q^{79} +(2363.93 - 1613.65i) q^{80} +729.000 q^{81} +(2951.75 - 4000.66i) q^{82} +5992.78i q^{83} +(473.040 + 1532.03i) q^{84} -3243.69 q^{85} +(-2135.16 - 1575.36i) q^{86} -5932.99i q^{87} +(-594.726 + 1701.93i) q^{88} +10839.6 q^{89} +(716.887 - 971.634i) q^{90} +552.244i q^{91} +(-963.600 + 297.528i) q^{92} -6939.59 q^{93} +(12669.8 + 9347.95i) q^{94} +5132.17i q^{95} +(5317.28 + 195.216i) q^{96} +5581.91 q^{97} +(4818.66 - 6530.97i) q^{98} +760.577i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	\( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) \) 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 50 * q^10 - 352 * q^13 - 804 * q^14 - 190 * q^16 + 324 * q^18 + 600 * q^20 + 288 * q^21 + 436 * q^22 - 1998 * q^24 + 2000 * q^25 - 852 * q^26 - 1156 * q^28 - 3456 * q^29 + 7668 * q^32 + 4772 * q^34 - 702 * q^36 + 9376 * q^37 - 1320 * q^38 + 550 * q^40 + 1248 * q^41 - 324 * q^42 - 6420 * q^44 - 1112 * q^46 - 4176 * q^48 - 3952 * q^49 - 1500 * q^50 + 12704 * q^52 - 5184 * q^53 - 486 * q^54 - 2604 * q^56 - 11232 * q^57 + 12708 * q^58 + 3150 * q^60 - 3808 * q^61 - 16152 * q^62 - 11902 * q^64 + 2400 * q^65 - 2916 * q^66 - 12312 * q^68 + 9792 * q^69 - 17100 * q^70 + 4860 * q^72 + 11040 * q^73 + 30516 * q^74 - 5160 * q^76 - 27456 * q^77 - 3600 * q^78 + 10800 * q^80 + 11664 * q^81 - 54040 * q^82 - 2052 * q^84 - 11200 * q^85 + 39768 * q^86 - 7220 * q^88 + 7584 * q^89 - 1350 * q^90 + 28848 * q^92 + 19872 * q^93 + 49776 * q^94 + 18882 * q^96 - 14496 * q^97 + 23940 * q^98

Introduction

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