LMFDB - Embedded newform 225.4.e.a.151.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,4,Mod(76,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.76"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.4.e.a.76.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18614 - 2.05446i) q^{2} +(1.50000 - 4.97494i) q^{3} +(1.18614 + 2.05446i) q^{4} +(-8.44158 - 8.98266i) q^{6} +(3.68614 - 6.38458i) q^{7} +24.6060 q^{8} +(-22.5000 - 14.9248i) q^{9} +(2.06930 - 3.58413i) q^{11} +(12.0000 - 2.81929i) q^{12} +(-39.4891 - 68.3972i) q^{13} +(-8.74456 - 15.1460i) q^{14} +(19.6970 - 34.1162i) q^{16} +33.3070 q^{17} +(-57.3505 + 28.5223i) q^{18} +89.3070 q^{19} +(-26.2337 - 27.9152i) q^{21} +(-4.90895 - 8.50256i) q^{22} +(-99.7812 - 172.826i) q^{23} +(36.9090 - 122.413i) q^{24} -187.359 q^{26} +(-108.000 + 89.5489i) q^{27} +17.4891 q^{28} +(-25.2405 + 43.7179i) q^{29} +(3.00000 + 5.19615i) q^{31} +(51.6970 + 89.5419i) q^{32} +(-14.7269 - 15.6708i) q^{33} +(39.5068 - 68.4278i) q^{34} +(3.97420 - 63.9282i) q^{36} +290.277 q^{37} +(105.931 - 183.477i) q^{38} +(-399.505 + 93.8602i) q^{39} +(26.6684 + 46.1911i) q^{41} +(-88.4674 + 20.7846i) q^{42} +(-149.194 + 258.412i) q^{43} +9.81791 q^{44} -473.418 q^{46} +(-209.452 + 362.782i) q^{47} +(-140.181 - 149.166i) q^{48} +(144.325 + 249.978i) q^{49} +(49.9605 - 165.700i) q^{51} +(93.6793 - 162.257i) q^{52} -399.228 q^{53} +(55.8710 + 328.099i) q^{54} +(90.7011 - 157.099i) q^{56} +(133.961 - 444.297i) q^{57} +(59.8776 + 103.711i) q^{58} +(-49.1209 - 85.0799i) q^{59} +(341.797 - 592.011i) q^{61} +14.2337 q^{62} +(-178.227 + 88.6382i) q^{63} +560.432 q^{64} +(-49.6631 + 11.6679i) q^{66} +(112.750 + 195.289i) q^{67} +(39.5068 + 68.4278i) q^{68} +(-1009.47 + 237.166i) q^{69} +512.951 q^{71} +(-553.634 - 367.239i) q^{72} +994.318 q^{73} +(344.310 - 596.362i) q^{74} +(105.931 + 183.477i) q^{76} +(-15.2554 - 26.4232i) q^{77} +(-281.038 + 932.097i) q^{78} +(100.853 - 174.683i) q^{79} +(283.500 + 671.617i) q^{81} +126.530 q^{82} +(553.822 - 959.247i) q^{83} +(26.2337 - 87.0073i) q^{84} +(353.931 + 613.026i) q^{86} +(179.633 + 191.147i) q^{87} +(50.9171 - 88.1909i) q^{88} +372.269 q^{89} -582.250 q^{91} +(236.709 - 409.992i) q^{92} +(30.3505 - 7.13058i) q^{93} +(496.880 + 860.622i) q^{94} +(523.011 - 122.877i) q^{96} +(-69.6156 + 120.578i) q^{97} +684.758 q^{98} +(-100.052 + 49.7590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 6 q^{3} - q^{4} - 51 q^{6} + 9 q^{7} + 18 q^{8} - 90 q^{9} + 37 q^{11} + 48 q^{12} - 112 q^{13} - 12 q^{14} + 119 q^{16} - 154 q^{17} - 126 q^{18} + 70 q^{19} - 36 q^{21} + 101 q^{22} - 267 q^{23}+ \cdots - 90 q^{99}+O(q^{100}) $ 4 * q - q^2 + 6 * q^3 - q^4 - 51 * q^6 + 9 * q^7 + 18 * q^8 - 90 * q^9 + 37 * q^11 + 48 * q^12 - 112 * q^13 - 12 * q^14 + 119 * q^16 - 154 * q^17 - 126 * q^18 + 70 * q^19 - 36 * q^21 + 101 * q^22 - 267 * q^23 + 27 * q^24 - 152 * q^26 - 432 * q^27 + 24 * q^28 - 325 * q^29 + 12 * q^31 + 247 * q^32 + 303 * q^33 + 451 * q^34 + 171 * q^36 + 1276 * q^37 + 395 * q^38 - 564 * q^39 - 238 * q^41 - 216 * q^42 - 97 * q^43 - 202 * q^44 - 492 * q^46 - 901 * q^47 + 525 * q^48 + 629 * q^49 - 231 * q^51 + 76 * q^52 - 448 * q^53 + 999 * q^54 + 156 * q^56 + 105 * q^57 - 806 * q^58 + 85 * q^59 + 247 * q^61 - 12 * q^62 - 351 * q^63 + 1426 * q^64 - 888 * q^66 - 606 * q^67 + 451 * q^68 - 1539 * q^69 + 788 * q^71 - 405 * q^72 + 1622 * q^73 - 484 * q^74 + 395 * q^76 - 84 * q^77 - 228 * q^78 + 840 * q^79 + 1134 * q^81 + 2218 * q^82 - 387 * q^83 + 36 * q^84 + 1387 * q^86 - 2418 * q^87 - 411 * q^88 - 2130 * q^89 - 1272 * q^91 + 246 * q^92 + 18 * q^93 - 632 * q^94 + 24 * q^96 - 1031 * q^97 - 926 * q^98 - 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.18614	−	2.05446i	0.419364	−	0.726360i	−0.576512	−	0.817089i	$-0.695586\pi$
$2$	1.18614	−	2.05446i	0.419364	−	0.726360i	0.995876	+	0.0907292i	$0.0289198\pi$
$3$	1.50000	−	4.97494i	0.288675	−	0.957427i
$3$	1.50000	−	4.97494i	0.288675	−	0.957427i
$4$	1.18614	+	2.05446i	0.148268	+	0.256807i
$5$		0			0
$5$		0			0
$6$	−8.44158	−	8.98266i	−0.574377	−	0.611193i
$7$	3.68614	−	6.38458i	0.199033	−	0.344735i	−0.749182	−	0.662364i	$-0.769553\pi$
$7$	3.68614	−	6.38458i	0.199033	−	0.344735i	0.948215	+	0.317629i	$0.102887\pi$
$8$	24.6060			1.08744
$9$	−22.5000	−	14.9248i	−0.833333	−	0.552771i
$10$		0			0
$11$	2.06930	−	3.58413i	0.0567197	−	0.0982414i	−0.836271	−	0.548316i	$-0.815269\pi$
$11$	2.06930	−	3.58413i	0.0567197	−	0.0982414i	0.892991	+	0.450074i	$0.148603\pi$
$12$	12.0000	−	2.81929i	0.288675	−	0.0678216i
$13$	−39.4891	−	68.3972i	−0.842486	−	1.45923i	−0.887787	−	0.460254i	$-0.847758\pi$
$13$	−39.4891	−	68.3972i	−0.842486	−	1.45923i	0.0453014	−	0.998973i	$-0.485575\pi$
$14$	−8.74456	−	15.1460i	−0.166934	−	0.289139i
$15$		0			0
$16$	19.6970	−	34.1162i	0.307766	−	0.533066i
$17$	33.3070			0.475185			0.237592	−	0.971365i	$-0.423642\pi$
$17$	33.3070			0.475185			0.237592	+	0.971365i	$0.423642\pi$
$18$	−57.3505	+	28.5223i	−0.750981	+	0.373488i
$19$	89.3070			1.07834			0.539169	−	0.842197i	$-0.318738\pi$
$19$	89.3070			1.07834			0.539169	+	0.842197i	$0.318738\pi$
$20$		0			0
$21$	−26.2337	−	27.9152i	−0.272603	−	0.290076i
$22$	−4.90895	−	8.50256i	−0.0475724	−	0.0823978i
$23$	−99.7812	−	172.826i	−0.904601	−	1.56682i	−0.821452	−	0.570278i	$-0.806835\pi$
$23$	−99.7812	−	172.826i	−0.904601	−	1.56682i	−0.0831494	−	0.996537i	$-0.526498\pi$
$24$	36.9090	−	122.413i	0.313917	−	1.04114i
$25$		0			0
$26$	−187.359			−1.41323
$27$	−108.000	+	89.5489i	−0.769800	+	0.638285i
$28$	17.4891			0.118041
$29$	−25.2405	+	43.7179i	−0.161622	+	0.279938i	−0.935451	−	0.353457i	$-0.885006\pi$
$29$	−25.2405	+	43.7179i	−0.161622	+	0.279938i	0.773828	+	0.633395i	$0.218339\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.0173812	+	0.0301050i	0.874585	−	0.484872i	$-0.161134\pi$
$31$	3.00000	+	5.19615i	0.0173812	+	0.0301050i	−0.857204	+	0.514977i	$0.827800\pi$
$32$	51.6970	+	89.5419i	0.285588	+	0.494654i
$33$	−14.7269	−	15.6708i	−0.0776854	−	0.0826648i
$34$	39.5068	−	68.4278i	0.199275	−	0.345155i
$35$		0			0
$36$	3.97420	−	63.9282i	0.0183991	−	0.295964i
$37$	290.277			1.28976			0.644882	−	0.764282i	$-0.276906\pi$
$37$	290.277			1.28976			0.644882	+	0.764282i	$0.276906\pi$
$38$	105.931	−	183.477i	0.452217	−	0.783262i
$39$	−399.505	+	93.8602i	−1.64031	+	0.385376i
$40$		0			0
$41$	26.6684	+	46.1911i	0.101583	+	0.175947i	0.912337	−	0.409440i	$-0.134276\pi$
$41$	26.6684	+	46.1911i	0.101583	+	0.175947i	−0.810754	+	0.585387i	$0.800943\pi$
$42$	−88.4674	+	20.7846i	−0.325019	+	0.0763604i
$43$	−149.194	+	258.412i	−0.529114	+	0.916453i	0.470309	+	0.882502i	$0.344142\pi$
$43$	−149.194	+	258.412i	−0.529114	+	0.916453i	−0.999424	+	0.0339510i	$0.989191\pi$
$44$	9.81791			0.0336388
$45$		0			0
$46$	−473.418			−1.51743
$47$	−209.452	+	362.782i	−0.650038	+	1.12590i	0.333075	+	0.942900i	$0.391914\pi$
$47$	−209.452	+	362.782i	−0.650038	+	1.12590i	−0.983113	+	0.182998i	$0.941420\pi$
$48$	−140.181	−	149.166i	−0.421528	−	0.448546i
$49$	144.325	+	249.978i	0.420772	+	0.728798i
$50$		0			0
$51$	49.9605	−	165.700i	0.137174	−	0.454955i
$52$	93.6793	−	162.257i	0.249827	−	0.432712i
$53$	−399.228			−1.03468			−0.517342	−	0.855779i	$-0.673078\pi$
$53$	−399.228			−1.03468			−0.517342	+	0.855779i	$0.673078\pi$
$54$	55.8710	+	328.099i	0.140798	+	0.826826i
$55$		0			0
$56$	90.7011	−	157.099i	0.216436	−	0.374879i
$57$	133.961	−	444.297i	0.311290	−	1.03243i
$58$	59.8776	+	103.711i	0.135557	+	0.234792i
$59$	−49.1209	−	85.0799i	−0.108390	−	0.187737i	0.806728	−	0.590923i	$-0.201236\pi$
$59$	−49.1209	−	85.0799i	−0.108390	−	0.187737i	−0.915118	+	0.403186i	$0.867903\pi$
$60$		0			0
$61$	341.797	−	592.011i	0.717421	−	1.24261i	−0.244597	−	0.969625i	$-0.578656\pi$
$61$	341.797	−	592.011i	0.717421	−	1.24261i	0.962018	−	0.272985i	$-0.0880109\pi$
$62$	14.2337			0.0291561
$63$	−178.227	+	88.6382i	−0.356420	+	0.177260i
$64$	560.432			1.09459
$65$		0			0
$66$	−49.6631	+	11.6679i	−0.0926228	+	0.0217609i
$67$	112.750	+	195.289i	0.205591	+	0.356094i	0.950321	−	0.311272i	$-0.100755\pi$
$67$	112.750	+	195.289i	0.205591	+	0.356094i	−0.744730	+	0.667366i	$0.767422\pi$
$68$	39.5068	+	68.4278i	0.0704545	+	0.122031i
$69$	−1009.47	+	237.166i	−1.76125	+	0.413789i
$70$		0			0
$71$	512.951			0.857410			0.428705	−	0.903445i	$-0.358970\pi$
$71$	512.951			0.857410			0.428705	+	0.903445i	$0.358970\pi$
$72$	−553.634	−	367.239i	−0.906200	−	0.601105i
$73$	994.318			1.59419			0.797096	−	0.603852i	$-0.206368\pi$
$73$	994.318			1.59419			0.797096	+	0.603852i	$0.206368\pi$
$74$	344.310	−	596.362i	0.540881	−	0.936833i
$75$		0			0
$76$	105.931	+	183.477i	0.159883	+	0.276925i
$77$	−15.2554	−	26.4232i	−0.0225782	−	0.0391065i
$78$	−281.038	+	932.097i	−0.407965	+	1.35307i
$79$	100.853	−	174.683i	0.143631	−	0.248777i	−0.785230	−	0.619204i	$-0.787455\pi$
$79$	100.853	−	174.683i	0.143631	−	0.248777i	0.928862	+	0.370427i	$0.120789\pi$
$80$		0			0
$81$	283.500	+	671.617i	0.388889	+	0.921285i
$82$	126.530			0.170401
$83$	553.822	−	959.247i	0.732408	−	1.26857i	−0.223444	−	0.974717i	$-0.571730\pi$
$83$	553.822	−	959.247i	0.732408	−	1.26857i	0.955851	−	0.293850i	$-0.0949367\pi$
$84$	26.2337	−	87.0073i	0.0340754	−	0.113015i
$85$		0			0
$86$	353.931	+	613.026i	0.443783	+	0.768655i
$87$	179.633	+	191.147i	0.221364	+	0.235553i
$88$	50.9171	−	88.1909i	0.0616793	−	0.106832i
$89$	372.269			0.443375			0.221688	−	0.975118i	$-0.428843\pi$
$89$	372.269			0.443375			0.221688	+	0.975118i	$0.428843\pi$
$90$		0			0
$91$	−582.250			−0.670729
$92$	236.709	−	409.992i	0.268246	−	0.464616i
$93$	30.3505	−	7.13058i	0.0338409	−	0.00795061i
$94$	496.880	+	860.622i	0.545205	+	0.944323i
$95$		0			0
$96$	523.011	−	122.877i	0.556037	−	0.130636i
$97$	−69.6156	+	120.578i	−0.0728700	+	0.126215i	−0.900158	−	0.435563i	$-0.856549\pi$
$97$	−69.6156	+	120.578i	−0.0728700	+	0.126215i	0.827288	+	0.561778i	$0.189882\pi$
$98$	684.758			0.705826
$99$	−100.052	+	49.7590i	−0.101571	+	0.0505148i
$100$		0			0
$101$	−985.872	+	1707.58i	−0.971267	+	1.68228i	−0.279525	+	0.960139i	$0.590177\pi$
$101$	−985.872	+	1707.58i	−0.971267	+	1.68228i	−0.691742	+	0.722145i	$0.743156\pi$
$102$	−281.164	−	299.186i	−0.272935	−	0.290429i
$103$	906.353	+	1569.85i	0.867045	+	1.50177i	0.865002	+	0.501768i	$0.167317\pi$
$103$	906.353	+	1569.85i	0.867045	+	1.50177i	0.00204255	+	0.999998i	$0.499350\pi$
$104$	−971.668	−	1682.98i	−0.916153	−	1.58682i
$105$		0			0
$106$	−473.541	+	820.197i	−0.433909	+	0.751552i
$107$	259.217			0.234201			0.117100	−	0.993120i	$-0.462640\pi$
$107$	259.217			0.234201			0.117100	+	0.993120i	$0.462640\pi$
$108$	−312.077	−	115.664i	−0.278052	−	0.103053i
$109$	775.556			0.681512			0.340756	−	0.940152i	$-0.389317\pi$
$109$	775.556			0.681512			0.340756	+	0.940152i	$0.389317\pi$
$110$		0			0
$111$	435.416	−	1444.11i	0.372323	−	1.23486i
$112$	−145.212	−	251.514i	−0.122511	−	0.212195i
$113$	−107.628	−	186.417i	−0.0895997	−	0.155191i	0.817742	−	0.575585i	$-0.195225\pi$
$113$	−107.628	−	186.417i	−0.0895997	−	0.155191i	−0.907342	+	0.420393i	$0.861892\pi$
$114$	−753.892	−	802.215i	−0.619373	−	0.659073i
$115$		0			0
$116$	−119.755			−0.0958534
$117$	−132.310	+	2128.30i	−0.104547	+	1.68172i
$118$	−233.057			−0.181819
$119$	122.774	−	212.652i	0.0945774	−	0.163813i
$120$		0			0
$121$	656.936	+	1137.85i	0.493566	+	0.854881i
$122$	−810.840	−	1404.42i	−0.601721	−	1.04221i
$123$	269.800	−	63.3872i	0.197781	−	0.0464669i
$124$	−7.11684	+	12.3267i	−0.00515412	+	0.00892721i
$125$		0			0
$126$	−29.2989	+	471.297i	−0.0207155	+	0.333226i
$127$	−2424.76			−1.69420			−0.847098	−	0.531436i	$-0.821652\pi$
$127$	−2424.76			−1.69420			−0.847098	+	0.531436i	$0.821652\pi$
$128$	251.175	−	435.048i	0.173445	−	0.300415i
$129$	1061.79	+	1129.85i	0.724694	+	0.771145i
$130$		0			0
$131$	−130.247	−	225.595i	−0.0868684	−	0.150461i	0.819317	−	0.573340i	$-0.194353\pi$
$131$	−130.247	−	225.595i	−0.0868684	−	0.150461i	−0.906186	+	0.422880i	$0.861019\pi$
$132$	14.7269	−	48.8435i	0.00971067	−	0.0322067i
$133$	329.198	−	570.188i	0.214625	−	0.371741i
$134$	534.949			0.344870
$135$		0			0
$136$	819.552			0.516735
$137$	−202.319	+	350.427i	−0.126170	+	0.218533i	−0.922190	−	0.386738i	$-0.873602\pi$
$137$	−202.319	+	350.427i	−0.126170	+	0.218533i	0.796020	+	0.605271i	$0.206935\pi$
$138$	−710.127	+	2355.23i	−0.438044	+	1.45283i
$139$	883.841	+	1530.86i	0.539327	+	0.934141i	0.998940	+	0.0460221i	$0.0146545\pi$
$139$	883.841	+	1530.86i	0.539327	+	0.934141i	−0.459614	+	0.888119i	$0.652012\pi$
$140$		0			0
$141$	1490.64	+	1586.19i	0.890316	+	0.947383i
$142$	608.432	−	1053.84i	0.359567	−	0.622788i
$143$	−326.859			−0.191142
$144$	−952.361	+	473.641i	−0.551135	+	0.274098i
$145$		0			0
$146$	1179.40	−	2042.78i	0.668547	−	1.15796i
$147$	1460.11	−	343.040i	0.819237	−	0.192472i
$148$	344.310	+	596.362i	0.191230	+	0.331220i
$149$	−960.344	−	1663.36i	−0.528016	−	0.914551i	−0.999467	−	0.0326584i	$-0.989603\pi$
$149$	−960.344	−	1663.36i	−0.528016	−	0.914551i	0.471450	−	0.881893i	$-0.343731\pi$
$150$		0			0
$151$	1262.28	−	2186.33i	0.680284	−	1.17829i	−0.294611	−	0.955617i	$-0.595190\pi$
$151$	1262.28	−	2186.33i	0.680284	−	1.17829i	0.974894	−	0.222668i	$-0.0714767\pi$
$152$	2197.49			1.17263
$153$	−749.408	−	497.101i	−0.395987	−	0.262668i
$154$	−72.3804			−0.0378739
$155$		0			0
$156$	−666.701	−	709.435i	−0.342172	−	0.364104i
$157$	971.350	+	1682.43i	0.493772	+	0.855238i	0.999974	−	0.00717683i	$-0.00228447\pi$
$157$	971.350	+	1682.43i	0.493772	+	0.855238i	−0.506202	+	0.862415i	$0.668951\pi$
$158$	−239.252	−	414.397i	−0.120468	−	0.208656i
$159$	−598.842	+	1986.13i	−0.298687	+	0.990634i
$160$		0			0
$161$	−1471.23			−0.720181
$162$	1716.08	+	214.193i	0.832270	+	0.103880i
$163$	1051.21			0.505134			0.252567	−	0.967579i	$-0.418725\pi$
$163$	1051.21			0.505134			0.252567	+	0.967579i	$0.418725\pi$
$164$	−63.2650	+	109.578i	−0.0301230	+	0.0521745i
$165$		0			0
$166$	−1313.82	−	2275.60i	−0.614291	−	1.06398i
$167$	−1408.22	−	2439.11i	−0.652524	−	1.13020i	−0.982508	−	0.186218i	$-0.940377\pi$
$167$	−1408.22	−	2439.11i	−0.652524	−	1.13020i	0.329985	−	0.943986i	$-0.392956\pi$
$168$	−645.505	−	686.880i	−0.296439	−	0.315440i
$169$	−2020.28	+	3499.23i	−0.919564	+	1.59273i
$170$		0			0
$171$	−2009.41	−	1332.89i	−0.898616	−	0.596074i
$172$	−707.861			−0.313802
$173$	−721.225	+	1249.20i	−0.316958	+	0.548987i	−0.979852	−	0.199726i	$-0.935995\pi$
$173$	−721.225	+	1249.20i	−0.316958	+	0.548987i	0.662894	+	0.748713i	$0.269328\pi$
$174$	605.772	−	142.321i	0.263928	−	0.0620075i
$175$		0			0
$176$	−81.5179	−	141.193i	−0.0349128	−	0.0604707i
$177$	−496.948	+	116.754i	−0.211033	+	0.0495804i
$178$	441.563	−	764.809i	0.185936	−	0.322050i
$179$	1534.89			0.640912			0.320456	−	0.947263i	$-0.396164\pi$
$179$	1534.89			0.640912			0.320456	+	0.947263i	$0.396164\pi$
$180$		0			0
$181$	−3650.43			−1.49908			−0.749542	−	0.661956i	$-0.769726\pi$
$181$	−3650.43			−1.49908			−0.749542	+	0.661956i	$0.769726\pi$
$182$	−690.630	+	1196.21i	−0.281280	+	0.487191i
$183$	−2432.52	−	2588.44i	−0.982606	−	1.04559i
$184$	−2455.21	−	4252.56i	−0.983700	−	1.70382i
$185$		0			0
$186$	21.3505	−	70.8117i	0.00841665	−	0.0279149i
$187$	68.9221	−	119.377i	0.0269523	−	0.0466828i
$188$	−993.760			−0.385518
$189$	173.629	+	1019.62i	0.0668235	+	0.392417i
$190$		0			0
$191$	−678.644	+	1175.45i	−0.257094	+	0.445300i	−0.965462	−	0.260543i	$-0.916098\pi$
$191$	−678.644	+	1175.45i	−0.257094	+	0.445300i	0.708368	+	0.705843i	$0.249432\pi$
$192$	840.648	−	2788.11i	0.315982	−	1.04799i
$193$	−901.520	−	1561.48i	−0.336232	−	0.582371i	0.647488	−	0.762075i	$-0.275819\pi$
$193$	−901.520	−	1561.48i	−0.336232	−	0.582371i	−0.983721	+	0.179704i	$0.942486\pi$
$194$	165.148	+	286.044i	0.0611181	+	0.105860i
$195$		0			0
$196$	−342.379	+	593.018i	−0.124774	+	0.216114i
$197$	263.403			0.0952624			0.0476312	−	0.998865i	$-0.484833\pi$
$197$	263.403			0.0952624			0.0476312	+	0.998865i	$0.484833\pi$
$198$	−16.4476	+	264.573i	−0.00590344	+	0.0949614i
$199$	492.853			0.175565			0.0877824	−	0.996140i	$-0.472022\pi$
$199$	492.853			0.175565			0.0877824	+	0.996140i	$0.472022\pi$
$200$		0			0
$201$	1140.67	−	267.991i	0.400283	−	0.0940429i
$202$	2338.77	+	4050.86i	0.814629	+	1.41098i
$203$	186.080	+	322.300i	0.0643363	+	0.111434i
$204$	399.684	−	93.9022i	0.137174	−	0.0322278i
$205$		0			0
$206$	4300.25			1.45443
$207$	−334.320	+	5377.80i	−0.112255	+	1.80572i
$208$	−3111.27			−1.03715
$209$	184.803	−	320.088i	0.0611630	−	0.105937i
$210$		0			0
$211$	500.772	+	867.362i	0.163387	+	0.282994i	0.936081	−	0.351784i	$-0.114425\pi$
$211$	500.772	+	867.362i	0.163387	+	0.282994i	−0.772695	+	0.634778i	$0.781092\pi$
$212$	−473.541	−	820.197i	−0.153410	−	0.265714i
$213$	769.426	−	2551.90i	0.247513	−	0.820907i
$214$	307.468	−	532.551i	0.0982155	−	0.170114i
$215$		0			0
$216$	−2657.44	+	2203.44i	−0.837112	+	0.694097i
$217$	44.2337			0.0138377
$218$	919.919	−	1593.35i	0.285802	−	0.495023i
$219$	1491.48	−	4946.67i	0.460204	−	1.52632i
$220$		0			0
$221$	−1315.27	−	2278.11i	−0.400336	−	0.693403i
$222$	−2450.40	−	2607.46i	−0.740810	−	0.788294i
$223$	280.574	−	485.969i	0.0842540	−	0.145932i	−0.820819	−	0.571188i	$-0.806483\pi$
$223$	280.574	−	485.969i	0.0842540	−	0.145932i	0.905073	+	0.425256i	$0.139816\pi$
$224$	762.250			0.227366
$225$		0			0
$226$	−510.646			−0.150300
$227$	−1953.23	+	3383.09i	−0.571103	+	0.989180i	0.425350	+	0.905029i	$0.360151\pi$
$227$	−1953.23	+	3383.09i	−0.571103	+	0.989180i	−0.996453	+	0.0841506i	$0.973182\pi$
$228$	1071.68	−	251.783i	0.311290	−	0.0731347i
$229$	−1498.45	−	2595.40i	−0.432405	−	0.748947i	0.564675	−	0.825313i	$-0.309001\pi$
$229$	−1498.45	−	2595.40i	−0.432405	−	0.748947i	−0.997080	+	0.0763664i	$0.975668\pi$
$230$		0			0
$231$	−154.337	+	36.2601i	−0.0439594	+	0.0103279i
$232$	−621.067	+	1075.72i	−0.175755	+	0.304416i
$233$	−4194.30			−1.17930			−0.589651	−	0.807658i	$-0.700735\pi$
$233$	−4194.30			−1.17930			−0.589651	+	0.807658i	$0.700735\pi$
$234$	4215.57	+	2796.29i	1.17769	+	0.781194i
$235$		0			0
$236$	116.529	−	201.833i	0.0321414	−	0.0556705i
$237$	−717.757	−	763.763i	−0.196723	−	0.209332i
$238$	−291.255	−	504.469i	−0.0793247	−	0.137394i
$239$	83.2362	+	144.169i	0.0225276	+	0.0390190i	0.877069	−	0.480364i	$-0.159495\pi$
$239$	83.2362	+	144.169i	0.0225276	+	0.0390190i	−0.854542	+	0.519383i	$0.826162\pi$
$240$		0			0
$241$	−307.272	+	532.210i	−0.0821291	+	0.142252i	−0.904164	−	0.427185i	$-0.859505\pi$
$241$	−307.272	+	532.210i	−0.0821291	+	0.142252i	0.822035	+	0.569437i	$0.192839\pi$
$242$	3116.87			0.827935
$243$	3766.50	−	402.970i	0.994325	−	0.106381i
$244$	1621.68			0.425481
$245$		0			0
$246$	189.795	−	629.479i	0.0491906	−	0.163147i
$247$	−3526.66	−	6108.35i	−0.908485	−	1.57354i
$248$	73.8179	+	127.856i	0.0189010	+	0.0327374i
$249$	−3941.46	−	4194.10i	−1.00313	−	1.06743i
$250$		0			0
$251$	−6136.16			−1.54307			−0.771536	−	0.636185i	$-0.780511\pi$
$251$	−6136.16			−1.54307			−0.771536	+	0.636185i	$0.780511\pi$
$252$	−393.505	−	261.022i	−0.0983671	−	0.0652493i
$253$	−825.908			−0.205235
$254$	−2876.11	+	4981.57i	−0.710485	+	1.23060i
$255$		0			0
$256$	1645.87	+	2850.73i	0.401824	+	0.695979i
$257$	2725.20	+	4720.19i	0.661453	+	1.14567i	0.980234	+	0.197842i	$0.0633932\pi$
$257$	2725.20	+	4720.19i	0.661453	+	1.14567i	−0.318781	+	0.947828i	$0.603273\pi$
$258$	3580.66	−	841.244i	0.864040	−	0.202998i
$259$	1070.00	−	1853.30i	0.256705	−	0.444627i
$260$		0			0
$261$	1220.39	−	606.942i	0.289427	−	0.143942i
$262$	−617.967			−0.145718
$263$	−391.620	+	678.305i	−0.0918186	+	0.159035i	−0.908276	−	0.418371i	$-0.862601\pi$
$263$	−391.620	+	678.305i	−0.0918186	+	0.159035i	0.816458	+	0.577405i	$0.195935\pi$
$264$	−362.369	−	385.596i	−0.0844782	−	0.0898930i
$265$		0			0
$266$	−780.951	−	1352.65i	−0.180012	−	0.311790i
$267$	558.403	−	1852.01i	0.127991	−	0.424499i
$268$	−267.474	+	463.279i	−0.0609649	+	0.105594i
$269$	141.019			0.0319632			0.0159816	−	0.999872i	$-0.494913\pi$
$269$	141.019			0.0319632			0.0159816	+	0.999872i	$0.494913\pi$
$270$		0			0
$271$	6375.83			1.42917			0.714583	−	0.699551i	$-0.246616\pi$
$271$	6375.83			1.42917			0.714583	+	0.699551i	$0.246616\pi$
$272$	656.049	−	1136.31i	0.146246	−	0.253305i
$273$	−873.375	+	2896.66i	−0.193623	+	0.642174i
$274$	479.958	+	831.312i	0.105822	+	0.183290i
$275$		0			0
$276$	−1684.62	−	1792.60i	−0.367400	−	0.390949i
$277$	3411.59	−	5909.04i	0.740008	−	1.28173i	−0.212482	−	0.977165i	$-0.568155\pi$
$277$	3411.59	−	5909.04i	0.740008	−	1.28173i	0.952491	−	0.304567i	$-0.0985118\pi$
$278$	4193.44			0.904697
$279$	10.0516	−	161.688i	0.00215689	−	0.0346953i
$280$		0			0
$281$	−294.846	+	510.689i	−0.0625945	+	0.108417i	−0.895624	−	0.444811i	$-0.853271\pi$
$281$	−294.846	+	510.689i	−0.0625945	+	0.108417i	0.833030	+	0.553228i	$0.186604\pi$
$282$	5026.86	−	1181.02i	1.06151	−	0.249392i
$283$	−2988.01	−	5175.39i	−0.627629	−	1.08709i	−0.988026	−	0.154286i	$-0.950692\pi$
$283$	−2988.01	−	5175.39i	−0.627629	−	1.08709i	0.360397	−	0.932799i	$-0.382641\pi$
$284$	608.432	+	1053.84i	0.127126	+	0.220189i
$285$		0			0
$286$	−387.701	+	671.517i	−0.0801581	+	0.138838i
$287$	393.214			0.0808736
$288$	173.212	−	2786.26i	0.0354397	−	0.570076i
$289$	−3803.64			−0.774199
$290$		0			0
$291$	495.443	+	527.200i	0.0998055	+	0.106203i
$292$	1179.40	+	2042.78i	0.236367	+	0.409400i
$293$	4028.74	+	6977.99i	0.803282	+	1.39133i	0.917445	+	0.397864i	$0.130248\pi$
$293$	4028.74	+	6977.99i	0.803282	+	1.39133i	−0.114162	+	0.993462i	$0.536418\pi$
$294$	1027.14	−	3406.63i	0.203755	−	0.675777i
$295$		0			0
$296$	7142.55			1.40254
$297$	97.4705	+	572.389i	0.0190431	+	0.111830i
$298$	−4556.41			−0.885724
$299$	−7880.55	+	13649.5i	−1.52423	+	2.64004i
$300$		0			0
$301$	1099.90	+	1905.09i	0.210622	+	0.364808i
$302$	−2994.48	−	5186.59i	−0.570573	−	0.988261i
$303$	7016.30	+	7466.02i	1.33028	+	1.41555i
$304$	1759.08	−	3046.82i	0.331876	−	0.574826i
$305$		0			0
$306$	−1910.18	+	949.994i	−0.356855	+	0.177476i
$307$	4546.58			0.845235			0.422618	−	0.906308i	$-0.361111\pi$
$307$	4546.58			0.845235			0.422618	+	0.906308i	$0.361111\pi$
$308$	36.1902	−	62.6832i	0.00669522	−	0.0115965i
$309$	9169.43	−	2154.28i	1.68813	−	0.396610i
$310$		0			0
$311$	2101.40	+	3639.73i	0.383149	+	0.663633i	0.991510	−	0.130027i	$-0.0415063\pi$
$311$	2101.40	+	3639.73i	0.383149	+	0.663633i	−0.608362	+	0.793660i	$0.708173\pi$
$312$	−9830.22	+	2309.52i	−1.78374	+	0.419073i
$313$	−3486.64	+	6039.04i	−0.629637	+	1.09056i	0.357987	+	0.933727i	$0.383463\pi$
$313$	−3486.64	+	6039.04i	−0.629637	+	1.09056i	−0.987624	+	0.156838i	$0.949870\pi$
$314$	4608.63			0.828281
$315$		0			0
$316$	478.505			0.0851835
$317$	−3680.02	+	6373.97i	−0.652020	+	1.12933i	0.330612	+	0.943767i	$0.392745\pi$
$317$	−3680.02	+	6373.97i	−0.652020	+	1.12933i	−0.982632	+	0.185565i	$0.940589\pi$
$318$	3370.12	+	3586.13i	0.594298	+	0.632391i
$319$	104.460	+	180.930i	0.0183343	+	0.0317560i
$320$		0			0
$321$	388.826	−	1289.59i	0.0676080	−	0.224230i
$322$	−1745.09	+	3022.58i	−0.302018	+	0.523111i
$323$	2974.55			0.512410
$324$	−1043.54	+	1379.07i	−0.178933	+	0.236466i
$325$		0			0
$326$	1246.88	−	2159.66i	0.211835	−	0.366909i
$327$	1163.33	−	3858.34i	0.196736	−	0.652498i
$328$	656.203	+	1136.58i	0.110466	+	0.191332i
$329$	1544.14	+	2674.53i	0.258758	+	0.448182i
$330$		0			0
$331$	3417.06	−	5918.52i	0.567428	−	0.982814i	−0.429391	−	0.903119i	$-0.641272\pi$
$331$	3417.06	−	5918.52i	0.567428	−	0.982814i	0.996819	−	0.0796957i	$-0.0253949\pi$
$332$	2627.64			0.434369
$333$	−6531.24	−	4332.33i	−1.07480	−	0.712944i
$334$	−6681.39			−1.09458
$335$		0			0
$336$	−1469.09	+	345.149i	−0.238528	+	0.0560399i
$337$	−3464.24	−	6000.24i	−0.559968	−	0.969893i	−0.997498	−	0.0706891i	$-0.977480\pi$
$337$	−3464.24	−	6000.24i	−0.559968	−	0.969893i	0.437531	−	0.899204i	$-0.355853\pi$
$338$	4792.68	+	8301.16i	0.771264	+	1.33587i
$339$	−1088.85	+	255.816i	−0.174449	+	0.0409853i
$340$		0			0
$341$	24.8316			0.00394341
$342$	−5121.81	+	2547.24i	−0.809812	+	0.402746i
$343$	4656.70			0.733055
$344$	−3671.07	+	6358.48i	−0.575380	+	0.996588i
$345$		0			0
$346$	1710.95	+	2963.45i	0.265842	+	0.460451i
$347$	−3770.30	−	6530.35i	−0.583286	−	1.01028i	−0.995087	−	0.0990071i	$-0.968433\pi$
$347$	−3770.30	−	6530.35i	−0.583286	−	1.01028i	0.411801	−	0.911274i	$-0.364900\pi$
$348$	−179.633	+	595.775i	−0.0276705	+	0.0917726i
$349$	922.084	−	1597.10i	0.141427	−	0.244959i	−0.786607	−	0.617454i	$-0.788164\pi$
$349$	922.084	−	1597.10i	0.141427	−	0.244959i	0.928034	+	0.372495i	$0.121498\pi$
$350$		0			0
$351$	10389.7	+	3850.69i	1.57995	+	0.585568i
$352$	427.906			0.0647939
$353$	−3548.74	+	6146.61i	−0.535073	+	0.926773i	0.464087	+	0.885789i	$0.346382\pi$
$353$	−3548.74	+	6146.61i	−0.535073	+	0.926773i	−0.999160	+	0.0409833i	$0.986951\pi$
$354$	−349.586	+	1159.44i	−0.0524866	+	0.174079i
$355$		0			0
$356$	441.563	+	764.809i	0.0657382	+	0.113862i
$357$	−873.766	−	929.772i	−0.129537	−	0.137840i
$358$	1820.60	−	3153.37i	0.268775	−	0.465532i
$359$	7709.65			1.13342			0.566712	−	0.823916i	$-0.308215\pi$
$359$	7709.65			1.13342			0.566712	+	0.823916i	$0.308215\pi$
$360$		0			0
$361$	1116.75			0.162815
$362$	−4329.92	+	7499.65i	−0.628662	+	1.08888i
$363$	6646.12	−	1561.45i	0.960966	−	0.225770i
$364$	−690.630	−	1196.21i	−0.0994474	−	0.172248i
$365$		0			0
$366$	−8203.14	+	1927.25i	−1.17154	+	0.275244i
$367$	−2628.19	+	4552.17i	−0.373816	+	0.647469i	−0.990149	−	0.140017i	$-0.955284\pi$
$367$	−2628.19	+	4552.17i	−0.373816	+	0.647469i	0.616333	+	0.787486i	$0.288618\pi$
$368$	−7861.57			−1.11362
$369$	89.3535	−	1437.32i	0.0126058	−	0.202775i
$370$		0			0
$371$	−1471.61	+	2548.91i	−0.205936	+	0.356692i
$372$	50.6495	+	53.8960i	0.00705928	+	0.00751176i
$373$	498.227	+	862.955i	0.0691615	+	0.119791i	0.898532	−	0.438907i	$-0.144634\pi$
$373$	498.227	+	862.955i	0.0691615	+	0.119791i	−0.829371	+	0.558698i	$0.811301\pi$
$374$	−163.503	−	283.195i	−0.0226057	−	0.0391542i
$375$		0			0
$376$	−5153.78	+	8926.61i	−0.706878	+	1.22435i
$377$	3986.90			0.544658
$378$	2300.72	+	852.705i	0.313059	+	0.116028i
$379$	−2735.20			−0.370707			−0.185354	−	0.982672i	$-0.559343\pi$
$379$	−2735.20			−0.370707			−0.185354	+	0.982672i	$0.559343\pi$
$380$		0			0
$381$	−3637.14	+	12063.0i	−0.489072	+	1.62207i
$382$	1609.93	+	2788.49i	0.215632	+	0.373485i
$383$	−4469.73	−	7741.80i	−0.596325	−	1.03287i	−0.993358	−	0.115062i	$-0.963293\pi$
$383$	−4469.73	−	7741.80i	−0.596325	−	1.03287i	0.397033	−	0.917804i	$-0.370040\pi$
$384$	−1787.57	−	1902.15i	−0.237557	−	0.252783i
$385$		0			0
$386$	−4277.32			−0.564015
$387$	7213.62	−	3587.57i	0.947517	−	0.471232i
$388$	−330.295			−0.0432170
$389$	5566.93	−	9642.21i	0.725590	−	1.25676i	−0.233140	−	0.972443i	$-0.574900\pi$
$389$	5566.93	−	9642.21i	0.725590	−	1.25676i	0.958731	−	0.284316i	$-0.0917666\pi$
$390$		0			0
$391$	−3323.42	−	5756.33i	−0.429853	−	0.744527i
$392$	3551.25	+	6150.95i	0.457564	+	0.792525i
$393$	−1317.69	+	309.580i	−0.169132	+	0.0397360i
$394$	312.433	−	541.150i	0.0399496	−	0.0691948i
$395$		0			0
$396$	−220.903	−	146.530i	−0.0280323	−	0.0185945i
$397$	9479.40			1.19838			0.599191	−	0.800606i	$-0.295489\pi$
$397$	9479.40			1.19838			0.599191	+	0.800606i	$0.295489\pi$
$398$	584.593	−	1012.54i	0.0736256	−	0.127523i
$399$	−2342.85	−	2493.02i	−0.293958	−	0.312800i
$400$		0			0
$401$	−4713.80	−	8164.54i	−0.587022	−	1.01675i	−0.994620	−	0.103591i	$-0.966967\pi$
$401$	−4713.80	−	8164.54i	−0.587022	−	1.01675i	0.407598	−	0.913162i	$-0.366367\pi$
$402$	802.423	−	2661.34i	0.0995553	−	0.330188i
$403$	236.935	−	410.383i	0.0292868	−	0.0507261i
$404$	−4677.53			−0.576029
$405$		0			0
$406$	882.869			0.107921
$407$	600.670	−	1040.39i	0.0731550	−	0.126708i
$408$	1229.33	−	4077.22i	0.149169	−	0.494736i
$409$	−204.093	−	353.500i	−0.0246742	−	0.0427370i	0.853425	−	0.521216i	$-0.174522\pi$
$409$	−204.093	−	353.500i	−0.0246742	−	0.0427370i	−0.878099	+	0.478479i	$0.841188\pi$
$410$		0			0
$411$	1439.87	+	1532.17i	0.172807	+	0.183884i
$412$	−2150.12	+	3724.12i	−0.257109	+	0.445326i
$413$	−724.266			−0.0862925
$414$	10651.9	+	7065.68i	1.26452	+	0.838790i
$415$		0			0
$416$	4082.94	−	7071.86i	0.481208	−	0.833477i
$417$	8941.68	−	2100.77i	1.05006	−	0.246703i
$418$	−438.404	−	759.338i	−0.0512992	−	0.0888527i
$419$	−4406.94	−	7633.05i	−0.513826	−	0.889973i	−0.999871	−	0.0160393i	$-0.994894\pi$
$419$	−4406.94	−	7633.05i	−0.513826	−	0.889973i	0.486045	−	0.873934i	$-0.338439\pi$
$420$		0			0
$421$	1174.68	−	2034.61i	0.135987	−	0.235537i	−0.789987	−	0.613124i	$-0.789913\pi$
$421$	1174.68	−	2034.61i	0.135987	−	0.235537i	0.925974	+	0.377587i	$0.123246\pi$
$422$	2375.94			0.274074
$423$	10127.1	−	5036.56i	1.16406	−	0.578927i
$424$	−9823.40			−1.12516
$425$		0			0
$426$	−4330.12	−	4607.66i	−0.492476	−	0.524042i
$427$	−2519.83	−	4364.47i	−0.285581	−	0.494640i
$428$	307.468	+	532.551i	0.0347244	+	0.0601444i
$429$	−490.288	+	1626.10i	−0.0551780	+	0.183005i
$430$		0			0
$431$	4481.16			0.500812			0.250406	−	0.968141i	$-0.419436\pi$
$431$	4481.16			0.500812			0.250406	+	0.968141i	$0.419436\pi$
$432$	927.792	+	5448.40i	0.103330	+	0.606797i
$433$	−3422.69			−0.379871			−0.189935	−	0.981797i	$-0.560828\pi$
$433$	−3422.69			−0.379871			−0.189935	+	0.981797i	$0.560828\pi$
$434$	52.4674	−	90.8762i	0.00580303	−	0.0100511i
$435$		0			0
$436$	919.919	+	1593.35i	0.101046	+	0.175017i
$437$	−8911.17	−	15434.6i	−0.975467	−	1.68956i
$438$	−8393.61	−	8931.62i	−0.915667	−	0.974359i
$439$	4064.59	−	7040.07i	0.441896	−	0.765386i	−0.555934	−	0.831226i	$-0.687639\pi$
$439$	4064.59	−	7040.07i	0.441896	−	0.765386i	0.997830	+	0.0658402i	$0.0209728\pi$
$440$		0			0
$441$	483.565	−	7778.52i	0.0522152	−	0.839922i
$442$	−6240.36			−0.671547
$443$	1175.39	−	2035.83i	0.126060	−	0.218342i	−0.796087	−	0.605182i	$-0.793100\pi$
$443$	1175.39	−	2035.83i	0.126060	−	0.218342i	0.922147	+	0.386840i	$0.126434\pi$
$444$	3483.33	−	818.376i	0.372323	−	0.0874739i
$445$		0			0
$446$	−665.601	−	1152.86i	−0.0706662	−	0.122397i
$447$	−9715.65	+	2282.60i	−1.02804	+	0.241529i
$448$	2065.83	−	3578.12i	0.217860	−	0.377345i
$449$	4760.99			0.500412			0.250206	−	0.968193i	$-0.419502\pi$
$449$	4760.99			0.500412			0.250206	+	0.968193i	$0.419502\pi$
$450$		0			0
$451$	220.740			0.0230471
$452$	255.323	−	442.233i	0.0265695	−	0.0460196i
$453$	−8983.44	−	9559.26i	−0.931742	−	0.991464i
$454$	4633.61	+	8025.65i	0.479000	+	0.829653i
$455$		0			0
$456$	3296.23	−	10932.4i	0.338509	−	1.12271i
$457$	1114.54	−	1930.44i	0.114083	−	0.197598i	−0.803330	−	0.595535i	$-0.796940\pi$
$457$	1114.54	−	1930.44i	0.114083	−	0.197598i	0.917413	+	0.397937i	$0.130274\pi$
$458$	−7109.51			−0.725340
$459$	−3597.16	+	2982.61i	−0.365797	+	0.303303i
$460$		0			0
$461$	−2868.31	+	4968.06i	−0.289784	+	0.501921i	−0.973758	−	0.227585i	$-0.926917\pi$
$461$	−2868.31	+	4968.06i	−0.289784	+	0.501921i	0.683974	+	0.729507i	$0.260250\pi$
$462$	−108.571	+	360.088i	−0.0109332	+	0.0362615i
$463$	−1801.99	−	3121.13i	−0.180876	−	0.313286i	0.761303	−	0.648396i	$-0.224560\pi$
$463$	−1801.99	−	3121.13i	−0.180876	−	0.313286i	−0.942179	+	0.335110i	$0.891227\pi$
$464$	994.326	+	1722.22i	0.0994836	+	0.172311i
$465$		0			0
$466$	−4975.03	+	8617.00i	−0.494557	+	0.856598i
$467$	3780.37			0.374593			0.187296	−	0.982303i	$-0.440028\pi$
$467$	3780.37			0.374593			0.187296	+	0.982303i	$0.440028\pi$
$468$	−4529.44	+	2252.64i	−0.447380	+	0.222497i
$469$	1662.45			0.163677
$470$		0			0
$471$	9827.00	−	2308.76i	0.961368	−	0.225865i
$472$	−1208.67	−	2093.47i	−0.117867	−	0.204152i
$473$	617.454	+	1069.46i	0.0600224	+	0.103962i
$474$	−2420.48	+	568.670i	−0.234549	+	0.0551052i
$475$		0			0
$476$	582.511			0.0560911
$477$	8982.63	+	5958.40i	0.862236	+	0.571943i
$478$	394.920			0.0377891
$479$	7230.58	−	12523.7i	0.689715	−	1.19462i	−0.282215	−	0.959351i	$-0.591069\pi$
$479$	7230.58	−	12523.7i	0.689715	−	1.19462i	0.971930	−	0.235271i	$-0.0755977\pi$
$480$		0			0
$481$	−11462.8	−	19854.1i	−1.08661	−	1.88206i
$482$	728.935	+	1262.55i	0.0688840	+	0.119311i
$483$	−2206.85	+	7319.28i	−0.207898	+	0.689521i
$484$	−1558.44	+	2699.29i	−0.146360	+	0.253502i
$485$		0			0
$486$	3639.71	−	8216.09i	0.339714	−	0.766850i
$487$	−3581.74			−0.333273			−0.166636	−	0.986018i	$-0.553291\pi$
$487$	−3581.74			−0.333273			−0.166636	+	0.986018i	$0.553291\pi$
$488$	8410.26	−	14567.0i	0.780153	−	1.35126i
$489$	1576.81	−	5229.69i	0.145820	−	0.483629i
$490$		0			0
$491$	3507.69	+	6075.50i	0.322403	+	0.558419i	0.980983	−	0.194092i	$-0.0621760\pi$
$491$	3507.69	+	6075.50i	0.322403	+	0.558419i	−0.658580	+	0.752511i	$0.728843\pi$
$492$	450.247	+	479.107i	0.0412576	+	0.0439021i
$493$	−840.687	+	1456.11i	−0.0768005	+	0.133022i
$494$	−16732.4			−1.52394
$495$		0			0
$496$	236.364			0.0213973
$497$	1890.81	−	3274.98i	0.170653	−	0.295579i
$498$	−13291.7	+	3122.77i	−1.19602	+	0.280993i
$499$	−1259.90	−	2182.21i	−0.113028	−	0.195769i	0.803962	−	0.594681i	$-0.202721\pi$
$499$	−1259.90	−	2182.21i	−0.113028	−	0.195769i	−0.916990	+	0.398911i	$0.869388\pi$
$500$		0			0
$501$	−14246.8	+	3347.15i	−1.27046	+	0.298482i
$502$	−7278.35	+	12606.5i	−0.647109	+	1.12083i
$503$	4989.32			0.442272			0.221136	−	0.975243i	$-0.429024\pi$
$503$	4989.32			0.442272			0.221136	+	0.975243i	$0.429024\pi$
$504$	−4385.44	+	2181.03i	−0.387586	+	0.192759i
$505$		0			0
$506$	−979.643	+	1696.79i	−0.0860681	+	0.149074i
$507$	14378.0	+	15299.6i	1.25947	+	1.34020i
$508$	−2876.11	−	4981.57i	−0.251194	−	0.435081i
$509$	−2359.76	−	4087.22i	−0.205490	−	0.355919i	0.744799	−	0.667289i	$-0.232546\pi$
$509$	−2359.76	−	4087.22i	−0.205490	−	0.355919i	−0.950289	+	0.311370i	$0.899212\pi$
$510$		0			0
$511$	3665.19	−	6348.30i	0.317297	−	0.549574i
$512$	11827.7			1.02093
$513$	−9645.16	+	7997.34i	−0.830106	+	0.688287i
$514$	12929.9			1.10956
$515$		0			0
$516$	−1061.79	+	3521.57i	−0.0905868	+	0.300442i
$517$	866.839	+	1501.41i	0.0737399	+	0.127721i
$518$	−2538.35	−	4396.55i	−0.215306	−	0.372921i
$519$	5132.85	+	5461.85i	0.434117	+	0.461943i
$520$		0			0
$521$	−10711.0			−0.900682			−0.450341	−	0.892857i	$-0.648698\pi$
$521$	−10711.0			−0.900682			−0.450341	+	0.892857i	$0.648698\pi$
$522$	200.622	−	3227.16i	0.0168218	−	0.270592i
$523$	10566.4			0.883433			0.441717	−	0.897155i	$-0.354370\pi$
$523$	10566.4			0.883433			0.441717	+	0.897155i	$0.354370\pi$
$524$	308.983	−	535.175i	0.0257595	−	0.0446168i
$525$		0			0
$526$	929.032	+	1609.13i	0.0770109	+	0.133387i
$527$	99.9211	+	173.068i	0.00825926	+	0.0143055i
$528$	−824.704	+	193.757i	−0.0679747	+	0.0159700i
$529$	−13829.1	+	23952.7i	−1.13661	+	1.96866i
$530$		0			0
$531$	−164.581	+	2647.42i	−0.0134505	+	0.216362i
$532$	1561.90			0.127288
$533$	2106.23	−	3648.09i	0.171165	−	0.296466i
$534$	−3142.53	−	3343.96i	−0.254664	−	0.270988i
$535$		0			0
$536$	2774.32	+	4805.26i	0.223568	+	0.387231i
$537$	2302.34	−	7635.99i	0.185015	−	0.613626i
$538$	167.269	−	289.718i	0.0134042	−	0.0232168i
$539$	1194.60			0.0954642
$540$		0			0
$541$	−6595.81			−0.524170			−0.262085	−	0.965045i	$-0.584410\pi$
$541$	−6595.81			−0.524170			−0.262085	+	0.965045i	$0.584410\pi$
$542$	7562.63	−	13098.9i	0.599341	−	1.03809i
$543$	−5475.65	+	18160.7i	−0.432749	+	1.43526i
$544$	1721.87	+	2982.37i	0.135707	+	0.235052i
$545$		0			0
$546$	4915.11	+	5230.15i	0.385251	+	0.409945i
$547$	−3194.39	+	5532.85i	−0.249693	+	0.432482i	−0.963441	−	0.267922i	$-0.913663\pi$
$547$	−3194.39	+	5532.85i	−0.249693	+	0.432482i	0.713747	+	0.700403i	$0.246997\pi$
$548$	−959.916			−0.0748277
$549$	−16526.1	+	8218.97i	−1.28473	+	0.638939i
$550$		0			0
$551$	−2254.16	+	3904.31i	−0.174284	+	0.301868i
$552$	−24839.0	+	5835.70i	−1.91525	+	0.449971i
$553$	−743.519	−	1287.81i	−0.0571748	−	0.0990296i
$554$	−8093.24	−	14017.9i	−0.620666	−	1.07502i
$555$		0			0
$556$	−2096.72	+	3631.62i	−0.159929	+	0.277006i
$557$	−15992.4			−1.21655			−0.608276	−	0.793726i	$-0.708138\pi$
$557$	−15992.4			−1.21655			−0.608276	+	0.793726i	$0.708138\pi$
$558$	−320.258	−	212.435i	−0.0242968	−	0.0161167i
$559$	23566.2			1.78308
$560$		0			0
$561$	−490.508	−	521.948i	−0.0369149	−	0.0392811i
$562$	699.459	+	1211.50i	0.0524998	+	0.0909323i
$563$	−3175.56	−	5500.23i	−0.237716	−	0.411736i	0.722343	−	0.691535i	$-0.243065\pi$
$563$	−3175.56	−	5500.23i	−0.237716	−	0.411736i	−0.960058	+	0.279800i	$0.909732\pi$
$564$	−1490.64	+	4943.89i	−0.111290	+	0.369106i
$565$		0			0
$566$	−14176.8			−1.05282
$567$	5333.01	+	665.644i	0.395001	+	0.0493023i
$568$	12621.7			0.932382
$569$	−4810.21	+	8331.53i	−0.354402	+	0.613842i	−0.987015	−	0.160626i	$-0.948649\pi$
$569$	−4810.21	+	8331.53i	−0.354402	+	0.613842i	0.632614	+	0.774468i	$0.281982\pi$
$570$		0			0
$571$	2532.30	+	4386.08i	0.185593	+	0.321456i	0.943776	−	0.330585i	$-0.107246\pi$
$571$	2532.30	+	4386.08i	0.185593	+	0.321456i	−0.758183	+	0.652042i	$0.773913\pi$
$572$	−387.701	−	671.517i	−0.0283402	−	0.0490866i
$573$	4829.80	+	5139.38i	0.352125	+	0.374696i
$574$	466.408	−	807.842i	0.0339155	−	0.0587433i
$575$		0			0
$576$	−12609.7	−	8364.34i	−0.912161	−	0.605059i
$577$	−11355.1			−0.819273			−0.409637	−	0.912249i	$-0.634345\pi$
$577$	−11355.1			−0.819273			−0.409637	+	0.912249i	$0.634345\pi$
$578$	−4511.65	+	7814.41i	−0.324671	+	0.562347i
$579$	−9120.54	+	2142.79i	−0.654640	+	0.153802i
$580$		0			0
$581$	−4082.93	−	7071.84i	−0.291546	−	0.504973i
$582$	1670.77	−	392.533i	0.118996	−	0.0279571i
$583$	−826.121	+	1430.88i	−0.0586869	+	0.101649i
$584$	24466.2			1.73359
$585$		0			0
$586$	19114.6			1.34747
$587$	−5016.00	+	8687.96i	−0.352696	+	0.610887i	−0.986721	−	0.162426i	$-0.948068\pi$
$587$	−5016.00	+	8687.96i	−0.352696	+	0.610887i	0.634025	+	0.773312i	$0.281402\pi$
$588$	2436.66	+	2592.84i	0.170895	+	0.181848i
$589$	267.921	+	464.053i	0.0187428	+	0.0324634i
$590$		0			0
$591$	395.105	−	1310.41i	0.0274999	−	0.0912068i
$592$	5717.59	−	9903.16i	0.396945	−	0.687530i
$593$	1325.12			0.0917643			0.0458821	−	0.998947i	$-0.485390\pi$
$593$	1325.12			0.0917643			0.0458821	+	0.998947i	$0.485390\pi$
$594$	1291.56	+	478.685i	0.0892145	+	0.0330651i
$595$		0			0
$596$	2278.21	−	3945.97i	0.156575	−	0.271197i
$597$	739.279	−	2451.91i	0.0506812	−	0.168091i
$598$	18694.9	+	32380.5i	1.27841	+	2.21427i
$599$	−8285.78	−	14351.4i	−0.565188	−	0.978935i	−0.997032	−	0.0769865i	$-0.975470\pi$
$599$	−8285.78	−	14351.4i	−0.565188	−	0.978935i	0.431844	−	0.901948i	$-0.357863\pi$
$600$		0			0
$601$	−8604.49	+	14903.4i	−0.584001	+	1.01152i	0.410998	+	0.911636i	$0.365180\pi$
$601$	−8604.49	+	14903.4i	−0.584001	+	1.01152i	−0.994999	+	0.0998833i	$0.968153\pi$
$602$	5218.55			0.353310
$603$	377.772	−	6076.76i	0.0255126	−	0.410390i
$604$	5988.96			0.403456
$605$		0			0
$606$	23660.9	−	5558.92i	1.58607	−	0.372633i
$607$	2088.99	+	3618.24i	0.139686	+	0.241944i	0.927378	−	0.374126i	$-0.122057\pi$
$607$	2088.99	+	3618.24i	0.139686	+	0.241944i	−0.787692	+	0.616070i	$0.788724\pi$
$608$	4616.91	+	7996.72i	0.307961	+	0.533404i
$609$	1882.54	−	442.287i	0.125262	−	0.0294292i
$610$		0			0
$611$	33084.4			2.19059
$612$	132.369	−	2129.26i	0.00874297	−	0.140638i
$613$	−14944.2			−0.984649			−0.492324	−	0.870412i	$-0.663853\pi$
$613$	−14944.2			−0.984649			−0.492324	+	0.870412i	$0.663853\pi$
$614$	5392.89	−	9340.75i	0.354461	−	0.613945i
$615$		0			0
$616$	−375.375	−	650.168i	−0.0245524	−	0.0425260i
$617$	10251.4	+	17756.0i	0.668893	+	1.15856i	0.978214	+	0.207600i	$0.0665651\pi$
$617$	10251.4	+	17756.0i	0.668893	+	1.15856i	−0.309320	+	0.950958i	$0.600102\pi$
$618$	6450.37	−	21393.5i	0.419858	−	1.39251i
$619$	−1364.26	+	2362.97i	−0.0885854	+	0.153434i	−0.906913	−	0.421317i	$-0.861568\pi$
$619$	−1364.26	+	2362.97i	−0.0885854	+	0.153434i	0.818328	+	0.574751i	$0.194901\pi$
$620$		0			0
$621$	26252.8	+	9729.93i	1.69644	+	0.628742i
$622$	9970.21			0.642715
$623$	1372.23	−	2376.78i	0.0882463	−	0.152847i
$624$	−4666.91	+	15478.4i	−0.299400	+	0.992999i
$625$		0			0
$626$	8271.29	+	14326.3i	0.528095	+	0.914687i
$627$	−1315.21	−	1399.51i	−0.0837712	−	0.0891407i
$628$	−2304.32	+	3991.19i	−0.146421	+	0.253608i
$629$	9668.27			0.612876
$630$		0			0
$631$	−3393.08			−0.214067			−0.107034	−	0.994255i	$-0.534135\pi$
$631$	−3393.08			−0.214067			−0.107034	+	0.994255i	$0.534135\pi$
$632$	2481.59	−	4298.25i	0.156191	−	0.270530i
$633$	5066.23	−	1190.27i	0.318112	−	0.0747374i
$634$	8730.03	+	15120.9i	0.546867	+	0.947202i
$635$		0			0
$636$	−4790.74	+	1125.54i	−0.298687	+	0.0701739i
$637$	11398.5	−	19742.8i	0.708988	−	1.22800i
$638$	495.618			0.0307550
$639$	−11541.4	−	7655.70i	−0.714508	−	0.473951i
$640$		0			0
$641$	−6780.88	+	11744.8i	−0.417830	+	0.723702i	−0.995721	−	0.0924116i	$-0.970542\pi$
$641$	−6780.88	+	11744.8i	−0.417830	+	0.723702i	0.577891	+	0.816114i	$0.303876\pi$
$642$	−2188.20	−	2328.46i	−0.134520	−	0.143142i
$643$	6483.44	+	11229.7i	0.397639	+	0.688731i	0.993434	−	0.114405i	$-0.0364962\pi$
$643$	6483.44	+	11229.7i	0.397639	+	0.688731i	−0.595795	+	0.803137i	$0.703163\pi$
$644$	−1745.09	−	3022.58i	−0.106780	−	0.184948i
$645$		0			0
$646$	3528.24	−	6111.09i	0.214886	−	0.372194i
$647$	−25837.9			−1.57000			−0.785001	−	0.619495i	$-0.787337\pi$
$647$	−25837.9			−1.57000			−0.785001	+	0.619495i	$0.787337\pi$
$648$	6975.79	+	16525.8i	0.422894	+	1.00184i
$649$	−406.583			−0.0245913
$650$		0			0
$651$	66.3505	−	220.060i	0.00399460	−	0.0132486i
$652$	1246.88	+	2159.66i	0.0748950	+	0.129722i
$653$	−14133.4	−	24479.8i	−0.846989	−	1.46703i	−0.883883	−	0.467709i	$-0.845080\pi$
$653$	−14133.4	−	24479.8i	−0.846989	−	1.46703i	0.0368938	−	0.999319i	$-0.488254\pi$
$654$	−6546.92	−	6966.56i	−0.391445	−	0.416535i
$655$		0			0
$656$	2101.15			0.125055
$657$	−22372.1	−	14840.0i	−1.32849	−	0.881223i
$658$	7326.28			0.434055
$659$	7978.92	−	13819.9i	0.471646	−	0.816914i	−0.527828	−	0.849351i	$-0.676993\pi$
$659$	7978.92	−	13819.9i	0.471646	−	0.816914i	0.999474	+	0.0324369i	$0.0103268\pi$
$660$		0			0
$661$	−12028.9	−	20834.6i	−0.707821	−	1.22598i	−0.965664	−	0.259795i	$-0.916345\pi$
$661$	−12028.9	−	20834.6i	−0.707821	−	1.22598i	0.257843	−	0.966187i	$-0.416988\pi$
$662$	−8106.23	−	14040.4i	−0.475918	−	0.824314i
$663$	−13306.3	+	3126.20i	−0.779450	+	0.183125i
$664$	13627.3	−	23603.2i	0.796450	−	1.37949i
$665$		0			0
$666$	−16647.6	+	8279.38i	−0.968588	+	0.481711i
$667$	10074.1			0.584815
$668$	3340.70	−	5786.26i	0.193496	−	0.335145i
$669$	−1996.80	−	2124.79i	−0.115397	−	0.122794i
$670$		0			0
$671$	−1414.56	−	2450.09i	−0.0813838	−	0.140961i
$672$	1143.37	−	3792.15i	0.0656349	−	0.217686i
$673$	626.519	−	1085.16i	0.0358849	−	0.0621545i	−0.847525	−	0.530755i	$-0.821908\pi$
$673$	626.519	−	1085.16i	0.0358849	−	0.0621545i	0.883410	+	0.468601i	$0.155242\pi$
$674$	−16436.3			−0.939321
$675$		0			0
$676$	−9585.35			−0.545366
$677$	440.364	−	762.733i	0.0249994	−	0.0433002i	−0.853255	−	0.521494i	$-0.825375\pi$
$677$	440.364	−	762.733i	0.0249994	−	0.0433002i	0.878254	+	0.478194i	$0.158708\pi$
$678$	−765.970	+	2540.43i	−0.0433877	+	0.143901i
$679$	513.226	+	888.933i	0.0290071	+	0.0502417i
$680$		0			0
$681$	13900.8	+	14791.8i	0.782204	+	0.832341i
$682$	29.4537	−	51.0153i	0.00165373	−	0.00286434i
$683$	26686.4			1.49506			0.747531	−	0.664227i	$-0.231239\pi$
$683$	26686.4			1.49506			0.747531	+	0.664227i	$0.231239\pi$
$684$	354.924	−	5709.24i	0.0198404	−	0.319149i
$685$		0			0
$686$	5523.50	−	9566.98i	0.307417	−	0.532462i
$687$	−15159.6	+	3561.62i	−0.841886	+	0.197794i
$688$	5877.36	+	10179.9i	0.325687	+	0.564106i
$689$	15765.2	+	27306.1i	0.871706	+	1.50984i
$690$		0			0
$691$	85.7060	−	148.447i	0.00471839	−	0.00817249i	−0.863657	−	0.504081i	$-0.831831\pi$
$691$	85.7060	−	148.447i	0.00471839	−	0.00817249i	0.868375	+	0.495908i	$0.165165\pi$
$692$	−3421.90			−0.187978
$693$	−51.1138	+	822.206i	−0.00280181	+	0.0450693i
$694$	−17888.4			−0.978437
$695$		0			0
$696$	4420.04	+	4703.35i	0.240720	+	0.256150i
$697$	888.247	+	1538.49i	0.0482708	+	0.0836075i
$698$	−2187.44	−	3788.76i	−0.118619	−	0.205454i
$699$	−6291.44	+	20866.4i	−0.340435	+	1.12910i
$700$		0			0
$701$	−14229.6			−0.766684			−0.383342	−	0.923607i	$-0.625227\pi$
$701$	−14229.6			−0.766684			−0.383342	+	0.923607i	$0.625227\pi$
$702$	20234.7	−	16777.8i	1.08791	−	0.902045i
$703$	25923.8			1.39080
$704$	1159.70	−	2008.66i	0.0620850	−	0.107534i
$705$		0			0
$706$	8418.62	+	14581.5i	0.448780	+	0.777310i
$707$	7268.13	+	12588.8i	0.386628	+	0.669659i
$708$	−829.316	−	882.472i	−0.0440220	−	0.0468437i
$709$	3887.04	−	6732.55i	0.205897	−	0.356624i	−0.744521	−	0.667599i	$-0.767322\pi$
$709$	3887.04	−	6732.55i	0.205897	−	0.356624i	0.950418	+	0.310975i	$0.100656\pi$
$710$		0			0
$711$	−4876.31	+	2425.15i	−0.257210	+	0.127919i
$712$	9160.03			0.482144
$713$	598.687	−	1036.96i	0.0314460	−	0.0544661i
$714$	−2946.59	+	692.274i	−0.154444	+	0.0362853i
$715$		0			0
$716$	1820.60	+	3153.37i	0.0950264	+	0.164591i
$717$	842.088	−	197.841i	0.0438610	−	0.0103047i
$718$	9144.72	−	15839.1i	0.475318	−	0.823274i
$719$	−22091.8			−1.14588			−0.572939	−	0.819598i	$-0.694197\pi$
$719$	−22091.8			−1.14588			−0.572939	+	0.819598i	$0.694197\pi$
$720$		0			0
$721$	13363.8			0.690282
$722$	1324.62	−	2294.31i	0.0682786	−	0.118262i
$723$	2186.81	+	2326.97i	0.112487	+	0.119697i
$724$	−4329.92	−	7499.65i	−0.222266	−	0.384975i
$725$		0			0
$726$	4675.31	−	15506.3i	0.239004	−	0.792687i
$727$	3321.74	−	5753.42i	0.169459	−	0.293511i	−0.768771	−	0.639524i	$-0.779131\pi$
$727$	3321.74	−	5753.42i	0.169459	−	0.293511i	0.938230	+	0.346013i	$0.112465\pi$
$728$	−14326.8			−0.729378
$729$	3645.00	−	19342.6i	0.185185	−	0.982704i
$730$		0			0
$731$	−4969.22	+	8606.94i	−0.251427	+	0.435484i
$732$	2432.52	−	8067.75i	0.122826	−	0.407367i
$733$	−1561.40	−	2704.43i	−0.0786791	−	0.136276i	0.824001	−	0.566588i	$-0.191737\pi$
$733$	−1561.40	−	2704.43i	−0.0786791	−	0.136276i	−0.902680	+	0.430312i	$0.858404\pi$
$734$	6234.82	+	10799.0i	0.313530	+	0.543050i
$735$		0			0
$736$	10316.8	−	17869.2i	0.516687	−	0.894928i
$737$	933.252			0.0466442
$738$	−2846.93	−	1888.44i	−0.142001	−	0.0941929i
$739$	19549.5			0.973127			0.486563	−	0.873645i	$-0.338250\pi$
$739$	19549.5			0.973127			0.486563	+	0.873645i	$0.338250\pi$
$740$		0			0
$741$	−35678.6	+	8382.37i	−1.76881	+	0.415566i
$742$	3491.08	+	6046.72i	0.172724	+	0.299167i
$743$	4695.92	+	8133.58i	0.231866	+	0.401604i	0.958357	−	0.285572i	$-0.0921834\pi$
$743$	4695.92	+	8133.58i	0.231866	+	0.401604i	−0.726491	+	0.687176i	$0.758850\pi$
$744$	746.804	−	175.455i	0.0368000	−	0.00864582i
$745$		0			0
$746$	2363.87			0.116015
$747$	−26777.6	+	13317.4i	−1.31157	+	0.652286i
$748$	327.005			0.0159846
$749$	955.512	−	1655.00i	0.0466137	−	0.0807373i
$750$		0			0
$751$	9136.01	+	15824.0i	0.443912	+	0.768878i	0.997976	−	0.0635962i	$-0.0202570\pi$
$751$	9136.01	+	15824.0i	0.443912	+	0.768878i	−0.554064	+	0.832474i	$0.686924\pi$
$752$	8251.18	+	14291.5i	0.400119	+	0.693026i
$753$	−9204.25	+	30527.0i	−0.445447	+	1.47738i
$754$	4729.03	−	8190.92i	0.228410	−	0.395618i
$755$		0			0
$756$	−1888.83	+	1566.13i	−0.0908676	+	0.0753434i
$757$	−2016.30			−0.0968082			−0.0484041	−	0.998828i	$-0.515414\pi$
$757$	−2016.30			−0.0968082			−0.0484041	+	0.998828i	$0.515414\pi$
$758$	−3244.34	+	5619.36i	−0.155461	+	0.269267i
$759$	−1238.86	+	4108.84i	−0.0592462	+	0.196497i
$760$		0			0
$761$	8846.39	+	15322.4i	0.421395	+	0.729877i	0.996076	−	0.0885001i	$-0.0282074\pi$
$761$	8846.39	+	15322.4i	0.421395	+	0.729877i	−0.574681	+	0.818377i	$0.694874\pi$
$762$	20468.8	+	21780.8i	0.973107	+	1.03548i
$763$	2858.81	−	4951.60i	0.135643	−	0.234941i
$764$	−3219.87			−0.152475
$765$		0			0
$766$	−21206.9			−1.00031
$767$	−3879.48	+	6719.46i	−0.182634	+	0.316331i
$768$	16651.0	−	3912.00i	0.782346	−	0.183805i
$769$	4879.86	+	8452.16i	0.228833	+	0.396350i	0.957462	−	0.288558i	$-0.0931759\pi$
$769$	4879.86	+	8452.16i	0.228833	+	0.396350i	−0.728630	+	0.684908i	$0.759843\pi$
$770$		0			0
$771$	27570.4	−	6477.43i	1.28784	−	0.302567i
$772$	2138.66	−	3704.27i	0.0997047	−	0.172694i
$773$	10338.3			0.481038			0.240519	−	0.970644i	$-0.422682\pi$
$773$	10338.3			0.481038			0.240519	+	0.970644i	$0.422682\pi$
$774$	1185.86	−	19075.4i	0.0550707	−	0.885856i
$775$		0			0
$776$	−1712.96	+	2966.93i	−0.0792418	+	0.137251i
$777$	−7615.04	−	8103.14i	−0.351593	−	0.374130i
$778$	−13206.3	−	22874.0i	−0.608573	−	1.05408i
$779$	2381.68	+	4125.19i	0.109541	+	0.189731i
$780$		0			0
$781$	1061.45	−	1838.48i	0.0486320	−	0.0842331i
$782$	−15768.2			−0.721059
$783$	−1188.91	−	6981.79i	−0.0542633	−	0.318657i
$784$	11371.1			0.517997
$785$		0			0
$786$	−926.950	+	3074.35i	−0.0420652	+	0.139514i
$787$	2363.64	+	4093.95i	0.107058	+	0.185430i	0.914577	−	0.404411i	$-0.132524\pi$
$787$	2363.64	+	4093.95i	0.107058	+	0.185430i	−0.807519	+	0.589842i	$0.799190\pi$
$788$	312.433	+	541.150i	0.0141243	+	0.0244640i
$789$	2787.10	+	2965.74i	0.125758	+	0.133819i
$790$		0			0
$791$	−1586.92			−0.0713331
$792$	−2461.87	+	1224.37i	−0.110453	+	0.0549319i
$793$	−53989.1			−2.41767
$794$	11243.9	−	19475.0i	0.502558	−	0.870456i
$795$		0			0
$796$	584.593	+	1012.54i	0.0260306	+	0.0450863i
$797$	14099.4	+	24420.9i	0.626634	+	1.08536i	0.988222	+	0.153025i	$0.0489014\pi$
$797$	14099.4	+	24420.9i	0.626634	+	1.08536i	−0.361588	+	0.932338i	$0.617765\pi$
$798$	−7900.76	+	1856.21i	−0.350481	+	0.0823423i
$799$	−6976.24	+	12083.2i	−0.308888	+	0.535010i
$800$		0			0
$801$	−8376.04	−	5556.04i	−0.369479	−	0.245085i
$802$	−22364.9			−0.984704
$803$	2057.54	−	3563.76i	0.0904221	−	0.156616i
$804$	1903.57	+	2025.59i	0.0834998	+	0.0888519i
$805$		0			0
$806$	−562.076	−	973.544i	−0.0245636	−	0.0425454i
$807$	211.529	−	701.562i	0.00922697	−	0.0306024i
$808$	−24258.3	+	42016.7i	−1.05619	+	1.82938i
$809$	−27310.5			−1.18688			−0.593439	−	0.804879i	$-0.702230\pi$
$809$	−27310.5			−1.18688			−0.593439	+	0.804879i	$0.702230\pi$
$810$		0			0
$811$	−18045.0			−0.781312			−0.390656	−	0.920537i	$-0.627752\pi$
$811$	−18045.0			−0.781312			−0.390656	+	0.920537i	$0.627752\pi$
$812$	−441.435	+	764.587i	−0.0190780	+	0.0330440i
$813$	9563.74	−	31719.3i	0.412565	−	1.36832i
$814$	−1424.96	−	2468.10i	−0.0613572	−	0.106274i
$815$		0			0
$816$	−4669.00	−	4968.27i	−0.200304	−	0.213142i
$817$	−13324.1	+	23078.0i	−0.570564	+	0.988246i
$818$	−968.333			−0.0413899
$819$	13100.6	+	8689.97i	0.558941	+	0.370760i
$820$		0			0
$821$	6288.85	−	10892.6i	0.267335	−	0.463038i	−0.700837	−	0.713321i	$-0.747190\pi$
$821$	6288.85	−	10892.6i	0.267335	−	0.463038i	0.968173	+	0.250283i	$0.0805235\pi$
$822$	4855.66	−	1140.79i	0.206035	−	0.0484060i
$823$	−17484.2	−	30283.6i	−0.740537	−	1.28265i	−0.952251	−	0.305316i	$-0.901238\pi$
$823$	−17484.2	−	30283.6i	−0.740537	−	1.28265i	0.211714	−	0.977332i	$-0.432096\pi$
$824$	22301.7	+	38627.7i	0.942860	+	1.63308i
$825$		0			0
$826$	−859.081	+	1487.97i	−0.0361880	+	0.0626794i
$827$	6735.01			0.283191			0.141596	−	0.989925i	$-0.454777\pi$
$827$	6735.01			0.283191			0.141596	+	0.989925i	$0.454777\pi$
$828$	−11445.0	+	5691.99i	−0.480364	+	0.238901i
$829$	−2867.97			−0.120155			−0.0600777	−	0.998194i	$-0.519135\pi$
$829$	−2867.97			−0.120155			−0.0600777	+	0.998194i	$0.519135\pi$
$830$		0			0
$831$	−24279.7	−	25836.0i	−1.01354	−	1.07851i
$832$	−22131.0	−	38332.0i	−0.922179	−	1.59726i
$833$	4807.03	+	8326.02i	0.199944	+	0.346314i
$834$	6290.16	−	20862.1i	0.261163	−	0.866181i
$835$		0			0
$836$	876.808			0.0362740
$837$	−789.310	−	292.538i	−0.0325956	−	0.0120807i
$838$	−20909.0			−0.861921
$839$	−13927.9	+	24123.8i	−0.573116	+	0.992666i	0.423128	+	0.906070i	$0.360932\pi$
$839$	−13927.9	+	24123.8i	−0.573116	+	0.992666i	−0.996244	+	0.0865958i	$0.972401\pi$
$840$		0			0
$841$	10920.3	+	18914.6i	0.447756	+	0.775537i
$842$	−2786.68	−	4826.67i	−0.114056	−	0.197551i
$843$	2098.38	+	2232.88i	0.0857318	+	0.0912270i
$844$	−1187.97	+	2057.63i	−0.0484499	+	0.0839176i
$845$		0			0
$846$	1664.81	−	26779.8i	0.0676566	−	1.08831i
$847$	9686.23			0.392943
$848$	−7863.60	+	13620.2i	−0.318440	+	0.551554i
$849$	−30229.3	+	7102.09i	−1.22199	+	0.287094i
$850$		0			0
$851$	−28964.2	−	50167.5i	−1.16672	−	2.02082i
$852$	6155.41	−	1446.16i	0.247513	−	0.0581509i
$853$	5463.05	−	9462.29i	0.219287	−	0.379815i	−0.735304	−	0.677738i	$-0.762960\pi$
$853$	5463.05	−	9462.29i	0.219287	−	0.379815i	0.954590	+	0.297923i	$0.0962937\pi$
$854$	−11955.5			−0.479049
$855$		0			0
$856$	6378.30			0.254680
$857$	22584.6	−	39117.7i	0.900206	−	1.55920i	0.0729799	−	0.997333i	$-0.476749\pi$
$857$	22584.6	−	39117.7i	0.900206	−	1.55920i	0.827226	−	0.561869i	$-0.189918\pi$
$858$	2759.20	+	2936.06i	0.109788	+	0.116825i
$859$	3525.95	+	6107.12i	0.140051	+	0.242576i	0.927516	−	0.373784i	$-0.121940\pi$
$859$	3525.95	+	6107.12i	0.140051	+	0.242576i	−0.787465	+	0.616360i	$0.788607\pi$
$860$		0			0
$861$	589.822	−	1956.22i	0.0233462	−	0.0774306i
$862$	5315.29	−	9206.35i	0.210022	−	0.363770i
$863$	−6882.52			−0.271476			−0.135738	−	0.990745i	$-0.543341\pi$
$863$	−6882.52			−0.271476			−0.135738	+	0.990745i	$0.543341\pi$
$864$	−13601.6	−	5041.11i	−0.535576	−	0.198498i
$865$		0			0
$866$	−4059.80	+	7031.77i	−0.159304	+	0.275923i
$867$	−5705.46	+	18922.9i	−0.223492	+	0.741239i
$868$	52.4674	+	90.8762i	0.00205168	+	0.00355362i
$869$	−417.391	−	722.942i	−0.0162935	−	0.0282211i
$870$		0			0
$871$	8904.79	−	15423.5i	0.346415	−	0.600008i
$872$	19083.3			0.741104
$873$	3365.95	−	1674.00i	0.130493	−	0.0648984i
$874$	−42279.6			−1.63630
$875$		0			0
$876$	11931.8	−	2803.27i	0.460204	−	0.108121i
$877$	18684.3	+	32362.2i	0.719413	+	1.24606i	0.961233	+	0.275738i	$0.0889224\pi$
$877$	18684.3	+	32362.2i	0.719413	+	1.24606i	−0.241820	+	0.970321i	$0.577744\pi$
$878$	−9642.35	−	16701.0i	−0.370630	−	0.641951i
$879$	40758.2	−	9575.76i	1.56398	−	0.367443i
$880$		0			0
$881$	−23880.5			−0.913229			−0.456614	−	0.889665i	$-0.650938\pi$
$881$	−23880.5			−0.913229			−0.456614	+	0.889665i	$0.650938\pi$
$882$	−15407.0	−	10219.9i	−0.588189	−	0.390160i
$883$	33107.0			1.26177			0.630883	−	0.775878i	$-0.282693\pi$
$883$	33107.0			1.26177			0.630883	+	0.775878i	$0.282693\pi$
$884$	3120.18	−	5404.31i	0.118714	−	0.205618i
$885$		0			0
$886$	−2788.36	−	4829.57i	−0.105730	−	0.183129i
$887$	5651.07	+	9787.95i	0.213917	+	0.370515i	0.952937	−	0.303168i	$-0.0980444\pi$
$887$	5651.07	+	9787.95i	0.213917	+	0.370515i	−0.739020	+	0.673684i	$0.764711\pi$
$888$	10713.8	−	35533.7i	0.404879	−	1.34283i
$889$	−8938.02	+	15481.1i	−0.337201	+	0.584049i
$890$		0			0
$891$	2993.80	+	373.674i	0.112566	+	0.0140500i
$892$	1331.20			0.0499686
$893$	−18705.6	+	32399.0i	−0.700961	+	1.21410i
$894$	−6834.62	+	22667.9i	−0.255687	+	0.848016i
$895$		0			0
$896$	−1851.73	−	3207.30i	−0.0690425	−	0.119585i
$897$	56084.6	+	59679.5i	2.08764	+	2.22145i
$898$	5647.21	−	9781.25i	0.209855	−	0.363479i
$899$	−302.886			−0.0112367
$900$		0			0
$901$	−13297.1			−0.491666
$902$	261.828	−	453.500i	0.00966511	−	0.0167405i
$903$	11127.5	−	2614.31i	0.410079	−	0.0963443i
$904$	−2648.28	−	4586.96i	−0.0974343	−	0.168761i
$905$		0			0
$906$	−30294.7	+	7117.47i	−1.11090	+	0.260996i
$907$	1981.12	−	3431.40i	0.0725270	−	0.125620i	−0.827481	−	0.561493i	$-0.810227\pi$
$907$	1981.12	−	3431.40i	0.0725270	−	0.125620i	0.900008	+	0.435873i	$0.143560\pi$
$908$	−9267.22			−0.338704
$909$	47667.4	−	23706.6i	1.73931	−	0.865015i
$910$		0			0
$911$	17023.1	−	29484.8i	0.619100	−	1.07231i	−0.370551	−	0.928812i	$-0.620831\pi$
$911$	17023.1	−	29484.8i	0.619100	−	1.07231i	0.989650	−	0.143500i	$-0.0458356\pi$
$912$	−12519.1	−	13321.6i	−0.454550	−	0.483685i
$913$	−2292.04	−	3969.93i	−0.0830838	−	0.143905i
$914$	−2644.01	−	4579.56i	−0.0956849	−	0.165731i
$915$		0			0
$916$	3554.76	−	6157.02i	0.128223	−	0.222089i
$917$	−1920.44			−0.0691587
$918$	1860.90	+	10928.0i	0.0669050	+	0.392895i
$919$	−35121.5			−1.26066			−0.630332	−	0.776326i	$-0.717081\pi$
$919$	−35121.5			−1.26066			−0.630332	+	0.776326i	$0.717081\pi$
$920$		0			0
$921$	6819.87	−	22619.0i	0.243998	−	0.809251i
$922$	6804.44	+	11785.6i	0.243050	+	0.420975i
$923$	−20256.0	−	35084.4i	−0.722355	−	1.25116i
$924$	−257.560	−	274.069i	−0.00917002	−	0.00975779i
$925$		0			0
$926$	−8549.64			−0.303411
$927$	3036.76	−	48848.8i	0.107595	−	1.73075i
$928$	−5219.44			−0.184630
$929$	−12228.9	+	21181.1i	−0.431881	+	0.748039i	−0.997035	−	0.0769459i	$-0.975483\pi$
$929$	−12228.9	+	21181.1i	−0.431881	+	0.748039i	0.565155	+	0.824985i	$0.308816\pi$
$930$		0			0
$931$	12889.2	+	22324.8i	0.453735	+	0.785891i
$932$	−4975.03	−	8617.00i	−0.174852	−	0.302853i
$933$	21259.5	−	4994.73i	0.745986	−	0.175263i
$934$	4484.05	−	7766.61i	0.157091	−	0.272089i
$935$		0			0
$936$	−3255.61	+	52369.0i	−0.113689	+	1.82878i
$937$	−41877.5			−1.46006			−0.730032	−	0.683413i	$-0.760495\pi$
$937$	−41877.5			−1.46006			−0.730032	+	0.683413i	$0.760495\pi$
$938$	1971.90	−	3415.43i	0.0686404	−	0.118889i
$939$	24813.9	+	26404.4i	0.862375	+	0.917651i
$940$		0			0
$941$	4599.48	+	7966.54i	0.159340	+	0.275985i	0.934631	−	0.355619i	$-0.115730\pi$
$941$	4599.48	+	7966.54i	0.159340	+	0.275985i	−0.775291	+	0.631604i	$0.782397\pi$
$942$	6912.95	−	22927.7i	0.239104	−	0.793018i
$943$	5322.02	−	9218.01i	0.183785	−	0.318324i
$944$	−3870.14			−0.133435
$945$		0			0
$946$	2929.55			0.100685
$947$	10481.8	−	18155.0i	0.359675	−	0.622976i	−0.628231	−	0.778027i	$-0.716221\pi$
$947$	10481.8	−	18155.0i	0.359675	−	0.622976i	0.987906	+	0.155051i	$0.0495541\pi$
$948$	717.757	−	2380.53i	0.0245904	−	0.0815570i
$949$	−39264.7	−	68008.5i	−1.34308	−	2.32629i
$950$		0			0
$951$	26190.1	+	27868.8i	0.893030	+	0.950271i
$952$	3020.98	−	5232.50i	0.102847	−	0.178137i
$953$	27943.7			0.949828			0.474914	−	0.880032i	$-0.342479\pi$
$953$	27943.7			0.949828			0.474914	+	0.880032i	$0.342479\pi$
$954$	22895.9	−	11386.9i	0.777027	−	0.386441i
$955$		0			0
$956$	−197.460	+	342.010i	−0.00668024	+	0.0115705i
$957$	1056.81	−	248.287i	0.0356967	−	0.00838662i
$958$	−17153.0	−	29709.8i	−0.578484	−	1.00196i
$959$	1491.55	+	2583.45i	0.0502240	+	0.0869905i
$960$		0			0
$961$	14877.5	−	25768.6i	0.499396	−	0.864979i
$962$	−54385.9			−1.82274
$963$	−5832.39	−	3868.77i	−0.195167	−	0.129459i
$964$	−1457.87			−0.0487084
$965$		0			0
$966$	12419.5	+	13215.6i	0.413655	+	0.440170i
$967$	1121.76	+	1942.95i	0.0373045	+	0.0646132i	0.884075	−	0.467345i	$-0.154790\pi$
$967$	1121.76	+	1942.95i	0.0373045	+	0.0646132i	−0.846770	+	0.531959i	$0.821456\pi$
$968$	16164.5	+	27997.8i	0.536723	+	0.929632i
$969$	4461.83	−	14798.2i	0.147920	−	0.490595i
$970$		0			0
$971$	57345.0			1.89525			0.947626	−	0.319381i	$-0.103475\pi$
$971$	57345.0			1.89525			0.947626	+	0.319381i	$0.103475\pi$
$972$	5295.48	+	7260.13i	0.174746	+	0.239577i
$973$	13031.8			0.429375
$974$	−4248.44	+	7358.52i	−0.139763	+	0.242076i
$975$		0			0
$976$	−13464.8	−	23321.7i	−0.441595	−	0.764866i
$977$	9395.44	+	16273.4i	0.307663	+	0.532888i	0.977851	−	0.209304i	$-0.0671197\pi$
$977$	9395.44	+	16273.4i	0.307663	+	0.532888i	−0.670188	+	0.742192i	$0.733786\pi$
$978$	−8873.84	−	9442.63i	−0.290137	−	0.308734i
$979$	770.334	−	1334.26i	0.0251481	−	0.0435578i
$980$		0			0
$981$	−17450.0	−	11575.0i	−0.567927	−	0.376720i
$982$	16642.5			0.540817
$983$	−17298.8	+	29962.4i	−0.561289	+	0.972181i	0.436096	+	0.899900i	$0.356361\pi$
$983$	−17298.8	+	29962.4i	−0.561289	+	0.972181i	−0.997384	+	0.0722803i	$0.976972\pi$
$984$	6638.70	−	1559.70i	0.215075	−	0.0505300i
$985$		0			0
$986$	1994.35	+	3454.31i	0.0644147	+	0.111570i
$987$	15621.8	−	3670.21i	0.503798	−	0.118363i
$988$	8366.22	−	14490.7i	0.269398	−	0.466611i
$989$	59547.1			1.91455
$990$		0			0
$991$	−45026.3			−1.44330			−0.721649	−	0.692259i	$-0.756616\pi$
$991$	−45026.3			−1.44330			−0.721649	+	0.692259i	$0.756616\pi$
$992$	−310.182	+	537.251i	−0.00992771	+	0.0171953i
$993$	−24318.7	−	25877.5i	−0.777171	−	0.826985i
$994$	−4485.53	−	7769.17i	−0.143131	−	0.247911i
$995$		0			0
$996$	3941.46	−	13072.4i	0.125392	−	0.415877i
$997$	−5986.04	+	10368.1i	−0.190150	+	0.329350i	−0.945300	−	0.326202i	$-0.894231\pi$
$997$	−5986.04	+	10368.1i	−0.190150	+	0.329350i	0.755150	+	0.655552i	$0.227564\pi$
$998$	−5977.66			−0.189599
$999$	−31349.9	+	25994.0i	−0.992861	+	0.823237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.a.151.2		4
5.2	odd	4		225.4.k.a.124.3		8
5.3	odd	4		225.4.k.a.124.2		8
5.4	even	2		45.4.e.a.16.1	✓	4
9.2	odd	6		2025.4.a.j.1.2		2
9.4	even	3	inner	225.4.e.a.76.2		4
9.7	even	3		2025.4.a.l.1.1		2
15.14	odd	2		135.4.e.a.46.2		4
45.4	even	6		45.4.e.a.31.1	yes	4
45.13	odd	12		225.4.k.a.49.3		8
45.14	odd	6		135.4.e.a.91.2		4
45.22	odd	12		225.4.k.a.49.2		8
45.29	odd	6		405.4.a.e.1.1		2
45.34	even	6		405.4.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.a.16.1	✓	4	5.4	even	2
45.4.e.a.31.1	yes	4	45.4	even	6
135.4.e.a.46.2		4	15.14	odd	2
135.4.e.a.91.2		4	45.14	odd	6
225.4.e.a.76.2		4	9.4	even	3	inner
225.4.e.a.151.2		4	1.1	even	1	trivial
225.4.k.a.49.2		8	45.22	odd	12
225.4.k.a.49.3		8	45.13	odd	12
225.4.k.a.124.2		8	5.3	odd	4
225.4.k.a.124.3		8	5.2	odd	4
405.4.a.d.1.2		2	45.34	even	6
405.4.a.e.1.1		2	45.29	odd	6
2025.4.a.j.1.2		2	9.2	odd	6
2025.4.a.l.1.1		2	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18614 - 2.05446i) q^{2} +(1.50000 - 4.97494i) q^{3} +(1.18614 + 2.05446i) q^{4} +(-8.44158 - 8.98266i) q^{6} +(3.68614 - 6.38458i) q^{7} +24.6060 q^{8} +(-22.5000 - 14.9248i) q^{9} +(2.06930 - 3.58413i) q^{11} +(12.0000 - 2.81929i) q^{12} +(-39.4891 - 68.3972i) q^{13} +(-8.74456 - 15.1460i) q^{14} +(19.6970 - 34.1162i) q^{16} +33.3070 q^{17} +(-57.3505 + 28.5223i) q^{18} +89.3070 q^{19} +(-26.2337 - 27.9152i) q^{21} +(-4.90895 - 8.50256i) q^{22} +(-99.7812 - 172.826i) q^{23} +(36.9090 - 122.413i) q^{24} -187.359 q^{26} +(-108.000 + 89.5489i) q^{27} +17.4891 q^{28} +(-25.2405 + 43.7179i) q^{29} +(3.00000 + 5.19615i) q^{31} +(51.6970 + 89.5419i) q^{32} +(-14.7269 - 15.6708i) q^{33} +(39.5068 - 68.4278i) q^{34} +(3.97420 - 63.9282i) q^{36} +290.277 q^{37} +(105.931 - 183.477i) q^{38} +(-399.505 + 93.8602i) q^{39} +(26.6684 + 46.1911i) q^{41} +(-88.4674 + 20.7846i) q^{42} +(-149.194 + 258.412i) q^{43} +9.81791 q^{44} -473.418 q^{46} +(-209.452 + 362.782i) q^{47} +(-140.181 - 149.166i) q^{48} +(144.325 + 249.978i) q^{49} +(49.9605 - 165.700i) q^{51} +(93.6793 - 162.257i) q^{52} -399.228 q^{53} +(55.8710 + 328.099i) q^{54} +(90.7011 - 157.099i) q^{56} +(133.961 - 444.297i) q^{57} +(59.8776 + 103.711i) q^{58} +(-49.1209 - 85.0799i) q^{59} +(341.797 - 592.011i) q^{61} +14.2337 q^{62} +(-178.227 + 88.6382i) q^{63} +560.432 q^{64} +(-49.6631 + 11.6679i) q^{66} +(112.750 + 195.289i) q^{67} +(39.5068 + 68.4278i) q^{68} +(-1009.47 + 237.166i) q^{69} +512.951 q^{71} +(-553.634 - 367.239i) q^{72} +994.318 q^{73} +(344.310 - 596.362i) q^{74} +(105.931 + 183.477i) q^{76} +(-15.2554 - 26.4232i) q^{77} +(-281.038 + 932.097i) q^{78} +(100.853 - 174.683i) q^{79} +(283.500 + 671.617i) q^{81} +126.530 q^{82} +(553.822 - 959.247i) q^{83} +(26.2337 - 87.0073i) q^{84} +(353.931 + 613.026i) q^{86} +(179.633 + 191.147i) q^{87} +(50.9171 - 88.1909i) q^{88} +372.269 q^{89} -582.250 q^{91} +(236.709 - 409.992i) q^{92} +(30.3505 - 7.13058i) q^{93} +(496.880 + 860.622i) q^{94} +(523.011 - 122.877i) q^{96} +(-69.6156 + 120.578i) q^{97} +684.758 q^{98} +(-100.052 + 49.7590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 6 q^{3} - q^{4} - 51 q^{6} + 9 q^{7} + 18 q^{8} - 90 q^{9} + 37 q^{11} + 48 q^{12} - 112 q^{13} - 12 q^{14} + 119 q^{16} - 154 q^{17} - 126 q^{18} + 70 q^{19} - 36 q^{21} + 101 q^{22} - 267 q^{23}+ \cdots - 90 q^{99}+O(q^{100}) \) 4 * q - q^2 + 6 * q^3 - q^4 - 51 * q^6 + 9 * q^7 + 18 * q^8 - 90 * q^9 + 37 * q^11 + 48 * q^12 - 112 * q^13 - 12 * q^14 + 119 * q^16 - 154 * q^17 - 126 * q^18 + 70 * q^19 - 36 * q^21 + 101 * q^22 - 267 * q^23 + 27 * q^24 - 152 * q^26 - 432 * q^27 + 24 * q^28 - 325 * q^29 + 12 * q^31 + 247 * q^32 + 303 * q^33 + 451 * q^34 + 171 * q^36 + 1276 * q^37 + 395 * q^38 - 564 * q^39 - 238 * q^41 - 216 * q^42 - 97 * q^43 - 202 * q^44 - 492 * q^46 - 901 * q^47 + 525 * q^48 + 629 * q^49 - 231 * q^51 + 76 * q^52 - 448 * q^53 + 999 * q^54 + 156 * q^56 + 105 * q^57 - 806 * q^58 + 85 * q^59 + 247 * q^61 - 12 * q^62 - 351 * q^63 + 1426 * q^64 - 888 * q^66 - 606 * q^67 + 451 * q^68 - 1539 * q^69 + 788 * q^71 - 405 * q^72 + 1622 * q^73 - 484 * q^74 + 395 * q^76 - 84 * q^77 - 228 * q^78 + 840 * q^79 + 1134 * q^81 + 2218 * q^82 - 387 * q^83 + 36 * q^84 + 1387 * q^86 - 2418 * q^87 - 411 * q^88 - 2130 * q^89 - 1272 * q^91 + 246 * q^92 + 18 * q^93 - 632 * q^94 + 24 * q^96 - 1031 * q^97 - 926 * q^98 - 90 * q^99

Introduction

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