LMFDB - Embedded newform 294.5.g.c.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,5,Mod(19,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("294.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	294.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$30.3907691467$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.31
Dual form			294.5.g.c.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 + 2.44949i) q^{2} +(4.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(20.7426 - 11.9758i) q^{5} +14.6969i q^{6} -22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +O(q^{10})$	\(q+(1.41421 + 2.44949i) q^{2} +(4.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(20.7426 - 11.9758i) q^{5} +14.6969i q^{6} -22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +(58.6690 + 33.8726i) q^{10} +(-48.9853 + 84.8450i) q^{11} +(-36.0000 + 20.7846i) q^{12} +104.211i q^{13} +124.456 q^{15} +(-32.0000 - 55.4256i) q^{16} +(-93.2498 - 53.8378i) q^{17} +(-38.1838 + 66.1362i) q^{18} +(-33.2498 + 19.1968i) q^{19} +191.612i q^{20} -277.103 q^{22} +(510.749 + 884.644i) q^{23} +(-101.823 - 58.7878i) q^{24} +(-25.6619 + 44.4477i) q^{25} +(-255.265 + 147.377i) q^{26} +140.296i q^{27} +621.603 q^{29} +(176.007 + 304.853i) q^{30} +(1315.61 + 759.568i) q^{31} +(90.5097 - 156.767i) q^{32} +(-440.868 + 254.535i) q^{33} -304.553i q^{34} -216.000 q^{36} +(281.118 + 486.910i) q^{37} +(-94.0446 - 54.2967i) q^{38} +(-270.749 + 468.952i) q^{39} +(-469.352 + 270.981i) q^{40} +1023.20i q^{41} -3382.41 q^{43} +(-391.882 - 678.760i) q^{44} +(560.051 + 323.346i) q^{45} +(-1444.62 + 2502.15i) q^{46} +(3416.50 - 1972.52i) q^{47} -332.554i q^{48} -145.166 q^{50} +(-279.749 - 484.540i) q^{51} +(-721.998 - 416.846i) q^{52} +(-1095.30 + 1897.12i) q^{53} +(-343.654 + 198.409i) q^{54} +2346.55i q^{55} -199.499 q^{57} +(879.079 + 1522.61i) q^{58} +(-2541.67 - 1467.44i) q^{59} +(-497.823 + 862.255i) q^{60} +(-576.207 + 332.673i) q^{61} +4296.76i q^{62} +512.000 q^{64} +(1248.01 + 2161.62i) q^{65} +(-1246.96 - 719.934i) q^{66} +(2962.69 - 5131.53i) q^{67} +(745.998 - 430.702i) q^{68} +5307.86i q^{69} -4494.41 q^{71} +(-305.470 - 529.090i) q^{72} +(-7767.32 - 4484.46i) q^{73} +(-795.121 + 1377.19i) q^{74} +(-230.957 + 133.343i) q^{75} -307.148i q^{76} -1531.59 q^{78} +(5223.41 + 9047.22i) q^{79} +(-1327.53 - 766.449i) q^{80} +(-364.500 + 631.333i) q^{81} +(-2506.31 + 1447.02i) q^{82} -1269.28i q^{83} -2579.00 q^{85} +(-4783.45 - 8285.17i) q^{86} +(2797.21 + 1614.97i) q^{87} +(1108.41 - 1919.82i) q^{88} +(3121.46 - 1802.18i) q^{89} +1829.12i q^{90} -8171.99 q^{92} +(3946.83 + 6836.11i) q^{93} +(9663.32 + 5579.12i) q^{94} +(-459.792 + 796.383i) q^{95} +(814.587 - 470.302i) q^{96} +1950.53i q^{97} -2645.21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} - 16 q^{4} + 66 q^{5} + 54 q^{9}+O(q^{10}) $ 4 * q + 18 * q^3 - 16 * q^4 + 66 * q^5 + 54 * q^9	$ 4 q + 18 q^{3} - 16 q^{4} + 66 q^{5} + 54 q^{9} + 48 q^{10} - 162 q^{11} - 144 q^{12} + 396 q^{15} - 128 q^{16} + 204 q^{17} + 444 q^{19} - 192 q^{22} + 312 q^{23} - 476 q^{25} - 1632 q^{26} + 2724 q^{29} + 144 q^{30} + 3786 q^{31} - 1458 q^{33} - 864 q^{36} + 1396 q^{37} - 1632 q^{38} + 648 q^{39} - 384 q^{40} - 632 q^{43} - 1296 q^{44} + 1782 q^{45} - 4896 q^{46} + 7896 q^{47} + 2112 q^{50} + 612 q^{51} + 1728 q^{52} - 1038 q^{53} + 2664 q^{57} - 336 q^{58} + 966 q^{59} - 1584 q^{60} - 5088 q^{61} + 2048 q^{64} - 744 q^{65} - 864 q^{66} + 14600 q^{67} - 1632 q^{68} - 9696 q^{71} - 22584 q^{73} + 768 q^{74} - 4284 q^{75} - 9792 q^{78} + 3974 q^{79} - 4224 q^{80} - 1458 q^{81} - 18816 q^{82} + 1224 q^{85} - 18240 q^{86} + 12258 q^{87} + 768 q^{88} + 33156 q^{89} - 4992 q^{92} + 11358 q^{93} + 16320 q^{94} + 3252 q^{95} - 8748 q^{99}+O(q^{100}) $ 4 * q + 18 * q^3 - 16 * q^4 + 66 * q^5 + 54 * q^9 + 48 * q^10 - 162 * q^11 - 144 * q^12 + 396 * q^15 - 128 * q^16 + 204 * q^17 + 444 * q^19 - 192 * q^22 + 312 * q^23 - 476 * q^25 - 1632 * q^26 + 2724 * q^29 + 144 * q^30 + 3786 * q^31 - 1458 * q^33 - 864 * q^36 + 1396 * q^37 - 1632 * q^38 + 648 * q^39 - 384 * q^40 - 632 * q^43 - 1296 * q^44 + 1782 * q^45 - 4896 * q^46 + 7896 * q^47 + 2112 * q^50 + 612 * q^51 + 1728 * q^52 - 1038 * q^53 + 2664 * q^57 - 336 * q^58 + 966 * q^59 - 1584 * q^60 - 5088 * q^61 + 2048 * q^64 - 744 * q^65 - 864 * q^66 + 14600 * q^67 - 1632 * q^68 - 9696 * q^71 - 22584 * q^73 + 768 * q^74 - 4284 * q^75 - 9792 * q^78 + 3974 * q^79 - 4224 * q^80 - 1458 * q^81 - 18816 * q^82 + 1224 * q^85 - 18240 * q^86 + 12258 * q^87 + 768 * q^88 + 33156 * q^89 - 4992 * q^92 + 11358 * q^93 + 16320 * q^94 + 3252 * q^95 - 8748 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.41421	+	2.44949i	0.353553	+	0.612372i
$2$	1.41421	+	2.44949i	0.353553	+	0.612372i
$3$	4.50000	+	2.59808i	0.500000	+	0.288675i
$3$	4.50000	+	2.59808i	0.500000	+	0.288675i
$4$	−4.00000	+	6.92820i	−0.250000	+	0.433013i
$5$	20.7426	−	11.9758i	0.829706	−	0.479031i	−0.0240462	−	0.999711i	$-0.507655\pi$
$5$	20.7426	−	11.9758i	0.829706	−	0.479031i	0.853752	+	0.520680i	$0.174322\pi$
$6$			14.6969i			0.408248i
$7$		0			0
$7$		0			0
$8$	−22.6274			−0.353553
$9$	13.5000	+	23.3827i	0.166667	+	0.288675i
$10$	58.6690	+	33.8726i	0.586690	+	0.338726i
$11$	−48.9853	+	84.8450i	−0.404837	+	0.701198i	−0.994302	−	0.106595i	$-0.966005\pi$
$11$	−48.9853	+	84.8450i	−0.404837	+	0.701198i	0.589465	+	0.807794i	$0.299338\pi$
$12$	−36.0000	+	20.7846i	−0.250000	+	0.144338i
$13$			104.211i			0.616636i	0.951283	+	0.308318i	$0.0997661\pi$
$13$			104.211i			0.616636i	−0.951283	+	0.308318i	$0.900234\pi$
$14$		0			0
$15$	124.456			0.553137
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−93.2498	−	53.8378i	−0.322664	−	0.186290i	0.329916	−	0.944010i	$-0.392980\pi$
$17$	−93.2498	−	53.8378i	−0.322664	−	0.186290i	−0.652579	+	0.757721i	$0.726313\pi$
$18$	−38.1838	+	66.1362i	−0.117851	+	0.204124i
$19$	−33.2498	+	19.1968i	−0.0921047	+	0.0531767i	−0.545345	−	0.838212i	$-0.683601\pi$
$19$	−33.2498	+	19.1968i	−0.0921047	+	0.0531767i	0.453240	+	0.891388i	$0.350268\pi$
$20$			191.612i			0.479031i
$21$		0			0
$22$	−277.103			−0.572526
$23$	510.749	+	884.644i	0.965500	+	1.67229i	0.708266	+	0.705945i	$0.249478\pi$
$23$	510.749	+	884.644i	0.965500	+	1.67229i	0.257233	+	0.966349i	$0.417189\pi$
$24$	−101.823	−	58.7878i	−0.176777	−	0.102062i
$25$	−25.6619	+	44.4477i	−0.0410590	+	0.0711164i
$26$	−255.265	+	147.377i	−0.377611	+	0.218014i
$27$			140.296i			0.192450i
$28$		0			0
$29$	621.603			0.739124			0.369562	−	0.929206i	$-0.379508\pi$
$29$	621.603			0.739124			0.369562	+	0.929206i	$0.379508\pi$
$30$	176.007	+	304.853i	0.195563	+	0.338726i
$31$	1315.61	+	759.568i	1.36900	+	0.790393i	0.990800	−	0.135331i	$-0.0432097\pi$
$31$	1315.61	+	759.568i	1.36900	+	0.790393i	0.378200	+	0.925724i	$0.376543\pi$
$32$	90.5097	−	156.767i	0.0883883	−	0.153093i
$33$	−440.868	+	254.535i	−0.404837	+	0.233733i
$34$		−	304.553i		−	0.263454i
$35$		0			0
$36$	−216.000			−0.166667
$37$	281.118	+	486.910i	0.205345	+	0.355669i	0.950243	−	0.311511i	$-0.100835\pi$
$37$	281.118	+	486.910i	0.205345	+	0.355669i	−0.744897	+	0.667179i	$0.767502\pi$
$38$	−94.0446	−	54.2967i	−0.0651278	−	0.0376016i
$39$	−270.749	+	468.952i	−0.178007	+	0.308318i
$40$	−469.352	+	270.981i	−0.293345	+	0.169363i
$41$			1023.20i			0.608684i	0.952563	+	0.304342i	$0.0984365\pi$
$41$			1023.20i			0.608684i	−0.952563	+	0.304342i	$0.901563\pi$
$42$		0			0
$43$	−3382.41			−1.82932			−0.914658	−	0.404228i	$-0.867540\pi$
$43$	−3382.41			−1.82932			−0.914658	+	0.404228i	$0.867540\pi$
$44$	−391.882	−	678.760i	−0.202419	−	0.350599i
$45$	560.051	+	323.346i	0.276569	+	0.159677i
$46$	−1444.62	+	2502.15i	−0.682711	+	1.18249i
$47$	3416.50	−	1972.52i	1.54663	−	0.892945i	0.548231	−	0.836327i	$-0.315302\pi$
$47$	3416.50	−	1972.52i	1.54663	−	0.892945i	0.998396	−	0.0566179i	$-0.0180317\pi$
$48$		−	332.554i		−	0.144338i
$49$		0			0
$50$	−145.166			−0.0580663
$51$	−279.749	−	484.540i	−0.107555	−	0.186290i
$52$	−721.998	−	416.846i	−0.267011	−	0.154159i
$53$	−1095.30	+	1897.12i	−0.389925	+	0.675370i	−0.992439	−	0.122738i	$-0.960833\pi$
$53$	−1095.30	+	1897.12i	−0.389925	+	0.675370i	0.602514	+	0.798108i	$0.294166\pi$
$54$	−343.654	+	198.409i	−0.117851	+	0.0680414i
$55$			2346.55i			0.775718i
$56$		0			0
$57$	−199.499			−0.0614031
$58$	879.079	+	1522.61i	0.261320	+	0.452619i
$59$	−2541.67	−	1467.44i	−0.730156	−	0.421556i	0.0883234	−	0.996092i	$-0.471849\pi$
$59$	−2541.67	−	1467.44i	−0.730156	−	0.421556i	−0.818479	+	0.574536i	$0.805182\pi$
$60$	−497.823	+	862.255i	−0.138284	+	0.239515i
$61$	−576.207	+	332.673i	−0.154853	+	0.0894043i	−0.575424	−	0.817855i	$-0.695163\pi$
$61$	−576.207	+	332.673i	−0.154853	+	0.0894043i	0.420571	+	0.907259i	$0.361830\pi$
$62$			4296.76i			1.11778i
$63$		0			0
$64$	512.000			0.125000
$65$	1248.01	+	2161.62i	0.295388	+	0.511626i
$66$	−1246.96	−	719.934i	−0.286263	−	0.165274i
$67$	2962.69	−	5131.53i	0.659989	−	1.14314i	−0.320629	−	0.947205i	$-0.603894\pi$
$67$	2962.69	−	5131.53i	0.659989	−	1.14314i	0.980618	−	0.195930i	$-0.0627726\pi$
$68$	745.998	−	430.702i	0.161332	−	0.0931450i
$69$			5307.86i			1.11486i
$70$		0			0
$71$	−4494.41			−0.891571			−0.445785	−	0.895140i	$-0.647076\pi$
$71$	−4494.41			−0.891571			−0.445785	+	0.895140i	$0.647076\pi$
$72$	−305.470	−	529.090i	−0.0589256	−	0.102062i
$73$	−7767.32	−	4484.46i	−1.45756	−	0.841521i	−0.458666	−	0.888609i	$-0.651673\pi$
$73$	−7767.32	−	4484.46i	−1.45756	−	0.841521i	−0.998891	+	0.0470879i	$0.985006\pi$
$74$	−795.121	+	1377.19i	−0.145201	+	0.251496i
$75$	−230.957	+	133.343i	−0.0410590	+	0.0237055i
$76$		−	307.148i		−	0.0531767i
$77$		0			0
$78$	−1531.59			−0.251741
$79$	5223.41	+	9047.22i	0.836951	+	1.44964i	0.892432	+	0.451182i	$0.148998\pi$
$79$	5223.41	+	9047.22i	0.836951	+	1.44964i	−0.0554805	+	0.998460i	$0.517669\pi$
$80$	−1327.53	−	766.449i	−0.207426	−	0.119758i
$81$	−364.500	+	631.333i	−0.0555556	+	0.0962250i
$82$	−2506.31	+	1447.02i	−0.372741	+	0.215202i
$83$		−	1269.28i		−	0.184247i	−0.995748	−	0.0921234i	$-0.970635\pi$
$83$		−	1269.28i		−	0.184247i	0.995748	−	0.0921234i	$-0.0293654\pi$
$84$		0			0
$85$	−2579.00			−0.356954
$86$	−4783.45	−	8285.17i	−0.646761	−	1.12022i
$87$	2797.21	+	1614.97i	0.369562	+	0.213367i
$88$	1108.41	−	1919.82i	0.143132	−	0.247911i
$89$	3121.46	−	1802.18i	0.394074	−	0.227519i	−0.289850	−	0.957072i	$-0.593605\pi$
$89$	3121.46	−	1802.18i	0.394074	−	0.227519i	0.683924	+	0.729553i	$0.260272\pi$
$90$			1829.12i			0.225817i
$91$		0			0
$92$	−8171.99			−0.965500
$93$	3946.83	+	6836.11i	0.456334	+	0.790393i
$94$	9663.32	+	5579.12i	1.09363	+	0.631408i
$95$	−459.792	+	796.383i	−0.0509465	+	0.0882419i
$96$	814.587	−	470.302i	0.0883883	−	0.0510310i
$97$			1950.53i			0.207304i	0.994614	+	0.103652i	$0.0330529\pi$
$97$			1950.53i			0.207304i	−0.994614	+	0.103652i	$0.966947\pi$
$98$		0			0
$99$	−2645.21			−0.269891
$100$	−205.295	−	355.582i	−0.0205295	−	0.0355582i
$101$	−9808.81	−	5663.12i	−0.961554	−	0.555153i	−0.0649030	−	0.997892i	$-0.520674\pi$
$101$	−9808.81	−	5663.12i	−0.961554	−	0.555153i	−0.896651	+	0.442738i	$0.854007\pi$
$102$	791.251	−	1370.49i	0.0760525	−	0.131727i
$103$	14141.2	−	8164.43i	1.33294	−	0.769576i	0.347195	−	0.937793i	$-0.387134\pi$
$103$	14141.2	−	8164.43i	1.33294	−	0.769576i	0.985750	+	0.168217i	$0.0538010\pi$
$104$		−	2358.04i		−	0.218014i
$105$		0			0
$106$	−6195.95			−0.551438
$107$	−2198.23	−	3807.45i	−0.192002	−	0.332557i	0.753912	−	0.656976i	$-0.228165\pi$
$107$	−2198.23	−	3807.45i	−0.192002	−	0.332557i	−0.945914	+	0.324419i	$0.894831\pi$
$108$	−972.000	−	561.184i	−0.0833333	−	0.0481125i
$109$	7348.89	−	12728.6i	0.618541	−	1.07134i	−0.371211	−	0.928548i	$-0.621057\pi$
$109$	7348.89	−	12728.6i	0.618541	−	1.07134i	0.989752	−	0.142796i	$-0.0456093\pi$
$110$	−5747.84	+	3318.52i	−0.475028	+	0.274258i
$111$			2921.46i			0.237112i
$112$		0			0
$113$	2124.36			0.166368			0.0831842	−	0.996534i	$-0.473491\pi$
$113$	2124.36			0.166368			0.0831842	+	0.996534i	$0.473491\pi$
$114$	−282.134	−	488.670i	−0.0217093	−	0.0376016i
$115$	21188.6	+	12233.2i	1.60216	+	0.925008i
$116$	−2486.41	+	4306.59i	−0.184781	+	0.320050i
$117$	−2436.74	+	1406.85i	−0.178007	+	0.102773i
$118$		−	8301.07i		−	0.596170i
$119$		0			0
$120$	−2816.11			−0.195563
$121$	2521.38	+	4367.17i	0.172214	+	0.298283i
$122$	−1629.76	−	940.942i	−0.109497	−	0.0632184i
$123$	−2658.35	+	4604.39i	−0.175712	+	0.304342i
$124$	−10524.9	+	6076.54i	−0.684500	+	0.395196i
$125$			16199.0i			1.03674i
$126$		0			0
$127$	8498.07			0.526881			0.263441	−	0.964676i	$-0.415143\pi$
$127$	8498.07			0.526881			0.263441	+	0.964676i	$0.415143\pi$
$128$	724.077	+	1254.14i	0.0441942	+	0.0765466i
$129$	−15220.8	−	8787.75i	−0.914658	−	0.528078i
$130$	−3529.91	+	6113.99i	−0.208871	+	0.361774i
$131$	−12533.4	+	7236.14i	−0.730340	+	0.421662i	−0.818547	−	0.574440i	$-0.805220\pi$
$131$	−12533.4	+	7236.14i	−0.730340	+	0.421662i	0.0882063	+	0.996102i	$0.471887\pi$
$132$		−	4072.56i		−	0.233733i
$133$		0			0
$134$	16759.5			0.933366
$135$	1680.15	+	2910.11i	0.0921895	+	0.159677i
$136$	2110.00	+	1218.21i	0.114079	+	0.0658634i
$137$	−6427.59	+	11132.9i	−0.342458	+	0.593154i	−0.984888	−	0.173190i	$-0.944593\pi$
$137$	−6427.59	+	11132.9i	−0.342458	+	0.593154i	0.642431	+	0.766344i	$0.277926\pi$
$138$	−13001.6	+	7506.45i	−0.682711	+	0.394164i
$139$		−	5009.46i		−	0.259275i	−0.991561	−	0.129638i	$-0.958619\pi$
$139$		−	5009.46i		−	0.259275i	0.991561	−	0.129638i	$-0.0413814\pi$
$140$		0			0
$141$	20499.0			1.03108
$142$	−6356.05	−	11009.0i	−0.315218	−	0.545973i
$143$	−8841.82	−	5104.83i	−0.432384	−	0.249637i
$144$	864.000	−	1496.49i	0.0416667	−	0.0721688i
$145$	12893.7	−	7444.17i	0.613255	−	0.354063i
$146$		−	25368.0i		−	1.19009i
$147$		0			0
$148$	−4497.88			−0.205345
$149$	−12699.5	−	21996.1i	−0.572022	−	0.990771i	−0.996358	−	0.0852664i	$-0.972826\pi$
$149$	−12699.5	−	21996.1i	−0.572022	−	0.990771i	0.424336	−	0.905505i	$-0.360507\pi$
$150$	−653.245	−	377.151i	−0.0290331	−	0.0167623i
$151$	9154.39	−	15855.9i	0.401491	−	0.695402i	−0.592415	−	0.805633i	$-0.701826\pi$
$151$	9154.39	−	15855.9i	0.401491	−	0.695402i	0.993906	+	0.110230i	$0.0351589\pi$
$152$	752.357	−	434.373i	0.0325639	−	0.0188008i
$153$		−	2907.24i		−	0.124193i
$154$		0			0
$155$	36385.6			1.51449
$156$	−2165.99	−	3751.61i	−0.0890037	−	0.154159i
$157$	30522.6	+	17622.2i	1.23829	+	0.714926i	0.968744	−	0.248062i	$-0.0797935\pi$
$157$	30522.6	+	17622.2i	1.23829	+	0.714926i	0.269544	+	0.962988i	$0.413127\pi$
$158$	−14774.0	+	25589.4i	−0.591814	+	1.02505i
$159$	−9857.70	+	5691.35i	−0.389925	+	0.225123i
$160$		−	4335.69i		−	0.169363i
$161$		0			0
$162$	−2061.92			−0.0785674
$163$	−72.9693	−	126.386i	−0.00274641	−	0.00475691i	0.864649	−	0.502377i	$-0.167541\pi$
$163$	−72.9693	−	126.386i	−0.00274641	−	0.00475691i	−0.867395	+	0.497620i	$0.834208\pi$
$164$	−7088.92	−	4092.79i	−0.263568	−	0.152171i
$165$	−6096.50	+	10559.5i	−0.223930	+	0.387859i
$166$	3109.08	−	1795.03i	0.112828	−	0.0651411i
$167$		−	31314.1i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$167$		−	31314.1i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$168$		0			0
$169$	17701.0			0.619760
$170$	−3647.25	−	6317.22i	−0.126202	−	0.218589i
$171$	−897.744	−	518.313i	−0.0307016	−	0.0177256i
$172$	13529.6	−	23434.0i	0.457329	−	0.792117i
$173$	34741.3	−	20057.9i	1.16079	−	0.670183i	0.209298	−	0.977852i	$-0.432882\pi$
$173$	34741.3	−	20057.9i	1.16079	−	0.670183i	0.951494	+	0.307669i	$0.0995489\pi$
$174$			9135.66i			0.301746i
$175$		0			0
$176$	6270.12			0.202419
$177$	−7625.02	−	13206.9i	−0.243385	−	0.421556i
$178$	8828.83	+	5097.33i	0.278653	+	0.160880i
$179$	25077.2	−	43435.0i	0.782661	−	1.35561i	−0.147726	−	0.989028i	$-0.547195\pi$
$179$	25077.2	−	43435.0i	0.782661	−	1.35561i	0.930387	−	0.366580i	$-0.119471\pi$
$180$	−4480.41	+	2586.77i	−0.138284	+	0.0798385i
$181$		−	63974.3i		−	1.95276i	−0.216069	−	0.976378i	$-0.569323\pi$
$181$		−	63974.3i		−	1.95276i	0.216069	−	0.976378i	$-0.430677\pi$
$182$		0			0
$183$	−3457.24			−0.103235
$184$	−11556.9	−	20017.2i	−0.341356	−	0.591245i
$185$	11662.2	+	6733.20i	0.340752	+	0.196733i
$186$	−11163.3	+	19335.4i	−0.322677	+	0.558892i
$187$	9135.73	−	5274.52i	0.261252	−	0.150834i
$188$			31560.3i			0.892945i
$189$		0			0
$190$	−2600.98			−0.0720492
$191$	21384.4	+	37039.0i	0.586180	+	1.01529i	0.994727	+	0.102557i	$0.0327024\pi$
$191$	21384.4	+	37039.0i	0.586180	+	1.01529i	−0.408547	+	0.912737i	$0.633964\pi$
$192$	2304.00	+	1330.22i	0.0625000	+	0.0360844i
$193$	4386.29	−	7597.28i	0.117756	−	0.203959i	−0.801122	−	0.598501i	$-0.795763\pi$
$193$	4386.29	−	7597.28i	0.117756	−	0.203959i	0.918878	+	0.394542i	$0.129097\pi$
$194$	−4777.80	+	2758.46i	−0.126947	+	0.0732932i
$195$			12969.7i			0.341084i
$196$		0			0
$197$	−32825.0			−0.845808			−0.422904	−	0.906174i	$-0.638989\pi$
$197$	−32825.0			−0.845808			−0.422904	+	0.906174i	$0.638989\pi$
$198$	−3740.89	−	6479.40i	−0.0954210	−	0.165274i
$199$	22918.7	+	13232.1i	0.578740	+	0.334136i	0.760632	−	0.649183i	$-0.224889\pi$
$199$	22918.7	+	13232.1i	0.578740	+	0.334136i	−0.181893	+	0.983318i	$0.558222\pi$
$200$	580.663	−	1005.74i	0.0145166	−	0.0251434i
$201$	26664.2	−	15394.6i	0.659989	−	0.381045i
$202$		−	32035.4i		−	0.785106i
$203$		0			0
$204$	4475.99			0.107555
$205$	12253.6	+	21223.8i	0.291578	+	0.505028i
$206$	39997.4	+	23092.5i	0.942534	+	0.544172i
$207$	−13790.2	+	23885.4i	−0.321833	+	0.557432i
$208$	5775.99	−	3334.77i	0.133506	−	0.0770795i
$209$		−	3761.44i		−	0.0861115i
$210$		0			0
$211$	67056.3			1.50617			0.753087	−	0.657921i	$-0.228564\pi$
$211$	67056.3			1.50617			0.753087	+	0.657921i	$0.228564\pi$
$212$	−8762.40	−	15176.9i	−0.194963	−	0.337685i
$213$	−20224.8	−	11676.8i	−0.445785	−	0.257374i
$214$	6217.54	−	10769.1i	0.135766	−	0.235154i
$215$	−70160.1	+	40506.9i	−1.51779	+	0.876299i
$216$		−	3174.54i		−	0.0680414i
$217$		0			0
$218$	41571.6			0.874749
$219$	−23302.0	−	40360.2i	−0.485852	−	0.841521i
$220$	−16257.3	−	9386.18i	−0.335896	−	0.193929i
$221$	5610.52	−	9717.70i	0.114873	−	0.198966i
$222$	−7156.09	+	4131.57i	−0.145201	+	0.0838319i
$223$		−	56260.1i		−	1.13133i	−0.824634	−	0.565666i	$-0.808619\pi$
$223$		−	56260.1i		−	1.13133i	0.824634	−	0.565666i	$-0.191381\pi$
$224$		0			0
$225$	−1385.74			−0.0273727
$226$	3004.30	+	5203.59i	0.0588201	+	0.101879i
$227$	−52955.8	−	30574.1i	−1.02769	−	0.593337i	−0.111368	−	0.993779i	$-0.535523\pi$
$227$	−52955.8	−	30574.1i	−1.02769	−	0.593337i	−0.916322	+	0.400442i	$0.868857\pi$
$228$	797.995	−	1382.17i	0.0153508	−	0.0265883i
$229$	−29274.9	+	16901.9i	−0.558244	+	0.322303i	−0.752441	−	0.658660i	$-0.771123\pi$
$229$	−29274.9	+	16901.9i	−0.558244	+	0.322303i	0.194196	+	0.980963i	$0.437790\pi$
$230$			69201.6i			1.30816i
$231$		0			0
$232$	−14065.3			−0.261320
$233$	−4343.63	−	7523.39i	−0.0800094	−	0.138580i	0.823244	−	0.567687i	$-0.192162\pi$
$233$	−4343.63	−	7523.39i	−0.0800094	−	0.138580i	−0.903254	+	0.429107i	$0.858828\pi$
$234$	−6892.15	−	3979.19i	−0.125870	−	0.0726712i
$235$	47244.8	−	81830.4i	0.855496	−	1.48176i
$236$	20333.4	−	11739.5i	0.365078	−	0.210778i
$237$			54283.3i			0.966428i
$238$		0			0
$239$	−15715.0			−0.275118			−0.137559	−	0.990494i	$-0.543926\pi$
$239$	−15715.0			−0.275118			−0.137559	+	0.990494i	$0.543926\pi$
$240$	−3982.59	−	6898.04i	−0.0691421	−	0.119758i
$241$	4744.80	+	2739.41i	0.0816928	+	0.0471654i	0.540290	−	0.841479i	$-0.318315\pi$
$241$	4744.80	+	2739.41i	0.0816928	+	0.0471654i	−0.458597	+	0.888644i	$0.651648\pi$
$242$	−7131.55	+	12352.2i	−0.121774	+	0.210918i
$243$	−3280.50	+	1894.00i	−0.0555556	+	0.0320750i
$244$		−	5322.77i		−	0.0894043i
$245$		0			0
$246$	−15037.9			−0.248494
$247$	−2000.52	−	3465.01i	−0.0327906	−	0.0567950i
$248$	−29768.9	−	17187.1i	−0.484015	−	0.279446i
$249$	3297.68	−	5711.74i	0.0531875	−	0.0921234i
$250$	−39679.3	+	22908.8i	−0.634868	+	0.366541i
$251$			24350.9i			0.386516i	0.981148	+	0.193258i	$0.0619054\pi$
$251$			24350.9i			0.386516i	−0.981148	+	0.193258i	$0.938095\pi$
$252$		0			0
$253$	−100077.			−1.56348
$254$	12018.1	+	20815.9i	0.186281	+	0.322647i
$255$	−11605.5	−	6700.43i	−0.178477	−	0.103044i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−10051.7	+	5803.37i	−0.152186	+	0.0878647i	−0.574159	−	0.818744i	$-0.694671\pi$
$257$	−10051.7	+	5803.37i	−0.152186	+	0.0878647i	0.421973	+	0.906608i	$0.361338\pi$
$258$		−	49711.0i		−	0.746815i
$259$		0			0
$260$	−19968.2			−0.295388
$261$	8391.64	+	14534.7i	0.123187	+	0.213367i
$262$	−35449.7	−	20466.9i	−0.516429	−	0.298160i
$263$	−60333.8	+	104501.i	−0.872266	+	1.51081i	−0.0126200	+	0.999920i	$0.504017\pi$
$263$	−60333.8	+	104501.i	−0.872266	+	1.51081i	−0.859646	+	0.510889i	$0.829316\pi$
$264$	9975.69	−	5759.47i	0.143132	−	0.0826370i
$265$			52468.3i			0.747145i
$266$		0			0
$267$	18728.8			0.262716
$268$	23701.5	+	41052.3i	0.329995	+	0.571568i
$269$	23596.3	+	13623.3i	0.326091	+	0.188269i	0.654104	−	0.756404i	$-0.273046\pi$
$269$	23596.3	+	13623.3i	0.326091	+	0.188269i	−0.328013	+	0.944673i	$0.606379\pi$
$270$	−4752.19	+	8231.04i	−0.0651878	+	0.112909i
$271$	84041.9	−	48521.6i	1.14435	−	0.660689i	0.196843	−	0.980435i	$-0.436931\pi$
$271$	84041.9	−	48521.6i	1.14435	−	0.660689i	0.947503	+	0.319746i	$0.103598\pi$
$272$			6891.24i			0.0931450i
$273$		0			0
$274$	−36359.9			−0.484308
$275$	−2514.11	−	4354.57i	−0.0332444	−	0.0575811i
$276$	−36774.0	−	21231.5i	−0.482750	−	0.278716i
$277$	−14876.4	+	25766.7i	−0.193882	+	0.335814i	−0.946534	−	0.322605i	$-0.895441\pi$
$277$	−14876.4	+	25766.7i	−0.193882	+	0.335814i	0.752651	+	0.658419i	$0.228775\pi$
$278$	12270.6	−	7084.44i	0.158773	−	0.0916676i
$279$			41016.7i			0.526929i
$280$		0			0
$281$	−122275.			−1.54855			−0.774276	−	0.632849i	$-0.781886\pi$
$281$	−122275.			−1.54855			−0.774276	+	0.632849i	$0.781886\pi$
$282$	28989.9	+	50212.1i	0.364543	+	0.631408i
$283$	52568.4	+	30350.4i	0.656374	+	0.378958i	0.790894	−	0.611953i	$-0.209616\pi$
$283$	52568.4	+	30350.4i	0.656374	+	0.378958i	−0.134520	+	0.990911i	$0.542949\pi$
$284$	17977.6	−	31138.2i	0.222893	−	0.386062i
$285$	−4138.13	+	2389.15i	−0.0509465	+	0.0294140i
$286$		−	28877.3i		−	0.353040i
$287$		0			0
$288$	4887.52			0.0589256
$289$	−35963.5	−	62290.6i	−0.430592	−	0.745807i
$290$	36468.9	+	21055.3i	0.433637	+	0.250360i
$291$	−5067.62	+	8777.37i	−0.0598436	+	0.103652i
$292$	62138.6	−	35875.7i	0.728778	−	0.420760i
$293$			29557.4i			0.344296i	0.985071	+	0.172148i	$0.0550707\pi$
$293$			29557.4i			0.344296i	−0.985071	+	0.172148i	$0.944929\pi$
$294$		0			0
$295$	−70294.7			−0.807752
$296$	−6360.97	−	11017.5i	−0.0726005	−	0.125748i
$297$	−11903.4	−	6872.44i	−0.134946	−	0.0779109i
$298$	35919.5	−	62214.4i	0.404481	−	0.700581i
$299$	−92190.0	+	53225.9i	−1.03120	+	0.595362i
$300$		−	2133.49i		−	0.0237055i
$301$		0			0
$302$	51785.0			0.567794
$303$	−29426.4	−	50968.1i	−0.320518	−	0.555153i
$304$	2127.99	+	1228.59i	0.0230262	+	0.0132942i
$305$	−7968.04	+	13801.0i	−0.0856548	+	0.148358i
$306$	7121.26	−	4111.46i	0.0760525	−	0.0439090i
$307$			107567.i			1.14131i	0.821191	+	0.570654i	$0.193310\pi$
$307$			107567.i			1.14131i	−0.821191	+	0.570654i	$0.806690\pi$
$308$		0			0
$309$	84847.3			0.888630
$310$	51457.0	+	89126.2i	0.535453	+	0.927432i
$311$	−37561.0	−	21685.9i	−0.388344	−	0.224211i	0.293098	−	0.956082i	$-0.405314\pi$
$311$	−37561.0	−	21685.9i	−0.388344	−	0.224211i	−0.681442	+	0.731872i	$0.738647\pi$
$312$	6126.36	−	10611.2i	0.0629351	−	0.109007i
$313$	93311.1	−	53873.2i	0.952455	−	0.549900i	0.0586125	−	0.998281i	$-0.481332\pi$
$313$	93311.1	−	53873.2i	0.952455	−	0.549900i	0.893843	+	0.448381i	$0.147999\pi$
$314$			99686.3i			1.01106i
$315$		0			0
$316$	−83574.6			−0.836951
$317$	77996.9	+	135095.i	0.776174	+	1.34437i	0.934133	+	0.356926i	$0.116175\pi$
$317$	77996.9	+	135095.i	0.776174	+	1.34437i	−0.157959	+	0.987446i	$0.550491\pi$
$318$	−27881.8	−	16097.6i	−0.275719	−	0.159186i
$319$	−30449.4	+	52739.9i	−0.299225	+	0.518272i
$320$	10620.2	−	6131.59i	0.103713	−	0.0598788i
$321$		−	22844.7i		−	0.221705i
$322$		0			0
$323$	4134.05			0.0396251
$324$	−2916.00	−	5050.66i	−0.0277778	−	0.0481125i
$325$	−4631.96	−	2674.26i	−0.0438529	−	0.0253185i
$326$	206.388	−	357.475i	0.00194200	−	0.00336365i
$327$	66140.0	−	38185.9i	0.618541	−	0.357115i
$328$		−	23152.3i		−	0.215202i
$329$		0			0
$330$	−34487.0			−0.316685
$331$	−20109.4	−	34830.4i	−0.183545	−	0.317909i	0.759540	−	0.650460i	$-0.225424\pi$
$331$	−20109.4	−	34830.4i	−0.183545	−	0.317909i	−0.943085	+	0.332551i	$0.892091\pi$
$332$	8793.80	+	5077.10i	0.0797812	+	0.0460617i
$333$	−7590.18	+	13146.6i	−0.0684484	+	0.118556i
$334$	76703.5	−	44284.8i	0.687578	−	0.396974i
$335$		−	141922.i		−	1.26462i
$336$		0			0
$337$	90476.4			0.796665			0.398332	−	0.917241i	$-0.369589\pi$
$337$	90476.4			0.796665			0.398332	+	0.917241i	$0.369589\pi$
$338$	25033.0	+	43358.3i	0.219118	+	0.379524i
$339$	9559.61	+	5519.25i	0.0831842	+	0.0480264i
$340$	10316.0	−	17867.8i	0.0892386	−	0.154566i
$341$	−128891.	+	74415.3i	−1.10844	+	0.639961i
$342$		−	2932.02i		−	0.0250677i
$343$		0			0
$344$	76535.1			0.646761
$345$	63565.7	+	110099.i	0.534054	+	0.925008i
$346$	98263.3	+	56732.3i	0.820803	+	0.473891i
$347$	−16037.2	+	27777.3i	−0.133190	+	0.230691i	−0.924904	−	0.380200i	$-0.875855\pi$
$347$	−16037.2	+	27777.3i	−0.133190	+	0.230691i	0.791715	+	0.610891i	$0.209189\pi$
$348$	−22377.7	+	12919.8i	−0.184781	+	0.106683i
$349$			116783.i			0.958805i	0.877595	+	0.479402i	$0.159147\pi$
$349$			116783.i			0.958805i	−0.877595	+	0.479402i	$0.840853\pi$
$350$		0			0
$351$	−14620.5			−0.118672
$352$	8867.28	+	15358.6i	0.0715658	+	0.123956i
$353$	−107957.	−	62329.1i	−0.866367	−	0.500197i	−0.000227639	−	1.00000i	$-0.500072\pi$
$353$	−107957.	−	62329.1i	−0.866367	−	0.500197i	−0.866139	+	0.499803i	$0.833406\pi$
$354$	21566.8	−	37354.8i	0.172099	−	0.298085i
$355$	−93225.9	+	53824.0i	−0.739741	+	0.427090i
$356$			28834.8i			0.227519i
$357$		0			0
$358$	141858.			1.10685
$359$	−49721.0	−	86119.4i	−0.385790	−	0.668208i	0.606088	−	0.795397i	$-0.292738\pi$
$359$	−49721.0	−	86119.4i	−0.385790	−	0.668208i	−0.991878	+	0.127189i	$0.959404\pi$
$360$	−12672.5	−	7316.48i	−0.0977817	−	0.0564543i
$361$	−64423.5	+	111585.i	−0.494344	+	0.856230i
$362$	156704.	−	90473.3i	1.19581	−	0.690404i
$363$			26203.0i			0.198856i
$364$		0			0
$365$	−214820.			−1.61246
$366$	−4889.28	−	8468.48i	−0.0364991	−	0.0632184i
$367$	−77002.3	−	44457.3i	−0.571704	−	0.330074i	0.186126	−	0.982526i	$-0.440407\pi$
$367$	−77002.3	−	44457.3i	−0.571704	−	0.330074i	−0.757830	+	0.652452i	$0.773740\pi$
$368$	32688.0	−	56617.2i	0.241375	−	0.418074i
$369$	−23925.1	+	13813.2i	−0.175712	+	0.101447i
$370$			38088.7i			0.278223i
$371$		0			0
$372$	−63149.3			−0.456334
$373$	45676.4	+	79113.9i	0.328303	+	0.568637i	0.982175	−	0.187968i	$-0.0601900\pi$
$373$	45676.4	+	79113.9i	0.328303	+	0.568637i	−0.653872	+	0.756605i	$0.726857\pi$
$374$	25839.8	+	14918.6i	0.184733	+	0.106656i
$375$	−42086.2	+	72895.5i	−0.299280	+	0.518368i
$376$	−77306.5	+	44632.9i	−0.546815	+	0.315704i
$377$			64778.2i			0.455770i
$378$		0			0
$379$	6328.51			0.0440578			0.0220289	−	0.999757i	$-0.492987\pi$
$379$	6328.51			0.0440578			0.0220289	+	0.999757i	$0.492987\pi$
$380$	−3678.34	−	6371.07i	−0.0254733	−	0.0441210i
$381$	38241.3	+	22078.6i	0.263441	+	0.152097i
$382$	−60484.4	+	104762.i	−0.414492	+	0.717922i
$383$	11635.9	−	6717.98i	0.0793235	−	0.0457974i	−0.459814	−	0.888015i	$-0.652084\pi$
$383$	11635.9	−	6717.98i	0.0793235	−	0.0457974i	0.539137	+	0.842218i	$0.318750\pi$
$384$			7524.83i			0.0510310i
$385$		0			0
$386$	24812.6			0.166532
$387$	−45662.5	−	79089.8i	−0.304886	−	0.528078i
$388$	−13513.6	−	7802.11i	−0.0897654	−	0.0518261i
$389$	−44148.1	+	76466.8i	−0.291752	+	0.505328i	−0.974224	−	0.225583i	$-0.927571\pi$
$389$	−44148.1	+	76466.8i	−0.291752	+	0.505328i	0.682472	+	0.730911i	$0.260905\pi$
$390$	−31769.2	+	18342.0i	−0.208871	+	0.120591i
$391$		−	109990.i		−	0.719451i
$392$		0			0
$393$	−75200.2			−0.486894
$394$	−46421.5	−	80404.4i	−0.299038	−	0.517950i
$395$	216695.	+	125109.i	1.38885	+	0.801851i
$396$	10580.8	−	18326.5i	0.0674728	−	0.116866i
$397$	−187570.	+	108294.i	−1.19010	+	0.687103i	−0.958329	−	0.285668i	$-0.907785\pi$
$397$	−187570.	+	108294.i	−1.19010	+	0.687103i	−0.231769	+	0.972771i	$0.574451\pi$
$398$			74852.1i			0.472539i
$399$		0			0
$400$	3284.72			0.0205295
$401$	2583.42	+	4474.61i	0.0160659	+	0.0278270i	0.873947	−	0.486022i	$-0.161553\pi$
$401$	2583.42	+	4474.61i	0.0160659	+	0.0278270i	−0.857881	+	0.513849i	$0.828219\pi$
$402$	75417.8	+	43542.5i	0.466683	+	0.269440i
$403$	−79155.7	+	137102.i	−0.487385	+	0.844175i
$404$	78470.5	−	45305.0i	0.480777	−	0.277577i
$405$			17460.7i			0.106451i
$406$		0			0
$407$	−55082.5			−0.332526
$408$	6330.01	+	10963.9i	0.0380263	+	0.0658634i
$409$	−33697.7	−	19455.3i	−0.201443	−	0.116303i	0.395885	−	0.918300i	$-0.370438\pi$
$409$	−33697.7	−	19455.3i	−0.201443	−	0.116303i	−0.597329	+	0.801997i	$0.703771\pi$
$410$	−34658.4	+	60030.0i	−0.206177	+	0.357109i
$411$	−57848.3	+	33398.7i	−0.342458	+	0.197718i
$412$			130631.i			0.769576i
$413$		0			0
$414$	−78009.3			−0.455141
$415$	−15200.6	−	26328.1i	−0.0882599	−	0.152871i
$416$	16337.0	+	9432.15i	0.0944027	+	0.0545034i
$417$	13015.0	−	22542.6i	0.0748463	−	0.129638i
$418$	9213.60	−	5319.48i	0.0527323	−	0.0304450i
$419$		−	263425.i		−	1.50048i	−0.661167	−	0.750239i	$-0.729938\pi$
$419$		−	263425.i		−	1.50048i	0.661167	−	0.750239i	$-0.270062\pi$
$420$		0			0
$421$	−16375.1			−0.0923889			−0.0461944	−	0.998932i	$-0.514709\pi$
$421$	−16375.1			−0.0923889			−0.0461944	+	0.998932i	$0.514709\pi$
$422$	94832.0	+	164254.i	0.532513	+	0.922339i
$423$	92245.4	+	53257.9i	0.515542	+	0.297648i
$424$	24783.8	−	42926.8i	0.137859	−	0.238780i
$425$	4785.93	−	2763.16i	0.0264965	−	0.0152978i
$426$		−	66054.0i		−	0.363982i
$427$		0			0
$428$	35171.7			0.192002
$429$	−26525.5	−	45943.5i	−0.144128	−	0.249637i
$430$	−198443.	−	114571.i	−1.07324	−	0.619637i
$431$	125208.	−	216867.i	0.674028	−	1.16745i	−0.302724	−	0.953078i	$-0.597896\pi$
$431$	125208.	−	216867.i	0.674028	−	1.16745i	0.976752	−	0.214373i	$-0.0687708\pi$
$432$	7776.00	−	4489.48i	0.0416667	−	0.0240563i
$433$			91495.1i			0.488002i	0.969775	+	0.244001i	$0.0784601\pi$
$433$			91495.1i			0.488002i	−0.969775	+	0.244001i	$0.921540\pi$
$434$		0			0
$435$	77362.1			0.408837
$436$	58791.1	+	101829.i	0.309270	+	0.535672i
$437$	−33964.6	−	19609.5i	−0.177854	−	0.102684i
$438$	65907.9	−	114156.i	0.343549	−	0.595045i
$439$	−7672.44	+	4429.69i	−0.0398111	+	0.0229850i	−0.519773	−	0.854304i	$-0.673984\pi$
$439$	−7672.44	+	4429.69i	−0.0398111	+	0.0229850i	0.479962	+	0.877289i	$0.340650\pi$
$440$		−	53096.3i		−	0.274258i
$441$		0			0
$442$	31737.9			0.162455
$443$	−150105.	−	259989.i	−0.764868	−	1.32479i	−0.940316	−	0.340302i	$-0.889471\pi$
$443$	−150105.	−	259989.i	−0.764868	−	1.32479i	0.175448	−	0.984489i	$-0.443863\pi$
$444$	−20240.5	−	11685.8i	−0.102673	−	0.0592781i
$445$	43164.9	−	74763.9i	0.217977	−	0.377548i
$446$	137808.	−	79563.7i	0.692797	−	0.399987i
$447$		−	131977.i		−	0.660514i
$448$		0			0
$449$	116866.			0.579691			0.289846	−	0.957073i	$-0.406396\pi$
$449$	116866.			0.579691			0.289846	+	0.957073i	$0.406396\pi$
$450$	−1959.74	−	3394.36i	−0.00967771	−	0.0167623i
$451$	−86813.2	−	50121.6i	−0.426808	−	0.246418i
$452$	−8497.43	+	14718.0i	−0.0415921	+	0.0720396i
$453$	82389.5	−	47567.6i	0.401491	−	0.231801i
$454$		−	172953.i		−	0.839105i
$455$		0			0
$456$	4514.14			0.0217093
$457$	−36872.9	−	63865.7i	−0.176553	−	0.305798i	0.764145	−	0.645045i	$-0.223161\pi$
$457$	−36872.9	−	63865.7i	−0.176553	−	0.305798i	−0.940698	+	0.339246i	$0.889828\pi$
$458$	−82801.9	−	47805.7i	−0.394738	−	0.227902i
$459$	7553.23	−	13082.6i	0.0358515	−	0.0620966i
$460$	−169509.	+	97865.9i	−0.801081	+	0.462504i
$461$			88219.1i			0.415108i	0.978224	+	0.207554i	$0.0665502\pi$
$461$			88219.1i			0.415108i	−0.978224	+	0.207554i	$0.933450\pi$
$462$		0			0
$463$	297880.			1.38957			0.694784	−	0.719219i	$-0.255500\pi$
$463$	297880.			1.38957			0.694784	+	0.719219i	$0.255500\pi$
$464$	−19891.3	−	34452.7i	−0.0923905	−	0.160025i
$465$	163735.	+	94532.6i	0.757245	+	0.437196i
$466$	12285.6	−	21279.4i	0.0565752	−	0.0979911i
$467$	162353.	−	93734.8i	0.744436	−	0.429801i	−0.0792437	−	0.996855i	$-0.525251\pi$
$467$	162353.	−	93734.8i	0.744436	−	0.429801i	0.823680	+	0.567055i	$0.191917\pi$
$468$		−	22509.7i		−	0.102773i
$469$		0			0
$470$	267257.			1.20985
$471$	91567.7	+	158600.i	0.412763	+	0.714926i
$472$	57511.5	+	33204.3i	0.258149	+	0.149042i
$473$	165688.	−	286980.i	0.740575	−	1.28271i
$474$	−132966.	+	76768.2i	−0.591814	+	0.341684i
$475$		−	1970.50i		−	0.00873353i
$476$		0			0
$477$	−59146.2			−0.259950
$478$	−22224.4	−	38493.8i	−0.0972690	−	0.168475i
$479$	104347.	+	60244.5i	0.454786	+	0.262571i	0.709849	−	0.704354i	$-0.248763\pi$
$479$	104347.	+	60244.5i	0.454786	+	0.262571i	−0.255063	+	0.966924i	$0.582096\pi$
$480$	11264.5	−	19510.6i	0.0488909	−	0.0846815i
$481$	−50741.6	+	29295.7i	−0.219318	+	0.126623i
$482$			15496.4i			0.0667019i
$483$		0			0
$484$	−40342.2			−0.172214
$485$	23359.1	+	40459.1i	0.0993052	+	0.172002i
$486$	−9278.66	−	5357.03i	−0.0392837	−	0.0226805i
$487$	133697.	−	231570.i	0.563721	−	0.976393i	−0.433447	−	0.901179i	$-0.642703\pi$
$487$	133697.	−	231570.i	0.563721	−	0.976393i	0.997167	−	0.0752136i	$-0.0239639\pi$
$488$	13038.1	−	7527.54i	0.0547487	−	0.0316092i
$489$		−	758.319i		−	0.00317128i
$490$		0			0
$491$	178364.			0.739851			0.369926	−	0.929061i	$-0.379383\pi$
$491$	178364.			0.739851			0.369926	+	0.929061i	$0.379383\pi$
$492$	−21266.8	−	36835.1i	−0.0878560	−	0.152171i
$493$	−57964.3	−	33465.7i	−0.238488	−	0.137691i
$494$	5658.34	−	9800.53i	0.0231865	−	0.0401602i
$495$	−54868.5	+	31678.4i	−0.223930	+	0.129286i
$496$		−	97224.7i		−	0.395196i
$497$		0			0
$498$	18654.5			0.0752184
$499$	−131873.	−	228411.i	−0.529610	−	0.917311i	−0.999403	−	0.0345349i	$-0.989005\pi$
$499$	−131873.	−	228411.i	−0.529610	−	0.917311i	0.469794	−	0.882776i	$-0.344328\pi$
$500$	−112230.	−	64796.0i	−0.448920	−	0.259184i
$501$	81356.3	−	140913.i	0.324128	−	0.561405i
$502$	−59647.2	+	34437.4i	−0.236692	+	0.136654i
$503$		−	480056.i		−	1.89739i	−0.316197	−	0.948694i	$-0.602406\pi$
$503$		−	480056.i		−	1.89739i	0.316197	−	0.948694i	$-0.397594\pi$
$504$		0			0
$505$	−271281.			−1.06374
$506$	−141530.	−	245137.i	−0.552774	−	0.957432i
$507$	79654.4	+	45988.5i	0.309880	+	0.178909i
$508$	−33992.3	+	58876.3i	−0.131720	+	0.228146i
$509$	52192.6	−	30133.4i	0.201453	−	0.116309i	−0.395880	−	0.918302i	$-0.629560\pi$
$509$	52192.6	−	30133.4i	0.201453	−	0.116309i	0.597333	+	0.801993i	$0.296227\pi$
$510$		−	37903.3i		−	0.145726i
$511$		0			0
$512$	−11585.2			−0.0441942
$513$	−2693.23	−	4664.82i	−0.0102339	−	0.0177256i
$514$	−28430.6	−	16414.4i	−0.107612	−	0.0621297i
$515$	195551.	−	338704.i	0.737301	−	1.27704i
$516$	121767.	−	70302.0i	0.457329	−	0.264039i
$517$			386497.i			1.44599i
$518$		0			0
$519$	208448.			0.773861
$520$	−28239.3	−	48911.9i	−0.104435	−	0.180887i
$521$	−248823.	−	143658.i	−0.916674	−	0.529242i	−0.0341018	−	0.999418i	$-0.510857\pi$
$521$	−248823.	−	143658.i	−0.916674	−	0.529242i	−0.882573	+	0.470176i	$0.844190\pi$
$522$	−23735.1	+	41110.5i	−0.0871066	+	0.150873i
$523$	239407.	−	138222.i	0.875254	−	0.505328i	0.00616355	−	0.999981i	$-0.498038\pi$
$523$	239407.	−	138222.i	0.875254	−	0.505328i	0.869091	+	0.494653i	$0.164705\pi$
$524$		−	115778.i		−	0.421662i
$525$		0			0
$526$	−341300.			−1.23357
$527$	−81786.9	−	141659.i	−0.294484	−	0.510062i
$528$	28215.5	+	16290.2i	0.101209	+	0.0584332i
$529$	−381809.	+	661313.i	−1.36438	+	2.36317i
$530$	−128520.	+	74201.3i	−0.457531	+	0.264156i
$531$		−	79241.5i		−	0.281037i
$532$		0			0
$533$	−106629.			−0.375336
$534$	26486.5	+	45876.0i	0.0928842	+	0.160880i
$535$	−91194.3	−	52651.0i	−0.318610	−	0.183950i
$536$	−67038.1	+	116113.i	−0.233341	+	0.404159i
$537$	225695.	−	130305.i	0.782661	−	0.451869i
$538$			77065.1i			0.266252i
$539$		0			0
$540$	−26882.5			−0.0921895
$541$	29832.0	+	51670.6i	0.101927	+	0.176542i	0.912478	−	0.409125i	$-0.134166\pi$
$541$	29832.0	+	51670.6i	0.101927	+	0.176542i	−0.810552	+	0.585667i	$0.800833\pi$
$542$	237707.	+	137240.i	0.809175	+	0.467177i
$543$	166210.	−	287884.i	0.563712	−	0.976378i
$544$	−16880.0	+	9745.68i	−0.0570394	+	0.0329317i
$545$		−	352034.i		−	1.18520i
$546$		0			0
$547$	489585.			1.63627			0.818133	−	0.575030i	$-0.195010\pi$
$547$	489585.			1.63627			0.818133	+	0.575030i	$0.195010\pi$
$548$	−51420.7	−	89063.3i	−0.171229	−	0.296577i
$549$	−15557.6	−	8982.18i	−0.0516176	−	0.0298014i
$550$	7110.98	−	12316.6i	0.0235074	−	0.0407160i
$551$	−20668.2	+	11932.8i	−0.0680767	+	0.0393041i
$552$		−	120103.i		−	0.394164i
$553$		0			0
$554$	−84153.6			−0.274191
$555$	34986.7	+	60598.8i	0.113584	+	0.196733i
$556$	34706.5	+	20037.8i	0.112269	+	0.0648188i
$557$	−254267.	+	440404.i	−0.819558	+	1.41952i	0.0864495	+	0.996256i	$0.472448\pi$
$557$	−254267.	+	440404.i	−0.819558	+	1.41952i	−0.906008	+	0.423261i	$0.860885\pi$
$558$	−100470.	+	58006.3i	−0.322677	+	0.186297i
$559$		−	352486.i		−	1.12802i
$560$		0			0
$561$	54814.4			0.174168
$562$	−172923.	−	299512.i	−0.547496	−	0.948290i
$563$	−103765.	−	59908.5i	−0.327365	−	0.189004i	0.327306	−	0.944919i	$-0.393859\pi$
$563$	−103765.	−	59908.5i	−0.327365	−	0.189004i	−0.654671	+	0.755914i	$0.727193\pi$
$564$	−81995.9	+	142021.i	−0.257771	+	0.446473i
$565$	44064.8	−	25440.8i	0.138037	−	0.0796956i
$566$			171688.i			0.535927i
$567$		0			0
$568$	101697.			0.315218
$569$	48829.7	+	84575.5i	0.150820	+	0.261228i	0.931529	−	0.363667i	$-0.118475\pi$
$569$	48829.7	+	84575.5i	0.150820	+	0.261228i	−0.780709	+	0.624895i	$0.785142\pi$
$570$	−11704.4	−	6757.54i	−0.0360246	−	0.0207988i
$571$	−23825.7	+	41267.3i	−0.0730757	+	0.126571i	−0.900248	−	0.435378i	$-0.856615\pi$
$571$	−23825.7	+	41267.3i	−0.0730757	+	0.126571i	0.827172	+	0.561949i	$0.189948\pi$
$572$	70734.6	−	40838.6i	0.216192	−	0.124819i
$573$			222234.i			0.676863i
$574$		0			0
$575$	−52427.2			−0.158570
$576$	6912.00	+	11971.9i	0.0208333	+	0.0360844i
$577$	113845.	+	65728.4i	0.341949	+	0.197425i	0.661134	−	0.750268i	$-0.270076\pi$
$577$	113845.	+	65728.4i	0.341949	+	0.197425i	−0.319184	+	0.947693i	$0.603409\pi$
$578$	101720.	−	176184.i	0.304475	−	0.527366i
$579$	39476.6	−	22791.8i	0.117756	−	0.0679864i
$580$			119107.i			0.354063i
$581$		0			0
$582$	−28666.8			−0.0846316
$583$	−107307.	−	185861.i	−0.315712	−	0.546830i
$584$	175754.	+	101472.i	0.515324	+	0.297523i
$585$	−33696.3	+	58363.8i	−0.0984625	+	0.170542i
$586$	−72400.6	+	41800.5i	−0.210837	+	0.121727i
$587$			135493.i			0.393224i	0.980481	+	0.196612i	$0.0629940\pi$
$587$			135493.i			0.393224i	−0.980481	+	0.196612i	$0.937006\pi$
$588$		0			0
$589$	−58325.0			−0.168122
$590$	−99411.7	−	172186.i	−0.285584	−	0.494645i
$591$	−147712.	−	85281.8i	−0.422904	−	0.244164i
$592$	17991.5	−	31162.3i	0.0513363	−	0.0889171i
$593$	−162993.	+	94104.0i	−0.463510	+	0.267608i	−0.713519	−	0.700636i	$-0.752900\pi$
$593$	−162993.	+	94104.0i	−0.463510	+	0.267608i	0.250009	+	0.968244i	$0.419567\pi$
$594$		−	38876.4i		−	0.110183i
$595$		0			0
$596$	203191.			0.572022
$597$	68756.0	+	119089.i	0.192913	+	0.334136i
$598$	−260753.	−	150546.i	−0.729166	−	0.420984i
$599$	39202.4	−	67900.5i	0.109259	−	0.189243i	−0.806211	−	0.591628i	$-0.798485\pi$
$599$	39202.4	−	67900.5i	0.109259	−	0.189243i	0.915470	+	0.402385i	$0.131819\pi$
$600$	5225.96	−	3017.21i	0.0145166	−	0.00838114i
$601$			254898.i			0.705695i	0.935681	+	0.352848i	$0.114787\pi$
$601$			254898.i			0.705695i	−0.935681	+	0.352848i	$0.885213\pi$
$602$		0			0
$603$	159985.			0.439993
$604$	73235.1	+	126847.i	0.200745	+	0.347701i
$605$	104600.	+	60391.0i	0.285774	+	0.164992i
$606$	83230.5	−	144160.i	0.226640	−	0.392553i
$607$	−489896.	+	282842.i	−1.32962	+	0.767655i	−0.985241	−	0.171176i	$-0.945243\pi$
$607$	−489896.	+	282842.i	−1.32962	+	0.767655i	−0.344378	+	0.938831i	$0.611910\pi$
$608$			6949.97i			0.0188008i
$609$		0			0
$610$	−45074.0			−0.121134
$611$	205559.	+	356038.i	0.550622	+	0.953705i
$612$	20142.0	+	11629.0i	0.0537773	+	0.0310483i
$613$	207111.	−	358726.i	0.551164	−	0.954645i	−0.447026	−	0.894521i	$-0.647517\pi$
$613$	207111.	−	358726.i	0.551164	−	0.954645i	0.998191	−	0.0601241i	$-0.0191496\pi$
$614$	−263485.	+	152123.i	−0.698905	+	0.403513i
$615$			127343.i			0.336686i
$616$		0			0
$617$	22896.0			0.0601435			0.0300717	−	0.999548i	$-0.490426\pi$
$617$	22896.0			0.0601435			0.0300717	+	0.999548i	$0.490426\pi$
$618$	119992.	+	207832.i	0.314178	+	0.544172i
$619$	−139564.	−	80577.4i	−0.364244	−	0.210296i	0.306697	−	0.951807i	$-0.400776\pi$
$619$	−139564.	−	80577.4i	−0.364244	−	0.210296i	−0.670941	+	0.741511i	$0.734110\pi$
$620$	−145543.	+	252087.i	−0.378623	+	0.655793i
$621$	−124112.	+	71656.1i	−0.321833	+	0.185811i
$622$		−	122674.i		−	0.317082i
$623$		0			0
$624$	34655.9			0.0890037
$625$	177957.	+	308230.i	0.455569	+	0.789069i
$626$	263924.	+	152376.i	0.673488	+	0.388838i
$627$	9772.50	−	16926.5i	0.0248583	−	0.0430558i
$628$	−244181.	+	140978.i	−0.619144	+	0.357463i
$629$		−	60539.0i		−	0.153015i
$630$		0			0
$631$	489038.			1.22824			0.614121	−	0.789212i	$-0.289511\pi$
$631$	489038.			1.22824			0.614121	+	0.789212i	$0.289511\pi$
$632$	−118192.	−	204715.i	−0.295907	−	0.512526i
$633$	301754.	+	174217.i	0.753087	+	0.434795i
$634$	−220609.	+	382105.i	−0.548838	+	0.950615i
$635$	176272.	−	101771.i	0.437156	−	0.252392i
$636$		−	91061.5i		−	0.225123i
$637$		0			0
$638$	−172248.			−0.423168
$639$	−60674.5	−	105091.i	−0.148595	−	0.257374i
$640$	30038.6	+	17342.8i	0.0733363	+	0.0423407i
$641$	−59669.8	+	103351.i	−0.145224	+	0.251536i	−0.929457	−	0.368932i	$-0.879724\pi$
$641$	−59669.8	+	103351.i	−0.145224	+	0.251536i	0.784232	+	0.620467i	$0.213057\pi$
$642$	55957.8	−	32307.3i	0.135766	−	0.0783845i
$643$			324224.i			0.784194i	0.919924	+	0.392097i	$0.128250\pi$
$643$			324224.i			0.784194i	−0.919924	+	0.392097i	$0.871750\pi$
$644$		0			0
$645$	−420960.			−1.01186
$646$	5846.43	+	10126.3i	0.0140096	+	0.0242653i
$647$	399048.	+	230391.i	0.953272	+	0.550372i	0.894096	−	0.447876i	$-0.147819\pi$
$647$	399048.	+	230391.i	0.953272	+	0.550372i	0.0591759	+	0.998248i	$0.481153\pi$
$648$	8247.69	−	14285.4i	0.0196419	−	0.0340207i
$649$	249009.	−	143765.i	0.591188	−	0.341323i
$650$		−	15127.9i		−	0.0358057i
$651$		0			0
$652$	1167.51			0.00274641
$653$	279562.	+	484216.i	0.655620	+	1.13557i	0.981738	+	0.190238i	$0.0609260\pi$
$653$	279562.	+	484216.i	0.655620	+	1.13557i	−0.326118	+	0.945329i	$0.605741\pi$
$654$	187072.	+	108006.i	0.437375	+	0.252518i
$655$	−173317.	+	300193.i	−0.403978	+	0.699711i
$656$	56711.4	−	32742.3i	0.131784	−	0.0760855i
$657$		−	242161.i		−	0.561014i
$658$		0			0
$659$	−184372.			−0.424546			−0.212273	−	0.977210i	$-0.568087\pi$
$659$	−184372.			−0.424546			−0.212273	+	0.977210i	$0.568087\pi$
$660$	−48772.0	−	84475.6i	−0.111965	−	0.193929i
$661$	−68612.1	−	39613.2i	−0.157035	−	0.0906645i	0.419423	−	0.907791i	$-0.362232\pi$
$661$	−68612.1	−	39613.2i	−0.157035	−	0.0906645i	−0.576458	+	0.817126i	$0.695566\pi$
$662$	56877.9	−	98515.3i	0.129786	−	0.224796i
$663$	50494.6	−	29153.1i	0.114873	−	0.0663220i
$664$			28720.4i			0.0651411i
$665$		0			0
$666$	−42936.5			−0.0968007
$667$	317483.	+	549897.i	0.713624	+	1.23603i
$668$	216950.	+	125256.i	0.486191	+	0.280703i
$669$	146168.	−	253170.i	0.326588	−	0.565666i
$670$	347637.	−	200708.i	0.774419	−	0.447111i
$671$		−	65184.4i		−	0.144777i
$672$		0			0
$673$	−482896.			−1.06616			−0.533082	−	0.846064i	$-0.678966\pi$
$673$	−482896.			−1.06616			−0.533082	+	0.846064i	$0.678966\pi$
$674$	127953.	+	221621.i	0.281663	+	0.487855i
$675$	−6235.84	−	3600.27i	−0.0136863	−	0.00790182i
$676$	−70803.9	+	122636.i	−0.154940	+	0.268364i
$677$	329375.	−	190165.i	0.718642	−	0.414908i	−0.0956105	−	0.995419i	$-0.530480\pi$
$677$	329375.	−	190165.i	0.718642	−	0.414908i	0.814253	+	0.580511i	$0.197147\pi$
$678$			31221.6i			0.0679196i
$679$		0			0
$680$	58356.0			0.126202
$681$	−158868.	−	275167.i	−0.342563	−	0.593337i
$682$	−364559.	−	210478.i	−0.783789	−	0.452521i
$683$	171034.	−	296240.i	0.366642	−	0.635042i	−0.622396	−	0.782702i	$-0.713841\pi$
$683$	171034.	−	296240.i	0.366642	−	0.635042i	0.989038	+	0.147660i	$0.0471742\pi$
$684$	7181.95	−	4146.50i	0.0153508	−	0.00886278i
$685$			307901.i			0.656191i
$686$		0			0
$687$	−175649.			−0.372163
$688$	108237.	+	187472.i	0.228665	+	0.396059i
$689$	−197701.	−	114143.i	−0.416458	−	0.240442i
$690$	−179791.	+	311407.i	−0.377633	+	0.654080i
$691$	−63274.0	+	36531.3i	−0.132516	+	0.0765084i	−0.564793	−	0.825233i	$-0.691044\pi$
$691$	−63274.0	+	36531.3i	−0.132516	+	0.0765084i	0.432276	+	0.901741i	$0.357711\pi$
$692$			320927.i			0.670183i
$693$		0			0
$694$	−90720.3			−0.188359
$695$	−59992.1	−	103909.i	−0.124201	−	0.215122i
$696$	−63293.7	−	36542.6i	−0.130660	−	0.0754365i
$697$	55086.7	−	95413.0i	0.113392	−	0.196400i
$698$	−286060.	+	165157.i	−0.587145	+	0.338989i
$699$		−	45140.3i		−	0.0923869i
$700$		0			0
$701$	−288287.			−0.586664			−0.293332	−	0.956011i	$-0.594764\pi$
$701$	−288287.			−0.586664			−0.293332	+	0.956011i	$0.594764\pi$
$702$	−20676.5	−	35812.7i	−0.0419568	−	0.0726712i
$703$	−18694.2	−	10793.1i	−0.0378265	−	0.0218392i
$704$	−25080.5	+	43440.6i	−0.0506046	+	0.0876498i
$705$	425203.	−	245491.i	0.855496	−	0.493921i
$706$		−	352586.i		−	0.707386i
$707$		0			0
$708$	122000.			0.243385
$709$	155256.	+	268911.i	0.308856	+	0.534954i	0.978112	−	0.208078i	$-0.0667206\pi$
$709$	155256.	+	268911.i	0.308856	+	0.534954i	−0.669257	+	0.743031i	$0.733387\pi$
$710$	−263683.	−	152237.i	−0.523076	−	0.301998i
$711$	−141032.	+	244275.i	−0.278984	+	0.483214i
$712$	−70630.7	+	40778.6i	−0.139326	+	0.0804401i
$713$			1.55179e6i			3.05250i
$714$		0			0
$715$	−244537.			−0.478335
$716$	200618.	+	347480.i	0.391330	+	0.677804i
$717$	−70717.6	−	40828.8i	−0.137559	−	0.0794198i
$718$	140632.	−	243582.i	0.272795	−	0.472495i
$719$	−8733.60	+	5042.35i	−0.0168941	+	0.00975383i	−0.508423	−	0.861107i	$-0.669771\pi$
$719$	−8733.60	+	5042.35i	−0.0168941	+	0.00975383i	0.491529	+	0.870861i	$0.336438\pi$
$720$		−	41388.3i		−	0.0798385i
$721$		0			0
$722$	−364434.			−0.699109
$723$	14234.4	+	24654.7i	0.0272309	+	0.0471654i
$724$	443227.	+	255897.i	0.845568	+	0.488189i
$725$	−15951.5	+	27628.8i	−0.0303477	+	0.0525638i
$726$	−64184.0	+	37056.6i	−0.121774	+	0.0703060i
$727$			638552.i			1.20817i	0.796921	+	0.604084i	$0.206461\pi$
$727$			638552.i			1.20817i	−0.796921	+	0.604084i	$0.793539\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$	−303801.	−	526199.i	−0.570090	−	0.987425i
$731$	315409.	+	182101.i	0.590254	+	0.340783i
$732$	13829.0	−	23952.5i	0.0258088	−	0.0447021i
$733$	715410.	−	413042.i	1.33152	−	0.768752i	0.345985	−	0.938240i	$-0.387545\pi$
$733$	715410.	−	413042.i	1.33152	−	0.768752i	0.985532	+	0.169488i	$0.0542115\pi$
$734$		−	251488.i		−	0.466795i
$735$		0			0
$736$	184911.			0.341356
$737$	290257.	+	502739.i	0.534376	+	0.925567i
$738$	−67670.4	−	39069.5i	−0.124247	−	0.0717341i
$739$	−384995.	+	666831.i	−0.704962	+	1.22103i	0.261743	+	0.965138i	$0.415703\pi$
$739$	−384995.	+	666831.i	−0.704962	+	1.22103i	−0.966705	+	0.255893i	$0.917630\pi$
$740$	−93298.0	+	53865.6i	−0.170376	+	0.0983667i
$741$		−	20790.1i		−	0.0378634i
$742$		0			0
$743$	−611777.			−1.10819			−0.554097	−	0.832452i	$-0.686936\pi$
$743$	−611777.			−1.10819			−0.554097	+	0.832452i	$0.686936\pi$
$744$	−89306.6	−	154683.i	−0.161338	−	0.279446i
$745$	−526841.	−	304172.i	−0.949220	−	0.548032i
$746$	−129193.	+	223768.i	−0.232145	+	0.402087i
$747$	29679.1	−	17135.2i	0.0531875	−	0.0307078i
$748$			84392.3i			0.150834i
$749$		0			0
$750$	−238076.			−0.423246
$751$	−185311.	−	320968.i	−0.328565	−	0.569091i	0.653663	−	0.756786i	$-0.273232\pi$
$751$	−185311.	−	320968.i	−0.328565	−	0.569091i	−0.982227	+	0.187695i	$0.939898\pi$
$752$	−218656.	−	126241.i	−0.386657	−	0.223236i
$753$	−63265.5	+	109579.i	−0.111578	+	0.193258i
$754$	−158673.	+	91610.2i	−0.279101	+	0.161139i
$755$		−	438523.i		−	0.769305i
$756$		0			0
$757$	298778.			0.521384			0.260692	−	0.965422i	$-0.416049\pi$
$757$	298778.			0.521384			0.260692	+	0.965422i	$0.416049\pi$
$758$	8949.87	+	15501.6i	0.0155768	+	0.0269798i
$759$	−450346.	−	260007.i	−0.781740	−	0.451338i
$760$	10403.9	−	18020.1i	0.0180123	−	0.0311982i
$761$	−695541.	+	401571.i	−1.20103	+	0.693414i	−0.960784	−	0.277298i	$-0.910561\pi$
$761$	−695541.	+	401571.i	−1.20103	+	0.693414i	−0.240245	+	0.970712i	$0.577228\pi$
$762$			124896.i			0.215098i
$763$		0			0
$764$	−342151.			−0.586180
$765$	−34816.4	−	60303.8i	−0.0594924	−	0.103044i
$766$	32911.2	+	19001.3i	0.0560902	+	0.0323837i
$767$	152924.	−	264871.i	0.259946	−	0.450240i
$768$	−18432.0	+	10641.7i	−0.0312500	+	0.0180422i
$769$		−	452541.i		−	0.765253i	−0.923903	−	0.382626i	$-0.875020\pi$
$769$		−	452541.i		−	0.765253i	0.923903	−	0.382626i	$-0.124980\pi$
$770$		0			0
$771$	−60310.4			−0.101457
$772$	35090.3	+	60778.2i	0.0588780	+	0.101980i
$773$	−908057.	−	524267.i	−1.51969	−	0.877392i	−0.999731	−	0.0231996i	$-0.992615\pi$
$773$	−908057.	−	524267.i	−1.51969	−	0.877392i	−0.519957	−	0.854193i	$-0.674052\pi$
$774$	129153.	−	223700.i	0.215587	−	0.373408i
$775$	−67522.1	+	38983.9i	−0.112420	+	0.0649056i
$776$		−	44135.4i		−	0.0732932i
$777$		0			0
$778$	−249740.			−0.412599
$779$	−19642.1	−	34021.1i	−0.0323678	−	0.0560626i
$780$	−89856.9	−	51878.9i	−0.147694	−	0.0852711i
$781$	220160.	−	381328.i	0.360941	−	0.625168i
$782$	269421.	−	155550.i	0.440572	−	0.254365i
$783$			87208.5i			0.142244i
$784$		0			0
$785$	844159.			1.36989
$786$	−106349.	−	184202.i	−0.172143	−	0.298160i
$787$	−169712.	−	97983.5i	−0.274009	−	0.158199i	0.356699	−	0.934219i	$-0.383902\pi$
$787$	−169712.	−	97983.5i	−0.274009	−	0.158199i	−0.630708	+	0.776020i	$0.717235\pi$
$788$	131300.	−	227418.i	0.211452	−	0.366246i
$789$	−543004.	+	313504.i	−0.872266	+	0.503603i
$790$			707722.i			1.13399i
$791$		0			0
$792$	59854.2			0.0954210
$793$	−34668.4	−	60047.4i	−0.0551299	−	0.0954877i
$794$	−530528.	−	306301.i	−0.841526	−	0.485855i
$795$	−136317.	+	236107.i	−0.215682	+	0.373572i
$796$	−183349.	+	105857.i	−0.289370	+	0.167068i
$797$		−	66453.8i		−	0.104617i	−0.998631	−	0.0523086i	$-0.983342\pi$
$797$		−	66453.8i		−	0.104617i	0.998631	−	0.0523086i	$-0.0166579\pi$
$798$		0			0
$799$	−424784.			−0.665387
$800$	4645.30	+	8045.90i	0.00725828	+	0.0125717i
$801$	84279.5	+	48658.8i	0.131358	+	0.0758397i
$802$	−7307.01	+	12656.1i	−0.0113603	+	0.0196767i
$803$	760969.	−	439346.i	1.18015	−	0.681358i
$804$			246314.i			0.381045i
$805$		0			0
$806$	−447772.			−0.689266
$807$	70788.8	+	122610.i	0.108697	+	0.188269i
$808$	221948.	+	128142.i	0.339961	+	0.196276i
$809$	−41152.3	+	71277.9i	−0.0628777	+	0.108907i	−0.895751	−	0.444557i	$-0.853361\pi$
$809$	−41152.3	+	71277.9i	−0.0628777	+	0.108907i	0.832873	+	0.553464i	$0.186694\pi$
$810$	−42769.7	+	24693.1i	−0.0651878	+	0.0376362i
$811$		−	469097.i		−	0.713215i	−0.934254	−	0.356608i	$-0.883933\pi$
$811$		−	469097.i		−	0.713215i	0.934254	−	0.356608i	$-0.116067\pi$
$812$		0			0
$813$	504252.			0.762898
$814$	−77898.5	−	134924.i	−0.117566	−	0.203629i
$815$	−3027.15	−	1747.73i	−0.00455742	−	0.00263123i
$816$	−17904.0	+	31010.6i	−0.0268886	+	0.0465725i
$817$	112464.	−	64931.3i	0.168489	−	0.0972769i
$818$		−	110056.i		−	0.164478i
$819$		0			0
$820$	−196057.			−0.291578
$821$	2689.76	+	4658.80i	0.00399050	+	0.00691174i	0.868014	−	0.496540i	$-0.165396\pi$
$821$	2689.76	+	4658.80i	0.00399050	+	0.00691174i	−0.864023	+	0.503452i	$0.832063\pi$
$822$	−163620.	−	94465.8i	−0.242154	−	0.139808i
$823$	484903.	−	839877.i	0.715905	−	1.23998i	−0.246704	−	0.969091i	$-0.579348\pi$
$823$	484903.	−	839877.i	0.715905	−	1.23998i	0.962609	−	0.270893i	$-0.0873190\pi$
$824$	−319979.	+	184740.i	−0.471267	+	0.272086i
$825$		−	26127.4i		−	0.0383874i
$826$		0			0
$827$	838747.			1.22637			0.613183	−	0.789941i	$-0.289889\pi$
$827$	838747.			1.22637			0.613183	+	0.789941i	$0.289889\pi$
$828$	−110322.	−	191083.i	−0.160917	−	0.278716i
$829$	765309.	+	441852.i	1.11360	+	0.642935i	0.939759	−	0.341839i	$-0.111050\pi$
$829$	765309.	+	441852.i	1.11360	+	0.642935i	0.173838	+	0.984774i	$0.444383\pi$
$830$	42993.7	−	74467.2i	0.0624091	−	0.108096i
$831$	−133888.	+	77300.0i	−0.193882	+	0.111938i
$832$			53356.3i			0.0770795i
$833$		0			0
$834$	73623.7			0.105849
$835$	−375010.	−	649536.i	−0.537861	−	0.931602i
$836$	26060.0	+	15045.7i	0.0372874	+	0.0215279i
$837$	−106564.	+	184575.i	−0.152111	+	0.263464i
$838$	645258.	−	372540.i	0.918852	−	0.530499i
$839$			1.12626e6i			1.59998i	0.600011	+	0.799992i	$0.295163\pi$
$839$			1.12626e6i			1.59998i	−0.600011	+	0.799992i	$0.704837\pi$
$840$		0			0
$841$	−320891.			−0.453696
$842$	−23157.9	−	40110.6i	−0.0326644	−	0.0565764i
$843$	−550238.	−	317680.i	−0.774276	−	0.447028i
$844$	−268225.	+	464580.i	−0.376543	+	0.652192i
$845$	367165.	−	211983.i	0.514218	−	0.296884i
$846$			301272.i			0.420938i
$847$		0			0
$848$	140198.			0.194963
$849$	157705.	+	273153.i	0.218791	+	0.378958i
$850$	13536.7	+	7815.40i	0.0187359	+	0.0108172i
$851$	−287161.	+	497378.i	−0.396522	+	0.686796i
$852$	161799.	−	93414.5i	0.222893	−	0.128687i
$853$		−	805486.i		−	1.10703i	−0.832839	−	0.553516i	$-0.813286\pi$
$853$		−	805486.i		−	1.10703i	0.832839	−	0.553516i	$-0.186714\pi$
$854$		0			0
$855$	−24828.8			−0.0339643
$856$	49740.3	+	86152.7i	0.0678830	+	0.117577i
$857$	849118.	+	490238.i	1.15613	+	0.667491i	0.950373	−	0.311112i	$-0.100701\pi$
$857$	849118.	+	490238.i	1.15613	+	0.667491i	0.205756	+	0.978603i	$0.434035\pi$
$858$	75025.3	−	129948.i	0.101914	−	0.176520i
$859$	375665.	−	216890.i	0.509113	−	0.293936i	−0.223356	−	0.974737i	$-0.571701\pi$
$859$	375665.	−	216890.i	0.509113	−	0.293936i	0.732469	+	0.680800i	$0.238368\pi$
$860$		−	648111.i		−	0.876299i
$861$		0			0
$862$	708284.			0.953220
$863$	151578.	+	262542.i	0.203524	+	0.352514i	0.949661	−	0.313278i	$-0.101427\pi$
$863$	151578.	+	262542.i	0.203524	+	0.352514i	−0.746137	+	0.665792i	$0.768094\pi$
$864$	21993.8	+	12698.2i	0.0294628	+	0.0170103i
$865$	480418.	−	832108.i	0.642077	−	1.11211i
$866$	−224116.	+	129394.i	−0.298839	+	0.172535i
$867$		−	373744.i		−	0.497205i
$868$		0			0
$869$	−1.02348e6			−1.35532
$870$	109407.	+	189498.i	0.144546	+	0.250360i
$871$	534765.	+	308747.i	0.704898	+	0.406973i
$872$	−166286.	+	288016.i	−0.218687	+	0.378777i
$873$	−45608.6	+	26332.1i	−0.0598436	+	0.0345507i
$874$		−	110928.i		−	0.145217i
$875$		0			0
$876$	372831.			0.485852
$877$	−177500.	−	307439.i	−0.230781	−	0.399724i	0.727257	−	0.686365i	$-0.240795\pi$
$877$	−177500.	−	307439.i	−0.230781	−	0.399724i	−0.958038	+	0.286641i	$0.907461\pi$
$878$	−21700.9	−	12529.0i	−0.0281507	−	0.0162528i
$879$	−76792.5	+	133008.i	−0.0993896	+	0.172148i
$880$	130059.	−	75089.5i	0.167948	−	0.0969647i
$881$			320002.i			0.412288i	0.978522	+	0.206144i	$0.0660915\pi$
$881$			320002.i			0.412288i	−0.978522	+	0.206144i	$0.933909\pi$
$882$		0			0
$883$	−1.08605e6			−1.39293			−0.696467	−	0.717589i	$-0.745246\pi$
$883$	−1.08605e6			−1.39293			−0.696467	+	0.717589i	$0.745246\pi$
$884$	44884.1	+	77741.6i	0.0574365	+	0.0994830i
$885$	−316326.	−	182631.i	−0.403876	−	0.233178i
$886$	424560.	−	735360.i	0.540844	−	0.936769i
$887$	−1.11218e6	+	642117.i	−1.41360	+	0.816144i	−0.995726	−	0.0923591i	$-0.970559\pi$
$887$	−1.11218e6	+	642117.i	−1.41360	+	0.816144i	−0.417878	+	0.908503i	$0.637226\pi$
$888$		−	66105.1i		−	0.0838319i
$889$		0			0
$890$	244178.			0.308266
$891$	−35710.3	−	61852.0i	−0.0449819	−	0.0779109i
$892$	389781.	+	225040.i	0.489882	+	0.282833i
$893$	−75731.9	+	131171.i	−0.0949677	+	0.164489i
$894$	323275.	−	186643.i	0.404481	−	0.233527i
$895$		−	1.20128e6i		−	1.49967i
$896$		0			0
$897$	−553140.			−0.687465
$898$	165274.	+	286263.i	0.204952	+	0.354987i
$899$	817787.	+	472150.i	1.01186	+	0.584198i
$900$	5542.97	−	9600.71i	0.00684317	−	0.0118527i
$901$	204273.	−	117937.i	0.251629	−	0.145278i
$902$		−	283531.i		−	0.348487i
$903$		0			0
$904$	−48068.7			−0.0588201
$905$	−766141.	−	1.32699e6i	−0.935430	−	1.62021i
$906$	233033.	+	134541.i	0.283897	+	0.163908i
$907$	−24217.8	+	41946.4i	−0.0294388	+	0.0509894i	−0.880369	−	0.474289i	$-0.842705\pi$
$907$	−24217.8	+	41946.4i	−0.0294388	+	0.0509894i	0.850931	+	0.525278i	$0.176039\pi$
$908$	423647.	−	244593.i	0.513845	−	0.296669i
$909$		−	305808.i		−	0.370102i
$910$		0			0
$911$	727675.			0.876801			0.438400	−	0.898780i	$-0.355545\pi$
$911$	727675.			0.876801			0.438400	+	0.898780i	$0.355545\pi$
$912$	6383.96	+	11057.3i	0.00767539	+	0.0132942i
$913$	107692.	+	62175.8i	0.129194	+	0.0745899i
$914$	104292.	−	180639.i	0.124842	−	0.216232i
$915$	−71712.3	+	41403.1i	−0.0856548	+	0.0494528i
$916$		−	270430.i		−	0.322303i
$917$		0			0
$918$	42727.5			0.0507017
$919$	−43858.0	−	75964.2i	−0.0519299	−	0.0899452i	0.838892	−	0.544298i	$-0.183204\pi$
$919$	−43858.0	−	75964.2i	−0.0519299	−	0.0899452i	−0.890822	+	0.454353i	$0.849871\pi$
$920$	−479443.	−	276806.i	−0.566449	−	0.327040i
$921$	−279468.	+	484052.i	−0.329467	+	0.570654i
$922$	−216092.	+	124761.i	−0.254201	+	0.146763i
$923$		−	468369.i		−	0.549775i
$924$		0			0
$925$	−28856.1			−0.0337251
$926$	421266.	+	729655.i	0.491286	+	0.850933i
$927$	381813.	+	220440.i	0.444315	+	0.256525i
$928$	56261.1	−	97447.1i	0.0653299	−	0.113155i
$929$	−781079.	+	450956.i	−0.905032	+	0.522520i	−0.878829	−	0.477136i	$-0.841675\pi$
$929$	−781079.	+	450956.i	−0.905032	+	0.522520i	−0.0262024	+	0.999657i	$0.508341\pi$
$930$			534757.i			0.618288i
$931$		0			0
$932$	69498.1			0.0800094
$933$	−112683.	−	195173.i	−0.129448	−	0.224211i
$934$	459205.	+	265122.i	0.526396	+	0.303915i
$935$	126333.	−	218815.i	0.144508	−	0.250296i
$936$	55137.2	−	31833.5i	0.0629351	−	0.0363356i
$937$		−	1.24186e6i		−	1.41447i	−0.706978	−	0.707236i	$-0.749942\pi$
$937$		−	1.24186e6i		−	1.41447i	0.706978	−	0.707236i	$-0.250058\pi$
$938$		0			0
$939$	559867.			0.634970
$940$	377958.	+	654643.i	0.427748	+	0.740882i
$941$	−369139.	−	213122.i	−0.416879	−	0.240685i	0.276862	−	0.960910i	$-0.410706\pi$
$941$	−369139.	−	213122.i	−0.416879	−	0.240685i	−0.693741	+	0.720224i	$0.744039\pi$
$942$	−258993.	+	448588.i	−0.291867	+	0.505529i
$943$	−905165.	+	522598.i	−1.01790	+	0.587684i
$944$			187832.i			0.210778i
$945$		0			0
$946$	937274.			1.04733
$947$	−13665.2	−	23668.9i	−0.0152376	−	0.0263923i	0.858306	−	0.513138i	$-0.171517\pi$
$947$	−13665.2	−	23668.9i	−0.0152376	−	0.0263923i	−0.873544	+	0.486746i	$0.838184\pi$
$948$	−376086.	−	217133.i	−0.418476	−	0.241607i
$949$	467333.	−	809444.i	0.518912	−	0.898782i
$950$	4826.73	−	2786.71i	0.00534817	−	0.00308777i
$951$			810568.i			0.896248i
$952$		0			0
$953$	1.30093e6			1.43242			0.716208	−	0.697887i	$-0.245876\pi$
$953$	1.30093e6			1.43242			0.716208	+	0.697887i	$0.245876\pi$
$954$	−83645.4	−	144878.i	−0.0919063	−	0.159186i
$955$	887140.	+	512190.i	0.972714	+	0.561597i
$956$	62860.1	−	108877.i	0.0687796	−	0.119130i
$957$	−274045.	+	158220.i	−0.299225	+	0.172757i
$958$			340794.i			0.371331i
$959$		0			0
$960$	63721.4			0.0691421
$961$	692125.	+	1.19880e6i	0.749442	+	1.29807i
$962$	−143519.	−	82860.7i	−0.155081	−	0.0895362i
$963$	59352.3	−	102801.i	0.0640007	−	0.110852i
$964$	−37958.4	+	21915.3i	−0.0408464	+	0.0235827i
$965$		−	210117.i		−	0.225635i
$966$		0			0
$967$	463079.			0.495225			0.247612	−	0.968859i	$-0.420354\pi$
$967$	463079.			0.495225			0.247612	+	0.968859i	$0.420354\pi$
$968$	−57052.4	−	98817.7i	−0.0608868	−	0.105459i
$969$	18603.2	+	10740.6i	0.0198125	+	0.0114388i
$970$	−66069.4	+	114436.i	−0.0702194	+	0.121623i
$971$	−54723.1	+	31594.4i	−0.0580406	+	0.0335098i	−0.528739	−	0.848784i	$-0.677335\pi$
$971$	−54723.1	+	31594.4i	−0.0580406	+	0.0335098i	0.470699	+	0.882294i	$0.344002\pi$
$972$		−	30304.0i		−	0.0320750i
$973$		0			0
$974$	756305.			0.797221
$975$	−13895.9	−	24068.4i	−0.0146176	−	0.0253185i
$976$	36877.2	+	21291.1i	0.0387132	+	0.0223511i
$977$	−719497.	+	1.24621e6i	−0.753772	+	1.30557i	0.192210	+	0.981354i	$0.438434\pi$
$977$	−719497.	+	1.24621e6i	−0.753772	+	1.30557i	−0.945982	+	0.324218i	$0.894899\pi$
$978$	1857.49	−	1072.42i	0.00194200	−	0.00112122i
$979$			353121.i			0.368432i
$980$		0			0
$981$	396840.			0.412361
$982$	252245.	+	436901.i	0.261577	+	0.453064i
$983$	−346926.	−	200298.i	−0.359030	−	0.207286i	0.309625	−	0.950859i	$-0.399796\pi$
$983$	−346926.	−	200298.i	−0.359030	−	0.207286i	−0.668655	+	0.743573i	$0.733130\pi$
$984$	60151.5	−	104185.i	0.0621235	−	0.107601i
$985$	−680877.	+	393104.i	−0.701772	+	0.405168i
$986$		−	189311.i		−	0.194725i
$987$		0			0
$988$	32008.4			0.0327906
$989$	−1.72756e6	−	2.99223e6i	−1.76620	−	3.05916i
$990$	−155192.	−	89600.0i	−0.158343	−	0.0914192i
$991$	−99274.5	+	171949.i	−0.101086	+	0.175086i	−0.912132	−	0.409896i	$-0.865565\pi$
$991$	−99274.5	+	171949.i	−0.101086	+	0.175086i	0.811046	+	0.584982i	$0.198898\pi$
$992$	238151.	−	137496.i	0.242007	−	0.139723i
$993$		−	208983.i		−	0.211939i
$994$		0			0
$995$	633858.			0.640245
$996$	26381.4	+	45693.9i	0.0265937	+	0.0460617i
$997$	−792228.	−	457393.i	−0.797003	−	0.460150i	0.0454194	−	0.998968i	$-0.485538\pi$
$997$	−792228.	−	457393.i	−0.797003	−	0.460150i	−0.842422	+	0.538818i	$0.818871\pi$
$998$	372994.	−	646045.i	0.374491	−	0.648637i
$999$	−68311.6	+	39439.7i	−0.0684484	+	0.0395187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.5.g.c.31.2		4
7.2	even	3		42.5.g.a.19.2	✓	4
7.3	odd	6		294.5.c.a.97.2		4
7.4	even	3		294.5.c.a.97.1		4
7.5	odd	6	inner	294.5.g.c.19.2		4
7.6	odd	2		42.5.g.a.31.2	yes	4
21.2	odd	6		126.5.n.b.19.1		4
21.11	odd	6		882.5.c.a.685.3		4
21.17	even	6		882.5.c.a.685.4		4
21.20	even	2		126.5.n.b.73.1		4
28.23	odd	6		336.5.bh.d.145.1		4
28.27	even	2		336.5.bh.d.241.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.g.a.19.2	✓	4	7.2	even	3
42.5.g.a.31.2	yes	4	7.6	odd	2
126.5.n.b.19.1		4	21.2	odd	6
126.5.n.b.73.1		4	21.20	even	2
294.5.c.a.97.1		4	7.4	even	3
294.5.c.a.97.2		4	7.3	odd	6
294.5.g.c.19.2		4	7.5	odd	6	inner
294.5.g.c.31.2		4	1.1	even	1	trivial
336.5.bh.d.145.1		4	28.23	odd	6
336.5.bh.d.241.1		4	28.27	even	2
882.5.c.a.685.3		4	21.11	odd	6
882.5.c.a.685.4		4	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	294.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 + 2.44949i) q^{2} +(4.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(20.7426 - 11.9758i) q^{5} +14.6969i q^{6} -22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +O(q^{10})\)	\(q+(1.41421 + 2.44949i) q^{2} +(4.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(20.7426 - 11.9758i) q^{5} +14.6969i q^{6} -22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +(58.6690 + 33.8726i) q^{10} +(-48.9853 + 84.8450i) q^{11} +(-36.0000 + 20.7846i) q^{12} +104.211i q^{13} +124.456 q^{15} +(-32.0000 - 55.4256i) q^{16} +(-93.2498 - 53.8378i) q^{17} +(-38.1838 + 66.1362i) q^{18} +(-33.2498 + 19.1968i) q^{19} +191.612i q^{20} -277.103 q^{22} +(510.749 + 884.644i) q^{23} +(-101.823 - 58.7878i) q^{24} +(-25.6619 + 44.4477i) q^{25} +(-255.265 + 147.377i) q^{26} +140.296i q^{27} +621.603 q^{29} +(176.007 + 304.853i) q^{30} +(1315.61 + 759.568i) q^{31} +(90.5097 - 156.767i) q^{32} +(-440.868 + 254.535i) q^{33} -304.553i q^{34} -216.000 q^{36} +(281.118 + 486.910i) q^{37} +(-94.0446 - 54.2967i) q^{38} +(-270.749 + 468.952i) q^{39} +(-469.352 + 270.981i) q^{40} +1023.20i q^{41} -3382.41 q^{43} +(-391.882 - 678.760i) q^{44} +(560.051 + 323.346i) q^{45} +(-1444.62 + 2502.15i) q^{46} +(3416.50 - 1972.52i) q^{47} -332.554i q^{48} -145.166 q^{50} +(-279.749 - 484.540i) q^{51} +(-721.998 - 416.846i) q^{52} +(-1095.30 + 1897.12i) q^{53} +(-343.654 + 198.409i) q^{54} +2346.55i q^{55} -199.499 q^{57} +(879.079 + 1522.61i) q^{58} +(-2541.67 - 1467.44i) q^{59} +(-497.823 + 862.255i) q^{60} +(-576.207 + 332.673i) q^{61} +4296.76i q^{62} +512.000 q^{64} +(1248.01 + 2161.62i) q^{65} +(-1246.96 - 719.934i) q^{66} +(2962.69 - 5131.53i) q^{67} +(745.998 - 430.702i) q^{68} +5307.86i q^{69} -4494.41 q^{71} +(-305.470 - 529.090i) q^{72} +(-7767.32 - 4484.46i) q^{73} +(-795.121 + 1377.19i) q^{74} +(-230.957 + 133.343i) q^{75} -307.148i q^{76} -1531.59 q^{78} +(5223.41 + 9047.22i) q^{79} +(-1327.53 - 766.449i) q^{80} +(-364.500 + 631.333i) q^{81} +(-2506.31 + 1447.02i) q^{82} -1269.28i q^{83} -2579.00 q^{85} +(-4783.45 - 8285.17i) q^{86} +(2797.21 + 1614.97i) q^{87} +(1108.41 - 1919.82i) q^{88} +(3121.46 - 1802.18i) q^{89} +1829.12i q^{90} -8171.99 q^{92} +(3946.83 + 6836.11i) q^{93} +(9663.32 + 5579.12i) q^{94} +(-459.792 + 796.383i) q^{95} +(814.587 - 470.302i) q^{96} +1950.53i q^{97} -2645.21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} - 16 q^{4} + 66 q^{5} + 54 q^{9}+O(q^{10}) \) 4 * q + 18 * q^3 - 16 * q^4 + 66 * q^5 + 54 * q^9	\( 4 q + 18 q^{3} - 16 q^{4} + 66 q^{5} + 54 q^{9} + 48 q^{10} - 162 q^{11} - 144 q^{12} + 396 q^{15} - 128 q^{16} + 204 q^{17} + 444 q^{19} - 192 q^{22} + 312 q^{23} - 476 q^{25} - 1632 q^{26} + 2724 q^{29} + 144 q^{30} + 3786 q^{31} - 1458 q^{33} - 864 q^{36} + 1396 q^{37} - 1632 q^{38} + 648 q^{39} - 384 q^{40} - 632 q^{43} - 1296 q^{44} + 1782 q^{45} - 4896 q^{46} + 7896 q^{47} + 2112 q^{50} + 612 q^{51} + 1728 q^{52} - 1038 q^{53} + 2664 q^{57} - 336 q^{58} + 966 q^{59} - 1584 q^{60} - 5088 q^{61} + 2048 q^{64} - 744 q^{65} - 864 q^{66} + 14600 q^{67} - 1632 q^{68} - 9696 q^{71} - 22584 q^{73} + 768 q^{74} - 4284 q^{75} - 9792 q^{78} + 3974 q^{79} - 4224 q^{80} - 1458 q^{81} - 18816 q^{82} + 1224 q^{85} - 18240 q^{86} + 12258 q^{87} + 768 q^{88} + 33156 q^{89} - 4992 q^{92} + 11358 q^{93} + 16320 q^{94} + 3252 q^{95} - 8748 q^{99}+O(q^{100}) \) 4 * q + 18 * q^3 - 16 * q^4 + 66 * q^5 + 54 * q^9 + 48 * q^10 - 162 * q^11 - 144 * q^12 + 396 * q^15 - 128 * q^16 + 204 * q^17 + 444 * q^19 - 192 * q^22 + 312 * q^23 - 476 * q^25 - 1632 * q^26 + 2724 * q^29 + 144 * q^30 + 3786 * q^31 - 1458 * q^33 - 864 * q^36 + 1396 * q^37 - 1632 * q^38 + 648 * q^39 - 384 * q^40 - 632 * q^43 - 1296 * q^44 + 1782 * q^45 - 4896 * q^46 + 7896 * q^47 + 2112 * q^50 + 612 * q^51 + 1728 * q^52 - 1038 * q^53 + 2664 * q^57 - 336 * q^58 + 966 * q^59 - 1584 * q^60 - 5088 * q^61 + 2048 * q^64 - 744 * q^65 - 864 * q^66 + 14600 * q^67 - 1632 * q^68 - 9696 * q^71 - 22584 * q^73 + 768 * q^74 - 4284 * q^75 - 9792 * q^78 + 3974 * q^79 - 4224 * q^80 - 1458 * q^81 - 18816 * q^82 + 1224 * q^85 - 18240 * q^86 + 12258 * q^87 + 768 * q^88 + 33156 * q^89 - 4992 * q^92 + 11358 * q^93 + 16320 * q^94 + 3252 * q^95 - 8748 * q^99

Introduction

L-functions

Modular forms

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