LMFDB - Embedded newform 98.5.d.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,5,Mod(19,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("98.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	98.d (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:	$10.1302563822$
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 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.5.d.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 + 2.44949i) q^{2} +(12.9853 - 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-21.9853 - 12.6932i) q^{5} +42.4098i q^{6} +22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +O(q^{10})$	\(q+(-1.41421 + 2.44949i) q^{2} +(12.9853 - 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-21.9853 - 12.6932i) q^{5} +42.4098i q^{6} +22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +(62.1838 - 35.9018i) q^{10} +(-21.9853 - 38.0796i) q^{11} +(-103.882 - 59.9764i) q^{12} -162.507i q^{13} -380.647 q^{15} +(-32.0000 + 55.4256i) q^{16} +(-93.7355 + 54.1182i) q^{17} +(203.397 + 352.294i) q^{18} +(-389.338 - 224.784i) q^{19} +203.091i q^{20} +124.368 q^{22} +(217.911 - 377.433i) q^{23} +(293.823 - 169.639i) q^{24} +(9.73506 + 16.8616i) q^{25} +(398.059 + 229.819i) q^{26} -941.981i q^{27} +742.118 q^{29} +(538.316 - 932.390i) q^{30} +(900.175 - 519.716i) q^{31} +(-90.5097 - 156.767i) q^{32} +(-570.970 - 329.650i) q^{33} -306.139i q^{34} -1150.59 q^{36} +(-493.338 + 854.486i) q^{37} +(1101.21 - 635.786i) q^{38} +(-1218.32 - 2110.20i) q^{39} +(-497.470 - 287.215i) q^{40} +1143.70i q^{41} +2418.82 q^{43} +(-175.882 + 304.637i) q^{44} +(-3162.00 + 1825.58i) q^{45} +(616.346 + 1067.54i) q^{46} +(1165.17 + 672.714i) q^{47} +959.623i q^{48} -55.0698 q^{50} +(-811.455 + 1405.48i) q^{51} +(-1125.88 + 650.027i) q^{52} +(1783.10 + 3088.42i) q^{53} +(2307.37 + 1332.16i) q^{54} +1116.26i q^{55} -6740.88 q^{57} +(-1049.51 + 1817.81i) q^{58} +(-3710.93 + 2142.50i) q^{59} +(1522.59 + 2637.20i) q^{60} +(1209.57 + 698.345i) q^{61} +2939.96i q^{62} +512.000 q^{64} +(-2062.73 + 3572.76i) q^{65} +(1614.95 - 932.390i) q^{66} +(-3632.89 - 6292.36i) q^{67} +(749.884 + 432.946i) q^{68} -6534.77i q^{69} +5987.76 q^{71} +(1627.18 - 2818.35i) q^{72} +(500.123 - 288.746i) q^{73} +(-1395.37 - 2416.85i) q^{74} +(252.825 + 145.969i) q^{75} +3596.55i q^{76} +6891.88 q^{78} +(1573.12 - 2724.72i) q^{79} +(1407.06 - 812.365i) q^{80} +(-1237.24 - 2142.95i) q^{81} +(-2801.47 - 1617.43i) q^{82} +4729.96i q^{83} +2747.74 q^{85} +(-3420.73 + 5924.88i) q^{86} +(9636.61 - 5563.70i) q^{87} +(-497.470 - 861.644i) q^{88} +(725.651 + 418.955i) q^{89} -10327.0i q^{90} -3486.58 q^{92} +(7792.69 - 13497.3i) q^{93} +(-3295.61 + 1902.72i) q^{94} +(5706.47 + 9883.89i) q^{95} +(-2350.59 - 1357.11i) q^{96} -5622.23i q^{97} -6323.99 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} - 16 q^{4} - 54 q^{5} + 84 q^{9}+O(q^{10}) $ 4 * q + 18 * q^3 - 16 * q^4 - 54 * q^5 + 84 * q^9	$ 4 q + 18 q^{3} - 16 q^{4} - 54 q^{5} + 84 q^{9} + 96 q^{10} - 54 q^{11} - 144 q^{12} - 708 q^{15} - 128 q^{16} - 918 q^{17} + 576 q^{18} - 30 q^{19} + 192 q^{22} - 486 q^{23} + 768 q^{24} - 572 q^{25} + 1728 q^{26} + 3240 q^{29} + 1152 q^{30} + 546 q^{31} - 1062 q^{33} - 1344 q^{36} - 446 q^{37} + 4320 q^{38} - 3312 q^{39} - 768 q^{40} + 2344 q^{43} - 432 q^{44} - 5724 q^{45} + 3840 q^{46} - 702 q^{47} - 3456 q^{50} + 318 q^{51} + 384 q^{52} + 2754 q^{53} + 1440 q^{54} - 17460 q^{57} + 384 q^{58} - 12366 q^{59} + 2832 q^{60} - 7686 q^{61} + 2048 q^{64} - 3024 q^{65} + 3456 q^{66} - 5062 q^{67} + 7344 q^{68} + 18792 q^{71} + 4608 q^{72} + 17274 q^{73} - 4320 q^{74} + 5220 q^{75} + 8832 q^{78} + 794 q^{79} + 3456 q^{80} - 4338 q^{81} - 9984 q^{82} + 10380 q^{85} - 10368 q^{86} + 12276 q^{87} - 768 q^{88} + 12474 q^{89} + 7776 q^{92} + 18918 q^{93} - 15168 q^{94} + 8910 q^{95} - 6144 q^{96} - 11448 q^{99}+O(q^{100}) $ 4 * q + 18 * q^3 - 16 * q^4 - 54 * q^5 + 84 * q^9 + 96 * q^10 - 54 * q^11 - 144 * q^12 - 708 * q^15 - 128 * q^16 - 918 * q^17 + 576 * q^18 - 30 * q^19 + 192 * q^22 - 486 * q^23 + 768 * q^24 - 572 * q^25 + 1728 * q^26 + 3240 * q^29 + 1152 * q^30 + 546 * q^31 - 1062 * q^33 - 1344 * q^36 - 446 * q^37 + 4320 * q^38 - 3312 * q^39 - 768 * q^40 + 2344 * q^43 - 432 * q^44 - 5724 * q^45 + 3840 * q^46 - 702 * q^47 - 3456 * q^50 + 318 * q^51 + 384 * q^52 + 2754 * q^53 + 1440 * q^54 - 17460 * q^57 + 384 * q^58 - 12366 * q^59 + 2832 * q^60 - 7686 * q^61 + 2048 * q^64 - 3024 * q^65 + 3456 * q^66 - 5062 * q^67 + 7344 * q^68 + 18792 * q^71 + 4608 * q^72 + 17274 * q^73 - 4320 * q^74 + 5220 * q^75 + 8832 * q^78 + 794 * q^79 + 3456 * q^80 - 4338 * q^81 - 9984 * q^82 + 10380 * q^85 - 10368 * q^86 + 12276 * q^87 - 768 * q^88 + 12474 * q^89 + 7776 * q^92 + 18918 * q^93 - 15168 * q^94 + 8910 * q^95 - 6144 * q^96 - 11448 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.41421	+	2.44949i	−0.353553	+	0.612372i
$2$	−1.41421	+	2.44949i	−0.353553	+	0.612372i
$3$	12.9853	−	7.49706i	1.44281	−	0.833006i	0.444773	−	0.895643i	$-0.353284\pi$
$3$	12.9853	−	7.49706i	1.44281	−	0.833006i	0.998036	+	0.0626373i	$0.0199511\pi$
$4$	−4.00000	−	6.92820i	−0.250000	−	0.433013i
$5$	−21.9853	−	12.6932i	−0.879411	−	0.507728i	−0.00894701	−	0.999960i	$-0.502848\pi$
$5$	−21.9853	−	12.6932i	−0.879411	−	0.507728i	−0.870464	+	0.492232i	$0.836181\pi$
$6$			42.4098i			1.17805i
$7$		0			0
$7$		0			0
$8$	22.6274			0.353553
$9$	71.9117	−	124.555i	0.887799	−	1.53771i
$10$	62.1838	−	35.9018i	0.621838	−	0.359018i
$11$	−21.9853	−	38.0796i	−0.181697	−	0.314708i	0.760762	−	0.649031i	$-0.224826\pi$
$11$	−21.9853	−	38.0796i	−0.181697	−	0.314708i	−0.942458	+	0.334324i	$0.891492\pi$
$12$	−103.882	−	59.9764i	−0.721405	−	0.416503i
$13$		−	162.507i		−	0.961579i	−0.876836	−	0.480790i	$-0.840350\pi$
$13$		−	162.507i		−	0.961579i	0.876836	−	0.480790i	$-0.159650\pi$
$14$		0			0
$15$	−380.647			−1.69176
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	−93.7355	+	54.1182i	−0.324344	+	0.187260i	−0.653327	−	0.757076i	$-0.726627\pi$
$17$	−93.7355	+	54.1182i	−0.324344	+	0.187260i	0.328983	+	0.944336i	$0.393294\pi$
$18$	203.397	+	352.294i	0.627768	+	1.08733i
$19$	−389.338	−	224.784i	−1.07850	−	0.622671i	−0.148007	−	0.988986i	$-0.547286\pi$
$19$	−389.338	−	224.784i	−1.07850	−	0.622671i	−0.930491	+	0.366315i	$0.880619\pi$
$20$			203.091i			0.507728i
$21$		0			0
$22$	124.368			0.256958
$23$	217.911	−	377.433i	0.411931	−	0.713485i	−0.583170	−	0.812350i	$-0.698188\pi$
$23$	217.911	−	377.433i	0.411931	−	0.713485i	0.995101	+	0.0988653i	$0.0315213\pi$
$24$	293.823	−	169.639i	0.510110	−	0.294512i
$25$	9.73506	+	16.8616i	0.0155761	+	0.0269786i
$26$	398.059	+	229.819i	0.588844	+	0.339970i
$27$		−	941.981i		−	1.29215i
$28$		0			0
$29$	742.118			0.882423			0.441212	−	0.897403i	$-0.354549\pi$
$29$	742.118			0.882423			0.441212	+	0.897403i	$0.354549\pi$
$30$	538.316	−	932.390i	0.598129	−	1.03599i
$31$	900.175	−	519.716i	0.936707	−	0.540808i	0.0477804	−	0.998858i	$-0.484785\pi$
$31$	900.175	−	519.716i	0.936707	−	0.540808i	0.888926	+	0.458050i	$0.151452\pi$
$32$	−90.5097	−	156.767i	−0.0883883	−	0.153093i
$33$	−570.970	−	329.650i	−0.524307	−	0.302709i
$34$		−	306.139i		−	0.264826i
$35$		0			0
$36$	−1150.59			−0.887799
$37$	−493.338	+	854.486i	−0.360364	+	0.624168i	−0.988021	−	0.154322i	$-0.950681\pi$
$37$	−493.338	+	854.486i	−0.360364	+	0.624168i	0.627657	+	0.778490i	$0.284014\pi$
$38$	1101.21	−	635.786i	0.762613	−	0.440295i
$39$	−1218.32	−	2110.20i	−0.801001	−	1.38737i
$40$	−497.470	−	287.215i	−0.310919	−	0.179509i
$41$			1143.70i			0.680366i	0.940359	+	0.340183i	$0.110489\pi$
$41$			1143.70i			0.680366i	−0.940359	+	0.340183i	$0.889511\pi$
$42$		0			0
$43$	2418.82			1.30818			0.654089	−	0.756418i	$-0.273052\pi$
$43$	2418.82			1.30818			0.654089	+	0.756418i	$0.273052\pi$
$44$	−175.882	+	304.637i	−0.0908483	+	0.157354i
$45$	−3162.00	+	1825.58i	−1.56148	+	0.901521i
$46$	616.346	+	1067.54i	0.291279	+	0.504510i
$47$	1165.17	+	672.714i	0.527467	+	0.304533i	0.739984	−	0.672624i	$-0.234833\pi$
$47$	1165.17	+	672.714i	0.527467	+	0.304533i	−0.212517	+	0.977157i	$0.568166\pi$
$48$			959.623i			0.416503i
$49$		0			0
$50$	−55.0698			−0.0220279
$51$	−811.455	+	1405.48i	−0.311978	+	0.540362i
$52$	−1125.88	+	650.027i	−0.416376	+	0.240395i
$53$	1783.10	+	3088.42i	0.634782	+	1.09947i	0.986561	+	0.163391i	$0.0522432\pi$
$53$	1783.10	+	3088.42i	0.634782	+	1.09947i	−0.351780	+	0.936083i	$0.614423\pi$
$54$	2307.37	+	1332.16i	0.791280	+	0.456846i
$55$			1116.26i			0.369010i
$56$		0			0
$57$	−6740.88			−2.07475
$58$	−1049.51	+	1817.81i	−0.311984	+	0.540372i
$59$	−3710.93	+	2142.50i	−1.06605	+	0.615485i	−0.927100	−	0.374814i	$-0.877707\pi$
$59$	−3710.93	+	2142.50i	−1.06605	+	0.615485i	−0.138952	+	0.990299i	$0.544373\pi$
$60$	1522.59	+	2637.20i	0.422941	+	0.732555i
$61$	1209.57	+	698.345i	0.325066	+	0.187677i	0.653648	−	0.756799i	$-0.273238\pi$
$61$	1209.57	+	698.345i	0.325066	+	0.187677i	−0.328583	+	0.944475i	$0.606571\pi$
$62$			2939.96i			0.764818i
$63$		0			0
$64$	512.000			0.125000
$65$	−2062.73	+	3572.76i	−0.488221	+	0.845623i
$66$	1614.95	−	932.390i	0.370741	−	0.214047i
$67$	−3632.89	−	6292.36i	−0.809288	−	1.40173i	−0.913358	−	0.407158i	$-0.866520\pi$
$67$	−3632.89	−	6292.36i	−0.809288	−	1.40173i	0.104070	−	0.994570i	$-0.466813\pi$
$68$	749.884	+	432.946i	0.162172	+	0.0936301i
$69$		−	6534.77i		−	1.37256i
$70$		0			0
$71$	5987.76			1.18781			0.593906	−	0.804534i	$-0.297585\pi$
$71$	5987.76			1.18781			0.593906	+	0.804534i	$0.297585\pi$
$72$	1627.18	−	2818.35i	0.313884	−	0.543663i
$73$	500.123	−	288.746i	0.0938494	−	0.0541840i	−0.452341	−	0.891845i	$-0.649411\pi$
$73$	500.123	−	288.746i	0.0938494	−	0.0541840i	0.546190	+	0.837661i	$0.316078\pi$
$74$	−1395.37	−	2416.85i	−0.254815	−	0.441353i
$75$	252.825	+	145.969i	0.0449467	+	0.0259500i
$76$			3596.55i			0.622671i
$77$		0			0
$78$	6891.88			1.13279
$79$	1573.12	−	2724.72i	0.252061	−	0.436583i	−0.712032	−	0.702147i	$-0.752225\pi$
$79$	1573.12	−	2724.72i	0.252061	−	0.436583i	0.964093	+	0.265564i	$0.0855582\pi$
$80$	1407.06	−	812.365i	0.219853	−	0.126932i
$81$	−1237.24	−	2142.95i	−0.188574	−	0.326620i
$82$	−2801.47	−	1617.43i	−0.416637	−	0.240546i
$83$			4729.96i			0.686596i	0.939227	+	0.343298i	$0.111544\pi$
$83$			4729.96i			0.686596i	−0.939227	+	0.343298i	$0.888456\pi$
$84$		0			0
$85$	2747.74			0.380309
$86$	−3420.73	+	5924.88i	−0.462511	+	0.801092i
$87$	9636.61	−	5563.70i	1.27317	−	0.735064i
$88$	−497.470	−	861.644i	−0.0642394	−	0.111266i
$89$	725.651	+	418.955i	0.0916110	+	0.0528916i	0.545106	−	0.838367i	$-0.316490\pi$
$89$	725.651	+	418.955i	0.0916110	+	0.0528916i	−0.453495	+	0.891259i	$0.649823\pi$
$90$		−	10327.0i		−	1.27494i
$91$		0			0
$92$	−3486.58			−0.411931
$93$	7792.69	−	13497.3i	0.900993	−	1.56057i
$94$	−3295.61	+	1902.72i	−0.372975	+	0.215337i
$95$	5706.47	+	9883.89i	0.632295	+	1.09517i
$96$	−2350.59	−	1357.11i	−0.255055	−	0.147256i
$97$		−	5622.23i		−	0.597537i	−0.954326	−	0.298769i	$-0.903424\pi$
$97$		−	5622.23i		−	0.597537i	0.954326	−	0.298769i	$-0.0965759\pi$
$98$		0			0
$99$	−6323.99			−0.645240
$100$	77.8805	−	134.893i	0.00778805	−	0.0134893i
$101$	5703.21	−	3292.75i	0.559083	−	0.322787i	−0.193694	−	0.981062i	$-0.562047\pi$
$101$	5703.21	−	3292.75i	0.559083	−	0.322787i	0.752778	+	0.658275i	$0.228714\pi$
$102$	−2295.14	−	3975.30i	−0.220602	−	0.382093i
$103$	−1320.25	−	762.249i	−0.124447	−	0.0718492i	0.436484	−	0.899712i	$-0.356223\pi$
$103$	−1320.25	−	762.249i	−0.124447	−	0.0718492i	−0.560931	+	0.827863i	$0.689557\pi$
$104$		−	3677.11i		−	0.339970i
$105$		0			0
$106$	−10086.7			−0.897717
$107$	−5303.31	+	9185.61i	−0.463212	+	0.802306i	−0.999119	−	0.0419706i	$-0.986636\pi$
$107$	−5303.31	+	9185.61i	−0.463212	+	0.802306i	0.535907	+	0.844277i	$0.319970\pi$
$108$	−6526.23	+	3767.92i	−0.559519	+	0.323039i
$109$	6976.13	+	12083.0i	0.587167	+	1.01700i	0.994601	+	0.103769i	$0.0330902\pi$
$109$	6976.13	+	12083.0i	0.587167	+	1.01700i	−0.407434	+	0.913235i	$0.633576\pi$
$110$	−2734.26	−	1578.62i	−0.225972	−	0.130465i
$111$			14794.3i			1.20074i
$112$		0			0
$113$	−8811.30			−0.690054			−0.345027	−	0.938593i	$-0.612130\pi$
$113$	−8811.30			−0.690054			−0.345027	+	0.938593i	$0.612130\pi$
$114$	9533.04	−	16511.7i	0.733537	−	1.27052i
$115$	−9581.68	+	5531.99i	−0.724513	+	0.418298i
$116$	−2968.47	−	5141.54i	−0.220606	−	0.382100i
$117$	−20241.0	−	11686.1i	−1.47863	−	0.853689i
$118$		−	12119.8i		−	0.870427i
$119$		0			0
$120$	−8613.05			−0.598129
$121$	6353.79	−	11005.1i	0.433973	−	0.751663i
$122$	−3421.18	+	1975.22i	−0.229856	+	0.132707i
$123$	8574.35	+	14851.2i	0.566749	+	0.981638i
$124$	−7201.40	−	4157.73i	−0.468353	−	0.270404i
$125$			15372.2i			0.983823i
$126$		0			0
$127$	3992.70			0.247548			0.123774	−	0.992310i	$-0.460500\pi$
$127$	3992.70			0.247548			0.123774	+	0.992310i	$0.460500\pi$
$128$	−724.077	+	1254.14i	−0.0441942	+	0.0765466i
$129$	31409.1	−	18134.0i	1.88745	−	1.08972i
$130$	−5834.29	−	10105.3i	−0.345224	−	0.597946i
$131$	17515.4	+	10112.5i	1.02065	+	0.589272i	0.914292	−	0.405056i	$-0.132748\pi$
$131$	17515.4	+	10112.5i	1.02065	+	0.589272i	0.106357	+	0.994328i	$0.466081\pi$
$132$			5274.40i			0.302709i
$133$		0			0
$134$	20550.7			1.14451
$135$	−11956.8	+	20709.7i	−0.656063	+	1.13634i
$136$	−2120.99	+	1224.56i	−0.114673	+	0.0662065i
$137$	−12528.9	−	21700.6i	−0.667530	−	1.15620i	−0.978593	−	0.205807i	$-0.934018\pi$
$137$	−12528.9	−	21700.6i	−0.667530	−	1.15620i	0.311062	−	0.950389i	$-0.399315\pi$
$138$	16006.9	+	9241.56i	0.840520	+	0.485274i
$139$		−	20070.1i		−	1.03877i	−0.854541	−	0.519385i	$-0.826161\pi$
$139$		−	20070.1i		−	1.03877i	0.854541	−	0.519385i	$-0.173839\pi$
$140$		0			0
$141$	20173.5			1.01471
$142$	−8467.98	+	14667.0i	−0.419955	+	0.727384i
$143$	−6188.20	+	3572.76i	−0.302616	+	0.174716i
$144$	4602.35	+	7971.50i	0.221950	+	0.384428i
$145$	−16315.7	−	9419.86i	−0.776013	−	0.448031i
$146$			1633.40i			0.0766277i
$147$		0			0
$148$	7893.40			0.360364
$149$	21353.9	−	36986.1i	0.961846	−	1.66597i	0.243986	−	0.969779i	$-0.421545\pi$
$149$	21353.9	−	36986.1i	0.961846	−	1.66597i	0.717860	−	0.696188i	$-0.245122\pi$
$150$	−715.097	+	412.862i	−0.0317821	+	0.0183494i
$151$	−14803.7	−	25640.8i	−0.649258	−	1.12455i	−0.983301	−	0.181989i	$-0.941746\pi$
$151$	−14803.7	−	25640.8i	−0.649258	−	1.12455i	0.334043	−	0.942558i	$-0.391587\pi$
$152$	−8809.71	−	5086.29i	−0.381307	−	0.220147i
$153$			15566.9i			0.664998i
$154$		0			0
$155$	−26387.5			−1.09833
$156$	−9746.58	+	16881.6i	−0.400501	+	0.693687i
$157$	−10597.6	+	6118.53i	−0.429940	+	0.248226i	−0.699321	−	0.714808i	$-0.746514\pi$
$157$	−10597.6	+	6118.53i	−0.429940	+	0.248226i	0.269381	+	0.963034i	$0.413181\pi$
$158$	4449.44	+	7706.66i	0.178234	+	0.308711i
$159$	46308.1	+	26736.0i	1.83174	+	1.05755i
$160$			4595.43i			0.179509i
$161$		0			0
$162$	6998.86			0.266684
$163$	−10765.6	+	18646.5i	−0.405193	+	0.701814i	−0.994344	−	0.106209i	$-0.966129\pi$
$163$	−10765.6	+	18646.5i	−0.405193	+	0.701814i	0.589151	+	0.808023i	$0.299462\pi$
$164$	7923.75	−	4574.78i	0.294607	−	0.170092i
$165$	8368.63	+	14494.9i	0.307388	+	0.532411i
$166$	−11586.0	−	6689.17i	−0.420452	−	0.242748i
$167$		−	16578.9i		−	0.594461i	−0.954806	−	0.297230i	$-0.903937\pi$
$167$		−	16578.9i		−	0.594461i	0.954806	−	0.297230i	$-0.0960629\pi$
$168$		0			0
$169$	2152.52			0.0753658
$170$	−3885.88	+	6730.55i	−0.134460	+	0.232891i
$171$	−55995.9	+	32329.2i	−1.91498	+	1.10561i
$172$	−9675.28	−	16758.1i	−0.327044	−	0.566458i
$173$	34972.8	+	20191.5i	1.16852	+	0.674648i	0.953332	−	0.301924i	$-0.0976289\pi$
$173$	34972.8	+	20191.5i	1.16852	+	0.674648i	0.215192	+	0.976572i	$0.430962\pi$
$174$			31473.0i			1.03954i
$175$		0			0
$176$	2814.12			0.0908483
$177$	−32124.9	+	55642.0i	−1.02541	+	1.77606i
$178$	−2052.45	+	1184.98i	−0.0647788	+	0.0374000i
$179$	26747.2	+	46327.5i	0.834780	+	1.44588i	0.894209	+	0.447649i	$0.147739\pi$
$179$	26747.2	+	46327.5i	0.834780	+	1.44588i	−0.0594290	+	0.998233i	$0.518928\pi$
$180$	25296.0	+	14604.6i	0.780740	+	0.450761i
$181$		−	54202.1i		−	1.65447i	−0.561857	−	0.827235i	$-0.689913\pi$
$181$		−	54202.1i		−	1.65447i	0.561857	−	0.827235i	$-0.310087\pi$
$182$		0			0
$183$	20942.1			0.625343
$184$	4930.77	−	8540.34i	0.145639	−	0.252255i
$185$	21692.3	−	12524.1i	0.633815	−	0.365934i
$186$	22041.0	+	38176.2i	0.637098	+	1.10349i
$187$	4121.60	+	2379.61i	0.117864	+	0.0680491i
$188$		−	10763.4i		−	0.304533i
$189$		0			0
$190$	−32280.6			−0.894201
$191$	601.936	−	1042.58i	0.0165000	−	0.0285788i	−0.857658	−	0.514221i	$-0.828081\pi$
$191$	601.936	−	1042.58i	0.0165000	−	0.0285788i	0.874158	+	0.485643i	$0.161414\pi$
$192$	6648.46	−	3838.49i	0.180351	−	0.104126i
$193$	−25656.5	−	44438.3i	−0.688783	−	1.19301i	−0.972232	−	0.234019i	$-0.924812\pi$
$193$	−25656.5	−	44438.3i	−0.688783	−	1.19301i	0.283449	−	0.958987i	$-0.408521\pi$
$194$	13771.6	+	7951.03i	0.365915	+	0.211261i
$195$			61857.7i			1.62676i
$196$		0			0
$197$	−1456.28			−0.0375242			−0.0187621	−	0.999824i	$-0.505973\pi$
$197$	−1456.28			−0.0375242			−0.0187621	+	0.999824i	$0.505973\pi$
$198$	8943.48	−	15490.6i	0.228127	−	0.395127i
$199$	−59546.3	+	34379.1i	−1.50366	+	0.868137i	−0.503667	+	0.863898i	$0.668016\pi$
$199$	−59546.3	+	34379.1i	−1.50366	+	0.868137i	−0.999991	+	0.00423890i	$0.998651\pi$
$200$	220.279	+	381.535i	0.00550698	+	0.00953838i
$201$	−94348.3	−	54472.0i	−2.33530	−	1.34828i
$202$			18626.6i			0.456490i
$203$		0			0
$204$	12983.3			0.311978
$205$	14517.2	−	25144.5i	0.345441	−	0.598322i
$206$	3734.24	−	2155.96i	0.0879970	−	0.0508051i
$207$	−31340.7	−	54283.7i	−0.731423	−	1.26686i
$208$	9007.04	+	5200.22i	0.208188	+	0.120197i
$209$			19767.8i			0.452549i
$210$		0			0
$211$	−622.821			−0.0139894			−0.00699469	−	0.999976i	$-0.502226\pi$
$211$	−622.821			−0.0139894			−0.00699469	+	0.999976i	$0.502226\pi$
$212$	14264.8	−	24707.4i	0.317391	−	0.549737i
$213$	77752.8	−	44890.6i	1.71379	−	0.989455i
$214$	−15000.0	−	25980.8i	−0.327540	−	0.567316i
$215$	−53178.5	−	30702.6i	−1.15043	−	0.664199i
$216$		−	21314.6i		−	0.456846i
$217$		0			0
$218$	−39463.0			−0.830380
$219$	4329.50	−	7498.91i	0.0902712	−	0.156354i
$220$	7733.64	−	4465.02i	0.159786	−	0.0922525i
$221$	8794.58	+	15232.7i	0.180066	+	0.311883i
$222$	−36238.5	−	20922.3i	−0.735300	−	0.424526i
$223$		−	11509.7i		−	0.231449i	−0.993281	−	0.115725i	$-0.963081\pi$
$223$		−	11509.7i		−	0.231449i	0.993281	−	0.115725i	$-0.0369190\pi$
$224$		0			0
$225$	2800.26			0.0553138
$226$	12461.1	−	21583.2i	0.243971	−	0.422570i
$227$	48815.4	−	28183.6i	0.947339	−	0.546946i	0.0550855	−	0.998482i	$-0.482457\pi$
$227$	48815.4	−	28183.6i	0.947339	−	0.546946i	0.892253	+	0.451535i	$0.149124\pi$
$228$	26963.5	+	46702.2i	0.518689	+	0.898395i
$229$	36484.4	+	21064.3i	0.695722	+	0.401675i	0.805752	−	0.592253i	$-0.201761\pi$
$229$	36484.4	+	21064.3i	0.695722	+	0.401675i	−0.110030	+	0.993928i	$0.535095\pi$
$230$		−	31293.6i		−	0.591562i
$231$		0			0
$232$	16792.2			0.311984
$233$	27550.9	−	47719.6i	0.507486	−	0.878992i	−0.492476	−	0.870326i	$-0.663908\pi$
$233$	27550.9	−	47719.6i	0.507486	−	0.878992i	0.999962	−	0.00866633i	$-0.00275861\pi$
$234$	57250.2	−	33053.4i	1.04555	−	0.603649i
$235$	−17077.8	−	29579.6i	−0.309240	−	0.535620i
$236$	29687.4	+	17140.0i	0.533026	+	0.307743i
$237$		−	47174.9i		−	0.839875i
$238$		0			0
$239$	23082.5			0.404098			0.202049	−	0.979375i	$-0.435240\pi$
$239$	23082.5			0.404098			0.202049	+	0.979375i	$0.435240\pi$
$240$	12180.7	−	21097.6i	0.211470	−	0.366278i
$241$	−70643.9	+	40786.3i	−1.21630	+	0.702231i	−0.964124	−	0.265451i	$-0.914479\pi$
$241$	−70643.9	+	40786.3i	−1.21630	+	0.702231i	−0.252175	+	0.967682i	$0.581146\pi$
$242$	17971.2	+	31127.1i	0.306865	+	0.531506i
$243$	33946.4	+	19599.0i	0.574886	+	0.331910i
$244$		−	11173.5i		−	0.187677i
$245$		0			0
$246$	−48503.8			−0.801504
$247$	−36529.0	+	63270.0i	−0.598747	+	1.03706i
$248$	20368.6	−	11759.8i	0.331176	−	0.191204i
$249$	35460.8	+	61419.8i	0.571939	+	0.990627i
$250$	−37654.1	−	21739.6i	−0.602466	−	0.347834i
$251$			27207.6i			0.431859i	0.976409	+	0.215930i	$0.0692782\pi$
$251$			27207.6i			0.431859i	−0.976409	+	0.215930i	$0.930722\pi$
$252$		0			0
$253$	−19163.4			−0.299385
$254$	−5646.53	+	9780.08i	−0.0875214	+	0.151592i
$255$	35680.1	−	20599.9i	0.548714	−	0.316800i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−93469.3	−	53964.5i	−1.41515	−	0.817038i	−0.419283	−	0.907856i	$-0.637719\pi$
$257$	−93469.3	−	53964.5i	−1.41515	−	0.817038i	−0.995868	+	0.0908179i	$0.971052\pi$
$258$			102582.i			1.54110i
$259$		0			0
$260$	33003.7			0.488221
$261$	53366.9	−	92434.3i	0.783414	−	1.35691i
$262$	−49540.9	+	28602.5i	−0.721708	+	0.416678i
$263$	20072.0	+	34765.8i	0.290188	+	0.502621i	0.973854	−	0.227174i	$-0.0729487\pi$
$263$	20072.0	+	34765.8i	0.290188	+	0.502621i	−0.683666	+	0.729795i	$0.739615\pi$
$264$	−12919.6	−	7459.12i	−0.185370	−	0.107024i
$265$		−	90533.1i		−	1.28919i
$266$		0			0
$267$	12563.7			0.176236
$268$	−29063.1	+	50338.8i	−0.404644	+	0.700864i
$269$	−91239.0	+	52676.9i	−1.26089	+	0.727973i	−0.973246	−	0.229765i	$-0.926204\pi$
$269$	−91239.0	+	52676.9i	−1.26089	+	0.727973i	−0.287641	+	0.957738i	$0.592871\pi$
$270$	−33818.8	−	58575.9i	−0.463907	−	0.803510i
$271$	13189.3	+	7614.84i	0.179590	+	0.103687i	0.587100	−	0.809514i	$-0.300269\pi$
$271$	13189.3	+	7614.84i	0.179590	+	0.103687i	−0.407510	+	0.913201i	$0.633603\pi$
$272$		−	6927.13i		−	0.0936301i
$273$		0			0
$274$	70874.0			0.944030
$275$	428.056	−	741.415i	0.00566025	−	0.00980384i
$276$	−45274.2	+	26139.1i	−0.594337	+	0.343141i
$277$	4935.81	+	8549.07i	0.0643278	+	0.111419i	0.896396	−	0.443255i	$-0.146176\pi$
$277$	4935.81	+	8549.07i	0.0643278	+	0.111419i	−0.832068	+	0.554674i	$0.812843\pi$
$278$	49161.4	+	28383.4i	0.636114	+	0.367260i
$279$		−	149495.i		−	1.92051i
$280$		0			0
$281$	−155117.			−1.96448			−0.982240	−	0.187631i	$-0.939919\pi$
$281$	−155117.			−1.96448			−0.982240	+	0.187631i	$0.939919\pi$
$282$	−28529.6	+	49414.8i	−0.358755	+	0.621382i
$283$	94970.0	−	54831.0i	1.18581	−	0.684626i	0.228456	−	0.973554i	$-0.426632\pi$
$283$	94970.0	−	54831.0i	1.18581	−	0.684626i	0.957351	+	0.288929i	$0.0932990\pi$
$284$	−23951.1	−	41484.4i	−0.296953	−	0.514338i
$285$	148200.	+	85563.4i	1.82456	+	1.05341i
$286$		−	20210.6i		−	0.247085i
$287$		0			0
$288$	−26034.8			−0.313884
$289$	−35902.9	+	62185.7i	−0.429867	+	0.744552i
$290$	46147.7	−	26643.4i	0.548724	−	0.316806i
$291$	−42150.2	−	73006.2i	−0.497752	−	0.862132i
$292$	−4000.99	−	2309.97i	−0.0469247	−	0.0270920i
$293$			89912.4i			1.04733i	0.851924	+	0.523666i	$0.175436\pi$
$293$			89912.4i			1.04733i	−0.851924	+	0.523666i	$0.824564\pi$
$294$		0			0
$295$	108781.			1.25000
$296$	−11163.0	+	19334.8i	−0.127408	+	0.220677i
$297$	−35870.3	+	20709.7i	−0.406651	+	0.234780i
$298$	60398.1	+	104613.i	0.680128	+	1.17802i
$299$	−61335.5	−	35412.1i	−0.686072	−	0.396104i
$300$		−	2335.50i		−	0.0259500i
$301$		0			0
$302$	83742.5			0.918189
$303$	49371.9	−	85514.6i	0.537767	−	0.931440i
$304$	24917.6	−	14386.2i	0.269624	−	0.155668i
$305$	−17728.5	−	30706.6i	−0.190578	−	0.330090i
$306$	−38131.0	−	22015.0i	−0.407226	−	0.235112i
$307$			141681.i			1.50327i	0.659582	+	0.751633i	$0.270733\pi$
$307$			141681.i			1.50327i	−0.659582	+	0.751633i	$0.729267\pi$
$308$		0			0
$309$	−22858.5			−0.239403
$310$	37317.5	−	64635.9i	0.388320	−	0.672590i
$311$	74171.3	−	42822.8i	0.766858	−	0.442746i	−0.0648948	−	0.997892i	$-0.520671\pi$
$311$	74171.3	−	42822.8i	0.766858	−	0.442746i	0.831753	+	0.555147i	$0.187338\pi$
$312$	−27567.5	−	47748.3i	−0.283197	−	0.490511i
$313$	−15442.6	−	8915.78i	−0.157627	−	0.0910061i	0.419112	−	0.907935i	$-0.362342\pi$
$313$	−15442.6	−	8915.78i	−0.157627	−	0.0910061i	−0.576739	+	0.816929i	$0.695675\pi$
$314$		−	34611.6i		−	0.351045i
$315$		0			0
$316$	−25169.8			−0.252061
$317$	−40402.6	+	69979.4i	−0.402060	+	0.696388i	−0.993974	−	0.109613i	$-0.965039\pi$
$317$	−40402.6	+	69979.4i	−0.402060	+	0.696388i	0.591914	+	0.806001i	$0.298372\pi$
$318$	−130979.	+	75620.9i	−1.29523	+	0.747804i
$319$	−16315.7	−	28259.6i	−0.160333	−	0.277705i
$320$	−11256.5	−	6498.92i	−0.109926	−	0.0634660i
$321$			159037.i			1.54343i
$322$		0			0
$323$	48659.7			0.466406
$324$	−9897.88	+	17143.6i	−0.0942871	+	0.163310i
$325$	2740.13	−	1582.01i	0.0259421	−	0.0149777i
$326$	−30449.6	−	52740.3i	−0.286514	−	0.496258i
$327$	181174.	+	104601.i	1.69434	+	0.978228i
$328$			25878.9i			0.240546i
$329$		0			0
$330$	−47340.1			−0.434712
$331$	−36402.1	+	63050.3i	−0.332254	+	0.575482i	−0.982954	−	0.183854i	$-0.941143\pi$
$331$	−36402.1	+	63050.3i	−0.332254	+	0.575482i	0.650699	+	0.759336i	$0.274476\pi$
$332$	32770.1	−	18919.8i	0.297305	−	0.171649i
$333$	70953.5	+	122895.i	0.639860	+	1.10827i
$334$	40609.9	+	23446.1i	0.364031	+	0.210174i
$335$			184452.i			1.64359i
$336$		0			0
$337$	126538.			1.11419			0.557095	−	0.830449i	$-0.311916\pi$
$337$	126538.			1.11419			0.557095	+	0.830449i	$0.311916\pi$
$338$	−3044.13	+	5272.58i	−0.0266458	+	0.0461519i
$339$	−114417.	+	66058.8i	−0.995616	+	0.574819i
$340$	−10990.9	−	19036.9i	−0.0950773	−	0.164679i
$341$	−39581.2	−	22852.2i	−0.340393	−	0.196526i
$342$		−	182882.i		−	1.56357i
$343$		0			0
$344$	54731.7			0.462511
$345$	−82947.2	+	143669.i	−0.696889	+	1.20705i
$346$	−98917.9	+	57110.3i	−0.826271	+	0.477048i
$347$	33474.6	+	57979.8i	0.278008	+	0.481524i	0.970890	−	0.239528i	$-0.0769926\pi$
$347$	33474.6	+	57979.8i	0.278008	+	0.481524i	−0.692882	+	0.721051i	$0.743659\pi$
$348$	−77092.9	−	44509.6i	−0.636584	−	0.367532i
$349$		−	25527.5i		−	0.209583i	−0.994494	−	0.104792i	$-0.966582\pi$
$349$		−	25527.5i		−	0.209583i	0.994494	−	0.104792i	$-0.0334176\pi$
$350$		0			0
$351$	−153078.			−1.24251
$352$	−3979.76	+	6893.15i	−0.0321197	+	0.0556330i
$353$	48995.9	−	28287.8i	0.393197	−	0.227013i	−0.290347	−	0.956921i	$-0.593771\pi$
$353$	48995.9	−	28287.8i	0.393197	−	0.227013i	0.683545	+	0.729909i	$0.260437\pi$
$354$	−90863.1	−	157379.i	−0.725071	−	1.25586i
$355$	−131643.	−	76003.9i	−1.04458	−	0.603086i
$356$		−	6703.27i		−	0.0528916i
$357$		0			0
$358$	−151305.			−1.18056
$359$	−18902.4	+	32739.9i	−0.146665	+	0.254032i	−0.929993	−	0.367577i	$-0.880187\pi$
$359$	−18902.4	+	32739.9i	−0.146665	+	0.254032i	0.783328	+	0.621609i	$0.213521\pi$
$360$	−71547.8	+	41308.2i	−0.552067	+	0.318736i
$361$	35895.4	+	62172.6i	0.275438	+	0.477073i
$362$	132767.	+	76653.3i	1.01315	+	0.584943i
$363$		−	190539.i		−	1.44601i
$364$		0			0
$365$	−14660.5			−0.110043
$366$	−29616.6	+	51297.5i	−0.221092	+	0.382943i
$367$	−9367.27	+	5408.20i	−0.0695474	+	0.0401532i	−0.534370	−	0.845250i	$-0.679451\pi$
$367$	−9367.27	+	5408.20i	−0.0695474	+	0.0401532i	0.464823	+	0.885404i	$0.346118\pi$
$368$	13946.3	+	24155.7i	0.102983	+	0.178371i
$369$	142453.	+	82245.1i	1.04621	+	0.604028i
$370$			70846.9i			0.517508i
$371$		0			0
$372$	−124683.			−0.900993
$373$	15511.7	−	26867.0i	0.111491	−	0.193109i	−0.804880	−	0.593437i	$-0.797771\pi$
$373$	15511.7	−	26867.0i	0.111491	−	0.193109i	0.916372	+	0.400328i	$0.131104\pi$
$374$	−11657.7	+	6730.55i	−0.0833428	+	0.0481180i
$375$	115246.	+	199613.i	0.819531	+	1.41947i
$376$	26364.9	+	15221.8i	0.186488	+	0.107669i
$377$		−	120599.i		−	0.848519i
$378$		0			0
$379$	−98527.5			−0.685929			−0.342964	−	0.939348i	$-0.611431\pi$
$379$	−98527.5			−0.685929			−0.342964	+	0.939348i	$0.611431\pi$
$380$	45651.7	−	79071.1i	0.316148	−	0.547584i
$381$	51846.3	−	29933.5i	0.357164	−	0.206209i
$382$	1702.53	+	2948.87i	0.0116673	+	0.0202083i
$383$	4454.26	+	2571.67i	0.0303653	+	0.0175314i	0.515106	−	0.857127i	$-0.327753\pi$
$383$	4454.26	+	2571.67i	0.0303653	+	0.0175314i	−0.484741	+	0.874658i	$0.661086\pi$
$384$			21713.8i			0.147256i
$385$		0			0
$386$	145135.			0.974086
$387$	173941.	−	301275.i	1.16140	−	2.01160i
$388$	−38951.9	+	22488.9i	−0.258741	+	0.149384i
$389$	−43141.0	−	74722.4i	−0.285096	−	0.493801i	0.687537	−	0.726150i	$-0.258692\pi$
$389$	−43141.0	−	74722.4i	−0.285096	−	0.493801i	−0.972632	+	0.232349i	$0.925359\pi$
$390$	−151520.	−	87480.0i	−0.996186	−	0.575148i
$391$			47171.9i			0.308553i
$392$		0			0
$393$	303256.			1.96347
$394$	2059.48	−	3567.13i	0.0132668	−	0.0229788i
$395$	−69170.8	+	39935.8i	−0.443331	+	0.255957i
$396$	25296.0	+	43813.9i	0.161310	+	0.279397i
$397$	135036.	+	77963.1i	0.856778	+	0.494661i	0.862932	−	0.505320i	$-0.168625\pi$
$397$	135036.	+	77963.1i	0.856778	+	0.494661i	−0.00615368	+	0.999981i	$0.501959\pi$
$398$		−	194478.i		−	1.22773i
$399$		0			0
$400$	−1246.09			−0.00778805
$401$	−17307.2	+	29977.0i	−0.107631	+	0.186423i	−0.914810	−	0.403884i	$-0.867660\pi$
$401$	−17307.2	+	29977.0i	−0.107631	+	0.186423i	0.807179	+	0.590307i	$0.200993\pi$
$402$	266857.	−	154070.i	1.65130	−	0.953381i
$403$	−84457.5	−	146285.i	−0.520030	−	0.900718i
$404$	−45625.7	−	26342.0i	−0.279542	−	0.161393i
$405$			62817.9i			0.382978i
$406$		0			0
$407$	43384.7			0.261907
$408$	−18361.1	+	31802.4i	−0.110301	+	0.191047i
$409$	271749.	−	156894.i	1.62450	−	0.937907i	0.638809	−	0.769366i	$-0.279428\pi$
$409$	271749.	−	156894.i	1.62450	−	0.937907i	0.985695	−	0.168542i	$-0.0539058\pi$
$410$	41060.7	+	71119.3i	0.244264	+	0.423077i
$411$	−325382.	−	187859.i	−1.92624	−	1.11211i
$412$			12196.0i			0.0718492i
$413$		0			0
$414$	177290.			1.03439
$415$	60038.3	−	103989.i	0.348604	−	0.603800i
$416$	−25475.8	+	14708.4i	−0.147211	+	0.0849924i
$417$	−150466.	−	260615.i	−0.865301	−	1.49875i
$418$	−48421.0	−	27955.9i	−0.277128	−	0.160000i
$419$			7324.74i			0.0417219i	0.999782	+	0.0208609i	$0.00664073\pi$
$419$			7324.74i			0.0417219i	−0.999782	+	0.0208609i	$0.993359\pi$
$420$		0			0
$421$	−25178.3			−0.142057			−0.0710285	−	0.997474i	$-0.522628\pi$
$421$	−25178.3			−0.142057			−0.0710285	+	0.997474i	$0.522628\pi$
$422$	880.802	−	1525.59i	0.00494599	−	0.00856671i
$423$	167579.	−	96752.0i	0.936569	−	0.540728i
$424$	40347.0	+	69883.0i	0.224429	+	0.388723i
$425$	−1825.04	−	1053.69i	−0.0101040	−	0.00583357i
$426$			253940.i			1.39930i
$427$		0			0
$428$	84853.0			0.463212
$429$	−53570.3	+	92786.6i	−0.291078	+	0.504162i
$430$	150411.	−	86840.1i	0.813474	−	0.469660i
$431$	−6913.59	−	11974.7i	−0.0372176	−	0.0644629i	0.846817	−	0.531885i	$-0.178516\pi$
$431$	−6913.59	−	11974.7i	−0.0372176	−	0.0644629i	−0.884034	+	0.467422i	$0.845183\pi$
$432$	52209.9	+	30143.4i	0.279760	+	0.161519i
$433$			47438.8i			0.253022i	0.991965	+	0.126511i	$0.0403779\pi$
$433$			47438.8i			0.253022i	−0.991965	+	0.126511i	$0.959622\pi$
$434$		0			0
$435$	−282485.			−1.49285
$436$	55809.1	−	96664.1i	0.293584	−	0.508502i
$437$	−169682.	+	97966.0i	−0.888532	+	0.512994i
$438$	12245.7	+	21210.1i	0.0638314	+	0.110559i
$439$	−95101.7	−	54907.0i	−0.493469	−	0.284904i	0.232544	−	0.972586i	$-0.425295\pi$
$439$	−95101.7	−	54907.0i	−0.493469	−	0.284904i	−0.726012	+	0.687682i	$0.758628\pi$
$440$			25258.0i			0.130465i
$441$		0			0
$442$	−49749.7			−0.254651
$443$	41280.4	−	71499.7i	0.210347	−	0.364331i	−0.741476	−	0.670979i	$-0.765874\pi$
$443$	41280.4	−	71499.7i	0.210347	−	0.364331i	0.951823	+	0.306648i	$0.0992073\pi$
$444$	102498.	−	59177.3i	0.519936	−	0.300185i
$445$	−10635.8	−	18421.7i	−0.0537092	−	0.0930270i
$446$	28193.0	+	16277.2i	0.141733	+	0.0818297i
$447$		−	640367.i		−	3.20490i
$448$		0			0
$449$	−330438.			−1.63907			−0.819534	−	0.573030i	$-0.805768\pi$
$449$	−330438.			−1.63907			−0.819534	+	0.573030i	$0.805768\pi$
$450$	−3960.17	+	6859.21i	−0.0195564	+	0.0338726i
$451$	43551.5	−	25144.5i	0.214116	−	0.123620i
$452$	35245.2	+	61046.4i	0.172513	+	0.298802i
$453$	−384461.	−	221969.i	−1.87351	−	1.08167i
$454$			159430.i			0.773499i
$455$		0			0
$456$	−152529.			−0.733537
$457$	186644.	−	323276.i	0.893677	−	1.54789i	0.0582431	−	0.998302i	$-0.481450\pi$
$457$	186644.	−	323276.i	0.893677	−	1.54789i	0.835434	−	0.549591i	$-0.185217\pi$
$458$	−103193.	+	59578.7i	−0.491950	+	0.284027i
$459$	50978.3	+	88297.0i	0.241969	+	0.419103i
$460$	76653.4	+	44255.9i	0.362256	+	0.209149i
$461$			20355.2i			0.0957798i	0.998853	+	0.0478899i	$0.0152497\pi$
$461$			20355.2i			0.0957798i	−0.998853	+	0.0478899i	$0.984750\pi$
$462$		0			0
$463$	−31552.7			−0.147189			−0.0735944	−	0.997288i	$-0.523447\pi$
$463$	−31552.7			−0.147189			−0.0735944	+	0.997288i	$0.523447\pi$
$464$	−23747.8	+	41132.3i	−0.110303	+	0.191050i
$465$	−342649.	+	197828.i	−1.58469	+	0.914919i
$466$	77925.8	+	134971.i	0.358847	+	0.621541i
$467$	209452.	+	120927.i	0.960397	+	0.554486i	0.896295	−	0.443458i	$-0.146248\pi$
$467$	209452.	+	120927.i	0.960397	+	0.554486i	0.0641019	+	0.997943i	$0.479582\pi$
$468$			186978.i			0.853689i
$469$		0			0
$470$	96606.6			0.437332
$471$	−91741.9	+	158902.i	−0.413548	+	0.716286i
$472$	−83968.7	+	48479.3i	−0.376906	+	0.217607i
$473$	−53178.5	−	92107.8i	−0.237691	−	0.411694i
$474$	115555.	+	66715.4i	0.514316	+	0.296941i
$475$		−	8753.16i		−	0.0387951i
$476$		0			0
$477$	512903.			2.25423
$478$	−32643.5	+	56540.3i	−0.142870	+	0.247458i
$479$	−235631.	+	136042.i	−1.02698	+	0.592926i	−0.916117	−	0.400910i	$-0.868694\pi$
$479$	−235631.	+	136042.i	−1.02698	+	0.592926i	−0.110861	+	0.993836i	$0.535361\pi$
$480$	34452.2	+	59673.0i	0.149532	+	0.258997i
$481$	138860.	+	80170.8i	0.600187	+	0.346518i
$482$		−	230722.i		−	0.993104i
$483$		0			0
$484$	−101661.			−0.433973
$485$	−71364.1	+	123606.i	−0.303387	+	0.525481i
$486$	−96015.0	+	55434.3i	−0.406506	+	0.234696i
$487$	203873.	+	353119.i	0.859611	+	1.48889i	0.872300	+	0.488971i	$0.162628\pi$
$487$	203873.	+	353119.i	0.859611	+	1.48889i	−0.0126891	+	0.999919i	$0.504039\pi$
$488$	27369.4	+	15801.7i	0.114928	+	0.0663537i
$489$			322840.i			1.35011i
$490$		0			0
$491$	−286772.			−1.18953			−0.594763	−	0.803901i	$-0.702754\pi$
$491$	−286772.			−1.18953			−0.594763	+	0.803901i	$0.702754\pi$
$492$	68594.8	−	118810.i	0.283375	−	0.490819i
$493$	−69562.8	+	40162.1i	−0.286209	+	0.165243i
$494$	−103320.	−	178955.i	−0.423378	−	0.733313i
$495$	139035.	+	80271.8i	0.567431	+	0.327606i
$496$			66523.7i			0.270404i
$497$		0			0
$498$	−200596.			−0.808843
$499$	−175718.	+	304352.i	−0.705690	+	1.22229i	0.260751	+	0.965406i	$0.416030\pi$
$499$	−175718.	+	304352.i	−0.705690	+	1.22229i	−0.966442	+	0.256886i	$0.917304\pi$
$500$	106502.	−	61488.9i	0.426008	−	0.245956i
$501$	−124293.	−	215282.i	−0.495189	−	0.857693i
$502$	−66644.7	−	38477.3i	−0.264459	−	0.152685i
$503$			116045.i			0.458660i	0.973349	+	0.229330i	$0.0736535\pi$
$503$			116045.i			0.458660i	−0.973349	+	0.229330i	$0.926347\pi$
$504$		0			0
$505$	−167182.			−0.655552
$506$	27101.1	−	46940.5i	0.105849	−	0.183335i
$507$	27951.1	−	16137.6i	0.108738	−	0.0627802i
$508$	−15970.8	−	27662.2i	−0.0618870	−	0.107191i
$509$	−72030.7	−	41586.9i	−0.278024	−	0.160517i	0.354505	−	0.935054i	$-0.384649\pi$
$509$	−72030.7	−	41586.9i	−0.278024	−	0.160517i	−0.632528	+	0.774537i	$0.717983\pi$
$510$			116531.i			0.448023i
$511$		0			0
$512$	11585.2			0.0441942
$513$	−211742.	+	366749.i	−0.804587	+	1.39359i
$514$	264371.	−	152635.i	1.00066	−	0.577733i
$515$	19350.8	+	33516.5i	0.0729598	+	0.126370i
$516$	−251273.	−	145072.i	−0.943725	−	0.544860i
$517$		−	59159.2i		−	0.221330i
$518$		0			0
$519$	605508.			2.24794
$520$	−46674.3	+	80842.3i	−0.172612	+	0.298973i
$521$	−174948.	+	101006.i	−0.644517	+	0.372112i	−0.786352	−	0.617778i	$-0.788033\pi$
$521$	−174948.	+	101006.i	−0.644517	+	0.372112i	0.141835	+	0.989890i	$0.454700\pi$
$522$	150945.	+	261444.i	0.553957	+	0.959482i
$523$	24134.0	+	13933.8i	0.0882321	+	0.0509408i	0.543467	−	0.839431i	$-0.317111\pi$
$523$	24134.0	+	13933.8i	0.0882321	+	0.0509408i	−0.455235	+	0.890371i	$0.650445\pi$
$524$		−	161800.i		−	0.589272i
$525$		0			0
$526$	−113545.			−0.410389
$527$	−56252.3	+	97431.8i	−0.202544	+	0.350816i
$528$	36542.1	−	21097.6i	0.131077	−	0.0756772i
$529$	44949.9	+	77855.5i	0.160626	+	0.278213i
$530$	221760.	+	128033.i	0.789462	+	0.455796i
$531$			616284.i			2.18571i
$532$		0			0
$533$	185858.			0.654226
$534$	−17767.8	+	30774.7i	−0.0623089	+	0.107922i
$535$	233190.	−	134632.i	0.814707	−	0.470372i
$536$	−82203.0	−	142380.i	−0.286126	−	0.495586i
$537$	694640.	+	401050.i	2.40886	+	1.39075i
$538$		−	297985.i		−	1.02951i
$539$		0			0
$540$	191308.			0.656063
$541$	18996.8	−	32903.4i	0.0649062	−	0.112421i	−0.831746	−	0.555156i	$-0.812659\pi$
$541$	18996.8	−	32903.4i	0.0649062	−	0.112421i	0.896652	+	0.442735i	$0.145992\pi$
$542$	−37305.0	+	21538.0i	−0.126990	+	0.0733175i
$543$	−406356.	−	703829.i	−1.37818	−	2.38708i
$544$	16967.9	+	9796.44i	0.0573365	+	0.0331032i
$545$		−	354198.i		−	1.19249i
$546$		0			0
$547$	360160.			1.20371			0.601854	−	0.798606i	$-0.294429\pi$
$547$	360160.			1.20371			0.601854	+	0.798606i	$0.294429\pi$
$548$	−100231.	+	173605.i	−0.333765	+	0.578098i
$549$	173964.	−	100438.i	0.577185	−	0.333238i
$550$	1210.73	+	2097.04i	0.00400240	+	0.00693236i
$551$	−288934.	−	166816.i	−0.951691	−	0.549459i
$552$		−	147865.i		−	0.485274i
$553$		0			0
$554$	−27921.1			−0.0909732
$555$	187787.	−	325257.i	0.609650	−	1.05594i
$556$	−139049.	+	80280.2i	−0.449800	+	0.259692i
$557$	−155272.	−	268938.i	−0.500474	−	0.866847i	−1.00000		0.000547960i	$-0.999826\pi$
$557$	−155272.	−	268938.i	−0.500474	−	0.866847i	0.499525	−	0.866299i	$-0.333508\pi$
$558$	366186.	+	211418.i	1.17607	+	0.679004i
$559$		−	393075.i		−	1.25792i
$560$		0			0
$561$	71360.2			0.226741
$562$	219369.	−	379958.i	0.694548	−	1.20299i
$563$	−14453.4	+	8344.68i	−0.0455988	+	0.0263265i	−0.522626	−	0.852562i	$-0.675048\pi$
$563$	−14453.4	+	8344.68i	−0.0455988	+	0.0263265i	0.477027	+	0.878888i	$0.341714\pi$
$564$	−80694.0	−	139766.i	−0.253678	−	0.439383i
$565$	193719.	+	111844.i	0.606841	+	0.350360i
$566$			310171.i			0.968207i
$567$		0			0
$568$	135488.			0.419955
$569$	65131.1	−	112810.i	0.201170	−	0.348437i	−0.747736	−	0.663997i	$-0.768859\pi$
$569$	65131.1	−	112810.i	0.201170	−	0.348437i	0.948906	+	0.315560i	$0.102192\pi$
$570$	−419173.	+	242010.i	−1.29016	+	0.744875i
$571$	249119.	+	431487.i	0.764073	+	1.32341i	0.940735	+	0.339142i	$0.110137\pi$
$571$	249119.	+	431487.i	0.764073	+	1.32341i	−0.176662	+	0.984272i	$0.556530\pi$
$572$	49505.6	+	28582.1i	0.151308	+	0.0873578i
$573$		−	18051.0i		−	0.0549784i
$574$		0			0
$575$	8485.52			0.0256651
$576$	36818.8	−	63772.0i	0.110975	−	0.192214i
$577$	29199.1	−	16858.1i	0.0877035	−	0.0506357i	−0.455507	−	0.890232i	$-0.650542\pi$
$577$	29199.1	−	16858.1i	0.0877035	−	0.0506357i	0.543210	+	0.839597i	$0.317209\pi$
$578$	−101549.	−	175888.i	−0.303962	−	0.526478i
$579$	−666313.	−	384696.i	−1.98756	−	1.14752i
$580$			150718.i			0.448031i
$581$		0			0
$582$	238437.			0.703928
$583$	78404.0	−	135800.i	0.230675	−	0.399541i
$584$	11316.5	−	6533.58i	0.0331808	−	0.0191569i
$585$	296669.	+	513846.i	0.866884	+	1.50149i
$586$	−220240.	−	127155.i	−0.641357	−	0.370288i
$587$			356809.i			1.03552i	0.855525	+	0.517762i	$0.173235\pi$
$587$			356809.i			1.03552i	−0.855525	+	0.517762i	$0.826765\pi$
$588$		0			0
$589$	−467296.			−1.34698
$590$	−153840.	+	266458.i	−0.441941	+	0.765464i
$591$	−18910.1	+	10917.8i	−0.0541402	+	0.0312579i
$592$	−31573.6	−	54687.1i	−0.0900909	−	0.156042i
$593$	28872.6	+	16669.6i	0.0821063	+	0.0474041i	0.540491	−	0.841350i	$-0.318238\pi$
$593$	28872.6	+	16669.6i	0.0821063	+	0.0474041i	−0.458385	+	0.888754i	$0.651572\pi$
$594$		−	117152.i		−	0.332029i
$595$		0			0
$596$	−341663.			−0.961846
$597$	−515484.	+	892844.i	−1.44633	+	2.50511i
$598$	173483.	−	100160.i	0.485126	−	0.280088i
$599$	−162165.	−	280878.i	−0.451963	−	0.782824i	0.546545	−	0.837430i	$-0.315943\pi$
$599$	−162165.	−	280878.i	−0.451963	−	0.782824i	−0.998508	+	0.0546064i	$0.982610\pi$
$600$	5720.78	+	3302.89i	0.0158911	+	0.00917470i
$601$			66322.0i			0.183615i	0.995777	+	0.0918076i	$0.0292645\pi$
$601$			66322.0i			0.183615i	−0.995777	+	0.0918076i	$0.970736\pi$
$602$		0			0
$603$	−1.04499e6			−2.87394
$604$	−118430.	+	205126.i	−0.324629	+	0.562274i
$605$	−279380.	+	161300.i	−0.763281	+	0.440680i
$606$	139645.	+	241872.i	0.380259	+	0.658628i
$607$	422322.	+	243828.i	1.14622	+	0.661768i	0.947962	−	0.318383i	$-0.103140\pi$
$607$	422322.	+	243828.i	1.14622	+	0.661768i	0.198253	+	0.980151i	$0.436473\pi$
$608$			81380.6i			0.220147i
$609$		0			0
$610$	100287.			0.269517
$611$	109321.	−	189349.i	0.292833	−	0.507201i
$612$	107851.	−	62267.7i	0.287952	−	0.166249i
$613$	170755.	+	295757.i	0.454415	+	0.787070i	0.998654	−	0.0518597i	$-0.0165149\pi$
$613$	170755.	+	295757.i	0.454415	+	0.787070i	−0.544239	+	0.838930i	$0.683182\pi$
$614$	−347047.	−	200368.i	−0.920558	−	0.531484i
$615$		−	435344.i		−	1.15102i
$616$		0			0
$617$	240873.			0.632728			0.316364	−	0.948638i	$-0.397538\pi$
$617$	240873.			0.632728			0.316364	+	0.948638i	$0.397538\pi$
$618$	32326.8	−	55991.6i	0.0846419	−	0.146604i
$619$	133658.	−	77167.4i	0.348830	−	0.201397i	−0.315340	−	0.948979i	$-0.602119\pi$
$619$	133658.	−	77167.4i	0.348830	−	0.201397i	0.664170	+	0.747582i	$0.268785\pi$
$620$	105550.	+	182818.i	0.274584	+	0.475593i
$621$	−355535.	−	205268.i	−0.921932	−	0.532278i
$622$			242242.i			0.626137i
$623$		0			0
$624$	155945.			0.400501
$625$	201207.	−	348501.i	0.515091	−	0.892164i
$626$	43678.2	−	25217.6i	0.111459	−	0.0643510i
$627$	148200.	+	256690.i	0.376976	+	0.652941i
$628$	84780.8	+	48948.2i	0.214970	+	0.124113i
$629$		−	106794.i		−	0.269927i
$630$		0			0
$631$	220248.			0.553164			0.276582	−	0.960990i	$-0.410798\pi$
$631$	220248.			0.553164			0.276582	+	0.960990i	$0.410798\pi$
$632$	35595.5	−	61653.3i	0.0891172	−	0.154355i
$633$	−8087.50	+	4669.32i	−0.0201840	+	0.0116532i
$634$	−114276.	−	197932.i	−0.284299	−	0.492421i
$635$	−87780.7	−	50680.2i	−0.217696	−	0.125687i
$636$		−	427776.i		−	1.05755i
$637$		0			0
$638$	92295.4			0.226745
$639$	430590.	−	745804.i	1.05454	−	1.82651i
$640$	31838.1	−	18381.7i	0.0777297	−	0.0448773i
$641$	340604.	+	589943.i	0.828960	+	1.43580i	0.898855	+	0.438247i	$0.144400\pi$
$641$	340604.	+	589943.i	0.828960	+	1.43580i	−0.0698947	+	0.997554i	$0.522266\pi$
$642$	−389559.	−	224912.i	−0.945156	−	0.545686i
$643$			572102.i			1.38373i	0.722027	+	0.691865i	$0.243211\pi$
$643$			572102.i			1.38373i	−0.722027	+	0.691865i	$0.756789\pi$
$644$		0			0
$645$	−920716.			−2.21313
$646$	−68815.2	+	119191.i	−0.164899	+	0.285614i
$647$	525915.	−	303637.i	1.25634	−	0.725348i	0.283979	−	0.958830i	$-0.408345\pi$
$647$	525915.	−	303637.i	1.25634	−	0.725348i	0.972361	+	0.233482i	$0.0750120\pi$
$648$	−27995.4	−	48489.5i	−0.0666710	−	0.115478i
$649$	163171.	+	94207.1i	0.387396	+	0.223663i
$650$			8949.23i			0.0211816i
$651$		0			0
$652$	172249.			0.405193
$653$	242335.	−	419737.i	0.568316	−	0.984353i	−0.428416	−	0.903581i	$-0.640928\pi$
$653$	242335.	−	419737.i	0.568316	−	0.984353i	0.996733	−	0.0807713i	$-0.0257383\pi$
$654$	−512438.	+	295856.i	−1.19808	+	0.691711i
$655$	−256720.	−	444652.i	−0.598380	−	1.03642i
$656$	−63390.0	−	36598.3i	−0.147304	−	0.0850458i
$657$		−	83057.0i		−	0.192418i
$658$		0			0
$659$	329627.			0.759017			0.379509	−	0.925188i	$-0.376093\pi$
$659$	329627.			0.759017			0.379509	+	0.925188i	$0.376093\pi$
$660$	66949.0	−	115959.i	0.153694	−	0.266205i
$661$	182392.	−	105304.i	0.417449	−	0.241014i	−0.276536	−	0.961003i	$-0.589187\pi$
$661$	182392.	−	105304.i	0.417449	−	0.241014i	0.693985	+	0.719989i	$0.255853\pi$
$662$	−102961.	−	178333.i	−0.234939	−	0.406927i
$663$	228400.	+	131867.i	0.519600	+	0.299991i
$664$			107027.i			0.242748i
$665$		0			0
$666$	−401374.			−0.904899
$667$	161716.	−	280100.i	0.363497	−	0.629595i
$668$	−114862.	+	66315.7i	−0.257409	+	0.148615i
$669$	−86289.2	−	149457.i	−0.192799	−	0.333937i
$670$	−451814.	−	260855.i	−1.00649	−	0.581098i
$671$		−	61413.2i		−	0.136401i
$672$		0			0
$673$	94709.8			0.209105			0.104553	−	0.994519i	$-0.466659\pi$
$673$	94709.8			0.209105			0.104553	+	0.994519i	$0.466659\pi$
$674$	−178951.	+	309952.i	−0.393926	+	0.682300i
$675$	15883.3	−	9170.24i	0.0348605	−	0.0201267i
$676$	−8610.09	−	14913.1i	−0.0188414	−	0.0326343i
$677$	−466400.	−	269276.i	−1.01761	−	0.587517i	−0.104199	−	0.994556i	$-0.533228\pi$
$677$	−466400.	−	269276.i	−1.01761	−	0.587517i	−0.913411	+	0.407039i	$0.866561\pi$
$678$		−	373685.i		−	0.812917i
$679$		0			0
$680$	62174.1			0.134460
$681$	422588.	−	731944.i	0.911219	−	1.57828i
$682$	111953.	−	64635.9i	0.240694	−	0.138965i
$683$	64535.9	+	111779.i	0.138344	+	0.239618i	0.926870	−	0.375383i	$-0.122489\pi$
$683$	64535.9	+	111779.i	0.138344	+	0.239618i	−0.788526	+	0.615001i	$0.789155\pi$
$684$	447967.	+	258634.i	0.957489	+	0.552806i
$685$			636126.i			1.35570i
$686$		0			0
$687$	631680.			1.33839
$688$	−77402.3	+	134065.i	−0.163522	+	0.283229i
$689$	501890.	−	289766.i	1.05723	−	0.610393i
$690$	−234610.	−	406357.i	−0.492775	−	0.853511i
$691$	−113201.	−	65356.6i	−0.237079	−	0.136878i	0.376754	−	0.926313i	$-0.377040\pi$
$691$	−113201.	−	65356.6i	−0.237079	−	0.136878i	−0.613834	+	0.789435i	$0.710373\pi$
$692$		−	323064.i		−	0.674648i
$693$		0			0
$694$	−189361.			−0.393162
$695$	−254753.	+	441246.i	−0.527413	+	0.913505i
$696$	218052.	−	125892.i	0.450133	−	0.259884i
$697$	−61894.8	−	107205.i	−0.127406	−	0.220673i
$698$	62529.3	+	36101.3i	0.128343	+	0.0740989i
$699$		−	826204.i		−	1.69096i
$700$		0			0
$701$	−182501.			−0.371389			−0.185694	−	0.982608i	$-0.559453\pi$
$701$	−182501.			−0.371389			−0.185694	+	0.982608i	$0.559453\pi$
$702$	216485.	−	374964.i	0.439293	−	0.760878i
$703$	384150.	−	221789.i	0.777302	−	0.448776i
$704$	−11256.5	−	19496.8i	−0.0227121	−	0.0393385i
$705$	−443520.	−	256066.i	−0.892349	−	0.515198i
$706$			160020.i			0.321044i
$707$		0			0
$708$	513999.			1.02541
$709$	−406899.	+	704770.i	−0.809458	+	1.40202i	0.103783	+	0.994600i	$0.466905\pi$
$709$	−406899.	+	704770.i	−0.809458	+	1.40202i	−0.913240	+	0.407422i	$0.866428\pi$
$710$	372342.	−	214972.i	0.738627	−	0.426446i
$711$	−226251.	−	391878.i	−0.447560	−	0.775196i
$712$	16419.6	+	9479.86i	0.0323894	+	0.0187000i
$713$		−	453008.i		−	0.891101i
$714$		0			0
$715$	181399.			0.354832
$716$	213978.	−	370620.i	0.417390	−	0.722941i
$717$	299732.	−	173051.i	0.583036	−	0.336616i
$718$	−53464.0	−	92602.4i	−0.103708	−	0.179628i
$719$	364222.	+	210283.i	0.704544	+	0.406769i	0.809038	−	0.587757i	$-0.199989\pi$
$719$	364222.	+	210283.i	0.704544	+	0.406769i	−0.104494	+	0.994526i	$0.533322\pi$
$720$		−	233674.i		−	0.450761i
$721$		0			0
$722$	−203055.			−0.389528
$723$	−611554.	+	1.05924e6i	−1.16992	+	2.02637i
$724$	−375523.	+	216808.i	−0.716406	+	0.413617i
$725$	7224.56	+	12513.3i	0.0137447	+	0.0238065i
$726$	466723.	+	269463.i	0.885495	+	0.511241i
$727$			172948.i			0.327225i	0.986525	+	0.163613i	$0.0523147\pi$
$727$			172948.i			0.327225i	−0.986525	+	0.163613i	$0.947685\pi$
$728$		0			0
$729$	788171.			1.48308
$730$	20733.0	−	35910.7i	0.0389061	−	0.0673873i
$731$	−226729.	+	130902.i	−0.424300	+	0.244970i
$732$	−83768.5	−	145091.i	−0.156336	−	0.270782i
$733$	−113936.	−	65780.9i	−0.212057	−	0.122431i	0.390210	−	0.920726i	$-0.372402\pi$
$733$	−113936.	−	65780.9i	−0.212057	−	0.122431i	−0.602267	+	0.798295i	$0.705736\pi$
$734$		−	30593.4i		−	0.0567852i
$735$		0			0
$736$	−78892.3			−0.145639
$737$	−159740.	+	276678.i	−0.294090	+	0.509378i
$738$	−402917.	+	232624.i	−0.739780	+	0.427112i
$739$	244884.	+	424151.i	0.448406	+	0.776662i	0.998282	−	0.0585842i	$-0.0186586\pi$
$739$	244884.	+	424151.i	0.448406	+	0.776662i	−0.549877	+	0.835246i	$0.685325\pi$
$740$	−173539.	−	100193.i	−0.316908	−	0.182967i
$741$			1.09544e6i			1.99504i
$742$		0			0
$743$	580258.			1.05110			0.525549	−	0.850763i	$-0.323860\pi$
$743$	580258.			1.05110			0.525549	+	0.850763i	$0.323860\pi$
$744$	176328.	−	305410.i	0.318549	−	0.551743i
$745$	−938945.	+	542100.i	−1.69172	+	0.976713i
$746$	43873.7	+	75991.5i	0.0788364	+	0.136549i
$747$	589139.	+	340139.i	1.05579	+	0.609559i
$748$		−	38073.7i		−	0.0680491i
$749$		0			0
$750$	−651933.			−1.15899
$751$	−218698.	+	378797.i	−0.387763	+	0.671624i	−0.992148	−	0.125067i	$-0.960085\pi$
$751$	−218698.	+	378797.i	−0.387763	+	0.671624i	0.604386	+	0.796692i	$0.293419\pi$
$752$	−74571.2	+	43053.7i	−0.131867	+	0.0761333i
$753$	203977.	+	353298.i	0.359742	+	0.623091i
$754$	295407.	+	170553.i	0.519610	+	0.299997i
$755$			751627.i			1.31859i
$756$		0			0
$757$	−24171.7			−0.0421809			−0.0210905	−	0.999778i	$-0.506714\pi$
$757$	−24171.7			−0.0421809			−0.0210905	+	0.999778i	$0.506714\pi$
$758$	139339.	−	241342.i	0.242512	−	0.420044i
$759$	−248842.	+	143669.i	−0.431956	+	0.249390i
$760$	129123.	+	223647.i	0.223550	+	0.387200i
$761$	561376.	+	324111.i	0.969359	+	0.559659i	0.899041	−	0.437865i	$-0.144265\pi$
$761$	561376.	+	324111.i	0.969359	+	0.559659i	0.0703180	+	0.997525i	$0.477599\pi$
$762$			169329.i			0.291624i
$763$		0			0
$764$	−9630.98			−0.0165000
$765$	197594.	−	342243.i	0.337638	−	0.584806i
$766$	−12598.5	+	7273.77i	−0.0214715	+	0.0123966i
$767$	348172.	+	603051.i	0.591838	+	1.02509i
$768$	−53187.7	−	30707.9i	−0.0901756	−	0.0520629i
$769$		−	179564.i		−	0.303646i	−0.988408	−	0.151823i	$-0.951486\pi$
$769$		−	179564.i		−	0.303646i	0.988408	−	0.151823i	$-0.0485143\pi$
$770$		0			0
$771$	−1.61830e6			−2.72239
$772$	−205252.	+	355506.i	−0.344391	+	0.596503i
$773$	−529068.	+	305457.i	−0.885426	+	0.511201i	−0.872444	−	0.488715i	$-0.837466\pi$
$773$	−529068.	+	305457.i	−0.885426	+	0.511201i	−0.0129823	+	0.999916i	$0.504133\pi$
$774$	491981.	+	852136.i	0.821233	+	1.42242i
$775$	17526.5	+	10118.9i	0.0291805	+	0.0168474i
$776$		−	127216.i		−	0.211261i
$777$		0			0
$778$	244042.			0.403186
$779$	257085.	−	445284.i	0.423644	−	0.733773i
$780$	428563.	−	247431.i	0.704410	−	0.406691i
$781$	−131643.	−	228012.i	−0.215821	−	0.373814i
$782$	−115547.	−	66711.1i	−0.188949	−	0.109090i
$783$		−	699061.i		−	1.14023i
$784$		0			0
$785$	310655.			0.504126
$786$	−428868.	+	742822.i	−0.694191	+	1.20237i
$787$	−1.03191e6	+	595774.i	−1.66607	+	0.961905i	−0.696342	+	0.717710i	$0.745190\pi$
$787$	−1.03191e6	+	595774.i	−1.66607	+	0.961905i	−0.969726	+	0.244195i	$0.921476\pi$
$788$	5825.10	+	10089.4i	0.00938104	+	0.0162484i
$789$	521282.	+	300963.i	0.837373	+	0.483458i
$790$		−	225911.i		−	0.361979i
$791$		0			0
$792$	−143096.			−0.228127
$793$	113486.	−	196563.i	0.180466	−	0.312576i
$794$	−381939.	+	220513.i	−0.605834	+	0.349778i
$795$	−678732.	−	1.17560e6i	−1.07390	−	1.86005i
$796$	476371.	+	275033.i	0.751829	+	0.434069i
$797$		−	900495.i		−	1.41764i	−0.705392	−	0.708818i	$-0.749229\pi$
$797$		−	900495.i		−	1.41764i	0.705392	−	0.708818i	$-0.250771\pi$
$798$		0			0
$799$	−145624.			−0.228108
$800$	1762.23	−	3052.28i	0.00275349	−	0.00476919i
$801$	104366.	−	60255.5i	0.162664	−	0.0939142i
$802$	−48952.2	−	84787.8i	−0.0761069	−	0.131821i
$803$	−21990.7	−	12696.3i	−0.0341042	−	0.0196901i
$804$			871552.i			1.34828i
$805$		0			0
$806$	477764.			0.735433
$807$	−789843.	+	1.36805e6i	−1.21281	+	2.10065i
$808$	129049.	−	74506.4i	0.197666	−	0.114122i
$809$	−277882.	−	481306.i	−0.424584	−	0.735401i	0.571798	−	0.820395i	$-0.306246\pi$
$809$	−277882.	−	481306.i	−0.424584	−	0.735401i	−0.996381	+	0.0849939i	$0.972913\pi$
$810$	−153872.	−	88838.0i	−0.234525	−	0.135403i
$811$			70954.2i			0.107879i	0.998544	+	0.0539395i	$0.0171778\pi$
$811$			70954.2i			0.107879i	−0.998544	+	0.0539395i	$0.982822\pi$
$812$		0			0
$813$	228356.			0.345486
$814$	−61355.2	+	106270.i	−0.0925982	+	0.160385i
$815$	473368.	−	273299.i	0.712662	−	0.411455i
$816$	−51933.1	−	89950.8i	−0.0779945	−	0.135090i
$817$	−941738.	−	543713.i	−1.41087	−	0.814564i
$818$			887527.i			1.32640i
$819$		0			0
$820$	−232275.			−0.345441
$821$	312356.	−	541016.i	0.463408	−	0.802646i	−0.535720	−	0.844396i	$-0.679960\pi$
$821$	312356.	−	541016.i	0.463408	−	0.802646i	0.999128	+	0.0417495i	$0.0132931\pi$
$822$	920319.	−	531346.i	1.36206	−	0.786383i
$823$	105029.	+	181916.i	0.155064	+	0.268579i	0.933082	−	0.359663i	$-0.117108\pi$
$823$	105029.	+	181916.i	0.155064	+	0.268579i	−0.778018	+	0.628242i	$0.783775\pi$
$824$	−29873.9	−	17247.7i	−0.0439985	−	0.0254025i
$825$		−	12836.6i		−	0.0188601i
$826$		0			0
$827$	−880910.			−1.28801			−0.644007	−	0.765020i	$-0.722729\pi$
$827$	−880910.			−1.28801			−0.644007	+	0.765020i	$0.722729\pi$
$828$	−250726.	+	434270.i	−0.365711	+	0.633431i
$829$	1.11951e6	−	646349.i	1.62899	−	0.940498i	0.644595	−	0.764524i	$-0.277026\pi$
$829$	1.11951e6	−	646349.i	1.62899	−	0.940498i	0.984395	−	0.175974i	$-0.0563075\pi$
$830$	169814.	+	294127.i	0.246500	+	0.426951i
$831$	128186.	+	74008.1i	0.185625	+	0.107171i
$832$		−	83203.5i		−	0.120197i
$833$		0			0
$834$	851166.			1.22372
$835$	−210440.	+	364492.i	−0.301825	+	0.522775i
$836$	136955.	−	79071.1i	0.195959	−	0.113137i
$837$	−489563.	−	847948.i	−0.698808	−	1.21037i
$838$	−17941.9	−	10358.7i	−0.0255493	−	0.0147509i
$839$			1.11586e6i			1.58520i	0.609741	+	0.792601i	$0.291274\pi$
$839$			1.11586e6i			1.58520i	−0.609741	+	0.792601i	$0.708726\pi$
$840$		0			0
$841$	−156542.			−0.221330
$842$	35607.5	−	61674.1i	0.0502247	−	0.0869918i
$843$	−2.01424e6	+	1.16292e6i	−2.83437	+	1.63642i
$844$	2491.28	+	4315.03i	0.00349734	+	0.00605758i
$845$	−47323.8	−	27322.4i	−0.0662775	−	0.0382653i
$846$			547312.i			0.764705i
$847$		0			0
$848$	−228237.			−0.317391
$849$	822142.	−	1.42399e6i	1.14059	−	1.97557i
$850$	5162.00	−	2980.28i	0.00714464	−	0.00412496i
$851$	215008.	+	372404.i	0.296889	+	0.514228i
$852$	−622022.	−	359125.i	−0.856893	−	0.494728i
$853$		−	1.28959e6i		−	1.77236i	−0.463341	−	0.886180i	$-0.653350\pi$
$853$		−	1.28959e6i		−	1.77236i	0.463341	−	0.886180i	$-0.346650\pi$
$854$		0			0
$855$	1.64145e6			2.24540
$856$	−120000.	+	207847.i	−0.163770	+	0.283658i
$857$	566854.	−	327273.i	0.771809	−	0.445604i	−0.0617109	−	0.998094i	$-0.519656\pi$
$857$	566854.	−	327273.i	0.771809	−	0.445604i	0.833519	+	0.552490i	$0.186322\pi$
$858$	−151520.	−	262440.i	−0.205823	−	0.356497i
$859$	−211796.	−	122281.i	−0.287033	−	0.165718i	0.349570	−	0.936910i	$-0.386328\pi$
$859$	−211796.	−	122281.i	−0.287033	−	0.165718i	−0.636603	+	0.771192i	$0.719661\pi$
$860$			491242.i			0.664199i
$861$		0			0
$862$	39109.2			0.0526337
$863$	232638.	−	402942.i	0.312363	−	0.541029i	−0.666510	−	0.745496i	$-0.732213\pi$
$863$	232638.	−	402942.i	0.312363	−	0.541029i	0.978873	+	0.204467i	$0.0655461\pi$
$864$	−147672.	+	85258.4i	−0.197820	+	0.114211i
$865$	−512591.	−	887833.i	−0.685075	−	1.18659i
$866$	−116201.	−	67088.6i	−0.154944	−	0.0894567i
$867$			1.07667e6i			1.43233i
$868$		0			0
$869$	−138342.			−0.183195
$870$	399494.	−	691943.i	0.527802	−	0.914181i
$871$	−1.02255e6	+	590370.i	−1.34787	+	0.778194i
$872$	157852.	+	273407.i	0.207595	+	0.359565i
$873$	−700275.	−	404304.i	−0.918840	−	0.530493i
$874$		−	554179.i		−	0.725484i
$875$		0			0
$876$	−69271.9			−0.0902712
$877$	−152086.	+	263420.i	−0.197738	+	0.342492i	−0.947795	−	0.318882i	$-0.896693\pi$
$877$	−152086.	+	263420.i	−0.197738	+	0.342492i	0.750057	+	0.661373i	$0.230026\pi$
$878$	268988.	−	155301.i	0.348935	−	0.201458i
$879$	674078.	+	1.16754e6i	0.872434	+	1.51110i
$880$	−61869.1	−	35720.2i	−0.0798930	−	0.0461262i
$881$		−	697876.i		−	0.899138i	−0.893246	−	0.449569i	$-0.851578\pi$
$881$		−	697876.i		−	0.899138i	0.893246	−	0.449569i	$-0.148422\pi$
$882$		0			0
$883$	891773.			1.14375			0.571877	−	0.820339i	$-0.306215\pi$
$883$	891773.			1.14375			0.571877	+	0.820339i	$0.306215\pi$
$884$	70356.6	−	121861.i	0.0900328	−	0.155941i
$885$	1.41255e6	−	815537.i	1.80351	−	1.04126i
$886$	116758.	+	202232.i	0.148738	+	0.257621i
$887$	1.09340e6	+	631278.i	1.38974	+	0.802367i	0.993286	−	0.115687i	$-0.0369070\pi$
$887$	1.09340e6	+	631278.i	1.38974	+	0.802367i	0.396455	+	0.918054i	$0.370240\pi$
$888$			334757.i			0.424526i
$889$		0			0
$890$	60164.9			0.0759562
$891$	−54401.9	+	94226.9i	−0.0685265	+	0.118691i
$892$	−79741.8	+	46039.0i	−0.100220	+	0.0578623i
$893$	−302431.	−	523826.i	−0.379248	−	0.656877i
$894$	1.56857e6	+	905616.i	1.96259	+	1.13310i
$895$		−	1.35803e6i		−	1.69537i
$896$		0			0
$897$	−1.06195e6			−1.31983
$898$	467310.	−	809404.i	0.579498	−	1.00372i
$899$	668036.	−	385691.i	0.826572	−	0.477221i
$900$	−11201.0	−	19400.8i	−0.0138284	−	0.0239516i
$901$	−334280.	−	192997.i	−0.411776	−	0.237739i
$902$			142239.i			0.174825i
$903$		0			0
$904$	−199377.			−0.243971
$905$	−687998.	+	1.19165e6i	−0.840021	+	1.45496i
$906$	1.08742e6	−	627822.i	1.32477	−	0.764857i
$907$	−475990.	−	824439.i	−0.578607	−	1.00218i	−0.995639	−	0.0932848i	$-0.970263\pi$
$907$	−475990.	−	824439.i	−0.578607	−	1.00218i	0.417033	−	0.908891i	$-0.363070\pi$
$908$	−390523.	−	225469.i	−0.473669	−	0.273473i
$909$		−	947149.i		−	1.14628i
$910$		0			0
$911$	−743243.			−0.895559			−0.447779	−	0.894144i	$-0.647785\pi$
$911$	−743243.			−0.895559			−0.447779	+	0.894144i	$0.647785\pi$
$912$	215708.	−	373617.i	0.259344	−	0.449198i
$913$	180115.	−	103989.i	0.216077	−	0.124752i
$914$	527908.	+	914363.i	0.631925	+	1.09453i
$915$	−460418.	−	265823.i	−0.549934	−	0.317505i
$916$		−	337028.i		−	0.401675i
$917$		0			0
$918$	−288377.			−0.342196
$919$	262150.	−	454057.i	0.310398	−	0.537625i	−0.668050	−	0.744116i	$-0.732871\pi$
$919$	262150.	−	454057.i	0.310398	−	0.537625i	0.978449	+	0.206491i	$0.0662043\pi$
$920$	−216809.	+	125175.i	−0.256154	+	0.147891i
$921$	1.06219e6	+	1.83977e6i	1.25223	+	2.16892i
$922$	−49859.9	−	28786.6i	−0.0586529	−	0.0338633i
$923$		−	973052.i		−	1.14218i
$924$		0			0
$925$	−19210.7			−0.0224522
$926$	44622.3	−	77288.1i	0.0520391	−	0.0901344i
$927$	−189883.	+	109629.i	−0.220967	+	0.127575i
$928$	−67168.8	−	116340.i	−0.0779959	−	0.135093i
$929$	−848178.	−	489696.i	−0.982779	−	0.567408i	−0.0796709	−	0.996821i	$-0.525387\pi$
$929$	−848178.	−	489696.i	−0.982779	−	0.567408i	−0.903108	+	0.429414i	$0.858720\pi$
$930$		−	1.11909e6i		−	1.29389i
$931$		0			0
$932$	−440815.			−0.507486
$933$	642090.	−	1.11213e6i	0.737620	−	1.27759i
$934$	−592420.	+	342034.i	−0.679103	+	0.392081i
$935$	−60409.7	−	104633.i	−0.0691009	−	0.119686i
$936$	−458001.	−	264427.i	−0.522775	−	0.301824i
$937$			1.13988e6i			1.29831i	0.760656	+	0.649155i	$0.224877\pi$
$937$			1.13988e6i			1.29831i	−0.760656	+	0.649155i	$0.775123\pi$
$938$		0			0
$939$	−267368.			−0.303235
$940$	−136622.	+	236637.i	−0.154620	+	0.267810i
$941$	−693791.	+	400561.i	−0.783519	+	0.452365i	−0.837676	−	0.546167i	$-0.816086\pi$
$941$	−693791.	+	400561.i	−0.783519	+	0.452365i	0.0541569	+	0.998532i	$0.482753\pi$
$942$	−259485.	−	449441.i	−0.292422	−	0.506491i
$943$	431669.	+	249224.i	0.485431	+	0.280264i
$944$		−	274240.i		−	0.307743i
$945$		0			0
$946$	300823.			0.336146
$947$	−340143.	+	589145.i	−0.379282	+	0.656935i	−0.990958	−	0.134173i	$-0.957162\pi$
$947$	−340143.	+	589145.i	−0.379282	+	0.656935i	0.611676	+	0.791108i	$0.290496\pi$
$948$	−326838.	+	188700.i	−0.363677	+	0.209969i
$949$	−46923.3	−	81273.5i	−0.0521022	−	0.0902436i
$950$	21440.8	+	12378.8i	0.0237571	+	0.0137162i
$951$			1.21160e6i			1.33967i
$952$		0			0
$953$	−394774.			−0.434673			−0.217337	−	0.976097i	$-0.569737\pi$
$953$	−394774.			−0.434673			−0.217337	+	0.976097i	$0.569737\pi$
$954$	−725355.	+	1.25635e6i	−0.796992	+	1.38043i
$955$	−26467.5	+	15281.0i	−0.0290206	+	0.0167550i
$956$	−92329.9	−	159920.i	−0.101024	−	0.174979i
$957$	−423727.	−	244639.i	−0.462660	−	0.267117i
$958$		−	769567.i		−	0.838524i
$959$		0			0
$960$	−194891.			−0.211470
$961$	78449.9	−	135879.i	0.0849465	−	0.147132i
$962$	−392755.	+	226757.i	−0.424396	+	0.245025i
$963$	762740.	+	1.32110e6i	0.822478	+	1.42457i
$964$	565151.	+	326290.i	0.608150	+	0.351115i
$965$			1.30265e6i			1.39886i
$966$		0			0
$967$	−604328.			−0.646279			−0.323140	−	0.946351i	$-0.604738\pi$
$967$	−604328.			−0.646279			−0.323140	+	0.946351i	$0.604738\pi$
$968$	143770.	−	249017.i	0.153433	−	0.265753i
$969$	631860.	−	364804.i	0.672935	−	0.388519i
$970$	−201848.	−	349611.i	−0.214527	−	0.371571i
$971$	−657301.	−	379493.i	−0.697149	−	0.402499i	0.109136	−	0.994027i	$-0.465192\pi$
$971$	−657301.	−	379493.i	−0.697149	−	0.402499i	−0.806285	+	0.591528i	$0.798525\pi$
$972$		−	313584.i		−	0.331910i
$973$		0			0
$974$	−1.15328e6			−1.21567
$975$	23720.9	−	41085.8i	0.0249530	−	0.0432198i
$976$	−77412.4	+	44694.1i	−0.0812664	+	0.0469192i
$977$	−612591.	−	1.06104e6i	−0.641773	−	1.11158i	−0.985037	−	0.172345i	$-0.944866\pi$
$977$	−612591.	−	1.06104e6i	−0.641773	−	1.11158i	0.343263	−	0.939239i	$-0.388468\pi$
$978$	−790793.	−	456565.i	−0.826771	−	0.477337i
$979$		−	36843.3i		−	0.0384409i
$980$		0			0
$981$	2.00666e6			2.08514
$982$	405557.	−	702446.i	0.420561	−	0.728434i
$983$	1.03964e6	−	600236.i	1.07591	−	0.621177i	0.146120	−	0.989267i	$-0.453322\pi$
$983$	1.03964e6	−	600236.i	1.07591	−	0.621177i	0.929790	+	0.368090i	$0.119988\pi$
$984$	194015.	+	336044.i	0.200376	+	0.347062i
$985$	32016.6	+	18484.8i	0.0329992	+	0.0190521i
$986$		−	227191.i		−	0.233689i
$987$		0			0
$988$	584464.			0.598747
$989$	527088.	−	912944.i	0.538878	−	0.933365i
$990$	−393250.	+	227043.i	−0.401234	+	0.231653i
$991$	−904963.	−	1.56744e6i	−0.921475	−	1.59604i	−0.797134	−	0.603802i	$-0.793652\pi$
$991$	−904963.	−	1.56744e6i	−0.921475	−	1.59604i	−0.124340	−	0.992240i	$-0.539682\pi$
$992$	−162949.	−	94078.7i	−0.165588	−	0.0956022i
$993$			1.09164e6i			1.10708i
$994$		0			0
$995$	1.74552e6			1.76311
$996$	283686.	−	491359.i	0.285969	−	0.495313i
$997$	−648903.	+	374644.i	−0.652814	+	0.376902i	−0.789534	−	0.613707i	$-0.789677\pi$
$997$	−648903.	+	374644.i	−0.652814	+	0.376902i	0.136719	+	0.990610i	$0.456344\pi$
$998$	−497004.	−	860837.i	−0.498998	−	0.864291i
$999$	804909.	+	464715.i	0.806521	+	0.465645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.5.d.a.19.1		4
7.2	even	3		98.5.b.b.97.4		4
7.3	odd	6	inner	98.5.d.a.31.1		4
7.4	even	3		14.5.d.a.3.1	✓	4
7.5	odd	6		98.5.b.b.97.3		4
7.6	odd	2		14.5.d.a.5.1	yes	4
21.2	odd	6		882.5.c.b.685.1		4
21.5	even	6		882.5.c.b.685.2		4
21.11	odd	6		126.5.n.a.73.2		4
21.20	even	2		126.5.n.a.19.2		4
28.11	odd	6		112.5.s.b.17.2		4
28.19	even	6		784.5.c.b.97.4		4
28.23	odd	6		784.5.c.b.97.1		4
28.27	even	2		112.5.s.b.33.2		4
35.4	even	6		350.5.k.a.101.2		4
35.13	even	4		350.5.i.a.299.3		8
35.18	odd	12		350.5.i.a.199.2		8
35.27	even	4		350.5.i.a.299.2		8
35.32	odd	12		350.5.i.a.199.3		8
35.34	odd	2		350.5.k.a.201.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.1	✓	4	7.4	even	3
14.5.d.a.5.1	yes	4	7.6	odd	2
98.5.b.b.97.3		4	7.5	odd	6
98.5.b.b.97.4		4	7.2	even	3
98.5.d.a.19.1		4	1.1	even	1	trivial
98.5.d.a.31.1		4	7.3	odd	6	inner
112.5.s.b.17.2		4	28.11	odd	6
112.5.s.b.33.2		4	28.27	even	2
126.5.n.a.19.2		4	21.20	even	2
126.5.n.a.73.2		4	21.11	odd	6
350.5.i.a.199.2		8	35.18	odd	12
350.5.i.a.199.3		8	35.32	odd	12
350.5.i.a.299.2		8	35.27	even	4
350.5.i.a.299.3		8	35.13	even	4
350.5.k.a.101.2		4	35.4	even	6
350.5.k.a.201.2		4	35.34	odd	2
784.5.c.b.97.1		4	28.23	odd	6
784.5.c.b.97.4		4	28.19	even	6
882.5.c.b.685.1		4	21.2	odd	6
882.5.c.b.685.2		4	21.5	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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 2.44949i) q^{2} +(12.9853 - 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-21.9853 - 12.6932i) q^{5} +42.4098i q^{6} +22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +O(q^{10})\)	\(q+(-1.41421 + 2.44949i) q^{2} +(12.9853 - 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-21.9853 - 12.6932i) q^{5} +42.4098i q^{6} +22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +(62.1838 - 35.9018i) q^{10} +(-21.9853 - 38.0796i) q^{11} +(-103.882 - 59.9764i) q^{12} -162.507i q^{13} -380.647 q^{15} +(-32.0000 + 55.4256i) q^{16} +(-93.7355 + 54.1182i) q^{17} +(203.397 + 352.294i) q^{18} +(-389.338 - 224.784i) q^{19} +203.091i q^{20} +124.368 q^{22} +(217.911 - 377.433i) q^{23} +(293.823 - 169.639i) q^{24} +(9.73506 + 16.8616i) q^{25} +(398.059 + 229.819i) q^{26} -941.981i q^{27} +742.118 q^{29} +(538.316 - 932.390i) q^{30} +(900.175 - 519.716i) q^{31} +(-90.5097 - 156.767i) q^{32} +(-570.970 - 329.650i) q^{33} -306.139i q^{34} -1150.59 q^{36} +(-493.338 + 854.486i) q^{37} +(1101.21 - 635.786i) q^{38} +(-1218.32 - 2110.20i) q^{39} +(-497.470 - 287.215i) q^{40} +1143.70i q^{41} +2418.82 q^{43} +(-175.882 + 304.637i) q^{44} +(-3162.00 + 1825.58i) q^{45} +(616.346 + 1067.54i) q^{46} +(1165.17 + 672.714i) q^{47} +959.623i q^{48} -55.0698 q^{50} +(-811.455 + 1405.48i) q^{51} +(-1125.88 + 650.027i) q^{52} +(1783.10 + 3088.42i) q^{53} +(2307.37 + 1332.16i) q^{54} +1116.26i q^{55} -6740.88 q^{57} +(-1049.51 + 1817.81i) q^{58} +(-3710.93 + 2142.50i) q^{59} +(1522.59 + 2637.20i) q^{60} +(1209.57 + 698.345i) q^{61} +2939.96i q^{62} +512.000 q^{64} +(-2062.73 + 3572.76i) q^{65} +(1614.95 - 932.390i) q^{66} +(-3632.89 - 6292.36i) q^{67} +(749.884 + 432.946i) q^{68} -6534.77i q^{69} +5987.76 q^{71} +(1627.18 - 2818.35i) q^{72} +(500.123 - 288.746i) q^{73} +(-1395.37 - 2416.85i) q^{74} +(252.825 + 145.969i) q^{75} +3596.55i q^{76} +6891.88 q^{78} +(1573.12 - 2724.72i) q^{79} +(1407.06 - 812.365i) q^{80} +(-1237.24 - 2142.95i) q^{81} +(-2801.47 - 1617.43i) q^{82} +4729.96i q^{83} +2747.74 q^{85} +(-3420.73 + 5924.88i) q^{86} +(9636.61 - 5563.70i) q^{87} +(-497.470 - 861.644i) q^{88} +(725.651 + 418.955i) q^{89} -10327.0i q^{90} -3486.58 q^{92} +(7792.69 - 13497.3i) q^{93} +(-3295.61 + 1902.72i) q^{94} +(5706.47 + 9883.89i) q^{95} +(-2350.59 - 1357.11i) q^{96} -5622.23i q^{97} -6323.99 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} - 16 q^{4} - 54 q^{5} + 84 q^{9}+O(q^{10}) \) 4 * q + 18 * q^3 - 16 * q^4 - 54 * q^5 + 84 * q^9	\( 4 q + 18 q^{3} - 16 q^{4} - 54 q^{5} + 84 q^{9} + 96 q^{10} - 54 q^{11} - 144 q^{12} - 708 q^{15} - 128 q^{16} - 918 q^{17} + 576 q^{18} - 30 q^{19} + 192 q^{22} - 486 q^{23} + 768 q^{24} - 572 q^{25} + 1728 q^{26} + 3240 q^{29} + 1152 q^{30} + 546 q^{31} - 1062 q^{33} - 1344 q^{36} - 446 q^{37} + 4320 q^{38} - 3312 q^{39} - 768 q^{40} + 2344 q^{43} - 432 q^{44} - 5724 q^{45} + 3840 q^{46} - 702 q^{47} - 3456 q^{50} + 318 q^{51} + 384 q^{52} + 2754 q^{53} + 1440 q^{54} - 17460 q^{57} + 384 q^{58} - 12366 q^{59} + 2832 q^{60} - 7686 q^{61} + 2048 q^{64} - 3024 q^{65} + 3456 q^{66} - 5062 q^{67} + 7344 q^{68} + 18792 q^{71} + 4608 q^{72} + 17274 q^{73} - 4320 q^{74} + 5220 q^{75} + 8832 q^{78} + 794 q^{79} + 3456 q^{80} - 4338 q^{81} - 9984 q^{82} + 10380 q^{85} - 10368 q^{86} + 12276 q^{87} - 768 q^{88} + 12474 q^{89} + 7776 q^{92} + 18918 q^{93} - 15168 q^{94} + 8910 q^{95} - 6144 q^{96} - 11448 q^{99}+O(q^{100}) \) 4 * q + 18 * q^3 - 16 * q^4 - 54 * q^5 + 84 * q^9 + 96 * q^10 - 54 * q^11 - 144 * q^12 - 708 * q^15 - 128 * q^16 - 918 * q^17 + 576 * q^18 - 30 * q^19 + 192 * q^22 - 486 * q^23 + 768 * q^24 - 572 * q^25 + 1728 * q^26 + 3240 * q^29 + 1152 * q^30 + 546 * q^31 - 1062 * q^33 - 1344 * q^36 - 446 * q^37 + 4320 * q^38 - 3312 * q^39 - 768 * q^40 + 2344 * q^43 - 432 * q^44 - 5724 * q^45 + 3840 * q^46 - 702 * q^47 - 3456 * q^50 + 318 * q^51 + 384 * q^52 + 2754 * q^53 + 1440 * q^54 - 17460 * q^57 + 384 * q^58 - 12366 * q^59 + 2832 * q^60 - 7686 * q^61 + 2048 * q^64 - 3024 * q^65 + 3456 * q^66 - 5062 * q^67 + 7344 * q^68 + 18792 * q^71 + 4608 * q^72 + 17274 * q^73 - 4320 * q^74 + 5220 * q^75 + 8832 * q^78 + 794 * q^79 + 3456 * q^80 - 4338 * q^81 - 9984 * q^82 + 10380 * q^85 - 10368 * q^86 + 12276 * q^87 - 768 * q^88 + 12474 * q^89 + 7776 * q^92 + 18918 * q^93 - 15168 * q^94 + 8910 * q^95 - 6144 * q^96 - 11448 * q^99

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