LMFDB - Embedded newform 350.5.k.a.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,5,Mod(101,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("350.101");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	350.k (of order $6$, degree $2$, 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:	$36.1794870793$
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			201.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	350.201
Dual form			350.5.k.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 - 2.44949i) q^{2} +(12.9853 - 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} -42.4098i q^{6} +(7.00000 - 48.4974i) q^{7} -22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +O(q^{10})$	\(q+(1.41421 - 2.44949i) q^{2} +(12.9853 - 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} -42.4098i q^{6} +(7.00000 - 48.4974i) q^{7} -22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +(-21.9853 - 38.0796i) q^{11} +(-103.882 - 59.9764i) q^{12} -162.507i q^{13} +(-108.894 - 85.7321i) q^{14} +(-32.0000 + 55.4256i) q^{16} +(-93.7355 + 54.1182i) q^{17} +(-203.397 - 352.294i) q^{18} +(389.338 + 224.784i) q^{19} +(-272.691 - 682.232i) q^{21} -124.368 q^{22} +(-217.911 + 377.433i) q^{23} +(-293.823 + 169.639i) q^{24} +(-398.059 - 229.819i) q^{26} -941.981i q^{27} +(-364.000 + 145.492i) q^{28} +742.118 q^{29} +(-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} -1143.70i q^{41} +(-2056.76 - 296.868i) q^{42} -2418.82 q^{43} +(-175.882 + 304.637i) q^{44} +(616.346 + 1067.54i) q^{46} +(1165.17 + 672.714i) q^{47} +959.623i q^{48} +(-2303.00 - 678.964i) q^{49} +(-811.455 + 1405.48i) q^{51} +(-1125.88 + 650.027i) q^{52} +(-1783.10 - 3088.42i) q^{53} +(-2307.37 - 1332.16i) q^{54} +(-158.392 + 1097.37i) q^{56} +6740.88 q^{57} +(1049.51 - 1817.81i) q^{58} +(3710.93 - 2142.50i) q^{59} +(-1209.57 - 698.345i) q^{61} +2939.96i q^{62} +(-5537.20 - 4359.41i) q^{63} +512.000 q^{64} +(-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} -3596.55i q^{76} +(-2000.66 + 799.672i) q^{77} -6891.88 q^{78} +(1573.12 - 2724.72i) q^{79} +(-1237.24 - 2142.95i) q^{81} +(-2801.47 - 1617.43i) q^{82} +4729.96i q^{83} +(-3635.88 + 4618.19i) q^{84} +(-3420.73 + 5924.88i) q^{86} +(9636.61 - 5563.70i) q^{87} +(497.470 + 861.644i) q^{88} +(-725.651 - 418.955i) q^{89} +(-7881.16 - 1137.55i) q^{91} +3486.58 q^{92} +(-7792.69 + 13497.3i) q^{93} +(3295.61 - 1902.72i) q^{94} +(2350.59 + 1357.11i) q^{96} -5622.23i q^{97} +(-4920.05 + 4680.97i) q^{98} -6323.99 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} - 16 q^{4} + 28 q^{7} + 84 q^{9}+O(q^{10}) $ 4 * q + 18 * q^3 - 16 * q^4 + 28 * q^7 + 84 * q^9	$ 4 q + 18 q^{3} - 16 q^{4} + 28 q^{7} + 84 q^{9} - 54 q^{11} - 144 q^{12} - 128 q^{16} - 918 q^{17} - 576 q^{18} + 30 q^{19} - 378 q^{21} - 192 q^{22} + 486 q^{23} - 768 q^{24} - 1728 q^{26} - 1456 q^{28} + 3240 q^{29} - 546 q^{31} - 1062 q^{33} - 1344 q^{36} + 446 q^{37} + 4320 q^{38} - 3312 q^{39} - 5376 q^{42} - 2344 q^{43} - 432 q^{44} + 3840 q^{46} - 702 q^{47} - 9212 q^{49} + 318 q^{51} + 384 q^{52} - 2754 q^{53} - 1440 q^{54} + 17460 q^{57} - 384 q^{58} + 12366 q^{59} + 7686 q^{61} - 6468 q^{63} + 2048 q^{64} - 3456 q^{66} + 5062 q^{67} + 7344 q^{68} + 18792 q^{71} - 4608 q^{72} + 17274 q^{73} - 4320 q^{74} - 4914 q^{77} - 8832 q^{78} + 794 q^{79} - 4338 q^{81} - 9984 q^{82} - 5040 q^{84} - 10368 q^{86} + 12276 q^{87} + 768 q^{88} - 12474 q^{89} + 2688 q^{91} - 7776 q^{92} - 18918 q^{93} + 15168 q^{94} + 6144 q^{96} - 11448 q^{99}+O(q^{100}) $ 4 * q + 18 * q^3 - 16 * q^4 + 28 * q^7 + 84 * q^9 - 54 * q^11 - 144 * q^12 - 128 * q^16 - 918 * q^17 - 576 * q^18 + 30 * q^19 - 378 * q^21 - 192 * q^22 + 486 * q^23 - 768 * q^24 - 1728 * q^26 - 1456 * q^28 + 3240 * q^29 - 546 * q^31 - 1062 * q^33 - 1344 * q^36 + 446 * q^37 + 4320 * q^38 - 3312 * q^39 - 5376 * q^42 - 2344 * q^43 - 432 * q^44 + 3840 * q^46 - 702 * q^47 - 9212 * q^49 + 318 * q^51 + 384 * q^52 - 2754 * q^53 - 1440 * q^54 + 17460 * q^57 - 384 * q^58 + 12366 * q^59 + 7686 * q^61 - 6468 * q^63 + 2048 * q^64 - 3456 * q^66 + 5062 * q^67 + 7344 * q^68 + 18792 * q^71 - 4608 * q^72 + 17274 * q^73 - 4320 * q^74 - 4914 * q^77 - 8832 * q^78 + 794 * q^79 - 4338 * q^81 - 9984 * q^82 - 5040 * q^84 - 10368 * q^86 + 12276 * q^87 + 768 * q^88 - 12474 * q^89 + 2688 * q^91 - 7776 * q^92 - 18918 * q^93 + 15168 * q^94 + 6144 * q^96 - 11448 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.41421	−	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
$5$		0			0
$5$		0			0
$6$		−	42.4098i		−	1.17805i
$7$	7.00000	−	48.4974i	0.142857	−	0.989743i
$7$	7.00000	−	48.4974i	0.142857	−	0.989743i
$8$	−22.6274			−0.353553
$9$	71.9117	−	124.555i	0.887799	−	1.53771i
$10$		0			0
$11$	−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	$-0.159650\pi$
$14$	−108.894	−	85.7321i	−0.555584	−	0.437409i
$15$		0			0
$16$	−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	0.930491	−	0.366315i	$-0.119381\pi$
$19$	389.338	+	224.784i	1.07850	+	0.622671i	0.148007	+	0.988986i	$0.452714\pi$
$20$		0			0
$21$	−272.691	−	682.232i	−0.618347	−	1.54701i
$22$	−124.368			−0.256958
$23$	−217.911	+	377.433i	−0.411931	+	0.713485i	−0.995101	−	0.0988653i	$-0.968479\pi$
$23$	−217.911	+	377.433i	−0.411931	+	0.713485i	0.583170	+	0.812350i	$0.301812\pi$
$24$	−293.823	+	169.639i	−0.510110	+	0.294512i
$25$		0			0
$26$	−398.059	−	229.819i	−0.588844	−	0.339970i
$27$		−	941.981i		−	1.29215i
$28$	−364.000	+	145.492i	−0.464286	+	0.185577i
$29$	742.118			0.882423			0.441212	−	0.897403i	$-0.354549\pi$
$29$	742.118			0.882423			0.441212	+	0.897403i	$0.354549\pi$
$30$		0			0
$31$	−900.175	+	519.716i	−0.936707	+	0.540808i	−0.888926	−	0.458050i	$-0.848548\pi$
$31$	−900.175	+	519.716i	−0.936707	+	0.540808i	−0.0477804	+	0.998858i	$0.515215\pi$
$32$	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	−0.627657	−	0.778490i	$-0.715986\pi$
$37$	493.338	−	854.486i	0.360364	−	0.624168i	0.988021	+	0.154322i	$0.0493193\pi$
$38$	1101.21	−	635.786i	0.762613	−	0.440295i
$39$	−1218.32	−	2110.20i	−0.801001	−	1.38737i
$40$		0			0
$41$		−	1143.70i		−	0.680366i	−0.940359	−	0.340183i	$-0.889511\pi$
$41$		−	1143.70i		−	0.680366i	0.940359	−	0.340183i	$-0.110489\pi$
$42$	−2056.76	−	296.868i	−1.16597	−	0.168293i
$43$	−2418.82			−1.30818			−0.654089	−	0.756418i	$-0.726948\pi$
$43$	−2418.82			−1.30818			−0.654089	+	0.756418i	$0.726948\pi$
$44$	−175.882	+	304.637i	−0.0908483	+	0.157354i
$45$		0			0
$46$	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
$49$	−2303.00	−	678.964i	−0.959184	−	0.282784i
$50$		0			0
$51$	−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	$-0.947757\pi$
$53$	−1783.10	−	3088.42i	−0.634782	−	1.09947i	0.351780	−	0.936083i	$-0.385577\pi$
$54$	−2307.37	−	1332.16i	−0.791280	−	0.456846i
$55$		0			0
$56$	−158.392	+	1097.37i	−0.0505076	+	0.349927i
$57$	6740.88			2.07475
$58$	1049.51	−	1817.81i	0.311984	−	0.540372i
$59$	3710.93	−	2142.50i	1.06605	−	0.615485i	0.138952	−	0.990299i	$-0.455627\pi$
$59$	3710.93	−	2142.50i	1.06605	−	0.615485i	0.927100	+	0.374814i	$0.122293\pi$
$60$		0			0
$61$	−1209.57	−	698.345i	−0.325066	−	0.187677i	0.328583	−	0.944475i	$-0.393429\pi$
$61$	−1209.57	−	698.345i	−0.325066	−	0.187677i	−0.653648	+	0.756799i	$0.726762\pi$
$62$			2939.96i			0.764818i
$63$	−5537.20	−	4359.41i	−1.39511	−	1.09837i
$64$	512.000			0.125000
$65$		0			0
$66$	−1614.95	+	932.390i	−0.370741	+	0.214047i
$67$	3632.89	+	6292.36i	0.809288	+	1.40173i	0.913358	+	0.407158i	$0.133480\pi$
$67$	3632.89	+	6292.36i	0.809288	+	1.40173i	−0.104070	+	0.994570i	$0.533187\pi$
$68$	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
$75$		0			0
$76$		−	3596.55i		−	0.622671i
$77$	−2000.66	+	799.672i	−0.337436	+	0.134875i
$78$	−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	$0.0855582\pi$
$80$		0			0
$81$	−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	$0.888456\pi$
$84$	−3635.88	+	4618.19i	−0.515289	+	0.654505i
$85$		0			0
$86$	−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	0.453495	−	0.891259i	$-0.350177\pi$
$89$	−725.651	−	418.955i	−0.0916110	−	0.0528916i	−0.545106	+	0.838367i	$0.683510\pi$
$90$		0			0
$91$	−7881.16	−	1137.55i	−0.951716	−	0.137368i
$92$	3486.58			0.411931
$93$	−7792.69	+	13497.3i	−0.900993	+	1.56057i
$94$	3295.61	−	1902.72i	0.372975	−	0.215337i
$95$		0			0
$96$	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	$-0.0965759\pi$
$98$	−4920.05	+	4680.97i	−0.512292	+	0.487398i
$99$	−6323.99			−0.645240
$100$		0			0
$101$	−5703.21	+	3292.75i	−0.559083	+	0.322787i	−0.752778	−	0.658275i	$-0.771286\pi$
$101$	−5703.21	+	3292.75i	−0.559083	+	0.322787i	0.193694	+	0.981062i	$0.437953\pi$
$102$	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	−0.535907	−	0.844277i	$-0.680030\pi$
$107$	5303.31	−	9185.61i	0.463212	−	0.802306i	0.999119	+	0.0419706i	$0.0133636\pi$
$108$	−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	$0.633576\pi$
$110$		0			0
$111$		−	14794.3i		−	1.20074i
$112$	2464.00	+	1939.90i	0.196429	+	0.154647i
$113$	8811.30			0.690054			0.345027	−	0.938593i	$-0.387870\pi$
$113$	8811.30			0.690054			0.345027	+	0.938593i	$0.387870\pi$
$114$	9533.04	−	16511.7i	0.733537	−	1.27052i
$115$		0			0
$116$	−2968.47	−	5141.54i	−0.220606	−	0.382100i
$117$	−20241.0	−	11686.1i	−1.47863	−	0.853689i
$118$		−	12119.8i		−	0.870427i
$119$	1968.45	+	4924.76i	0.139005	+	0.347769i
$120$		0			0
$121$	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
$125$		0			0
$126$	−18509.1	+	7398.17i	−1.16586	+	0.465997i
$127$	−3992.70			−0.247548			−0.123774	−	0.992310i	$-0.539500\pi$
$127$	−3992.70			−0.247548			−0.123774	+	0.992310i	$0.539500\pi$
$128$	724.077	−	1254.14i	0.0441942	−	0.0765466i
$129$	−31409.1	+	18134.0i	−1.88745	+	1.08972i
$130$		0			0
$131$	−17515.4	−	10112.5i	−1.02065	−	0.589272i	−0.106357	−	0.994328i	$-0.533919\pi$
$131$	−17515.4	−	10112.5i	−1.02065	−	0.589272i	−0.914292	+	0.405056i	$0.867252\pi$
$132$			5274.40i			0.302709i
$133$	13626.8	−	17308.4i	0.770355	−	0.978483i
$134$	20550.7			1.14451
$135$		0			0
$136$	2120.99	−	1224.56i	0.114673	−	0.0662065i
$137$	12528.9	+	21700.6i	0.667530	+	1.15620i	0.978593	+	0.205807i	$0.0659818\pi$
$137$	12528.9	+	21700.6i	0.667530	+	1.15620i	−0.311062	+	0.950389i	$0.600685\pi$
$138$	16006.9	+	9241.56i	0.840520	+	0.485274i
$139$			20070.1i			1.03877i	0.854541	+	0.519385i	$0.173839\pi$
$139$			20070.1i			1.03877i	−0.854541	+	0.519385i	$0.826161\pi$
$140$		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
$145$		0			0
$146$		−	1633.40i		−	0.0766277i
$147$	−34995.3	+	8449.18i	−1.61948	+	0.391003i
$148$	−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	$-0.245122\pi$
$150$		0			0
$151$	−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
$154$	−870.573	+	6031.50i	−0.0367082	+	0.254322i
$155$		0			0
$156$	−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
$160$		0			0
$161$	16779.2	+	13210.2i	0.647319	+	0.509632i
$162$	−6998.86			−0.266684
$163$	10765.6	−	18646.5i	0.405193	−	0.701814i	−0.589151	−	0.808023i	$-0.700538\pi$
$163$	10765.6	−	18646.5i	0.405193	−	0.701814i	0.994344	+	0.106209i	$0.0338711\pi$
$164$	−7923.75	+	4574.78i	−0.294607	+	0.170092i
$165$		0			0
$166$	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	$-0.0960629\pi$
$168$	6170.29	+	15437.1i	0.218619	+	0.546951i
$169$	2152.52			0.0753658
$170$		0			0
$171$	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	$0.518928\pi$
$180$		0			0
$181$			54202.1i			1.65447i	0.561857	+	0.827235i	$0.310087\pi$
$181$			54202.1i			1.65447i	−0.561857	+	0.827235i	$0.689913\pi$
$182$	−13932.1	+	17696.1i	−0.420603	+	0.534238i
$183$	−20942.1			−0.625343
$184$	4930.77	−	8540.34i	0.145639	−	0.252255i
$185$		0			0
$186$	22041.0	+	38176.2i	0.637098	+	1.10349i
$187$	4121.60	+	2379.61i	0.117864	+	0.0680491i
$188$		−	10763.4i		−	0.304533i
$189$	−45683.6	−	6593.86i	−1.27890	−	0.184594i
$190$		0			0
$191$	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	$0.0751879\pi$
$193$	25656.5	+	44438.3i	0.688783	+	1.19301i	−0.283449	+	0.958987i	$0.591479\pi$
$194$	−13771.6	−	7951.03i	−0.365915	−	0.211261i
$195$		0			0
$196$	4508.00	+	18671.5i	0.117347	+	0.486035i
$197$	1456.28			0.0375242			0.0187621	−	0.999824i	$-0.494027\pi$
$197$	1456.28			0.0375242			0.0187621	+	0.999824i	$0.494027\pi$
$198$	−8943.48	+	15490.6i	−0.228127	+	0.395127i
$199$	59546.3	−	34379.1i	1.50366	−	0.868137i	0.503667	−	0.863898i	$-0.331984\pi$
$199$	59546.3	−	34379.1i	1.50366	−	0.868137i	0.999991	−	0.00423890i	$-0.00134929\pi$
$200$		0			0
$201$	94348.3	+	54472.0i	2.33530	+	1.34828i
$202$			18626.6i			0.456490i
$203$	5194.82	−	35990.8i	0.126060	−	0.873372i
$204$	12983.3			0.311978
$205$		0			0
$206$	−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
$215$		0			0
$216$			21314.6i			0.456846i
$217$	18903.7	+	47294.2i	0.401446	+	1.00436i
$218$	39463.0			0.830380
$219$	4329.50	−	7498.91i	0.0902712	−	0.156354i
$220$		0			0
$221$	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	$-0.0369190\pi$
$224$	8236.38	−	3292.11i	0.164150	−	0.0656113i
$225$		0			0
$226$	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	0.110030	−	0.993928i	$-0.464905\pi$
$229$	−36484.4	−	21064.3i	−0.695722	−	0.401675i	−0.805752	+	0.592253i	$0.798239\pi$
$230$		0			0
$231$	−19984.0	+	25383.0i	−0.374505	+	0.475685i
$232$	−16792.2			−0.311984
$233$	−27550.9	+	47719.6i	−0.507486	+	0.878992i	0.492476	+	0.870326i	$0.336092\pi$
$233$	−27550.9	+	47719.6i	−0.507486	+	0.878992i	−0.999962	+	0.00866633i	$0.997241\pi$
$234$	−57250.2	+	33053.4i	−1.04555	+	0.603649i
$235$		0			0
$236$	−29687.4	−	17140.0i	−0.533026	−	0.307743i
$237$		−	47174.9i		−	0.839875i
$238$	14846.9	+	2142.97i	0.262110	+	0.0378323i
$239$	23082.5			0.404098			0.202049	−	0.979375i	$-0.435240\pi$
$239$	23082.5			0.404098			0.202049	+	0.979375i	$0.435240\pi$
$240$		0			0
$241$	70643.9	−	40786.3i	1.21630	−	0.702231i	0.252175	−	0.967682i	$-0.418854\pi$
$241$	70643.9	−	40786.3i	1.21630	−	0.702231i	0.964124	+	0.265451i	$0.0855209\pi$
$242$	−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
$250$		0			0
$251$		−	27207.6i		−	0.431859i	−0.976409	−	0.215930i	$-0.930722\pi$
$251$		−	27207.6i		−	0.431859i	0.976409	−	0.215930i	$-0.0692782\pi$
$252$	−8054.11	+	55800.5i	−0.126828	+	0.878693i
$253$	19163.4			0.299385
$254$	−5646.53	+	9780.08i	−0.0875214	+	0.151592i
$255$		0			0
$256$	−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
$259$	−37987.0	−	29907.0i	−0.566286	−	0.445834i
$260$		0			0
$261$	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	0.683666	−	0.729795i	$-0.260385\pi$
$263$	−20072.0	−	34765.8i	−0.290188	−	0.502621i	−0.973854	+	0.227174i	$0.927051\pi$
$264$	12919.6	+	7459.12i	0.185370	+	0.107024i
$265$		0			0
$266$	−23125.5	−	57856.5i	−0.326834	−	0.817690i
$267$	−12563.7			−0.176236
$268$	29063.1	−	50338.8i	0.404644	−	0.700864i
$269$	91239.0	−	52676.9i	1.26089	−	0.727973i	0.287641	−	0.957738i	$-0.407129\pi$
$269$	91239.0	−	52676.9i	1.26089	−	0.727973i	0.973246	+	0.229765i	$0.0737958\pi$
$270$		0			0
$271$	−13189.3	−	7614.84i	−0.179590	−	0.103687i	0.407510	−	0.913201i	$-0.366397\pi$
$271$	−13189.3	−	7614.84i	−0.179590	−	0.103687i	−0.587100	+	0.809514i	$0.699731\pi$
$272$		−	6927.13i		−	0.0936301i
$273$	−110867.	+	44314.1i	−1.48757	+	0.594589i
$274$	70874.0			0.944030
$275$		0			0
$276$	45274.2	−	26139.1i	0.594337	−	0.343141i
$277$	−4935.81	−	8549.07i	−0.0643278	−	0.111419i	0.832068	−	0.554674i	$-0.187157\pi$
$277$	−4935.81	−	8549.07i	−0.0643278	−	0.111419i	−0.896396	+	0.443255i	$0.853824\pi$
$278$	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
$285$		0			0
$286$			20210.6i			0.247085i
$287$	−55466.3	−	8005.87i	−0.673388	−	0.0971952i
$288$	26034.8			0.313884
$289$	−35902.9	+	62185.7i	−0.429867	+	0.744552i
$290$		0			0
$291$	−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	$0.824564\pi$
$294$	−28794.7	+	97669.7i	−0.333133	+	1.12997i
$295$		0			0
$296$	−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
$300$		0			0
$301$	−16931.7	+	117307.i	−0.186883	+	1.29476i
$302$	−83742.5			−0.918189
$303$	−49371.9	+	85514.6i	−0.537767	+	0.931440i
$304$	−24917.6	+	14386.2i	−0.269624	+	0.155668i
$305$		0			0
$306$	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	$0.729267\pi$
$308$	13542.9	+	10662.3i	0.142762	+	0.112396i
$309$	−22858.5			−0.239403
$310$		0			0
$311$	−74171.3	+	42822.8i	−0.766858	+	0.442746i	−0.831753	−	0.555147i	$-0.812662\pi$
$311$	−74171.3	+	42822.8i	−0.766858	+	0.442746i	0.0648948	+	0.997892i	$0.479329\pi$
$312$	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	−0.591914	−	0.806001i	$-0.701628\pi$
$317$	40402.6	−	69979.4i	0.402060	−	0.696388i	0.993974	+	0.109613i	$0.0349610\pi$
$318$	−130979.	+	75620.9i	−1.29523	+	0.747804i
$319$	−16315.7	−	28259.6i	−0.160333	−	0.277705i
$320$		0			0
$321$		−	159037.i		−	1.54343i
$322$	56087.5	−	22418.4i	0.540946	−	0.216218i
$323$	−48659.7			−0.466406
$324$	−9897.88	+	17143.6i	−0.0942871	+	0.163310i
$325$		0			0
$326$	−30449.6	−	52740.3i	−0.286514	−	0.496258i
$327$	181174.	+	104601.i	1.69434	+	0.978228i
$328$			25878.9i			0.240546i
$329$	40781.1	−	51799.0i	0.376762	−	0.478552i
$330$		0			0
$331$	−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
$335$		0			0
$336$	46539.2	+	6717.36i	0.412231	+	0.0595004i
$337$	−126538.			−1.11419			−0.557095	−	0.830449i	$-0.688084\pi$
$337$	−126538.			−1.11419			−0.557095	+	0.830449i	$0.688084\pi$
$338$	3044.13	−	5272.58i	0.0266458	−	0.0461519i
$339$	114417.	−	66058.8i	0.995616	−	0.574819i
$340$		0			0
$341$	39581.2	+	22852.2i	0.340393	+	0.196526i
$342$		−	182882.i		−	1.56357i
$343$	−49049.0	+	106937.i	−0.416910	+	0.908948i
$344$	54731.7			0.462511
$345$		0			0
$346$	98917.9	−	57110.3i	0.826271	−	0.477048i
$347$	−33474.6	−	57979.8i	−0.278008	−	0.481524i	0.692882	−	0.721051i	$-0.256341\pi$
$347$	−33474.6	−	57979.8i	−0.278008	−	0.481524i	−0.970890	+	0.239528i	$0.923007\pi$
$348$	−77092.9	−	44509.6i	−0.636584	−	0.367532i
$349$			25527.5i			0.209583i	0.994494	+	0.104792i	$0.0334176\pi$
$349$			25527.5i			0.209583i	−0.994494	+	0.104792i	$0.966582\pi$
$350$		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
$355$		0			0
$356$			6703.27i			0.0528916i
$357$	62482.0	+	49191.8i	0.490251	+	0.385973i
$358$	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	$0.213521\pi$
$360$		0			0
$361$	35895.4	+	62172.6i	0.275438	+	0.477073i
$362$	132767.	+	76653.3i	1.01315	+	0.584943i
$363$		−	190539.i		−	1.44601i
$364$	23643.5	+	59152.5i	0.178447	+	0.446447i
$365$		0			0
$366$	−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
$370$		0			0
$371$	−162262.	+	64856.9i	−1.17888	+	0.471203i
$372$	124683.			0.900993
$373$	−15511.7	+	26867.0i	−0.111491	+	0.193109i	−0.916372	−	0.400328i	$-0.868896\pi$
$373$	−15511.7	+	26867.0i	−0.111491	+	0.193109i	0.804880	+	0.593437i	$0.202229\pi$
$374$	11657.7	−	6730.55i	0.0833428	−	0.0481180i
$375$		0			0
$376$	−26364.9	−	15221.8i	−0.186488	−	0.107669i
$377$		−	120599.i		−	0.848519i
$378$	−80758.0	+	102576.i	−0.565200	+	0.717900i
$379$	−98527.5			−0.685929			−0.342964	−	0.939348i	$-0.611431\pi$
$379$	−98527.5			−0.685929			−0.342964	+	0.939348i	$0.611431\pi$
$380$		0			0
$381$	−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	$0.925359\pi$
$390$		0			0
$391$		−	47171.9i		−	0.308553i
$392$	52110.9	+	15363.2i	0.339123	+	0.0999792i
$393$	−303256.			−1.96347
$394$	2059.48	−	3567.13i	0.0132668	−	0.0229788i
$395$		0			0
$396$	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
$399$	47186.2	−	326915.i	0.296394	−	2.05347i
$400$		0			0
$401$	−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
$405$		0			0
$406$	−80812.5	−	63623.3i	−0.490260	−	0.385980i
$407$	−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	$0.720572\pi$
$409$	−271749.	+	156894.i	−1.62450	+	0.937907i	−0.985695	+	0.168542i	$0.946094\pi$
$410$		0			0
$411$	325382.	+	187859.i	1.92624	+	1.11211i
$412$			12196.0i			0.0718492i
$413$	−77929.4	−	194968.i	−0.456879	−	1.14304i
$414$	177290.			1.03439
$415$		0			0
$416$	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	$-0.993359\pi$
$419$		−	7324.74i		−	0.0417219i	0.999782	−	0.0208609i	$-0.00664073\pi$
$420$		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
$425$		0			0
$426$		−	253940.i		−	1.39930i
$427$	−42334.9	+	53772.6i	−0.232190	+	0.294920i
$428$	−84853.0			−0.463212
$429$	−53570.3	+	92786.6i	−0.291078	+	0.504162i
$430$		0			0
$431$	−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	$0.959622\pi$
$434$	142580.	+	20579.7i	0.756973	+	0.109260i
$435$		0			0
$436$	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	0.726012	−	0.687682i	$-0.241372\pi$
$439$	95101.7	+	54907.0i	0.493469	+	0.284904i	−0.232544	+	0.972586i	$0.574705\pi$
$440$		0			0
$441$	−250181.	+	238024.i	−1.28640	+	1.22389i
$442$	49749.7			0.254651
$443$	−41280.4	+	71499.7i	−0.210347	+	0.364331i	−0.951823	−	0.306648i	$-0.900793\pi$
$443$	−41280.4	+	71499.7i	−0.210347	+	0.364331i	0.741476	+	0.670979i	$0.234126\pi$
$444$	−102498.	+	59177.3i	−0.519936	+	0.300185i
$445$		0			0
$446$	−28193.0	−	16277.2i	−0.141733	−	0.0818297i
$447$		−	640367.i		−	3.20490i
$448$	3584.00	−	24830.7i	0.0178571	−	0.123718i
$449$	−330438.			−1.63907			−0.819534	−	0.573030i	$-0.805768\pi$
$449$	−330438.			−1.63907			−0.819534	+	0.573030i	$0.805768\pi$
$450$		0			0
$451$	−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	$0.518550\pi$
$457$	−186644.	+	323276.i	−0.893677	+	1.54789i	−0.835434	+	0.549591i	$0.814783\pi$
$458$	−103193.	+	59578.7i	−0.491950	+	0.284027i
$459$	50978.3	+	88297.0i	0.241969	+	0.419103i
$460$		0			0
$461$		−	20355.2i		−	0.0957798i	−0.998853	−	0.0478899i	$-0.984750\pi$
$461$		−	20355.2i		−	0.0957798i	0.998853	−	0.0478899i	$-0.0152497\pi$
$462$	33913.9	+	84847.5i	0.158889	+	0.397517i
$463$	31552.7			0.147189			0.0735944	−	0.997288i	$-0.476553\pi$
$463$	31552.7			0.147189			0.0735944	+	0.997288i	$0.476553\pi$
$464$	−23747.8	+	41132.3i	−0.110303	+	0.191050i
$465$		0			0
$466$	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
$469$	330593.	−	132139.i	1.50296	−	0.600740i
$470$		0			0
$471$	−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
$475$		0			0
$476$	26245.9	−	33336.8i	0.115837	−	0.147133i
$477$	−512903.			−2.25423
$478$	32643.5	−	56540.3i	0.142870	−	0.247458i
$479$	235631.	−	136042.i	1.02698	−	0.592926i	0.110861	−	0.993836i	$-0.464639\pi$
$479$	235631.	−	136042.i	1.02698	−	0.592926i	0.916117	+	0.400910i	$0.131306\pi$
$480$		0			0
$481$	−138860.	−	80170.8i	−0.600187	−	0.346518i
$482$		−	230722.i		−	0.993104i
$483$	316920.	+	45743.4i	1.35848	+	0.196080i
$484$	−101661.			−0.433973
$485$		0			0
$486$	96015.0	−	55434.3i	0.406506	−	0.234696i
$487$	−203873.	−	353119.i	−0.859611	−	1.48889i	−0.872300	−	0.488971i	$-0.837372\pi$
$487$	−203873.	−	353119.i	−0.859611	−	1.48889i	0.0126891	−	0.999919i	$-0.495961\pi$
$488$	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
$495$		0			0
$496$		−	66523.7i		−	0.270404i
$497$	41914.3	−	290391.i	0.169687	−	1.17563i
$498$	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	$0.917304\pi$
$500$		0			0
$501$	−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	$0.926347\pi$
$504$	125293.	+	98642.3i	0.493247	+	0.388331i
$505$		0			0
$506$	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	0.632528	−	0.774537i	$-0.282017\pi$
$509$	72030.7	+	41586.9i	0.278024	+	0.160517i	−0.354505	+	0.935054i	$0.615351\pi$
$510$		0			0
$511$	−10502.6	−	26275.9i	−0.0402212	−	0.100627i
$512$	−11585.2			−0.0441942
$513$	211742.	−	366749.i	0.804587	−	1.39359i
$514$	−264371.	+	152635.i	−1.00066	+	0.577733i
$515$		0			0
$516$	251273.	+	145072.i	0.943725	+	0.544860i
$517$		−	59159.2i		−	0.221330i
$518$	−126979.	+	50753.9i	−0.473229	+	0.189151i
$519$	605508.			2.24794
$520$		0			0
$521$	174948.	−	101006.i	0.644517	−	0.372112i	−0.141835	−	0.989890i	$-0.545300\pi$
$521$	174948.	−	101006.i	0.644517	−	0.372112i	0.786352	+	0.617778i	$0.211967\pi$
$522$	−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
$530$		0			0
$531$		−	616284.i		−	2.18571i
$532$	−174423.	−	25175.8i	−0.616284	−	0.0889530i
$533$	−185858.			−0.654226
$534$	−17767.8	+	30774.7i	−0.0623089	+	0.107922i
$535$		0			0
$536$	−82203.0	−	142380.i	−0.286126	−	0.495586i
$537$	694640.	+	401050.i	2.40886	+	1.39075i
$538$		−	297985.i		−	1.02951i
$539$	24777.4	+	102625.i	0.0852861	+	0.353243i
$540$		0			0
$541$	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
$545$		0			0
$546$	−48243.1	+	334238.i	−0.161827	+	1.12117i
$547$	−360160.			−1.20371			−0.601854	−	0.798606i	$-0.705571\pi$
$547$	−360160.			−1.20371			−0.601854	+	0.798606i	$0.705571\pi$
$548$	100231.	−	173605.i	0.333765	−	0.578098i
$549$	−173964.	+	100438.i	−0.577185	+	0.333238i
$550$		0			0
$551$	288934.	+	166816.i	0.951691	+	0.549459i
$552$		−	147865.i		−	0.485274i
$553$	−121130.	−	95365.1i	−0.396097	−	0.311845i
$554$	−27921.1			−0.0909732
$555$		0			0
$556$	139049.	−	80280.2i	0.449800	−	0.259692i
$557$	155272.	+	268938.i	0.500474	+	0.866847i	1.00000		0.000547960i	$0.000174421\pi$
$557$	155272.	+	268938.i	0.500474	+	0.866847i	−0.499525	+	0.866299i	$0.666492\pi$
$558$	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
$565$		0			0
$566$		−	310171.i		−	0.968207i
$567$	−112588.	+	45002.0i	−0.350209	+	0.139980i
$568$	−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	$0.102192\pi$
$570$		0			0
$571$	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
$574$	−98051.5	+	124542.i	−0.297598	+	0.378000i
$575$		0			0
$576$	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
$580$		0			0
$581$	229391.	+	33109.7i	0.679554	+	0.0980851i
$582$	−238437.			−0.703928
$583$	−78404.0	+	135800.i	−0.230675	+	0.399541i
$584$	−11316.5	+	6533.58i	−0.0331808	+	0.0191569i
$585$		0			0
$586$	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	$0.826765\pi$
$588$	198519.	+	208658.i	0.574179	+	0.603504i
$589$	−467296.			−1.34698
$590$		0			0
$591$	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	$0.982610\pi$
$600$		0			0
$601$		−	66322.0i		−	0.183615i	−0.995777	−	0.0918076i	$-0.970736\pi$
$601$		−	66322.0i		−	0.183615i	0.995777	−	0.0918076i	$-0.0292645\pi$
$602$	263396.	+	207371.i	0.726803	+	0.572209i
$603$	1.04499e6			2.87394
$604$	−118430.	+	205126.i	−0.324629	+	0.562274i
$605$		0			0
$606$	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
$609$	−202369.	−	506297.i	−0.545643	−	1.36512i
$610$		0			0
$611$	109321.	−	189349.i	0.292833	−	0.507201i
$612$	107851.	−	62267.7i	0.287952	−	0.166249i
$613$	−170755.	−	295757.i	−0.454415	−	0.787070i	0.544239	−	0.838930i	$-0.316818\pi$
$613$	−170755.	−	295757.i	−0.454415	−	0.787070i	−0.998654	+	0.0518597i	$0.983485\pi$
$614$	347047.	+	200368.i	0.920558	+	0.531484i
$615$		0			0
$616$	45269.8	−	18094.5i	0.119302	−	0.0476854i
$617$	−240873.			−0.632728			−0.316364	−	0.948638i	$-0.602462\pi$
$617$	−240873.			−0.632728			−0.316364	+	0.948638i	$0.602462\pi$
$618$	−32326.8	+	55991.6i	−0.0846419	+	0.146604i
$619$	−133658.	+	77167.4i	−0.348830	+	0.201397i	−0.664170	−	0.747582i	$-0.731215\pi$
$619$	−133658.	+	77167.4i	−0.348830	+	0.201397i	0.315340	+	0.948979i	$0.397881\pi$
$620$		0			0
$621$	355535.	+	205268.i	0.921932	+	0.532278i
$622$			242242.i			0.626137i
$623$	−25397.8	+	32259.5i	−0.0654364	+	0.0831154i
$624$	155945.			0.400501
$625$		0			0
$626$	−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
$635$		0			0
$636$			427776.i			1.05755i
$637$	−110336.	+	374253.i	−0.271919	+	0.922331i
$638$	−92295.4			−0.226745
$639$	430590.	−	745804.i	1.05454	−	1.82651i
$640$		0			0
$641$	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	$0.756789\pi$
$644$	24406.1	−	169090.i	0.0588472	−	0.407705i
$645$		0			0
$646$	−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
$650$		0			0
$651$	600037.	+	472407.i	1.41585	+	1.11469i
$652$	−172249.			−0.405193
$653$	−242335.	+	419737.i	−0.568316	+	0.984353i	0.428416	+	0.903581i	$0.359072\pi$
$653$	−242335.	+	419737.i	−0.568316	+	0.984353i	−0.996733	+	0.0807713i	$0.974262\pi$
$654$	512438.	−	295856.i	1.19808	−	0.691711i
$655$		0			0
$656$	63390.0	+	36598.3i	0.147304	+	0.0850458i
$657$		−	83057.0i		−	0.192418i
$658$	−69207.8	−	173148.i	−0.159847	−	0.399912i
$659$	329627.			0.759017			0.379509	−	0.925188i	$-0.376093\pi$
$659$	329627.			0.759017			0.379509	+	0.925188i	$0.376093\pi$
$660$		0			0
$661$	−182392.	+	105304.i	−0.417449	+	0.241014i	−0.693985	−	0.719989i	$-0.744147\pi$
$661$	−182392.	+	105304.i	−0.417449	+	0.241014i	0.276536	+	0.961003i	$0.410813\pi$
$662$	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
$670$		0			0
$671$			61413.2i			0.136401i
$672$	82270.5	−	104498.i	0.182182	−	0.231402i
$673$	−94709.8			−0.209105			−0.104553	−	0.994519i	$-0.533341\pi$
$673$	−94709.8			−0.209105			−0.104553	+	0.994519i	$0.533341\pi$
$674$	−178951.	+	309952.i	−0.393926	+	0.682300i
$675$		0			0
$676$	−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
$679$	−272664.	−	39355.6i	−0.591408	−	0.0853625i
$680$		0			0
$681$	422588.	−	731944.i	0.911219	−	1.57828i
$682$	111953.	−	64635.9i	0.240694	−	0.138965i
$683$	−64535.9	−	111779.i	−0.138344	−	0.239618i	0.788526	−	0.615001i	$-0.210845\pi$
$683$	−64535.9	−	111779.i	−0.138344	−	0.239618i	−0.926870	+	0.375383i	$0.877511\pi$
$684$	−447967.	−	258634.i	−0.957489	−	0.552806i
$685$		0			0
$686$	192575.	+	271377.i	0.409215	+	0.576666i
$687$	−631680.			−1.33839
$688$	77402.3	−	134065.i	0.163522	−	0.283229i
$689$	−501890.	+	289766.i	−1.05723	+	0.610393i
$690$		0			0
$691$	113201.	+	65356.6i	0.237079	+	0.136878i	0.613834	−	0.789435i	$-0.289627\pi$
$691$	113201.	+	65356.6i	0.237079	+	0.136878i	−0.376754	+	0.926313i	$0.622960\pi$
$692$		−	323064.i		−	0.674648i
$693$	−44268.0	+	306697.i	−0.0921771	+	0.638622i
$694$	−189361.			−0.393162
$695$		0			0
$696$	−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
$705$		0			0
$706$		−	160020.i		−	0.321044i
$707$	119767.	+	299640.i	0.239607	+	0.599462i
$708$	−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	$0.866428\pi$
$710$		0			0
$711$	−226251.	−	391878.i	−0.447560	−	0.775196i
$712$	16419.6	+	9479.86i	0.0323894	+	0.0187000i
$713$		−	453008.i		−	0.891101i
$714$	208858.	−	83481.3i	0.409689	−	0.163754i
$715$		0			0
$716$	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	0.104494	−	0.994526i	$-0.466678\pi$
$719$	−364222.	−	210283.i	−0.704544	−	0.406769i	−0.809038	+	0.587757i	$0.800011\pi$
$720$		0			0
$721$	−46208.9	+	58693.1i	−0.0888904	+	0.112906i
$722$	203055.			0.389528
$723$	611554.	−	1.05924e6i	1.16992	−	2.02637i
$724$	375523.	−	216808.i	0.716406	−	0.413617i
$725$		0			0
$726$	−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	$0.947685\pi$
$728$	178330.	+	25739.8i	0.336483	+	0.0485671i
$729$	788171.			1.48308
$730$		0			0
$731$	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	$0.685325\pi$
$740$		0			0
$741$		−	1.09544e6i		−	1.99504i
$742$	−70607.2	+	489181.i	−0.128245	+	0.888509i
$743$	−580258.			−1.05110			−0.525549	−	0.850763i	$-0.676140\pi$
$743$	−580258.			−1.05110			−0.525549	+	0.850763i	$0.676140\pi$
$744$	176328.	−	305410.i	0.318549	−	0.551743i
$745$		0			0
$746$	43873.7	+	75991.5i	0.0788364	+	0.136549i
$747$	589139.	+	340139.i	1.05579	+	0.609559i
$748$		−	38073.7i		−	0.0680491i
$749$	−408355.	−	321496.i	−0.727904	−	0.573076i
$750$		0			0
$751$	−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
$755$		0			0
$756$	137051.	+	342881.i	0.239794	+	0.599929i
$757$	24171.7			0.0421809			0.0210905	−	0.999778i	$-0.493286\pi$
$757$	24171.7			0.0421809			0.0210905	+	0.999778i	$0.493286\pi$
$758$	−139339.	+	241342.i	−0.242512	+	0.420044i
$759$	248842.	−	143669.i	0.431956	−	0.249390i
$760$		0			0
$761$	−561376.	−	324111.i	−0.969359	−	0.559659i	−0.0703180	−	0.997525i	$-0.522401\pi$
$761$	−561376.	−	324111.i	−0.969359	−	0.559659i	−0.899041	+	0.437865i	$0.855735\pi$
$762$			169329.i			0.291624i
$763$	634828.	−	253743.i	1.09045	−	0.435859i
$764$	−9630.98			−0.0165000
$765$		0			0
$766$	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	$0.0485143\pi$
$769$			179564.i			0.303646i	−0.988408	+	0.151823i	$0.951486\pi$
$770$		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
$775$		0			0
$776$			127216.i			0.211261i
$777$	−717486.	−	103560.i	−1.18842	−	0.171534i
$778$	−244042.			−0.403186
$779$	257085.	−	445284.i	0.423644	−	0.733773i
$780$		0			0
$781$	−131643.	−	228012.i	−0.215821	−	0.373814i
$782$	−115547.	−	66711.1i	−0.188949	−	0.109090i
$783$		−	699061.i		−	1.14023i
$784$	111328.	−	105918.i	0.181122	−	0.172321i
$785$		0			0
$786$	−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
$790$		0			0
$791$	61679.1	−	427325.i	0.0985791	−	0.682976i
$792$	143096.			0.228127
$793$	−113486.	+	196563.i	−0.180466	+	0.312576i
$794$	381939.	−	220513.i	0.605834	−	0.349778i
$795$		0			0
$796$	−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	$-0.250771\pi$
$798$	−734044.	−	577910.i	−1.15270	−	0.907516i
$799$	−145624.			−0.228108
$800$		0			0
$801$	−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	$0.972913\pi$
$810$		0			0
$811$		−	70954.2i		−	0.107879i	−0.998544	−	0.0539395i	$-0.982822\pi$
$811$		−	70954.2i		−	0.107879i	0.998544	−	0.0539395i	$-0.0171778\pi$
$812$	−270131.	+	107972.i	−0.409696	+	0.163757i
$813$	−228356.			−0.345486
$814$	−61355.2	+	106270.i	−0.0925982	+	0.160385i
$815$		0			0
$816$	−51933.1	−	89950.8i	−0.0779945	−	0.135090i
$817$	−941738.	−	543713.i	−1.41087	−	0.814564i
$818$			887527.i			1.32640i
$819$	−708435.	+	899833.i	−1.05617	+	1.34151i
$820$		0			0
$821$	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	0.778018	−	0.628242i	$-0.216225\pi$
$823$	−105029.	−	181916.i	−0.155064	−	0.268579i	−0.933082	+	0.359663i	$0.882892\pi$
$824$	29873.9	+	17247.7i	0.0439985	+	0.0254025i
$825$		0			0
$826$	−587781.	−	84838.8i	−0.861500	−	0.124347i
$827$	880910.			1.28801			0.644007	−	0.765020i	$-0.277271\pi$
$827$	880910.			1.28801			0.644007	+	0.765020i	$0.277271\pi$
$828$	250726.	−	434270.i	0.365711	−	0.633431i
$829$	−1.11951e6	+	646349.i	−1.62899	+	0.940498i	−0.644595	+	0.764524i	$0.722974\pi$
$829$	−1.11951e6	+	646349.i	−1.62899	+	0.940498i	−0.984395	+	0.175974i	$0.943692\pi$
$830$		0			0
$831$	−128186.	−	74008.1i	−0.185625	−	0.107171i
$832$		−	83203.5i		−	0.120197i
$833$	252617.	−	60991.2i	0.364060	−	0.0878977i
$834$	851166.			1.22372
$835$		0			0
$836$	−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	$-0.708726\pi$
$839$		−	1.11586e6i		−	1.58520i	0.609741	−	0.792601i	$-0.291274\pi$
$840$		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
$845$		0			0
$846$		−	547312.i		−	0.764705i
$847$	−489242.	−	385178.i	−0.681957	−	0.536902i
$848$	228237.			0.317391
$849$	822142.	−	1.42399e6i	1.14059	−	1.97557i
$850$		0			0
$851$	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	$-0.346650\pi$
$854$	71844.7	+	179745.i	0.0985097	+	0.246457i
$855$		0			0
$856$	−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	0.636603	−	0.771192i	$-0.280339\pi$
$859$	211796.	+	122281.i	0.287033	+	0.165718i	−0.349570	+	0.936910i	$0.613672\pi$
$860$		0			0
$861$	−780266.	+	311875.i	−1.05253	+	0.420702i
$862$	−39109.2			−0.0526337
$863$	−232638.	+	402942.i	−0.312363	+	0.541029i	−0.978873	−	0.204467i	$-0.934454\pi$
$863$	−232638.	+	402942.i	−0.312363	+	0.541029i	0.666510	+	0.745496i	$0.267787\pi$
$864$	147672.	−	85258.4i	0.197820	−	0.114211i
$865$		0			0
$866$	116201.	+	67088.6i	0.154944	+	0.0894567i
$867$			1.07667e6i			1.43233i
$868$	252049.	−	320145.i	0.334538	−	0.424921i
$869$	−138342.			−0.183195
$870$		0			0
$871$	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	−0.750057	−	0.661373i	$-0.769974\pi$
$877$	152086.	−	263420.i	0.197738	−	0.342492i	0.947795	+	0.318882i	$0.103307\pi$
$878$	268988.	−	155301.i	0.348935	−	0.201458i
$879$	674078.	+	1.16754e6i	0.872434	+	1.51110i
$880$		0			0
$881$			697876.i			0.899138i	0.893246	+	0.449569i	$0.148422\pi$
$881$			697876.i			0.899138i	−0.893246	+	0.449569i	$0.851578\pi$
$882$	229228.	+	949432.i	0.294667	+	1.22047i
$883$	−891773.			−1.14375			−0.571877	−	0.820339i	$-0.693785\pi$
$883$	−891773.			−1.14375			−0.571877	+	0.820339i	$0.693785\pi$
$884$	70356.6	−	121861.i	0.0900328	−	0.155941i
$885$		0			0
$886$	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
$889$	−27948.9	+	193636.i	−0.0353640	+	0.245009i
$890$		0			0
$891$	−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
$895$		0			0
$896$	−55754.0	−	43894.9i	−0.0694480	−	0.0546761i
$897$	1.06195e6			1.31983
$898$	−467310.	+	809404.i	−0.579498	+	1.00372i
$899$	−668036.	+	385691.i	−0.826572	+	0.477221i
$900$		0			0
$901$	334280.	+	192997.i	0.411776	+	0.237739i
$902$			142239.i			0.174825i
$903$	659590.	+	1.65020e6i	0.808907	+	2.02377i
$904$	−199377.			−0.243971
$905$		0			0
$906$	−1.08742e6	+	627822.i	−1.32477	+	0.764857i
$907$	475990.	+	824439.i	0.578607	+	1.00218i	0.995639	+	0.0932848i	$0.0297367\pi$
$907$	475990.	+	824439.i	0.578607	+	1.00218i	−0.417033	+	0.908891i	$0.636930\pi$
$908$	−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
$915$		0			0
$916$			337028.i			0.401675i
$917$	−613038.	+	778662.i	−0.729035	+	0.925999i
$918$	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	$0.0662043\pi$
$920$		0			0
$921$	1.06219e6	+	1.83977e6i	1.25223	+	2.16892i
$922$	−49859.9	−	28786.6i	−0.0586529	−	0.0338633i
$923$		−	973052.i		−	1.14218i
$924$	255795.	+	36920.8i	0.299604	+	0.0432441i
$925$		0			0
$926$	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	0.903108	−	0.429414i	$-0.141280\pi$
$929$	848178.	+	489696.i	0.982779	+	0.567408i	0.0796709	+	0.996821i	$0.474613\pi$
$930$		0			0
$931$	−744024.	−	782024.i	−0.858396	−	0.902237i
$932$	440815.			0.507486
$933$	−642090.	+	1.11213e6i	−0.737620	+	1.27759i
$934$	592420.	−	342034.i	0.679103	−	0.392081i
$935$		0			0
$936$	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	$0.775123\pi$
$938$	143855.	−	996658.i	0.163501	−	1.13277i
$939$	−267368.			−0.303235
$940$		0			0
$941$	693791.	−	400561.i	0.783519	−	0.452365i	−0.0541569	−	0.998532i	$-0.517247\pi$
$941$	693791.	−	400561.i	0.783519	−	0.452365i	0.837676	+	0.546167i	$0.183914\pi$
$942$	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	−0.611676	−	0.791108i	$-0.709504\pi$
$947$	340143.	−	589145.i	0.379282	−	0.656935i	0.990958	+	0.134173i	$0.0428378\pi$
$948$	−326838.	+	188700.i	−0.363677	+	0.209969i
$949$	−46923.3	−	81273.5i	−0.0521022	−	0.0902436i
$950$		0			0
$951$		−	1.21160e6i		−	1.33967i
$952$	−44540.8	−	111435.i	−0.0491456	−	0.122955i
$953$	394774.			0.434673			0.217337	−	0.976097i	$-0.430263\pi$
$953$	394774.			0.434673			0.217337	+	0.976097i	$0.430263\pi$
$954$	−725355.	+	1.25635e6i	−0.796992	+	1.38043i
$955$		0			0
$956$	−92329.9	−	159920.i	−0.101024	−	0.174979i
$957$	−423727.	−	244639.i	−0.462660	−	0.267117i
$958$		−	769567.i		−	0.838524i
$959$	1.14013e6	−	455714.i	1.23970	−	0.495513i
$960$		0			0
$961$	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
$965$		0			0
$966$	560240.	−	711600.i	0.600371	−	0.762574i
$967$	604328.			0.646279			0.323140	−	0.946351i	$-0.395262\pi$
$967$	604328.			0.646279			0.323140	+	0.946351i	$0.395262\pi$
$968$	−143770.	+	249017.i	−0.153433	+	0.265753i
$969$	−631860.	+	364804.i	−0.672935	+	0.388519i
$970$		0			0
$971$	657301.	+	379493.i	0.697149	+	0.402499i	0.806285	−	0.591528i	$-0.201475\pi$
$971$	657301.	+	379493.i	0.697149	+	0.402499i	−0.109136	+	0.994027i	$0.534808\pi$
$972$		−	313584.i		−	0.331910i
$973$	973346.	+	140490.i	1.02811	+	0.148396i
$974$	−1.15328e6			−1.21567
$975$		0			0
$976$	77412.4	−	44694.1i	0.0812664	−	0.0469192i
$977$	612591.	+	1.06104e6i	0.641773	+	1.11158i	0.985037	+	0.172345i	$0.0551344\pi$
$977$	612591.	+	1.06104e6i	0.641773	+	1.11158i	−0.343263	+	0.939239i	$0.611532\pi$
$978$	−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
$985$		0			0
$986$			227191.i			0.233689i
$987$	141214.	−	978362.i	0.144959	−	1.00430i
$988$	−584464.			−0.598747
$989$	527088.	−	912944.i	0.538878	−	0.933365i
$990$		0			0
$991$	−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
$994$	−652034.	−	513344.i	−0.659929	−	0.519560i
$995$		0			0
$996$	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	350.5.k.a.201.2		4
5.2	odd	4		350.5.i.a.299.3		8
5.3	odd	4		350.5.i.a.299.2		8
5.4	even	2		14.5.d.a.5.1	yes	4
7.3	odd	6	inner	350.5.k.a.101.2		4
15.14	odd	2		126.5.n.a.19.2		4
20.19	odd	2		112.5.s.b.33.2		4
35.3	even	12		350.5.i.a.199.3		8
35.4	even	6		98.5.d.a.31.1		4
35.9	even	6		98.5.b.b.97.3		4
35.17	even	12		350.5.i.a.199.2		8
35.19	odd	6		98.5.b.b.97.4		4
35.24	odd	6		14.5.d.a.3.1	✓	4
35.34	odd	2		98.5.d.a.19.1		4
105.44	odd	6		882.5.c.b.685.2		4
105.59	even	6		126.5.n.a.73.2		4
105.89	even	6		882.5.c.b.685.1		4
140.19	even	6		784.5.c.b.97.1		4
140.59	even	6		112.5.s.b.17.2		4
140.79	odd	6		784.5.c.b.97.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.1	✓	4	35.24	odd	6
14.5.d.a.5.1	yes	4	5.4	even	2
98.5.b.b.97.3		4	35.9	even	6
98.5.b.b.97.4		4	35.19	odd	6
98.5.d.a.19.1		4	35.34	odd	2
98.5.d.a.31.1		4	35.4	even	6
112.5.s.b.17.2		4	140.59	even	6
112.5.s.b.33.2		4	20.19	odd	2
126.5.n.a.19.2		4	15.14	odd	2
126.5.n.a.73.2		4	105.59	even	6
350.5.i.a.199.2		8	35.17	even	12
350.5.i.a.199.3		8	35.3	even	12
350.5.i.a.299.2		8	5.3	odd	4
350.5.i.a.299.3		8	5.2	odd	4
350.5.k.a.101.2		4	7.3	odd	6	inner
350.5.k.a.201.2		4	1.1	even	1	trivial
784.5.c.b.97.1		4	140.19	even	6
784.5.c.b.97.4		4	140.79	odd	6
882.5.c.b.685.1		4	105.89	even	6
882.5.c.b.685.2		4	105.44	odd	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	350.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 - 2.44949i) q^{2} +(12.9853 - 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} -42.4098i q^{6} +(7.00000 - 48.4974i) q^{7} -22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +O(q^{10})\)	\(q+(1.41421 - 2.44949i) q^{2} +(12.9853 - 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} -42.4098i q^{6} +(7.00000 - 48.4974i) q^{7} -22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +(-21.9853 - 38.0796i) q^{11} +(-103.882 - 59.9764i) q^{12} -162.507i q^{13} +(-108.894 - 85.7321i) q^{14} +(-32.0000 + 55.4256i) q^{16} +(-93.7355 + 54.1182i) q^{17} +(-203.397 - 352.294i) q^{18} +(389.338 + 224.784i) q^{19} +(-272.691 - 682.232i) q^{21} -124.368 q^{22} +(-217.911 + 377.433i) q^{23} +(-293.823 + 169.639i) q^{24} +(-398.059 - 229.819i) q^{26} -941.981i q^{27} +(-364.000 + 145.492i) q^{28} +742.118 q^{29} +(-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} -1143.70i q^{41} +(-2056.76 - 296.868i) q^{42} -2418.82 q^{43} +(-175.882 + 304.637i) q^{44} +(616.346 + 1067.54i) q^{46} +(1165.17 + 672.714i) q^{47} +959.623i q^{48} +(-2303.00 - 678.964i) q^{49} +(-811.455 + 1405.48i) q^{51} +(-1125.88 + 650.027i) q^{52} +(-1783.10 - 3088.42i) q^{53} +(-2307.37 - 1332.16i) q^{54} +(-158.392 + 1097.37i) q^{56} +6740.88 q^{57} +(1049.51 - 1817.81i) q^{58} +(3710.93 - 2142.50i) q^{59} +(-1209.57 - 698.345i) q^{61} +2939.96i q^{62} +(-5537.20 - 4359.41i) q^{63} +512.000 q^{64} +(-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} -3596.55i q^{76} +(-2000.66 + 799.672i) q^{77} -6891.88 q^{78} +(1573.12 - 2724.72i) q^{79} +(-1237.24 - 2142.95i) q^{81} +(-2801.47 - 1617.43i) q^{82} +4729.96i q^{83} +(-3635.88 + 4618.19i) q^{84} +(-3420.73 + 5924.88i) q^{86} +(9636.61 - 5563.70i) q^{87} +(497.470 + 861.644i) q^{88} +(-725.651 - 418.955i) q^{89} +(-7881.16 - 1137.55i) q^{91} +3486.58 q^{92} +(-7792.69 + 13497.3i) q^{93} +(3295.61 - 1902.72i) q^{94} +(2350.59 + 1357.11i) q^{96} -5622.23i q^{97} +(-4920.05 + 4680.97i) q^{98} -6323.99 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} - 16 q^{4} + 28 q^{7} + 84 q^{9}+O(q^{10}) \) 4 * q + 18 * q^3 - 16 * q^4 + 28 * q^7 + 84 * q^9	\( 4 q + 18 q^{3} - 16 q^{4} + 28 q^{7} + 84 q^{9} - 54 q^{11} - 144 q^{12} - 128 q^{16} - 918 q^{17} - 576 q^{18} + 30 q^{19} - 378 q^{21} - 192 q^{22} + 486 q^{23} - 768 q^{24} - 1728 q^{26} - 1456 q^{28} + 3240 q^{29} - 546 q^{31} - 1062 q^{33} - 1344 q^{36} + 446 q^{37} + 4320 q^{38} - 3312 q^{39} - 5376 q^{42} - 2344 q^{43} - 432 q^{44} + 3840 q^{46} - 702 q^{47} - 9212 q^{49} + 318 q^{51} + 384 q^{52} - 2754 q^{53} - 1440 q^{54} + 17460 q^{57} - 384 q^{58} + 12366 q^{59} + 7686 q^{61} - 6468 q^{63} + 2048 q^{64} - 3456 q^{66} + 5062 q^{67} + 7344 q^{68} + 18792 q^{71} - 4608 q^{72} + 17274 q^{73} - 4320 q^{74} - 4914 q^{77} - 8832 q^{78} + 794 q^{79} - 4338 q^{81} - 9984 q^{82} - 5040 q^{84} - 10368 q^{86} + 12276 q^{87} + 768 q^{88} - 12474 q^{89} + 2688 q^{91} - 7776 q^{92} - 18918 q^{93} + 15168 q^{94} + 6144 q^{96} - 11448 q^{99}+O(q^{100}) \) 4 * q + 18 * q^3 - 16 * q^4 + 28 * q^7 + 84 * q^9 - 54 * q^11 - 144 * q^12 - 128 * q^16 - 918 * q^17 - 576 * q^18 + 30 * q^19 - 378 * q^21 - 192 * q^22 + 486 * q^23 - 768 * q^24 - 1728 * q^26 - 1456 * q^28 + 3240 * q^29 - 546 * q^31 - 1062 * q^33 - 1344 * q^36 + 446 * q^37 + 4320 * q^38 - 3312 * q^39 - 5376 * q^42 - 2344 * q^43 - 432 * q^44 + 3840 * q^46 - 702 * q^47 - 9212 * q^49 + 318 * q^51 + 384 * q^52 - 2754 * q^53 - 1440 * q^54 + 17460 * q^57 - 384 * q^58 + 12366 * q^59 + 7686 * q^61 - 6468 * q^63 + 2048 * q^64 - 3456 * q^66 + 5062 * q^67 + 7344 * q^68 + 18792 * q^71 - 4608 * q^72 + 17274 * q^73 - 4320 * q^74 - 4914 * q^77 - 8832 * q^78 + 794 * q^79 - 4338 * q^81 - 9984 * q^82 - 5040 * q^84 - 10368 * q^86 + 12276 * q^87 + 768 * q^88 - 12474 * q^89 + 2688 * q^91 - 7776 * q^92 - 18918 * q^93 + 15168 * q^94 + 6144 * q^96 - 11448 * q^99

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