LMFDB - Embedded newform 124.5.b.a.63.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(63,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("124.63");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			63.19
Character	$\chi$	$=$	124.63
Dual form			124.5.b.a.63.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86128 - 3.54057i) q^{2} -8.93980i q^{3} +(-9.07128 + 13.1800i) q^{4} +0.767532 q^{5} +(-31.6520 + 16.6395i) q^{6} +40.1374i q^{7} +(63.5488 + 7.58587i) q^{8} +1.07989 q^{9} +O(q^{10})$	\(q+(-1.86128 - 3.54057i) q^{2} -8.93980i q^{3} +(-9.07128 + 13.1800i) q^{4} +0.767532 q^{5} +(-31.6520 + 16.6395i) q^{6} +40.1374i q^{7} +(63.5488 + 7.58587i) q^{8} +1.07989 q^{9} +(-1.42859 - 2.71750i) q^{10} +138.297i q^{11} +(117.826 + 81.0954i) q^{12} +126.860 q^{13} +(142.109 - 74.7070i) q^{14} -6.86159i q^{15} +(-91.4238 - 239.119i) q^{16} +110.913 q^{17} +(-2.00998 - 3.82343i) q^{18} +603.442i q^{19} +(-6.96250 + 10.1161i) q^{20} +358.821 q^{21} +(489.650 - 257.409i) q^{22} -273.153i q^{23} +(67.8162 - 568.114i) q^{24} -624.411 q^{25} +(-236.122 - 449.157i) q^{26} -733.778i q^{27} +(-529.011 - 364.098i) q^{28} +753.664 q^{29} +(-24.2939 + 12.7713i) q^{30} -172.601i q^{31} +(-676.451 + 768.759i) q^{32} +1236.35 q^{33} +(-206.440 - 392.695i) q^{34} +30.8068i q^{35} +(-9.79600 + 14.2330i) q^{36} +983.087 q^{37} +(2136.53 - 1123.17i) q^{38} -1134.10i q^{39} +(48.7758 + 5.82240i) q^{40} +1207.54 q^{41} +(-667.866 - 1270.43i) q^{42} -870.173i q^{43} +(-1822.75 - 1254.53i) q^{44} +0.828851 q^{45} +(-967.116 + 508.413i) q^{46} +2681.15i q^{47} +(-2137.67 + 817.311i) q^{48} +789.986 q^{49} +(1162.20 + 2210.77i) q^{50} -991.539i q^{51} +(-1150.78 + 1672.01i) q^{52} +3362.66 q^{53} +(-2597.99 + 1365.77i) q^{54} +106.147i q^{55} +(-304.477 + 2550.69i) q^{56} +5394.66 q^{57} +(-1402.78 - 2668.40i) q^{58} +5958.82i q^{59} +(90.4356 + 62.2433i) q^{60} -5724.63 q^{61} +(-611.105 + 321.258i) q^{62} +43.3441i q^{63} +(3980.91 + 964.146i) q^{64} +97.3692 q^{65} +(-2301.19 - 4377.38i) q^{66} -3716.51i q^{67} +(-1006.12 + 1461.83i) q^{68} -2441.93 q^{69} +(109.074 - 57.3400i) q^{70} +5272.14i q^{71} +(68.6259 + 8.19191i) q^{72} +3280.39 q^{73} +(-1829.80 - 3480.69i) q^{74} +5582.11i q^{75} +(-7953.36 - 5473.99i) q^{76} -5550.89 q^{77} +(-4015.38 + 2110.89i) q^{78} +5810.95i q^{79} +(-70.1707 - 183.531i) q^{80} -6472.36 q^{81} +(-2247.58 - 4275.39i) q^{82} -1216.24i q^{83} +(-3254.96 + 4729.25i) q^{84} +85.1292 q^{85} +(-3080.91 + 1619.64i) q^{86} -6737.61i q^{87} +(-1049.10 + 8788.62i) q^{88} +5925.99 q^{89} +(-1.54272 - 2.93461i) q^{90} +5091.84i q^{91} +(3600.15 + 2477.84i) q^{92} -1543.02 q^{93} +(9492.82 - 4990.38i) q^{94} +463.161i q^{95} +(6872.56 + 6047.34i) q^{96} +9767.51 q^{97} +(-1470.38 - 2797.00i) q^{98} +149.346i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9}+O(q^{10}) $ 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9	$ 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9} + 53 q^{10} + 130 q^{12} + 120 q^{13} - 231 q^{14} - 590 q^{16} - 648 q^{17} + 230 q^{18} + 1113 q^{20} + 608 q^{21} + 1080 q^{22} - 1028 q^{24} + 8340 q^{25} - 1554 q^{26} - 165 q^{28} - 168 q^{29} - 2238 q^{30} - 1674 q^{32} - 1120 q^{33} + 1844 q^{34} + 1966 q^{36} - 2248 q^{37} - 5055 q^{38} - 1716 q^{40} + 6072 q^{41} + 5794 q^{42} - 120 q^{44} - 4040 q^{45} + 8850 q^{46} + 2276 q^{48} - 17604 q^{49} - 4539 q^{50} + 5896 q^{52} + 3480 q^{53} + 5148 q^{54} - 396 q^{56} - 10912 q^{57} - 7484 q^{58} + 22812 q^{60} + 2200 q^{61} - 19299 q^{64} - 9168 q^{65} - 468 q^{66} - 21930 q^{68} + 6496 q^{69} - 9615 q^{70} - 10079 q^{72} + 13752 q^{73} - 2106 q^{74} + 20099 q^{76} + 16608 q^{77} + 39460 q^{78} - 5787 q^{80} + 20732 q^{81} - 30525 q^{82} - 21760 q^{84} - 21200 q^{85} - 13398 q^{86} + 34690 q^{88} + 22296 q^{89} - 25419 q^{90} - 18852 q^{92} + 3196 q^{94} + 20790 q^{96} + 12120 q^{97} + 21921 q^{98}+O(q^{100}) $ 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9 + 53 * q^10 + 130 * q^12 + 120 * q^13 - 231 * q^14 - 590 * q^16 - 648 * q^17 + 230 * q^18 + 1113 * q^20 + 608 * q^21 + 1080 * q^22 - 1028 * q^24 + 8340 * q^25 - 1554 * q^26 - 165 * q^28 - 168 * q^29 - 2238 * q^30 - 1674 * q^32 - 1120 * q^33 + 1844 * q^34 + 1966 * q^36 - 2248 * q^37 - 5055 * q^38 - 1716 * q^40 + 6072 * q^41 + 5794 * q^42 - 120 * q^44 - 4040 * q^45 + 8850 * q^46 + 2276 * q^48 - 17604 * q^49 - 4539 * q^50 + 5896 * q^52 + 3480 * q^53 + 5148 * q^54 - 396 * q^56 - 10912 * q^57 - 7484 * q^58 + 22812 * q^60 + 2200 * q^61 - 19299 * q^64 - 9168 * q^65 - 468 * q^66 - 21930 * q^68 + 6496 * q^69 - 9615 * q^70 - 10079 * q^72 + 13752 * q^73 - 2106 * q^74 + 20099 * q^76 + 16608 * q^77 + 39460 * q^78 - 5787 * q^80 + 20732 * q^81 - 30525 * q^82 - 21760 * q^84 - 21200 * q^85 - 13398 * q^86 + 34690 * q^88 + 22296 * q^89 - 25419 * q^90 - 18852 * q^92 + 3196 * q^94 + 20790 * q^96 + 12120 * q^97 + 21921 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.86128	−	3.54057i	−0.465320	−	0.885143i
$2$	−1.86128	−	3.54057i	−0.465320	−	0.885143i
$3$		−	8.93980i		−	0.993312i	−0.867948	−	0.496656i	$-0.834561\pi$
$3$		−	8.93980i		−	0.993312i	0.867948	−	0.496656i	$-0.165439\pi$
$4$	−9.07128	+	13.1800i	−0.566955	+	0.823749i
$5$	0.767532			0.0307013			0.0153506	−	0.999882i	$-0.495114\pi$
$5$	0.767532			0.0307013			0.0153506	+	0.999882i	$0.495114\pi$
$6$	−31.6520	+	16.6395i	−0.879222	+	0.462208i
$7$			40.1374i			0.819131i	0.912281	+	0.409566i	$0.134320\pi$
$7$			40.1374i			0.819131i	−0.912281	+	0.409566i	$0.865680\pi$
$8$	63.5488	+	7.58587i	0.992951	+	0.118529i
$9$	1.07989			0.0133320
$10$	−1.42859	−	2.71750i	−0.0142859	−	0.0271750i
$11$			138.297i			1.14295i	0.820619	+	0.571475i	$0.193629\pi$
$11$			138.297i			1.14295i	−0.820619	+	0.571475i	$0.806371\pi$
$12$	117.826	+	81.0954i	0.818239	+	0.563163i
$13$	126.860			0.750651			0.375326	−	0.926893i	$-0.377531\pi$
$13$	126.860			0.750651			0.375326	+	0.926893i	$0.377531\pi$
$14$	142.109	−	74.7070i	0.725048	−	0.381158i
$15$		−	6.86159i		−	0.0304959i
$16$	−91.4238	−	239.119i	−0.357124	−	0.934057i
$17$	110.913			0.383782			0.191891	−	0.981416i	$-0.438538\pi$
$17$	110.913			0.383782			0.191891	+	0.981416i	$0.438538\pi$
$18$	−2.00998	−	3.82343i	−0.00620364	−	0.0118007i
$19$			603.442i			1.67159i	0.549045	+	0.835793i	$0.314991\pi$
$19$			603.442i			1.67159i	−0.549045	+	0.835793i	$0.685009\pi$
$20$	−6.96250	+	10.1161i	−0.0174062	+	0.0252901i
$21$	358.821			0.813653
$22$	489.650	−	257.409i	1.01167	−	0.531838i
$23$		−	273.153i		−	0.516357i	−0.966097	−	0.258178i	$-0.916878\pi$
$23$		−	273.153i		−	0.516357i	0.966097	−	0.258178i	$-0.0831222\pi$
$24$	67.8162	−	568.114i	0.117736	−	0.986309i
$25$	−624.411			−0.999057
$26$	−236.122	−	449.157i	−0.349293	−	0.664433i
$27$		−	733.778i		−	1.00655i
$28$	−529.011	−	364.098i	−0.674759	−	0.464411i
$29$	753.664			0.896152			0.448076	−	0.893995i	$-0.352109\pi$
$29$	753.664			0.896152			0.448076	+	0.893995i	$0.352109\pi$
$30$	−24.2939	+	12.7713i	−0.0269933	+	0.0141904i
$31$		−	172.601i		−	0.179605i
$31$		−	172.601i		−	0.179605i
$32$	−676.451	+	768.759i	−0.660596	+	0.750741i
$33$	1236.35			1.13531
$34$	−206.440	−	392.695i	−0.178581	−	0.339701i
$35$			30.8068i			0.0251484i
$36$	−9.79600	+	14.2330i	−0.00755864	+	0.0109822i
$37$	983.087			0.718106			0.359053	−	0.933317i	$-0.383100\pi$
$37$	983.087			0.718106			0.359053	+	0.933317i	$0.383100\pi$
$38$	2136.53	−	1123.17i	1.47959	−	0.777822i
$39$		−	1134.10i		−	0.745631i
$40$	48.7758	+	5.82240i	0.0304849	+	0.00363900i
$41$	1207.54			0.718348			0.359174	−	0.933271i	$-0.383058\pi$
$41$	1207.54			0.718348			0.359174	+	0.933271i	$0.383058\pi$
$42$	−667.866	−	1270.43i	−0.378609	−	0.720199i
$43$		−	870.173i		−	0.470618i	−0.971921	−	0.235309i	$-0.924390\pi$
$43$		−	870.173i		−	0.470618i	0.971921	−	0.235309i	$-0.0756103\pi$
$44$	−1822.75	−	1254.53i	−0.941504	−	0.648001i
$45$	0.828851			0.000409309
$46$	−967.116	+	508.413i	−0.457049	+	0.240271i
$47$			2681.15i			1.21374i	0.794801	+	0.606871i	$0.207575\pi$
$47$			2681.15i			1.21374i	−0.794801	+	0.606871i	$0.792425\pi$
$48$	−2137.67	+	817.311i	−0.927810	+	0.354736i
$49$	789.986			0.329024
$50$	1162.20	+	2210.77i	0.464881	+	0.884308i
$51$		−	991.539i		−	0.381215i
$52$	−1150.78	+	1672.01i	−0.425585	+	0.618348i
$53$	3362.66			1.19710			0.598550	−	0.801085i	$-0.295744\pi$
$53$	3362.66			1.19710			0.598550	+	0.801085i	$0.295744\pi$
$54$	−2597.99	+	1365.77i	−0.890944	+	0.468370i
$55$			106.147i			0.0350900i
$56$	−304.477	+	2550.69i	−0.0970910	+	0.813357i
$57$	5394.66			1.66040
$58$	−1402.78	−	2668.40i	−0.416997	−	0.793222i
$59$			5958.82i			1.71181i	0.517130	+	0.855907i	$0.327000\pi$
$59$			5958.82i			1.71181i	−0.517130	+	0.855907i	$0.673000\pi$
$60$	90.4356	+	62.2433i	0.0251210	+	0.0172898i
$61$	−5724.63			−1.53846			−0.769232	−	0.638969i	$-0.779361\pi$
$61$	−5724.63			−1.53846			−0.769232	+	0.638969i	$0.779361\pi$
$62$	−611.105	+	321.258i	−0.158976	+	0.0835739i
$63$			43.3441i			0.0109207i
$64$	3980.91	+	964.146i	0.971902	+	0.235387i
$65$	97.3692			0.0230460
$66$	−2301.19	−	4377.38i	−0.528281	−	1.00491i
$67$		−	3716.51i		−	0.827914i	−0.910296	−	0.413957i	$-0.864146\pi$
$67$		−	3716.51i		−	0.827914i	0.910296	−	0.413957i	$-0.135854\pi$
$68$	−1006.12	+	1461.83i	−0.217587	+	0.316140i
$69$	−2441.93			−0.512903
$70$	109.074	−	57.3400i	0.0222599	−	0.0117020i
$71$			5272.14i			1.04585i	0.852378	+	0.522926i	$0.175160\pi$
$71$			5272.14i			1.04585i	−0.852378	+	0.522926i	$0.824840\pi$
$72$	68.6259	+	8.19191i	0.0132380	+	0.00158023i
$73$	3280.39			0.615572			0.307786	−	0.951456i	$-0.400412\pi$
$73$	3280.39			0.615572			0.307786	+	0.951456i	$0.400412\pi$
$74$	−1829.80	−	3480.69i	−0.334149	−	0.635626i
$75$			5582.11i			0.992375i
$76$	−7953.36	−	5473.99i	−1.37697	−	0.947713i
$77$	−5550.89			−0.936227
$78$	−4015.38	+	2110.89i	−0.659990	+	0.346957i
$79$			5810.95i			0.931092i	0.885024	+	0.465546i	$0.154142\pi$
$79$			5810.95i			0.931092i	−0.885024	+	0.465546i	$0.845858\pi$
$80$	−70.1707	−	183.531i	−0.0109642	−	0.0286767i
$81$	−6472.36			−0.986490
$82$	−2247.58	−	4275.39i	−0.334262	−	0.635841i
$83$		−	1216.24i		−	0.176548i	−0.996096	−	0.0882740i	$-0.971865\pi$
$83$		−	1216.24i		−	0.176548i	0.996096	−	0.0882740i	$-0.0281351\pi$
$84$	−3254.96	+	4729.25i	−0.461304	+	0.670246i
$85$	85.1292			0.0117826
$86$	−3080.91	+	1619.64i	−0.416564	+	0.218988i
$87$		−	6737.61i		−	0.890158i
$88$	−1049.10	+	8788.62i	−0.135473	+	1.13489i
$89$	5925.99			0.748137			0.374069	−	0.927401i	$-0.377962\pi$
$89$	5925.99			0.748137			0.374069	+	0.927401i	$0.377962\pi$
$90$	−1.54272	−	2.93461i	−0.000190460	−	0.000362297i
$91$			5091.84i			0.614882i
$92$	3600.15	+	2477.84i	0.425348	+	0.292751i
$93$	−1543.02			−0.178404
$94$	9492.82	−	4990.38i	1.07433	−	0.564778i
$95$			463.161i			0.0513198i
$96$	6872.56	+	6047.34i	0.745720	+	0.656178i
$97$	9767.51			1.03810			0.519052	−	0.854743i	$-0.326285\pi$
$97$	9767.51			1.03810			0.519052	+	0.854743i	$0.326285\pi$
$98$	−1470.38	−	2797.00i	−0.153101	−	0.291233i
$99$			149.346i			0.0152378i
$100$	5664.20	−	8229.72i	0.566420	−	0.822972i
$101$	−10724.2			−1.05129			−0.525643	−	0.850705i	$-0.676175\pi$
$101$	−10724.2			−1.05129			−0.525643	+	0.850705i	$0.676175\pi$
$102$	−3510.62	+	1845.53i	−0.337429	+	0.177387i
$103$			3054.07i			0.287876i	0.989587	+	0.143938i	$0.0459765\pi$
$103$			3054.07i			0.287876i	−0.989587	+	0.143938i	$0.954023\pi$
$104$	8061.81	+	962.344i	0.745360	+	0.0889741i
$105$	275.406			0.0249802
$106$	−6258.84	−	11905.7i	−0.557035	−	1.05960i
$107$		−	4225.34i		−	0.369058i	−0.982827	−	0.184529i	$-0.940924\pi$
$107$		−	4225.34i		−	0.369058i	0.982827	−	0.184529i	$-0.0590759\pi$
$108$	9671.18	+	6656.31i	0.829148	+	0.570671i
$109$	3631.66			0.305670			0.152835	−	0.988252i	$-0.451160\pi$
$109$	3631.66			0.305670			0.152835	+	0.988252i	$0.451160\pi$
$110$	375.822	−	197.570i	0.0310597	−	0.0163281i
$111$		−	8788.60i		−	0.713303i
$112$	9597.61	−	3669.52i	0.765115	−	0.292532i
$113$	3574.26			0.279917			0.139958	−	0.990157i	$-0.455303\pi$
$113$	3574.26			0.279917			0.139958	+	0.990157i	$0.455303\pi$
$114$	−10041.0	−	19100.2i	−0.772619	−	1.46970i
$115$		−	209.653i		−	0.0158528i
$116$	−6836.69	+	9933.28i	−0.508078	+	0.738204i
$117$	136.995			0.0100077
$118$	21097.6	−	11091.0i	1.51520	−	0.796541i
$119$			4451.76i			0.314368i
$120$	52.0511	−	436.046i	0.00361466	−	0.0302810i
$121$	−4485.07			−0.306336
$122$	10655.1	+	20268.4i	0.715878	+	1.36176i
$123$		−	10795.2i		−	0.713544i
$124$	2274.87	+	1565.71i	0.147950	+	0.101828i
$125$	−958.963			−0.0613736
$126$	153.463	−	80.6755i	0.00966634	−	0.00508160i
$127$		−	5495.74i		−	0.340737i	−0.985380	−	0.170368i	$-0.945504\pi$
$127$		−	5495.74i		−	0.340737i	0.985380	−	0.170368i	$-0.0544957\pi$
$128$	−3995.96	−	15889.2i	−0.243894	−	0.969802i
$129$	−7779.18			−0.467471
$130$	−181.231	−	344.742i	−0.0107237	−	0.0203990i
$131$		−	19271.0i		−	1.12296i	−0.827492	−	0.561478i	$-0.810233\pi$
$131$		−	19271.0i		−	1.12296i	0.827492	−	0.561478i	$-0.189767\pi$
$132$	−11215.3	+	16295.1i	−0.643667	+	0.935207i
$133$	−24220.6			−1.36925
$134$	−13158.6	+	6917.46i	−0.732822	+	0.385245i
$135$		−	563.198i		−	0.0309025i
$136$	7048.38	+	841.370i	0.381076	+	0.0454893i
$137$	−2692.59			−0.143459			−0.0717296	−	0.997424i	$-0.522852\pi$
$137$	−2692.59			−0.143459			−0.0717296	+	0.997424i	$0.522852\pi$
$138$	4545.12	+	8645.83i	0.238664	+	0.453992i
$139$		−	32396.6i		−	1.67675i	−0.545091	−	0.838377i	$-0.683505\pi$
$139$		−	32396.6i		−	1.67675i	0.545091	−	0.838377i	$-0.316495\pi$
$140$	−406.033	−	279.457i	−0.0207159	−	0.0142580i
$141$	23969.0			1.20562
$142$	18666.4	−	9812.93i	0.925729	−	0.486656i
$143$			17544.4i			0.857957i
$144$	−98.7279	−	258.222i	−0.00476118	−	0.0124528i
$145$	578.461			0.0275130
$146$	−6105.71	−	11614.4i	−0.286438	−	0.544869i
$147$		−	7062.32i		−	0.326823i
$148$	−8917.85	+	12957.1i	−0.407134	+	0.591539i
$149$	−11107.4			−0.500312			−0.250156	−	0.968206i	$-0.580482\pi$
$149$	−11107.4			−0.500312			−0.250156	+	0.968206i	$0.580482\pi$
$150$	19763.9	−	10389.9i	0.878394	−	0.461772i
$151$		−	15303.0i		−	0.671153i	−0.942013	−	0.335576i	$-0.891069\pi$
$151$		−	15303.0i		−	0.671153i	0.942013	−	0.335576i	$-0.108931\pi$
$152$	−4577.63	+	38348.0i	−0.198132	+	1.65980i
$153$	119.774			0.00511657
$154$	10331.8	+	19653.3i	0.435645	+	0.828694i
$155$		−	132.477i		−	0.00551411i
$156$	14947.5	+	10287.8i	0.614212	+	0.422739i
$157$	18965.6			0.769427			0.384713	−	0.923036i	$-0.374300\pi$
$157$	18965.6			0.769427			0.384713	+	0.923036i	$0.374300\pi$
$158$	20574.1	−	10815.8i	0.824149	−	0.433256i
$159$		−	30061.5i		−	1.18909i
$160$	−519.198	+	590.047i	−0.0202812	+	0.0230487i
$161$	10963.6			0.422964
$162$	12046.9	+	22915.9i	0.459034	+	0.873185i
$163$			24654.9i			0.927958i	0.885846	+	0.463979i	$0.153579\pi$
$163$			24654.9i			0.927958i	−0.885846	+	0.463979i	$0.846421\pi$
$164$	−10954.0	+	15915.4i	−0.407271	+	0.591738i
$165$	948.937			0.0348554
$166$	−4306.18	+	2263.76i	−0.156270	+	0.0821513i
$167$			13724.4i			0.492110i	0.969256	+	0.246055i	$0.0791343\pi$
$167$			13724.4i			0.492110i	−0.969256	+	0.246055i	$0.920866\pi$
$168$	22802.6	+	2721.97i	0.807917	+	0.0964416i
$169$	−12467.5			−0.436523
$170$	−158.449	−	301.406i	−0.00548267	−	0.0104293i
$171$			651.652i			0.0222856i
$172$	11468.9	+	7893.58i	0.387671	+	0.266819i
$173$	−48425.7			−1.61802			−0.809010	−	0.587795i	$-0.799996\pi$
$173$	−48425.7			−1.61802			−0.809010	+	0.587795i	$0.799996\pi$
$174$	−23855.0	+	12540.6i	−0.787917	+	0.414208i
$175$		−	25062.3i		−	0.818359i
$176$	33069.4	−	12643.6i	1.06758	−	0.408176i
$177$	53270.7			1.70036
$178$	−11029.9	−	20981.4i	−0.348123	−	0.662208i
$179$			18108.7i			0.565173i	0.959242	+	0.282587i	$0.0911925\pi$
$179$			18108.7i			0.565173i	−0.959242	+	0.282587i	$0.908808\pi$
$180$	−7.51874	+	10.9242i	−0.000232060	+	0.000337168i
$181$	−59393.4			−1.81293			−0.906466	−	0.422279i	$-0.861230\pi$
$181$	−59393.4			−1.81293			−0.906466	+	0.422279i	$0.861230\pi$
$182$	18028.0	−	9477.33i	0.544258	−	0.286117i
$183$			51177.1i			1.52817i
$184$	2072.10	−	17358.5i	0.0612033	−	0.512716i
$185$	754.550			0.0220468
$186$	2871.98	+	5463.16i	0.0830149	+	0.157913i
$187$			15338.9i			0.438643i
$188$	−35337.6	−	24321.5i	−0.999818	−	0.688137i
$189$	29452.0			0.824500
$190$	1639.85	−	862.072i	0.0454253	−	0.0238801i
$191$			60461.3i			1.65734i	0.559741	+	0.828668i	$0.310901\pi$
$191$			60461.3i			1.65734i	−0.559741	+	0.828668i	$0.689099\pi$
$192$	8619.28	−	35588.6i	0.233813	−	0.965401i
$193$	−14990.8			−0.402449			−0.201225	−	0.979545i	$-0.564492\pi$
$193$	−14990.8			−0.402449			−0.201225	+	0.979545i	$0.564492\pi$
$194$	−18180.1	−	34582.6i	−0.483050	−	0.918869i
$195$		−	870.461i		−	0.0228918i
$196$	−7166.18	+	10412.0i	−0.186542	+	0.271033i
$197$	−50805.0			−1.30910			−0.654551	−	0.756018i	$-0.727142\pi$
$197$	−50805.0			−1.30910			−0.654551	+	0.756018i	$0.727142\pi$
$198$	528.769	−	277.974i	0.0134876	−	0.00709046i
$199$		−	46599.4i		−	1.17672i	−0.808598	−	0.588362i	$-0.799773\pi$
$199$		−	46599.4i		−	1.17672i	0.808598	−	0.588362i	$-0.200227\pi$
$200$	−39680.6	−	4736.70i	−0.992015	−	0.118417i
$201$	−33224.9			−0.822377
$202$	19960.7	+	37969.7i	0.489184	+	0.930538i
$203$			30250.1i			0.734066i
$204$	13068.5	+	8994.53i	0.314025	+	0.216132i
$205$	926.828			0.0220542
$206$	10813.2	−	5684.48i	0.254811	−	0.133954i
$207$		−	294.975i		−	0.00688406i
$208$	−11598.0	−	30334.6i	−0.268076	−	0.701151i
$209$	−83454.3			−1.91054
$210$	−512.608	−	975.096i	−0.0116238	−	0.0221110i
$211$		−	67668.1i		−	1.51992i	−0.649973	−	0.759958i	$-0.725220\pi$
$211$		−	67668.1i		−	1.51992i	0.649973	−	0.759958i	$-0.274780\pi$
$212$	−30503.6	+	44319.7i	−0.678702	+	0.986110i
$213$	47131.9			1.03886
$214$	−14960.1	+	7864.54i	−0.326669	+	0.171730i
$215$		−	667.886i		−	0.0144486i
$216$	5566.34	−	46630.8i	0.119306	−	0.999459i
$217$	6927.75			0.147120
$218$	−6759.53	−	12858.1i	−0.142234	−	0.270561i
$219$		−	29326.0i		−	0.611455i
$220$	−1399.02	−	962.892i	−0.0289054	−	0.0198945i
$221$	14070.4			0.288086
$222$	−31116.7	+	16358.0i	−0.631375	+	0.331914i
$223$		−	32892.7i		−	0.661439i	−0.943729	−	0.330719i	$-0.892709\pi$
$223$		−	32892.7i		−	0.661439i	0.943729	−	0.330719i	$-0.107291\pi$
$224$	−30856.0	−	27151.0i	−0.614956	−	0.541115i
$225$	−674.296			−0.0133194
$226$	−6652.69	−	12654.9i	−0.130251	−	0.247766i
$227$			13785.5i			0.267530i	0.991013	+	0.133765i	$0.0427067\pi$
$227$			13785.5i			0.267530i	−0.991013	+	0.133765i	$0.957293\pi$
$228$	−48936.4	+	71101.5i	−0.941375	+	1.36776i
$229$	26409.8			0.503611			0.251805	−	0.967778i	$-0.418976\pi$
$229$	26409.8			0.503611			0.251805	+	0.967778i	$0.418976\pi$
$230$	−742.292	+	390.223i	−0.0140320	+	0.00737662i
$231$			49623.9i			0.929965i
$232$	47894.5	+	5717.19i	0.889835	+	0.106220i
$233$	−59506.9			−1.09611			−0.548057	−	0.836441i	$-0.684632\pi$
$233$	−59506.9			−1.09611			−0.548057	+	0.836441i	$0.684632\pi$
$234$	−254.986	−	485.041i	−0.00465677	−	0.00885822i
$235$			2057.87i			0.0372634i
$236$	−78537.2	−	54054.1i	−1.41010	−	0.970521i
$237$	51948.7			0.924865
$238$	15761.8	−	8285.97i	0.278260	−	0.146281i
$239$			45080.3i			0.789207i	0.918851	+	0.394604i	$0.129118\pi$
$239$			45080.3i			0.789207i	−0.918851	+	0.394604i	$0.870882\pi$
$240$	−1640.73	+	627.313i	−0.0284849	+	0.0108908i
$241$	80833.7			1.39174			0.695871	−	0.718167i	$-0.255019\pi$
$241$	80833.7			1.39174			0.695871	+	0.718167i	$0.255019\pi$
$242$	8347.97	+	15879.7i	0.142544	+	0.271151i
$243$		−	1574.38i		−	0.0266622i
$244$	51929.7	−	75450.5i	0.872240	−	1.26731i
$245$	606.340			0.0101015
$246$	−38221.2	+	20092.9i	−0.631588	+	0.332026i
$247$			76552.7i			1.25478i
$248$	1309.33	−	10968.6i	0.0212885	−	0.178339i
$249$	−10872.9			−0.175367
$250$	1784.90	+	3395.28i	0.0285584	+	0.0543244i
$251$		−	19590.0i		−	0.310948i	−0.987840	−	0.155474i	$-0.950309\pi$
$251$		−	19590.0i		−	0.310948i	0.987840	−	0.155474i	$-0.0496905\pi$
$252$	−571.274	−	393.186i	−0.00899588	−	0.00619152i
$253$	37776.2			0.590170
$254$	−19458.1	+	10229.1i	−0.301600	+	0.158552i
$255$		−	761.038i		−	0.0117038i
$256$	−48819.4	+	43722.3i	−0.744924	+	0.667149i
$257$	94773.4			1.43490			0.717448	−	0.696612i	$-0.245310\pi$
$257$	94773.4			1.43490			0.717448	+	0.696612i	$0.245310\pi$
$258$	14479.2	+	27542.7i	0.217523	+	0.413778i
$259$			39458.6i			0.588223i
$260$	−883.263	+	1283.32i	−0.0130660	+	0.0189841i
$261$	813.875			0.0119475
$262$	−68230.5	+	35868.8i	−0.993976	+	0.522534i
$263$			70021.0i			1.01232i	0.862440	+	0.506158i	$0.168935\pi$
$263$			70021.0i			1.01232i	−0.862440	+	0.506158i	$0.831065\pi$
$264$	78568.5	+	9378.77i	1.12730	+	0.134567i
$265$	2580.95			0.0367525
$266$	45081.3	+	85754.8i	0.637138	+	1.21198i
$267$		−	52977.2i		−	0.743133i
$268$	48983.5	+	33713.5i	0.681994	+	0.469390i
$269$	102740.			1.41983			0.709913	−	0.704290i	$-0.248734\pi$
$269$	102740.			1.41983			0.709913	+	0.704290i	$0.248734\pi$
$270$	−1994.04	+	1048.27i	−0.0273531	+	0.0143796i
$271$			5243.99i			0.0714041i	0.999362	+	0.0357020i	$0.0113667\pi$
$271$			5243.99i			0.0714041i	−0.999362	+	0.0357020i	$0.988633\pi$
$272$	−10140.1	−	26521.3i	−0.137058	−	0.358474i
$273$	45520.0			0.610770
$274$	5011.66	+	9533.29i	0.0667544	+	0.126982i
$275$		−	86354.2i		−	1.14187i
$276$	22151.4	−	32184.6i	0.290793	−	0.422503i
$277$	−95914.8			−1.25005			−0.625023	−	0.780606i	$-0.714910\pi$
$277$	−95914.8			−1.25005			−0.625023	+	0.780606i	$0.714910\pi$
$278$	−114702.	+	60299.1i	−1.48417	+	0.780227i
$279$		−	186.390i		−	0.00239450i
$280$	−233.696	+	1957.73i	−0.00298082	+	0.0249711i
$281$	138124.			1.74927			0.874634	−	0.484785i	$-0.161102\pi$
$281$	138124.			1.74927			0.874634	+	0.484785i	$0.161102\pi$
$282$	−44613.0	−	84863.9i	−0.561001	−	1.06715i
$283$			74803.3i			0.934003i	0.884257	+	0.467001i	$0.154666\pi$
$283$			74803.3i			0.934003i	−0.884257	+	0.467001i	$0.845334\pi$
$284$	−69486.7	−	47825.1i	−0.861520	−	0.592951i
$285$	4140.57			0.0509765
$286$	62117.1	−	32655.0i	0.759415	−	0.399225i
$287$			48467.7i			0.588422i
$288$	−730.494	+	830.176i	−0.00880707	+	0.0100089i
$289$	−71219.3			−0.852712
$290$	−1076.68	−	2048.08i	−0.0128024	−	0.0243529i
$291$		−	87319.7i		−	1.03116i
$292$	−29757.3	+	43235.4i	−0.349002	+	0.507077i
$293$	−72805.0			−0.848059			−0.424030	−	0.905648i	$-0.639385\pi$
$293$	−72805.0			−0.848059			−0.424030	+	0.905648i	$0.639385\pi$
$294$	−25004.6	+	13145.0i	−0.289285	+	0.152077i
$295$			4573.59i			0.0525549i
$296$	62474.0	+	7457.57i	0.713043	+	0.0851165i
$297$	101479.			1.15044
$298$	20674.0	+	39326.6i	0.232805	+	0.442847i
$299$		−	34652.2i		−	0.387604i
$300$	−73572.1	−	50636.9i	−0.817468	−	0.562632i
$301$	34926.5			0.385498
$302$	−54181.2	+	28483.1i	−0.594066	+	0.312301i
$303$			95872.0i			1.04426i
$304$	144294.	−	55169.0i	1.56136	−	0.596964i
$305$	−4393.83			−0.0472328
$306$	−222.933	−	424.068i	−0.00238084	−	0.00452890i
$307$		−	98516.3i		−	1.04528i	−0.852554	−	0.522638i	$-0.824948\pi$
$307$		−	98516.3i		−	1.04528i	0.852554	−	0.522638i	$-0.175052\pi$
$308$	50353.7	−	73160.6i	0.530798	−	0.771216i
$309$	27302.8			0.285950
$310$	−469.043	+	246.576i	−0.00488078	+	0.00256583i
$311$		−	179374.i		−	1.85455i	−0.374378	−	0.927276i	$-0.622144\pi$
$311$		−	179374.i		−	1.85455i	0.374378	−	0.927276i	$-0.377856\pi$
$312$	8603.16	−	72071.0i	0.0883790	−	0.740374i
$313$	127215.			1.29852			0.649259	−	0.760567i	$-0.275079\pi$
$313$	127215.			1.29852			0.649259	+	0.760567i	$0.275079\pi$
$314$	−35300.3	−	67149.0i	−0.358030	−	0.681052i
$315$			33.2680i			0.000335278i
$316$	−76588.2	−	52712.7i	−0.766986	−	0.527887i
$317$	120207.			1.19622			0.598110	−	0.801414i	$-0.295919\pi$
$317$	120207.			1.19622			0.598110	+	0.801414i	$0.295919\pi$
$318$	−106435.	+	55952.8i	−1.05252	+	0.553309i
$319$			104229.i			1.02426i
$320$	3055.47	+	740.013i	0.0298386	+	0.00722669i
$321$	−37773.7			−0.366589
$322$	−20406.4	−	38817.6i	−0.196813	−	0.374383i
$323$			66929.5i			0.641524i
$324$	58712.6	−	85305.6i	0.559295	−	0.812620i
$325$	−79212.8			−0.749944
$326$	87292.4	−	45889.7i	0.821375	−	0.431797i
$327$		−	32466.3i		−	0.303625i
$328$	76738.0	+	9160.26i	0.713284	+	0.0851452i
$329$	−107615.			−0.994214
$330$	−1766.24	−	3359.78i	−0.0162189	−	0.0308520i
$331$		−	131089.i		−	1.19649i	−0.801312	−	0.598246i	$-0.795864\pi$
$331$		−	131089.i		−	1.19649i	0.801312	−	0.598246i	$-0.204136\pi$
$332$	16030.0	+	11032.8i	0.145431	+	0.100095i
$333$	1061.63			0.00957378
$334$	48592.4	−	25545.0i	0.435587	−	0.228988i
$335$		−	2852.54i		−	0.0254180i
$336$	−32804.8	−	85800.7i	−0.290575	−	0.759998i
$337$	146788.			1.29250			0.646249	−	0.763126i	$-0.276337\pi$
$337$	146788.			1.29250			0.646249	+	0.763126i	$0.276337\pi$
$338$	23205.5	+	44142.1i	0.203123	+	0.386385i
$339$		−	31953.1i		−	0.278044i
$340$	−772.230	+	1122.00i	−0.00668019	+	0.00970589i
$341$	23870.2			0.205280
$342$	2307.22	−	1212.91i	0.0197259	−	0.0103699i
$343$			128078.i			1.08865i
$344$	6601.02	−	55298.5i	0.0557820	−	0.467301i
$345$	−1874.26			−0.0157468
$346$	90133.8	+	171455.i	0.752897	+	1.43218i
$347$		−	37360.8i		−	0.310282i	−0.987892	−	0.155141i	$-0.950417\pi$
$347$		−	37360.8i		−	0.310282i	0.987892	−	0.155141i	$-0.0495832\pi$
$348$	88801.6	+	61118.7i	0.733267	+	0.504680i
$349$	−169309.			−1.39005			−0.695024	−	0.718987i	$-0.744606\pi$
$349$	−169309.			−1.39005			−0.695024	+	0.718987i	$0.744606\pi$
$350$	−88734.7	+	46647.9i	−0.724365	+	0.380799i
$351$		−	93087.2i		−	0.755571i
$352$	−106317.	−	93551.1i	−0.858060	−	0.755029i
$353$	−126322.			−1.01375			−0.506875	−	0.862020i	$-0.669199\pi$
$353$	−126322.			−1.01375			−0.506875	+	0.862020i	$0.669199\pi$
$354$	−99151.7	−	188609.i	−0.791213	−	1.50507i
$355$			4046.54i			0.0321090i
$356$	−53756.3	+	78104.5i	−0.424160	+	0.616277i
$357$	39797.9			0.312265
$358$	64115.2	−	33705.4i	0.500259	−	0.262986i
$359$			5194.61i			0.0403055i	0.999797	+	0.0201527i	$0.00641525\pi$
$359$			5194.61i			0.0403055i	−0.999797	+	0.0201527i	$0.993585\pi$
$360$	52.6725	+	6.28756i	0.000406424	+	4.85151e-5i
$361$	−233821.			−1.79420
$362$	110548.	+	210287.i	0.843593	+	1.60470i
$363$			40095.6i			0.304287i
$364$	−67110.3	−	46189.5i	−0.506508	−	0.348610i
$365$	2517.80			0.0188989
$366$	181196.	−	95254.8i	1.35265	−	0.711090i
$367$		−	25559.1i		−	0.189764i	−0.995489	−	0.0948820i	$-0.969753\pi$
$367$		−	25559.1i		−	0.189764i	0.995489	−	0.0948820i	$-0.0302474\pi$
$368$	−65315.9	+	24972.7i	−0.482306	+	0.184404i
$369$	1304.02			0.00957701
$370$	−1404.43	−	2671.54i	−0.0102588	−	0.0195145i
$371$			134968.i			0.980583i
$372$	13997.1	−	20336.9i	0.101147	−	0.146960i
$373$	−119158.			−0.856457			−0.428228	−	0.903671i	$-0.640862\pi$
$373$	−119158.			−0.856457			−0.428228	+	0.903671i	$0.640862\pi$
$374$	54308.5	−	28550.0i	0.388262	−	0.204110i
$375$			8572.94i			0.0609631i
$376$	−20338.9	+	170384.i	−0.143864	+	1.20519i
$377$	95609.9			0.672698
$378$	−54818.4	−	104277.i	−0.383656	−	0.729800i
$379$			23302.7i			0.162229i	0.996705	+	0.0811143i	$0.0258479\pi$
$379$			23302.7i			0.162229i	−0.996705	+	0.0811143i	$0.974152\pi$
$380$	−6104.46	−	4201.46i	−0.0422746	−	0.0290960i
$381$	−49130.8			−0.338458
$382$	214067.	−	112535.i	1.46698	−	0.771191i
$383$			68283.7i			0.465500i	0.972537	+	0.232750i	$0.0747723\pi$
$383$			68283.7i			0.465500i	−0.972537	+	0.232750i	$0.925228\pi$
$384$	−142047.	+	35723.1i	−0.963316	+	0.242263i
$385$	−4260.48			−0.0287434
$386$	27902.1	+	53076.1i	0.187268	+	0.356225i
$387$		−	939.693i		−	0.00627428i
$388$	−88603.8	+	128736.i	−0.588558	+	0.855136i
$389$	248009.			1.63896			0.819480	−	0.573108i	$-0.194263\pi$
$389$	248009.			1.63896			0.819480	+	0.573108i	$0.194263\pi$
$390$	−3081.93	+	1620.17i	−0.0202625	+	0.0106520i
$391$		−	30296.1i		−	0.198168i
$392$	50202.7	+	5992.73i	0.326704	+	0.0389989i
$393$	−172279.			−1.11545
$394$	94562.2	+	179879.i	0.609152	+	1.15874i
$395$			4460.09i			0.0285857i
$396$	−1968.38	−	1354.76i	−0.0125521	−	0.00863915i
$397$	−49399.7			−0.313432			−0.156716	−	0.987644i	$-0.550091\pi$
$397$	−49399.7			−0.313432			−0.156716	+	0.987644i	$0.550091\pi$
$398$	−164989.	+	86734.6i	−1.04157	+	0.547553i
$399$			216528.i			1.36009i
$400$	57086.0	+	149308.i	0.356788	+	0.933176i
$401$	−54629.2			−0.339732			−0.169866	−	0.985467i	$-0.554333\pi$
$401$	−54629.2			−0.339732			−0.169866	+	0.985467i	$0.554333\pi$
$402$	61840.7	+	117635.i	0.382668	+	0.727921i
$403$		−	21896.1i		−	0.134821i
$404$	97281.9	−	141344.i	0.596032	−	0.865996i
$405$	−4967.74			−0.0302865
$406$	107103.	−	56304.0i	0.649753	−	0.341576i
$407$			135958.i			0.820759i
$408$	7521.69	−	63011.2i	0.0451851	−	0.378527i
$409$	−155212.			−0.927852			−0.463926	−	0.885874i	$-0.653560\pi$
$409$	−155212.			−0.927852			−0.463926	+	0.885874i	$0.653560\pi$
$410$	−1725.09	−	3281.50i	−0.0102623	−	0.0195211i
$411$			24071.2i			0.142500i
$412$	−40252.6	−	27704.3i	−0.237137	−	0.163212i
$413$	−239172.			−1.40220
$414$	−1044.38	+	549.031i	−0.00609338	+	0.00320329i
$415$		−	933.503i		−	0.00542025i
$416$	−85814.6	+	97524.8i	−0.495878	+	0.563545i
$417$	−289619.			−1.66554
$418$	155332.	+	295476.i	0.889012	+	1.69110i
$419$		−	196974.i		−	1.12197i	−0.827826	−	0.560985i	$-0.810423\pi$
$419$		−	196974.i		−	1.12197i	0.827826	−	0.560985i	$-0.189577\pi$
$420$	−2498.29	+	3629.85i	−0.0141626	+	0.0205774i
$421$	126999.			0.716531			0.358265	−	0.933620i	$-0.383368\pi$
$421$	126999.			0.716531			0.358265	+	0.933620i	$0.383368\pi$
$422$	−239584.	+	125949.i	−1.34534	+	0.707247i
$423$			2895.36i			0.0161816i
$424$	213693.	+	25508.7i	1.18866	+	0.141891i
$425$	−69255.2			−0.383420
$426$	−87725.7	−	166874.i	−0.483401	−	0.919537i
$427$		−	229772.i		−	1.26020i
$428$	55689.9	+	38329.2i	0.304011	+	0.209239i
$429$	156843.			0.852219
$430$	−2364.70	+	1243.12i	−0.0127891	+	0.00672321i
$431$			220890.i			1.18911i	0.804055	+	0.594555i	$0.202672\pi$
$431$			220890.i			1.18911i	−0.804055	+	0.594555i	$0.797328\pi$
$432$	−175460.	+	67084.8i	−0.940179	+	0.359465i
$433$	−118056.			−0.629671			−0.314835	−	0.949146i	$-0.601949\pi$
$433$	−118056.			−0.629671			−0.314835	+	0.949146i	$0.601949\pi$
$434$	−12894.5	−	24528.2i	−0.0684580	−	0.130222i
$435$		−	5171.33i		−	0.0273290i
$436$	−32943.8	+	47865.2i	−0.173301	+	0.251795i
$437$	164832.			0.863134
$438$	−103831.	+	54583.9i	−0.541225	+	0.284522i
$439$		−	59927.6i		−	0.310955i	−0.987839	−	0.155477i	$-0.950308\pi$
$439$		−	59927.6i		−	0.310955i	0.987839	−	0.155477i	$-0.0496916\pi$
$440$	−805.220	+	6745.54i	−0.00415919	+	0.0348427i
$441$	853.099			0.00438654
$442$	−26189.0	−	49817.3i	−0.134052	−	0.254997i
$443$		−	234294.i		−	1.19386i	−0.802293	−	0.596931i	$-0.796387\pi$
$443$		−	234294.i		−	1.19386i	0.802293	−	0.596931i	$-0.203613\pi$
$444$	115834.	+	79723.9i	0.587582	+	0.404410i
$445$	4548.39			0.0229688
$446$	−116459.	+	61222.5i	−0.585468	+	0.307781i
$447$			99298.1i			0.496965i
$448$	−38698.4	+	159783.i	−0.192813	+	0.796115i
$449$	−260070.			−1.29002			−0.645012	−	0.764173i	$-0.723147\pi$
$449$	−260070.			−1.29002			−0.645012	+	0.764173i	$0.723147\pi$
$450$	1255.05	+	2387.39i	0.00619780	+	0.0117896i
$451$			167000.i			0.821036i
$452$	−32423.1	+	47108.6i	−0.158700	+	0.230581i
$453$	−136805.			−0.666664
$454$	48808.7	−	25658.7i	0.236802	−	0.124487i
$455$			3908.15i			0.0188777i
$456$	342824.	+	40923.1i	1.64870	+	0.196806i
$457$	−260884.			−1.24915			−0.624576	−	0.780964i	$-0.714728\pi$
$457$	−260884.			−1.24915			−0.624576	+	0.780964i	$0.714728\pi$
$458$	−49156.1	−	93505.9i	−0.234340	−	0.445767i
$459$		−	81385.5i		−	0.386297i
$460$	2763.23	+	1901.82i	0.0130587	+	0.00898782i
$461$	282393.			1.32878			0.664388	−	0.747388i	$-0.268692\pi$
$461$	282393.			1.32878			0.664388	+	0.747388i	$0.268692\pi$
$462$	175697.	−	92363.9i	0.823152	−	0.432731i
$463$		−	146650.i		−	0.684101i	−0.939682	−	0.342051i	$-0.888879\pi$
$463$		−	146650.i		−	0.684101i	0.939682	−	0.342051i	$-0.111121\pi$
$464$	−68902.9	−	180215.i	−0.320038	−	0.837057i
$465$	−1184.31			−0.00547723
$466$	110759.	+	210688.i	0.510043	+	0.970217i
$467$		−	278928.i		−	1.27896i	−0.768806	−	0.639482i	$-0.779149\pi$
$467$		−	278928.i		−	1.27896i	0.768806	−	0.639482i	$-0.220851\pi$
$468$	−1242.72	+	1805.59i	−0.00567390	+	0.00824382i
$469$	149171.			0.678171
$470$	7286.04	−	3830.27i	0.0329834	−	0.0173394i
$471$		−	169549.i		−	0.764281i
$472$	−45202.8	+	378676.i	−0.202900	+	1.69975i
$473$	120342.			0.537894
$474$	−96691.1	−	183928.i	−0.430358	−	0.818637i
$475$		−	376796.i		−	1.67001i
$476$	−58674.1	−	40383.1i	−0.258960	−	0.178232i
$477$	3631.30			0.0159597
$478$	159610.	−	83907.1i	0.698561	−	0.367234i
$479$		−	118462.i		−	0.516305i	−0.966104	−	0.258153i	$-0.916886\pi$
$479$		−	118462.i		−	0.516305i	0.966104	−	0.258153i	$-0.0831137\pi$
$480$	5274.91	+	4641.52i	0.0228946	+	0.0201455i
$481$	124714.			0.539047
$482$	−150454.	−	286198.i	−0.647605	−	1.23189i
$483$		−	98012.8i		−	0.420135i
$484$	40685.3	−	59113.1i	0.173679	−	0.252344i
$485$	7496.88			0.0318711
$486$	−5574.19	+	2930.35i	−0.0235999	+	0.0124065i
$487$		−	145968.i		−	0.615462i	−0.951473	−	0.307731i	$-0.900430\pi$
$487$		−	145968.i		−	0.615462i	0.951473	−	0.307731i	$-0.0995697\pi$
$488$	−363793.	−	43426.3i	−1.52762	−	0.182353i
$489$	220410.			0.921751
$490$	−1128.57	−	2146.79i	−0.00470041	−	0.00894122i
$491$			125356.i			0.519976i	0.965612	+	0.259988i	$0.0837185\pi$
$491$			125356.i			0.519976i	−0.965612	+	0.259988i	$0.916281\pi$
$492$	142281.	+	97926.3i	0.587781	+	0.404547i
$493$	83591.0			0.343927
$494$	271040.	−	142486.i	1.11066	−	0.583873i
$495$			114.628i			0.000467820i
$496$	−41272.0	+	15779.8i	−0.167762	+	0.0641414i
$497$	−211610.			−0.856691
$498$	20237.6	+	38496.4i	0.0816019	+	0.155225i
$499$		−	49361.2i		−	0.198237i	−0.995076	−	0.0991184i	$-0.968398\pi$
$499$		−	49361.2i		−	0.198237i	0.995076	−	0.0991184i	$-0.0316023\pi$
$500$	8699.02	−	12639.1i	0.0347961	−	0.0505564i
$501$	122694.			0.488818
$502$	−69359.9	+	36462.5i	−0.275233	+	0.144690i
$503$			44625.9i			0.176381i	0.996104	+	0.0881903i	$0.0281084\pi$
$503$			44625.9i			0.176381i	−0.996104	+	0.0881903i	$0.971892\pi$
$504$	−328.802	+	2754.47i	−0.00129442	+	0.0108437i
$505$	−8231.15			−0.0322758
$506$	−70312.1	−	133749.i	−0.274618	−	0.522385i
$507$			111457.i			0.433603i
$508$	72433.8	+	49853.4i	0.280681	+	0.193182i
$509$	5362.20			0.0206970			0.0103485	−	0.999946i	$-0.496706\pi$
$509$	5362.20			0.0206970			0.0103485	+	0.999946i	$0.496706\pi$
$510$	−2694.51	+	1416.50i	−0.0103595	+	0.00544600i
$511$			131666.i			0.504235i
$512$	245668.	+	91469.0i	0.937150	+	0.348927i
$513$	442793.			1.68254
$514$	−176400.	−	335552.i	−0.667685	−	1.27009i
$515$			2344.10i			0.00883815i
$516$	70567.1	−	102529.i	0.265035	−	0.385078i
$517$	−370796.			−1.38725
$518$	139706.	−	73443.4i	0.520661	−	0.273712i
$519$			432917.i			1.60720i
$520$	6187.70	+	738.630i	0.0228835	+	0.00273162i
$521$	−294880.			−1.08635			−0.543175	−	0.839620i	$-0.682778\pi$
$521$	−294880.			−1.08635			−0.543175	+	0.839620i	$0.682778\pi$
$522$	−1514.85	−	2881.58i	−0.00555941	−	0.0105752i
$523$			297894.i			1.08908i	0.838736	+	0.544538i	$0.183295\pi$
$523$			297894.i			1.08908i	−0.838736	+	0.544538i	$0.816705\pi$
$524$	253992.	+	174813.i	0.925034	+	0.636665i
$525$	−224052.			−0.812886
$526$	247914.	−	130329.i	0.896045	−	0.471051i
$527$		−	19143.6i		−	0.0689292i
$528$	−113032.	−	295634.i	−0.405446	−	1.06044i
$529$	205229.			0.733376
$530$	−4803.86	−	9138.02i	−0.0171017	−	0.0325312i
$531$			6434.88i			0.0228219i
$532$	219712.	−	319227.i	0.776302	−	1.12792i
$533$	153189.			0.539229
$534$	−187570.	+	98605.4i	−0.657779	+	0.345795i
$535$		−	3243.08i		−	0.0113305i
$536$	28192.9	−	236180.i	0.0981320	−	0.822078i
$537$	161888.			0.561393
$538$	−191228.	−	363758.i	−0.660673	−	1.25675i
$539$			109253.i			0.376058i
$540$	7422.94	+	5108.93i	0.0254559	+	0.0175203i
$541$	−327963.			−1.12055			−0.560274	−	0.828307i	$-0.689304\pi$
$541$	−327963.			−1.12055			−0.560274	+	0.828307i	$0.689304\pi$
$542$	18566.7	−	9760.52i	0.0632028	−	0.0332257i
$543$			530966.i			1.80081i
$544$	−75027.1	+	85265.3i	−0.253525	+	0.288121i
$545$	2787.42			0.00938445
$546$	−84725.5	−	161167.i	−0.284203	−	0.540618i
$547$		−	578452.i		−	1.93327i	−0.256157	−	0.966635i	$-0.582457\pi$
$547$		−	578452.i		−	1.93327i	0.256157	−	0.966635i	$-0.417543\pi$
$548$	24425.2	−	35488.2i	0.0813349	−	0.118174i
$549$	−6181.98			−0.0205108
$550$	−305743.	+	160729.i	−1.01072	+	0.531336i
$551$			454793.i			1.49799i
$552$	−155182.	−	18524.2i	−0.509287	−	0.0607940i
$553$	−233236.			−0.762687
$554$	178524.	+	339593.i	0.581671	+	1.10647i
$555$		−	6745.53i		−	0.0218993i
$556$	426986.	+	293878.i	1.38122	+	0.950644i
$557$	560502.			1.80662			0.903309	−	0.428990i	$-0.141130\pi$
$557$	560502.			1.80662			0.903309	+	0.428990i	$0.141130\pi$
$558$	−659.927	+	346.924i	−0.00211947	+	0.00111421i
$559$		−	110390.i		−	0.353270i
$560$	7366.47	−	2816.47i	0.0234900	−	0.00898110i
$561$	137127.			0.435710
$562$	−257087.	−	489037.i	−0.813969	−	1.54835i
$563$		−	101557.i		−	0.320401i	−0.987085	−	0.160200i	$-0.948786\pi$
$563$		−	101557.i		−	0.320401i	0.987085	−	0.160200i	$-0.0512140\pi$
$564$	−217429.	+	315911.i	−0.683534	+	0.993131i
$565$	2743.35			0.00859380
$566$	264846.	−	139230.i	0.826726	−	0.434610i
$567$		−	259784.i		−	0.808065i
$568$	−39993.8	+	335038.i	−0.123964	+	1.03848i
$569$	315615.			0.974840			0.487420	−	0.873168i	$-0.337938\pi$
$569$	315615.			0.974840			0.487420	+	0.873168i	$0.337938\pi$
$570$	−7706.76	−	14660.0i	−0.0237204	−	0.0451215i
$571$		−	368649.i		−	1.13068i	−0.824857	−	0.565342i	$-0.808744\pi$
$571$		−	368649.i		−	1.13068i	0.824857	−	0.565342i	$-0.191256\pi$
$572$	−231235.	−	159150.i	−0.706742	−	0.486423i
$573$	540512.			1.64625
$574$	171603.	−	90211.9i	0.520837	−	0.273804i
$575$			170559.i			0.515870i
$576$	4298.95	+	1041.17i	0.0129574	+	0.00313818i
$577$	262601.			0.788761			0.394380	−	0.918947i	$-0.370959\pi$
$577$	262601.			0.788761			0.394380	+	0.918947i	$0.370959\pi$
$578$	132559.	+	252157.i	0.396784	+	0.754771i
$579$			134015.i			0.399758i
$580$	−5247.38	+	7624.11i	−0.0155986	+	0.0226638i
$581$	48816.7			0.144616
$582$	−309161.	+	162526.i	−0.912724	+	0.479819i
$583$			465045.i			1.36823i
$584$	208465.	+	24884.6i	0.611233	+	0.0729633i
$585$	105.148			0.000307249
$586$	135511.	+	257771.i	0.394619	+	0.750653i
$587$		−	155308.i		−	0.450731i	−0.974274	−	0.225365i	$-0.927642\pi$
$587$		−	155308.i		−	0.450731i	0.974274	−	0.225365i	$-0.0723576\pi$
$588$	93081.3	+	64064.3i	0.269220	+	0.185294i
$589$	104155.			0.300226
$590$	16193.1	−	8512.73i	0.0465186	−	0.0244548i
$591$			454186.i			1.30035i
$592$	−89877.6	−	235074.i	−0.256453	−	0.670752i
$593$	331684.			0.943225			0.471612	−	0.881806i	$-0.343672\pi$
$593$	331684.			0.943225			0.471612	+	0.881806i	$0.343672\pi$
$594$	−188881.	−	359295.i	−0.535324	−	1.01831i
$595$			3416.87i			0.00965149i
$596$	100758.	−	146396.i	0.283654	−	0.412131i
$597$	−416590.			−1.16885
$598$	−122688.	+	64497.4i	−0.343085	+	0.180360i
$599$		−	396372.i		−	1.10471i	−0.833608	−	0.552357i	$-0.813729\pi$
$599$		−	396372.i		−	1.10471i	0.833608	−	0.552357i	$-0.186271\pi$
$600$	−42345.2	+	354737.i	−0.117625	+	0.985380i
$601$	142541.			0.394631			0.197316	−	0.980340i	$-0.436778\pi$
$601$	142541.			0.394631			0.197316	+	0.980340i	$0.436778\pi$
$602$	−65008.0	−	123660.i	−0.179380	−	0.341221i
$603$		−	4013.43i		−	0.0110378i
$604$	201693.	+	138817.i	0.552861	+	0.380513i
$605$	−3442.43			−0.00940491
$606$	339442.	−	178445.i	0.924315	−	0.485913i
$607$		−	418490.i		−	1.13581i	−0.823093	−	0.567907i	$-0.807753\pi$
$607$		−	418490.i		−	1.13581i	0.823093	−	0.567907i	$-0.192247\pi$
$608$	−463902.	−	408199.i	−1.25493	−	1.10424i
$609$	270430.			0.729157
$610$	8178.15	+	15556.7i	0.0219784	+	0.0418078i
$611$			340132.i			0.911097i
$612$	−1086.50	+	1578.62i	−0.00290087	+	0.00421477i
$613$	−593662.			−1.57986			−0.789930	−	0.613198i	$-0.789883\pi$
$613$	−593662.			−1.57986			−0.789930	+	0.613198i	$0.789883\pi$
$614$	−348804.	+	183366.i	−0.925219	+	0.486388i
$615$		−	8285.66i		−	0.0219067i
$616$	−352753.	−	42108.3i	−0.929627	−	0.110970i
$617$	637931.			1.67573			0.837864	−	0.545879i	$-0.183804\pi$
$617$	637931.			1.67573			0.837864	+	0.545879i	$0.183804\pi$
$618$	−50818.2	−	96667.5i	−0.133058	−	0.253107i
$619$			636948.i			1.66235i	0.556010	+	0.831175i	$0.312332\pi$
$619$			636948.i			1.66235i	−0.556010	+	0.831175i	$0.687668\pi$
$620$	1746.04	+	1201.73i	0.00454224	+	0.00312625i
$621$	−200433.			−0.519741
$622$	−635087.	+	333865.i	−1.64154	+	0.862960i
$623$			237854.i			0.612823i
$624$	−271185.	+	103684.i	−0.696461	+	0.266283i
$625$	389521.			0.997173
$626$	−236782.	−	450412.i	−0.604226	−	1.14937i
$627$			746065.i			1.89776i
$628$	−172042.	+	249966.i	−0.436230	+	0.633814i
$629$	109037.			0.275596
$630$	117.788	−	61.9210i	0.000296769	−	0.000156012i
$631$		−	232438.i		−	0.583778i	−0.956452	−	0.291889i	$-0.905716\pi$
$631$		−	232438.i		−	0.583778i	0.956452	−	0.291889i	$-0.0942838\pi$
$632$	−44081.1	+	369279.i	−0.110362	+	0.924528i
$633$	−604940.			−1.50975
$634$	−223739.	−	425601.i	−0.556625	−	1.05883i
$635$		−	4218.16i		−	0.0104610i
$636$	396210.	+	272696.i	0.979515	+	0.674163i
$637$	100218.			0.246982
$638$	369032.	−	194000.i	0.906614	−	0.476607i
$639$			5693.34i			0.0139433i
$640$	−3067.03	−	12195.5i	−0.00748785	−	0.0297742i
$641$	−136294.			−0.331713			−0.165856	−	0.986150i	$-0.553039\pi$
$641$	−136294.			−0.331713			−0.165856	+	0.986150i	$0.553039\pi$
$642$	70307.4	+	133740.i	0.170581	+	0.324484i
$643$		−	775485.i		−	1.87565i	−0.347109	−	0.937825i	$-0.612837\pi$
$643$		−	775485.i		−	1.87565i	0.347109	−	0.937825i	$-0.387163\pi$
$644$	−99454.3	+	144501.i	−0.239801	+	0.348416i
$645$	−5970.77			−0.0143519
$646$	236969.	−	124575.i	0.567840	−	0.298514i
$647$			150951.i			0.360601i	0.983612	+	0.180300i	$0.0577070\pi$
$647$			150951.i			0.360601i	−0.983612	+	0.180300i	$0.942293\pi$
$648$	−411311.	−	49098.5i	−0.979536	−	0.116928i
$649$	−824088.			−1.95652
$650$	147437.	+	280459.i	0.348964	+	0.663807i
$651$		−	61932.7i		−	0.146136i
$652$	−324951.	−	223651.i	−0.764404	−	0.526110i
$653$	−332611.			−0.780027			−0.390014	−	0.920809i	$-0.627530\pi$
$653$	−332611.			−0.780027			−0.390014	+	0.920809i	$0.627530\pi$
$654$	−114949.	+	60428.9i	−0.268752	+	0.141283i
$655$		−	14791.1i		−	0.0344762i
$656$	−110398.	−	288746.i	−0.256540	−	0.670978i
$657$	3542.46			0.00820681
$658$	200301.	+	381017.i	0.462627	+	0.880021i
$659$		−	638802.i		−	1.47094i	−0.677556	−	0.735471i	$-0.736961\pi$
$659$		−	638802.i		−	1.47094i	0.677556	−	0.735471i	$-0.263039\pi$
$660$	−8608.07	+	12507.0i	−0.0197614	+	0.0287121i
$661$	−492818.			−1.12793			−0.563967	−	0.825798i	$-0.690725\pi$
$661$	−492818.			−1.12793			−0.563967	+	0.825798i	$0.690725\pi$
$662$	−464130.	+	243993.i	−1.05907	+	0.556752i
$663$		−	125787.i		−	0.286159i
$664$	9226.23	−	77290.6i	0.0209261	−	0.175303i
$665$	−18590.1			−0.0420377
$666$	−1975.98	−	3758.77i	−0.00445487	−	0.00847416i
$667$		−	205865.i		−	0.462734i
$668$	−180888.	−	124498.i	−0.405375	−	0.279004i
$669$	−294054.			−0.657015
$670$	−10099.6	+	5309.37i	−0.0224986	+	0.0118275i
$671$		−	791699.i		−	1.75839i
$672$	−242725.	+	275847.i	−0.537496	+	0.610843i
$673$	630657.			1.39240			0.696198	−	0.717850i	$-0.254873\pi$
$673$	630657.			1.39240			0.696198	+	0.717850i	$0.254873\pi$
$674$	−273213.	−	519713.i	−0.601425	−	1.14405i
$675$			458179.i			1.00561i
$676$	113096.	−	164322.i	0.247489	−	0.359585i
$677$	662249.			1.44492			0.722460	−	0.691413i	$-0.243011\pi$
$677$	662249.			1.44492			0.722460	+	0.691413i	$0.243011\pi$
$678$	−113132.	+	59473.7i	−0.246109	+	0.129380i
$679$			392043.i			0.850343i
$680$	5409.86	+	645.779i	0.0116995	+	0.00139658i
$681$	123240.			0.265740
$682$	−44429.0	−	84514.0i	−0.0955209	−	0.181702i
$683$			810382.i			1.73719i	0.495520	+	0.868597i	$0.334978\pi$
$683$			810382.i			1.73719i	−0.495520	+	0.868597i	$0.665022\pi$
$684$	−8588.76	−	5911.32i	−0.0183577	−	0.0126349i
$685$	−2066.65			−0.00440438
$686$	453469.	−	238389.i	0.963606	−	0.506568i
$687$		−	236099.i		−	0.500242i
$688$	−208075.	+	79554.6i	−0.439584	+	0.168069i
$689$	426587.			0.898605
$690$	3488.52	+	6635.95i	0.00732729	+	0.0139381i
$691$		−	144457.i		−	0.302540i	−0.988493	−	0.151270i	$-0.951664\pi$
$691$		−	144457.i		−	0.302540i	0.988493	−	0.151270i	$-0.0483362\pi$
$692$	439283.	−	638250.i	0.917344	−	1.33284i
$693$	−5994.36			−0.0124818
$694$	−132278.	+	69538.8i	−0.274644	+	0.144380i
$695$		−	24865.4i		−	0.0514785i
$696$	51110.6	−	428167.i	0.105510	−	0.883883i
$697$	133932.			0.275689
$698$	315132.	+	599451.i	0.646817	+	1.23039i
$699$			531980.i			1.08878i
$700$	330320.	+	227347.i	0.674123	+	0.463973i
$701$	576995.			1.17418			0.587091	−	0.809521i	$-0.300273\pi$
$701$	576995.			1.17418			0.587091	+	0.809521i	$0.300273\pi$
$702$	−329582.	+	173261.i	−0.668789	+	0.351582i
$703$			593236.i			1.20037i
$704$	−133339.	+	550548.i	−0.269036	+	1.11084i
$705$	18397.0			0.0370142
$706$	235121.	+	447253.i	0.471718	+	0.897313i
$707$		−	430441.i		−	0.861142i
$708$	−483234.	+	702107.i	−0.964030	+	1.40067i
$709$	−599389.			−1.19238			−0.596192	−	0.802842i	$-0.703320\pi$
$709$	−599389.			−1.19238			−0.596192	+	0.802842i	$0.703320\pi$
$710$	14327.1	−	7531.74i	0.0284210	−	0.0149410i
$711$			6275.19i			0.0124133i
$712$	376590.	+	44953.8i	0.742863	+	0.0886761i
$713$	−47146.3			−0.0927404
$714$	−74074.9	−	140907.i	−0.145303	−	0.276399i
$715$			13465.9i			0.0263404i
$716$	−238673.	−	164269.i	−0.465561	−	0.320428i
$717$	403009.			0.783929
$718$	18391.9	−	9668.62i	0.0356761	−	0.0187549i
$719$			41835.0i			0.0809249i	0.999181	+	0.0404624i	$0.0128831\pi$
$719$			41835.0i			0.0809249i	−0.999181	+	0.0404624i	$0.987117\pi$
$720$	−75.7768	−	198.194i	−0.000146174	−	0.000382318i
$721$	−122583.			−0.235808
$722$	435207.	+	827861.i	0.834875	+	1.58812i
$723$		−	722638.i		−	1.38243i
$724$	538774.	−	782805.i	1.02785	−	1.49340i
$725$	−470596.			−0.895307
$726$	141961.	−	74629.2i	0.269338	−	0.141591i
$727$			411955.i			0.779436i	0.920934	+	0.389718i	$0.127428\pi$
$727$			411955.i			0.779436i	−0.920934	+	0.389718i	$0.872572\pi$
$728$	−38626.0	+	323580.i	−0.0728815	+	0.610548i
$729$	−538336.			−1.01297
$730$	−4686.33	−	8914.45i	−0.00879401	−	0.0167282i
$731$		−	96513.4i		−	0.180615i
$732$	−674513.	−	464241.i	−1.25883	−	0.866406i
$733$	−776133.			−1.44454			−0.722268	−	0.691613i	$-0.756900\pi$
$733$	−776133.			−1.44454			−0.722268	+	0.691613i	$0.756900\pi$
$734$	−90493.9	+	47572.7i	−0.167968	+	0.0883010i
$735$		−	5420.56i		−	0.0100339i
$736$	209989.	+	184774.i	0.387650	+	0.341103i
$737$	513982.			0.946265
$738$	−2427.14	−	4616.96i	−0.00445638	−	0.00847702i
$739$		−	500937.i		−	0.917264i	−0.888626	−	0.458632i	$-0.848340\pi$
$739$		−	500937.i		−	0.917264i	0.888626	−	0.458632i	$-0.151660\pi$
$740$	−6844.74	+	9944.96i	−0.0124995	+	0.0181610i
$741$	684366.			1.24639
$742$	477865.	−	251214.i	0.867956	−	0.456285i
$743$		−	117762.i		−	0.213319i	−0.994296	−	0.106659i	$-0.965985\pi$
$743$		−	117762.i		−	0.213319i	0.994296	−	0.106659i	$-0.0340154\pi$
$744$	−98056.9	−	11705.1i	−0.177146	−	0.0211461i
$745$	−8525.30			−0.0153602
$746$	221786.	+	421887.i	0.398526	+	0.758086i
$747$		−	1313.41i		−	0.00235374i
$748$	−202167.	−	139144.i	−0.361332	−	0.248691i
$749$	169594.			0.302307
$750$	30353.1	−	15956.6i	0.0539611	−	0.0283674i
$751$		−	331435.i		−	0.587650i	−0.955859	−	0.293825i	$-0.905072\pi$
$751$		−	331435.i		−	0.587650i	0.955859	−	0.293825i	$-0.0949283\pi$
$752$	641114.	−	245121.i	1.13370	−	0.433457i
$753$	−175131.			−0.308868
$754$	−177957.	−	338513.i	−0.313020	−	0.595434i
$755$		−	11745.5i		−	0.0206052i
$756$	−267167.	+	388177.i	−0.467454	+	0.679181i
$757$	−987313.			−1.72291			−0.861456	−	0.507832i	$-0.830447\pi$
$757$	−987313.			−1.72291			−0.861456	+	0.507832i	$0.830447\pi$
$758$	82504.8	−	43372.8i	0.143596	−	0.0754882i
$759$		−	337712.i		−	0.586223i
$760$	−3513.48	+	29433.4i	−0.00608289	+	0.0509580i
$761$	204145.			0.352508			0.176254	−	0.984345i	$-0.443602\pi$
$761$	204145.			0.352508			0.176254	+	0.984345i	$0.443602\pi$
$762$	91446.2	+	173951.i	0.157491	+	0.299583i
$763$			145766.i			0.250384i
$764$	−796878.	−	548461.i	−1.36523	−	0.939635i
$765$	91.9303			0.000157085
$766$	241763.	−	127095.i	0.412034	−	0.216606i
$767$			755937.i			1.28498i
$768$	390869.	+	436436.i	0.662687	+	0.739942i
$769$	−315321.			−0.533212			−0.266606	−	0.963806i	$-0.585902\pi$
$769$	−315321.			−0.533212			−0.266606	+	0.963806i	$0.585902\pi$
$770$	7929.95	+	15084.5i	0.0133749	+	0.0254420i
$771$		−	847256.i		−	1.42530i
$772$	135986.	−	197579.i	0.228171	−	0.331517i
$773$	−816115.			−1.36582			−0.682909	−	0.730504i	$-0.739285\pi$
$773$	−816115.			−1.36582			−0.682909	+	0.730504i	$0.739285\pi$
$774$	−3327.05	+	1749.03i	−0.00555363	+	0.00291955i
$775$			107774.i			0.179436i
$776$	620714.	+	74095.0i	1.03079	+	0.123045i
$777$	352752.			0.584289
$778$	−461614.	−	878093.i	−0.762640	−	1.45071i
$779$			728683.i			1.20078i
$780$	11472.7	+	7896.20i	0.0188571	+	0.0129786i
$781$	−729122.			−1.19536
$782$	−107266.	+	56389.6i	−0.175407	+	0.0922116i
$783$		−	553022.i		−	0.902026i
$784$	−72223.6	−	188900.i	−0.117502	−	0.307327i
$785$	14556.7			0.0236224
$786$	320660.	+	609967.i	0.519039	+	0.987328i
$787$			654648.i			1.05696i	0.848946	+	0.528480i	$0.177238\pi$
$787$			654648.i			1.05696i	−0.848946	+	0.528480i	$0.822762\pi$
$788$	460866.	−	669609.i	0.742202	−	1.07837i
$789$	625974.			1.00555
$790$	15791.2	−	8301.47i	0.0253024	−	0.0133015i
$791$			143461.i			0.229288i
$792$	−1132.92	+	9490.75i	−0.00180613	+	0.0151304i
$793$	−726227.			−1.15485
$794$	91946.6	+	174903.i	0.145846	+	0.277432i
$795$		−	23073.2i		−	0.0365067i
$796$	614180.	+	422717.i	0.969325	+	0.667149i
$797$	208224.			0.327804			0.163902	−	0.986477i	$-0.447592\pi$
$797$	208224.			0.327804			0.163902	+	0.986477i	$0.447592\pi$
$798$	766631.	−	403018.i	1.20387	−	0.632877i
$799$			297375.i			0.465812i
$800$	422383.	−	480022.i	0.659974	−	0.750034i
$801$	6399.43			0.00997416
$802$	101680.	+	193419.i	0.158084	+	0.300711i
$803$			453668.i			0.703569i
$804$	301392.	−	437903.i	0.466251	−	0.677432i
$805$	8414.95			0.0129855
$806$	−77524.8	+	40754.8i	−0.119336	+	0.0627349i
$807$		−	918476.i		−	1.41033i
$808$	−681509.	−	81352.1i	−1.04388	−	0.124608i
$809$	−738797.			−1.12883			−0.564414	−	0.825492i	$-0.690898\pi$
$809$	−738797.			−1.12883			−0.564414	+	0.825492i	$0.690898\pi$
$810$	9246.36	+	17588.7i	0.0140929	+	0.0268079i
$811$		−	745390.i		−	1.13329i	−0.823961	−	0.566646i	$-0.808241\pi$
$811$		−	745390.i		−	1.13329i	0.823961	−	0.566646i	$-0.191759\pi$
$812$	−398696.	−	274407.i	−0.604686	−	0.416182i
$813$	46880.2			0.0709265
$814$	481369.	−	253056.i	0.726489	−	0.381916i
$815$			18923.4i			0.0284895i
$816$	−237095.	+	90650.4i	−0.356076	+	0.136141i
$817$	525099.			0.786678
$818$	288893.	+	549539.i	0.431748	+	0.821282i
$819$			5498.63i			0.00819761i
$820$	−8407.51	+	12215.6i	−0.0125037	+	0.0181671i
$821$	−368819.			−0.547176			−0.273588	−	0.961847i	$-0.588211\pi$
$821$	−368819.			−0.547176			−0.273588	+	0.961847i	$0.588211\pi$
$822$	85225.8	−	44803.2i	0.126133	−	0.0663080i
$823$			1.00833e6i			1.48868i	0.667798	+	0.744342i	$0.267237\pi$
$823$			1.00833e6i			1.48868i	−0.667798	+	0.744342i	$0.732763\pi$
$824$	−23167.8	+	194083.i	−0.0341217	+	0.285846i
$825$	−771989.			−1.13424
$826$	445166.	+	846805.i	0.652472	+	1.24115i
$827$		−	126381.i		−	0.184786i	−0.995723	−	0.0923932i	$-0.970548\pi$
$827$		−	126381.i		−	0.184786i	0.995723	−	0.0923932i	$-0.0294517\pi$
$828$	3887.77	+	2675.80i	0.00567074	+	0.00390295i
$829$	680049.			0.989536			0.494768	−	0.869025i	$-0.335253\pi$
$829$	680049.			0.989536			0.494768	+	0.869025i	$0.335253\pi$
$830$	−3305.13	+	1737.51i	−0.00479769	+	0.00252215i
$831$			857460.i			1.24169i
$832$	505018.	+	122312.i	0.729559	+	0.176694i
$833$	87619.6			0.126273
$834$	539062.	+	1.02542e6i	0.775008	+	1.47424i
$835$			10534.0i			0.0151084i
$836$	757037.	−	1.09993e6i	1.08319	−	1.57380i
$837$	−126651.			−0.180783
$838$	−697401.	+	366624.i	−0.993103	+	0.522075i
$839$		−	640868.i		−	0.910426i	−0.890383	−	0.455213i	$-0.849563\pi$
$839$		−	640868.i		−	0.910426i	0.890383	−	0.455213i	$-0.150437\pi$
$840$	17501.8	+	2089.20i	0.0248041	+	0.00296088i
$841$	−139272.			−0.196911
$842$	−236380.	−	449647.i	−0.333416	−	0.634232i
$843$		−	1.23480e6i		−	1.73757i
$844$	891865.	+	613836.i	1.25203	+	0.861723i
$845$	−9569.22			−0.0134018
$846$	10251.2	−	5389.07i	0.0143230	−	0.00752962i
$847$		−	180019.i		−	0.250930i
$848$	−307427.	−	804073.i	−0.427514	−	1.11816i
$849$	668727.			0.927756
$850$	128903.	+	245203.i	0.178413	+	0.339381i
$851$		−	268533.i		−	0.370799i
$852$	−427547.	+	621198.i	−0.588985	+	0.855758i
$853$	1.06221e6			1.45986			0.729929	−	0.683523i	$-0.239553\pi$
$853$	1.06221e6			1.45986			0.729929	+	0.683523i	$0.239553\pi$
$854$	−813524.	+	427670.i	−1.11546	+	0.586398i
$855$			500.164i			0.000684195i
$856$	32052.9	−	268515.i	0.0437441	−	0.366456i
$857$	−34175.9			−0.0465327			−0.0232663	−	0.999729i	$-0.507407\pi$
$857$	−34175.9			−0.0465327			−0.0232663	+	0.999729i	$0.507407\pi$
$858$	−291929.	−	555315.i	−0.396555	−	0.754335i
$859$			813949.i			1.10309i	0.834145	+	0.551545i	$0.185961\pi$
$859$			813949.i			1.10309i	−0.834145	+	0.551545i	$0.814039\pi$
$860$	8802.72	+	6058.58i	0.0119020	+	0.00819169i
$861$	433292.			0.584486
$862$	782078.	−	411139.i	1.05253	−	0.553317i
$863$		−	701831.i		−	0.942348i	−0.882040	−	0.471174i	$-0.843830\pi$
$863$		−	701831.i		−	0.942348i	0.882040	−	0.471174i	$-0.156170\pi$
$864$	564099.	+	496365.i	0.755662	+	0.664926i
$865$	−37168.3			−0.0496753
$866$	219736.	+	417987.i	0.292998	+	0.557348i
$867$			636687.i			0.847008i
$868$	−62843.5	+	91307.6i	−0.0834106	+	0.121190i
$869$	−803636.			−1.06419
$870$	−18309.5	+	9625.29i	−0.0241901	+	0.0127167i
$871$		−	471476.i		−	0.621475i
$872$	230788.	+	27549.3i	0.303515	+	0.0362308i
$873$	10547.9			0.0138400
$874$	−306798.	−	583599.i	−0.401633	−	0.763996i
$875$		−	38490.3i		−	0.0502731i
$876$	386516.	+	266024.i	0.503686	+	0.346667i
$877$	707217.			0.919504			0.459752	−	0.888047i	$-0.347938\pi$
$877$	707217.			0.919504			0.459752	+	0.888047i	$0.347938\pi$
$878$	−212178.	+	111542.i	−0.275240	+	0.144694i
$879$			650863.i			0.842387i
$880$	25381.8	−	9704.40i	0.0327761	−	0.0125315i
$881$	615739.			0.793313			0.396657	−	0.917967i	$-0.370170\pi$
$881$	615739.			0.793313			0.396657	+	0.917967i	$0.370170\pi$
$882$	−1587.86	−	3020.46i	−0.00204115	−	0.00388272i
$883$			144063.i			0.184770i	0.995723	+	0.0923849i	$0.0294490\pi$
$883$			144063.i			0.184770i	−0.995723	+	0.0923849i	$0.970551\pi$
$884$	−127637.	+	185448.i	−0.163332	+	0.237311i
$885$	40887.0			0.0522034
$886$	−829535.	+	436087.i	−1.05674	+	0.555527i
$887$		−	1.34077e6i		−	1.70415i	−0.523423	−	0.852073i	$-0.675345\pi$
$887$		−	1.34077e6i		−	1.70415i	0.523423	−	0.852073i	$-0.324655\pi$
$888$	66669.2	−	558506.i	0.0845472	−	0.708274i
$889$	220585.			0.279108
$890$	−8465.82	−	16103.9i	−0.0106878	−	0.0203306i
$891$		−	895109.i		−	1.12751i
$892$	433525.	+	298379.i	0.544859	+	0.375006i
$893$	−1.61792e6			−2.02887
$894$	351572.	−	184822.i	0.439885	−	0.231248i
$895$			13899.0i			0.0173515i
$896$	637753.	−	160388.i	0.794395	−	0.199781i
$897$	−309784.			−0.385011
$898$	484063.	+	920796.i	0.600273	+	1.14185i
$899$		−	130083.i		−	0.160954i
$900$	6116.73	−	8887.21i	0.00755152	−	0.0109719i
$901$	372962.			0.459425
$902$	591274.	−	310833.i	0.726734	−	0.382045i
$903$		−	312236.i		−	0.382920i
$904$	227140.	+	27113.8i	0.277943	+	0.0331783i
$905$	−45586.4			−0.0556593
$906$	254633.	+	484369.i	0.310212	+	0.590093i
$907$			817933.i			0.994267i	0.867674	+	0.497133i	$0.165614\pi$
$907$			817933.i			0.994267i	−0.867674	+	0.497133i	$0.834386\pi$
$908$	−181693.	−	125052.i	−0.220377	−	0.151677i
$909$	−11580.9			−0.0140157
$910$	13837.1	−	7274.16i	0.0167094	−	0.00878415i
$911$		−	1.39488e6i		−	1.68074i	−0.542012	−	0.840371i	$-0.682337\pi$
$911$		−	1.39488e6i		−	1.68074i	0.542012	−	0.840371i	$-0.317663\pi$
$912$	−493200.	−	1.28996e6i	−0.592971	−	1.55091i
$913$	168202.			0.201786
$914$	485578.	+	923678.i	0.581255	+	1.10568i
$915$			39280.0i			0.0469169i
$916$	−239571.	+	348081.i	−0.285524	+	0.414849i
$917$	773490.			0.919848
$918$	−288151.	+	151481.i	−0.341928	+	0.179752i
$919$		−	205734.i		−	0.243599i	−0.992555	−	0.121799i	$-0.961134\pi$
$919$		−	205734.i		−	0.243599i	0.992555	−	0.121799i	$-0.0388665\pi$
$920$	1590.40	−	13323.2i	0.00187902	−	0.0157411i
$921$	−880716.			−1.03829
$922$	−525612.	−	999832.i	−0.618306	−	1.17616i
$923$			668824.i			0.785071i
$924$	−654042.	−	450152.i	−0.766058	−	0.527248i
$925$	−613850.			−0.717429
$926$	−519225.	+	272957.i	−0.605527	+	0.318326i
$927$			3298.07i			0.00383796i
$928$	−509817.	+	579386.i	−0.591995	+	0.672778i
$929$	−353614.			−0.409730			−0.204865	−	0.978790i	$-0.565676\pi$
$929$	−353614.			−0.409730			−0.204865	+	0.978790i	$0.565676\pi$
$930$	2204.34	+	4193.15i	0.00254866	+	0.00484813i
$931$			476711.i			0.549991i
$932$	539804.	−	784300.i	0.621447	−	0.902922i
$933$	−1.60357e6			−1.84215
$934$	−987564.	+	519163.i	−1.13206	+	0.595127i
$935$			11773.1i			0.0134669i
$936$	8705.88	+	1039.23i	0.00993713	+	0.00118620i
$937$	855961.			0.974933			0.487467	−	0.873142i	$-0.337921\pi$
$937$	855961.			0.974933			0.487467	+	0.873142i	$0.337921\pi$
$938$	−277649.	−	528151.i	−0.315566	−	0.600278i
$939$		−	1.13727e6i		−	1.28983i
$940$	−27122.7	−	18667.5i	−0.0306957	−	0.0211267i
$941$	−458198.			−0.517456			−0.258728	−	0.965950i	$-0.583303\pi$
$941$	−458198.			−0.517456			−0.258728	+	0.965950i	$0.583303\pi$
$942$	−600299.	+	315578.i	−0.676497	+	0.355635i
$943$		−	329844.i		−	0.370924i
$944$	1.42487e6	−	544779.i	1.59893	−	0.611331i
$945$	22605.3			0.0253132
$946$	−223991.	−	426081.i	−0.250293	−	0.476112i
$947$			1.42575e6i			1.58980i	0.606741	+	0.794900i	$0.292477\pi$
$947$			1.42575e6i			1.58980i	−0.606741	+	0.794900i	$0.707523\pi$
$948$	−471241.	+	684683.i	−0.524356	+	0.761856i
$949$	416150.			0.462080
$950$	−1.33407e6	+	701322.i	−1.47820	+	0.777089i
$951$		−	1.07463e6i		−	1.18822i
$952$	−33770.5	+	282904.i	−0.0372617	+	0.312151i
$953$	261524.			0.287956			0.143978	−	0.989581i	$-0.454011\pi$
$953$	261524.			0.287956			0.143978	+	0.989581i	$0.454011\pi$
$954$	−6758.87	−	12856.9i	−0.00742638	−	0.0141266i
$955$			46406.0i			0.0508823i
$956$	−594158.	−	408936.i	−0.650109	−	0.447445i
$957$	931791.			1.01741
$958$	−419422.	+	220490.i	−0.457004	+	0.240247i
$959$		−	108074.i		−	0.117512i
$960$	6615.57	−	27315.3i	0.00717835	−	0.0296391i
$961$	−29791.0			−0.0322581
$962$	−232128.	−	441560.i	−0.250829	−	0.477133i
$963$		−	4562.91i		−	0.00492027i
$964$	−733265.	+	1.06539e6i	−0.789054	+	1.14645i
$965$	−11505.9			−0.0123557
$966$	−347021.	+	182429.i	−0.371879	+	0.195497i
$967$		−	1.60117e6i		−	1.71232i	−0.516713	−	0.856159i	$-0.672845\pi$
$967$		−	1.60117e6i		−	1.71232i	0.516713	−	0.856159i	$-0.327155\pi$
$968$	−285021.	−	34023.1i	−0.304177	−	0.0363098i
$969$	598337.			0.637233
$970$	−13953.8	−	26543.2i	−0.0148303	−	0.0282105i
$971$		−	1.04157e6i		−	1.10471i	−0.833609	−	0.552355i	$-0.813729\pi$
$971$		−	1.04157e6i		−	1.10471i	0.833609	−	0.552355i	$-0.186271\pi$
$972$	20750.3	+	14281.6i	0.0219630	+	0.0151163i
$973$	1.30031e6			1.37348
$974$	−516812.	+	271688.i	−0.544772	+	0.286387i
$975$			708147.i			0.744928i
$976$	523367.	+	1.36886e6i	0.549423	+	1.43701i
$977$	413587.			0.433289			0.216645	−	0.976251i	$-0.430489\pi$
$977$	413587.			0.433289			0.216645	+	0.976251i	$0.430489\pi$
$978$	−410245.	−	780377.i	−0.428909	−	0.815881i
$979$			819547.i			0.855084i
$980$	−5500.27	+	7991.54i	−0.00572707	+	0.00832106i
$981$	3921.80			0.00407519
$982$	443833.	−	233323.i	0.460253	−	0.241955i
$983$			673208.i			0.696694i	0.937366	+	0.348347i	$0.113257\pi$
$983$			673208.i			0.696694i	−0.937366	+	0.348347i	$0.886743\pi$
$984$	81891.0	−	686022.i	0.0845757	−	0.708513i
$985$	−38994.4			−0.0401911
$986$	−155586.	−	295960.i	−0.160036	−	0.304424i
$987$			962054.i			0.987564i
$988$	−1.00896e6	−	694431.i	−1.03362	−	0.711402i
$989$	−237690.			−0.243007
$990$	405.847	−	213.354i	0.000414088	−	0.000217686i
$991$			1.49262e6i			1.51986i	0.650007	+	0.759928i	$0.274766\pi$
$991$			1.49262e6i			1.51986i	−0.650007	+	0.759928i	$0.725234\pi$
$992$	132688.	+	116756.i	0.134837	+	0.118647i
$993$	−1.17191e6			−1.18849
$994$	393866.	+	749221.i	0.398635	+	0.758293i
$995$		−	35766.6i		−	0.0361269i
$996$	98631.5	−	143305.i	0.0994253	−	0.144459i
$997$	−188423.			−0.189559			−0.0947795	−	0.995498i	$-0.530215\pi$
$997$	−188423.			−0.189559			−0.0947795	+	0.995498i	$0.530215\pi$
$998$	−174767.	+	91874.9i	−0.175468	+	0.0922435i
$999$		−	721368.i		−	0.722813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.b.a.63.19	✓	60
4.3	odd	2	inner	124.5.b.a.63.20	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.b.a.63.19	✓	60	1.1	even	1	trivial
124.5.b.a.63.20	yes	60	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86128 - 3.54057i) q^{2} -8.93980i q^{3} +(-9.07128 + 13.1800i) q^{4} +0.767532 q^{5} +(-31.6520 + 16.6395i) q^{6} +40.1374i q^{7} +(63.5488 + 7.58587i) q^{8} +1.07989 q^{9} +O(q^{10})\)	\(q+(-1.86128 - 3.54057i) q^{2} -8.93980i q^{3} +(-9.07128 + 13.1800i) q^{4} +0.767532 q^{5} +(-31.6520 + 16.6395i) q^{6} +40.1374i q^{7} +(63.5488 + 7.58587i) q^{8} +1.07989 q^{9} +(-1.42859 - 2.71750i) q^{10} +138.297i q^{11} +(117.826 + 81.0954i) q^{12} +126.860 q^{13} +(142.109 - 74.7070i) q^{14} -6.86159i q^{15} +(-91.4238 - 239.119i) q^{16} +110.913 q^{17} +(-2.00998 - 3.82343i) q^{18} +603.442i q^{19} +(-6.96250 + 10.1161i) q^{20} +358.821 q^{21} +(489.650 - 257.409i) q^{22} -273.153i q^{23} +(67.8162 - 568.114i) q^{24} -624.411 q^{25} +(-236.122 - 449.157i) q^{26} -733.778i q^{27} +(-529.011 - 364.098i) q^{28} +753.664 q^{29} +(-24.2939 + 12.7713i) q^{30} -172.601i q^{31} +(-676.451 + 768.759i) q^{32} +1236.35 q^{33} +(-206.440 - 392.695i) q^{34} +30.8068i q^{35} +(-9.79600 + 14.2330i) q^{36} +983.087 q^{37} +(2136.53 - 1123.17i) q^{38} -1134.10i q^{39} +(48.7758 + 5.82240i) q^{40} +1207.54 q^{41} +(-667.866 - 1270.43i) q^{42} -870.173i q^{43} +(-1822.75 - 1254.53i) q^{44} +0.828851 q^{45} +(-967.116 + 508.413i) q^{46} +2681.15i q^{47} +(-2137.67 + 817.311i) q^{48} +789.986 q^{49} +(1162.20 + 2210.77i) q^{50} -991.539i q^{51} +(-1150.78 + 1672.01i) q^{52} +3362.66 q^{53} +(-2597.99 + 1365.77i) q^{54} +106.147i q^{55} +(-304.477 + 2550.69i) q^{56} +5394.66 q^{57} +(-1402.78 - 2668.40i) q^{58} +5958.82i q^{59} +(90.4356 + 62.2433i) q^{60} -5724.63 q^{61} +(-611.105 + 321.258i) q^{62} +43.3441i q^{63} +(3980.91 + 964.146i) q^{64} +97.3692 q^{65} +(-2301.19 - 4377.38i) q^{66} -3716.51i q^{67} +(-1006.12 + 1461.83i) q^{68} -2441.93 q^{69} +(109.074 - 57.3400i) q^{70} +5272.14i q^{71} +(68.6259 + 8.19191i) q^{72} +3280.39 q^{73} +(-1829.80 - 3480.69i) q^{74} +5582.11i q^{75} +(-7953.36 - 5473.99i) q^{76} -5550.89 q^{77} +(-4015.38 + 2110.89i) q^{78} +5810.95i q^{79} +(-70.1707 - 183.531i) q^{80} -6472.36 q^{81} +(-2247.58 - 4275.39i) q^{82} -1216.24i q^{83} +(-3254.96 + 4729.25i) q^{84} +85.1292 q^{85} +(-3080.91 + 1619.64i) q^{86} -6737.61i q^{87} +(-1049.10 + 8788.62i) q^{88} +5925.99 q^{89} +(-1.54272 - 2.93461i) q^{90} +5091.84i q^{91} +(3600.15 + 2477.84i) q^{92} -1543.02 q^{93} +(9492.82 - 4990.38i) q^{94} +463.161i q^{95} +(6872.56 + 6047.34i) q^{96} +9767.51 q^{97} +(-1470.38 - 2797.00i) q^{98} +149.346i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9}+O(q^{10}) \) 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9	\( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9} + 53 q^{10} + 130 q^{12} + 120 q^{13} - 231 q^{14} - 590 q^{16} - 648 q^{17} + 230 q^{18} + 1113 q^{20} + 608 q^{21} + 1080 q^{22} - 1028 q^{24} + 8340 q^{25} - 1554 q^{26} - 165 q^{28} - 168 q^{29} - 2238 q^{30} - 1674 q^{32} - 1120 q^{33} + 1844 q^{34} + 1966 q^{36} - 2248 q^{37} - 5055 q^{38} - 1716 q^{40} + 6072 q^{41} + 5794 q^{42} - 120 q^{44} - 4040 q^{45} + 8850 q^{46} + 2276 q^{48} - 17604 q^{49} - 4539 q^{50} + 5896 q^{52} + 3480 q^{53} + 5148 q^{54} - 396 q^{56} - 10912 q^{57} - 7484 q^{58} + 22812 q^{60} + 2200 q^{61} - 19299 q^{64} - 9168 q^{65} - 468 q^{66} - 21930 q^{68} + 6496 q^{69} - 9615 q^{70} - 10079 q^{72} + 13752 q^{73} - 2106 q^{74} + 20099 q^{76} + 16608 q^{77} + 39460 q^{78} - 5787 q^{80} + 20732 q^{81} - 30525 q^{82} - 21760 q^{84} - 21200 q^{85} - 13398 q^{86} + 34690 q^{88} + 22296 q^{89} - 25419 q^{90} - 18852 q^{92} + 3196 q^{94} + 20790 q^{96} + 12120 q^{97} + 21921 q^{98}+O(q^{100}) \) 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9 + 53 * q^10 + 130 * q^12 + 120 * q^13 - 231 * q^14 - 590 * q^16 - 648 * q^17 + 230 * q^18 + 1113 * q^20 + 608 * q^21 + 1080 * q^22 - 1028 * q^24 + 8340 * q^25 - 1554 * q^26 - 165 * q^28 - 168 * q^29 - 2238 * q^30 - 1674 * q^32 - 1120 * q^33 + 1844 * q^34 + 1966 * q^36 - 2248 * q^37 - 5055 * q^38 - 1716 * q^40 + 6072 * q^41 + 5794 * q^42 - 120 * q^44 - 4040 * q^45 + 8850 * q^46 + 2276 * q^48 - 17604 * q^49 - 4539 * q^50 + 5896 * q^52 + 3480 * q^53 + 5148 * q^54 - 396 * q^56 - 10912 * q^57 - 7484 * q^58 + 22812 * q^60 + 2200 * q^61 - 19299 * q^64 - 9168 * q^65 - 468 * q^66 - 21930 * q^68 + 6496 * q^69 - 9615 * q^70 - 10079 * q^72 + 13752 * q^73 - 2106 * q^74 + 20099 * q^76 + 16608 * q^77 + 39460 * q^78 - 5787 * q^80 + 20732 * q^81 - 30525 * q^82 - 21760 * q^84 - 21200 * q^85 - 13398 * q^86 + 34690 * q^88 + 22296 * q^89 - 25419 * q^90 - 18852 * q^92 + 3196 * q^94 + 20790 * q^96 + 12120 * q^97 + 21921 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more