LMFDB - Embedded newform 115.5.f.a.93.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,5,Mod(47,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

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("115.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	115.f (of order $4$, 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:	$11.8875457546$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.11
Character	$\chi$	$=$	115.93
Dual form			115.5.f.a.47.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.55253 + 3.55253i) q^{2} +(-5.80472 - 5.80472i) q^{3} -9.24088i q^{4} +(-21.4504 + 12.8406i) q^{5} +41.2428 q^{6} +(2.81474 - 2.81474i) q^{7} +(-24.0119 - 24.0119i) q^{8} -13.6105i q^{9} +(30.5864 - 121.820i) q^{10} -184.488 q^{11} +(-53.6407 + 53.6407i) q^{12} +(-37.0012 - 37.0012i) q^{13} +19.9989i q^{14} +(199.050 + 49.9772i) q^{15} +318.460 q^{16} +(250.449 - 250.449i) q^{17} +(48.3516 + 48.3516i) q^{18} +597.288i q^{19} +(118.659 + 198.220i) q^{20} -32.6775 q^{21} +(655.399 - 655.399i) q^{22} +(77.9968 + 77.9968i) q^{23} +278.765i q^{24} +(295.237 - 550.872i) q^{25} +262.895 q^{26} +(-549.187 + 549.187i) q^{27} +(-26.0107 - 26.0107i) q^{28} +947.586i q^{29} +(-884.674 + 529.584i) q^{30} +1231.51 q^{31} +(-747.147 + 747.147i) q^{32} +(1070.90 + 1070.90i) q^{33} +1779.46i q^{34} +(-24.2342 + 96.5202i) q^{35} -125.773 q^{36} +(636.569 - 636.569i) q^{37} +(-2121.88 - 2121.88i) q^{38} +429.563i q^{39} +(823.393 + 206.737i) q^{40} -1338.23 q^{41} +(116.088 - 116.088i) q^{42} +(1237.70 + 1237.70i) q^{43} +1704.83i q^{44} +(174.767 + 291.950i) q^{45} -554.171 q^{46} +(2390.39 - 2390.39i) q^{47} +(-1848.57 - 1848.57i) q^{48} +2385.15i q^{49} +(908.151 + 3005.82i) q^{50} -2907.58 q^{51} +(-341.924 + 341.924i) q^{52} +(-1149.05 - 1149.05i) q^{53} -3902.00i q^{54} +(3957.34 - 2368.94i) q^{55} -135.175 q^{56} +(3467.09 - 3467.09i) q^{57} +(-3366.32 - 3366.32i) q^{58} -6455.33i q^{59} +(461.833 - 1839.39i) q^{60} -2543.50 q^{61} +(-4374.96 + 4374.96i) q^{62} +(-38.3099 - 38.3099i) q^{63} -213.155i q^{64} +(1268.81 + 318.571i) q^{65} -7608.81 q^{66} +(4108.36 - 4108.36i) q^{67} +(-2314.37 - 2314.37i) q^{68} -905.499i q^{69} +(-256.798 - 428.983i) q^{70} +7900.01 q^{71} +(-326.814 + 326.814i) q^{72} +(-2910.79 - 2910.79i) q^{73} +4522.86i q^{74} +(-4911.43 + 1483.89i) q^{75} +5519.46 q^{76} +(-519.286 + 519.286i) q^{77} +(-1526.03 - 1526.03i) q^{78} +5119.73i q^{79} +(-6831.09 + 4089.23i) q^{80} +5273.31 q^{81} +(4754.09 - 4754.09i) q^{82} +(-1562.28 - 1562.28i) q^{83} +301.969i q^{84} +(-2156.31 + 8588.16i) q^{85} -8793.93 q^{86} +(5500.47 - 5500.47i) q^{87} +(4429.92 + 4429.92i) q^{88} +8134.38i q^{89} +(-1658.02 - 416.295i) q^{90} -208.297 q^{91} +(720.759 - 720.759i) q^{92} +(-7148.55 - 7148.55i) q^{93} +16983.8i q^{94} +(-7669.55 - 12812.0i) q^{95} +8673.96 q^{96} +(4131.07 - 4131.07i) q^{97} +(-8473.32 - 8473.32i) q^{98} +2510.97i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 48 q^{5} + 160 q^{7} + 180 q^{8} + 16 q^{10} + 312 q^{11} - 720 q^{12} - 760 q^{13} - 60 q^{15} - 4528 q^{16} + 420 q^{17} + 980 q^{18} + 1344 q^{20} + 1976 q^{21} + 720 q^{22} - 1176 q^{25} + 1872 q^{26}+ \cdots - 22320 q^{98}+O(q^{100}) $ 88 * q - 48 * q^5 + 160 * q^7 + 180 * q^8 + 16 * q^10 + 312 * q^11 - 720 * q^12 - 760 * q^13 - 60 * q^15 - 4528 * q^16 + 420 * q^17 + 980 * q^18 + 1344 * q^20 + 1976 * q^21 + 720 * q^22 - 1176 * q^25 + 1872 * q^26 + 2820 * q^27 - 1140 * q^28 - 1160 * q^30 - 820 * q^31 - 3720 * q^32 + 820 * q^33 - 1728 * q^35 + 9504 * q^36 + 180 * q^37 + 3180 * q^38 + 8560 * q^40 + 1956 * q^41 + 5320 * q^42 - 8960 * q^43 + 2064 * q^45 - 5640 * q^47 + 3820 * q^48 - 5448 * q^50 - 6648 * q^51 - 2800 * q^52 - 2160 * q^53 - 11796 * q^55 - 1464 * q^56 - 160 * q^57 + 3740 * q^58 - 6700 * q^60 - 4496 * q^61 - 30300 * q^62 - 2740 * q^63 - 3336 * q^65 - 4104 * q^66 + 640 * q^67 + 13440 * q^68 + 6508 * q^70 + 14916 * q^71 + 44280 * q^72 + 3660 * q^73 + 15732 * q^75 - 53552 * q^76 + 10980 * q^77 + 4340 * q^78 + 10404 * q^80 - 35864 * q^81 + 32860 * q^82 + 7920 * q^83 + 14216 * q^85 + 59352 * q^86 - 38440 * q^87 - 19140 * q^88 + 7160 * q^90 + 52584 * q^91 - 20960 * q^93 + 28224 * q^95 - 26624 * q^96 + 13480 * q^97 - 22320 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−3.55253	+	3.55253i	−0.888131	+	0.888131i	−0.994344	−	0.106212i	$-0.966128\pi$
$2$	−3.55253	+	3.55253i	−0.888131	+	0.888131i	0.106212	+	0.994344i	$0.466128\pi$
$3$	−5.80472	−	5.80472i	−0.644969	−	0.644969i	0.306804	−	0.951773i	$-0.400740\pi$
$3$	−5.80472	−	5.80472i	−0.644969	−	0.644969i	−0.951773	+	0.306804i	$0.900740\pi$
$4$		−	9.24088i		−	0.577555i
$5$	−21.4504	+	12.8406i	−0.858015	+	0.513625i
$5$	−21.4504	+	12.8406i	−0.858015	+	0.513625i
$6$	41.2428			1.14563
$7$	2.81474	−	2.81474i	0.0574436	−	0.0574436i	−0.677801	−	0.735245i	$-0.737067\pi$
$7$	2.81474	−	2.81474i	0.0574436	−	0.0574436i	0.735245	+	0.677801i	$0.237067\pi$
$8$	−24.0119	−	24.0119i	−0.375187	−	0.375187i
$9$		−	13.6105i		−	0.168031i
$10$	30.5864	−	121.820i	0.305864	−	1.21820i
$11$	−184.488			−1.52470			−0.762348	−	0.647168i	$-0.775953\pi$
$11$	−184.488			−1.52470			−0.762348	+	0.647168i	$0.775953\pi$
$12$	−53.6407	+	53.6407i	−0.372505	+	0.372505i
$13$	−37.0012	−	37.0012i	−0.218942	−	0.218942i	0.589110	−	0.808053i	$-0.299478\pi$
$13$	−37.0012	−	37.0012i	−0.218942	−	0.218942i	−0.808053	+	0.589110i	$0.799478\pi$
$14$			19.9989i			0.102035i
$15$	199.050	+	49.9772i	0.884665	+	0.222121i
$16$	318.460			1.24399
$17$	250.449	−	250.449i	0.866607	−	0.866607i	−0.125488	−	0.992095i	$-0.540050\pi$
$17$	250.449	−	250.449i	0.866607	−	0.866607i	0.992095	+	0.125488i	$0.0400496\pi$
$18$	48.3516	+	48.3516i	0.149233	+	0.149233i
$19$			597.288i			1.65454i	0.561807	+	0.827268i	$0.310106\pi$
$19$			597.288i			1.65454i	−0.561807	+	0.827268i	$0.689894\pi$
$20$	118.659	+	198.220i	0.296647	+	0.495551i
$21$	−32.6775			−0.0740987
$22$	655.399	−	655.399i	1.35413	−	1.35413i
$23$	77.9968	+	77.9968i	0.147442	+	0.147442i
$23$	77.9968	+	77.9968i	0.147442	+	0.147442i
$24$			278.765i			0.483967i
$25$	295.237	−	550.872i	0.472379	−	0.881395i
$26$	262.895			0.388899
$27$	−549.187	+	549.187i	−0.753343	+	0.753343i
$28$	−26.0107	−	26.0107i	−0.0331769	−	0.0331769i
$29$			947.586i			1.12674i	0.826206	+	0.563368i	$0.190495\pi$
$29$			947.586i			1.12674i	−0.826206	+	0.563368i	$0.809505\pi$
$30$	−884.674	+	529.584i	−0.982971	+	0.588426i
$31$	1231.51			1.28148			0.640742	−	0.767756i	$-0.278627\pi$
$31$	1231.51			1.28148			0.640742	+	0.767756i	$0.278627\pi$
$32$	−747.147	+	747.147i	−0.729636	+	0.729636i
$33$	1070.90	+	1070.90i	0.983381	+	0.983381i
$34$			1779.46i			1.53932i
$35$	−24.2342	+	96.5202i	−0.0197830	+	0.0787920i
$36$	−125.773			−0.0970469
$37$	636.569	−	636.569i	0.464988	−	0.464988i	−0.435298	−	0.900286i	$-0.643357\pi$
$37$	636.569	−	636.569i	0.464988	−	0.464988i	0.900286	+	0.435298i	$0.143357\pi$
$38$	−2121.88	−	2121.88i	−1.46945	−	1.46945i
$39$			429.563i			0.282422i
$40$	823.393	+	206.737i	0.514621	+	0.129211i
$41$	−1338.23			−0.796090			−0.398045	−	0.917366i	$-0.630311\pi$
$41$	−1338.23			−0.796090			−0.398045	+	0.917366i	$0.630311\pi$
$42$	116.088	−	116.088i	0.0658094	−	0.0658094i
$43$	1237.70	+	1237.70i	0.669390	+	0.669390i	0.957575	−	0.288185i	$-0.0930518\pi$
$43$	1237.70	+	1237.70i	0.669390	+	0.669390i	−0.288185	+	0.957575i	$0.593052\pi$
$44$			1704.83i			0.880596i
$45$	174.767	+	291.950i	0.0863047	+	0.144173i
$46$	−554.171			−0.261896
$47$	2390.39	−	2390.39i	1.08211	−	1.08211i	0.0858006	−	0.996312i	$-0.472655\pi$
$47$	2390.39	−	2390.39i	1.08211	−	1.08211i	0.996312	−	0.0858006i	$-0.0273448\pi$
$48$	−1848.57	−	1848.57i	−0.802332	−	0.802332i
$49$			2385.15i			0.993400i
$50$	908.151	+	3005.82i	0.363260	+	1.20233i
$51$	−2907.58			−1.11787
$52$	−341.924	+	341.924i	−0.126451	+	0.126451i
$53$	−1149.05	−	1149.05i	−0.409060	−	0.409060i	0.472351	−	0.881411i	$-0.343406\pi$
$53$	−1149.05	−	1149.05i	−0.409060	−	0.409060i	−0.881411	+	0.472351i	$0.843406\pi$
$54$		−	3902.00i		−	1.33814i
$55$	3957.34	−	2368.94i	1.30821	−	0.783121i
$56$	−135.175			−0.0431042
$57$	3467.09	−	3467.09i	1.06712	−	1.06712i
$58$	−3366.32	−	3366.32i	−1.00069	−	1.00069i
$59$		−	6455.33i		−	1.85445i	−0.374509	−	0.927223i	$-0.622189\pi$
$59$		−	6455.33i		−	1.85445i	0.374509	−	0.927223i	$-0.377811\pi$
$60$	461.833	−	1839.39i	0.128287	−	0.510943i
$61$	−2543.50			−0.683553			−0.341777	−	0.939781i	$-0.611029\pi$
$61$	−2543.50			−0.683553			−0.341777	+	0.939781i	$0.611029\pi$
$62$	−4374.96	+	4374.96i	−1.13813	+	1.13813i
$63$	−38.3099	−	38.3099i	−0.00965229	−	0.00965229i
$64$		−	213.155i		−	0.0520398i
$65$	1268.81	+	318.571i	0.300310	+	0.0754015i
$66$	−7608.81			−1.74674
$67$	4108.36	−	4108.36i	0.915207	−	0.915207i	−0.0814689	−	0.996676i	$-0.525961\pi$
$67$	4108.36	−	4108.36i	0.915207	−	0.915207i	0.996676	+	0.0814689i	$0.0259611\pi$
$68$	−2314.37	−	2314.37i	−0.500513	−	0.500513i
$69$		−	905.499i		−	0.190191i
$70$	−256.798	−	428.983i	−0.0524077	−	0.0875475i
$71$	7900.01			1.56715			0.783576	−	0.621296i	$-0.213393\pi$
$71$	7900.01			1.56715			0.783576	+	0.621296i	$0.213393\pi$
$72$	−326.814	+	326.814i	−0.0630428	+	0.0630428i
$73$	−2910.79	−	2910.79i	−0.546218	−	0.546218i	0.379127	−	0.925345i	$-0.376224\pi$
$73$	−2910.79	−	2910.79i	−0.546218	−	0.546218i	−0.925345	+	0.379127i	$0.876224\pi$
$74$			4522.86i			0.825942i
$75$	−4911.43	+	1483.89i	−0.873142	+	0.263803i
$76$	5519.46			0.955586
$77$	−519.286	+	519.286i	−0.0875840	+	0.0875840i
$78$	−1526.03	−	1526.03i	−0.250827	−	0.250827i
$79$			5119.73i			0.820338i	0.912010	+	0.410169i	$0.134530\pi$
$79$			5119.73i			0.820338i	−0.912010	+	0.410169i	$0.865470\pi$
$80$	−6831.09	+	4089.23i	−1.06736	+	0.638942i
$81$	5273.31			0.803735
$82$	4754.09	−	4754.09i	0.707033	−	0.707033i
$83$	−1562.28	−	1562.28i	−0.226779	−	0.226779i	0.584566	−	0.811346i	$-0.301265\pi$
$83$	−1562.28	−	1562.28i	−0.226779	−	0.226779i	−0.811346	+	0.584566i	$0.801265\pi$
$84$			301.969i			0.0427961i
$85$	−2156.31	+	8588.16i	−0.298451	+	1.18867i
$86$	−8793.93			−1.18901
$87$	5500.47	−	5500.47i	0.726710	−	0.726710i
$88$	4429.92	+	4429.92i	0.572045	+	0.572045i
$89$			8134.38i			1.02694i	0.858108	+	0.513469i	$0.171640\pi$
$89$			8134.38i			1.02694i	−0.858108	+	0.513469i	$0.828360\pi$
$90$	−1658.02	−	416.295i	−0.204694	−	0.0513944i
$91$	−208.297			−0.0251536
$92$	720.759	−	720.759i	0.0851558	−	0.0851558i
$93$	−7148.55	−	7148.55i	−0.826517	−	0.826517i
$94$			16983.8i			1.92212i
$95$	−7669.55	−	12812.0i	−0.849811	−	1.41962i
$96$	8673.96			0.941185
$97$	4131.07	−	4131.07i	0.439055	−	0.439055i	−0.452639	−	0.891694i	$-0.649517\pi$
$97$	4131.07	−	4131.07i	0.439055	−	0.439055i	0.891694	+	0.452639i	$0.149517\pi$
$98$	−8473.32	−	8473.32i	−0.882270	−	0.882270i
$99$			2510.97i			0.256195i
$100$	−5090.54	−	2728.25i	−0.509054	−	0.272825i
$101$	−4631.78			−0.454052			−0.227026	−	0.973889i	$-0.572900\pi$
$101$	−4631.78			−0.454052			−0.227026	+	0.973889i	$0.572900\pi$
$102$	10329.2	−	10329.2i	0.992815	−	0.992815i
$103$	3386.02	+	3386.02i	0.319165	+	0.319165i	0.848446	−	0.529281i	$-0.177538\pi$
$103$	3386.02	+	3386.02i	0.319165	+	0.319165i	−0.529281	+	0.848446i	$0.677538\pi$
$104$			1776.94i			0.164288i
$105$	700.945	−	419.600i	0.0635778	−	0.0380589i
$106$	8164.06			0.726598
$107$	−14295.8	+	14295.8i	−1.24865	+	1.24865i	−0.292332	+	0.956317i	$0.594431\pi$
$107$	−14295.8	+	14295.8i	−1.24865	+	1.24865i	−0.956317	+	0.292332i	$0.905569\pi$
$108$	5074.97	+	5074.97i	0.435097	+	0.435097i
$109$		−	11279.1i		−	0.949335i	−0.880165	−	0.474668i	$-0.842568\pi$
$109$		−	11279.1i		−	0.949335i	0.880165	−	0.474668i	$-0.157432\pi$
$110$	−5642.82	+	22474.3i	−0.466349	+	1.85738i
$111$	−7390.21			−0.599806
$112$	896.382	−	896.382i	0.0714590	−	0.0714590i
$113$	4876.21	+	4876.21i	0.381878	+	0.381878i	0.871779	−	0.489900i	$-0.162967\pi$
$113$	4876.21	+	4876.21i	0.381878	+	0.381878i	−0.489900	+	0.871779i	$0.662967\pi$
$114$			24633.8i			1.89549i
$115$	−2674.59	−	671.533i	−0.202237	−	0.0507775i
$116$	8756.53			0.650753
$117$	−503.604	+	503.604i	−0.0367890	+	0.0367890i
$118$	22932.7	+	22932.7i	1.64699	+	1.64699i
$119$		−	1409.90i		−	0.0995621i
$120$	−3579.52	−	5979.62i	−0.248578	−	0.415251i
$121$	19394.9			1.32470
$122$	9035.86	−	9035.86i	0.607085	−	0.607085i
$123$	7768.04	+	7768.04i	0.513453	+	0.513453i
$124$		−	11380.2i		−	0.740128i
$125$	740.599	+	15607.4i	0.0473983	+	0.998876i
$126$	272.194			0.0171450
$127$	17482.6	−	17482.6i	1.08392	−	1.08392i	0.0877818	−	0.996140i	$-0.472022\pi$
$127$	17482.6	−	17482.6i	1.08392	−	1.08392i	0.996140	−	0.0877818i	$-0.0279778\pi$
$128$	−11197.1	−	11197.1i	−0.683418	−	0.683418i
$129$		−	14369.0i		−	0.863471i
$130$	−5639.21	+	3375.74i	−0.333681	+	0.199748i
$131$	21656.5			1.26196			0.630981	−	0.775798i	$-0.282653\pi$
$131$	21656.5			1.26196			0.630981	+	0.775798i	$0.282653\pi$
$132$	9896.08	−	9896.08i	0.567957	−	0.567957i
$133$	1681.21	+	1681.21i	0.0950426	+	0.0950426i
$134$			29190.1i			1.62565i
$135$	4728.37	−	18832.2i	0.259444	−	1.03332i
$136$	−12027.6			−0.650279
$137$	−11090.1	+	11090.1i	−0.590872	+	0.590872i	−0.937867	−	0.346995i	$-0.887202\pi$
$137$	−11090.1	+	11090.1i	−0.590872	+	0.590872i	0.346995	+	0.937867i	$0.387202\pi$
$138$	3216.81	+	3216.81i	0.168915	+	0.168915i
$139$		−	9088.05i		−	0.470371i	−0.971950	−	0.235186i	$-0.924430\pi$
$139$		−	9088.05i		−	0.470371i	0.971950	−	0.235186i	$-0.0755698\pi$
$140$	891.931	+	223.945i	0.0455067	+	0.0114258i
$141$	−27751.1			−1.39586
$142$	−28065.0	+	28065.0i	−1.39184	+	1.39184i
$143$	6826.28	+	6826.28i	0.333820	+	0.333820i
$144$		−	4334.40i		−	0.209028i
$145$	−12167.6	−	20326.1i	−0.578720	−	0.966757i
$146$	20681.3			0.970226
$147$	13845.2	−	13845.2i	0.640712	−	0.640712i
$148$	−5882.46	−	5882.46i	−0.268556	−	0.268556i
$149$		−	15283.6i		−	0.688420i	−0.938893	−	0.344210i	$-0.888147\pi$
$149$		−	15283.6i		−	0.688420i	0.938893	−	0.344210i	$-0.111853\pi$
$150$	12176.4	−	22719.5i	0.541174	−	1.00976i
$151$	17214.9			0.755006			0.377503	−	0.926008i	$-0.376783\pi$
$151$	17214.9			0.755006			0.377503	+	0.926008i	$0.376783\pi$
$152$	14342.0	−	14342.0i	0.620760	−	0.620760i
$153$	−3408.74	−	3408.74i	−0.145617	−	0.145617i
$154$		−	3689.55i		−	0.155572i
$155$	−26416.3	+	15813.3i	−1.09953	+	0.658202i
$156$	3969.54			0.163114
$157$	2011.48	−	2011.48i	0.0816051	−	0.0816051i	−0.665126	−	0.746731i	$-0.731622\pi$
$157$	2011.48	−	2011.48i	0.0816051	−	0.0816051i	0.746731	+	0.665126i	$0.231622\pi$
$158$	−18188.0	−	18188.0i	−0.728568	−	0.728568i
$159$			13339.8i			0.527662i
$160$	6432.75	−	25620.4i	0.251279	−	1.00080i
$161$	439.081			0.0169392
$162$	−18733.6	+	18733.6i	−0.713822	+	0.713822i
$163$	11789.4	+	11789.4i	0.443727	+	0.443727i	0.893263	−	0.449535i	$-0.148410\pi$
$163$	11789.4	+	11789.4i	0.443727	+	0.443727i	−0.449535	+	0.893263i	$0.648410\pi$
$164$			12366.4i			0.459786i
$165$	−36722.3	−	9220.20i	−1.34884	−	0.338667i
$166$	11100.1			0.402820
$167$	5270.11	−	5270.11i	0.188967	−	0.188967i	−0.606282	−	0.795250i	$-0.707340\pi$
$167$	5270.11	−	5270.11i	0.188967	−	0.188967i	0.795250	+	0.606282i	$0.207340\pi$
$168$	784.651	+	784.651i	0.0278008	+	0.0278008i
$169$		−	25822.8i		−	0.904129i
$170$	−22849.3	−	38170.0i	−0.790634	−	1.32076i
$171$	8129.37			0.278013
$172$	11437.5	−	11437.5i	0.386609	−	0.386609i
$173$	36577.3	+	36577.3i	1.22214	+	1.22214i	0.966871	+	0.255264i	$0.0821624\pi$
$173$	36577.3	+	36577.3i	1.22214	+	1.22214i	0.255264	+	0.966871i	$0.417838\pi$
$174$			39081.1i			1.29083i
$175$	−719.546	−	2381.58i	−0.0234954	−	0.0777657i
$176$	−58752.1			−1.89670
$177$	−37471.4	+	37471.4i	−1.19606	+	1.19606i
$178$	−28897.6	−	28897.6i	−0.912056	−	0.912056i
$179$			20451.5i			0.638292i	0.947706	+	0.319146i	$0.103396\pi$
$179$			20451.5i			0.638292i	−0.947706	+	0.319146i	$0.896604\pi$
$180$	2697.87	−	1615.00i	0.0832677	−	0.0498457i
$181$	1374.32			0.0419497			0.0209749	−	0.999780i	$-0.493323\pi$
$181$	1374.32			0.0419497			0.0209749	+	0.999780i	$0.493323\pi$
$182$	739.982	−	739.982i	0.0223397	−	0.0223397i
$183$	14764.3	+	14764.3i	0.440871	+	0.440871i
$184$		−	3745.71i		−	0.110637i
$185$	−5480.70	+	21828.6i	−0.160137	+	0.637797i
$186$	50790.8			1.46811
$187$	−46205.0	+	46205.0i	−1.32131	+	1.32131i
$188$	−22089.3	−	22089.3i	−0.624980	−	0.624980i
$189$			3091.64i			0.0865495i
$190$	72761.4	+	18268.9i	2.01555	+	0.506063i
$191$	24341.8			0.667247			0.333624	−	0.942706i	$-0.391729\pi$
$191$	24341.8			0.667247			0.333624	+	0.942706i	$0.391729\pi$
$192$	−1237.30	+	1237.30i	−0.0335640	+	0.0335640i
$193$	−26283.8	−	26283.8i	−0.705624	−	0.705624i	0.259988	−	0.965612i	$-0.416282\pi$
$193$	−26283.8	−	26283.8i	−0.705624	−	0.705624i	−0.965612	+	0.259988i	$0.916282\pi$
$194$			29351.5i			0.779877i
$195$	−5515.86	−	9214.29i	−0.145059	−	0.242322i
$196$	22040.9			0.573743
$197$	−19169.8	+	19169.8i	−0.493952	+	0.493952i	−0.909549	−	0.415597i	$-0.863573\pi$
$197$	−19169.8	+	19169.8i	−0.493952	+	0.493952i	0.415597	+	0.909549i	$0.363573\pi$
$198$	−8920.29	−	8920.29i	−0.227535	−	0.227535i
$199$			54177.6i			1.36809i	0.729441	+	0.684043i	$0.239780\pi$
$199$			54177.6i			1.36809i	−0.729441	+	0.684043i	$0.760220\pi$
$200$	−20316.7	+	6138.30i	−0.507918	+	0.153457i
$201$	−47695.8			−1.18056
$202$	16454.5	−	16454.5i	0.403258	−	0.403258i
$203$	2667.21	+	2667.21i	0.0647239	+	0.0647239i
$204$			26868.6i			0.645631i
$205$	28705.5	−	17183.7i	0.683057	−	0.408892i
$206$	−24057.9			−0.566921
$207$	1061.57	−	1061.57i	0.0247748	−	0.0247748i
$208$	−11783.4	−	11783.4i	−0.272361	−	0.272361i
$209$		−	110193.i		−	2.52266i
$210$	−999.487	+	3980.76i	−0.0226641	+	0.0902668i
$211$	73142.2			1.64287			0.821435	−	0.570302i	$-0.193174\pi$
$211$	73142.2			1.64287			0.821435	+	0.570302i	$0.193174\pi$
$212$	−10618.2	+	10618.2i	−0.236255	+	0.236255i
$213$	−45857.4	−	45857.4i	−1.01076	−	1.01076i
$214$		−	101572.i		−	2.21793i
$215$	−42442.0	−	10656.3i	−0.918162	−	0.230531i
$216$	26374.1			0.565289
$217$	3466.37	−	3466.37i	0.0736131	−	0.0736131i
$218$	40069.1	+	40069.1i	0.843135	+	0.843135i
$219$			33792.7i			0.704586i
$220$	−21891.1	−	36569.3i	−0.452296	−	0.755564i
$221$	−18533.9			−0.379473
$222$	26253.9	−	26253.9i	0.532707	−	0.532707i
$223$	−3617.58	−	3617.58i	−0.0727458	−	0.0727458i	0.669798	−	0.742544i	$-0.266381\pi$
$223$	−3617.58	−	3617.58i	−0.0727458	−	0.0727458i	−0.742544	+	0.669798i	$0.766381\pi$
$224$			4206.05i			0.0838259i
$225$	−7497.63	−	4018.32i	−0.148101	−	0.0793741i
$226$	−34645.7			−0.678316
$227$	20111.1	−	20111.1i	0.390287	−	0.390287i	−0.484502	−	0.874790i	$-0.660999\pi$
$227$	20111.1	−	20111.1i	0.390287	−	0.390287i	0.874790	+	0.484502i	$0.160999\pi$
$228$	−32038.9	−	32038.9i	−0.616323	−	0.616323i
$229$		−	22418.6i		−	0.427501i	−0.976888	−	0.213751i	$-0.931432\pi$
$229$		−	22418.6i		−	0.427501i	0.976888	−	0.213751i	$-0.0685680\pi$
$230$	11887.2	−	7115.90i	0.224710	−	0.134516i
$231$	6028.62			0.112978
$232$	22753.4	−	22753.4i	0.422737	−	0.422737i
$233$	31110.1	+	31110.1i	0.573046	+	0.573046i	0.932978	−	0.359933i	$-0.117200\pi$
$233$	31110.1	+	31110.1i	0.573046	+	0.573046i	−0.359933	+	0.932978i	$0.617200\pi$
$234$		−	3578.13i		−	0.0653469i
$235$	−20580.6	+	81968.8i	−0.372669	+	1.48427i
$236$	−59652.9			−1.07104
$237$	29718.6	−	29718.6i	0.529092	−	0.529092i
$238$	5008.70	+	5008.70i	0.0884243	+	0.0884243i
$239$		−	18817.0i		−	0.329423i	−0.986342	−	0.164711i	$-0.947331\pi$
$239$		−	18817.0i		−	0.329423i	0.986342	−	0.164711i	$-0.0526693\pi$
$240$	63389.4	+	15915.7i	1.10051	+	0.276315i
$241$	73856.4			1.27161			0.635805	−	0.771849i	$-0.280668\pi$
$241$	73856.4			1.27161			0.635805	+	0.771849i	$0.280668\pi$
$242$	−68900.8	+	68900.8i	−1.17650	+	1.17650i
$243$	13874.1	+	13874.1i	0.234959	+	0.234959i
$244$			23504.2i			0.394790i
$245$	−30626.9	−	51162.5i	−0.510235	−	0.852352i
$246$	−55192.3			−0.912028
$247$	22100.4	−	22100.4i	0.362248	−	0.362248i
$248$	−29570.9	−	29570.9i	−0.480796	−	0.480796i
$249$			18137.2i			0.292531i
$250$	−58076.8	−	52814.8i	−0.929229	−	0.845037i
$251$	77295.7			1.22690			0.613448	−	0.789735i	$-0.289782\pi$
$251$	77295.7			1.22690			0.613448	+	0.789735i	$0.289782\pi$
$252$	−354.017	+	354.017i	−0.00557473	+	0.00557473i
$253$	−14389.5	−	14389.5i	−0.224804	−	0.224804i
$254$			124215.i			1.92533i
$255$	62368.6	−	37335.1i	0.959148	−	0.574165i
$256$	82966.6			1.26597
$257$	−46347.9	+	46347.9i	−0.701720	+	0.701720i	−0.964780	−	0.263060i	$-0.915268\pi$
$257$	−46347.9	+	46347.9i	−0.701720	+	0.701720i	0.263060	+	0.964780i	$0.415268\pi$
$258$	51046.3	+	51046.3i	0.766876	+	0.766876i
$259$		−	3583.55i		−	0.0534213i
$260$	2943.88	−	11724.9i	0.0435485	−	0.173445i
$261$	12897.1			0.189326
$262$	−76935.4	+	76935.4i	−1.12079	+	1.12079i
$263$	−25093.0	−	25093.0i	−0.362777	−	0.362777i	0.502057	−	0.864835i	$-0.332577\pi$
$263$	−25093.0	−	25093.0i	−0.362777	−	0.362777i	−0.864835	+	0.502057i	$0.832577\pi$
$264$		−	51428.9i		−	0.737903i
$265$	39402.1	+	9893.03i	0.561083	+	0.140876i
$266$	−11945.1			−0.168821
$267$	47217.8	−	47217.8i	0.662343	−	0.662343i
$268$	−37964.9	−	37964.9i	−0.528582	−	0.528582i
$269$			35536.6i			0.491102i	0.969384	+	0.245551i	$0.0789689\pi$
$269$			35536.6i			0.491102i	−0.969384	+	0.245551i	$0.921031\pi$
$270$	50104.1	+	83699.4i	0.687300	+	1.14814i
$271$	−134131.			−1.82638			−0.913189	−	0.407536i	$-0.866388\pi$
$271$	−134131.			−1.82638			−0.913189	+	0.407536i	$0.866388\pi$
$272$	79758.2	−	79758.2i	1.07805	−	1.07805i
$273$	1209.11	+	1209.11i	0.0162233	+	0.0162233i
$274$		−	78795.5i		−	1.04954i
$275$	−54467.7	+	101629.i	−0.720234	+	1.34386i
$276$	−8367.61			−0.109846
$277$	−21251.3	+	21251.3i	−0.276966	+	0.276966i	−0.831896	−	0.554931i	$-0.812745\pi$
$277$	−21251.3	+	21251.3i	−0.276966	+	0.276966i	0.554931	+	0.831896i	$0.312745\pi$
$278$	32285.5	+	32285.5i	0.417752	+	0.417752i
$279$		−	16761.4i		−	0.215329i
$280$	2899.55	−	1735.73i	0.0369840	−	0.0221394i
$281$	−28206.2			−0.357216			−0.178608	−	0.983920i	$-0.557159\pi$
$281$	−28206.2			−0.357216			−0.178608	+	0.983920i	$0.557159\pi$
$282$	98586.3	−	98586.3i	1.23971	−	1.23971i
$283$	7699.00	+	7699.00i	0.0961305	+	0.0961305i	0.753537	−	0.657406i	$-0.228346\pi$
$283$	7699.00	+	7699.00i	0.0961305	+	0.0961305i	−0.657406	+	0.753537i	$0.728346\pi$
$284$		−	73003.1i		−	0.905117i
$285$	−29850.8	+	118890.i	−0.367507	+	1.46371i
$286$	−48501.1			−0.592952
$287$	−3766.76	+	3766.76i	−0.0457303	+	0.0457303i
$288$	10169.0	+	10169.0i	0.122601	+	0.122601i
$289$		−	41928.9i		−	0.502016i
$290$	115435.	+	28983.2i	1.37259	+	0.344628i
$291$	−47959.4			−0.566354
$292$	−26898.3	+	26898.3i	−0.315471	+	0.315471i
$293$	−14289.1	−	14289.1i	−0.166445	−	0.166445i	0.618970	−	0.785415i	$-0.287550\pi$
$293$	−14289.1	−	14289.1i	−0.166445	−	0.166445i	−0.785415	+	0.618970i	$0.787550\pi$
$294$			98370.5i			1.13807i
$295$	82890.4	+	138469.i	0.952490	+	1.59114i
$296$	−30570.5			−0.348915
$297$	101319.	−	101319.i	1.14862	−	1.14862i
$298$	54295.4	+	54295.4i	0.611408	+	0.611408i
$299$		−	5771.95i		−	0.0645625i
$300$	13712.5	+	45385.9i	0.152361	+	0.504288i
$301$	6967.61			0.0769044
$302$	−61156.3	+	61156.3i	−0.670544	+	0.670544i
$303$	26886.2	+	26886.2i	0.292849	+	0.292849i
$304$			190212.i			2.05822i
$305$	54559.1	−	32660.1i	0.586499	−	0.351090i
$306$	24219.3			0.258653
$307$	−48387.2	+	48387.2i	−0.513397	+	0.513397i	−0.915566	−	0.402169i	$-0.868257\pi$
$307$	−48387.2	+	48387.2i	−0.513397	+	0.513397i	0.402169	+	0.915566i	$0.368257\pi$
$308$	4798.66	+	4798.66i	0.0505846	+	0.0505846i
$309$		−	39309.8i		−	0.411703i
$310$	37667.3	−	150022.i	0.391960	−	1.56110i
$311$	−39390.4			−0.407258			−0.203629	−	0.979048i	$-0.565274\pi$
$311$	−39390.4			−0.407258			−0.203629	+	0.979048i	$0.565274\pi$
$312$	10314.6	−	10314.6i	0.105961	−	0.105961i
$313$	40352.4	+	40352.4i	0.411889	+	0.411889i	0.882396	−	0.470507i	$-0.155929\pi$
$313$	40352.4	+	40352.4i	0.411889	+	0.411889i	−0.470507	+	0.882396i	$0.655929\pi$
$314$			14291.7i			0.144952i
$315$	1313.69	+	329.839i	0.0132395	+	0.00332415i
$316$	47310.8			0.473790
$317$	−20437.7	+	20437.7i	−0.203383	+	0.203383i	−0.801448	−	0.598065i	$-0.795936\pi$
$317$	−20437.7	+	20437.7i	−0.203383	+	0.203383i	0.598065	+	0.801448i	$0.295936\pi$
$318$	−47390.1	−	47390.1i	−0.468633	−	0.468633i
$319$		−	174818.i		−	1.71793i
$320$	2737.04	+	4572.25i	0.0267289	+	0.0446509i
$321$	165966.			1.61068
$322$	−1559.85	+	1559.85i	−0.0150442	+	0.0150442i
$323$	149590.	+	149590.i	1.43383	+	1.43383i
$324$		−	48730.0i		−	0.464201i
$325$	−31307.1	+	9458.81i	−0.296398	+	0.0895509i
$326$	−83764.2			−0.788176
$327$	−65471.7	+	65471.7i	−0.612292	+	0.612292i
$328$	32133.5	+	32133.5i	0.298682	+	0.298682i
$329$		−	13456.6i		−	0.124321i
$330$	163212.	−	97701.9i	1.49873	−	0.897171i
$331$	−106355.			−0.970740			−0.485370	−	0.874309i	$-0.661315\pi$
$331$	−106355.			−0.970740			−0.485370	+	0.874309i	$0.661315\pi$
$332$	−14436.9	+	14436.9i	−0.130978	+	0.130978i
$333$	−8664.01	−	8664.01i	−0.0781323	−	0.0781323i
$334$			37444.4i			0.335655i
$335$	−35372.0	+	140880.i	−0.315188	+	1.25533i
$336$	−10406.5			−0.0921777
$337$	−92531.5	+	92531.5i	−0.814760	+	0.814760i	−0.985343	−	0.170583i	$-0.945435\pi$
$337$	−92531.5	+	92531.5i	−0.814760	+	0.814760i	0.170583	+	0.985343i	$0.445435\pi$
$338$	91736.2	+	91736.2i	0.802985	+	0.802985i
$339$		−	56610.0i		−	0.492599i
$340$	79362.2	+	19926.2i	0.686524	+	0.172372i
$341$	−227198.			−1.95387
$342$	−28879.8	+	28879.8i	−0.246912	+	0.246912i
$343$	13471.8	+	13471.8i	0.114508	+	0.114508i
$344$		−	59439.2i		−	0.502292i
$345$	11627.2	+	19423.3i	0.0976868	+	0.163187i
$346$	−259884.			−2.17083
$347$	151780.	−	151780.i	1.26053	−	1.26053i	0.309698	−	0.950835i	$-0.399772\pi$
$347$	151780.	−	151780.i	1.26053	−	1.26053i	0.950835	−	0.309698i	$-0.100228\pi$
$348$	−50829.2	−	50829.2i	−0.419715	−	0.419715i
$349$			100880.i			0.828239i	0.910223	+	0.414119i	$0.135910\pi$
$349$			100880.i			0.828239i	−0.910223	+	0.414119i	$0.864090\pi$
$350$	11016.8	+	5904.40i	0.0899332	+	0.0481992i
$351$	40641.2			0.329877
$352$	137840.	−	137840.i	1.11247	−	1.11247i
$353$	44859.7	+	44859.7i	0.360004	+	0.360004i	0.863814	−	0.503810i	$-0.168069\pi$
$353$	44859.7	+	44859.7i	0.360004	+	0.360004i	−0.503810	+	0.863814i	$0.668069\pi$
$354$		−	266236.i		−	2.12452i
$355$	−169458.	+	101441.i	−1.34464	+	0.804928i
$356$	75168.8			0.593113
$357$	−8184.07	+	8184.07i	−0.0642145	+	0.0642145i
$358$	−72654.5	−	72654.5i	−0.566887	−	0.566887i
$359$		−	72835.5i		−	0.565138i	−0.959247	−	0.282569i	$-0.908813\pi$
$359$		−	72835.5i		−	0.565138i	0.959247	−	0.282569i	$-0.0911866\pi$
$360$	2813.79	−	11206.8i	0.0217113	−	0.0864720i
$361$	−226432.			−1.73749
$362$	−4882.29	+	4882.29i	−0.0372569	+	0.0372569i
$363$	−112582.	−	112582.i	−0.854388	−	0.854388i
$364$			1924.85i			0.0145276i
$365$	99814.0	+	25061.2i	0.749214	+	0.188112i
$366$	−104901.			−0.783102
$367$	−64183.5	+	64183.5i	−0.476531	+	0.476531i	−0.904020	−	0.427489i	$-0.859398\pi$
$367$	−64183.5	+	64183.5i	−0.476531	+	0.476531i	0.427489	+	0.904020i	$0.359398\pi$
$368$	24838.9	+	24838.9i	0.183416	+	0.183416i
$369$			18213.9i			0.133768i
$370$	−58076.3	−	97017.0i	−0.424224	−	0.708670i
$371$	−6468.55			−0.0469958
$372$	−66058.9	+	66058.9i	−0.477359	+	0.477359i
$373$	−167651.	−	167651.i	−1.20501	−	1.20501i	−0.972624	−	0.232383i	$-0.925348\pi$
$373$	−167651.	−	167651.i	−1.20501	−	1.20501i	−0.232383	−	0.972624i	$-0.574652\pi$
$374$		−	328289.i		−	2.34700i
$375$	86297.8	−	94895.8i	0.613673	−	0.674814i
$376$	−114796.			−0.811989
$377$	35061.8	−	35061.8i	0.246690	−	0.246690i
$378$	−10983.1	−	10983.1i	−0.0768674	−	0.0768674i
$379$		−	52795.3i		−	0.367550i	−0.982968	−	0.183775i	$-0.941168\pi$
$379$		−	52795.3i		−	0.367550i	0.982968	−	0.183775i	$-0.0588318\pi$
$380$	−118395.	+	70873.4i	−0.819907	+	0.490813i
$381$	−202963.			−1.39819
$382$	−86475.1	+	86475.1i	−0.592603	+	0.592603i
$383$	81271.5	+	81271.5i	0.554040	+	0.554040i	0.927604	−	0.373565i	$-0.121865\pi$
$383$	81271.5	+	81271.5i	0.554040	+	0.554040i	−0.373565	+	0.927604i	$0.621865\pi$
$384$			129992.i			0.881566i
$385$	4470.92	−	17806.8i	0.0301631	−	0.120134i
$386$	186748.			1.25337
$387$	16845.7	−	16845.7i	0.112478	−	0.112478i
$388$	−38174.7	−	38174.7i	−0.253578	−	0.253578i
$389$			63912.5i			0.422364i	0.977447	+	0.211182i	$0.0677312\pi$
$389$			63912.5i			0.422364i	−0.977447	+	0.211182i	$0.932269\pi$
$390$	52329.2	+	13138.8i	0.344045	+	0.0863825i
$391$	39068.5			0.255549
$392$	57272.2	−	57272.2i	0.372711	−	0.372711i
$393$	−125710.	−	125710.i	−0.813926	−	0.813926i
$394$		−	136202.i		−	0.877388i
$395$	−65740.5	−	109820.i	−0.421346	−	0.703862i
$396$	23203.6			0.147967
$397$	185435.	−	185435.i	1.17655	−	1.17655i	0.195936	−	0.980617i	$-0.437225\pi$
$397$	185435.	−	185435.i	1.17655	−	1.17655i	0.980617	−	0.195936i	$-0.0627745\pi$
$398$	−192467.	−	192467.i	−1.21504	−	1.21504i
$399$		−	19517.9i		−	0.122599i
$400$	94021.2	−	175431.i	0.587633	−	1.09644i
$401$	159570.			0.992345			0.496172	−	0.868224i	$-0.334738\pi$
$401$	159570.			0.992345			0.496172	+	0.868224i	$0.334738\pi$
$402$	169441.	−	169441.i	1.04849	−	1.04849i
$403$	−45567.2	−	45567.2i	−0.280571	−	0.280571i
$404$			42801.7i			0.262240i
$405$	−113114.	+	67712.5i	−0.689617	+	0.412818i
$406$	−18950.6			−0.114967
$407$	−117439.	+	117439.i	−0.708966	+	0.708966i
$408$	69816.6	+	69816.6i	0.419410	+	0.419410i
$409$			15836.9i			0.0946727i	0.998879	+	0.0473363i	$0.0150733\pi$
$409$			15836.9i			0.0946727i	−0.998879	+	0.0473363i	$0.984927\pi$
$410$	−40931.5	+	163022.i	−0.243495	+	0.969794i
$411$	128749.			0.762188
$412$	31289.8	−	31289.8i	0.184335	−	0.184335i
$413$	−18170.1	−	18170.1i	−0.106526	−	0.106526i
$414$			7542.53i			0.0440065i
$415$	53572.3	+	13450.9i	0.311060	+	0.0781006i
$416$	55290.7			0.319496
$417$	−52753.6	+	52753.6i	−0.303375	+	0.303375i
$418$	391462.	+	391462.i	2.24046	+	2.24046i
$419$			15156.5i			0.0863318i	0.999068	+	0.0431659i	$0.0137444\pi$
$419$			15156.5i			0.0863318i	−0.999068	+	0.0431659i	$0.986256\pi$
$420$	−3877.47	−	6477.35i	−0.0219811	−	0.0367197i
$421$	140633.			0.793456			0.396728	−	0.917936i	$-0.370146\pi$
$421$	140633.			0.793456			0.396728	+	0.917936i	$0.370146\pi$
$422$	−259840.	+	259840.i	−1.45908	+	1.45908i
$423$	−32534.3	−	32534.3i	−0.181828	−	0.181828i
$424$			55181.9i			0.306948i
$425$	−64023.7	−	211908.i	−0.354457	−	1.17319i
$426$	325819.			1.79538
$427$	−7159.29	+	7159.29i	−0.0392658	+	0.0392658i
$428$	132106.	+	132106.i	0.721163	+	0.721163i
$429$		−	79249.3i		−	0.430607i
$430$	188633.	−	112920.i	1.02019	−	0.610706i
$431$	−83775.8			−0.450987			−0.225493	−	0.974245i	$-0.572399\pi$
$431$	−83775.8			−0.450987			−0.225493	+	0.974245i	$0.572399\pi$
$432$	−174894.	+	174894.i	−0.937148	+	0.937148i
$433$	93346.8	+	93346.8i	0.497879	+	0.497879i	0.910777	−	0.412898i	$-0.135484\pi$
$433$	93346.8	+	93346.8i	0.497879	+	0.497879i	−0.412898	+	0.910777i	$0.635484\pi$
$434$			24628.7i			0.130756i
$435$	−47357.7	+	188617.i	−0.250272	+	0.996784i
$436$	−104228.			−0.548293
$437$	−46586.5	+	46586.5i	−0.243948	+	0.243948i
$438$	−120049.	−	120049.i	−0.625765	−	0.625765i
$439$			131771.i			0.683737i	0.939748	+	0.341869i	$0.111060\pi$
$439$			131771.i			0.683737i	−0.939748	+	0.341869i	$0.888940\pi$
$440$	−151906.	−	38140.5i	−0.784640	−	0.197007i
$441$	32463.1			0.166922
$442$	65842.0	−	65842.0i	0.337022	−	0.337022i
$443$	−1523.66	−	1523.66i	−0.00776389	−	0.00776389i	0.703214	−	0.710978i	$-0.251747\pi$
$443$	−1523.66	−	1523.66i	−0.00776389	−	0.00776389i	−0.710978	+	0.703214i	$0.751747\pi$
$444$			68292.1i			0.346421i
$445$	−104450.	−	174485.i	−0.527461	−	0.881128i
$446$	25703.1			0.129216
$447$	−88717.1	+	88717.1i	−0.444010	+	0.444010i
$448$	−599.975	−	599.975i	−0.00298935	−	0.00298935i
$449$		−	171320.i		−	0.849795i	−0.905241	−	0.424898i	$-0.860310\pi$
$449$		−	171320.i		−	0.849795i	0.905241	−	0.424898i	$-0.139690\pi$
$450$	40910.7	−	12360.4i	0.202028	−	0.0610388i
$451$	246887.			1.21380
$452$	45060.4	−	45060.4i	0.220556	−	0.220556i
$453$	−99927.6	−	99927.6i	−0.486955	−	0.486955i
$454$			142891.i			0.693253i
$455$	4468.06	−	2674.67i	0.0215822	−	0.0129195i
$456$	−166503.			−0.800742
$457$	−73654.8	+	73654.8i	−0.352670	+	0.352670i	−0.861102	−	0.508432i	$-0.830225\pi$
$457$	−73654.8	+	73654.8i	−0.352670	+	0.352670i	0.508432	+	0.861102i	$0.330225\pi$
$458$	79642.7	+	79642.7i	0.379677	+	0.379677i
$459$			275087.i			1.30571i
$460$	−6205.56	+	24715.5i	−0.0293268	+	0.116803i
$461$	274304.			1.29072			0.645358	−	0.763881i	$-0.276708\pi$
$461$	274304.			1.29072			0.645358	+	0.763881i	$0.276708\pi$
$462$	−21416.8	+	21416.8i	−0.100339	+	0.100339i
$463$	−1734.02	−	1734.02i	−0.00808894	−	0.00808894i	0.703051	−	0.711140i	$-0.251821\pi$
$463$	−1734.02	−	1734.02i	−0.00808894	−	0.00808894i	−0.711140	+	0.703051i	$0.751821\pi$
$464$			301768.i			1.40164i
$465$	245131.	+	61547.2i	1.13368	+	0.284644i
$466$	−221039.			−1.01788
$467$	222292.	−	222292.i	1.01927	−	1.01927i	0.0194620	−	0.999811i	$-0.493805\pi$
$467$	222292.	−	222292.i	1.01927	−	1.01927i	0.999811	−	0.0194620i	$-0.00619532\pi$
$468$	4653.74	+	4653.74i	0.0212476	+	0.0212476i
$469$		−	23127.9i		−	0.105146i
$470$	−218083.	−	364309.i	−0.987247	−	1.64921i
$471$	−23352.2			−0.105265
$472$	−155005.	+	155005.i	−0.695764	+	0.695764i
$473$	−228341.	−	228341.i	−1.02062	−	1.02062i
$474$			211152.i			0.939807i
$475$	329029.	+	176341.i	1.45830	+	0.781569i
$476$	−13028.7			−0.0575026
$477$	−15639.1	+	15639.1i	−0.0687346	+	0.0687346i
$478$	66847.8	+	66847.8i	0.292571	+	0.292571i
$479$			69849.2i			0.304432i	0.988347	+	0.152216i	$0.0486410\pi$
$479$			69849.2i			0.304432i	−0.988347	+	0.152216i	$0.951359\pi$
$480$	−186060.	+	111379.i	−0.807550	+	0.483416i
$481$	−47107.7			−0.203611
$482$	−262377.	+	262377.i	−1.12936	+	1.12936i
$483$	−2548.74	−	2548.74i	−0.0109253	−	0.0109253i
$484$		−	179226.i		−	0.765085i
$485$	−35567.5	+	141658.i	−0.151206	+	0.602225i
$486$	−98576.2			−0.417349
$487$	−3885.73	+	3885.73i	−0.0163838	+	0.0163838i	−0.715251	−	0.698867i	$-0.753688\pi$
$487$	−3885.73	+	3885.73i	−0.0163838	+	0.0163838i	0.698867	+	0.715251i	$0.253688\pi$
$488$	61074.4	+	61074.4i	0.256460	+	0.256460i
$489$		−	136868.i		−	0.572380i
$490$	290559.	+	72953.2i	1.21016	+	0.303845i
$491$	323891.			1.34349			0.671747	−	0.740781i	$-0.265544\pi$
$491$	323891.			1.34349			0.671747	+	0.740781i	$0.265544\pi$
$492$	71783.5	−	71783.5i	0.296548	−	0.296548i
$493$	237322.	+	237322.i	0.976438	+	0.976438i
$494$			157024.i			0.643447i
$495$	−32242.4	−	53861.3i	−0.131588	−	0.219820i
$496$	392186.			1.59415
$497$	22236.5	−	22236.5i	0.0900229	−	0.0900229i
$498$	−64433.0	−	64433.0i	−0.259806	−	0.259806i
$499$			216973.i			0.871373i	0.900099	+	0.435686i	$0.143494\pi$
$499$			216973.i			0.871373i	−0.900099	+	0.435686i	$0.856506\pi$
$500$	144226.	−	6843.78i	0.576906	−	0.0273751i
$501$	−61183.0			−0.243756
$502$	−274595.	+	274595.i	−1.08964	+	1.08964i
$503$	308050.	+	308050.i	1.21755	+	1.21755i	0.968489	+	0.249056i	$0.0801204\pi$
$503$	308050.	+	308050.i	1.21755	+	1.21755i	0.249056	+	0.968489i	$0.419880\pi$
$504$			1839.79i			0.00724282i
$505$	99353.4	−	59474.9i	0.389583	−	0.233212i
$506$	102238.			0.399311
$507$	−149894.	+	149894.i	−0.583135	+	0.583135i
$508$	−161554.	−	161554.i	−0.626024	−	0.626024i
$509$		−	480107.i		−	1.85311i	−0.376154	−	0.926557i	$-0.622754\pi$
$509$		−	480107.i		−	1.85311i	0.376154	−	0.926557i	$-0.377246\pi$
$510$	−88932.2	+	354200.i	−0.341916	+	1.36178i
$511$	−16386.2			−0.0627534
$512$	−115587.	+	115587.i	−0.440929	+	0.440929i
$513$	−328023.	−	328023.i	−1.24643	−	1.24643i
$514$		−	329304.i		−	1.24644i
$515$	−116110.	−	29152.8i	−0.437779	−	0.109917i
$516$	−132782.			−0.498702
$517$	−440998.	+	440998.i	−1.64989	+	1.64989i
$518$	12730.7	+	12730.7i	0.0474451	+	0.0474451i
$519$		−	424642.i		−	1.57648i
$520$	−22817.0	−	38116.1i	−0.0843825	−	0.140962i
$521$	409811.			1.50976			0.754880	−	0.655863i	$-0.227695\pi$
$521$	409811.			1.50976			0.754880	+	0.655863i	$0.227695\pi$
$522$	−45817.3	+	45817.3i	−0.168147	+	0.168147i
$523$	−24703.1	−	24703.1i	−0.0903125	−	0.0903125i	0.660507	−	0.750820i	$-0.270341\pi$
$523$	−24703.1	−	24703.1i	−0.0903125	−	0.0903125i	−0.750820	+	0.660507i	$0.770341\pi$
$524$		−	200125.i		−	0.728852i
$525$	−9647.61	+	18001.1i	−0.0350027	+	0.0653103i
$526$	178287.			0.644388
$527$	308430.	−	308430.i	1.11054	−	1.11054i
$528$	341040.	+	341040.i	1.22331	+	1.22331i
$529$			12167.0i			0.0434783i
$530$	−175122.	+	104832.i	−0.623432	+	0.373199i
$531$	−87860.1			−0.311604
$532$	15535.8	−	15535.8i	0.0548923	−	0.0548923i
$533$	49516.0	+	49516.0i	0.174298	+	0.174298i
$534$			335485.i			1.17650i
$535$	123083.	−	490216.i	0.430022	−	1.71270i
$536$	−197300.			−0.686747
$537$	118715.	−	118715.i	0.411678	−	0.411678i
$538$	−126245.	−	126245.i	−0.436163	−	0.436163i
$539$		−	440033.i		−	1.51463i
$540$	−174026.	−	43694.3i	−0.596797	−	0.149843i
$541$	300988.			1.02838			0.514191	−	0.857675i	$-0.328092\pi$
$541$	300988.			1.02838			0.514191	+	0.857675i	$0.328092\pi$
$542$	476504.	−	476504.i	1.62206	−	1.62206i
$543$	−7977.51	−	7977.51i	−0.0270563	−	0.0270563i
$544$			374245.i			1.26462i
$545$	144830.	+	241940.i	0.487602	+	0.814544i
$546$	−8590.77			−0.0288169
$547$	26389.6	−	26389.6i	0.0881978	−	0.0881978i	−0.661631	−	0.749829i	$-0.730136\pi$
$547$	26389.6	−	26389.6i	0.0881978	−	0.0881978i	0.749829	+	0.661631i	$0.230136\pi$
$548$	102482.	+	102482.i	0.341261	+	0.341261i
$549$			34618.3i			0.114858i
$550$	−167543.	−	554539.i	−0.553861	−	1.83319i
$551$	−565981.			−1.86423
$552$	−21742.8	+	21742.8i	−0.0713571	+	0.0713571i
$553$	14410.7	+	14410.7i	0.0471232	+	0.0471232i
$554$		−	150992.i		−	0.491964i
$555$	158523.	−	94894.9i	0.514643	−	0.308075i
$556$	−83981.6			−0.271665
$557$	−142081.	+	142081.i	−0.457959	+	0.457959i	−0.897985	−	0.440026i	$-0.854969\pi$
$557$	−142081.	+	142081.i	−0.457959	+	0.457959i	0.440026	+	0.897985i	$0.354969\pi$
$558$	59545.3	+	59545.3i	0.191240	+	0.191240i
$559$		−	91592.9i		−	0.293115i
$560$	−7717.63	+	30737.8i	−0.0246098	+	0.0980160i
$561$	536414.			1.70441
$562$	100203.	−	100203.i	0.317255	−	0.317255i
$563$	115383.	+	115383.i	0.364021	+	0.364021i	0.865291	−	0.501270i	$-0.167134\pi$
$563$	115383.	+	115383.i	0.364021	+	0.364021i	−0.501270	+	0.865291i	$0.667134\pi$
$564$			256444.i			0.806185i
$565$	−167210.	−	41982.9i	−0.523800	−	0.131515i
$566$	−54701.8			−0.170753
$567$	14843.0	−	14843.0i	0.0461695	−	0.0461695i
$568$	−189695.	−	189695.i	−0.587975	−	0.587975i
$569$			25415.5i			0.0785008i	0.999229	+	0.0392504i	$0.0124970\pi$
$569$			25415.5i			0.0785008i	−0.999229	+	0.0392504i	$0.987503\pi$
$570$	−316314.	−	528405.i	−0.973573	−	1.62636i
$571$	196811.			0.603639			0.301820	−	0.953365i	$-0.402406\pi$
$571$	196811.			0.603639			0.301820	+	0.953365i	$0.402406\pi$
$572$	63080.9	−	63080.9i	0.192799	−	0.192799i
$573$	−141298.	−	141298.i	−0.430354	−	0.430354i
$574$		−	26763.0i		−	0.0812291i
$575$	65993.8	−	19938.7i	0.199603	−	0.0603062i
$576$	−2901.14			−0.00874427
$577$	167061.	−	167061.i	0.501793	−	0.501793i	−0.410202	−	0.911995i	$-0.634542\pi$
$577$	167061.	−	167061.i	0.501793	−	0.501793i	0.911995	+	0.410202i	$0.134542\pi$
$578$	148953.	+	148953.i	0.445856	+	0.445856i
$579$			305140.i			0.910211i
$580$	−187831.	+	112439.i	−0.558355	+	0.334243i
$581$	−8794.84			−0.0260541
$582$	170377.	−	170377.i	0.502996	−	0.502996i
$583$	211986.	+	211986.i	0.623692	+	0.623692i
$584$			139788.i			0.409867i
$585$	4335.91	−	17269.1i	0.0126697	−	0.0504612i
$586$	101525.			0.295650
$587$	−115256.	+	115256.i	−0.334494	+	0.334494i	−0.854290	−	0.519796i	$-0.826008\pi$
$587$	−115256.	+	115256.i	−0.334494	+	0.334494i	0.519796	+	0.854290i	$0.326008\pi$
$588$	−127941.	−	127941.i	−0.370047	−	0.370047i
$589$			735564.i			2.12026i
$590$	−786386.	−	197445.i	−2.25908	−	0.567208i
$591$	222550.			0.637167
$592$	202722.	−	202722.i	0.578439	−	0.578439i
$593$	−100599.	−	100599.i	−0.286077	−	0.286077i	0.549449	−	0.835527i	$-0.314837\pi$
$593$	−100599.	−	100599.i	−0.286077	−	0.286077i	−0.835527	+	0.549449i	$0.814837\pi$
$594$			719873.i			2.04025i
$595$	18104.0	+	30242.9i	0.0511376	+	0.0854258i
$596$	−141234.			−0.397601
$597$	314486.	−	314486.i	0.882373	−	0.882373i
$598$	20505.0	+	20505.0i	0.0573400	+	0.0573400i
$599$		−	505775.i		−	1.40962i	−0.709394	−	0.704812i	$-0.751031\pi$
$599$		−	505775.i		−	1.40962i	0.709394	−	0.704812i	$-0.248969\pi$
$600$	153564.	+	82301.8i	0.426567	+	0.228616i
$601$	−420577.			−1.16439			−0.582193	−	0.813051i	$-0.697805\pi$
$601$	−420577.			−1.16439			−0.582193	+	0.813051i	$0.697805\pi$
$602$	−24752.6	+	24752.6i	−0.0683012	+	0.0683012i
$603$	−55916.8	−	55916.8i	−0.153783	−	0.153783i
$604$		−	159081.i		−	0.436057i
$605$	−416027.	+	249042.i	−1.13661	+	0.680397i
$606$	−191028.			−0.520177
$607$	466115.	−	466115.i	1.26507	−	1.26507i	0.316470	−	0.948602i	$-0.397502\pi$
$607$	466115.	−	466115.i	1.26507	−	1.26507i	0.948602	−	0.316470i	$-0.102498\pi$
$608$	−446262.	−	446262.i	−1.20721	−	1.20721i
$609$		−	30964.8i		−	0.0834897i
$610$	−77796.5	+	309849.i	−0.209074	+	0.832702i
$611$	−176894.			−0.473840
$612$	−31499.7	+	31499.7i	−0.0841015	+	0.0841015i
$613$	−425779.	−	425779.i	−1.13309	−	1.13309i	−0.989661	−	0.143426i	$-0.954188\pi$
$613$	−425779.	−	425779.i	−1.13309	−	1.13309i	−0.143426	−	0.989661i	$-0.545812\pi$
$614$		−	343793.i		−	0.911928i
$615$	−266374.	−	66880.9i	−0.704273	−	0.176828i
$616$	24938.1			0.0657207
$617$	371023.	−	371023.i	0.974609	−	0.974609i	−0.0250764	−	0.999686i	$-0.507983\pi$
$617$	371023.	−	371023.i	0.974609	−	0.974609i	0.999686	+	0.0250764i	$0.00798290\pi$
$618$	139649.	+	139649.i	0.365646	+	0.365646i
$619$			735915.i			1.92064i	0.278895	+	0.960322i	$0.410032\pi$
$619$			735915.i			1.92064i	−0.278895	+	0.960322i	$0.589968\pi$
$620$	146129.	+	244110.i	0.380148	+	0.635041i
$621$	−85669.7			−0.222149
$622$	139935.	−	139935.i	0.361699	−	0.361699i
$623$	22896.1	+	22896.1i	0.0589911	+	0.0589911i
$624$			136799.i			0.351328i
$625$	−216295.	−	325276.i	−0.553716	−	0.832706i
$626$	−286706.			−0.731624
$627$	−639637.	+	639637.i	−1.62704	+	1.62704i
$628$	−18587.9	−	18587.9i	−0.0471314	−	0.0471314i
$629$		−	318857.i		−	0.805925i
$630$	−5838.66	+	3495.14i	−0.0147107	+	0.00880610i
$631$	610188.			1.53252			0.766258	−	0.642533i	$-0.222117\pi$
$631$	610188.			1.53252			0.766258	+	0.642533i	$0.222117\pi$
$632$	122935.	−	122935.i	0.307780	−	0.307780i
$633$	−424570.	−	424570.i	−1.05960	−	1.05960i
$634$		−	145211.i		−	0.361261i
$635$	−150521.	+	599495.i	−0.373292	+	1.48675i
$636$	123272.			0.304754
$637$	88253.6	−	88253.6i	0.217497	−	0.217497i
$638$	621047.	+	621047.i	1.52575	+	1.52575i
$639$		−	107523.i		−	0.263329i
$640$	383960.	+	96404.4i	0.937403	+	0.235362i
$641$	−251941.			−0.613172			−0.306586	−	0.951843i	$-0.599187\pi$
$641$	−251941.			−0.613172			−0.306586	+	0.951843i	$0.599187\pi$
$642$	−589598.	+	589598.i	−1.43049	+	1.43049i
$643$	43628.3	+	43628.3i	0.105523	+	0.105523i	0.757897	−	0.652374i	$-0.226227\pi$
$643$	43628.3	+	43628.3i	0.105523	+	0.105523i	−0.652374	+	0.757897i	$0.726227\pi$
$644$		−	4057.50i		−	0.00978332i
$645$	184507.	+	308221.i	0.443500	+	0.740871i
$646$	−1.06285e6			−2.54687
$647$	440782.	−	440782.i	1.05297	−	1.05297i	0.0544523	−	0.998516i	$-0.482659\pi$
$647$	440782.	−	440782.i	1.05297	−	1.05297i	0.998516	−	0.0544523i	$-0.0173413\pi$
$648$	−126622.	−	126622.i	−0.301551	−	0.301551i
$649$			1.19093e6i			2.82747i
$650$	77616.4	−	144822.i	0.183708	−	0.342773i
$651$	−40242.6			−0.0949563
$652$	108944.	−	108944.i	0.256277	−	0.256277i
$653$	−265254.	−	265254.i	−0.622064	−	0.622064i	0.323995	−	0.946059i	$-0.394974\pi$
$653$	−265254.	−	265254.i	−0.622064	−	0.622064i	−0.946059	+	0.323995i	$0.894974\pi$
$654$		−	465180.i		−	1.08759i
$655$	−464540.	+	278083.i	−1.08278	+	0.648175i
$656$	−426172.			−0.990325
$657$	−39617.3	+	39617.3i	−0.0917812	+	0.0917812i
$658$	47805.0	+	47805.0i	0.110413	+	0.110413i
$659$			456316.i			1.05074i	0.850874	+	0.525369i	$0.176073\pi$
$659$			456316.i			1.05074i	−0.850874	+	0.525369i	$0.823927\pi$
$660$	−85202.8	+	339346.i	−0.195599	+	0.779032i
$661$	350242.			0.801614			0.400807	−	0.916162i	$-0.368730\pi$
$661$	350242.			0.801614			0.400807	+	0.916162i	$0.368730\pi$
$662$	377830.	−	377830.i	0.862145	−	0.862145i
$663$	107584.	+	107584.i	0.244749	+	0.244749i
$664$			75026.9i			0.170169i
$665$	−57650.3	−	14474.8i	−0.130364	−	0.0327317i
$666$	61558.2			0.138783
$667$	−73908.6	+	73908.6i	−0.166128	+	0.166128i
$668$	−48700.4	−	48700.4i	−0.109139	−	0.109139i
$669$			41998.0i			0.0938375i
$670$	−374820.	−	626139.i	−0.834973	−	1.39483i
$671$	469246.			1.04221
$672$	24414.9	−	24414.9i	0.0540651	−	0.0540651i
$673$	−522535.	−	522535.i	−1.15368	−	1.15368i	−0.985809	−	0.167871i	$-0.946311\pi$
$673$	−522535.	−	522535.i	−1.15368	−	1.15368i	−0.167871	−	0.985809i	$-0.553689\pi$
$674$		−	657441.i		−	1.44723i
$675$	140392.	+	464672.i	0.308130	+	1.01986i
$676$	−238626.			−0.522184
$677$	−220817.	+	220817.i	−0.481788	+	0.481788i	−0.905702	−	0.423914i	$-0.860656\pi$
$677$	−220817.	+	220817.i	−0.481788	+	0.481788i	0.423914	+	0.905702i	$0.360656\pi$
$678$	201109.	+	201109.i	0.437493	+	0.437493i
$679$		−	23255.7i		−	0.0504418i
$680$	257996.	−	154441.i	0.557949	−	0.333999i
$681$	−233479.			−0.503446
$682$	807128.	−	807128.i	1.73530	−	1.73530i
$683$	17459.2	+	17459.2i	0.0374268	+	0.0374268i	0.725572	−	0.688146i	$-0.241575\pi$
$683$	17459.2	+	17459.2i	0.0374268	+	0.0374268i	−0.688146	+	0.725572i	$0.741575\pi$
$684$		−	75122.5i		−	0.160568i
$685$	95482.7	−	380290.i	0.203490	−	0.810463i
$686$	−95717.6			−0.203397
$687$	−130134.	+	130134.i	−0.275725	+	0.275725i
$688$	394159.	+	394159.i	0.832711	+	0.832711i
$689$			85032.5i			0.179121i
$690$	−110308.	−	27695.9i	−0.231690	−	0.0581725i
$691$	637693.			1.33553			0.667767	−	0.744370i	$-0.267250\pi$
$691$	637693.			1.33553			0.667767	+	0.744370i	$0.267250\pi$
$692$	338006.	−	338006.i	0.705851	−	0.705851i
$693$	7067.73	+	7067.73i	0.0147168	+	0.0147168i
$694$			1.07840e6i			2.23904i
$695$	116696.	+	194942.i	0.241594	+	0.403586i
$696$	−264154.			−0.545304
$697$	−335158.	+	335158.i	−0.689898	+	0.689898i
$698$	−358380.	−	358380.i	−0.735585	−	0.735585i
$699$		−	361171.i		−	0.739193i
$700$	−22007.9	+	6649.24i	−0.0449140	+	0.0135699i
$701$	−125311.			−0.255008			−0.127504	−	0.991838i	$-0.540697\pi$
$701$	−125311.			−0.255008			−0.127504	+	0.991838i	$0.540697\pi$
$702$	−144379.	+	144379.i	−0.292974	+	0.292974i
$703$	380215.	+	380215.i	0.769340	+	0.769340i
$704$			39324.6i			0.0793448i
$705$	595270.	−	356341.i	1.19767	−	0.716947i
$706$	−318731.			−0.639462
$707$	−13037.2	+	13037.2i	−0.0260824	+	0.0260824i
$708$	346268.	+	346268.i	0.690791	+	0.690791i
$709$		−	719014.i		−	1.43036i	−0.698942	−	0.715179i	$-0.746345\pi$
$709$		−	719014.i		−	1.43036i	0.698942	−	0.715179i	$-0.253655\pi$
$710$	241633.	−	962377.i	0.479335	−	1.90910i
$711$	69682.0			0.137842
$712$	195322.	−	195322.i	0.385294	−	0.385294i
$713$	96053.6	+	96053.6i	0.188945	+	0.188945i
$714$		−	58148.2i		−	0.114062i
$715$	−234080.	−	58772.6i	−0.457881	−	0.114964i
$716$	188990.			0.368649
$717$	−109227.	+	109227.i	−0.212467	+	0.212467i
$718$	258750.	+	258750.i	0.501917	+	0.501917i
$719$			784081.i			1.51671i	0.651841	+	0.758356i	$0.273997\pi$
$719$			784081.i			1.51671i	−0.651841	+	0.758356i	$0.726003\pi$
$720$	55656.3	+	92974.4i	0.107362	+	0.179349i
$721$	19061.5			0.0366680
$722$	804404.	−	804404.i	1.54312	−	1.54312i
$723$	−428716.	−	428716.i	−0.820149	−	0.820149i
$724$		−	12699.9i		−	0.0242283i
$725$	521999.	+	279762.i	0.993101	+	0.532247i
$726$	799900.			1.51762
$727$	−288195.	+	288195.i	−0.545277	+	0.545277i	−0.925071	−	0.379794i	$-0.875995\pi$
$727$	−288195.	+	288195.i	−0.545277	+	0.545277i	0.379794	+	0.925071i	$0.375995\pi$
$728$	5001.63	+	5001.63i	0.00943731	+	0.00943731i
$729$		−	588208.i		−	1.10682i
$730$	−443622.	+	265561.i	−0.832468	+	0.498332i
$731$	619963.			1.16020
$732$	136435.	−	136435.i	0.254627	−	0.254627i
$733$	−369280.	−	369280.i	−0.687302	−	0.687302i	0.274333	−	0.961635i	$-0.411543\pi$
$733$	−369280.	−	369280.i	−0.687302	−	0.687302i	−0.961635	+	0.274333i	$0.911543\pi$
$734$		−	456027.i		−	0.846444i
$735$	−119203.	+	474764.i	−0.220655	+	0.878826i
$736$	−116550.			−0.215158
$737$	−757945.	+	757945.i	−1.39541	+	1.39541i
$738$	−64705.4	−	64705.4i	−0.118803	−	0.118803i
$739$			123689.i			0.226486i	0.993567	+	0.113243i	$0.0361239\pi$
$739$			123689.i			0.226486i	−0.993567	+	0.113243i	$0.963876\pi$
$740$	201715.	+	50646.5i	0.368363	+	0.0924882i
$741$	−256573.			−0.467277
$742$	22979.7	−	22979.7i	0.0417384	−	0.0417384i
$743$	−702418.	−	702418.i	−1.27238	−	1.27238i	−0.944834	−	0.327549i	$-0.893777\pi$
$743$	−702418.	−	702418.i	−1.27238	−	1.27238i	−0.327549	−	0.944834i	$-0.606223\pi$
$744$			343301.i			0.620197i
$745$	196251.	+	327839.i	0.353590	+	0.590675i
$746$	1.19117e6			2.14041
$747$	−21263.4	+	21263.4i	−0.0381059	+	0.0381059i
$748$	426975.	+	426975.i	0.763130	+	0.763130i
$749$			80477.7i			0.143454i
$750$	30544.4	+	643695.i	0.0543011	+	1.14435i
$751$	−453211.			−0.803565			−0.401783	−	0.915735i	$-0.631609\pi$
$751$	−453211.			−0.803565			−0.401783	+	0.915735i	$0.631609\pi$
$752$	761243.	−	761243.i	1.34613	−	1.34613i
$753$	−448680.	−	448680.i	−0.791309	−	0.791309i
$754$			249116.i			0.438186i
$755$	−369266.	+	221050.i	−0.647806	+	0.387790i
$756$	28569.4			0.0499871
$757$	−169459.	+	169459.i	−0.295715	+	0.295715i	−0.839333	−	0.543618i	$-0.817054\pi$
$757$	−169459.	+	169459.i	−0.295715	+	0.295715i	0.543618	+	0.839333i	$0.317054\pi$
$758$	187557.	+	187557.i	0.326433	+	0.326433i
$759$			167054.i			0.289983i
$760$	−123481.	+	491803.i	−0.213784	+	0.851459i
$761$	−163848.			−0.282925			−0.141462	−	0.989944i	$-0.545180\pi$
$761$	−163848.			−0.282925			−0.141462	+	0.989944i	$0.545180\pi$
$762$	721031.	−	721031.i	1.24178	−	1.24178i
$763$	−31747.6	−	31747.6i	−0.0545333	−	0.0545333i
$764$		−	224940.i		−	0.385372i
$765$	116889.	+	29348.4i	0.199733	+	0.0501489i
$766$	−577438.			−0.984120
$767$	−238855.	+	238855.i	−0.406016	+	0.406016i
$768$	−481598.	−	481598.i	−0.816511	−	0.816511i
$769$			574664.i			0.971765i	0.874024	+	0.485883i	$0.161502\pi$
$769$			574664.i			0.971765i	−0.874024	+	0.485883i	$0.838498\pi$
$770$	47376.1	+	79142.3i	0.0799058	+	0.133483i
$771$	538073.			0.905175
$772$	−242885.	+	242885.i	−0.407537	+	0.407537i
$773$	250860.	+	250860.i	0.419828	+	0.419828i	0.885144	−	0.465316i	$-0.154059\pi$
$773$	250860.	+	250860.i	0.419828	+	0.419828i	−0.465316	+	0.885144i	$0.654059\pi$
$774$			119690.i			0.199790i
$775$	363586.	−	678403.i	0.605346	−	1.12949i
$776$	−198390.			−0.329455
$777$	−20801.5	+	20801.5i	−0.0344550	+	0.0344550i
$778$	−227051.	−	227051.i	−0.375115	−	0.375115i
$779$		−	799307.i		−	1.31716i
$780$	−85148.2	+	50971.4i	−0.139954	+	0.0837794i
$781$	−1.45746e6			−2.38943
$782$	−138792.	+	138792.i	−0.226961	+	0.226961i
$783$	−520402.	−	520402.i	−0.848820	−	0.848820i
$784$			759577.i			1.23578i
$785$	−17318.4	+	68975.8i	−0.0281040	+	0.111933i
$786$	893176.			1.44575
$787$	565274.	−	565274.i	0.912661	−	0.912661i	−0.0838197	−	0.996481i	$-0.526712\pi$
$787$	565274.	−	565274.i	0.912661	−	0.912661i	0.996481	+	0.0838197i	$0.0267120\pi$
$788$	177146.	+	177146.i	0.285284	+	0.285284i
$789$			291315.i			0.467960i
$790$	623684.	+	156594.i	0.999333	+	0.250912i
$791$	27450.5			0.0438730
$792$	60293.3	−	60293.3i	0.0961211	−	0.0961211i
$793$	94112.6	+	94112.6i	0.149659	+	0.149659i
$794$			1.31753e6i			2.08987i
$795$	−171292.	−	286144.i	−0.271020	−	0.452742i
$796$	500649.			0.790146
$797$	242456.	−	242456.i	0.381695	−	0.381695i	−0.490017	−	0.871713i	$-0.663010\pi$
$797$	242456.	−	242456.i	0.381695	−	0.381695i	0.871713	+	0.490017i	$0.163010\pi$
$798$	69337.8	+	69337.8i	0.108884	+	0.108884i
$799$		−	1.19734e6i		−	1.87553i
$800$	190997.	+	632168.i	0.298433	+	0.987762i
$801$	110713.			0.172557
$802$	−566877.	+	566877.i	−0.881333	+	0.881333i
$803$	537007.	+	537007.i	0.832815	+	0.832815i
$804$			440751.i			0.681838i
$805$	−9418.45	+	5638.07i	−0.0145341	+	0.00870039i
$806$	323757.			0.498368
$807$	206280.	−	206280.i	0.316745	−	0.316745i
$808$	111218.	+	111218.i	0.170354	+	0.170354i
$809$		−	293367.i		−	0.448243i	−0.974561	−	0.224122i	$-0.928049\pi$
$809$		−	293367.i		−	0.448243i	0.974561	−	0.224122i	$-0.0719513\pi$
$810$	161291.	−	642392.i	0.245833	−	0.979107i
$811$	−484540.			−0.736696			−0.368348	−	0.929688i	$-0.620076\pi$
$811$	−484540.			−0.736696			−0.368348	+	0.929688i	$0.620076\pi$
$812$	24647.3	−	24647.3i	0.0373816	−	0.0373816i
$813$	778593.	+	778593.i	1.17796	+	1.17796i
$814$		−	834414.i		−	1.25931i
$815$	−404270.	−	101504.i	−0.608634	−	0.152815i
$816$	−925948.			−1.39061
$817$	−739264.	+	739264.i	−1.10753	+	1.10753i
$818$	−56261.1	−	56261.1i	−0.0840818	−	0.0840818i
$819$			2835.03i			0.00422658i
$820$	−158792.	−	265264.i	−0.236158	−	0.394503i
$821$	972880.			1.44335			0.721677	−	0.692229i	$-0.243371\pi$
$821$	972880.			1.44335			0.721677	+	0.692229i	$0.243371\pi$
$822$	−457386.	+	457386.i	−0.676923	+	0.676923i
$823$	−244515.	−	244515.i	−0.361000	−	0.361000i	0.503181	−	0.864181i	$-0.332163\pi$
$823$	−244515.	−	244515.i	−0.361000	−	0.361000i	−0.864181	+	0.503181i	$0.832163\pi$
$824$		−	162610.i		−	0.239493i
$825$	906100.	−	273760.i	1.33128	−	0.402219i
$826$	129099.			0.189218
$827$	−301109.	+	301109.i	−0.440263	+	0.440263i	−0.892100	−	0.451837i	$-0.850769\pi$
$827$	−301109.	+	301109.i	−0.440263	+	0.440263i	0.451837	+	0.892100i	$0.350769\pi$
$828$	−9809.87	−	9809.87i	−0.0143088	−	0.0143088i
$829$			954722.i			1.38921i	0.719391	+	0.694605i	$0.244421\pi$
$829$			954722.i			1.38921i	−0.719391	+	0.694605i	$0.755579\pi$
$830$	−238101.	+	142532.i	−0.345625	+	0.206898i
$831$	246716.			0.357268
$832$	−7886.99	+	7886.99i	−0.0113937	+	0.0113937i
$833$	597361.	+	597361.i	0.860888	+	0.860888i
$834$		−	374817.i		−	0.538874i
$835$	−45374.3	+	180717.i	−0.0650784	+	0.259195i
$836$	−1.01828e6			−1.45698
$837$	−676328.	+	676328.i	−0.965398	+	0.965398i
$838$	−53843.8	−	53843.8i	−0.0766740	−	0.0766740i
$839$			1.09935e6i			1.56175i	0.624685	+	0.780877i	$0.285227\pi$
$839$			1.09935e6i			1.56175i	−0.624685	+	0.780877i	$0.714773\pi$
$840$	−26906.5	−	6755.65i	−0.0381327	−	0.00957433i
$841$	−190638.			−0.269536
$842$	−499602.	+	499602.i	−0.704693	+	0.704693i
$843$	163729.	+	163729.i	0.230393	+	0.230393i
$844$		−	675898.i		−	0.948848i
$845$	331581.	+	553909.i	0.464383	+	0.775756i
$846$	231158.			0.322974
$847$	54591.5	−	54591.5i	0.0760954	−	0.0760954i
$848$	−365927.	−	365927.i	−0.508865	−	0.508865i
$849$		−	89381.0i		−	0.124002i
$850$	980253.	+	525361.i	1.35675	+	0.727144i
$851$	99300.7			0.137118
$852$	−423762.	+	423762.i	−0.583772	+	0.583772i
$853$	207155.	+	207155.i	0.284706	+	0.284706i	0.834982	−	0.550277i	$-0.185478\pi$
$853$	207155.	+	207155.i	0.284706	+	0.284706i	−0.550277	+	0.834982i	$0.685478\pi$
$854$		−	50867.1i		−	0.0697464i
$855$	−174378.	+	104386.i	−0.238539	+	0.142794i
$856$	686539.			0.936953
$857$	285095.	−	285095.i	0.388176	−	0.388176i	−0.485860	−	0.874036i	$-0.661494\pi$
$857$	285095.	−	285095.i	0.388176	−	0.388176i	0.874036	+	0.485860i	$0.161494\pi$
$858$	281535.	+	281535.i	0.382435	+	0.382435i
$859$		−	868658.i		−	1.17723i	−0.808412	−	0.588617i	$-0.799673\pi$
$859$		−	868658.i		−	1.17723i	0.808412	−	0.588617i	$-0.200327\pi$
$860$	−98473.6	+	392202.i	−0.133144	+	0.530289i
$861$	43730.0			0.0589893
$862$	297616.	−	297616.i	0.400536	−	0.400536i
$863$	−572841.	−	572841.i	−0.769152	−	0.769152i	0.208805	−	0.977957i	$-0.433043\pi$
$863$	−572841.	−	572841.i	−0.769152	−	0.769152i	−0.977957	+	0.208805i	$0.933043\pi$
$864$		−	820647.i		−	1.09933i
$865$	−1.25427e6	−	314921.i	−1.67633	−	0.420891i
$866$	−663234.			−0.884363
$867$	−243385.	+	243385.i	−0.323785	+	0.323785i
$868$	−32032.3	−	32032.3i	−0.0425156	−	0.0425156i
$869$		−	944529.i		−	1.25077i
$870$	−501826.	−	838304.i	−0.663001	−	1.10755i
$871$	−304029.			−0.400755
$872$	−270832.	+	270832.i	−0.356178	+	0.356178i
$873$	−56225.8	−	56225.8i	−0.0737747	−	0.0737747i
$874$		−	331000.i		−	0.433316i
$875$	46015.4	+	41846.3i	0.0601018	+	0.0546563i
$876$	312274.			0.406937
$877$	−253892.	+	253892.i	−0.330104	+	0.330104i	−0.852626	−	0.522522i	$-0.824991\pi$
$877$	−253892.	+	253892.i	−0.330104	+	0.330104i	0.522522	+	0.852626i	$0.324991\pi$
$878$	−468118.	−	468118.i	−0.607249	−	0.607249i
$879$			165889.i			0.214704i
$880$	1.26026e6	−	754414.i	1.62740	−	0.974191i
$881$	826450.			1.06479			0.532396	−	0.846496i	$-0.321292\pi$
$881$	826450.			1.06479			0.532396	+	0.846496i	$0.321292\pi$
$882$	−115326.	+	115326.i	−0.148248	+	0.148248i
$883$	−575862.	−	575862.i	−0.738578	−	0.738578i	0.233724	−	0.972303i	$-0.424909\pi$
$883$	−575862.	−	575862.i	−0.738578	−	0.738578i	−0.972303	+	0.233724i	$0.924909\pi$
$884$			171269.i			0.219167i
$885$	322619.	−	1.28493e6i	0.411911	−	1.64056i
$886$	10825.6			0.0137907
$887$	−461037.	+	461037.i	−0.585988	+	0.585988i	−0.936542	−	0.350555i	$-0.885993\pi$
$887$	−461037.	+	461037.i	−0.585988	+	0.585988i	0.350555	+	0.936542i	$0.385993\pi$
$888$	177453.	+	177453.i	0.225039	+	0.225039i
$889$		−	98417.7i		−	0.124529i
$890$	990927.	+	248801.i	1.25101	+	0.314103i
$891$	−972863.			−1.22545
$892$	−33429.6	+	33429.6i	−0.0420147	+	0.0420147i
$893$	1.42775e6	+	1.42775e6i	1.79040	+	1.79040i
$894$		−	630340.i		−	0.788678i
$895$	−262610.	−	438692.i	−0.327842	−	0.547664i
$896$	−63033.9			−0.0785160
$897$	−33504.5	+	33504.5i	−0.0416408	+	0.0416408i
$898$	608617.	+	608617.i	0.754730	+	0.754730i
$899$			1.16696e6i			1.44390i
$900$	−37132.8	+	69284.7i	−0.0458429	+	0.0855367i
$901$	−575558.			−0.708989
$902$	−877073.	+	877073.i	−1.07801	+	1.07801i
$903$	−40445.0	−	40445.0i	−0.0496009	−	0.0496009i
$904$		−	234174.i		−	0.286551i
$905$	−29479.6	+	17647.1i	−0.0359935	+	0.0215464i
$906$	709991.			0.864960
$907$	663568.	−	663568.i	0.806624	−	0.806624i	−0.177498	−	0.984121i	$-0.556800\pi$
$907$	663568.	−	663568.i	0.806624	−	0.806624i	0.984121	+	0.177498i	$0.0568002\pi$
$908$	−185844.	−	185844.i	−0.225412	−	0.225412i
$909$			63040.7i			0.0762946i
$910$	−6371.06	+	25374.7i	−0.00769359	+	0.0306421i
$911$	−746557.			−0.899552			−0.449776	−	0.893141i	$-0.648496\pi$
$911$	−746557.			−0.899552			−0.449776	+	0.893141i	$0.648496\pi$
$912$	1.10413e6	−	1.10413e6i	1.32749	−	1.32749i
$913$	288223.	+	288223.i	0.345770	+	0.345770i
$914$		−	523321.i		−	0.626435i
$915$	−506283.	−	127117.i	−0.604716	−	0.151831i
$916$	−207168.			−0.246906
$917$	60957.4	−	60957.4i	0.0724917	−	0.0724917i
$918$	−977255.	−	977255.i	−1.15964	−	1.15964i
$919$			431660.i			0.511106i	0.966795	+	0.255553i	$0.0822575\pi$
$919$			431660.i			0.511106i	−0.966795	+	0.255553i	$0.917743\pi$
$920$	48097.2	+	80346.9i	0.0568257	+	0.0949278i
$921$	561748.			0.662250
$922$	−974473.	+	974473.i	−1.14633	+	1.14633i
$923$	−292310.	−	292310.i	−0.343115	−	0.343115i
$924$		−	55709.7i		−	0.0652510i
$925$	−162730.	−	538607.i	−0.190188	−	0.629490i
$926$	12320.3			0.0143681
$927$	46085.4	−	46085.4i	0.0536295	−	0.0536295i
$928$	−707986.	−	707986.i	−0.822107	−	0.822107i
$929$			338533.i			0.392256i	0.980578	+	0.196128i	$0.0628369\pi$
$929$			338533.i			0.392256i	−0.980578	+	0.196128i	$0.937163\pi$
$930$	−1.08948e6	+	652186.i	−1.25966	+	0.754059i
$931$	−1.42462e6			−1.64362
$932$	287485.	−	287485.i	0.330965	−	0.330965i
$933$	228650.	+	228650.i	0.262669	+	0.262669i
$934$			1.57940e6i			1.81050i
$935$	397813.	−	1.58441e6i	0.455047	−	1.81236i
$936$	24185.0			0.0276054
$937$	374415.	−	374415.i	0.426456	−	0.426456i	−0.460963	−	0.887419i	$-0.652496\pi$
$937$	374415.	−	374415.i	0.426456	−	0.426456i	0.887419	+	0.460963i	$0.152496\pi$
$938$	82162.6	+	82162.6i	0.0933831	+	0.0933831i
$939$		−	468468.i		−	0.531311i
$940$	757464.	+	190183.i	0.857247	+	0.215237i
$941$	419785.			0.474075			0.237038	−	0.971500i	$-0.423824\pi$
$941$	419785.			0.474075			0.237038	+	0.971500i	$0.423824\pi$
$942$	82959.3	−	82959.3i	0.0934896	−	0.0934896i
$943$	−104377.	−	104377.i	−0.117377	−	0.117377i
$944$		−	2.05577e6i		−	2.30690i
$945$	−39698.5	−	66316.7i	−0.0444540	−	0.0742608i
$946$	1.62238e6			1.81288
$947$	−114973.	+	114973.i	−0.128202	+	0.128202i	−0.768296	−	0.640094i	$-0.778895\pi$
$947$	−114973.	+	114973.i	−0.128202	+	0.128202i	0.640094	+	0.768296i	$0.278895\pi$
$948$	−274626.	−	274626.i	−0.305580	−	0.305580i
$949$			215406.i			0.239180i
$950$	−1.79534e6	+	542427.i	−1.98930	+	0.601028i
$951$	237270.			0.262351
$952$	−33854.4	+	33854.4i	−0.0373544	+	0.0373544i
$953$	447662.	+	447662.i	0.492906	+	0.492906i	0.909221	−	0.416315i	$-0.136679\pi$
$953$	447662.	+	447662.i	0.492906	+	0.492906i	−0.416315	+	0.909221i	$0.636679\pi$
$954$		−	111117.i		−	0.122091i
$955$	−522142.	+	312564.i	−0.572508	+	0.342715i
$956$	−173885.			−0.190260
$957$	−1.01477e6	+	1.01477e6i	−1.10801	+	1.10801i
$958$	−248141.	−	248141.i	−0.270376	−	0.270376i
$959$			62431.3i			0.0678836i
$960$	10652.9	−	42428.4i	0.0115591	−	0.0460378i
$961$	593087.			0.642202
$962$	167351.	−	167351.i	0.180833	−	0.180833i
$963$	194572.	+	194572.i	0.209811	+	0.209811i
$964$		−	682499.i		−	0.734425i
$965$	901298.	+	226297.i	0.967862	+	0.243010i
$966$	18108.9			0.0194061
$967$	372268.	−	372268.i	0.398110	−	0.398110i	−0.479456	−	0.877566i	$-0.659166\pi$
$967$	372268.	−	372268.i	0.398110	−	0.398110i	0.877566	+	0.479456i	$0.159166\pi$
$968$	−465709.	−	465709.i	−0.497008	−	0.497008i
$969$		−	1.73666e6i		−	1.84956i
$970$	−376891.	−	629600.i	−0.400564	−	0.669146i
$971$	563807.			0.597987			0.298993	−	0.954255i	$-0.403349\pi$
$971$	563807.			0.597987			0.298993	+	0.954255i	$0.403349\pi$
$972$	128209.	−	128209.i	0.135702	−	0.135702i
$973$	−25580.5	−	25580.5i	−0.0270198	−	0.0270198i
$974$		−	27608.3i		−	0.0291020i
$975$	236634.	+	126823.i	0.248925	+	0.133410i
$976$	−810004.			−0.850330
$977$	455228.	−	455228.i	0.476914	−	0.476914i	−0.427230	−	0.904143i	$-0.640510\pi$
$977$	455228.	−	455228.i	0.476914	−	0.476914i	0.904143	+	0.427230i	$0.140510\pi$
$978$	486228.	+	486228.i	0.508349	+	0.508349i
$979$		−	1.50070e6i		−	1.56577i
$980$	−472786.	+	283019.i	−0.492280	+	0.294689i
$981$	−153513.			−0.159517
$982$	−1.15063e6	+	1.15063e6i	−1.19320	+	1.19320i
$983$	608097.	+	608097.i	0.629312	+	0.629312i	0.947895	−	0.318583i	$-0.103207\pi$
$983$	608097.	+	608097.i	0.629312	+	0.629312i	−0.318583	+	0.947895i	$0.603207\pi$
$984$		−	373051.i		−	0.385282i
$985$	165047.	−	657350.i	0.170112	−	0.677524i
$986$	−1.68619e6			−1.73441
$987$	−78111.9	+	78111.9i	−0.0801832	+	0.0801832i
$988$	−204227.	−	204227.i	−0.209218	−	0.209218i
$989$			193074.i			0.197392i
$990$	305886.	+	76801.5i	0.312096	+	0.0783609i
$991$	1.03618e6			1.05508			0.527541	−	0.849529i	$-0.323114\pi$
$991$	1.03618e6			1.05508			0.527541	+	0.849529i	$0.323114\pi$
$992$	−920116.	+	920116.i	−0.935017	+	0.935017i
$993$	617362.	+	617362.i	0.626097	+	0.626097i
$994$			157991.i			0.159904i
$995$	−695674.	−	1.16213e6i	−0.702683	−	1.17384i
$996$	167604.			0.168953
$997$	524380.	−	524380.i	0.527541	−	0.527541i	−0.392298	−	0.919838i	$-0.628320\pi$
$997$	524380.	−	524380.i	0.527541	−	0.527541i	0.919838	+	0.392298i	$0.128320\pi$
$998$	−770801.	−	770801.i	−0.773894	−	0.773894i
$999$			699191.i			0.700592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.5.f.a.93.11	yes	88
5.2	odd	4	inner	115.5.f.a.47.11	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.f.a.47.11	✓	88	5.2	odd	4	inner
115.5.f.a.93.11	yes	88	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.55253 + 3.55253i) q^{2} +(-5.80472 - 5.80472i) q^{3} -9.24088i q^{4} +(-21.4504 + 12.8406i) q^{5} +41.2428 q^{6} +(2.81474 - 2.81474i) q^{7} +(-24.0119 - 24.0119i) q^{8} -13.6105i q^{9} +(30.5864 - 121.820i) q^{10} -184.488 q^{11} +(-53.6407 + 53.6407i) q^{12} +(-37.0012 - 37.0012i) q^{13} +19.9989i q^{14} +(199.050 + 49.9772i) q^{15} +318.460 q^{16} +(250.449 - 250.449i) q^{17} +(48.3516 + 48.3516i) q^{18} +597.288i q^{19} +(118.659 + 198.220i) q^{20} -32.6775 q^{21} +(655.399 - 655.399i) q^{22} +(77.9968 + 77.9968i) q^{23} +278.765i q^{24} +(295.237 - 550.872i) q^{25} +262.895 q^{26} +(-549.187 + 549.187i) q^{27} +(-26.0107 - 26.0107i) q^{28} +947.586i q^{29} +(-884.674 + 529.584i) q^{30} +1231.51 q^{31} +(-747.147 + 747.147i) q^{32} +(1070.90 + 1070.90i) q^{33} +1779.46i q^{34} +(-24.2342 + 96.5202i) q^{35} -125.773 q^{36} +(636.569 - 636.569i) q^{37} +(-2121.88 - 2121.88i) q^{38} +429.563i q^{39} +(823.393 + 206.737i) q^{40} -1338.23 q^{41} +(116.088 - 116.088i) q^{42} +(1237.70 + 1237.70i) q^{43} +1704.83i q^{44} +(174.767 + 291.950i) q^{45} -554.171 q^{46} +(2390.39 - 2390.39i) q^{47} +(-1848.57 - 1848.57i) q^{48} +2385.15i q^{49} +(908.151 + 3005.82i) q^{50} -2907.58 q^{51} +(-341.924 + 341.924i) q^{52} +(-1149.05 - 1149.05i) q^{53} -3902.00i q^{54} +(3957.34 - 2368.94i) q^{55} -135.175 q^{56} +(3467.09 - 3467.09i) q^{57} +(-3366.32 - 3366.32i) q^{58} -6455.33i q^{59} +(461.833 - 1839.39i) q^{60} -2543.50 q^{61} +(-4374.96 + 4374.96i) q^{62} +(-38.3099 - 38.3099i) q^{63} -213.155i q^{64} +(1268.81 + 318.571i) q^{65} -7608.81 q^{66} +(4108.36 - 4108.36i) q^{67} +(-2314.37 - 2314.37i) q^{68} -905.499i q^{69} +(-256.798 - 428.983i) q^{70} +7900.01 q^{71} +(-326.814 + 326.814i) q^{72} +(-2910.79 - 2910.79i) q^{73} +4522.86i q^{74} +(-4911.43 + 1483.89i) q^{75} +5519.46 q^{76} +(-519.286 + 519.286i) q^{77} +(-1526.03 - 1526.03i) q^{78} +5119.73i q^{79} +(-6831.09 + 4089.23i) q^{80} +5273.31 q^{81} +(4754.09 - 4754.09i) q^{82} +(-1562.28 - 1562.28i) q^{83} +301.969i q^{84} +(-2156.31 + 8588.16i) q^{85} -8793.93 q^{86} +(5500.47 - 5500.47i) q^{87} +(4429.92 + 4429.92i) q^{88} +8134.38i q^{89} +(-1658.02 - 416.295i) q^{90} -208.297 q^{91} +(720.759 - 720.759i) q^{92} +(-7148.55 - 7148.55i) q^{93} +16983.8i q^{94} +(-7669.55 - 12812.0i) q^{95} +8673.96 q^{96} +(4131.07 - 4131.07i) q^{97} +(-8473.32 - 8473.32i) q^{98} +2510.97i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 48 q^{5} + 160 q^{7} + 180 q^{8} + 16 q^{10} + 312 q^{11} - 720 q^{12} - 760 q^{13} - 60 q^{15} - 4528 q^{16} + 420 q^{17} + 980 q^{18} + 1344 q^{20} + 1976 q^{21} + 720 q^{22} - 1176 q^{25} + 1872 q^{26}+ \cdots - 22320 q^{98}+O(q^{100}) \) 88 * q - 48 * q^5 + 160 * q^7 + 180 * q^8 + 16 * q^10 + 312 * q^11 - 720 * q^12 - 760 * q^13 - 60 * q^15 - 4528 * q^16 + 420 * q^17 + 980 * q^18 + 1344 * q^20 + 1976 * q^21 + 720 * q^22 - 1176 * q^25 + 1872 * q^26 + 2820 * q^27 - 1140 * q^28 - 1160 * q^30 - 820 * q^31 - 3720 * q^32 + 820 * q^33 - 1728 * q^35 + 9504 * q^36 + 180 * q^37 + 3180 * q^38 + 8560 * q^40 + 1956 * q^41 + 5320 * q^42 - 8960 * q^43 + 2064 * q^45 - 5640 * q^47 + 3820 * q^48 - 5448 * q^50 - 6648 * q^51 - 2800 * q^52 - 2160 * q^53 - 11796 * q^55 - 1464 * q^56 - 160 * q^57 + 3740 * q^58 - 6700 * q^60 - 4496 * q^61 - 30300 * q^62 - 2740 * q^63 - 3336 * q^65 - 4104 * q^66 + 640 * q^67 + 13440 * q^68 + 6508 * q^70 + 14916 * q^71 + 44280 * q^72 + 3660 * q^73 + 15732 * q^75 - 53552 * q^76 + 10980 * q^77 + 4340 * q^78 + 10404 * q^80 - 35864 * q^81 + 32860 * q^82 + 7920 * q^83 + 14216 * q^85 + 59352 * q^86 - 38440 * q^87 - 19140 * q^88 + 7160 * q^90 + 52584 * q^91 - 20960 * q^93 + 28224 * q^95 - 26624 * q^96 + 13480 * q^97 - 22320 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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