LMFDB - Embedded newform 115.5.f.a.47.11

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			47.11
Character	$\chi$	$=$	115.47
Dual form			115.5.f.a.93.11

$q$-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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

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

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	0.106212	−	0.994344i	$-0.466128\pi$
$2$	−3.55253	−	3.55253i	−0.888131	−	0.888131i	−0.994344	+	0.106212i	$0.966128\pi$
$3$	−5.80472	+	5.80472i	−0.644969	+	0.644969i	−0.951773	−	0.306804i	$-0.900740\pi$
$3$	−5.80472	+	5.80472i	−0.644969	+	0.644969i	0.306804	+	0.951773i	$0.400740\pi$
$4$			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	0.735245	−	0.677801i	$-0.237067\pi$
$7$	2.81474	+	2.81474i	0.0574436	+	0.0574436i	−0.677801	+	0.735245i	$0.737067\pi$
$8$	−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	−0.808053	−	0.589110i	$-0.799478\pi$
$13$	−37.0012	+	37.0012i	−0.218942	+	0.218942i	0.589110	+	0.808053i	$0.299478\pi$
$14$		−	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	0.992095	−	0.125488i	$-0.0400496\pi$
$17$	250.449	+	250.449i	0.866607	+	0.866607i	−0.125488	+	0.992095i	$0.540050\pi$
$18$	48.3516	−	48.3516i	0.149233	−	0.149233i
$19$		−	597.288i		−	1.65454i	−0.561807	−	0.827268i	$-0.689894\pi$
$19$		−	597.288i		−	1.65454i	0.561807	−	0.827268i	$-0.310106\pi$
$20$	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	$-0.809505\pi$
$29$		−	947.586i		−	1.12674i	0.826206	−	0.563368i	$-0.190495\pi$
$30$	−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	0.900286	−	0.435298i	$-0.143357\pi$
$37$	636.569	+	636.569i	0.464988	+	0.464988i	−0.435298	+	0.900286i	$0.643357\pi$
$38$	−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	−0.288185	−	0.957575i	$-0.593052\pi$
$43$	1237.70	−	1237.70i	0.669390	−	0.669390i	0.957575	+	0.288185i	$0.0930518\pi$
$44$		−	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	0.996312	+	0.0858006i	$0.0273448\pi$
$47$	2390.39	+	2390.39i	1.08211	+	1.08211i	0.0858006	+	0.996312i	$0.472655\pi$
$48$	−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	−0.881411	−	0.472351i	$-0.843406\pi$
$53$	−1149.05	+	1149.05i	−0.409060	+	0.409060i	0.472351	+	0.881411i	$0.343406\pi$
$54$			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	$0.377811\pi$
$59$			6455.33i			1.85445i	−0.374509	+	0.927223i	$0.622189\pi$
$60$	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	0.996676	−	0.0814689i	$-0.0259611\pi$
$67$	4108.36	+	4108.36i	0.915207	+	0.915207i	−0.0814689	+	0.996676i	$0.525961\pi$
$68$	−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	−0.925345	−	0.379127i	$-0.876224\pi$
$73$	−2910.79	+	2910.79i	−0.546218	+	0.546218i	0.379127	+	0.925345i	$0.376224\pi$
$74$		−	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	$-0.865470\pi$
$79$		−	5119.73i		−	0.820338i	0.912010	−	0.410169i	$-0.134530\pi$
$80$	−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	−0.811346	−	0.584566i	$-0.801265\pi$
$83$	−1562.28	+	1562.28i	−0.226779	+	0.226779i	0.584566	+	0.811346i	$0.301265\pi$
$84$		−	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	$-0.828360\pi$
$89$		−	8134.38i		−	1.02694i	0.858108	−	0.513469i	$-0.171640\pi$
$90$	−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	0.891694	−	0.452639i	$-0.149517\pi$
$97$	4131.07	+	4131.07i	0.439055	+	0.439055i	−0.452639	+	0.891694i	$0.649517\pi$
$98$	−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	−0.529281	−	0.848446i	$-0.677538\pi$
$103$	3386.02	−	3386.02i	0.319165	−	0.319165i	0.848446	+	0.529281i	$0.177538\pi$
$104$		−	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	−0.956317	−	0.292332i	$-0.905569\pi$
$107$	−14295.8	−	14295.8i	−1.24865	−	1.24865i	−0.292332	−	0.956317i	$-0.594431\pi$
$108$	5074.97	−	5074.97i	0.435097	−	0.435097i
$109$			11279.1i			0.949335i	0.880165	+	0.474668i	$0.157432\pi$
$109$			11279.1i			0.949335i	−0.880165	+	0.474668i	$0.842568\pi$
$110$	−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	−0.489900	−	0.871779i	$-0.662967\pi$
$113$	4876.21	−	4876.21i	0.381878	−	0.381878i	0.871779	+	0.489900i	$0.162967\pi$
$114$		−	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	0.996140	+	0.0877818i	$0.0279778\pi$
$127$	17482.6	+	17482.6i	1.08392	+	1.08392i	0.0877818	+	0.996140i	$0.472022\pi$
$128$	−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	0.346995	−	0.937867i	$-0.387202\pi$
$137$	−11090.1	−	11090.1i	−0.590872	−	0.590872i	−0.937867	+	0.346995i	$0.887202\pi$
$138$	3216.81	−	3216.81i	0.168915	−	0.168915i
$139$			9088.05i			0.470371i	0.971950	+	0.235186i	$0.0755698\pi$
$139$			9088.05i			0.470371i	−0.971950	+	0.235186i	$0.924430\pi$
$140$	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	$0.111853\pi$
$149$			15283.6i			0.688420i	−0.938893	+	0.344210i	$0.888147\pi$
$150$	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	0.746731	−	0.665126i	$-0.231622\pi$
$157$	2011.48	+	2011.48i	0.0816051	+	0.0816051i	−0.665126	+	0.746731i	$0.731622\pi$
$158$	−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	−0.449535	−	0.893263i	$-0.648410\pi$
$163$	11789.4	−	11789.4i	0.443727	−	0.443727i	0.893263	+	0.449535i	$0.148410\pi$
$164$		−	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	0.795250	−	0.606282i	$-0.207340\pi$
$167$	5270.11	+	5270.11i	0.188967	+	0.188967i	−0.606282	+	0.795250i	$0.707340\pi$
$168$	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	0.255264	−	0.966871i	$-0.417838\pi$
$173$	36577.3	−	36577.3i	1.22214	−	1.22214i	0.966871	−	0.255264i	$-0.0821624\pi$
$174$		−	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	$-0.896604\pi$
$179$		−	20451.5i		−	0.638292i	0.947706	−	0.319146i	$-0.103396\pi$
$180$	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	−0.965612	−	0.259988i	$-0.916282\pi$
$193$	−26283.8	+	26283.8i	−0.705624	+	0.705624i	0.259988	+	0.965612i	$0.416282\pi$
$194$		−	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	0.415597	−	0.909549i	$-0.363573\pi$
$197$	−19169.8	−	19169.8i	−0.493952	−	0.493952i	−0.909549	+	0.415597i	$0.863573\pi$
$198$	−8920.29	+	8920.29i	−0.227535	+	0.227535i
$199$		−	54177.6i		−	1.36809i	−0.729441	−	0.684043i	$-0.760220\pi$
$199$		−	54177.6i		−	1.36809i	0.729441	−	0.684043i	$-0.239780\pi$
$200$	−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	−0.742544	−	0.669798i	$-0.766381\pi$
$223$	−3617.58	+	3617.58i	−0.0727458	+	0.0727458i	0.669798	+	0.742544i	$0.266381\pi$
$224$		−	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	0.874790	−	0.484502i	$-0.160999\pi$
$227$	20111.1	+	20111.1i	0.390287	+	0.390287i	−0.484502	+	0.874790i	$0.660999\pi$
$228$	−32038.9	+	32038.9i	−0.616323	+	0.616323i
$229$			22418.6i			0.427501i	0.976888	+	0.213751i	$0.0685680\pi$
$229$			22418.6i			0.427501i	−0.976888	+	0.213751i	$0.931432\pi$
$230$	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	−0.359933	−	0.932978i	$-0.617200\pi$
$233$	31110.1	−	31110.1i	0.573046	−	0.573046i	0.932978	+	0.359933i	$0.117200\pi$
$234$			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	$0.0526693\pi$
$239$			18817.0i			0.329423i	−0.986342	+	0.164711i	$0.947331\pi$
$240$	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	0.263060	−	0.964780i	$-0.415268\pi$
$257$	−46347.9	−	46347.9i	−0.701720	−	0.701720i	−0.964780	+	0.263060i	$0.915268\pi$
$258$	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	−0.864835	−	0.502057i	$-0.832577\pi$
$263$	−25093.0	+	25093.0i	−0.362777	+	0.362777i	0.502057	+	0.864835i	$0.332577\pi$
$264$			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	$-0.921031\pi$
$269$		−	35536.6i		−	0.491102i	0.969384	−	0.245551i	$-0.0789689\pi$
$270$	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	0.554931	−	0.831896i	$-0.312745\pi$
$277$	−21251.3	−	21251.3i	−0.276966	−	0.276966i	−0.831896	+	0.554931i	$0.812745\pi$
$278$	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	−0.657406	−	0.753537i	$-0.728346\pi$
$283$	7699.00	−	7699.00i	0.0961305	−	0.0961305i	0.753537	+	0.657406i	$0.228346\pi$
$284$			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	−0.785415	−	0.618970i	$-0.787550\pi$
$293$	−14289.1	+	14289.1i	−0.166445	+	0.166445i	0.618970	+	0.785415i	$0.287550\pi$
$294$		−	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	0.402169	−	0.915566i	$-0.368257\pi$
$307$	−48387.2	−	48387.2i	−0.513397	−	0.513397i	−0.915566	+	0.402169i	$0.868257\pi$
$308$	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	−0.470507	−	0.882396i	$-0.655929\pi$
$313$	40352.4	−	40352.4i	0.411889	−	0.411889i	0.882396	+	0.470507i	$0.155929\pi$
$314$		−	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	0.598065	−	0.801448i	$-0.295936\pi$
$317$	−20437.7	−	20437.7i	−0.203383	−	0.203383i	−0.801448	+	0.598065i	$0.795936\pi$
$318$	−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	0.170583	−	0.985343i	$-0.445435\pi$
$337$	−92531.5	−	92531.5i	−0.814760	−	0.814760i	−0.985343	+	0.170583i	$0.945435\pi$
$338$	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	0.950835	+	0.309698i	$0.100228\pi$
$347$	151780.	+	151780.i	1.26053	+	1.26053i	0.309698	+	0.950835i	$0.399772\pi$
$348$	−50829.2	+	50829.2i	−0.419715	+	0.419715i
$349$		−	100880.i		−	0.828239i	−0.910223	−	0.414119i	$-0.864090\pi$
$349$		−	100880.i		−	0.828239i	0.910223	−	0.414119i	$-0.135910\pi$
$350$	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	−0.503810	−	0.863814i	$-0.668069\pi$
$353$	44859.7	−	44859.7i	0.360004	−	0.360004i	0.863814	+	0.503810i	$0.168069\pi$
$354$			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	$0.0911866\pi$
$359$			72835.5i			0.565138i	−0.959247	+	0.282569i	$0.908813\pi$
$360$	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	0.427489	−	0.904020i	$-0.359398\pi$
$367$	−64183.5	−	64183.5i	−0.476531	−	0.476531i	−0.904020	+	0.427489i	$0.859398\pi$
$368$	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	−0.232383	+	0.972624i	$0.574652\pi$
$373$	−167651.	+	167651.i	−1.20501	+	1.20501i	−0.972624	+	0.232383i	$0.925348\pi$
$374$			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	$0.0588318\pi$
$379$			52795.3i			0.367550i	−0.982968	+	0.183775i	$0.941168\pi$
$380$	−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	−0.373565	−	0.927604i	$-0.621865\pi$
$383$	81271.5	−	81271.5i	0.554040	−	0.554040i	0.927604	+	0.373565i	$0.121865\pi$
$384$		−	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	$-0.932269\pi$
$389$		−	63912.5i		−	0.422364i	0.977447	−	0.211182i	$-0.0677312\pi$
$390$	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	0.980617	+	0.195936i	$0.0627745\pi$
$397$	185435.	+	185435.i	1.17655	+	1.17655i	0.195936	+	0.980617i	$0.437225\pi$
$398$	−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	$-0.984927\pi$
$409$		−	15836.9i		−	0.0946727i	0.998879	−	0.0473363i	$-0.0150733\pi$
$410$	−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	$-0.986256\pi$
$419$		−	15156.5i		−	0.0863318i	0.999068	−	0.0431659i	$-0.0137444\pi$
$420$	−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	−0.412898	−	0.910777i	$-0.635484\pi$
$433$	93346.8	−	93346.8i	0.497879	−	0.497879i	0.910777	+	0.412898i	$0.135484\pi$
$434$		−	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	$-0.888940\pi$
$439$		−	131771.i		−	0.683737i	0.939748	−	0.341869i	$-0.111060\pi$
$440$	−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	−0.710978	−	0.703214i	$-0.751747\pi$
$443$	−1523.66	+	1523.66i	−0.00776389	+	0.00776389i	0.703214	+	0.710978i	$0.251747\pi$
$444$		−	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	$0.139690\pi$
$449$			171320.i			0.849795i	−0.905241	+	0.424898i	$0.860310\pi$
$450$	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	0.508432	−	0.861102i	$-0.330225\pi$
$457$	−73654.8	−	73654.8i	−0.352670	−	0.352670i	−0.861102	+	0.508432i	$0.830225\pi$
$458$	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	−0.711140	−	0.703051i	$-0.751821\pi$
$463$	−1734.02	+	1734.02i	−0.00808894	+	0.00808894i	0.703051	+	0.711140i	$0.251821\pi$
$464$		−	301768.i		−	1.40164i
$465$	245131.	−	61547.2i	1.13368	−	0.284644i
$466$	−221039.			−1.01788
$467$	222292.	+	222292.i	1.01927	+	1.01927i	0.999811	+	0.0194620i	$0.00619532\pi$
$467$	222292.	+	222292.i	1.01927	+	1.01927i	0.0194620	+	0.999811i	$0.493805\pi$
$468$	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	$-0.951359\pi$
$479$		−	69849.2i		−	0.304432i	0.988347	−	0.152216i	$-0.0486410\pi$
$480$	−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	0.698867	−	0.715251i	$-0.253688\pi$
$487$	−3885.73	−	3885.73i	−0.0163838	−	0.0163838i	−0.715251	+	0.698867i	$0.753688\pi$
$488$	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	$-0.856506\pi$
$499$		−	216973.i		−	0.871373i	0.900099	−	0.435686i	$-0.143494\pi$
$500$	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	0.249056	−	0.968489i	$-0.419880\pi$
$503$	308050.	−	308050.i	1.21755	−	1.21755i	0.968489	−	0.249056i	$-0.0801204\pi$
$504$		−	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	$0.377246\pi$
$509$			480107.i			1.85311i	−0.376154	+	0.926557i	$0.622754\pi$
$510$	−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	−0.750820	−	0.660507i	$-0.770341\pi$
$523$	−24703.1	+	24703.1i	−0.0903125	+	0.0903125i	0.660507	+	0.750820i	$0.270341\pi$
$524$			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	0.749829	−	0.661631i	$-0.230136\pi$
$547$	26389.6	+	26389.6i	0.0881978	+	0.0881978i	−0.661631	+	0.749829i	$0.730136\pi$
$548$	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	0.440026	−	0.897985i	$-0.354969\pi$
$557$	−142081.	−	142081.i	−0.457959	−	0.457959i	−0.897985	+	0.440026i	$0.854969\pi$
$558$	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	−0.501270	−	0.865291i	$-0.667134\pi$
$563$	115383.	−	115383.i	0.364021	−	0.364021i	0.865291	+	0.501270i	$0.167134\pi$
$564$		−	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	$-0.987503\pi$
$569$		−	25415.5i		−	0.0785008i	0.999229	−	0.0392504i	$-0.0124970\pi$
$570$	−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	0.911995	−	0.410202i	$-0.134542\pi$
$577$	167061.	+	167061.i	0.501793	+	0.501793i	−0.410202	+	0.911995i	$0.634542\pi$
$578$	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	0.519796	−	0.854290i	$-0.326008\pi$
$587$	−115256.	−	115256.i	−0.334494	−	0.334494i	−0.854290	+	0.519796i	$0.826008\pi$
$588$	−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	−0.835527	−	0.549449i	$-0.814837\pi$
$593$	−100599.	+	100599.i	−0.286077	+	0.286077i	0.549449	+	0.835527i	$0.314837\pi$
$594$		−	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	$0.248969\pi$
$599$			505775.i			1.40962i	−0.709394	+	0.704812i	$0.751031\pi$
$600$	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	0.948602	+	0.316470i	$0.102498\pi$
$607$	466115.	+	466115.i	1.26507	+	1.26507i	0.316470	+	0.948602i	$0.397502\pi$
$608$	−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	−0.143426	+	0.989661i	$0.545812\pi$
$613$	−425779.	+	425779.i	−1.13309	+	1.13309i	−0.989661	+	0.143426i	$0.954188\pi$
$614$			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	0.999686	−	0.0250764i	$-0.00798290\pi$
$617$	371023.	+	371023.i	0.974609	+	0.974609i	−0.0250764	+	0.999686i	$0.507983\pi$
$618$	139649.	−	139649.i	0.365646	−	0.365646i
$619$		−	735915.i		−	1.92064i	−0.278895	−	0.960322i	$-0.589968\pi$
$619$		−	735915.i		−	1.92064i	0.278895	−	0.960322i	$-0.410032\pi$
$620$	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	−0.652374	−	0.757897i	$-0.726227\pi$
$643$	43628.3	−	43628.3i	0.105523	−	0.105523i	0.757897	+	0.652374i	$0.226227\pi$
$644$			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	0.998516	+	0.0544523i	$0.0173413\pi$
$647$	440782.	+	440782.i	1.05297	+	1.05297i	0.0544523	+	0.998516i	$0.482659\pi$
$648$	−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	−0.946059	−	0.323995i	$-0.894974\pi$
$653$	−265254.	+	265254.i	−0.622064	+	0.622064i	0.323995	+	0.946059i	$0.394974\pi$
$654$			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	$-0.823927\pi$
$659$		−	456316.i		−	1.05074i	0.850874	−	0.525369i	$-0.176073\pi$
$660$	−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	−0.167871	+	0.985809i	$0.553689\pi$
$673$	−522535.	+	522535.i	−1.15368	+	1.15368i	−0.985809	+	0.167871i	$0.946311\pi$
$674$			657441.i			1.44723i
$675$	140392.	−	464672.i	0.308130	−	1.01986i
$676$	−238626.			−0.522184
$677$	−220817.	−	220817.i	−0.481788	−	0.481788i	0.423914	−	0.905702i	$-0.360656\pi$
$677$	−220817.	−	220817.i	−0.481788	−	0.481788i	−0.905702	+	0.423914i	$0.860656\pi$
$678$	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	−0.688146	−	0.725572i	$-0.741575\pi$
$683$	17459.2	−	17459.2i	0.0374268	−	0.0374268i	0.725572	+	0.688146i	$0.241575\pi$
$684$			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	$0.253655\pi$
$709$			719014.i			1.43036i	−0.698942	+	0.715179i	$0.746345\pi$
$710$	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	$-0.726003\pi$
$719$		−	784081.i		−	1.51671i	0.651841	−	0.758356i	$-0.273997\pi$
$720$	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	0.379794	−	0.925071i	$-0.375995\pi$
$727$	−288195.	−	288195.i	−0.545277	−	0.545277i	−0.925071	+	0.379794i	$0.875995\pi$
$728$	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	−0.961635	−	0.274333i	$-0.911543\pi$
$733$	−369280.	+	369280.i	−0.687302	+	0.687302i	0.274333	+	0.961635i	$0.411543\pi$
$734$			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	$-0.963876\pi$
$739$		−	123689.i		−	0.226486i	0.993567	−	0.113243i	$-0.0361239\pi$
$740$	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	−0.327549	+	0.944834i	$0.606223\pi$
$743$	−702418.	+	702418.i	−1.27238	+	1.27238i	−0.944834	+	0.327549i	$0.893777\pi$
$744$		−	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	0.543618	−	0.839333i	$-0.317054\pi$
$757$	−169459.	−	169459.i	−0.295715	−	0.295715i	−0.839333	+	0.543618i	$0.817054\pi$
$758$	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	$-0.838498\pi$
$769$		−	574664.i		−	0.971765i	0.874024	−	0.485883i	$-0.161502\pi$
$770$	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	−0.465316	−	0.885144i	$-0.654059\pi$
$773$	250860.	−	250860.i	0.419828	−	0.419828i	0.885144	+	0.465316i	$0.154059\pi$
$774$		−	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	0.996481	−	0.0838197i	$-0.0267120\pi$
$787$	565274.	+	565274.i	0.912661	+	0.912661i	−0.0838197	+	0.996481i	$0.526712\pi$
$788$	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	0.871713	−	0.490017i	$-0.163010\pi$
$797$	242456.	+	242456.i	0.381695	+	0.381695i	−0.490017	+	0.871713i	$0.663010\pi$
$798$	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	$0.0719513\pi$
$809$			293367.i			0.448243i	−0.974561	+	0.224122i	$0.928049\pi$
$810$	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	−0.864181	−	0.503181i	$-0.832163\pi$
$823$	−244515.	+	244515.i	−0.361000	+	0.361000i	0.503181	+	0.864181i	$0.332163\pi$
$824$			162610.i			0.239493i
$825$	906100.	+	273760.i	1.33128	+	0.402219i
$826$	129099.			0.189218
$827$	−301109.	−	301109.i	−0.440263	−	0.440263i	0.451837	−	0.892100i	$-0.350769\pi$
$827$	−301109.	−	301109.i	−0.440263	−	0.440263i	−0.892100	+	0.451837i	$0.850769\pi$
$828$	−9809.87	+	9809.87i	−0.0143088	+	0.0143088i
$829$		−	954722.i		−	1.38921i	−0.719391	−	0.694605i	$-0.755579\pi$
$829$		−	954722.i		−	1.38921i	0.719391	−	0.694605i	$-0.244421\pi$
$830$	−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	$-0.714773\pi$
$839$		−	1.09935e6i		−	1.56175i	0.624685	−	0.780877i	$-0.285227\pi$
$840$	−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	−0.550277	−	0.834982i	$-0.685478\pi$
$853$	207155.	−	207155.i	0.284706	−	0.284706i	0.834982	+	0.550277i	$0.185478\pi$
$854$			50867.1i			0.0697464i
$855$	−174378.	−	104386.i	−0.238539	−	0.142794i
$856$	686539.			0.936953
$857$	285095.	+	285095.i	0.388176	+	0.388176i	0.874036	−	0.485860i	$-0.161494\pi$
$857$	285095.	+	285095.i	0.388176	+	0.388176i	−0.485860	+	0.874036i	$0.661494\pi$
$858$	281535.	−	281535.i	0.382435	−	0.382435i
$859$			868658.i			1.17723i	0.808412	+	0.588617i	$0.200327\pi$
$859$			868658.i			1.17723i	−0.808412	+	0.588617i	$0.799673\pi$
$860$	−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	−0.977957	−	0.208805i	$-0.933043\pi$
$863$	−572841.	+	572841.i	−0.769152	+	0.769152i	0.208805	+	0.977957i	$0.433043\pi$
$864$			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	0.522522	−	0.852626i	$-0.324991\pi$
$877$	−253892.	−	253892.i	−0.330104	−	0.330104i	−0.852626	+	0.522522i	$0.824991\pi$
$878$	−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	−0.972303	−	0.233724i	$-0.924909\pi$
$883$	−575862.	+	575862.i	−0.738578	+	0.738578i	0.233724	+	0.972303i	$0.424909\pi$
$884$		−	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	0.350555	−	0.936542i	$-0.385993\pi$
$887$	−461037.	−	461037.i	−0.585988	−	0.585988i	−0.936542	+	0.350555i	$0.885993\pi$
$888$	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	0.984121	−	0.177498i	$-0.0568002\pi$
$907$	663568.	+	663568.i	0.806624	+	0.806624i	−0.177498	+	0.984121i	$0.556800\pi$
$908$	−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	$-0.917743\pi$
$919$		−	431660.i		−	0.511106i	0.966795	−	0.255553i	$-0.0822575\pi$
$920$	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	$-0.937163\pi$
$929$		−	338533.i		−	0.392256i	0.980578	−	0.196128i	$-0.0628369\pi$
$930$	−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	0.887419	−	0.460963i	$-0.152496\pi$
$937$	374415.	+	374415.i	0.426456	+	0.426456i	−0.460963	+	0.887419i	$0.652496\pi$
$938$	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	0.640094	−	0.768296i	$-0.278895\pi$
$947$	−114973.	−	114973.i	−0.128202	−	0.128202i	−0.768296	+	0.640094i	$0.778895\pi$
$948$	−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	−0.416315	−	0.909221i	$-0.636679\pi$
$953$	447662.	−	447662.i	0.492906	−	0.492906i	0.909221	+	0.416315i	$0.136679\pi$
$954$			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	0.877566	−	0.479456i	$-0.159166\pi$
$967$	372268.	+	372268.i	0.398110	+	0.398110i	−0.479456	+	0.877566i	$0.659166\pi$
$968$	−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	0.904143	−	0.427230i	$-0.140510\pi$
$977$	455228.	+	455228.i	0.476914	+	0.476914i	−0.427230	+	0.904143i	$0.640510\pi$
$978$	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	−0.318583	−	0.947895i	$-0.603207\pi$
$983$	608097.	−	608097.i	0.629312	−	0.629312i	0.947895	+	0.318583i	$0.103207\pi$
$984$			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	0.919838	−	0.392298i	$-0.128320\pi$
$997$	524380.	+	524380.i	0.527541	+	0.527541i	−0.392298	+	0.919838i	$0.628320\pi$
$998$	−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.47.11	✓	88
5.3	odd	4	inner	115.5.f.a.93.11	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.f.a.47.11	✓	88	1.1	even	1	trivial
115.5.f.a.93.11	yes	88	5.3	odd	4	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
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

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