LMFDB - Embedded newform 289.4.b.d.288.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(288,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("289.288");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.0515519917$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 43x^{6} + 505x^{4} + 1528x^{2} + 1296 $ x^8 + 43x^6 + 505x^4 + 1528*x^2 + 1296
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			288.7
Root			$-3.68488i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.4.b.d.288.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.68488 q^{2} -9.05894i q^{3} +5.57832 q^{4} +7.08909i q^{5} -33.3811i q^{6} -28.1854i q^{7} -8.92359 q^{8} -55.0643 q^{9} +O(q^{10})$	\(q+3.68488 q^{2} -9.05894i q^{3} +5.57832 q^{4} +7.08909i q^{5} -33.3811i q^{6} -28.1854i q^{7} -8.92359 q^{8} -55.0643 q^{9} +26.1224i q^{10} +15.3047i q^{11} -50.5336i q^{12} +2.51532 q^{13} -103.860i q^{14} +64.2196 q^{15} -77.5089 q^{16} -202.905 q^{18} -14.3453 q^{19} +39.5452i q^{20} -255.330 q^{21} +56.3958i q^{22} -180.191i q^{23} +80.8383i q^{24} +74.7448 q^{25} +9.26864 q^{26} +254.233i q^{27} -157.227i q^{28} +41.2425i q^{29} +236.641 q^{30} +155.242i q^{31} -214.222 q^{32} +138.644 q^{33} +199.809 q^{35} -307.167 q^{36} -225.676i q^{37} -52.8606 q^{38} -22.7861i q^{39} -63.2602i q^{40} -234.306i q^{41} -940.860 q^{42} +321.875 q^{43} +85.3743i q^{44} -390.356i q^{45} -663.983i q^{46} -326.183 q^{47} +702.148i q^{48} -451.418 q^{49} +275.425 q^{50} +14.0313 q^{52} +57.1579 q^{53} +936.818i q^{54} -108.496 q^{55} +251.515i q^{56} +129.953i q^{57} +151.974i q^{58} +241.623 q^{59} +358.238 q^{60} -460.925i q^{61} +572.046i q^{62} +1552.01i q^{63} -169.311 q^{64} +17.8313i q^{65} +510.886 q^{66} +392.696 q^{67} -1632.34 q^{69} +736.272 q^{70} +615.558i q^{71} +491.372 q^{72} -697.452i q^{73} -831.587i q^{74} -677.109i q^{75} -80.0226 q^{76} +431.369 q^{77} -83.9641i q^{78} -991.317i q^{79} -549.468i q^{80} +816.345 q^{81} -863.387i q^{82} +98.9057 q^{83} -1424.31 q^{84} +1186.07 q^{86} +373.613 q^{87} -136.573i q^{88} +698.470 q^{89} -1438.41i q^{90} -70.8954i q^{91} -1005.16i q^{92} +1406.32 q^{93} -1201.94 q^{94} -101.695i q^{95} +1940.62i q^{96} -1428.66i q^{97} -1663.42 q^{98} -842.741i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 22 q^{4} - 120 q^{8} - 12 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 22 * q^4 - 120 * q^8 - 12 * q^9	$ 8 q - 2 q^{2} + 22 q^{4} - 120 q^{8} - 12 q^{9} - 44 q^{13} - 108 q^{15} + 126 q^{16} - 668 q^{18} - 44 q^{19} - 704 q^{21} - 756 q^{25} + 896 q^{26} + 626 q^{30} - 662 q^{32} + 188 q^{33} - 484 q^{35} - 282 q^{36} - 1048 q^{38} - 2910 q^{42} + 228 q^{43} + 20 q^{47} - 2012 q^{49} + 1610 q^{50} - 3074 q^{52} - 100 q^{53} - 2632 q^{55} - 1992 q^{59} + 434 q^{60} - 300 q^{64} + 2180 q^{66} - 1736 q^{67} - 2256 q^{69} - 2104 q^{70} - 78 q^{72} + 1746 q^{76} + 1788 q^{77} + 2160 q^{81} - 1700 q^{83} + 886 q^{84} + 4822 q^{86} + 768 q^{87} + 1568 q^{89} + 3100 q^{93} - 2238 q^{94} - 3754 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 22 * q^4 - 120 * q^8 - 12 * q^9 - 44 * q^13 - 108 * q^15 + 126 * q^16 - 668 * q^18 - 44 * q^19 - 704 * q^21 - 756 * q^25 + 896 * q^26 + 626 * q^30 - 662 * q^32 + 188 * q^33 - 484 * q^35 - 282 * q^36 - 1048 * q^38 - 2910 * q^42 + 228 * q^43 + 20 * q^47 - 2012 * q^49 + 1610 * q^50 - 3074 * q^52 - 100 * q^53 - 2632 * q^55 - 1992 * q^59 + 434 * q^60 - 300 * q^64 + 2180 * q^66 - 1736 * q^67 - 2256 * q^69 - 2104 * q^70 - 78 * q^72 + 1746 * q^76 + 1788 * q^77 + 2160 * q^81 - 1700 * q^83 + 886 * q^84 + 4822 * q^86 + 768 * q^87 + 1568 * q^89 + 3100 * q^93 - 2238 * q^94 - 3754 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	3.68488	1.30280	0.651400	−	0.758734i	$-0.274182\pi$
$2$	3.68488	1.30280	0.651400	+	0.758734i	$0.274182\pi$
$3$	− 9.05894i	− 1.74339i	−0.490046	−	0.871697i	$-0.663020\pi$
$3$	− 9.05894i	− 1.74339i	0.490046	−	0.871697i	$-0.336980\pi$
$4$	5.57832	0.697290
$5$	7.08909i	0.634067i	0.948414	+	0.317034i	$0.102687\pi$
$5$	7.08909i	0.634067i	−0.948414	+	0.317034i	$0.897313\pi$
$6$	− 33.3811i	− 2.27129i
$7$	− 28.1854i	− 1.52187i	−0.648828	−	0.760935i	$-0.724741\pi$
$7$	− 28.1854i	− 1.52187i	0.648828	−	0.760935i	$-0.275259\pi$
$8$	−8.92359	−0.394371
$9$	−55.0643	−2.03942
$10$	26.1224i	0.826064i
$11$	15.3047i	0.419503i	0.977755	+	0.209751i	$0.0672655\pi$
$11$	15.3047i	0.419503i	−0.977755	+	0.209751i	$0.932735\pi$
$12$	− 50.5336i	− 1.21565i
$13$	2.51532	0.0536634	0.0268317	−	0.999640i	$-0.491458\pi$
$13$	2.51532	0.0536634	0.0268317	+	0.999640i	$0.491458\pi$
$14$	− 103.860i	− 1.98269i
$15$	64.2196	1.10543
$16$	−77.5089	−1.21108
$17$	0	0
$17$	0	0
$18$	−202.905	−2.65696
$19$	−14.3453	−0.173212	−0.0866062	−	0.996243i	$-0.527602\pi$
$19$	−14.3453	−0.173212	−0.0866062	+	0.996243i	$0.527602\pi$
$20$	39.5452i	0.442129i
$21$	−255.330	−2.65322
$22$	56.3958i	0.546529i
$23$	− 180.191i	− 1.63359i	−0.576931	−	0.816793i	$-0.695750\pi$
$23$	− 180.191i	− 1.63359i	0.576931	−	0.816793i	$-0.304250\pi$
$24$	80.8383i	0.687544i
$25$	74.7448	0.597958
$26$	9.26864	0.0699127
$27$	254.233i	1.81212i
$28$	− 157.227i	− 1.06118i
$29$	41.2425i	0.264088i	0.991244	+	0.132044i	$0.0421540\pi$
$29$	41.2425i	0.264088i	−0.991244	+	0.132044i	$0.957846\pi$
$30$	236.641	1.44015
$31$	155.242i	0.899426i	0.893173	+	0.449713i	$0.148474\pi$
$31$	155.242i	0.899426i	−0.893173	+	0.449713i	$0.851526\pi$
$32$	−214.222	−1.18342
$33$	138.644	0.731358
$34$	0	0
$35$	199.809	0.964968
$36$	−307.167	−1.42207
$37$	− 225.676i	− 1.00273i	−0.865237	−	0.501363i	$-0.832832\pi$
$37$	− 225.676i	− 1.00273i	0.865237	−	0.501363i	$-0.167168\pi$
$38$	−52.8606	−0.225661
$39$	− 22.7861i	− 0.0935564i
$40$	− 63.2602i	− 0.250058i
$41$	− 234.306i	− 0.892497i	−0.894909	−	0.446249i	$-0.852760\pi$
$41$	− 234.306i	− 0.892497i	0.894909	−	0.446249i	$-0.147240\pi$
$42$	−940.860	−3.45661
$43$	321.875	1.14152	0.570761	−	0.821117i	$-0.306648\pi$
$43$	321.875	1.14152	0.570761	+	0.821117i	$0.306648\pi$
$44$	85.3743i	0.292515i
$45$	− 390.356i	− 1.29313i
$46$	− 663.983i	− 2.12824i
$47$	−326.183	−1.01231	−0.506156	−	0.862442i	$-0.668934\pi$
$47$	−326.183	−1.01231	−0.506156	+	0.862442i	$0.668934\pi$
$48$	702.148i	2.11138i
$49$	−451.418	−1.31609
$50$	275.425	0.779021
$51$	0	0
$52$	14.0313	0.0374189
$53$	57.1579	0.148137	0.0740683	−	0.997253i	$-0.476402\pi$
$53$	57.1579	0.148137	0.0740683	+	0.997253i	$0.476402\pi$
$54$	936.818i	2.36083i
$55$	−108.496	−0.265993
$56$	251.515i	0.600181i
$57$	129.953i	0.301977i
$58$	151.974i	0.344054i
$59$	241.623	0.533164	0.266582	−	0.963812i	$-0.414106\pi$
$59$	241.623	0.533164	0.266582	+	0.963812i	$0.414106\pi$
$60$	358.238	0.770805
$61$	− 460.925i	− 0.967465i	−0.875216	−	0.483732i	$-0.839281\pi$
$61$	− 460.925i	− 0.967465i	0.875216	−	0.483732i	$-0.160719\pi$
$62$	572.046i	1.17177i
$63$	1552.01i	3.10373i
$64$	−169.311	−0.330685
$65$	17.8313i	0.0340262i
$66$	510.886	0.952814
$67$	392.696	0.716052	0.358026	−	0.933712i	$-0.383450\pi$
$67$	392.696	0.716052	0.358026	+	0.933712i	$0.383450\pi$
$68$	0	0
$69$	−1632.34	−2.84798
$70$	736.272	1.25716
$71$	615.558i	1.02892i	0.857515	+	0.514460i	$0.172007\pi$
$71$	615.558i	1.02892i	−0.857515	+	0.514460i	$0.827993\pi$
$72$	491.372	0.804288
$73$	− 697.452i	− 1.11823i	−0.829091	−	0.559114i	$-0.811142\pi$
$73$	− 697.452i	− 1.11823i	0.829091	−	0.559114i	$-0.188858\pi$
$74$	− 831.587i	− 1.30635i
$75$	− 677.109i	− 1.04248i
$76$	−80.0226	−0.120779
$77$	431.369	0.638429
$78$	− 83.9641i	− 0.121885i
$79$	− 991.317i	− 1.41180i	−0.708313	−	0.705898i	$-0.750544\pi$
$79$	− 991.317i	− 1.41180i	0.708313	−	0.705898i	$-0.249456\pi$
$80$	− 549.468i	− 0.767904i
$81$	816.345	1.11981
$82$	− 863.387i	− 1.16275i
$83$	98.9057	0.130799	0.0653995	−	0.997859i	$-0.479168\pi$
$83$	98.9057	0.130799	0.0653995	+	0.997859i	$0.479168\pi$
$84$	−1424.31	−1.85006
$85$	0	0
$86$	1186.07	1.48717
$87$	373.613	0.460409
$88$	− 136.573i	− 0.165440i
$89$	698.470	0.831884	0.415942	−	0.909391i	$-0.363452\pi$
$89$	698.470	0.831884	0.415942	+	0.909391i	$0.363452\pi$
$90$	− 1438.41i	− 1.68469i
$91$	− 70.8954i	− 0.0816687i
$92$	− 1005.16i	− 1.13908i
$93$	1406.32	1.56805
$94$	−1201.94	−1.31884
$95$	− 101.695i	− 0.109828i
$96$	1940.62i	2.06317i
$97$	− 1428.66i	− 1.49545i	−0.664009	−	0.747725i	$-0.731146\pi$
$97$	− 1428.66i	− 1.49545i	0.664009	−	0.747725i	$-0.268854\pi$
$98$	−1663.42	−1.71460
$99$	− 842.741i	− 0.855542i
$100$	416.950	0.416950
$101$	408.671	0.402617	0.201308	−	0.979528i	$-0.435481\pi$
$101$	408.671	0.402617	0.201308	+	0.979528i	$0.435481\pi$
$102$	0	0
$103$	1649.55	1.57801	0.789007	−	0.614384i	$-0.210596\pi$
$103$	1649.55	1.57801	0.789007	+	0.614384i	$0.210596\pi$
$104$	−22.4457	−0.0211633
$105$	− 1810.06i	− 1.68232i
$106$	210.620	0.192993
$107$	2055.01i	1.85668i	0.371731	+	0.928340i	$0.378764\pi$
$107$	2055.01i	1.85668i	−0.371731	+	0.928340i	$0.621236\pi$
$108$	1418.19i	1.26357i
$109$	445.064i	0.391095i	0.980694	+	0.195548i	$0.0626485\pi$
$109$	445.064i	0.391095i	−0.980694	+	0.195548i	$0.937352\pi$
$110$	−399.795	−0.346536
$111$	−2044.38	−1.74814
$112$	2184.62i	1.84310i
$113$	− 1226.02i	− 1.02066i	−0.859979	−	0.510330i	$-0.829523\pi$
$113$	− 1226.02i	− 1.02066i	0.859979	−	0.510330i	$-0.170477\pi$
$114$	478.861i	0.393416i
$115$	1277.39	1.03580
$116$	230.064i	0.184146i
$117$	−138.504	−0.109442
$118$	890.352	0.694607
$119$	0	0
$120$	−573.070	−0.435949
$121$	1096.77	0.824017
$122$	− 1698.45i	− 1.26041i
$123$	−2122.56	−1.55597
$124$	865.987i	0.627161i
$125$	1416.01i	1.01321i
$126$	5718.97i	4.04354i
$127$	591.124	0.413022	0.206511	−	0.978444i	$-0.433789\pi$
$127$	591.124	0.413022	0.206511	+	0.978444i	$0.433789\pi$
$128$	1089.89	0.752604
$129$	− 2915.84i	− 1.99012i
$130$	65.7063i	0.0443294i
$131$	2025.27i	1.35075i	0.737474	+	0.675375i	$0.236018\pi$
$131$	2025.27i	1.35075i	−0.737474	+	0.675375i	$0.763982\pi$
$132$	773.401	0.509969
$133$	404.328i	0.263607i
$134$	1447.04	0.932873
$135$	−1802.28	−1.14901
$136$	0	0
$137$	623.919	0.389087	0.194544	−	0.980894i	$-0.437677\pi$
$137$	623.919	0.389087	0.194544	+	0.980894i	$0.437677\pi$
$138$	−6014.98	−3.71036
$139$	− 1033.14i	− 0.630429i	−0.949020	−	0.315214i	$-0.897924\pi$
$139$	− 1033.14i	− 0.630429i	0.949020	−	0.315214i	$-0.102076\pi$
$140$	1114.60	0.672863
$141$	2954.87i	1.76486i
$142$	2268.25i	1.34048i
$143$	38.4961i	0.0225119i
$144$	4267.98	2.46989
$145$	−292.372	−0.167449
$146$	− 2570.02i	− 1.45683i
$147$	4089.37i	2.29446i
$148$	− 1258.89i	− 0.699190i
$149$	−284.476	−0.156411	−0.0782054	−	0.996937i	$-0.524919\pi$
$149$	−284.476	−0.156411	−0.0782054	+	0.996937i	$0.524919\pi$
$150$	− 2495.06i	− 1.35814i
$151$	−3153.25	−1.69939	−0.849696	−	0.527273i	$-0.823214\pi$
$151$	−3153.25	−1.69939	−0.849696	+	0.527273i	$0.823214\pi$
$152$	128.012	0.0683099
$153$	0	0
$154$	1589.54	0.831745
$155$	−1100.52	−0.570297
$156$	− 127.108i	− 0.0652359i
$157$	−482.335	−0.245188	−0.122594	−	0.992457i	$-0.539121\pi$
$157$	−482.335	−0.245188	−0.122594	+	0.992457i	$0.539121\pi$
$158$	− 3652.88i	− 1.83929i
$159$	− 517.790i	− 0.258261i
$160$	− 1518.64i	− 0.750369i
$161$	−5078.77	−2.48611
$162$	3008.13	1.45890
$163$	3717.39i	1.78631i	0.449749	+	0.893155i	$0.351513\pi$
$163$	3717.39i	1.78631i	−0.449749	+	0.893155i	$0.648487\pi$
$164$	− 1307.03i	− 0.622329i
$165$	982.860i	0.463731i
$166$	364.455	0.170405
$167$	2128.93i	0.986475i	0.869895	+	0.493237i	$0.164187\pi$
$167$	2128.93i	0.986475i	−0.869895	+	0.493237i	$0.835813\pi$
$168$	2278.46	1.04635
$169$	−2190.67	−0.997120
$170$	0	0
$171$	789.914	0.353253
$172$	1795.52	0.795971
$173$	− 1197.86i	− 0.526426i	−0.964738	−	0.263213i	$-0.915218\pi$
$173$	− 1197.86i	− 0.526426i	0.964738	−	0.263213i	$-0.0847822\pi$
$174$	1376.72	0.599821
$175$	− 2106.71i	− 0.910015i
$176$	− 1186.25i	− 0.508050i
$177$	− 2188.85i	− 0.929515i
$178$	2573.78	1.08378
$179$	−4095.63	−1.71018	−0.855089	−	0.518482i	$-0.826497\pi$
$179$	−4095.63	−1.71018	−0.855089	+	0.518482i	$0.826497\pi$
$180$	− 2177.53i	− 0.901687i
$181$	− 1297.08i	− 0.532660i	−0.963882	−	0.266330i	$-0.914189\pi$
$181$	− 1297.08i	− 0.532660i	0.963882	−	0.266330i	$-0.0858110\pi$
$182$	− 261.241i	− 0.106398i
$183$	−4175.49	−1.68667
$184$	1607.95i	0.644239i
$185$	1599.83	0.635795
$186$	5182.13	2.04286
$187$	0	0
$188$	−1819.55	−0.705876
$189$	7165.67	2.75781
$190$	− 374.734i	− 0.143084i
$191$	4381.72	1.65995	0.829974	−	0.557803i	$-0.188355\pi$
$191$	4381.72	1.65995	0.829974	+	0.557803i	$0.188355\pi$
$192$	1533.77i	0.576514i
$193$	1022.20i	0.381240i	0.981664	+	0.190620i	$0.0610498\pi$
$193$	1022.20i	0.381240i	−0.981664	+	0.190620i	$0.938950\pi$
$194$	− 5264.44i	− 1.94827i
$195$	161.533	0.0593211
$196$	−2518.15	−0.917695
$197$	− 2202.50i	− 0.796555i	−0.917265	−	0.398278i	$-0.869608\pi$
$197$	− 2202.50i	− 0.796555i	0.917265	−	0.398278i	$-0.130392\pi$
$198$	− 3105.40i	− 1.11460i
$199$	76.0165i	0.0270787i	0.999908	+	0.0135394i	$0.00430985\pi$
$199$	76.0165i	0.0270787i	−0.999908	+	0.0135394i	$0.995690\pi$
$200$	−666.992	−0.235817
$201$	− 3557.41i	− 1.24836i
$202$	1505.90	0.524529
$203$	1162.44	0.401907
$204$	0	0
$205$	1661.01	0.565904
$206$	6078.40	2.05584
$207$	9922.12i	3.33157i
$208$	−194.960	−0.0649905
$209$	− 219.550i	− 0.0726631i
$210$	− 6669.84i	− 2.19173i
$211$	1972.63i	0.643609i	0.946806	+	0.321804i	$0.104289\pi$
$211$	1972.63i	0.643609i	−0.946806	+	0.321804i	$0.895711\pi$
$212$	318.845	0.103294
$213$	5576.30	1.79381
$214$	7572.44i	2.41889i
$215$	2281.80i	0.723801i
$216$	− 2268.67i	− 0.714647i
$217$	4375.55	1.36881
$218$	1640.01i	0.509520i
$219$	−6318.17	−1.94951
$220$	−605.226	−0.185474
$221$	0	0
$222$	−7533.29	−2.27748
$223$	−1177.47	−0.353584	−0.176792	−	0.984248i	$-0.556572\pi$
$223$	−1177.47	−0.353584	−0.176792	+	0.984248i	$0.556572\pi$
$224$	6037.94i	1.80101i
$225$	−4115.77	−1.21949
$226$	− 4517.75i	− 1.32972i
$227$	2845.44i	0.831976i	0.909370	+	0.415988i	$0.136564\pi$
$227$	2845.44i	0.831976i	−0.909370	+	0.415988i	$0.863436\pi$
$228$	724.920i	0.210566i
$229$	−3605.93	−1.04055	−0.520277	−	0.853998i	$-0.674171\pi$
$229$	−3605.93	−1.04055	−0.520277	+	0.853998i	$0.674171\pi$
$230$	4707.03	1.34945
$231$	− 3907.74i	− 1.11303i
$232$	− 368.032i	− 0.104149i
$233$	835.204i	0.234833i	0.993083	+	0.117416i	$0.0374612\pi$
$233$	835.204i	0.234833i	−0.993083	+	0.117416i	$0.962539\pi$
$234$	−510.372	−0.142581
$235$	− 2312.34i	− 0.641875i
$236$	1347.85	0.371770
$237$	−8980.28	−2.46132
$238$	0	0
$239$	−4057.52	−1.09816	−0.549078	−	0.835771i	$-0.685021\pi$
$239$	−4057.52	−1.09816	−0.549078	+	0.835771i	$0.685021\pi$
$240$	−4977.59	−1.33876
$241$	2130.64i	0.569487i	0.958604	+	0.284743i	$0.0919084\pi$
$241$	2130.64i	0.569487i	−0.958604	+	0.284743i	$0.908092\pi$
$242$	4041.45	1.07353
$243$	− 530.923i	− 0.140159i
$244$	− 2571.19i	− 0.674604i
$245$	− 3200.14i	− 0.834489i
$246$	−7821.37	−2.02712
$247$	−36.0830	−0.00929516
$248$	− 1385.31i	− 0.354708i
$249$	− 895.981i	− 0.228034i
$250$	5217.82i	1.32002i
$251$	2164.17	0.544227	0.272113	−	0.962265i	$-0.412277\pi$
$251$	2164.17	0.544227	0.272113	+	0.962265i	$0.412277\pi$
$252$	8657.62i	2.16420i
$253$	2757.77	0.685294
$254$	2178.22	0.538085
$255$	0	0
$256$	5370.59	1.31118
$257$	−6991.31	−1.69691	−0.848456	−	0.529267i	$-0.822467\pi$
$257$	−6991.31	−1.69691	−0.848456	+	0.529267i	$0.822467\pi$
$258$	− 10744.5i	− 2.59273i
$259$	−6360.76	−1.52602
$260$	99.4688i	0.0237261i
$261$	− 2270.99i	− 0.538586i
$262$	7462.85i	1.75976i
$263$	2985.57	0.699993	0.349996	−	0.936751i	$-0.386183\pi$
$263$	2985.57	0.699993	0.349996	+	0.936751i	$0.386183\pi$
$264$	−1237.20	−0.288426
$265$	405.198i	0.0939287i
$266$	1489.90i	0.343427i
$267$	− 6327.40i	− 1.45030i
$268$	2190.58	0.499296
$269$	4063.25i	0.920969i	0.887668	+	0.460484i	$0.152324\pi$
$269$	4063.25i	0.920969i	−0.887668	+	0.460484i	$0.847676\pi$
$270$	−6641.19	−1.49693
$271$	6295.85	1.41124	0.705619	−	0.708591i	$-0.250669\pi$
$271$	6295.85	1.41124	0.705619	+	0.708591i	$0.250669\pi$
$272$	0	0
$273$	−642.237	−0.142381
$274$	2299.06	0.506903
$275$	1143.94i	0.250845i
$276$	−9105.72	−1.98587
$277$	4710.13i	1.02168i	0.859677	+	0.510838i	$0.170665\pi$
$277$	4710.13i	1.02168i	−0.859677	+	0.510838i	$0.829335\pi$
$278$	− 3806.99i	− 0.821323i
$279$	− 8548.28i	− 1.83431i
$280$	−1783.01	−0.380555
$281$	2458.26	0.521878	0.260939	−	0.965355i	$-0.415968\pi$
$281$	2458.26	0.521878	0.260939	+	0.965355i	$0.415968\pi$
$282$	10888.3i	2.29926i
$283$	− 9204.70i	− 1.93344i	−0.255843	−	0.966718i	$-0.582353\pi$
$283$	− 9204.70i	− 1.93344i	0.255843	−	0.966718i	$-0.417647\pi$
$284$	3433.78i	0.717455i
$285$	−921.249	−0.191474
$286$	141.854i	0.0293286i
$287$	−6604.00	−1.35826
$288$	11796.0	2.41349
$289$	0	0
$290$	−1077.35	−0.218153
$291$	−12942.2	−2.60716
$292$	− 3890.61i	− 0.779729i
$293$	423.010	0.0843431	0.0421716	−	0.999110i	$-0.486572\pi$
$293$	423.010	0.0843431	0.0421716	+	0.999110i	$0.486572\pi$
$294$	15068.8i	2.98922i
$295$	1712.89i	0.338062i
$296$	2013.84i	0.395446i
$297$	−3890.95	−0.760189
$298$	−1048.26	−0.203772
$299$	− 453.239i	− 0.0876638i
$300$	− 3777.13i	− 0.726909i
$301$	− 9072.17i	− 1.73725i
$302$	−11619.4	−2.21397
$303$	− 3702.12i	− 0.701919i
$304$	1111.89	0.209773
$305$	3267.54	0.613438
$306$	0	0
$307$	632.590	0.117602	0.0588010	−	0.998270i	$-0.481272\pi$
$307$	632.590	0.117602	0.0588010	+	0.998270i	$0.481272\pi$
$308$	2406.31	0.445170
$309$	− 14943.2i	− 2.75110i
$310$	−4055.29	−0.742983
$311$	− 5293.07i	− 0.965089i	−0.875872	−	0.482544i	$-0.839713\pi$
$311$	− 5293.07i	− 0.965089i	0.875872	−	0.482544i	$-0.160287\pi$
$312$	203.334i	0.0368959i
$313$	3817.93i	0.689464i	0.938701	+	0.344732i	$0.112030\pi$
$313$	3817.93i	0.689464i	−0.938701	+	0.344732i	$0.887970\pi$
$314$	−1777.35	−0.319431
$315$	−11002.4	−1.96798
$316$	− 5529.88i	− 0.984431i
$317$	1389.54i	0.246197i	0.992394	+	0.123098i	$0.0392830\pi$
$317$	1389.54i	0.246197i	−0.992394	+	0.123098i	$0.960717\pi$
$318$	− 1907.99i	− 0.336462i
$319$	−631.203	−0.110786
$320$	− 1200.26i	− 0.209677i
$321$	18616.2	3.23692
$322$	−18714.6	−3.23890
$323$	0	0
$324$	4553.83	0.780836
$325$	188.007	0.0320885
$326$	13698.1i	2.32721i
$327$	4031.81	0.681833
$328$	2090.85i	0.351975i
$329$	9193.61i	1.54061i
$330$	3621.72i	0.604149i
$331$	5736.36	0.952565	0.476282	−	0.879292i	$-0.341984\pi$
$331$	5736.36	0.952565	0.476282	+	0.879292i	$0.341984\pi$
$332$	551.728	0.0912048
$333$	12426.7i	2.04498i
$334$	7844.83i	1.28518i
$335$	2783.86i	0.454025i
$336$	19790.3	3.21325
$337$	− 3997.46i	− 0.646159i	−0.946372	−	0.323080i	$-0.895282\pi$
$337$	− 3997.46i	− 0.646159i	0.946372	−	0.323080i	$-0.104718\pi$
$338$	−8072.36	−1.29905
$339$	−11106.5	−1.77941
$340$	0	0
$341$	−2375.92	−0.377312
$342$	2910.74	0.460218
$343$	3055.81i	0.481045i
$344$	−2872.28	−0.450183
$345$	− 11571.8i	− 1.80581i
$346$	− 4413.97i	− 0.685828i
$347$	2485.37i	0.384500i	0.981346	+	0.192250i	$0.0615785\pi$
$347$	2485.37i	0.384500i	−0.981346	+	0.192250i	$0.938422\pi$
$348$	2084.14	0.321038
$349$	9518.10	1.45986	0.729932	−	0.683520i	$-0.239552\pi$
$349$	9518.10	1.45986	0.729932	+	0.683520i	$0.239552\pi$
$350$	− 7762.98i	− 1.18557i
$351$	639.478i	0.0972444i
$352$	− 3278.60i	− 0.496448i
$353$	174.509	0.0263121	0.0131561	−	0.999913i	$-0.495812\pi$
$353$	174.509	0.0263121	0.0131561	+	0.999913i	$0.495812\pi$
$354$	− 8065.65i	− 1.21097i
$355$	−4363.74	−0.652404
$356$	3896.29	0.580065
$357$	0	0
$358$	−15091.9	−2.22802
$359$	8112.87	1.19270	0.596352	−	0.802723i	$-0.296616\pi$
$359$	8112.87	1.19270	0.596352	+	0.802723i	$0.296616\pi$
$360$	3483.38i	0.509973i
$361$	−6653.21	−0.969997
$362$	− 4779.59i	− 0.693949i
$363$	− 9935.55i	− 1.43659i
$364$	− 395.477i	− 0.0569468i
$365$	4944.30	0.709031
$366$	−15386.2	−2.19740
$367$	− 41.1424i	− 0.00585181i	−0.999996	−	0.00292591i	$-0.999069\pi$
$367$	− 41.1424i	− 0.00585181i	0.999996	−	0.00292591i	$-0.000931346\pi$
$368$	13966.4i	1.97840i
$369$	12901.9i	1.82018i
$370$	5895.19	0.828315
$371$	− 1611.02i	− 0.225445i
$372$	7844.93	1.09339
$373$	1275.50	0.177059	0.0885296	−	0.996074i	$-0.471783\pi$
$373$	1275.50	0.177059	0.0885296	+	0.996074i	$0.471783\pi$
$374$	0	0
$375$	12827.5	1.76643
$376$	2910.73	0.399227
$377$	103.738i	0.0141718i
$378$	26404.6	3.59288
$379$	4101.12i	0.555832i	0.960605	+	0.277916i	$0.0896438\pi$
$379$	4101.12i	0.555832i	−0.960605	+	0.277916i	$0.910356\pi$
$380$	− 567.287i	− 0.0765822i
$381$	− 5354.95i	− 0.720059i
$382$	16146.1	2.16258
$383$	10390.1	1.38619	0.693094	−	0.720848i	$-0.256247\pi$
$383$	10390.1	1.38619	0.693094	+	0.720848i	$0.256247\pi$
$384$	− 9873.22i	− 1.31209i
$385$	3058.01i	0.404807i
$386$	3766.67i	0.496679i
$387$	−17723.8	−2.32804
$388$	− 7969.53i	− 1.04276i
$389$	−6213.37	−0.809846	−0.404923	−	0.914351i	$-0.632702\pi$
$389$	−6213.37	−0.809846	−0.404923	+	0.914351i	$0.632702\pi$
$390$	595.229	0.0772835
$391$	0	0
$392$	4028.27	0.519027
$393$	18346.8	2.35489
$394$	− 8115.93i	− 1.03775i
$395$	7027.54	0.895174
$396$	− 4701.08i	− 0.596561i
$397$	− 171.318i	− 0.0216580i	−0.999941	−	0.0108290i	$-0.996553\pi$
$397$	− 171.318i	− 0.0216580i	0.999941	−	0.0108290i	$-0.00344704\pi$
$398$	280.111i	0.0352782i
$399$	3662.78	0.459570
$400$	−5793.39	−0.724174
$401$	− 9328.60i	− 1.16172i	−0.814005	−	0.580858i	$-0.802717\pi$
$401$	− 9328.60i	− 1.16172i	0.814005	−	0.580858i	$-0.197283\pi$
$402$	− 13108.6i	− 1.62636i
$403$	390.482i	0.0482663i
$404$	2279.70	0.280741
$405$	5787.14i	0.710038i
$406$	4283.44	0.523605
$407$	3453.89	0.420646
$408$	0	0
$409$	−6370.74	−0.770202	−0.385101	−	0.922874i	$-0.625833\pi$
$409$	−6370.74	−0.770202	−0.385101	+	0.922874i	$0.625833\pi$
$410$	6120.63	0.737260
$411$	− 5652.04i	− 0.678332i
$412$	9201.74	1.10033
$413$	− 6810.26i	− 0.811406i
$414$	36561.8i	4.34037i
$415$	701.152i	0.0829354i
$416$	−538.837	−0.0635064
$417$	−9359.13	−1.09909
$418$	− 809.014i	− 0.0946655i
$419$	− 8067.75i	− 0.940657i	−0.882491	−	0.470329i	$-0.844135\pi$
$419$	− 8067.75i	− 0.940657i	0.882491	−	0.470329i	$-0.155865\pi$
$420$	− 10097.1i	− 1.17306i
$421$	−6254.81	−0.724088	−0.362044	−	0.932161i	$-0.617921\pi$
$421$	−6254.81	−0.724088	−0.362044	+	0.932161i	$0.617921\pi$
$422$	7268.90i	0.838494i
$423$	17961.1	2.06453
$424$	−510.054	−0.0584208
$425$	0	0
$426$	20548.0	2.33698
$427$	−12991.4	−1.47236
$428$	11463.5i	1.29464i
$429$	348.734	0.0392472
$430$	8408.14i	0.942969i
$431$	− 5910.99i	− 0.660609i	−0.943874	−	0.330305i	$-0.892849\pi$
$431$	− 5910.99i	− 0.660609i	0.943874	−	0.330305i	$-0.107151\pi$
$432$	− 19705.3i	− 2.19461i
$433$	−11833.5	−1.31335	−0.656677	−	0.754172i	$-0.728038\pi$
$433$	−11833.5	−1.31335	−0.656677	+	0.754172i	$0.728038\pi$
$434$	16123.4	1.78329
$435$	2648.58i	0.291930i
$436$	2482.71i	0.272707i
$437$	2584.90i	0.282957i
$438$	−23281.7	−2.53982
$439$	7520.94i	0.817665i	0.912609	+	0.408833i	$0.134064\pi$
$439$	7520.94i	0.817665i	−0.912609	+	0.408833i	$0.865936\pi$
$440$	968.176	0.104900
$441$	24857.0	2.68406
$442$	0	0
$443$	8478.34	0.909296	0.454648	−	0.890671i	$-0.349765\pi$
$443$	8478.34	0.909296	0.454648	+	0.890671i	$0.349765\pi$
$444$	−11404.2	−1.21896
$445$	4951.52i	0.527471i
$446$	−4338.83	−0.460649
$447$	2577.05i	0.272685i
$448$	4772.09i	0.503259i
$449$	1078.67i	0.113375i	0.998392	+	0.0566877i	$0.0180539\pi$
$449$	1078.67i	0.113375i	−0.998392	+	0.0566877i	$0.981946\pi$
$450$	−15166.1	−1.58875
$451$	3585.97	0.374405
$452$	− 6839.15i	− 0.711696i
$453$	28565.1i	2.96271i
$454$	10485.1i	1.08390i
$455$	502.584	0.0517835
$456$	− 1159.65i	− 0.119091i
$457$	−5664.74	−0.579837	−0.289918	−	0.957051i	$-0.593628\pi$
$457$	−5664.74	−0.579837	−0.289918	+	0.957051i	$0.593628\pi$
$458$	−13287.4	−1.35563
$459$	0	0
$460$	7125.70	0.722256
$461$	−710.717	−0.0718034	−0.0359017	−	0.999355i	$-0.511430\pi$
$461$	−710.717	−0.0718034	−0.0359017	+	0.999355i	$0.511430\pi$
$462$	− 14399.5i	− 1.45006i
$463$	8328.23	0.835952	0.417976	−	0.908458i	$-0.362740\pi$
$463$	8328.23	0.835952	0.417976	+	0.908458i	$0.362740\pi$
$464$	− 3196.66i	− 0.319831i
$465$	9969.56i	0.994252i
$466$	3077.62i	0.305940i
$467$	14132.8	1.40040	0.700201	−	0.713946i	$-0.253094\pi$
$467$	14132.8	1.40040	0.700201	+	0.713946i	$0.253094\pi$
$468$	−772.622	−0.0763130
$469$	− 11068.3i	− 1.08974i
$470$	− 8520.69i	− 0.836235i
$471$	4369.44i	0.427459i
$472$	−2156.15	−0.210264
$473$	4926.18i	0.478871i
$474$	−33091.2	−3.20660
$475$	−1072.24	−0.103574
$476$	0	0
$477$	−3147.36	−0.302113
$478$	−14951.5	−1.43068
$479$	6522.89i	0.622210i	0.950376	+	0.311105i	$0.100699\pi$
$479$	6522.89i	0.622210i	−0.950376	+	0.311105i	$0.899301\pi$
$480$	−13757.3	−1.30819
$481$	− 567.646i	− 0.0538096i
$482$	7851.13i	0.741928i
$483$	46008.3i	4.33426i
$484$	6118.12	0.574579
$485$	10127.9	0.948216
$486$	− 1956.39i	− 0.182600i
$487$	2178.49i	0.202704i	0.994851	+	0.101352i	$0.0323168\pi$
$487$	2178.49i	0.202704i	−0.994851	+	0.101352i	$0.967683\pi$
$488$	4113.11i	0.381540i
$489$	33675.6	3.11424
$490$	− 11792.1i	− 1.08717i
$491$	12618.8	1.15983	0.579915	−	0.814677i	$-0.303086\pi$
$491$	12618.8	1.15983	0.579915	+	0.814677i	$0.303086\pi$
$492$	−11840.3	−1.08496
$493$	0	0
$494$	−132.961	−0.0121097
$495$	5974.27	0.542472
$496$	− 12032.6i	− 1.08927i
$497$	17349.8	1.56588
$498$	− 3301.58i	− 0.297083i
$499$	− 13762.8i	− 1.23469i	−0.786694	−	0.617343i	$-0.788209\pi$
$499$	− 13762.8i	− 1.23469i	0.786694	−	0.617343i	$-0.211791\pi$
$500$	7898.95i	0.706504i
$501$	19285.8	1.71981
$502$	7974.69	0.709019
$503$	− 491.671i	− 0.0435836i	−0.999763	−	0.0217918i	$-0.993063\pi$
$503$	− 491.671i	− 0.0435836i	0.999763	−	0.0217918i	$-0.00693709\pi$
$504$	− 13849.5i	− 1.22402i
$505$	2897.11i	0.255286i
$506$	10162.0	0.892802
$507$	19845.2i	1.73837i
$508$	3297.48	0.287996
$509$	576.514	0.0502034	0.0251017	−	0.999685i	$-0.492009\pi$
$509$	576.514	0.0502034	0.0251017	+	0.999685i	$0.492009\pi$
$510$	0	0
$511$	−19658.0	−1.70180
$512$	11070.9	0.955600
$513$	− 3647.05i	− 0.313881i
$514$	−25762.1	−2.21074
$515$	11693.8i	1.00057i
$516$	− 16265.5i	− 1.38769i
$517$	− 4992.12i	− 0.424668i
$518$	−23438.6	−1.98810
$519$	−10851.4	−0.917768
$520$	− 159.120i	− 0.0134189i
$521$	− 6102.95i	− 0.513196i	−0.966518	−	0.256598i	$-0.917398\pi$
$521$	− 6102.95i	− 0.513196i	0.966518	−	0.256598i	$-0.0826016\pi$
$522$	− 8368.33i	− 0.701670i
$523$	13593.3	1.13651	0.568255	−	0.822853i	$-0.307619\pi$
$523$	13593.3	1.13651	0.568255	+	0.822853i	$0.307619\pi$
$524$	11297.6i	0.941864i
$525$	−19084.6	−1.58651
$526$	11001.5	0.911951
$527$	0	0
$528$	−10746.1	−0.885731
$529$	−20301.9	−1.66860
$530$	1493.10i	0.122370i
$531$	−13304.8	−1.08735
$532$	2255.47i	0.183810i
$533$	− 589.354i	− 0.0478944i
$534$	− 23315.7i	− 1.88945i
$535$	−14568.1	−1.17726
$536$	−3504.26	−0.282390
$537$	37102.1i	2.98151i
$538$	14972.6i	1.19984i
$539$	− 6908.80i	− 0.552103i
$540$	−10053.7	−0.801190
$541$	− 20360.3i	− 1.61803i	−0.587786	−	0.809017i	$-0.700000\pi$
$541$	− 20360.3i	− 1.61803i	0.587786	−	0.809017i	$-0.300000\pi$
$542$	23199.4	1.83856
$543$	−11750.2	−0.928635
$544$	0	0
$545$	−3155.10	−0.247981
$546$	−2366.56	−0.185494
$547$	− 253.860i	− 0.0198433i	−0.999951	−	0.00992164i	$-0.996842\pi$
$547$	− 253.860i	− 0.0198433i	0.999951	−	0.00992164i	$-0.00315821\pi$
$548$	3480.42	0.271307
$549$	25380.5i	1.97307i
$550$	4215.29i	0.326801i
$551$	− 591.636i	− 0.0457433i
$552$	14566.4	1.12316
$553$	−27940.7	−2.14857
$554$	17356.2i	1.33104i
$555$	− 14492.8i	− 1.10844i
$556$	− 5763.17i	− 0.439592i
$557$	1519.94	0.115623	0.0578116	−	0.998328i	$-0.481588\pi$
$557$	1519.94	0.115623	0.0578116	+	0.998328i	$0.481588\pi$
$558$	− 31499.4i	− 2.38974i
$559$	809.617	0.0612579
$560$	−15487.0	−1.16865
$561$	0	0
$562$	9058.40	0.679903
$563$	25112.9	1.87990	0.939948	−	0.341317i	$-0.110873\pi$
$563$	25112.9	1.87990	0.939948	+	0.341317i	$0.110873\pi$
$564$	16483.2i	1.23062i
$565$	8691.39	0.647168
$566$	− 33918.2i	− 2.51888i
$567$	− 23009.0i	− 1.70421i
$568$	− 5492.99i	− 0.405776i
$569$	−3649.16	−0.268859	−0.134430	−	0.990923i	$-0.542920\pi$
$569$	−3649.16	−0.268859	−0.134430	+	0.990923i	$0.542920\pi$
$570$	−3394.69	−0.249452
$571$	− 4111.91i	− 0.301362i	−0.988582	−	0.150681i	$-0.951853\pi$
$571$	− 4111.91i	− 0.301362i	0.988582	−	0.150681i	$-0.0481467\pi$
$572$	214.744i	0.0156974i
$573$	− 39693.7i	− 2.89394i
$574$	−24334.9	−1.76955
$575$	− 13468.4i	− 0.976817i
$576$	9322.98	0.674405
$577$	25307.1	1.82591	0.912954	−	0.408062i	$-0.133795\pi$
$577$	25307.1	1.82591	0.912954	+	0.408062i	$0.133795\pi$
$578$	0	0
$579$	9260.01	0.664651
$580$	−1630.94	−0.116761
$581$	− 2787.70i	− 0.199059i
$582$	−47690.3	−3.39661
$583$	874.783i	0.0621438i
$584$	6223.78i	0.440996i
$585$	− 981.870i	− 0.0693938i
$586$	1558.74	0.109882
$587$	−6734.14	−0.473506	−0.236753	−	0.971570i	$-0.576083\pi$
$587$	−6734.14	−0.473506	−0.236753	+	0.971570i	$0.576083\pi$
$588$	22811.8i	1.59990i
$589$	− 2226.99i	− 0.155792i
$590$	6311.79i	0.440427i
$591$	−19952.3	−1.38871
$592$	17491.9i	1.21438i
$593$	−885.596	−0.0613273	−0.0306636	−	0.999530i	$-0.509762\pi$
$593$	−885.596	−0.0613273	−0.0306636	+	0.999530i	$0.509762\pi$
$594$	−14337.7	−0.990374
$595$	0	0
$596$	−1586.90	−0.109064
$597$	688.629	0.0472089
$598$	− 1670.13i	− 0.114208i
$599$	7411.88	0.505578	0.252789	−	0.967521i	$-0.418652\pi$
$599$	7411.88	0.505578	0.252789	+	0.967521i	$0.418652\pi$
$600$	6042.24i	0.411123i
$601$	− 19232.0i	− 1.30531i	−0.757657	−	0.652653i	$-0.773656\pi$
$601$	− 19232.0i	− 1.30531i	0.757657	−	0.652653i	$-0.226344\pi$
$602$	− 33429.8i	− 2.26329i
$603$	−21623.6	−1.46033
$604$	−17589.9	−1.18497
$605$	7775.08i	0.522483i
$606$	− 13641.9i	− 0.914461i
$607$	− 3485.07i	− 0.233039i	−0.993188	−	0.116519i	$-0.962826\pi$
$607$	− 3485.07i	− 0.233039i	0.993188	−	0.116519i	$-0.0371737\pi$
$608$	3073.08	0.204983
$609$	− 10530.5i	− 0.700682i
$610$	12040.5	0.799188
$611$	−820.455	−0.0543241
$612$	0	0
$613$	−27347.9	−1.80191	−0.900954	−	0.433915i	$-0.857132\pi$
$613$	−27347.9	−1.80191	−0.900954	+	0.433915i	$0.857132\pi$
$614$	2331.02	0.153212
$615$	− 15047.0i	− 0.986592i
$616$	−3849.36	−0.251778
$617$	12625.9i	0.823822i	0.911224	+	0.411911i	$0.135139\pi$
$617$	12625.9i	0.823822i	−0.911224	+	0.411911i	$0.864861\pi$
$618$	− 55063.9i	− 3.58413i
$619$	− 16469.8i	− 1.06943i	−0.845033	−	0.534714i	$-0.820419\pi$
$619$	− 16469.8i	− 1.06943i	0.845033	−	0.534714i	$-0.179581\pi$
$620$	−6139.06	−0.397662
$621$	45810.6	2.96025
$622$	− 19504.3i	− 1.25732i
$623$	− 19686.7i	− 1.26602i
$624$	1766.13i	0.113304i
$625$	−695.113	−0.0444872
$626$	14068.6i	0.898235i
$627$	−1988.89	−0.126680
$628$	−2690.62	−0.170967
$629$	0	0
$630$	−40542.3	−2.56388
$631$	−6691.13	−0.422139	−0.211069	−	0.977471i	$-0.567695\pi$
$631$	−6691.13	−0.422139	−0.211069	+	0.977471i	$0.567695\pi$
$632$	8846.11i	0.556771i
$633$	17869.9	1.12206
$634$	5120.28i	0.320745i
$635$	4190.53i	0.261884i
$636$	− 2888.40i	− 0.180082i
$637$	−1135.46	−0.0706258
$638$	−2325.91	−0.144332
$639$	− 33895.3i	− 2.09840i
$640$	7726.31i	0.477202i
$641$	14335.5i	0.883335i	0.897179	+	0.441668i	$0.145613\pi$
$641$	14335.5i	0.883335i	−0.897179	+	0.441668i	$0.854387\pi$
$642$	68598.3	4.21707
$643$	30421.9i	1.86582i	0.360109	+	0.932910i	$0.382740\pi$
$643$	30421.9i	1.86582i	−0.360109	+	0.932910i	$0.617260\pi$
$644$	−28331.0	−1.73354
$645$	20670.7	1.26187
$646$	0	0
$647$	−9221.00	−0.560301	−0.280151	−	0.959956i	$-0.590384\pi$
$647$	−9221.00	−0.560301	−0.280151	+	0.959956i	$0.590384\pi$
$648$	−7284.73	−0.441622
$649$	3697.96i	0.223664i
$650$	692.783	0.0418049
$651$	− 39637.8i	− 2.38637i
$652$	20736.8i	1.24558i
$653$	24958.5i	1.49572i	0.663859	+	0.747858i	$0.268918\pi$
$653$	24958.5i	1.49572i	−0.663859	+	0.747858i	$0.731082\pi$
$654$	14856.7	0.888293
$655$	−14357.3	−0.856467
$656$	18160.8i	1.08088i
$657$	38404.7i	2.28054i
$658$	33877.3i	2.00711i
$659$	−3367.32	−0.199047	−0.0995236	−	0.995035i	$-0.531732\pi$
$659$	−3367.32	−0.199047	−0.0995236	+	0.995035i	$0.531732\pi$
$660$	5482.71i	0.323355i
$661$	6389.67	0.375990	0.187995	−	0.982170i	$-0.439801\pi$
$661$	6389.67	0.375990	0.187995	+	0.982170i	$0.439801\pi$
$662$	21137.8	1.24100
$663$	0	0
$664$	−882.595	−0.0515833
$665$	−2866.32	−0.167144
$666$	45790.8i	2.66420i
$667$	7431.55	0.431410
$668$	11875.8i	0.687859i
$669$	10666.6i	0.616436i
$670$	10258.2i	0.591504i
$671$	7054.30	0.405854
$672$	54697.3	3.13987
$673$	27441.4i	1.57175i	0.618383	+	0.785877i	$0.287788\pi$
$673$	27441.4i	1.57175i	−0.618383	+	0.785877i	$0.712212\pi$
$674$	− 14730.2i	− 0.841817i
$675$	19002.6i	1.08357i
$676$	−12220.3	−0.695282
$677$	− 16931.5i	− 0.961194i	−0.876941	−	0.480597i	$-0.840420\pi$
$677$	− 16931.5i	− 0.961194i	0.876941	−	0.480597i	$-0.159580\pi$
$678$	−40926.0	−2.31822
$679$	−40267.4	−2.27588
$680$	0	0
$681$	25776.7	1.45046
$682$	−8754.98	−0.491562
$683$	69.2829i	0.00388146i	0.999998	+	0.00194073i	$0.000617754\pi$
$683$	69.2829i	0.00388146i	−0.999998	+	0.00194073i	$0.999382\pi$
$684$	4406.39	0.246320
$685$	4423.01i	0.246708i
$686$	11260.3i	0.626705i
$687$	32665.9i	1.81409i
$688$	−24948.1	−1.38247
$689$	143.770	0.00794952
$690$	− 42640.7i	− 2.35262i
$691$	1509.96i	0.0831282i	0.999136	+	0.0415641i	$0.0132341\pi$
$691$	1509.96i	0.0831282i	−0.999136	+	0.0415641i	$0.986766\pi$
$692$	− 6682.05i	− 0.367072i
$693$	−23753.0	−1.30202
$694$	9158.27i	0.500927i
$695$	7324.01	0.399734
$696$	−3333.98	−0.181572
$697$	0	0
$698$	35073.0	1.90191
$699$	7566.06	0.409406
$700$	− 11751.9i	− 0.634544i
$701$	−16452.5	−0.886449	−0.443224	−	0.896411i	$-0.646165\pi$
$701$	−16452.5	−0.886449	−0.443224	+	0.896411i	$0.646165\pi$
$702$	2356.40i	0.126690i
$703$	3237.38i	0.173684i
$704$	− 2591.24i	− 0.138723i
$705$	−20947.4	−1.11904
$706$	643.045	0.0342795
$707$	− 11518.6i	− 0.612730i
$708$	− 12210.1i	− 0.648141i
$709$	− 4602.45i	− 0.243792i	−0.992543	−	0.121896i	$-0.961103\pi$
$709$	− 4602.45i	− 0.243792i	0.992543	−	0.121896i	$-0.0388975\pi$
$710$	−16079.9	−0.849953
$711$	54586.2i	2.87925i
$712$	−6232.87	−0.328071
$713$	27973.2	1.46929
$714$	0	0
$715$	−272.903	−0.0142741
$716$	−22846.7	−1.19249
$717$	36756.8i	1.91452i
$718$	29894.9	1.55386
$719$	− 23515.7i	− 1.21973i	−0.792505	−	0.609865i	$-0.791224\pi$
$719$	− 23515.7i	− 1.21973i	0.792505	−	0.609865i	$-0.208776\pi$
$720$	30256.1i	1.56608i
$721$	− 46493.4i	− 2.40153i
$722$	−24516.3	−1.26371
$723$	19301.3	0.992839
$724$	− 7235.54i	− 0.371418i
$725$	3082.66i	0.157914i
$726$	− 36611.3i	− 1.87159i
$727$	−8389.04	−0.427968	−0.213984	−	0.976837i	$-0.568644\pi$
$727$	−8389.04	−0.427968	−0.213984	+	0.976837i	$0.568644\pi$
$728$	632.641i	0.0322078i
$729$	17231.7	0.875462
$730$	18219.1	0.923727
$731$	0	0
$732$	−23292.2	−1.17610
$733$	7677.37	0.386863	0.193431	−	0.981114i	$-0.438038\pi$
$733$	7677.37	0.386863	0.193431	+	0.981114i	$0.438038\pi$
$734$	− 151.605i	− 0.00762374i
$735$	−28989.9	−1.45484
$736$	38601.0i	1.93322i
$737$	6010.08i	0.300386i
$738$	47541.9i	2.37133i
$739$	−26617.3	−1.32494	−0.662472	−	0.749087i	$-0.730493\pi$
$739$	−26617.3	−1.32494	−0.662472	+	0.749087i	$0.730493\pi$
$740$	8924.39	0.443334
$741$	326.873i	0.0162051i
$742$	− 5936.41i	− 0.293710i
$743$	− 20951.6i	− 1.03451i	−0.855832	−	0.517253i	$-0.826954\pi$
$743$	− 20951.6i	− 1.03451i	0.855832	−	0.517253i	$-0.173046\pi$
$744$	−12549.5	−0.618395
$745$	− 2016.68i	− 0.0991750i
$746$	4700.07	0.230673
$747$	−5446.18	−0.266754
$748$	0	0
$749$	57921.2	2.82563
$750$	47267.9	2.30131
$751$	− 8252.35i	− 0.400975i	−0.979696	−	0.200488i	$-0.935747\pi$
$751$	− 8252.35i	− 0.400975i	0.979696	−	0.200488i	$-0.0642527\pi$
$752$	25282.1	1.22599
$753$	− 19605.0i	− 0.948801i
$754$	382.262i	0.0184631i
$755$	− 22353.7i	− 1.07753i
$756$	39972.4	1.92299
$757$	21203.1	1.01802	0.509010	−	0.860760i	$-0.330012\pi$
$757$	21203.1	1.01802	0.509010	+	0.860760i	$0.330012\pi$
$758$	15112.1i	0.724139i
$759$	− 24982.4i	− 1.19474i
$760$	907.485i	0.0433131i
$761$	29378.2	1.39942	0.699711	−	0.714426i	$-0.253312\pi$
$761$	29378.2	1.39942	0.699711	+	0.714426i	$0.253312\pi$
$762$	− 19732.3i	− 0.938094i
$763$	12544.3	0.595196
$764$	24442.6	1.15746
$765$	0	0
$766$	38286.3	1.80593
$767$	607.760	0.0286114
$768$	− 48651.8i	− 2.28590i
$769$	−16559.6	−0.776532	−0.388266	−	0.921547i	$-0.626926\pi$
$769$	−16559.6	−0.776532	−0.388266	+	0.921547i	$0.626926\pi$
$770$	11268.4i	0.527383i
$771$	63333.9i	2.95838i
$772$	5702.13i	0.265835i
$773$	39537.3	1.83966	0.919830	−	0.392317i	$-0.128327\pi$
$773$	39537.3	1.83966	0.919830	+	0.392317i	$0.128327\pi$
$774$	−65310.1	−3.03297
$775$	11603.5i	0.537820i
$776$	12748.8i	0.589762i
$777$	57621.7i	2.66045i
$778$	−22895.5	−1.05507
$779$	3361.18i	0.154592i
$780$	901.082	0.0413640
$781$	−9420.91	−0.431634
$782$	0	0
$783$	−10485.2	−0.478558
$784$	34988.9	1.59388
$785$	− 3419.32i	− 0.155466i
$786$	67605.5	3.06795
$787$	− 17801.2i	− 0.806280i	−0.915138	−	0.403140i	$-0.867919\pi$
$787$	− 17801.2i	− 0.806280i	0.915138	−	0.403140i	$-0.132081\pi$
$788$	− 12286.2i	− 0.555430i
$789$	− 27046.1i	− 1.22036i
$790$	25895.6	1.16623
$791$	−34556.0	−1.55331
$792$	7520.28i	0.337401i
$793$	− 1159.37i	− 0.0519175i
$794$	− 631.287i	− 0.0282161i
$795$	3670.66	0.163755
$796$	424.044i	0.0188817i
$797$	−34006.4	−1.51138	−0.755688	−	0.654932i	$-0.772697\pi$
$797$	−34006.4	−1.51138	−0.755688	+	0.654932i	$0.772697\pi$
$798$	13496.9	0.598728
$799$	0	0
$800$	−16012.0	−0.707636
$801$	−38460.8	−1.69656
$802$	− 34374.7i	− 1.51348i
$803$	10674.3	0.469099
$804$	− 19844.4i	− 0.870469i
$805$	− 36003.8i	− 1.57636i
$806$	1438.88i	0.0628813i
$807$	36808.7	1.60561
$808$	−3646.81	−0.158780
$809$	− 7943.98i	− 0.345235i	−0.984989	−	0.172618i	$-0.944777\pi$
$809$	− 7943.98i	− 0.345235i	0.984989	−	0.172618i	$-0.0552225\pi$
$810$	21324.9i	0.925038i
$811$	− 29182.7i	− 1.26355i	−0.775150	−	0.631777i	$-0.782326\pi$
$811$	− 29182.7i	− 1.26355i	0.775150	−	0.631777i	$-0.217674\pi$
$812$	6484.45	0.280246
$813$	− 57033.7i	− 2.46034i
$814$	12727.2	0.548018
$815$	−26352.9	−1.13264
$816$	0	0
$817$	−4617.38	−0.197726
$818$	−23475.4	−1.00342
$819$	3903.81i	0.166557i
$820$	9265.66	0.394599
$821$	29589.4i	1.25783i	0.777475	+	0.628913i	$0.216500\pi$
$821$	29589.4i	1.25783i	−0.777475	+	0.628913i	$0.783500\pi$
$822$	− 20827.1i	− 0.883732i
$823$	11121.5i	0.471046i	0.971869	+	0.235523i	$0.0756803\pi$
$823$	11121.5i	0.471046i	−0.971869	+	0.235523i	$0.924320\pi$
$824$	−14720.0	−0.622323
$825$	10362.9	0.437322
$826$	− 25095.0i	− 1.05710i
$827$	12401.7i	0.521461i	0.965412	+	0.260730i	$0.0839634\pi$
$827$	12401.7i	0.521461i	−0.965412	+	0.260730i	$0.916037\pi$
$828$	55348.7i	2.32307i
$829$	−6224.06	−0.260761	−0.130380	−	0.991464i	$-0.541620\pi$
$829$	−6224.06	−0.260761	−0.130380	+	0.991464i	$0.541620\pi$
$830$	2583.66i	0.108048i
$831$	42668.8	1.78118
$832$	−425.870	−0.0177457
$833$	0	0
$834$	−34487.3	−1.43189
$835$	−15092.1	−0.625491
$836$	− 1224.72i	− 0.0506672i
$837$	−39467.6	−1.62987
$838$	− 29728.7i	− 1.22549i
$839$	− 36811.6i	− 1.51475i	−0.652978	−	0.757377i	$-0.726481\pi$
$839$	− 36811.6i	− 1.51475i	0.652978	−	0.757377i	$-0.273519\pi$
$840$	16152.2i	0.663458i
$841$	22688.1	0.930258
$842$	−23048.2	−0.943342
$843$	− 22269.3i	− 0.909839i
$844$	11004.0i	0.448782i
$845$	− 15529.9i	− 0.632241i
$846$	66184.3	2.68967
$847$	− 30912.8i	− 1.25405i
$848$	−4430.25	−0.179405
$849$	−83384.8	−3.37074
$850$	0	0
$851$	−40664.8	−1.63804
$852$	31106.4	1.25081
$853$	3319.10i	0.133228i	0.997779	+	0.0666141i	$0.0212196\pi$
$853$	3319.10i	0.133228i	−0.997779	+	0.0666141i	$0.978780\pi$
$854$	−47871.6	−1.91819
$855$	5599.77i	0.223986i
$856$	− 18338.0i	− 0.732221i
$857$	8084.66i	0.322248i	0.986934	+	0.161124i	$0.0515119\pi$
$857$	8084.66i	0.322248i	−0.986934	+	0.161124i	$0.948488\pi$
$858$	1285.04	0.0511313
$859$	23619.8	0.938181	0.469091	−	0.883150i	$-0.344582\pi$
$859$	23619.8	0.938181	0.469091	+	0.883150i	$0.344582\pi$
$860$	12728.6i	0.504699i
$861$	59825.3i	2.36799i
$862$	− 21781.3i	− 0.860642i
$863$	−34938.3	−1.37812	−0.689058	−	0.724706i	$-0.741975\pi$
$863$	−34938.3	−1.37812	−0.689058	+	0.724706i	$0.741975\pi$
$864$	− 54462.4i	− 2.14450i
$865$	8491.75	0.333790
$866$	−43605.0	−1.71104
$867$	0	0
$868$	24408.2	0.954457
$869$	15171.8	0.592252
$870$	9759.69i	0.380327i
$871$	987.756	0.0384258
$872$	− 3971.57i	− 0.154237i
$873$	78668.3i	3.04985i
$874$	9525.02i	0.368637i
$875$	39910.8	1.54198
$876$	−35244.8	−1.35937
$877$	− 20700.0i	− 0.797022i	−0.917164	−	0.398511i	$-0.869527\pi$
$877$	− 20700.0i	− 0.797022i	0.917164	−	0.398511i	$-0.130473\pi$
$878$	27713.8i	1.06525i
$879$	− 3832.02i	− 0.147043i
$880$	8409.42	0.322138
$881$	− 5183.11i	− 0.198211i	−0.995077	−	0.0991053i	$-0.968402\pi$
$881$	− 5183.11i	− 0.198211i	0.995077	−	0.0991053i	$-0.0315981\pi$
$882$	91595.2	3.49679
$883$	7357.34	0.280401	0.140201	−	0.990123i	$-0.455225\pi$
$883$	7357.34	0.280401	0.140201	+	0.990123i	$0.455225\pi$
$884$	0	0
$885$	15517.0	0.589375
$886$	31241.6	1.18463
$887$	− 35702.2i	− 1.35148i	−0.737140	−	0.675740i	$-0.763824\pi$
$887$	− 35702.2i	− 1.35148i	0.737140	−	0.675740i	$-0.236176\pi$
$888$	18243.2	0.689417
$889$	− 16661.1i	− 0.628565i
$890$	18245.7i	0.687189i
$891$	12493.9i	0.469765i
$892$	−6568.30	−0.246550
$893$	4679.19	0.175345
$894$	9496.12i	0.355255i
$895$	− 29034.3i	− 1.08437i
$896$	− 30718.9i	− 1.14537i
$897$	−4105.86	−0.152832
$898$	3974.77i	0.147706i
$899$	−6402.56	−0.237528
$900$	−22959.1	−0.850337
$901$	0	0
$902$	13213.9	0.487775
$903$	−82184.2	−3.02870
$904$	10940.5i	0.402519i
$905$	9195.14	0.337742
$906$	105259.i	3.85982i
$907$	5660.56i	0.207228i	0.994618	+	0.103614i	$0.0330407\pi$
$907$	5660.56i	0.207228i	−0.994618	+	0.103614i	$0.966959\pi$
$908$	15872.8i	0.580128i
$909$	−22503.2	−0.821105
$910$	1851.96	0.0674636
$911$	11754.9i	0.427506i	0.976888	+	0.213753i	$0.0685687\pi$
$911$	11754.9i	0.427506i	−0.976888	+	0.213753i	$0.931431\pi$
$912$	− 10072.5i	− 0.365718i
$913$	1513.72i	0.0548705i
$914$	−20873.9	−0.755412
$915$	− 29600.4i	− 1.06946i
$916$	−20115.0	−0.725567
$917$	57083.0	2.05567
$918$	0	0
$919$	4513.88	0.162023	0.0810116	−	0.996713i	$-0.474185\pi$
$919$	4513.88	0.162023	0.0810116	+	0.996713i	$0.474185\pi$
$920$	−11398.9	−0.408491
$921$	− 5730.59i	− 0.205027i
$922$	−2618.90	−0.0935455
$923$	1548.32i	0.0552153i
$924$	− 21798.6i	− 0.776106i
$925$	− 16868.1i	− 0.599588i
$926$	30688.5	1.08908
$927$	−90831.6	−3.21823
$928$	− 8835.06i	− 0.312527i
$929$	15124.4i	0.534138i	0.963677	+	0.267069i	$0.0860552\pi$
$929$	15124.4i	0.534138i	−0.963677	+	0.267069i	$0.913945\pi$
$930$	36736.6i	1.29531i
$931$	6475.72	0.227963
$932$	4659.03i	0.163746i
$933$	−47949.6	−1.68253
$934$	52077.6	1.82444
$935$	0	0
$936$	1235.96	0.0431608
$937$	19918.8	0.694470	0.347235	−	0.937778i	$-0.387121\pi$
$937$	19918.8	0.694470	0.347235	+	0.937778i	$0.387121\pi$
$938$	− 40785.4i	− 1.41971i
$939$	34586.4	1.20201
$940$	− 12899.0i	− 0.447573i
$941$	− 2072.11i	− 0.0717843i	−0.999356	−	0.0358921i	$-0.988573\pi$
$941$	− 2072.11i	− 0.0717843i	0.999356	−	0.0358921i	$-0.0114273\pi$
$942$	16100.9i	0.556894i
$943$	−42219.8	−1.45797
$944$	−18728.0	−0.645703
$945$	50798.1i	1.74864i
$946$	18152.4i	0.623874i
$947$	− 5522.83i	− 0.189512i	−0.995501	−	0.0947560i	$-0.969793\pi$
$947$	− 5522.83i	− 0.189512i	0.995501	−	0.0947560i	$-0.0302071\pi$
$948$	−50094.9	−1.71625
$949$	− 1754.31i	− 0.0600079i
$950$	−3951.06	−0.134936
$951$	12587.8	0.429217
$952$	0	0
$953$	−39192.3	−1.33218	−0.666089	−	0.745873i	$-0.732033\pi$
$953$	−39192.3	−1.33218	−0.666089	+	0.745873i	$0.732033\pi$
$954$	−11597.6	−0.393593
$955$	31062.4i	1.05252i
$956$	−22634.1	−0.765733
$957$	5718.03i	0.193143i
$958$	24036.1i	0.810616i
$959$	− 17585.4i	− 0.592140i
$960$	−10873.1	−0.365549
$961$	5691.04	0.191032
$962$	− 2091.71i	− 0.0701033i
$963$	− 113158.i	− 3.78655i
$964$	11885.4i	0.397097i
$965$	−7246.44	−0.241732
$966$	169535.i	5.64668i
$967$	−53414.4	−1.77631	−0.888155	−	0.459543i	$-0.848013\pi$
$967$	−53414.4	−1.77631	−0.888155	+	0.459543i	$0.848013\pi$
$968$	−9787.11	−0.324968
$969$	0	0
$970$	37320.1	1.23534
$971$	39644.8	1.31026	0.655130	−	0.755516i	$-0.272614\pi$
$971$	39644.8	1.31026	0.655130	+	0.755516i	$0.272614\pi$
$972$	− 2961.66i	− 0.0977317i
$973$	−29119.4	−0.959431
$974$	8027.47i	0.264083i
$975$	− 1703.14i	− 0.0559428i
$976$	35725.8i	1.17167i
$977$	−40232.8	−1.31746	−0.658732	−	0.752378i	$-0.728907\pi$
$977$	−40232.8	−1.31746	−0.658732	+	0.752378i	$0.728907\pi$
$978$	124090.	4.05723
$979$	10689.9i	0.348978i
$980$	− 17851.4i	− 0.581880i
$981$	− 24507.2i	− 0.797608i
$982$	46498.6	1.51103
$983$	− 40449.2i	− 1.31244i	−0.754569	−	0.656220i	$-0.772154\pi$
$983$	− 40449.2i	− 1.31244i	0.754569	−	0.656220i	$-0.227846\pi$
$984$	18940.9	0.613631
$985$	15613.7	0.505070
$986$	0	0
$987$	83284.3	2.68589
$988$	−201.282	−0.00648142
$989$	− 57999.0i	− 1.86477i
$990$	22014.5	0.706733
$991$	41635.0i	1.33459i	0.744793	+	0.667296i	$0.232548\pi$
$991$	41635.0i	1.33459i	−0.744793	+	0.667296i	$0.767452\pi$
$992$	− 33256.2i	− 1.06440i
$993$	− 51965.4i	− 1.66070i
$994$	63931.7	2.04003
$995$	−538.888	−0.0171697
$996$	− 4998.07i	− 0.159006i
$997$	− 33986.6i	− 1.07960i	−0.841792	−	0.539802i	$-0.818499\pi$
$997$	− 33986.6i	− 1.07960i	0.841792	−	0.539802i	$-0.181501\pi$
$998$	− 50714.3i	− 1.60855i
$999$	57374.2	1.81706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.d.288.7		8
17.4	even	4		289.4.a.c.1.1	✓	4
17.13	even	4		289.4.a.d.1.1	yes	4
17.16	even	2	inner	289.4.b.d.288.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.c.1.1	✓	4	17.4	even	4
289.4.a.d.1.1	yes	4	17.13	even	4
289.4.b.d.288.7		8	1.1	even	1	trivial
289.4.b.d.288.8		8	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.68488 q^{2} -9.05894i q^{3} +5.57832 q^{4} +7.08909i q^{5} -33.3811i q^{6} -28.1854i q^{7} -8.92359 q^{8} -55.0643 q^{9} +O(q^{10})\)	\(q+3.68488 q^{2} -9.05894i q^{3} +5.57832 q^{4} +7.08909i q^{5} -33.3811i q^{6} -28.1854i q^{7} -8.92359 q^{8} -55.0643 q^{9} +26.1224i q^{10} +15.3047i q^{11} -50.5336i q^{12} +2.51532 q^{13} -103.860i q^{14} +64.2196 q^{15} -77.5089 q^{16} -202.905 q^{18} -14.3453 q^{19} +39.5452i q^{20} -255.330 q^{21} +56.3958i q^{22} -180.191i q^{23} +80.8383i q^{24} +74.7448 q^{25} +9.26864 q^{26} +254.233i q^{27} -157.227i q^{28} +41.2425i q^{29} +236.641 q^{30} +155.242i q^{31} -214.222 q^{32} +138.644 q^{33} +199.809 q^{35} -307.167 q^{36} -225.676i q^{37} -52.8606 q^{38} -22.7861i q^{39} -63.2602i q^{40} -234.306i q^{41} -940.860 q^{42} +321.875 q^{43} +85.3743i q^{44} -390.356i q^{45} -663.983i q^{46} -326.183 q^{47} +702.148i q^{48} -451.418 q^{49} +275.425 q^{50} +14.0313 q^{52} +57.1579 q^{53} +936.818i q^{54} -108.496 q^{55} +251.515i q^{56} +129.953i q^{57} +151.974i q^{58} +241.623 q^{59} +358.238 q^{60} -460.925i q^{61} +572.046i q^{62} +1552.01i q^{63} -169.311 q^{64} +17.8313i q^{65} +510.886 q^{66} +392.696 q^{67} -1632.34 q^{69} +736.272 q^{70} +615.558i q^{71} +491.372 q^{72} -697.452i q^{73} -831.587i q^{74} -677.109i q^{75} -80.0226 q^{76} +431.369 q^{77} -83.9641i q^{78} -991.317i q^{79} -549.468i q^{80} +816.345 q^{81} -863.387i q^{82} +98.9057 q^{83} -1424.31 q^{84} +1186.07 q^{86} +373.613 q^{87} -136.573i q^{88} +698.470 q^{89} -1438.41i q^{90} -70.8954i q^{91} -1005.16i q^{92} +1406.32 q^{93} -1201.94 q^{94} -101.695i q^{95} +1940.62i q^{96} -1428.66i q^{97} -1663.42 q^{98} -842.741i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 22 q^{4} - 120 q^{8} - 12 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 22 * q^4 - 120 * q^8 - 12 * q^9	\( 8 q - 2 q^{2} + 22 q^{4} - 120 q^{8} - 12 q^{9} - 44 q^{13} - 108 q^{15} + 126 q^{16} - 668 q^{18} - 44 q^{19} - 704 q^{21} - 756 q^{25} + 896 q^{26} + 626 q^{30} - 662 q^{32} + 188 q^{33} - 484 q^{35} - 282 q^{36} - 1048 q^{38} - 2910 q^{42} + 228 q^{43} + 20 q^{47} - 2012 q^{49} + 1610 q^{50} - 3074 q^{52} - 100 q^{53} - 2632 q^{55} - 1992 q^{59} + 434 q^{60} - 300 q^{64} + 2180 q^{66} - 1736 q^{67} - 2256 q^{69} - 2104 q^{70} - 78 q^{72} + 1746 q^{76} + 1788 q^{77} + 2160 q^{81} - 1700 q^{83} + 886 q^{84} + 4822 q^{86} + 768 q^{87} + 1568 q^{89} + 3100 q^{93} - 2238 q^{94} - 3754 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 22 * q^4 - 120 * q^8 - 12 * q^9 - 44 * q^13 - 108 * q^15 + 126 * q^16 - 668 * q^18 - 44 * q^19 - 704 * q^21 - 756 * q^25 + 896 * q^26 + 626 * q^30 - 662 * q^32 + 188 * q^33 - 484 * q^35 - 282 * q^36 - 1048 * q^38 - 2910 * q^42 + 228 * q^43 + 20 * q^47 - 2012 * q^49 + 1610 * q^50 - 3074 * q^52 - 100 * q^53 - 2632 * q^55 - 1992 * q^59 + 434 * q^60 - 300 * q^64 + 2180 * q^66 - 1736 * q^67 - 2256 * q^69 - 2104 * q^70 - 78 * q^72 + 1746 * q^76 + 1788 * q^77 + 2160 * q^81 - 1700 * q^83 + 886 * q^84 + 4822 * q^86 + 768 * q^87 + 1568 * q^89 + 3100 * q^93 - 2238 * q^94 - 3754 * q^98

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