LMFDB - Embedded newform 1682.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1682,4,Mod(1,1682)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1682, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1682.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1682 = 2 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1682.a (trivial)

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:	yes
Analytic conductor:	$99.2412126297$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.19816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 42x - 54 $ x^3 - x^2 - 42*x - 54
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-5.13291$ of defining polynomial
Character	$\chi$	$=$	1682.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -6.13291 q^{3} +4.00000 q^{4} +2.36031 q^{5} +12.2658 q^{6} -18.5045 q^{7} -8.00000 q^{8} +10.6126 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -6.13291 q^{3} +4.00000 q^{4} +2.36031 q^{5} +12.2658 q^{6} -18.5045 q^{7} -8.00000 q^{8} +10.6126 q^{9} -4.72062 q^{10} +15.3852 q^{11} -24.5316 q^{12} +27.8241 q^{13} +37.0090 q^{14} -14.4756 q^{15} +16.0000 q^{16} +62.4231 q^{17} -21.2251 q^{18} -55.3245 q^{19} +9.44123 q^{20} +113.486 q^{21} -30.7703 q^{22} +44.3109 q^{23} +49.0633 q^{24} -119.429 q^{25} -55.6482 q^{26} +100.503 q^{27} -74.0180 q^{28} +28.9511 q^{30} +207.078 q^{31} -32.0000 q^{32} -94.3557 q^{33} -124.846 q^{34} -43.6763 q^{35} +42.4502 q^{36} -303.388 q^{37} +110.649 q^{38} -170.643 q^{39} -18.8825 q^{40} -125.712 q^{41} -226.973 q^{42} -101.246 q^{43} +61.5406 q^{44} +25.0489 q^{45} -88.6218 q^{46} -50.8663 q^{47} -98.1265 q^{48} -0.583766 q^{49} +238.858 q^{50} -382.835 q^{51} +111.296 q^{52} +692.512 q^{53} -201.005 q^{54} +36.3137 q^{55} +148.036 q^{56} +339.300 q^{57} +557.935 q^{59} -57.9022 q^{60} -809.678 q^{61} -414.157 q^{62} -196.380 q^{63} +64.0000 q^{64} +65.6734 q^{65} +188.711 q^{66} -749.866 q^{67} +249.692 q^{68} -271.755 q^{69} +87.3526 q^{70} -54.7703 q^{71} -84.9004 q^{72} +184.533 q^{73} +606.775 q^{74} +732.447 q^{75} -221.298 q^{76} -284.694 q^{77} +341.285 q^{78} +752.875 q^{79} +37.7649 q^{80} -902.913 q^{81} +251.423 q^{82} -902.018 q^{83} +453.945 q^{84} +147.338 q^{85} +202.492 q^{86} -123.081 q^{88} -953.385 q^{89} -50.0978 q^{90} -514.871 q^{91} +177.244 q^{92} -1269.99 q^{93} +101.733 q^{94} -130.583 q^{95} +196.253 q^{96} +1114.68 q^{97} +1.16753 q^{98} +163.276 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} - 2 q^{3} + 12 q^{4} + 20 q^{5} + 4 q^{6} + 24 q^{7} - 24 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q - 6 * q^2 - 2 * q^3 + 12 * q^4 + 20 * q^5 + 4 * q^6 + 24 * q^7 - 24 * q^8 + 5 * q^9	\( 3 q - 6 q^{2} - 2 q^{3} + 12 q^{4} + 20 q^{5} + 4 q^{6} + 24 q^{7} - 24 q^{8} + 5 q^{9} - 40 q^{10} - 10 q^{11} - 8 q^{12} - 4 q^{13} - 48 q^{14} + 130 q^{15} + 48 q^{16} + 66 q^{17} - 10 q^{18} + 164 q^{19} + 80 q^{20} + 88 q^{21} + 20 q^{22} - 204 q^{23} + 16 q^{24} + 79 q^{25} + 8 q^{26} + 142 q^{27} + 96 q^{28} - 260 q^{30} + 86 q^{31} - 96 q^{32} - 130 q^{33} - 132 q^{34} + 24 q^{35} + 20 q^{36} + 42 q^{37} - 328 q^{38} + 394 q^{39} - 160 q^{40} - 562 q^{41} - 176 q^{42} - 18 q^{43} - 40 q^{44} + 422 q^{45} + 408 q^{46} - 654 q^{47} - 32 q^{48} + 539 q^{49} - 158 q^{50} + 556 q^{51} - 16 q^{52} + 712 q^{53} - 284 q^{54} - 142 q^{55} - 192 q^{56} + 828 q^{57} + 184 q^{59} + 520 q^{60} - 322 q^{61} - 172 q^{62} - 784 q^{63} + 192 q^{64} + 1494 q^{65} + 260 q^{66} - 228 q^{67} + 264 q^{68} - 684 q^{69} - 48 q^{70} - 52 q^{71} - 40 q^{72} + 494 q^{73} - 84 q^{74} + 3048 q^{75} + 656 q^{76} - 872 q^{77} - 788 q^{78} + 2110 q^{79} + 320 q^{80} - 1513 q^{81} + 1124 q^{82} - 288 q^{83} + 352 q^{84} + 2704 q^{85} + 36 q^{86} + 80 q^{88} - 914 q^{89} - 844 q^{90} - 2984 q^{91} - 816 q^{92} - 62 q^{93} + 1308 q^{94} + 1900 q^{95} + 64 q^{96} - 218 q^{97} - 1078 q^{98} + 304 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - 2 * q^3 + 12 * q^4 + 20 * q^5 + 4 * q^6 + 24 * q^7 - 24 * q^8 + 5 * q^9 - 40 * q^10 - 10 * q^11 - 8 * q^12 - 4 * q^13 - 48 * q^14 + 130 * q^15 + 48 * q^16 + 66 * q^17 - 10 * q^18 + 164 * q^19 + 80 * q^20 + 88 * q^21 + 20 * q^22 - 204 * q^23 + 16 * q^24 + 79 * q^25 + 8 * q^26 + 142 * q^27 + 96 * q^28 - 260 * q^30 + 86 * q^31 - 96 * q^32 - 130 * q^33 - 132 * q^34 + 24 * q^35 + 20 * q^36 + 42 * q^37 - 328 * q^38 + 394 * q^39 - 160 * q^40 - 562 * q^41 - 176 * q^42 - 18 * q^43 - 40 * q^44 + 422 * q^45 + 408 * q^46 - 654 * q^47 - 32 * q^48 + 539 * q^49 - 158 * q^50 + 556 * q^51 - 16 * q^52 + 712 * q^53 - 284 * q^54 - 142 * q^55 - 192 * q^56 + 828 * q^57 + 184 * q^59 + 520 * q^60 - 322 * q^61 - 172 * q^62 - 784 * q^63 + 192 * q^64 + 1494 * q^65 + 260 * q^66 - 228 * q^67 + 264 * q^68 - 684 * q^69 - 48 * q^70 - 52 * q^71 - 40 * q^72 + 494 * q^73 - 84 * q^74 + 3048 * q^75 + 656 * q^76 - 872 * q^77 - 788 * q^78 + 2110 * q^79 + 320 * q^80 - 1513 * q^81 + 1124 * q^82 - 288 * q^83 + 352 * q^84 + 2704 * q^85 + 36 * q^86 + 80 * q^88 - 914 * q^89 - 844 * q^90 - 2984 * q^91 - 816 * q^92 - 62 * q^93 + 1308 * q^94 + 1900 * q^95 + 64 * q^96 - 218 * q^97 - 1078 * q^98 + 304 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−6.13291	−1.18028	−0.590139	−	0.807301i	$-0.700927\pi$
$3$	−6.13291	−1.18028	−0.590139	+	0.807301i	$0.700927\pi$
$4$	4.00000	0.500000
$5$	2.36031	0.211112	0.105556	−	0.994413i	$-0.466338\pi$
$5$	2.36031	0.211112	0.105556	+	0.994413i	$0.466338\pi$
$6$	12.2658	0.834583
$7$	−18.5045	−0.999149	−0.499574	−	0.866271i	$-0.666510\pi$
$7$	−18.5045	−0.999149	−0.499574	+	0.866271i	$0.666510\pi$
$8$	−8.00000	−0.353553
$9$	10.6126	0.393058
$10$	−4.72062	−0.149279
$11$	15.3852	0.421709	0.210854	−	0.977517i	$-0.432375\pi$
$11$	15.3852	0.421709	0.210854	+	0.977517i	$0.432375\pi$
$12$	−24.5316	−0.590139
$13$	27.8241	0.593617	0.296808	−	0.954937i	$-0.404078\pi$
$13$	27.8241	0.593617	0.296808	+	0.954937i	$0.404078\pi$
$14$	37.0090	0.706505
$15$	−14.4756	−0.249171
$16$	16.0000	0.250000
$17$	62.4231	0.890578	0.445289	−	0.895387i	$-0.353101\pi$
$17$	62.4231	0.890578	0.445289	+	0.895387i	$0.353101\pi$
$18$	−21.2251	−0.277934
$19$	−55.3245	−0.668016	−0.334008	−	0.942570i	$-0.608401\pi$
$19$	−55.3245	−0.668016	−0.334008	+	0.942570i	$0.608401\pi$
$20$	9.44123	0.105556
$21$	113.486	1.17927
$22$	−30.7703	−0.298193
$23$	44.3109	0.401716	0.200858	−	0.979620i	$-0.435627\pi$
$23$	44.3109	0.401716	0.200858	+	0.979620i	$0.435627\pi$
$24$	49.0633	0.417291
$25$	−119.429	−0.955432
$26$	−55.6482	−0.419750
$27$	100.503	0.716361
$28$	−74.0180	−0.499574
$29$	0	0
$29$	0	0
$30$	28.9511	0.176191
$31$	207.078	1.19975	0.599877	−	0.800092i	$-0.295216\pi$
$31$	207.078	1.19975	0.599877	+	0.800092i	$0.295216\pi$
$32$	−32.0000	−0.176777
$33$	−94.3557	−0.497734
$34$	−124.846	−0.629734
$35$	−43.6763	−0.210933
$36$	42.4502	0.196529
$37$	−303.388	−1.34802	−0.674008	−	0.738724i	$-0.735429\pi$
$37$	−303.388	−1.34802	−0.674008	+	0.738724i	$0.735429\pi$
$38$	110.649	0.472359
$39$	−170.643	−0.700633
$40$	−18.8825	−0.0746395
$41$	−125.712	−0.478850	−0.239425	−	0.970915i	$-0.576959\pi$
$41$	−125.712	−0.478850	−0.239425	+	0.970915i	$0.576959\pi$
$42$	−226.973	−0.833872
$43$	−101.246	−0.359066	−0.179533	−	0.983752i	$-0.557459\pi$
$43$	−101.246	−0.359066	−0.179533	+	0.983752i	$0.557459\pi$
$44$	61.5406	0.210854
$45$	25.0489	0.0829793
$46$	−88.6218	−0.284056
$47$	−50.8663	−0.157864	−0.0789320	−	0.996880i	$-0.525151\pi$
$47$	−50.8663	−0.157864	−0.0789320	+	0.996880i	$0.525151\pi$
$48$	−98.1265	−0.295070
$49$	−0.583766	−0.00170194
$50$	238.858	0.675592
$51$	−382.835	−1.05113
$52$	111.296	0.296808
$53$	692.512	1.79479	0.897395	−	0.441229i	$-0.145457\pi$
$53$	692.512	1.79479	0.897395	+	0.441229i	$0.145457\pi$
$54$	−201.005	−0.506544
$55$	36.3137	0.0890280
$56$	148.036	0.353252
$57$	339.300	0.788445
$58$	0	0
$59$	557.935	1.23113	0.615567	−	0.788085i	$-0.288927\pi$
$59$	557.935	1.23113	0.615567	+	0.788085i	$0.288927\pi$
$60$	−57.9022	−0.124586
$61$	−809.678	−1.69948	−0.849742	−	0.527198i	$-0.823243\pi$
$61$	−809.678	−1.69948	−0.849742	+	0.527198i	$0.823243\pi$
$62$	−414.157	−0.848354
$63$	−196.380	−0.392723
$64$	64.0000	0.125000
$65$	65.6734	0.125320
$66$	188.711	0.351951
$67$	−749.866	−1.36732	−0.683662	−	0.729799i	$-0.739614\pi$
$67$	−749.866	−1.36732	−0.683662	+	0.729799i	$0.739614\pi$
$68$	249.692	0.445289
$69$	−271.755	−0.474137
$70$	87.3526	0.149152
$71$	−54.7703	−0.0915499	−0.0457749	−	0.998952i	$-0.514576\pi$
$71$	−54.7703	−0.0915499	−0.0457749	+	0.998952i	$0.514576\pi$
$72$	−84.9004	−0.138967
$73$	184.533	0.295862	0.147931	−	0.988998i	$-0.452739\pi$
$73$	184.533	0.295862	0.147931	+	0.988998i	$0.452739\pi$
$74$	606.775	0.953192
$75$	732.447	1.12768
$76$	−221.298	−0.334008
$77$	−284.694	−0.421350
$78$	341.285	0.495422
$79$	752.875	1.07222	0.536108	−	0.844149i	$-0.319894\pi$
$79$	752.875	1.07222	0.536108	+	0.844149i	$0.319894\pi$
$80$	37.7649	0.0527781
$81$	−902.913	−1.23856
$82$	251.423	0.338598
$83$	−902.018	−1.19288	−0.596441	−	0.802657i	$-0.703419\pi$
$83$	−902.018	−1.19288	−0.596441	+	0.802657i	$0.703419\pi$
$84$	453.945	0.589637
$85$	147.338	0.188012
$86$	202.492	0.253898
$87$	0	0
$88$	−123.081	−0.149097
$89$	−953.385	−1.13549	−0.567745	−	0.823204i	$-0.692184\pi$
$89$	−953.385	−1.13549	−0.567745	+	0.823204i	$0.692184\pi$
$90$	−50.0978	−0.0586752
$91$	−514.871	−0.593111
$92$	177.244	0.200858
$93$	−1269.99	−1.41604
$94$	101.733	0.111627
$95$	−130.583	−0.141026
$96$	196.253	0.208646
$97$	1114.68	1.16679	0.583395	−	0.812189i	$-0.301724\pi$
$97$	1114.68	1.16679	0.583395	+	0.812189i	$0.301724\pi$
$98$	1.16753	0.00120345
$99$	163.276	0.165756
$100$	−477.716	−0.477716
$101$	−742.802	−0.731798	−0.365899	−	0.930655i	$-0.619238\pi$
$101$	−742.802	−0.731798	−0.365899	+	0.930655i	$0.619238\pi$
$102$	765.670	0.743261
$103$	−1782.16	−1.70487	−0.852434	−	0.522835i	$-0.824874\pi$
$103$	−1782.16	−1.70487	−0.852434	+	0.522835i	$0.824874\pi$
$104$	−222.593	−0.209875
$105$	267.863	0.248959
$106$	−1385.02	−1.26911
$107$	1758.89	1.58914	0.794571	−	0.607172i	$-0.207696\pi$
$107$	1758.89	1.58914	0.794571	+	0.607172i	$0.207696\pi$
$108$	402.011	0.358181
$109$	1596.84	1.40321	0.701604	−	0.712567i	$-0.252468\pi$
$109$	1596.84	1.40321	0.701604	+	0.712567i	$0.252468\pi$
$110$	−72.6274	−0.0629523
$111$	1860.65	1.59103
$112$	−296.072	−0.249787
$113$	−991.893	−0.825747	−0.412874	−	0.910788i	$-0.635475\pi$
$113$	−991.893	−0.825747	−0.412874	+	0.910788i	$0.635475\pi$
$114$	−678.600	−0.557515
$115$	104.587	0.0848072
$116$	0	0
$117$	295.285	0.233325
$118$	−1115.87	−0.870543
$119$	−1155.11	−0.889819
$120$	115.804	0.0880954
$121$	−1094.30	−0.822162
$122$	1619.36	1.20172
$123$	770.978	0.565177
$124$	828.314	0.599877
$125$	−576.928	−0.412816
$126$	392.760	0.277697
$127$	−363.708	−0.254125	−0.127063	−	0.991895i	$-0.540555\pi$
$127$	−363.708	−0.254125	−0.127063	+	0.991895i	$0.540555\pi$
$128$	−128.000	−0.0883883
$129$	620.931	0.423798
$130$	−131.347	−0.0886145
$131$	665.920	0.444135	0.222068	−	0.975031i	$-0.428719\pi$
$131$	665.920	0.444135	0.222068	+	0.975031i	$0.428719\pi$
$132$	−377.423	−0.248867
$133$	1023.75	0.667448
$134$	1499.73	0.966844
$135$	237.217	0.151233
$136$	−499.385	−0.314867
$137$	−343.259	−0.214063	−0.107031	−	0.994256i	$-0.534135\pi$
$137$	−343.259	−0.214063	−0.107031	+	0.994256i	$0.534135\pi$
$138$	543.510	0.335265
$139$	−755.103	−0.460770	−0.230385	−	0.973100i	$-0.573999\pi$
$139$	−755.103	−0.460770	−0.230385	+	0.973100i	$0.573999\pi$
$140$	−174.705	−0.105466
$141$	311.958	0.186324
$142$	109.541	0.0647355
$143$	428.078	0.250333
$144$	169.801	0.0982644
$145$	0	0
$146$	−369.065	−0.209206
$147$	3.58018	0.00200877
$148$	−1213.55	−0.674008
$149$	−3033.96	−1.66813	−0.834066	−	0.551664i	$-0.813993\pi$
$149$	−3033.96	−1.66813	−0.834066	+	0.551664i	$0.813993\pi$
$150$	−1464.89	−0.797387
$151$	−723.924	−0.390146	−0.195073	−	0.980789i	$-0.562494\pi$
$151$	−723.924	−0.390146	−0.195073	+	0.980789i	$0.562494\pi$
$152$	442.596	0.236179
$153$	662.468	0.350048
$154$	569.389	0.297939
$155$	488.769	0.253283
$156$	−682.570	−0.350316
$157$	−647.348	−0.329070	−0.164535	−	0.986371i	$-0.552612\pi$
$157$	−647.348	−0.329070	−0.164535	+	0.986371i	$0.552612\pi$
$158$	−1505.75	−0.758171
$159$	−4247.11	−2.11835
$160$	−75.5299	−0.0373197
$161$	−819.951	−0.401374
$162$	1805.83	0.875797
$163$	1514.06	0.727546	0.363773	−	0.931488i	$-0.381488\pi$
$163$	1514.06	0.727546	0.363773	+	0.931488i	$0.381488\pi$
$164$	−502.847	−0.239425
$165$	−222.709	−0.105078
$166$	1804.04	0.843496
$167$	1841.05	0.853084	0.426542	−	0.904468i	$-0.359732\pi$
$167$	1841.05	0.853084	0.426542	+	0.904468i	$0.359732\pi$
$168$	−907.891	−0.416936
$169$	−1422.82	−0.647619
$170$	−294.675	−0.132945
$171$	−587.134	−0.262569
$172$	−404.983	−0.179533
$173$	−303.426	−0.133347	−0.0666736	−	0.997775i	$-0.521239\pi$
$173$	−303.426	−0.133347	−0.0666736	+	0.997775i	$0.521239\pi$
$174$	0	0
$175$	2209.97	0.954618
$176$	246.162	0.105427
$177$	−3421.76	−1.45308
$178$	1906.77	0.802913
$179$	−3036.60	−1.26797	−0.633983	−	0.773347i	$-0.718581\pi$
$179$	−3036.60	−1.26797	−0.633983	+	0.773347i	$0.718581\pi$
$180$	100.196	0.0414897
$181$	−2339.77	−0.960851	−0.480425	−	0.877036i	$-0.659518\pi$
$181$	−2339.77	−0.960851	−0.480425	+	0.877036i	$0.659518\pi$
$182$	1029.74	0.419393
$183$	4965.68	2.00587
$184$	−354.487	−0.142028
$185$	−716.088	−0.284583
$186$	2539.99	1.00129
$187$	960.389	0.375565
$188$	−203.465	−0.0789320
$189$	−1859.75	−0.715751
$190$	261.166	0.0997208
$191$	4217.47	1.59772	0.798862	−	0.601514i	$-0.205436\pi$
$191$	4217.47	1.59772	0.798862	+	0.601514i	$0.205436\pi$
$192$	−392.506	−0.147535
$193$	1962.59	0.731969	0.365985	−	0.930621i	$-0.380732\pi$
$193$	1962.59	0.731969	0.365985	+	0.930621i	$0.380732\pi$
$194$	−2229.36	−0.825045
$195$	−402.769	−0.147912
$196$	−2.33506	−0.000850971 0
$197$	2040.68	0.738032	0.369016	−	0.929423i	$-0.379695\pi$
$197$	2040.68	0.738032	0.369016	+	0.929423i	$0.379695\pi$
$198$	−326.552	−0.117207
$199$	3235.68	1.15262	0.576310	−	0.817231i	$-0.304492\pi$
$199$	3235.68	1.15262	0.576310	+	0.817231i	$0.304492\pi$
$200$	955.432	0.337796
$201$	4598.86	1.61382
$202$	1485.60	0.517459
$203$	0	0
$204$	−1531.34	−0.525565
$205$	−296.718	−0.101091
$206$	3564.32	1.20552
$207$	470.252	0.157897
$208$	445.186	0.148404
$209$	−851.176	−0.281708
$210$	−535.725	−0.176041
$211$	3943.15	1.28653	0.643264	−	0.765645i	$-0.277580\pi$
$211$	3943.15	1.28653	0.643264	+	0.765645i	$0.277580\pi$
$212$	2770.05	0.897395
$213$	335.901	0.108054
$214$	−3517.78	−1.12369
$215$	−238.971	−0.0758033
$216$	−804.022	−0.253272
$217$	−3831.88	−1.19873
$218$	−3193.68	−0.992218
$219$	−1131.72	−0.349199
$220$	145.255	0.0445140
$221$	1736.87	0.528662
$222$	−3721.30	−1.12503
$223$	−2530.83	−0.759987	−0.379993	−	0.924989i	$-0.624074\pi$
$223$	−2530.83	−0.759987	−0.379993	+	0.924989i	$0.624074\pi$
$224$	592.144	0.176626
$225$	−1267.45	−0.375540
$226$	1983.79	0.583892
$227$	5429.77	1.58761	0.793803	−	0.608175i	$-0.208098\pi$
$227$	5429.77	1.58761	0.793803	+	0.608175i	$0.208098\pi$
$228$	1357.20	0.394223
$229$	−5597.57	−1.61527	−0.807637	−	0.589680i	$-0.799254\pi$
$229$	−5597.57	−1.61527	−0.807637	+	0.589680i	$0.799254\pi$
$230$	−209.175	−0.0599677
$231$	1746.00	0.497310
$232$	0	0
$233$	−1736.74	−0.488316	−0.244158	−	0.969735i	$-0.578512\pi$
$233$	−1736.74	−0.488316	−0.244158	+	0.969735i	$0.578512\pi$
$234$	−590.569	−0.164986
$235$	−120.060	−0.0333271
$236$	2231.74	0.615567
$237$	−4617.31	−1.26551
$238$	2310.21	0.629197
$239$	4205.18	1.13812	0.569059	−	0.822296i	$-0.307307\pi$
$239$	4205.18	1.13812	0.569059	+	0.822296i	$0.307307\pi$
$240$	−231.609	−0.0622929
$241$	6050.05	1.61709	0.808543	−	0.588436i	$-0.200256\pi$
$241$	6050.05	1.61709	0.808543	+	0.588436i	$0.200256\pi$
$242$	2188.59	0.581356
$243$	2823.91	0.745489
$244$	−3238.71	−0.849742
$245$	−1.37787	−0.000359301 0
$246$	−1541.96	−0.399640
$247$	−1539.35	−0.396545
$248$	−1656.63	−0.424177
$249$	5531.99	1.40793
$250$	1153.86	0.291905
$251$	6533.19	1.64291	0.821457	−	0.570271i	$-0.193162\pi$
$251$	6533.19	1.64291	0.821457	+	0.570271i	$0.193162\pi$
$252$	−785.520	−0.196361
$253$	681.730	0.169407
$254$	727.417	0.179694
$255$	−903.608	−0.221907
$256$	256.000	0.0625000
$257$	2423.49	0.588222	0.294111	−	0.955771i	$-0.404976\pi$
$257$	2423.49	0.588222	0.294111	+	0.955771i	$0.404976\pi$
$258$	−1241.86	−0.299671
$259$	5614.03	1.34687
$260$	262.694	0.0626599
$261$	0	0
$262$	−1331.84	−0.314051
$263$	2692.44	0.631266	0.315633	−	0.948881i	$-0.397783\pi$
$263$	2692.44	0.631266	0.315633	+	0.948881i	$0.397783\pi$
$264$	754.846	0.175976
$265$	1634.54	0.378902
$266$	−2047.50	−0.471957
$267$	5847.02	1.34019
$268$	−2999.46	−0.683662
$269$	6688.58	1.51602	0.758011	−	0.652241i	$-0.226171\pi$
$269$	6688.58	1.51602	0.758011	+	0.652241i	$0.226171\pi$
$270$	−474.435	−0.106938
$271$	−1273.30	−0.285415	−0.142707	−	0.989765i	$-0.545581\pi$
$271$	−1273.30	−0.285415	−0.142707	+	0.989765i	$0.545581\pi$
$272$	998.769	0.222644
$273$	3157.65	0.700036
$274$	686.517	0.151365
$275$	−1837.43	−0.402914
$276$	−1087.02	−0.237068
$277$	−1660.50	−0.360179	−0.180090	−	0.983650i	$-0.557639\pi$
$277$	−1660.50	−0.360179	−0.180090	+	0.983650i	$0.557639\pi$
$278$	1510.21	0.325814
$279$	2197.63	0.471573
$280$	349.410	0.0745760
$281$	−1247.71	−0.264883	−0.132442	−	0.991191i	$-0.542282\pi$
$281$	−1247.71	−0.264883	−0.132442	+	0.991191i	$0.542282\pi$
$282$	−623.917	−0.131751
$283$	6592.72	1.38479	0.692396	−	0.721517i	$-0.256555\pi$
$283$	6592.72	1.38479	0.692396	+	0.721517i	$0.256555\pi$
$284$	−219.081	−0.0457749
$285$	800.852	0.166451
$286$	−856.156	−0.177012
$287$	2326.23	0.478443
$288$	−339.602	−0.0694834
$289$	−1016.36	−0.206871
$290$	0	0
$291$	−6836.23	−1.37714
$292$	738.130	0.147931
$293$	−837.525	−0.166992	−0.0834962	−	0.996508i	$-0.526609\pi$
$293$	−837.525	−0.166992	−0.0834962	+	0.996508i	$0.526609\pi$
$294$	−7.16037	−0.00142041
$295$	1316.90	0.259908
$296$	2427.10	0.476596
$297$	1546.25	0.302096
$298$	6067.92	1.17955
$299$	1232.91	0.238465
$300$	2929.79	0.563838
$301$	1873.50	0.358761
$302$	1447.85	0.275875
$303$	4555.54	0.863726
$304$	−885.192	−0.167004
$305$	−1911.09	−0.358782
$306$	−1324.94	−0.247522
$307$	−500.495	−0.0930448	−0.0465224	−	0.998917i	$-0.514814\pi$
$307$	−500.495	−0.0930448	−0.0465224	+	0.998917i	$0.514814\pi$
$308$	−1138.78	−0.210675
$309$	10929.8	2.01222
$310$	−977.538	−0.179098
$311$	−2016.48	−0.367667	−0.183833	−	0.982957i	$-0.558851\pi$
$311$	−2016.48	−0.367667	−0.183833	+	0.982957i	$0.558851\pi$
$312$	1365.14	0.247711
$313$	8739.06	1.57815	0.789075	−	0.614296i	$-0.210560\pi$
$313$	8739.06	1.57815	0.789075	+	0.614296i	$0.210560\pi$
$314$	1294.70	0.232688
$315$	−463.517	−0.0829087
$316$	3011.50	0.536108
$317$	1690.73	0.299560	0.149780	−	0.988719i	$-0.452143\pi$
$317$	1690.73	0.299560	0.149780	+	0.988719i	$0.452143\pi$
$318$	8494.22	1.49790
$319$	0	0
$320$	151.060	0.0263890
$321$	−10787.1	−1.87563
$322$	1639.90	0.283814
$323$	−3453.53	−0.594920
$324$	−3611.65	−0.619282
$325$	−3323.00	−0.567160
$326$	−3028.11	−0.514453
$327$	−9793.28	−1.65618
$328$	1005.69	0.169299
$329$	941.255	0.157730
$330$	445.417	0.0743012
$331$	7446.19	1.23649	0.618247	−	0.785984i	$-0.287843\pi$
$331$	7446.19	1.23649	0.618247	+	0.785984i	$0.287843\pi$
$332$	−3608.07	−0.596441
$333$	−3219.72	−0.529848
$334$	−3682.11	−0.603221
$335$	−1769.91	−0.288659
$336$	1815.78	0.294818
$337$	9366.72	1.51406	0.757030	−	0.653381i	$-0.226650\pi$
$337$	9366.72	1.51406	0.757030	+	0.653381i	$0.226650\pi$
$338$	2845.64	0.457936
$339$	6083.19	0.974612
$340$	589.351	0.0940060
$341$	3185.93	0.505947
$342$	1174.27	0.185664
$343$	6357.84	1.00085
$344$	809.967	0.126949
$345$	−641.425	−0.100096
$346$	606.852	0.0942907
$347$	7951.11	1.23008	0.615040	−	0.788496i	$-0.289140\pi$
$347$	7951.11	1.23008	0.615040	+	0.788496i	$0.289140\pi$
$348$	0	0
$349$	−1256.74	−0.192755	−0.0963776	−	0.995345i	$-0.530726\pi$
$349$	−1256.74	−0.192755	−0.0963776	+	0.995345i	$0.530726\pi$
$350$	−4419.94	−0.675017
$351$	2796.40	0.425244
$352$	−492.325	−0.0745483
$353$	7309.17	1.10206	0.551031	−	0.834485i	$-0.314235\pi$
$353$	7309.17	1.10206	0.551031	+	0.834485i	$0.314235\pi$
$354$	6843.52	1.02748
$355$	−129.275	−0.0193273
$356$	−3813.54	−0.567745
$357$	7084.17	1.05023
$358$	6073.20	0.896588
$359$	−11555.1	−1.69876	−0.849379	−	0.527783i	$-0.823024\pi$
$359$	−11555.1	−1.69876	−0.849379	+	0.527783i	$0.823024\pi$
$360$	−200.391	−0.0293376
$361$	−3798.20	−0.553754
$362$	4679.55	0.679424
$363$	6711.22	0.970380
$364$	−2059.48	−0.296556
$365$	435.554	0.0624601
$366$	−9931.35	−1.41836
$367$	2097.86	0.298386	0.149193	−	0.988808i	$-0.452332\pi$
$367$	2097.86	0.298386	0.149193	+	0.988808i	$0.452332\pi$
$368$	708.975	0.100429
$369$	−1334.12	−0.188216
$370$	1432.18	0.201231
$371$	−12814.6	−1.79326
$372$	−5079.97	−0.708022
$373$	13979.4	1.94055	0.970277	−	0.241996i	$-0.0778022\pi$
$373$	13979.4	1.94055	0.970277	+	0.241996i	$0.0778022\pi$
$374$	−1920.78	−0.265564
$375$	3538.24	0.487238
$376$	406.930	0.0558134
$377$	0	0
$378$	3719.50	0.506113
$379$	894.071	0.121175	0.0605875	−	0.998163i	$-0.480703\pi$
$379$	894.071	0.121175	0.0605875	+	0.998163i	$0.480703\pi$
$380$	−522.331	−0.0705132
$381$	2230.59	0.299939
$382$	−8434.94	−1.12976
$383$	5312.26	0.708730	0.354365	−	0.935107i	$-0.384697\pi$
$383$	5312.26	0.708730	0.354365	+	0.935107i	$0.384697\pi$
$384$	785.012	0.104323
$385$	−671.967	−0.0889522
$386$	−3925.17	−0.517580
$387$	−1074.48	−0.141134
$388$	4458.72	0.583395
$389$	4206.27	0.548242	0.274121	−	0.961695i	$-0.411613\pi$
$389$	4206.27	0.548242	0.274121	+	0.961695i	$0.411613\pi$
$390$	805.538	0.104590
$391$	2766.02	0.357759
$392$	4.67013	0.000601727 0
$393$	−4084.03	−0.524204
$394$	−4081.36	−0.521868
$395$	1777.02	0.226358
$396$	653.103	0.0828779
$397$	5702.43	0.720898	0.360449	−	0.932779i	$-0.382623\pi$
$397$	5702.43	0.720898	0.360449	+	0.932779i	$0.382623\pi$
$398$	−6471.36	−0.815025
$399$	−6278.57	−0.787774
$400$	−1910.86	−0.238858
$401$	9803.05	1.22080	0.610400	−	0.792093i	$-0.291009\pi$
$401$	9803.05	1.22080	0.610400	+	0.792093i	$0.291009\pi$
$402$	−9197.71	−1.14114
$403$	5761.77	0.712194
$404$	−2971.21	−0.365899
$405$	−2131.15	−0.261476
$406$	0	0
$407$	−4667.66	−0.568471
$408$	3062.68	0.371630
$409$	−8384.14	−1.01362	−0.506808	−	0.862059i	$-0.669175\pi$
$409$	−8384.14	−1.01362	−0.506808	+	0.862059i	$0.669175\pi$
$410$	593.436	0.0714823
$411$	2105.17	0.252653
$412$	−7128.64	−0.852434
$413$	−10324.3	−1.23009
$414$	−940.504	−0.111650
$415$	−2129.04	−0.251832
$416$	−890.371	−0.104938
$417$	4630.98	0.543837
$418$	1702.35	0.199198
$419$	−12350.2	−1.43997	−0.719986	−	0.693989i	$-0.755852\pi$
$419$	−12350.2	−1.43997	−0.719986	+	0.693989i	$0.755852\pi$
$420$	1071.45	0.124480
$421$	4776.65	0.552968	0.276484	−	0.961018i	$-0.410831\pi$
$421$	4776.65	0.552968	0.276484	+	0.961018i	$0.410831\pi$
$422$	−7886.29	−0.909712
$423$	−539.821	−0.0620497
$424$	−5540.10	−0.634554
$425$	−7455.12	−0.850886
$426$	−671.802	−0.0764060
$427$	14982.7	1.69804
$428$	7035.55	0.794571
$429$	−2625.36	−0.295463
$430$	477.943	0.0536010
$431$	−536.087	−0.0599128	−0.0299564	−	0.999551i	$-0.509537\pi$
$431$	−536.087	−0.0599128	−0.0299564	+	0.999551i	$0.509537\pi$
$432$	1608.04	0.179090
$433$	−3530.09	−0.391790	−0.195895	−	0.980625i	$-0.562761\pi$
$433$	−3530.09	−0.391790	−0.195895	+	0.980625i	$0.562761\pi$
$434$	7663.76	0.847632
$435$	0	0
$436$	6387.37	0.701604
$437$	−2451.48	−0.268353
$438$	2263.44	0.246921
$439$	−11536.6	−1.25425	−0.627123	−	0.778920i	$-0.715768\pi$
$439$	−11536.6	−1.25425	−0.627123	+	0.778920i	$0.715768\pi$
$440$	−290.510	−0.0314761
$441$	−6.19525	−0.000668961 0
$442$	−3473.73	−0.373820
$443$	−6775.94	−0.726715	−0.363357	−	0.931650i	$-0.618370\pi$
$443$	−6775.94	−0.726715	−0.363357	+	0.931650i	$0.618370\pi$
$444$	7442.59	0.795517
$445$	−2250.28	−0.239716
$446$	5061.67	0.537392
$447$	18607.0	1.96886
$448$	−1184.29	−0.124894
$449$	6601.58	0.693870	0.346935	−	0.937889i	$-0.387222\pi$
$449$	6601.58	0.693870	0.346935	+	0.937889i	$0.387222\pi$
$450$	2534.89	0.265547
$451$	−1934.09	−0.201935
$452$	−3967.57	−0.412874
$453$	4439.76	0.460481
$454$	−10859.5	−1.12261
$455$	−1215.25	−0.125213
$456$	−2714.40	−0.278757
$457$	−4454.94	−0.456003	−0.228001	−	0.973661i	$-0.573219\pi$
$457$	−4454.94	−0.456003	−0.228001	+	0.973661i	$0.573219\pi$
$458$	11195.1	1.14217
$459$	6273.69	0.637975
$460$	418.350	0.0424036
$461$	−1861.62	−0.188078	−0.0940392	−	0.995568i	$-0.529978\pi$
$461$	−1861.62	−0.188078	−0.0940392	+	0.995568i	$0.529978\pi$
$462$	−3492.01	−0.351651
$463$	−7795.98	−0.782527	−0.391263	−	0.920279i	$-0.627962\pi$
$463$	−7795.98	−0.782527	−0.391263	+	0.920279i	$0.627962\pi$
$464$	0	0
$465$	−2997.57	−0.298945
$466$	3473.48	0.345291
$467$	−13072.0	−1.29529	−0.647646	−	0.761941i	$-0.724247\pi$
$467$	−13072.0	−1.29529	−0.647646	+	0.761941i	$0.724247\pi$
$468$	1181.14	0.116663
$469$	13875.9	1.36616
$470$	240.120	0.0235658
$471$	3970.12	0.388394
$472$	−4463.48	−0.435272
$473$	−1557.68	−0.151421
$474$	9234.63	0.894853
$475$	6607.35	0.638244
$476$	−4620.43	−0.444910
$477$	7349.32	0.705455
$478$	−8410.36	−0.804771
$479$	−4847.90	−0.462435	−0.231218	−	0.972902i	$-0.574271\pi$
$479$	−4847.90	−0.462435	−0.231218	+	0.972902i	$0.574271\pi$
$480$	463.218	0.0440477
$481$	−8441.48	−0.800205
$482$	−12100.1	−1.14345
$483$	5028.68	0.473733
$484$	−4377.19	−0.411081
$485$	2630.99	0.246324
$486$	−5647.81	−0.527140
$487$	15092.4	1.40432	0.702160	−	0.712020i	$-0.252219\pi$
$487$	15092.4	1.40432	0.702160	+	0.712020i	$0.252219\pi$
$488$	6477.42	0.600859
$489$	−9285.56	−0.858707
$490$	2.75574	0.000254064 0
$491$	4438.48	0.407955	0.203978	−	0.978976i	$-0.434613\pi$
$491$	4438.48	0.407955	0.203978	+	0.978976i	$0.434613\pi$
$492$	3083.91	0.282588
$493$	0	0
$494$	3078.71	0.280400
$495$	385.381	0.0349931
$496$	3313.26	0.299939
$497$	1013.50	0.0914719
$498$	−11064.0	−0.995560
$499$	1648.66	0.147904	0.0739519	−	0.997262i	$-0.476439\pi$
$499$	1648.66	0.147904	0.0739519	+	0.997262i	$0.476439\pi$
$500$	−2307.71	−0.206408
$501$	−11291.0	−1.00688
$502$	−13066.4	−1.16172
$503$	−16870.8	−1.49549	−0.747746	−	0.663984i	$-0.768864\pi$
$503$	−16870.8	−1.49549	−0.747746	+	0.663984i	$0.768864\pi$
$504$	1571.04	0.138849
$505$	−1753.24	−0.154492
$506$	−1363.46	−0.119789
$507$	8726.02	0.764371
$508$	−1454.83	−0.127063
$509$	11051.6	0.962384	0.481192	−	0.876615i	$-0.340204\pi$
$509$	11051.6	0.962384	0.481192	+	0.876615i	$0.340204\pi$
$510$	1807.22	0.156912
$511$	−3414.68	−0.295610
$512$	−512.000	−0.0441942
$513$	−5560.26	−0.478541
$514$	−4846.98	−0.415936
$515$	−4206.45	−0.359919
$516$	2483.73	0.211899
$517$	−782.586	−0.0665727
$518$	−11228.1	−0.952380
$519$	1860.88	0.157387
$520$	−525.387	−0.0443072
$521$	−15369.3	−1.29240	−0.646201	−	0.763167i	$-0.723643\pi$
$521$	−15369.3	−1.29240	−0.646201	+	0.763167i	$0.723643\pi$
$522$	0	0
$523$	779.256	0.0651520	0.0325760	−	0.999469i	$-0.489629\pi$
$523$	779.256	0.0651520	0.0325760	+	0.999469i	$0.489629\pi$
$524$	2663.68	0.222068
$525$	−13553.6	−1.12672
$526$	−5384.88	−0.446373
$527$	12926.5	1.06847
$528$	−1509.69	−0.124434
$529$	−10203.5	−0.838624
$530$	−3269.08	−0.267924
$531$	5921.11	0.483906
$532$	4095.01	0.333724
$533$	−3497.81	−0.284253
$534$	−11694.0	−0.947661
$535$	4151.52	0.335487
$536$	5998.92	0.483422
$537$	18623.2	1.49655
$538$	−13377.2	−1.07199
$539$	−8.98133	−0.000717724 0
$540$	948.869	0.0756164
$541$	−18847.1	−1.49778	−0.748889	−	0.662695i	$-0.769413\pi$
$541$	−18847.1	−1.49778	−0.748889	+	0.662695i	$0.769413\pi$
$542$	2546.60	0.201819
$543$	14349.6	1.13407
$544$	−1997.54	−0.157433
$545$	3769.04	0.296235
$546$	−6315.31	−0.495001
$547$	−3422.52	−0.267525	−0.133763	−	0.991013i	$-0.542706\pi$
$547$	−3422.52	−0.267525	−0.133763	+	0.991013i	$0.542706\pi$
$548$	−1373.03	−0.107031
$549$	−8592.75	−0.667995
$550$	3674.87	0.284903
$551$	0	0
$552$	2174.04	0.167633
$553$	−13931.6	−1.07130
$554$	3321.00	0.254685
$555$	4391.70	0.335887
$556$	−3020.41	−0.230385
$557$	−24115.0	−1.83445	−0.917224	−	0.398373i	$-0.869575\pi$
$557$	−24115.0	−1.83445	−0.917224	+	0.398373i	$0.869575\pi$
$558$	−4395.26	−0.333452
$559$	−2817.07	−0.213148
$560$	−698.821	−0.0527332
$561$	−5889.97	−0.443271
$562$	2495.42	0.187301
$563$	−18904.9	−1.41518	−0.707591	−	0.706622i	$-0.750218\pi$
$563$	−18904.9	−1.41518	−0.707591	+	0.706622i	$0.750218\pi$
$564$	1247.83	0.0931618
$565$	−2341.17	−0.174325
$566$	−13185.4	−0.979196
$567$	16707.9	1.23751
$568$	438.162	0.0323678
$569$	14072.1	1.03679	0.518394	−	0.855142i	$-0.326530\pi$
$569$	14072.1	1.03679	0.518394	+	0.855142i	$0.326530\pi$
$570$	−1601.70	−0.117698
$571$	16218.7	1.18867	0.594334	−	0.804218i	$-0.297416\pi$
$571$	16218.7	1.18867	0.594334	+	0.804218i	$0.297416\pi$
$572$	1712.31	0.125167
$573$	−25865.3	−1.88576
$574$	−4652.46	−0.338310
$575$	−5292.01	−0.383812
$576$	679.203	0.0491322
$577$	−5122.09	−0.369559	−0.184779	−	0.982780i	$-0.559157\pi$
$577$	−5122.09	−0.369559	−0.184779	+	0.982780i	$0.559157\pi$
$578$	2032.72	0.146280
$579$	−12036.4	−0.863928
$580$	0	0
$581$	16691.4	1.19187
$582$	13672.5	0.973783
$583$	10654.4	0.756879
$584$	−1476.26	−0.104603
$585$	696.963	0.0492579
$586$	1675.05	0.118081
$587$	22661.7	1.59344	0.796721	−	0.604347i	$-0.206566\pi$
$587$	22661.7	1.59344	0.796721	+	0.604347i	$0.206566\pi$
$588$	14.3207	0.00100438
$589$	−11456.5	−0.801455
$590$	−2633.79	−0.183782
$591$	−12515.3	−0.871084
$592$	−4854.20	−0.337004
$593$	−13919.5	−0.963921	−0.481960	−	0.876193i	$-0.660075\pi$
$593$	−13919.5	−0.963921	−0.481960	+	0.876193i	$0.660075\pi$
$594$	−3092.50	−0.213614
$595$	−2726.41	−0.187852
$596$	−12135.8	−0.834066
$597$	−19844.1	−1.36041
$598$	−2465.82	−0.168620
$599$	10239.3	0.698441	0.349221	−	0.937041i	$-0.386446\pi$
$599$	10239.3	0.698441	0.349221	+	0.937041i	$0.386446\pi$
$600$	−5859.57	−0.398693
$601$	6948.34	0.471595	0.235798	−	0.971802i	$-0.424230\pi$
$601$	6948.34	0.471595	0.235798	+	0.971802i	$0.424230\pi$
$602$	−3747.01	−0.253682
$603$	−7957.99	−0.537437
$604$	−2895.70	−0.195073
$605$	−2582.88	−0.173568
$606$	−9111.08	−0.610746
$607$	15449.1	1.03305	0.516525	−	0.856272i	$-0.327225\pi$
$607$	15449.1	1.03305	0.516525	+	0.856272i	$0.327225\pi$
$608$	1770.38	0.118090
$609$	0	0
$610$	3822.18	0.253697
$611$	−1415.31	−0.0937107
$612$	2649.87	0.175024
$613$	8873.06	0.584632	0.292316	−	0.956322i	$-0.405574\pi$
$613$	8873.06	0.584632	0.292316	+	0.956322i	$0.405574\pi$
$614$	1000.99	0.0657926
$615$	1819.75	0.119316
$616$	2277.56	0.148970
$617$	16549.2	1.07981	0.539906	−	0.841725i	$-0.318460\pi$
$617$	16549.2	1.07981	0.539906	+	0.841725i	$0.318460\pi$
$618$	−21859.6	−1.42285
$619$	1121.37	0.0728140	0.0364070	−	0.999337i	$-0.488409\pi$
$619$	1121.37	0.0728140	0.0364070	+	0.999337i	$0.488409\pi$
$620$	1955.08	0.126642
$621$	4453.37	0.287774
$622$	4032.97	0.259980
$623$	17641.9	1.13452
$624$	−2730.28	−0.175158
$625$	13566.9	0.868281
$626$	−17478.1	−1.11592
$627$	5220.18	0.332494
$628$	−2589.39	−0.164535
$629$	−18938.4	−1.20051
$630$	927.034	0.0586253
$631$	1944.05	0.122649	0.0613245	−	0.998118i	$-0.480468\pi$
$631$	1944.05	0.122649	0.0613245	+	0.998118i	$0.480468\pi$
$632$	−6023.00	−0.379086
$633$	−24182.9	−1.51846
$634$	−3381.45	−0.211821
$635$	−858.464	−0.0536490
$636$	−16988.4	−1.05918
$637$	−16.2428	−0.00101030
$638$	0	0
$639$	−581.253	−0.0359844
$640$	−302.119	−0.0186599
$641$	11807.0	0.727530	0.363765	−	0.931491i	$-0.381491\pi$
$641$	11807.0	0.727530	0.363765	+	0.931491i	$0.381491\pi$
$642$	21574.2	1.32627
$643$	14848.2	0.910665	0.455333	−	0.890321i	$-0.349520\pi$
$643$	14848.2	0.910665	0.455333	+	0.890321i	$0.349520\pi$
$644$	−3279.80	−0.200687
$645$	1465.59	0.0894690
$646$	6907.05	0.420672
$647$	−4933.68	−0.299788	−0.149894	−	0.988702i	$-0.547893\pi$
$647$	−4933.68	−0.299788	−0.149894	+	0.988702i	$0.547893\pi$
$648$	7223.30	0.437898
$649$	8583.91	0.519180
$650$	6646.00	0.401043
$651$	23500.6	1.41484
$652$	6056.22	0.363773
$653$	27029.7	1.61984	0.809919	−	0.586541i	$-0.199511\pi$
$653$	27029.7	1.61984	0.809919	+	0.586541i	$0.199511\pi$
$654$	19586.6	1.17109
$655$	1571.78	0.0937625
$656$	−2011.39	−0.119713
$657$	1958.36	0.116291
$658$	−1882.51	−0.111532
$659$	−12211.1	−0.721817	−0.360908	−	0.932601i	$-0.617533\pi$
$659$	−12211.1	−0.721817	−0.360908	+	0.932601i	$0.617533\pi$
$660$	−890.834	−0.0525389
$661$	−864.848	−0.0508906	−0.0254453	−	0.999676i	$-0.508100\pi$
$661$	−864.848	−0.0508906	−0.0254453	+	0.999676i	$0.508100\pi$
$662$	−14892.4	−0.874333
$663$	−10652.0	−0.623968
$664$	7216.14	0.421748
$665$	2416.37	0.140906
$666$	6439.43	0.374659
$667$	0	0
$668$	7364.21	0.426542
$669$	15521.4	0.896996
$670$	3539.83	0.204113
$671$	−12457.0	−0.716688
$672$	−3631.56	−0.208468
$673$	−7448.31	−0.426614	−0.213307	−	0.976985i	$-0.568423\pi$
$673$	−7448.31	−0.426614	−0.213307	+	0.976985i	$0.568423\pi$
$674$	−18733.4	−1.07060
$675$	−12002.9	−0.684434
$676$	−5691.28	−0.323810
$677$	−9281.19	−0.526891	−0.263446	−	0.964674i	$-0.584859\pi$
$677$	−9281.19	−0.526891	−0.263446	+	0.964674i	$0.584859\pi$
$678$	−12166.4	−0.689155
$679$	−20626.6	−1.16580
$680$	−1178.70	−0.0664723
$681$	−33300.3	−1.87382
$682$	−6371.87	−0.357759
$683$	32252.9	1.80691	0.903456	−	0.428680i	$-0.141021\pi$
$683$	32252.9	1.80691	0.903456	+	0.428680i	$0.141021\pi$
$684$	−2348.54	−0.131284
$685$	−810.196	−0.0451913
$686$	−12715.7	−0.707707
$687$	34329.4	1.90647
$688$	−1619.93	−0.0897666
$689$	19268.5	1.06542
$690$	1282.85	0.0707786
$691$	4915.05	0.270590	0.135295	−	0.990805i	$-0.456802\pi$
$691$	4915.05	0.270590	0.135295	+	0.990805i	$0.456802\pi$
$692$	−1213.70	−0.0666736
$693$	−3021.34	−0.165615
$694$	−15902.2	−0.869798
$695$	−1782.28	−0.0972742
$696$	0	0
$697$	−7847.31	−0.426453
$698$	2513.47	0.136298
$699$	10651.3	0.576349
$700$	8839.89	0.477309
$701$	11610.7	0.625577	0.312788	−	0.949823i	$-0.398737\pi$
$701$	11610.7	0.625577	0.312788	+	0.949823i	$0.398737\pi$
$702$	−5592.79	−0.300693
$703$	16784.8	0.900497
$704$	984.650	0.0527136
$705$	736.318	0.0393352
$706$	−14618.3	−0.779275
$707$	13745.2	0.731175
$708$	−13687.0	−0.726540
$709$	−6350.02	−0.336361	−0.168180	−	0.985756i	$-0.553789\pi$
$709$	−6350.02	−0.336361	−0.168180	+	0.985756i	$0.553789\pi$
$710$	258.550	0.0136665
$711$	7989.93	0.421443
$712$	7627.08	0.401456
$713$	9175.84	0.481960
$714$	−14168.3	−0.742628
$715$	1010.40	0.0528485
$716$	−12146.4	−0.633983
$717$	−25790.0	−1.34330
$718$	23110.2	1.20120
$719$	−22323.6	−1.15790	−0.578949	−	0.815364i	$-0.696537\pi$
$719$	−22323.6	−1.15790	−0.578949	+	0.815364i	$0.696537\pi$
$720$	400.782	0.0207448
$721$	32978.0	1.70342
$722$	7596.40	0.391563
$723$	−37104.4	−1.90861
$724$	−9359.10	−0.480425
$725$	0	0
$726$	−13422.4	−0.686162
$727$	24589.5	1.25443	0.627217	−	0.778844i	$-0.284194\pi$
$727$	24589.5	1.25443	0.627217	+	0.778844i	$0.284194\pi$
$728$	4118.97	0.209696
$729$	7059.88	0.358679
$730$	−871.108	−0.0441659
$731$	−6320.08	−0.319776
$732$	19862.7	1.00293
$733$	35064.1	1.76688	0.883438	−	0.468548i	$-0.155223\pi$
$733$	35064.1	1.76688	0.883438	+	0.468548i	$0.155223\pi$
$734$	−4195.73	−0.210991
$735$	8.45034	0.000424075 0
$736$	−1417.95	−0.0710140
$737$	−11536.8	−0.576612
$738$	2668.24	0.133089
$739$	33877.0	1.68631	0.843157	−	0.537668i	$-0.180695\pi$
$739$	33877.0	1.68631	0.843157	+	0.537668i	$0.180695\pi$
$740$	−2864.35	−0.142291
$741$	9440.71	0.468034
$742$	25629.2	1.26803
$743$	−3119.59	−0.154033	−0.0770166	−	0.997030i	$-0.524539\pi$
$743$	−3119.59	−0.154033	−0.0770166	+	0.997030i	$0.524539\pi$
$744$	10159.9	0.500647
$745$	−7161.08	−0.352163
$746$	−27958.8	−1.37218
$747$	−9572.71	−0.468872
$748$	3841.55	0.187782
$749$	−32547.3	−1.58779
$750$	−7076.49	−0.344529
$751$	26359.7	1.28080	0.640398	−	0.768043i	$-0.278769\pi$
$751$	26359.7	1.28080	0.640398	+	0.768043i	$0.278769\pi$
$752$	−813.861	−0.0394660
$753$	−40067.4	−1.93910
$754$	0	0
$755$	−1708.68	−0.0823647
$756$	−7439.00	−0.357876
$757$	10385.9	0.498654	0.249327	−	0.968419i	$-0.419791\pi$
$757$	10385.9	0.498654	0.249327	+	0.968419i	$0.419791\pi$
$758$	−1788.14	−0.0856837
$759$	−4180.99	−0.199948
$760$	1044.66	0.0498604
$761$	24007.6	1.14360	0.571798	−	0.820395i	$-0.306246\pi$
$761$	24007.6	1.14360	0.571798	+	0.820395i	$0.306246\pi$
$762$	−4461.18	−0.212089
$763$	−29548.7	−1.40201
$764$	16869.9	0.798862
$765$	1563.63	0.0738995
$766$	−10624.5	−0.501148
$767$	15524.0	0.730821
$768$	−1570.02	−0.0737674
$769$	−12607.2	−0.591195	−0.295597	−	0.955313i	$-0.595519\pi$
$769$	−12607.2	−0.591195	−0.295597	+	0.955313i	$0.595519\pi$
$770$	1343.93	0.0628987
$771$	−14863.0	−0.694266
$772$	7850.35	0.365985
$773$	−6237.38	−0.290224	−0.145112	−	0.989415i	$-0.546354\pi$
$773$	−6237.38	−0.290224	−0.145112	+	0.989415i	$0.546354\pi$
$774$	2148.95	0.0997966
$775$	−24731.2	−1.14628
$776$	−8917.44	−0.412522
$777$	−34430.3	−1.58968
$778$	−8412.54	−0.387666
$779$	6954.93	0.319880
$780$	−1611.08	−0.0739561
$781$	−842.650	−0.0386074
$782$	−5532.05	−0.252974
$783$	0	0
$784$	−9.34026	−0.000425486 0
$785$	−1527.94	−0.0694707
$786$	8168.06	0.370668
$787$	−6005.74	−0.272022	−0.136011	−	0.990707i	$-0.543428\pi$
$787$	−6005.74	−0.272022	−0.136011	+	0.990707i	$0.543428\pi$
$788$	8162.72	0.369016
$789$	−16512.5	−0.745070
$790$	−3554.03	−0.160059
$791$	18354.5	0.825044
$792$	−1306.21	−0.0586036
$793$	−22528.5	−1.00884
$794$	−11404.9	−0.509752
$795$	−10024.5	−0.447210
$796$	12942.7	0.576310
$797$	6169.00	0.274175	0.137087	−	0.990559i	$-0.456226\pi$
$797$	6169.00	0.274175	0.137087	+	0.990559i	$0.456226\pi$
$798$	12557.1	0.557040
$799$	−3175.23	−0.140590
$800$	3821.73	0.168898
$801$	−10117.9	−0.446313
$802$	−19606.1	−0.863236
$803$	2839.06	0.124768
$804$	18395.4	0.806911
$805$	−1935.34	−0.0847350
$806$	−11523.5	−0.503597
$807$	−41020.5	−1.78933
$808$	5942.42	0.258730
$809$	−40910.3	−1.77791	−0.888956	−	0.457993i	$-0.848568\pi$
$809$	−40910.3	−1.77791	−0.888956	+	0.457993i	$0.848568\pi$
$810$	4262.30	0.184891
$811$	−28340.0	−1.22707	−0.613534	−	0.789669i	$-0.710252\pi$
$811$	−28340.0	−1.22707	−0.613534	+	0.789669i	$0.710252\pi$
$812$	0	0
$813$	7809.02	0.336869
$814$	9335.33	0.401969
$815$	3573.64	0.153594
$816$	−6125.36	−0.262782
$817$	5601.38	0.239862
$818$	16768.3	0.716735
$819$	−5464.09	−0.233127
$820$	−1186.87	−0.0505456
$821$	−17791.4	−0.756303	−0.378151	−	0.925744i	$-0.623440\pi$
$821$	−17791.4	−0.756303	−0.378151	+	0.925744i	$0.623440\pi$
$822$	−4210.35	−0.178653
$823$	−5375.77	−0.227688	−0.113844	−	0.993499i	$-0.536316\pi$
$823$	−5375.77	−0.227688	−0.113844	+	0.993499i	$0.536316\pi$
$824$	14257.3	0.602762
$825$	11268.8	0.475551
$826$	20648.6	0.869802
$827$	−17894.5	−0.752422	−0.376211	−	0.926534i	$-0.622773\pi$
$827$	−17894.5	−0.752422	−0.376211	+	0.926534i	$0.622773\pi$
$828$	1881.01	0.0789487
$829$	−14195.1	−0.594713	−0.297357	−	0.954766i	$-0.596105\pi$
$829$	−14195.1	−0.594713	−0.297357	+	0.954766i	$0.596105\pi$
$830$	4258.08	0.178072
$831$	10183.7	0.425112
$832$	1780.74	0.0742021
$833$	−36.4405	−0.00151571
$834$	−9261.96	−0.384551
$835$	4345.45	0.180097
$836$	−3404.70	−0.140854
$837$	20811.9	0.859457
$838$	24700.5	1.01821
$839$	18312.2	0.753524	0.376762	−	0.926310i	$-0.377038\pi$
$839$	18312.2	0.753524	0.376762	+	0.926310i	$0.377038\pi$
$840$	−2142.90	−0.0880204
$841$	0	0
$842$	−9553.30	−0.391008
$843$	7652.09	0.312636
$844$	15772.6	0.643264
$845$	−3358.29	−0.136720
$846$	1079.64	0.0438757
$847$	20249.4	0.821462
$848$	11080.2	0.448697
$849$	−40432.5	−1.63444
$850$	14910.2	0.601667
$851$	−13443.4	−0.541520
$852$	1343.60	0.0540272
$853$	−192.909	−0.00774335	−0.00387168	−	0.999993i	$-0.501232\pi$
$853$	−192.909	−0.00774335	−0.00387168	+	0.999993i	$0.501232\pi$
$854$	−29965.3	−1.20069
$855$	−1385.82	−0.0554315
$856$	−14071.1	−0.561846
$857$	−20355.5	−0.811355	−0.405678	−	0.914016i	$-0.632964\pi$
$857$	−20355.5	−0.811355	−0.405678	+	0.914016i	$0.632964\pi$
$858$	5250.73	0.208924
$859$	−35959.3	−1.42831	−0.714153	−	0.699990i	$-0.753188\pi$
$859$	−35959.3	−1.42831	−0.714153	+	0.699990i	$0.753188\pi$
$860$	−955.886	−0.0379017
$861$	−14266.6	−0.564695
$862$	1072.17	0.0423648
$863$	7302.77	0.288052	0.144026	−	0.989574i	$-0.453995\pi$
$863$	7302.77	0.288052	0.144026	+	0.989574i	$0.453995\pi$
$864$	−3216.09	−0.126636
$865$	−716.179	−0.0281512
$866$	7060.17	0.277038
$867$	6233.24	0.244166
$868$	−15327.5	−0.599367
$869$	11583.1	0.452163
$870$	0	0
$871$	−20864.3	−0.811666
$872$	−12774.7	−0.496109
$873$	11829.6	0.458615
$874$	4902.96	0.189754
$875$	10675.8	0.412464
$876$	−4526.89	−0.174600
$877$	36855.5	1.41907	0.709533	−	0.704673i	$-0.248906\pi$
$877$	36855.5	1.41907	0.709533	+	0.704673i	$0.248906\pi$
$878$	23073.3	0.886886
$879$	5136.47	0.197098
$880$	581.019	0.0222570
$881$	−9615.17	−0.367699	−0.183850	−	0.982954i	$-0.558856\pi$
$881$	−9615.17	−0.367699	−0.183850	+	0.982954i	$0.558856\pi$
$882$	12.3905	0.000473027 0
$883$	46143.6	1.75861	0.879306	−	0.476257i	$-0.158007\pi$
$883$	46143.6	1.75861	0.879306	+	0.476257i	$0.158007\pi$
$884$	6947.46	0.264331
$885$	−8076.41	−0.306763
$886$	13551.9	0.513865
$887$	28495.0	1.07866	0.539328	−	0.842096i	$-0.318678\pi$
$887$	28495.0	1.07866	0.539328	+	0.842096i	$0.318678\pi$
$888$	−14885.2	−0.562516
$889$	6730.24	0.253909
$890$	4500.57	0.169505
$891$	−13891.4	−0.522313
$892$	−10123.3	−0.379993
$893$	2814.15	0.105456
$894$	−37214.0	−1.39220
$895$	−7167.31	−0.267684
$896$	2368.58	0.0883131
$897$	−7561.33	−0.281455
$898$	−13203.2	−0.490640
$899$	0	0
$900$	−5069.78	−0.187770
$901$	43228.7	1.59840
$902$	3868.19	0.142790
$903$	−11490.0	−0.423437
$904$	7935.14	0.291946
$905$	−5522.59	−0.202848
$906$	−8879.52	−0.325610
$907$	−21873.4	−0.800764	−0.400382	−	0.916348i	$-0.631123\pi$
$907$	−21873.4	−0.800764	−0.400382	+	0.916348i	$0.631123\pi$
$908$	21719.1	0.793803
$909$	−7883.03	−0.287639
$910$	2430.51	0.0885390
$911$	−32308.0	−1.17498	−0.587492	−	0.809230i	$-0.699885\pi$
$911$	−32308.0	−1.17498	−0.587492	+	0.809230i	$0.699885\pi$
$912$	5428.80	0.197111
$913$	−13877.7	−0.503049
$914$	8909.88	0.322443
$915$	11720.5	0.423463
$916$	−22390.3	−0.807637
$917$	−12322.5	−0.443757
$918$	−12547.4	−0.451117
$919$	4297.83	0.154268	0.0771340	−	0.997021i	$-0.475423\pi$
$919$	4297.83	0.154268	0.0771340	+	0.997021i	$0.475423\pi$
$920$	−836.699	−0.0299839
$921$	3069.49	0.109819
$922$	3723.23	0.132991
$923$	−1523.93	−0.0543455
$924$	6984.02	0.248655
$925$	36233.3	1.28794
$926$	15592.0	0.553330
$927$	−18913.3	−0.670111
$928$	0	0
$929$	36879.6	1.30245	0.651227	−	0.758883i	$-0.274254\pi$
$929$	36879.6	1.30245	0.651227	+	0.758883i	$0.274254\pi$
$930$	5995.15	0.211386
$931$	32.2966	0.00113692
$932$	−6946.96	−0.244158
$933$	12366.9	0.433949
$934$	26144.1	0.915910
$935$	2266.81	0.0792863
$936$	−2362.28	−0.0824930
$937$	−15770.1	−0.549824	−0.274912	−	0.961469i	$-0.588649\pi$
$937$	−15770.1	−0.549824	−0.274912	+	0.961469i	$0.588649\pi$
$938$	−27751.8	−0.966020
$939$	−53595.9	−1.86266
$940$	−480.241	−0.0166635
$941$	−485.478	−0.0168184	−0.00840921	−	0.999965i	$-0.502677\pi$
$941$	−485.478	−0.0168184	−0.00840921	+	0.999965i	$0.502677\pi$
$942$	−7940.25	−0.274636
$943$	−5570.40	−0.192362
$944$	8926.95	0.307783
$945$	−4389.59	−0.151104
$946$	3115.37	0.107071
$947$	−8167.18	−0.280251	−0.140126	−	0.990134i	$-0.544751\pi$
$947$	−8167.18	−0.280251	−0.140126	+	0.990134i	$0.544751\pi$
$948$	−18469.3	−0.632757
$949$	5134.45	0.175628
$950$	−13214.7	−0.451307
$951$	−10369.1	−0.353565
$952$	9240.86	0.314599
$953$	−29839.4	−1.01426	−0.507132	−	0.861868i	$-0.669294\pi$
$953$	−29839.4	−1.01426	−0.507132	+	0.861868i	$0.669294\pi$
$954$	−14698.6	−0.498832
$955$	9954.53	0.337299
$956$	16820.7	0.569059
$957$	0	0
$958$	9695.81	0.326991
$959$	6351.83	0.213880
$960$	−926.435	−0.0311464
$961$	13090.5	0.439411
$962$	16883.0	0.565830
$963$	18666.3	0.624624
$964$	24200.2	0.808543
$965$	4632.31	0.154528
$966$	−10057.4	−0.334980
$967$	8150.60	0.271050	0.135525	−	0.990774i	$-0.456728\pi$
$967$	8150.60	0.271050	0.135525	+	0.990774i	$0.456728\pi$
$968$	8754.38	0.290678
$969$	21180.1	0.702172
$970$	−5261.98	−0.174177
$971$	34617.7	1.14411	0.572057	−	0.820214i	$-0.306146\pi$
$971$	34617.7	1.14411	0.572057	+	0.820214i	$0.306146\pi$
$972$	11295.6	0.372744
$973$	13972.8	0.460378
$974$	−30184.9	−0.993004
$975$	20379.7	0.669407
$976$	−12954.8	−0.424871
$977$	−40762.0	−1.33479	−0.667395	−	0.744704i	$-0.732591\pi$
$977$	−40762.0	−1.33479	−0.667395	+	0.744704i	$0.732591\pi$
$978$	18571.1	0.607197
$979$	−14668.0	−0.478846
$980$	−5.51147	−0.000179651 0
$981$	16946.6	0.551542
$982$	−8876.97	−0.288468
$983$	15737.6	0.510631	0.255315	−	0.966858i	$-0.417821\pi$
$983$	15737.6	0.510631	0.255315	+	0.966858i	$0.417821\pi$
$984$	−6167.82	−0.199820
$985$	4816.63	0.155808
$986$	0	0
$987$	−5772.63	−0.186165
$988$	−6157.42	−0.198273
$989$	−4486.30	−0.144243
$990$	−770.762	−0.0247439
$991$	−47989.9	−1.53829	−0.769146	−	0.639073i	$-0.779318\pi$
$991$	−47989.9	−1.53829	−0.769146	+	0.639073i	$0.779318\pi$
$992$	−6626.51	−0.212089
$993$	−45666.8	−1.45941
$994$	−2026.99	−0.0646804
$995$	7637.20	0.243332
$996$	22128.0	0.703967
$997$	51443.4	1.63413	0.817066	−	0.576545i	$-0.195599\pi$
$997$	51443.4	1.63413	0.817066	+	0.576545i	$0.195599\pi$
$998$	−3297.31	−0.104584
$999$	−30491.3	−0.965667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1682.4.a.d.1.1		3
29.28	even	2		58.4.a.d.1.3	✓	3
87.86	odd	2		522.4.a.k.1.2		3
116.115	odd	2		464.4.a.i.1.1		3
145.144	even	2		1450.4.a.h.1.1		3
232.115	odd	2		1856.4.a.s.1.3		3
232.173	even	2		1856.4.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.4.a.d.1.3	✓	3	29.28	even	2
464.4.a.i.1.1		3	116.115	odd	2
522.4.a.k.1.2		3	87.86	odd	2
1450.4.a.h.1.1		3	145.144	even	2
1682.4.a.d.1.1		3	1.1	even	1	trivial
1856.4.a.r.1.1		3	232.173	even	2
1856.4.a.s.1.3		3	232.115	odd	2

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:	\( N \)	\(=\)	\( 1682 = 2 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1682.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -6.13291 q^{3} +4.00000 q^{4} +2.36031 q^{5} +12.2658 q^{6} -18.5045 q^{7} -8.00000 q^{8} +10.6126 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -6.13291 q^{3} +4.00000 q^{4} +2.36031 q^{5} +12.2658 q^{6} -18.5045 q^{7} -8.00000 q^{8} +10.6126 q^{9} -4.72062 q^{10} +15.3852 q^{11} -24.5316 q^{12} +27.8241 q^{13} +37.0090 q^{14} -14.4756 q^{15} +16.0000 q^{16} +62.4231 q^{17} -21.2251 q^{18} -55.3245 q^{19} +9.44123 q^{20} +113.486 q^{21} -30.7703 q^{22} +44.3109 q^{23} +49.0633 q^{24} -119.429 q^{25} -55.6482 q^{26} +100.503 q^{27} -74.0180 q^{28} +28.9511 q^{30} +207.078 q^{31} -32.0000 q^{32} -94.3557 q^{33} -124.846 q^{34} -43.6763 q^{35} +42.4502 q^{36} -303.388 q^{37} +110.649 q^{38} -170.643 q^{39} -18.8825 q^{40} -125.712 q^{41} -226.973 q^{42} -101.246 q^{43} +61.5406 q^{44} +25.0489 q^{45} -88.6218 q^{46} -50.8663 q^{47} -98.1265 q^{48} -0.583766 q^{49} +238.858 q^{50} -382.835 q^{51} +111.296 q^{52} +692.512 q^{53} -201.005 q^{54} +36.3137 q^{55} +148.036 q^{56} +339.300 q^{57} +557.935 q^{59} -57.9022 q^{60} -809.678 q^{61} -414.157 q^{62} -196.380 q^{63} +64.0000 q^{64} +65.6734 q^{65} +188.711 q^{66} -749.866 q^{67} +249.692 q^{68} -271.755 q^{69} +87.3526 q^{70} -54.7703 q^{71} -84.9004 q^{72} +184.533 q^{73} +606.775 q^{74} +732.447 q^{75} -221.298 q^{76} -284.694 q^{77} +341.285 q^{78} +752.875 q^{79} +37.7649 q^{80} -902.913 q^{81} +251.423 q^{82} -902.018 q^{83} +453.945 q^{84} +147.338 q^{85} +202.492 q^{86} -123.081 q^{88} -953.385 q^{89} -50.0978 q^{90} -514.871 q^{91} +177.244 q^{92} -1269.99 q^{93} +101.733 q^{94} -130.583 q^{95} +196.253 q^{96} +1114.68 q^{97} +1.16753 q^{98} +163.276 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} - 2 q^{3} + 12 q^{4} + 20 q^{5} + 4 q^{6} + 24 q^{7} - 24 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q - 6 * q^2 - 2 * q^3 + 12 * q^4 + 20 * q^5 + 4 * q^6 + 24 * q^7 - 24 * q^8 + 5 * q^9	\( 3 q - 6 q^{2} - 2 q^{3} + 12 q^{4} + 20 q^{5} + 4 q^{6} + 24 q^{7} - 24 q^{8} + 5 q^{9} - 40 q^{10} - 10 q^{11} - 8 q^{12} - 4 q^{13} - 48 q^{14} + 130 q^{15} + 48 q^{16} + 66 q^{17} - 10 q^{18} + 164 q^{19} + 80 q^{20} + 88 q^{21} + 20 q^{22} - 204 q^{23} + 16 q^{24} + 79 q^{25} + 8 q^{26} + 142 q^{27} + 96 q^{28} - 260 q^{30} + 86 q^{31} - 96 q^{32} - 130 q^{33} - 132 q^{34} + 24 q^{35} + 20 q^{36} + 42 q^{37} - 328 q^{38} + 394 q^{39} - 160 q^{40} - 562 q^{41} - 176 q^{42} - 18 q^{43} - 40 q^{44} + 422 q^{45} + 408 q^{46} - 654 q^{47} - 32 q^{48} + 539 q^{49} - 158 q^{50} + 556 q^{51} - 16 q^{52} + 712 q^{53} - 284 q^{54} - 142 q^{55} - 192 q^{56} + 828 q^{57} + 184 q^{59} + 520 q^{60} - 322 q^{61} - 172 q^{62} - 784 q^{63} + 192 q^{64} + 1494 q^{65} + 260 q^{66} - 228 q^{67} + 264 q^{68} - 684 q^{69} - 48 q^{70} - 52 q^{71} - 40 q^{72} + 494 q^{73} - 84 q^{74} + 3048 q^{75} + 656 q^{76} - 872 q^{77} - 788 q^{78} + 2110 q^{79} + 320 q^{80} - 1513 q^{81} + 1124 q^{82} - 288 q^{83} + 352 q^{84} + 2704 q^{85} + 36 q^{86} + 80 q^{88} - 914 q^{89} - 844 q^{90} - 2984 q^{91} - 816 q^{92} - 62 q^{93} + 1308 q^{94} + 1900 q^{95} + 64 q^{96} - 218 q^{97} - 1078 q^{98} + 304 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - 2 * q^3 + 12 * q^4 + 20 * q^5 + 4 * q^6 + 24 * q^7 - 24 * q^8 + 5 * q^9 - 40 * q^10 - 10 * q^11 - 8 * q^12 - 4 * q^13 - 48 * q^14 + 130 * q^15 + 48 * q^16 + 66 * q^17 - 10 * q^18 + 164 * q^19 + 80 * q^20 + 88 * q^21 + 20 * q^22 - 204 * q^23 + 16 * q^24 + 79 * q^25 + 8 * q^26 + 142 * q^27 + 96 * q^28 - 260 * q^30 + 86 * q^31 - 96 * q^32 - 130 * q^33 - 132 * q^34 + 24 * q^35 + 20 * q^36 + 42 * q^37 - 328 * q^38 + 394 * q^39 - 160 * q^40 - 562 * q^41 - 176 * q^42 - 18 * q^43 - 40 * q^44 + 422 * q^45 + 408 * q^46 - 654 * q^47 - 32 * q^48 + 539 * q^49 - 158 * q^50 + 556 * q^51 - 16 * q^52 + 712 * q^53 - 284 * q^54 - 142 * q^55 - 192 * q^56 + 828 * q^57 + 184 * q^59 + 520 * q^60 - 322 * q^61 - 172 * q^62 - 784 * q^63 + 192 * q^64 + 1494 * q^65 + 260 * q^66 - 228 * q^67 + 264 * q^68 - 684 * q^69 - 48 * q^70 - 52 * q^71 - 40 * q^72 + 494 * q^73 - 84 * q^74 + 3048 * q^75 + 656 * q^76 - 872 * q^77 - 788 * q^78 + 2110 * q^79 + 320 * q^80 - 1513 * q^81 + 1124 * q^82 - 288 * q^83 + 352 * q^84 + 2704 * q^85 + 36 * q^86 + 80 * q^88 - 914 * q^89 - 844 * q^90 - 2984 * q^91 - 816 * q^92 - 62 * q^93 + 1308 * q^94 + 1900 * q^95 + 64 * q^96 - 218 * q^97 - 1078 * q^98 + 304 * q^99

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