LMFDB - Embedded newform 547.3.b.b.546.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,3,Mod(546,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("547.546");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	547.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.9046704605$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			546.5
Character	$\chi$	$=$	547.546
Dual form			547.3.b.b.546.84

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.58531i q^{2} -0.541221i q^{3} -8.85444 q^{4} -2.75520i q^{5} -1.94044 q^{6} +8.99411i q^{7} +17.4047i q^{8} +8.70708 q^{9} +O(q^{10})$	\(q-3.58531i q^{2} -0.541221i q^{3} -8.85444 q^{4} -2.75520i q^{5} -1.94044 q^{6} +8.99411i q^{7} +17.4047i q^{8} +8.70708 q^{9} -9.87823 q^{10} +7.21359 q^{11} +4.79221i q^{12} +19.2495 q^{13} +32.2467 q^{14} -1.49117 q^{15} +26.9833 q^{16} +30.2473i q^{17} -31.2176i q^{18} +6.85377 q^{19} +24.3957i q^{20} +4.86780 q^{21} -25.8630i q^{22} -14.7026i q^{23} +9.41977 q^{24} +17.4089 q^{25} -69.0153i q^{26} -9.58344i q^{27} -79.6378i q^{28} -46.1503 q^{29} +5.34631i q^{30} +39.8232i q^{31} -27.1249i q^{32} -3.90415i q^{33} +108.446 q^{34} +24.7805 q^{35} -77.0963 q^{36} +22.6762i q^{37} -24.5729i q^{38} -10.4182i q^{39} +47.9533 q^{40} -38.3553i q^{41} -17.4526i q^{42} +33.7176i q^{43} -63.8723 q^{44} -23.9897i q^{45} -52.7133 q^{46} +32.5387 q^{47} -14.6039i q^{48} -31.8940 q^{49} -62.4162i q^{50} +16.3705 q^{51} -170.443 q^{52} +6.88090 q^{53} -34.3596 q^{54} -19.8749i q^{55} -156.539 q^{56} -3.70940i q^{57} +165.463i q^{58} -68.4638i q^{59} +13.2035 q^{60} -58.5952i q^{61} +142.778 q^{62} +78.3124i q^{63} +10.6821 q^{64} -53.0361i q^{65} -13.9976 q^{66} -2.96403 q^{67} -267.823i q^{68} -7.95734 q^{69} -88.8459i q^{70} +29.9436i q^{71} +151.544i q^{72} +53.6290 q^{73} +81.3011 q^{74} -9.42206i q^{75} -60.6863 q^{76} +64.8798i q^{77} -37.3525 q^{78} +14.5648i q^{79} -74.3444i q^{80} +73.1770 q^{81} -137.516 q^{82} +114.405i q^{83} -43.1016 q^{84} +83.3373 q^{85} +120.888 q^{86} +24.9775i q^{87} +125.550i q^{88} -174.185i q^{89} -86.0105 q^{90} +173.132i q^{91} +130.183i q^{92} +21.5531 q^{93} -116.661i q^{94} -18.8835i q^{95} -14.6806 q^{96} -66.5823 q^{97} +114.350i q^{98} +62.8093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 192 q^{4} - 306 q^{9}+O(q^{10}) $ 88 * q - 192 * q^4 - 306 * q^9	$ 88 q - 192 q^{4} - 306 q^{9} - 4 q^{10} - 32 q^{11} + 26 q^{13} - 26 q^{14} + 22 q^{15} + 236 q^{16} - 12 q^{19} - 16 q^{21} - 2 q^{24} - 544 q^{25} - 96 q^{29} + 26 q^{34} + 10 q^{35} + 364 q^{36} + 44 q^{40} + 124 q^{44} - 288 q^{46} - 310 q^{47} - 694 q^{49} + 86 q^{51} - 316 q^{52} + 24 q^{53} - 266 q^{54} + 158 q^{56} - 80 q^{60} + 40 q^{62} - 652 q^{64} + 528 q^{66} + 28 q^{67} + 16 q^{69} + 94 q^{73} - 614 q^{74} - 28 q^{76} - 98 q^{78} + 928 q^{81} - 772 q^{82} + 358 q^{84} + 74 q^{85} - 410 q^{86} - 214 q^{90} + 656 q^{93} - 724 q^{96} + 346 q^{97} + 50 q^{99}+O(q^{100}) $ 88 * q - 192 * q^4 - 306 * q^9 - 4 * q^10 - 32 * q^11 + 26 * q^13 - 26 * q^14 + 22 * q^15 + 236 * q^16 - 12 * q^19 - 16 * q^21 - 2 * q^24 - 544 * q^25 - 96 * q^29 + 26 * q^34 + 10 * q^35 + 364 * q^36 + 44 * q^40 + 124 * q^44 - 288 * q^46 - 310 * q^47 - 694 * q^49 + 86 * q^51 - 316 * q^52 + 24 * q^53 - 266 * q^54 + 158 * q^56 - 80 * q^60 + 40 * q^62 - 652 * q^64 + 528 * q^66 + 28 * q^67 + 16 * q^69 + 94 * q^73 - 614 * q^74 - 28 * q^76 - 98 * q^78 + 928 * q^81 - 772 * q^82 + 358 * q^84 + 74 * q^85 - 410 * q^86 - 214 * q^90 + 656 * q^93 - 724 * q^96 + 346 * q^97 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	3.58531i		−	1.79265i	−0.443393	−	0.896327i	$-0.646225\pi$
$2$		−	3.58531i		−	1.79265i	0.443393	−	0.896327i	$-0.353775\pi$
$3$		−	0.541221i		−	0.180407i	−0.995923	−	0.0902035i	$-0.971248\pi$
$3$		−	0.541221i		−	0.180407i	0.995923	−	0.0902035i	$-0.0287518\pi$
$4$	−8.85444			−2.21361
$5$		−	2.75520i		−	0.551039i	−0.961295	−	0.275520i	$-0.911150\pi$
$5$		−	2.75520i		−	0.551039i	0.961295	−	0.275520i	$-0.0888499\pi$
$6$	−1.94044			−0.323407
$7$			8.99411i			1.28487i	0.766339	+	0.642436i	$0.222076\pi$
$7$			8.99411i			1.28487i	−0.766339	+	0.642436i	$0.777924\pi$
$8$			17.4047i			2.17558i
$9$	8.70708			0.967453
$10$	−9.87823			−0.987823
$11$	7.21359			0.655781			0.327891	−	0.944716i	$-0.393662\pi$
$11$	7.21359			0.655781			0.327891	+	0.944716i	$0.393662\pi$
$12$			4.79221i			0.399351i
$13$	19.2495			1.48073			0.740364	−	0.672206i	$-0.234653\pi$
$13$	19.2495			1.48073			0.740364	+	0.672206i	$0.234653\pi$
$14$	32.2467			2.30333
$15$	−1.49117			−0.0994114
$16$	26.9833			1.68646
$17$			30.2473i			1.77925i	0.456689	+	0.889626i	$0.349035\pi$
$17$			30.2473i			1.77925i	−0.456689	+	0.889626i	$0.650965\pi$
$18$		−	31.2176i		−	1.73431i
$19$	6.85377			0.360725			0.180362	−	0.983600i	$-0.442273\pi$
$19$	6.85377			0.360725			0.180362	+	0.983600i	$0.442273\pi$
$20$			24.3957i			1.21979i
$21$	4.86780			0.231800
$22$		−	25.8630i		−	1.17559i
$23$		−	14.7026i		−	0.639242i	−0.947545	−	0.319621i	$-0.896444\pi$
$23$		−	14.7026i		−	0.639242i	0.947545	−	0.319621i	$-0.103556\pi$
$24$	9.41977			0.392490
$25$	17.4089			0.696356
$26$		−	69.0153i		−	2.65443i
$27$		−	9.58344i		−	0.354942i
$28$		−	79.6378i		−	2.84421i
$29$	−46.1503			−1.59139			−0.795694	−	0.605699i	$-0.792894\pi$
$29$	−46.1503			−1.59139			−0.795694	+	0.605699i	$0.792894\pi$
$30$			5.34631i			0.178210i
$31$			39.8232i			1.28462i	0.766446	+	0.642309i	$0.222023\pi$
$31$			39.8232i			1.28462i	−0.766446	+	0.642309i	$0.777977\pi$
$32$		−	27.1249i		−	0.847653i
$33$		−	3.90415i		−	0.118308i
$34$	108.446			3.18959
$35$	24.7805			0.708015
$36$	−77.0963			−2.14156
$37$			22.6762i			0.612870i	0.951892	+	0.306435i	$0.0991362\pi$
$37$			22.6762i			0.612870i	−0.951892	+	0.306435i	$0.900864\pi$
$38$		−	24.5729i		−	0.646655i
$39$		−	10.4182i		−	0.267134i
$40$	47.9533			1.19883
$41$		−	38.3553i		−	0.935496i	−0.883862	−	0.467748i	$-0.845065\pi$
$41$		−	38.3553i		−	0.935496i	0.883862	−	0.467748i	$-0.154935\pi$
$42$		−	17.4526i		−	0.415537i
$43$			33.7176i			0.784130i	0.919938	+	0.392065i	$0.128239\pi$
$43$			33.7176i			0.784130i	−0.919938	+	0.392065i	$0.871761\pi$
$44$	−63.8723			−1.45164
$45$		−	23.9897i		−	0.533105i
$46$	−52.7133			−1.14594
$47$	32.5387			0.692312			0.346156	−	0.938177i	$-0.387487\pi$
$47$	32.5387			0.692312			0.346156	+	0.938177i	$0.387487\pi$
$48$		−	14.6039i		−	0.304249i
$49$	−31.8940			−0.650898
$50$		−	62.4162i		−	1.24832i
$51$	16.3705			0.320990
$52$	−170.443			−3.27775
$53$	6.88090			0.129828			0.0649141	−	0.997891i	$-0.479323\pi$
$53$	6.88090			0.129828			0.0649141	+	0.997891i	$0.479323\pi$
$54$	−34.3596			−0.636289
$55$		−	19.8749i		−	0.361361i
$56$	−156.539			−2.79535
$57$		−	3.70940i		−	0.0650773i
$58$			165.463i			2.85281i
$59$		−	68.4638i		−	1.16040i	−0.814473	−	0.580202i	$-0.802974\pi$
$59$		−	68.4638i		−	1.16040i	0.814473	−	0.580202i	$-0.197026\pi$
$60$	13.2035			0.220058
$61$		−	58.5952i		−	0.960577i	−0.877111	−	0.480288i	$-0.840532\pi$
$61$		−	58.5952i		−	0.960577i	0.877111	−	0.480288i	$-0.159468\pi$
$62$	142.778			2.30288
$63$			78.3124i			1.24305i
$64$	10.6821			0.166908
$65$		−	53.0361i		−	0.815940i
$66$	−13.9976			−0.212085
$67$	−2.96403			−0.0442393			−0.0221197	−	0.999755i	$-0.507041\pi$
$67$	−2.96403			−0.0442393			−0.0221197	+	0.999755i	$0.507041\pi$
$68$		−	267.823i		−	3.93857i
$69$	−7.95734			−0.115324
$70$		−	88.8459i		−	1.26923i
$71$			29.9436i			0.421741i	0.977514	+	0.210871i	$0.0676299\pi$
$71$			29.9436i			0.421741i	−0.977514	+	0.210871i	$0.932370\pi$
$72$			151.544i			2.10477i
$73$	53.6290			0.734643			0.367322	−	0.930094i	$-0.380275\pi$
$73$	53.6290			0.734643			0.367322	+	0.930094i	$0.380275\pi$
$74$	81.3011			1.09866
$75$		−	9.42206i		−	0.125627i
$76$	−60.6863			−0.798503
$77$			64.8798i			0.842595i
$78$	−37.3525			−0.478879
$79$			14.5648i			0.184365i	0.995742	+	0.0921823i	$0.0293842\pi$
$79$			14.5648i			0.184365i	−0.995742	+	0.0921823i	$0.970616\pi$
$80$		−	74.3444i		−	0.929305i
$81$	73.1770			0.903419
$82$	−137.516			−1.67702
$83$			114.405i			1.37837i	0.724585	+	0.689185i	$0.242031\pi$
$83$			114.405i			1.37837i	−0.724585	+	0.689185i	$0.757969\pi$
$84$	−43.1016			−0.513115
$85$	83.3373			0.980438
$86$	120.888			1.40567
$87$			24.9775i			0.287098i
$88$			125.550i			1.42671i
$89$		−	174.185i		−	1.95714i	−0.205922	−	0.978568i	$-0.566019\pi$
$89$		−	174.185i		−	1.95714i	0.205922	−	0.978568i	$-0.433981\pi$
$90$	−86.0105			−0.955673
$91$			173.132i			1.90255i
$92$			130.183i			1.41503i
$93$	21.5531			0.231754
$94$		−	116.661i		−	1.24108i
$95$		−	18.8835i		−	0.198773i
$96$	−14.6806			−0.152923
$97$	−66.5823			−0.686415			−0.343208	−	0.939260i	$-0.611513\pi$
$97$	−66.5823			−0.686415			−0.343208	+	0.939260i	$0.611513\pi$
$98$			114.350i			1.16683i
$99$	62.8093			0.634438
$100$	−154.146			−1.54146
$101$			136.054i			1.34707i	0.739157	+	0.673533i	$0.235224\pi$
$101$			136.054i			1.34707i	−0.739157	+	0.673533i	$0.764776\pi$
$102$		−	58.6932i		−	0.575424i
$103$			43.0609i			0.418067i	0.977909	+	0.209033i	$0.0670317\pi$
$103$			43.0609i			0.418067i	−0.977909	+	0.209033i	$0.932968\pi$
$104$			335.030i			3.22145i
$105$		−	13.4117i		−	0.127731i
$106$		−	24.6701i		−	0.232737i
$107$		−	203.115i		−	1.89827i	−0.314872	−	0.949134i	$-0.601961\pi$
$107$		−	203.115i		−	1.89827i	0.314872	−	0.949134i	$-0.398039\pi$
$108$			84.8560i			0.785704i
$109$		−	38.2561i		−	0.350973i	−0.984482	−	0.175487i	$-0.943850\pi$
$109$		−	38.2561i		−	0.350973i	0.984482	−	0.175487i	$-0.0561499\pi$
$110$	−71.2575			−0.647796
$111$	12.2728			0.110566
$112$			242.691i			2.16688i
$113$	26.7301			0.236550			0.118275	−	0.992981i	$-0.462264\pi$
$113$	26.7301			0.236550			0.118275	+	0.992981i	$0.462264\pi$
$114$	−13.2994			−0.116661
$115$	−40.5085			−0.352248
$116$	408.635			3.52271
$117$	167.607			1.43254
$118$	−245.464			−2.08020
$119$	−272.047			−2.28611
$120$		−	25.9533i		−	0.216278i
$121$	−68.9641			−0.569951
$122$	−210.082			−1.72198
$123$	−20.7587			−0.168770
$124$		−	352.612i		−	2.84364i
$125$		−	116.845i		−	0.934759i
$126$	280.774			2.22837
$127$	41.3001			0.325198			0.162599	−	0.986692i	$-0.448012\pi$
$127$	41.3001			0.325198			0.162599	+	0.986692i	$0.448012\pi$
$128$		−	146.798i		−	1.14686i
$129$	18.2487			0.141463
$130$	−190.151			−1.46270
$131$	30.8812			0.235734			0.117867	−	0.993029i	$-0.462394\pi$
$131$	30.8812			0.235734			0.117867	+	0.993029i	$0.462394\pi$
$132$			34.5690i			0.261887i
$133$			61.6435i			0.463485i
$134$			10.6270i			0.0793058i
$135$	−26.4043			−0.195587
$136$	−526.444			−3.87091
$137$	−195.035			−1.42362			−0.711808	−	0.702374i	$-0.752123\pi$
$137$	−195.035			−1.42362			−0.711808	+	0.702374i	$0.752123\pi$
$138$			28.5295i			0.206736i
$139$	−102.812			−0.739657			−0.369829	−	0.929100i	$-0.620584\pi$
$139$	−102.812			−0.739657			−0.369829	+	0.929100i	$0.620584\pi$
$140$	−219.418			−1.56727
$141$		−	17.6106i		−	0.124898i
$142$	107.357			0.756036
$143$	138.858			0.971034
$144$	234.946			1.63157
$145$			127.153i			0.876918i
$146$		−	192.276i		−	1.31696i
$147$			17.2617i			0.117427i
$148$		−	200.785i		−	1.35665i
$149$	257.342			1.72712			0.863562	−	0.504242i	$-0.168228\pi$
$149$	257.342			1.72712			0.863562	+	0.504242i	$0.168228\pi$
$150$	−33.7810			−0.225207
$151$			198.605i			1.31526i	0.753340	+	0.657631i	$0.228442\pi$
$151$			198.605i			1.31526i	−0.753340	+	0.657631i	$0.771558\pi$
$152$			119.287i			0.784786i
$153$			263.366i			1.72134i
$154$	232.614			1.51048
$155$	109.721			0.707875
$156$			92.2475i			0.591330i
$157$	215.873			1.37498			0.687492	−	0.726192i	$-0.258712\pi$
$157$	215.873			1.37498			0.687492	+	0.726192i	$0.258712\pi$
$158$	52.2193			0.330502
$159$		−	3.72409i		−	0.0234219i
$160$	−74.7345			−0.467090
$161$	132.237			0.821345
$162$		−	262.362i		−	1.61952i
$163$		−	47.9710i		−	0.294301i	−0.989114	−	0.147150i	$-0.952990\pi$
$163$		−	47.9710i		−	0.294301i	0.989114	−	0.147150i	$-0.0470101\pi$
$164$			339.615i			2.07082i
$165$	−10.7567			−0.0651921
$166$	410.176			2.47094
$167$	−139.444			−0.834994			−0.417497	−	0.908678i	$-0.637093\pi$
$167$	−139.444			−0.834994			−0.417497	+	0.908678i	$0.637093\pi$
$168$			84.7224i			0.504300i
$169$	201.542			1.19256
$170$		−	298.790i		−	1.75759i
$171$	59.6763			0.348984
$172$		−	298.550i		−	1.73576i
$173$		−	208.523i		−	1.20533i	−0.797993	−	0.602667i	$-0.794105\pi$
$173$		−	208.523i		−	1.20533i	0.797993	−	0.602667i	$-0.205895\pi$
$174$	89.5520			0.514667
$175$			156.577i			0.894728i
$176$	194.647			1.10595
$177$	−37.0541			−0.209345
$178$	−624.508			−3.50847
$179$	−129.017			−0.720767			−0.360383	−	0.932804i	$-0.617354\pi$
$179$	−129.017			−0.720767			−0.360383	+	0.932804i	$0.617354\pi$
$180$			212.415i			1.18009i
$181$	282.126			1.55871			0.779353	−	0.626585i	$-0.215548\pi$
$181$	282.126			1.55871			0.779353	+	0.626585i	$0.215548\pi$
$182$	620.731			3.41061
$183$	−31.7130			−0.173295
$184$	255.893			1.39072
$185$	62.4773			0.337715
$186$		−	77.2746i		−	0.415455i
$187$			218.192i			1.16680i
$188$	−288.112			−1.53251
$189$	86.1945			0.456056
$190$	−67.7031			−0.356332
$191$	164.827			0.862967			0.431483	−	0.902121i	$-0.357990\pi$
$191$	164.827			0.862967			0.431483	+	0.902121i	$0.357990\pi$
$192$		−	5.78139i		−	0.0301114i
$193$	−32.2294			−0.166992			−0.0834958	−	0.996508i	$-0.526609\pi$
$193$	−32.2294			−0.166992			−0.0834958	+	0.996508i	$0.526609\pi$
$194$			238.718i			1.23051i
$195$	−28.7042			−0.147201
$196$	282.403			1.44083
$197$		−	62.8239i		−	0.318903i	−0.987206	−	0.159451i	$-0.949027\pi$
$197$		−	62.8239i		−	0.318903i	0.987206	−	0.159451i	$-0.0509725\pi$
$198$		−	225.191i		−	1.13733i
$199$	−235.559			−1.18371			−0.591857	−	0.806043i	$-0.701605\pi$
$199$	−235.559			−1.18371			−0.591857	+	0.806043i	$0.701605\pi$
$200$			302.996i			1.51498i
$201$			1.60420i			0.00798109i
$202$	487.794			2.41482
$203$		−	415.080i		−	2.04473i
$204$	−144.951			−0.710546
$205$	−105.676			−0.515495
$206$	154.386			0.749449
$207$		−	128.017i		−	0.618437i
$208$	519.415			2.49719
$209$	49.4403			0.236556
$210$	−48.0853			−0.228977
$211$			205.981i			0.976212i	0.872784	+	0.488106i	$0.162312\pi$
$211$			205.981i			0.976212i	−0.872784	+	0.488106i	$0.837688\pi$
$212$	−60.9265			−0.287389
$213$	16.2061			0.0760851
$214$	−728.229			−3.40294
$215$	92.8986			0.432086
$216$	166.797			0.772206
$217$	−358.174			−1.65057
$218$	−137.160			−0.629174
$219$		−	29.0251i		−	0.132535i
$220$			175.981i			0.799913i
$221$			582.244i			2.63459i
$222$		−	44.0019i		−	0.198207i
$223$			297.844i			1.33562i	0.744330	+	0.667812i	$0.232769\pi$
$223$			297.844i			1.33562i	−0.744330	+	0.667812i	$0.767231\pi$
$224$	243.964			1.08913
$225$	151.581			0.673692
$226$		−	95.8357i		−	0.424052i
$227$	332.675			1.46553			0.732765	−	0.680482i	$-0.238229\pi$
$227$	332.675			1.46553			0.732765	+	0.680482i	$0.238229\pi$
$228$			32.8447i			0.144056i
$229$		−	309.703i		−	1.35241i	−0.736712	−	0.676207i	$-0.763623\pi$
$229$		−	309.703i		−	1.35241i	0.736712	−	0.676207i	$-0.236377\pi$
$230$			145.235i			0.631458i
$231$	35.1143			0.152010
$232$		−	803.230i		−	3.46220i
$233$	−1.70893			−0.00733448			−0.00366724	−	0.999993i	$-0.501167\pi$
$233$	−1.70893			−0.00733448			−0.00366724	+	0.999993i	$0.501167\pi$
$234$		−	600.922i		−	2.56804i
$235$		−	89.6504i		−	0.381491i
$236$			606.209i			2.56868i
$237$	7.88278			0.0332607
$238$			975.374i			4.09821i
$239$	−104.386			−0.436763			−0.218381	−	0.975864i	$-0.570078\pi$
$239$	−104.386			−0.436763			−0.218381	+	0.975864i	$0.570078\pi$
$240$	−40.2367			−0.167653
$241$		−	142.092i		−	0.589592i	−0.955560	−	0.294796i	$-0.904748\pi$
$241$		−	142.092i		−	0.589592i	0.955560	−	0.294796i	$-0.0952516\pi$
$242$			247.257i			1.02173i
$243$		−	125.856i		−	0.517926i
$244$			518.828i			2.12634i
$245$			87.8742i			0.358670i
$246$			74.4264i			0.302546i
$247$	131.931			0.534135
$248$	−693.109			−2.79479
$249$	61.9183			0.248668
$250$	−418.925			−1.67570
$251$			57.9767i			0.230983i	0.993308	+	0.115491i	$0.0368443\pi$
$251$			57.9767i			0.230983i	−0.993308	+	0.115491i	$0.963156\pi$
$252$		−	693.412i		−	2.75164i
$253$		−	106.058i		−	0.419203i
$254$		−	148.074i		−	0.582967i
$255$		−	45.1039i		−	0.176878i
$256$	−483.589			−1.88902
$257$		−	96.2805i		−	0.374632i	−0.982300	−	0.187316i	$-0.940021\pi$
$257$		−	96.2805i		−	0.374632i	0.982300	−	0.187316i	$-0.0599789\pi$
$258$		−	65.4271i		−	0.253593i
$259$	−203.952			−0.787460
$260$			469.605i			1.80617i
$261$	−401.834			−1.53959
$262$		−	110.719i		−	0.422590i
$263$	151.831			0.577303			0.288652	−	0.957434i	$-0.406793\pi$
$263$	151.831			0.577303			0.288652	+	0.957434i	$0.406793\pi$
$264$	67.9504			0.257388
$265$		−	18.9582i		−	0.0715405i
$266$	221.011			0.830869
$267$	−94.2727			−0.353081
$268$	26.2449			0.0979286
$269$	−42.1050			−0.156524			−0.0782620	−	0.996933i	$-0.524937\pi$
$269$	−42.1050			−0.156524			−0.0782620	+	0.996933i	$0.524937\pi$
$270$			94.6675i			0.350620i
$271$		−	287.389i		−	1.06048i	−0.847848	−	0.530239i	$-0.822102\pi$
$271$		−	287.389i		−	1.06048i	0.847848	−	0.530239i	$-0.177898\pi$
$272$			816.173i			3.00063i
$273$	93.7026			0.343233
$274$			699.262i			2.55205i
$275$	125.581			0.456657
$276$	70.4578			0.255282
$277$	229.779			0.829526			0.414763	−	0.909929i	$-0.363864\pi$
$277$	229.779			0.829526			0.414763	+	0.909929i	$0.363864\pi$
$278$			368.614i			1.32595i
$279$			346.743i			1.24281i
$280$			431.297i			1.54035i
$281$			237.898i			0.846613i	0.905987	+	0.423307i	$0.139131\pi$
$281$			237.898i			0.846613i	−0.905987	+	0.423307i	$0.860869\pi$
$282$	−63.1395			−0.223899
$283$			407.426i			1.43967i	0.694145	+	0.719835i	$0.255782\pi$
$283$			407.426i			1.43967i	−0.694145	+	0.719835i	$0.744218\pi$
$284$		−	265.134i		−	0.933570i
$285$	−10.2201			−0.0358601
$286$		−	497.848i		−	1.74073i
$287$	344.972			1.20199
$288$		−	236.179i		−	0.820065i
$289$	−625.899			−2.16574
$290$	455.883			1.57201
$291$			36.0357i			0.123834i
$292$	−474.854			−1.62621
$293$	−420.917			−1.43658			−0.718288	−	0.695746i	$-0.755074\pi$
$293$	−420.917			−1.43658			−0.718288	+	0.695746i	$0.755074\pi$
$294$	61.8885			0.210505
$295$	−188.631			−0.639428
$296$	−394.671			−1.33335
$297$		−	69.1311i		−	0.232765i
$298$		−	922.649i		−	3.09614i
$299$		−	283.017i		−	0.946545i
$300$			83.4270i			0.278090i
$301$	−303.260			−1.00751
$302$	712.059			2.35781
$303$	73.6351			0.243020
$304$	184.937			0.608347
$305$	−161.441			−0.529316
$306$	944.247			3.08577
$307$			48.9075i			0.159308i	0.996823	+	0.0796539i	$0.0253815\pi$
$307$			48.9075i			0.159308i	−0.996823	+	0.0796539i	$0.974618\pi$
$308$		−	574.475i		−	1.86518i
$309$	23.3054			0.0754222
$310$		−	393.382i		−	1.26898i
$311$	−325.509			−1.04665			−0.523326	−	0.852133i	$-0.675309\pi$
$311$	−325.509			−1.04665			−0.523326	+	0.852133i	$0.675309\pi$
$312$	181.326			0.581172
$313$	81.9928			0.261958			0.130979	−	0.991385i	$-0.458188\pi$
$313$	81.9928			0.261958			0.130979	+	0.991385i	$0.458188\pi$
$314$		−	773.970i		−	2.46487i
$315$	215.766			0.684972
$316$		−	128.963i		−	0.408111i
$317$	−538.849			−1.69984			−0.849920	−	0.526912i	$-0.823350\pi$
$317$	−538.849			−1.69984			−0.849920	+	0.526912i	$0.823350\pi$
$318$	−13.3520			−0.0419874
$319$	−332.909			−1.04360
$320$		−	29.4314i		−	0.0919730i
$321$	−109.930			−0.342461
$322$		−	474.109i		−	1.47239i
$323$			207.308i			0.641820i
$324$	−647.941			−1.99982
$325$	335.112			1.03111
$326$	−171.991			−0.527580
$327$	−20.7050			−0.0633180
$328$	667.562			2.03525
$329$			292.656i			0.889533i
$330$			38.5661i			0.116867i
$331$		−	501.981i		−	1.51656i	−0.651929	−	0.758280i	$-0.726040\pi$
$331$		−	501.981i		−	1.51656i	0.651929	−	0.758280i	$-0.273960\pi$
$332$		−	1012.99i		−	3.05117i
$333$			197.443i			0.592923i
$334$			499.950i			1.49686i
$335$			8.16650i			0.0243776i
$336$	131.349			0.390921
$337$			91.6852i			0.272063i	0.990705	+	0.136031i	$0.0434348\pi$
$337$			91.6852i			0.272063i	−0.990705	+	0.136031i	$0.956565\pi$
$338$		−	722.591i		−	2.13784i
$339$		−	14.4669i		−	0.0426752i
$340$	−737.905			−2.17031
$341$			287.268i			0.842428i
$342$		−	213.958i		−	0.625608i
$343$			153.853i			0.448552i
$344$	−586.843			−1.70594
$345$			21.9241i			0.0635480i
$346$	−747.619			−2.16075
$347$	−157.814			−0.454795			−0.227397	−	0.973802i	$-0.573022\pi$
$347$	−157.814			−0.454795			−0.227397	+	0.973802i	$0.573022\pi$
$348$		−	221.162i		−	0.635522i
$349$	4.79104			0.0137279			0.00686396	−	0.999976i	$-0.497815\pi$
$349$	4.79104			0.0137279			0.00686396	+	0.999976i	$0.497815\pi$
$350$	561.379			1.60394
$351$		−	184.476i		−	0.525573i
$352$		−	195.668i		−	0.555875i
$353$	−139.099			−0.394050			−0.197025	−	0.980399i	$-0.563128\pi$
$353$	−139.099			−0.394050			−0.197025	+	0.980399i	$0.563128\pi$
$354$			132.850i			0.375283i
$355$	82.5006			0.232396
$356$			1542.31i			4.33234i
$357$			147.238i			0.412431i
$358$			462.567i			1.29209i
$359$			642.483i			1.78965i	0.446420	+	0.894824i	$0.352699\pi$
$359$			642.483i			1.78965i	−0.446420	+	0.894824i	$0.647301\pi$
$360$	417.533			1.15981
$361$	−314.026			−0.869878
$362$		−	1011.51i		−	2.79422i
$363$			37.3248i			0.102823i
$364$		−	1532.99i		−	4.21150i
$365$		−	147.758i		−	0.404817i
$366$			113.701i			0.310658i
$367$	−276.164			−0.752491			−0.376246	−	0.926520i	$-0.622785\pi$
$367$	−276.164			−0.752491			−0.376246	+	0.926520i	$0.622785\pi$
$368$		−	396.724i		−	1.07806i
$369$		−	333.963i		−	0.905049i
$370$		−	224.001i		−	0.605407i
$371$			61.8875i			0.166813i
$372$	−190.841			−0.513013
$373$		−	532.102i		−	1.42655i	−0.700885	−	0.713274i	$-0.747211\pi$
$373$		−	532.102i		−	1.42655i	0.700885	−	0.713274i	$-0.252789\pi$
$374$	782.285			2.09167
$375$	−63.2389			−0.168637
$376$			566.324i			1.50618i
$377$	−888.368			−2.35641
$378$		−	309.034i		−	0.817550i
$379$	473.938			1.25050			0.625248	−	0.780426i	$-0.284998\pi$
$379$	473.938			1.25050			0.625248	+	0.780426i	$0.284998\pi$
$380$			167.203i			0.440007i
$381$		−	22.3525i		−	0.0586679i
$382$		−	590.955i		−	1.54700i
$383$	−671.118			−1.75227			−0.876133	−	0.482070i	$-0.839885\pi$
$383$	−671.118			−1.75227			−0.876133	+	0.482070i	$0.839885\pi$
$384$	−79.4504			−0.206902
$385$	178.757			0.464303
$386$			115.552i			0.299358i
$387$			293.582i			0.758609i
$388$	589.549			1.51946
$389$		−	245.917i		−	0.632178i	−0.948730	−	0.316089i	$-0.897630\pi$
$389$		−	245.917i		−	0.632178i	0.948730	−	0.316089i	$-0.102370\pi$
$390$			102.914i			0.263881i
$391$	444.713			1.13737
$392$		−	555.104i		−	1.41608i
$393$		−	16.7135i		−	0.0425281i
$394$	−225.243			−0.571683
$395$	40.1289			0.101592
$396$	−556.141			−1.40440
$397$		−	278.778i		−	0.702212i	−0.936336	−	0.351106i	$-0.885806\pi$
$397$		−	278.778i		−	0.702212i	0.936336	−	0.351106i	$-0.114194\pi$
$398$			844.552i			2.12199i
$399$	33.3628			0.0836160
$400$	469.750			1.17437
$401$	−448.345			−1.11807			−0.559033	−	0.829145i	$-0.688828\pi$
$401$	−448.345			−1.11807			−0.559033	+	0.829145i	$0.688828\pi$
$402$	5.75155			0.0143073
$403$			766.575i			1.90217i
$404$		−	1204.68i		−	2.98188i
$405$		−	201.617i		−	0.497820i
$406$	−1488.19			−3.66550
$407$			163.577i			0.401908i
$408$			284.923i			0.698340i
$409$	−368.292			−0.900468			−0.450234	−	0.892910i	$-0.648660\pi$
$409$	−368.292			−0.900468			−0.450234	+	0.892910i	$0.648660\pi$
$410$			378.883i			0.924104i
$411$			105.557i			0.256830i
$412$		−	381.280i		−	0.925436i
$413$	615.771			1.49097
$414$	−458.979			−1.10864
$415$	315.208			0.759536
$416$		−	522.140i		−	1.25514i
$417$			55.6442i			0.133439i
$418$		−	177.259i		−	0.424064i
$419$	−670.397			−1.59999			−0.799996	−	0.600006i	$-0.795165\pi$
$419$	−670.397			−1.59999			−0.799996	+	0.600006i	$0.795165\pi$
$420$			118.754i			0.282746i
$421$			502.485i			1.19355i	0.802409	+	0.596775i	$0.203551\pi$
$421$			502.485i			1.19355i	−0.802409	+	0.596775i	$0.796449\pi$
$422$	738.504			1.75001
$423$	283.317			0.669779
$424$			119.760i			0.282452i
$425$			526.572i			1.23899i
$426$		−	58.1039i		−	0.136394i
$427$	527.012			1.23422
$428$			1798.47i			4.20203i
$429$		−	75.1528i		−	0.175181i
$430$		−	333.070i		−	0.774582i
$431$			196.432i			0.455759i	0.973689	+	0.227879i	$0.0731792\pi$
$431$			196.432i			0.455759i	−0.973689	+	0.227879i	$0.926821\pi$
$432$		−	258.593i		−	0.598595i
$433$		−	437.218i		−	1.00974i	−0.863195	−	0.504871i	$-0.831540\pi$
$433$		−	437.218i		−	1.00974i	0.863195	−	0.504871i	$-0.168460\pi$
$434$			1284.16i			2.95890i
$435$	68.8179			0.158202
$436$			338.736i			0.776918i
$437$		−	100.768i		−	0.230591i
$438$	−104.064			−0.237589
$439$	−730.736			−1.66455			−0.832274	−	0.554365i	$-0.812961\pi$
$439$	−730.736			−1.66455			−0.832274	+	0.554365i	$0.812961\pi$
$440$	345.915			0.786171
$441$	−277.703			−0.629713
$442$	2087.53			4.72291
$443$	568.584			1.28349			0.641743	−	0.766920i	$-0.278212\pi$
$443$	568.584			1.28349			0.641743	+	0.766920i	$0.278212\pi$
$444$	−108.669			−0.244750
$445$	−479.914			−1.07846
$446$	1067.86			2.39431
$447$		−	139.279i		−	0.311585i
$448$			96.0762i			0.214456i
$449$	834.013			1.85749			0.928745	−	0.370720i	$-0.120889\pi$
$449$	834.013			1.85749			0.928745	+	0.370720i	$0.120889\pi$
$450$		−	543.463i		−	1.20770i
$451$		−	276.680i		−	0.613481i
$452$	−236.680			−0.523628
$453$	107.489			0.237283
$454$		−	1192.74i		−	2.62719i
$455$	477.012			1.04838
$456$	64.5609			0.141581
$457$		−	480.792i		−	1.05206i	−0.850465	−	0.526031i	$-0.823680\pi$
$457$		−	480.792i		−	1.05206i	0.850465	−	0.526031i	$-0.176320\pi$
$458$	−1110.38			−2.42441
$459$	289.873			0.631532
$460$	358.680			0.779739
$461$			564.467i			1.22444i	0.790688	+	0.612220i	$0.209723\pi$
$461$			564.467i			1.22444i	−0.790688	+	0.612220i	$0.790277\pi$
$462$		−	125.896i		−	0.272502i
$463$		−	285.066i		−	0.615692i	−0.951436	−	0.307846i	$-0.900392\pi$
$463$		−	285.066i		−	0.615692i	0.951436	−	0.307846i	$-0.0996082\pi$
$464$	−1245.29			−2.68381
$465$		−	59.3831i		−	0.127706i
$466$			6.12706i			0.0131482i
$467$	834.718			1.78740			0.893702	−	0.448660i	$-0.148099\pi$
$467$	834.718			1.78740			0.893702	+	0.448660i	$0.148099\pi$
$468$	−1484.06			−3.17107
$469$		−	26.6589i		−	0.0568419i
$470$	−321.424			−0.683882
$471$		−	116.835i		−	0.248057i
$472$	1191.59			2.52455
$473$			243.225i			0.514218i
$474$		−	28.2622i		−	0.0596249i
$475$	119.316			0.251193
$476$	2408.83			5.06056
$477$	59.9125			0.125603
$478$			374.257i			0.782964i
$479$	608.594			1.27055			0.635275	−	0.772286i	$-0.280887\pi$
$479$	608.594			1.27055			0.635275	+	0.772286i	$0.280887\pi$
$480$			40.4479i			0.0842664i
$481$			436.504i			0.907494i
$482$	−509.442			−1.05693
$483$		−	71.5692i		−	0.148176i
$484$	610.638			1.26165
$485$			183.447i			0.378242i
$486$	−451.232			−0.928462
$487$			286.801i			0.588914i	0.955665	+	0.294457i	$0.0951388\pi$
$487$			286.801i			0.588914i	−0.955665	+	0.294457i	$0.904861\pi$
$488$	1019.83			2.08981
$489$	−25.9629			−0.0530939
$490$	315.056			0.642972
$491$			339.698i			0.691849i	0.938262	+	0.345924i	$0.112435\pi$
$491$			339.698i			0.691849i	−0.938262	+	0.345924i	$0.887565\pi$
$492$	183.807			0.373591
$493$		−	1395.92i		−	2.83148i
$494$		−	473.015i		−	0.957520i
$495$		−	173.052i		−	0.349600i
$496$			1074.56i			2.16645i
$497$	−269.316			−0.541884
$498$		−	221.996i		−	0.445775i
$499$	−415.728			−0.833122			−0.416561	−	0.909108i	$-0.636765\pi$
$499$	−415.728			−0.833122			−0.416561	+	0.909108i	$0.636765\pi$
$500$			1034.60i			2.06919i
$501$			75.4701i			0.150639i
$502$	207.864			0.414072
$503$		−	604.321i		−	1.20143i	−0.799462	−	0.600716i	$-0.794882\pi$
$503$		−	604.321i		−	1.20143i	0.799462	−	0.600716i	$-0.205118\pi$
$504$	−1363.00			−2.70437
$505$	374.855			0.742287
$506$	−380.252			−0.751486
$507$		−	109.079i		−	0.215146i
$508$	−365.689			−0.719860
$509$	−345.863			−0.679494			−0.339747	−	0.940517i	$-0.610341\pi$
$509$	−345.863			−0.679494			−0.339747	+	0.940517i	$0.610341\pi$
$510$	−161.711			−0.317081
$511$			482.345i			0.943923i
$512$			1146.62i			2.23950i
$513$		−	65.6827i		−	0.128036i
$514$	−345.195			−0.671586
$515$	118.641			0.230371
$516$	−161.582			−0.313143
$517$	234.721			0.454005
$518$			731.231i			1.41164i
$519$	−112.857			−0.217451
$520$	923.075			1.77514
$521$	−199.057			−0.382068			−0.191034	−	0.981583i	$-0.561184\pi$
$521$	−199.057			−0.382068			−0.191034	+	0.981583i	$0.561184\pi$
$522$			1440.70i			2.75996i
$523$		−	68.1917i		−	0.130386i	−0.997873	−	0.0651928i	$-0.979234\pi$
$523$		−	68.1917i		−	0.130386i	0.997873	−	0.0651928i	$-0.0207662\pi$
$524$	−273.435			−0.521823
$525$	84.7430			0.161415
$526$		−	544.360i		−	1.03491i
$527$	−1204.54			−2.28566
$528$		−	105.347i		−	0.199521i
$529$	312.834			0.591369
$530$	−67.9711			−0.128247
$531$		−	596.120i		−	1.12264i
$532$		−	545.819i		−	1.02598i
$533$		−	738.320i		−	1.38522i
$534$			337.997i			0.632953i
$535$	−559.621			−1.04602
$536$		−	51.5880i		−	0.0962463i
$537$			69.8269i			0.130031i
$538$			150.959i			0.280593i
$539$	−230.070			−0.426846
$540$	233.795			0.432954
$541$			305.795i			0.565241i	0.959232	+	0.282621i	$0.0912037\pi$
$541$			305.795i			0.565241i	−0.959232	+	0.282621i	$0.908796\pi$
$542$	−1030.38			−1.90107
$543$		−	152.692i		−	0.281202i
$544$	820.455			1.50819
$545$	−105.403			−0.193400
$546$		−	335.953i		−	0.615298i
$547$	117.473	−	534.237i	0.214758	−	0.976667i
$547$	117.473	−	534.237i	0.214758	−	0.976667i
$548$	1726.93			3.15133
$549$		−	510.193i		−	0.929313i
$550$		−	450.245i		−	0.818628i
$551$	−316.303			−0.574053
$552$		−	138.495i		−	0.250897i
$553$	−130.997			−0.236885
$554$		−	823.828i		−	1.48705i
$555$		−	33.8141i		−	0.0609262i
$556$	910.346			1.63731
$557$	229.406			0.411859			0.205930	−	0.978567i	$-0.433978\pi$
$557$	229.406			0.411859			0.205930	+	0.978567i	$0.433978\pi$
$558$	1243.18			2.22793
$559$			649.046i			1.16108i
$560$	668.661			1.19404
$561$	118.090			0.210499
$562$	852.939			1.51768
$563$	57.1909			0.101582			0.0507912	−	0.998709i	$-0.483826\pi$
$563$	57.1909			0.101582			0.0507912	+	0.998709i	$0.483826\pi$
$564$			155.932i			0.276475i
$565$		−	73.6467i		−	0.130348i
$566$	1460.75			2.58083
$567$			658.161i			1.16078i
$568$	−521.159			−0.917533
$569$		−	983.257i		−	1.72804i	−0.503455	−	0.864022i	$-0.667938\pi$
$569$		−	983.257i		−	1.72804i	0.503455	−	0.864022i	$-0.332062\pi$
$570$			36.6423i			0.0642848i
$571$	−916.025			−1.60425			−0.802123	−	0.597158i	$-0.796296\pi$
$571$	−916.025			−1.60425			−0.802123	+	0.597158i	$0.796296\pi$
$572$	−1229.51			−2.14949
$573$		−	89.2077i		−	0.155685i
$574$		−	1236.83i		−	2.15476i
$575$		−	255.956i		−	0.445140i
$576$	93.0101			0.161476
$577$		−	576.974i		−	0.999956i	−0.866038	−	0.499978i	$-0.833342\pi$
$577$		−	576.974i		−	0.999956i	0.866038	−	0.499978i	$-0.166658\pi$
$578$			2244.04i			3.88242i
$579$			17.4432i			0.0301265i
$580$		−	1125.87i		−	1.94115i
$581$	−1028.97			−1.77103
$582$	129.199			0.221992
$583$	49.6360			0.0851389
$584$			933.394i			1.59828i
$585$		−	461.789i		−	0.789384i
$586$			1509.12i			2.57528i
$587$	691.576			1.17815			0.589077	−	0.808077i	$-0.299492\pi$
$587$	691.576			1.17815			0.589077	+	0.808077i	$0.299492\pi$
$588$		−	152.843i		−	0.259936i
$589$			272.939i			0.463393i
$590$			676.301i			1.14627i
$591$	−34.0016			−0.0575323
$592$			611.879i			1.03358i
$593$	969.672			1.63520			0.817599	−	0.575788i	$-0.195305\pi$
$593$	969.672			1.63520			0.817599	+	0.575788i	$0.195305\pi$
$594$	−247.856			−0.417266
$595$			749.544i			1.25974i
$596$	−2278.61			−3.82318
$597$			127.490i			0.213550i
$598$	−1014.70			−1.69683
$599$	386.189			0.644723			0.322362	−	0.946617i	$-0.395523\pi$
$599$	386.189			0.644723			0.322362	+	0.946617i	$0.395523\pi$
$600$	163.988			0.273313
$601$	344.672			0.573497			0.286749	−	0.958006i	$-0.407426\pi$
$601$	344.672			0.573497			0.286749	+	0.958006i	$0.407426\pi$
$602$			1087.28i			1.80611i
$603$	−25.8081			−0.0427995
$604$		−	1758.53i		−	2.91148i
$605$			190.010i			0.314065i
$606$		−	264.005i		−	0.435651i
$607$	252.010			0.415172			0.207586	−	0.978217i	$-0.433439\pi$
$607$	252.010			0.415172			0.207586	+	0.978217i	$0.433439\pi$
$608$		−	185.908i		−	0.305769i
$609$	−224.650			−0.368884
$610$			578.817i			0.948880i
$611$	626.352			1.02513
$612$		−	2331.95i		−	3.81038i
$613$	183.724			0.299712			0.149856	−	0.988708i	$-0.452119\pi$
$613$	183.724			0.299712			0.149856	+	0.988708i	$0.452119\pi$
$614$	175.348			0.285584
$615$			57.1943i			0.0929989i
$616$	−1129.21			−1.83314
$617$		−	1098.71i		−	1.78073i	−0.455252	−	0.890363i	$-0.650451\pi$
$617$		−	1098.71i		−	1.78073i	0.455252	−	0.890363i	$-0.349549\pi$
$618$		−	83.5572i		−	0.135206i
$619$		−	232.666i		−	0.375875i	−0.982181	−	0.187937i	$-0.939820\pi$
$619$		−	232.666i		−	0.375875i	0.982181	−	0.187937i	$-0.0601802\pi$
$620$	−971.515			−1.56696
$621$	−140.901			−0.226894
$622$			1167.05i			1.87628i
$623$	1566.64			2.51467
$624$		−	281.118i		−	0.450510i
$625$	113.292			0.181267
$626$		−	293.970i		−	0.469600i
$627$		−	26.7581i		−	0.0426764i
$628$	−1911.43			−3.04368
$629$	−685.893			−1.09045
$630$		−	773.588i		−	1.22792i
$631$	−756.343			−1.19864			−0.599321	−	0.800509i	$-0.704563\pi$
$631$	−756.343			−1.19864			−0.599321	+	0.800509i	$0.704563\pi$
$632$	−253.495			−0.401100
$633$	111.481			0.176115
$634$			1931.94i			3.04723i
$635$		−	113.790i		−	0.179197i
$636$			32.9747i			0.0518470i
$637$	−613.942			−0.963803
$638$			1193.58i			1.87082i
$639$			260.722i			0.408015i
$640$	−404.458			−0.631966
$641$		−	596.790i		−	0.931029i	−0.885040	−	0.465515i	$-0.845869\pi$
$641$		−	596.790i		−	0.931029i	0.885040	−	0.465515i	$-0.154131\pi$
$642$			394.133i			0.613914i
$643$	−127.258			−0.197914			−0.0989568	−	0.995092i	$-0.531551\pi$
$643$	−127.258			−0.197914			−0.0989568	+	0.995092i	$0.531551\pi$
$644$	−1170.88			−1.81814
$645$		−	50.2787i		−	0.0779514i
$646$	743.263			1.15056
$647$	763.210			1.17961			0.589807	−	0.807544i	$-0.299204\pi$
$647$	763.210			1.17961			0.589807	+	0.807544i	$0.299204\pi$
$648$			1273.62i			1.96546i
$649$		−	493.870i		−	0.760971i
$650$		−	1201.48i		−	1.84843i
$651$			193.851i			0.297775i
$652$			424.757i			0.651467i
$653$			19.6457i			0.0300854i	0.999887	+	0.0150427i	$0.00478841\pi$
$653$			19.6457i			0.0300854i	−0.999887	+	0.0150427i	$0.995212\pi$
$654$			74.2338i			0.113507i
$655$		−	85.0837i		−	0.129899i
$656$		−	1034.95i		−	1.57767i
$657$	466.952			0.710733
$658$	1049.26			1.59462
$659$			244.669i			0.371274i	0.982618	+	0.185637i	$0.0594348\pi$
$659$			244.669i			0.371274i	−0.982618	+	0.185637i	$0.940565\pi$
$660$	95.2445			0.144310
$661$	398.417			0.602748			0.301374	−	0.953506i	$-0.402555\pi$
$661$	398.417			0.602748			0.301374	+	0.953506i	$0.402555\pi$
$662$	−1799.76			−2.71867
$663$	315.123			0.475299
$664$	−1991.18			−2.99876
$665$	169.840			0.255399
$666$	707.895			1.06291
$667$			678.528i			1.01728i
$668$	1234.70			1.84835
$669$	161.200			0.240956
$670$	29.2794			0.0437006
$671$		−	422.682i		−	0.629928i
$672$		−	132.039i		−	0.196486i
$673$	−1160.90			−1.72496			−0.862479	−	0.506094i	$-0.831089\pi$
$673$	−1160.90			−1.72496			−0.862479	+	0.506094i	$0.831089\pi$
$674$	328.720			0.487715
$675$		−	166.837i		−	0.247166i
$676$	−1784.54			−2.63986
$677$	873.810			1.29071			0.645355	−	0.763883i	$-0.276710\pi$
$677$	873.810			1.29071			0.645355	+	0.763883i	$0.276710\pi$
$678$	−51.8683			−0.0765019
$679$		−	598.848i		−	0.881956i
$680$			1450.46i			2.13302i
$681$		−	180.051i		−	0.264392i
$682$	1029.94			1.51018
$683$	1184.57			1.73436			0.867180	−	0.497994i	$-0.165930\pi$
$683$	1184.57			1.73436			0.867180	+	0.497994i	$0.165930\pi$
$684$	−528.400			−0.772515
$685$			537.361i			0.784468i
$686$	551.612			0.804099
$687$	−167.618			−0.243985
$688$			909.813i			1.32240i
$689$	132.454			0.192240
$690$	78.6045			0.113920
$691$	171.543			0.248254			0.124127	−	0.992266i	$-0.460387\pi$
$691$	171.543			0.248254			0.124127	+	0.992266i	$0.460387\pi$
$692$			1846.35i			2.66814i
$693$			564.914i			0.815172i
$694$			565.811i			0.815290i
$695$			283.268i			0.407580i
$696$	−434.725			−0.624605
$697$	1160.15			1.66448
$698$		−	17.1774i		−	0.0246094i
$699$			0.924912i			0.00132319i
$700$		−	1386.41i		−	1.98058i
$701$	−301.205			−0.429680			−0.214840	−	0.976649i	$-0.568923\pi$
$701$	−301.205			−0.429680			−0.214840	+	0.976649i	$0.568923\pi$
$702$	−661.404			−0.942171
$703$			155.417i			0.221077i
$704$	77.0565			0.109455
$705$	−48.5207			−0.0688237
$706$			498.715i			0.706395i
$707$	−1223.68			−1.73081
$708$	328.093			0.463408
$709$			468.407i			0.660659i	0.943866	+	0.330330i	$0.107160\pi$
$709$			468.407i			0.660659i	−0.943866	+	0.330330i	$0.892840\pi$
$710$		−	295.790i		−	0.416606i
$711$			126.817i			0.178364i
$712$	3031.63			4.25791
$713$	585.503			0.821183
$714$	527.893			0.739346
$715$		−	382.581i		−	0.535078i
$716$	1142.38			1.59550
$717$			56.4961i			0.0787951i
$718$	2303.50			3.20822
$719$			44.5101i			0.0619056i	0.999521	+	0.0309528i	$0.00985415\pi$
$719$			44.5101i			0.0619056i	−0.999521	+	0.0309528i	$0.990146\pi$
$720$		−	647.322i		−	0.899059i
$721$	−387.294			−0.537162
$722$			1125.88i			1.55939i
$723$	−76.9029			−0.106366
$724$	−2498.07			−3.45037
$725$	−803.425			−1.10817
$726$	133.821			0.184326
$727$			176.775i			0.243157i	0.992582	+	0.121578i	$0.0387956\pi$
$727$			176.775i			0.243157i	−0.992582	+	0.121578i	$0.961204\pi$
$728$	−3013.30			−4.13915
$729$	590.477			0.809982
$730$	−529.759			−0.725698
$731$	−1019.87			−1.39517
$732$	280.800			0.383607
$733$		−	534.609i		−	0.729344i	−0.931136	−	0.364672i	$-0.881181\pi$
$733$		−	534.609i		−	0.729344i	0.931136	−	0.364672i	$-0.118819\pi$
$734$			990.134i			1.34896i
$735$	47.5594			0.0647066
$736$	−398.806			−0.541856
$737$	−21.3813			−0.0290113
$738$	−1197.36			−1.62244
$739$			534.160i			0.722815i	0.932408	+	0.361408i	$0.117704\pi$
$739$			534.160i			0.722815i	−0.932408	+	0.361408i	$0.882296\pi$
$740$	−553.202			−0.747570
$741$		−	71.4041i		−	0.0963617i
$742$	221.886			0.299038
$743$	−1314.61			−1.76932			−0.884662	−	0.466233i	$-0.845611\pi$
$743$	−1314.61			−1.76932			−0.884662	+	0.466233i	$0.845611\pi$
$744$			375.125i			0.504200i
$745$		−	709.027i		−	0.951713i
$746$	−1907.75			−2.55731
$747$			996.131i			1.33351i
$748$		−	1931.97i		−	2.58284i
$749$	1826.84			2.43903
$750$			226.731i			0.302308i
$751$	98.4534			0.131096			0.0655482	−	0.997849i	$-0.479120\pi$
$751$	98.4534			0.131096			0.0655482	+	0.997849i	$0.479120\pi$
$752$	878.001			1.16755
$753$	31.3782			0.0416709
$754$			3185.07i			4.22424i
$755$	547.195			0.724762
$756$	−763.204			−1.00953
$757$	−864.539			−1.14206			−0.571029	−	0.820930i	$-0.693456\pi$
$757$	−864.539			−1.14206			−0.571029	+	0.820930i	$0.693456\pi$
$758$		−	1699.21i		−	2.24171i
$759$	−57.4011			−0.0756272
$760$	328.661			0.432448
$761$	−1229.27			−1.61534			−0.807670	−	0.589635i	$-0.799271\pi$
$761$	−1229.27			−1.61534			−0.807670	+	0.589635i	$0.799271\pi$
$762$	−80.1405			−0.105171
$763$	344.079			0.450956
$764$	−1459.45			−1.91027
$765$	725.624			0.948528
$766$			2406.16i			3.14121i
$767$		−	1317.89i		−	1.71824i
$768$			261.729i			0.340792i
$769$			782.205i			1.01717i	0.861011	+	0.508586i	$0.169831\pi$
$769$			782.205i			1.01717i	−0.861011	+	0.508586i	$0.830169\pi$
$770$		−	640.898i		−	0.832335i
$771$	−52.1090			−0.0675863
$772$	285.373			0.369654
$773$			841.128i			1.08813i	0.839042	+	0.544067i	$0.183116\pi$
$773$			841.128i			1.08813i	−0.839042	+	0.544067i	$0.816884\pi$
$774$	1052.58			1.35992
$775$			693.277i			0.894551i
$776$		−	1158.84i		−	1.49335i
$777$			110.383i			0.142063i
$778$	−881.689			−1.13328
$779$		−	262.879i		−	0.337456i
$780$	254.160			0.325846
$781$			216.001i			0.276570i
$782$		−	1594.43i		−	2.03892i
$783$			442.278i			0.564851i
$784$	−860.606			−1.09771
$785$		−	594.771i		−	0.757670i
$786$	−59.9232			−0.0762382
$787$	−369.033			−0.468911			−0.234456	−	0.972127i	$-0.575331\pi$
$787$	−369.033			−0.468911			−0.234456	+	0.972127i	$0.575331\pi$
$788$			556.270i			0.705926i
$789$		−	82.1740i		−	0.104150i
$790$		−	143.874i		−	0.182120i
$791$			240.413i			0.303936i
$792$			1093.18i			1.38027i
$793$		−	1127.93i		−	1.42235i
$794$	−999.506			−1.25882
$795$	−10.2606			−0.0129064
$796$	2085.74			2.62028
$797$	403.223			0.505926			0.252963	−	0.967476i	$-0.418595\pi$
$797$	403.223			0.505926			0.252963	+	0.967476i	$0.418595\pi$
$798$		−	119.616i		−	0.149895i
$799$			984.207i			1.23180i
$800$		−	472.215i		−	0.590268i
$801$		−	1516.64i		−	1.89344i
$802$			1607.45i			2.00431i
$803$	386.858			0.481765
$804$		−	14.2043i		−	0.0176670i
$805$		−	364.338i		−	0.452593i
$806$	2748.41			3.40993
$807$			22.7881i			0.0282380i
$808$	−2367.97			−2.93065
$809$		−	874.911i		−	1.08147i	−0.841192	−	0.540736i	$-0.818146\pi$
$809$		−	874.911i		−	1.08147i	0.841192	−	0.540736i	$-0.181854\pi$
$810$	−722.859			−0.892418
$811$	−780.338			−0.962192			−0.481096	−	0.876668i	$-0.659761\pi$
$811$	−780.338			−0.962192			−0.481096	+	0.876668i	$0.659761\pi$
$812$			3675.30i			4.52624i
$813$	−155.541			−0.191318
$814$	586.473			0.720483
$815$	−132.170			−0.162171
$816$	441.730			0.541336
$817$			231.093i			0.282855i
$818$			1320.44i			1.61423i
$819$			1507.47i			1.84063i
$820$	935.706			1.14110
$821$			605.473i			0.737483i	0.929532	+	0.368741i	$0.120211\pi$
$821$			605.473i			0.737483i	−0.929532	+	0.368741i	$0.879789\pi$
$822$	378.455			0.460408
$823$	−273.576			−0.332413			−0.166206	−	0.986091i	$-0.553152\pi$
$823$	−273.576			−0.332413			−0.166206	+	0.986091i	$0.553152\pi$
$824$	−749.460			−0.909538
$825$		−	67.9669i		−	0.0823841i
$826$		−	2207.73i		−	2.67280i
$827$		−	1498.42i		−	1.81187i	−0.423412	−	0.905937i	$-0.639168\pi$
$827$		−	1498.42i		−	1.81187i	0.423412	−	0.905937i	$-0.360832\pi$
$828$			1133.51i			1.36898i
$829$	−942.059			−1.13638			−0.568190	−	0.822898i	$-0.692356\pi$
$829$	−942.059			−1.13638			−0.568190	+	0.822898i	$0.692356\pi$
$830$		−	1130.12i		−	1.36159i
$831$		−	124.361i		−	0.149652i
$832$	205.625			0.247146
$833$		−	964.707i		−	1.15811i
$834$	199.502			0.239211
$835$			384.196i			0.460115i
$836$	−437.766			−0.523644
$837$	381.643			0.455965
$838$			2403.58i			2.86823i
$839$	−686.958			−0.818782			−0.409391	−	0.912359i	$-0.634259\pi$
$839$	−686.958			−0.818782			−0.409391	+	0.912359i	$0.634259\pi$
$840$	233.427			0.277889
$841$	1288.85			1.53252
$842$	1801.56			2.13962
$843$	128.756			0.152735
$844$		−	1823.84i		−	2.16095i
$845$		−	555.288i		−	0.657146i
$846$		−	1015.78i		−	1.20068i
$847$		−	620.270i		−	0.732314i
$848$	185.670			0.218950
$849$	220.508			0.259726
$850$	1887.92			2.22109
$851$	333.398			0.391772
$852$	−143.496			−0.168423
$853$	−1052.52			−1.23391			−0.616954	−	0.786999i	$-0.711634\pi$
$853$	−1052.52			−1.23391			−0.616954	+	0.786999i	$0.711634\pi$
$854$		−	1889.50i		−	2.21253i
$855$		−	164.420i		−	0.192304i
$856$	3535.14			4.12984
$857$		−	53.7959i		−	0.0627724i	−0.999507	−	0.0313862i	$-0.990008\pi$
$857$		−	53.7959i		−	0.0627724i	0.999507	−	0.0313862i	$-0.00999218\pi$
$858$	−269.446			−0.314040
$859$	412.222			0.479886			0.239943	−	0.970787i	$-0.422871\pi$
$859$	412.222			0.479886			0.239943	+	0.970787i	$0.422871\pi$
$860$	−822.565			−0.956471
$861$		−	186.706i		−	0.216848i
$862$	704.270			0.817018
$863$		−	361.202i		−	0.418543i	−0.977858	−	0.209271i	$-0.932891\pi$
$863$		−	361.202i		−	0.418543i	0.977858	−	0.209271i	$-0.0671092\pi$
$864$	−259.950			−0.300868
$865$	−574.521			−0.664187
$866$	−1567.56			−1.81012
$867$			338.750i			0.390715i
$868$	3171.43			3.65372
$869$			105.065i			0.120903i
$870$		−	246.733i		−	0.283602i
$871$	−57.0561			−0.0655064
$872$	665.834			0.763571
$873$	−579.737			−0.664075
$874$	−361.285			−0.413369
$875$	1050.92			1.20105
$876$			257.001i			0.293380i
$877$		−	5.06477i		−	0.00577511i	−0.999996	−	0.00288755i	$-0.999081\pi$
$877$		−	5.06477i		−	0.00577511i	0.999996	−	0.00288755i	$-0.000919138\pi$
$878$			2619.92i			2.98396i
$879$			227.809i			0.259168i
$880$		−	536.290i		−	0.609420i
$881$		−	1384.21i		−	1.57119i	−0.618744	−	0.785593i	$-0.712358\pi$
$881$		−	1384.21i		−	1.57119i	0.618744	−	0.785593i	$-0.287642\pi$
$882$			995.653i			1.12886i
$883$	556.549			0.630293			0.315147	−	0.949043i	$-0.397946\pi$
$883$	556.549			0.630293			0.315147	+	0.949043i	$0.397946\pi$
$884$		−	5155.45i		−	5.83195i
$885$			102.091i			0.115357i
$886$		−	2038.55i		−	2.30085i
$887$	−378.604			−0.426837			−0.213418	−	0.976961i	$-0.568460\pi$
$887$	−378.604			−0.426837			−0.213418	+	0.976961i	$0.568460\pi$
$888$			213.604i			0.240545i
$889$			371.457i			0.417837i
$890$			1720.64i			1.93330i
$891$	527.869			0.592445
$892$		−	2637.24i		−	2.95655i
$893$	223.012			0.249734
$894$	−499.357			−0.558565
$895$			355.468i			0.397171i
$896$	1320.32			1.47357
$897$	−153.175			−0.170763
$898$		−	2990.19i		−	3.32984i
$899$		−	1837.85i		−	2.04433i
$900$	−1342.16			−1.49129
$901$			208.129i			0.230997i
$902$	−991.982			−1.09976
$903$			164.131i			0.181761i
$904$			465.228i			0.514633i
$905$		−	777.312i		−	0.858909i
$906$		−	385.381i		−	0.425366i
$907$	1513.93			1.66916			0.834579	−	0.550888i	$-0.185711\pi$
$907$	1513.93			1.66916			0.834579	+	0.550888i	$0.185711\pi$
$908$	−2945.65			−3.24411
$909$			1184.63i			1.30322i
$910$		−	1710.24i		−	1.87938i
$911$		−	376.145i		−	0.412892i	−0.978458	−	0.206446i	$-0.933810\pi$
$911$		−	376.145i		−	0.412892i	0.978458	−	0.206446i	$-0.0661899\pi$
$912$		−	100.092i		−	0.109750i
$913$			825.269i			0.903910i
$914$	−1723.79			−1.88598
$915$			87.3754i			0.0954923i
$916$			2742.24i			2.99371i
$917$			277.749i			0.302888i
$918$		−	1039.29i		−	1.13212i
$919$	444.784			0.483987			0.241994	−	0.970278i	$-0.422199\pi$
$919$	444.784			0.483987			0.241994	+	0.970278i	$0.422199\pi$
$920$		−	705.037i		−	0.766344i
$921$	26.4698			0.0287402
$922$	2023.79			2.19500
$923$			576.399i			0.624484i
$924$	−310.918			−0.336491
$925$			394.767i			0.426775i
$926$	−1022.05			−1.10372
$927$			374.934i			0.404460i
$928$			1251.82i			1.34895i
$929$		−	886.649i		−	0.954412i	−0.878791	−	0.477206i	$-0.841650\pi$
$929$		−	886.649i		−	0.954412i	0.878791	−	0.477206i	$-0.158350\pi$
$930$	−212.907			−0.228932
$931$	−218.594			−0.234795
$932$	15.1317			0.0162357
$933$			176.172i			0.188823i
$934$		−	2992.72i		−	3.20420i
$935$	601.161			0.642953
$936$			2917.14i			3.11660i
$937$		−	357.607i		−	0.381651i	−0.981624	−	0.190825i	$-0.938884\pi$
$937$		−	357.607i		−	0.381651i	0.981624	−	0.190825i	$-0.0611164\pi$
$938$	−95.5802			−0.101898
$939$		−	44.3762i		−	0.0472590i
$940$			793.804i			0.844472i
$941$	1176.24			1.24999			0.624997	−	0.780627i	$-0.285100\pi$
$941$	1176.24			1.24999			0.624997	+	0.780627i	$0.285100\pi$
$942$	−418.889			−0.444680
$943$	−563.922			−0.598009
$944$		−	1847.38i		−	1.95697i
$945$		−	237.483i		−	0.251305i
$946$	872.037			0.921815
$947$	−1096.31			−1.15767			−0.578833	−	0.815446i	$-0.696492\pi$
$947$	−1096.31			−1.15767			−0.578833	+	0.815446i	$0.696492\pi$
$948$	−69.7975			−0.0736261
$949$	1032.33			1.08781
$950$		−	427.786i		−	0.450302i
$951$			291.637i			0.306663i
$952$		−	4734.89i		−	4.97363i
$953$	−531.967			−0.558202			−0.279101	−	0.960262i	$-0.590036\pi$
$953$	−531.967			−0.558202			−0.279101	+	0.960262i	$0.590036\pi$
$954$		−	214.805i		−	0.225162i
$955$		−	454.130i		−	0.475529i
$956$	924.282			0.966822
$957$			180.177i			0.188273i
$958$		−	2182.00i		−	2.27766i
$959$		−	1754.17i		−	1.82917i
$960$	−15.9289			−0.0165926
$961$	−624.884			−0.650244
$962$	1565.00			1.62682
$963$		−	1768.54i		−	1.83649i
$964$			1258.14i			1.30513i
$965$			88.7983i			0.0920190i
$966$	−256.598			−0.265629
$967$			99.8687i			0.103277i	0.998666	+	0.0516384i	$0.0164443\pi$
$967$			99.8687i			0.103277i	−0.998666	+	0.0516384i	$0.983556\pi$
$968$		−	1200.30i		−	1.23998i
$969$	112.199			0.115789
$970$	657.715			0.678057
$971$			887.060i			0.913553i	0.889582	+	0.456776i	$0.150996\pi$
$971$			887.060i			0.913553i	−0.889582	+	0.456776i	$0.849004\pi$
$972$			1114.38i			1.14649i
$973$		−	924.706i		−	0.950366i
$974$	1028.27			1.05572
$975$		−	181.370i		−	0.186020i
$976$		−	1581.09i		−	1.61997i
$977$			1246.68i			1.27603i	0.770025	+	0.638014i	$0.220244\pi$
$977$			1246.68i			1.27603i	−0.770025	+	0.638014i	$0.779756\pi$
$978$			93.0851i			0.0951791i
$979$		−	1256.50i		−	1.28345i
$980$		−	778.077i		−	0.793956i
$981$		−	333.099i		−	0.339550i
$982$	1217.92			1.24025
$983$		−	297.577i		−	0.302723i	−0.988478	−	0.151361i	$-0.951634\pi$
$983$		−	297.577i		−	0.302723i	0.988478	−	0.151361i	$-0.0483657\pi$
$984$		−	361.298i		−	0.367173i
$985$	−173.092			−0.175728
$986$	−5004.81			−5.07587
$987$	158.392			0.160478
$988$	−1168.18			−1.18237
$989$	495.735			0.501249
$990$	−620.445			−0.626712
$991$	433.588			0.437526			0.218763	−	0.975778i	$-0.429798\pi$
$991$	433.588			0.437526			0.218763	+	0.975778i	$0.429798\pi$
$992$	1080.20			1.08891
$993$	−271.683			−0.273598
$994$			965.582i			0.971410i
$995$			649.012i			0.652273i
$996$	−548.251			−0.550453
$997$			116.074i			0.116423i	0.998304	+	0.0582115i	$0.0185398\pi$
$997$			116.074i			0.116423i	−0.998304	+	0.0582115i	$0.981460\pi$
$998$			1490.51i			1.49350i
$999$	217.316			0.217533

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.3.b.b.546.5	✓	88
547.546	odd	2	inner	547.3.b.b.546.84	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.3.b.b.546.5	✓	88	1.1	even	1	trivial
547.3.b.b.546.84	yes	88	547.546	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	547.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.58531i q^{2} -0.541221i q^{3} -8.85444 q^{4} -2.75520i q^{5} -1.94044 q^{6} +8.99411i q^{7} +17.4047i q^{8} +8.70708 q^{9} +O(q^{10})\)	\(q-3.58531i q^{2} -0.541221i q^{3} -8.85444 q^{4} -2.75520i q^{5} -1.94044 q^{6} +8.99411i q^{7} +17.4047i q^{8} +8.70708 q^{9} -9.87823 q^{10} +7.21359 q^{11} +4.79221i q^{12} +19.2495 q^{13} +32.2467 q^{14} -1.49117 q^{15} +26.9833 q^{16} +30.2473i q^{17} -31.2176i q^{18} +6.85377 q^{19} +24.3957i q^{20} +4.86780 q^{21} -25.8630i q^{22} -14.7026i q^{23} +9.41977 q^{24} +17.4089 q^{25} -69.0153i q^{26} -9.58344i q^{27} -79.6378i q^{28} -46.1503 q^{29} +5.34631i q^{30} +39.8232i q^{31} -27.1249i q^{32} -3.90415i q^{33} +108.446 q^{34} +24.7805 q^{35} -77.0963 q^{36} +22.6762i q^{37} -24.5729i q^{38} -10.4182i q^{39} +47.9533 q^{40} -38.3553i q^{41} -17.4526i q^{42} +33.7176i q^{43} -63.8723 q^{44} -23.9897i q^{45} -52.7133 q^{46} +32.5387 q^{47} -14.6039i q^{48} -31.8940 q^{49} -62.4162i q^{50} +16.3705 q^{51} -170.443 q^{52} +6.88090 q^{53} -34.3596 q^{54} -19.8749i q^{55} -156.539 q^{56} -3.70940i q^{57} +165.463i q^{58} -68.4638i q^{59} +13.2035 q^{60} -58.5952i q^{61} +142.778 q^{62} +78.3124i q^{63} +10.6821 q^{64} -53.0361i q^{65} -13.9976 q^{66} -2.96403 q^{67} -267.823i q^{68} -7.95734 q^{69} -88.8459i q^{70} +29.9436i q^{71} +151.544i q^{72} +53.6290 q^{73} +81.3011 q^{74} -9.42206i q^{75} -60.6863 q^{76} +64.8798i q^{77} -37.3525 q^{78} +14.5648i q^{79} -74.3444i q^{80} +73.1770 q^{81} -137.516 q^{82} +114.405i q^{83} -43.1016 q^{84} +83.3373 q^{85} +120.888 q^{86} +24.9775i q^{87} +125.550i q^{88} -174.185i q^{89} -86.0105 q^{90} +173.132i q^{91} +130.183i q^{92} +21.5531 q^{93} -116.661i q^{94} -18.8835i q^{95} -14.6806 q^{96} -66.5823 q^{97} +114.350i q^{98} +62.8093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 192 q^{4} - 306 q^{9}+O(q^{10}) \) 88 * q - 192 * q^4 - 306 * q^9	\( 88 q - 192 q^{4} - 306 q^{9} - 4 q^{10} - 32 q^{11} + 26 q^{13} - 26 q^{14} + 22 q^{15} + 236 q^{16} - 12 q^{19} - 16 q^{21} - 2 q^{24} - 544 q^{25} - 96 q^{29} + 26 q^{34} + 10 q^{35} + 364 q^{36} + 44 q^{40} + 124 q^{44} - 288 q^{46} - 310 q^{47} - 694 q^{49} + 86 q^{51} - 316 q^{52} + 24 q^{53} - 266 q^{54} + 158 q^{56} - 80 q^{60} + 40 q^{62} - 652 q^{64} + 528 q^{66} + 28 q^{67} + 16 q^{69} + 94 q^{73} - 614 q^{74} - 28 q^{76} - 98 q^{78} + 928 q^{81} - 772 q^{82} + 358 q^{84} + 74 q^{85} - 410 q^{86} - 214 q^{90} + 656 q^{93} - 724 q^{96} + 346 q^{97} + 50 q^{99}+O(q^{100}) \) 88 * q - 192 * q^4 - 306 * q^9 - 4 * q^10 - 32 * q^11 + 26 * q^13 - 26 * q^14 + 22 * q^15 + 236 * q^16 - 12 * q^19 - 16 * q^21 - 2 * q^24 - 544 * q^25 - 96 * q^29 + 26 * q^34 + 10 * q^35 + 364 * q^36 + 44 * q^40 + 124 * q^44 - 288 * q^46 - 310 * q^47 - 694 * q^49 + 86 * q^51 - 316 * q^52 + 24 * q^53 - 266 * q^54 + 158 * q^56 - 80 * q^60 + 40 * q^62 - 652 * q^64 + 528 * q^66 + 28 * q^67 + 16 * q^69 + 94 * q^73 - 614 * q^74 - 28 * q^76 - 98 * q^78 + 928 * q^81 - 772 * q^82 + 358 * q^84 + 74 * q^85 - 410 * q^86 - 214 * q^90 + 656 * q^93 - 724 * q^96 + 346 * q^97 + 50 * q^99

Introduction

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