LMFDB - Embedded newform 495.3.h.d.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,3,Mod(109,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.109"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	495.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4877730858$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{5}, \sqrt{-21})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} + 41x^{2} - 40x + 505 $ x^4 - 2x^3 + 41x^2 - 40*x + 505
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.1
Root			$-0.618034 - 4.58258i$ of defining polynomial
Character	$\chi$	$=$	495.109
Dual form			495.3.h.d.109.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.23607 q^{2} +1.00000 q^{4} +(2.00000 - 4.58258i) q^{5} +11.1803 q^{7} +6.70820 q^{8} +(-4.47214 + 10.2470i) q^{10} +(4.00000 - 10.2470i) q^{11} +8.94427 q^{13} -25.0000 q^{14} -19.0000 q^{16} +15.6525 q^{17} +10.2470i q^{19} +(2.00000 - 4.58258i) q^{20} +(-8.94427 + 22.9129i) q^{22} +27.4955i q^{23} +(-17.0000 - 18.3303i) q^{25} -20.0000 q^{26} +11.1803 q^{28} +10.2470i q^{29} -3.00000 q^{31} +15.6525 q^{32} -35.0000 q^{34} +(22.3607 - 51.2348i) q^{35} -4.58258i q^{37} -22.9129i q^{38} +(13.4164 - 30.7409i) q^{40} +20.4939i q^{41} +22.3607 q^{43} +(4.00000 - 10.2470i) q^{44} -61.4817i q^{46} -64.1561i q^{47} +76.0000 q^{49} +(38.0132 + 40.9878i) q^{50} +8.94427 q^{52} +4.58258i q^{53} +(-38.9574 - 38.8242i) q^{55} +75.0000 q^{56} -22.9129i q^{58} +18.0000 q^{59} +71.7287i q^{61} +6.70820 q^{62} +41.0000 q^{64} +(17.8885 - 40.9878i) q^{65} -27.4955i q^{67} +15.6525 q^{68} +(-50.0000 + 114.564i) q^{70} -27.0000 q^{71} +58.1378 q^{73} +10.2470i q^{74} +10.2470i q^{76} +(44.7214 - 114.564i) q^{77} -61.4817i q^{79} +(-38.0000 + 87.0689i) q^{80} -45.8258i q^{82} +71.5542 q^{83} +(31.3050 - 71.7287i) q^{85} -50.0000 q^{86} +(26.8328 - 68.7386i) q^{88} -37.0000 q^{89} +100.000 q^{91} +27.4955i q^{92} +143.457i q^{94} +(46.9574 + 20.4939i) q^{95} -119.147i q^{97} -169.941 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 8 q^{5} + 16 q^{11} - 100 q^{14} - 76 q^{16} + 8 q^{20} - 68 q^{25} - 80 q^{26} - 12 q^{31} - 140 q^{34} + 16 q^{44} + 304 q^{49} + 32 q^{55} + 300 q^{56} + 72 q^{59} + 164 q^{64} - 200 q^{70}+ \cdots + 400 q^{91}+O(q^{100}) $ 4 * q + 4 * q^4 + 8 * q^5 + 16 * q^11 - 100 * q^14 - 76 * q^16 + 8 * q^20 - 68 * q^25 - 80 * q^26 - 12 * q^31 - 140 * q^34 + 16 * q^44 + 304 * q^49 + 32 * q^55 + 300 * q^56 + 72 * q^59 + 164 * q^64 - 200 * q^70 - 108 * q^71 - 152 * q^80 - 200 * q^86 - 148 * q^89 + 400 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−2.23607			−1.11803			−0.559017	−	0.829156i	$-0.688821\pi$
$2$	−2.23607			−1.11803			−0.559017	+	0.829156i	$0.688821\pi$
$3$		0			0
$3$		0			0
$4$	1.00000			0.250000
$5$	2.00000	−	4.58258i	0.400000	−	0.916515i
$5$	2.00000	−	4.58258i	0.400000	−	0.916515i
$6$		0			0
$7$	11.1803			1.59719			0.798596	−	0.601868i	$-0.205577\pi$
$7$	11.1803			1.59719			0.798596	+	0.601868i	$0.205577\pi$
$8$	6.70820			0.838525
$9$		0			0
$10$	−4.47214	+	10.2470i	−0.447214	+	1.02470i
$11$	4.00000	−	10.2470i	0.363636	−	0.931541i
$11$	4.00000	−	10.2470i	0.363636	−	0.931541i
$12$		0			0
$13$	8.94427			0.688021			0.344010	−	0.938966i	$-0.388214\pi$
$13$	8.94427			0.688021			0.344010	+	0.938966i	$0.388214\pi$
$14$	−25.0000			−1.78571
$15$		0			0
$16$	−19.0000			−1.18750
$17$	15.6525			0.920734			0.460367	−	0.887729i	$-0.347718\pi$
$17$	15.6525			0.920734			0.460367	+	0.887729i	$0.347718\pi$
$18$		0			0
$19$			10.2470i			0.539313i	0.962957	+	0.269657i	$0.0869102\pi$
$19$			10.2470i			0.539313i	−0.962957	+	0.269657i	$0.913090\pi$
$20$	2.00000	−	4.58258i	0.100000	−	0.229129i
$21$		0			0
$22$	−8.94427	+	22.9129i	−0.406558	+	1.04149i
$23$			27.4955i			1.19545i	0.801700	+	0.597727i	$0.203929\pi$
$23$			27.4955i			1.19545i	−0.801700	+	0.597727i	$0.796071\pi$
$24$		0			0
$25$	−17.0000	−	18.3303i	−0.680000	−	0.733212i
$26$	−20.0000			−0.769231
$27$		0			0
$28$	11.1803			0.399298
$29$			10.2470i			0.353343i	0.984270	+	0.176672i	$0.0565330\pi$
$29$			10.2470i			0.353343i	−0.984270	+	0.176672i	$0.943467\pi$
$30$		0			0
$31$	−3.00000			−0.0967742			−0.0483871	−	0.998829i	$-0.515408\pi$
$31$	−3.00000			−0.0967742			−0.0483871	+	0.998829i	$0.515408\pi$
$32$	15.6525			0.489140
$33$		0			0
$34$	−35.0000			−1.02941
$35$	22.3607	−	51.2348i	0.638877	−	1.46385i
$36$		0			0
$37$		−	4.58258i		−	0.123853i	−0.998081	−	0.0619267i	$-0.980275\pi$
$37$		−	4.58258i		−	0.123853i	0.998081	−	0.0619267i	$-0.0197245\pi$
$38$		−	22.9129i		−	0.602970i
$39$		0			0
$40$	13.4164	−	30.7409i	0.335410	−	0.768521i
$41$			20.4939i			0.499851i	0.968265	+	0.249926i	$0.0804062\pi$
$41$			20.4939i			0.499851i	−0.968265	+	0.249926i	$0.919594\pi$
$42$		0			0
$43$	22.3607			0.520016			0.260008	−	0.965606i	$-0.416275\pi$
$43$	22.3607			0.520016			0.260008	+	0.965606i	$0.416275\pi$
$44$	4.00000	−	10.2470i	0.0909091	−	0.232885i
$45$		0			0
$46$		−	61.4817i		−	1.33656i
$47$		−	64.1561i		−	1.36502i	−0.730875	−	0.682511i	$-0.760888\pi$
$47$		−	64.1561i		−	1.36502i	0.730875	−	0.682511i	$-0.239112\pi$
$48$		0			0
$49$	76.0000			1.55102
$50$	38.0132	+	40.9878i	0.760263	+	0.819756i
$51$		0			0
$52$	8.94427			0.172005
$53$			4.58258i			0.0864637i	0.999065	+	0.0432318i	$0.0137654\pi$
$53$			4.58258i			0.0864637i	−0.999065	+	0.0432318i	$0.986235\pi$
$54$		0			0
$55$	−38.9574	−	38.8242i	−0.708317	−	0.705895i
$56$	75.0000			1.33929
$57$		0			0
$58$		−	22.9129i		−	0.395050i
$59$	18.0000			0.305085			0.152542	−	0.988297i	$-0.451254\pi$
$59$	18.0000			0.305085			0.152542	+	0.988297i	$0.451254\pi$
$60$		0			0
$61$			71.7287i			1.17588i	0.808905	+	0.587940i	$0.200061\pi$
$61$			71.7287i			1.17588i	−0.808905	+	0.587940i	$0.799939\pi$
$62$	6.70820			0.108197
$63$		0			0
$64$	41.0000			0.640625
$65$	17.8885	−	40.9878i	0.275208	−	0.630582i
$66$		0			0
$67$		−	27.4955i		−	0.410380i	−0.978722	−	0.205190i	$-0.934219\pi$
$67$		−	27.4955i		−	0.410380i	0.978722	−	0.205190i	$-0.0657812\pi$
$68$	15.6525			0.230183
$69$		0			0
$70$	−50.0000	+	114.564i	−0.714286	+	1.63663i
$71$	−27.0000			−0.380282			−0.190141	−	0.981757i	$-0.560894\pi$
$71$	−27.0000			−0.380282			−0.190141	+	0.981757i	$0.560894\pi$
$72$		0			0
$73$	58.1378			0.796408			0.398204	−	0.917297i	$-0.369634\pi$
$73$	58.1378			0.796408			0.398204	+	0.917297i	$0.369634\pi$
$74$			10.2470i			0.138472i
$75$		0			0
$76$			10.2470i			0.134828i
$77$	44.7214	−	114.564i	0.580797	−	1.48785i
$78$		0			0
$79$		−	61.4817i		−	0.778249i	−0.921185	−	0.389125i	$-0.872778\pi$
$79$		−	61.4817i		−	0.778249i	0.921185	−	0.389125i	$-0.127222\pi$
$80$	−38.0000	+	87.0689i	−0.475000	+	1.08836i
$81$		0			0
$82$		−	45.8258i		−	0.558851i
$83$	71.5542			0.862098			0.431049	−	0.902328i	$-0.358144\pi$
$83$	71.5542			0.862098			0.431049	+	0.902328i	$0.358144\pi$
$84$		0			0
$85$	31.3050	−	71.7287i	0.368294	−	0.843867i
$86$	−50.0000			−0.581395
$87$		0			0
$88$	26.8328	−	68.7386i	0.304918	−	0.781121i
$89$	−37.0000			−0.415730			−0.207865	−	0.978157i	$-0.566652\pi$
$89$	−37.0000			−0.415730			−0.207865	+	0.978157i	$0.566652\pi$
$90$		0			0
$91$	100.000			1.09890
$92$			27.4955i			0.298864i
$93$		0			0
$94$			143.457i			1.52614i
$95$	46.9574	+	20.4939i	0.494289	+	0.215725i
$96$		0			0
$97$		−	119.147i		−	1.22832i	−0.789182	−	0.614160i	$-0.789495\pi$
$97$		−	119.147i		−	1.22832i	0.789182	−	0.614160i	$-0.210505\pi$
$98$	−169.941			−1.73409
$99$		0			0
$100$	−17.0000	−	18.3303i	−0.170000	−	0.183303i
$101$		−	102.470i		−	1.01455i	−0.861784	−	0.507275i	$-0.830653\pi$
$101$		−	102.470i		−	1.01455i	0.861784	−	0.507275i	$-0.169347\pi$
$102$		0			0
$103$			18.3303i			0.177964i	0.996033	+	0.0889821i	$0.0283614\pi$
$103$			18.3303i			0.177964i	−0.996033	+	0.0889821i	$0.971639\pi$
$104$	60.0000			0.576923
$105$		0			0
$106$		−	10.2470i		−	0.0966693i
$107$	−156.525			−1.46285			−0.731424	−	0.681923i	$-0.761144\pi$
$107$	−156.525			−1.46285			−0.731424	+	0.681923i	$0.761144\pi$
$108$		0			0
$109$		−	20.4939i		−	0.188017i	−0.995571	−	0.0940087i	$-0.970032\pi$
$109$		−	20.4939i		−	0.188017i	0.995571	−	0.0940087i	$-0.0299682\pi$
$110$	87.1115	+	86.8136i	0.791922	+	0.789214i
$111$		0			0
$112$	−212.426			−1.89666
$113$			164.973i			1.45994i	0.683482	+	0.729968i	$0.260465\pi$
$113$			164.973i			1.45994i	−0.683482	+	0.729968i	$0.739535\pi$
$114$		0			0
$115$	126.000	+	54.9909i	1.09565	+	0.478182i
$116$			10.2470i			0.0883358i
$117$		0			0
$118$	−40.2492			−0.341095
$119$	175.000			1.47059
$120$		0			0
$121$	−89.0000	−	81.9756i	−0.735537	−	0.677484i
$122$		−	160.390i		−	1.31467i
$123$		0			0
$124$	−3.00000			−0.0241935
$125$	−118.000	+	41.2432i	−0.944000	+	0.329945i
$126$		0			0
$127$	−31.3050			−0.246496			−0.123248	−	0.992376i	$-0.539331\pi$
$127$	−31.3050			−0.246496			−0.123248	+	0.992376i	$0.539331\pi$
$128$	−154.289			−1.20538
$129$		0			0
$130$	−40.0000	+	91.6515i	−0.307692	+	0.705012i
$131$		−	215.186i		−	1.64264i	−0.570467	−	0.821320i	$-0.693238\pi$
$131$		−	215.186i		−	1.64264i	0.570467	−	0.821320i	$-0.306762\pi$
$132$		0			0
$133$			114.564i			0.861386i
$134$			61.4817i			0.458819i
$135$		0			0
$136$	105.000			0.772059
$137$		−	64.1561i		−	0.468292i	−0.972201	−	0.234146i	$-0.924771\pi$
$137$		−	64.1561i		−	0.468292i	0.972201	−	0.234146i	$-0.0752294\pi$
$138$		0			0
$139$			225.433i			1.62182i	0.585171	+	0.810910i	$0.301027\pi$
$139$			225.433i			1.62182i	−0.585171	+	0.810910i	$0.698973\pi$
$140$	22.3607	−	51.2348i	0.159719	−	0.365963i
$141$		0			0
$142$	60.3738			0.425168
$143$	35.7771	−	91.6515i	0.250189	−	0.640920i
$144$		0			0
$145$	46.9574	+	20.4939i	0.323844	+	0.141337i
$146$	−130.000			−0.890411
$147$		0			0
$148$		−	4.58258i		−	0.0309633i
$149$			153.704i			1.03157i	0.856717	+	0.515786i	$0.172500\pi$
$149$			153.704i			1.03157i	−0.856717	+	0.515786i	$0.827500\pi$
$150$		0			0
$151$		−	102.470i		−	0.678606i	−0.940677	−	0.339303i	$-0.889809\pi$
$151$		−	102.470i		−	0.678606i	0.940677	−	0.339303i	$-0.110191\pi$
$152$			68.7386i			0.452228i
$153$		0			0
$154$	−100.000	+	256.174i	−0.649351	+	1.66347i
$155$	−6.00000	+	13.7477i	−0.0387097	+	0.0886950i
$156$		0			0
$157$		−	50.4083i		−	0.321072i	−0.987030	−	0.160536i	$-0.948678\pi$
$157$		−	50.4083i		−	0.321072i	0.987030	−	0.160536i	$-0.0513223\pi$
$158$			137.477i			0.870109i
$159$		0			0
$160$	31.3050	−	71.7287i	0.195656	−	0.448304i
$161$			307.409i			1.90937i
$162$		0			0
$163$			270.372i			1.65872i	0.558712	+	0.829362i	$0.311296\pi$
$163$			270.372i			1.65872i	−0.558712	+	0.829362i	$0.688704\pi$
$164$			20.4939i			0.124963i
$165$		0			0
$166$	−160.000			−0.963855
$167$	−297.397			−1.78082			−0.890410	−	0.455159i	$-0.849583\pi$
$167$	−297.397			−1.78082			−0.890410	+	0.455159i	$0.849583\pi$
$168$		0			0
$169$	−89.0000			−0.526627
$170$	−70.0000	+	160.390i	−0.411765	+	0.943471i
$171$		0			0
$172$	22.3607			0.130004
$173$	143.108			0.827216			0.413608	−	0.910455i	$-0.364268\pi$
$173$	143.108			0.827216			0.413608	+	0.910455i	$0.364268\pi$
$174$		0			0
$175$	−190.066	−	204.939i	−1.08609	−	1.17108i
$176$	−76.0000	+	194.692i	−0.431818	+	1.10620i
$177$		0			0
$178$	82.7345			0.464801
$179$	−242.000			−1.35196			−0.675978	−	0.736922i	$-0.736278\pi$
$179$	−242.000			−1.35196			−0.675978	+	0.736922i	$0.736278\pi$
$180$		0			0
$181$	−258.000			−1.42541			−0.712707	−	0.701462i	$-0.752531\pi$
$181$	−258.000			−1.42541			−0.712707	+	0.701462i	$0.752531\pi$
$182$	−223.607			−1.22861
$183$		0			0
$184$			184.445i			1.00242i
$185$	−21.0000	−	9.16515i	−0.113514	−	0.0495414i
$186$		0			0
$187$	62.6099	−	160.390i	0.334812	−	0.857701i
$188$		−	64.1561i		−	0.341256i
$189$		0			0
$190$	−105.000	−	45.8258i	−0.552632	−	0.241188i
$191$	278.000			1.45550			0.727749	−	0.685844i	$-0.240567\pi$
$191$	278.000			1.45550			0.727749	+	0.685844i	$0.240567\pi$
$192$		0			0
$193$	−78.2624			−0.405505			−0.202752	−	0.979230i	$-0.564989\pi$
$193$	−78.2624			−0.405505			−0.202752	+	0.979230i	$0.564989\pi$
$194$			266.421i			1.37330i
$195$		0			0
$196$	76.0000			0.387755
$197$	196.774			0.998853			0.499426	−	0.866356i	$-0.333544\pi$
$197$	196.774			0.998853			0.499426	+	0.866356i	$0.333544\pi$
$198$		0			0
$199$	−53.0000			−0.266332			−0.133166	−	0.991094i	$-0.542514\pi$
$199$	−53.0000			−0.266332			−0.133166	+	0.991094i	$0.542514\pi$
$200$	−114.039	−	122.963i	−0.570197	−	0.614817i
$201$		0			0
$202$			229.129i			1.13430i
$203$			114.564i			0.564357i
$204$		0			0
$205$	93.9149	+	40.9878i	0.458121	+	0.199941i
$206$		−	40.9878i		−	0.198970i
$207$		0			0
$208$	−169.941			−0.817025
$209$	105.000	+	40.9878i	0.502392	+	0.196114i
$210$		0			0
$211$			174.198i			0.825584i	0.910825	+	0.412792i	$0.135446\pi$
$211$			174.198i			0.825584i	−0.910825	+	0.412792i	$0.864554\pi$
$212$			4.58258i			0.0216159i
$213$		0			0
$214$	350.000			1.63551
$215$	44.7214	−	102.470i	0.208006	−	0.476602i
$216$		0			0
$217$	−33.5410			−0.154567
$218$			45.8258i			0.210210i
$219$		0			0
$220$	−38.9574	−	38.8242i	−0.177079	−	0.176474i
$221$	140.000			0.633484
$222$		0			0
$223$		−	394.102i		−	1.76727i	−0.468175	−	0.883636i	$-0.655088\pi$
$223$		−	394.102i		−	1.76727i	0.468175	−	0.883636i	$-0.344912\pi$
$224$	175.000			0.781250
$225$		0			0
$226$		−	368.890i		−	1.63226i
$227$	277.272			1.22146			0.610732	−	0.791837i	$-0.290875\pi$
$227$	277.272			1.22146			0.610732	+	0.791837i	$0.290875\pi$
$228$		0			0
$229$	292.000			1.27511			0.637555	−	0.770405i	$-0.279946\pi$
$229$	292.000			1.27511			0.637555	+	0.770405i	$0.279946\pi$
$230$	−281.745	−	122.963i	−1.22498	−	0.534624i
$231$		0			0
$232$			68.7386i			0.296287i
$233$	172.177			0.738958			0.369479	−	0.929239i	$-0.379536\pi$
$233$	172.177			0.738958			0.369479	+	0.929239i	$0.379536\pi$
$234$		0			0
$235$	−294.000	−	128.312i	−1.25106	−	0.546009i
$236$	18.0000			0.0762712
$237$		0			0
$238$	−391.312			−1.64417
$239$		−	225.433i		−	0.943234i	−0.881804	−	0.471617i	$-0.843671\pi$
$239$		−	225.433i		−	0.943234i	0.881804	−	0.471617i	$-0.156329\pi$
$240$		0			0
$241$		−	327.902i		−	1.36059i	−0.732938	−	0.680295i	$-0.761851\pi$
$241$		−	327.902i		−	1.36059i	0.732938	−	0.680295i	$-0.238149\pi$
$242$	199.010	+	183.303i	0.822356	+	0.757451i
$243$		0			0
$244$			71.7287i			0.293970i
$245$	152.000	−	348.276i	0.620408	−	1.42153i
$246$		0			0
$247$			91.6515i			0.371059i
$248$	−20.1246			−0.0811476
$249$		0			0
$250$	263.856	−	92.2226i	1.05542	−	0.368890i
$251$	−282.000			−1.12351			−0.561753	−	0.827305i	$-0.689873\pi$
$251$	−282.000			−1.12351			−0.561753	+	0.827305i	$0.689873\pi$
$252$		0			0
$253$	281.745	+	109.982i	1.11361	+	0.434711i
$254$	70.0000			0.275591
$255$		0			0
$256$	181.000			0.707031
$257$		−	64.1561i		−	0.249634i	−0.992180	−	0.124817i	$-0.960166\pi$
$257$		−	64.1561i		−	0.249634i	0.992180	−	0.124817i	$-0.0398345\pi$
$258$		0			0
$259$		−	51.2348i		−	0.197818i
$260$	17.8885	−	40.9878i	0.0688021	−	0.157645i
$261$		0			0
$262$			481.170i			1.83653i
$263$	−199.010			−0.756692			−0.378346	−	0.925664i	$-0.623507\pi$
$263$	−199.010			−0.756692			−0.378346	+	0.925664i	$0.623507\pi$
$264$		0			0
$265$	21.0000	+	9.16515i	0.0792453	+	0.0345855i
$266$		−	256.174i		−	0.963059i
$267$		0			0
$268$		−	27.4955i		−	0.102595i
$269$	−162.000			−0.602230			−0.301115	−	0.953588i	$-0.597359\pi$
$269$	−162.000			−0.602230			−0.301115	+	0.953588i	$0.597359\pi$
$270$		0			0
$271$			245.927i			0.907479i	0.891134	+	0.453740i	$0.149910\pi$
$271$			245.927i			0.907479i	−0.891134	+	0.453740i	$0.850090\pi$
$272$	−297.397			−1.09337
$273$		0			0
$274$			143.457i			0.523567i
$275$	−255.830	+	100.877i	−0.930290	+	0.366825i
$276$		0			0
$277$	58.1378			0.209884			0.104942	−	0.994478i	$-0.466534\pi$
$277$	58.1378			0.209884			0.104942	+	0.994478i	$0.466534\pi$
$278$		−	504.083i		−	1.81325i
$279$		0			0
$280$	150.000	−	343.693i	0.535714	−	1.22748i
$281$		−	163.951i		−	0.583456i	−0.956501	−	0.291728i	$-0.905770\pi$
$281$		−	163.951i		−	0.583456i	0.956501	−	0.291728i	$-0.0942303\pi$
$282$		0			0
$283$	−250.440			−0.884946			−0.442473	−	0.896782i	$-0.645899\pi$
$283$	−250.440			−0.884946			−0.442473	+	0.896782i	$0.645899\pi$
$284$	−27.0000			−0.0950704
$285$		0			0
$286$	−80.0000	+	204.939i	−0.279720	+	0.716570i
$287$			229.129i			0.798358i
$288$		0			0
$289$	−44.0000			−0.152249
$290$	−105.000	−	45.8258i	−0.362069	−	0.158020i
$291$		0			0
$292$	58.1378			0.199102
$293$	447.214			1.52633			0.763163	−	0.646206i	$-0.223645\pi$
$293$	447.214			1.52633			0.763163	+	0.646206i	$0.223645\pi$
$294$		0			0
$295$	36.0000	−	82.4864i	0.122034	−	0.279615i
$296$		−	30.7409i		−	0.103854i
$297$		0			0
$298$		−	343.693i		−	1.15333i
$299$			245.927i			0.822498i
$300$		0			0
$301$	250.000			0.830565
$302$			229.129i			0.758705i
$303$		0			0
$304$		−	194.692i		−	0.640434i
$305$	328.702	+	143.457i	1.07771	+	0.470352i
$306$		0			0
$307$	447.214			1.45672			0.728361	−	0.685194i	$-0.240282\pi$
$307$	447.214			1.45672			0.728361	+	0.685194i	$0.240282\pi$
$308$	44.7214	−	114.564i	0.145199	−	0.371962i
$309$		0			0
$310$	13.4164	−	30.7409i	0.0432787	−	0.0991640i
$311$	−87.0000			−0.279743			−0.139871	−	0.990170i	$-0.544669\pi$
$311$	−87.0000			−0.279743			−0.139871	+	0.990170i	$0.544669\pi$
$312$		0			0
$313$			293.285i			0.937012i	0.883460	+	0.468506i	$0.155208\pi$
$313$			293.285i			0.937012i	−0.883460	+	0.468506i	$0.844792\pi$
$314$			112.716i			0.358970i
$315$		0			0
$316$		−	61.4817i		−	0.194562i
$317$			50.4083i			0.159017i	0.996834	+	0.0795084i	$0.0253351\pi$
$317$			50.4083i			0.159017i	−0.996834	+	0.0795084i	$0.974665\pi$
$318$		0			0
$319$	105.000	+	40.9878i	0.329154	+	0.128488i
$320$	82.0000	−	187.886i	0.256250	−	0.587143i
$321$		0			0
$322$		−	687.386i		−	2.13474i
$323$			160.390i			0.496564i
$324$		0			0
$325$	−152.053	−	163.951i	−0.467854	−	0.504465i
$326$		−	604.570i		−	1.85451i
$327$		0			0
$328$			137.477i			0.419138i
$329$		−	717.287i		−	2.18020i
$330$		0			0
$331$	−138.000			−0.416918			−0.208459	−	0.978031i	$-0.566845\pi$
$331$	−138.000			−0.416918			−0.208459	+	0.978031i	$0.566845\pi$
$332$	71.5542			0.215525
$333$		0			0
$334$	665.000			1.99102
$335$	−126.000	−	54.9909i	−0.376119	−	0.164152i
$336$		0			0
$337$	243.731			0.723239			0.361619	−	0.932326i	$-0.382224\pi$
$337$	243.731			0.723239			0.361619	+	0.932326i	$0.382224\pi$
$338$	199.010			0.588787
$339$		0			0
$340$	31.3050	−	71.7287i	0.0920734	−	0.210967i
$341$	−12.0000	+	30.7409i	−0.0351906	+	0.0901491i
$342$		0			0
$343$	301.869			0.880085
$344$	150.000			0.436047
$345$		0			0
$346$	−320.000			−0.924855
$347$	−4.47214			−0.0128880			−0.00644400	−	0.999979i	$-0.502051\pi$
$347$	−4.47214			−0.0128880			−0.00644400	+	0.999979i	$0.502051\pi$
$348$		0			0
$349$			512.348i			1.46804i	0.679125	+	0.734022i	$0.262359\pi$
$349$			512.348i			1.46804i	−0.679125	+	0.734022i	$0.737641\pi$
$350$	425.000	+	458.258i	1.21429	+	1.30931i
$351$		0			0
$352$	62.6099	−	160.390i	0.177869	−	0.455654i
$353$		−	293.285i		−	0.830835i	−0.909631	−	0.415418i	$-0.863635\pi$
$353$		−	293.285i		−	0.830835i	0.909631	−	0.415418i	$-0.136365\pi$
$354$		0			0
$355$	−54.0000	+	123.730i	−0.152113	+	0.348534i
$356$	−37.0000			−0.103933
$357$		0			0
$358$	541.128			1.51153
$359$			635.311i			1.76967i	0.465906	+	0.884834i	$0.345728\pi$
$359$			635.311i			1.76967i	−0.465906	+	0.884834i	$0.654272\pi$
$360$		0			0
$361$	256.000			0.709141
$362$	576.906			1.59366
$363$		0			0
$364$	100.000			0.274725
$365$	116.276	−	266.421i	0.318563	−	0.729920i
$366$		0			0
$367$			430.762i			1.17374i	0.809682	+	0.586869i	$0.199640\pi$
$367$			430.762i			1.17374i	−0.809682	+	0.586869i	$0.800360\pi$
$368$		−	522.414i		−	1.41960i
$369$		0			0
$370$	46.9574	+	20.4939i	0.126912	+	0.0553889i
$371$			51.2348i			0.138099i
$372$		0			0
$373$	−545.601			−1.46274			−0.731368	−	0.681983i	$-0.761118\pi$
$373$	−545.601			−1.46274			−0.731368	+	0.681983i	$0.761118\pi$
$374$	−140.000	+	358.643i	−0.374332	+	0.958939i
$375$		0			0
$376$		−	430.372i		−	1.14461i
$377$			91.6515i			0.243107i
$378$		0			0
$379$	−428.000			−1.12929			−0.564644	−	0.825335i	$-0.690986\pi$
$379$	−428.000			−1.12929			−0.564644	+	0.825335i	$0.690986\pi$
$380$	46.9574	+	20.4939i	0.123572	+	0.0539313i
$381$		0			0
$382$	−621.627			−1.62730
$383$			164.973i			0.430738i	0.976533	+	0.215369i	$0.0690955\pi$
$383$			164.973i			0.430738i	−0.976533	+	0.215369i	$0.930905\pi$
$384$		0			0
$385$	−435.557	−	434.068i	−1.13132	−	1.12745i
$386$	175.000			0.453368
$387$		0			0
$388$		−	119.147i		−	0.307080i
$389$	228.000			0.586118			0.293059	−	0.956094i	$-0.405327\pi$
$389$	228.000			0.586118			0.293059	+	0.956094i	$0.405327\pi$
$390$		0			0
$391$			430.372i			1.10070i
$392$	509.823			1.30057
$393$		0			0
$394$	−440.000			−1.11675
$395$	−281.745	−	122.963i	−0.713277	−	0.311300i
$396$		0			0
$397$		−	669.056i		−	1.68528i	−0.538478	−	0.842640i	$-0.681000\pi$
$397$		−	669.056i		−	1.68528i	0.538478	−	0.842640i	$-0.319000\pi$
$398$	118.512			0.297768
$399$		0			0
$400$	323.000	+	348.276i	0.807500	+	0.870689i
$401$	−107.000			−0.266833			−0.133416	−	0.991060i	$-0.542595\pi$
$401$	−107.000			−0.266833			−0.133416	+	0.991060i	$0.542595\pi$
$402$		0			0
$403$	−26.8328			−0.0665827
$404$		−	102.470i		−	0.253637i
$405$		0			0
$406$		−	256.174i		−	0.630970i
$407$	−46.9574	−	18.3303i	−0.115375	−	0.0450376i
$408$		0			0
$409$		−	327.902i		−	0.801717i	−0.916140	−	0.400859i	$-0.868712\pi$
$409$		−	327.902i		−	0.801717i	0.916140	−	0.400859i	$-0.131288\pi$
$410$	−210.000	−	91.6515i	−0.512195	−	0.223540i
$411$		0			0
$412$			18.3303i			0.0444910i
$413$	201.246			0.487279
$414$		0			0
$415$	143.108	−	327.902i	0.344839	−	0.790126i
$416$	140.000			0.336538
$417$		0			0
$418$	−234.787	−	91.6515i	−0.561692	−	0.219262i
$419$	−722.000			−1.72315			−0.861575	−	0.507630i	$-0.830522\pi$
$419$	−722.000			−1.72315			−0.861575	+	0.507630i	$0.830522\pi$
$420$		0			0
$421$	−408.000			−0.969121			−0.484561	−	0.874758i	$-0.661020\pi$
$421$	−408.000			−0.969121			−0.484561	+	0.874758i	$0.661020\pi$
$422$		−	389.519i		−	0.923031i
$423$		0			0
$424$			30.7409i			0.0725020i
$425$	−266.092	−	286.915i	−0.626099	−	0.675093i
$426$		0			0
$427$			801.951i			1.87810i
$428$	−156.525			−0.365712
$429$		0			0
$430$	−100.000	+	229.129i	−0.232558	+	0.532858i
$431$		−	61.4817i		−	0.142649i	−0.997453	−	0.0713245i	$-0.977277\pi$
$431$		−	61.4817i		−	0.142649i	0.997453	−	0.0713245i	$-0.0227226\pi$
$432$		0			0
$433$			247.459i			0.571499i	0.958304	+	0.285750i	$0.0922425\pi$
$433$			247.459i			0.571499i	−0.958304	+	0.285750i	$0.907757\pi$
$434$	75.0000			0.172811
$435$		0			0
$436$		−	20.4939i		−	0.0470044i
$437$	−281.745			−0.644724
$438$		0			0
$439$			430.372i			0.980346i	0.871625	+	0.490173i	$0.163066\pi$
$439$			430.372i			0.980346i	−0.871625	+	0.490173i	$0.836934\pi$
$440$	−261.334	−	260.441i	−0.593942	−	0.591911i
$441$		0			0
$442$	−313.050			−0.708257
$443$			302.450i			0.682731i	0.939931	+	0.341366i	$0.110889\pi$
$443$			302.450i			0.682731i	−0.939931	+	0.341366i	$0.889111\pi$
$444$		0			0
$445$	−74.0000	+	169.555i	−0.166292	+	0.381023i
$446$			881.238i			1.97587i
$447$		0			0
$448$	458.394			1.02320
$449$	−22.0000			−0.0489978			−0.0244989	−	0.999700i	$-0.507799\pi$
$449$	−22.0000			−0.0489978			−0.0244989	+	0.999700i	$0.507799\pi$
$450$		0			0
$451$	210.000	+	81.9756i	0.465632	+	0.181764i
$452$			164.973i			0.364984i
$453$		0			0
$454$	−620.000			−1.36564
$455$	200.000	−	458.258i	0.439560	−	1.00716i
$456$		0			0
$457$	346.591			0.758404			0.379202	−	0.925314i	$-0.376199\pi$
$457$	346.591			0.758404			0.379202	+	0.925314i	$0.376199\pi$
$458$	−652.932			−1.42562
$459$		0			0
$460$	126.000	+	54.9909i	0.273913	+	0.119545i
$461$			338.149i			0.733513i	0.930317	+	0.366756i	$0.119532\pi$
$461$			338.149i			0.733513i	−0.930317	+	0.366756i	$0.880468\pi$
$462$		0			0
$463$		−	623.230i		−	1.34607i	−0.739611	−	0.673035i	$-0.764990\pi$
$463$		−	623.230i		−	1.34607i	0.739611	−	0.673035i	$-0.235010\pi$
$464$		−	194.692i		−	0.419595i
$465$		0			0
$466$	−385.000			−0.826180
$467$			554.492i			1.18735i	0.804706	+	0.593674i	$0.202323\pi$
$467$			554.492i			1.18735i	−0.804706	+	0.593674i	$0.797677\pi$
$468$		0			0
$469$		−	307.409i		−	0.655455i
$470$	657.404	+	286.915i	1.39873	+	0.610457i
$471$		0			0
$472$	120.748			0.255821
$473$	89.4427	−	229.129i	0.189097	−	0.484416i
$474$		0			0
$475$	187.830	−	174.198i	0.395431	−	0.366733i
$476$	175.000			0.367647
$477$		0			0
$478$			504.083i			1.05457i
$479$		−	40.9878i		−	0.0855695i	−0.999084	−	0.0427848i	$-0.986377\pi$
$479$		−	40.9878i		−	0.0855695i	0.999084	−	0.0427848i	$-0.0136230\pi$
$480$		0			0
$481$		−	40.9878i		−	0.0852137i
$482$			733.212i			1.52119i
$483$		0			0
$484$	−89.0000	−	81.9756i	−0.183884	−	0.169371i
$485$	−546.000	−	238.294i	−1.12577	−	0.491328i
$486$		0			0
$487$			339.111i			0.696326i	0.937434	+	0.348163i	$0.113194\pi$
$487$			339.111i			0.696326i	−0.937434	+	0.348163i	$0.886806\pi$
$488$			481.170i			0.986005i
$489$		0			0
$490$	−339.882	+	778.768i	−0.693637	+	1.58932i
$491$			584.076i			1.18956i	0.803887	+	0.594782i	$0.202762\pi$
$491$			584.076i			1.18956i	−0.803887	+	0.594782i	$0.797238\pi$
$492$		0			0
$493$			160.390i			0.325335i
$494$		−	204.939i		−	0.414856i
$495$		0			0
$496$	57.0000			0.114919
$497$	−301.869			−0.607383
$498$		0			0
$499$	−268.000			−0.537074			−0.268537	−	0.963269i	$-0.586540\pi$
$499$	−268.000			−0.537074			−0.268537	+	0.963269i	$0.586540\pi$
$500$	−118.000	+	41.2432i	−0.236000	+	0.0824864i
$501$		0			0
$502$	630.571			1.25612
$503$	−541.128			−1.07580			−0.537901	−	0.843008i	$-0.680783\pi$
$503$	−541.128			−1.07580			−0.537901	+	0.843008i	$0.680783\pi$
$504$		0			0
$505$	−469.574	−	204.939i	−0.929850	−	0.405820i
$506$	−630.000	−	245.927i	−1.24506	−	0.486021i
$507$		0			0
$508$	−31.3050			−0.0616239
$509$	828.000			1.62672			0.813360	−	0.581761i	$-0.197636\pi$
$509$	828.000			1.62672			0.813360	+	0.581761i	$0.197636\pi$
$510$		0			0
$511$	650.000			1.27202
$512$	212.426			0.414895
$513$		0			0
$514$			143.457i			0.279100i
$515$	84.0000	+	36.6606i	0.163107	+	0.0711856i
$516$		0			0
$517$	−657.404	−	256.624i	−1.27157	−	0.496372i
$518$			114.564i			0.221167i
$519$		0			0
$520$	120.000	−	274.955i	0.230769	−	0.528759i
$521$	−242.000			−0.464491			−0.232246	−	0.972657i	$-0.574607\pi$
$521$	−242.000			−0.464491			−0.232246	+	0.972657i	$0.574607\pi$
$522$		0			0
$523$	−143.108			−0.273630			−0.136815	−	0.990597i	$-0.543687\pi$
$523$	−143.108			−0.273630			−0.136815	+	0.990597i	$0.543687\pi$
$524$		−	215.186i		−	0.410660i
$525$		0			0
$526$	445.000			0.846008
$527$	−46.9574			−0.0891033
$528$		0			0
$529$	−227.000			−0.429112
$530$	−46.9574	−	20.4939i	−0.0885989	−	0.0386677i
$531$		0			0
$532$			114.564i			0.215347i
$533$			183.303i			0.343908i
$534$		0			0
$535$	−313.050	+	717.287i	−0.585139	+	1.34072i
$536$		−	184.445i		−	0.344114i
$537$		0			0
$538$	362.243			0.673314
$539$	304.000	−	778.768i	0.564007	−	1.44484i
$540$		0			0
$541$			440.619i			0.814453i	0.913327	+	0.407226i	$0.133504\pi$
$541$			440.619i			0.814453i	−0.913327	+	0.407226i	$0.866496\pi$
$542$		−	549.909i		−	1.01459i
$543$		0			0
$544$	245.000			0.450368
$545$	−93.9149	−	40.9878i	−0.172321	−	0.0752070i
$546$		0			0
$547$	−398.020			−0.727642			−0.363821	−	0.931469i	$-0.618528\pi$
$547$	−398.020			−0.727642			−0.363821	+	0.931469i	$0.618528\pi$
$548$		−	64.1561i		−	0.117073i
$549$		0			0
$550$	572.053	−	225.568i	1.04010	−	0.410123i
$551$	−105.000			−0.190563
$552$		0			0
$553$		−	687.386i		−	1.24301i
$554$	−130.000			−0.234657
$555$		0			0
$556$			225.433i			0.405455i
$557$	−156.525			−0.281014			−0.140507	−	0.990080i	$-0.544873\pi$
$557$	−156.525			−0.281014			−0.140507	+	0.990080i	$0.544873\pi$
$558$		0			0
$559$	200.000			0.357782
$560$	−424.853	+	973.460i	−0.758666	+	1.73832i
$561$		0			0
$562$			366.606i			0.652324i
$563$	−881.011			−1.56485			−0.782425	−	0.622745i	$-0.786018\pi$
$563$	−881.011			−1.56485			−0.782425	+	0.622745i	$0.786018\pi$
$564$		0			0
$565$	756.000	+	329.945i	1.33805	+	0.583974i
$566$	560.000			0.989399
$567$		0			0
$568$	−181.122			−0.318876
$569$			143.457i			0.252122i	0.992023	+	0.126061i	$0.0402335\pi$
$569$			143.457i			0.252122i	−0.992023	+	0.126061i	$0.959767\pi$
$570$		0			0
$571$			604.570i			1.05879i	0.848375	+	0.529396i	$0.177581\pi$
$571$			604.570i			1.05879i	−0.848375	+	0.529396i	$0.822419\pi$
$572$	35.7771	−	91.6515i	0.0625474	−	0.160230i
$573$		0			0
$574$		−	512.348i		−	0.892592i
$575$	504.000	−	467.423i	0.876522	−	0.812909i
$576$		0			0
$577$		−	164.973i		−	0.285915i	−0.989729	−	0.142957i	$-0.954339\pi$
$577$		−	164.973i		−	0.285915i	0.989729	−	0.142957i	$-0.0456612\pi$
$578$	98.3870			0.170220
$579$		0			0
$580$	46.9574	+	20.4939i	0.0809611	+	0.0353343i
$581$	800.000			1.37694
$582$		0			0
$583$	46.9574	+	18.3303i	0.0805445	+	0.0314413i
$584$	390.000			0.667808
$585$		0			0
$586$	−1000.00			−1.70648
$587$			875.272i			1.49109i	0.666453	+	0.745547i	$0.267812\pi$
$587$			875.272i			1.49109i	−0.666453	+	0.745547i	$0.732188\pi$
$588$		0			0
$589$		−	30.7409i		−	0.0521916i
$590$	−80.4984	+	184.445i	−0.136438	+	0.312619i
$591$		0			0
$592$			87.0689i			0.147076i
$593$	111.803			0.188539			0.0942693	−	0.995547i	$-0.469949\pi$
$593$	111.803			0.188539			0.0942693	+	0.995547i	$0.469949\pi$
$594$		0			0
$595$	350.000	−	801.951i	0.588235	−	1.34782i
$596$			153.704i			0.257893i
$597$		0			0
$598$		−	549.909i		−	0.919580i
$599$	493.000			0.823038			0.411519	−	0.911401i	$-0.364998\pi$
$599$	493.000			0.823038			0.411519	+	0.911401i	$0.364998\pi$
$600$		0			0
$601$		−	102.470i		−	0.170498i	−0.996360	−	0.0852492i	$-0.972831\pi$
$601$		−	102.470i		−	0.170498i	0.996360	−	0.0852492i	$-0.0271686\pi$
$602$	−559.017			−0.928600
$603$		0			0
$604$		−	102.470i		−	0.169652i
$605$	−553.659	+	243.898i	−0.915140	+	0.403137i
$606$		0			0
$607$	−816.165			−1.34459			−0.672294	−	0.740284i	$-0.734691\pi$
$607$	−816.165			−1.34459			−0.672294	+	0.740284i	$0.734691\pi$
$608$			160.390i			0.263800i
$609$		0			0
$610$	−735.000	−	320.780i	−1.20492	−	0.525869i
$611$		−	573.829i		−	0.939164i
$612$		0			0
$613$	881.011			1.43721			0.718606	−	0.695418i	$-0.244781\pi$
$613$	881.011			1.43721			0.718606	+	0.695418i	$0.244781\pi$
$614$	−1000.00			−1.62866
$615$		0			0
$616$	300.000	−	768.521i	0.487013	−	1.24760i
$617$		−	293.285i		−	0.475340i	−0.971346	−	0.237670i	$-0.923616\pi$
$617$		−	293.285i		−	0.475340i	0.971346	−	0.237670i	$-0.0763837\pi$
$618$		0			0
$619$	972.000			1.57027			0.785137	−	0.619322i	$-0.212592\pi$
$619$	972.000			1.57027			0.785137	+	0.619322i	$0.212592\pi$
$620$	−6.00000	+	13.7477i	−0.00967742	+	0.0221738i
$621$		0			0
$622$	194.538			0.312762
$623$	−413.673			−0.664001
$624$		0			0
$625$	−47.0000	+	623.230i	−0.0752000	+	0.997168i
$626$		−	655.805i		−	1.04761i
$627$		0			0
$628$		−	50.4083i		−	0.0802680i
$629$		−	71.7287i		−	0.114036i
$630$		0			0
$631$	−113.000			−0.179081			−0.0895404	−	0.995983i	$-0.528540\pi$
$631$	−113.000			−0.179081			−0.0895404	+	0.995983i	$0.528540\pi$
$632$		−	412.432i		−	0.652582i
$633$		0			0
$634$		−	112.716i		−	0.177786i
$635$	−62.6099	+	143.457i	−0.0985983	+	0.225917i
$636$		0			0
$637$	679.765			1.06713
$638$	−234.787	−	91.6515i	−0.368005	−	0.143654i
$639$		0			0
$640$	−308.577	+	707.040i	−0.482152	+	1.10475i
$641$	−1007.00			−1.57098			−0.785491	−	0.618873i	$-0.787590\pi$
$641$	−1007.00			−1.57098			−0.785491	+	0.618873i	$0.787590\pi$
$642$		0			0
$643$			270.372i			0.420485i	0.977649	+	0.210243i	$0.0674254\pi$
$643$			270.372i			0.420485i	−0.977649	+	0.210243i	$0.932575\pi$
$644$			307.409i			0.477342i
$645$		0			0
$646$		−	358.643i		−	0.555175i
$647$		−	18.3303i		−	0.0283312i	−0.999900	−	0.0141656i	$-0.995491\pi$
$647$		−	18.3303i		−	0.0283312i	0.999900	−	0.0141656i	$-0.00450921\pi$
$648$		0			0
$649$	72.0000	−	184.445i	0.110940	−	0.284199i
$650$	340.000	+	366.606i	0.523077	+	0.564009i
$651$		0			0
$652$			270.372i			0.414681i
$653$			691.969i			1.05968i	0.848099	+	0.529838i	$0.177747\pi$
$653$			691.969i			1.05968i	−0.848099	+	0.529838i	$0.822253\pi$
$654$		0			0
$655$	−986.106	−	430.372i	−1.50551	−	0.657056i
$656$		−	389.384i		−	0.593573i
$657$		0			0
$658$			1603.90i			2.43754i
$659$			1096.42i			1.66377i	0.554949	+	0.831884i	$0.312738\pi$
$659$			1096.42i			1.66377i	−0.554949	+	0.831884i	$0.687262\pi$
$660$		0			0
$661$	862.000			1.30408			0.652042	−	0.758183i	$-0.273912\pi$
$661$	862.000			1.30408			0.652042	+	0.758183i	$0.273912\pi$
$662$	308.577			0.466129
$663$		0			0
$664$	480.000			0.722892
$665$	525.000	+	229.129i	0.789474	+	0.344555i
$666$		0			0
$667$	−281.745			−0.422406
$668$	−297.397			−0.445205
$669$		0			0
$670$	281.745	+	122.963i	0.420514	+	0.183527i
$671$	735.000	+	286.915i	1.09538	+	0.427593i
$672$		0			0
$673$	−713.306			−1.05989			−0.529945	−	0.848032i	$-0.677787\pi$
$673$	−713.306			−1.05989			−0.529945	+	0.848032i	$0.677787\pi$
$674$	−545.000			−0.808605
$675$		0			0
$676$	−89.0000			−0.131657
$677$	31.3050			0.0462407			0.0231203	−	0.999733i	$-0.492640\pi$
$677$	31.3050			0.0462407			0.0231203	+	0.999733i	$0.492640\pi$
$678$		0			0
$679$		−	1332.10i		−	1.96186i
$680$	210.000	−	481.170i	0.308824	−	0.707604i
$681$		0			0
$682$	26.8328	−	68.7386i	0.0393443	−	0.100790i
$683$			600.317i			0.878942i	0.898257	+	0.439471i	$0.144834\pi$
$683$			600.317i			0.878942i	−0.898257	+	0.439471i	$0.855166\pi$
$684$		0			0
$685$	−294.000	−	128.312i	−0.429197	−	0.187317i
$686$	−675.000			−0.983965
$687$		0			0
$688$	−424.853			−0.617519
$689$			40.9878i			0.0594888i
$690$		0			0
$691$	872.000			1.26194			0.630970	−	0.775808i	$-0.282657\pi$
$691$	872.000			1.26194			0.630970	+	0.775808i	$0.282657\pi$
$692$	143.108			0.206804
$693$		0			0
$694$	10.0000			0.0144092
$695$	1033.06	+	450.866i	1.48642	+	0.648728i
$696$		0			0
$697$			320.780i			0.460230i
$698$		−	1145.64i		−	1.64132i
$699$		0			0
$700$	−190.066	−	204.939i	−0.271523	−	0.292770i
$701$			870.991i			1.24250i	0.783613	+	0.621249i	$0.213374\pi$
$701$			870.991i			1.24250i	−0.783613	+	0.621249i	$0.786626\pi$
$702$		0			0
$703$	46.9574			0.0667958
$704$	164.000	−	420.125i	0.232955	−	0.596768i
$705$		0			0
$706$			655.805i			0.928902i
$707$		−	1145.64i		−	1.62043i
$708$		0			0
$709$	−768.000			−1.08322			−0.541608	−	0.840631i	$-0.682184\pi$
$709$	−768.000			−1.08322			−0.541608	+	0.840631i	$0.682184\pi$
$710$	120.748	−	276.668i	0.170067	−	0.389673i
$711$		0			0
$712$	−248.204			−0.348600
$713$		−	82.4864i		−	0.115689i
$714$		0			0
$715$	−348.446	−	347.254i	−0.487337	−	0.485670i
$716$	−242.000			−0.337989
$717$		0			0
$718$		−	1420.60i		−	1.97855i
$719$	263.000			0.365786			0.182893	−	0.983133i	$-0.441454\pi$
$719$	263.000			0.365786			0.182893	+	0.983133i	$0.441454\pi$
$720$		0			0
$721$			204.939i			0.284243i
$722$	−572.433			−0.792844
$723$		0			0
$724$	−258.000			−0.356354
$725$	187.830	−	174.198i	0.259075	−	0.240273i
$726$		0			0
$727$			293.285i			0.403418i	0.979446	+	0.201709i	$0.0646495\pi$
$727$			293.285i			0.403418i	−0.979446	+	0.201709i	$0.935350\pi$
$728$	670.820			0.921457
$729$		0			0
$730$	−260.000	+	595.735i	−0.356164	+	0.816075i
$731$	350.000			0.478796
$732$		0			0
$733$	219.135			0.298956			0.149478	−	0.988765i	$-0.452241\pi$
$733$	219.135			0.298956			0.149478	+	0.988765i	$0.452241\pi$
$734$		−	963.213i		−	1.31228i
$735$		0			0
$736$			430.372i			0.584744i
$737$	−281.745	−	109.982i	−0.382286	−	0.149229i
$738$		0			0
$739$		−	389.384i		−	0.526907i	−0.964672	−	0.263453i	$-0.915138\pi$
$739$		−	389.384i		−	0.526907i	0.964672	−	0.263453i	$-0.0848615\pi$
$740$	−21.0000	−	9.16515i	−0.0283784	−	0.0123853i
$741$		0			0
$742$		−	114.564i		−	0.154399i
$743$	−682.001			−0.917901			−0.458951	−	0.888462i	$-0.651775\pi$
$743$	−682.001			−0.917901			−0.458951	+	0.888462i	$0.651775\pi$
$744$		0			0
$745$	704.361	+	307.409i	0.945452	+	0.412629i
$746$	1220.00			1.63539
$747$		0			0
$748$	62.6099	−	160.390i	0.0837031	−	0.214425i
$749$	−1750.00			−2.33645
$750$		0			0
$751$	−1003.00			−1.33555			−0.667776	−	0.744362i	$-0.732754\pi$
$751$	−1003.00			−1.33555			−0.667776	+	0.744362i	$0.732754\pi$
$752$			1218.97i			1.62096i
$753$		0			0
$754$		−	204.939i		−	0.271802i
$755$	−469.574	−	204.939i	−0.621953	−	0.271442i
$756$		0			0
$757$		−	1218.97i		−	1.61026i	−0.593100	−	0.805129i	$-0.702096\pi$
$757$		−	1218.97i		−	1.61026i	0.593100	−	0.805129i	$-0.297904\pi$
$758$	957.037			1.26258
$759$		0			0
$760$	315.000	+	137.477i	0.414474	+	0.180891i
$761$			184.445i			0.242372i	0.992630	+	0.121186i	$0.0386698\pi$
$761$			184.445i			0.242372i	−0.992630	+	0.121186i	$0.961330\pi$
$762$		0			0
$763$		−	229.129i		−	0.300300i
$764$	278.000			0.363874
$765$		0			0
$766$		−	368.890i		−	0.481580i
$767$	160.997			0.209905
$768$		0			0
$769$		−	245.927i		−	0.319801i	−0.987133	−	0.159900i	$-0.948883\pi$
$769$		−	245.927i		−	0.319801i	0.987133	−	0.159900i	$-0.0511173\pi$
$770$	973.936	+	970.605i	1.26485	+	1.26053i
$771$		0			0
$772$	−78.2624			−0.101376
$773$			279.537i			0.361626i	0.983517	+	0.180813i	$0.0578729\pi$
$773$			279.537i			0.361626i	−0.983517	+	0.180813i	$0.942127\pi$
$774$		0			0
$775$	51.0000	+	54.9909i	0.0658065	+	0.0709560i
$776$		−	799.262i		−	1.02998i
$777$		0			0
$778$	−509.823			−0.655300
$779$	−210.000			−0.269576
$780$		0			0
$781$	−108.000	+	276.668i	−0.138284	+	0.354248i
$782$		−	962.341i		−	1.23061i
$783$		0			0
$784$	−1444.00			−1.84184
$785$	−231.000	−	100.817i	−0.294268	−	0.128429i
$786$		0			0
$787$	746.847			0.948979			0.474490	−	0.880261i	$-0.342633\pi$
$787$	746.847			0.948979			0.474490	+	0.880261i	$0.342633\pi$
$788$	196.774			0.249713
$789$		0			0
$790$	630.000	+	274.955i	0.797468	+	0.348044i
$791$			1844.45i			2.33180i
$792$		0			0
$793$			641.561i			0.809030i
$794$			1496.05i			1.88420i
$795$		0			0
$796$	−53.0000			−0.0665829
$797$		−	705.717i		−	0.885466i	−0.896653	−	0.442733i	$-0.854009\pi$
$797$		−	705.717i		−	0.885466i	0.896653	−	0.442733i	$-0.145991\pi$
$798$		0			0
$799$		−	1004.20i		−	1.25682i
$800$	−266.092	−	286.915i	−0.332615	−	0.358643i
$801$		0			0
$802$	239.259			0.298328
$803$	232.551	−	595.735i	0.289603	−	0.741886i
$804$		0			0
$805$	1408.72	+	614.817i	1.74997	+	0.763748i
$806$	60.0000			0.0744417
$807$		0			0
$808$		−	687.386i		−	0.850726i
$809$		−	1209.14i		−	1.49461i	−0.664481	−	0.747305i	$-0.731347\pi$
$809$		−	1209.14i		−	1.49461i	0.664481	−	0.747305i	$-0.268653\pi$
$810$		0			0
$811$			1096.42i			1.35194i	0.736929	+	0.675970i	$0.236275\pi$
$811$			1096.42i			1.35194i	−0.736929	+	0.675970i	$0.763725\pi$
$812$			114.564i			0.141089i
$813$		0			0
$814$	105.000	+	40.9878i	0.128993	+	0.0503536i
$815$	1239.00	+	540.744i	1.52025	+	0.663489i
$816$		0			0
$817$			229.129i			0.280451i
$818$			733.212i			0.896347i
$819$		0			0
$820$	93.9149	+	40.9878i	0.114530	+	0.0499851i
$821$		−	758.274i		−	0.923598i	−0.886984	−	0.461799i	$-0.847204\pi$
$821$		−	758.274i		−	0.923598i	0.886984	−	0.461799i	$-0.152796\pi$
$822$		0			0
$823$			293.285i			0.356361i	0.983998	+	0.178180i	$0.0570210\pi$
$823$			293.285i			0.356361i	−0.983998	+	0.178180i	$0.942979\pi$
$824$			122.963i			0.149227i
$825$		0			0
$826$	−450.000			−0.544794
$827$	−594.794			−0.719219			−0.359609	−	0.933103i	$-0.617090\pi$
$827$	−594.794			−0.719219			−0.359609	+	0.933103i	$0.617090\pi$
$828$		0			0
$829$	102.000			0.123040			0.0615199	−	0.998106i	$-0.480405\pi$
$829$	102.000			0.123040			0.0615199	+	0.998106i	$0.480405\pi$
$830$	−320.000	+	733.212i	−0.385542	+	0.883388i
$831$		0			0
$832$	366.715			0.440763
$833$	1189.59			1.42808
$834$		0			0
$835$	−594.794	+	1362.84i	−0.712328	+	1.63215i
$836$	105.000	+	40.9878i	0.125598	+	0.0490285i
$837$		0			0
$838$	1614.44			1.92654
$839$	138.000			0.164482			0.0822408	−	0.996612i	$-0.473792\pi$
$839$	138.000			0.164482			0.0822408	+	0.996612i	$0.473792\pi$
$840$		0			0
$841$	736.000			0.875149
$842$	912.316			1.08351
$843$		0			0
$844$			174.198i			0.206396i
$845$	−178.000	+	407.849i	−0.210651	+	0.482662i
$846$		0			0
$847$	−995.050	−	916.515i	−1.17479	−	1.08207i
$848$		−	87.0689i		−	0.102676i
$849$		0			0
$850$	595.000	+	641.561i	0.700000	+	0.754777i
$851$	126.000			0.148061
$852$		0			0
$853$	−532.184			−0.623897			−0.311949	−	0.950099i	$-0.600982\pi$
$853$	−532.184			−0.623897			−0.311949	+	0.950099i	$0.600982\pi$
$854$		−	1793.22i		−	2.09978i
$855$		0			0
$856$	−1050.00			−1.22664
$857$	950.329			1.10890			0.554451	−	0.832216i	$-0.312928\pi$
$857$	950.329			1.10890			0.554451	+	0.832216i	$0.312928\pi$
$858$		0			0
$859$	−1068.00			−1.24331			−0.621653	−	0.783293i	$-0.713539\pi$
$859$	−1068.00			−1.24331			−0.621653	+	0.783293i	$0.713539\pi$
$860$	44.7214	−	102.470i	0.0520016	−	0.119151i
$861$		0			0
$862$			137.477i			0.159486i
$863$			73.3212i			0.0849608i	0.999097	+	0.0424804i	$0.0135260\pi$
$863$			73.3212i			0.0849608i	−0.999097	+	0.0424804i	$0.986474\pi$
$864$		0			0
$865$	286.217	−	655.805i	0.330886	−	0.758156i
$866$		−	553.335i		−	0.638955i
$867$		0			0
$868$	−33.5410			−0.0386417
$869$	−630.000	−	245.927i	−0.724971	−	0.283000i
$870$		0			0
$871$		−	245.927i		−	0.282350i
$872$		−	137.477i		−	0.157657i
$873$		0			0
$874$	630.000			0.720824
$875$	−1319.28	+	461.113i	−1.50775	+	0.526986i
$876$		0			0
$877$	169.941			0.193776			0.0968878	−	0.995295i	$-0.469111\pi$
$877$	169.941			0.193776			0.0968878	+	0.995295i	$0.469111\pi$
$878$		−	962.341i		−	1.09606i
$879$		0			0
$880$	740.191	+	737.660i	0.841126	+	0.838250i
$881$	78.0000			0.0885358			0.0442679	−	0.999020i	$-0.485904\pi$
$881$	78.0000			0.0885358			0.0442679	+	0.999020i	$0.485904\pi$
$882$		0			0
$883$			1553.49i			1.75934i	0.475589	+	0.879668i	$0.342235\pi$
$883$			1553.49i			1.75934i	−0.475589	+	0.879668i	$0.657765\pi$
$884$	140.000			0.158371
$885$		0			0
$886$		−	676.299i		−	0.763317i
$887$	−299.633			−0.337805			−0.168903	−	0.985633i	$-0.554022\pi$
$887$	−299.633			−0.337805			−0.168903	+	0.985633i	$0.554022\pi$
$888$		0			0
$889$	−350.000			−0.393701
$890$	165.469	−	379.137i	0.185920	−	0.425997i
$891$		0			0
$892$		−	394.102i		−	0.441818i
$893$	657.404			0.736175
$894$		0			0
$895$	−484.000	+	1108.98i	−0.540782	+	1.23909i
$896$	−1725.00			−1.92522
$897$		0			0
$898$	49.1935			0.0547812
$899$		−	30.7409i		−	0.0341945i
$900$		0			0
$901$			71.7287i			0.0796101i
$902$	−469.574	−	183.303i	−0.520592	−	0.203218i
$903$		0			0
$904$			1106.67i			1.22419i
$905$	−516.000	+	1182.30i	−0.570166	+	1.30641i
$906$		0			0
$907$		−	691.969i		−	0.762921i	−0.924385	−	0.381460i	$-0.875421\pi$
$907$		−	691.969i		−	0.762921i	0.924385	−	0.381460i	$-0.124579\pi$
$908$	277.272			0.305366
$909$		0			0
$910$	−447.214	+	1024.70i	−0.491444	+	1.12604i
$911$	−1037.00			−1.13831			−0.569155	−	0.822230i	$-0.692729\pi$
$911$	−1037.00			−1.13831			−0.569155	+	0.822230i	$0.692729\pi$
$912$		0			0
$913$	286.217	−	733.212i	0.313490	−	0.803080i
$914$	−775.000			−0.847921
$915$		0			0
$916$	292.000			0.318777
$917$		−	2405.85i		−	2.62361i
$918$		0			0
$919$		−	1782.97i		−	1.94012i	−0.242867	−	0.970060i	$-0.578088\pi$
$919$		−	1782.97i		−	1.94012i	0.242867	−	0.970060i	$-0.421912\pi$
$920$	845.234	+	368.890i	0.918732	+	0.400968i
$921$		0			0
$922$		−	756.125i		−	0.820092i
$923$	−241.495			−0.261642
$924$		0			0
$925$	−84.0000	+	77.9038i	−0.0908108	+	0.0842203i
$926$			1393.59i			1.50495i
$927$		0			0
$928$			160.390i			0.172834i
$929$	633.000			0.681378			0.340689	−	0.940176i	$-0.389340\pi$
$929$	633.000			0.681378			0.340689	+	0.940176i	$0.389340\pi$
$930$		0			0
$931$			778.768i			0.836486i
$932$	172.177			0.184740
$933$		0			0
$934$		−	1239.88i		−	1.32750i
$935$	−609.780	−	607.695i	−0.652171	−	0.649941i
$936$		0			0
$937$	−728.958			−0.777970			−0.388985	−	0.921244i	$-0.627174\pi$
$937$	−728.958			−0.777970			−0.388985	+	0.921244i	$0.627174\pi$
$938$			687.386i			0.732821i
$939$		0			0
$940$	−294.000	−	128.312i	−0.312766	−	0.136502i
$941$		−	850.497i		−	0.903822i	−0.892063	−	0.451911i	$-0.850742\pi$
$941$		−	850.497i		−	0.903822i	0.892063	−	0.451911i	$-0.149258\pi$
$942$		0			0
$943$	−563.489			−0.597549
$944$	−342.000			−0.362288
$945$		0			0
$946$	−200.000	+	512.348i	−0.211416	+	0.541594i
$947$		−	911.933i		−	0.962970i	−0.876454	−	0.481485i	$-0.840098\pi$
$947$		−	911.933i		−	0.962970i	0.876454	−	0.481485i	$-0.159902\pi$
$948$		0			0
$949$	520.000			0.547945
$950$	−420.000	+	389.519i	−0.442105	+	0.410020i
$951$		0			0
$952$	1173.94			1.23313
$953$	1236.55			1.29753			0.648765	−	0.760989i	$-0.275286\pi$
$953$	1236.55			1.29753			0.648765	+	0.760989i	$0.275286\pi$
$954$		0			0
$955$	556.000	−	1273.96i	0.582199	−	1.33399i
$956$		−	225.433i		−	0.235808i
$957$		0			0
$958$			91.6515i			0.0956696i
$959$		−	717.287i		−	0.747953i
$960$		0			0
$961$	−952.000			−0.990635
$962$			91.6515i			0.0952718i
$963$		0			0
$964$		−	327.902i		−	0.340148i
$965$	−156.525	+	358.643i	−0.162202	+	0.371651i
$966$		0			0
$967$	431.561			0.446289			0.223144	−	0.974785i	$-0.428368\pi$
$967$	431.561			0.446289			0.223144	+	0.974785i	$0.428368\pi$
$968$	−597.030	−	549.909i	−0.616767	−	0.568088i
$969$		0			0
$970$	1220.89	+	532.841i	1.25865	+	0.549321i
$971$	1048.00			1.07930			0.539650	−	0.841890i	$-0.318557\pi$
$971$	1048.00			1.07930			0.539650	+	0.841890i	$0.318557\pi$
$972$		0			0
$973$			2520.42i			2.59036i
$974$		−	758.274i		−	0.778516i
$975$		0			0
$976$		−	1362.84i		−	1.39636i
$977$		−	247.459i		−	0.253285i	−0.991948	−	0.126642i	$-0.959580\pi$
$977$		−	247.459i		−	0.253285i	0.991948	−	0.126642i	$-0.0404200\pi$
$978$		0			0
$979$	−148.000	+	379.137i	−0.151175	+	0.387270i
$980$	152.000	−	348.276i	0.155102	−	0.355383i
$981$		0			0
$982$		−	1306.03i		−	1.32997i
$983$			27.4955i			0.0279710i	0.999902	+	0.0139855i	$0.00445186\pi$
$983$			27.4955i			0.0279710i	−0.999902	+	0.0139855i	$0.995548\pi$
$984$		0			0
$985$	393.548	−	901.732i	0.399541	−	0.915464i
$986$		−	358.643i		−	0.363736i
$987$		0			0
$988$			91.6515i			0.0927647i
$989$			614.817i			0.621655i
$990$		0			0
$991$	1182.00			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$991$	1182.00			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$992$	−46.9574			−0.0473361
$993$		0			0
$994$	675.000			0.679074
$995$	−106.000	+	242.877i	−0.106533	+	0.244097i
$996$		0			0
$997$	−1694.94			−1.70004			−0.850020	−	0.526751i	$-0.823410\pi$
$997$	−1694.94			−1.70004			−0.850020	+	0.526751i	$0.823410\pi$
$998$	599.266			0.600467
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.3.h.d.109.1		4
3.2	odd	2		55.3.d.d.54.3	yes	4
5.4	even	2	inner	495.3.h.d.109.4		4
11.10	odd	2	inner	495.3.h.d.109.3		4
12.11	even	2		880.3.i.d.769.3		4
15.2	even	4		275.3.c.e.76.3		4
15.8	even	4		275.3.c.e.76.2		4
15.14	odd	2		55.3.d.d.54.2	yes	4
33.32	even	2		55.3.d.d.54.1	✓	4
55.54	odd	2	inner	495.3.h.d.109.2		4
60.59	even	2		880.3.i.d.769.2		4
132.131	odd	2		880.3.i.d.769.4		4
165.32	odd	4		275.3.c.e.76.1		4
165.98	odd	4		275.3.c.e.76.4		4
165.164	even	2		55.3.d.d.54.4	yes	4
660.659	odd	2		880.3.i.d.769.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.d.d.54.1	✓	4	33.32	even	2
55.3.d.d.54.2	yes	4	15.14	odd	2
55.3.d.d.54.3	yes	4	3.2	odd	2
55.3.d.d.54.4	yes	4	165.164	even	2
275.3.c.e.76.1		4	165.32	odd	4
275.3.c.e.76.2		4	15.8	even	4
275.3.c.e.76.3		4	15.2	even	4
275.3.c.e.76.4		4	165.98	odd	4
495.3.h.d.109.1		4	1.1	even	1	trivial
495.3.h.d.109.2		4	55.54	odd	2	inner
495.3.h.d.109.3		4	11.10	odd	2	inner
495.3.h.d.109.4		4	5.4	even	2	inner
880.3.i.d.769.1		4	660.659	odd	2
880.3.i.d.769.2		4	60.59	even	2
880.3.i.d.769.3		4	12.11	even	2
880.3.i.d.769.4		4	132.131	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} +1.00000 q^{4} +(2.00000 - 4.58258i) q^{5} +11.1803 q^{7} +6.70820 q^{8} +(-4.47214 + 10.2470i) q^{10} +(4.00000 - 10.2470i) q^{11} +8.94427 q^{13} -25.0000 q^{14} -19.0000 q^{16} +15.6525 q^{17} +10.2470i q^{19} +(2.00000 - 4.58258i) q^{20} +(-8.94427 + 22.9129i) q^{22} +27.4955i q^{23} +(-17.0000 - 18.3303i) q^{25} -20.0000 q^{26} +11.1803 q^{28} +10.2470i q^{29} -3.00000 q^{31} +15.6525 q^{32} -35.0000 q^{34} +(22.3607 - 51.2348i) q^{35} -4.58258i q^{37} -22.9129i q^{38} +(13.4164 - 30.7409i) q^{40} +20.4939i q^{41} +22.3607 q^{43} +(4.00000 - 10.2470i) q^{44} -61.4817i q^{46} -64.1561i q^{47} +76.0000 q^{49} +(38.0132 + 40.9878i) q^{50} +8.94427 q^{52} +4.58258i q^{53} +(-38.9574 - 38.8242i) q^{55} +75.0000 q^{56} -22.9129i q^{58} +18.0000 q^{59} +71.7287i q^{61} +6.70820 q^{62} +41.0000 q^{64} +(17.8885 - 40.9878i) q^{65} -27.4955i q^{67} +15.6525 q^{68} +(-50.0000 + 114.564i) q^{70} -27.0000 q^{71} +58.1378 q^{73} +10.2470i q^{74} +10.2470i q^{76} +(44.7214 - 114.564i) q^{77} -61.4817i q^{79} +(-38.0000 + 87.0689i) q^{80} -45.8258i q^{82} +71.5542 q^{83} +(31.3050 - 71.7287i) q^{85} -50.0000 q^{86} +(26.8328 - 68.7386i) q^{88} -37.0000 q^{89} +100.000 q^{91} +27.4955i q^{92} +143.457i q^{94} +(46.9574 + 20.4939i) q^{95} -119.147i q^{97} -169.941 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 8 q^{5} + 16 q^{11} - 100 q^{14} - 76 q^{16} + 8 q^{20} - 68 q^{25} - 80 q^{26} - 12 q^{31} - 140 q^{34} + 16 q^{44} + 304 q^{49} + 32 q^{55} + 300 q^{56} + 72 q^{59} + 164 q^{64} - 200 q^{70}+ \cdots + 400 q^{91}+O(q^{100}) \) 4 * q + 4 * q^4 + 8 * q^5 + 16 * q^11 - 100 * q^14 - 76 * q^16 + 8 * q^20 - 68 * q^25 - 80 * q^26 - 12 * q^31 - 140 * q^34 + 16 * q^44 + 304 * q^49 + 32 * q^55 + 300 * q^56 + 72 * q^59 + 164 * q^64 - 200 * q^70 - 108 * q^71 - 152 * q^80 - 200 * q^86 - 148 * q^89 + 400 * q^91

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