LMFDB - Embedded newform 275.3.c.e.76.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,3,Mod(76,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("275.76");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.c (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:	$7.49320726991$
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} + x^{2} + 105 $ x^4 - 2*x^3 + x^2 + 105
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			76.3
Root			$-1.79129 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	275.76
Dual form			275.3.c.e.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.23607i q^{2} -4.58258 q^{3} -1.00000 q^{4} -10.2470i q^{6} +11.1803i q^{7} +6.70820i q^{8} +12.0000 q^{9} +(-4.00000 + 10.2470i) q^{11} +4.58258 q^{12} -8.94427i q^{13} -25.0000 q^{14} -19.0000 q^{16} -15.6525i q^{17} +26.8328i q^{18} -10.2470i q^{19} -51.2348i q^{21} +(-22.9129 - 8.94427i) q^{22} -27.4955 q^{23} -30.7409i q^{24} +20.0000 q^{26} -13.7477 q^{27} -11.1803i q^{28} +10.2470i q^{29} -3.00000 q^{31} -15.6525i q^{32} +(18.3303 - 46.9574i) q^{33} +35.0000 q^{34} -12.0000 q^{36} +4.58258 q^{37} +22.9129 q^{38} +40.9878i q^{39} -20.4939i q^{41} +114.564 q^{42} -22.3607i q^{43} +(4.00000 - 10.2470i) q^{44} -61.4817i q^{46} -64.1561 q^{47} +87.0689 q^{48} -76.0000 q^{49} +71.7287i q^{51} +8.94427i q^{52} -4.58258 q^{53} -30.7409i q^{54} -75.0000 q^{56} +46.9574i q^{57} -22.9129 q^{58} +18.0000 q^{59} +71.7287i q^{61} -6.70820i q^{62} +134.164i q^{63} -41.0000 q^{64} +(105.000 + 40.9878i) q^{66} +27.4955 q^{67} +15.6525i q^{68} +126.000 q^{69} +27.0000 q^{71} +80.4984i q^{72} -58.1378i q^{73} +10.2470i q^{74} +10.2470i q^{76} +(-114.564 - 44.7214i) q^{77} -91.6515 q^{78} +61.4817i q^{79} -45.0000 q^{81} +45.8258 q^{82} +71.5542i q^{83} +51.2348i q^{84} +50.0000 q^{86} -46.9574i q^{87} +(-68.7386 - 26.8328i) q^{88} -37.0000 q^{89} +100.000 q^{91} +27.4955 q^{92} +13.7477 q^{93} -143.457i q^{94} +71.7287i q^{96} +119.147 q^{97} -169.941i q^{98} +(-48.0000 + 122.963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 48 q^{9} - 16 q^{11} - 100 q^{14} - 76 q^{16} + 80 q^{26} - 12 q^{31} + 140 q^{34} - 48 q^{36} + 16 q^{44} - 304 q^{49} - 300 q^{56} + 72 q^{59} - 164 q^{64} + 420 q^{66} + 504 q^{69} + 108 q^{71}+ \cdots - 192 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 48 * q^9 - 16 * q^11 - 100 * q^14 - 76 * q^16 + 80 * q^26 - 12 * q^31 + 140 * q^34 - 48 * q^36 + 16 * q^44 - 304 * q^49 - 300 * q^56 + 72 * q^59 - 164 * q^64 + 420 * q^66 + 504 * q^69 + 108 * q^71 - 180 * q^81 + 200 * q^86 - 148 * q^89 + 400 * q^91 - 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$-1$	$1$

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 $

$2$			2.23607i			1.11803i	0.829156	+	0.559017i	$0.188821\pi$
$2$			2.23607i			1.11803i	−0.829156	+	0.559017i	$0.811179\pi$
$3$	−4.58258			−1.52753			−0.763763	−	0.645497i	$-0.776650\pi$
$3$	−4.58258			−1.52753			−0.763763	+	0.645497i	$0.776650\pi$
$4$	−1.00000			−0.250000
$5$		0			0
$5$		0			0
$6$		−	10.2470i		−	1.70783i
$7$			11.1803i			1.59719i	0.601868	+	0.798596i	$0.294423\pi$
$7$			11.1803i			1.59719i	−0.601868	+	0.798596i	$0.705577\pi$
$8$			6.70820i			0.838525i
$9$	12.0000			1.33333
$10$		0			0
$11$	−4.00000	+	10.2470i	−0.363636	+	0.931541i
$11$	−4.00000	+	10.2470i	−0.363636	+	0.931541i
$12$	4.58258			0.381881
$13$		−	8.94427i		−	0.688021i	−0.938966	−	0.344010i	$-0.888214\pi$
$13$		−	8.94427i		−	0.688021i	0.938966	−	0.344010i	$-0.111786\pi$
$14$	−25.0000			−1.78571
$15$		0			0
$16$	−19.0000			−1.18750
$17$		−	15.6525i		−	0.920734i	−0.887729	−	0.460367i	$-0.847718\pi$
$17$		−	15.6525i		−	0.920734i	0.887729	−	0.460367i	$-0.152282\pi$
$18$			26.8328i			1.49071i
$19$		−	10.2470i		−	0.539313i	−0.962957	−	0.269657i	$-0.913090\pi$
$19$		−	10.2470i		−	0.539313i	0.962957	−	0.269657i	$-0.0869102\pi$
$20$		0			0
$21$		−	51.2348i		−	2.43975i
$22$	−22.9129	−	8.94427i	−1.04149	−	0.406558i
$23$	−27.4955			−1.19545			−0.597727	−	0.801700i	$-0.703929\pi$
$23$	−27.4955			−1.19545			−0.597727	+	0.801700i	$0.703929\pi$
$24$		−	30.7409i		−	1.28087i
$25$		0			0
$26$	20.0000			0.769231
$27$	−13.7477			−0.509175
$28$		−	11.1803i		−	0.399298i
$29$			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	$0.515408\pi$
$32$		−	15.6525i		−	0.489140i
$33$	18.3303	−	46.9574i	0.555464	−	1.42295i
$34$	35.0000			1.02941
$35$		0			0
$36$	−12.0000			−0.333333
$37$	4.58258			0.123853			0.0619267	−	0.998081i	$-0.480275\pi$
$37$	4.58258			0.123853			0.0619267	+	0.998081i	$0.480275\pi$
$38$	22.9129			0.602970
$39$			40.9878i			1.05097i
$40$		0			0
$41$		−	20.4939i		−	0.499851i	−0.968265	−	0.249926i	$-0.919594\pi$
$41$		−	20.4939i		−	0.499851i	0.968265	−	0.249926i	$-0.0804062\pi$
$42$	114.564			2.72772
$43$		−	22.3607i		−	0.520016i	−0.965606	−	0.260008i	$-0.916275\pi$
$43$		−	22.3607i		−	0.520016i	0.965606	−	0.260008i	$-0.0837252\pi$
$44$	4.00000	−	10.2470i	0.0909091	−	0.232885i
$45$		0			0
$46$		−	61.4817i		−	1.33656i
$47$	−64.1561			−1.36502			−0.682511	−	0.730875i	$-0.739112\pi$
$47$	−64.1561			−1.36502			−0.682511	+	0.730875i	$0.739112\pi$
$48$	87.0689			1.81394
$49$	−76.0000			−1.55102
$50$		0			0
$51$			71.7287i			1.40644i
$52$			8.94427i			0.172005i
$53$	−4.58258			−0.0864637			−0.0432318	−	0.999065i	$-0.513765\pi$
$53$	−4.58258			−0.0864637			−0.0432318	+	0.999065i	$0.513765\pi$
$54$		−	30.7409i		−	0.569275i
$55$		0			0
$56$	−75.0000			−1.33929
$57$			46.9574i			0.823815i
$58$	−22.9129			−0.395050
$59$	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	$0.799939\pi$
$62$		−	6.70820i		−	0.108197i
$63$			134.164i			2.12959i
$64$	−41.0000			−0.640625
$65$		0			0
$66$	105.000	+	40.9878i	1.59091	+	0.621027i
$67$	27.4955			0.410380			0.205190	−	0.978722i	$-0.434219\pi$
$67$	27.4955			0.410380			0.205190	+	0.978722i	$0.434219\pi$
$68$			15.6525i			0.230183i
$69$	126.000			1.82609
$70$		0			0
$71$	27.0000			0.380282			0.190141	−	0.981757i	$-0.439106\pi$
$71$	27.0000			0.380282			0.190141	+	0.981757i	$0.439106\pi$
$72$			80.4984i			1.11803i
$73$		−	58.1378i		−	0.796408i	−0.917297	−	0.398204i	$-0.869634\pi$
$73$		−	58.1378i		−	0.796408i	0.917297	−	0.398204i	$-0.130366\pi$
$74$			10.2470i			0.138472i
$75$		0			0
$76$			10.2470i			0.134828i
$77$	−114.564	−	44.7214i	−1.48785	−	0.580797i
$78$	−91.6515			−1.17502
$79$			61.4817i			0.778249i	0.921185	+	0.389125i	$0.127222\pi$
$79$			61.4817i			0.778249i	−0.921185	+	0.389125i	$0.872778\pi$
$80$		0			0
$81$	−45.0000			−0.555556
$82$	45.8258			0.558851
$83$			71.5542i			0.862098i	0.902328	+	0.431049i	$0.141856\pi$
$83$			71.5542i			0.862098i	−0.902328	+	0.431049i	$0.858144\pi$
$84$			51.2348i			0.609938i
$85$		0			0
$86$	50.0000			0.581395
$87$		−	46.9574i		−	0.539741i
$88$	−68.7386	−	26.8328i	−0.781121	−	0.304918i
$89$	−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
$92$	27.4955			0.298864
$93$	13.7477			0.147825
$94$		−	143.457i		−	1.52614i
$95$		0			0
$96$			71.7287i			0.747173i
$97$	119.147			1.22832			0.614160	−	0.789182i	$-0.289495\pi$
$97$	119.147			1.22832			0.614160	+	0.789182i	$0.289495\pi$
$98$		−	169.941i		−	1.73409i
$99$	−48.0000	+	122.963i	−0.484848	+	1.24205i
$100$		0			0
$101$			102.470i			1.01455i	0.861784	+	0.507275i	$0.169347\pi$
$101$			102.470i			1.01455i	−0.861784	+	0.507275i	$0.830653\pi$
$102$	−160.390			−1.57245
$103$	18.3303			0.177964			0.0889821	−	0.996033i	$-0.471639\pi$
$103$	18.3303			0.177964			0.0889821	+	0.996033i	$0.471639\pi$
$104$	60.0000			0.576923
$105$		0			0
$106$		−	10.2470i		−	0.0966693i
$107$			156.525i			1.46285i	0.681923	+	0.731424i	$0.261144\pi$
$107$			156.525i			1.46285i	−0.681923	+	0.731424i	$0.738856\pi$
$108$	13.7477			0.127294
$109$			20.4939i			0.188017i	0.995571	+	0.0940087i	$0.0299682\pi$
$109$			20.4939i			0.188017i	−0.995571	+	0.0940087i	$0.970032\pi$
$110$		0			0
$111$	−21.0000			−0.189189
$112$		−	212.426i		−	1.89666i
$113$	−164.973			−1.45994			−0.729968	−	0.683482i	$-0.760465\pi$
$113$	−164.973			−1.45994			−0.729968	+	0.683482i	$0.760465\pi$
$114$	−105.000			−0.921053
$115$		0			0
$116$		−	10.2470i		−	0.0883358i
$117$		−	107.331i		−	0.917361i
$118$			40.2492i			0.341095i
$119$	175.000			1.47059
$120$		0			0
$121$	−89.0000	−	81.9756i	−0.735537	−	0.677484i
$122$	−160.390			−1.31467
$123$			93.9149i			0.763535i
$124$	3.00000			0.0241935
$125$		0			0
$126$	−300.000			−2.38095
$127$		−	31.3050i		−	0.246496i	−0.992376	−	0.123248i	$-0.960669\pi$
$127$		−	31.3050i		−	0.246496i	0.992376	−	0.123248i	$-0.0393310\pi$
$128$		−	154.289i		−	1.20538i
$129$			102.470i			0.794337i
$130$		0			0
$131$			215.186i			1.64264i	0.570467	+	0.821320i	$0.306762\pi$
$131$			215.186i			1.64264i	−0.570467	+	0.821320i	$0.693238\pi$
$132$	−18.3303	+	46.9574i	−0.138866	+	0.355738i
$133$	114.564			0.861386
$134$			61.4817i			0.458819i
$135$		0			0
$136$	105.000			0.772059
$137$	−64.1561			−0.468292			−0.234146	−	0.972201i	$-0.575229\pi$
$137$	−64.1561			−0.468292			−0.234146	+	0.972201i	$0.575229\pi$
$138$			281.745i			2.04163i
$139$		−	225.433i		−	1.62182i	−0.585171	−	0.810910i	$-0.698973\pi$
$139$		−	225.433i		−	1.62182i	0.585171	−	0.810910i	$-0.301027\pi$
$140$		0			0
$141$	294.000			2.08511
$142$			60.3738i			0.425168i
$143$	91.6515	+	35.7771i	0.640920	+	0.250189i
$144$	−228.000			−1.58333
$145$		0			0
$146$	130.000			0.890411
$147$	348.276			2.36922
$148$	−4.58258			−0.0309633
$149$			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	$-0.110191\pi$
$152$	68.7386			0.452228
$153$		−	187.830i		−	1.22765i
$154$	100.000	−	256.174i	0.649351	−	1.66347i
$155$		0			0
$156$		−	40.9878i		−	0.262742i
$157$	50.4083			0.321072			0.160536	−	0.987030i	$-0.448678\pi$
$157$	50.4083			0.321072			0.160536	+	0.987030i	$0.448678\pi$
$158$	−137.477			−0.870109
$159$	21.0000			0.132075
$160$		0			0
$161$		−	307.409i		−	1.90937i
$162$		−	100.623i		−	0.621130i
$163$	270.372			1.65872			0.829362	−	0.558712i	$-0.188704\pi$
$163$	270.372			1.65872			0.829362	+	0.558712i	$0.188704\pi$
$164$			20.4939i			0.124963i
$165$		0			0
$166$	−160.000			−0.963855
$167$			297.397i			1.78082i	0.455159	+	0.890410i	$0.349583\pi$
$167$			297.397i			1.78082i	−0.455159	+	0.890410i	$0.650417\pi$
$168$	343.693			2.04579
$169$	89.0000			0.526627
$170$		0			0
$171$		−	122.963i		−	0.719084i
$172$			22.3607i			0.130004i
$173$			143.108i			0.827216i	0.910455	+	0.413608i	$0.135732\pi$
$173$			143.108i			0.827216i	−0.910455	+	0.413608i	$0.864268\pi$
$174$	105.000			0.603448
$175$		0			0
$176$	76.0000	−	194.692i	0.431818	−	1.10620i
$177$	−82.4864			−0.466025
$178$		−	82.7345i		−	0.464801i
$179$	−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	$0.752531\pi$
$182$			223.607i			1.22861i
$183$		−	328.702i		−	1.79619i
$184$		−	184.445i		−	1.00242i
$185$		0			0
$186$			30.7409i			0.165273i
$187$	160.390	+	62.6099i	0.857701	+	0.334812i
$188$	64.1561			0.341256
$189$		−	153.704i		−	0.813250i
$190$		0			0
$191$	−278.000			−1.45550			−0.727749	−	0.685844i	$-0.759433\pi$
$191$	−278.000			−1.45550			−0.727749	+	0.685844i	$0.759433\pi$
$192$	187.886			0.978571
$193$			78.2624i			0.405505i	0.979230	+	0.202752i	$0.0649886\pi$
$193$			78.2624i			0.405505i	−0.979230	+	0.202752i	$0.935011\pi$
$194$			266.421i			1.37330i
$195$		0			0
$196$	76.0000			0.387755
$197$		−	196.774i		−	0.998853i	−0.866356	−	0.499426i	$-0.833544\pi$
$197$		−	196.774i		−	0.998853i	0.866356	−	0.499426i	$-0.166456\pi$
$198$	−274.955	−	107.331i	−1.38866	−	0.542077i
$199$	53.0000			0.266332			0.133166	−	0.991094i	$-0.457486\pi$
$199$	53.0000			0.266332			0.133166	+	0.991094i	$0.457486\pi$
$200$		0			0
$201$	−126.000			−0.626866
$202$	−229.129			−1.13430
$203$	−114.564			−0.564357
$204$		−	71.7287i		−	0.351611i
$205$		0			0
$206$			40.9878i			0.198970i
$207$	−329.945			−1.59394
$208$			169.941i			0.817025i
$209$	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	$0.864554\pi$
$212$	4.58258			0.0216159
$213$	−123.730			−0.580890
$214$	−350.000			−1.63551
$215$		0			0
$216$		−	92.2226i		−	0.426956i
$217$		−	33.5410i		−	0.154567i
$218$	−45.8258			−0.210210
$219$			266.421i			1.21653i
$220$		0			0
$221$	−140.000			−0.633484
$222$		−	46.9574i		−	0.211520i
$223$	−394.102			−1.76727			−0.883636	−	0.468175i	$-0.844912\pi$
$223$	−394.102			−1.76727			−0.883636	+	0.468175i	$0.844912\pi$
$224$	175.000			0.781250
$225$		0			0
$226$		−	368.890i		−	1.63226i
$227$		−	277.272i		−	1.22146i	−0.791837	−	0.610732i	$-0.790875\pi$
$227$		−	277.272i		−	1.22146i	0.791837	−	0.610732i	$-0.209125\pi$
$228$		−	46.9574i		−	0.205954i
$229$	−292.000			−1.27511			−0.637555	−	0.770405i	$-0.720054\pi$
$229$	−292.000			−1.27511			−0.637555	+	0.770405i	$0.720054\pi$
$230$		0			0
$231$	525.000	+	204.939i	2.27273	+	0.887182i
$232$	−68.7386			−0.296287
$233$			172.177i			0.738958i	0.929239	+	0.369479i	$0.120464\pi$
$233$			172.177i			0.738958i	−0.929239	+	0.369479i	$0.879536\pi$
$234$	240.000			1.02564
$235$		0			0
$236$	−18.0000			−0.0762712
$237$		−	281.745i		−	1.18880i
$238$			391.312i			1.64417i
$239$		−	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	$-0.238149\pi$
$242$	183.303	−	199.010i	0.757451	−	0.822356i
$243$	329.945			1.35780
$244$		−	71.7287i		−	0.293970i
$245$		0			0
$246$	−210.000			−0.853659
$247$	−91.6515			−0.371059
$248$		−	20.1246i		−	0.0811476i
$249$		−	327.902i		−	1.31688i
$250$		0			0
$251$	282.000			1.12351			0.561753	−	0.827305i	$-0.310127\pi$
$251$	282.000			1.12351			0.561753	+	0.827305i	$0.310127\pi$
$252$		−	134.164i		−	0.532397i
$253$	109.982	−	281.745i	0.434711	−	1.11361i
$254$	70.0000			0.275591
$255$		0			0
$256$	181.000			0.707031
$257$	−64.1561			−0.249634			−0.124817	−	0.992180i	$-0.539834\pi$
$257$	−64.1561			−0.249634			−0.124817	+	0.992180i	$0.539834\pi$
$258$	−229.129			−0.888096
$259$			51.2348i			0.197818i
$260$		0			0
$261$			122.963i			0.471124i
$262$	−481.170			−1.83653
$263$		−	199.010i		−	0.756692i	−0.925664	−	0.378346i	$-0.876493\pi$
$263$		−	199.010i		−	0.756692i	0.925664	−	0.378346i	$-0.123507\pi$
$264$	315.000	+	122.963i	1.19318	+	0.465770i
$265$		0			0
$266$			256.174i			0.963059i
$267$	169.555			0.635039
$268$	−27.4955			−0.102595
$269$	−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	$0.850090\pi$
$272$			297.397i			1.09337i
$273$	−458.258			−1.67860
$274$		−	143.457i		−	0.523567i
$275$		0			0
$276$	−126.000			−0.456522
$277$			58.1378i			0.209884i	0.994478	+	0.104942i	$0.0334656\pi$
$277$			58.1378i			0.209884i	−0.994478	+	0.104942i	$0.966534\pi$
$278$	504.083			1.81325
$279$	−36.0000			−0.129032
$280$		0			0
$281$			163.951i			0.583456i	0.956501	+	0.291728i	$0.0942303\pi$
$281$			163.951i			0.583456i	−0.956501	+	0.291728i	$0.905770\pi$
$282$			657.404i			2.33122i
$283$			250.440i			0.884946i	0.896782	+	0.442473i	$0.145899\pi$
$283$			250.440i			0.884946i	−0.896782	+	0.442473i	$0.854101\pi$
$284$	−27.0000			−0.0950704
$285$		0			0
$286$	−80.0000	+	204.939i	−0.279720	+	0.716570i
$287$	229.129			0.798358
$288$		−	187.830i		−	0.652186i
$289$	44.0000			0.152249
$290$		0			0
$291$	−546.000			−1.87629
$292$			58.1378i			0.199102i
$293$			447.214i			1.52633i	0.646206	+	0.763163i	$0.276355\pi$
$293$			447.214i			1.52633i	−0.646206	+	0.763163i	$0.723645\pi$
$294$			778.768i			2.64887i
$295$		0			0
$296$			30.7409i			0.103854i
$297$	54.9909	−	140.872i	0.185155	−	0.474317i
$298$	−343.693			−1.15333
$299$			245.927i			0.822498i
$300$		0			0
$301$	250.000			0.830565
$302$	229.129			0.758705
$303$		−	469.574i		−	1.54975i
$304$			194.692i			0.640434i
$305$		0			0
$306$	420.000			1.37255
$307$			447.214i			1.45672i	0.685194	+	0.728361i	$0.259718\pi$
$307$			447.214i			1.45672i	−0.685194	+	0.728361i	$0.740282\pi$
$308$	114.564	+	44.7214i	0.371962	+	0.145199i
$309$	−84.0000			−0.271845
$310$		0			0
$311$	87.0000			0.279743			0.139871	−	0.990170i	$-0.455331\pi$
$311$	87.0000			0.279743			0.139871	+	0.990170i	$0.455331\pi$
$312$	−274.955			−0.881265
$313$	293.285			0.937012			0.468506	−	0.883460i	$-0.344792\pi$
$313$	293.285			0.937012			0.468506	+	0.883460i	$0.344792\pi$
$314$			112.716i			0.358970i
$315$		0			0
$316$		−	61.4817i		−	0.194562i
$317$	50.4083			0.159017			0.0795084	−	0.996834i	$-0.474665\pi$
$317$	50.4083			0.159017			0.0795084	+	0.996834i	$0.474665\pi$
$318$			46.9574i			0.147665i
$319$	−105.000	−	40.9878i	−0.329154	−	0.128488i
$320$		0			0
$321$		−	717.287i		−	2.23454i
$322$	687.386			2.13474
$323$	−160.390			−0.496564
$324$	45.0000			0.138889
$325$		0			0
$326$			604.570i			1.85451i
$327$		−	93.9149i		−	0.287201i
$328$	137.477			0.419138
$329$		−	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	$0.566845\pi$
$332$		−	71.5542i		−	0.215525i
$333$	54.9909			0.165138
$334$	−665.000			−1.99102
$335$		0			0
$336$			973.460i			2.89720i
$337$			243.731i			0.723239i	0.932326	+	0.361619i	$0.117776\pi$
$337$			243.731i			0.723239i	−0.932326	+	0.361619i	$0.882224\pi$
$338$			199.010i			0.588787i
$339$	756.000			2.23009
$340$		0			0
$341$	12.0000	−	30.7409i	0.0351906	−	0.0901491i
$342$	274.955			0.803961
$343$		−	301.869i		−	0.880085i
$344$	150.000			0.436047
$345$		0			0
$346$	−320.000			−0.924855
$347$			4.47214i			0.0128880i	0.999979	+	0.00644400i	$0.00205120\pi$
$347$			4.47214i			0.0128880i	−0.999979	+	0.00644400i	$0.997949\pi$
$348$			46.9574i			0.134935i
$349$		−	512.348i		−	1.46804i	−0.679125	−	0.734022i	$-0.737641\pi$
$349$		−	512.348i		−	1.46804i	0.679125	−	0.734022i	$-0.262359\pi$
$350$		0			0
$351$			122.963i			0.350323i
$352$	160.390	+	62.6099i	0.455654	+	0.177869i
$353$	293.285			0.830835			0.415418	−	0.909631i	$-0.363635\pi$
$353$	293.285			0.830835			0.415418	+	0.909631i	$0.363635\pi$
$354$		−	184.445i		−	0.521031i
$355$		0			0
$356$	37.0000			0.103933
$357$	−801.951			−2.24636
$358$		−	541.128i		−	1.51153i
$359$			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
$362$		−	576.906i		−	1.59366i
$363$	407.849	+	375.659i	1.12355	+	1.03487i
$364$	−100.000			−0.274725
$365$		0			0
$366$	735.000			2.00820
$367$	−430.762			−1.17374			−0.586869	−	0.809682i	$-0.699640\pi$
$367$	−430.762			−1.17374			−0.586869	+	0.809682i	$0.699640\pi$
$368$	522.414			1.41960
$369$		−	245.927i		−	0.666468i
$370$		0			0
$371$		−	51.2348i		−	0.138099i
$372$	−13.7477			−0.0369563
$373$			545.601i			1.46274i	0.681983	+	0.731368i	$0.261118\pi$
$373$			545.601i			1.46274i	−0.681983	+	0.731368i	$0.738882\pi$
$374$	−140.000	+	358.643i	−0.374332	+	0.958939i
$375$		0			0
$376$		−	430.372i		−	1.14461i
$377$	91.6515			0.243107
$378$	343.693			0.909241
$379$	428.000			1.12929			0.564644	−	0.825335i	$-0.309014\pi$
$379$	428.000			1.12929			0.564644	+	0.825335i	$0.309014\pi$
$380$		0			0
$381$			143.457i			0.376528i
$382$		−	621.627i		−	1.62730i
$383$	−164.973			−0.430738			−0.215369	−	0.976533i	$-0.569095\pi$
$383$	−164.973			−0.430738			−0.215369	+	0.976533i	$0.569095\pi$
$384$			707.040i			1.84125i
$385$		0			0
$386$	−175.000			−0.453368
$387$		−	268.328i		−	0.693354i
$388$	−119.147			−0.307080
$389$	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
$392$		−	509.823i		−	1.30057i
$393$		−	986.106i		−	2.50918i
$394$	440.000			1.11675
$395$		0			0
$396$	48.0000	−	122.963i	0.121212	−	0.310514i
$397$	669.056			1.68528			0.842640	−	0.538478i	$-0.181000\pi$
$397$	669.056			1.68528			0.842640	+	0.538478i	$0.181000\pi$
$398$			118.512i			0.297768i
$399$	−525.000			−1.31579
$400$		0			0
$401$	107.000			0.266833			0.133416	−	0.991060i	$-0.457405\pi$
$401$	107.000			0.266833			0.133416	+	0.991060i	$0.457405\pi$
$402$		−	281.745i		−	0.700857i
$403$			26.8328i			0.0665827i
$404$		−	102.470i		−	0.253637i
$405$		0			0
$406$		−	256.174i		−	0.630970i
$407$	−18.3303	+	46.9574i	−0.0450376	+	0.115375i
$408$	−481.170			−1.17934
$409$			327.902i			0.801717i	0.916140	+	0.400859i	$0.131288\pi$
$409$			327.902i			0.801717i	−0.916140	+	0.400859i	$0.868712\pi$
$410$		0			0
$411$	294.000			0.715328
$412$	−18.3303			−0.0444910
$413$			201.246i			0.487279i
$414$		−	737.780i		−	1.78208i
$415$		0			0
$416$	−140.000			−0.336538
$417$			1033.06i			2.47737i
$418$	−91.6515	+	234.787i	−0.219262	+	0.561692i
$419$	−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	$0.661020\pi$
$422$	−389.519			−0.923031
$423$	−769.873			−1.82003
$424$		−	30.7409i		−	0.0725020i
$425$		0			0
$426$		−	276.668i		−	0.649455i
$427$	−801.951			−1.87810
$428$		−	156.525i		−	0.365712i
$429$	−420.000	−	163.951i	−0.979021	−	0.382171i
$430$		0			0
$431$			61.4817i			0.142649i	0.997453	+	0.0713245i	$0.0227226\pi$
$431$			61.4817i			0.142649i	−0.997453	+	0.0713245i	$0.977277\pi$
$432$	261.207			0.604645
$433$	247.459			0.571499			0.285750	−	0.958304i	$-0.407757\pi$
$433$	247.459			0.571499			0.285750	+	0.958304i	$0.407757\pi$
$434$	75.0000			0.172811
$435$		0			0
$436$		−	20.4939i		−	0.0470044i
$437$			281.745i			0.644724i
$438$	−595.735			−1.36013
$439$		−	430.372i		−	0.980346i	−0.871625	−	0.490173i	$-0.836934\pi$
$439$		−	430.372i		−	0.980346i	0.871625	−	0.490173i	$-0.163066\pi$
$440$		0			0
$441$	−912.000			−2.06803
$442$		−	313.050i		−	0.708257i
$443$	−302.450			−0.682731			−0.341366	−	0.939931i	$-0.610889\pi$
$443$	−302.450			−0.682731			−0.341366	+	0.939931i	$0.610889\pi$
$444$	21.0000			0.0472973
$445$		0			0
$446$		−	881.238i		−	1.97587i
$447$		−	704.361i		−	1.57575i
$448$		−	458.394i		−	1.02320i
$449$	−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
$452$	164.973			0.364984
$453$			469.574i			1.03659i
$454$	620.000			1.36564
$455$		0			0
$456$	−315.000			−0.690789
$457$			346.591i			0.758404i	0.925314	+	0.379202i	$0.123801\pi$
$457$			346.591i			0.758404i	−0.925314	+	0.379202i	$0.876199\pi$
$458$		−	652.932i		−	1.42562i
$459$			215.186i			0.468815i
$460$		0			0
$461$		−	338.149i		−	0.733513i	−0.930317	−	0.366756i	$-0.880468\pi$
$461$		−	338.149i		−	0.733513i	0.930317	−	0.366756i	$-0.119532\pi$
$462$	−458.258	+	1173.94i	−0.991900	+	2.54099i
$463$	−623.230			−1.34607			−0.673035	−	0.739611i	$-0.735010\pi$
$463$	−623.230			−1.34607			−0.673035	+	0.739611i	$0.735010\pi$
$464$		−	194.692i		−	0.419595i
$465$		0			0
$466$	−385.000			−0.826180
$467$	554.492			1.18735			0.593674	−	0.804706i	$-0.297677\pi$
$467$	554.492			1.18735			0.593674	+	0.804706i	$0.297677\pi$
$468$			107.331i			0.229340i
$469$			307.409i			0.655455i
$470$		0			0
$471$	−231.000			−0.490446
$472$			120.748i			0.255821i
$473$	229.129	+	89.4427i	0.484416	+	0.189097i
$474$	630.000			1.32911
$475$		0			0
$476$	−175.000			−0.367647
$477$	−54.9909			−0.115285
$478$	504.083			1.05457
$479$		−	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
$482$	733.212			1.52119
$483$			1408.72i			2.91661i
$484$	89.0000	+	81.9756i	0.183884	+	0.169371i
$485$		0			0
$486$			737.780i			1.51807i
$487$	−339.111			−0.696326			−0.348163	−	0.937434i	$-0.613194\pi$
$487$	−339.111			−0.696326			−0.348163	+	0.937434i	$0.613194\pi$
$488$	−481.170			−0.986005
$489$	−1239.00			−2.53374
$490$		0			0
$491$		−	584.076i		−	1.18956i	−0.803887	−	0.594782i	$-0.797238\pi$
$491$		−	584.076i		−	1.18956i	0.803887	−	0.594782i	$-0.202762\pi$
$492$		−	93.9149i		−	0.190884i
$493$	160.390			0.325335
$494$		−	204.939i		−	0.414856i
$495$		0			0
$496$	57.0000			0.114919
$497$			301.869i			0.607383i
$498$	733.212			1.47231
$499$	268.000			0.537074			0.268537	−	0.963269i	$-0.413460\pi$
$499$	268.000			0.537074			0.268537	+	0.963269i	$0.413460\pi$
$500$		0			0
$501$		−	1362.84i		−	2.72025i
$502$			630.571i			1.25612i
$503$		−	541.128i		−	1.07580i	−0.843008	−	0.537901i	$-0.819217\pi$
$503$		−	541.128i		−	1.07580i	0.843008	−	0.537901i	$-0.180783\pi$
$504$	−900.000			−1.78571
$505$		0			0
$506$	630.000	+	245.927i	1.24506	+	0.486021i
$507$	−407.849			−0.804436
$508$			31.3050i			0.0616239i
$509$	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
$512$		−	212.426i		−	0.414895i
$513$			140.872i			0.274605i
$514$		−	143.457i		−	0.279100i
$515$		0			0
$516$		−	102.470i		−	0.198584i
$517$	256.624	−	657.404i	0.496372	−	1.27157i
$518$	−114.564			−0.221167
$519$		−	655.805i		−	1.26359i
$520$		0			0
$521$	242.000			0.464491			0.232246	−	0.972657i	$-0.425393\pi$
$521$	242.000			0.464491			0.232246	+	0.972657i	$0.425393\pi$
$522$	−274.955			−0.526733
$523$			143.108i			0.273630i	0.990597	+	0.136815i	$0.0436865\pi$
$523$			143.108i			0.273630i	−0.990597	+	0.136815i	$0.956313\pi$
$524$		−	215.186i		−	0.410660i
$525$		0			0
$526$	445.000			0.846008
$527$			46.9574i			0.0891033i
$528$	−348.276	+	892.191i	−0.659613	+	1.68976i
$529$	227.000			0.429112
$530$		0			0
$531$	216.000			0.406780
$532$	−114.564			−0.215347
$533$	−183.303			−0.343908
$534$			379.137i			0.709995i
$535$		0			0
$536$			184.445i			0.344114i
$537$	1108.98			2.06515
$538$		−	362.243i		−	0.673314i
$539$	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	$0.866496\pi$
$542$	−549.909			−1.01459
$543$	1182.30			2.17736
$544$	−245.000			−0.450368
$545$		0			0
$546$		−	1024.70i		−	1.87673i
$547$		−	398.020i		−	0.727642i	−0.931469	−	0.363821i	$-0.881472\pi$
$547$		−	398.020i		−	0.727642i	0.931469	−	0.363821i	$-0.118528\pi$
$548$	64.1561			0.117073
$549$			860.744i			1.56784i
$550$		0			0
$551$	105.000			0.190563
$552$			845.234i			1.53122i
$553$	−687.386			−1.24301
$554$	−130.000			−0.234657
$555$		0			0
$556$			225.433i			0.405455i
$557$			156.525i			0.281014i	0.990080	+	0.140507i	$0.0448732\pi$
$557$			156.525i			0.281014i	−0.990080	+	0.140507i	$0.955127\pi$
$558$		−	80.4984i		−	0.144262i
$559$	−200.000			−0.357782
$560$		0			0
$561$	−735.000	−	286.915i	−1.31016	−	0.511434i
$562$	−366.606			−0.652324
$563$		−	881.011i		−	1.56485i	−0.622745	−	0.782425i	$-0.713982\pi$
$563$		−	881.011i		−	1.56485i	0.622745	−	0.782425i	$-0.286018\pi$
$564$	−294.000			−0.521277
$565$		0			0
$566$	−560.000			−0.989399
$567$		−	503.115i		−	0.887329i
$568$			181.122i			0.318876i
$569$			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	$0.822419\pi$
$572$	−91.6515	−	35.7771i	−0.160230	−	0.0625474i
$573$	1273.96			2.22331
$574$			512.348i			0.892592i
$575$		0			0
$576$	−492.000			−0.854167
$577$	164.973			0.285915			0.142957	−	0.989729i	$-0.454339\pi$
$577$	164.973			0.285915			0.142957	+	0.989729i	$0.454339\pi$
$578$			98.3870i			0.170220i
$579$		−	358.643i		−	0.619418i
$580$		0			0
$581$	−800.000			−1.37694
$582$		−	1220.89i		−	2.09775i
$583$	18.3303	−	46.9574i	0.0314413	−	0.0805445i
$584$	390.000			0.667808
$585$		0			0
$586$	−1000.00			−1.70648
$587$	875.272			1.49109			0.745547	−	0.666453i	$-0.232188\pi$
$587$	875.272			1.49109			0.745547	+	0.666453i	$0.232188\pi$
$588$	−348.276			−0.592306
$589$			30.7409i			0.0521916i
$590$		0			0
$591$			901.732i			1.52577i
$592$	−87.0689			−0.147076
$593$			111.803i			0.188539i	0.995547	+	0.0942693i	$0.0300515\pi$
$593$			111.803i			0.188539i	−0.995547	+	0.0942693i	$0.969949\pi$
$594$	315.000	+	122.963i	0.530303	+	0.207009i
$595$		0			0
$596$		−	153.704i		−	0.257893i
$597$	−242.877			−0.406828
$598$	−549.909			−0.919580
$599$	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	$-0.0271686\pi$
$602$			559.017i			0.928600i
$603$	329.945			0.547173
$604$			102.470i			0.169652i
$605$		0			0
$606$	1050.00			1.73267
$607$		−	816.165i		−	1.34459i	−0.740284	−	0.672294i	$-0.765309\pi$
$607$		−	816.165i		−	1.34459i	0.740284	−	0.672294i	$-0.234691\pi$
$608$	−160.390			−0.263800
$609$	525.000			0.862069
$610$		0			0
$611$			573.829i			0.939164i
$612$			187.830i			0.306911i
$613$		−	881.011i		−	1.43721i	−0.695418	−	0.718606i	$-0.744781\pi$
$613$		−	881.011i		−	1.43721i	0.695418	−	0.718606i	$-0.255219\pi$
$614$	−1000.00			−1.62866
$615$		0			0
$616$	300.000	−	768.521i	0.487013	−	1.24760i
$617$	−293.285			−0.475340			−0.237670	−	0.971346i	$-0.576384\pi$
$617$	−293.285			−0.475340			−0.237670	+	0.971346i	$0.576384\pi$
$618$		−	187.830i		−	0.303932i
$619$	−972.000			−1.57027			−0.785137	−	0.619322i	$-0.787408\pi$
$619$	−972.000			−1.57027			−0.785137	+	0.619322i	$0.787408\pi$
$620$		0			0
$621$	378.000			0.608696
$622$			194.538i			0.312762i
$623$		−	413.673i		−	0.664001i
$624$		−	778.768i		−	1.24803i
$625$		0			0
$626$			655.805i			1.04761i
$627$	−481.170	−	187.830i	−0.767417	−	0.299569i
$628$	−50.4083			−0.0802680
$629$		−	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	$0.528540\pi$
$632$	−412.432			−0.652582
$633$		−	798.276i		−	1.26110i
$634$			112.716i			0.177786i
$635$		0			0
$636$	−21.0000			−0.0330189
$637$			679.765i			1.06713i
$638$	91.6515	−	234.787i	0.143654	−	0.368005i
$639$	324.000			0.507042
$640$		0			0
$641$	1007.00			1.57098			0.785491	−	0.618873i	$-0.212410\pi$
$641$	1007.00			1.57098			0.785491	+	0.618873i	$0.212410\pi$
$642$	1603.90			2.49829
$643$	270.372			0.420485			0.210243	−	0.977649i	$-0.432575\pi$
$643$	270.372			0.420485			0.210243	+	0.977649i	$0.432575\pi$
$644$			307.409i			0.477342i
$645$		0			0
$646$		−	358.643i		−	0.555175i
$647$	−18.3303			−0.0283312			−0.0141656	−	0.999900i	$-0.504509\pi$
$647$	−18.3303			−0.0283312			−0.0141656	+	0.999900i	$0.504509\pi$
$648$		−	301.869i		−	0.465847i
$649$	−72.0000	+	184.445i	−0.110940	+	0.284199i
$650$		0			0
$651$			153.704i			0.236105i
$652$	−270.372			−0.414681
$653$	−691.969			−1.05968			−0.529838	−	0.848099i	$-0.677747\pi$
$653$	−691.969			−1.05968			−0.529838	+	0.848099i	$0.677747\pi$
$654$	210.000			0.321101
$655$		0			0
$656$			389.384i			0.593573i
$657$		−	697.653i		−	1.06188i
$658$	1603.90			2.43754
$659$			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	$0.273912\pi$
$662$		−	308.577i		−	0.466129i
$663$	641.561			0.967663
$664$	−480.000			−0.722892
$665$		0			0
$666$			122.963i			0.184630i
$667$		−	281.745i		−	0.422406i
$668$		−	297.397i		−	0.445205i
$669$	1806.00			2.69955
$670$		0			0
$671$	−735.000	−	286.915i	−1.09538	−	0.427593i
$672$	−801.951			−1.19338
$673$			713.306i			1.05989i	0.848032	+	0.529945i	$0.177787\pi$
$673$			713.306i			1.05989i	−0.848032	+	0.529945i	$0.822213\pi$
$674$	−545.000			−0.808605
$675$		0			0
$676$	−89.0000			−0.131657
$677$		−	31.3050i		−	0.0462407i	−0.999733	−	0.0231203i	$-0.992640\pi$
$677$		−	31.3050i		−	0.0462407i	0.999733	−	0.0231203i	$-0.00736009\pi$
$678$			1690.47i			2.49331i
$679$			1332.10i			1.96186i
$680$		0			0
$681$			1270.62i			1.86582i
$682$	68.7386	+	26.8328i	0.100790	+	0.0393443i
$683$	−600.317			−0.878942			−0.439471	−	0.898257i	$-0.644834\pi$
$683$	−600.317			−0.878942			−0.439471	+	0.898257i	$0.644834\pi$
$684$			122.963i			0.179771i
$685$		0			0
$686$	675.000			0.983965
$687$	1338.11			1.94776
$688$			424.853i			0.617519i
$689$			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	$0.282657\pi$
$692$		−	143.108i		−	0.206804i
$693$	−1374.77	−	536.656i	−1.98380	−	0.774396i
$694$	−10.0000			−0.0144092
$695$		0			0
$696$	315.000			0.452586
$697$	−320.780			−0.460230
$698$	1145.64			1.64132
$699$		−	789.015i		−	1.12878i
$700$		0			0
$701$		−	870.991i		−	1.24250i	−0.783613	−	0.621249i	$-0.786626\pi$
$701$		−	870.991i		−	1.24250i	0.783613	−	0.621249i	$-0.213374\pi$
$702$	−274.955			−0.391673
$703$		−	46.9574i		−	0.0667958i
$704$	164.000	−	420.125i	0.232955	−	0.596768i
$705$		0			0
$706$			655.805i			0.928902i
$707$	−1145.64			−1.62043
$708$	82.4864			0.116506
$709$	768.000			1.08322			0.541608	−	0.840631i	$-0.317816\pi$
$709$	768.000			1.08322			0.541608	+	0.840631i	$0.317816\pi$
$710$		0			0
$711$			737.780i			1.03767i
$712$		−	248.204i		−	0.348600i
$713$	82.4864			0.115689
$714$		−	1793.22i		−	2.51151i
$715$		0			0
$716$	242.000			0.337989
$717$			1033.06i			1.44081i
$718$	−1420.60			−1.97855
$719$	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
$722$			572.433i			0.792844i
$723$			1502.64i			2.07834i
$724$	258.000			0.356354
$725$		0			0
$726$	−840.000	+	911.979i	−1.15702	+	1.25617i
$727$	−293.285			−0.403418			−0.201709	−	0.979446i	$-0.564650\pi$
$727$	−293.285			−0.403418			−0.201709	+	0.979446i	$0.564650\pi$
$728$			670.820i			0.921457i
$729$	−1107.00			−1.51852
$730$		0			0
$731$	−350.000			−0.478796
$732$			328.702i			0.449046i
$733$		−	219.135i		−	0.298956i	−0.988765	−	0.149478i	$-0.952241\pi$
$733$		−	219.135i		−	0.298956i	0.988765	−	0.149478i	$-0.0477593\pi$
$734$		−	963.213i		−	1.31228i
$735$		0			0
$736$			430.372i			0.584744i
$737$	−109.982	+	281.745i	−0.149229	+	0.382286i
$738$	549.909			0.745134
$739$			389.384i			0.526907i	0.964672	+	0.263453i	$0.0848615\pi$
$739$			389.384i			0.526907i	−0.964672	+	0.263453i	$0.915138\pi$
$740$		0			0
$741$	420.000			0.566802
$742$	114.564			0.154399
$743$		−	682.001i		−	0.917901i	−0.888462	−	0.458951i	$-0.848225\pi$
$743$		−	682.001i		−	0.917901i	0.888462	−	0.458951i	$-0.151775\pi$
$744$			92.2226i			0.123955i
$745$		0			0
$746$	−1220.00			−1.63539
$747$			858.650i			1.14946i
$748$	−160.390	−	62.6099i	−0.214425	−	0.0837031i
$749$	−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	$0.732754\pi$
$752$	1218.97			1.62096
$753$	−1292.29			−1.71618
$754$			204.939i			0.271802i
$755$		0			0
$756$			153.704i			0.203313i
$757$	1218.97			1.61026			0.805129	−	0.593100i	$-0.202096\pi$
$757$	1218.97			1.61026			0.805129	+	0.593100i	$0.202096\pi$
$758$			957.037i			1.26258i
$759$	−504.000	+	1291.12i	−0.664032	+	1.70107i
$760$		0			0
$761$		−	184.445i		−	0.242372i	−0.992630	−	0.121186i	$-0.961330\pi$
$761$		−	184.445i		−	0.242372i	0.992630	−	0.121186i	$-0.0386698\pi$
$762$	−320.780			−0.420972
$763$	−229.129			−0.300300
$764$	278.000			0.363874
$765$		0			0
$766$		−	368.890i		−	0.481580i
$767$		−	160.997i		−	0.209905i
$768$	−829.446			−1.08001
$769$			245.927i			0.319801i	0.987133	+	0.159900i	$0.0511173\pi$
$769$			245.927i			0.319801i	−0.987133	+	0.159900i	$0.948883\pi$
$770$		0			0
$771$	294.000			0.381323
$772$		−	78.2624i		−	0.101376i
$773$	−279.537			−0.361626			−0.180813	−	0.983517i	$-0.557873\pi$
$773$	−279.537			−0.361626			−0.180813	+	0.983517i	$0.557873\pi$
$774$	600.000			0.775194
$775$		0			0
$776$			799.262i			1.02998i
$777$		−	234.787i		−	0.302171i
$778$			509.823i			0.655300i
$779$	−210.000			−0.269576
$780$		0			0
$781$	−108.000	+	276.668i	−0.138284	+	0.354248i
$782$	−962.341			−1.23061
$783$		−	140.872i		−	0.179914i
$784$	1444.00			1.84184
$785$		0			0
$786$	2205.00			2.80534
$787$			746.847i			0.948979i	0.880261	+	0.474490i	$0.157367\pi$
$787$			746.847i			0.948979i	−0.880261	+	0.474490i	$0.842633\pi$
$788$			196.774i			0.249713i
$789$			911.979i			1.15587i
$790$		0			0
$791$		−	1844.45i		−	2.33180i
$792$	−824.864	−	321.994i	−1.04149	−	0.406558i
$793$	641.561			0.809030
$794$			1496.05i			1.88420i
$795$		0			0
$796$	−53.0000			−0.0665829
$797$	−705.717			−0.885466			−0.442733	−	0.896653i	$-0.645991\pi$
$797$	−705.717			−0.885466			−0.442733	+	0.896653i	$0.645991\pi$
$798$		−	1173.94i		−	1.47110i
$799$			1004.20i			1.25682i
$800$		0			0
$801$	−444.000			−0.554307
$802$			239.259i			0.298328i
$803$	595.735	+	232.551i	0.741886	+	0.289603i
$804$	126.000			0.156716
$805$		0			0
$806$	−60.0000			−0.0744417
$807$	742.377			0.919922
$808$	−687.386			−0.850726
$809$		−	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	$0.763725\pi$
$812$	114.564			0.141089
$813$		−	1126.98i		−	1.38620i
$814$	−105.000	−	40.9878i	−0.128993	−	0.0503536i
$815$		0			0
$816$		−	1362.84i		−	1.67015i
$817$	−229.129			−0.280451
$818$	−733.212			−0.896347
$819$	1200.00			1.46520
$820$		0			0
$821$			758.274i			0.923598i	0.886984	+	0.461799i	$0.152796\pi$
$821$			758.274i			0.923598i	−0.886984	+	0.461799i	$0.847204\pi$
$822$			657.404i			0.799762i
$823$	293.285			0.356361			0.178180	−	0.983998i	$-0.442979\pi$
$823$	293.285			0.356361			0.178180	+	0.983998i	$0.442979\pi$
$824$			122.963i			0.149227i
$825$		0			0
$826$	−450.000			−0.544794
$827$			594.794i			0.719219i	0.933103	+	0.359609i	$0.117090\pi$
$827$			594.794i			0.719219i	−0.933103	+	0.359609i	$0.882910\pi$
$828$	329.945			0.398485
$829$	−102.000			−0.123040			−0.0615199	−	0.998106i	$-0.519595\pi$
$829$	−102.000			−0.123040			−0.0615199	+	0.998106i	$0.519595\pi$
$830$		0			0
$831$		−	266.421i		−	0.320603i
$832$			366.715i			0.440763i
$833$			1189.59i			1.42808i
$834$	−2310.00			−2.76978
$835$		0			0
$836$	−105.000	−	40.9878i	−0.125598	−	0.0490285i
$837$	41.2432			0.0492750
$838$		−	1614.44i		−	1.92654i
$839$	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
$842$		−	912.316i		−	1.08351i
$843$		−	751.319i		−	0.891244i
$844$		−	174.198i		−	0.206396i
$845$		0			0
$846$		−	1721.49i		−	2.03486i
$847$	916.515	−	995.050i	1.08207	−	1.17479i
$848$	87.0689			0.102676
$849$		−	1147.66i		−	1.35178i
$850$		0			0
$851$	−126.000			−0.148061
$852$	123.730			0.145222
$853$			532.184i			0.623897i	0.950099	+	0.311949i	$0.100982\pi$
$853$			532.184i			0.623897i	−0.950099	+	0.311949i	$0.899018\pi$
$854$		−	1793.22i		−	2.09978i
$855$		0			0
$856$	−1050.00			−1.22664
$857$		−	950.329i		−	1.10890i	−0.832216	−	0.554451i	$-0.812928\pi$
$857$		−	950.329i		−	1.10890i	0.832216	−	0.554451i	$-0.187072\pi$
$858$	366.606	−	939.149i	0.427280	−	1.09458i
$859$	1068.00			1.24331			0.621653	−	0.783293i	$-0.286461\pi$
$859$	1068.00			1.24331			0.621653	+	0.783293i	$0.286461\pi$
$860$		0			0
$861$	−1050.00			−1.21951
$862$	−137.477			−0.159486
$863$	−73.3212			−0.0849608			−0.0424804	−	0.999097i	$-0.513526\pi$
$863$	−73.3212			−0.0849608			−0.0424804	+	0.999097i	$0.513526\pi$
$864$			215.186i			0.249058i
$865$		0			0
$866$			553.335i			0.638955i
$867$	−201.633			−0.232564
$868$			33.5410i			0.0386417i
$869$	−630.000	−	245.927i	−0.724971	−	0.283000i
$870$		0			0
$871$		−	245.927i		−	0.282350i
$872$	−137.477			−0.157657
$873$	1429.76			1.63776
$874$	−630.000			−0.720824
$875$		0			0
$876$		−	266.421i		−	0.304133i
$877$			169.941i			0.193776i	0.995295	+	0.0968878i	$0.0308888\pi$
$877$			169.941i			0.193776i	−0.995295	+	0.0968878i	$0.969111\pi$
$878$	962.341			1.09606
$879$		−	2049.39i		−	2.33150i
$880$		0			0
$881$	−78.0000			−0.0885358			−0.0442679	−	0.999020i	$-0.514096\pi$
$881$	−78.0000			−0.0885358			−0.0442679	+	0.999020i	$0.514096\pi$
$882$		−	2039.29i		−	2.31212i
$883$	1553.49			1.75934			0.879668	−	0.475589i	$-0.157765\pi$
$883$	1553.49			1.75934			0.879668	+	0.475589i	$0.157765\pi$
$884$	140.000			0.158371
$885$		0			0
$886$		−	676.299i		−	0.763317i
$887$			299.633i			0.337805i	0.985633	+	0.168903i	$0.0540223\pi$
$887$			299.633i			0.337805i	−0.985633	+	0.168903i	$0.945978\pi$
$888$		−	140.872i		−	0.158640i
$889$	350.000			0.393701
$890$		0			0
$891$	180.000	−	461.113i	0.202020	−	0.517523i
$892$	394.102			0.441818
$893$			657.404i			0.736175i
$894$	1575.00			1.76174
$895$		0			0
$896$	1725.00			1.92522
$897$		−	1126.98i		−	1.25639i
$898$		−	49.1935i		−	0.0547812i
$899$		−	30.7409i		−	0.0341945i
$900$		0			0
$901$			71.7287i			0.0796101i
$902$	−183.303	+	469.574i	−0.203218	+	0.520592i
$903$	−1145.64			−1.26871
$904$		−	1106.67i		−	1.22419i
$905$		0			0
$906$	−1050.00			−1.15894
$907$	691.969			0.762921			0.381460	−	0.924385i	$-0.375421\pi$
$907$	691.969			0.762921			0.381460	+	0.924385i	$0.375421\pi$
$908$			277.272i			0.305366i
$909$			1229.63i			1.35273i
$910$		0			0
$911$	1037.00			1.13831			0.569155	−	0.822230i	$-0.307271\pi$
$911$	1037.00			1.13831			0.569155	+	0.822230i	$0.307271\pi$
$912$		−	892.191i		−	0.978280i
$913$	−733.212	−	286.217i	−0.803080	−	0.313490i
$914$	−775.000			−0.847921
$915$		0			0
$916$	292.000			0.318777
$917$	−2405.85			−2.62361
$918$	−481.170			−0.524151
$919$			1782.97i			1.94012i	0.242867	+	0.970060i	$0.421912\pi$
$919$			1782.97i			1.94012i	−0.242867	+	0.970060i	$0.578088\pi$
$920$		0			0
$921$		−	2049.39i		−	2.22518i
$922$	756.125			0.820092
$923$		−	241.495i		−	0.261642i
$924$	−525.000	−	204.939i	−0.568182	−	0.221795i
$925$		0			0
$926$		−	1393.59i		−	1.50495i
$927$	219.964			0.237285
$928$	160.390			0.172834
$929$	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
$932$		−	172.177i		−	0.184740i
$933$	−398.684			−0.427314
$934$			1239.88i			1.32750i
$935$		0			0
$936$	720.000			0.769231
$937$		−	728.958i		−	0.777970i	−0.921244	−	0.388985i	$-0.872826\pi$
$937$		−	728.958i		−	0.777970i	0.921244	−	0.388985i	$-0.127174\pi$
$938$	−687.386			−0.732821
$939$	−1344.00			−1.43131
$940$		0			0
$941$			850.497i			0.903822i	0.892063	+	0.451911i	$0.149258\pi$
$941$			850.497i			0.903822i	−0.892063	+	0.451911i	$0.850742\pi$
$942$		−	516.532i		−	0.548335i
$943$			563.489i			0.597549i
$944$	−342.000			−0.362288
$945$		0			0
$946$	−200.000	+	512.348i	−0.211416	+	0.541594i
$947$	−911.933			−0.962970			−0.481485	−	0.876454i	$-0.659902\pi$
$947$	−911.933			−0.962970			−0.481485	+	0.876454i	$0.659902\pi$
$948$			281.745i			0.297199i
$949$	−520.000			−0.547945
$950$		0			0
$951$	−231.000			−0.242902
$952$			1173.94i			1.23313i
$953$			1236.55i			1.29753i	0.760989	+	0.648765i	$0.224714\pi$
$953$			1236.55i			1.29753i	−0.760989	+	0.648765i	$0.775286\pi$
$954$		−	122.963i		−	0.128892i
$955$		0			0
$956$			225.433i			0.235808i
$957$	481.170	+	187.830i	0.502790	+	0.196269i
$958$	91.6515			0.0956696
$959$		−	717.287i		−	0.747953i
$960$		0			0
$961$	−952.000			−0.990635
$962$	91.6515			0.0952718
$963$			1878.30i			1.95046i
$964$			327.902i			0.340148i
$965$		0			0
$966$	−3150.00			−3.26087
$967$			431.561i			0.446289i	0.974785	+	0.223144i	$0.0716321\pi$
$967$			431.561i			0.446289i	−0.974785	+	0.223144i	$0.928368\pi$
$968$	549.909	−	597.030i	0.568088	−	0.616767i
$969$	735.000			0.758514
$970$		0			0
$971$	−1048.00			−1.07930			−0.539650	−	0.841890i	$-0.681443\pi$
$971$	−1048.00			−1.07930			−0.539650	+	0.841890i	$0.681443\pi$
$972$	−329.945			−0.339450
$973$	2520.42			2.59036
$974$		−	758.274i		−	0.778516i
$975$		0			0
$976$		−	1362.84i		−	1.39636i
$977$	−247.459			−0.253285			−0.126642	−	0.991948i	$-0.540420\pi$
$977$	−247.459			−0.253285			−0.126642	+	0.991948i	$0.540420\pi$
$978$		−	2770.49i		−	2.83281i
$979$	148.000	−	379.137i	0.151175	−	0.387270i
$980$		0			0
$981$			245.927i			0.250690i
$982$	1306.03			1.32997
$983$	−27.4955			−0.0279710			−0.0139855	−	0.999902i	$-0.504452\pi$
$983$	−27.4955			−0.0279710			−0.0139855	+	0.999902i	$0.504452\pi$
$984$	−630.000			−0.640244
$985$		0			0
$986$			358.643i			0.363736i
$987$			3287.02i			3.33031i
$988$	91.6515			0.0927647
$989$			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	$0.296610\pi$
$992$			46.9574i			0.0473361i
$993$	632.395			0.636853
$994$	−675.000			−0.679074
$995$		0			0
$996$			327.902i			0.329219i
$997$		−	1694.94i		−	1.70004i	−0.526751	−	0.850020i	$-0.676590\pi$
$997$		−	1694.94i		−	1.70004i	0.526751	−	0.850020i	$-0.323410\pi$
$998$			599.266i			0.600467i
$999$	−63.0000			−0.0630631

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.c.e.76.3		4
5.2	odd	4		55.3.d.d.54.2	yes	4
5.3	odd	4		55.3.d.d.54.3	yes	4
5.4	even	2	inner	275.3.c.e.76.2		4
11.10	odd	2	inner	275.3.c.e.76.1		4
15.2	even	4		495.3.h.d.109.4		4
15.8	even	4		495.3.h.d.109.1		4
20.3	even	4		880.3.i.d.769.3		4
20.7	even	4		880.3.i.d.769.2		4
55.32	even	4		55.3.d.d.54.4	yes	4
55.43	even	4		55.3.d.d.54.1	✓	4
55.54	odd	2	inner	275.3.c.e.76.4		4
165.32	odd	4		495.3.h.d.109.2		4
165.98	odd	4		495.3.h.d.109.3		4
220.43	odd	4		880.3.i.d.769.4		4
220.87	odd	4		880.3.i.d.769.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.d.d.54.1	✓	4	55.43	even	4
55.3.d.d.54.2	yes	4	5.2	odd	4
55.3.d.d.54.3	yes	4	5.3	odd	4
55.3.d.d.54.4	yes	4	55.32	even	4
275.3.c.e.76.1		4	11.10	odd	2	inner
275.3.c.e.76.2		4	5.4	even	2	inner
275.3.c.e.76.3		4	1.1	even	1	trivial
275.3.c.e.76.4		4	55.54	odd	2	inner
495.3.h.d.109.1		4	15.8	even	4
495.3.h.d.109.2		4	165.32	odd	4
495.3.h.d.109.3		4	165.98	odd	4
495.3.h.d.109.4		4	15.2	even	4
880.3.i.d.769.1		4	220.87	odd	4
880.3.i.d.769.2		4	20.7	even	4
880.3.i.d.769.3		4	20.3	even	4
880.3.i.d.769.4		4	220.43	odd	4

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.23607i q^{2} -4.58258 q^{3} -1.00000 q^{4} -10.2470i q^{6} +11.1803i q^{7} +6.70820i q^{8} +12.0000 q^{9} +(-4.00000 + 10.2470i) q^{11} +4.58258 q^{12} -8.94427i q^{13} -25.0000 q^{14} -19.0000 q^{16} -15.6525i q^{17} +26.8328i q^{18} -10.2470i q^{19} -51.2348i q^{21} +(-22.9129 - 8.94427i) q^{22} -27.4955 q^{23} -30.7409i q^{24} +20.0000 q^{26} -13.7477 q^{27} -11.1803i q^{28} +10.2470i q^{29} -3.00000 q^{31} -15.6525i q^{32} +(18.3303 - 46.9574i) q^{33} +35.0000 q^{34} -12.0000 q^{36} +4.58258 q^{37} +22.9129 q^{38} +40.9878i q^{39} -20.4939i q^{41} +114.564 q^{42} -22.3607i q^{43} +(4.00000 - 10.2470i) q^{44} -61.4817i q^{46} -64.1561 q^{47} +87.0689 q^{48} -76.0000 q^{49} +71.7287i q^{51} +8.94427i q^{52} -4.58258 q^{53} -30.7409i q^{54} -75.0000 q^{56} +46.9574i q^{57} -22.9129 q^{58} +18.0000 q^{59} +71.7287i q^{61} -6.70820i q^{62} +134.164i q^{63} -41.0000 q^{64} +(105.000 + 40.9878i) q^{66} +27.4955 q^{67} +15.6525i q^{68} +126.000 q^{69} +27.0000 q^{71} +80.4984i q^{72} -58.1378i q^{73} +10.2470i q^{74} +10.2470i q^{76} +(-114.564 - 44.7214i) q^{77} -91.6515 q^{78} +61.4817i q^{79} -45.0000 q^{81} +45.8258 q^{82} +71.5542i q^{83} +51.2348i q^{84} +50.0000 q^{86} -46.9574i q^{87} +(-68.7386 - 26.8328i) q^{88} -37.0000 q^{89} +100.000 q^{91} +27.4955 q^{92} +13.7477 q^{93} -143.457i q^{94} +71.7287i q^{96} +119.147 q^{97} -169.941i q^{98} +(-48.0000 + 122.963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 48 q^{9} - 16 q^{11} - 100 q^{14} - 76 q^{16} + 80 q^{26} - 12 q^{31} + 140 q^{34} - 48 q^{36} + 16 q^{44} - 304 q^{49} - 300 q^{56} + 72 q^{59} - 164 q^{64} + 420 q^{66} + 504 q^{69} + 108 q^{71}+ \cdots - 192 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 48 * q^9 - 16 * q^11 - 100 * q^14 - 76 * q^16 + 80 * q^26 - 12 * q^31 + 140 * q^34 - 48 * q^36 + 16 * q^44 - 304 * q^49 - 300 * q^56 + 72 * q^59 - 164 * q^64 + 420 * q^66 + 504 * q^69 + 108 * q^71 - 180 * q^81 + 200 * q^86 - 148 * q^89 + 400 * q^91 - 192 * q^99

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