LMFDB - Embedded newform 275.3.c.g.76.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(76,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [8,0,-4,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 21x^{6} + 130x^{4} + 215x^{2} + 25 $ x^8 + 21x^6 + 130x^4 + 215*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.6
Root			$1.54705i$ of defining polynomial
Character	$\chi$	$=$	275.76
Dual form			275.3.c.g.76.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.54705i q^{2} +4.06604 q^{3} +1.60665 q^{4} +6.29036i q^{6} -8.53587i q^{7} +8.67374i q^{8} +7.53270 q^{9} +(7.63571 - 7.91807i) q^{11} +6.53270 q^{12} +16.6490i q^{13} +13.2054 q^{14} -6.99209 q^{16} +5.33961i q^{17} +11.6534i q^{18} +0.884280i q^{19} -34.7072i q^{21} +(12.2496 + 11.8128i) q^{22} +20.2635 q^{23} +35.2678i q^{24} -25.7568 q^{26} -5.96611 q^{27} -13.7141i q^{28} -40.3082i q^{29} -51.5865 q^{31} +23.8779i q^{32} +(31.0471 - 32.1952i) q^{33} -8.26062 q^{34} +12.1024 q^{36} +10.7964 q^{37} -1.36802 q^{38} +67.6956i q^{39} -36.1941i q^{41} +53.6937 q^{42} +74.3649i q^{43} +(12.2679 - 12.7216i) q^{44} +31.3486i q^{46} -72.2589 q^{47} -28.4301 q^{48} -23.8611 q^{49} +21.7111i q^{51} +26.7491i q^{52} -13.8913 q^{53} -9.22985i q^{54} +74.0380 q^{56} +3.59552i q^{57} +62.3587 q^{58} -26.9285 q^{59} +45.5691i q^{61} -79.8067i q^{62} -64.2981i q^{63} -64.9086 q^{64} +(49.8075 + 48.0314i) q^{66} -78.3584 q^{67} +8.57887i q^{68} +82.3923 q^{69} +66.9670 q^{71} +65.3367i q^{72} -27.9462i q^{73} +16.7026i q^{74} +1.42073i q^{76} +(-67.5876 - 65.1775i) q^{77} -104.728 q^{78} -10.4721i q^{79} -92.0527 q^{81} +55.9939 q^{82} -121.282i q^{83} -55.7623i q^{84} -115.046 q^{86} -163.895i q^{87} +(68.6793 + 66.2302i) q^{88} +19.7361 q^{89} +142.114 q^{91} +32.5563 q^{92} -209.753 q^{93} -111.788i q^{94} +97.0885i q^{96} +148.321 q^{97} -36.9142i q^{98} +(57.5175 - 59.6444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 10 q^{4} + 32 q^{9} - q^{11} + 24 q^{12} + 18 q^{14} - 14 q^{16} + 35 q^{22} - 4 q^{23} + 68 q^{26} - 142 q^{27} - 42 q^{31} + 31 q^{33} - 142 q^{34} - 84 q^{36} + 104 q^{37} - 190 q^{38}+ \cdots + 368 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 10 * q^4 + 32 * q^9 - q^11 + 24 * q^12 + 18 * q^14 - 14 * q^16 + 35 * q^22 - 4 * q^23 + 68 * q^26 - 142 * q^27 - 42 * q^31 + 31 * q^33 - 142 * q^34 - 84 * q^36 + 104 * q^37 - 190 * q^38 - 50 * q^42 + 69 * q^44 + 64 * q^47 + 86 * q^48 - 50 * q^49 + 286 * q^53 + 166 * q^56 + 130 * q^58 - 160 * q^59 + 288 * q^64 - 315 * q^66 - 46 * q^67 - 16 * q^69 + 246 * q^71 - 80 * q^77 - 620 * q^78 + 304 * q^81 - 280 * q^82 - 282 * q^86 + 365 * q^88 - 18 * q^89 - 142 * q^91 - 26 * q^92 - 818 * q^93 + 264 * q^97 + 368 * 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 $

$2$			1.54705i			0.773523i	0.922180	+	0.386762i	$0.126406\pi$
$2$			1.54705i			0.773523i	−0.922180	+	0.386762i	$0.873594\pi$
$3$	4.06604			1.35535			0.677674	−	0.735363i	$-0.262988\pi$
$3$	4.06604			1.35535			0.677674	+	0.735363i	$0.262988\pi$
$4$	1.60665			0.401662
$5$		0			0
$5$		0			0
$6$			6.29036i			1.04839i
$7$		−	8.53587i		−	1.21941i	−0.792628	−	0.609705i	$-0.791288\pi$
$7$		−	8.53587i		−	1.21941i	0.792628	−	0.609705i	$-0.208712\pi$
$8$			8.67374i			1.08422i
$9$	7.53270			0.836966
$10$		0			0
$11$	7.63571	−	7.91807i	0.694156	−	0.719825i
$11$	7.63571	−	7.91807i	0.694156	−	0.719825i
$12$	6.53270			0.544391
$13$			16.6490i			1.28069i	0.768086	+	0.640347i	$0.221209\pi$
$13$			16.6490i			1.28069i	−0.768086	+	0.640347i	$0.778791\pi$
$14$	13.2054			0.943242
$15$		0			0
$16$	−6.99209			−0.437006
$17$			5.33961i			0.314095i	0.987591	+	0.157047i	$0.0501975\pi$
$17$			5.33961i			0.314095i	−0.987591	+	0.157047i	$0.949802\pi$
$18$			11.6534i			0.647413i
$19$			0.884280i			0.0465410i	0.999729	+	0.0232705i	$0.00740790\pi$
$19$			0.884280i			0.0465410i	−0.999729	+	0.0232705i	$0.992592\pi$
$20$		0			0
$21$		−	34.7072i		−	1.65272i
$22$	12.2496	+	11.8128i	0.556801	+	0.536946i
$23$	20.2635			0.881023			0.440511	−	0.897747i	$-0.354797\pi$
$23$	20.2635			0.881023			0.440511	+	0.897747i	$0.354797\pi$
$24$			35.2678i			1.46949i
$25$		0			0
$26$	−25.7568			−0.990646
$27$	−5.96611			−0.220967
$28$		−	13.7141i		−	0.489791i
$29$		−	40.3082i		−	1.38994i	−0.719040	−	0.694969i	$-0.755418\pi$
$29$		−	40.3082i		−	1.38994i	0.719040	−	0.694969i	$-0.244582\pi$
$30$		0			0
$31$	−51.5865			−1.66408			−0.832040	−	0.554716i	$-0.812827\pi$
$31$	−51.5865			−1.66408			−0.832040	+	0.554716i	$0.812827\pi$
$32$			23.8779i			0.746184i
$33$	31.0471	−	32.1952i	0.940822	−	0.975613i
$34$	−8.26062			−0.242959
$35$		0			0
$36$	12.1024			0.336178
$37$	10.7964			0.291795			0.145898	−	0.989300i	$-0.453393\pi$
$37$	10.7964			0.291795			0.145898	+	0.989300i	$0.453393\pi$
$38$	−1.36802			−0.0360006
$39$			67.6956i			1.73578i
$40$		0			0
$41$		−	36.1941i		−	0.882783i	−0.897315	−	0.441391i	$-0.854485\pi$
$41$		−	36.1941i		−	0.882783i	0.897315	−	0.441391i	$-0.145515\pi$
$42$	53.6937			1.27842
$43$			74.3649i			1.72942i	0.502275	+	0.864708i	$0.332496\pi$
$43$			74.3649i			1.72942i	−0.502275	+	0.864708i	$0.667504\pi$
$44$	12.2679	−	12.7216i	0.278816	−	0.289126i
$45$		0			0
$46$			31.3486i			0.681491i
$47$	−72.2589			−1.53742			−0.768712	−	0.639595i	$-0.779102\pi$
$47$	−72.2589			−1.53742			−0.768712	+	0.639595i	$0.779102\pi$
$48$	−28.4301			−0.592295
$49$	−23.8611			−0.486961
$50$		0			0
$51$			21.7111i			0.425707i
$52$			26.7491i			0.514406i
$53$	−13.8913			−0.262101			−0.131050	−	0.991376i	$-0.541835\pi$
$53$	−13.8913			−0.262101			−0.131050	+	0.991376i	$0.541835\pi$
$54$		−	9.22985i		−	0.170923i
$55$		0			0
$56$	74.0380			1.32211
$57$			3.59552i			0.0630793i
$58$	62.3587			1.07515
$59$	−26.9285			−0.456415			−0.228208	−	0.973612i	$-0.573287\pi$
$59$	−26.9285			−0.456415			−0.228208	+	0.973612i	$0.573287\pi$
$60$		0			0
$61$			45.5691i			0.747035i	0.927623	+	0.373517i	$0.121848\pi$
$61$			45.5691i			0.747035i	−0.927623	+	0.373517i	$0.878152\pi$
$62$		−	79.8067i		−	1.28720i
$63$		−	64.2981i		−	1.02061i
$64$	−64.9086			−1.01420
$65$		0			0
$66$	49.8075	+	48.0314i	0.754659	+	0.727748i
$67$	−78.3584			−1.16953			−0.584764	−	0.811203i	$-0.698813\pi$
$67$	−78.3584			−1.16953			−0.584764	+	0.811203i	$0.698813\pi$
$68$			8.57887i			0.126160i
$69$	82.3923			1.19409
$70$		0			0
$71$	66.9670			0.943197			0.471598	−	0.881813i	$-0.343677\pi$
$71$	66.9670			0.943197			0.471598	+	0.881813i	$0.343677\pi$
$72$			65.3367i			0.907454i
$73$		−	27.9462i		−	0.382825i	−0.981510	−	0.191412i	$-0.938693\pi$
$73$		−	27.9462i		−	0.382825i	0.981510	−	0.191412i	$-0.0613067\pi$
$74$			16.7026i			0.225710i
$75$		0			0
$76$			1.42073i			0.0186938i
$77$	−67.5876	−	65.1775i	−0.877762	−	0.846461i
$78$	−104.728			−1.34267
$79$		−	10.4721i		−	0.132558i	−0.997801	−	0.0662789i	$-0.978887\pi$
$79$		−	10.4721i		−	0.132558i	0.997801	−	0.0662789i	$-0.0211127\pi$
$80$		0			0
$81$	−92.0527			−1.13645
$82$	55.9939			0.682853
$83$		−	121.282i		−	1.46123i	−0.682791	−	0.730614i	$-0.739234\pi$
$83$		−	121.282i		−	1.46123i	0.682791	−	0.730614i	$-0.260766\pi$
$84$		−	55.7623i		−	0.663836i
$85$		0			0
$86$	−115.046			−1.33774
$87$		−	163.895i		−	1.88385i
$88$	68.6793	+	66.2302i	0.780447	+	0.752616i
$89$	19.7361			0.221754			0.110877	−	0.993834i	$-0.464634\pi$
$89$	19.7361			0.221754			0.110877	+	0.993834i	$0.464634\pi$
$90$		0			0
$91$	142.114			1.56169
$92$	32.5563			0.353873
$93$	−209.753			−2.25541
$94$		−	111.788i		−	1.18923i
$95$		0			0
$96$			97.0885i			1.01134i
$97$	148.321			1.52909			0.764543	−	0.644573i	$-0.222965\pi$
$97$	148.321			1.52909			0.764543	+	0.644573i	$0.222965\pi$
$98$		−	36.9142i		−	0.376676i
$99$	57.5175	−	59.6444i	0.580985	−	0.602469i
$100$		0			0
$101$		−	119.352i		−	1.18171i	−0.806779	−	0.590853i	$-0.798791\pi$
$101$		−	119.352i		−	1.18171i	0.806779	−	0.590853i	$-0.201209\pi$
$102$	−33.5880			−0.329294
$103$	−163.050			−1.58300			−0.791502	−	0.611166i	$-0.790701\pi$
$103$	−163.050			−1.58300			−0.791502	+	0.611166i	$0.790701\pi$
$104$	−144.409			−1.38855
$105$		0			0
$106$		−	21.4906i		−	0.202741i
$107$			96.1684i			0.898770i	0.893338	+	0.449385i	$0.148357\pi$
$107$			96.1684i			0.898770i	−0.893338	+	0.449385i	$0.851643\pi$
$108$	−9.58544			−0.0887541
$109$		−	156.781i		−	1.43836i	−0.694823	−	0.719181i	$-0.744517\pi$
$109$		−	156.781i		−	1.43836i	0.694823	−	0.719181i	$-0.255483\pi$
$110$		0			0
$111$	43.8987			0.395484
$112$			59.6836i			0.532889i
$113$	72.2303			0.639206			0.319603	−	0.947552i	$-0.396450\pi$
$113$	72.2303			0.639206			0.319603	+	0.947552i	$0.396450\pi$
$114$	−5.56243			−0.0487933
$115$		0			0
$116$		−	64.7611i		−	0.558285i
$117$			125.412i			1.07190i
$118$		−	41.6597i		−	0.353048i
$119$	45.5782			0.383010
$120$		0			0
$121$	−4.39172	−	120.920i	−0.0362952	−	0.999341i
$122$	−70.4975			−0.577849
$123$		−	147.167i		−	1.19648i
$124$	−82.8813			−0.668397
$125$		0			0
$126$	99.4722			0.789462
$127$		−	113.469i		−	0.893454i	−0.894670	−	0.446727i	$-0.852590\pi$
$127$		−	113.469i		−	0.893454i	0.894670	−	0.446727i	$-0.147410\pi$
$128$		−	4.90501i		−	0.0383204i
$129$			302.371i			2.34396i
$130$		0			0
$131$			125.812i			0.960398i	0.877160	+	0.480199i	$0.159435\pi$
$131$			125.812i			0.960398i	−0.877160	+	0.480199i	$0.840565\pi$
$132$	49.8818	−	51.7264i	0.377893	−	0.391866i
$133$	7.54810			0.0567526
$134$		−	121.224i		−	0.904658i
$135$		0			0
$136$	−46.3144			−0.340547
$137$	−79.0330			−0.576883			−0.288442	−	0.957497i	$-0.593137\pi$
$137$	−79.0330			−0.576883			−0.288442	+	0.957497i	$0.593137\pi$
$138$			127.465i			0.923658i
$139$			105.709i			0.760496i	0.924885	+	0.380248i	$0.124161\pi$
$139$			105.709i			0.760496i	−0.924885	+	0.380248i	$0.875839\pi$
$140$		0			0
$141$	−293.808			−2.08374
$142$			103.601i			0.729585i
$143$	131.828	+	127.127i	0.921875	+	0.889001i
$144$	−52.6693			−0.365759
$145$		0			0
$146$	43.2341			0.296124
$147$	−97.0202			−0.660001
$148$	17.3461			0.117203
$149$			238.710i			1.60208i	0.598609	+	0.801041i	$0.295720\pi$
$149$			238.710i			1.60208i	−0.598609	+	0.801041i	$0.704280\pi$
$150$		0			0
$151$			284.704i			1.88545i	0.333565	+	0.942727i	$0.391748\pi$
$151$			284.704i			1.88545i	−0.333565	+	0.942727i	$0.608252\pi$
$152$	−7.67002			−0.0504606
$153$			40.2217i			0.262887i
$154$	100.833	−	104.561i	0.654757	−	0.678969i
$155$		0			0
$156$			108.763i			0.697199i
$157$	152.650			0.972293			0.486146	−	0.873877i	$-0.338402\pi$
$157$	152.650			0.972293			0.486146	+	0.873877i	$0.338402\pi$
$158$	16.2008			0.102537
$159$	−56.4828			−0.355238
$160$		0			0
$161$		−	172.967i		−	1.07433i
$162$		−	142.410i		−	0.879073i
$163$	246.798			1.51410			0.757048	−	0.653359i	$-0.226641\pi$
$163$	246.798			1.51410			0.757048	+	0.653359i	$0.226641\pi$
$164$		−	58.1511i		−	0.354580i
$165$		0			0
$166$	187.629			1.13029
$167$		−	124.912i		−	0.747978i	−0.927433	−	0.373989i	$-0.877990\pi$
$167$		−	124.912i		−	0.747978i	0.927433	−	0.373989i	$-0.122010\pi$
$168$	301.041			1.79191
$169$	−108.190			−0.640176
$170$		0			0
$171$			6.66101i			0.0389533i
$172$			119.478i			0.694641i
$173$		−	79.2272i		−	0.457961i	−0.973431	−	0.228980i	$-0.926461\pi$
$173$		−	79.2272i		−	0.457961i	0.973431	−	0.228980i	$-0.0735392\pi$
$174$	253.553			1.45720
$175$		0			0
$176$	−53.3896	+	55.3639i	−0.303350	+	0.314568i
$177$	−109.492			−0.618602
$178$			30.5327i			0.171532i
$179$	320.405			1.78997			0.894985	−	0.446097i	$-0.147186\pi$
$179$	320.405			1.78997			0.894985	+	0.446097i	$0.147186\pi$
$180$		0			0
$181$	62.4120			0.344818			0.172409	−	0.985025i	$-0.444845\pi$
$181$	62.4120			0.344818			0.172409	+	0.985025i	$0.444845\pi$
$182$			219.857i			1.20800i
$183$			185.286i			1.01249i
$184$			175.761i			0.955221i
$185$		0			0
$186$		−	324.497i		−	1.74461i
$187$	42.2794	+	40.7717i	0.226093	+	0.218031i
$188$	−116.095			−0.617525
$189$			50.9260i			0.269450i
$190$		0			0
$191$	45.7787			0.239679			0.119840	−	0.992793i	$-0.461762\pi$
$191$	45.7787			0.239679			0.119840	+	0.992793i	$0.461762\pi$
$192$	−263.921			−1.37459
$193$			273.871i			1.41902i	0.704694	+	0.709511i	$0.251084\pi$
$193$			273.871i			1.41902i	−0.704694	+	0.709511i	$0.748916\pi$
$194$			229.460i			1.18278i
$195$		0			0
$196$	−38.3364			−0.195594
$197$		−	168.083i		−	0.853214i	−0.904437	−	0.426607i	$-0.859709\pi$
$197$		−	168.083i		−	0.853214i	0.904437	−	0.426607i	$-0.140291\pi$
$198$	92.2727	+	88.9823i	0.466024	+	0.449405i
$199$	−304.174			−1.52851			−0.764256	−	0.644913i	$-0.776894\pi$
$199$	−304.174			−1.52851			−0.764256	+	0.644913i	$0.776894\pi$
$200$		0			0
$201$	−318.609			−1.58512
$202$	184.644			0.914078
$203$	−344.066			−1.69490
$204$			34.8820i			0.170990i
$205$		0			0
$206$		−	252.245i		−	1.22449i
$207$	152.639			0.737386
$208$		−	116.411i		−	0.559670i
$209$	7.00179	+	6.75211i	0.0335014	+	0.0323067i
$210$		0			0
$211$			31.8928i			0.151151i	0.997140	+	0.0755754i	$0.0240793\pi$
$211$			31.8928i			0.151151i	−0.997140	+	0.0755754i	$0.975921\pi$
$212$	−22.3185			−0.105276
$213$	272.291			1.27836
$214$	−148.777			−0.695219
$215$		0			0
$216$		−	51.7485i		−	0.239577i
$217$			440.335i			2.02920i
$218$	242.548			1.11261
$219$		−	113.630i		−	0.518860i
$220$		0			0
$221$	−88.8992			−0.402259
$222$			67.9134i			0.305916i
$223$	−140.029			−0.627931			−0.313965	−	0.949434i	$-0.601658\pi$
$223$	−140.029			−0.627931			−0.313965	+	0.949434i	$0.601658\pi$
$224$	203.819			0.909904
$225$		0			0
$226$			111.744i			0.494441i
$227$		−	153.141i		−	0.674629i	−0.941392	−	0.337314i	$-0.890481\pi$
$227$		−	153.141i		−	0.674629i	0.941392	−	0.337314i	$-0.109519\pi$
$228$			5.77673i			0.0253365i
$229$	199.559			0.871435			0.435717	−	0.900084i	$-0.356495\pi$
$229$	199.559			0.871435			0.435717	+	0.900084i	$0.356495\pi$
$230$		0			0
$231$	−274.814	−	265.014i	−1.18967	−	1.14725i
$232$	349.623			1.50700
$233$			102.599i			0.440338i	0.975462	+	0.220169i	$0.0706609\pi$
$233$			102.599i			0.440338i	−0.975462	+	0.220169i	$0.929339\pi$
$234$	−194.018			−0.829138
$235$		0			0
$236$	−43.2646			−0.183325
$237$		−	42.5799i		−	0.179662i
$238$			70.5116i			0.296267i
$239$		−	366.949i		−	1.53535i	−0.640838	−	0.767676i	$-0.721413\pi$
$239$		−	366.949i		−	1.53535i	0.640838	−	0.767676i	$-0.278587\pi$
$240$		0			0
$241$			199.190i			0.826513i	0.910615	+	0.413256i	$0.135609\pi$
$241$			199.190i			0.826513i	−0.910615	+	0.413256i	$0.864391\pi$
$242$	187.069	−	6.79420i	0.773013	−	0.0280752i
$243$	−320.595			−1.31932
$244$			73.2135i			0.300055i
$245$		0			0
$246$	227.674			0.925503
$247$	−14.7224			−0.0596048
$248$		−	447.448i		−	1.80423i
$249$		−	493.137i		−	1.98047i
$250$		0			0
$251$	267.673			1.06643			0.533213	−	0.845981i	$-0.320984\pi$
$251$	267.673			1.06643			0.533213	+	0.845981i	$0.320984\pi$
$252$		−	103.304i		−	0.409938i
$253$	154.726	−	160.448i	0.611567	−	0.634182i
$254$	175.541			0.691107
$255$		0			0
$256$	−252.046			−0.984555
$257$	170.577			0.663725			0.331862	−	0.943328i	$-0.392323\pi$
$257$	170.577			0.663725			0.331862	+	0.943328i	$0.392323\pi$
$258$	−467.781			−1.81311
$259$		−	92.1569i		−	0.355818i
$260$		0			0
$261$		−	303.629i		−	1.16333i
$262$	−194.637			−0.742890
$263$			252.398i			0.959688i	0.877354	+	0.479844i	$0.159307\pi$
$263$			252.398i			0.959688i	−0.877354	+	0.479844i	$0.840693\pi$
$264$	279.253	+	269.295i	1.05778	+	1.02006i
$265$		0			0
$266$			11.6773i			0.0438995i
$267$	80.2480			0.300554
$268$	−125.894			−0.469755
$269$	10.5405			0.0391840			0.0195920	−	0.999808i	$-0.493763\pi$
$269$	10.5405			0.0391840			0.0195920	+	0.999808i	$0.493763\pi$
$270$		0			0
$271$			310.989i			1.14756i	0.819009	+	0.573781i	$0.194524\pi$
$271$			310.989i			1.14756i	−0.819009	+	0.573781i	$0.805476\pi$
$272$		−	37.3350i		−	0.137261i
$273$	577.841			2.11663
$274$		−	122.268i		−	0.446233i
$275$		0			0
$276$	132.375			0.479621
$277$		−	1.23402i		−	0.00445494i	−0.999998	−	0.00222747i	$-0.999291\pi$
$277$		−	1.23402i		−	0.00445494i	0.999998	−	0.00222747i	$-0.000709026\pi$
$278$	−163.537			−0.588261
$279$	−388.585			−1.39278
$280$		0			0
$281$		−	138.442i		−	0.492675i	−0.969184	−	0.246337i	$-0.920773\pi$
$281$		−	138.442i		−	0.492675i	0.969184	−	0.246337i	$-0.0792271\pi$
$282$		−	454.534i		−	1.61182i
$283$		−	15.0453i		−	0.0531637i	−0.999647	−	0.0265819i	$-0.991538\pi$
$283$		−	15.0453i		−	0.0531637i	0.999647	−	0.0265819i	$-0.00846227\pi$
$284$	107.592			0.378846
$285$		0			0
$286$	−196.672	+	203.944i	−0.687663	+	0.713092i
$287$	−308.948			−1.07647
$288$			179.865i			0.624531i
$289$	260.489			0.901345
$290$		0			0
$291$	603.081			2.07244
$292$		−	44.8997i		−	0.153766i
$293$			95.4236i			0.325678i	0.986653	+	0.162839i	$0.0520651\pi$
$293$			95.4236i			0.325678i	−0.986653	+	0.162839i	$0.947935\pi$
$294$		−	150.095i		−	0.510526i
$295$		0			0
$296$			93.6455i			0.316370i
$297$	−45.5555	+	47.2401i	−0.153386	+	0.159058i
$298$	−369.296			−1.23925
$299$			337.368i			1.12832i
$300$		0			0
$301$	634.769			2.10887
$302$	−440.450			−1.45844
$303$		−	485.292i		−	1.60162i
$304$		−	6.18296i		−	0.0203387i
$305$		0			0
$306$	−62.2248			−0.203349
$307$			273.765i			0.891742i	0.895097	+	0.445871i	$0.147106\pi$
$307$			273.765i			0.891742i	−0.895097	+	0.445871i	$0.852894\pi$
$308$	−108.590	−	104.717i	−0.352563	−	0.339991i
$309$	−662.966			−2.14552
$310$		0			0
$311$	−277.610			−0.892635			−0.446318	−	0.894875i	$-0.647265\pi$
$311$	−277.610			−0.892635			−0.446318	+	0.894875i	$0.647265\pi$
$312$	−587.174			−1.88197
$313$	−171.212			−0.547004			−0.273502	−	0.961871i	$-0.588182\pi$
$313$	−171.212			−0.547004			−0.273502	+	0.961871i	$0.588182\pi$
$314$			236.157i			0.752091i
$315$		0			0
$316$		−	16.8249i		−	0.0532434i
$317$	−107.731			−0.339847			−0.169923	−	0.985457i	$-0.554352\pi$
$317$	−107.731			−0.339847			−0.169923	+	0.985457i	$0.554352\pi$
$318$		−	87.3815i		−	0.274785i
$319$	−319.163	−	307.782i	−1.00051	−	0.964834i
$320$		0			0
$321$			391.025i			1.21815i
$322$	267.588			0.831018
$323$	−4.72171			−0.0146183
$324$	−147.896			−0.456470
$325$		0			0
$326$			381.808i			1.17119i
$327$		−	637.480i		−	1.94948i
$328$	313.938			0.957129
$329$			616.793i			1.87475i
$330$		0			0
$331$	226.936			0.685606			0.342803	−	0.939407i	$-0.388624\pi$
$331$	226.936			0.685606			0.342803	+	0.939407i	$0.388624\pi$
$332$		−	194.857i		−	0.586920i
$333$	81.3262			0.244223
$334$	193.245			0.578578
$335$		0			0
$336$			242.676i			0.722250i
$337$			164.018i			0.486701i	0.969938	+	0.243350i	$0.0782465\pi$
$337$			164.018i			0.486701i	−0.969938	+	0.243350i	$0.921753\pi$
$338$		−	167.375i		−	0.495191i
$339$	293.691			0.866346
$340$		0			0
$341$	−393.900	+	408.465i	−1.15513	+	1.19785i
$342$	−10.3049			−0.0301313
$343$		−	214.582i		−	0.625605i
$344$	−645.022			−1.87506
$345$		0			0
$346$	122.568			0.354243
$347$			283.936i			0.818260i	0.912476	+	0.409130i	$0.134168\pi$
$347$			283.936i			0.818260i	−0.912476	+	0.409130i	$0.865832\pi$
$348$		−	263.321i		−	0.756670i
$349$		−	107.964i		−	0.309352i	−0.987965	−	0.154676i	$-0.950567\pi$
$349$		−	107.964i		−	0.309352i	0.987965	−	0.154676i	$-0.0494333\pi$
$350$		0			0
$351$		−	99.3299i		−	0.282991i
$352$	189.067	+	182.325i	0.537122	+	0.517968i
$353$	−299.299			−0.847871			−0.423936	−	0.905692i	$-0.639352\pi$
$353$	−299.299			−0.847871			−0.423936	+	0.905692i	$0.639352\pi$
$354$		−	169.390i		−	0.478503i
$355$		0			0
$356$	31.7090			0.0890703
$357$	185.323			0.519112
$358$			495.681i			1.38458i
$359$		−	315.451i		−	0.878694i	−0.898318	−	0.439347i	$-0.855210\pi$
$359$		−	315.451i		−	0.878694i	0.898318	−	0.439347i	$-0.144790\pi$
$360$		0			0
$361$	360.218			0.997834
$362$			96.5542i			0.266724i
$363$	−17.8569	−	491.667i	−0.0491927	−	1.35445i
$364$	228.327			0.627272
$365$		0			0
$366$	−286.646			−0.783185
$367$	−170.851			−0.465535			−0.232768	−	0.972532i	$-0.574778\pi$
$367$	−170.851			−0.465535			−0.232768	+	0.972532i	$0.574778\pi$
$368$	−141.684			−0.385012
$369$		−	272.639i		−	0.738859i
$370$		0			0
$371$			118.575i			0.319609i
$372$	−336.999			−0.905911
$373$			63.4196i			0.170026i	0.996380	+	0.0850129i	$0.0270932\pi$
$373$			63.4196i			0.170026i	−0.996380	+	0.0850129i	$0.972907\pi$
$374$	−63.0757	+	65.4082i	−0.168652	+	0.174888i
$375$		0			0
$376$		−	626.756i		−	1.66690i
$377$	671.092			1.78008
$378$	−78.7848			−0.208426
$379$	−395.811			−1.04436			−0.522178	−	0.852837i	$-0.674880\pi$
$379$	−395.811			−1.04436			−0.522178	+	0.852837i	$0.674880\pi$
$380$		0			0
$381$		−	461.368i		−	1.21094i
$382$			70.8218i			0.185397i
$383$	239.493			0.625308			0.312654	−	0.949867i	$-0.398782\pi$
$383$	239.493			0.625308			0.312654	+	0.949867i	$0.398782\pi$
$384$		−	19.9440i		−	0.0519374i
$385$		0			0
$386$	−423.691			−1.09765
$387$			560.168i			1.44746i
$388$	238.300			0.614175
$389$	225.687			0.580172			0.290086	−	0.957001i	$-0.406316\pi$
$389$	225.687			0.580172			0.290086	+	0.957001i	$0.406316\pi$
$390$		0			0
$391$			108.199i			0.276724i
$392$		−	206.965i		−	0.527972i
$393$			511.557i			1.30167i
$394$	260.032			0.659981
$395$		0			0
$396$	92.4104	−	95.8276i	0.233360	−	0.241989i
$397$	−46.1196			−0.116170			−0.0580851	−	0.998312i	$-0.518499\pi$
$397$	−46.1196			−0.116170			−0.0580851	+	0.998312i	$0.518499\pi$
$398$		−	470.571i		−	1.18234i
$399$	30.6909			0.0769195
$400$		0			0
$401$	273.371			0.681722			0.340861	−	0.940114i	$-0.389281\pi$
$401$	273.371			0.681722			0.340861	+	0.940114i	$0.389281\pi$
$402$		−	492.902i		−	1.22613i
$403$		−	858.864i		−	2.13118i
$404$		−	191.757i		−	0.474647i
$405$		0			0
$406$		−	532.285i		−	1.31105i
$407$	82.4385	−	85.4869i	0.202551	−	0.210042i
$408$	−188.316			−0.461559
$409$		−	355.118i		−	0.868259i	−0.900850	−	0.434130i	$-0.857056\pi$
$409$		−	355.118i		−	0.868259i	0.900850	−	0.434130i	$-0.142944\pi$
$410$		0			0
$411$	−321.352			−0.781877
$412$	−261.963			−0.635833
$413$			229.858i			0.556558i
$414$			236.140i			0.570385i
$415$		0			0
$416$	−397.543			−0.955633
$417$			429.817i			1.03074i
$418$	−10.4458	+	10.8321i	−0.0249900	+	0.0259141i
$419$	−137.679			−0.328590			−0.164295	−	0.986411i	$-0.552535\pi$
$419$	−137.679			−0.328590			−0.164295	+	0.986411i	$0.552535\pi$
$420$		0			0
$421$	42.5093			0.100972			0.0504861	−	0.998725i	$-0.483923\pi$
$421$	42.5093			0.100972			0.0504861	+	0.998725i	$0.483923\pi$
$422$	−49.3396			−0.116919
$423$	−544.305			−1.28677
$424$		−	120.490i		−	0.284175i
$425$		0			0
$426$			421.246i			0.988841i
$427$	388.972			0.910941
$428$			154.509i			0.361002i
$429$	536.019	+	516.904i	1.24946	+	1.20491i
$430$		0			0
$431$			18.0213i			0.0418128i	0.999781	+	0.0209064i	$0.00665520\pi$
$431$			18.0213i			0.0418128i	−0.999781	+	0.0209064i	$0.993345\pi$
$432$	41.7156			0.0965639
$433$	443.870			1.02510			0.512552	−	0.858656i	$-0.328700\pi$
$433$	443.870			1.02510			0.512552	+	0.858656i	$0.328700\pi$
$434$	−681.219			−1.56963
$435$		0			0
$436$		−	251.892i		−	0.577735i
$437$			17.9186i			0.0410037i
$438$	175.791			0.401350
$439$			420.410i			0.957654i	0.877909	+	0.478827i	$0.158938\pi$
$439$			420.410i			0.957654i	−0.877909	+	0.478827i	$0.841062\pi$
$440$		0			0
$441$	−179.738			−0.407570
$442$		−	137.531i		−	0.311157i
$443$	−526.465			−1.18841			−0.594204	−	0.804314i	$-0.702533\pi$
$443$	−526.465			−1.18841			−0.594204	+	0.804314i	$0.702533\pi$
$444$	70.5298			0.158851
$445$		0			0
$446$		−	216.631i		−	0.485719i
$447$			970.606i			2.17138i
$448$			554.051i			1.23672i
$449$	115.197			0.256564			0.128282	−	0.991738i	$-0.459054\pi$
$449$	115.197			0.256564			0.128282	+	0.991738i	$0.459054\pi$
$450$		0			0
$451$	−286.587	−	276.368i	−0.635449	−	0.612789i
$452$	116.049			0.256745
$453$			1157.62i			2.55544i
$454$	236.916			0.521841
$455$		0			0
$456$	−31.1866			−0.0683917
$457$		−	331.393i		−	0.725148i	−0.931955	−	0.362574i	$-0.881898\pi$
$457$		−	331.393i		−	0.725148i	0.931955	−	0.362574i	$-0.118102\pi$
$458$			308.726i			0.674075i
$459$		−	31.8567i		−	0.0694046i
$460$		0			0
$461$			440.253i			0.954997i	0.878633	+	0.477498i	$0.158456\pi$
$461$			440.253i			0.954997i	−0.878633	+	0.477498i	$0.841544\pi$
$462$	409.989	−	425.150i	0.887423	−	0.920239i
$463$	119.267			0.257595			0.128798	−	0.991671i	$-0.458888\pi$
$463$	119.267			0.257595			0.128798	+	0.991671i	$0.458888\pi$
$464$			281.839i			0.607411i
$465$		0			0
$466$	−158.725			−0.340612
$467$	411.442			0.881031			0.440516	−	0.897745i	$-0.354796\pi$
$467$	411.442			0.881031			0.440516	+	0.897745i	$0.354796\pi$
$468$			201.493i			0.430540i
$469$			668.858i			1.42614i
$470$		0			0
$471$	620.681			1.31779
$472$		−	233.571i		−	0.494854i
$473$	588.826	+	567.829i	1.24488	+	1.20048i
$474$	65.8730			0.138973
$475$		0			0
$476$	73.2281			0.153841
$477$	−104.639			−0.219370
$478$	567.687			1.18763
$479$		−	923.838i		−	1.92868i	−0.264666	−	0.964340i	$-0.585262\pi$
$479$		−	923.838i		−	1.92868i	0.264666	−	0.964340i	$-0.414738\pi$
$480$		0			0
$481$			179.750i			0.373701i
$482$	−308.155			−0.639327
$483$		−	703.290i		−	1.45609i
$484$	−7.05596	−	194.276i	−0.0145784	−	0.401397i
$485$		0			0
$486$		−	495.976i		−	1.02053i
$487$	−277.052			−0.568895			−0.284447	−	0.958692i	$-0.591810\pi$
$487$	−277.052			−0.568895			−0.284447	+	0.958692i	$0.591810\pi$
$488$	−395.255			−0.809948
$489$	1003.49			2.05213
$490$		0			0
$491$		−	98.0225i		−	0.199639i	−0.995006	−	0.0998193i	$-0.968174\pi$
$491$		−	98.0225i		−	0.199639i	0.995006	−	0.0998193i	$-0.0318265\pi$
$492$		−	236.445i		−	0.480579i
$493$	215.230			0.436572
$494$		−	22.7762i		−	0.0461057i
$495$		0			0
$496$	360.697			0.727212
$497$		−	571.622i		−	1.15014i
$498$	762.907			1.53194
$499$	252.147			0.505305			0.252653	−	0.967557i	$-0.418697\pi$
$499$	252.147			0.505305			0.252653	+	0.967557i	$0.418697\pi$
$500$		0			0
$501$		−	507.899i		−	1.01377i
$502$			414.103i			0.824906i
$503$			438.637i			0.872041i	0.899937	+	0.436021i	$0.143613\pi$
$503$			438.637i			0.872041i	−0.899937	+	0.436021i	$0.856387\pi$
$504$	557.706			1.10656
$505$		0			0
$506$	248.221	+	239.369i	0.490554	+	0.473061i
$507$	−439.904			−0.867661
$508$		−	182.304i		−	0.358866i
$509$	869.942			1.70912			0.854560	−	0.519352i	$-0.173827\pi$
$509$	869.942			1.70912			0.854560	+	0.519352i	$0.173827\pi$
$510$		0			0
$511$	−238.545			−0.466820
$512$		−	409.547i		−	0.799896i
$513$		−	5.27571i		−	0.0102840i
$514$			263.891i			0.513407i
$515$		0			0
$516$			485.803i			0.941479i
$517$	−551.749	+	572.152i	−1.06721	+	1.10668i
$518$	142.571			0.275234
$519$		−	322.141i		−	0.620696i
$520$		0			0
$521$	387.883			0.744498			0.372249	−	0.928133i	$-0.378587\pi$
$521$	387.883			0.744498			0.372249	+	0.928133i	$0.378587\pi$
$522$	469.729			0.899864
$523$			284.445i			0.543872i	0.962315	+	0.271936i	$0.0876639\pi$
$523$			284.445i			0.543872i	−0.962315	+	0.271936i	$0.912336\pi$
$524$			202.136i			0.385755i
$525$		0			0
$526$	−390.471			−0.742341
$527$		−	275.452i		−	0.522678i
$528$	−217.084	+	225.112i	−0.411145	+	0.426348i
$529$	−118.390			−0.223799
$530$		0			0
$531$	−202.844			−0.382004
$532$	12.1271			0.0227954
$533$	602.596			1.13057
$534$			124.147i			0.232486i
$535$		0			0
$536$		−	679.661i		−	1.26802i
$537$	1302.78			2.42603
$538$			16.3066i			0.0303097i
$539$	−182.196	+	188.934i	−0.338027	+	0.350527i
$540$		0			0
$541$		−	181.011i		−	0.334585i	−0.985907	−	0.167293i	$-0.946498\pi$
$541$		−	181.011i		−	0.334585i	0.985907	−	0.167293i	$-0.0535025\pi$
$542$	−481.114			−0.887665
$543$	253.770			0.467347
$544$	−127.499			−0.234372
$545$		0			0
$546$			893.947i			1.63726i
$547$		−	602.153i		−	1.10083i	−0.834892	−	0.550414i	$-0.814470\pi$
$547$		−	602.153i		−	1.10083i	0.834892	−	0.550414i	$-0.185530\pi$
$548$	−126.978			−0.231712
$549$			343.258i			0.625243i
$550$		0			0
$551$	35.6437			0.0646891
$552$			714.650i			1.29466i
$553$	−89.3882			−0.161642
$554$	1.90908			0.00344600
$555$		0			0
$556$			169.837i			0.305462i
$557$		−	264.253i		−	0.474422i	−0.971458	−	0.237211i	$-0.923767\pi$
$557$		−	264.253i		−	0.474422i	0.971458	−	0.237211i	$-0.0762333\pi$
$558$		−	601.159i		−	1.07735i
$559$	−1238.10			−2.21485
$560$		0			0
$561$	171.910	+	165.780i	0.306435	+	0.295507i
$562$	214.176			0.381095
$563$		−	210.532i		−	0.373946i	−0.982365	−	0.186973i	$-0.940132\pi$
$563$		−	210.532i		−	0.373946i	0.982365	−	0.186973i	$-0.0598678\pi$
$564$	−472.046			−0.836961
$565$		0			0
$566$	23.2758			0.0411234
$567$			785.750i			1.38580i
$568$			580.854i			1.02263i
$569$		−	93.1571i		−	0.163721i	−0.996644	−	0.0818604i	$-0.973914\pi$
$569$		−	93.1571i		−	0.163721i	0.996644	−	0.0818604i	$-0.0260862\pi$
$570$		0			0
$571$			823.255i			1.44178i	0.693051	+	0.720889i	$0.256266\pi$
$571$			823.255i			1.44178i	−0.693051	+	0.720889i	$0.743734\pi$
$572$	211.801	+	204.249i	0.370282	+	0.357078i
$573$	186.138			0.324848
$574$		−	477.957i		−	0.832678i
$575$		0			0
$576$	−488.937			−0.848848
$577$	−750.486			−1.30067			−0.650335	−	0.759648i	$-0.725371\pi$
$577$	−750.486			−1.30067			−0.650335	+	0.759648i	$0.725371\pi$
$578$			402.988i			0.697211i
$579$			1113.57i			1.92327i
$580$		0			0
$581$	−1035.25			−1.78184
$582$			932.993i			1.60308i
$583$	−106.070	+	109.993i	−0.181939	+	0.188667i
$584$	242.398			0.415065
$585$		0			0
$586$	−147.625			−0.251919
$587$	1050.85			1.79021			0.895106	−	0.445854i	$-0.147100\pi$
$587$	1050.85			1.79021			0.895106	+	0.445854i	$0.147100\pi$
$588$	−155.877			−0.265097
$589$		−	45.6169i		−	0.0774480i
$590$		0			0
$591$		−	683.433i		−	1.15640i
$592$	−75.4896			−0.127516
$593$		−	172.160i		−	0.290321i	−0.989408	−	0.145161i	$-0.953630\pi$
$593$		−	172.160i		−	0.290321i	0.989408	−	0.145161i	$-0.0463699\pi$
$594$	−73.0826	−	70.4765i	−0.123035	−	0.118647i
$595$		0			0
$596$			383.523i			0.643496i
$597$	−1236.78			−2.07167
$598$	−521.923			−0.872782
$599$	−674.329			−1.12576			−0.562879	−	0.826539i	$-0.690306\pi$
$599$	−674.329			−1.12576			−0.562879	+	0.826539i	$0.690306\pi$
$600$		0			0
$601$		−	521.125i		−	0.867096i	−0.901131	−	0.433548i	$-0.857261\pi$
$601$		−	521.125i		−	0.867096i	0.901131	−	0.433548i	$-0.142739\pi$
$602$			982.017i			1.63126i
$603$	−590.250			−0.978856
$604$			457.418i			0.757315i
$605$		0			0
$606$	750.769			1.23889
$607$		−	719.195i		−	1.18484i	−0.805631	−	0.592418i	$-0.798174\pi$
$607$		−	719.195i		−	1.18484i	0.805631	−	0.592418i	$-0.201826\pi$
$608$	−21.1147			−0.0347282
$609$	−1398.99			−2.29718
$610$		0			0
$611$		−	1203.04i		−	1.96897i
$612$			64.6220i			0.105592i
$613$		−	802.668i		−	1.30941i	−0.755884	−	0.654705i	$-0.772793\pi$
$613$		−	802.668i		−	1.30941i	0.755884	−	0.654705i	$-0.227207\pi$
$614$	−423.527			−0.689783
$615$		0			0
$616$	565.333	−	586.238i	0.917748	−	0.951685i
$617$	−15.2837			−0.0247710			−0.0123855	−	0.999923i	$-0.503943\pi$
$617$	−15.2837			−0.0247710			−0.0123855	+	0.999923i	$0.503943\pi$
$618$		−	1025.64i		−	1.65961i
$619$	511.627			0.826537			0.413269	−	0.910609i	$-0.364387\pi$
$619$	511.627			0.826537			0.413269	+	0.910609i	$0.364387\pi$
$620$		0			0
$621$	−120.894			−0.194677
$622$		−	429.475i		−	0.690474i
$623$		−	168.465i		−	0.270410i
$624$		−	473.334i		−	0.758548i
$625$		0			0
$626$		−	264.873i		−	0.423120i
$627$	28.4696	+	27.4544i	0.0454060	+	0.0437868i
$628$	245.255			0.390533
$629$			57.6487i			0.0916514i
$630$		0			0
$631$	−1120.05			−1.77503			−0.887517	−	0.460775i	$-0.847571\pi$
$631$	−1120.05			−1.77503			−0.887517	+	0.460775i	$0.847571\pi$
$632$	90.8320			0.143722
$633$			129.677i			0.204862i
$634$		−	166.665i		−	0.262879i
$635$		0			0
$636$	−90.7480			−0.142686
$637$		−	397.264i		−	0.623648i
$638$	476.153	−	493.760i	0.746321	−	0.773919i
$639$	504.442			0.789424
$640$		0			0
$641$	782.877			1.22134			0.610668	−	0.791886i	$-0.290901\pi$
$641$	782.877			1.22134			0.610668	+	0.791886i	$0.290901\pi$
$642$	−604.933			−0.942264
$643$	−865.718			−1.34637			−0.673186	−	0.739473i	$-0.735075\pi$
$643$	−865.718			−1.34637			−0.673186	+	0.739473i	$0.735075\pi$
$644$		−	277.897i		−	0.431517i
$645$		0			0
$646$		−	7.30470i		−	0.0113076i
$647$	−464.538			−0.717987			−0.358994	−	0.933340i	$-0.616880\pi$
$647$	−464.538			−0.717987			−0.358994	+	0.933340i	$0.616880\pi$
$648$		−	798.442i		−	1.23216i
$649$	−205.618	+	213.222i	−0.316823	+	0.328539i
$650$		0			0
$651$			1790.42i			2.75026i
$652$	396.517			0.608155
$653$	−48.3757			−0.0740823			−0.0370412	−	0.999314i	$-0.511793\pi$
$653$	−48.3757			−0.0740823			−0.0370412	+	0.999314i	$0.511793\pi$
$654$	986.211			1.50797
$655$		0			0
$656$			253.072i			0.385781i
$657$		−	210.510i		−	0.320411i
$658$	−954.207			−1.45016
$659$		−	1071.21i		−	1.62551i	−0.582603	−	0.812757i	$-0.697966\pi$
$659$		−	1071.21i		−	1.62551i	0.582603	−	0.812757i	$-0.302034\pi$
$660$		0			0
$661$	−809.703			−1.22497			−0.612483	−	0.790484i	$-0.709829\pi$
$661$	−809.703			−1.22497			−0.612483	+	0.790484i	$0.709829\pi$
$662$			351.080i			0.530332i
$663$	−361.468			−0.545201
$664$	1051.97			1.58429
$665$		0			0
$666$			125.815i			0.188912i
$667$		−	816.786i		−	1.22457i
$668$		−	200.690i		−	0.300434i
$669$	−569.362			−0.851064
$670$		0			0
$671$	360.819	+	347.953i	0.537734	+	0.518558i
$672$	828.735			1.23324
$673$		−	230.577i		−	0.342611i	−0.985218	−	0.171305i	$-0.945201\pi$
$673$		−	230.577i		−	0.342611i	0.985218	−	0.171305i	$-0.0547985\pi$
$674$	−253.744			−0.376474
$675$		0			0
$676$	−173.823			−0.257134
$677$			229.733i			0.339339i	0.985501	+	0.169670i	$0.0542701\pi$
$677$			229.733i			0.339339i	−0.985501	+	0.169670i	$0.945730\pi$
$678$			454.354i			0.670139i
$679$		−	1266.05i		−	1.86458i
$680$		0			0
$681$		−	622.677i		−	0.914356i
$682$	−631.915	−	609.381i	−0.926561	−	0.893520i
$683$	830.100			1.21537			0.607687	−	0.794177i	$-0.292098\pi$
$683$	830.100			1.21537			0.607687	+	0.794177i	$0.292098\pi$
$684$			10.7019i			0.0156461i
$685$		0			0
$686$	331.969			0.483920
$687$	811.413			1.18110
$688$		−	519.966i		−	0.755765i
$689$		−	231.277i		−	0.335671i
$690$		0			0
$691$	−35.7315			−0.0517098			−0.0258549	−	0.999666i	$-0.508231\pi$
$691$	−35.7315			−0.0517098			−0.0258549	+	0.999666i	$0.508231\pi$
$692$		−	127.290i		−	0.183945i
$693$	−509.117	−	490.962i	−0.734657	−	0.708459i
$694$	−439.263			−0.632943
$695$		0			0
$696$	1421.58			2.04250
$697$	193.262			0.277277
$698$	167.025			0.239291
$699$			417.171i			0.596811i
$700$		0			0
$701$			663.222i			0.946109i	0.881033	+	0.473054i	$0.156849\pi$
$701$			663.222i			0.946109i	−0.881033	+	0.473054i	$0.843151\pi$
$702$	153.668			0.218900
$703$			9.54706i			0.0135805i
$704$	−495.623	+	513.951i	−0.704010	+	0.730044i
$705$		0			0
$706$		−	463.029i		−	0.655848i
$707$	−1018.78			−1.44099
$708$	−175.916			−0.248469
$709$	44.6451			0.0629691			0.0314845	−	0.999504i	$-0.489977\pi$
$709$	44.6451			0.0629691			0.0314845	+	0.999504i	$0.489977\pi$
$710$		0			0
$711$		−	78.8829i		−	0.110946i
$712$			171.186i			0.240430i
$713$	−1045.32			−1.46609
$714$			286.703i			0.401545i
$715$		0			0
$716$	514.777			0.718963
$717$		−	1492.03i		−	2.08094i
$718$	488.017			0.679690
$719$	−166.507			−0.231582			−0.115791	−	0.993274i	$-0.536940\pi$
$719$	−166.507			−0.231582			−0.115791	+	0.993274i	$0.536940\pi$
$720$		0			0
$721$			1391.77i			1.93033i
$722$			557.274i			0.771848i
$723$			809.913i			1.12021i
$724$	100.274			0.138500
$725$		0			0
$726$	760.631	−	27.6255i	1.04770	−	0.0380517i
$727$	−844.769			−1.16199			−0.580996	−	0.813906i	$-0.697337\pi$
$727$	−844.769			−1.16199			−0.580996	+	0.813906i	$0.697337\pi$
$728$			1232.66i			1.69321i
$729$	−475.079			−0.651686
$730$		0			0
$731$	−397.079			−0.543200
$732$			297.689i			0.406679i
$733$			136.236i			0.185861i	0.995673	+	0.0929303i	$0.0296234\pi$
$733$			136.236i			0.185861i	−0.995673	+	0.0929303i	$0.970377\pi$
$734$		−	264.315i		−	0.360102i
$735$		0			0
$736$			483.850i			0.657405i
$737$	−598.323	+	620.448i	−0.811835	+	0.841856i
$738$	421.785			0.571525
$739$			867.760i			1.17424i	0.809502	+	0.587118i	$0.199737\pi$
$739$			867.760i			1.17424i	−0.809502	+	0.587118i	$0.800263\pi$
$740$		0			0
$741$	−59.8618			−0.0807852
$742$	−183.441			−0.247225
$743$		−	366.969i		−	0.493902i	−0.969028	−	0.246951i	$-0.920571\pi$
$743$		−	366.969i		−	0.493902i	0.969028	−	0.246951i	$-0.0794286\pi$
$744$		−	1819.34i		−	2.44535i
$745$		0			0
$746$	−98.1131			−0.131519
$747$		−	913.580i		−	1.22300i
$748$	67.9281	+	65.5058i	0.0908130	+	0.0875746i
$749$	820.881			1.09597
$750$		0			0
$751$	674.177			0.897705			0.448853	−	0.893606i	$-0.351833\pi$
$751$	674.177			0.897705			0.448853	+	0.893606i	$0.351833\pi$
$752$	505.241			0.671863
$753$	1088.37			1.44538
$754$			1038.21i			1.37694i
$755$		0			0
$756$			81.8201i			0.108228i
$757$	−65.4072			−0.0864032			−0.0432016	−	0.999066i	$-0.513756\pi$
$757$	−65.4072			−0.0864032			−0.0432016	+	0.999066i	$0.513756\pi$
$758$		−	612.337i		−	0.807833i
$759$	629.124	−	652.388i	0.828886	−	0.859537i
$760$		0			0
$761$			21.0476i			0.0276578i	0.999904	+	0.0138289i	$0.00440201\pi$
$761$			21.0476i			0.0276578i	−0.999904	+	0.0138289i	$0.995598\pi$
$762$	713.758			0.936690
$763$	−1338.27			−1.75395
$764$	73.5503			0.0962700
$765$		0			0
$766$			370.507i			0.483690i
$767$		−	448.333i		−	0.584528i
$768$	−1024.83			−1.33441
$769$		−	66.0422i		−	0.0858806i	−0.999078	−	0.0429403i	$-0.986327\pi$
$769$		−	66.0422i		−	0.0858806i	0.999078	−	0.0429403i	$-0.0136725\pi$
$770$		0			0
$771$	693.575			0.899578
$772$			440.015i			0.569967i
$773$	16.5144			0.0213640			0.0106820	−	0.999943i	$-0.496600\pi$
$773$	16.5144			0.0213640			0.0106820	+	0.999943i	$0.496600\pi$
$774$	−866.606			−1.11965
$775$		0			0
$776$			1286.50i			1.65786i
$777$		−	374.714i		−	0.482257i
$778$			349.148i			0.448777i
$779$	32.0057			0.0410856
$780$		0			0
$781$	511.341	−	530.249i	0.654726	−	0.678937i
$782$	−167.389			−0.214053
$783$			240.483i			0.307131i
$784$	166.839			0.212805
$785$		0			0
$786$	−791.403			−1.00687
$787$		−	778.394i		−	0.989065i	−0.869159	−	0.494533i	$-0.835339\pi$
$787$		−	778.394i		−	0.989065i	0.869159	−	0.494533i	$-0.164661\pi$
$788$		−	270.051i		−	0.342704i
$789$			1026.26i			1.30071i
$790$		0			0
$791$		−	616.548i		−	0.779454i
$792$	517.341	+	498.892i	0.653208	+	0.629915i
$793$	−758.681			−0.956722
$794$		−	71.3491i		−	0.0898604i
$795$		0			0
$796$	−488.700			−0.613945
$797$	318.852			0.400066			0.200033	−	0.979789i	$-0.435895\pi$
$797$	318.852			0.400066			0.200033	+	0.979789i	$0.435895\pi$
$798$			47.4802i			0.0594990i
$799$		−	385.834i		−	0.482897i
$800$		0			0
$801$	148.666			0.185601
$802$			422.917i			0.527328i
$803$	−221.280	−	213.389i	−0.275567	−	0.265740i
$804$	−511.892			−0.636682
$805$		0			0
$806$	1328.70			1.64851
$807$	42.8581			0.0531079
$808$	1035.23			1.28123
$809$		−	253.404i		−	0.313231i	−0.987660	−	0.156616i	$-0.949942\pi$
$809$		−	253.404i		−	0.313231i	0.987660	−	0.156616i	$-0.0500584\pi$
$810$		0			0
$811$		−	1021.32i		−	1.25934i	−0.776864	−	0.629668i	$-0.783191\pi$
$811$		−	1021.32i		−	1.25934i	0.776864	−	0.629668i	$-0.216809\pi$
$812$	−552.792			−0.680779
$813$			1264.49i			1.55534i
$814$	132.252	+	127.536i	0.162472	+	0.156678i
$815$		0			0
$816$		−	151.806i		−	0.186037i
$817$	−65.7593			−0.0804888
$818$	549.384			0.671619
$819$	1070.50			1.30708
$820$		0			0
$821$		−	889.675i		−	1.08365i	−0.840492	−	0.541824i	$-0.817734\pi$
$821$		−	889.675i		−	1.08365i	0.840492	−	0.541824i	$-0.182266\pi$
$822$		−	497.146i		−	0.604800i
$823$	−92.7923			−0.112749			−0.0563744	−	0.998410i	$-0.517954\pi$
$823$	−92.7923			−0.112749			−0.0563744	+	0.998410i	$0.517954\pi$
$824$		−	1414.25i		−	1.71632i
$825$		0			0
$826$	−355.601			−0.430510
$827$			1582.62i			1.91369i	0.290597	+	0.956845i	$0.406146\pi$
$827$			1582.62i			1.91369i	−0.290597	+	0.956845i	$0.593854\pi$
$828$	245.237			0.296180
$829$	925.797			1.11676			0.558382	−	0.829584i	$-0.311422\pi$
$829$	925.797			1.11676			0.558382	+	0.829584i	$0.311422\pi$
$830$		0			0
$831$		−	5.01757i		−	0.00603799i
$832$		−	1080.66i		−	1.29887i
$833$		−	127.409i		−	0.152952i
$834$	−664.947			−0.797298
$835$		0			0
$836$	11.2494	+	10.8483i	0.0134562	+	0.0129764i
$837$	307.771			0.367707
$838$		−	212.996i		−	0.254172i
$839$	169.321			0.201813			0.100907	−	0.994896i	$-0.467826\pi$
$839$	169.321			0.201813			0.100907	+	0.994896i	$0.467826\pi$
$840$		0			0
$841$	−783.751			−0.931927
$842$			65.7639i			0.0781044i
$843$		−	562.909i		−	0.667746i
$844$			51.2405i			0.0607115i
$845$		0			0
$846$		−	842.065i		−	0.995348i
$847$	−1032.16	+	37.4872i	−1.21861	+	0.0442588i
$848$	97.1296			0.114540
$849$		−	61.1750i		−	0.0720553i
$850$		0			0
$851$	218.774			0.257078
$852$	437.475			0.513468
$853$		−	1296.08i		−	1.51943i	−0.650254	−	0.759717i	$-0.725338\pi$
$853$		−	1296.08i		−	1.51943i	0.650254	−	0.759717i	$-0.274662\pi$
$854$			601.758i			0.704634i
$855$		0			0
$856$	−834.140			−0.974462
$857$			1439.08i			1.67921i	0.543197	+	0.839605i	$0.317214\pi$
$857$			1439.08i			1.67921i	−0.543197	+	0.839605i	$0.682786\pi$
$858$	−799.675	+	829.246i	−0.932022	+	0.966487i
$859$	1287.02			1.49827			0.749137	−	0.662415i	$-0.230468\pi$
$859$	1287.02			1.49827			0.749137	+	0.662415i	$0.230468\pi$
$860$		0			0
$861$	−1256.20			−1.45900
$862$	−27.8798			−0.0323432
$863$	1467.32			1.70026			0.850130	−	0.526573i	$-0.176523\pi$
$863$	1467.32			1.70026			0.850130	+	0.526573i	$0.176523\pi$
$864$		−	142.458i		−	0.164882i
$865$		0			0
$866$			686.687i			0.792941i
$867$	1059.16			1.22163
$868$			707.464i			0.815051i
$869$	−82.9186	−	79.9617i	−0.0954184	−	0.0920158i
$870$		0			0
$871$		−	1304.59i		−	1.49781i
$872$	1359.88			1.55950
$873$	1117.26			1.27979
$874$	−27.7209			−0.0317173
$875$		0			0
$876$		−	182.564i		−	0.208406i
$877$		−	267.438i		−	0.304947i	−0.988308	−	0.152473i	$-0.951276\pi$
$877$		−	267.438i		−	0.304947i	0.988308	−	0.152473i	$-0.0487238\pi$
$878$	−650.394			−0.740768
$879$			387.996i			0.441407i
$880$		0			0
$881$	−1753.38			−1.99022			−0.995109	−	0.0987811i	$-0.968506\pi$
$881$	−1753.38			−1.99022			−0.995109	+	0.0987811i	$0.968506\pi$
$882$		−	278.064i		−	0.315265i
$883$	−525.703			−0.595360			−0.297680	−	0.954666i	$-0.596213\pi$
$883$	−525.703			−0.595360			−0.297680	+	0.954666i	$0.596213\pi$
$884$	−142.830			−0.161572
$885$		0			0
$886$		−	814.465i		−	0.919261i
$887$			21.4678i			0.0242027i	0.999927	+	0.0121014i	$0.00385207\pi$
$887$			21.4678i			0.0242027i	−0.999927	+	0.0121014i	$0.996148\pi$
$888$			380.766i			0.428791i
$889$	−968.553			−1.08949
$890$		0			0
$891$	−702.888	+	728.880i	−0.788876	+	0.818047i
$892$	−224.977			−0.252216
$893$		−	63.8971i		−	0.0715533i
$894$	−1501.57			−1.67961
$895$		0			0
$896$	−41.8685			−0.0467282
$897$			1371.75i			1.52927i
$898$			178.216i			0.198458i
$899$			2079.36i			2.31297i
$900$		0			0
$901$		−	74.1744i		−	0.0823245i
$902$	427.554	−	443.364i	0.474006	−	0.491534i
$903$	2581.00			2.85825
$904$			626.507i			0.693039i
$905$		0			0
$906$	−1790.89			−1.97670
$907$	16.7154			0.0184294			0.00921469	−	0.999958i	$-0.497067\pi$
$907$	16.7154			0.0184294			0.00921469	+	0.999958i	$0.497067\pi$
$908$		−	246.043i		−	0.270973i
$909$		−	899.046i		−	0.989049i
$910$		0			0
$911$	1401.06			1.53793			0.768967	−	0.639289i	$-0.220771\pi$
$911$	1401.06			1.53793			0.768967	+	0.639289i	$0.220771\pi$
$912$		−	25.1402i		−	0.0275660i
$913$	−960.319	−	926.074i	−1.05183	−	1.01432i
$914$	512.680			0.560919
$915$		0			0
$916$	320.620			0.350022
$917$	1073.92			1.17112
$918$	49.2838			0.0536861
$919$			1598.11i			1.73896i	0.493965	+	0.869482i	$0.335547\pi$
$919$			1598.11i			1.73896i	−0.493965	+	0.869482i	$0.664453\pi$
$920$		0			0
$921$			1113.14i			1.20862i
$922$	−681.092			−0.738712
$923$			1114.93i			1.20795i
$924$	−441.530	−	425.785i	−0.477846	−	0.460806i
$925$		0			0
$926$			184.511i			0.199256i
$927$	−1228.20			−1.32492
$928$	962.475			1.03715
$929$	−149.678			−0.161117			−0.0805585	−	0.996750i	$-0.525670\pi$
$929$	−149.678			−0.161117			−0.0805585	+	0.996750i	$0.525670\pi$
$930$		0			0
$931$		−	21.0999i		−	0.0226637i
$932$			164.840i			0.176867i
$933$	−1128.77			−1.20983
$934$			636.519i			0.681498i
$935$		0			0
$936$	−1087.79			−1.16217
$937$			1699.25i			1.81351i	0.421663	+	0.906753i	$0.361447\pi$
$937$			1699.25i			1.81351i	−0.421663	+	0.906753i	$0.638553\pi$
$938$	−1034.75			−1.10315
$939$	−696.156			−0.741380
$940$		0			0
$941$		−	1130.78i		−	1.20168i	−0.799368	−	0.600841i	$-0.794832\pi$
$941$		−	1130.78i		−	1.20168i	0.799368	−	0.600841i	$-0.205168\pi$
$942$			960.223i			1.01934i
$943$		−	733.420i		−	0.777751i
$944$	188.287			0.199456
$945$		0			0
$946$	−878.458	+	910.942i	−0.928602	+	0.962941i
$947$	−346.852			−0.366264			−0.183132	−	0.983088i	$-0.558624\pi$
$947$	−346.852			−0.366264			−0.183132	+	0.983088i	$0.558624\pi$
$948$		−	68.4108i		−	0.0721633i
$949$	465.277			0.490281
$950$		0			0
$951$	−438.040			−0.460610
$952$			395.334i			0.415266i
$953$		−	116.543i		−	0.122291i	−0.998129	−	0.0611453i	$-0.980525\pi$
$953$		−	116.543i		−	0.122291i	0.998129	−	0.0611453i	$-0.0194753\pi$
$954$		−	161.882i		−	0.169688i
$955$		0			0
$956$		−	589.558i		−	0.616693i
$957$	−1297.73	−	1251.45i	−1.35604	−	1.30768i
$958$	1429.22			1.49188
$959$			674.616i			0.703457i
$960$		0			0
$961$	1700.16			1.76916
$962$	−278.081			−0.289066
$963$			724.407i			0.752240i
$964$			320.027i			0.331979i
$965$		0			0
$966$	1088.02			1.12632
$967$		−	1721.69i		−	1.78044i	−0.455527	−	0.890222i	$-0.650549\pi$
$967$		−	1721.69i		−	1.78044i	0.455527	−	0.890222i	$-0.349451\pi$
$968$	1048.83	−	38.0927i	1.08350	−	0.0393520i
$969$	−19.1987			−0.0198129
$970$		0			0
$971$	−333.995			−0.343970			−0.171985	−	0.985100i	$-0.555018\pi$
$971$	−333.995			−0.343970			−0.171985	+	0.985100i	$0.555018\pi$
$972$	−515.084			−0.529922
$973$	902.318			0.927356
$974$		−	428.612i		−	0.440053i
$975$		0			0
$976$		−	318.623i		−	0.326458i
$977$	685.606			0.701746			0.350873	−	0.936423i	$-0.385885\pi$
$977$	685.606			0.701746			0.350873	+	0.936423i	$0.385885\pi$
$978$			1552.45i			1.58737i
$979$	150.700	−	156.272i	0.153932	−	0.159624i
$980$		0			0
$981$		−	1180.99i		−	1.20386i
$982$	151.645			0.154425
$983$	443.589			0.451260			0.225630	−	0.974213i	$-0.427556\pi$
$983$	443.589			0.451260			0.225630	+	0.974213i	$0.427556\pi$
$984$	1276.49			1.29724
$985$		0			0
$986$			332.971i			0.337699i
$987$			2507.91i			2.54094i
$988$	−23.6537			−0.0239410
$989$			1506.89i			1.52365i
$990$		0			0
$991$	458.627			0.462792			0.231396	−	0.972860i	$-0.425671\pi$
$991$	458.627			0.462792			0.231396	+	0.972860i	$0.425671\pi$
$992$		−	1231.78i		−	1.24171i
$993$	922.730			0.929234
$994$	884.325			0.889663
$995$		0			0
$996$		−	792.298i		−	0.795480i
$997$		−	166.538i		−	0.167040i	−0.996506	−	0.0835198i	$-0.973384\pi$
$997$		−	166.538i		−	0.167040i	0.996506	−	0.0835198i	$-0.0266162\pi$
$998$			390.084i			0.390865i
$999$	−64.4127			−0.0644772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.c.g.76.6	yes	8
5.2	odd	4		275.3.d.b.274.5		16
5.3	odd	4		275.3.d.b.274.12		16
5.4	even	2		275.3.c.h.76.3	yes	8
11.10	odd	2	inner	275.3.c.g.76.3	✓	8
55.32	even	4		275.3.d.b.274.11		16
55.43	even	4		275.3.d.b.274.6		16
55.54	odd	2		275.3.c.h.76.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.c.g.76.3	✓	8	11.10	odd	2	inner
275.3.c.g.76.6	yes	8	1.1	even	1	trivial
275.3.c.h.76.3	yes	8	5.4	even	2
275.3.c.h.76.6	yes	8	55.54	odd	2
275.3.d.b.274.5		16	5.2	odd	4
275.3.d.b.274.6		16	55.43	even	4
275.3.d.b.274.11		16	55.32	even	4
275.3.d.b.274.12		16	5.3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+1.54705i q^{2} +4.06604 q^{3} +1.60665 q^{4} +6.29036i q^{6} -8.53587i q^{7} +8.67374i q^{8} +7.53270 q^{9} +(7.63571 - 7.91807i) q^{11} +6.53270 q^{12} +16.6490i q^{13} +13.2054 q^{14} -6.99209 q^{16} +5.33961i q^{17} +11.6534i q^{18} +0.884280i q^{19} -34.7072i q^{21} +(12.2496 + 11.8128i) q^{22} +20.2635 q^{23} +35.2678i q^{24} -25.7568 q^{26} -5.96611 q^{27} -13.7141i q^{28} -40.3082i q^{29} -51.5865 q^{31} +23.8779i q^{32} +(31.0471 - 32.1952i) q^{33} -8.26062 q^{34} +12.1024 q^{36} +10.7964 q^{37} -1.36802 q^{38} +67.6956i q^{39} -36.1941i q^{41} +53.6937 q^{42} +74.3649i q^{43} +(12.2679 - 12.7216i) q^{44} +31.3486i q^{46} -72.2589 q^{47} -28.4301 q^{48} -23.8611 q^{49} +21.7111i q^{51} +26.7491i q^{52} -13.8913 q^{53} -9.22985i q^{54} +74.0380 q^{56} +3.59552i q^{57} +62.3587 q^{58} -26.9285 q^{59} +45.5691i q^{61} -79.8067i q^{62} -64.2981i q^{63} -64.9086 q^{64} +(49.8075 + 48.0314i) q^{66} -78.3584 q^{67} +8.57887i q^{68} +82.3923 q^{69} +66.9670 q^{71} +65.3367i q^{72} -27.9462i q^{73} +16.7026i q^{74} +1.42073i q^{76} +(-67.5876 - 65.1775i) q^{77} -104.728 q^{78} -10.4721i q^{79} -92.0527 q^{81} +55.9939 q^{82} -121.282i q^{83} -55.7623i q^{84} -115.046 q^{86} -163.895i q^{87} +(68.6793 + 66.2302i) q^{88} +19.7361 q^{89} +142.114 q^{91} +32.5563 q^{92} -209.753 q^{93} -111.788i q^{94} +97.0885i q^{96} +148.321 q^{97} -36.9142i q^{98} +(57.5175 - 59.6444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 10 q^{4} + 32 q^{9} - q^{11} + 24 q^{12} + 18 q^{14} - 14 q^{16} + 35 q^{22} - 4 q^{23} + 68 q^{26} - 142 q^{27} - 42 q^{31} + 31 q^{33} - 142 q^{34} - 84 q^{36} + 104 q^{37} - 190 q^{38}+ \cdots + 368 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 10 * q^4 + 32 * q^9 - q^11 + 24 * q^12 + 18 * q^14 - 14 * q^16 + 35 * q^22 - 4 * q^23 + 68 * q^26 - 142 * q^27 - 42 * q^31 + 31 * q^33 - 142 * q^34 - 84 * q^36 + 104 * q^37 - 190 * q^38 - 50 * q^42 + 69 * q^44 + 64 * q^47 + 86 * q^48 - 50 * q^49 + 286 * q^53 + 166 * q^56 + 130 * q^58 - 160 * q^59 + 288 * q^64 - 315 * q^66 - 46 * q^67 - 16 * q^69 + 246 * q^71 - 80 * q^77 - 620 * q^78 + 304 * q^81 - 280 * q^82 - 282 * q^86 + 365 * q^88 - 18 * q^89 - 142 * q^91 - 26 * q^92 - 818 * q^93 + 264 * q^97 + 368 * q^99

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