LMFDB - Embedded newform 275.3.c.h.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.h.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	$-0.737012\pi$
$3$	−4.06604			−1.35535			−0.677674	+	0.735363i	$0.737012\pi$
$4$	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	$-0.992592\pi$
$19$		−	0.884280i		−	0.0465410i	0.999729	−	0.0232705i	$-0.00740790\pi$
$20$		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	$-0.645203\pi$
$23$	−20.2635			−0.881023			−0.440511	+	0.897747i	$0.645203\pi$
$24$		−	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	$0.244582\pi$
$29$			40.3082i			1.38994i	−0.719040	+	0.694969i	$0.755418\pi$
$30$		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	$-0.546607\pi$
$37$	−10.7964			−0.291795			−0.145898	+	0.989300i	$0.546607\pi$
$38$	1.36802			0.0360006
$39$		−	67.6956i		−	1.73578i
$40$		0			0
$41$			36.1941i			0.882783i	0.897315	+	0.441391i	$0.145515\pi$
$41$			36.1941i			0.882783i	−0.897315	+	0.441391i	$0.854485\pi$
$42$	−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	$-0.220898\pi$
$47$	72.2589			1.53742			0.768712	+	0.639595i	$0.220898\pi$
$48$	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	$-0.458165\pi$
$53$	13.8913			0.262101			0.131050	+	0.991376i	$0.458165\pi$
$54$			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	$-0.878152\pi$
$61$		−	45.5691i		−	0.747035i	0.927623	−	0.373517i	$-0.121848\pi$
$62$		−	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	$-0.301187\pi$
$67$	78.3584			1.16953			0.584764	+	0.811203i	$0.301187\pi$
$68$			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	$0.0211127\pi$
$79$			10.4721i			0.132558i	−0.997801	+	0.0662789i	$0.978887\pi$
$80$		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	$-0.777035\pi$
$97$	−148.321			−1.52909			−0.764543	+	0.644573i	$0.777035\pi$
$98$		−	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	$0.201209\pi$
$101$			119.352i			1.18171i	−0.806779	+	0.590853i	$0.798791\pi$
$102$	33.5880			0.329294
$103$	163.050			1.58300			0.791502	−	0.611166i	$-0.209299\pi$
$103$	163.050			1.58300			0.791502	+	0.611166i	$0.209299\pi$
$104$	−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	$0.255483\pi$
$109$			156.781i			1.43836i	−0.694823	+	0.719181i	$0.744517\pi$
$110$		0			0
$111$	43.8987			0.395484
$112$			59.6836i			0.532889i
$113$	−72.2303			−0.639206			−0.319603	−	0.947552i	$-0.603550\pi$
$113$	−72.2303			−0.639206			−0.319603	+	0.947552i	$0.603550\pi$
$114$	−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	$-0.840565\pi$
$131$		−	125.812i		−	0.960398i	0.877160	−	0.480199i	$-0.159435\pi$
$132$	−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	$-0.406863\pi$
$137$	79.0330			0.576883			0.288442	+	0.957497i	$0.406863\pi$
$138$			127.465i			0.923658i
$139$		−	105.709i		−	0.760496i	−0.924885	−	0.380248i	$-0.875839\pi$
$139$		−	105.709i		−	0.760496i	0.924885	−	0.380248i	$-0.124161\pi$
$140$		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	$-0.704280\pi$
$149$		−	238.710i		−	1.60208i	0.598609	−	0.801041i	$-0.295720\pi$
$150$		0			0
$151$		−	284.704i		−	1.88545i	−0.333565	−	0.942727i	$-0.608252\pi$
$151$		−	284.704i		−	1.88545i	0.333565	−	0.942727i	$-0.391748\pi$
$152$	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	$-0.661598\pi$
$157$	−152.650			−0.972293			−0.486146	+	0.873877i	$0.661598\pi$
$158$	−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	$-0.773359\pi$
$163$	−246.798			−1.51410			−0.757048	+	0.653359i	$0.773359\pi$
$164$			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	$-0.975921\pi$
$211$		−	31.8928i		−	0.151151i	0.997140	−	0.0755754i	$-0.0240793\pi$
$212$	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	$-0.398342\pi$
$223$	140.029			0.627931			0.313965	+	0.949434i	$0.398342\pi$
$224$	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	$0.278587\pi$
$239$			366.949i			1.53535i	−0.640838	+	0.767676i	$0.721413\pi$
$240$		0			0
$241$		−	199.190i		−	0.826513i	−0.910615	−	0.413256i	$-0.864391\pi$
$241$		−	199.190i		−	0.826513i	0.910615	−	0.413256i	$-0.135609\pi$
$242$	−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	$-0.607677\pi$
$257$	−170.577			−0.663725			−0.331862	+	0.943328i	$0.607677\pi$
$258$	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	$-0.805476\pi$
$271$		−	310.989i		−	1.14756i	0.819009	−	0.573781i	$-0.194524\pi$
$272$		−	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	$0.0792271\pi$
$281$			138.442i			0.492675i	−0.969184	+	0.246337i	$0.920773\pi$
$282$		−	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	$-0.411818\pi$
$313$	171.212			0.547004			0.273502	+	0.961871i	$0.411818\pi$
$314$		−	236.157i		−	0.752091i
$315$		0			0
$316$			16.8249i			0.0532434i
$317$	107.731			0.339847			0.169923	−	0.985457i	$-0.445648\pi$
$317$	107.731			0.339847			0.169923	+	0.985457i	$0.445648\pi$
$318$		−	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	$0.0494333\pi$
$349$			107.964i			0.309352i	−0.987965	+	0.154676i	$0.950567\pi$
$350$		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	$-0.360648\pi$
$353$	299.299			0.847871			0.423936	+	0.905692i	$0.360648\pi$
$354$			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	$0.144790\pi$
$359$			315.451i			0.878694i	−0.898318	+	0.439347i	$0.855210\pi$
$360$		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	$-0.425222\pi$
$367$	170.851			0.465535			0.232768	+	0.972532i	$0.425222\pi$
$368$	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	$-0.601218\pi$
$383$	−239.493			−0.625308			−0.312654	+	0.949867i	$0.601218\pi$
$384$			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	$-0.481501\pi$
$397$	46.1196			0.116170			0.0580851	+	0.998312i	$0.481501\pi$
$398$		−	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	$0.142944\pi$
$409$			355.118i			0.868259i	−0.900850	+	0.434130i	$0.857056\pi$
$410$		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	$-0.993345\pi$
$431$		−	18.0213i		−	0.0418128i	0.999781	−	0.0209064i	$-0.00665520\pi$
$432$	−41.7156			−0.0965639
$433$	−443.870			−1.02510			−0.512552	−	0.858656i	$-0.671300\pi$
$433$	−443.870			−1.02510			−0.512552	+	0.858656i	$0.671300\pi$
$434$	−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	$-0.841062\pi$
$439$		−	420.410i		−	0.957654i	0.877909	−	0.478827i	$-0.158938\pi$
$440$		0			0
$441$	−179.738			−0.407570
$442$		−	137.531i		−	0.311157i
$443$	526.465			1.18841			0.594204	−	0.804314i	$-0.297467\pi$
$443$	526.465			1.18841			0.594204	+	0.804314i	$0.297467\pi$
$444$	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	$-0.841544\pi$
$461$		−	440.253i		−	0.954997i	0.878633	−	0.477498i	$-0.158456\pi$
$462$	−409.989	−	425.150i	−0.887423	−	0.920239i
$463$	−119.267			−0.257595			−0.128798	−	0.991671i	$-0.541112\pi$
$463$	−119.267			−0.257595			−0.128798	+	0.991671i	$0.541112\pi$
$464$		−	281.839i		−	0.607411i
$465$		0			0
$466$	−158.725			−0.340612
$467$	−411.442			−0.881031			−0.440516	−	0.897745i	$-0.645204\pi$
$467$	−411.442			−0.881031			−0.440516	+	0.897745i	$0.645204\pi$
$468$			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	$0.414738\pi$
$479$			923.838i			1.92868i	−0.264666	+	0.964340i	$0.585262\pi$
$480$		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	$-0.408190\pi$
$487$	277.052			0.568895			0.284447	+	0.958692i	$0.408190\pi$
$488$	395.255			0.809948
$489$	1003.49			2.05213
$490$		0			0
$491$			98.0225i			0.199639i	0.995006	+	0.0998193i	$0.0318265\pi$
$491$			98.0225i			0.199639i	−0.995006	+	0.0998193i	$0.968174\pi$
$492$		−	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	$0.0535025\pi$
$541$			181.011i			0.334585i	−0.985907	+	0.167293i	$0.946498\pi$
$542$	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	$0.0260862\pi$
$569$			93.1571i			0.163721i	−0.996644	+	0.0818604i	$0.973914\pi$
$570$		0			0
$571$		−	823.255i		−	1.44178i	−0.693051	−	0.720889i	$-0.743734\pi$
$571$		−	823.255i		−	1.44178i	0.693051	−	0.720889i	$-0.256266\pi$
$572$	−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	$-0.274629\pi$
$577$	750.486			1.30067			0.650335	+	0.759648i	$0.274629\pi$
$578$			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	$-0.852900\pi$
$587$	−1050.85			−1.79021			−0.895106	+	0.445854i	$0.852900\pi$
$588$	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	$0.142739\pi$
$601$			521.125i			0.867096i	−0.901131	+	0.433548i	$0.857261\pi$
$602$			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	$-0.496057\pi$
$617$	15.2837			0.0247710			0.0123855	+	0.999923i	$0.496057\pi$
$618$		−	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	$-0.264925\pi$
$643$	865.718			1.34637			0.673186	+	0.739473i	$0.264925\pi$
$644$			277.897i			0.431517i
$645$		0			0
$646$			7.30470i			0.0113076i
$647$	464.538			0.717987			0.358994	−	0.933340i	$-0.383120\pi$
$647$	464.538			0.717987			0.358994	+	0.933340i	$0.383120\pi$
$648$		−	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	$-0.488207\pi$
$653$	48.3757			0.0740823			0.0370412	+	0.999314i	$0.488207\pi$
$654$	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	$0.302034\pi$
$659$			1071.21i			1.62551i	−0.582603	+	0.812757i	$0.697966\pi$
$660$		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	$-0.707902\pi$
$683$	−830.100			−1.21537			−0.607687	+	0.794177i	$0.707902\pi$
$684$		−	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	$-0.843151\pi$
$701$		−	663.222i		−	0.946109i	0.881033	−	0.473054i	$-0.156849\pi$
$702$	−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	$-0.302663\pi$
$727$	844.769			1.16199			0.580996	+	0.813906i	$0.302663\pi$
$728$			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	$-0.800263\pi$
$739$		−	867.760i		−	1.17424i	0.809502	−	0.587118i	$-0.199737\pi$
$740$		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	$-0.486244\pi$
$757$	65.4072			0.0864032			0.0432016	+	0.999066i	$0.486244\pi$
$758$		−	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	$-0.995598\pi$
$761$		−	21.0476i		−	0.0276578i	0.999904	−	0.0138289i	$-0.00440201\pi$
$762$	−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	$0.0136725\pi$
$769$			66.0422i			0.0858806i	−0.999078	+	0.0429403i	$0.986327\pi$
$770$		0			0
$771$	693.575			0.899578
$772$			440.015i			0.569967i
$773$	−16.5144			−0.0213640			−0.0106820	−	0.999943i	$-0.503400\pi$
$773$	−16.5144			−0.0213640			−0.0106820	+	0.999943i	$0.503400\pi$
$774$	−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	$-0.564105\pi$
$797$	−318.852			−0.400066			−0.200033	+	0.979789i	$0.564105\pi$
$798$			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	$0.0500584\pi$
$809$			253.404i			0.313231i	−0.987660	+	0.156616i	$0.949942\pi$
$810$		0			0
$811$			1021.32i			1.25934i	0.776864	+	0.629668i	$0.216809\pi$
$811$			1021.32i			1.25934i	−0.776864	+	0.629668i	$0.783191\pi$
$812$	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	$0.182266\pi$
$821$			889.675i			1.08365i	−0.840492	+	0.541824i	$0.817734\pi$
$822$		−	497.146i		−	0.604800i
$823$	92.7923			0.112749			0.0563744	−	0.998410i	$-0.482046\pi$
$823$	92.7923			0.112749			0.0563744	+	0.998410i	$0.482046\pi$
$824$			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	$-0.823477\pi$
$863$	−1467.32			−1.70026			−0.850130	+	0.526573i	$0.823477\pi$
$864$			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	$-0.403787\pi$
$883$	525.703			0.595360			0.297680	+	0.954666i	$0.403787\pi$
$884$	−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	$-0.502933\pi$
$907$	−16.7154			−0.0184294			−0.00921469	+	0.999958i	$0.502933\pi$
$908$		−	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	$-0.664453\pi$
$919$		−	1598.11i		−	1.73896i	0.493965	−	0.869482i	$-0.335547\pi$
$920$		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	$0.205168\pi$
$941$			1130.78i			1.20168i	−0.799368	+	0.600841i	$0.794832\pi$
$942$			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	$-0.441376\pi$
$947$	346.852			0.366264			0.183132	+	0.983088i	$0.441376\pi$
$948$		−	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	$-0.614115\pi$
$977$	−685.606			−0.701746			−0.350873	+	0.936423i	$0.614115\pi$
$978$			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	$-0.572444\pi$
$983$	−443.589			−0.451260			−0.225630	+	0.974213i	$0.572444\pi$
$984$	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.h.76.6	yes	8
5.2	odd	4		275.3.d.b.274.6		16
5.3	odd	4		275.3.d.b.274.11		16
5.4	even	2		275.3.c.g.76.3	✓	8
11.10	odd	2	inner	275.3.c.h.76.3	yes	8
55.32	even	4		275.3.d.b.274.12		16
55.43	even	4		275.3.d.b.274.5		16
55.54	odd	2		275.3.c.g.76.6	yes	8

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