LMFDB - Embedded newform 275.3.d.b.274.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(274,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.274"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,20] 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 50x^{14} + 939x^{12} + 8450x^{10} + 39245x^{8} + 93316x^{6} + 104420x^{4} + 45264x^{2} + 6400 $ x^16 + 50x^14 + 939x^12 + 8450x^10 + 39245x^8 + 93316x^6 + 104420x^4 + 45264*x^2 + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.12
Root			$0.547046i$ of defining polynomial
Character	$\chi$	$=$	275.274
Dual form			275.3.d.b.274.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.54705 q^{2} +4.06604i q^{3} -1.60665 q^{4} +6.29036i q^{6} -8.53587 q^{7} -8.67374 q^{8} -7.53270 q^{9} +(7.63571 - 7.91807i) q^{11} -6.53270i q^{12} -16.6490 q^{13} -13.2054 q^{14} -6.99209 q^{16} +5.33961 q^{17} -11.6534 q^{18} -0.884280i q^{19} -34.7072i q^{21} +(11.8128 - 12.2496i) q^{22} +20.2635i q^{23} -35.2678i q^{24} -25.7568 q^{26} +5.96611i q^{27} +13.7141 q^{28} +40.3082i q^{29} -51.5865 q^{31} +23.8779 q^{32} +(32.1952 + 31.0471i) q^{33} +8.26062 q^{34} +12.1024 q^{36} -10.7964i q^{37} -1.36802i q^{38} -67.6956i q^{39} -36.1941i q^{41} -53.6937i q^{42} -74.3649 q^{43} +(-12.2679 + 12.7216i) q^{44} +31.3486i q^{46} +72.2589i q^{47} -28.4301i q^{48} +23.8611 q^{49} +21.7111i q^{51} +26.7491 q^{52} -13.8913i q^{53} +9.22985i q^{54} +74.0380 q^{56} +3.59552 q^{57} +62.3587i q^{58} +26.9285 q^{59} +45.5691i q^{61} -79.8067 q^{62} +64.2981 q^{63} +64.9086 q^{64} +(49.8075 + 48.0314i) q^{66} +78.3584i q^{67} -8.57887 q^{68} -82.3923 q^{69} +66.9670 q^{71} +65.3367 q^{72} +27.9462 q^{73} -16.7026i q^{74} +1.42073i q^{76} +(-65.1775 + 67.5876i) q^{77} -104.728i q^{78} +10.4721i q^{79} -92.0527 q^{81} -55.9939i q^{82} +121.282 q^{83} +55.7623i q^{84} -115.046 q^{86} -163.895 q^{87} +(-66.2302 + 68.6793i) q^{88} -19.7361 q^{89} +142.114 q^{91} -32.5563i q^{92} -209.753i q^{93} +111.788i q^{94} +97.0885i q^{96} -148.321i q^{97} +36.9142 q^{98} +(-57.5175 + 59.6444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{4} - 64 q^{9} - 2 q^{11} - 36 q^{14} - 28 q^{16} + 136 q^{26} - 84 q^{31} + 284 q^{34} - 168 q^{36} - 138 q^{44} + 100 q^{49} + 332 q^{56} + 320 q^{59} - 576 q^{64} - 630 q^{66} + 32 q^{69}+ \cdots - 736 q^{99}+O(q^{100}) $ 16 * q + 20 * q^4 - 64 * q^9 - 2 * q^11 - 36 * q^14 - 28 * q^16 + 136 * q^26 - 84 * q^31 + 284 * q^34 - 168 * q^36 - 138 * q^44 + 100 * q^49 + 332 * q^56 + 320 * q^59 - 576 * q^64 - 630 * q^66 + 32 * q^69 + 492 * q^71 + 608 * q^81 - 564 * q^86 + 36 * q^89 - 284 * q^91 - 736 * 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 $

$2$	1.54705			0.773523			0.386762	−	0.922180i	$-0.373594\pi$
$2$	1.54705			0.773523			0.386762	+	0.922180i	$0.373594\pi$
$3$			4.06604i			1.35535i	0.735363	+	0.677674i	$0.237012\pi$
$3$			4.06604i			1.35535i	−0.735363	+	0.677674i	$0.762988\pi$
$4$	−1.60665			−0.401662
$5$		0			0
$5$		0			0
$6$			6.29036i			1.04839i
$7$	−8.53587			−1.21941			−0.609705	−	0.792628i	$-0.708712\pi$
$7$	−8.53587			−1.21941			−0.609705	+	0.792628i	$0.708712\pi$
$8$	−8.67374			−1.08422
$9$	−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
$12$		−	6.53270i		−	0.544391i
$13$	−16.6490			−1.28069			−0.640347	−	0.768086i	$-0.721209\pi$
$13$	−16.6490			−1.28069			−0.640347	+	0.768086i	$0.721209\pi$
$14$	−13.2054			−0.943242
$15$		0			0
$16$	−6.99209			−0.437006
$17$	5.33961			0.314095			0.157047	−	0.987591i	$-0.449802\pi$
$17$	5.33961			0.314095			0.157047	+	0.987591i	$0.449802\pi$
$18$	−11.6534			−0.647413
$19$		−	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
$22$	11.8128	−	12.2496i	0.536946	−	0.556801i
$23$			20.2635i			0.881023i	0.897747	+	0.440511i	$0.145203\pi$
$23$			20.2635i			0.881023i	−0.897747	+	0.440511i	$0.854797\pi$
$24$		−	35.2678i		−	1.46949i
$25$		0			0
$26$	−25.7568			−0.990646
$27$			5.96611i			0.220967i
$28$	13.7141			0.489791
$29$			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	$0.812827\pi$
$32$	23.8779			0.746184
$33$	32.1952	+	31.0471i	0.975613	+	0.940822i
$34$	8.26062			0.242959
$35$		0			0
$36$	12.1024			0.336178
$37$		−	10.7964i		−	0.291795i	−0.989300	−	0.145898i	$-0.953393\pi$
$37$		−	10.7964i		−	0.291795i	0.989300	−	0.145898i	$-0.0466070\pi$
$38$		−	1.36802i		−	0.0360006i
$39$		−	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	$-0.145515\pi$
$42$		−	53.6937i		−	1.27842i
$43$	−74.3649			−1.72942			−0.864708	−	0.502275i	$-0.832496\pi$
$43$	−74.3649			−1.72942			−0.864708	+	0.502275i	$0.832496\pi$
$44$	−12.2679	+	12.7216i	−0.278816	+	0.289126i
$45$		0			0
$46$			31.3486i			0.681491i
$47$			72.2589i			1.53742i	0.639595	+	0.768712i	$0.279102\pi$
$47$			72.2589i			1.53742i	−0.639595	+	0.768712i	$0.720898\pi$
$48$		−	28.4301i		−	0.592295i
$49$	23.8611			0.486961
$50$		0			0
$51$			21.7111i			0.425707i
$52$	26.7491			0.514406
$53$		−	13.8913i		−	0.262101i	−0.991376	−	0.131050i	$-0.958165\pi$
$53$		−	13.8913i		−	0.262101i	0.991376	−	0.131050i	$-0.0418350\pi$
$54$			9.22985i			0.170923i
$55$		0			0
$56$	74.0380			1.32211
$57$	3.59552			0.0630793
$58$			62.3587i			1.07515i
$59$	26.9285			0.456415			0.228208	−	0.973612i	$-0.426713\pi$
$59$	26.9285			0.456415			0.228208	+	0.973612i	$0.426713\pi$
$60$		0			0
$61$			45.5691i			0.747035i	0.927623	+	0.373517i	$0.121848\pi$
$61$			45.5691i			0.747035i	−0.927623	+	0.373517i	$0.878152\pi$
$62$	−79.8067			−1.28720
$63$	64.2981			1.02061
$64$	64.9086			1.01420
$65$		0			0
$66$	49.8075	+	48.0314i	0.754659	+	0.727748i
$67$			78.3584i			1.16953i	0.811203	+	0.584764i	$0.198813\pi$
$67$			78.3584i			1.16953i	−0.811203	+	0.584764i	$0.801187\pi$
$68$	−8.57887			−0.126160
$69$	−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	$0.343677\pi$
$72$	65.3367			0.907454
$73$	27.9462			0.382825			0.191412	−	0.981510i	$-0.438693\pi$
$73$	27.9462			0.382825			0.191412	+	0.981510i	$0.438693\pi$
$74$		−	16.7026i		−	0.225710i
$75$		0			0
$76$			1.42073i			0.0186938i
$77$	−65.1775	+	67.5876i	−0.846461	+	0.877762i
$78$		−	104.728i		−	1.34267i
$79$			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
$82$		−	55.9939i		−	0.682853i
$83$	121.282			1.46123			0.730614	−	0.682791i	$-0.239234\pi$
$83$	121.282			1.46123			0.730614	+	0.682791i	$0.239234\pi$
$84$			55.7623i			0.663836i
$85$		0			0
$86$	−115.046			−1.33774
$87$	−163.895			−1.88385
$88$	−66.2302	+	68.6793i	−0.752616	+	0.780447i
$89$	−19.7361			−0.221754			−0.110877	−	0.993834i	$-0.535366\pi$
$89$	−19.7361			−0.221754			−0.110877	+	0.993834i	$0.535366\pi$
$90$		0			0
$91$	142.114			1.56169
$92$		−	32.5563i		−	0.353873i
$93$		−	209.753i		−	2.25541i
$94$			111.788i			1.18923i
$95$		0			0
$96$			97.0885i			1.01134i
$97$		−	148.321i		−	1.52909i	−0.644573	−	0.764543i	$-0.722965\pi$
$97$		−	148.321i		−	1.52909i	0.644573	−	0.764543i	$-0.277035\pi$
$98$	36.9142			0.376676
$99$	−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	$-0.201209\pi$
$102$			33.5880i			0.329294i
$103$		−	163.050i		−	1.58300i	−0.611166	−	0.791502i	$-0.709299\pi$
$103$		−	163.050i		−	1.58300i	0.611166	−	0.791502i	$-0.290701\pi$
$104$	144.409			1.38855
$105$		0			0
$106$		−	21.4906i		−	0.202741i
$107$	96.1684			0.898770			0.449385	−	0.893338i	$-0.351643\pi$
$107$	96.1684			0.898770			0.449385	+	0.893338i	$0.351643\pi$
$108$		−	9.58544i		−	0.0887541i
$109$			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
$112$	59.6836			0.532889
$113$			72.2303i			0.639206i	0.947552	+	0.319603i	$0.103550\pi$
$113$			72.2303i			0.639206i	−0.947552	+	0.319603i	$0.896450\pi$
$114$	5.56243			0.0487933
$115$		0			0
$116$		−	64.7611i		−	0.558285i
$117$	125.412			1.07190
$118$	41.6597			0.353048
$119$	−45.5782			−0.383010
$120$		0			0
$121$	−4.39172	−	120.920i	−0.0362952	−	0.999341i
$122$			70.4975i			0.577849i
$123$	147.167			1.19648
$124$	82.8813			0.668397
$125$		0			0
$126$	99.4722			0.789462
$127$	−113.469			−0.893454			−0.446727	−	0.894670i	$-0.647410\pi$
$127$	−113.469			−0.893454			−0.446727	+	0.894670i	$0.647410\pi$
$128$	4.90501			0.0383204
$129$		−	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	$0.840565\pi$
$132$	−51.7264	−	49.8818i	−0.391866	−	0.377893i
$133$			7.54810i			0.0567526i
$134$			121.224i			0.904658i
$135$		0			0
$136$	−46.3144			−0.340547
$137$			79.0330i			0.576883i	0.957497	+	0.288442i	$0.0931371\pi$
$137$			79.0330i			0.576883i	−0.957497	+	0.288442i	$0.906863\pi$
$138$	−127.465			−0.923658
$139$		−	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
$142$	103.601			0.729585
$143$	−127.127	+	131.828i	−0.889001	+	0.921875i
$144$	52.6693			0.365759
$145$		0			0
$146$	43.2341			0.296124
$147$			97.0202i			0.660001i
$148$			17.3461i			0.117203i
$149$		−	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	$0.391748\pi$
$151$			284.704i			1.88545i	−0.333565	+	0.942727i	$0.608252\pi$
$152$			7.67002i			0.0504606i
$153$	−40.2217			−0.262887
$154$	−100.833	+	104.561i	−0.654757	+	0.678969i
$155$		0			0
$156$			108.763i			0.697199i
$157$		−	152.650i		−	0.972293i	−0.873877	−	0.486146i	$-0.838402\pi$
$157$		−	152.650i		−	0.972293i	0.873877	−	0.486146i	$-0.161598\pi$
$158$			16.2008i			0.102537i
$159$	56.4828			0.355238
$160$		0			0
$161$		−	172.967i		−	1.07433i
$162$	−142.410			−0.879073
$163$			246.798i			1.51410i	0.653359	+	0.757048i	$0.273359\pi$
$163$			246.798i			1.51410i	−0.653359	+	0.757048i	$0.726641\pi$
$164$			58.1511i			0.354580i
$165$		0			0
$166$	187.629			1.13029
$167$	−124.912			−0.747978			−0.373989	−	0.927433i	$-0.622010\pi$
$167$	−124.912			−0.747978			−0.373989	+	0.927433i	$0.622010\pi$
$168$			301.041i			1.79191i
$169$	108.190			0.640176
$170$		0			0
$171$			6.66101i			0.0389533i
$172$	119.478			0.694641
$173$	79.2272			0.457961			0.228980	−	0.973431i	$-0.426461\pi$
$173$	79.2272			0.457961			0.228980	+	0.973431i	$0.426461\pi$
$174$	−253.553			−1.45720
$175$		0			0
$176$	−53.3896	+	55.3639i	−0.303350	+	0.314568i
$177$			109.492i			0.618602i
$178$	−30.5327			−0.171532
$179$	−320.405			−1.78997			−0.894985	−	0.446097i	$-0.852814\pi$
$179$	−320.405			−1.78997			−0.894985	+	0.446097i	$0.852814\pi$
$180$		0			0
$181$	62.4120			0.344818			0.172409	−	0.985025i	$-0.444845\pi$
$181$	62.4120			0.344818			0.172409	+	0.985025i	$0.444845\pi$
$182$	219.857			1.20800
$183$	−185.286			−1.01249
$184$		−	175.761i		−	0.955221i
$185$		0			0
$186$		−	324.497i		−	1.74461i
$187$	40.7717	−	42.2794i	0.218031	−	0.226093i
$188$		−	116.095i		−	0.617525i
$189$		−	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	$0.461762\pi$
$192$			263.921i			1.37459i
$193$	−273.871			−1.41902			−0.709511	−	0.704694i	$-0.751084\pi$
$193$	−273.871			−1.41902			−0.709511	+	0.704694i	$0.751084\pi$
$194$		−	229.460i		−	1.18278i
$195$		0			0
$196$	−38.3364			−0.195594
$197$	−168.083			−0.853214			−0.426607	−	0.904437i	$-0.640291\pi$
$197$	−168.083			−0.853214			−0.426607	+	0.904437i	$0.640291\pi$
$198$	−88.9823	+	92.2727i	−0.449405	+	0.466024i
$199$	304.174			1.52851			0.764256	−	0.644913i	$-0.223106\pi$
$199$	304.174			1.52851			0.764256	+	0.644913i	$0.223106\pi$
$200$		0			0
$201$	−318.609			−1.58512
$202$		−	184.644i		−	0.914078i
$203$		−	344.066i		−	1.69490i
$204$		−	34.8820i		−	0.170990i
$205$		0			0
$206$		−	252.245i		−	1.22449i
$207$		−	152.639i		−	0.737386i
$208$	116.411			0.559670
$209$	−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	$0.975921\pi$
$212$			22.3185i			0.105276i
$213$			272.291i			1.27836i
$214$	148.777			0.695219
$215$		0			0
$216$		−	51.7485i		−	0.239577i
$217$	440.335			2.02920
$218$			242.548i			1.11261i
$219$			113.630i			0.518860i
$220$		0			0
$221$	−88.8992			−0.402259
$222$	67.9134			0.305916
$223$		−	140.029i		−	0.627931i	−0.949434	−	0.313965i	$-0.898342\pi$
$223$		−	140.029i		−	0.627931i	0.949434	−	0.313965i	$-0.101658\pi$
$224$	−203.819			−0.909904
$225$		0			0
$226$			111.744i			0.494441i
$227$	−153.141			−0.674629			−0.337314	−	0.941392i	$-0.609519\pi$
$227$	−153.141			−0.674629			−0.337314	+	0.941392i	$0.609519\pi$
$228$	−5.77673			−0.0253365
$229$	−199.559			−0.871435			−0.435717	−	0.900084i	$-0.643505\pi$
$229$	−199.559			−0.871435			−0.435717	+	0.900084i	$0.643505\pi$
$230$		0			0
$231$	−274.814	−	265.014i	−1.18967	−	1.14725i
$232$		−	349.623i		−	1.50700i
$233$	−102.599			−0.440338			−0.220169	−	0.975462i	$-0.570661\pi$
$233$	−102.599			−0.440338			−0.220169	+	0.975462i	$0.570661\pi$
$234$	194.018			0.829138
$235$		0			0
$236$	−43.2646			−0.183325
$237$	−42.5799			−0.179662
$238$	−70.5116			−0.296267
$239$			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	$0.135609\pi$
$241$			199.190i			0.826513i	−0.910615	+	0.413256i	$0.864391\pi$
$242$	−6.79420	−	187.069i	−0.0280752	−	0.773013i
$243$		−	320.595i		−	1.31932i
$244$		−	73.2135i		−	0.300055i
$245$		0			0
$246$	227.674			0.925503
$247$			14.7224i			0.0596048i
$248$	447.448			1.80423
$249$			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	$0.320984\pi$
$252$	−103.304			−0.409938
$253$	160.448	+	154.726i	0.634182	+	0.611567i
$254$	−175.541			−0.691107
$255$		0			0
$256$	−252.046			−0.984555
$257$		−	170.577i		−	0.663725i	−0.943328	−	0.331862i	$-0.892323\pi$
$257$		−	170.577i		−	0.663725i	0.943328	−	0.331862i	$-0.107677\pi$
$258$		−	467.781i		−	1.81311i
$259$			92.1569i			0.355818i
$260$		0			0
$261$		−	303.629i		−	1.16333i
$262$			194.637i			0.742890i
$263$	−252.398			−0.959688			−0.479844	−	0.877354i	$-0.659307\pi$
$263$	−252.398			−0.959688			−0.479844	+	0.877354i	$0.659307\pi$
$264$	−279.253	−	269.295i	−1.05778	−	1.02006i
$265$		0			0
$266$			11.6773i			0.0438995i
$267$		−	80.2480i		−	0.300554i
$268$		−	125.894i		−	0.469755i
$269$	−10.5405			−0.0391840			−0.0195920	−	0.999808i	$-0.506237\pi$
$269$	−10.5405			−0.0391840			−0.0195920	+	0.999808i	$0.506237\pi$
$270$		0			0
$271$			310.989i			1.14756i	0.819009	+	0.573781i	$0.194524\pi$
$271$			310.989i			1.14756i	−0.819009	+	0.573781i	$0.805476\pi$
$272$	−37.3350			−0.137261
$273$			577.841i			2.11663i
$274$			122.268i			0.446233i
$275$		0			0
$276$	132.375			0.479621
$277$	−1.23402			−0.00445494			−0.00222747	−	0.999998i	$-0.500709\pi$
$277$	−1.23402			−0.00445494			−0.00222747	+	0.999998i	$0.500709\pi$
$278$		−	163.537i		−	0.588261i
$279$	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	$-0.0792271\pi$
$282$	−454.534			−1.61182
$283$	15.0453			0.0531637			0.0265819	−	0.999647i	$-0.491538\pi$
$283$	15.0453			0.0531637			0.0265819	+	0.999647i	$0.491538\pi$
$284$	−107.592			−0.378846
$285$		0			0
$286$	−196.672	+	203.944i	−0.687663	+	0.713092i
$287$			308.948i			1.07647i
$288$	−179.865			−0.624531
$289$	−260.489			−0.901345
$290$		0			0
$291$	603.081			2.07244
$292$	−44.8997			−0.153766
$293$	−95.4236			−0.325678			−0.162839	−	0.986653i	$-0.552065\pi$
$293$	−95.4236			−0.325678			−0.162839	+	0.986653i	$0.552065\pi$
$294$			150.095i			0.510526i
$295$		0			0
$296$			93.6455i			0.316370i
$297$	47.2401	+	45.5555i	0.159058	+	0.153386i
$298$		−	369.296i		−	1.23925i
$299$		−	337.368i		−	1.12832i
$300$		0			0
$301$	634.769			2.10887
$302$			440.450i			1.45844i
$303$	485.292			1.60162
$304$			6.18296i			0.0203387i
$305$		0			0
$306$	−62.2248			−0.203349
$307$	273.765			0.891742			0.445871	−	0.895097i	$-0.352894\pi$
$307$	273.765			0.891742			0.445871	+	0.895097i	$0.352894\pi$
$308$	104.717	−	108.590i	0.339991	−	0.352563i
$309$	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	$0.647265\pi$
$312$			587.174i			1.88197i
$313$		−	171.212i		−	0.547004i	−0.961871	−	0.273502i	$-0.911818\pi$
$313$		−	171.212i		−	0.547004i	0.961871	−	0.273502i	$-0.0881820\pi$
$314$		−	236.157i		−	0.752091i
$315$		0			0
$316$		−	16.8249i		−	0.0532434i
$317$			107.731i			0.339847i	0.985457	+	0.169923i	$0.0543520\pi$
$317$			107.731i			0.339847i	−0.985457	+	0.169923i	$0.945648\pi$
$318$	87.3815			0.274785
$319$	319.163	+	307.782i	1.00051	+	0.964834i
$320$		0			0
$321$			391.025i			1.21815i
$322$		−	267.588i		−	0.831018i
$323$		−	4.72171i		−	0.0146183i
$324$	147.896			0.456470
$325$		0			0
$326$			381.808i			1.17119i
$327$	−637.480			−1.94948
$328$			313.938i			0.957129i
$329$		−	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	$0.388624\pi$
$332$	−194.857			−0.586920
$333$			81.3262i			0.244223i
$334$	−193.245			−0.578578
$335$		0			0
$336$			242.676i			0.722250i
$337$	164.018			0.486701			0.243350	−	0.969938i	$-0.421753\pi$
$337$	164.018			0.486701			0.243350	+	0.969938i	$0.421753\pi$
$338$	167.375			0.495191
$339$	−293.691			−0.866346
$340$		0			0
$341$	−393.900	+	408.465i	−1.15513	+	1.19785i
$342$			10.3049i			0.0301313i
$343$	214.582			0.625605
$344$	645.022			1.87506
$345$		0			0
$346$	122.568			0.354243
$347$	283.936			0.818260			0.409130	−	0.912476i	$-0.365832\pi$
$347$	283.936			0.818260			0.409130	+	0.912476i	$0.365832\pi$
$348$	263.321			0.756670
$349$			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
$352$	182.325	−	189.067i	0.517968	−	0.537122i
$353$		−	299.299i		−	0.847871i	−0.905692	−	0.423936i	$-0.860648\pi$
$353$		−	299.299i		−	0.847871i	0.905692	−	0.423936i	$-0.139352\pi$
$354$			169.390i			0.478503i
$355$		0			0
$356$	31.7090			0.0890703
$357$		−	185.323i		−	0.519112i
$358$	−495.681			−1.38458
$359$			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
$362$	96.5542			0.266724
$363$	491.667	−	17.8569i	1.35445	−	0.0491927i
$364$	−228.327			−0.627272
$365$		0			0
$366$	−286.646			−0.783185
$367$			170.851i			0.465535i	0.972532	+	0.232768i	$0.0747782\pi$
$367$			170.851i			0.465535i	−0.972532	+	0.232768i	$0.925222\pi$
$368$		−	141.684i		−	0.385012i
$369$			272.639i			0.738859i
$370$		0			0
$371$			118.575i			0.319609i
$372$			336.999i			0.905911i
$373$	−63.4196			−0.170026			−0.0850129	−	0.996380i	$-0.527093\pi$
$373$	−63.4196			−0.170026			−0.0850129	+	0.996380i	$0.527093\pi$
$374$	63.0757	−	65.4082i	0.168652	−	0.174888i
$375$		0			0
$376$		−	626.756i		−	1.66690i
$377$		−	671.092i		−	1.78008i
$378$		−	78.7848i		−	0.208426i
$379$	395.811			1.04436			0.522178	−	0.852837i	$-0.325120\pi$
$379$	395.811			1.04436			0.522178	+	0.852837i	$0.325120\pi$
$380$		0			0
$381$		−	461.368i		−	1.21094i
$382$	70.8218			0.185397
$383$			239.493i			0.625308i	0.949867	+	0.312654i	$0.101218\pi$
$383$			239.493i			0.625308i	−0.949867	+	0.312654i	$0.898782\pi$
$384$			19.9440i			0.0519374i
$385$		0			0
$386$	−423.691			−1.09765
$387$	560.168			1.44746
$388$			238.300i			0.614175i
$389$	−225.687			−0.580172			−0.290086	−	0.957001i	$-0.593684\pi$
$389$	−225.687			−0.580172			−0.290086	+	0.957001i	$0.593684\pi$
$390$		0			0
$391$			108.199i			0.276724i
$392$	−206.965			−0.527972
$393$	−511.557			−1.30167
$394$	−260.032			−0.659981
$395$		0			0
$396$	92.4104	−	95.8276i	0.233360	−	0.241989i
$397$			46.1196i			0.116170i	0.998312	+	0.0580851i	$0.0184995\pi$
$397$			46.1196i			0.116170i	−0.998312	+	0.0580851i	$0.981501\pi$
$398$	470.571			1.18234
$399$	−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	$0.389281\pi$
$402$	−492.902			−1.22613
$403$	858.864			2.13118
$404$			191.757i			0.474647i
$405$		0			0
$406$		−	532.285i		−	1.31105i
$407$	−85.4869	−	82.4385i	−0.210042	−	0.202551i
$408$		−	188.316i		−	0.461559i
$409$			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
$412$			261.963i			0.635833i
$413$	−229.858			−0.556558
$414$		−	236.140i		−	0.570385i
$415$		0			0
$416$	−397.543			−0.955633
$417$	429.817			1.03074
$418$	−10.8321	−	10.4458i	−0.0259141	−	0.0249900i
$419$	137.679			0.328590			0.164295	−	0.986411i	$-0.447465\pi$
$419$	137.679			0.328590			0.164295	+	0.986411i	$0.447465\pi$
$420$		0			0
$421$	42.5093			0.100972			0.0504861	−	0.998725i	$-0.483923\pi$
$421$	42.5093			0.100972			0.0504861	+	0.998725i	$0.483923\pi$
$422$			49.3396i			0.116919i
$423$		−	544.305i		−	1.28677i
$424$			120.490i			0.284175i
$425$		0			0
$426$			421.246i			0.988841i
$427$		−	388.972i		−	0.910941i
$428$	−154.509			−0.361002
$429$	−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	$0.993345\pi$
$432$		−	41.7156i		−	0.0965639i
$433$			443.870i			1.02510i	0.858656	+	0.512552i	$0.171300\pi$
$433$			443.870i			1.02510i	−0.858656	+	0.512552i	$0.828700\pi$
$434$	681.219			1.56963
$435$		0			0
$436$		−	251.892i		−	0.577735i
$437$	17.9186			0.0410037
$438$			175.791i			0.401350i
$439$		−	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
$442$	−137.531			−0.311157
$443$		−	526.465i		−	1.18841i	−0.804314	−	0.594204i	$-0.797467\pi$
$443$		−	526.465i		−	1.18841i	0.804314	−	0.594204i	$-0.202533\pi$
$444$	−70.5298			−0.158851
$445$		0			0
$446$		−	216.631i		−	0.485719i
$447$	970.606			2.17138
$448$	−554.051			−1.23672
$449$	−115.197			−0.256564			−0.128282	−	0.991738i	$-0.540946\pi$
$449$	−115.197			−0.256564			−0.128282	+	0.991738i	$0.540946\pi$
$450$		0			0
$451$	−286.587	−	276.368i	−0.635449	−	0.612789i
$452$		−	116.049i		−	0.256745i
$453$	−1157.62			−2.55544
$454$	−236.916			−0.521841
$455$		0			0
$456$	−31.1866			−0.0683917
$457$	−331.393			−0.725148			−0.362574	−	0.931955i	$-0.618102\pi$
$457$	−331.393			−0.725148			−0.362574	+	0.931955i	$0.618102\pi$
$458$	−308.726			−0.674075
$459$			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	$0.841544\pi$
$462$	−425.150	−	409.989i	−0.920239	−	0.887423i
$463$			119.267i			0.257595i	0.991671	+	0.128798i	$0.0411118\pi$
$463$			119.267i			0.257595i	−0.991671	+	0.128798i	$0.958888\pi$
$464$		−	281.839i		−	0.607411i
$465$		0			0
$466$	−158.725			−0.340612
$467$		−	411.442i		−	0.881031i	−0.897745	−	0.440516i	$-0.854796\pi$
$467$		−	411.442i		−	0.881031i	0.897745	−	0.440516i	$-0.145204\pi$
$468$	−201.493			−0.430540
$469$		−	668.858i		−	1.42614i
$470$		0			0
$471$	620.681			1.31779
$472$	−233.571			−0.494854
$473$	−567.829	+	588.826i	−1.20048	+	1.24488i
$474$	−65.8730			−0.138973
$475$		0			0
$476$	73.2281			0.153841
$477$			104.639i			0.219370i
$478$			567.687i			1.18763i
$479$			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
$482$			308.155i			0.639327i
$483$	703.290			1.45609
$484$	7.05596	+	194.276i	0.0145784	+	0.401397i
$485$		0			0
$486$		−	495.976i		−	1.02053i
$487$			277.052i			0.568895i	0.958692	+	0.284447i	$0.0918101\pi$
$487$			277.052i			0.568895i	−0.958692	+	0.284447i	$0.908190\pi$
$488$		−	395.255i		−	0.809948i
$489$	−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	$-0.0318265\pi$
$492$	−236.445			−0.480579
$493$			215.230i			0.436572i
$494$			22.7762i			0.0461057i
$495$		0			0
$496$	360.697			0.727212
$497$	−571.622			−1.15014
$498$			762.907i			1.53194i
$499$	−252.147			−0.505305			−0.252653	−	0.967557i	$-0.581303\pi$
$499$	−252.147			−0.505305			−0.252653	+	0.967557i	$0.581303\pi$
$500$		0			0
$501$		−	507.899i		−	1.01377i
$502$	414.103			0.824906
$503$	−438.637			−0.872041			−0.436021	−	0.899937i	$-0.643613\pi$
$503$	−438.637			−0.872041			−0.436021	+	0.899937i	$0.643613\pi$
$504$	−557.706			−1.10656
$505$		0			0
$506$	248.221	+	239.369i	0.490554	+	0.473061i
$507$			439.904i			0.867661i
$508$	182.304			0.358866
$509$	−869.942			−1.70912			−0.854560	−	0.519352i	$-0.826173\pi$
$509$	−869.942			−1.70912			−0.854560	+	0.519352i	$0.826173\pi$
$510$		0			0
$511$	−238.545			−0.466820
$512$	−409.547			−0.799896
$513$	5.27571			0.0102840
$514$		−	263.891i		−	0.513407i
$515$		0			0
$516$			485.803i			0.941479i
$517$	572.152	+	551.749i	1.10668	+	1.06721i
$518$			142.571i			0.275234i
$519$			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	$0.378587\pi$
$522$		−	469.729i		−	0.899864i
$523$	−284.445			−0.543872			−0.271936	−	0.962315i	$-0.587664\pi$
$523$	−284.445			−0.543872			−0.271936	+	0.962315i	$0.587664\pi$
$524$		−	202.136i		−	0.385755i
$525$		0			0
$526$	−390.471			−0.742341
$527$	−275.452			−0.522678
$528$	−225.112	−	217.084i	−0.426348	−	0.411145i
$529$	118.390			0.223799
$530$		0			0
$531$	−202.844			−0.382004
$532$		−	12.1271i		−	0.0227954i
$533$			602.596i			1.13057i
$534$		−	124.147i		−	0.232486i
$535$		0			0
$536$		−	679.661i		−	1.26802i
$537$		−	1302.78i		−	2.42603i
$538$	−16.3066			−0.0303097
$539$	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	$-0.0535025\pi$
$542$			481.114i			0.887665i
$543$			253.770i			0.467347i
$544$	127.499			0.234372
$545$		0			0
$546$			893.947i			1.63726i
$547$	−602.153			−1.10083			−0.550414	−	0.834892i	$-0.685530\pi$
$547$	−602.153			−1.10083			−0.550414	+	0.834892i	$0.685530\pi$
$548$		−	126.978i		−	0.231712i
$549$		−	343.258i		−	0.625243i
$550$		0			0
$551$	35.6437			0.0646891
$552$	714.650			1.29466
$553$		−	89.3882i		−	0.161642i
$554$	−1.90908			−0.00344600
$555$		0			0
$556$			169.837i			0.305462i
$557$	−264.253			−0.474422			−0.237211	−	0.971458i	$-0.576233\pi$
$557$	−264.253			−0.474422			−0.237211	+	0.971458i	$0.576233\pi$
$558$	601.159			1.07735
$559$	1238.10			2.21485
$560$		0			0
$561$	171.910	+	165.780i	0.306435	+	0.295507i
$562$		−	214.176i		−	0.381095i
$563$	210.532			0.373946			0.186973	−	0.982365i	$-0.440132\pi$
$563$	210.532			0.373946			0.186973	+	0.982365i	$0.440132\pi$
$564$	472.046			0.836961
$565$		0			0
$566$	23.2758			0.0411234
$567$	785.750			1.38580
$568$	−580.854			−1.02263
$569$			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	$0.256266\pi$
$571$			823.255i			1.44178i	−0.693051	+	0.720889i	$0.743734\pi$
$572$	204.249	−	211.801i	0.357078	−	0.370282i
$573$			186.138i			0.324848i
$574$			477.957i			0.832678i
$575$		0			0
$576$	−488.937			−0.848848
$577$			750.486i			1.30067i	0.759648	+	0.650335i	$0.225371\pi$
$577$			750.486i			1.30067i	−0.759648	+	0.650335i	$0.774629\pi$
$578$	−402.988			−0.697211
$579$		−	1113.57i		−	1.92327i
$580$		0			0
$581$	−1035.25			−1.78184
$582$	932.993			1.60308
$583$	−109.993	−	106.070i	−0.188667	−	0.181939i
$584$	−242.398			−0.415065
$585$		0			0
$586$	−147.625			−0.251919
$587$		−	1050.85i		−	1.79021i	−0.445854	−	0.895106i	$-0.647100\pi$
$587$		−	1050.85i		−	1.79021i	0.445854	−	0.895106i	$-0.352900\pi$
$588$		−	155.877i		−	0.265097i
$589$			45.6169i			0.0774480i
$590$		0			0
$591$		−	683.433i		−	1.15640i
$592$			75.4896i			0.127516i
$593$	172.160			0.290321			0.145161	−	0.989408i	$-0.453630\pi$
$593$	172.160			0.290321			0.145161	+	0.989408i	$0.453630\pi$
$594$	73.0826	+	70.4765i	0.123035	+	0.118647i
$595$		0			0
$596$			383.523i			0.643496i
$597$			1236.78i			2.07167i
$598$		−	521.923i		−	0.872782i
$599$	674.329			1.12576			0.562879	−	0.826539i	$-0.309694\pi$
$599$	674.329			1.12576			0.562879	+	0.826539i	$0.309694\pi$
$600$		0			0
$601$		−	521.125i		−	0.867096i	−0.901131	−	0.433548i	$-0.857261\pi$
$601$		−	521.125i		−	0.867096i	0.901131	−	0.433548i	$-0.142739\pi$
$602$	982.017			1.63126
$603$		−	590.250i		−	0.978856i
$604$		−	457.418i		−	0.757315i
$605$		0			0
$606$	750.769			1.23889
$607$	−719.195			−1.18484			−0.592418	−	0.805631i	$-0.701826\pi$
$607$	−719.195			−1.18484			−0.592418	+	0.805631i	$0.701826\pi$
$608$		−	21.1147i		−	0.0347282i
$609$	1398.99			2.29718
$610$		0			0
$611$		−	1203.04i		−	1.96897i
$612$	64.6220			0.105592
$613$	802.668			1.30941			0.654705	−	0.755884i	$-0.272793\pi$
$613$	802.668			1.30941			0.654705	+	0.755884i	$0.272793\pi$
$614$	423.527			0.689783
$615$		0			0
$616$	565.333	−	586.238i	0.917748	−	0.951685i
$617$			15.2837i			0.0247710i	0.999923	+	0.0123855i	$0.00394253\pi$
$617$			15.2837i			0.0247710i	−0.999923	+	0.0123855i	$0.996057\pi$
$618$	1025.64			1.65961
$619$	−511.627			−0.826537			−0.413269	−	0.910609i	$-0.635613\pi$
$619$	−511.627			−0.826537			−0.413269	+	0.910609i	$0.635613\pi$
$620$		0			0
$621$	−120.894			−0.194677
$622$	−429.475			−0.690474
$623$	168.465			0.270410
$624$			473.334i			0.758548i
$625$		0			0
$626$		−	264.873i		−	0.423120i
$627$	27.4544	−	28.4696i	0.0437868	−	0.0454060i
$628$			245.255i			0.390533i
$629$		−	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	$0.847571\pi$
$632$		−	90.8320i		−	0.143722i
$633$	−129.677			−0.204862
$634$			166.665i			0.262879i
$635$		0			0
$636$	−90.7480			−0.142686
$637$	−397.264			−0.623648
$638$	493.760	+	476.153i	0.773919	+	0.746321i
$639$	−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	$0.290901\pi$
$642$			604.933i			0.942264i
$643$		−	865.718i		−	1.34637i	−0.739473	−	0.673186i	$-0.764925\pi$
$643$		−	865.718i		−	1.34637i	0.739473	−	0.673186i	$-0.235075\pi$
$644$			277.897i			0.431517i
$645$		0			0
$646$		−	7.30470i		−	0.0113076i
$647$			464.538i			0.717987i	0.933340	+	0.358994i	$0.116880\pi$
$647$			464.538i			0.717987i	−0.933340	+	0.358994i	$0.883120\pi$
$648$	798.442			1.23216
$649$	205.618	−	213.222i	0.316823	−	0.328539i
$650$		0			0
$651$			1790.42i			2.75026i
$652$		−	396.517i		−	0.608155i
$653$		−	48.3757i		−	0.0740823i	−0.999314	−	0.0370412i	$-0.988207\pi$
$653$		−	48.3757i		−	0.0740823i	0.999314	−	0.0370412i	$-0.0117933\pi$
$654$	−986.211			−1.50797
$655$		0			0
$656$			253.072i			0.385781i
$657$	−210.510			−0.320411
$658$		−	954.207i		−	1.45016i
$659$			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	$0.709829\pi$
$662$	351.080			0.530332
$663$		−	361.468i		−	0.545201i
$664$	−1051.97			−1.58429
$665$		0			0
$666$			125.815i			0.188912i
$667$	−816.786			−1.22457
$668$	200.690			0.300434
$669$	569.362			0.851064
$670$		0			0
$671$	360.819	+	347.953i	0.537734	+	0.518558i
$672$		−	828.735i		−	1.23324i
$673$	230.577			0.342611			0.171305	−	0.985218i	$-0.445201\pi$
$673$	230.577			0.342611			0.171305	+	0.985218i	$0.445201\pi$
$674$	253.744			0.376474
$675$		0			0
$676$	−173.823			−0.257134
$677$	229.733			0.339339			0.169670	−	0.985501i	$-0.445730\pi$
$677$	229.733			0.339339			0.169670	+	0.985501i	$0.445730\pi$
$678$	−454.354			−0.670139
$679$			1266.05i			1.86458i
$680$		0			0
$681$		−	622.677i		−	0.914356i
$682$	−609.381	+	631.915i	−0.893520	+	0.926561i
$683$			830.100i			1.21537i	0.794177	+	0.607687i	$0.207902\pi$
$683$			830.100i			1.21537i	−0.794177	+	0.607687i	$0.792098\pi$
$684$		−	10.7019i		−	0.0156461i
$685$		0			0
$686$	331.969			0.483920
$687$		−	811.413i		−	1.18110i
$688$	519.966			0.755765
$689$			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	$0.508231\pi$
$692$	−127.290			−0.183945
$693$	490.962	−	509.117i	0.708459	−	0.734657i
$694$	439.263			0.632943
$695$		0			0
$696$	1421.58			2.04250
$697$		−	193.262i		−	0.277277i
$698$			167.025i			0.239291i
$699$		−	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	$0.843151\pi$
$702$		−	153.668i		−	0.218900i
$703$	−9.54706			−0.0135805
$704$	495.623	−	513.951i	0.704010	−	0.730044i
$705$		0			0
$706$		−	463.029i		−	0.655848i
$707$			1018.78i			1.44099i
$708$		−	175.916i		−	0.248469i
$709$	−44.6451			−0.0629691			−0.0314845	−	0.999504i	$-0.510023\pi$
$709$	−44.6451			−0.0629691			−0.0314845	+	0.999504i	$0.510023\pi$
$710$		0			0
$711$		−	78.8829i		−	0.110946i
$712$	171.186			0.240430
$713$		−	1045.32i		−	1.46609i
$714$		−	286.703i		−	0.401545i
$715$		0			0
$716$	514.777			0.718963
$717$	−1492.03			−2.08094
$718$			488.017i			0.679690i
$719$	166.507			0.231582			0.115791	−	0.993274i	$-0.463060\pi$
$719$	166.507			0.231582			0.115791	+	0.993274i	$0.463060\pi$
$720$		0			0
$721$			1391.77i			1.93033i
$722$	557.274			0.771848
$723$	−809.913			−1.12021
$724$	−100.274			−0.138500
$725$		0			0
$726$	760.631	−	27.6255i	1.04770	−	0.0380517i
$727$			844.769i			1.16199i	0.813906	+	0.580996i	$0.197337\pi$
$727$			844.769i			1.16199i	−0.813906	+	0.580996i	$0.802663\pi$
$728$	−1232.66			−1.69321
$729$	475.079			0.651686
$730$		0			0
$731$	−397.079			−0.543200
$732$	297.689			0.406679
$733$	−136.236			−0.185861			−0.0929303	−	0.995673i	$-0.529623\pi$
$733$	−136.236			−0.185861			−0.0929303	+	0.995673i	$0.529623\pi$
$734$			264.315i			0.360102i
$735$		0			0
$736$			483.850i			0.657405i
$737$	620.448	+	598.323i	0.841856	+	0.811835i
$738$			421.785i			0.571525i
$739$		−	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
$742$			183.441i			0.247225i
$743$	366.969			0.493902			0.246951	−	0.969028i	$-0.420571\pi$
$743$	366.969			0.493902			0.246951	+	0.969028i	$0.420571\pi$
$744$			1819.34i			2.44535i
$745$		0			0
$746$	−98.1131			−0.131519
$747$	−913.580			−1.22300
$748$	−65.5058	+	67.9281i	−0.0875746	+	0.0908130i
$749$	−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	$0.351833\pi$
$752$		−	505.241i		−	0.671863i
$753$			1088.37i			1.44538i
$754$		−	1038.21i		−	1.37694i
$755$		0			0
$756$			81.8201i			0.108228i
$757$			65.4072i			0.0864032i	0.999066	+	0.0432016i	$0.0137558\pi$
$757$			65.4072i			0.0864032i	−0.999066	+	0.0432016i	$0.986244\pi$
$758$	612.337			0.807833
$759$	−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	$0.995598\pi$
$762$		−	713.758i		−	0.936690i
$763$		−	1338.27i		−	1.75395i
$764$	−73.5503			−0.0962700
$765$		0			0
$766$			370.507i			0.483690i
$767$	−448.333			−0.584528
$768$		−	1024.83i		−	1.33441i
$769$			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
$772$	440.015			0.569967
$773$			16.5144i			0.0213640i	0.999943	+	0.0106820i	$0.00340026\pi$
$773$			16.5144i			0.0213640i	−0.999943	+	0.0106820i	$0.996600\pi$
$774$	866.606			1.11965
$775$		0			0
$776$			1286.50i			1.65786i
$777$	−374.714			−0.482257
$778$	−349.148			−0.448777
$779$	−32.0057			−0.0410856
$780$		0			0
$781$	511.341	−	530.249i	0.654726	−	0.678937i
$782$			167.389i			0.214053i
$783$	−240.483			−0.307131
$784$	−166.839			−0.212805
$785$		0			0
$786$	−791.403			−1.00687
$787$	−778.394			−0.989065			−0.494533	−	0.869159i	$-0.664661\pi$
$787$	−778.394			−0.989065			−0.494533	+	0.869159i	$0.664661\pi$
$788$	270.051			0.342704
$789$		−	1026.26i		−	1.30071i
$790$		0			0
$791$		−	616.548i		−	0.779454i
$792$	498.892	−	517.341i	0.629915	−	0.653208i
$793$		−	758.681i		−	0.956722i
$794$			71.3491i			0.0898604i
$795$		0			0
$796$	−488.700			−0.613945
$797$		−	318.852i		−	0.400066i	−0.979789	−	0.200033i	$-0.935895\pi$
$797$		−	318.852i		−	0.400066i	0.979789	−	0.200033i	$-0.0641049\pi$
$798$	−47.4802			−0.0594990
$799$			385.834i			0.482897i
$800$		0			0
$801$	148.666			0.185601
$802$	422.917			0.527328
$803$	213.389	−	221.280i	0.265740	−	0.275567i
$804$	511.892			0.636682
$805$		0			0
$806$	1328.70			1.64851
$807$		−	42.8581i		−	0.0531079i
$808$			1035.23i			1.28123i
$809$			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	$-0.783191\pi$
$811$		−	1021.32i		−	1.25934i	0.776864	−	0.629668i	$-0.216809\pi$
$812$			552.792i			0.680779i
$813$	−1264.49			−1.55534
$814$	−132.252	−	127.536i	−0.162472	−	0.156678i
$815$		0			0
$816$		−	151.806i		−	0.186037i
$817$			65.7593i			0.0804888i
$818$			549.384i			0.671619i
$819$	−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	$-0.182266\pi$
$822$	−497.146			−0.604800
$823$		−	92.7923i		−	0.112749i	−0.998410	−	0.0563744i	$-0.982046\pi$
$823$		−	92.7923i		−	0.112749i	0.998410	−	0.0563744i	$-0.0179541\pi$
$824$			1414.25i			1.71632i
$825$		0			0
$826$	−355.601			−0.430510
$827$	1582.62			1.91369			0.956845	−	0.290597i	$-0.0938540\pi$
$827$	1582.62			1.91369			0.956845	+	0.290597i	$0.0938540\pi$
$828$			245.237i			0.296180i
$829$	−925.797			−1.11676			−0.558382	−	0.829584i	$-0.688578\pi$
$829$	−925.797			−1.11676			−0.558382	+	0.829584i	$0.688578\pi$
$830$		0			0
$831$		−	5.01757i		−	0.00603799i
$832$	−1080.66			−1.29887
$833$	127.409			0.152952
$834$	664.947			0.797298
$835$		0			0
$836$	11.2494	+	10.8483i	0.0134562	+	0.0129764i
$837$		−	307.771i		−	0.367707i
$838$	212.996			0.254172
$839$	−169.321			−0.201813			−0.100907	−	0.994896i	$-0.532174\pi$
$839$	−169.321			−0.201813			−0.100907	+	0.994896i	$0.532174\pi$
$840$		0			0
$841$	−783.751			−0.931927
$842$	65.7639			0.0781044
$843$	562.909			0.667746
$844$		−	51.2405i		−	0.0607115i
$845$		0			0
$846$		−	842.065i		−	0.995348i
$847$	37.4872	+	1032.16i	0.0442588	+	1.21861i
$848$			97.1296i			0.114540i
$849$			61.1750i			0.0720553i
$850$		0			0
$851$	218.774			0.257078
$852$		−	437.475i		−	0.513468i
$853$	1296.08			1.51943			0.759717	−	0.650254i	$-0.225338\pi$
$853$	1296.08			1.51943			0.759717	+	0.650254i	$0.225338\pi$
$854$		−	601.758i		−	0.704634i
$855$		0			0
$856$	−834.140			−0.974462
$857$	1439.08			1.67921			0.839605	−	0.543197i	$-0.182786\pi$
$857$	1439.08			1.67921			0.839605	+	0.543197i	$0.182786\pi$
$858$	−829.246	−	799.675i	−0.966487	−	0.932022i
$859$	−1287.02			−1.49827			−0.749137	−	0.662415i	$-0.769532\pi$
$859$	−1287.02			−1.49827			−0.749137	+	0.662415i	$0.769532\pi$
$860$		0			0
$861$	−1256.20			−1.45900
$862$			27.8798i			0.0323432i
$863$			1467.32i			1.70026i	0.526573	+	0.850130i	$0.323477\pi$
$863$			1467.32i			1.70026i	−0.526573	+	0.850130i	$0.676523\pi$
$864$			142.458i			0.164882i
$865$		0			0
$866$			686.687i			0.792941i
$867$		−	1059.16i		−	1.22163i
$868$	−707.464			−0.815051
$869$	82.9186	+	79.9617i	0.0954184	+	0.0920158i
$870$		0			0
$871$		−	1304.59i		−	1.49781i
$872$		−	1359.88i		−	1.55950i
$873$			1117.26i			1.27979i
$874$	27.7209			0.0317173
$875$		0			0
$876$		−	182.564i		−	0.208406i
$877$	−267.438			−0.304947			−0.152473	−	0.988308i	$-0.548724\pi$
$877$	−267.438			−0.304947			−0.152473	+	0.988308i	$0.548724\pi$
$878$		−	650.394i		−	0.740768i
$879$		−	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	$0.968506\pi$
$882$	−278.064			−0.315265
$883$		−	525.703i		−	0.595360i	−0.954666	−	0.297680i	$-0.903787\pi$
$883$		−	525.703i		−	0.595360i	0.954666	−	0.297680i	$-0.0962128\pi$
$884$	142.830			0.161572
$885$		0			0
$886$		−	814.465i		−	0.919261i
$887$	21.4678			0.0242027			0.0121014	−	0.999927i	$-0.496148\pi$
$887$	21.4678			0.0242027			0.0121014	+	0.999927i	$0.496148\pi$
$888$	−380.766			−0.428791
$889$	968.553			1.08949
$890$		0			0
$891$	−702.888	+	728.880i	−0.788876	+	0.818047i
$892$			224.977i			0.252216i
$893$	63.8971			0.0715533
$894$	1501.57			1.67961
$895$		0			0
$896$	−41.8685			−0.0467282
$897$	1371.75			1.52927
$898$	−178.216			−0.198458
$899$		−	2079.36i		−	2.31297i
$900$		0			0
$901$		−	74.1744i		−	0.0823245i
$902$	−443.364	−	427.554i	−0.491534	−	0.474006i
$903$			2581.00i			2.85825i
$904$		−	626.507i		−	0.693039i
$905$		0			0
$906$	−1790.89			−1.97670
$907$		−	16.7154i		−	0.0184294i	−0.999958	−	0.00921469i	$-0.997067\pi$
$907$		−	16.7154i		−	0.0184294i	0.999958	−	0.00921469i	$-0.00293317\pi$
$908$	246.043			0.270973
$909$			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	$0.220771\pi$
$912$	−25.1402			−0.0275660
$913$	926.074	−	960.319i	1.01432	−	1.05183i
$914$	−512.680			−0.560919
$915$		0			0
$916$	320.620			0.350022
$917$		−	1073.92i		−	1.17112i
$918$			49.2838i			0.0536861i
$919$		−	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
$922$			681.092i			0.738712i
$923$	−1114.93			−1.20795
$924$	441.530	+	425.785i	0.477846	+	0.460806i
$925$		0			0
$926$			184.511i			0.199256i
$927$			1228.20i			1.32492i
$928$			962.475i			1.03715i
$929$	149.678			0.161117			0.0805585	−	0.996750i	$-0.474330\pi$
$929$	149.678			0.161117			0.0805585	+	0.996750i	$0.474330\pi$
$930$		0			0
$931$		−	21.0999i		−	0.0226637i
$932$	164.840			0.176867
$933$		−	1128.77i		−	1.20983i
$934$		−	636.519i		−	0.681498i
$935$		0			0
$936$	−1087.79			−1.16217
$937$	1699.25			1.81351			0.906753	−	0.421663i	$-0.138553\pi$
$937$	1699.25			1.81351			0.906753	+	0.421663i	$0.138553\pi$
$938$		−	1034.75i		−	1.10315i
$939$	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	$-0.205168\pi$
$942$	960.223			1.01934
$943$	733.420			0.777751
$944$	−188.287			−0.199456
$945$		0			0
$946$	−878.458	+	910.942i	−0.928602	+	0.962941i
$947$			346.852i			0.366264i	0.983088	+	0.183132i	$0.0586236\pi$
$947$			346.852i			0.366264i	−0.983088	+	0.183132i	$0.941376\pi$
$948$	68.4108			0.0721633
$949$	−465.277			−0.490281
$950$		0			0
$951$	−438.040			−0.460610
$952$	395.334			0.415266
$953$	116.543			0.122291			0.0611453	−	0.998129i	$-0.480525\pi$
$953$	116.543			0.122291			0.0611453	+	0.998129i	$0.480525\pi$
$954$			161.882i			0.169688i
$955$		0			0
$956$		−	589.558i		−	0.616693i
$957$	−1251.45	+	1297.73i	−1.30768	+	1.35604i
$958$			1429.22i			1.49188i
$959$		−	674.616i		−	0.703457i
$960$		0			0
$961$	1700.16			1.76916
$962$			278.081i			0.289066i
$963$	−724.407			−0.752240
$964$		−	320.027i		−	0.331979i
$965$		0			0
$966$	1088.02			1.12632
$967$	−1721.69			−1.78044			−0.890222	−	0.455527i	$-0.849451\pi$
$967$	−1721.69			−1.78044			−0.890222	+	0.455527i	$0.849451\pi$
$968$	38.0927	+	1048.83i	0.0393520	+	1.08350i
$969$	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	$0.555018\pi$
$972$			515.084i			0.529922i
$973$			902.318i			0.927356i
$974$			428.612i			0.440053i
$975$		0			0
$976$		−	318.623i		−	0.326458i
$977$		−	685.606i		−	0.701746i	−0.936423	−	0.350873i	$-0.885885\pi$
$977$		−	685.606i		−	0.701746i	0.936423	−	0.350873i	$-0.114115\pi$
$978$	−1552.45			−1.58737
$979$	−150.700	+	156.272i	−0.153932	+	0.159624i
$980$		0			0
$981$		−	1180.99i		−	1.20386i
$982$		−	151.645i		−	0.154425i
$983$			443.589i			0.451260i	0.974213	+	0.225630i	$0.0724440\pi$
$983$			443.589i			0.451260i	−0.974213	+	0.225630i	$0.927556\pi$
$984$	−1276.49			−1.29724
$985$		0			0
$986$			332.971i			0.337699i
$987$	2507.91			2.54094
$988$		−	23.6537i		−	0.0239410i
$989$		−	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	$0.425671\pi$
$992$	−1231.78			−1.24171
$993$			922.730i			0.929234i
$994$	−884.325			−0.889663
$995$		0			0
$996$		−	792.298i		−	0.795480i
$997$	−166.538			−0.167040			−0.0835198	−	0.996506i	$-0.526616\pi$
$997$	−166.538			−0.167040			−0.0835198	+	0.996506i	$0.526616\pi$
$998$	−390.084			−0.390865
$999$	64.4127			0.0644772

Twists

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

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

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.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.54705 q^{2} +4.06604i q^{3} -1.60665 q^{4} +6.29036i q^{6} -8.53587 q^{7} -8.67374 q^{8} -7.53270 q^{9} +(7.63571 - 7.91807i) q^{11} -6.53270i q^{12} -16.6490 q^{13} -13.2054 q^{14} -6.99209 q^{16} +5.33961 q^{17} -11.6534 q^{18} -0.884280i q^{19} -34.7072i q^{21} +(11.8128 - 12.2496i) q^{22} +20.2635i q^{23} -35.2678i q^{24} -25.7568 q^{26} +5.96611i q^{27} +13.7141 q^{28} +40.3082i q^{29} -51.5865 q^{31} +23.8779 q^{32} +(32.1952 + 31.0471i) q^{33} +8.26062 q^{34} +12.1024 q^{36} -10.7964i q^{37} -1.36802i q^{38} -67.6956i q^{39} -36.1941i q^{41} -53.6937i q^{42} -74.3649 q^{43} +(-12.2679 + 12.7216i) q^{44} +31.3486i q^{46} +72.2589i q^{47} -28.4301i q^{48} +23.8611 q^{49} +21.7111i q^{51} +26.7491 q^{52} -13.8913i q^{53} +9.22985i q^{54} +74.0380 q^{56} +3.59552 q^{57} +62.3587i q^{58} +26.9285 q^{59} +45.5691i q^{61} -79.8067 q^{62} +64.2981 q^{63} +64.9086 q^{64} +(49.8075 + 48.0314i) q^{66} +78.3584i q^{67} -8.57887 q^{68} -82.3923 q^{69} +66.9670 q^{71} +65.3367 q^{72} +27.9462 q^{73} -16.7026i q^{74} +1.42073i q^{76} +(-65.1775 + 67.5876i) q^{77} -104.728i q^{78} +10.4721i q^{79} -92.0527 q^{81} -55.9939i q^{82} +121.282 q^{83} +55.7623i q^{84} -115.046 q^{86} -163.895 q^{87} +(-66.2302 + 68.6793i) q^{88} -19.7361 q^{89} +142.114 q^{91} -32.5563i q^{92} -209.753i q^{93} +111.788i q^{94} +97.0885i q^{96} -148.321i q^{97} +36.9142 q^{98} +(-57.5175 + 59.6444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{4} - 64 q^{9} - 2 q^{11} - 36 q^{14} - 28 q^{16} + 136 q^{26} - 84 q^{31} + 284 q^{34} - 168 q^{36} - 138 q^{44} + 100 q^{49} + 332 q^{56} + 320 q^{59} - 576 q^{64} - 630 q^{66} + 32 q^{69}+ \cdots - 736 q^{99}+O(q^{100}) \) 16 * q + 20 * q^4 - 64 * q^9 - 2 * q^11 - 36 * q^14 - 28 * q^16 + 136 * q^26 - 84 * q^31 + 284 * q^34 - 168 * q^36 - 138 * q^44 + 100 * q^49 + 332 * q^56 + 320 * q^59 - 576 * q^64 - 630 * q^66 + 32 * q^69 + 492 * q^71 + 608 * q^81 - 564 * q^86 + 36 * q^89 - 284 * q^91 - 736 * q^99

Introduction

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