LMFDB - Embedded newform 315.3.h.d.181.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(181,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("315.181");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.8
Root			$-1.01714 - 1.76174i$ of defining polynomial
Character	$\chi$	$=$	315.181
Dual form			315.3.h.d.181.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.71214 q^{2} -1.06857 q^{4} +2.23607i q^{5} +(-3.33344 - 6.15534i) q^{7} -8.67811 q^{8} +O(q^{10})$	\(q+1.71214 q^{2} -1.06857 q^{4} +2.23607i q^{5} +(-3.33344 - 6.15534i) q^{7} -8.67811 q^{8} +3.82847i q^{10} -17.0001 q^{11} -16.3319i q^{13} +(-5.70733 - 10.5388i) q^{14} -10.5839 q^{16} +13.4266i q^{17} -13.7499i q^{19} -2.38940i q^{20} -29.1066 q^{22} +16.6179 q^{23} -5.00000 q^{25} -27.9626i q^{26} +(3.56202 + 6.57741i) q^{28} -32.1793 q^{29} +6.74366i q^{31} +16.5913 q^{32} +22.9883i q^{34} +(13.7637 - 7.45380i) q^{35} -69.2141 q^{37} -23.5418i q^{38} -19.4048i q^{40} -39.7391i q^{41} +43.2210 q^{43} +18.1658 q^{44} +28.4522 q^{46} +40.1384i q^{47} +(-26.7763 + 41.0369i) q^{49} -8.56071 q^{50} +17.4518i q^{52} -22.5002 q^{53} -38.0134i q^{55} +(28.9280 + 53.4167i) q^{56} -55.0956 q^{58} +81.6005i q^{59} -14.9859i q^{61} +11.5461i q^{62} +70.7422 q^{64} +36.5193 q^{65} +72.0872 q^{67} -14.3473i q^{68} +(23.5655 - 12.7620i) q^{70} +25.7338 q^{71} -75.0647i q^{73} -118.504 q^{74} +14.6927i q^{76} +(56.6689 + 104.641i) q^{77} +80.0480 q^{79} -23.6663i q^{80} -68.0389i q^{82} -102.112i q^{83} -30.0228 q^{85} +74.0005 q^{86} +147.529 q^{88} -128.381i q^{89} +(-100.529 + 54.4416i) q^{91} -17.7574 q^{92} +68.7227i q^{94} +30.7457 q^{95} +159.448i q^{97} +(-45.8449 + 70.2610i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8	$ 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8} + 16 q^{11} + 40 q^{14} + 92 q^{16} - 88 q^{22} + 64 q^{23} - 60 q^{25} + 88 q^{28} - 104 q^{29} + 228 q^{32} - 60 q^{35} + 32 q^{37} + 152 q^{43} - 192 q^{44} + 200 q^{46} + 60 q^{49} - 20 q^{50} - 176 q^{53} + 368 q^{56} - 400 q^{58} - 20 q^{64} + 240 q^{65} + 168 q^{67} - 60 q^{70} - 32 q^{71} - 184 q^{74} - 8 q^{77} + 120 q^{79} + 120 q^{85} - 400 q^{86} - 536 q^{88} + 24 q^{91} - 192 q^{92} - 884 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8 + 16 * q^11 + 40 * q^14 + 92 * q^16 - 88 * q^22 + 64 * q^23 - 60 * q^25 + 88 * q^28 - 104 * q^29 + 228 * q^32 - 60 * q^35 + 32 * q^37 + 152 * q^43 - 192 * q^44 + 200 * q^46 + 60 * q^49 - 20 * q^50 - 176 * q^53 + 368 * q^56 - 400 * q^58 - 20 * q^64 + 240 * q^65 + 168 * q^67 - 60 * q^70 - 32 * q^71 - 184 * q^74 - 8 * q^77 + 120 * q^79 + 120 * q^85 - 400 * q^86 - 536 * q^88 + 24 * q^91 - 192 * q^92 - 884 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.71214			0.856071			0.428035	−	0.903762i	$-0.359206\pi$
$2$	1.71214			0.856071			0.428035	+	0.903762i	$0.359206\pi$
$3$		0			0
$3$		0			0
$4$	−1.06857			−0.267143
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$		0			0
$7$	−3.33344	−	6.15534i	−0.476206	−	0.879334i
$7$	−3.33344	−	6.15534i	−0.476206	−	0.879334i
$8$	−8.67811			−1.08476
$9$		0			0
$10$			3.82847i			0.382847i
$11$	−17.0001			−1.54546			−0.772732	−	0.634732i	$-0.781110\pi$
$11$	−17.0001			−1.54546			−0.772732	+	0.634732i	$0.781110\pi$
$12$		0			0
$13$		−	16.3319i		−	1.25630i	−0.778091	−	0.628152i	$-0.783812\pi$
$13$		−	16.3319i		−	1.25630i	0.778091	−	0.628152i	$-0.216188\pi$
$14$	−5.70733	−	10.5388i	−0.407666	−	0.752772i
$15$		0			0
$16$	−10.5839			−0.661492
$17$			13.4266i			0.789801i	0.918724	+	0.394900i	$0.129221\pi$
$17$			13.4266i			0.789801i	−0.918724	+	0.394900i	$0.870779\pi$
$18$		0			0
$19$		−	13.7499i		−	0.723679i	−0.932240	−	0.361839i	$-0.882149\pi$
$19$		−	13.7499i		−	0.723679i	0.932240	−	0.361839i	$-0.117851\pi$
$20$		−	2.38940i		−	0.119470i
$21$		0			0
$22$	−29.1066			−1.32303
$23$	16.6179			0.722518			0.361259	−	0.932466i	$-0.382347\pi$
$23$	16.6179			0.722518			0.361259	+	0.932466i	$0.382347\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$		−	27.9626i		−	1.07548i
$27$		0			0
$28$	3.56202	+	6.57741i	0.127215	+	0.234907i
$29$	−32.1793			−1.10963			−0.554816	−	0.831973i	$-0.687211\pi$
$29$	−32.1793			−1.10963			−0.554816	+	0.831973i	$0.687211\pi$
$30$		0			0
$31$			6.74366i			0.217538i	0.994067	+	0.108769i	$0.0346908\pi$
$31$			6.74366i			0.217538i	−0.994067	+	0.108769i	$0.965309\pi$
$32$	16.5913			0.518480
$33$		0			0
$34$			22.9883i			0.676125i
$35$	13.7637	−	7.45380i	0.393250	−	0.212966i
$36$		0			0
$37$	−69.2141			−1.87065			−0.935325	−	0.353789i	$-0.884893\pi$
$37$	−69.2141			−1.87065			−0.935325	+	0.353789i	$0.884893\pi$
$38$		−	23.5418i		−	0.619520i
$39$		0			0
$40$		−	19.4048i		−	0.485121i
$41$		−	39.7391i		−	0.969246i	−0.874723	−	0.484623i	$-0.838957\pi$
$41$		−	39.7391i		−	0.969246i	0.874723	−	0.484623i	$-0.161043\pi$
$42$		0			0
$43$	43.2210			1.00514			0.502570	−	0.864537i	$-0.332388\pi$
$43$	43.2210			1.00514			0.502570	+	0.864537i	$0.332388\pi$
$44$	18.1658			0.412859
$45$		0			0
$46$	28.4522			0.618526
$47$			40.1384i			0.854009i	0.904249	+	0.427005i	$0.140431\pi$
$47$			40.1384i			0.854009i	−0.904249	+	0.427005i	$0.859569\pi$
$48$		0			0
$49$	−26.7763	+	41.0369i	−0.546456	+	0.837488i
$50$	−8.56071			−0.171214
$51$		0			0
$52$			17.4518i			0.335612i
$53$	−22.5002			−0.424533			−0.212266	−	0.977212i	$-0.568084\pi$
$53$	−22.5002			−0.424533			−0.212266	+	0.977212i	$0.568084\pi$
$54$		0			0
$55$		−	38.0134i		−	0.691153i
$56$	28.9280	+	53.4167i	0.516571	+	0.953869i
$57$		0			0
$58$	−55.0956			−0.949924
$59$			81.6005i			1.38306i	0.722348	+	0.691529i	$0.243063\pi$
$59$			81.6005i			1.38306i	−0.722348	+	0.691529i	$0.756937\pi$
$60$		0			0
$61$		−	14.9859i		−	0.245671i	−0.992427	−	0.122836i	$-0.960801\pi$
$61$		−	14.9859i		−	0.245671i	0.992427	−	0.122836i	$-0.0391988\pi$
$62$			11.5461i			0.186228i
$63$		0			0
$64$	70.7422			1.10535
$65$	36.5193			0.561836
$66$		0			0
$67$	72.0872			1.07593			0.537964	−	0.842968i	$-0.319194\pi$
$67$	72.0872			1.07593			0.537964	+	0.842968i	$0.319194\pi$
$68$		−	14.3473i		−	0.210989i
$69$		0			0
$70$	23.5655	−	12.7620i	0.336650	−	0.182314i
$71$	25.7338			0.362448			0.181224	−	0.983442i	$-0.441994\pi$
$71$	25.7338			0.362448			0.181224	+	0.983442i	$0.441994\pi$
$72$		0			0
$73$		−	75.0647i		−	1.02828i	−0.857705	−	0.514142i	$-0.828110\pi$
$73$		−	75.0647i		−	1.02828i	0.857705	−	0.514142i	$-0.171890\pi$
$74$	−118.504			−1.60141
$75$		0			0
$76$			14.6927i			0.193325i
$77$	56.6689	+	104.641i	0.735959	+	1.35898i
$78$		0			0
$79$	80.0480			1.01327			0.506633	−	0.862162i	$-0.330890\pi$
$79$	80.0480			1.01327			0.506633	+	0.862162i	$0.330890\pi$
$80$		−	23.6663i		−	0.295828i
$81$		0			0
$82$		−	68.0389i		−	0.829743i
$83$		−	102.112i		−	1.23027i	−0.788421	−	0.615135i	$-0.789101\pi$
$83$		−	102.112i		−	1.23027i	0.788421	−	0.615135i	$-0.210899\pi$
$84$		0			0
$85$	−30.0228			−0.353210
$86$	74.0005			0.860471
$87$		0			0
$88$	147.529			1.67646
$89$		−	128.381i		−	1.44248i	−0.692683	−	0.721242i	$-0.743571\pi$
$89$		−	128.381i		−	1.44248i	0.692683	−	0.721242i	$-0.256429\pi$
$90$		0			0
$91$	−100.529	+	54.4416i	−1.10471	+	0.598259i
$92$	−17.7574			−0.193015
$93$		0			0
$94$			68.7227i			0.731092i
$95$	30.7457			0.323639
$96$		0			0
$97$			159.448i			1.64379i	0.569636	+	0.821897i	$0.307084\pi$
$97$			159.448i			1.64379i	−0.569636	+	0.821897i	$0.692916\pi$
$98$	−45.8449	+	70.2610i	−0.467805	+	0.716949i
$99$		0			0
$100$	5.34285			0.0534285
$101$		−	24.1380i		−	0.238990i	−0.992835	−	0.119495i	$-0.961872\pi$
$101$		−	24.1380i		−	0.238990i	0.992835	−	0.119495i	$-0.0381276\pi$
$102$		0			0
$103$		−	87.3469i		−	0.848028i	−0.905656	−	0.424014i	$-0.860621\pi$
$103$		−	87.3469i		−	0.848028i	0.905656	−	0.424014i	$-0.139379\pi$
$104$			141.730i			1.36279i
$105$		0			0
$106$	−38.5236			−0.363430
$107$	−168.359			−1.57344			−0.786722	−	0.617307i	$-0.788224\pi$
$107$	−168.359			−1.57344			−0.786722	+	0.617307i	$0.788224\pi$
$108$		0			0
$109$	−155.570			−1.42725			−0.713624	−	0.700529i	$-0.752947\pi$
$109$	−155.570			−1.42725			−0.713624	+	0.700529i	$0.752947\pi$
$110$		−	65.0843i		−	0.591676i
$111$		0			0
$112$	35.2807	+	65.1473i	0.315007	+	0.581672i
$113$	20.9965			0.185810			0.0929050	−	0.995675i	$-0.470385\pi$
$113$	20.9965			0.185810			0.0929050	+	0.995675i	$0.470385\pi$
$114$		0			0
$115$			37.1588i			0.323120i
$116$	34.3859			0.296430
$117$		0			0
$118$			139.712i			1.18400i
$119$	82.6453	−	44.7568i	0.694498	−	0.376108i
$120$		0			0
$121$	168.004			1.38846
$122$		−	25.6581i		−	0.210312i
$123$		0			0
$124$		−	7.20608i		−	0.0581135i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	−59.8712			−0.471427			−0.235713	−	0.971823i	$-0.575743\pi$
$127$	−59.8712			−0.471427			−0.235713	+	0.971823i	$0.575743\pi$
$128$	54.7554			0.427776
$129$		0			0
$130$	62.5263			0.480971
$131$		−	166.868i		−	1.27380i	−0.770947	−	0.636899i	$-0.780217\pi$
$131$		−	166.868i		−	1.27380i	0.770947	−	0.636899i	$-0.219783\pi$
$132$		0			0
$133$	−84.6352	+	45.8345i	−0.636355	+	0.344620i
$134$	123.423			0.921071
$135$		0			0
$136$		−	116.518i		−	0.856747i
$137$	−126.139			−0.920726			−0.460363	−	0.887731i	$-0.652281\pi$
$137$	−126.139			−0.920726			−0.460363	+	0.887731i	$0.652281\pi$
$138$		0			0
$139$		−	211.650i		−	1.52266i	−0.648365	−	0.761330i	$-0.724547\pi$
$139$		−	211.650i		−	1.52266i	0.648365	−	0.761330i	$-0.275453\pi$
$140$	−14.7075	+	7.96491i	−0.105054	+	0.0568922i
$141$		0			0
$142$	44.0599			0.310281
$143$			277.645i			1.94157i
$144$		0			0
$145$		−	71.9552i		−	0.496243i
$146$		−	128.521i		−	0.880284i
$147$		0			0
$148$	73.9601			0.499730
$149$	64.1825			0.430755			0.215377	−	0.976531i	$-0.430902\pi$
$149$	64.1825			0.430755			0.215377	+	0.976531i	$0.430902\pi$
$150$		0			0
$151$	110.915			0.734538			0.367269	−	0.930115i	$-0.380293\pi$
$151$	110.915			0.734538			0.367269	+	0.930115i	$0.380293\pi$
$152$			119.323i			0.785021i
$153$		0			0
$154$	97.0252	+	179.161i	0.630033	+	1.16338i
$155$	−15.0793			−0.0972858
$156$		0			0
$157$			290.451i			1.85001i	0.379956	+	0.925004i	$0.375939\pi$
$157$			290.451i			1.85001i	−0.379956	+	0.925004i	$0.624061\pi$
$158$	137.053			0.867427
$159$		0			0
$160$			37.0994i			0.231871i
$161$	−55.3948	−	102.289i	−0.344067	−	0.635334i
$162$		0			0
$163$	−53.8559			−0.330404			−0.165202	−	0.986260i	$-0.552828\pi$
$163$	−53.8559			−0.330404			−0.165202	+	0.986260i	$0.552828\pi$
$164$			42.4640i			0.258927i
$165$		0			0
$166$		−	174.831i		−	1.05320i
$167$			41.7927i			0.250255i	0.992141	+	0.125128i	$0.0399341\pi$
$167$			41.7927i			0.250255i	−0.992141	+	0.125128i	$0.960066\pi$
$168$		0			0
$169$	−97.7324			−0.578298
$170$	−51.4033			−0.302372
$171$		0			0
$172$	−46.1847			−0.268515
$173$		−	130.344i		−	0.753434i	−0.926328	−	0.376717i	$-0.877053\pi$
$173$		−	130.344i		−	0.753434i	0.926328	−	0.376717i	$-0.122947\pi$
$174$		0			0
$175$	16.6672	+	30.7767i	0.0952412	+	0.175867i
$176$	179.927			1.02231
$177$		0			0
$178$		−	219.807i		−	1.23487i
$179$	−44.9934			−0.251360			−0.125680	−	0.992071i	$-0.540111\pi$
$179$	−44.9934			−0.251360			−0.125680	+	0.992071i	$0.540111\pi$
$180$		0			0
$181$		−	17.8944i		−	0.0988640i	−0.998777	−	0.0494320i	$-0.984259\pi$
$181$		−	17.8944i		−	0.0988640i	0.998777	−	0.0494320i	$-0.0157411\pi$
$182$	−172.119	+	93.2117i	−0.945710	+	0.512152i
$183$		0			0
$184$	−144.212			−0.783761
$185$		−	154.767i		−	0.836581i
$186$		0			0
$187$		−	228.254i		−	1.22061i
$188$		−	42.8907i		−	0.228142i
$189$		0			0
$190$	52.6410			0.277058
$191$	−178.314			−0.933583			−0.466791	−	0.884367i	$-0.654590\pi$
$191$	−178.314			−0.933583			−0.466791	+	0.884367i	$0.654590\pi$
$192$		0			0
$193$	−336.283			−1.74240			−0.871200	−	0.490928i	$-0.836658\pi$
$193$	−336.283			−1.74240			−0.871200	+	0.490928i	$0.836658\pi$
$194$			272.998i			1.40720i
$195$		0			0
$196$	28.6124	−	43.8508i	0.145982	−	0.223729i
$197$	−49.2082			−0.249788			−0.124894	−	0.992170i	$-0.539859\pi$
$197$	−49.2082			−0.249788			−0.124894	+	0.992170i	$0.539859\pi$
$198$		0			0
$199$		−	171.789i		−	0.863262i	−0.902050	−	0.431631i	$-0.857938\pi$
$199$		−	171.789i		−	0.863262i	0.902050	−	0.431631i	$-0.142062\pi$
$200$	43.3906			0.216953
$201$		0			0
$202$		−	41.3277i		−	0.204592i
$203$	107.268	+	198.075i	0.528414	+	0.975737i
$204$		0			0
$205$	88.8593			0.433460
$206$		−	149.550i		−	0.725972i
$207$		0			0
$208$			172.855i			0.831035i
$209$			233.750i			1.11842i
$210$		0			0
$211$	−5.09458			−0.0241449			−0.0120725	−	0.999927i	$-0.503843\pi$
$211$	−5.09458			−0.0241449			−0.0120725	+	0.999927i	$0.503843\pi$
$212$	24.0431			0.113411
$213$		0			0
$214$	−288.254			−1.34698
$215$			96.6451i			0.449512i
$216$		0			0
$217$	41.5095	−	22.4796i	0.191288	−	0.103593i
$218$	−266.358			−1.22183
$219$		0			0
$220$			40.6200i			0.184636i
$221$	219.283			0.992229
$222$		0			0
$223$			310.066i			1.39043i	0.718802	+	0.695215i	$0.244691\pi$
$223$			310.066i			1.39043i	−0.718802	+	0.695215i	$0.755309\pi$
$224$	−55.3063	−	102.125i	−0.246903	−	0.455917i
$225$		0			0
$226$	35.9490			0.159067
$227$		−	108.558i		−	0.478228i	−0.970991	−	0.239114i	$-0.923143\pi$
$227$		−	108.558i		−	0.478228i	0.970991	−	0.239114i	$-0.0768570\pi$
$228$		0			0
$229$		−	236.483i		−	1.03268i	−0.856384	−	0.516339i	$-0.827294\pi$
$229$		−	236.483i		−	1.03268i	0.856384	−	0.516339i	$-0.172706\pi$
$230$			63.6211i			0.276613i
$231$		0			0
$232$	279.256			1.20369
$233$	−151.290			−0.649312			−0.324656	−	0.945832i	$-0.605249\pi$
$233$	−151.290			−0.649312			−0.324656	+	0.945832i	$0.605249\pi$
$234$		0			0
$235$	−89.7523			−0.381925
$236$		−	87.1958i		−	0.369474i
$237$		0			0
$238$	141.500	−	76.6300i	0.594540	−	0.321975i
$239$	−48.2956			−0.202074			−0.101037	−	0.994883i	$-0.532216\pi$
$239$	−48.2956			−0.202074			−0.101037	+	0.994883i	$0.532216\pi$
$240$		0			0
$241$		−	230.735i		−	0.957406i	−0.877977	−	0.478703i	$-0.841107\pi$
$241$		−	230.735i		−	0.957406i	0.877977	−	0.478703i	$-0.158893\pi$
$242$	287.646			1.18862
$243$		0			0
$244$			16.0135i			0.0656292i
$245$	−91.7613	−	59.8737i	−0.374536	−	0.244382i
$246$		0			0
$247$	−224.563			−0.909160
$248$		−	58.5223i		−	0.235977i
$249$		0			0
$250$		−	19.1423i		−	0.0765693i
$251$		−	86.6812i		−	0.345343i	−0.984979	−	0.172672i	$-0.944760\pi$
$251$		−	86.6812i		−	0.345343i	0.984979	−	0.172672i	$-0.0552399\pi$
$252$		0			0
$253$	−282.506			−1.11663
$254$	−102.508			−0.403575
$255$		0			0
$256$	−189.220			−0.739141
$257$		−	141.110i		−	0.549065i	−0.961578	−	0.274532i	$-0.911477\pi$
$257$		−	141.110i		−	0.549065i	0.961578	−	0.274532i	$-0.0885231\pi$
$258$		0			0
$259$	230.721	+	426.036i	0.890815	+	1.64493i
$260$	−39.0235			−0.150090
$261$		0			0
$262$		−	285.701i		−	1.09046i
$263$	−38.0901			−0.144829			−0.0724147	−	0.997375i	$-0.523070\pi$
$263$	−38.0901			−0.144829			−0.0724147	+	0.997375i	$0.523070\pi$
$264$		0			0
$265$		−	50.3121i		−	0.189857i
$266$	−144.908	+	78.4752i	−0.544765	+	0.295019i
$267$		0			0
$268$	−77.0302			−0.287426
$269$		−	454.220i		−	1.68855i	−0.535909	−	0.844275i	$-0.680031\pi$
$269$		−	454.220i		−	1.68855i	0.535909	−	0.844275i	$-0.319969\pi$
$270$		0			0
$271$		−	78.7098i		−	0.290442i	−0.989399	−	0.145221i	$-0.953611\pi$
$271$		−	78.7098i		−	0.290442i	0.989399	−	0.145221i	$-0.0463893\pi$
$272$		−	142.106i		−	0.522447i
$273$		0			0
$274$	−215.969			−0.788207
$275$	85.0005			0.309093
$276$		0			0
$277$	−85.3396			−0.308085			−0.154043	−	0.988064i	$-0.549229\pi$
$277$	−85.3396			−0.308085			−0.154043	+	0.988064i	$0.549229\pi$
$278$		−	362.374i		−	1.30350i
$279$		0			0
$280$	−119.443	+	64.6849i	−0.426583	+	0.231018i
$281$	−167.376			−0.595643			−0.297821	−	0.954622i	$-0.596260\pi$
$281$	−167.376			−0.595643			−0.297821	+	0.954622i	$0.596260\pi$
$282$		0			0
$283$			149.591i			0.528588i	0.964442	+	0.264294i	$0.0851390\pi$
$283$			149.591i			0.528588i	−0.964442	+	0.264294i	$0.914861\pi$
$284$	−27.4984			−0.0968252
$285$		0			0
$286$			475.367i			1.66212i
$287$	−244.607	+	132.468i	−0.852291	+	0.461561i
$288$		0			0
$289$	108.726			0.376215
$290$		−	123.197i		−	0.424819i
$291$		0			0
$292$			80.2119i			0.274698i
$293$			145.805i			0.497627i	0.968551	+	0.248813i	$0.0800406\pi$
$293$			145.805i			0.497627i	−0.968551	+	0.248813i	$0.919959\pi$
$294$		0			0
$295$	−182.464			−0.618523
$296$	600.648			2.02921
$297$		0			0
$298$	109.889			0.368757
$299$		−	271.403i		−	0.907701i
$300$		0			0
$301$	−144.075	−	266.040i	−0.478653	−	0.883853i
$302$	189.903			0.628817
$303$		0			0
$304$			145.527i			0.478708i
$305$	33.5096			0.109868
$306$		0			0
$307$			205.594i			0.669686i	0.942274	+	0.334843i	$0.108683\pi$
$307$			205.594i			0.669686i	−0.942274	+	0.334843i	$0.891317\pi$
$308$	−60.5547	−	111.817i	−0.196606	−	0.363041i
$309$		0			0
$310$	−25.8179			−0.0832835
$311$			424.383i			1.36458i	0.731084	+	0.682288i	$0.239015\pi$
$311$			424.383i			1.36458i	−0.731084	+	0.682288i	$0.760985\pi$
$312$		0			0
$313$		−	363.503i		−	1.16135i	−0.814135	−	0.580676i	$-0.802788\pi$
$313$		−	363.503i		−	1.16135i	0.814135	−	0.580676i	$-0.197212\pi$
$314$			497.294i			1.58374i
$315$		0			0
$316$	−85.5369			−0.270686
$317$	−441.407			−1.39245			−0.696226	−	0.717822i	$-0.745139\pi$
$317$	−441.407			−1.39245			−0.696226	+	0.717822i	$0.745139\pi$
$318$		0			0
$319$	547.052			1.71490
$320$			158.184i			0.494326i
$321$		0			0
$322$	−94.8438	−	175.133i	−0.294546	−	0.543891i
$323$	184.615			0.571562
$324$		0			0
$325$			81.6597i			0.251261i
$326$	−92.2089			−0.282849
$327$		0			0
$328$			344.860i			1.05140i
$329$	247.066	−	133.799i	0.750959	−	0.406684i
$330$		0			0
$331$	509.327			1.53875			0.769376	−	0.638796i	$-0.220567\pi$
$331$	509.327			1.53875			0.769376	+	0.638796i	$0.220567\pi$
$332$			109.114i			0.328658i
$333$		0			0
$334$			71.5550i			0.214236i
$335$			161.192i			0.481170i
$336$		0			0
$337$	442.557			1.31323			0.656613	−	0.754228i	$-0.271988\pi$
$337$	442.557			1.31323			0.656613	+	0.754228i	$0.271988\pi$
$338$	−167.332			−0.495064
$339$		0			0
$340$	32.0815			0.0943573
$341$		−	114.643i		−	0.336197i
$342$		0			0
$343$	341.853	+	28.0231i	0.996657	+	0.0816999i
$344$	−375.077			−1.09034
$345$		0			0
$346$		−	223.167i		−	0.644993i
$347$	493.763			1.42295			0.711475	−	0.702712i	$-0.248028\pi$
$347$	493.763			1.42295			0.711475	+	0.702712i	$0.248028\pi$
$348$		0			0
$349$		−	324.460i		−	0.929686i	−0.885393	−	0.464843i	$-0.846111\pi$
$349$		−	324.460i		−	0.929686i	0.885393	−	0.464843i	$-0.153889\pi$
$350$	28.5366	+	52.6940i	0.0815332	+	0.150554i
$351$		0			0
$352$	−282.055			−0.801292
$353$			529.424i			1.49979i	0.661559	+	0.749893i	$0.269895\pi$
$353$			529.424i			1.49979i	−0.661559	+	0.749893i	$0.730105\pi$
$354$		0			0
$355$			57.5425i			0.162092i
$356$			137.184i			0.385349i
$357$		0			0
$358$	−77.0351			−0.215182
$359$	−64.2261			−0.178903			−0.0894514	−	0.995991i	$-0.528511\pi$
$359$	−64.2261			−0.178903			−0.0894514	+	0.995991i	$0.528511\pi$
$360$		0			0
$361$	171.940			0.476289
$362$		−	30.6377i		−	0.0846346i
$363$		0			0
$364$	107.422	−	58.1747i	0.295115	−	0.159821i
$365$	167.850			0.459863
$366$		0			0
$367$			10.8172i			0.0294747i	0.999891	+	0.0147373i	$0.00469121\pi$
$367$			10.8172i			0.0294747i	−0.999891	+	0.0147373i	$0.995309\pi$
$368$	−175.882			−0.477940
$369$		0			0
$370$		−	264.984i		−	0.716172i
$371$	75.0033	+	138.497i	0.202165	+	0.373306i
$372$		0			0
$373$	532.850			1.42855			0.714276	−	0.699864i	$-0.246756\pi$
$373$	532.850			1.42855			0.714276	+	0.699864i	$0.246756\pi$
$374$		−	390.803i		−	1.04493i
$375$		0			0
$376$		−	348.326i		−	0.926398i
$377$			525.551i			1.39403i
$378$		0			0
$379$	516.003			1.36149			0.680743	−	0.732523i	$-0.261657\pi$
$379$	516.003			1.36149			0.680743	+	0.732523i	$0.261657\pi$
$380$	−32.8539			−0.0864578
$381$		0			0
$382$	−305.299			−0.799213
$383$			415.069i			1.08373i	0.840465	+	0.541866i	$0.182282\pi$
$383$			415.069i			1.08373i	−0.840465	+	0.541866i	$0.817718\pi$
$384$		0			0
$385$	−233.985	+	126.715i	−0.607754	+	0.329131i
$386$	−575.765			−1.49162
$387$		0			0
$388$		−	170.381i		−	0.439127i
$389$	−54.8032			−0.140882			−0.0704411	−	0.997516i	$-0.522441\pi$
$389$	−54.8032			−0.140882			−0.0704411	+	0.997516i	$0.522441\pi$
$390$		0			0
$391$			223.122i			0.570645i
$392$	232.368	−	356.123i	0.592775	−	0.908477i
$393$		0			0
$394$	−84.2514			−0.213836
$395$			178.993i			0.453146i
$396$		0			0
$397$		−	19.9434i		−	0.0502352i	−0.999685	−	0.0251176i	$-0.992004\pi$
$397$		−	19.9434i		−	0.0502352i	0.999685	−	0.0251176i	$-0.00799602\pi$
$398$		−	294.127i		−	0.739013i
$399$		0			0
$400$	52.9194			0.132298
$401$	239.505			0.597269			0.298634	−	0.954368i	$-0.403469\pi$
$401$	239.505			0.597269			0.298634	+	0.954368i	$0.403469\pi$
$402$		0			0
$403$	110.137			0.273293
$404$			25.7931i			0.0638444i
$405$		0			0
$406$	183.658	+	339.132i	0.452359	+	0.835300i
$407$	1176.65			2.89102
$408$		0			0
$409$			663.541i			1.62235i	0.584804	+	0.811175i	$0.301171\pi$
$409$			663.541i			1.62235i	−0.584804	+	0.811175i	$0.698829\pi$
$410$	152.140			0.371072
$411$		0			0
$412$			93.3363i			0.226544i
$413$	502.278	−	272.010i	1.21617	−	0.658621i
$414$		0			0
$415$	228.330			0.550194
$416$		−	270.969i		−	0.651368i
$417$		0			0
$418$			400.213i			0.957447i
$419$			110.648i			0.264077i	0.991245	+	0.132039i	$0.0421523\pi$
$419$			110.648i			0.264077i	−0.991245	+	0.132039i	$0.957848\pi$
$420$		0			0
$421$	−521.325			−1.23830			−0.619151	−	0.785272i	$-0.712523\pi$
$421$	−521.325			−1.23830			−0.619151	+	0.785272i	$0.712523\pi$
$422$	−8.72264			−0.0206698
$423$		0			0
$424$	195.260			0.460518
$425$		−	67.1330i		−	0.157960i
$426$		0			0
$427$	−92.2435	+	49.9548i	−0.216027	+	0.116990i
$428$	179.903			0.420334
$429$		0			0
$430$			165.470i			0.384814i
$431$	−573.019			−1.32951			−0.664755	−	0.747062i	$-0.731464\pi$
$431$	−573.019			−1.32951			−0.664755	+	0.747062i	$0.731464\pi$
$432$		0			0
$433$			429.740i			0.992472i	0.868188	+	0.496236i	$0.165285\pi$
$433$			429.740i			0.992472i	−0.868188	+	0.496236i	$0.834715\pi$
$434$	71.0702	−	38.4883i	0.163756	−	0.0886827i
$435$		0			0
$436$	166.237			0.381279
$437$		−	228.495i		−	0.522871i
$438$		0			0
$439$		−	83.0494i		−	0.189179i	−0.995516	−	0.0945893i	$-0.969846\pi$
$439$		−	83.0494i		−	0.189179i	0.995516	−	0.0945893i	$-0.0301538\pi$
$440$			329.884i			0.749737i
$441$		0			0
$442$	375.443			0.849419
$443$	410.010			0.925530			0.462765	−	0.886481i	$-0.346857\pi$
$443$	410.010			0.925530			0.462765	+	0.886481i	$0.346857\pi$
$444$		0			0
$445$	287.069			0.645099
$446$			530.876i			1.19031i
$447$		0			0
$448$	−235.815	−	435.442i	−0.526373	−	0.971969i
$449$	205.948			0.458682			0.229341	−	0.973346i	$-0.426343\pi$
$449$	205.948			0.458682			0.229341	+	0.973346i	$0.426343\pi$
$450$		0			0
$451$			675.569i			1.49793i
$452$	−22.4363			−0.0496378
$453$		0			0
$454$		−	185.866i		−	0.409397i
$455$	−121.735	−	224.789i	−0.267550	−	0.494041i
$456$		0			0
$457$	−640.868			−1.40234			−0.701169	−	0.712995i	$-0.747338\pi$
$457$	−640.868			−1.40234			−0.701169	+	0.712995i	$0.747338\pi$
$458$		−	404.893i		−	0.884046i
$459$		0			0
$460$		−	39.7068i		−	0.0863190i
$461$			166.085i			0.360272i	0.983642	+	0.180136i	$0.0576538\pi$
$461$			166.085i			0.360272i	−0.983642	+	0.180136i	$0.942346\pi$
$462$		0			0
$463$	−10.4409			−0.0225505			−0.0112753	−	0.999936i	$-0.503589\pi$
$463$	−10.4409			−0.0225505			−0.0112753	+	0.999936i	$0.503589\pi$
$464$	340.582			0.734013
$465$		0			0
$466$	−259.029			−0.555857
$467$		−	269.736i		−	0.577592i	−0.957391	−	0.288796i	$-0.906745\pi$
$467$		−	269.736i		−	0.577592i	0.957391	−	0.288796i	$-0.0932550\pi$
$468$		0			0
$469$	−240.298	−	443.721i	−0.512364	−	0.946100i
$470$	−153.669			−0.326954
$471$		0			0
$472$		−	708.138i		−	1.50029i
$473$	−734.761			−1.55341
$474$		0			0
$475$			68.7495i			0.144736i
$476$	−88.3123	+	47.8258i	−0.185530	+	0.100474i
$477$		0			0
$478$	−82.6889			−0.172989
$479$		−	649.820i		−	1.35662i	−0.734777	−	0.678309i	$-0.762713\pi$
$479$		−	649.820i		−	1.35662i	0.734777	−	0.678309i	$-0.237287\pi$
$480$		0			0
$481$			1130.40i			2.35011i
$482$		−	395.051i		−	0.819608i
$483$		0			0
$484$	−179.524			−0.370917
$485$	−356.537			−0.735127
$486$		0			0
$487$	597.640			1.22719			0.613593	−	0.789622i	$-0.289723\pi$
$487$	597.640			1.22719			0.613593	+	0.789622i	$0.289723\pi$
$488$			130.050i			0.266495i
$489$		0			0
$490$	−157.108	−	102.512i	−0.320629	−	0.209209i
$491$	107.625			0.219195			0.109598	−	0.993976i	$-0.465044\pi$
$491$	107.625			0.219195			0.109598	+	0.993976i	$0.465044\pi$
$492$		0			0
$493$		−	432.059i		−	0.876388i
$494$	−384.483			−0.778306
$495$		0			0
$496$		−	71.3741i		−	0.143899i
$497$	−85.7821	−	158.400i	−0.172600	−	0.318713i
$498$		0			0
$499$	−420.611			−0.842908			−0.421454	−	0.906850i	$-0.638480\pi$
$499$	−420.611			−0.842908			−0.421454	+	0.906850i	$0.638480\pi$
$500$			11.9470i			0.0238940i
$501$		0			0
$502$		−	148.410i		−	0.295638i
$503$		−	837.716i		−	1.66544i	−0.553694	−	0.832720i	$-0.686782\pi$
$503$		−	837.716i		−	1.66544i	0.553694	−	0.832720i	$-0.313218\pi$
$504$		0			0
$505$	53.9742			0.106880
$506$	−483.691			−0.955910
$507$		0			0
$508$	63.9766			0.125938
$509$			511.304i			1.00453i	0.864715	+	0.502264i	$0.167499\pi$
$509$			511.304i			1.00453i	−0.864715	+	0.502264i	$0.832501\pi$
$510$		0			0
$511$	−462.049	+	250.224i	−0.904205	+	0.489675i
$512$	−542.993			−1.06053
$513$		0			0
$514$		−	241.600i		−	0.470038i
$515$	195.314			0.379250
$516$		0			0
$517$		−	682.358i		−	1.31984i
$518$	395.027	+	729.434i	0.762601	+	1.40817i
$519$		0			0
$520$	−316.919			−0.609459
$521$			958.401i			1.83954i	0.392455	+	0.919771i	$0.371626\pi$
$521$			958.401i			1.83954i	−0.392455	+	0.919771i	$0.628374\pi$
$522$		0			0
$523$			152.860i			0.292275i	0.989264	+	0.146138i	$0.0466843\pi$
$523$			152.860i			0.292275i	−0.989264	+	0.146138i	$0.953316\pi$
$524$			178.310i			0.340286i
$525$		0			0
$526$	−65.2157			−0.123984
$527$	−90.5445			−0.171811
$528$		0			0
$529$	−252.845			−0.477968
$530$		−	86.1414i		−	0.162531i
$531$		0			0
$532$	90.4387	−	48.9774i	0.169998	−	0.0920627i
$533$	−649.017			−1.21767
$534$		0			0
$535$		−	376.461i		−	0.703666i
$536$	−625.581			−1.16713
$537$		0			0
$538$		−	777.689i		−	1.44552i
$539$	455.200	−	697.632i	0.844527	−	1.29431i
$540$		0			0
$541$	−285.016			−0.526832			−0.263416	−	0.964682i	$-0.584849\pi$
$541$	−285.016			−0.526832			−0.263416	+	0.964682i	$0.584849\pi$
$542$		−	134.762i		−	0.248639i
$543$		0			0
$544$			222.766i			0.409495i
$545$		−	347.865i		−	0.638285i
$546$		0			0
$547$	−195.330			−0.357092			−0.178546	−	0.983932i	$-0.557139\pi$
$547$	−195.330			−0.357092			−0.178546	+	0.983932i	$0.557139\pi$
$548$	134.789			0.245965
$549$		0			0
$550$	145.533			0.264605
$551$			442.463i			0.803017i
$552$		0			0
$553$	−266.835	−	492.722i	−0.482523	−	0.890999i
$554$	−146.113			−0.263743
$555$		0			0
$556$			226.163i			0.406767i
$557$	27.9390			0.0501598			0.0250799	−	0.999685i	$-0.492016\pi$
$557$	27.9390			0.0501598			0.0250799	+	0.999685i	$0.492016\pi$
$558$		0			0
$559$		−	705.883i		−	1.26276i
$560$	−145.674	+	78.8901i	−0.260132	+	0.140875i
$561$		0			0
$562$	−286.571			−0.509912
$563$		−	459.585i		−	0.816314i	−0.912912	−	0.408157i	$-0.866172\pi$
$563$		−	459.585i		−	0.816314i	0.912912	−	0.408157i	$-0.133828\pi$
$564$		0			0
$565$			46.9497i			0.0830968i
$566$			256.120i			0.452509i
$567$		0			0
$568$	−223.321			−0.393170
$569$	635.353			1.11661			0.558306	−	0.829635i	$-0.311451\pi$
$569$	635.353			1.11661			0.558306	+	0.829635i	$0.311451\pi$
$570$		0			0
$571$	205.282			0.359513			0.179757	−	0.983711i	$-0.442469\pi$
$571$	205.282			0.359513			0.179757	+	0.983711i	$0.442469\pi$
$572$		−	296.683i		−	0.518676i
$573$		0			0
$574$	−418.803	+	226.804i	−0.729621	+	0.395129i
$575$	−83.0895			−0.144504
$576$		0			0
$577$			185.464i			0.321429i	0.987001	+	0.160714i	$0.0513798\pi$
$577$			185.464i			0.321429i	−0.987001	+	0.160714i	$0.948620\pi$
$578$	186.155			0.322067
$579$		0			0
$580$			76.8892i			0.132568i
$581$	−628.537	+	340.386i	−1.08182	+	0.585862i
$582$		0			0
$583$	382.506			0.656100
$584$			651.420i			1.11545i
$585$		0			0
$586$			249.638i			0.426004i
$587$		−	673.958i		−	1.14814i	−0.818806	−	0.574070i	$-0.805364\pi$
$587$		−	673.958i		−	1.14814i	0.818806	−	0.574070i	$-0.194636\pi$
$588$		0			0
$589$	92.7247			0.157427
$590$	−312.405			−0.529499
$591$		0			0
$592$	732.553			1.23742
$593$		−	0.486694i		−	0.000820731i	−1.00000		0.000410366i	$-0.999869\pi$
$593$		−	0.486694i		−	0.000820731i	1.00000		0.000410366i	$-0.000130623\pi$
$594$		0			0
$595$	100.079	+	184.800i	0.168201	+	0.310589i
$596$	−68.5835			−0.115073
$597$		0			0
$598$		−	464.680i		−	0.777057i
$599$	−580.285			−0.968756			−0.484378	−	0.874859i	$-0.660954\pi$
$599$	−580.285			−0.968756			−0.484378	+	0.874859i	$0.660954\pi$
$600$		0			0
$601$		−	781.851i		−	1.30092i	−0.759542	−	0.650459i	$-0.774577\pi$
$601$		−	781.851i		−	1.30092i	0.759542	−	0.650459i	$-0.225423\pi$
$602$	−246.676	−	455.498i	−0.409761	−	0.756641i
$603$		0			0
$604$	−118.521			−0.196226
$605$			375.667i			0.620938i
$606$		0			0
$607$			907.211i			1.49458i	0.664498	+	0.747290i	$0.268646\pi$
$607$			907.211i			1.49458i	−0.664498	+	0.747290i	$0.731354\pi$
$608$		−	228.129i		−	0.375213i
$609$		0			0
$610$	57.3732			0.0940544
$611$	655.539			1.07289
$612$		0			0
$613$	−911.642			−1.48718			−0.743590	−	0.668636i	$-0.766879\pi$
$613$	−911.642			−1.48718			−0.743590	+	0.668636i	$0.766879\pi$
$614$			352.006i			0.573299i
$615$		0			0
$616$	−491.779	−	908.089i	−0.798342	−	1.47417i
$617$	−637.918			−1.03390			−0.516951	−	0.856015i	$-0.672933\pi$
$617$	−637.918			−1.03390			−0.516951	+	0.856015i	$0.672933\pi$
$618$		0			0
$619$			862.604i			1.39354i	0.717292	+	0.696772i	$0.245381\pi$
$619$			862.604i			1.39354i	−0.717292	+	0.696772i	$0.754619\pi$
$620$	16.1133			0.0259892
$621$		0			0
$622$			726.604i			1.16817i
$623$	−790.229	+	427.951i	−1.26843	+	0.686920i
$624$		0			0
$625$	25.0000			0.0400000
$626$		−	622.369i		−	0.994200i
$627$		0			0
$628$		−	310.368i		−	0.494216i
$629$		−	929.310i		−	1.47744i
$630$		0			0
$631$	−601.057			−0.952547			−0.476273	−	0.879297i	$-0.658013\pi$
$631$	−601.057			−0.952547			−0.476273	+	0.879297i	$0.658013\pi$
$632$	−694.665			−1.09915
$633$		0			0
$634$	−755.752			−1.19204
$635$		−	133.876i		−	0.210828i
$636$		0			0
$637$	670.213	+	437.309i	1.05214	+	0.686514i
$638$	936.631			1.46807
$639$		0			0
$640$			122.437i			0.191307i
$641$	884.432			1.37977			0.689885	−	0.723919i	$-0.257661\pi$
$641$	884.432			1.37977			0.689885	+	0.723919i	$0.257661\pi$
$642$		0			0
$643$		−	385.448i		−	0.599453i	−0.954025	−	0.299726i	$-0.903105\pi$
$643$		−	385.448i		−	0.599453i	0.954025	−	0.299726i	$-0.0968954\pi$
$644$	59.1933	+	109.303i	0.0919150	+	0.169725i
$645$		0			0
$646$	316.086			0.489298
$647$			1096.93i			1.69540i	0.530473	+	0.847702i	$0.322014\pi$
$647$			1096.93i			1.69540i	−0.530473	+	0.847702i	$0.677986\pi$
$648$		0			0
$649$		−	1387.22i		−	2.13747i
$650$			139.813i			0.215097i
$651$		0			0
$652$	57.5488			0.0882650
$653$	556.888			0.852814			0.426407	−	0.904531i	$-0.359779\pi$
$653$	556.888			0.852814			0.426407	+	0.904531i	$0.359779\pi$
$654$		0			0
$655$	373.127			0.569660
$656$			420.594i			0.641149i
$657$		0			0
$658$	423.011	−	229.083i	0.642874	−	0.348151i
$659$	715.578			1.08585			0.542927	−	0.839780i	$-0.317316\pi$
$659$	715.578			1.08585			0.542927	+	0.839780i	$0.317316\pi$
$660$		0			0
$661$		−	280.365i		−	0.424152i	−0.977253	−	0.212076i	$-0.931978\pi$
$661$		−	280.365i		−	0.424152i	0.977253	−	0.212076i	$-0.0680225\pi$
$662$	872.040			1.31728
$663$		0			0
$664$			886.143i			1.33455i
$665$	−102.489	−	189.250i	−0.154119	−	0.284587i
$666$		0			0
$667$	−534.753			−0.801729
$668$		−	44.6584i		−	0.0668539i
$669$		0			0
$670$			275.983i			0.411915i
$671$			254.763i			0.379676i
$672$		0			0
$673$	1067.08			1.58556			0.792781	−	0.609506i	$-0.208632\pi$
$673$	1067.08			1.58556			0.792781	+	0.609506i	$0.208632\pi$
$674$	757.721			1.12421
$675$		0			0
$676$	104.434			0.154488
$677$		−	313.071i		−	0.462439i	−0.972902	−	0.231219i	$-0.925728\pi$
$677$		−	313.071i		−	0.462439i	0.972902	−	0.231219i	$-0.0742715\pi$
$678$		0			0
$679$	981.456	−	531.511i	1.44544	−	0.782785i
$680$	260.541			0.383149
$681$		0			0
$682$		−	196.285i		−	0.287808i
$683$	−505.514			−0.740138			−0.370069	−	0.929004i	$-0.620666\pi$
$683$	−505.514			−0.740138			−0.370069	+	0.929004i	$0.620666\pi$
$684$		0			0
$685$		−	282.056i		−	0.411761i
$686$	585.301	+	47.9795i	0.853209	+	0.0699409i
$687$		0			0
$688$	−457.446			−0.664892
$689$			367.473i			0.533342i
$690$		0			0
$691$			276.726i			0.400472i	0.979748	+	0.200236i	$0.0641709\pi$
$691$			276.726i			0.400472i	−0.979748	+	0.200236i	$0.935829\pi$
$692$			139.282i			0.201274i
$693$		0			0
$694$	845.393			1.21815
$695$	473.263			0.680954
$696$		0			0
$697$	533.561			0.765511
$698$		−	555.522i		−	0.795877i
$699$		0			0
$700$	−17.8101	−	32.8870i	−0.0254430	−	0.0469815i
$701$	−854.178			−1.21851			−0.609256	−	0.792973i	$-0.708532\pi$
$701$	−854.178			−1.21851			−0.609256	+	0.792973i	$0.708532\pi$
$702$		0			0
$703$			951.687i			1.35375i
$704$	−1202.63			−1.70828
$705$		0			0
$706$			906.450i			1.28392i
$707$	−148.577	+	80.4626i	−0.210152	+	0.113809i
$708$		0			0
$709$	−452.996			−0.638922			−0.319461	−	0.947599i	$-0.603502\pi$
$709$	−452.996			−0.638922			−0.319461	+	0.947599i	$0.603502\pi$
$710$			98.5210i			0.138762i
$711$		0			0
$712$			1114.11i			1.56476i
$713$			112.066i			0.157175i
$714$		0			0
$715$	−620.833			−0.868297
$716$	48.0786			0.0671489
$717$		0			0
$718$	−109.964			−0.153153
$719$		−	840.685i		−	1.16924i	−0.811306	−	0.584621i	$-0.801243\pi$
$719$		−	840.685i		−	1.16924i	0.811306	−	0.584621i	$-0.198757\pi$
$720$		0			0
$721$	−537.650	+	291.166i	−0.745700	+	0.403836i
$722$	294.386			0.407737
$723$		0			0
$724$			19.1214i			0.0264108i
$725$	160.897			0.221926
$726$		0			0
$727$		−	1339.58i		−	1.84262i	−0.388829	−	0.921310i	$-0.627120\pi$
$727$		−	1339.58i		−	1.84262i	0.388829	−	0.921310i	$-0.372880\pi$
$728$	872.398	−	472.450i	1.19835	−	0.648970i
$729$		0			0
$730$	287.383			0.393675
$731$			580.311i			0.793860i
$732$		0			0
$733$			536.275i			0.731616i	0.930690	+	0.365808i	$0.119207\pi$
$733$			536.275i			0.731616i	−0.930690	+	0.365808i	$0.880793\pi$
$734$			18.5206i			0.0252324i
$735$		0			0
$736$	275.713			0.374611
$737$	−1225.49			−1.66281
$738$		0			0
$739$	−898.552			−1.21590			−0.607951	−	0.793974i	$-0.708008\pi$
$739$	−898.552			−1.21590			−0.607951	+	0.793974i	$0.708008\pi$
$740$			165.380i			0.223486i
$741$		0			0
$742$	128.416	+	237.126i	0.173068	+	0.319576i
$743$	−532.720			−0.716985			−0.358493	−	0.933533i	$-0.616709\pi$
$743$	−532.720			−0.716985			−0.358493	+	0.933533i	$0.616709\pi$
$744$		0			0
$745$			143.516i			0.192639i
$746$	912.314			1.22294
$747$		0			0
$748$			243.905i			0.326076i
$749$	561.214	+	1036.30i	0.749284	+	1.38358i
$750$		0			0
$751$	342.085			0.455506			0.227753	−	0.973719i	$-0.426862\pi$
$751$	342.085			0.455506			0.227753	+	0.973719i	$0.426862\pi$
$752$		−	424.820i		−	0.564921i
$753$		0			0
$754$			899.818i			1.19339i
$755$			248.014i			0.328495i
$756$		0			0
$757$	405.961			0.536276			0.268138	−	0.963381i	$-0.413592\pi$
$757$	405.961			0.536276			0.268138	+	0.963381i	$0.413592\pi$
$758$	883.470			1.16553
$759$		0			0
$760$	−266.815			−0.351072
$761$		−	577.340i		−	0.758660i	−0.925261	−	0.379330i	$-0.876155\pi$
$761$		−	577.340i		−	0.758660i	0.925261	−	0.379330i	$-0.123845\pi$
$762$		0			0
$763$	518.584	+	957.586i	0.679664	+	1.25503i
$764$	190.541			0.249400
$765$		0			0
$766$			710.657i			0.927751i
$767$	1332.69			1.73754
$768$		0			0
$769$		−	828.522i		−	1.07740i	−0.842497	−	0.538701i	$-0.818915\pi$
$769$		−	828.522i		−	1.07740i	0.842497	−	0.538701i	$-0.181085\pi$
$770$	−400.616	+	216.955i	−0.520280	+	0.281760i
$771$		0			0
$772$	359.342			0.465469
$773$			438.991i			0.567906i	0.958838	+	0.283953i	$0.0916460\pi$
$773$			438.991i			0.567906i	−0.958838	+	0.283953i	$0.908354\pi$
$774$		0			0
$775$		−	33.7183i		−	0.0435075i
$776$		−	1383.71i		−	1.78313i
$777$		0			0
$778$	−93.8308			−0.120605
$779$	−546.408			−0.701423
$780$		0			0
$781$	−437.477			−0.560150
$782$			382.017i			0.488512i
$783$		0			0
$784$	283.397	−	434.330i	0.361476	−	0.553992i
$785$	−649.469			−0.827349
$786$		0			0
$787$			285.209i			0.362400i	0.983446	+	0.181200i	$0.0579982\pi$
$787$			285.209i			0.362400i	−0.983446	+	0.181200i	$0.942002\pi$
$788$	52.5824			0.0667289
$789$		0			0
$790$			306.461i			0.387925i
$791$	−69.9907	−	129.241i	−0.0884838	−	0.163389i
$792$		0			0
$793$	−244.750			−0.308638
$794$		−	34.1459i		−	0.0430049i
$795$		0			0
$796$			183.569i			0.230614i
$797$		−	1243.03i		−	1.55964i	−0.626006	−	0.779818i	$-0.715311\pi$
$797$		−	1243.03i		−	1.55964i	0.626006	−	0.779818i	$-0.284689\pi$
$798$		0			0
$799$	−538.923			−0.674497
$800$	−82.9567			−0.103696
$801$		0			0
$802$	410.066			0.511304
$803$			1276.11i			1.58918i
$804$		0			0
$805$	228.725	−	123.867i	0.284130	−	0.153872i
$806$	188.570			0.233958
$807$		0			0
$808$			209.472i			0.259248i
$809$	630.338			0.779157			0.389578	−	0.920993i	$-0.372621\pi$
$809$	630.338			0.779157			0.389578	+	0.920993i	$0.372621\pi$
$810$		0			0
$811$		−	1121.08i		−	1.38234i	−0.722692	−	0.691170i	$-0.757095\pi$
$811$		−	1121.08i		−	1.38234i	0.722692	−	0.691170i	$-0.242905\pi$
$812$	−114.623	−	211.657i	−0.141162	−	0.260661i
$813$		0			0
$814$	2014.59			2.47492
$815$		−	120.425i		−	0.147761i
$816$		0			0
$817$		−	594.284i		−	0.727398i
$818$			1136.08i			1.38885i
$819$		0			0
$820$	−94.9524			−0.115796
$821$	−544.285			−0.662954			−0.331477	−	0.943463i	$-0.607547\pi$
$821$	−544.285			−0.662954			−0.331477	+	0.943463i	$0.607547\pi$
$822$		0			0
$823$	83.7611			0.101775			0.0508877	−	0.998704i	$-0.483795\pi$
$823$	83.7611			0.101775			0.0508877	+	0.998704i	$0.483795\pi$
$824$			758.006i			0.919911i
$825$		0			0
$826$	859.972	−	465.721i	1.04113	−	0.563826i
$827$	957.378			1.15765			0.578826	−	0.815451i	$-0.303511\pi$
$827$	957.378			1.15765			0.578826	+	0.815451i	$0.303511\pi$
$828$		0			0
$829$			9.08184i			0.0109552i	0.999985	+	0.00547759i	$0.00174358\pi$
$829$			9.08184i			0.0109552i	−0.999985	+	0.00547759i	$0.998256\pi$
$830$	390.934			0.471005
$831$		0			0
$832$		−	1155.36i		−	1.38865i
$833$	−550.987	−	359.515i	−0.661449	−	0.431591i
$834$		0			0
$835$	−93.4512			−0.111918
$836$		−	249.778i		−	0.298778i
$837$		0			0
$838$			189.446i			0.226069i
$839$		−	492.860i		−	0.587437i	−0.955892	−	0.293719i	$-0.905107\pi$
$839$		−	492.860i		−	0.587437i	0.955892	−	0.293719i	$-0.0948929\pi$
$840$		0			0
$841$	194.509			0.231283
$842$	−892.583			−1.06007
$843$		0			0
$844$	5.44391			0.00645013
$845$		−	218.536i		−	0.258623i
$846$		0			0
$847$	−560.030	−	1034.12i	−0.661193	−	1.22092i
$848$	238.140			0.280825
$849$		0			0
$850$		−	114.941i		−	0.135225i
$851$	−1150.19			−1.35158
$852$		0			0
$853$		−	519.198i		−	0.608672i	−0.952565	−	0.304336i	$-0.901565\pi$
$853$		−	519.198i		−	0.608672i	0.952565	−	0.304336i	$-0.0984346\pi$
$854$	−157.934	+	85.5297i	−0.184934	+	0.100152i
$855$		0			0
$856$	1461.03			1.70682
$857$			479.468i			0.559473i	0.960077	+	0.279736i	$0.0902470\pi$
$857$			479.468i			0.559473i	−0.960077	+	0.279736i	$0.909753\pi$
$858$		0			0
$859$			1667.63i			1.94136i	0.240378	+	0.970679i	$0.422729\pi$
$859$			1667.63i			1.94136i	−0.240378	+	0.970679i	$0.577271\pi$
$860$		−	103.272i		−	0.120084i
$861$		0			0
$862$	−981.089			−1.13815
$863$	−1217.16			−1.41039			−0.705193	−	0.709016i	$-0.749139\pi$
$863$	−1217.16			−1.41039			−0.705193	+	0.709016i	$0.749139\pi$
$864$		0			0
$865$	291.458			0.336946
$866$			735.776i			0.849626i
$867$		0			0
$868$	−44.3558	+	24.0211i	−0.0511012	+	0.0276740i
$869$	−1360.82			−1.56597
$870$		0			0
$871$		−	1177.32i		−	1.35169i
$872$	1350.05			1.54823
$873$		0			0
$874$		−	391.215i		−	0.447615i
$875$	−68.8187	+	37.2690i	−0.0786500	+	0.0425932i
$876$		0			0
$877$	−1027.18			−1.17125			−0.585623	−	0.810583i	$-0.699150\pi$
$877$	−1027.18			−1.17125			−0.585623	+	0.810583i	$0.699150\pi$
$878$		−	142.192i		−	0.161950i
$879$		0			0
$880$			402.329i			0.457192i
$881$		−	149.054i		−	0.169187i	−0.996416	−	0.0845937i	$-0.973041\pi$
$881$		−	149.054i		−	0.169187i	0.996416	−	0.0845937i	$-0.0269592\pi$
$882$		0			0
$883$	201.243			0.227908			0.113954	−	0.993486i	$-0.463648\pi$
$883$	201.243			0.227908			0.113954	+	0.993486i	$0.463648\pi$
$884$	−234.319			−0.265067
$885$		0			0
$886$	701.995			0.792319
$887$			951.252i			1.07244i	0.844079	+	0.536219i	$0.180148\pi$
$887$			951.252i			1.07244i	−0.844079	+	0.536219i	$0.819852\pi$
$888$		0			0
$889$	199.577	+	368.527i	0.224496	+	0.414542i
$890$	491.503			0.552250
$891$		0			0
$892$		−	331.327i		−	0.371443i
$893$	551.899			0.618028
$894$		0			0
$895$		−	100.608i		−	0.112412i
$896$	−182.524	−	337.038i	−0.203710	−	0.376158i
$897$		0			0
$898$	352.613			0.392664
$899$		−	217.007i		−	0.241387i
$900$		0			0
$901$		−	302.102i		−	0.335296i
$902$			1156.67i			1.28234i
$903$		0			0
$904$	−182.210			−0.201560
$905$	40.0130			0.0442133
$906$		0			0
$907$	−559.990			−0.617409			−0.308705	−	0.951158i	$-0.599895\pi$
$907$	−559.990			−0.617409			−0.308705	+	0.951158i	$0.599895\pi$
$908$			116.002i			0.127755i
$909$		0			0
$910$	−208.428	−	384.870i	−0.229042	−	0.422934i
$911$	674.618			0.740525			0.370262	−	0.928927i	$-0.379268\pi$
$911$	674.618			0.740525			0.370262	+	0.928927i	$0.379268\pi$
$912$		0			0
$913$			1735.92i			1.90134i
$914$	−1097.26			−1.20050
$915$		0			0
$916$			252.699i			0.275872i
$917$	−1027.13	+	556.244i	−1.12009	+	0.606591i
$918$		0			0
$919$	982.395			1.06898			0.534491	−	0.845174i	$-0.320503\pi$
$919$	982.395			1.06898			0.534491	+	0.845174i	$0.320503\pi$
$920$		−	322.468i		−	0.350509i
$921$		0			0
$922$			284.362i			0.308419i
$923$		−	420.283i		−	0.455345i
$924$		0			0
$925$	346.070			0.374130
$926$	−17.8763			−0.0193049
$927$		0			0
$928$	−533.898			−0.575322
$929$			344.774i			0.371124i	0.982633	+	0.185562i	$0.0594105\pi$
$929$			344.774i			0.371124i	−0.982633	+	0.185562i	$0.940589\pi$
$930$		0			0
$931$	564.253	+	368.172i	0.606072	+	0.395458i
$932$	161.664			0.173459
$933$		0			0
$934$		−	461.826i		−	0.494460i
$935$	510.391			0.545873
$936$		0			0
$937$			635.256i			0.677967i	0.940792	+	0.338984i	$0.110083\pi$
$937$			635.256i			0.677967i	−0.940792	+	0.338984i	$0.889917\pi$
$938$	−411.425	−	759.713i	−0.438620	−	0.809929i
$939$		0			0
$940$	95.9066			0.102028
$941$		−	1207.78i		−	1.28351i	−0.766909	−	0.641756i	$-0.778206\pi$
$941$		−	1207.78i		−	1.28351i	0.766909	−	0.641756i	$-0.221794\pi$
$942$		0			0
$943$		−	660.380i		−	0.700297i
$944$		−	863.649i		−	0.914883i
$945$		0			0
$946$	−1258.02			−1.32983
$947$	254.133			0.268356			0.134178	−	0.990957i	$-0.457161\pi$
$947$	254.133			0.268356			0.134178	+	0.990957i	$0.457161\pi$
$948$		0			0
$949$	−1225.95			−1.29184
$950$			117.709i			0.123904i
$951$		0			0
$952$	−717.205	+	388.405i	−0.753367	+	0.407988i
$953$	−424.523			−0.445460			−0.222730	−	0.974880i	$-0.571497\pi$
$953$	−424.523			−0.445460			−0.222730	+	0.974880i	$0.571497\pi$
$954$		0			0
$955$		−	398.723i		−	0.417511i
$956$	51.6072			0.0539824
$957$		0			0
$958$		−	1112.58i		−	1.16136i
$959$	420.479	+	776.431i	0.438455	+	0.809625i
$960$		0			0
$961$	915.523			0.952677
$962$			1935.41i			2.01186i
$963$		0			0
$964$			246.557i			0.255764i
$965$		−	751.952i		−	0.779225i
$966$		0			0
$967$	−46.7338			−0.0483286			−0.0241643	−	0.999708i	$-0.507692\pi$
$967$	−46.7338			−0.0483286			−0.0241643	+	0.999708i	$0.507692\pi$
$968$	−1457.95			−1.50615
$969$		0			0
$970$	−610.441			−0.629321
$971$		−	1724.03i		−	1.77552i	−0.460303	−	0.887762i	$-0.652259\pi$
$971$		−	1724.03i		−	1.77552i	0.460303	−	0.887762i	$-0.347741\pi$
$972$		0			0
$973$	−1302.77	+	705.522i	−1.33893	+	0.725100i
$974$	1023.24			1.05056
$975$		0			0
$976$			158.609i			0.162510i
$977$	1613.20			1.65118			0.825589	−	0.564271i	$-0.190843\pi$
$977$	1613.20			1.65118			0.825589	+	0.564271i	$0.190843\pi$
$978$		0			0
$979$			2182.49i			2.22931i
$980$	98.0534	+	63.9792i	0.100055	+	0.0652849i
$981$		0			0
$982$	184.269			0.187647
$983$		−	31.6909i		−	0.0322389i	−0.999870	−	0.0161195i	$-0.994869\pi$
$983$		−	31.6909i		−	0.0322389i	0.999870	−	0.0161195i	$-0.00513121\pi$
$984$		0			0
$985$		−	110.033i		−	0.111708i
$986$		−	739.747i		−	0.750250i
$987$		0			0
$988$	239.961			0.242875
$989$	718.242			0.726231
$990$		0			0
$991$	−236.475			−0.238623			−0.119311	−	0.992857i	$-0.538069\pi$
$991$	−236.475			−0.238623			−0.119311	+	0.992857i	$0.538069\pi$
$992$			111.886i			0.112789i
$993$		0			0
$994$	−146.871	−	271.204i	−0.147758	−	0.272841i
$995$	384.132			0.386062
$996$		0			0
$997$			948.441i			0.951295i	0.879636	+	0.475648i	$0.157786\pi$
$997$			948.441i			0.951295i	−0.879636	+	0.475648i	$0.842214\pi$
$998$	−720.146			−0.721589
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.h.d.181.8		12
3.2	odd	2		105.3.h.a.76.6	yes	12
7.6	odd	2	inner	315.3.h.d.181.7		12
12.11	even	2		1680.3.s.c.1441.2		12
15.2	even	4		525.3.e.c.349.15		24
15.8	even	4		525.3.e.c.349.2		24
15.14	odd	2		525.3.h.d.76.7		12
21.20	even	2		105.3.h.a.76.5	✓	12
84.83	odd	2		1680.3.s.c.1441.11		12
105.62	odd	4		525.3.e.c.349.1		24
105.83	odd	4		525.3.e.c.349.16		24
105.104	even	2		525.3.h.d.76.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.5	✓	12	21.20	even	2
105.3.h.a.76.6	yes	12	3.2	odd	2
315.3.h.d.181.7		12	7.6	odd	2	inner
315.3.h.d.181.8		12	1.1	even	1	trivial
525.3.e.c.349.1		24	105.62	odd	4
525.3.e.c.349.2		24	15.8	even	4
525.3.e.c.349.15		24	15.2	even	4
525.3.e.c.349.16		24	105.83	odd	4
525.3.h.d.76.7		12	15.14	odd	2
525.3.h.d.76.8		12	105.104	even	2
1680.3.s.c.1441.2		12	12.11	even	2
1680.3.s.c.1441.11		12	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.71214 q^{2} -1.06857 q^{4} +2.23607i q^{5} +(-3.33344 - 6.15534i) q^{7} -8.67811 q^{8} +O(q^{10})\)	\(q+1.71214 q^{2} -1.06857 q^{4} +2.23607i q^{5} +(-3.33344 - 6.15534i) q^{7} -8.67811 q^{8} +3.82847i q^{10} -17.0001 q^{11} -16.3319i q^{13} +(-5.70733 - 10.5388i) q^{14} -10.5839 q^{16} +13.4266i q^{17} -13.7499i q^{19} -2.38940i q^{20} -29.1066 q^{22} +16.6179 q^{23} -5.00000 q^{25} -27.9626i q^{26} +(3.56202 + 6.57741i) q^{28} -32.1793 q^{29} +6.74366i q^{31} +16.5913 q^{32} +22.9883i q^{34} +(13.7637 - 7.45380i) q^{35} -69.2141 q^{37} -23.5418i q^{38} -19.4048i q^{40} -39.7391i q^{41} +43.2210 q^{43} +18.1658 q^{44} +28.4522 q^{46} +40.1384i q^{47} +(-26.7763 + 41.0369i) q^{49} -8.56071 q^{50} +17.4518i q^{52} -22.5002 q^{53} -38.0134i q^{55} +(28.9280 + 53.4167i) q^{56} -55.0956 q^{58} +81.6005i q^{59} -14.9859i q^{61} +11.5461i q^{62} +70.7422 q^{64} +36.5193 q^{65} +72.0872 q^{67} -14.3473i q^{68} +(23.5655 - 12.7620i) q^{70} +25.7338 q^{71} -75.0647i q^{73} -118.504 q^{74} +14.6927i q^{76} +(56.6689 + 104.641i) q^{77} +80.0480 q^{79} -23.6663i q^{80} -68.0389i q^{82} -102.112i q^{83} -30.0228 q^{85} +74.0005 q^{86} +147.529 q^{88} -128.381i q^{89} +(-100.529 + 54.4416i) q^{91} -17.7574 q^{92} +68.7227i q^{94} +30.7457 q^{95} +159.448i q^{97} +(-45.8449 + 70.2610i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8	\( 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8} + 16 q^{11} + 40 q^{14} + 92 q^{16} - 88 q^{22} + 64 q^{23} - 60 q^{25} + 88 q^{28} - 104 q^{29} + 228 q^{32} - 60 q^{35} + 32 q^{37} + 152 q^{43} - 192 q^{44} + 200 q^{46} + 60 q^{49} - 20 q^{50} - 176 q^{53} + 368 q^{56} - 400 q^{58} - 20 q^{64} + 240 q^{65} + 168 q^{67} - 60 q^{70} - 32 q^{71} - 184 q^{74} - 8 q^{77} + 120 q^{79} + 120 q^{85} - 400 q^{86} - 536 q^{88} + 24 q^{91} - 192 q^{92} - 884 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8 + 16 * q^11 + 40 * q^14 + 92 * q^16 - 88 * q^22 + 64 * q^23 - 60 * q^25 + 88 * q^28 - 104 * q^29 + 228 * q^32 - 60 * q^35 + 32 * q^37 + 152 * q^43 - 192 * q^44 + 200 * q^46 + 60 * q^49 - 20 * q^50 - 176 * q^53 + 368 * q^56 - 400 * q^58 - 20 * q^64 + 240 * q^65 + 168 * q^67 - 60 * q^70 - 32 * q^71 - 184 * q^74 - 8 * q^77 + 120 * q^79 + 120 * q^85 - 400 * q^86 - 536 * q^88 + 24 * q^91 - 192 * q^92 - 884 * q^98

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