LMFDB - Embedded newform 315.3.h.d.181.1

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			181.1
Root			$1.31896 - 2.28450i$ of defining polynomial
Character	$\chi$	$=$	315.181
Dual form			315.3.h.d.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.50369 q^{2} +8.27584 q^{4} -2.23607i q^{5} +(-6.69736 - 2.03600i) q^{7} -14.9812 q^{8} +O(q^{10})$	\(q-3.50369 q^{2} +8.27584 q^{4} -2.23607i q^{5} +(-6.69736 - 2.03600i) q^{7} -14.9812 q^{8} +7.83449i q^{10} +2.03112 q^{11} +18.0174i q^{13} +(23.4655 + 7.13352i) q^{14} +19.3861 q^{16} +1.07289i q^{17} -28.7852i q^{19} -18.5053i q^{20} -7.11640 q^{22} -24.8710 q^{23} -5.00000 q^{25} -63.1275i q^{26} +(-55.4263 - 16.8496i) q^{28} +38.4300 q^{29} +44.0899i q^{31} -7.99812 q^{32} -3.75906i q^{34} +(-4.55264 + 14.9758i) q^{35} +37.2832 q^{37} +100.855i q^{38} +33.4990i q^{40} +49.9206i q^{41} -9.58871 q^{43} +16.8092 q^{44} +87.1402 q^{46} +55.6978i q^{47} +(40.7094 + 27.2717i) q^{49} +17.5184 q^{50} +149.109i q^{52} -57.4656 q^{53} -4.54171i q^{55} +(100.335 + 30.5018i) q^{56} -134.647 q^{58} +101.697i q^{59} +31.9530i q^{61} -154.477i q^{62} -49.5215 q^{64} +40.2882 q^{65} +95.7318 q^{67} +8.87902i q^{68} +(15.9510 - 52.4704i) q^{70} +25.8039 q^{71} +95.6803i q^{73} -130.629 q^{74} -238.222i q^{76} +(-13.6031 - 4.13536i) q^{77} +28.1212 q^{79} -43.3487i q^{80} -174.906i q^{82} -103.374i q^{83} +2.39905 q^{85} +33.5959 q^{86} -30.4286 q^{88} +29.3629i q^{89} +(36.6835 - 120.669i) q^{91} -205.828 q^{92} -195.148i q^{94} -64.3658 q^{95} +67.6473i q^{97} +(-142.633 - 95.5515i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.50369			−1.75184			−0.875922	−	0.482452i	$-0.839746\pi$
$2$	−3.50369			−1.75184			−0.875922	+	0.482452i	$0.839746\pi$
$3$		0			0
$3$		0			0
$4$	8.27584			2.06896
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$		0			0
$7$	−6.69736	−	2.03600i	−0.956766	−	0.290857i
$7$	−6.69736	−	2.03600i	−0.956766	−	0.290857i
$8$	−14.9812			−1.87265
$9$		0			0
$10$			7.83449i			0.783449i
$11$	2.03112			0.184647			0.0923235	−	0.995729i	$-0.470571\pi$
$11$	2.03112			0.184647			0.0923235	+	0.995729i	$0.470571\pi$
$12$		0			0
$13$			18.0174i			1.38596i	0.720958	+	0.692978i	$0.243702\pi$
$13$			18.0174i			1.38596i	−0.720958	+	0.692978i	$0.756298\pi$
$14$	23.4655	+	7.13352i	1.67611	+	0.509537i
$15$		0			0
$16$	19.3861			1.21163
$17$			1.07289i			0.0631109i	0.999502	+	0.0315555i	$0.0100461\pi$
$17$			1.07289i			0.0631109i	−0.999502	+	0.0315555i	$0.989954\pi$
$18$		0			0
$19$		−	28.7852i		−	1.51501i	−0.652828	−	0.757506i	$-0.726417\pi$
$19$		−	28.7852i		−	1.51501i	0.652828	−	0.757506i	$-0.273583\pi$
$20$		−	18.5053i		−	0.925267i
$21$		0			0
$22$	−7.11640			−0.323473
$23$	−24.8710			−1.08135			−0.540674	−	0.841232i	$-0.681831\pi$
$23$	−24.8710			−1.08135			−0.540674	+	0.841232i	$0.681831\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$		−	63.1275i		−	2.42798i
$27$		0			0
$28$	−55.4263	−	16.8496i	−1.97951	−	0.601772i
$29$	38.4300			1.32517			0.662587	−	0.748985i	$-0.269458\pi$
$29$	38.4300			1.32517			0.662587	+	0.748985i	$0.269458\pi$
$30$		0			0
$31$			44.0899i			1.42225i	0.703064	+	0.711127i	$0.251815\pi$
$31$			44.0899i			1.42225i	−0.703064	+	0.711127i	$0.748185\pi$
$32$	−7.99812			−0.249941
$33$		0			0
$34$		−	3.75906i		−	0.110561i
$35$	−4.55264	+	14.9758i	−0.130075	+	0.427879i
$36$		0			0
$37$	37.2832			1.00765			0.503827	−	0.863804i	$-0.331925\pi$
$37$	37.2832			1.00765			0.503827	+	0.863804i	$0.331925\pi$
$38$			100.855i			2.65407i
$39$		0			0
$40$			33.4990i			0.837474i
$41$			49.9206i			1.21758i	0.793333	+	0.608788i	$0.208344\pi$
$41$			49.9206i			1.21758i	−0.793333	+	0.608788i	$0.791656\pi$
$42$		0			0
$43$	−9.58871			−0.222993			−0.111497	−	0.993765i	$-0.535564\pi$
$43$	−9.58871			−0.222993			−0.111497	+	0.993765i	$0.535564\pi$
$44$	16.8092			0.382027
$45$		0			0
$46$	87.1402			1.89435
$47$			55.6978i			1.18506i	0.805549	+	0.592529i	$0.201871\pi$
$47$			55.6978i			1.18506i	−0.805549	+	0.592529i	$0.798129\pi$
$48$		0			0
$49$	40.7094	+	27.2717i	0.830804	+	0.556565i
$50$	17.5184			0.350369
$51$		0			0
$52$			149.109i			2.86749i
$53$	−57.4656			−1.08426			−0.542128	−	0.840296i	$-0.682381\pi$
$53$	−57.4656			−1.08426			−0.542128	+	0.840296i	$0.682381\pi$
$54$		0			0
$55$		−	4.54171i		−	0.0825766i
$56$	100.335	+	30.5018i	1.79169	+	0.544674i
$57$		0			0
$58$	−134.647			−2.32150
$59$			101.697i			1.72368i	0.507178	+	0.861841i	$0.330689\pi$
$59$			101.697i			1.72368i	−0.507178	+	0.861841i	$0.669311\pi$
$60$		0			0
$61$			31.9530i			0.523819i	0.965092	+	0.261910i	$0.0843523\pi$
$61$			31.9530i			0.523819i	−0.965092	+	0.261910i	$0.915648\pi$
$62$		−	154.477i		−	2.49157i
$63$		0			0
$64$	−49.5215			−0.773774
$65$	40.2882			0.619819
$66$		0			0
$67$	95.7318			1.42883			0.714416	−	0.699721i	$-0.246692\pi$
$67$	95.7318			1.42883			0.714416	+	0.699721i	$0.246692\pi$
$68$			8.87902i			0.130574i
$69$		0			0
$70$	15.9510	−	52.4704i	0.227872	−	0.749577i
$71$	25.8039			0.363435			0.181718	−	0.983351i	$-0.441834\pi$
$71$	25.8039			0.363435			0.181718	+	0.983351i	$0.441834\pi$
$72$		0			0
$73$			95.6803i			1.31069i	0.755330	+	0.655345i	$0.227477\pi$
$73$			95.6803i			1.31069i	−0.755330	+	0.655345i	$0.772523\pi$
$74$	−130.629			−1.76525
$75$		0			0
$76$		−	238.222i		−	3.13450i
$77$	−13.6031	−	4.13536i	−0.176664	−	0.0537059i
$78$		0			0
$79$	28.1212			0.355965			0.177982	−	0.984034i	$-0.443043\pi$
$79$	28.1212			0.355965			0.177982	+	0.984034i	$0.443043\pi$
$80$		−	43.3487i		−	0.541858i
$81$		0			0
$82$		−	174.906i		−	2.13301i
$83$		−	103.374i		−	1.24547i	−0.782435	−	0.622733i	$-0.786022\pi$
$83$		−	103.374i		−	1.24547i	0.782435	−	0.622733i	$-0.213978\pi$
$84$		0			0
$85$	2.39905			0.0282241
$86$	33.5959			0.390650
$87$		0			0
$88$	−30.4286			−0.345779
$89$			29.3629i			0.329920i	0.986300	+	0.164960i	$0.0527496\pi$
$89$			29.3629i			0.329920i	−0.986300	+	0.164960i	$0.947250\pi$
$90$		0			0
$91$	36.6835	−	120.669i	0.403116	−	1.32604i
$92$	−205.828			−2.23726
$93$		0			0
$94$		−	195.148i		−	2.07604i
$95$	−64.3658			−0.677534
$96$		0			0
$97$			67.6473i			0.697395i	0.937235	+	0.348697i	$0.113376\pi$
$97$			67.6473i			0.697395i	−0.937235	+	0.348697i	$0.886624\pi$
$98$	−142.633	−	95.5515i	−1.45544	−	0.975016i
$99$		0			0
$100$	−41.3792			−0.413792
$101$			73.3301i			0.726040i	0.931781	+	0.363020i	$0.118254\pi$
$101$			73.3301i			0.726040i	−0.931781	+	0.363020i	$0.881746\pi$
$102$		0			0
$103$			57.3431i			0.556729i	0.960476	+	0.278365i	$0.0897923\pi$
$103$			57.3431i			0.556729i	−0.960476	+	0.278365i	$0.910208\pi$
$104$		−	269.923i		−	2.59541i
$105$		0			0
$106$	201.342			1.89945
$107$	39.8399			0.372336			0.186168	−	0.982518i	$-0.440393\pi$
$107$	39.8399			0.372336			0.186168	+	0.982518i	$0.440393\pi$
$108$		0			0
$109$	−185.052			−1.69773			−0.848863	−	0.528613i	$-0.822712\pi$
$109$	−185.052			−1.69773			−0.848863	+	0.528613i	$0.822712\pi$
$110$			15.9128i			0.144661i
$111$		0			0
$112$	−129.836	−	39.4702i	−1.15925	−	0.352412i
$113$	120.716			1.06829			0.534143	−	0.845394i	$-0.320634\pi$
$113$	120.716			1.06829			0.534143	+	0.845394i	$0.320634\pi$
$114$		0			0
$115$			55.6132i			0.483593i
$116$	318.041			2.74173
$117$		0			0
$118$		−	356.316i		−	3.01962i
$119$	2.18440	−	7.18551i	0.0183563	−	0.0603824i
$120$		0			0
$121$	−116.875			−0.965906
$122$		−	111.953i		−	0.917650i
$123$		0			0
$124$			364.880i			2.94258i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−83.5096			−0.657556			−0.328778	−	0.944407i	$-0.606637\pi$
$127$	−83.5096			−0.657556			−0.328778	+	0.944407i	$0.606637\pi$
$128$	205.501			1.60547
$129$		0			0
$130$	−141.157			−1.08583
$131$		−	198.248i		−	1.51334i	−0.653796	−	0.756671i	$-0.726825\pi$
$131$		−	198.248i		−	1.51334i	0.653796	−	0.756671i	$-0.273175\pi$
$132$		0			0
$133$	−58.6068	+	192.785i	−0.440653	+	1.44951i
$134$	−335.414			−2.50309
$135$		0			0
$136$		−	16.0731i		−	0.118185i
$137$	24.1635			0.176376			0.0881880	−	0.996104i	$-0.471892\pi$
$137$	24.1635			0.176376			0.0881880	+	0.996104i	$0.471892\pi$
$138$		0			0
$139$		−	61.6370i		−	0.443432i	−0.975111	−	0.221716i	$-0.928834\pi$
$139$		−	61.6370i		−	0.443432i	0.975111	−	0.221716i	$-0.0711658\pi$
$140$	−37.6769	+	123.937i	−0.269121	+	0.885264i
$141$		0			0
$142$	−90.4088			−0.636682
$143$			36.5955i			0.255913i
$144$		0			0
$145$		−	85.9322i		−	0.592636i
$146$		−	335.234i		−	2.29612i
$147$		0			0
$148$	308.550			2.08480
$149$	28.8271			0.193470			0.0967351	−	0.995310i	$-0.469160\pi$
$149$	28.8271			0.193470			0.0967351	+	0.995310i	$0.469160\pi$
$150$		0			0
$151$	248.311			1.64445			0.822223	−	0.569166i	$-0.192734\pi$
$151$	248.311			1.64445			0.822223	+	0.569166i	$0.192734\pi$
$152$			431.237i			2.83709i
$153$		0			0
$154$	47.6611	+	14.4890i	0.309488	+	0.0940844i
$155$	98.5879			0.636051
$156$		0			0
$157$		−	41.3848i		−	0.263597i	−0.991277	−	0.131799i	$-0.957925\pi$
$157$		−	41.3848i		−	0.263597i	0.991277	−	0.131799i	$-0.0420752\pi$
$158$	−98.5280			−0.623595
$159$		0			0
$160$			17.8843i			0.111777i
$161$	166.570	+	50.6374i	1.03460	+	0.314518i
$162$		0			0
$163$	−51.8103			−0.317855			−0.158927	−	0.987290i	$-0.550804\pi$
$163$	−51.8103			−0.317855			−0.158927	+	0.987290i	$0.550804\pi$
$164$			413.135i			2.51912i
$165$		0			0
$166$			362.189i			2.18186i
$167$			41.9711i			0.251324i	0.992073	+	0.125662i	$0.0401055\pi$
$167$			41.9711i			0.251324i	−0.992073	+	0.125662i	$0.959895\pi$
$168$		0			0
$169$	−155.628			−0.920876
$170$	−8.40551			−0.0494442
$171$		0			0
$172$	−79.3546			−0.461364
$173$		−	98.0199i		−	0.566589i	−0.959033	−	0.283295i	$-0.908573\pi$
$173$		−	98.0199i		−	0.566589i	0.959033	−	0.283295i	$-0.0914274\pi$
$174$		0			0
$175$	33.4868	+	10.1800i	0.191353	+	0.0581715i
$176$	39.3754			0.223724
$177$		0			0
$178$		−	102.879i		−	0.577969i
$179$	−68.5830			−0.383145			−0.191573	−	0.981478i	$-0.561359\pi$
$179$	−68.5830			−0.383145			−0.191573	+	0.981478i	$0.561359\pi$
$180$		0			0
$181$			105.124i			0.580798i	0.956906	+	0.290399i	$0.0937880\pi$
$181$			105.124i			0.580798i	−0.956906	+	0.290399i	$0.906212\pi$
$182$	−128.528	+	422.788i	−0.706196	+	2.32301i
$183$		0			0
$184$	372.597			2.02499
$185$		−	83.3678i		−	0.450637i
$186$		0			0
$187$			2.17916i			0.0116532i
$188$			460.946i			2.45184i
$189$		0			0
$190$	225.518			1.18693
$191$	−229.803			−1.20316			−0.601579	−	0.798813i	$-0.705461\pi$
$191$	−229.803			−1.20316			−0.601579	+	0.798813i	$0.705461\pi$
$192$		0			0
$193$	111.530			0.577877			0.288939	−	0.957348i	$-0.406698\pi$
$193$	111.530			0.577877			0.288939	+	0.957348i	$0.406698\pi$
$194$		−	237.015i		−	1.22173i
$195$		0			0
$196$	336.904	+	225.696i	1.71890	+	1.15151i
$197$	172.865			0.877486			0.438743	−	0.898613i	$-0.355424\pi$
$197$	172.865			0.877486			0.438743	+	0.898613i	$0.355424\pi$
$198$		0			0
$199$		−	117.944i		−	0.592685i	−0.955082	−	0.296343i	$-0.904233\pi$
$199$		−	117.944i		−	0.592685i	0.955082	−	0.296343i	$-0.0957670\pi$
$200$	74.9060			0.374530
$201$		0			0
$202$		−	256.926i		−	1.27191i
$203$	−257.380	−	78.2437i	−1.26788	−	0.385437i
$204$		0			0
$205$	111.626			0.544517
$206$		−	200.912i		−	0.975303i
$207$		0			0
$208$			349.288i			1.67927i
$209$		−	58.4662i		−	0.279742i
$210$		0			0
$211$	−391.940			−1.85754			−0.928769	−	0.370660i	$-0.879131\pi$
$211$	−391.940			−1.85754			−0.928769	+	0.370660i	$0.879131\pi$
$212$	−475.576			−2.24328
$213$		0			0
$214$	−139.587			−0.652274
$215$			21.4410i			0.0997256i
$216$		0			0
$217$	89.7670	−	295.286i	0.413673	−	1.36076i
$218$	648.365			2.97415
$219$		0			0
$220$		−	37.5865i		−	0.170848i
$221$	−19.3306			−0.0874690
$222$		0			0
$223$			96.2512i			0.431620i	0.976435	+	0.215810i	$0.0692391\pi$
$223$			96.2512i			0.431620i	−0.976435	+	0.215810i	$0.930761\pi$
$224$	53.5663	+	16.2842i	0.239135	+	0.0726972i
$225$		0			0
$226$	−422.952			−1.87147
$227$		−	91.6962i		−	0.403948i	−0.979391	−	0.201974i	$-0.935264\pi$
$227$		−	91.6962i		−	0.403948i	0.979391	−	0.201974i	$-0.0647357\pi$
$228$		0			0
$229$			323.972i			1.41472i	0.706852	+	0.707361i	$0.250115\pi$
$229$			323.972i			1.41472i	−0.706852	+	0.707361i	$0.749885\pi$
$230$		−	194.852i		−	0.847180i
$231$		0			0
$232$	−575.728			−2.48159
$233$	−182.918			−0.785055			−0.392528	−	0.919740i	$-0.628399\pi$
$233$	−182.918			−0.785055			−0.392528	+	0.919740i	$0.628399\pi$
$234$		0			0
$235$	124.544			0.529974
$236$			841.630i			3.56623i
$237$		0			0
$238$	−7.65345	+	25.1758i	−0.0321573	+	0.105781i
$239$	42.9240			0.179598			0.0897992	−	0.995960i	$-0.471377\pi$
$239$	42.9240			0.179598			0.0897992	+	0.995960i	$0.471377\pi$
$240$		0			0
$241$		−	99.8942i		−	0.414499i	−0.978288	−	0.207249i	$-0.933549\pi$
$241$		−	99.8942i		−	0.414499i	0.978288	−	0.207249i	$-0.0664511\pi$
$242$	409.492			1.69212
$243$		0			0
$244$			264.438i			1.08376i
$245$	60.9814	−	91.0290i	0.248904	−	0.371547i
$246$		0			0
$247$	518.636			2.09974
$248$		−	660.519i		−	2.66338i
$249$		0			0
$250$		−	39.1724i		−	0.156690i
$251$			404.945i			1.61333i	0.591011	+	0.806663i	$0.298729\pi$
$251$			404.945i			1.61333i	−0.591011	+	0.806663i	$0.701271\pi$
$252$		0			0
$253$	−50.5159			−0.199668
$254$	292.592			1.15194
$255$		0			0
$256$	−521.924			−2.03876
$257$		−	102.697i		−	0.399600i	−0.979837	−	0.199800i	$-0.935971\pi$
$257$		−	102.697i		−	0.399600i	0.979837	−	0.199800i	$-0.0640292\pi$
$258$		0			0
$259$	−249.699	−	75.9087i	−0.964090	−	0.293084i
$260$	333.419			1.28238
$261$		0			0
$262$			694.598i			2.65114i
$263$	−281.479			−1.07026			−0.535132	−	0.844769i	$-0.679738\pi$
$263$	−281.479			−1.07026			−0.535132	+	0.844769i	$0.679738\pi$
$264$		0			0
$265$			128.497i			0.484894i
$266$	205.340	−	675.460i	0.771955	−	2.53932i
$267$		0			0
$268$	792.260			2.95620
$269$			176.412i			0.655808i	0.944711	+	0.327904i	$0.106342\pi$
$269$			176.412i			0.655808i	−0.944711	+	0.327904i	$0.893658\pi$
$270$		0			0
$271$		−	306.041i		−	1.12930i	−0.825330	−	0.564651i	$-0.809011\pi$
$271$		−	306.041i		−	1.12930i	0.825330	−	0.564651i	$-0.190989\pi$
$272$			20.7991i			0.0764672i
$273$		0			0
$274$	−84.6614			−0.308983
$275$	−10.1556			−0.0369294
$276$		0			0
$277$	43.7993			0.158120			0.0790601	−	0.996870i	$-0.474808\pi$
$277$	43.7993			0.158120			0.0790601	+	0.996870i	$0.474808\pi$
$278$			215.957i			0.776824i
$279$		0			0
$280$	68.2040	−	224.355i	0.243586	−	0.801267i
$281$	−499.502			−1.77759			−0.888794	−	0.458307i	$-0.848456\pi$
$281$	−499.502			−1.77759			−0.888794	+	0.458307i	$0.848456\pi$
$282$		0			0
$283$		−	122.672i		−	0.433470i	−0.976231	−	0.216735i	$-0.930459\pi$
$283$		−	122.672i		−	0.433470i	0.976231	−	0.216735i	$-0.0695407\pi$
$284$	213.549			0.751932
$285$		0			0
$286$		−	128.219i		−	0.448319i
$287$	101.639	−	334.337i	0.354141	−	1.16494i
$288$		0			0
$289$	287.849			0.996017
$290$			301.080i			1.03821i
$291$		0			0
$292$			791.835i			2.71176i
$293$		−	123.871i		−	0.422769i	−0.977403	−	0.211385i	$-0.932203\pi$
$293$		−	123.871i		−	0.422769i	0.977403	−	0.211385i	$-0.0677972\pi$
$294$		0			0
$295$	227.402			0.770854
$296$	−558.547			−1.88698
$297$		0			0
$298$	−101.001			−0.338930
$299$		−	448.112i		−	1.49870i
$300$		0			0
$301$	64.2191	+	19.5226i	0.213352	+	0.0648593i
$302$	−870.006			−2.88081
$303$		0			0
$304$		−	558.034i		−	1.83564i
$305$	71.4490			0.234259
$306$		0			0
$307$		−	225.577i		−	0.734778i	−0.930067	−	0.367389i	$-0.880252\pi$
$307$		−	225.577i		−	0.734778i	0.930067	−	0.367389i	$-0.119748\pi$
$308$	−112.577	−	34.2235i	−0.365511	−	0.111115i
$309$		0			0
$310$	−345.421			−1.11426
$311$			52.9648i			0.170305i	0.996368	+	0.0851525i	$0.0271377\pi$
$311$			52.9648i			0.170305i	−0.996368	+	0.0851525i	$0.972862\pi$
$312$		0			0
$313$		−	374.563i		−	1.19669i	−0.801240	−	0.598343i	$-0.795826\pi$
$313$		−	374.563i		−	1.19669i	0.801240	−	0.598343i	$-0.204174\pi$
$314$			144.999i			0.461782i
$315$		0			0
$316$	232.727			0.736477
$317$	−12.0550			−0.0380283			−0.0190142	−	0.999819i	$-0.506053\pi$
$317$	−12.0550			−0.0380283			−0.0190142	+	0.999819i	$0.506053\pi$
$318$		0			0
$319$	78.0559			0.244689
$320$			110.734i			0.346042i
$321$		0			0
$322$	−583.610	−	177.418i	−1.81245	−	0.550987i
$323$	30.8833			0.0956138
$324$		0			0
$325$		−	90.0872i		−	0.277191i
$326$	181.527			0.556832
$327$		0			0
$328$		−	747.871i		−	2.28009i
$329$	113.401	−	373.028i	0.344683	−	1.13382i
$330$		0			0
$331$	−376.184			−1.13651			−0.568254	−	0.822853i	$-0.692381\pi$
$331$	−376.184			−1.13651			−0.568254	+	0.822853i	$0.692381\pi$
$332$		−	855.503i		−	2.57682i
$333$		0			0
$334$		−	147.054i		−	0.440281i
$335$		−	214.063i		−	0.638993i
$336$		0			0
$337$	−108.973			−0.323363			−0.161682	−	0.986843i	$-0.551692\pi$
$337$	−108.973			−0.323363			−0.161682	+	0.986843i	$0.551692\pi$
$338$	545.272			1.61323
$339$		0			0
$340$	19.8541			0.0583944
$341$			89.5516i			0.262615i
$342$		0			0
$343$	−217.120	−	265.533i	−0.633004	−	0.774148i
$344$	143.650			0.417588
$345$		0			0
$346$			343.431i			0.992576i
$347$	206.351			0.594671			0.297335	−	0.954773i	$-0.403902\pi$
$347$	206.351			0.594671			0.297335	+	0.954773i	$0.403902\pi$
$348$		0			0
$349$			373.475i			1.07013i	0.844811	+	0.535064i	$0.179713\pi$
$349$			373.475i			1.07013i	−0.844811	+	0.535064i	$0.820287\pi$
$350$	−117.327	−	35.6676i	−0.335221	−	0.101907i
$351$		0			0
$352$	−16.2451			−0.0461509
$353$			646.142i			1.83043i	0.402964	+	0.915216i	$0.367980\pi$
$353$			646.142i			1.83043i	−0.402964	+	0.915216i	$0.632020\pi$
$354$		0			0
$355$		−	57.6992i		−	0.162533i
$356$			243.003i			0.682592i
$357$		0			0
$358$	240.294			0.671211
$359$	−175.261			−0.488192			−0.244096	−	0.969751i	$-0.578491\pi$
$359$	−175.261			−0.488192			−0.244096	+	0.969751i	$0.578491\pi$
$360$		0			0
$361$	−467.590			−1.29526
$362$		−	368.323i		−	1.01747i
$363$		0			0
$364$	303.587	−	998.640i	0.834030	−	2.74352i
$365$	213.948			0.586158
$366$		0			0
$367$			106.477i			0.290127i	0.989422	+	0.145063i	$0.0463386\pi$
$367$			106.477i			0.290127i	−0.989422	+	0.145063i	$0.953661\pi$
$368$	−482.152			−1.31020
$369$		0			0
$370$			292.095i			0.789446i
$371$	384.868	+	117.000i	1.03738	+	0.315364i
$372$		0			0
$373$	223.324			0.598723			0.299362	−	0.954140i	$-0.403226\pi$
$373$	223.324			0.598723			0.299362	+	0.954140i	$0.403226\pi$
$374$		−	7.63508i		−	0.0204147i
$375$		0			0
$376$		−	834.419i		−	2.21920i
$377$			692.411i			1.83663i
$378$		0			0
$379$	119.075			0.314183			0.157092	−	0.987584i	$-0.449788\pi$
$379$	119.075			0.314183			0.157092	+	0.987584i	$0.449788\pi$
$380$	−532.680			−1.40179
$381$		0			0
$382$	805.159			2.10775
$383$			494.637i			1.29148i	0.763557	+	0.645740i	$0.223451\pi$
$383$			494.637i			1.29148i	−0.763557	+	0.645740i	$0.776549\pi$
$384$		0			0
$385$	−9.24694	+	30.4175i	−0.0240180	+	0.0790065i
$386$	−390.767			−1.01235
$387$		0			0
$388$			559.838i			1.44288i
$389$	270.578			0.695574			0.347787	−	0.937574i	$-0.386933\pi$
$389$	270.578			0.695574			0.347787	+	0.937574i	$0.386933\pi$
$390$		0			0
$391$		−	26.6837i		−	0.0682448i
$392$	−609.875	−	408.563i	−1.55580	−	1.04225i
$393$		0			0
$394$	−605.664			−1.53722
$395$		−	62.8810i		−	0.159192i
$396$		0			0
$397$			37.1881i			0.0936727i	0.998903	+	0.0468364i	$0.0149139\pi$
$397$			37.1881i			0.0936727i	−0.998903	+	0.0468364i	$0.985086\pi$
$398$			413.240i			1.03829i
$399$		0			0
$400$	−96.9306			−0.242326
$401$	36.7102			0.0915467			0.0457733	−	0.998952i	$-0.485425\pi$
$401$	36.7102			0.0915467			0.0457733	+	0.998952i	$0.485425\pi$
$402$		0			0
$403$	−794.386			−1.97118
$404$			606.868i			1.50215i
$405$		0			0
$406$	901.780	+	274.141i	2.22113	+	0.675225i
$407$	75.7266			0.186060
$408$		0			0
$409$			495.325i			1.21106i	0.795821	+	0.605532i	$0.207040\pi$
$409$			495.325i			1.21106i	−0.795821	+	0.605532i	$0.792960\pi$
$410$	−391.103			−0.953909
$411$		0			0
$412$			474.562i			1.15185i
$413$	207.056	−	681.104i	0.501346	−	1.64916i
$414$		0			0
$415$	−231.151			−0.556989
$416$		−	144.106i		−	0.346408i
$417$		0			0
$418$			204.847i			0.490065i
$419$			269.297i			0.642713i	0.946958	+	0.321357i	$0.104139\pi$
$419$			269.297i			0.642713i	−0.946958	+	0.321357i	$0.895861\pi$
$420$		0			0
$421$	756.722			1.79744			0.898719	−	0.438524i	$-0.144499\pi$
$421$	756.722			1.79744			0.898719	+	0.438524i	$0.144499\pi$
$422$	1373.24			3.25412
$423$		0			0
$424$	860.904			2.03043
$425$		−	5.36443i		−	0.0126222i
$426$		0			0
$427$	65.0563	−	214.001i	0.152357	−	0.501173i
$428$	329.709			0.770347
$429$		0			0
$430$		−	75.1226i		−	0.174704i
$431$	−185.182			−0.429657			−0.214828	−	0.976652i	$-0.568919\pi$
$431$	−185.182			−0.429657			−0.214828	+	0.976652i	$0.568919\pi$
$432$		0			0
$433$			642.846i			1.48463i	0.670049	+	0.742317i	$0.266273\pi$
$433$			642.846i			1.48463i	−0.670049	+	0.742317i	$0.733727\pi$
$434$	−314.516	+	1034.59i	−0.724691	+	2.38385i
$435$		0			0
$436$	−1531.46			−3.51253
$437$			715.918i			1.63826i
$438$		0			0
$439$		−	464.239i		−	1.05749i	−0.848780	−	0.528745i	$-0.822663\pi$
$439$		−	464.239i		−	1.05749i	0.848780	−	0.528745i	$-0.177337\pi$
$440$			68.0403i			0.154637i
$441$		0			0
$442$	67.7286			0.153232
$443$	115.228			0.260109			0.130054	−	0.991507i	$-0.458485\pi$
$443$	115.228			0.260109			0.130054	+	0.991507i	$0.458485\pi$
$444$		0			0
$445$	65.6575			0.147545
$446$		−	337.234i		−	0.756130i
$447$		0			0
$448$	331.664	+	100.826i	0.740321	+	0.225058i
$449$	−333.955			−0.743774			−0.371887	−	0.928278i	$-0.621289\pi$
$449$	−333.955			−0.743774			−0.371887	+	0.928278i	$0.621289\pi$
$450$		0			0
$451$			101.395i			0.224822i
$452$	999.028			2.21024
$453$		0			0
$454$			321.275i			0.707654i
$455$	−269.825	−	82.0269i	−0.593022	−	0.180279i
$456$		0			0
$457$	354.152			0.774949			0.387474	−	0.921880i	$-0.373348\pi$
$457$	354.152			0.774949			0.387474	+	0.921880i	$0.373348\pi$
$458$		−	1135.10i		−	2.47837i
$459$		0			0
$460$			460.246i			1.00053i
$461$			128.906i			0.279623i	0.990178	+	0.139811i	$0.0446497\pi$
$461$			128.906i			0.279623i	−0.990178	+	0.139811i	$0.955350\pi$
$462$		0			0
$463$	−302.175			−0.652645			−0.326322	−	0.945259i	$-0.605810\pi$
$463$	−302.175			−0.652645			−0.326322	+	0.945259i	$0.605810\pi$
$464$	745.009			1.60562
$465$		0			0
$466$	640.887			1.37530
$467$		−	808.227i		−	1.73068i	−0.501186	−	0.865339i	$-0.667103\pi$
$467$		−	808.227i		−	1.73068i	0.501186	−	0.865339i	$-0.332897\pi$
$468$		0			0
$469$	−641.151	−	194.910i	−1.36706	−	0.415587i
$470$	−436.363			−0.928433
$471$		0			0
$472$		−	1523.55i		−	3.22785i
$473$	−19.4758			−0.0411750
$474$		0			0
$475$			143.926i			0.303003i
$476$	18.0777	−	59.4661i	0.0379784	−	0.124929i
$477$		0			0
$478$	−150.392			−0.314628
$479$			48.8836i			0.102053i	0.998697	+	0.0510267i	$0.0162494\pi$
$479$			48.8836i			0.102053i	−0.998697	+	0.0510267i	$0.983751\pi$
$480$		0			0
$481$			671.748i			1.39657i
$482$			349.998i			0.726137i
$483$		0			0
$484$	−967.235			−1.99842
$485$	151.264			0.311884
$486$		0			0
$487$	334.433			0.686720			0.343360	−	0.939204i	$-0.388435\pi$
$487$	334.433			0.686720			0.343360	+	0.939204i	$0.388435\pi$
$488$		−	478.694i		−	0.980930i
$489$		0			0
$490$	−213.660	+	318.937i	−0.436040	+	0.650892i
$491$	549.151			1.11843			0.559217	−	0.829021i	$-0.311102\pi$
$491$	549.151			1.11843			0.559217	+	0.829021i	$0.311102\pi$
$492$		0			0
$493$			41.2310i			0.0836329i
$494$	−1817.14			−3.67842
$495$		0			0
$496$			854.731i			1.72325i
$497$	−172.818	−	52.5368i	−0.347722	−	0.105708i
$498$		0			0
$499$	−462.450			−0.926754			−0.463377	−	0.886161i	$-0.653362\pi$
$499$	−462.450			−0.926754			−0.463377	+	0.886161i	$0.653362\pi$
$500$			92.5267i			0.185053i
$501$		0			0
$502$		−	1418.80i		−	2.82630i
$503$			676.817i			1.34556i	0.739842	+	0.672781i	$0.234900\pi$
$503$			676.817i			1.34556i	−0.739842	+	0.672781i	$0.765100\pi$
$504$		0			0
$505$	163.971			0.324695
$506$	176.992			0.349786
$507$		0			0
$508$	−691.112			−1.36046
$509$			31.5959i			0.0620744i	0.999518	+	0.0310372i	$0.00988104\pi$
$509$			31.5959i			0.0620744i	−0.999518	+	0.0310372i	$0.990119\pi$
$510$		0			0
$511$	194.805	−	640.806i	0.381224	−	1.25402i
$512$	1006.66			1.96613
$513$		0			0
$514$			359.819i			0.700036i
$515$	128.223			0.248977
$516$		0			0
$517$			113.129i			0.218817i
$518$	874.869	+	265.961i	1.68894	+	0.513437i
$519$		0			0
$520$	−603.566			−1.16070
$521$		−	793.420i		−	1.52288i	−0.648236	−	0.761440i	$-0.724493\pi$
$521$		−	793.420i		−	1.52288i	0.648236	−	0.761440i	$-0.275507\pi$
$522$		0			0
$523$		−	593.508i		−	1.13481i	−0.823438	−	0.567407i	$-0.807947\pi$
$523$		−	593.508i		−	1.13481i	0.823438	−	0.567407i	$-0.192053\pi$
$524$		−	1640.67i		−	3.13104i
$525$		0			0
$526$	986.216			1.87494
$527$	−47.3034			−0.0897597
$528$		0			0
$529$	89.5666			0.169313
$530$		−	450.214i		−	0.849460i
$531$		0			0
$532$	−485.020	+	1595.46i	−0.911692	+	2.99898i
$533$	−899.442			−1.68751
$534$		0			0
$535$		−	89.0848i		−	0.166514i
$536$	−1434.18			−2.67570
$537$		0			0
$538$		−	618.094i		−	1.14887i
$539$	82.6855	+	55.3920i	0.153405	+	0.102768i
$540$		0			0
$541$	217.690			0.402385			0.201192	−	0.979552i	$-0.435518\pi$
$541$	217.690			0.402385			0.201192	+	0.979552i	$0.435518\pi$
$542$			1072.27i			1.97836i
$543$		0			0
$544$		−	8.58106i		−	0.0157740i
$545$			413.789i			0.759246i
$546$		0			0
$547$	−137.891			−0.252085			−0.126043	−	0.992025i	$-0.540228\pi$
$547$	−137.891			−0.252085			−0.126043	+	0.992025i	$0.540228\pi$
$548$	199.973			0.364915
$549$		0			0
$550$	35.5820			0.0646945
$551$		−	1106.22i		−	2.00766i
$552$		0			0
$553$	−188.338	−	57.2549i	−0.340575	−	0.103535i
$554$	−153.459			−0.277002
$555$		0			0
$556$		−	510.098i		−	0.917442i
$557$	316.337			0.567930			0.283965	−	0.958835i	$-0.408350\pi$
$557$	316.337			0.567930			0.283965	+	0.958835i	$0.408350\pi$
$558$		0			0
$559$		−	172.764i		−	0.309059i
$560$	−88.2580	+	290.322i	−0.157604	+	0.518432i
$561$		0			0
$562$	1750.10			3.11406
$563$		−	151.482i		−	0.269063i	−0.990909	−	0.134531i	$-0.957047\pi$
$563$		−	151.482i		−	0.269063i	0.990909	−	0.134531i	$-0.0429529\pi$
$564$		0			0
$565$		−	269.930i		−	0.477752i
$566$			429.804i			0.759371i
$567$		0			0
$568$	−386.573			−0.680586
$569$	213.993			0.376086			0.188043	−	0.982161i	$-0.439786\pi$
$569$	213.993			0.376086			0.188043	+	0.982161i	$0.439786\pi$
$570$		0			0
$571$	−204.492			−0.358129			−0.179065	−	0.983837i	$-0.557307\pi$
$571$	−204.492			−0.358129			−0.179065	+	0.983837i	$0.557307\pi$
$572$			302.858i			0.529473i
$573$		0			0
$574$	−356.110	+	1171.41i	−0.620400	+	2.04079i
$575$	124.355			0.216270
$576$		0			0
$577$		−	957.823i		−	1.66001i	−0.557759	−	0.830003i	$-0.688339\pi$
$577$		−	957.823i		−	1.66001i	0.557759	−	0.830003i	$-0.311661\pi$
$578$	−1008.53			−1.74487
$579$		0			0
$580$		−	711.161i		−	1.22614i
$581$	−210.469	+	692.331i	−0.362253	+	1.19162i
$582$		0			0
$583$	−116.719			−0.200205
$584$		−	1433.41i		−	2.45446i
$585$		0			0
$586$			434.007i			0.740626i
$587$		−	981.279i		−	1.67168i	−0.548969	−	0.835842i	$-0.684980\pi$
$587$		−	981.279i		−	1.67168i	0.548969	−	0.835842i	$-0.315020\pi$
$588$		0			0
$589$	1269.14			2.15473
$590$	−796.746			−1.35042
$591$		0			0
$592$	722.777			1.22091
$593$			708.384i			1.19458i	0.802026	+	0.597288i	$0.203755\pi$
$593$			708.384i			1.19458i	−0.802026	+	0.597288i	$0.796245\pi$
$594$		0			0
$595$	−16.0673	−	4.88446i	−0.0270038	−	0.00820918i
$596$	238.568			0.400282
$597$		0			0
$598$			1570.04i			2.62549i
$599$	928.994			1.55091			0.775454	−	0.631404i	$-0.217521\pi$
$599$	928.994			1.55091			0.775454	+	0.631404i	$0.217521\pi$
$600$		0			0
$601$		−	466.882i		−	0.776842i	−0.921482	−	0.388421i	$-0.873021\pi$
$601$		−	466.882i		−	0.776842i	0.921482	−	0.388421i	$-0.126979\pi$
$602$	−225.004	−	68.4012i	−0.373760	−	0.113623i
$603$		0			0
$604$	2054.98			3.40229
$605$			261.339i			0.431966i
$606$		0			0
$607$			988.757i			1.62892i	0.580216	+	0.814462i	$0.302968\pi$
$607$			988.757i			1.62892i	−0.580216	+	0.814462i	$0.697032\pi$
$608$			230.228i			0.378664i
$609$		0			0
$610$	−250.335			−0.410386
$611$	−1003.53			−1.64244
$612$		0			0
$613$	469.962			0.766660			0.383330	−	0.923612i	$-0.374777\pi$
$613$	469.962			0.766660			0.383330	+	0.923612i	$0.374777\pi$
$614$			790.351i			1.28722i
$615$		0			0
$616$	203.791	+	61.9526i	0.330830	+	0.100572i
$617$	−1081.72			−1.75320			−0.876598	−	0.481223i	$-0.840193\pi$
$617$	−1081.72			−1.75320			−0.876598	+	0.481223i	$0.840193\pi$
$618$		0			0
$619$		−	553.956i		−	0.894921i	−0.894304	−	0.447461i	$-0.852328\pi$
$619$		−	553.956i		−	0.894921i	0.894304	−	0.447461i	$-0.147672\pi$
$620$	815.897			1.31596
$621$		0			0
$622$		−	185.572i		−	0.298348i
$623$	59.7829	−	196.654i	0.0959598	−	0.315657i
$624$		0			0
$625$	25.0000			0.0400000
$626$			1312.35i			2.09641i
$627$		0			0
$628$		−	342.494i		−	0.545372i
$629$			40.0006i			0.0635940i
$630$		0			0
$631$	−77.8822			−0.123427			−0.0617133	−	0.998094i	$-0.519656\pi$
$631$	−77.8822			−0.123427			−0.0617133	+	0.998094i	$0.519656\pi$
$632$	−421.290			−0.666597
$633$		0			0
$634$	42.2369			0.0666197
$635$			186.733i			0.294068i
$636$		0			0
$637$	−491.366	+	733.479i	−0.771375	+	1.15146i
$638$	−273.484			−0.428658
$639$		0			0
$640$		−	459.513i		−	0.717989i
$641$	360.619			0.562589			0.281294	−	0.959622i	$-0.409236\pi$
$641$	360.619			0.562589			0.281294	+	0.959622i	$0.409236\pi$
$642$		0			0
$643$			793.158i			1.23353i	0.787148	+	0.616764i	$0.211557\pi$
$643$			793.158i			1.23353i	−0.787148	+	0.616764i	$0.788443\pi$
$644$	1378.51	+	419.067i	2.14054	+	0.650725i
$645$		0			0
$646$	−108.205			−0.167501
$647$			405.244i			0.626344i	0.949696	+	0.313172i	$0.101392\pi$
$647$			405.244i			0.626344i	−0.949696	+	0.313172i	$0.898608\pi$
$648$		0			0
$649$			206.559i			0.318273i
$650$			315.637i			0.485596i
$651$		0			0
$652$	−428.774			−0.657629
$653$	−493.508			−0.755755			−0.377877	−	0.925856i	$-0.623346\pi$
$653$	−493.508			−0.755755			−0.377877	+	0.925856i	$0.623346\pi$
$654$		0			0
$655$	−443.295			−0.676787
$656$			967.767i			1.47526i
$657$		0			0
$658$	−397.321	+	1306.97i	−0.603831	+	1.98628i
$659$	1120.88			1.70088			0.850441	−	0.526070i	$-0.176335\pi$
$659$	1120.88			1.70088			0.850441	+	0.526070i	$0.176335\pi$
$660$		0			0
$661$			1134.48i			1.71631i	0.513393	+	0.858154i	$0.328388\pi$
$661$			1134.48i			1.71631i	−0.513393	+	0.858154i	$0.671612\pi$
$662$	1318.03			1.99098
$663$		0			0
$664$			1548.66i			2.33232i
$665$	431.081	+	131.049i	0.648242	+	0.197066i
$666$		0			0
$667$	−955.794			−1.43297
$668$			347.346i			0.519979i
$669$		0			0
$670$			750.009i			1.11942i
$671$			64.9002i			0.0967216i
$672$		0			0
$673$	−763.267			−1.13413			−0.567063	−	0.823674i	$-0.691920\pi$
$673$	−763.267			−1.13413			−0.567063	+	0.823674i	$0.691920\pi$
$674$	381.809			0.566482
$675$		0			0
$676$	−1287.95			−1.90525
$677$			456.611i			0.674463i	0.941422	+	0.337232i	$0.109491\pi$
$677$			456.611i			0.674463i	−0.941422	+	0.337232i	$0.890509\pi$
$678$		0			0
$679$	137.730	−	453.058i	0.202842	−	0.667244i
$680$	−35.9406			−0.0528538
$681$		0			0
$682$		−	313.761i		−	0.460060i
$683$	219.276			0.321049			0.160524	−	0.987032i	$-0.448681\pi$
$683$	219.276			0.321049			0.160524	+	0.987032i	$0.448681\pi$
$684$		0			0
$685$		−	54.0313i		−	0.0788777i
$686$	760.722	+	930.345i	1.10892	+	1.35619i
$687$		0			0
$688$	−185.888			−0.270186
$689$		−	1035.38i		−	1.50273i
$690$		0			0
$691$			396.801i			0.574242i	0.957894	+	0.287121i	$0.0926982\pi$
$691$			396.801i			0.574242i	−0.957894	+	0.287121i	$0.907302\pi$
$692$		−	811.197i		−	1.17225i
$693$		0			0
$694$	−722.989			−1.04177
$695$	−137.825			−0.198309
$696$		0			0
$697$	−53.5591			−0.0768424
$698$		−	1308.54i		−	1.87470i
$699$		0			0
$700$	277.131	+	84.2481i	0.395902	+	0.120354i
$701$	493.156			0.703503			0.351752	−	0.936093i	$-0.385586\pi$
$701$	493.156			0.703503			0.351752	+	0.936093i	$0.385586\pi$
$702$		0			0
$703$		−	1073.21i		−	1.52661i
$704$	−100.584			−0.142875
$705$		0			0
$706$		−	2263.88i		−	3.20663i
$707$	149.300	−	491.118i	0.211174	−	0.694651i
$708$		0			0
$709$	859.326			1.21202			0.606012	−	0.795455i	$-0.292768\pi$
$709$	859.326			1.21202			0.606012	+	0.795455i	$0.292768\pi$
$710$			202.160i			0.284733i
$711$		0			0
$712$		−	439.892i		−	0.617825i
$713$		−	1096.56i		−	1.53795i
$714$		0			0
$715$	81.8300			0.114448
$716$	−567.582			−0.792712
$717$		0			0
$718$	614.060			0.855237
$719$			385.539i			0.536216i	0.963389	+	0.268108i	$0.0863983\pi$
$719$			385.539i			0.536216i	−0.963389	+	0.268108i	$0.913602\pi$
$720$		0			0
$721$	116.751	−	384.048i	0.161929	−	0.532660i
$722$	1638.29			2.26910
$723$		0			0
$724$			869.992i			1.20165i
$725$	−192.150			−0.265035
$726$		0			0
$727$		−	114.722i		−	0.157802i	−0.996882	−	0.0789012i	$-0.974859\pi$
$727$		−	114.722i		−	0.157802i	0.996882	−	0.0789012i	$-0.0251412\pi$
$728$	−549.563	+	1807.77i	−0.754895	+	2.48320i
$729$		0			0
$730$	−749.606			−1.02686
$731$		−	10.2876i		−	0.0140733i
$732$		0			0
$733$		−	140.433i		−	0.191586i	−0.995401	−	0.0957932i	$-0.969461\pi$
$733$		−	140.433i		−	0.191586i	0.995401	−	0.0957932i	$-0.0305388\pi$
$734$		−	373.061i		−	0.508257i
$735$		0			0
$736$	198.921			0.270273
$737$	194.442			0.263830
$738$		0			0
$739$	−50.8609			−0.0688239			−0.0344120	−	0.999408i	$-0.510956\pi$
$739$	−50.8609			−0.0688239			−0.0344120	+	0.999408i	$0.510956\pi$
$740$		−	689.939i		−	0.932349i
$741$		0			0
$742$	−1348.46	−	409.932i	−1.81733	−	0.552469i
$743$	−930.694			−1.25262			−0.626309	−	0.779575i	$-0.715435\pi$
$743$	−930.694			−1.25262			−0.626309	+	0.779575i	$0.715435\pi$
$744$		0			0
$745$		−	64.4593i		−	0.0865225i
$746$	−782.457			−1.04887
$747$		0			0
$748$			18.0343i			0.0241101i
$749$	−266.822	−	81.1142i	−0.356238	−	0.108297i
$750$		0			0
$751$	−446.702			−0.594809			−0.297404	−	0.954752i	$-0.596121\pi$
$751$	−446.702			−0.594809			−0.297404	+	0.954752i	$0.596121\pi$
$752$			1079.76i			1.43586i
$753$		0			0
$754$		−	2425.99i		−	3.21750i
$755$		−	555.241i		−	0.735419i
$756$		0			0
$757$	27.2042			0.0359369			0.0179684	−	0.999839i	$-0.494280\pi$
$757$	27.2042			0.0359369			0.0179684	+	0.999839i	$0.494280\pi$
$758$	−417.203			−0.550400
$759$		0			0
$760$	964.276			1.26878
$761$		−	333.536i		−	0.438287i	−0.975693	−	0.219143i	$-0.929674\pi$
$761$		−	333.536i		−	0.438287i	0.975693	−	0.219143i	$-0.0703262\pi$
$762$		0			0
$763$	1239.36	+	376.767i	1.62433	+	0.493796i
$764$	−1901.81			−2.48928
$765$		0			0
$766$		−	1733.05i		−	2.26247i
$767$	−1832.32			−2.38895
$768$		0			0
$769$		−	56.3903i		−	0.0733294i	−0.999328	−	0.0366647i	$-0.988327\pi$
$769$		−	56.3903i		−	0.0733294i	0.999328	−	0.0366647i	$-0.0116734\pi$
$770$	32.3984	−	106.574i	0.0420758	−	0.138407i
$771$		0			0
$772$	923.006			1.19560
$773$			296.398i			0.383438i	0.981450	+	0.191719i	$0.0614063\pi$
$773$			296.398i			0.383438i	−0.981450	+	0.191719i	$0.938594\pi$
$774$		0			0
$775$		−	220.449i		−	0.284451i
$776$		−	1013.44i		−	1.30598i
$777$		0			0
$778$	−948.022			−1.21854
$779$	1436.98			1.84464
$780$		0			0
$781$	52.4107			0.0671072
$782$			93.4915i			0.119554i
$783$		0			0
$784$	789.197	+	528.692i	1.00663	+	0.674352i
$785$	−92.5392			−0.117884
$786$		0			0
$787$			226.427i			0.287709i	0.989599	+	0.143854i	$0.0459497\pi$
$787$			226.427i			0.287709i	−0.989599	+	0.143854i	$0.954050\pi$
$788$	1430.60			1.81548
$789$		0			0
$790$			220.315i			0.278880i
$791$	−808.481	−	245.779i	−1.02210	−	0.310719i
$792$		0			0
$793$	−575.711			−0.725991
$794$		−	130.295i		−	0.164100i
$795$		0			0
$796$		−	976.088i		−	1.22624i
$797$			305.282i			0.383038i	0.981489	+	0.191519i	$0.0613414\pi$
$797$			305.282i			0.383038i	−0.981489	+	0.191519i	$0.938659\pi$
$798$		0			0
$799$	−59.7573			−0.0747901
$800$	39.9906			0.0499882
$801$		0			0
$802$	−128.621			−0.160375
$803$			194.338i			0.242015i
$804$		0			0
$805$	113.229	−	372.462i	0.140657	−	0.462686i
$806$	2783.28			3.45320
$807$		0			0
$808$		−	1098.57i		−	1.35962i
$809$	−592.651			−0.732573			−0.366286	−	0.930502i	$-0.619371\pi$
$809$	−592.651			−0.732573			−0.366286	+	0.930502i	$0.619371\pi$
$810$		0			0
$811$			731.348i			0.901785i	0.892578	+	0.450893i	$0.148894\pi$
$811$			731.348i			0.901785i	−0.892578	+	0.450893i	$0.851106\pi$
$812$	−2130.04	−	647.532i	−2.62320	−	0.797453i
$813$		0			0
$814$	−265.322			−0.325949
$815$			115.851i			0.142149i
$816$		0			0
$817$			276.013i			0.337838i
$818$		−	1735.47i		−	2.12160i
$819$		0			0
$820$	923.798			1.12658
$821$	−268.560			−0.327114			−0.163557	−	0.986534i	$-0.552297\pi$
$821$	−268.560			−0.327114			−0.163557	+	0.986534i	$0.552297\pi$
$822$		0			0
$823$	1213.35			1.47430			0.737151	−	0.675728i	$-0.236170\pi$
$823$	1213.35			1.47430			0.737151	+	0.675728i	$0.236170\pi$
$824$		−	859.068i		−	1.04256i
$825$		0			0
$826$	−725.459	+	2386.37i	−0.878280	+	2.88907i
$827$	1238.49			1.49757			0.748785	−	0.662813i	$-0.230637\pi$
$827$	1238.49			1.49757			0.748785	+	0.662813i	$0.230637\pi$
$828$		0			0
$829$		−	873.056i		−	1.05314i	−0.850131	−	0.526572i	$-0.823477\pi$
$829$		−	873.056i		−	1.05314i	0.850131	−	0.526572i	$-0.176523\pi$
$830$	809.879			0.975758
$831$		0			0
$832$		−	892.251i		−	1.07242i
$833$	−29.2594	+	43.6765i	−0.0351253	+	0.0524328i
$834$		0			0
$835$	93.8503			0.112396
$836$		−	483.856i		−	0.578776i
$837$		0			0
$838$		−	943.532i		−	1.12593i
$839$			100.572i			0.119871i	0.998202	+	0.0599355i	$0.0190895\pi$
$839$			100.572i			0.119871i	−0.998202	+	0.0599355i	$0.980910\pi$
$840$		0			0
$841$	635.869			0.756086
$842$	−2651.32			−3.14883
$843$		0			0
$844$	−3243.63			−3.84317
$845$			347.995i			0.411828i
$846$		0			0
$847$	782.752	+	237.957i	0.924146	+	0.280941i
$848$	−1114.03			−1.31372
$849$		0			0
$850$			18.7953i			0.0221121i
$851$	−927.271			−1.08963
$852$		0			0
$853$			1162.30i			1.36260i	0.732003	+	0.681302i	$0.238586\pi$
$853$			1162.30i			1.36260i	−0.732003	+	0.681302i	$0.761414\pi$
$854$	−227.937	+	749.792i	−0.266905	+	0.877977i
$855$		0			0
$856$	−596.850			−0.697254
$857$			87.8213i			0.102475i	0.998686	+	0.0512376i	$0.0163166\pi$
$857$			87.8213i			0.102475i	−0.998686	+	0.0512376i	$0.983683\pi$
$858$		0			0
$859$		−	200.580i		−	0.233504i	−0.993161	−	0.116752i	$-0.962752\pi$
$859$		−	200.580i		−	0.233504i	0.993161	−	0.116752i	$-0.0372482\pi$
$860$			177.442i			0.206328i
$861$		0			0
$862$	648.820			0.752691
$863$	617.914			0.716007			0.358004	−	0.933720i	$-0.383458\pi$
$863$	617.914			0.716007			0.358004	+	0.933720i	$0.383458\pi$
$864$		0			0
$865$	−219.179			−0.253386
$866$		−	2252.33i		−	2.60085i
$867$		0			0
$868$	742.897	−	2443.74i	0.855872	−	2.81537i
$869$	57.1175			0.0657278
$870$		0			0
$871$			1724.84i			1.98030i
$872$	2772.30			3.17925
$873$		0			0
$874$		−	2508.35i		−	2.86997i
$875$	22.7632	−	74.8788i	0.0260151	−	0.0855758i
$876$		0			0
$877$	−638.649			−0.728220			−0.364110	−	0.931356i	$-0.618627\pi$
$877$	−638.649			−0.728220			−0.364110	+	0.931356i	$0.618627\pi$
$878$			1626.55i			1.85256i
$879$		0			0
$880$		−	88.0462i		−	0.100052i
$881$		−	148.009i		−	0.168001i	−0.996466	−	0.0840003i	$-0.973230\pi$
$881$		−	148.009i		−	0.168001i	0.996466	−	0.0840003i	$-0.0267697\pi$
$882$		0			0
$883$	−784.505			−0.888454			−0.444227	−	0.895914i	$-0.646522\pi$
$883$	−784.505			−0.888454			−0.444227	+	0.895914i	$0.646522\pi$
$884$	−159.977			−0.180970
$885$		0			0
$886$	−403.724			−0.455670
$887$		−	1466.40i		−	1.65321i	−0.562783	−	0.826605i	$-0.690269\pi$
$887$		−	1466.40i		−	1.65321i	0.562783	−	0.826605i	$-0.309731\pi$
$888$		0			0
$889$	559.294	+	170.026i	0.629127	+	0.191255i
$890$	−230.043			−0.258476
$891$		0			0
$892$			796.559i			0.893003i
$893$	1603.27			1.79538
$894$		0			0
$895$			153.356i			0.171348i
$896$	−1376.31	−	418.400i	−1.53606	−	0.466964i
$897$		0			0
$898$	1170.07			1.30298
$899$			1694.38i			1.88473i
$900$		0			0
$901$		−	61.6540i		−	0.0684284i
$902$		−	355.255i		−	0.393853i
$903$		0			0
$904$	−1808.48			−2.00053
$905$	235.065			0.259741
$906$		0			0
$907$	488.454			0.538538			0.269269	−	0.963065i	$-0.413218\pi$
$907$	488.454			0.538538			0.269269	+	0.963065i	$0.413218\pi$
$908$		−	758.863i		−	0.835752i
$909$		0			0
$910$	945.382	+	287.397i	1.03888	+	0.315821i
$911$	−1329.44			−1.45932			−0.729658	−	0.683812i	$-0.760321\pi$
$911$	−1329.44			−1.45932			−0.729658	+	0.683812i	$0.760321\pi$
$912$		0			0
$913$		−	209.964i		−	0.229971i
$914$	−1240.84			−1.35759
$915$		0			0
$916$			2681.14i			2.92700i
$917$	−403.633	+	1327.74i	−0.440167	+	1.44791i
$918$		0			0
$919$	1369.52			1.49023			0.745113	−	0.666938i	$-0.232395\pi$
$919$	1369.52			1.49023			0.745113	+	0.666938i	$0.232395\pi$
$920$		−	833.153i		−	0.905601i
$921$		0			0
$922$		−	451.647i		−	0.489856i
$923$			464.920i			0.503705i
$924$		0			0
$925$	−186.416			−0.201531
$926$	1058.73			1.14333
$927$		0			0
$928$	−307.368			−0.331216
$929$		−	909.289i		−	0.978783i	−0.872064	−	0.489391i	$-0.837219\pi$
$929$		−	909.289i		−	0.978783i	0.872064	−	0.489391i	$-0.162781\pi$
$930$		0			0
$931$	785.022	−	1171.83i	0.843203	−	1.25868i
$932$	−1513.80			−1.62425
$933$		0			0
$934$			2831.78i			3.03188i
$935$	4.87274			0.00521149
$936$		0			0
$937$			184.883i			0.197313i	0.995122	+	0.0986566i	$0.0314545\pi$
$937$			184.883i			0.197313i	−0.995122	+	0.0986566i	$0.968545\pi$
$938$	2246.39	+	682.904i	2.39487	+	0.728043i
$939$		0			0
$940$	1030.71			1.09650
$941$		−	884.454i		−	0.939909i	−0.882691	−	0.469955i	$-0.844270\pi$
$941$		−	884.454i		−	0.939909i	0.882691	−	0.469955i	$-0.155730\pi$
$942$		0			0
$943$		−	1241.58i		−	1.31662i
$944$			1971.51i			2.08847i
$945$		0			0
$946$	68.2371			0.0721322
$947$	651.331			0.687784			0.343892	−	0.939009i	$-0.388255\pi$
$947$	651.331			0.687784			0.343892	+	0.939009i	$0.388255\pi$
$948$		0			0
$949$	−1723.91			−1.81656
$950$		−	504.273i		−	0.530813i
$951$		0			0
$952$	−32.7249	+	107.647i	−0.0343749	+	0.113075i
$953$	−1622.61			−1.70263			−0.851316	−	0.524654i	$-0.824195\pi$
$953$	−1622.61			−1.70263			−0.851316	+	0.524654i	$0.824195\pi$
$954$		0			0
$955$			513.855i			0.538069i
$956$	355.232			0.371582
$957$		0			0
$958$		−	171.273i		−	0.178782i
$959$	−161.832	−	49.1970i	−0.168751	−	0.0513003i
$960$		0			0
$961$	−982.915			−1.02280
$962$		−	2353.60i		−	2.44657i
$963$		0			0
$964$		−	826.708i		−	0.857581i
$965$		−	249.389i		−	0.258435i
$966$		0			0
$967$	−1491.24			−1.54213			−0.771067	−	0.636754i	$-0.780276\pi$
$967$	−1491.24			−1.54213			−0.771067	+	0.636754i	$0.780276\pi$
$968$	1750.92			1.80880
$969$		0			0
$970$	−529.982			−0.546373
$971$			1739.36i			1.79130i	0.444756	+	0.895652i	$0.353291\pi$
$971$			1739.36i			1.79130i	−0.444756	+	0.895652i	$0.646709\pi$
$972$		0			0
$973$	−125.493	+	412.806i	−0.128975	+	0.424261i
$974$	−1171.75			−1.20303
$975$		0			0
$976$			619.444i			0.634676i
$977$	62.8973			0.0643780			0.0321890	−	0.999482i	$-0.489752\pi$
$977$	62.8973			0.0643780			0.0321890	+	0.999482i	$0.489752\pi$
$978$		0			0
$979$			59.6395i			0.0609188i
$980$	504.672	−	753.341i	0.514971	−	0.768715i
$981$		0			0
$982$	−1924.06			−1.95932
$983$		−	1214.68i		−	1.23569i	−0.786299	−	0.617846i	$-0.788006\pi$
$983$		−	1214.68i		−	1.23569i	0.786299	−	0.617846i	$-0.211994\pi$
$984$		0			0
$985$		−	386.537i		−	0.392424i
$986$		−	144.461i		−	0.146512i
$987$		0			0
$988$	4292.15			4.34428
$989$	238.481			0.241133
$990$		0			0
$991$	114.216			0.115253			0.0576266	−	0.998338i	$-0.481647\pi$
$991$	114.216			0.115253			0.0576266	+	0.998338i	$0.481647\pi$
$992$		−	352.636i		−	0.355480i
$993$		0			0
$994$	605.501	+	184.072i	0.609156	+	0.185184i
$995$	−263.732			−0.265057
$996$		0			0
$997$		−	178.000i		−	0.178536i	−0.996008	−	0.0892678i	$-0.971547\pi$
$997$		−	178.000i		−	0.178536i	0.996008	−	0.0892678i	$-0.0284527\pi$
$998$	1620.28			1.62353
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.h.d.181.1		12
3.2	odd	2		105.3.h.a.76.11	✓	12
7.6	odd	2	inner	315.3.h.d.181.2		12
12.11	even	2		1680.3.s.c.1441.12		12
15.2	even	4		525.3.e.c.349.10		24
15.8	even	4		525.3.e.c.349.23		24
15.14	odd	2		525.3.h.d.76.2		12
21.20	even	2		105.3.h.a.76.12	yes	12
84.83	odd	2		1680.3.s.c.1441.3		12
105.62	odd	4		525.3.e.c.349.24		24
105.83	odd	4		525.3.e.c.349.9		24
105.104	even	2		525.3.h.d.76.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.11	✓	12	3.2	odd	2
105.3.h.a.76.12	yes	12	21.20	even	2
315.3.h.d.181.1		12	1.1	even	1	trivial
315.3.h.d.181.2		12	7.6	odd	2	inner
525.3.e.c.349.9		24	105.83	odd	4
525.3.e.c.349.10		24	15.2	even	4
525.3.e.c.349.23		24	15.8	even	4
525.3.e.c.349.24		24	105.62	odd	4
525.3.h.d.76.1		12	105.104	even	2
525.3.h.d.76.2		12	15.14	odd	2
1680.3.s.c.1441.3		12	84.83	odd	2
1680.3.s.c.1441.12		12	12.11	even	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)

\(f(q)\)	\(=\)	\(q-3.50369 q^{2} +8.27584 q^{4} -2.23607i q^{5} +(-6.69736 - 2.03600i) q^{7} -14.9812 q^{8} +O(q^{10})\)	\(q-3.50369 q^{2} +8.27584 q^{4} -2.23607i q^{5} +(-6.69736 - 2.03600i) q^{7} -14.9812 q^{8} +7.83449i q^{10} +2.03112 q^{11} +18.0174i q^{13} +(23.4655 + 7.13352i) q^{14} +19.3861 q^{16} +1.07289i q^{17} -28.7852i q^{19} -18.5053i q^{20} -7.11640 q^{22} -24.8710 q^{23} -5.00000 q^{25} -63.1275i q^{26} +(-55.4263 - 16.8496i) q^{28} +38.4300 q^{29} +44.0899i q^{31} -7.99812 q^{32} -3.75906i q^{34} +(-4.55264 + 14.9758i) q^{35} +37.2832 q^{37} +100.855i q^{38} +33.4990i q^{40} +49.9206i q^{41} -9.58871 q^{43} +16.8092 q^{44} +87.1402 q^{46} +55.6978i q^{47} +(40.7094 + 27.2717i) q^{49} +17.5184 q^{50} +149.109i q^{52} -57.4656 q^{53} -4.54171i q^{55} +(100.335 + 30.5018i) q^{56} -134.647 q^{58} +101.697i q^{59} +31.9530i q^{61} -154.477i q^{62} -49.5215 q^{64} +40.2882 q^{65} +95.7318 q^{67} +8.87902i q^{68} +(15.9510 - 52.4704i) q^{70} +25.8039 q^{71} +95.6803i q^{73} -130.629 q^{74} -238.222i q^{76} +(-13.6031 - 4.13536i) q^{77} +28.1212 q^{79} -43.3487i q^{80} -174.906i q^{82} -103.374i q^{83} +2.39905 q^{85} +33.5959 q^{86} -30.4286 q^{88} +29.3629i q^{89} +(36.6835 - 120.669i) q^{91} -205.828 q^{92} -195.148i q^{94} -64.3658 q^{95} +67.6473i q^{97} +(-142.633 - 95.5515i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) 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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