LMFDB - Embedded newform 315.2.ce.a.53.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(53,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("315.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.ce (of order $12$, degree $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.13
Character	$\chi$	$=$	315.53
Dual form			315.2.ce.a.107.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.494677 - 1.84616i) q^{2} +(-1.43155 - 0.826508i) q^{4} +(-0.541988 - 2.16939i) q^{5} +(2.64533 + 0.0471386i) q^{7} +(0.468944 - 0.468944i) q^{8} +O(q^{10})$	\(q+(0.494677 - 1.84616i) q^{2} +(-1.43155 - 0.826508i) q^{4} +(-0.541988 - 2.16939i) q^{5} +(2.64533 + 0.0471386i) q^{7} +(0.468944 - 0.468944i) q^{8} +(-4.27315 - 0.0725500i) q^{10} +(-0.971861 - 0.561104i) q^{11} +(0.830077 + 0.830077i) q^{13} +(1.39561 - 4.86039i) q^{14} +(-2.28679 - 3.96083i) q^{16} +(-2.16001 + 0.578772i) q^{17} +(-5.19853 + 3.00137i) q^{19} +(-1.01713 + 3.55355i) q^{20} +(-1.51665 + 1.51665i) q^{22} +(-0.641461 - 0.171879i) q^{23} +(-4.41250 + 2.35157i) q^{25} +(1.94308 - 1.12184i) q^{26} +(-3.74797 - 2.25387i) q^{28} +9.88857 q^{29} +(4.19734 - 7.27001i) q^{31} +(-7.16237 + 1.91915i) q^{32} +4.27403i q^{34} +(-1.33148 - 5.76430i) q^{35} +(5.51429 + 1.47755i) q^{37} +(2.96942 + 11.0820i) q^{38} +(-1.27148 - 0.763160i) q^{40} +3.31153i q^{41} +(5.26014 + 5.26014i) q^{43} +(0.927514 + 1.60650i) q^{44} +(-0.634632 + 1.09922i) q^{46} +(-2.55120 + 9.52122i) q^{47} +(6.99556 + 0.249395i) q^{49} +(2.15861 + 9.30945i) q^{50} +(-0.502235 - 1.87437i) q^{52} +(-0.211894 - 0.790799i) q^{53} +(-0.690516 + 2.41246i) q^{55} +(1.26262 - 1.21841i) q^{56} +(4.89165 - 18.2559i) q^{58} +(-1.75013 + 3.03132i) q^{59} +(2.57534 + 4.46061i) q^{61} +(-11.3453 - 11.3453i) q^{62} +5.02510i q^{64} +(1.35087 - 2.25065i) q^{65} +(1.66197 + 6.20255i) q^{67} +(3.57052 + 0.956719i) q^{68} +(-11.3005 - 0.393349i) q^{70} -12.1470i q^{71} +(-4.49672 + 1.20489i) q^{73} +(5.45559 - 9.44935i) q^{74} +9.92263 q^{76} +(-2.54444 - 1.53012i) q^{77} +(9.12881 - 5.27052i) q^{79} +(-7.35317 + 7.10765i) q^{80} +(6.11362 + 1.63814i) q^{82} +(-11.5106 + 11.5106i) q^{83} +(2.42628 + 4.37221i) q^{85} +(12.3131 - 7.10899i) q^{86} +(-0.718875 + 0.192622i) q^{88} +(-1.76847 - 3.06308i) q^{89} +(2.15670 + 2.23496i) q^{91} +(0.776226 + 0.776226i) q^{92} +(16.3157 + 9.41986i) q^{94} +(9.32868 + 9.65092i) q^{95} +(10.6773 - 10.6773i) q^{97} +(3.92097 - 12.7916i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{7}+O(q^{10}) $ 64 * q + 8 * q^7	$ 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73} - 320 q^{76} - 56 q^{82} + 16 q^{85} + 120 q^{88} - 128 q^{91} + 208 q^{97}+O(q^{100}) $ 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.494677	−	1.84616i	0.349790	−	1.30543i	−0.537126	−	0.843502i	$-0.680490\pi$
$2$	0.494677	−	1.84616i	0.349790	−	1.30543i	0.886916	−	0.461931i	$-0.152843\pi$
$3$		0			0
$3$		0			0
$4$	−1.43155	−	0.826508i	−0.715777	−	0.413254i
$5$	−0.541988	−	2.16939i	−0.242385	−	0.970180i
$5$	−0.541988	−	2.16939i	−0.242385	−	0.970180i
$6$		0			0
$7$	2.64533	+	0.0471386i	0.999841	+	0.0178167i
$7$	2.64533	+	0.0471386i	0.999841	+	0.0178167i
$8$	0.468944	−	0.468944i	0.165797	−	0.165797i
$9$		0			0
$10$	−4.27315	−	0.0725500i	−1.35129	−	0.0229423i
$11$	−0.971861	−	0.561104i	−0.293027	−	0.169179i	0.346279	−	0.938132i	$-0.387445\pi$
$11$	−0.971861	−	0.561104i	−0.293027	−	0.169179i	−0.639306	+	0.768952i	$0.720778\pi$
$12$		0			0
$13$	0.830077	+	0.830077i	0.230222	+	0.230222i	0.812785	−	0.582563i	$-0.197950\pi$
$13$	0.830077	+	0.830077i	0.230222	+	0.230222i	−0.582563	+	0.812785i	$0.697950\pi$
$14$	1.39561	−	4.86039i	0.372993	−	1.29899i
$15$		0			0
$16$	−2.28679	−	3.96083i	−0.571696	−	0.990207i
$17$	−2.16001	+	0.578772i	−0.523879	+	0.140373i	−0.511060	−	0.859545i	$-0.670747\pi$
$17$	−2.16001	+	0.578772i	−0.523879	+	0.140373i	−0.0128185	+	0.999918i	$0.504080\pi$
$18$		0			0
$19$	−5.19853	+	3.00137i	−1.19262	+	0.688562i	−0.958901	−	0.283741i	$-0.908424\pi$
$19$	−5.19853	+	3.00137i	−1.19262	+	0.688562i	−0.233723	+	0.972303i	$0.575091\pi$
$20$	−1.01713	+	3.55355i	−0.227438	+	0.794599i
$21$		0			0
$22$	−1.51665	+	1.51665i	−0.323350	+	0.323350i
$23$	−0.641461	−	0.171879i	−0.133754	−	0.0358392i	0.191321	−	0.981528i	$-0.438723\pi$
$23$	−0.641461	−	0.171879i	−0.133754	−	0.0358392i	−0.325075	+	0.945688i	$0.605390\pi$
$24$		0			0
$25$	−4.41250	+	2.35157i	−0.882499	+	0.470313i
$26$	1.94308	−	1.12184i	0.381069	−	0.220010i
$27$		0			0
$28$	−3.74797	−	2.25387i	−0.708300	−	0.425941i
$29$	9.88857			1.83626			0.918131	−	0.396277i	$-0.129698\pi$
$29$	9.88857			1.83626			0.918131	+	0.396277i	$0.129698\pi$
$30$		0			0
$31$	4.19734	−	7.27001i	0.753865	−	1.30573i	−0.192071	−	0.981381i	$-0.561521\pi$
$31$	4.19734	−	7.27001i	0.753865	−	1.30573i	0.945937	−	0.324352i	$-0.105146\pi$
$32$	−7.16237	+	1.91915i	−1.26614	+	0.339261i
$33$		0			0
$34$			4.27403i			0.732989i
$35$	−1.33148	−	5.76430i	−0.225061	−	0.974345i
$36$		0			0
$37$	5.51429	+	1.47755i	0.906543	+	0.242908i	0.681824	−	0.731516i	$-0.261187\pi$
$37$	5.51429	+	1.47755i	0.906543	+	0.242908i	0.224719	+	0.974424i	$0.427854\pi$
$38$	2.96942	+	11.0820i	0.481704	+	1.79774i
$39$		0			0
$40$	−1.27148	−	0.763160i	−0.201039	−	0.120666i
$41$			3.31153i			0.517175i	0.965988	+	0.258587i	$0.0832570\pi$
$41$			3.31153i			0.517175i	−0.965988	+	0.258587i	$0.916743\pi$
$42$		0			0
$43$	5.26014	+	5.26014i	0.802164	+	0.802164i	0.983433	−	0.181270i	$-0.0580207\pi$
$43$	5.26014	+	5.26014i	0.802164	+	0.802164i	−0.181270	+	0.983433i	$0.558021\pi$
$44$	0.927514	+	1.60650i	0.139828	+	0.242189i
$45$		0			0
$46$	−0.634632	+	1.09922i	−0.0935714	+	0.162070i
$47$	−2.55120	+	9.52122i	−0.372131	+	1.38881i	0.485360	+	0.874314i	$0.338689\pi$
$47$	−2.55120	+	9.52122i	−0.372131	+	1.38881i	−0.857491	+	0.514498i	$0.827978\pi$
$48$		0			0
$49$	6.99556	+	0.249395i	0.999365	+	0.0356278i
$50$	2.15861	+	9.30945i	0.305273	+	1.31655i
$51$		0			0
$52$	−0.502235	−	1.87437i	−0.0696474	−	0.259928i
$53$	−0.211894	−	0.790799i	−0.0291059	−	0.108625i	0.949845	−	0.312722i	$-0.101241\pi$
$53$	−0.211894	−	0.790799i	−0.0291059	−	0.108625i	−0.978951	+	0.204097i	$0.934574\pi$
$54$		0			0
$55$	−0.690516	+	2.41246i	−0.0931092	+	0.325296i
$56$	1.26262	−	1.21841i	0.168724	−	0.162816i
$57$		0			0
$58$	4.89165	−	18.2559i	0.642305	−	2.39712i
$59$	−1.75013	+	3.03132i	−0.227848	+	0.394644i	−0.957170	−	0.289526i	$-0.906502\pi$
$59$	−1.75013	+	3.03132i	−0.227848	+	0.394644i	0.729322	+	0.684170i	$0.239836\pi$
$60$		0			0
$61$	2.57534	+	4.46061i	0.329738	+	0.571123i	0.982460	−	0.186475i	$-0.0597063\pi$
$61$	2.57534	+	4.46061i	0.329738	+	0.571123i	−0.652722	+	0.757598i	$0.726373\pi$
$62$	−11.3453	−	11.3453i	−1.44085	−	1.44085i
$63$		0			0
$64$			5.02510i			0.628138i
$65$	1.35087	−	2.25065i	0.167555	−	0.279159i
$66$		0			0
$67$	1.66197	+	6.20255i	0.203042	+	0.757762i	0.990038	+	0.140804i	$0.0449687\pi$
$67$	1.66197	+	6.20255i	0.203042	+	0.757762i	−0.786996	+	0.616958i	$0.788365\pi$
$68$	3.57052	+	0.956719i	0.432990	+	0.116019i
$69$		0			0
$70$	−11.3005	−	0.393349i	−1.35067	−	0.0470142i
$71$		−	12.1470i		−	1.44159i	−0.693149	−	0.720795i	$-0.743777\pi$
$71$		−	12.1470i		−	1.44159i	0.693149	−	0.720795i	$-0.256223\pi$
$72$		0			0
$73$	−4.49672	+	1.20489i	−0.526301	+	0.141022i	−0.512179	−	0.858878i	$-0.671162\pi$
$73$	−4.49672	+	1.20489i	−0.526301	+	0.141022i	−0.0141212	+	0.999900i	$0.504495\pi$
$74$	5.45559	−	9.44935i	0.634199	−	1.09846i
$75$		0			0
$76$	9.92263			1.13820
$77$	−2.54444	−	1.53012i	−0.289966	−	0.174373i
$78$		0			0
$79$	9.12881	−	5.27052i	1.02707	−	0.592980i	0.110927	−	0.993829i	$-0.464618\pi$
$79$	9.12881	−	5.27052i	1.02707	−	0.592980i	0.916144	+	0.400849i	$0.131285\pi$
$80$	−7.35317	+	7.10765i	−0.822109	+	0.794659i
$81$		0			0
$82$	6.11362	+	1.63814i	0.675137	+	0.180902i
$83$	−11.5106	+	11.5106i	−1.26345	+	1.26345i	−0.314036	+	0.949411i	$0.601681\pi$
$83$	−11.5106	+	11.5106i	−1.26345	+	1.26345i	−0.949411	+	0.314036i	$0.898319\pi$
$84$		0			0
$85$	2.42628	+	4.37221i	0.263167	+	0.474232i
$86$	12.3131	−	7.10899i	1.32776	−	0.766582i
$87$		0			0
$88$	−0.718875	+	0.192622i	−0.0766323	+	0.0205336i
$89$	−1.76847	−	3.06308i	−0.187457	−	0.324686i	0.756944	−	0.653479i	$-0.226691\pi$
$89$	−1.76847	−	3.06308i	−0.187457	−	0.324686i	−0.944402	+	0.328793i	$0.893358\pi$
$90$		0			0
$91$	2.15670	+	2.23496i	0.226084	+	0.234287i
$92$	0.776226	+	0.776226i	0.0809272	+	0.0809272i
$93$		0			0
$94$	16.3157	+	9.41986i	1.68283	+	0.971585i
$95$	9.32868	+	9.65092i	0.957103	+	0.990164i
$96$		0			0
$97$	10.6773	−	10.6773i	1.08411	−	1.08411i	0.0879901	−	0.996121i	$-0.471956\pi$
$97$	10.6773	−	10.6773i	1.08411	−	1.08411i	0.996121	−	0.0879901i	$-0.0280444\pi$
$98$	3.92097	−	12.7916i	0.396077	−	1.29214i
$99$		0			0
$100$	8.26031	+	0.280570i	0.826031	+	0.0280570i
$101$	−2.76599	−	1.59694i	−0.275226	−	0.158902i	0.356034	−	0.934473i	$-0.384129\pi$
$101$	−2.76599	−	1.59694i	−0.275226	−	0.158902i	−0.631260	+	0.775571i	$0.717462\pi$
$102$		0			0
$103$	−0.554604	+	2.06981i	−0.0546468	+	0.203945i	−0.987852	−	0.155400i	$-0.950333\pi$
$103$	−0.554604	+	2.06981i	−0.0546468	+	0.203945i	0.933205	+	0.359345i	$0.117000\pi$
$104$	0.778519			0.0763401
$105$		0			0
$106$	−1.56476			−0.151983
$107$	0.164185	−	0.612745i	0.0158723	−	0.0592363i	−0.957535	−	0.288315i	$-0.906905\pi$
$107$	0.164185	−	0.612745i	0.0158723	−	0.0592363i	0.973408	+	0.229079i	$0.0735715\pi$
$108$		0			0
$109$	−11.9861	−	6.92020i	−1.14806	−	0.662835i	−0.199649	−	0.979867i	$-0.563980\pi$
$109$	−11.9861	−	6.92020i	−1.14806	−	0.662835i	−0.948415	+	0.317033i	$0.897314\pi$
$110$	4.11220	+	2.46819i	0.392083	+	0.235333i
$111$		0			0
$112$	−5.86260	−	10.5855i	−0.553963	−	1.00024i
$113$	−5.75515	+	5.75515i	−0.541399	+	0.541399i	−0.923939	−	0.382540i	$-0.875049\pi$
$113$	−5.75515	+	5.75515i	−0.541399	+	0.541399i	0.382540	+	0.923939i	$0.375049\pi$
$114$		0			0
$115$	−0.0252080	+	1.48473i	−0.00235066	+	0.138452i
$116$	−14.1560	−	8.17298i	−1.31435	−	0.758842i
$117$		0			0
$118$	4.73055	+	4.73055i	0.435483	+	0.435483i
$119$	−5.74122	+	1.42922i	−0.526296	+	0.131017i
$120$		0			0
$121$	−4.87032	−	8.43565i	−0.442757	−	0.766877i
$122$	9.50897	−	2.54792i	0.860901	−	0.230678i
$123$		0			0
$124$	−12.0174	+	6.93827i	−1.07920	+	0.623075i
$125$	7.49298	+	8.29790i	0.670193	+	0.742187i
$126$		0			0
$127$	−9.74796	+	9.74796i	−0.864992	+	0.864992i	−0.991913	−	0.126921i	$-0.959490\pi$
$127$	−9.74796	+	9.74796i	−0.864992	+	0.864992i	0.126921	+	0.991913i	$0.459490\pi$
$128$	−5.04759	−	1.35250i	−0.446148	−	0.119545i
$129$		0			0
$130$	−3.48682	−	3.60727i	−0.305815	−	0.316378i
$131$	−12.7957	+	7.38760i	−1.11796	+	0.645457i	−0.940881	−	0.338738i	$-0.890000\pi$
$131$	−12.7957	+	7.38760i	−1.11796	+	0.645457i	−0.177084	+	0.984196i	$0.556667\pi$
$132$		0			0
$133$	−13.8933	+	7.69457i	−1.20470	+	0.667204i
$134$	12.2730			1.06023
$135$		0			0
$136$	−0.741510	+	1.28433i	−0.0635840	+	0.110131i
$137$	19.2723	−	5.16400i	1.64655	−	0.441191i	0.687903	−	0.725803i	$-0.258531\pi$
$137$	19.2723	−	5.16400i	1.64655	−	0.441191i	0.958643	+	0.284612i	$0.0918648\pi$
$138$		0			0
$139$			1.87882i			0.159359i	0.996821	+	0.0796796i	$0.0253897\pi$
$139$			1.87882i			0.159359i	−0.996821	+	0.0796796i	$0.974610\pi$
$140$	−2.85816	+	9.35238i	−0.241559	+	0.790420i
$141$		0			0
$142$	−22.4254	−	6.00887i	−1.88190	−	0.504253i
$143$	−0.340960	−	1.27248i	−0.0285125	−	0.106410i
$144$		0			0
$145$	−5.35949	−	21.4522i	−0.445081	−	1.78150i
$146$			8.89769i			0.736378i
$147$		0			0
$148$	−6.67279	−	6.67279i	−0.548500	−	0.548500i
$149$	11.0437	+	19.1282i	0.904731	+	1.56704i	0.821278	+	0.570529i	$0.193262\pi$
$149$	11.0437	+	19.1282i	0.904731	+	1.56704i	0.0834535	+	0.996512i	$0.473405\pi$
$150$		0			0
$151$	−2.38598	+	4.13263i	−0.194168	+	0.336309i	−0.946627	−	0.322330i	$-0.895534\pi$
$151$	−2.38598	+	4.13263i	−0.194168	+	0.336309i	0.752459	+	0.658639i	$0.228867\pi$
$152$	−1.03034	+	3.84529i	−0.0835719	+	0.311894i
$153$		0			0
$154$	−4.08352	+	3.94054i	−0.329060	+	0.317538i
$155$	−18.0464	−	5.16541i	−1.44952	−	0.414896i
$156$		0			0
$157$	−3.79660	−	14.1691i	−0.303002	−	1.13082i	−0.934652	−	0.355564i	$-0.884289\pi$
$157$	−3.79660	−	14.1691i	−0.303002	−	1.13082i	0.631650	−	0.775253i	$-0.282378\pi$
$158$	−5.21442	−	19.4605i	−0.414837	−	1.54819i
$159$		0			0
$160$	8.04530	+	14.4978i	0.636037	+	1.14615i
$161$	−1.68877	−	0.484914i	−0.133094	−	0.0382166i
$162$		0			0
$163$	−3.19404	+	11.9203i	−0.250177	+	0.933672i	0.720534	+	0.693420i	$0.243897\pi$
$163$	−3.19404	+	11.9203i	−0.250177	+	0.933672i	−0.970711	+	0.240252i	$0.922770\pi$
$164$	2.73701	−	4.74064i	0.213724	−	0.370182i
$165$		0			0
$166$	15.5563	+	26.9443i	1.20740	+	2.09129i
$167$	−2.58291	−	2.58291i	−0.199871	−	0.199871i	0.600073	−	0.799945i	$-0.295138\pi$
$167$	−2.58291	−	2.58291i	−0.199871	−	0.199871i	−0.799945	+	0.600073i	$0.795138\pi$
$168$		0			0
$169$		−	11.6219i		−	0.893996i
$170$	9.27202	−	2.31647i	0.711132	−	0.177665i
$171$		0			0
$172$	−3.18262	−	11.8777i	−0.242673	−	0.905667i
$173$	−2.71673	−	0.727945i	−0.206549	−	0.0553446i	0.154061	−	0.988061i	$-0.450765\pi$
$173$	−2.71673	−	0.727945i	−0.206549	−	0.0553446i	−0.360610	+	0.932717i	$0.617431\pi$
$174$		0			0
$175$	−11.7834	+	6.01267i	−0.890739	+	0.454515i
$176$			5.13250i			0.386877i
$177$		0			0
$178$	−6.52976	+	1.74964i	−0.489426	+	0.131141i
$179$	−2.82676	+	4.89609i	−0.211282	+	0.365951i	−0.952116	−	0.305737i	$-0.901097\pi$
$179$	−2.82676	+	4.89609i	−0.211282	+	0.365951i	0.740834	+	0.671688i	$0.234430\pi$
$180$		0			0
$181$	−22.3247			−1.65938			−0.829690	−	0.558225i	$-0.811483\pi$
$181$	−22.3247			−1.65938			−0.829690	+	0.558225i	$0.811483\pi$
$182$	5.19296	−	2.87603i	0.384928	−	0.213186i
$183$		0			0
$184$	−0.381411	+	0.220208i	−0.0281180	+	0.0162339i
$185$	0.216699	−	12.7634i	0.0159320	−	0.938387i
$186$		0			0
$187$	2.42398	+	0.649503i	0.177259	+	0.0474964i
$188$	11.5215	−	11.5215i	0.840295	−	0.840295i
$189$		0			0
$190$	22.4318	−	12.4482i	1.62738	−	0.903084i
$191$	−5.11137	+	2.95105i	−0.369846	+	0.213531i	−0.673391	−	0.739286i	$-0.735163\pi$
$191$	−5.11137	+	2.95105i	−0.369846	+	0.213531i	0.303545	+	0.952817i	$0.401830\pi$
$192$		0			0
$193$	−11.0380	+	2.95761i	−0.794530	+	0.212894i	−0.633181	−	0.774004i	$-0.718251\pi$
$193$	−11.0380	+	2.95761i	−0.794530	+	0.212894i	−0.161349	+	0.986897i	$0.551585\pi$
$194$	−14.4301	−	24.9937i	−1.03602	−	1.79445i
$195$		0			0
$196$	−9.80839	−	6.13890i	−0.700599	−	0.438493i
$197$	−9.38019	−	9.38019i	−0.668311	−	0.668311i	0.289014	−	0.957325i	$-0.406673\pi$
$197$	−9.38019	−	9.38019i	−0.668311	−	0.668311i	−0.957325	+	0.289014i	$0.906673\pi$
$198$		0			0
$199$	10.5579	+	6.09559i	0.748428	+	0.432105i	0.825126	−	0.564949i	$-0.191104\pi$
$199$	10.5579	+	6.09559i	0.748428	+	0.432105i	−0.0766977	+	0.997054i	$0.524438\pi$
$200$	−0.966461	+	3.17197i	−0.0683391	+	0.224292i
$201$		0			0
$202$	−4.31648	+	4.31648i	−0.303707	+	0.303707i
$203$	26.1586	+	0.466134i	1.83597	+	0.0327162i
$204$		0			0
$205$	7.18401	−	1.79481i	0.501753	−	0.125355i
$206$	3.54685	+	2.04778i	0.247121	+	0.142675i
$207$		0			0
$208$	1.38959	−	5.18600i	0.0963504	−	0.359585i
$209$	6.73633			0.465962
$210$		0			0
$211$	−3.48159			−0.239683			−0.119841	−	0.992793i	$-0.538239\pi$
$211$	−3.48159			−0.239683			−0.119841	+	0.992793i	$0.538239\pi$
$212$	−0.350264	+	1.30720i	−0.0240562	+	0.0897791i
$213$		0			0
$214$	−1.05001	−	0.606222i	−0.0717770	−	0.0414405i
$215$	8.56036	−	14.2622i	0.583811	−	0.972676i
$216$		0			0
$217$	11.4461	−	19.0337i	0.777009	−	1.29209i
$218$	−18.7051	+	18.7051i	−1.26687	+	1.26687i
$219$		0			0
$220$	2.98242	−	2.88284i	0.201075	−	0.194361i
$221$	−2.27340	−	1.31255i	−0.152925	−	0.0882915i
$222$		0			0
$223$	11.8362	+	11.8362i	0.792608	+	0.792608i	0.981917	−	0.189310i	$-0.0606250\pi$
$223$	11.8362	+	11.8362i	0.792608	+	0.792608i	−0.189310	+	0.981917i	$0.560625\pi$
$224$	−19.0373	+	4.73917i	−1.27198	+	0.316649i
$225$		0			0
$226$	7.77799	+	13.4719i	0.517384	+	0.896135i
$227$	25.9887	−	6.96365i	1.72493	−	0.462194i	0.745926	−	0.666029i	$-0.232007\pi$
$227$	25.9887	−	6.96365i	1.72493	−	0.462194i	0.979005	+	0.203835i	$0.0653406\pi$
$228$		0			0
$229$	−5.91912	+	3.41741i	−0.391146	+	0.225829i	−0.682657	−	0.730739i	$-0.739176\pi$
$229$	−5.91912	+	3.41741i	−0.391146	+	0.225829i	0.291510	+	0.956568i	$0.405842\pi$
$230$	2.72859	+	0.781002i	0.179918	+	0.0514978i
$231$		0			0
$232$	4.63719	−	4.63719i	0.304446	−	0.304446i
$233$	−6.88187	−	1.84399i	−0.450846	−	0.120804i	0.0262490	−	0.999655i	$-0.491644\pi$
$233$	−6.88187	−	1.84399i	−0.450846	−	0.120804i	−0.477095	+	0.878852i	$0.658310\pi$
$234$		0			0
$235$	22.0380	+	0.374163i	1.43760	+	0.0244077i
$236$	5.01082	−	2.89300i	0.326176	−	0.188318i
$237$		0			0
$238$	−0.201472	+	11.3062i	−0.0130595	+	0.732873i
$239$	−18.7848			−1.21509			−0.607543	−	0.794287i	$-0.707845\pi$
$239$	−18.7848			−1.21509			−0.607543	+	0.794287i	$0.707845\pi$
$240$		0			0
$241$	12.7838	−	22.1421i	0.823474	−	1.42630i	−0.0796052	−	0.996826i	$-0.525366\pi$
$241$	12.7838	−	22.1421i	0.823474	−	1.42630i	0.903080	−	0.429473i	$-0.141301\pi$
$242$	−17.9828	+	4.81848i	−1.15598	+	0.309743i
$243$		0			0
$244$		−	8.51414i		−	0.545062i
$245$	−3.25048	−	15.3113i	−0.207665	−	0.978200i
$246$		0			0
$247$	−6.80655	−	1.82381i	−0.433091	−	0.116046i
$248$	−1.44091	−	5.37755i	−0.0914978	−	0.341475i
$249$		0			0
$250$	19.0259	−	9.72847i	1.20330	−	0.615283i
$251$			2.18106i			0.137667i	0.997628	+	0.0688336i	$0.0219277\pi$
$251$			2.18106i			0.137667i	−0.997628	+	0.0688336i	$0.978072\pi$
$252$		0			0
$253$	0.526969	+	0.526969i	0.0331302	+	0.0331302i
$254$	13.1742	+	22.8184i	0.826623	+	1.43175i
$255$		0			0
$256$	−10.0190	+	17.3533i	−0.626185	+	1.08458i
$257$	1.98298	−	7.40059i	0.123695	−	0.461636i	−0.876095	−	0.482139i	$-0.839860\pi$
$257$	1.98298	−	7.40059i	0.123695	−	0.461636i	0.999790	+	0.0205029i	$0.00652672\pi$
$258$		0			0
$259$	14.5175	+	4.16854i	0.902072	+	0.259021i
$260$	−3.79402	+	2.10543i	−0.235295	+	0.130573i
$261$		0			0
$262$	7.30895	+	27.2774i	0.451549	+	1.68520i
$263$	2.35526	+	8.78994i	0.145231	+	0.542011i	0.999745	+	0.0225820i	$0.00718867\pi$
$263$	2.35526	+	8.78994i	0.145231	+	0.542011i	−0.854514	+	0.519429i	$0.826145\pi$
$264$		0			0
$265$	−1.60071	+	0.888285i	−0.0983307	+	0.0545669i
$266$	7.33271	+	29.4556i	0.449597	+	1.80604i
$267$		0			0
$268$	2.74726	−	10.2529i	0.167816	−	0.626296i
$269$	3.66156	−	6.34200i	0.223249	−	0.386679i	−0.732544	−	0.680720i	$-0.761667\pi$
$269$	3.66156	−	6.34200i	0.223249	−	0.386679i	0.955793	+	0.294041i	$0.0950004\pi$
$270$		0			0
$271$	−8.97448	−	15.5443i	−0.545161	−	0.944246i	−0.998597	−	0.0529575i	$-0.983135\pi$
$271$	−8.97448	−	15.5443i	−0.545161	−	0.944246i	0.453436	−	0.891289i	$-0.350198\pi$
$272$	7.23189	+	7.23189i	0.438498	+	0.438498i
$273$		0			0
$274$		−	38.1343i		−	2.30378i
$275$	5.60781	+	0.190475i	0.338164	+	0.0114861i
$276$		0			0
$277$	7.24135	+	27.0251i	0.435091	+	1.62378i	0.740849	+	0.671672i	$0.234423\pi$
$277$	7.24135	+	27.0251i	0.435091	+	1.62378i	−0.305758	+	0.952109i	$0.598910\pi$
$278$	3.46860	+	0.929408i	0.208033	+	0.0557422i
$279$		0			0
$280$	−3.32752	−	2.07875i	−0.198857	−	0.124229i
$281$		−	20.0659i		−	1.19703i	−0.801111	−	0.598516i	$-0.795757\pi$
$281$		−	20.0659i		−	1.19703i	0.801111	−	0.598516i	$-0.204243\pi$
$282$		0			0
$283$	−10.1980	+	2.73254i	−0.606206	+	0.162432i	−0.548849	−	0.835921i	$-0.684934\pi$
$283$	−10.1980	+	2.73254i	−0.606206	+	0.162432i	−0.0573568	+	0.998354i	$0.518267\pi$
$284$	−10.0396	+	17.3891i	−0.595742	+	1.03186i
$285$		0			0
$286$	−2.51787			−0.148885
$287$	−0.156101	+	8.76010i	−0.00921436	+	0.517093i
$288$		0			0
$289$	−10.3918	+	5.99970i	−0.611281	+	0.352923i
$290$	−42.2554	−	0.717416i	−2.48132	−	0.0421281i
$291$		0			0
$292$	7.43314	+	1.99170i	0.434992	+	0.116556i
$293$	14.8561	−	14.8561i	0.867901	−	0.867901i	−0.124339	−	0.992240i	$-0.539681\pi$
$293$	14.8561	−	14.8561i	0.867901	−	0.867901i	0.992240	+	0.124339i	$0.0396810\pi$
$294$		0			0
$295$	7.52466	+	2.15378i	0.438103	+	0.125398i
$296$	3.27878	−	1.89300i	0.190575	−	0.110029i
$297$		0			0
$298$	40.7767	−	10.9261i	2.36213	−	0.632931i
$299$	−0.389789	−	0.675135i	−0.0225421	−	0.0390441i
$300$		0			0
$301$	13.6669	+	14.1628i	0.787745	+	0.816328i
$302$	6.44922	+	6.44922i	0.371111	+	0.371111i
$303$		0			0
$304$	23.7758	+	13.7270i	1.36364	+	0.787297i
$305$	8.28100	−	8.00450i	0.474169	−	0.458337i
$306$		0			0
$307$	−10.5560	+	10.5560i	−0.602461	+	0.602461i	−0.940965	−	0.338504i	$-0.890079\pi$
$307$	−10.5560	+	10.5560i	−0.602461	+	0.602461i	0.338504	+	0.940965i	$0.390079\pi$
$308$	2.37785	+	4.29345i	0.135491	+	0.244642i
$309$		0			0
$310$	−18.4633	+	30.7613i	−1.04865	+	1.74713i
$311$	−2.61258	−	1.50838i	−0.148146	−	0.0855322i	0.424095	−	0.905618i	$-0.360592\pi$
$311$	−2.61258	−	1.50838i	−0.148146	−	0.0855322i	−0.572241	+	0.820086i	$0.693926\pi$
$312$		0			0
$313$	7.27876	−	27.1647i	0.411420	−	1.53544i	−0.380480	−	0.924789i	$-0.624241\pi$
$313$	7.27876	−	27.1647i	0.411420	−	1.53544i	0.791900	−	0.610650i	$-0.209092\pi$
$314$	−28.0365			−1.58219
$315$		0			0
$316$	−17.4245			−0.980205
$317$	−4.43708	+	16.5594i	−0.249211	+	0.930069i	0.722009	+	0.691884i	$0.243219\pi$
$317$	−4.43708	+	16.5594i	−0.249211	+	0.930069i	−0.971220	+	0.238185i	$0.923448\pi$
$318$		0			0
$319$	−9.61032	−	5.54852i	−0.538075	−	0.310657i
$320$	10.9014	−	2.72355i	0.609407	−	0.152251i
$321$		0			0
$322$	−1.73063	+	2.87787i	−0.0964441	+	0.160378i
$323$	9.49175	−	9.49175i	0.528135	−	0.528135i
$324$		0			0
$325$	−5.61470	−	1.71073i	−0.311447	−	0.0948943i
$326$	20.4268	+	11.7934i	1.13134	+	0.653177i
$327$		0			0
$328$	1.55292	+	1.55292i	0.0857459	+	0.0857459i
$329$	−7.19760	+	25.0665i	−0.396816	+	1.38196i
$330$		0			0
$331$	−7.37160	−	12.7680i	−0.405180	−	0.701792i	0.589163	−	0.808014i	$-0.299458\pi$
$331$	−7.37160	−	12.7680i	−0.405180	−	0.701792i	−0.994342	+	0.106223i	$0.966124\pi$
$332$	25.9915	−	6.96441i	1.42647	−	0.382222i
$333$		0			0
$334$	−6.04617	+	3.49076i	−0.330832	+	0.191006i
$335$	12.5550	−	6.96717i	0.685952	−	0.380657i
$336$		0			0
$337$	−20.2173	+	20.2173i	−1.10131	+	1.10131i	−0.107055	+	0.994253i	$0.534142\pi$
$337$	−20.2173	+	20.2173i	−1.10131	+	1.10131i	−0.994253	+	0.107055i	$0.965858\pi$
$338$	−21.4560	−	5.74911i	−1.16705	−	0.312710i
$339$		0			0
$340$	0.140314	−	8.26439i	0.00760958	−	0.448199i
$341$	−8.15847	+	4.71029i	−0.441806	+	0.255077i
$342$		0			0
$343$	18.4938	+	0.989492i	0.998572	+	0.0534275i
$344$	4.93342			0.265992
$345$		0			0
$346$	−2.68781	+	4.65542i	−0.144497	+	0.250277i
$347$	−18.7190	+	5.01575i	−1.00489	+	0.269260i	−0.723493	−	0.690332i	$-0.757465\pi$
$347$	−18.7190	+	5.01575i	−1.00489	+	0.269260i	−0.281397	+	0.959591i	$0.590798\pi$
$348$		0			0
$349$		−	19.5132i		−	1.04452i	−0.852787	−	0.522258i	$-0.825090\pi$
$349$		−	19.5132i		−	1.04452i	0.852787	−	0.522258i	$-0.174910\pi$
$350$	5.27140	+	24.7283i	0.281768	+	1.32178i
$351$		0			0
$352$	8.03767	+	2.15369i	0.428409	+	0.114792i
$353$	5.15540	+	19.2402i	0.274394	+	1.02405i	0.956246	+	0.292564i	$0.0945083\pi$
$353$	5.15540	+	19.2402i	0.274394	+	1.02405i	−0.681852	+	0.731491i	$0.738825\pi$
$354$		0			0
$355$	−26.3517	+	6.58356i	−1.39860	+	0.349419i
$356$			5.84662i			0.309870i
$357$		0			0
$358$	7.64064	+	7.64064i	0.403820	+	0.403820i
$359$	−3.47927	−	6.02627i	−0.183629	−	0.318054i	0.759485	−	0.650525i	$-0.225451\pi$
$359$	−3.47927	−	6.02627i	−0.183629	−	0.318054i	−0.943114	+	0.332471i	$0.892118\pi$
$360$		0			0
$361$	8.51646	−	14.7509i	0.448235	−	0.776366i
$362$	−11.0435	+	41.2149i	−0.580434	+	2.16621i
$363$		0			0
$364$	−1.24022	−	4.98199i	−0.0650053	−	0.261127i
$365$	5.05104	+	9.10209i	0.264384	+	0.476425i
$366$		0			0
$367$	1.03003	+	3.84412i	0.0537671	+	0.200662i	0.987585	−	0.157088i	$-0.0502107\pi$
$367$	1.03003	+	3.84412i	0.0537671	+	0.200662i	−0.933817	+	0.357750i	$0.883544\pi$
$368$	0.786100	+	2.93377i	0.0409783	+	0.152933i
$369$		0			0
$370$	−23.4562	−	6.71385i	−1.21943	−	0.349036i
$371$	−0.523253	−	2.10191i	−0.0271659	−	0.109126i
$372$		0			0
$373$	2.78464	−	10.3924i	0.144183	−	0.538099i	−0.855607	−	0.517625i	$-0.826816\pi$
$373$	2.78464	−	10.3924i	0.144183	−	0.538099i	0.999790	−	0.0204732i	$-0.00651727\pi$
$374$	2.39817	−	4.15376i	0.124007	−	0.214786i
$375$		0			0
$376$	3.26855	+	5.66129i	0.168562	+	0.291959i
$377$	8.20828	+	8.20828i	0.422748	+	0.422748i
$378$		0			0
$379$		−	13.4948i		−	0.693180i	−0.938017	−	0.346590i	$-0.887339\pi$
$379$		−	13.4948i		−	0.693180i	0.938017	−	0.346590i	$-0.112661\pi$
$380$	−5.37795	−	21.5260i	−0.275883	−	1.10426i
$381$		0			0
$382$	2.91964	+	10.8962i	0.149382	+	0.557500i
$383$	−2.67081	−	0.715640i	−0.136472	−	0.0365675i	0.189937	−	0.981796i	$-0.439172\pi$
$383$	−2.67081	−	0.715640i	−0.136472	−	0.0365675i	−0.326408	+	0.945229i	$0.605838\pi$
$384$		0			0
$385$	−1.94036	+	6.34920i	−0.0988901	+	0.323585i
$386$			21.8409i			1.11167i
$387$		0			0
$388$	−24.1099	+	6.46023i	−1.22399	+	0.327968i
$389$	8.29427	−	14.3661i	0.420536	−	0.728390i	−0.575456	−	0.817833i	$-0.695175\pi$
$389$	8.29427	−	14.3661i	0.420536	−	0.728390i	0.995992	+	0.0894428i	$0.0285086\pi$
$390$		0			0
$391$	1.48504			0.0751016
$392$	3.39748	−	3.16357i	0.171598	−	0.159784i
$393$		0			0
$394$	−21.9575	+	12.6772i	−1.10620	+	0.638667i
$395$	−16.3815	−	16.9474i	−0.824244	−	0.852715i
$396$		0			0
$397$	13.5010	+	3.61757i	0.677594	+	0.181561i	0.581173	−	0.813780i	$-0.302594\pi$
$397$	13.5010	+	3.61757i	0.677594	+	0.181561i	0.0964210	+	0.995341i	$0.469260\pi$
$398$	16.4762	−	16.4762i	0.825876	−	0.825876i
$399$		0			0
$400$	19.4046	+	12.0996i	0.970229	+	0.604981i
$401$	7.99139	−	4.61383i	0.399071	−	0.230404i	−0.287012	−	0.957927i	$-0.592662\pi$
$401$	7.99139	−	4.61383i	0.399071	−	0.230404i	0.686083	+	0.727523i	$0.259329\pi$
$402$		0			0
$403$	9.51879	−	2.55055i	0.474165	−	0.127052i
$404$	2.63977	+	4.57222i	0.131333	+	0.227476i
$405$		0			0
$406$	13.8006	−	48.0623i	0.684912	−	2.38529i
$407$	−4.53006	−	4.53006i	−0.224547	−	0.224547i
$408$		0			0
$409$	−14.8468	−	8.57179i	−0.734125	−	0.423848i	0.0858041	−	0.996312i	$-0.472654\pi$
$409$	−14.8468	−	8.57179i	−0.734125	−	0.423848i	−0.819929	+	0.572465i	$0.805987\pi$
$410$	0.240252	−	14.1507i	0.0118652	−	0.698852i
$411$		0			0
$412$	2.50466	−	2.50466i	0.123396	−	0.123396i
$413$	−4.77257	+	7.93634i	−0.234843	+	0.390522i
$414$		0			0
$415$	31.2094	+	18.7323i	1.53201	+	0.919531i
$416$	−7.53836	−	4.35228i	−0.369599	−	0.213388i
$417$		0			0
$418$	3.33231	−	12.4363i	0.162989	−	0.608282i
$419$	−22.7475			−1.11129			−0.555645	−	0.831420i	$-0.687529\pi$
$419$	−22.7475			−1.11129			−0.555645	+	0.831420i	$0.687529\pi$
$420$		0			0
$421$	−8.08528			−0.394052			−0.197026	−	0.980398i	$-0.563128\pi$
$421$	−8.08528			−0.394052			−0.197026	+	0.980398i	$0.563128\pi$
$422$	−1.72227	+	6.42758i	−0.0838386	+	0.312890i
$423$		0			0
$424$	−0.470207	−	0.271474i	−0.0228353	−	0.0131839i
$425$	8.17000	−	7.63323i	0.396303	−	0.370266i
$426$		0			0
$427$	6.60235	+	11.9212i	0.319510	+	0.576907i
$428$	−0.741478	+	0.741478i	−0.0358407	+	0.0358407i
$429$		0			0
$430$	−22.0957	−	22.8590i	−1.06555	−	1.10236i
$431$	23.4131	+	13.5176i	1.12777	+	0.651119i	0.943373	−	0.331733i	$-0.107633\pi$
$431$	23.4131	+	13.5176i	1.12777	+	0.651119i	0.184398	+	0.982852i	$0.440966\pi$
$432$		0			0
$433$	−1.13772	−	1.13772i	−0.0546754	−	0.0546754i	0.679240	−	0.733916i	$-0.262309\pi$
$433$	−1.13772	−	1.13772i	−0.0546754	−	0.0546754i	−0.733916	+	0.679240i	$0.762309\pi$
$434$	−29.4772	−	30.5468i	−1.41495	−	1.46629i
$435$		0			0
$436$	11.4392	+	19.8133i	0.547838	+	0.948883i
$437$	3.85052	−	1.03174i	0.184196	−	0.0493551i
$438$		0			0
$439$	−27.2646	+	15.7412i	−1.30127	+	0.751287i	−0.980621	−	0.195912i	$-0.937233\pi$
$439$	−27.2646	+	15.7412i	−1.30127	+	0.751287i	−0.320646	+	0.947199i	$0.603900\pi$
$440$	0.807493	+	1.45512i	0.0384957	+	0.0693701i
$441$		0			0
$442$	−3.54777	+	3.54777i	−0.168750	+	0.168750i
$443$	−13.9059	−	3.72608i	−0.660690	−	0.177031i	−0.0871324	−	0.996197i	$-0.527770\pi$
$443$	−13.9059	−	3.72608i	−0.660690	−	0.177031i	−0.573557	+	0.819166i	$0.694437\pi$
$444$		0			0
$445$	−5.68652	+	5.49665i	−0.269567	+	0.260566i
$446$	27.7065	−	15.9964i	1.31194	−	0.757450i
$447$		0			0
$448$	−0.236876	+	13.2931i	−0.0111914	+	0.628038i
$449$	13.1001			0.618230			0.309115	−	0.951025i	$-0.399967\pi$
$449$	13.1001			0.618230			0.309115	+	0.951025i	$0.399967\pi$
$450$		0			0
$451$	1.85812	−	3.21835i	0.0874953	−	0.151546i
$452$	12.9955	−	3.48213i	0.611256	−	0.163785i
$453$		0			0
$454$		−	51.4241i		−	2.41345i
$455$	3.67959	−	5.89004i	0.172502	−	0.276130i
$456$		0			0
$457$	5.00463	+	1.34099i	0.234107	+	0.0627288i	0.373965	−	0.927443i	$-0.377998\pi$
$457$	5.00463	+	1.34099i	0.234107	+	0.0627288i	−0.139858	+	0.990172i	$0.544665\pi$
$458$	3.38103	+	12.6182i	0.157985	+	0.589608i
$459$		0			0
$460$	1.26323	−	2.10464i	0.0588985	−	0.0981294i
$461$		−	26.5137i		−	1.23486i	−0.786624	−	0.617432i	$-0.788173\pi$
$461$		−	26.5137i		−	1.23486i	0.786624	−	0.617432i	$-0.211827\pi$
$462$		0			0
$463$	−8.59270	−	8.59270i	−0.399337	−	0.399337i	0.478662	−	0.877999i	$-0.341122\pi$
$463$	−8.59270	−	8.59270i	−0.399337	−	0.399337i	−0.877999	+	0.478662i	$0.841122\pi$
$464$	−22.6130	−	39.1669i	−1.04978	−	1.81828i
$465$		0			0
$466$	−6.80861	+	11.7929i	−0.315403	+	0.546294i
$467$	2.64464	−	9.86992i	0.122379	−	0.456726i	−0.877353	−	0.479845i	$-0.840693\pi$
$467$	2.64464	−	9.86992i	0.122379	−	0.456726i	0.999733	+	0.0231190i	$0.00735968\pi$
$468$		0			0
$469$	4.10408	+	16.4861i	0.189509	+	0.761259i
$470$	11.5924	−	40.5005i	0.534719	−	1.86815i
$471$		0			0
$472$	0.600804	+	2.24223i	0.0276543	+	0.103207i
$473$	−2.16064	−	8.06361i	−0.0993462	−	0.370765i
$474$		0			0
$475$	15.8806	−	25.4682i	0.728650	−	1.16856i
$476$	9.40012	+	2.69915i	0.430854	+	0.123715i
$477$		0			0
$478$	−9.29240	+	34.6797i	−0.425025	+	1.58621i
$479$	2.60300	−	4.50853i	0.118934	−	0.206000i	−0.800411	−	0.599451i	$-0.795386\pi$
$479$	2.60300	−	4.50853i	0.118934	−	0.206000i	0.919346	+	0.393451i	$0.128719\pi$
$480$		0			0
$481$	3.35081	+	5.80377i	0.152784	+	0.264629i
$482$	−34.5541	−	34.5541i	−1.57390	−	1.57390i
$483$		0			0
$484$			16.1014i			0.731884i
$485$	−28.9501	−	17.3762i	−1.31456	−	0.789012i
$486$		0			0
$487$	−6.88081	−	25.6796i	−0.311799	−	1.16365i	−0.926932	−	0.375228i	$-0.877564\pi$
$487$	−6.88081	−	25.6796i	−0.311799	−	1.16365i	0.615133	−	0.788423i	$-0.289102\pi$
$488$	3.29946	+	0.884089i	0.149360	+	0.0400208i
$489$		0			0
$490$	−29.8750	−	1.57323i	−1.34961	−	0.0710712i
$491$		−	5.16035i		−	0.232883i	−0.993198	−	0.116442i	$-0.962851\pi$
$491$		−	5.16035i		−	0.232883i	0.993198	−	0.116442i	$-0.0371488\pi$
$492$		0			0
$493$	−21.3594	+	5.72323i	−0.961978	+	0.257761i
$494$	−6.73409	+	11.6638i	−0.302981	+	0.524779i
$495$		0			0
$496$	−38.3937			−1.72393
$497$	0.572595	−	32.1330i	0.0256844	−	1.44136i
$498$		0			0
$499$	6.70115	−	3.86891i	0.299985	−	0.173196i	−0.342451	−	0.939536i	$-0.611257\pi$
$499$	6.70115	−	3.86891i	0.299985	−	0.173196i	0.642436	+	0.766339i	$0.277924\pi$
$500$	−3.86833	−	18.0719i	−0.172997	−	0.808200i
$501$		0			0
$502$	4.02658	+	1.07892i	0.179715	+	0.0481545i
$503$	3.22778	−	3.22778i	0.143920	−	0.143920i	−0.631476	−	0.775395i	$-0.717551\pi$
$503$	3.22778	−	3.22778i	0.143920	−	0.143920i	0.775395	+	0.631476i	$0.217551\pi$
$504$		0			0
$505$	−1.96526	+	6.86602i	−0.0874528	+	0.305534i
$506$	1.23355	−	0.712190i	0.0548379	−	0.0316607i
$507$		0			0
$508$	22.0115	−	5.89796i	0.976602	−	0.261680i
$509$	8.98621	+	15.5646i	0.398307	+	0.689887i	0.993517	−	0.113682i	$-0.0362646\pi$
$509$	8.98621	+	15.5646i	0.398307	+	0.689887i	−0.595210	+	0.803570i	$0.702931\pi$
$510$		0			0
$511$	−11.9521	+	2.97537i	−0.528730	+	0.131623i
$512$	19.6907	+	19.6907i	0.870216	+	0.870216i
$513$		0			0
$514$	−12.6817	−	7.32181i	−0.559368	−	0.322951i
$515$	4.79081	+	0.0813390i	0.211109	+	0.00358422i
$516$		0			0
$517$	7.82181	−	7.82181i	0.344003	−	0.344003i
$518$	14.8773	−	24.7395i	0.653669	−	1.08699i
$519$		0			0
$520$	−0.421948	−	1.68891i	−0.0185037	−	0.0740637i
$521$	24.8083	+	14.3231i	1.08687	+	0.627505i	0.932741	−	0.360546i	$-0.117410\pi$
$521$	24.8083	+	14.3231i	1.08687	+	0.627505i	0.154129	+	0.988051i	$0.450743\pi$
$522$		0			0
$523$	−0.195886	+	0.731058i	−0.00856551	+	0.0319669i	−0.970076	−	0.242800i	$-0.921934\pi$
$523$	−0.195886	+	0.731058i	−0.00856551	+	0.0319669i	0.961511	+	0.274767i	$0.0886007\pi$
$524$	24.4236			1.06695
$525$		0			0
$526$	17.3927			0.758359
$527$	−4.85861	+	18.1326i	−0.211644	+	0.789868i
$528$		0			0
$529$	−19.5367	−	11.2795i	−0.849420	−	0.490413i
$530$	0.848083	+	3.39458i	0.0368384	+	0.147451i
$531$		0			0
$532$	26.2486	+	0.467739i	1.13802	+	0.0202791i
$533$	−2.74883	+	2.74883i	−0.119065	+	0.119065i
$534$		0			0
$535$	−1.41827	−	0.0240795i	−0.0613171	−	0.00104105i
$536$	3.68802	+	2.12928i	0.159298	+	0.0919708i
$537$		0			0
$538$	−9.89706	−	9.89706i	−0.426693	−	0.426693i
$539$	−6.65877	−	4.16761i	−0.286814	−	0.179512i
$540$		0			0
$541$	20.4118	+	35.3542i	0.877571	+	1.52000i	0.853999	+	0.520275i	$0.174170\pi$
$541$	20.4118	+	35.3542i	0.877571	+	1.52000i	0.0235718	+	0.999722i	$0.492496\pi$
$542$	−33.1367	+	8.87895i	−1.42334	+	0.381383i
$543$		0			0
$544$	14.3600	−	8.29076i	0.615681	−	0.355463i
$545$	−8.51626	+	29.7533i	−0.364796	+	1.27449i
$546$		0			0
$547$	−15.8647	+	15.8647i	−0.678325	+	0.678325i	−0.959621	−	0.281296i	$-0.909236\pi$
$547$	−15.8647	+	15.8647i	−0.678325	+	0.678325i	0.281296	+	0.959621i	$0.409236\pi$
$548$	−31.8574	−	8.53618i	−1.36088	−	0.364647i
$549$		0			0
$550$	3.12570	−	10.2587i	0.133280	−	0.437432i
$551$	−51.4060	+	29.6793i	−2.18997	+	1.26438i
$552$		0			0
$553$	24.3972	−	13.5120i	1.03747	−	0.574587i
$554$	53.4748			2.27193
$555$		0			0
$556$	1.55286	−	2.68963i	0.0658558	−	0.114066i
$557$	−5.32480	+	1.42678i	−0.225619	+	0.0604544i	−0.369857	−	0.929089i	$-0.620593\pi$
$557$	−5.32480	+	1.42678i	−0.225619	+	0.0604544i	0.144238	+	0.989543i	$0.453927\pi$
$558$		0			0
$559$			8.73265i			0.369352i
$560$	−19.7866	+	18.4555i	−0.836137	+	0.779886i
$561$		0			0
$562$	−37.0449	−	9.92615i	−1.56264	−	0.418709i
$563$	10.0547	+	37.5245i	0.423753	+	1.58147i	0.766630	+	0.642089i	$0.221932\pi$
$563$	10.0547	+	37.5245i	0.423753	+	1.58147i	−0.342877	+	0.939380i	$0.611401\pi$
$564$		0			0
$565$	15.6044	+	9.36593i	0.656481	+	0.394028i
$566$			20.1788i			0.848179i
$567$		0			0
$568$	−5.69628	−	5.69628i	−0.239011	−	0.239011i
$569$	2.56024	+	4.43446i	0.107331	+	0.185902i	0.914688	−	0.404161i	$-0.132436\pi$
$569$	2.56024	+	4.43446i	0.107331	+	0.185902i	−0.807357	+	0.590063i	$0.799103\pi$
$570$		0			0
$571$	17.4000	−	30.1377i	0.728169	−	1.26123i	−0.229487	−	0.973312i	$-0.573705\pi$
$571$	17.4000	−	30.1377i	0.728169	−	1.26123i	0.957656	−	0.287914i	$-0.0929617\pi$
$572$	−0.563612	+	2.10343i	−0.0235658	+	0.0879488i
$573$		0			0
$574$	16.0953	+	4.62161i	0.671807	+	0.192902i
$575$	3.23463	−	0.750023i	0.134893	−	0.0312781i
$576$		0			0
$577$	−1.89014	−	7.05409i	−0.0786874	−	0.293666i	0.915357	−	0.402644i	$-0.131909\pi$
$577$	−1.89014	−	7.05409i	−0.0786874	−	0.293666i	−0.994044	+	0.108978i	$0.965242\pi$
$578$	5.93583	+	22.1528i	0.246898	+	0.921435i
$579$		0			0
$580$	−10.0580	+	35.1396i	−0.417635	+	1.45909i
$581$	−30.9918	+	29.9066i	−1.28576	+	1.24074i
$582$		0			0
$583$	−0.237789	+	0.887442i	−0.00984823	+	0.0367541i
$584$	−1.54368	+	2.67373i	−0.0638780	+	0.110640i
$585$		0			0
$586$	−20.0777	−	34.7757i	−0.829403	−	1.43657i
$587$	21.2623	+	21.2623i	0.877588	+	0.877588i	0.993285	−	0.115696i	$-0.0369099\pi$
$587$	21.2623	+	21.2623i	0.877588	+	0.877588i	−0.115696	+	0.993285i	$0.536910\pi$
$588$		0			0
$589$			50.3912i			2.07633i
$590$	7.69850	−	12.8263i	0.316942	−	0.528051i
$591$		0			0
$592$	−6.75767	−	25.2200i	−0.277739	−	1.03653i
$593$	23.5608	+	6.31310i	0.967527	+	0.259248i	0.707783	−	0.706430i	$-0.249695\pi$
$593$	23.5608	+	6.31310i	0.967527	+	0.259248i	0.259744	+	0.965678i	$0.416362\pi$
$594$		0			0
$595$	6.21222	+	11.6803i	0.254676	+	0.478846i
$596$		−	36.5107i		−	1.49553i
$597$		0			0
$598$	−1.43923	+	0.385640i	−0.0588544	+	0.0157700i
$599$	−6.90412	+	11.9583i	−0.282095	+	0.488602i	−0.971900	−	0.235392i	$-0.924363\pi$
$599$	−6.90412	+	11.9583i	−0.282095	+	0.488602i	0.689806	+	0.723994i	$0.257696\pi$
$600$		0			0
$601$	2.66574			0.108738			0.0543690	−	0.998521i	$-0.482685\pi$
$601$	2.66574			0.108738			0.0543690	+	0.998521i	$0.482685\pi$
$602$	32.9074	−	18.2252i	1.34121	−	0.742804i
$603$		0			0
$604$	6.83130	−	3.94406i	0.277962	−	0.160481i
$605$	−15.6605	+	15.1377i	−0.636692	+	0.615433i
$606$		0			0
$607$	4.14832	+	1.11154i	0.168375	+	0.0451159i	0.342022	−	0.939692i	$-0.388888\pi$
$607$	4.14832	+	1.11154i	0.168375	+	0.0451159i	−0.173647	+	0.984808i	$0.555555\pi$
$608$	31.4737	−	31.4737i	1.27643	−	1.27643i
$609$		0			0
$610$	−10.6812	−	19.2477i	−0.432468	−	0.779317i
$611$	−10.0210	+	5.78565i	−0.405408	+	0.234062i
$612$		0			0
$613$	−24.4122	+	6.54122i	−0.985998	+	0.264197i	−0.715568	−	0.698543i	$-0.753832\pi$
$613$	−24.4122	+	6.54122i	−0.985998	+	0.264197i	−0.270429	+	0.962740i	$0.587166\pi$
$614$	14.2662	+	24.7098i	0.575738	+	0.997208i
$615$		0			0
$616$	−1.91074	+	0.475662i	−0.0769860	+	0.0191650i
$617$	10.0544	+	10.0544i	0.404774	+	0.404774i	0.879911	−	0.475138i	$-0.157602\pi$
$617$	10.0544	+	10.0544i	0.404774	+	0.404774i	−0.475138	+	0.879911i	$0.657602\pi$
$618$		0			0
$619$	−9.47268	−	5.46905i	−0.380739	−	0.219820i	0.297401	−	0.954753i	$-0.403880\pi$
$619$	−9.47268	−	5.46905i	−0.380739	−	0.219820i	−0.678140	+	0.734933i	$0.737214\pi$
$620$	21.5651	+	22.3100i	0.866076	+	0.895993i
$621$		0			0
$622$	−4.07709	+	4.07709i	−0.163476	+	0.163476i
$623$	−4.53380	−	8.18622i	−0.181643	−	0.327974i
$624$		0			0
$625$	13.9403	−	20.7526i	0.557611	−	0.830103i
$626$	−46.5498	−	26.8755i	−1.86050	−	1.07416i
$627$		0			0
$628$	−6.27584	+	23.4217i	−0.250433	+	0.934629i
$629$	−12.7661			−0.509016
$630$		0			0
$631$	−14.9321			−0.594439			−0.297219	−	0.954809i	$-0.596059\pi$
$631$	−14.9321			−0.594439			−0.297219	+	0.954809i	$0.596059\pi$
$632$	1.80932	−	6.75248i	0.0719709	−	0.268599i
$633$		0			0
$634$	28.3764	+	16.3831i	1.12697	+	0.650657i
$635$	26.4304	+	15.8638i	1.04886	+	0.629537i
$636$		0			0
$637$	5.59984	+	6.01387i	0.221874	+	0.238278i
$638$	−14.9975	+	14.9975i	−0.593755	+	0.593755i
$639$		0			0
$640$	−0.198359	+	11.6832i	−0.00784083	+	0.461820i
$641$	−8.48248	−	4.89736i	−0.335038	−	0.193434i	0.323038	−	0.946386i	$-0.395296\pi$
$641$	−8.48248	−	4.89736i	−0.335038	−	0.193434i	−0.658075	+	0.752952i	$0.728629\pi$
$642$		0			0
$643$	−3.43776	−	3.43776i	−0.135572	−	0.135572i	0.636064	−	0.771636i	$-0.280561\pi$
$643$	−3.43776	−	3.43776i	−0.135572	−	0.135572i	−0.771636	+	0.636064i	$0.780561\pi$
$644$	2.01679	+	2.08997i	0.0794725	+	0.0823562i
$645$		0			0
$646$	−12.8279	−	22.2186i	−0.504709	−	0.874181i
$647$	−18.7678	+	5.02881i	−0.737837	+	0.197703i	−0.608117	−	0.793848i	$-0.708075\pi$
$647$	−18.7678	+	5.02881i	−0.737837	+	0.197703i	−0.129720	+	0.991551i	$0.541408\pi$
$648$		0			0
$649$	3.40177	−	1.96401i	0.133531	−	0.0770943i
$650$	−5.93575	+	9.51937i	−0.232819	+	0.373381i
$651$		0			0
$652$	14.4247	−	14.4247i	0.564914	−	0.564914i
$653$	−12.5364	−	3.35912i	−0.490588	−	0.131453i	0.00504043	−	0.999987i	$-0.498396\pi$
$653$	−12.5364	−	3.35912i	−0.490588	−	0.131453i	−0.495629	+	0.868535i	$0.665062\pi$
$654$		0			0
$655$	22.9617	+	23.7548i	0.897187	+	0.928179i
$656$	13.1164	−	7.57277i	0.512110	−	0.295667i
$657$		0			0
$658$	42.7163	+	25.6878i	1.66526	+	1.00141i
$659$	1.48624			0.0578959			0.0289479	−	0.999581i	$-0.490784\pi$
$659$	1.48624			0.0578959			0.0289479	+	0.999581i	$0.490784\pi$
$660$		0			0
$661$	−9.29471	+	16.0989i	−0.361522	+	0.626175i	−0.988212	−	0.153094i	$-0.951076\pi$
$661$	−9.29471	+	16.0989i	−0.361522	+	0.626175i	0.626689	+	0.779269i	$0.284410\pi$
$662$	−27.2183	+	7.29312i	−1.05787	+	0.283455i
$663$		0			0
$664$			10.7956i			0.418951i
$665$	24.2225	+	25.9696i	0.939309	+	1.00706i
$666$		0			0
$667$	−6.34313	−	1.69964i	−0.245607	−	0.0658102i
$668$	1.56278	+	5.83237i	0.0604657	+	0.225661i
$669$		0			0
$670$	−6.65185	−	26.6250i	−0.256983	−	1.02861i
$671$		−	5.78013i		−	0.223139i
$672$		0			0
$673$	9.44812	+	9.44812i	0.364198	+	0.364198i	0.865356	−	0.501158i	$-0.167092\pi$
$673$	9.44812	+	9.44812i	0.364198	+	0.364198i	−0.501158	+	0.865356i	$0.667092\pi$
$674$	27.3234	+	47.3255i	1.05246	+	1.82291i
$675$		0			0
$676$	−9.60563	+	16.6374i	−0.369447	+	0.639901i
$677$	11.0601	−	41.2767i	0.425072	−	1.58639i	−0.338692	−	0.940897i	$-0.609985\pi$
$677$	11.0601	−	41.2767i	0.425072	−	1.58639i	0.763765	−	0.645495i	$-0.223349\pi$
$678$		0			0
$679$	28.7482	−	27.7416i	1.10325	−	1.06462i
$680$	3.18811	+	0.912531i	0.122258	+	0.0349940i
$681$		0			0
$682$	4.66015	+	17.3919i	0.178446	+	0.665971i
$683$	0.687686	+	2.56648i	0.0263136	+	0.0982036i	0.977834	−	0.209383i	$-0.0671454\pi$
$683$	0.687686	+	2.56648i	0.0263136	+	0.0982036i	−0.951520	+	0.307586i	$0.900479\pi$
$684$		0			0
$685$	−21.6481	−	39.0103i	−0.827132	−	1.49051i
$686$	10.9752	−	33.6531i	0.419036	−	1.28488i
$687$		0			0
$688$	8.80570	−	32.8633i	0.335714	−	1.25290i
$689$	0.480536	−	0.832313i	0.0183070	−	0.0317086i
$690$		0			0
$691$	15.5622	+	26.9545i	0.592014	+	1.02540i	0.993961	+	0.109735i	$0.0350002\pi$
$691$	15.5622	+	26.9545i	0.592014	+	1.02540i	−0.401947	+	0.915663i	$0.631667\pi$
$692$	3.28749	+	3.28749i	0.124972	+	0.124972i
$693$		0			0
$694$			37.0395i			1.40600i
$695$	4.07588	−	1.01830i	0.154607	−	0.0386262i
$696$		0			0
$697$	−1.91662	−	7.15294i	−0.0725973	−	0.270937i
$698$	−36.0245	−	9.65273i	−1.36355	−	0.365361i
$699$		0			0
$700$	21.8380	+	1.13158i	0.825400	+	0.0427697i
$701$			24.8143i			0.937224i	0.883404	+	0.468612i	$0.155246\pi$
$701$			24.8143i			0.937224i	−0.883404	+	0.468612i	$0.844754\pi$
$702$		0			0
$703$	−33.1009	+	8.86935i	−1.24842	+	0.334514i
$704$	2.81961	−	4.88370i	0.106268	−	0.184061i
$705$		0			0
$706$	38.0708			1.43281
$707$	−7.24167	−	4.35483i	−0.272351	−	0.163780i
$708$		0			0
$709$	−14.3464	+	8.28290i	−0.538791	+	0.311071i	−0.744589	−	0.667524i	$-0.767354\pi$
$709$	−14.3464	+	8.28290i	−0.538791	+	0.311071i	0.205798	+	0.978594i	$0.434021\pi$
$710$	−0.881269	+	51.9062i	−0.0330734	+	1.94800i
$711$		0			0
$712$	−2.26573	−	0.607099i	−0.0849117	−	0.0227520i
$713$	−3.94199	+	3.94199i	−0.147629	+	0.147629i
$714$		0			0
$715$	−2.57571	+	1.42934i	−0.0963260	+	0.0534544i
$716$	8.09331	−	4.67268i	0.302461	−	0.174626i
$717$		0			0
$718$	−12.8466	+	3.44223i	−0.479430	+	0.128463i
$719$	−8.28531	−	14.3506i	−0.308990	−	0.535186i	0.669152	−	0.743126i	$-0.266658\pi$
$719$	−8.28531	−	14.3506i	−0.308990	−	0.535186i	−0.978142	+	0.207939i	$0.933324\pi$
$720$		0			0
$721$	−1.56468	+	5.44919i	−0.0582717	+	0.202939i
$722$	−23.0197	−	23.0197i	−0.856705	−	0.856705i
$723$		0			0
$724$	31.9589	+	18.4515i	1.18774	+	0.685745i
$725$	−43.6333	+	23.2536i	−1.62050	+	0.863618i
$726$		0			0
$727$	10.4810	−	10.4810i	0.388721	−	0.388721i	−0.485510	−	0.874231i	$-0.661366\pi$
$727$	10.4810	−	10.4810i	0.388721	−	0.388721i	0.874231	+	0.485510i	$0.161366\pi$
$728$	2.05944	+	0.0366983i	0.0763280	+	0.00136013i
$729$		0			0
$730$	19.3026	−	4.82244i	0.714420	−	0.178487i
$731$	−14.4064	−	8.31752i	−0.532838	−	0.307634i
$732$		0			0
$733$	7.08056	−	26.4250i	0.261527	−	0.976030i	−0.702816	−	0.711372i	$-0.748074\pi$
$733$	7.08056	−	26.4250i	0.261527	−	0.976030i	0.964342	−	0.264658i	$-0.0852592\pi$
$734$	7.60640			0.280757
$735$		0			0
$736$	4.92424			0.181510
$737$	1.86508	−	6.96055i	0.0687009	−	0.256395i
$738$		0			0
$739$	24.2950	+	14.0267i	0.893707	+	0.515982i	0.875153	−	0.483846i	$-0.160760\pi$
$739$	24.2950	+	14.0267i	0.893707	+	0.515982i	0.0185537	+	0.999828i	$0.494094\pi$
$740$	−10.8593	+	18.0925i	−0.399196	+	0.665092i
$741$		0			0
$742$	−4.13931	−	0.0737607i	−0.151959	−	0.00270784i
$743$	13.7752	−	13.7752i	0.505363	−	0.505363i	−0.407737	−	0.913100i	$-0.633682\pi$
$743$	13.7752	−	13.7752i	0.505363	−	0.505363i	0.913100	+	0.407737i	$0.133682\pi$
$744$		0			0
$745$	35.5109	−	34.3252i	1.30102	−	1.25758i
$746$	−17.8086	−	10.2818i	−0.652018	−	0.376443i
$747$		0			0
$748$	−2.93323	−	2.93323i	−0.107250	−	0.107250i
$749$	0.463207	−	1.61317i	0.0169252	−	0.0589441i
$750$		0			0
$751$	17.1719	+	29.7426i	0.626611	+	1.08532i	0.988227	+	0.152994i	$0.0488916\pi$
$751$	17.1719	+	29.7426i	0.626611	+	1.08532i	−0.361617	+	0.932327i	$0.617775\pi$
$752$	43.5460	−	11.6681i	1.58796	−	0.425492i
$753$		0			0
$754$	19.2143	−	11.0934i	0.699742	−	0.403996i
$755$	10.2585	+	2.93627i	0.373344	+	0.106862i
$756$		0			0
$757$	14.6354	−	14.6354i	0.531932	−	0.531932i	−0.389215	−	0.921147i	$-0.627254\pi$
$757$	14.6354	−	14.6354i	0.531932	−	0.531932i	0.921147	+	0.389215i	$0.127254\pi$
$758$	−24.9135	−	6.67556i	−0.904900	−	0.242467i
$759$		0			0
$760$	8.90037	+	0.151111i	0.322850	+	0.00548139i
$761$	31.8819	−	18.4070i	1.15572	−	0.667254i	0.205443	−	0.978669i	$-0.434136\pi$
$761$	31.8819	−	18.4070i	1.15572	−	0.667254i	0.950274	+	0.311415i	$0.100803\pi$
$762$		0			0
$763$	−31.3811	−	18.8712i	−1.13607	−	0.683184i
$764$	9.75627			0.352969
$765$		0			0
$766$	−2.64237	+	4.57673i	−0.0954728	+	0.165364i
$767$	−3.96897	+	1.06348i	−0.143311	+	0.0384002i
$768$		0			0
$769$			24.6011i			0.887139i	0.896240	+	0.443569i	$0.146288\pi$
$769$			24.6011i			0.887139i	−0.896240	+	0.443569i	$0.853712\pi$
$770$	10.7618	+	6.72303i	0.387828	+	0.242281i
$771$		0			0
$772$	18.2459	+	4.88898i	0.656685	+	0.175958i
$773$	−2.47156	−	9.22398i	−0.0888958	−	0.331764i	0.907128	−	0.420856i	$-0.138270\pi$
$773$	−2.47156	−	9.22398i	−0.0888958	−	0.331764i	−0.996023	+	0.0890921i	$0.971603\pi$
$774$		0			0
$775$	−1.42485	+	41.9492i	−0.0511821	+	1.50686i
$776$		−	10.0141i		−	0.359484i
$777$		0			0
$778$	−22.4191	−	22.4191i	−0.803765	−	0.803765i
$779$	−9.93914	−	17.2151i	−0.356107	−	0.616795i
$780$		0			0
$781$	−6.81576	+	11.8052i	−0.243887	+	0.422425i
$782$	0.734615	−	2.74162i	0.0262698	−	0.0980401i
$783$		0			0
$784$	−15.0095	−	28.2785i	−0.536055	−	1.00995i
$785$	−28.6806	+	15.9158i	−1.02365	+	0.568059i
$786$		0			0
$787$	−10.2341	−	38.1941i	−0.364806	−	1.36147i	−0.867684	−	0.497116i	$-0.834392\pi$
$787$	−10.2341	−	38.1941i	−0.364806	−	1.36147i	0.502879	−	0.864357i	$-0.332274\pi$
$788$	5.67545	+	21.1810i	0.202179	+	0.754544i
$789$		0			0
$790$	−39.3912	+	21.8594i	−1.40147	+	0.777724i
$791$	−15.4956	+	14.9530i	−0.550959	+	0.531667i
$792$		0			0
$793$	−1.56493	+	5.84038i	−0.0555721	+	0.207398i
$794$	13.3572	−	23.1354i	0.474031	−	0.821046i
$795$		0			0
$796$	−10.0761	−	17.4523i	−0.357138	−	0.618581i
$797$	−10.0038	−	10.0038i	−0.354354	−	0.354354i	0.507373	−	0.861727i	$-0.330617\pi$
$797$	−10.0038	−	10.0038i	−0.354354	−	0.354354i	−0.861727	+	0.507373i	$0.830617\pi$
$798$		0			0
$799$		−	22.0425i		−	0.779806i
$800$	27.0909	−	25.3110i	0.957809	−	0.894880i
$801$		0			0
$802$	−4.56472	−	17.0358i	−0.161186	−	0.601553i
$803$	5.04625	+	1.35214i	0.178078	+	0.0477160i
$804$		0			0
$805$	−0.136672	+	3.92643i	−0.00481705	+	0.138388i
$806$		−	18.8349i		−	0.663432i
$807$		0			0
$808$	−2.04597	+	0.548215i	−0.0719769	+	0.0192862i
$809$	2.99072	−	5.18008i	0.105148	−	0.182122i	−0.808651	−	0.588289i	$-0.799802\pi$
$809$	2.99072	−	5.18008i	0.105148	−	0.182122i	0.913799	+	0.406167i	$0.133135\pi$
$810$		0			0
$811$	4.80074			0.168577			0.0842883	−	0.996441i	$-0.473138\pi$
$811$	4.80074			0.168577			0.0842883	+	0.996441i	$0.473138\pi$
$812$	−37.0621	−	22.2875i	−1.30062	−	0.782139i
$813$		0			0
$814$	−10.6041	+	6.12230i	−0.371675	+	0.214587i
$815$	27.5910	+	0.468442i	0.966469	+	0.0164088i
$816$		0			0
$817$	−43.1326	−	11.5574i	−1.50902	−	0.404340i
$818$	−23.1693	+	23.1693i	−0.810094	+	0.810094i
$819$		0			0
$820$	−11.7677	−	3.36827i	−0.410946	−	0.117625i
$821$	22.5254	−	13.0050i	0.786142	−	0.453879i	−0.0524609	−	0.998623i	$-0.516706\pi$
$821$	22.5254	−	13.0050i	0.786142	−	0.453879i	0.838602	+	0.544744i	$0.183373\pi$
$822$		0			0
$823$	11.2027	−	3.00174i	0.390500	−	0.104634i	−0.0582263	−	0.998303i	$-0.518545\pi$
$823$	11.2027	−	3.00174i	0.390500	−	0.104634i	0.448726	+	0.893669i	$0.351878\pi$
$824$	0.710547	+	1.23070i	0.0247531	+	0.0428736i
$825$		0			0
$826$	12.2909	+	12.7369i	0.427655	+	0.443172i
$827$	9.82938	+	9.82938i	0.341801	+	0.341801i	0.857044	−	0.515243i	$-0.172298\pi$
$827$	9.82938	+	9.82938i	0.341801	+	0.341801i	−0.515243	+	0.857044i	$0.672298\pi$
$828$		0			0
$829$	33.1815	+	19.1573i	1.15244	+	0.665362i	0.949481	−	0.313825i	$-0.101611\pi$
$829$	33.1815	+	19.1573i	1.15244	+	0.665362i	0.202960	+	0.979187i	$0.434944\pi$
$830$	50.0214	−	48.3512i	1.73627	−	1.67830i
$831$		0			0
$832$	−4.17123	+	4.17123i	−0.144611	+	0.144611i
$833$	−15.2548	+	3.51014i	−0.528547	+	0.121619i
$834$		0			0
$835$	−4.20343	+	7.00324i	−0.145466	+	0.242357i
$836$	−9.64341	−	5.56763i	−0.333524	−	0.192560i
$837$		0			0
$838$	−11.2527	+	41.9956i	−0.388718	+	1.45071i
$839$	−23.9846			−0.828039			−0.414020	−	0.910268i	$-0.635876\pi$
$839$	−23.9846			−0.828039			−0.414020	+	0.910268i	$0.635876\pi$
$840$		0			0
$841$	68.7839			2.37186
$842$	−3.99960	+	14.9267i	−0.137835	+	0.514409i
$843$		0			0
$844$	4.98409	+	2.87756i	0.171559	+	0.0990498i
$845$	−25.2125	+	6.29896i	−0.867337	+	0.216691i
$846$		0			0
$847$	−12.4860	−	22.5447i	−0.429023	−	0.774644i
$848$	−2.64766	+	2.64766i	−0.0909212	+	0.0909212i
$849$		0			0
$850$	−10.0507	−	18.8591i	−0.344735	−	0.646863i
$851$	−3.28324	−	1.89558i	−0.112548	−	0.0649796i
$852$		0			0
$853$	32.7833	+	32.7833i	1.12248	+	1.12248i	0.991368	+	0.131111i	$0.0418544\pi$
$853$	32.7833	+	32.7833i	1.12248	+	1.12248i	0.131111	+	0.991368i	$0.458146\pi$
$854$	25.2745	−	6.29185i	0.864875	−	0.215303i
$855$		0			0
$856$	−0.210350	−	0.364336i	−0.00718961	−	0.0124528i
$857$	6.84801	−	1.83492i	0.233924	−	0.0626796i	−0.139953	−	0.990158i	$-0.544695\pi$
$857$	6.84801	−	1.83492i	0.233924	−	0.0626796i	0.373876	+	0.927479i	$0.378028\pi$
$858$		0			0
$859$	35.3255	−	20.3952i	1.20529	−	0.695874i	0.243563	−	0.969885i	$-0.421684\pi$
$859$	35.3255	−	20.3952i	1.20529	−	0.695874i	0.961727	+	0.274011i	$0.0883504\pi$
$860$	−24.0424	+	13.3419i	−0.819841	+	0.454956i
$861$		0			0
$862$	36.5376	−	36.5376i	1.24448	−	1.24448i
$863$	26.6975	+	7.15357i	0.908793	+	0.243510i	0.682789	−	0.730616i	$-0.260767\pi$
$863$	26.6975	+	7.15357i	0.908793	+	0.243510i	0.226004	+	0.974126i	$0.427434\pi$
$864$		0			0
$865$	−0.106761	+	6.28818i	−0.00363000	+	0.213804i
$866$	−2.66322	+	1.53761i	−0.0904999	+	0.0522501i
$867$		0			0
$868$	−32.1172	+	17.7875i	−1.09013	+	0.603749i
$869$	−11.8292			−0.401280
$870$		0			0
$871$	−3.76903	+	6.52816i	−0.127709	+	0.221198i
$872$	−8.86601	+	2.37564i	−0.300241	+	0.0804493i
$873$		0			0
$874$		−	7.61907i		−	0.257719i
$875$	19.4303	+	22.3039i	0.656863	+	0.754010i
$876$		0			0
$877$	6.53819	+	1.75190i	0.220779	+	0.0591576i	0.367513	−	0.930018i	$-0.380209\pi$
$877$	6.53819	+	1.75190i	0.220779	+	0.0591576i	−0.146734	+	0.989176i	$0.546876\pi$
$878$	15.5736	+	58.1216i	0.525585	+	1.96151i
$879$		0			0
$880$	11.1344	−	2.78175i	0.375340	−	0.0937729i
$881$		−	54.4886i		−	1.83577i	−0.396848	−	0.917884i	$-0.629896\pi$
$881$		−	54.4886i		−	1.83577i	0.396848	−	0.917884i	$-0.370104\pi$
$882$		0			0
$883$	−26.9366	−	26.9366i	−0.906490	−	0.906490i	0.0894971	−	0.995987i	$-0.471474\pi$
$883$	−26.9366	−	26.9366i	−0.906490	−	0.906490i	−0.995987	+	0.0894971i	$0.971474\pi$
$884$	2.16966	+	3.75796i	0.0729736	+	0.126394i
$885$		0			0
$886$	−13.7579	+	23.8293i	−0.462205	+	0.800562i
$887$	11.7970	−	44.0271i	0.396105	−	1.47829i	−0.423784	−	0.905763i	$-0.639298\pi$
$887$	11.7970	−	44.0271i	0.396105	−	1.47829i	0.819889	−	0.572522i	$-0.194035\pi$
$888$		0			0
$889$	−26.2461	+	25.3271i	−0.880266	+	0.849443i
$890$	7.33471	+	13.2173i	0.245860	+	0.443045i
$891$		0			0
$892$	−7.16142	−	26.7268i	−0.239782	−	0.894879i
$893$	−15.3142	−	57.1534i	−0.512471	−	1.91257i
$894$		0			0
$895$	12.1536	+	3.47872i	0.406250	+	0.116281i
$896$	−13.2888	−	3.81574i	−0.443947	−	0.127475i
$897$		0			0
$898$	6.48030	−	24.1848i	0.216251	−	0.807058i
$899$	41.5057	−	71.8900i	1.38429	−	2.39767i
$900$		0			0
$901$	0.915385	+	1.58549i	0.0304959	+	0.0528205i
$902$	−5.02243	−	5.02243i	−0.167228	−	0.167228i
$903$		0			0
$904$			5.39768i			0.179524i
$905$	12.0997	+	48.4309i	0.402208	+	1.60990i
$906$		0			0
$907$	0.102828	+	0.383760i	0.00341435	+	0.0127425i	0.967612	−	0.252442i	$-0.0812337\pi$
$907$	0.102828	+	0.383760i	0.00341435	+	0.0127425i	−0.964198	+	0.265185i	$0.914567\pi$
$908$	−42.9597	−	11.5110i	−1.42567	−	0.382007i
$909$		0			0
$910$	−9.05376	−	9.70678i	−0.300129	−	0.321777i
$911$			21.8995i			0.725562i	0.931874	+	0.362781i	$0.118173\pi$
$911$			21.8995i			0.725562i	−0.931874	+	0.362781i	$0.881827\pi$
$912$		0			0
$913$	17.6453	−	4.72804i	0.583973	−	0.156475i
$914$	4.95136	−	8.57600i	0.163776	−	0.283669i
$915$		0			0
$916$	11.2980			0.373298
$917$	−34.1971	+	18.9395i	−1.12929	+	0.625436i
$918$		0			0
$919$	−27.8860	+	16.1000i	−0.919875	+	0.531090i	−0.883595	−	0.468252i	$-0.844884\pi$
$919$	−27.8860	+	16.1000i	−0.919875	+	0.531090i	−0.0362798	+	0.999342i	$0.511551\pi$
$920$	0.684436	+	0.708078i	0.0225652	+	0.0233446i
$921$		0			0
$922$	−48.9485	−	13.1157i	−1.61203	−	0.431943i
$923$	10.0830	−	10.0830i	0.331886	−	0.331886i
$924$		0			0
$925$	−27.8063	+	6.44753i	−0.914267	+	0.211994i
$926$	−20.1141	+	11.6129i	−0.660991	+	0.381623i
$927$		0			0
$928$	−70.8256	+	18.9777i	−2.32496	+	0.622972i
$929$	27.1770	+	47.0719i	0.891647	+	1.54438i	0.837900	+	0.545823i	$0.183783\pi$
$929$	27.1770	+	47.0719i	0.891647	+	1.54438i	0.0537466	+	0.998555i	$0.482884\pi$
$930$		0			0
$931$	−37.1151	+	19.6998i	−1.21640	+	0.645634i
$932$	8.32769	+	8.32769i	0.272783	+	0.272783i
$933$		0			0
$934$	−16.9132	−	9.76486i	−0.553418	−	0.319516i
$935$	0.0952570	−	5.61057i	0.00311524	−	0.183485i
$936$		0			0
$937$	−16.8346	+	16.8346i	−0.549964	+	0.549964i	−0.926430	−	0.376467i	$-0.877139\pi$
$937$	−16.8346	+	16.8346i	−0.549964	+	0.549964i	0.376467	+	0.926430i	$0.377139\pi$
$938$	32.4663	+	0.578534i	1.06006	+	0.0188898i
$939$		0			0
$940$	−31.2393	−	18.7502i	−1.01891	−	0.611563i
$941$	−10.4837	−	6.05274i	−0.341757	−	0.197314i	0.319292	−	0.947657i	$-0.396555\pi$
$941$	−10.4837	−	6.05274i	−0.341757	−	0.197314i	−0.661049	+	0.750343i	$0.729888\pi$
$942$		0			0
$943$	0.569183	−	2.12422i	0.0185351	−	0.0691741i
$944$	16.0087			0.521039
$945$		0			0
$946$	−15.9555			−0.518759
$947$	−5.75096	+	21.4629i	−0.186881	+	0.697450i	0.807339	+	0.590088i	$0.200907\pi$
$947$	−5.75096	+	21.4629i	−0.186881	+	0.697450i	−0.994220	+	0.107362i	$0.965760\pi$
$948$		0			0
$949$	−4.73278	−	2.73247i	−0.153632	−	0.0886997i
$950$	−39.1627	−	41.9166i	−1.27061	−	1.35996i
$951$		0			0
$952$	−2.02208	+	3.36253i	−0.0655361	+	0.108980i
$953$	−20.5298	+	20.5298i	−0.665024	+	0.665024i	−0.956560	−	0.291536i	$-0.905834\pi$
$953$	−20.5298	+	20.5298i	−0.665024	+	0.665024i	0.291536	+	0.956560i	$0.405834\pi$
$954$		0			0
$955$	9.17228	+	9.48911i	0.296808	+	0.307061i
$956$	26.8914	+	15.5258i	0.869730	+	0.502139i
$957$		0			0
$958$	−7.03582	−	7.03582i	−0.227317	−	0.227317i
$959$	51.2251	−	12.7520i	1.65414	−	0.411785i
$960$		0			0
$961$	−19.7354	−	34.1827i	−0.636625	−	1.10267i
$962$	12.3723	−	3.31513i	0.398897	−	0.106884i
$963$		0			0
$964$	−36.6013	+	21.1318i	−1.17885	+	0.680608i
$965$	12.3987	+	22.3427i	0.399127	+	0.719236i
$966$		0			0
$967$	−12.1981	+	12.1981i	−0.392263	+	0.392263i	−0.875493	−	0.483230i	$-0.839463\pi$
$967$	−12.1981	+	12.1981i	−0.392263	+	0.392263i	0.483230	+	0.875493i	$0.339463\pi$
$968$	−6.23975	−	1.67194i	−0.200553	−	0.0537381i
$969$		0			0
$970$	−46.4002	+	44.8509i	−1.48982	+	1.44008i
$971$	16.6289	−	9.60073i	0.533648	−	0.308102i	−0.208853	−	0.977947i	$-0.566973\pi$
$971$	16.6289	−	9.60073i	0.533648	−	0.308102i	0.742501	+	0.669845i	$0.233640\pi$
$972$		0			0
$973$	−0.0885648	+	4.97009i	−0.00283926	+	0.159334i
$974$	−50.8124			−1.62813
$975$		0			0
$976$	11.7785	−	20.4009i	0.377020	−	0.653018i
$977$	−8.86259	+	2.37472i	−0.283539	+	0.0759741i	−0.397786	−	0.917478i	$-0.630221\pi$
$977$	−8.86259	+	2.37472i	−0.283539	+	0.0759741i	0.114247	+	0.993452i	$0.463555\pi$
$978$		0			0
$979$			3.96918i			0.126856i
$980$	−8.00164	+	24.6054i	−0.255603	+	0.785991i
$981$		0			0
$982$	−9.52683	−	2.55271i	−0.304013	−	0.0814601i
$983$	−11.5884	−	43.2486i	−0.369614	−	1.37942i	−0.861057	−	0.508508i	$-0.830197\pi$
$983$	−11.5884	−	43.2486i	−0.369614	−	1.37942i	0.491443	−	0.870910i	$-0.336469\pi$
$984$		0			0
$985$	−15.2653	+	25.4332i	−0.486394	+	0.810371i
$986$			42.2640i			1.34596i
$987$		0			0
$988$	8.23655	+	8.23655i	0.262040	+	0.262040i
$989$	−2.47007	−	4.27828i	−0.0785435	−	0.136041i
$990$		0			0
$991$	22.5543	−	39.0653i	0.716462	−	1.24095i	−0.245930	−	0.969287i	$-0.579093\pi$
$991$	22.5543	−	39.0653i	0.716462	−	1.24095i	0.962393	−	0.271662i	$-0.0875732\pi$
$992$	−16.1107	+	60.1258i	−0.511514	+	1.90900i
$993$		0			0
$994$	−59.0394	−	16.9525i	−1.87262	−	0.537702i
$995$	7.50147	−	26.2079i	0.237812	−	0.830845i
$996$		0			0
$997$	13.3278	+	49.7401i	0.422096	+	1.57529i	0.770183	+	0.637823i	$0.220165\pi$
$997$	13.3278	+	49.7401i	0.422096	+	1.57529i	−0.348087	+	0.937462i	$0.613169\pi$
$998$	−3.82772	−	14.2853i	−0.121164	−	0.452192i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.53.13	yes	64
3.2	odd	2	inner	315.2.ce.a.53.4	✓	64
5.2	odd	4	inner	315.2.ce.a.242.13	yes	64
7.2	even	3	inner	315.2.ce.a.233.4	yes	64
15.2	even	4	inner	315.2.ce.a.242.4	yes	64
21.2	odd	6	inner	315.2.ce.a.233.13	yes	64
35.2	odd	12	inner	315.2.ce.a.107.4	yes	64
105.2	even	12	inner	315.2.ce.a.107.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.4	✓	64	3.2	odd	2	inner
315.2.ce.a.53.13	yes	64	1.1	even	1	trivial
315.2.ce.a.107.4	yes	64	35.2	odd	12	inner
315.2.ce.a.107.13	yes	64	105.2	even	12	inner
315.2.ce.a.233.4	yes	64	7.2	even	3	inner
315.2.ce.a.233.13	yes	64	21.2	odd	6	inner
315.2.ce.a.242.4	yes	64	15.2	even	4	inner
315.2.ce.a.242.13	yes	64	5.2	odd	4	inner

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.494677 - 1.84616i) q^{2} +(-1.43155 - 0.826508i) q^{4} +(-0.541988 - 2.16939i) q^{5} +(2.64533 + 0.0471386i) q^{7} +(0.468944 - 0.468944i) q^{8} +O(q^{10})\)	\(q+(0.494677 - 1.84616i) q^{2} +(-1.43155 - 0.826508i) q^{4} +(-0.541988 - 2.16939i) q^{5} +(2.64533 + 0.0471386i) q^{7} +(0.468944 - 0.468944i) q^{8} +(-4.27315 - 0.0725500i) q^{10} +(-0.971861 - 0.561104i) q^{11} +(0.830077 + 0.830077i) q^{13} +(1.39561 - 4.86039i) q^{14} +(-2.28679 - 3.96083i) q^{16} +(-2.16001 + 0.578772i) q^{17} +(-5.19853 + 3.00137i) q^{19} +(-1.01713 + 3.55355i) q^{20} +(-1.51665 + 1.51665i) q^{22} +(-0.641461 - 0.171879i) q^{23} +(-4.41250 + 2.35157i) q^{25} +(1.94308 - 1.12184i) q^{26} +(-3.74797 - 2.25387i) q^{28} +9.88857 q^{29} +(4.19734 - 7.27001i) q^{31} +(-7.16237 + 1.91915i) q^{32} +4.27403i q^{34} +(-1.33148 - 5.76430i) q^{35} +(5.51429 + 1.47755i) q^{37} +(2.96942 + 11.0820i) q^{38} +(-1.27148 - 0.763160i) q^{40} +3.31153i q^{41} +(5.26014 + 5.26014i) q^{43} +(0.927514 + 1.60650i) q^{44} +(-0.634632 + 1.09922i) q^{46} +(-2.55120 + 9.52122i) q^{47} +(6.99556 + 0.249395i) q^{49} +(2.15861 + 9.30945i) q^{50} +(-0.502235 - 1.87437i) q^{52} +(-0.211894 - 0.790799i) q^{53} +(-0.690516 + 2.41246i) q^{55} +(1.26262 - 1.21841i) q^{56} +(4.89165 - 18.2559i) q^{58} +(-1.75013 + 3.03132i) q^{59} +(2.57534 + 4.46061i) q^{61} +(-11.3453 - 11.3453i) q^{62} +5.02510i q^{64} +(1.35087 - 2.25065i) q^{65} +(1.66197 + 6.20255i) q^{67} +(3.57052 + 0.956719i) q^{68} +(-11.3005 - 0.393349i) q^{70} -12.1470i q^{71} +(-4.49672 + 1.20489i) q^{73} +(5.45559 - 9.44935i) q^{74} +9.92263 q^{76} +(-2.54444 - 1.53012i) q^{77} +(9.12881 - 5.27052i) q^{79} +(-7.35317 + 7.10765i) q^{80} +(6.11362 + 1.63814i) q^{82} +(-11.5106 + 11.5106i) q^{83} +(2.42628 + 4.37221i) q^{85} +(12.3131 - 7.10899i) q^{86} +(-0.718875 + 0.192622i) q^{88} +(-1.76847 - 3.06308i) q^{89} +(2.15670 + 2.23496i) q^{91} +(0.776226 + 0.776226i) q^{92} +(16.3157 + 9.41986i) q^{94} +(9.32868 + 9.65092i) q^{95} +(10.6773 - 10.6773i) q^{97} +(3.92097 - 12.7916i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7}+O(q^{10}) \) 64 * q + 8 * q^7	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73} - 320 q^{76} - 56 q^{82} + 16 q^{85} + 120 q^{88} - 128 q^{91} + 208 q^{97}+O(q^{100}) \) 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

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