LMFDB - Embedded newform 819.2.do.e.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(361,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("819.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.do (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$1.21245 - 0.727987i$ of defining polynomial
Character	$\chi$	$=$	819.361
Dual form			819.2.do.e.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99469 - 1.15163i) q^{2} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.09135 - 1.62057i) q^{7} -3.00585i q^{8} +O(q^{10})$	\(q+(-1.99469 - 1.15163i) q^{2} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.09135 - 1.62057i) q^{7} -3.00585i q^{8} -1.95154 q^{10} +1.50340i q^{11} +(-2.92329 - 2.11054i) q^{13} +(-6.03790 + 0.824057i) q^{14} +(-0.156597 + 0.271234i) q^{16} +(-1.03570 - 1.79389i) q^{17} +0.0474272i q^{19} +(2.42516 + 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} +(3.90935 - 6.77119i) q^{23} +(-2.14105 + 3.70840i) q^{25} +(3.40047 + 7.57643i) q^{26} +(8.09446 + 3.30795i) q^{28} +(0.679854 + 1.17754i) q^{29} +(6.80787 + 3.93052i) q^{31} +(-4.58156 + 2.64516i) q^{32} +4.77099i q^{34} +(0.848038 - 2.07513i) q^{35} +(-5.80427 - 3.35110i) q^{37} +(0.0546187 - 0.0946024i) q^{38} +(-1.27341 - 2.20562i) q^{40} +(8.67622 - 5.00922i) q^{41} +(4.63283 - 8.02430i) q^{43} +(-4.30311 + 2.48440i) q^{44} +(-15.5959 + 9.00428i) q^{46} +(-0.311781 + 0.180007i) q^{47} +(1.74751 - 6.77836i) q^{49} +(8.54144 - 4.93141i) q^{50} +(1.21011 - 11.8549i) q^{52} +(1.35591 - 2.34850i) q^{53} +(0.636910 + 1.10316i) q^{55} +(-4.87118 - 6.28629i) q^{56} -3.13177i q^{58} +(-1.42132 + 0.820598i) q^{59} +4.52194 q^{61} +(-9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(-3.03916 - 0.310229i) q^{65} +2.04266i q^{67} +(3.42303 - 5.92886i) q^{68} +(-4.08136 + 3.16260i) q^{70} +(-12.3096 - 7.10697i) q^{71} +(-5.85563 - 3.38075i) q^{73} +(7.71847 + 13.3688i) q^{74} +(-0.135748 + 0.0783743i) q^{76} +(2.43637 + 3.14414i) q^{77} +(-5.82952 - 10.0970i) q^{79} +0.265367i q^{80} -23.0751 q^{82} +11.5362i q^{83} +(-1.51994 - 0.877541i) q^{85} +(-18.4821 + 10.6706i) q^{86} +4.51900 q^{88} +(-15.1652 - 8.75561i) q^{89} +(-9.53391 + 0.323492i) q^{91} +25.8411 q^{92} +0.829208 q^{94} +(0.0200923 + 0.0348009i) q^{95} +(0.369125 + 0.213115i) q^{97} +(-11.2919 + 11.5082i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.99469	−	1.15163i	−1.41046	−	0.814328i	−0.415026	−	0.909810i	$-0.636227\pi$
$2$	−1.99469	−	1.15163i	−1.41046	−	0.814328i	−0.995431	+	0.0954820i	$0.969561\pi$
$3$		0			0
$3$		0			0
$4$	1.65252	+	2.86225i	0.826259	+	1.43112i
$5$	0.733776	−	0.423646i	0.328155	−	0.189460i	−0.326867	−	0.945070i	$-0.605993\pi$
$5$	0.733776	−	0.423646i	0.328155	−	0.189460i	0.655022	+	0.755610i	$0.272660\pi$
$6$		0			0
$7$	2.09135	−	1.62057i	0.790457	−	0.612517i
$7$	2.09135	−	1.62057i	0.790457	−	0.612517i
$8$		−	3.00585i		−	1.06273i
$9$		0			0
$10$	−1.95154			−0.617131
$11$			1.50340i			0.453293i	0.973977	+	0.226646i	$0.0727762\pi$
$11$			1.50340i			0.453293i	−0.973977	+	0.226646i	$0.927224\pi$
$12$		0			0
$13$	−2.92329	−	2.11054i	−0.810774	−	0.585360i
$13$	−2.92329	−	2.11054i	−0.810774	−	0.585360i
$14$	−6.03790	+	0.824057i	−1.61370	+	0.220238i
$15$		0			0
$16$	−0.156597	+	0.271234i	−0.0391492	+	0.0678085i
$17$	−1.03570	−	1.79389i	−0.251194	−	0.435081i	0.712661	−	0.701509i	$-0.247490\pi$
$17$	−1.03570	−	1.79389i	−0.251194	−	0.435081i	−0.963855	+	0.266428i	$0.914157\pi$
$18$		0			0
$19$			0.0474272i			0.0108805i	0.999985	+	0.00544027i	$0.00173170\pi$
$19$			0.0474272i			0.0108805i	−0.999985	+	0.00544027i	$0.998268\pi$
$20$	2.42516	+	1.40016i	0.542282	+	0.313086i
$21$		0			0
$22$	1.73137	−	2.99882i	0.369129	−	0.639350i
$23$	3.90935	−	6.77119i	0.815156	−	1.41189i	−0.0940598	−	0.995567i	$-0.529984\pi$
$23$	3.90935	−	6.77119i	0.815156	−	1.41189i	0.909216	−	0.416325i	$-0.136682\pi$
$24$		0			0
$25$	−2.14105	+	3.70840i	−0.428210	+	0.741681i
$26$	3.40047	+	7.57643i	0.666887	+	1.48586i
$27$		0			0
$28$	8.09446	+	3.30795i	1.52971	+	0.625143i
$29$	0.679854	+	1.17754i	0.126246	+	0.218664i	0.922219	−	0.386668i	$-0.126374\pi$
$29$	0.679854	+	1.17754i	0.126246	+	0.218664i	−0.795973	+	0.605331i	$0.793041\pi$
$30$		0			0
$31$	6.80787	+	3.93052i	1.22273	+	0.705943i	0.965499	−	0.260407i	$-0.0838567\pi$
$31$	6.80787	+	3.93052i	1.22273	+	0.705943i	0.257230	+	0.966350i	$0.417190\pi$
$32$	−4.58156	+	2.64516i	−0.809912	+	0.467603i
$33$		0			0
$34$			4.77099i			0.818218i
$35$	0.848038	−	2.07513i	0.143345	−	0.350761i
$36$		0			0
$37$	−5.80427	−	3.35110i	−0.954216	−	0.550917i	−0.0598278	−	0.998209i	$-0.519055\pi$
$37$	−5.80427	−	3.35110i	−0.954216	−	0.550917i	−0.894388	+	0.447292i	$0.852388\pi$
$38$	0.0546187	−	0.0946024i	0.00886032	−	0.0153465i
$39$		0			0
$40$	−1.27341	−	2.20562i	−0.201345	−	0.348739i
$41$	8.67622	−	5.00922i	1.35500	−	0.782309i	0.366054	−	0.930594i	$-0.380709\pi$
$41$	8.67622	−	5.00922i	1.35500	−	0.782309i	0.988945	+	0.148285i	$0.0473754\pi$
$42$		0			0
$43$	4.63283	−	8.02430i	0.706500	−	1.22369i	−0.259647	−	0.965704i	$-0.583606\pi$
$43$	4.63283	−	8.02430i	0.706500	−	1.22369i	0.966147	−	0.257991i	$-0.0830604\pi$
$44$	−4.30311	+	2.48440i	−0.648718	+	0.374537i
$45$		0			0
$46$	−15.5959	+	9.00428i	−2.29948	+	1.32761i
$47$	−0.311781	+	0.180007i	−0.0454779	+	0.0262567i	−0.522567	−	0.852598i	$-0.675025\pi$
$47$	−0.311781	+	0.180007i	−0.0454779	+	0.0262567i	0.477089	+	0.878855i	$0.341692\pi$
$48$		0			0
$49$	1.74751	−	6.77836i	0.249645	−	0.968337i
$50$	8.54144	−	4.93141i	1.20794	−	0.697406i
$51$		0			0
$52$	1.21011	−	11.8549i	0.167813	−	1.64398i
$53$	1.35591	−	2.34850i	0.186248	−	0.322591i	−0.757748	−	0.652547i	$-0.773701\pi$
$53$	1.35591	−	2.34850i	0.186248	−	0.322591i	0.943996	+	0.329956i	$0.107034\pi$
$54$		0			0
$55$	0.636910	+	1.10316i	0.0858809	+	0.148750i
$56$	−4.87118	−	6.28629i	−0.650939	−	0.840040i
$57$		0			0
$58$		−	3.13177i		−	0.411222i
$59$	−1.42132	+	0.820598i	−0.185040	+	0.106833i	−0.589658	−	0.807653i	$-0.700738\pi$
$59$	−1.42132	+	0.820598i	−0.185040	+	0.106833i	0.404619	+	0.914486i	$0.367404\pi$
$60$		0			0
$61$	4.52194			0.578975			0.289488	−	0.957182i	$-0.406515\pi$
$61$	4.52194			0.578975			0.289488	+	0.957182i	$0.406515\pi$
$62$	−9.05305	−	15.6803i	−1.14974	−	1.99140i
$63$		0			0
$64$	12.8114			1.60143
$65$	−3.03916	−	0.310229i	−0.376962	−	0.0384792i
$66$		0			0
$67$			2.04266i			0.249551i	0.992185	+	0.124775i	$0.0398210\pi$
$67$			2.04266i			0.249551i	−0.992185	+	0.124775i	$0.960179\pi$
$68$	3.42303	−	5.92886i	0.415103	−	0.718980i
$69$		0			0
$70$	−4.08136	+	3.16260i	−0.487815	+	0.378003i
$71$	−12.3096	−	7.10697i	−1.46088	−	0.843442i	−0.461832	−	0.886967i	$-0.652808\pi$
$71$	−12.3096	−	7.10697i	−1.46088	−	0.843442i	−0.999052	+	0.0435255i	$0.986141\pi$
$72$		0			0
$73$	−5.85563	−	3.38075i	−0.685349	−	0.395687i	0.116518	−	0.993189i	$-0.462827\pi$
$73$	−5.85563	−	3.38075i	−0.685349	−	0.395687i	−0.801867	+	0.597502i	$0.796160\pi$
$74$	7.71847	+	13.3688i	0.897253	+	1.55409i
$75$		0			0
$76$	−0.135748	+	0.0783743i	−0.0155714	+	0.00899015i
$77$	2.43637	+	3.14414i	0.277650	+	0.358308i
$78$		0			0
$79$	−5.82952	−	10.0970i	−0.655873	−	1.13600i	−0.981674	−	0.190567i	$-0.938967\pi$
$79$	−5.82952	−	10.0970i	−0.655873	−	1.13600i	0.325801	−	0.945438i	$-0.394366\pi$
$80$			0.265367i			0.0296689i
$81$		0			0
$82$	−23.0751			−2.54822
$83$			11.5362i			1.26627i	0.774043	+	0.633133i	$0.218232\pi$
$83$			11.5362i			1.26627i	−0.774043	+	0.633133i	$0.781768\pi$
$84$		0			0
$85$	−1.51994	−	0.877541i	−0.164861	−	0.0951826i
$86$	−18.4821	+	10.6706i	−1.99298	+	1.15065i
$87$		0			0
$88$	4.51900			0.481727
$89$	−15.1652	−	8.75561i	−1.60750	−	0.928093i	−0.989927	−	0.141582i	$-0.954781\pi$
$89$	−15.1652	−	8.75561i	−1.60750	−	0.928093i	−0.617577	−	0.786510i	$-0.711886\pi$
$90$		0			0
$91$	−9.53391	+	0.323492i	−0.999425	+	0.0339112i
$92$	25.8411			2.69412
$93$		0			0
$94$	0.829208			0.0855262
$95$	0.0200923	+	0.0348009i	0.00206143	+	0.00357050i
$96$		0			0
$97$	0.369125	+	0.213115i	0.0374790	+	0.0216385i	0.518622	−	0.855003i	$-0.326445\pi$
$97$	0.369125	+	0.213115i	0.0374790	+	0.0216385i	−0.481143	+	0.876642i	$0.659778\pi$
$98$	−11.2919	+	11.5082i	−1.14066	+	1.16251i
$99$		0			0
$100$	−14.1525			−1.41525
$101$	9.66997			0.962198			0.481099	−	0.876666i	$-0.340238\pi$
$101$	9.66997			0.962198			0.481099	+	0.876666i	$0.340238\pi$
$102$		0			0
$103$	−4.98912	−	8.64140i	−0.491592	−	0.851463i	0.508361	−	0.861144i	$-0.330252\pi$
$103$	−4.98912	−	8.64140i	−0.491592	−	0.851463i	−0.999953	+	0.00968129i	$0.996918\pi$
$104$	−6.34397	+	8.78695i	−0.622078	+	0.861631i
$105$		0			0
$106$	−5.40922	+	3.12301i	−0.525390	+	0.303334i
$107$	4.93111	−	8.54094i	0.476709	−	0.825684i	−0.522935	−	0.852373i	$-0.675163\pi$
$107$	4.93111	−	8.54094i	0.476709	−	0.825684i	0.999644	+	0.0266888i	$0.00849631\pi$
$108$		0			0
$109$	10.0507	+	5.80275i	0.962679	+	0.555803i	0.896996	−	0.442038i	$-0.145744\pi$
$109$	10.0507	+	5.80275i	0.962679	+	0.555803i	0.0656822	+	0.997841i	$0.479078\pi$
$110$		−	2.93395i		−	0.279741i
$111$		0			0
$112$	0.112054	+	0.821022i	0.0105881	+	0.0775793i
$113$	−1.73879	+	3.01167i	−0.163572	+	0.283314i	−0.936147	−	0.351609i	$-0.885635\pi$
$113$	−1.73879	+	3.01167i	−0.163572	+	0.283314i	0.772576	+	0.634923i	$0.218968\pi$
$114$		0			0
$115$		−	6.62472i		−	0.617758i
$116$	−2.24694	+	3.89182i	−0.208623	+	0.361346i
$117$		0			0
$118$	3.78011			0.347987
$119$	−5.07313	−	2.07322i	−0.465053	−	0.190052i
$120$		0			0
$121$	8.73978			0.794526
$122$	−9.01986	−	5.20762i	−0.816620	−	0.471476i
$123$		0			0
$124$			25.9811i			2.33317i
$125$			7.86464i			0.703435i
$126$		0			0
$127$	−7.84992	−	13.5965i	−0.696567	−	1.20649i	−0.969649	−	0.244499i	$-0.921376\pi$
$127$	−7.84992	−	13.5965i	−0.696567	−	1.20649i	0.273082	−	0.961991i	$-0.411957\pi$
$128$	−16.3917	−	9.46373i	−1.44883	−	0.836483i
$129$		0			0
$130$	5.70491	+	4.11881i	0.500353	+	0.361243i
$131$	−1.27259	−	2.20418i	−0.111186	−	0.192580i	0.805063	−	0.593190i	$-0.202132\pi$
$131$	−1.27259	−	2.20418i	−0.111186	−	0.192580i	−0.916249	+	0.400610i	$0.868798\pi$
$132$		0			0
$133$	0.0768590	+	0.0991869i	0.00666452	+	0.00860060i
$134$	2.35240	−	4.07447i	0.203216	−	0.351981i
$135$		0			0
$136$	−5.39215	+	3.11316i	−0.462373	+	0.266951i
$137$	1.61490	−	0.932362i	0.137970	−	0.0796571i	−0.429426	−	0.903102i	$-0.641284\pi$
$137$	1.61490	−	0.932362i	0.137970	−	0.0796571i	0.567396	+	0.823445i	$0.307951\pi$
$138$		0			0
$139$	−7.80462	+	13.5180i	−0.661979	+	1.14658i	0.318116	+	0.948052i	$0.396950\pi$
$139$	−7.80462	+	13.5180i	−0.661979	+	1.14658i	−0.980095	+	0.198530i	$0.936383\pi$
$140$	7.34092	−	1.00189i	0.620421	−	0.0846755i
$141$		0			0
$142$	16.3692	+	28.3524i	1.37368	+	2.37928i
$143$	3.17300	−	4.39487i	0.265339	−	0.367518i
$144$		0			0
$145$	0.997721	+	0.576035i	0.0828562	+	0.0478371i
$146$	7.78676	+	13.4871i	0.644437	+	1.11620i
$147$		0			0
$148$		−	22.1510i		−	1.82080i
$149$		−	6.36363i		−	0.521329i	−0.965429	−	0.260664i	$-0.916058\pi$
$149$		−	6.36363i		−	0.521329i	0.965429	−	0.260664i	$-0.0839416\pi$
$150$		0			0
$151$	−0.575122	−	0.332047i	−0.0468028	−	0.0270216i	0.476416	−	0.879220i	$-0.341936\pi$
$151$	−0.575122	−	0.332047i	−0.0468028	−	0.0270216i	−0.523219	+	0.852198i	$0.675269\pi$
$152$	0.142559			0.0115630
$153$		0			0
$154$	−1.23889	−	9.07739i	−0.0998325	−	0.731477i
$155$	6.66060			0.534992
$156$		0			0
$157$	8.28798	−	14.3552i	0.661453	−	1.14567i	−0.318781	−	0.947828i	$-0.603273\pi$
$157$	8.28798	−	14.3552i	0.661453	−	1.14567i	0.980234	−	0.197842i	$-0.0633933\pi$
$158$			26.8539i			2.13638i
$159$		0			0
$160$	−2.24122	+	3.88191i	−0.177184	+	0.306892i
$161$	−2.79735	−	20.4963i	−0.220462	−	1.61534i
$162$		0			0
$163$			9.05127i			0.708950i	0.935065	+	0.354475i	$0.115340\pi$
$163$			9.05127i			0.708950i	−0.935065	+	0.354475i	$0.884660\pi$
$164$	28.6752	+	16.5557i	2.23916	+	1.29278i
$165$		0			0
$166$	13.2855	−	23.0112i	1.03116	−	1.78601i
$167$	2.30156	−	1.32880i	0.178100	−	0.102826i	−0.408300	−	0.912848i	$-0.633878\pi$
$167$	2.30156	−	1.32880i	0.178100	−	0.102826i	0.586400	+	0.810022i	$0.300545\pi$
$168$		0			0
$169$	4.09120	+	12.3395i	0.314708	+	0.949189i
$170$	2.02121	+	3.50084i	0.155020	+	0.268502i
$171$		0			0
$172$	30.6234			2.33501
$173$	19.5870			1.48918			0.744588	−	0.667525i	$-0.232646\pi$
$173$	19.5870			1.48918			0.744588	+	0.667525i	$0.232646\pi$
$174$		0			0
$175$	1.53204	+	11.2253i	0.115811	+	0.848553i
$176$	−0.407774	−	0.235428i	−0.0307371	−	0.0177461i
$177$		0			0
$178$	20.1665	+	34.9294i	1.51154	+	2.61807i
$179$	−2.89332			−0.216257			−0.108129	−	0.994137i	$-0.534486\pi$
$179$	−2.89332			−0.216257			−0.108129	+	0.994137i	$0.534486\pi$
$180$		0			0
$181$	−1.36804			−0.101686			−0.0508429	−	0.998707i	$-0.516191\pi$
$181$	−1.36804			−0.101686			−0.0508429	+	0.998707i	$0.516191\pi$
$182$	19.3897	+	10.3343i	1.43726	+	0.766029i
$183$		0			0
$184$	−20.3532	−	11.7509i	−1.50046	−	0.866289i
$185$	−5.67871			−0.417507
$186$		0			0
$187$	2.69693	−	1.55707i	0.197219	−	0.113865i
$188$	−1.03045	−	0.594929i	−0.0751531	−	0.0433897i
$189$		0			0
$190$		−	0.0925559i		−	0.00671471i
$191$	1.51325			0.109495			0.0547475	−	0.998500i	$-0.482565\pi$
$191$	1.51325			0.109495			0.0547475	+	0.998500i	$0.482565\pi$
$192$		0			0
$193$			6.95394i			0.500556i	0.968174	+	0.250278i	$0.0805220\pi$
$193$			6.95394i			0.500556i	−0.968174	+	0.250278i	$0.919478\pi$
$194$	−0.490860	−	0.850194i	−0.0352417	−	0.0610404i
$195$		0			0
$196$	22.2891	−	6.19955i	1.59208	−	0.442825i
$197$	13.4037	−	7.73860i	0.954971	−	0.551353i	0.0603494	−	0.998177i	$-0.480779\pi$
$197$	13.4037	−	7.73860i	0.954971	−	0.551353i	0.894622	+	0.446825i	$0.147445\pi$
$198$		0			0
$199$	3.30764	+	5.72901i	0.234473	+	0.406118i	0.959119	−	0.283002i	$-0.0913304\pi$
$199$	3.30764	+	5.72901i	0.234473	+	0.406118i	−0.724647	+	0.689121i	$0.757997\pi$
$200$	11.1469	+	6.43566i	0.788205	+	0.455070i
$201$		0			0
$202$	−19.2886	−	11.1363i	−1.35714	−	0.783545i
$203$	3.33010	+	1.36090i	0.233727	+	0.0955168i
$204$		0			0
$205$	4.24427	−	7.35129i	0.296433	−	0.513436i
$206$			22.9825i			1.60127i
$207$		0			0
$208$	1.03023	−	0.462389i	0.0714335	−	0.0320609i
$209$	−0.0713021			−0.00493207
$210$		0			0
$211$	4.04714	+	7.00986i	0.278617	+	0.482578i	0.971041	−	0.238912i	$-0.0767907\pi$
$211$	4.04714	+	7.00986i	0.278617	+	0.482578i	−0.692424	+	0.721490i	$0.743457\pi$
$212$	8.96264			0.615557
$213$		0			0
$214$	−19.6721	+	11.3577i	−1.34475	+	0.776394i
$215$		−	7.85072i		−	0.535415i
$216$		0			0
$217$	20.6073	−	2.81251i	1.39892	−	0.190925i
$218$	−13.3653	−	23.1493i	−0.905211	−	1.56787i
$219$		0			0
$220$	−2.10501	+	3.64599i	−0.141920	+	0.245812i
$221$	−0.758428	+	7.42993i	−0.0510174	+	0.499791i
$222$		0			0
$223$	13.9067	−	8.02903i	0.931261	−	0.537664i	0.0440506	−	0.999029i	$-0.485974\pi$
$223$	13.9067	−	8.02903i	0.931261	−	0.537664i	0.887210	+	0.461366i	$0.152640\pi$
$224$	−5.29498	+	12.9567i	−0.353786	+	0.865706i
$225$		0			0
$226$	6.93668	−	4.00490i	0.461421	−	0.266402i
$227$	1.12220	−	0.647903i	0.0744831	−	0.0430029i	−0.462296	−	0.886726i	$-0.652974\pi$
$227$	1.12220	−	0.647903i	0.0744831	−	0.0430029i	0.536779	+	0.843723i	$0.319641\pi$
$228$		0			0
$229$	−18.0285	+	10.4088i	−1.19136	+	0.687831i	−0.958614	−	0.284707i	$-0.908104\pi$
$229$	−18.0285	+	10.4088i	−1.19136	+	0.687831i	−0.232743	+	0.972538i	$0.574770\pi$
$230$	−7.62925	+	13.2142i	−0.503058	+	0.871322i
$231$		0			0
$232$	3.53951	−	2.04354i	0.232380	−	0.134165i
$233$	6.65213	+	11.5218i	0.435796	+	0.754820i	0.997360	−	0.0726127i	$-0.0231337\pi$
$233$	6.65213	+	11.5218i	0.435796	+	0.754820i	−0.561565	+	0.827433i	$0.689800\pi$
$234$		0			0
$235$	−0.152518	+	0.264169i	−0.00994920	+	0.0172325i
$236$	−4.69751	−	2.71211i	−0.305782	−	0.176543i
$237$		0			0
$238$	7.73172	+	9.97782i	0.501173	+	0.646766i
$239$			13.3652i			0.864525i	0.901748	+	0.432263i	$0.142285\pi$
$239$			13.3652i			0.864525i	−0.901748	+	0.432263i	$0.857715\pi$
$240$		0			0
$241$	−0.722398	+	0.417076i	−0.0465337	+	0.0268663i	−0.523086	−	0.852280i	$-0.675219\pi$
$241$	−0.722398	+	0.417076i	−0.0465337	+	0.0268663i	0.476553	+	0.879146i	$0.341886\pi$
$242$	−17.4331	−	10.0650i	−1.12064	−	0.647004i
$243$		0			0
$244$	7.47259	+	12.9429i	0.478384	+	0.828585i
$245$	−1.58934	−	5.71413i	−0.101539	−	0.365062i
$246$		0			0
$247$	0.100097	−	0.138643i	0.00636903	−	0.00882165i
$248$	11.8146	−	20.4634i	0.750225	−	1.29943i
$249$		0			0
$250$	9.05718	−	15.6875i	0.572827	−	0.992165i
$251$	−13.6360	+	23.6183i	−0.860699	+	1.49078i	0.0105555	+	0.999944i	$0.496640\pi$
$251$	−13.6360	+	23.6183i	−0.860699	+	1.49078i	−0.871255	+	0.490831i	$0.836693\pi$
$252$		0			0
$253$	10.1798	+	5.87733i	0.640000	+	0.369504i
$254$			36.1609i			2.26894i
$255$		0			0
$256$	8.98607	+	15.5643i	0.561630	+	0.972771i
$257$	−3.27594	+	5.67409i	−0.204348	+	0.353940i	−0.949925	−	0.312479i	$-0.898841\pi$
$257$	−3.27594	+	5.67409i	−0.204348	+	0.353940i	0.745577	+	0.666419i	$0.232174\pi$
$258$		0			0
$259$	−17.5695	+	2.39789i	−1.09171	+	0.148998i
$260$	−4.13432	−	9.21148i	−0.256399	−	0.571272i
$261$		0			0
$262$			5.86221i			0.362168i
$263$	22.5891			1.39290			0.696450	−	0.717605i	$-0.254762\pi$
$263$	22.5891			1.39290			0.696450	+	0.717605i	$0.254762\pi$
$264$		0			0
$265$		−	2.29770i		−	0.141146i
$266$	−0.0390827	−	0.286360i	−0.00239631	−	0.0175579i
$267$		0			0
$268$	−5.84660	+	3.37553i	−0.357138	+	0.206194i
$269$	8.00065	+	13.8575i	0.487808	+	0.844909i	0.999902	−	0.0140210i	$-0.00446317\pi$
$269$	8.00065	+	13.8575i	0.487808	+	0.844909i	−0.512093	+	0.858930i	$0.671130\pi$
$270$		0			0
$271$	−7.58582	−	4.37967i	−0.460806	−	0.266046i	0.251577	−	0.967837i	$-0.419051\pi$
$271$	−7.58582	−	4.37967i	−0.460806	−	0.266046i	−0.712383	+	0.701791i	$0.752384\pi$
$272$	0.648750			0.0393363
$273$		0			0
$274$	−4.29496			−0.259468
$275$	−5.57522	−	3.21886i	−0.336199	−	0.194104i
$276$		0			0
$277$	−9.95914	−	17.2497i	−0.598387	−	1.03644i	−0.993059	−	0.117614i	$-0.962475\pi$
$277$	−9.95914	−	17.2497i	−0.598387	−	1.03644i	0.394673	−	0.918822i	$-0.370858\pi$
$278$	31.1355	−	17.9761i	1.86739	−	1.07814i
$279$		0			0
$280$	−6.23752	−	2.54907i	−0.372763	−	0.152336i
$281$		−	14.0234i		−	0.836566i	−0.908317	−	0.418283i	$-0.862632\pi$
$281$		−	14.0234i		−	0.836566i	0.908317	−	0.418283i	$-0.137368\pi$
$282$		0			0
$283$	−1.01259			−0.0601922			−0.0300961	−	0.999547i	$-0.509581\pi$
$283$	−1.01259			−0.0601922			−0.0300961	+	0.999547i	$0.509581\pi$
$284$		−	46.9776i		−	2.78761i
$285$		0			0
$286$	−11.3904	+	5.11227i	−0.673530	+	0.302295i
$287$	10.0273	−	24.5365i	0.591890	−	1.44834i
$288$		0			0
$289$	6.35465	−	11.0066i	0.373803	−	0.647446i
$290$	−1.32676	−	2.29802i	−0.0779101	−	0.134944i
$291$		0			0
$292$		−	22.3470i		−	1.30776i
$293$	0.172543	+	0.0996176i	0.0100801	+	0.00581972i	0.505032	−	0.863101i	$-0.331481\pi$
$293$	0.172543	+	0.0996176i	0.0100801	+	0.00581972i	−0.494952	+	0.868921i	$0.664814\pi$
$294$		0			0
$295$	−0.695286	+	1.20427i	−0.0404811	+	0.0701153i
$296$	−10.0729	+	17.4467i	−0.585474	+	1.01407i
$297$		0			0
$298$	−7.32857	+	12.6935i	−0.424532	+	0.735312i
$299$	−25.7191	+	11.5433i	−1.48737	+	0.667565i
$300$		0			0
$301$	−3.31504	−	24.2895i	−0.191076	−	1.40002i
$302$	0.764792	+	1.32466i	0.0440088	+	0.0762256i
$303$		0			0
$304$	−0.0128639	−	0.00742695i	−0.000737793	−	0.000425965i
$305$	3.31809	−	1.91570i	0.189993	−	0.109693i
$306$		0			0
$307$			27.2004i			1.55241i	0.630482	+	0.776204i	$0.282857\pi$
$307$			27.2004i			1.55241i	−0.630482	+	0.776204i	$0.717143\pi$
$308$	−4.97317	+	12.1692i	−0.283373	+	0.693407i
$309$		0			0
$310$	−13.2858	−	7.67057i	−0.754584	−	0.435659i
$311$	−13.5505	+	23.4701i	−0.768376	+	1.33087i	0.170067	+	0.985432i	$0.445602\pi$
$311$	−13.5505	+	23.4701i	−0.768376	+	1.33087i	−0.938443	+	0.345434i	$0.887732\pi$
$312$		0			0
$313$	11.0392	+	19.1205i	0.623975	+	1.08076i	0.988738	+	0.149656i	$0.0478165\pi$
$313$	11.0392	+	19.1205i	0.623975	+	1.08076i	−0.364763	+	0.931100i	$0.618850\pi$
$314$	−33.0639	+	19.0894i	−1.86590	+	1.07728i
$315$		0			0
$316$	19.2668	−	33.3711i	1.08384	−	1.87727i
$317$	−6.12126	+	3.53411i	−0.343804	+	0.198496i	−0.661953	−	0.749545i	$-0.730272\pi$
$317$	−6.12126	+	3.53411i	−0.343804	+	0.198496i	0.318149	+	0.948041i	$0.396939\pi$
$318$		0			0
$319$	−1.77032	+	1.02209i	−0.0991188	+	0.0572263i
$320$	9.40071	−	5.42750i	0.525516	−	0.303407i
$321$		0			0
$322$	−18.0244	+	44.1053i	−1.00446	+	2.45789i
$323$	0.0850789	−	0.0491204i	0.00473392	−	0.00273313i
$324$		0			0
$325$	14.0857	−	6.32195i	0.781331	−	0.350679i
$326$	10.4237	−	18.0544i	0.577318	−	0.999943i
$327$		0			0
$328$	−15.0569	−	26.0794i	−0.831381	−	1.43999i
$329$	−0.360331	+	0.881721i	−0.0198657	+	0.0486108i
$330$		0			0
$331$			6.58858i			0.362141i	0.983470	+	0.181071i	$0.0579563\pi$
$331$			6.58858i			0.362141i	−0.983470	+	0.181071i	$0.942044\pi$
$332$	−33.0195	+	19.0638i	−1.81218	+	1.04626i
$333$		0			0
$334$	−6.12118			−0.334936
$335$	0.865365	+	1.49886i	0.0472799	+	0.0818912i
$336$		0			0
$337$	−4.22290			−0.230036			−0.115018	−	0.993363i	$-0.536693\pi$
$337$	−4.22290			−0.230036			−0.115018	+	0.993363i	$0.536693\pi$
$338$	6.04985	−	29.3249i	0.329069	−	1.59506i
$339$		0			0
$340$		−	5.80061i		−	0.314582i
$341$	−5.90916	+	10.2350i	−0.319999	+	0.554254i
$342$		0			0
$343$	−7.33014	−	17.0079i	−0.395790	−	0.918341i
$344$	−24.1198	−	13.9256i	−1.30045	−	0.750817i
$345$		0			0
$346$	−39.0700	−	22.5571i	−2.10042	−	1.21268i
$347$	−4.54739	−	7.87631i	−0.244117	−	0.422822i	0.717766	−	0.696284i	$-0.245165\pi$
$347$	−4.54739	−	7.87631i	−0.244117	−	0.422822i	−0.961883	+	0.273462i	$0.911831\pi$
$348$		0			0
$349$	7.98521	−	4.61026i	0.427439	−	0.246782i	−0.270816	−	0.962631i	$-0.587294\pi$
$349$	7.98521	−	4.61026i	0.427439	−	0.246782i	0.698255	+	0.715849i	$0.253960\pi$
$350$	9.87149	−	24.1553i	0.527653	−	1.29116i
$351$		0			0
$352$	−3.97674	−	6.88792i	−0.211961	−	0.367127i
$353$			2.15449i			0.114672i	0.998355	+	0.0573359i	$0.0182606\pi$
$353$			2.15449i			0.114672i	−0.998355	+	0.0573359i	$0.981739\pi$
$354$		0			0
$355$	−12.0433			−0.639195
$356$		−	57.8752i		−	3.06738i
$357$		0			0
$358$	5.77128	+	3.33205i	0.305021	+	0.176104i
$359$	−7.41107	+	4.27878i	−0.391141	+	0.225825i	−0.682654	−	0.730741i	$-0.739175\pi$
$359$	−7.41107	+	4.27878i	−0.391141	+	0.225825i	0.291513	+	0.956567i	$0.405841\pi$
$360$		0			0
$361$	18.9978			0.999882
$362$	2.72881	+	1.57548i	0.143423	+	0.0828055i
$363$		0			0
$364$	−16.6809	−	26.7538i	−0.874315	−	1.40228i
$365$	−5.72896			−0.299867
$366$		0			0
$367$	2.29823			0.119967			0.0599833	−	0.998199i	$-0.480895\pi$
$367$	2.29823			0.119967			0.0599833	+	0.998199i	$0.480895\pi$
$368$	1.22438	+	2.12070i	0.0638255	+	0.110549i
$369$		0			0
$370$	11.3273	+	6.53979i	0.588876	+	0.339988i
$371$	−0.970225	−	7.10888i	−0.0503716	−	0.369075i
$372$		0			0
$373$	11.7684			0.609343			0.304672	−	0.952457i	$-0.401453\pi$
$373$	11.7684			0.609343			0.304672	+	0.952457i	$0.401453\pi$
$374$	−7.17271			−0.370892
$375$		0			0
$376$	0.541073	+	0.937166i	0.0279037	+	0.0483307i
$377$	0.497847	−	4.87715i	0.0256404	−	0.251186i
$378$		0			0
$379$	−6.92034	+	3.99546i	−0.355474	+	0.205233i	−0.667094	−	0.744974i	$-0.732462\pi$
$379$	−6.92034	+	3.99546i	−0.355474	+	0.205233i	0.311619	+	0.950207i	$0.399129\pi$
$380$	−0.0664059	+	0.115018i	−0.00340655	+	0.00590032i
$381$		0			0
$382$	−3.01846	−	1.74271i	−0.154438	−	0.0891647i
$383$			28.2446i			1.44323i	0.692294	+	0.721616i	$0.256600\pi$
$383$			28.2446i			1.44323i	−0.692294	+	0.721616i	$0.743400\pi$
$384$		0			0
$385$	3.11975	+	1.27494i	0.158997	+	0.0649770i
$386$	8.00839	−	13.8709i	0.407616	−	0.706012i
$387$		0			0
$388$			1.40870i			0.0715161i
$389$	−3.84043	+	6.65182i	−0.194717	+	0.337261i	−0.946808	−	0.321799i	$-0.895712\pi$
$389$	−3.84043	+	6.65182i	−0.194717	+	0.337261i	0.752090	+	0.659060i	$0.229046\pi$
$390$		0			0
$391$	−16.1957			−0.819050
$392$	−20.3747	−	5.25276i	−1.02908	−	0.265304i
$393$		0			0
$394$	−35.6481			−1.79593
$395$	−8.55513	−	4.93931i	−0.430455	−	0.248524i
$396$		0			0
$397$			7.45281i			0.374046i	0.982356	+	0.187023i	$0.0598839\pi$
$397$			7.45281i			0.374046i	−0.982356	+	0.187023i	$0.940116\pi$
$398$		−	15.2368i		−	0.763750i
$399$		0			0
$400$	−0.670563	−	1.16145i	−0.0335282	−	0.0580725i
$401$	15.7601	+	9.09912i	0.787024	+	0.454389i	0.838914	−	0.544264i	$-0.183191\pi$
$401$	15.7601	+	9.09912i	0.787024	+	0.454389i	−0.0518898	+	0.998653i	$0.516524\pi$
$402$		0			0
$403$	−11.6058	−	25.8584i	−0.578126	−	1.28810i
$404$	15.9798	+	27.6778i	0.795025	+	1.37702i
$405$		0			0
$406$	−5.07525	−	6.54964i	−0.251880	−	0.325053i
$407$	5.03804	−	8.72615i	0.249727	−	0.432539i
$408$		0			0
$409$	−25.3594	+	14.6413i	−1.25394	+	0.723964i	−0.971890	−	0.235435i	$-0.924349\pi$
$409$	−25.3594	+	14.6413i	−1.25394	+	0.723964i	−0.282053	+	0.959399i	$0.591015\pi$
$410$	−16.9320	+	9.77568i	−0.836211	+	0.482787i
$411$		0			0
$412$	16.4892	−	28.5602i	0.812365	−	1.40706i
$413$	−1.64264	+	4.01950i	−0.0808291	+	0.197787i
$414$		0			0
$415$	4.88728	+	8.46502i	0.239907	+	0.415531i
$416$	18.9759	+	1.93701i	0.930372	+	0.0949698i
$417$		0			0
$418$	0.142225	+	0.0821139i	0.00695647	+	0.00401632i
$419$	−10.3697	−	17.9608i	−0.506591	−	0.877441i	−0.999971	−	0.00762733i	$-0.997572\pi$
$419$	−10.3697	−	17.9608i	−0.506591	−	0.877441i	0.493380	−	0.869814i	$-0.335761\pi$
$420$		0			0
$421$			24.8696i			1.21207i	0.795437	+	0.606036i	$0.207241\pi$
$421$			24.8696i			1.21207i	−0.795437	+	0.606036i	$0.792759\pi$
$422$		−	18.6433i		−	0.907541i
$423$		0			0
$424$	−7.05923	−	4.07565i	−0.342826	−	0.197931i
$425$	8.86994			0.430255
$426$		0			0
$427$	9.45698	−	7.32812i	0.457655	−	0.354632i
$428$	32.5950			1.57554
$429$		0			0
$430$	−9.04115	+	15.6597i	−0.436003	+	0.755179i
$431$		−	21.1688i		−	1.01966i	−0.860274	−	0.509832i	$-0.829708\pi$
$431$		−	21.1688i		−	1.01966i	0.860274	−	0.509832i	$-0.170292\pi$
$432$		0			0
$433$	−11.7148	+	20.2906i	−0.562977	+	0.975105i	0.434258	+	0.900789i	$0.357011\pi$
$433$	−11.7148	+	20.2906i	−0.562977	+	0.975105i	−0.997235	+	0.0743163i	$0.976323\pi$
$434$	−44.3442	−	18.1220i	−2.12859	−	0.869885i
$435$		0			0
$436$			38.3566i			1.83695i
$437$	0.321139	+	0.185409i	0.0153621	+	0.00886934i
$438$		0			0
$439$	−6.01919	+	10.4256i	−0.287280	+	0.497584i	−0.973160	−	0.230131i	$-0.926085\pi$
$439$	−6.01919	+	10.4256i	−0.287280	+	0.497584i	0.685879	+	0.727715i	$0.259418\pi$
$440$	3.31593	−	1.91445i	0.158081	−	0.0912680i
$441$		0			0
$442$	10.0694	−	13.9470i	0.478952	−	0.663390i
$443$	7.86656	+	13.6253i	0.373752	+	0.647357i	0.990139	−	0.140086i	$-0.0447379\pi$
$443$	7.86656	+	13.6253i	0.373752	+	0.647357i	−0.616388	+	0.787443i	$0.711405\pi$
$444$		0			0
$445$	−14.8371			−0.703346
$446$	−36.9860			−1.75134
$447$		0			0
$448$	26.7932	−	20.7618i	1.26586	−	0.980902i
$449$	−22.5177	−	13.0006i	−1.06268	−	0.613536i	−0.136504	−	0.990640i	$-0.543587\pi$
$449$	−22.5177	−	13.0006i	−1.06268	−	0.613536i	−0.926171	+	0.377104i	$0.876920\pi$
$450$		0			0
$451$	7.53087	+	13.0438i	0.354615	+	0.614211i
$452$	−11.4935			−0.540610
$453$		0			0
$454$	−2.98459			−0.140074
$455$	−6.85871	+	4.27637i	−0.321541	+	0.200479i
$456$		0			0
$457$	26.6700	+	15.3979i	1.24757	+	0.720284i	0.970624	−	0.240602i	$-0.0773448\pi$
$457$	26.6700	+	15.3979i	1.24757	+	0.720284i	0.276945	+	0.960886i	$0.410678\pi$
$458$	47.9483			2.24048
$459$		0			0
$460$	18.9616	−	10.9475i	0.884088	−	0.510429i
$461$	29.5278	+	17.0479i	1.37525	+	0.794000i	0.991583	−	0.129472i	$-0.0413284\pi$
$461$	29.5278	+	17.0479i	1.37525	+	0.794000i	0.383665	+	0.923472i	$0.374662\pi$
$462$		0			0
$463$		−	1.69184i		−	0.0786263i	−0.999227	−	0.0393131i	$-0.987483\pi$
$463$		−	1.69184i		−	0.0786263i	0.999227	−	0.0393131i	$-0.0125170\pi$
$464$	−0.425852			−0.0197697
$465$		0			0
$466$		−	30.6433i		−	1.41952i
$467$	−14.1762	−	24.5539i	−0.655996	−	1.13622i	−0.981643	−	0.190727i	$-0.938916\pi$
$467$	−14.1762	−	24.5539i	−0.655996	−	1.13622i	0.325647	−	0.945491i	$-0.394418\pi$
$468$		0			0
$469$	3.31027	+	4.27192i	0.152854	+	0.197259i
$470$	0.608453	−	0.351290i	0.0280658	−	0.0162038i
$471$		0			0
$472$	2.46659	+	4.27226i	0.113534	+	0.196647i
$473$	12.0637	+	6.96501i	0.554692	+	0.320251i
$474$		0			0
$475$	−0.175879	−	0.101544i	−0.00806989	−	0.00465915i
$476$	−2.44936	−	17.9466i	−0.112266	−	0.822581i
$477$		0			0
$478$	15.3918	−	26.6595i	0.704007	−	1.21938i
$479$			6.28246i			0.287053i	0.989646	+	0.143526i	$0.0458442\pi$
$479$			6.28246i			0.287053i	−0.989646	+	0.143526i	$0.954156\pi$
$480$		0			0
$481$	9.89490	+	22.0464i	0.451169	+	1.00523i
$482$	1.92128			0.0875117
$483$		0			0
$484$	14.4427	+	25.0154i	0.656484	+	1.13706i
$485$	0.361140			0.0163985
$486$		0			0
$487$	−11.2736	+	6.50879i	−0.510854	+	0.294942i	−0.733185	−	0.680030i	$-0.761967\pi$
$487$	−11.2736	+	6.50879i	−0.510854	+	0.294942i	0.222331	+	0.974971i	$0.428634\pi$
$488$		−	13.5923i		−	0.615293i
$489$		0			0
$490$	−3.41034	+	13.2282i	−0.154063	+	0.597591i
$491$	6.17616	+	10.6974i	0.278726	+	0.482768i	0.971068	−	0.238801i	$-0.0767544\pi$
$491$	6.17616	+	10.6974i	0.278726	+	0.482768i	−0.692342	+	0.721569i	$0.743421\pi$
$492$		0			0
$493$	1.40825	−	2.43916i	0.0634244	−	0.109854i
$494$	−0.359329	+	0.161275i	−0.0161670	+	0.00725609i
$495$		0			0
$496$	−2.13218	+	1.23102i	−0.0957378	+	0.0552743i
$497$	−37.2611	+	5.08542i	−1.67139	+	0.228112i
$498$		0			0
$499$	−7.92708	+	4.57670i	−0.354865	+	0.204881i	−0.666826	−	0.745214i	$-0.732348\pi$
$499$	−7.92708	+	4.57670i	−0.354865	+	0.204881i	0.311961	+	0.950095i	$0.399014\pi$
$500$	−22.5105	+	12.9965i	−1.00670	+	0.581220i
$501$		0			0
$502$	54.3993	−	31.4074i	2.42796	−	1.40178i
$503$	11.2519	−	19.4888i	0.501696	−	0.868963i	−0.498302	−	0.867003i	$-0.666043\pi$
$503$	11.2519	−	19.4888i	0.501696	−	0.868963i	0.999998	−	0.00195935i	$-0.000623680\pi$
$504$		0			0
$505$	7.09559	−	4.09664i	0.315750	−	0.182298i
$506$	−13.5370	−	23.4469i	−0.601795	−	1.04234i
$507$		0			0
$508$	25.9443	−	44.9368i	1.15109	−	1.99375i
$509$	33.4811	+	19.3303i	1.48402	+	0.856800i	0.999835	−	0.0181646i	$-0.00578229\pi$
$509$	33.4811	+	19.3303i	1.48402	+	0.856800i	0.484187	+	0.874965i	$0.339116\pi$
$510$		0			0
$511$	−17.7249	+	2.41911i	−0.784104	+	0.107015i
$512$		−	3.53972i		−	0.156435i
$513$		0			0
$514$	13.0690	−	7.54536i	0.576447	−	0.332812i
$515$	−7.32179	−	4.22724i	−0.322637	−	0.186274i
$516$		0			0
$517$	−0.270623	−	0.468732i	−0.0119020	−	0.0206148i
$518$	37.8071	+	15.4505i	1.66115	+	0.678857i
$519$		0			0
$520$	−0.932502	+	9.13525i	−0.0408929	+	0.400607i
$521$	20.1176	−	34.8446i	0.881366	−	1.52657i	0.0315430	−	0.999502i	$-0.489958\pi$
$521$	20.1176	−	34.8446i	0.881366	−	1.52657i	0.849823	−	0.527068i	$-0.176709\pi$
$522$		0			0
$523$	0.366073	−	0.634057i	0.0160073	−	0.0277254i	−0.857911	−	0.513799i	$-0.828238\pi$
$523$	0.366073	−	0.634057i	0.0160073	−	0.0277254i	0.873918	+	0.486073i	$0.161571\pi$
$524$	4.20594	−	7.28491i	0.183737	−	0.318243i
$525$		0			0
$526$	−45.0581	−	26.0143i	−1.96463	−	1.13428i
$527$		−	16.2834i		−	0.709316i
$528$		0			0
$529$	−19.0660	−	33.0234i	−0.828959	−	1.43580i
$530$	−2.64610	+	4.58319i	−0.114939	+	0.199081i
$531$		0			0
$532$	−0.156887	+	0.383898i	−0.00680189	+	0.0166441i
$533$	−35.9353	−	3.66817i	−1.55653	−	0.158886i
$534$		0			0
$535$		−	8.35618i		−	0.361269i
$536$	6.13993			0.265204
$537$		0			0
$538$		−	36.8553i		−	1.58894i
$539$	10.1906	+	2.62722i	0.438940	+	0.113162i
$540$		0			0
$541$	20.4847	−	11.8268i	0.880705	−	0.508476i	0.00981448	−	0.999952i	$-0.496876\pi$
$541$	20.4847	−	11.8268i	0.880705	−	0.508476i	0.870891	+	0.491476i	$0.163543\pi$
$542$	10.0876	+	17.4722i	0.433298	+	0.750494i
$543$		0			0
$544$	9.49024	+	5.47919i	0.406891	+	0.234918i
$545$	9.83325			0.421210
$546$		0			0
$547$	−12.9472			−0.553582			−0.276791	−	0.960930i	$-0.589271\pi$
$547$	−12.9472			−0.553582			−0.276791	+	0.960930i	$0.589271\pi$
$548$	5.33730	+	3.08149i	0.227998	+	0.131635i
$549$		0			0
$550$	7.41388	+	12.8412i	0.316129	+	0.547552i
$551$	−0.0558475	+	0.0322436i	−0.00237918	+	0.00137362i
$552$		0			0
$553$	−28.5545	−	11.6693i	−1.21426	−	0.496230i
$554$			45.8771i			1.94913i
$555$		0			0
$556$	−51.5891			−2.18787
$557$			6.40680i			0.271465i	0.990746	+	0.135732i	$0.0433388\pi$
$557$			6.40680i			0.271465i	−0.990746	+	0.135732i	$0.956661\pi$
$558$		0			0
$559$	−30.4787	+	13.6795i	−1.28911	+	0.578582i
$560$	0.430045	+	0.554975i	0.0181727	+	0.0234520i
$561$		0			0
$562$	−16.1498	+	27.9723i	−0.681239	+	1.17994i
$563$	−3.66042	−	6.34004i	−0.154268	−	0.267201i	0.778524	−	0.627615i	$-0.215969\pi$
$563$	−3.66042	−	6.34004i	−0.154268	−	0.267201i	−0.932792	+	0.360414i	$0.882635\pi$
$564$		0			0
$565$			2.94652i			0.123961i
$566$	2.01980	+	1.16613i	0.0848986	+	0.0490162i
$567$		0			0
$568$	−21.3625	+	37.0009i	−0.896349	+	1.55252i
$569$	2.15872	−	3.73901i	0.0904981	−	0.156747i	−0.817223	−	0.576322i	$-0.804487\pi$
$569$	2.15872	−	3.73901i	0.0904981	−	0.156747i	0.907721	+	0.419575i	$0.137821\pi$
$570$		0			0
$571$	17.0847	−	29.5916i	0.714974	−	1.23837i	−0.247996	−	0.968761i	$-0.579772\pi$
$571$	17.0847	−	29.5916i	0.714974	−	1.23837i	0.962970	−	0.269610i	$-0.0868946\pi$
$572$	17.8226	+	1.81929i	0.745202	+	0.0760682i
$573$		0			0
$574$	−48.2582	+	37.3948i	−2.01426	+	1.56083i
$575$	16.7402	+	28.9949i	0.698115	+	1.20917i
$576$		0			0
$577$	5.50494	+	3.17828i	0.229174	+	0.132314i	0.610191	−	0.792254i	$-0.291093\pi$
$577$	5.50494	+	3.17828i	0.229174	+	0.132314i	−0.381017	+	0.924568i	$0.624426\pi$
$578$	−25.3511	+	14.6364i	−1.05447	+	0.608796i
$579$		0			0
$580$			3.80763i			0.158103i
$581$	18.6953	+	24.1263i	0.775610	+	1.00093i
$582$		0			0
$583$	3.53074	+	2.03847i	0.146228	+	0.0844249i
$584$	−10.1620	+	17.6011i	−0.420507	+	0.728339i
$585$		0			0
$586$	−0.229446	−	0.397412i	−0.00947832	−	0.0164169i
$587$	−27.2036	+	15.7060i	−1.12281	+	0.648256i	−0.942118	−	0.335283i	$-0.891168\pi$
$587$	−27.2036	+	15.7060i	−1.12281	+	0.648256i	−0.180695	+	0.983539i	$0.557835\pi$
$588$		0			0
$589$	−0.186414	+	0.322878i	−0.00768104	+	0.0133040i
$590$	2.77376	−	1.60143i	0.114194	−	0.0659298i
$591$		0			0
$592$	1.81786	−	1.04954i	0.0747136	−	0.0431359i
$593$	0.409641	−	0.236506i	0.0168219	−	0.00971215i	−0.491565	−	0.870841i	$-0.663575\pi$
$593$	0.409641	−	0.236506i	0.0168219	−	0.00971215i	0.508387	+	0.861128i	$0.330242\pi$
$594$		0			0
$595$	−4.60086	+	0.627928i	−0.188617	+	0.0257425i
$596$	18.2143	−	10.5160i	0.746086	−	0.430753i
$597$		0			0
$598$	64.5951	+	6.59369i	2.64149	+	0.269636i
$599$	−4.81348	+	8.33719i	−0.196673	+	0.340648i	−0.947448	−	0.319910i	$-0.896347\pi$
$599$	−4.81348	+	8.33719i	−0.196673	+	0.340648i	0.750774	+	0.660559i	$0.229680\pi$
$600$		0			0
$601$	20.5399	+	35.5762i	0.837842	+	1.45118i	0.891696	+	0.452635i	$0.149516\pi$
$601$	20.5399	+	35.5762i	0.837842	+	1.45118i	−0.0538542	+	0.998549i	$0.517151\pi$
$602$	−21.3601	+	52.2676i	−0.870572	+	2.13027i
$603$		0			0
$604$		−	2.19485i		−	0.0893073i
$605$	6.41304	−	3.70257i	0.260727	−	0.150531i
$606$		0			0
$607$	19.0858			0.774668			0.387334	−	0.921939i	$-0.373396\pi$
$607$	19.0858			0.774668			0.387334	+	0.921939i	$0.373396\pi$
$608$	−0.125453	−	0.217290i	−0.00508777	−	0.00881228i
$609$		0			0
$610$	−8.82474			−0.357303
$611$	1.29134	+	0.131816i	0.0522419	+	0.00533271i
$612$		0			0
$613$			38.0048i			1.53500i	0.641049	+	0.767500i	$0.278499\pi$
$613$			38.0048i			1.53500i	−0.641049	+	0.767500i	$0.721501\pi$
$614$	31.3249	−	54.2563i	1.26417	−	2.18961i
$615$		0			0
$616$	9.45082	−	7.32335i	0.380784	−	0.295066i
$617$	−7.20117	−	4.15759i	−0.289908	−	0.167378i	0.347992	−	0.937497i	$-0.386864\pi$
$617$	−7.20117	−	4.15759i	−0.289908	−	0.167378i	−0.637900	+	0.770119i	$0.720197\pi$
$618$		0			0
$619$	38.5146	+	22.2364i	1.54803	+	0.893756i	0.998292	+	0.0584199i	$0.0186062\pi$
$619$	38.5146	+	22.2364i	1.54803	+	0.893756i	0.549739	+	0.835336i	$0.314727\pi$
$620$	11.0068	+	19.0643i	0.442042	+	0.765640i
$621$		0			0
$622$	54.0579	−	31.2103i	2.16752	−	1.25142i
$623$	−45.9048	+	6.26512i	−1.83914	+	0.251007i
$624$		0			0
$625$	−7.37342	−	12.7711i	−0.294937	−	0.510845i
$626$		−	50.8526i		−	2.03248i
$627$		0			0
$628$	54.7842			2.18613
$629$			13.8829i			0.553549i
$630$		0			0
$631$	−10.1779	−	5.87622i	−0.405177	−	0.233929i	0.283539	−	0.958961i	$-0.408492\pi$
$631$	−10.1779	−	5.87622i	−0.405177	−	0.233929i	−0.688715	+	0.725032i	$0.741825\pi$
$632$	−30.3501	+	17.5227i	−1.20726	+	0.697014i
$633$		0			0
$634$	16.2800			0.646562
$635$	−11.5202	−	6.65117i	−0.457164	−	0.263944i
$636$		0			0
$637$	−19.4145	+	16.1269i	−0.769231	+	0.638971i
$638$	4.70831			0.186404
$639$		0			0
$640$	−16.0371			−0.633921
$641$	−5.24342	−	9.08186i	−0.207102	−	0.358712i	0.743698	−	0.668516i	$-0.233070\pi$
$641$	−5.24342	−	9.08186i	−0.207102	−	0.358712i	−0.950801	+	0.309804i	$0.899737\pi$
$642$		0			0
$643$	27.0912	+	15.6411i	1.06837	+	0.616825i	0.927736	−	0.373237i	$-0.121752\pi$
$643$	27.0912	+	15.6411i	1.06837	+	0.616825i	0.140635	+	0.990061i	$0.455085\pi$
$644$	54.0428	−	41.8773i	2.12959	−	1.65020i
$645$		0			0
$646$	−0.226275			−0.00890265
$647$	−26.8675			−1.05627			−0.528135	−	0.849160i	$-0.677109\pi$
$647$	−26.8675			−1.05627			−0.528135	+	0.849160i	$0.677109\pi$
$648$		0			0
$649$	−1.23369	−	2.13681i	−0.0484265	−	0.0838772i
$650$	−35.3770	−	3.61119i	−1.38760	−	0.141643i
$651$		0			0
$652$	−25.9070	+	14.9574i	−1.01459	+	0.585776i
$653$	−2.07081	+	3.58674i	−0.0810369	+	0.140360i	−0.903696	−	0.428176i	$-0.859156\pi$
$653$	−2.07081	+	3.58674i	−0.0810369	+	0.140360i	0.822659	+	0.568536i	$0.192490\pi$
$654$		0			0
$655$	−1.86759	−	1.07825i	−0.0729726	−	0.0421308i
$656$			3.13771i			0.122507i
$657$		0			0
$658$	1.73417	−	1.34379i	0.0676048	−	0.0523863i
$659$	10.7276	−	18.5807i	0.417887	−	0.723801i	−0.577840	−	0.816150i	$-0.696104\pi$
$659$	10.7276	−	18.5807i	0.417887	−	0.723801i	0.995727	+	0.0923492i	$0.0294376\pi$
$660$		0			0
$661$			42.3872i			1.64867i	0.566102	+	0.824335i	$0.308451\pi$
$661$			42.3872i			1.64867i	−0.566102	+	0.824335i	$0.691549\pi$
$662$	7.58763	−	13.1422i	0.294902	−	0.510785i
$663$		0			0
$664$	34.6762			1.34570
$665$	0.0984174	+	0.0402200i	0.00381646	+	0.00155967i
$666$		0			0
$667$	10.6312			0.411640
$668$	7.60673	+	4.39175i	0.294313	+	0.169922i
$669$		0			0
$670$		−	3.98633i		−	0.154005i
$671$			6.79830i			0.262445i
$672$		0			0
$673$	−14.7928	−	25.6219i	−0.570220	−	0.987650i	−0.996543	−	0.0830790i	$-0.973525\pi$
$673$	−14.7928	−	25.6219i	−0.570220	−	0.987650i	0.426323	−	0.904571i	$-0.359809\pi$
$674$	8.42336	+	4.86323i	0.324456	+	0.187324i
$675$		0			0
$676$	−28.5578	+	32.1012i	−1.09838	+	1.23466i
$677$	16.0830	+	27.8565i	0.618118	+	1.07061i	0.989829	+	0.142263i	$0.0454380\pi$
$677$	16.0830	+	27.8565i	0.618118	+	1.07061i	−0.371711	+	0.928349i	$0.621229\pi$
$678$		0			0
$679$	1.11734	−	0.152495i	0.0428795	−	0.00585223i
$680$	−2.63775	+	4.56872i	−0.101153	+	0.175202i
$681$		0			0
$682$	23.5738	−	13.6104i	0.902689	−	0.521168i
$683$	7.44986	−	4.30118i	0.285061	−	0.164580i	−0.350651	−	0.936506i	$-0.614040\pi$
$683$	7.44986	−	4.30118i	0.285061	−	0.164580i	0.635712	+	0.771926i	$0.280706\pi$
$684$		0			0
$685$	0.789983	−	1.36829i	0.0301837	−	0.0522797i
$686$	−4.96555	+	42.3671i	−0.189586	+	1.61758i
$687$		0			0
$688$	1.45097	+	2.51316i	0.0553179	+	0.0958134i
$689$	−8.92031	+	4.00363i	−0.339837	+	0.152526i
$690$		0			0
$691$	17.7033	+	10.2210i	0.673466	+	0.388826i	0.797388	−	0.603466i	$-0.206214\pi$
$691$	17.7033	+	10.2210i	0.673466	+	0.388826i	−0.123923	+	0.992292i	$0.539548\pi$
$692$	32.3680	+	56.0629i	1.23044	+	2.13119i
$693$		0			0
$694$			20.9477i			0.795164i
$695$			13.2256i			0.501675i
$696$		0			0
$697$	−17.9719	−	10.3761i	−0.680736	−	0.393023i
$698$	−21.2373			−0.803845
$699$		0			0
$700$	−29.5978	+	22.9351i	−1.11869	+	0.866864i
$701$	25.1373			0.949422			0.474711	−	0.880142i	$-0.342553\pi$
$701$	25.1373			0.949422			0.474711	+	0.880142i	$0.342553\pi$
$702$		0			0
$703$	0.158933	−	0.275280i	0.00599427	−	0.0103824i
$704$			19.2607i			0.725915i
$705$		0			0
$706$	2.48118	−	4.29753i	0.0933804	−	0.161740i
$707$	20.2233	−	15.6709i	0.760576	−	0.589363i
$708$		0			0
$709$		−	29.4929i		−	1.10763i	−0.832640	−	0.553814i	$-0.813172\pi$
$709$		−	29.4929i		−	1.10763i	0.832640	−	0.553814i	$-0.186828\pi$
$710$	24.0227	+	13.8695i	0.901556	+	0.520514i
$711$		0			0
$712$	−26.3180	+	45.5841i	−0.986309	+	1.70834i
$713$	53.2287	−	30.7316i	1.99343	−	1.15091i
$714$		0			0
$715$	0.466399	−	4.56908i	0.0174423	−	0.170874i
$716$	−4.78127	−	8.28140i	−0.178684	−	0.309491i
$717$		0			0
$718$	19.7104			0.735584
$719$	−8.33153			−0.310713			−0.155357	−	0.987858i	$-0.549653\pi$
$719$	−8.33153			−0.310713			−0.155357	+	0.987858i	$0.549653\pi$
$720$		0			0
$721$	−24.4380	−	9.98702i	−0.910118	−	0.371936i
$722$	−37.8946	−	21.8784i	−1.41029	−	0.814231i
$723$		0			0
$724$	−2.26071	−	3.91567i	−0.0840188	−	0.145525i
$725$	−5.82240			−0.216239
$726$		0			0
$727$	9.66141			0.358322			0.179161	−	0.983820i	$-0.442662\pi$
$727$	9.66141			0.358322			0.179161	+	0.983820i	$0.442662\pi$
$728$	0.972369	+	28.6575i	0.0360384	+	1.06212i
$729$		0			0
$730$	11.4275	+	6.59766i	0.422950	+	0.244190i
$731$	−19.1929			−0.709875
$732$		0			0
$733$	12.1398	−	7.00894i	0.448395	−	0.258881i	−0.258757	−	0.965942i	$-0.583313\pi$
$733$	12.1398	−	7.00894i	0.448395	−	0.258881i	0.707152	+	0.707061i	$0.249980\pi$
$734$	−4.58425	−	2.64672i	−0.169208	−	0.0976921i
$735$		0			0
$736$			41.3635i			1.52468i
$737$	−3.07094			−0.113120
$738$		0			0
$739$		−	38.8147i		−	1.42782i	−0.700237	−	0.713910i	$-0.746923\pi$
$739$		−	38.8147i		−	1.42782i	0.700237	−	0.713910i	$-0.253077\pi$
$740$	−9.38417	−	16.2539i	−0.344969	−	0.597504i
$741$		0			0
$742$	−6.25153	+	15.2973i	−0.229501	+	0.561583i
$743$	−29.7863	+	17.1971i	−1.09275	+	0.630901i	−0.934308	−	0.356467i	$-0.883981\pi$
$743$	−29.7863	+	17.1971i	−1.09275	+	0.630901i	−0.158445	+	0.987368i	$0.550648\pi$
$744$		0			0
$745$	−2.69592	−	4.66948i	−0.0987710	−	0.171076i
$746$	−23.4742	−	13.5528i	−0.859452	−	0.496205i
$747$		0			0
$748$	8.91346	+	5.14619i	0.325908	+	0.188163i
$749$	−3.52848	−	25.8533i	−0.128928	−	0.944660i
$750$		0			0
$751$	24.0735	−	41.6965i	0.878454	−	1.52153i	0.0254165	−	0.999677i	$-0.491909\pi$
$751$	24.0735	−	41.6965i	0.878454	−	1.52153i	0.853037	−	0.521850i	$-0.174758\pi$
$752$		−	0.112754i		−	0.00411172i
$753$		0			0
$754$	−6.60974	+	9.15506i	−0.240713	+	0.333408i
$755$	−0.562681			−0.0204781
$756$		0			0
$757$	3.45319	+	5.98110i	0.125508	+	0.217387i	0.921931	−	0.387353i	$-0.126611\pi$
$757$	3.45319	+	5.98110i	0.125508	+	0.217387i	−0.796423	+	0.604740i	$0.793277\pi$
$758$	18.4052			0.668508
$759$		0			0
$760$	0.104606	−	0.0603945i	0.00379447	−	0.00219074i
$761$			31.9730i			1.15902i	0.814965	+	0.579511i	$0.196756\pi$
$761$			31.9730i			1.15902i	−0.814965	+	0.579511i	$0.803244\pi$
$762$		0			0
$763$	30.4232	−	4.15219i	1.10139	−	0.150319i
$764$	2.50067	+	4.33129i	0.0904712	+	0.156701i
$765$		0			0
$766$	32.5274	−	56.3391i	1.17526	−	2.03562i
$767$	5.88683	+	0.600911i	0.212561	+	0.0216976i
$768$		0			0
$769$	12.4665	−	7.19752i	0.449553	−	0.259549i	−0.258089	−	0.966121i	$-0.583093\pi$
$769$	12.4665	−	7.19752i	0.449553	−	0.259549i	0.707641	+	0.706572i	$0.249759\pi$
$770$	−4.75466	−	6.13592i	−0.171346	−	0.221123i
$771$		0			0
$772$	−19.9039	+	11.4915i	−0.716357	+	0.413589i
$773$	32.2829	−	18.6385i	1.16114	−	0.670382i	0.209560	−	0.977796i	$-0.432797\pi$
$773$	32.2829	−	18.6385i	1.16114	−	0.670382i	0.951576	+	0.307414i	$0.0994636\pi$
$774$		0			0
$775$	−29.1520	+	16.8309i	−1.04717	+	0.604583i
$776$	0.640590	−	1.10953i	0.0229958	−	0.0398300i
$777$		0			0
$778$	15.3209	−	8.84553i	0.549281	−	0.317128i
$779$	0.237573	+	0.411489i	0.00851194	+	0.0147431i
$780$		0			0
$781$	10.6846	−	18.5063i	0.382326	−	0.662208i
$782$	32.3053	+	18.6515i	1.15524	+	0.666975i
$783$		0			0
$784$	1.56487	+	1.53546i	0.0558881	+	0.0548377i
$785$		−	14.0447i		−	0.501276i
$786$		0			0
$787$	−12.4263	+	7.17430i	−0.442948	+	0.255736i	−0.704847	−	0.709359i	$-0.748985\pi$
$787$	−12.4263	+	7.17430i	−0.442948	+	0.255736i	0.261899	+	0.965095i	$0.415651\pi$
$788$	44.2996	+	25.5764i	1.57811	+	0.911120i
$789$		0			0
$790$	11.3765	+	19.7047i	0.404759	+	0.701064i
$791$	1.24420	+	9.11630i	0.0442386	+	0.324138i
$792$		0			0
$793$	−13.2189	−	9.54376i	−0.469418	−	0.338909i
$794$	8.58291	−	14.8660i	0.304596	−	0.527576i
$795$		0			0
$796$	−10.9319	+	18.9346i	−0.387470	+	0.671118i
$797$	−5.54219	+	9.59935i	−0.196314	+	0.340026i	−0.947331	−	0.320257i	$-0.896231\pi$
$797$	−5.54219	+	9.59935i	−0.196314	+	0.340026i	0.751016	+	0.660284i	$0.229564\pi$
$798$		0			0
$799$	0.645824	+	0.372866i	0.0228476	+	0.0131911i
$800$		−	22.6537i		−	0.800929i
$801$		0			0
$802$	−20.9577	−	36.2998i	−0.740042	−	1.28179i
$803$	5.08262	−	8.80336i	0.179362	−	0.310664i
$804$		0			0
$805$	−10.7358	−	13.8546i	−0.378388	−	0.488312i
$806$	−6.62941	+	64.9450i	−0.233511	+	2.28759i
$807$		0			0
$808$		−	29.0665i		−	1.02255i
$809$	42.5536			1.49610			0.748052	−	0.663640i	$-0.230989\pi$
$809$	42.5536			1.49610			0.748052	+	0.663640i	$0.230989\pi$
$810$		0			0
$811$			16.3622i			0.574554i	0.957848	+	0.287277i	$0.0927500\pi$
$811$			16.3622i			0.574554i	−0.957848	+	0.287277i	$0.907250\pi$
$812$	1.60781	+	11.7805i	0.0564231	+	0.413414i
$813$		0			0
$814$	−20.0986	+	11.6040i	−0.704457	+	0.406719i
$815$	3.83453	+	6.64160i	0.134318	+	0.232645i
$816$		0			0
$817$	0.380570	+	0.219722i	0.0133145	+	0.00768710i
$818$	67.4455			2.35818
$819$		0			0
$820$	28.0549			0.979721
$821$	−2.68944	−	1.55275i	−0.0938621	−	0.0541913i	0.452334	−	0.891848i	$-0.350591\pi$
$821$	−2.68944	−	1.55275i	−0.0938621	−	0.0541913i	−0.546196	+	0.837657i	$0.683925\pi$
$822$		0			0
$823$	24.5082	+	42.4494i	0.854301	+	1.47969i	0.877292	+	0.479958i	$0.159348\pi$
$823$	24.5082	+	42.4494i	0.854301	+	1.47969i	−0.0229903	+	0.999736i	$0.507319\pi$
$824$	−25.9747	+	14.9965i	−0.904873	+	0.522429i
$825$		0			0
$826$	7.90555	−	6.12593i	0.275069	−	0.213148i
$827$			13.0887i			0.455140i	0.973762	+	0.227570i	$0.0730780\pi$
$827$			13.0887i			0.455140i	−0.973762	+	0.227570i	$0.926922\pi$
$828$		0			0
$829$	−49.2565			−1.71075			−0.855374	−	0.518010i	$-0.826673\pi$
$829$	−49.2565			−1.71075			−0.855374	+	0.518010i	$0.826673\pi$
$830$		−	22.5134i		−	0.781452i
$831$		0			0
$832$	−37.4514	−	27.0391i	−1.29839	−	0.937411i
$833$	−13.9695	+	3.88551i	−0.484015	+	0.134625i
$834$		0			0
$835$	1.12588	−	1.95009i	0.0389629	−	0.0674856i
$836$	−0.117828	−	0.204084i	−0.00407517	−	0.00705840i
$837$		0			0
$838$			47.7682i			1.65012i
$839$	−14.9508	−	8.63182i	−0.516157	−	0.298004i	0.219204	−	0.975679i	$-0.429654\pi$
$839$	−14.9508	−	8.63182i	−0.516157	−	0.298004i	−0.735361	+	0.677676i	$0.762987\pi$
$840$		0			0
$841$	13.5756	−	23.5136i	0.468124	−	0.810815i
$842$	28.6407	−	49.6071i	0.987024	−	1.70957i
$843$		0			0
$844$	−13.3760	+	23.1678i	−0.460419	+	0.797470i
$845$	8.22958	+	7.32117i	0.283106	+	0.251856i
$846$		0			0
$847$	18.2780	−	14.1634i	0.628038	−	0.486661i
$848$	0.424662	+	0.735535i	0.0145829	+	0.0252584i
$849$		0			0
$850$	−17.6928	−	10.2149i	−0.606857	−	0.350369i
$851$	−45.3818	+	26.2012i	−1.55567	+	0.898166i
$852$		0			0
$853$		−	52.4163i		−	1.79470i	−0.441319	−	0.897350i	$-0.645489\pi$
$853$		−	52.4163i		−	1.79470i	0.441319	−	0.897350i	$-0.354511\pi$
$854$	−27.3030	+	3.72634i	−0.934290	+	0.127513i
$855$		0			0
$856$	−25.6728	−	14.8222i	−0.877477	−	0.506611i
$857$	−5.06355	+	8.77032i	−0.172967	+	0.299588i	−0.939456	−	0.342670i	$-0.888669\pi$
$857$	−5.06355	+	8.77032i	−0.172967	+	0.299588i	0.766489	+	0.642258i	$0.222002\pi$
$858$		0			0
$859$	0.255118	+	0.441878i	0.00870452	+	0.0150767i	0.870345	−	0.492443i	$-0.163896\pi$
$859$	0.255118	+	0.441878i	0.00870452	+	0.0150767i	−0.861640	+	0.507519i	$0.830563\pi$
$860$	22.4707	−	12.9735i	0.766244	−	0.442391i
$861$		0			0
$862$	−24.3787	+	42.2251i	−0.830341	+	1.43819i
$863$	−17.7527	+	10.2495i	−0.604310	+	0.348898i	−0.770735	−	0.637156i	$-0.780111\pi$
$863$	−17.7527	+	10.2495i	−0.604310	+	0.348898i	0.166426	+	0.986054i	$0.446777\pi$
$864$		0			0
$865$	14.3725	−	8.29797i	0.488680	−	0.282139i
$866$	46.7347	−	26.9823i	1.58811	−	0.916896i
$867$		0			0
$868$	42.1041	+	54.3356i	1.42911	+	1.84427i
$869$	15.1799	−	8.76412i	0.514943	−	0.297302i
$870$		0			0
$871$	4.31113	−	5.97128i	0.146077	−	0.202329i
$872$	17.4422	−	30.2107i	0.590667	−	1.02306i
$873$		0			0
$874$	−0.427047	−	0.739668i	−0.0144451	−	0.0250196i
$875$	12.7452	+	16.4477i	0.430866	+	0.556035i
$876$		0			0
$877$		−	11.2906i		−	0.381256i	−0.981662	−	0.190628i	$-0.938948\pi$
$877$		−	11.2906i		−	0.381256i	0.981662	−	0.190628i	$-0.0610525\pi$
$878$	24.0128	−	13.8638i	0.810394	−	0.467881i
$879$		0			0
$880$	−0.398953			−0.0134487
$881$	−11.2634	−	19.5088i	−0.379474	−	0.657268i	0.611512	−	0.791235i	$-0.290562\pi$
$881$	−11.2634	−	19.5088i	−0.379474	−	0.657268i	−0.990986	+	0.133967i	$0.957228\pi$
$882$		0			0
$883$	−28.0268			−0.943178			−0.471589	−	0.881819i	$-0.656319\pi$
$883$	−28.0268			−0.943178			−0.471589	+	0.881819i	$0.656319\pi$
$884$	−22.5196	+	10.1073i	−0.757417	+	0.339945i
$885$		0			0
$886$		−	36.2376i		−	1.21743i
$887$	−10.3118	+	17.8605i	−0.346235	+	0.599696i	−0.985577	−	0.169226i	$-0.945873\pi$
$887$	−10.3118	+	17.8605i	−0.346235	+	0.599696i	0.639342	+	0.768922i	$0.279207\pi$
$888$		0			0
$889$	−38.4509	−	15.7137i	−1.28960	−	0.527019i
$890$	29.5954	+	17.0869i	0.992040	+	0.572754i
$891$		0			0
$892$	45.9621	+	26.5362i	1.53893	+	0.888499i
$893$	−0.00853722	−	0.0147869i	−0.000285687	−	0.000494824i
$894$		0			0
$895$	−2.12305	+	1.22574i	−0.0709658	+	0.0409721i
$896$	−49.6174	+	6.77181i	−1.65760	+	0.226230i
$897$		0			0
$898$	29.9438	+	51.8642i	0.999238	+	1.73073i
$899$			10.6887i			0.356489i
$900$		0			0
$901$	−5.61725			−0.187138
$902$		−	34.6912i		−	1.15509i
$903$		0			0
$904$	9.05263	+	5.22654i	0.301086	+	0.173832i
$905$	−1.00384	+	0.579565i	−0.0333686	+	0.0192654i
$906$		0			0
$907$	−41.4631			−1.37676			−0.688379	−	0.725351i	$-0.741678\pi$
$907$	−41.4631			−1.37676			−0.688379	+	0.725351i	$0.741678\pi$
$908$	3.70892	+	2.14134i	0.123085	+	0.0710630i
$909$		0			0
$910$	18.6058	−	0.631308i	0.616776	−	0.0209277i
$911$	−40.8187			−1.35239			−0.676193	−	0.736725i	$-0.736371\pi$
$911$	−40.8187			−1.35239			−0.676193	+	0.736725i	$0.736371\pi$
$912$		0			0
$913$	−17.3436			−0.573990
$914$	−35.4655	−	61.4280i	−1.17309	−	2.03186i
$915$		0			0
$916$	−59.5849	−	34.4014i	−1.96874	−	1.13665i
$917$	−6.23346	−	2.54741i	−0.205847	−	0.0841230i
$918$		0			0
$919$	−48.7678			−1.60870			−0.804350	−	0.594155i	$-0.797486\pi$
$919$	−48.7678			−1.60870			−0.804350	+	0.594155i	$0.797486\pi$
$920$	−19.9129			−0.656509
$921$		0			0
$922$	−39.2659	−	68.0105i	−1.29315	−	2.23981i
$923$	20.9850	+	46.7557i	0.690730	+	1.53898i
$924$		0			0
$925$	24.8544	−	14.3497i	0.817209	−	0.471816i
$926$	−1.94837	+	3.37468i	−0.0640275	+	0.110899i
$927$		0			0
$928$	−6.22958	−	3.59665i	−0.204496	−	0.118066i
$929$			29.3829i			0.964023i	0.876165	+	0.482012i	$0.160094\pi$
$929$			29.3829i			0.964023i	−0.876165	+	0.482012i	$0.839906\pi$
$930$		0			0
$931$	0.321479	+	0.0828796i	0.0105360	+	0.00271627i
$932$	−21.9855	+	38.0801i	−0.720160	+	1.24735i
$933$		0			0
$934$			65.3031i			2.13678i
$935$	1.31930	−	2.28509i	0.0431456	−	0.0747304i
$936$		0			0
$937$	−21.0196			−0.686681			−0.343340	−	0.939211i	$-0.611558\pi$
$937$	−21.0196			−0.686681			−0.343340	+	0.939211i	$0.611558\pi$
$938$	−1.68327	−	12.3334i	−0.0549606	−	0.402699i
$939$		0			0
$940$	−1.00816			−0.0328825
$941$	−20.8740	−	12.0516i	−0.680474	−	0.392872i	0.119560	−	0.992827i	$-0.461852\pi$
$941$	−20.8740	−	12.0516i	−0.680474	−	0.392872i	−0.800034	+	0.599955i	$0.795185\pi$
$942$		0			0
$943$		−	78.3312i		−	2.55081i
$944$		−	0.514013i		−	0.0167297i
$945$		0			0
$946$	−16.0423	−	27.7860i	−0.521579	−	0.903402i
$947$	2.89292	+	1.67023i	0.0940072	+	0.0542751i	0.546267	−	0.837611i	$-0.316049\pi$
$947$	2.89292	+	1.67023i	0.0940072	+	0.0542751i	−0.452259	+	0.891886i	$0.649382\pi$
$948$		0			0
$949$	9.98245	+	22.2415i	0.324044	+	0.721988i
$950$	0.233883	+	0.405097i	0.00758815	+	0.0131431i
$951$		0			0
$952$	−6.23180	+	15.2491i	−0.201974	+	0.494225i
$953$	2.48562	−	4.30522i	0.0805171	−	0.139460i	−0.822955	−	0.568106i	$-0.807676\pi$
$953$	2.48562	−	4.30522i	0.0805171	−	0.139460i	0.903472	+	0.428647i	$0.141009\pi$
$954$		0			0
$955$	1.11039	−	0.641082i	0.0359313	−	0.0207449i
$956$	−38.2546	+	22.0863i	−1.23724	+	0.714322i
$957$		0			0
$958$	7.23509	−	12.5315i	0.233755	−	0.404876i
$959$	1.86637	−	4.56695i	0.0602681	−	0.147475i
$960$		0			0
$961$	15.3981	+	26.6702i	0.496711	+	0.860329i
$962$	5.65211	−	55.3709i	0.182231	−	1.78523i
$963$		0			0
$964$	−2.38755	−	1.37845i	−0.0768978	−	0.0443970i
$965$	2.94601	+	5.10264i	0.0948354	+	0.164260i
$966$		0			0
$967$			47.4943i			1.52731i	0.645623	+	0.763657i	$0.276598\pi$
$967$			47.4943i			1.52731i	−0.645623	+	0.763657i	$0.723402\pi$
$968$		−	26.2705i		−	0.844364i
$969$		0			0
$970$	−0.720362	−	0.415901i	−0.0231294	−	0.0133538i
$971$	−34.4715			−1.10624			−0.553121	−	0.833101i	$-0.686563\pi$
$971$	−34.4715			−1.10624			−0.553121	+	0.833101i	$0.686563\pi$
$972$		0			0
$973$	5.58463	+	40.9188i	0.179035	+	1.31180i
$974$	29.9830			0.960717
$975$		0			0
$976$	−0.708122	+	1.22650i	−0.0226664	+	0.0392594i
$977$			13.3481i			0.427044i	0.976938	+	0.213522i	$0.0684936\pi$
$977$			13.3481i			0.427044i	−0.976938	+	0.213522i	$0.931506\pi$
$978$		0			0
$979$	13.1632	−	22.7993i	0.420698	−	0.728670i
$980$	13.7288	−	13.9918i	0.438551	−	0.446951i
$981$		0			0
$982$		−	28.4507i		−	0.907898i
$983$	−10.8551	−	6.26720i	−0.346224	−	0.199893i	0.316797	−	0.948493i	$-0.397393\pi$
$983$	−10.8551	−	6.26720i	−0.346224	−	0.199893i	−0.663021	+	0.748601i	$0.730726\pi$
$984$		0			0
$985$	6.55685	−	11.3568i	0.208919	−	0.361858i
$986$	−5.61804	+	3.24358i	−0.178915	+	0.103297i
$987$		0			0
$988$	0.562243	+	0.0573923i	0.0178873	+	0.00182589i
$989$	−36.2227	−	62.7396i	−1.15182	−	1.99500i
$990$		0			0
$991$	−10.4119			−0.330745			−0.165373	−	0.986231i	$-0.552883\pi$
$991$	−10.4119			−0.330745			−0.165373	+	0.986231i	$0.552883\pi$
$992$	−41.5875			−1.32040
$993$		0			0
$994$	80.1808	+	32.7673i	2.54318	+	1.03932i
$995$	4.85414	+	2.80254i	0.153887	+	0.0888464i
$996$		0			0
$997$	−2.87635	−	4.98198i	−0.0910949	−	0.157781i	0.816877	−	0.576812i	$-0.195703\pi$
$997$	−2.87635	−	4.98198i	−0.0910949	−	0.157781i	−0.907972	+	0.419031i	$0.862370\pi$
$998$	21.0827			0.667362
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.do.e.361.1		12
3.2	odd	2		91.2.u.b.88.6	yes	12
7.2	even	3		819.2.bm.f.478.6		12
13.4	even	6		819.2.bm.f.550.1		12
21.2	odd	6		91.2.k.b.23.1	yes	12
21.5	even	6		637.2.k.i.569.1		12
21.11	odd	6		637.2.q.g.491.1		12
21.17	even	6		637.2.q.i.491.1		12
21.20	even	2		637.2.u.g.361.6		12
39.2	even	12		1183.2.e.j.508.11		24
39.11	even	12		1183.2.e.j.508.2		24
39.17	odd	6		91.2.k.b.4.6	✓	12
91.30	even	6	inner	819.2.do.e.667.1		12
273.2	even	12		1183.2.e.j.170.11		24
273.11	even	12		8281.2.a.cp.1.11		12
273.17	even	6		637.2.q.i.589.1		12
273.80	odd	12		8281.2.a.co.1.2		12
273.95	odd	6		637.2.q.g.589.1		12
273.128	even	12		1183.2.e.j.170.2		24
273.158	even	12		8281.2.a.cp.1.2		12
273.173	even	6		637.2.u.g.30.6		12
273.206	odd	12		8281.2.a.co.1.11		12
273.212	odd	6		91.2.u.b.30.6	yes	12
273.251	even	6		637.2.k.i.459.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.6	✓	12	39.17	odd	6
91.2.k.b.23.1	yes	12	21.2	odd	6
91.2.u.b.30.6	yes	12	273.212	odd	6
91.2.u.b.88.6	yes	12	3.2	odd	2
637.2.k.i.459.6		12	273.251	even	6
637.2.k.i.569.1		12	21.5	even	6
637.2.q.g.491.1		12	21.11	odd	6
637.2.q.g.589.1		12	273.95	odd	6
637.2.q.i.491.1		12	21.17	even	6
637.2.q.i.589.1		12	273.17	even	6
637.2.u.g.30.6		12	273.173	even	6
637.2.u.g.361.6		12	21.20	even	2
819.2.bm.f.478.6		12	7.2	even	3
819.2.bm.f.550.1		12	13.4	even	6
819.2.do.e.361.1		12	1.1	even	1	trivial
819.2.do.e.667.1		12	91.30	even	6	inner
1183.2.e.j.170.2		24	273.128	even	12
1183.2.e.j.170.11		24	273.2	even	12
1183.2.e.j.508.2		24	39.11	even	12
1183.2.e.j.508.11		24	39.2	even	12
8281.2.a.co.1.2		12	273.80	odd	12
8281.2.a.co.1.11		12	273.206	odd	12
8281.2.a.cp.1.2		12	273.158	even	12
8281.2.a.cp.1.11		12	273.11	even	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.do (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99469 - 1.15163i) q^{2} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.09135 - 1.62057i) q^{7} -3.00585i q^{8} +O(q^{10})\)	\(q+(-1.99469 - 1.15163i) q^{2} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.09135 - 1.62057i) q^{7} -3.00585i q^{8} -1.95154 q^{10} +1.50340i q^{11} +(-2.92329 - 2.11054i) q^{13} +(-6.03790 + 0.824057i) q^{14} +(-0.156597 + 0.271234i) q^{16} +(-1.03570 - 1.79389i) q^{17} +0.0474272i q^{19} +(2.42516 + 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} +(3.90935 - 6.77119i) q^{23} +(-2.14105 + 3.70840i) q^{25} +(3.40047 + 7.57643i) q^{26} +(8.09446 + 3.30795i) q^{28} +(0.679854 + 1.17754i) q^{29} +(6.80787 + 3.93052i) q^{31} +(-4.58156 + 2.64516i) q^{32} +4.77099i q^{34} +(0.848038 - 2.07513i) q^{35} +(-5.80427 - 3.35110i) q^{37} +(0.0546187 - 0.0946024i) q^{38} +(-1.27341 - 2.20562i) q^{40} +(8.67622 - 5.00922i) q^{41} +(4.63283 - 8.02430i) q^{43} +(-4.30311 + 2.48440i) q^{44} +(-15.5959 + 9.00428i) q^{46} +(-0.311781 + 0.180007i) q^{47} +(1.74751 - 6.77836i) q^{49} +(8.54144 - 4.93141i) q^{50} +(1.21011 - 11.8549i) q^{52} +(1.35591 - 2.34850i) q^{53} +(0.636910 + 1.10316i) q^{55} +(-4.87118 - 6.28629i) q^{56} -3.13177i q^{58} +(-1.42132 + 0.820598i) q^{59} +4.52194 q^{61} +(-9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(-3.03916 - 0.310229i) q^{65} +2.04266i q^{67} +(3.42303 - 5.92886i) q^{68} +(-4.08136 + 3.16260i) q^{70} +(-12.3096 - 7.10697i) q^{71} +(-5.85563 - 3.38075i) q^{73} +(7.71847 + 13.3688i) q^{74} +(-0.135748 + 0.0783743i) q^{76} +(2.43637 + 3.14414i) q^{77} +(-5.82952 - 10.0970i) q^{79} +0.265367i q^{80} -23.0751 q^{82} +11.5362i q^{83} +(-1.51994 - 0.877541i) q^{85} +(-18.4821 + 10.6706i) q^{86} +4.51900 q^{88} +(-15.1652 - 8.75561i) q^{89} +(-9.53391 + 0.323492i) q^{91} +25.8411 q^{92} +0.829208 q^{94} +(0.0200923 + 0.0348009i) q^{95} +(0.369125 + 0.213115i) q^{97} +(-11.2919 + 11.5082i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

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