LMFDB - Embedded newform 819.2.bm.f.478.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (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			478.6
Root			$1.21245 + 0.727987i$ of defining polynomial
Character	$\chi$	$=$	819.478
Dual form			819.2.bm.f.550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30327i q^{2} -3.30504 q^{4} +(-0.733776 - 0.423646i) q^{5} +(-0.357777 + 2.62145i) q^{7} -3.00585i q^{8} +O(q^{10})$	\(q+2.30327i q^{2} -3.30504 q^{4} +(-0.733776 - 0.423646i) q^{5} +(-0.357777 + 2.62145i) q^{7} -3.00585i q^{8} +(0.975769 - 1.69008i) q^{10} +(-1.30198 - 0.751701i) q^{11} +(-2.92329 - 2.11054i) q^{13} +(-6.03790 - 0.824057i) q^{14} +0.313194 q^{16} +2.07140 q^{17} +(0.0410731 - 0.0237136i) q^{19} +(2.42516 + 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} -7.81870 q^{23} +(-2.14105 - 3.70840i) q^{25} +(4.86115 - 6.73311i) q^{26} +(1.18247 - 8.66399i) q^{28} +(0.679854 + 1.17754i) q^{29} +(-6.80787 + 3.93052i) q^{31} -5.29033i q^{32} +4.77099i q^{34} +(1.37309 - 1.77199i) q^{35} +6.70219i q^{37} +(0.0546187 + 0.0946024i) q^{38} +(-1.27341 + 2.20562i) q^{40} +(8.67622 - 5.00922i) q^{41} +(4.63283 - 8.02430i) q^{43} +(4.30311 + 2.48440i) q^{44} -18.0086i q^{46} +(0.311781 + 0.180007i) q^{47} +(-6.74399 - 1.87579i) q^{49} +(8.54144 - 4.93141i) q^{50} +(9.66157 + 6.97543i) q^{52} +(1.35591 + 2.34850i) q^{53} +(0.636910 + 1.10316i) q^{55} +(7.87968 + 1.07542i) q^{56} +(-2.71219 + 1.56588i) q^{58} -1.64120i q^{59} +(-2.26097 - 3.91612i) q^{61} +(-9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(1.25091 + 2.78711i) q^{65} +(-1.76900 - 1.02133i) q^{67} -6.84606 q^{68} +(4.08136 + 3.16260i) q^{70} +(-12.3096 - 7.10697i) q^{71} +(5.85563 - 3.38075i) q^{73} -15.4369 q^{74} +(-0.135748 + 0.0783743i) q^{76} +(2.43637 - 3.14414i) q^{77} +(-5.82952 + 10.0970i) q^{79} +(-0.229814 - 0.132683i) q^{80} +(11.5376 + 19.9837i) q^{82} +11.5362i q^{83} +(-1.51994 - 0.877541i) q^{85} +(18.4821 + 10.6706i) q^{86} +(-2.25950 + 3.91357i) q^{88} +17.5112i q^{89} +(6.57857 - 6.90814i) q^{91} +25.8411 q^{92} +(-0.414604 + 0.718115i) q^{94} -0.0401846 q^{95} +(0.369125 + 0.213115i) q^{97} +(4.32044 - 15.5332i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			2.30327i			1.62866i	0.580405	+	0.814328i	$0.302894\pi$
$2$			2.30327i			1.62866i	−0.580405	+	0.814328i	$0.697106\pi$
$3$		0			0
$3$		0			0
$4$	−3.30504			−1.65252
$5$	−0.733776	−	0.423646i	−0.328155	−	0.189460i	0.326867	−	0.945070i	$-0.394007\pi$
$5$	−0.733776	−	0.423646i	−0.328155	−	0.189460i	−0.655022	+	0.755610i	$0.727340\pi$
$6$		0			0
$7$	−0.357777	+	2.62145i	−0.135227	+	0.990815i
$7$	−0.357777	+	2.62145i	−0.135227	+	0.990815i
$8$		−	3.00585i		−	1.06273i
$9$		0			0
$10$	0.975769	−	1.69008i	0.308565	−	0.534451i
$11$	−1.30198	−	0.751701i	−0.392563	−	0.226646i	0.290707	−	0.956812i	$-0.406110\pi$
$11$	−1.30198	−	0.751701i	−0.392563	−	0.226646i	−0.683270	+	0.730166i	$0.739443\pi$
$12$		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
$16$	0.313194			0.0782985
$17$	2.07140			0.502389			0.251194	−	0.967937i	$-0.419177\pi$
$17$	2.07140			0.502389			0.251194	+	0.967937i	$0.419177\pi$
$18$		0			0
$19$	0.0410731	−	0.0237136i	0.00942282	−	0.00544027i	−0.495281	−	0.868733i	$-0.664935\pi$
$19$	0.0410731	−	0.0237136i	0.00942282	−	0.00544027i	0.504704	+	0.863292i	$0.331602\pi$
$20$	2.42516	+	1.40016i	0.542282	+	0.313086i
$21$		0			0
$22$	1.73137	−	2.99882i	0.369129	−	0.639350i
$23$	−7.81870			−1.63031			−0.815156	−	0.579241i	$-0.803349\pi$
$23$	−7.81870			−1.63031			−0.815156	+	0.579241i	$0.803349\pi$
$24$		0			0
$25$	−2.14105	−	3.70840i	−0.428210	−	0.741681i
$26$	4.86115	−	6.73311i	0.953349	−	1.32047i
$27$		0			0
$28$	1.18247	−	8.66399i	0.223465	−	1.63734i
$29$	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	$-0.916143\pi$
$31$	−6.80787	+	3.93052i	−1.22273	+	0.705943i	−0.257230	+	0.966350i	$0.582810\pi$
$32$		−	5.29033i		−	0.935206i
$33$		0			0
$34$			4.77099i			0.818218i
$35$	1.37309	−	1.77199i	0.232095	−	0.299520i
$36$		0			0
$37$			6.70219i			1.10183i	0.834560	+	0.550917i	$0.185722\pi$
$37$			6.70219i			1.10183i	−0.834560	+	0.550917i	$0.814278\pi$
$38$	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
$46$		−	18.0086i		−	2.65522i
$47$	0.311781	+	0.180007i	0.0454779	+	0.0262567i	0.522567	−	0.852598i	$-0.324975\pi$
$47$	0.311781	+	0.180007i	0.0454779	+	0.0262567i	−0.477089	+	0.878855i	$0.658308\pi$
$48$		0			0
$49$	−6.74399	−	1.87579i	−0.963427	−	0.267970i
$50$	8.54144	−	4.93141i	1.20794	−	0.697406i
$51$		0			0
$52$	9.66157	+	6.97543i	1.33982	+	0.967318i
$53$	1.35591	+	2.34850i	0.186248	+	0.322591i	0.943996	−	0.329956i	$-0.107034\pi$
$53$	1.35591	+	2.34850i	0.186248	+	0.322591i	−0.757748	+	0.652547i	$0.773701\pi$
$54$		0			0
$55$	0.636910	+	1.10316i	0.0858809	+	0.148750i
$56$	7.87968	+	1.07542i	1.05297	+	0.143710i
$57$		0			0
$58$	−2.71219	+	1.56588i	−0.356128	+	0.205611i
$59$		−	1.64120i		−	0.213666i	−0.994277	−	0.106833i	$-0.965929\pi$
$59$		−	1.64120i		−	0.213666i	0.994277	−	0.106833i	$-0.0340709\pi$
$60$		0			0
$61$	−2.26097	−	3.91612i	−0.289488	−	0.501407i	0.684200	−	0.729295i	$-0.260152\pi$
$61$	−2.26097	−	3.91612i	−0.289488	−	0.501407i	−0.973688	+	0.227887i	$0.926818\pi$
$62$	−9.05305	−	15.6803i	−1.14974	−	1.99140i
$63$		0			0
$64$	12.8114			1.60143
$65$	1.25091	+	2.78711i	0.155157	+	0.345698i
$66$		0			0
$67$	−1.76900	−	1.02133i	−0.216117	−	0.124775i	0.388034	−	0.921645i	$-0.373154\pi$
$67$	−1.76900	−	1.02133i	−0.216117	−	0.124775i	−0.604151	+	0.796870i	$0.706488\pi$
$68$	−6.84606			−0.830206
$69$		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	$-0.537173\pi$
$73$	5.85563	−	3.38075i	0.685349	−	0.395687i	0.801867	+	0.597502i	$0.203840\pi$
$74$	−15.4369			−1.79451
$75$		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	0.325801	+	0.945438i	$0.394366\pi$
$79$	−5.82952	+	10.0970i	−0.655873	+	1.13600i	−0.981674	+	0.190567i	$0.938967\pi$
$80$	−0.229814	−	0.132683i	−0.0256940	−	0.0148344i
$81$		0			0
$82$	11.5376	+	19.9837i	1.27411	+	2.20683i
$83$			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
$88$	−2.25950	+	3.91357i	−0.240863	+	0.417188i
$89$			17.5112i			1.85619i	0.372350	+	0.928093i	$0.378552\pi$
$89$			17.5112i			1.85619i	−0.372350	+	0.928093i	$0.621448\pi$
$90$		0			0
$91$	6.57857	−	6.90814i	0.689622	−	0.724170i
$92$	25.8411			2.69412
$93$		0			0
$94$	−0.414604	+	0.718115i	−0.0427631	+	0.0740679i
$95$	−0.0401846			−0.00412286
$96$		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	$0.659778\pi$
$98$	4.32044	−	15.5332i	0.436431	−	1.56909i
$99$		0			0
$100$	7.07624	+	12.2564i	0.707624	+	1.22564i
$101$	−4.83499	+	8.37444i	−0.481099	+	0.833288i	−0.999765	−	0.0216891i	$-0.993096\pi$
$101$	−4.83499	+	8.37444i	−0.481099	+	0.833288i	0.518666	+	0.854977i	$0.326429\pi$
$102$		0			0
$103$	−4.98912	+	8.64140i	−0.491592	+	0.851463i	−0.999953	−	0.00968129i	$-0.996918\pi$
$103$	−4.98912	+	8.64140i	−0.491592	+	0.851463i	0.508361	+	0.861144i	$0.330252\pi$
$104$	−6.34397	+	8.78695i	−0.622078	+	0.861631i
$105$		0			0
$106$	−5.40922	+	3.12301i	−0.525390	+	0.303334i
$107$	−9.86223			−0.953417			−0.476709	−	0.879061i	$-0.658170\pi$
$107$	−9.86223			−0.953417			−0.476709	+	0.879061i	$0.658170\pi$
$108$		0			0
$109$	−10.0507	+	5.80275i	−0.962679	+	0.555803i	−0.896996	−	0.442038i	$-0.854256\pi$
$109$	−10.0507	+	5.80275i	−0.962679	+	0.555803i	−0.0656822	+	0.997841i	$0.520922\pi$
$110$	−2.54087	+	1.46697i	−0.242263	+	0.139870i
$111$		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
$115$	5.73718	+	3.31236i	0.534994	+	0.308879i
$116$	−2.24694	−	3.89182i	−0.208623	−	0.361346i
$117$		0			0
$118$	3.78011			0.347987
$119$	−0.741100	+	5.43007i	−0.0679366	+	0.497774i
$120$		0			0
$121$	−4.36989	−	7.56887i	−0.397263	−	0.688079i
$122$	9.01986	−	5.20762i	0.816620	−	0.471476i
$123$		0			0
$124$	22.5003	−	12.9905i	2.02058	−	1.16658i
$125$			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	$-0.411957\pi$
$128$			18.9275i			1.67297i
$129$		0			0
$130$	−6.41945	+	2.88119i	−0.563023	+	0.252697i
$131$	−1.27259	+	2.20418i	−0.111186	+	0.192580i	−0.916249	−	0.400610i	$-0.868798\pi$
$131$	−1.27259	+	2.20418i	−0.111186	+	0.192580i	0.805063	+	0.593190i	$0.202132\pi$
$132$		0			0
$133$	0.0474689	+	0.116155i	0.00411608	+	0.0100719i
$134$	2.35240	−	4.07447i	0.203216	−	0.351981i
$135$		0			0
$136$		−	6.22632i		−	0.533902i
$137$			1.86472i			0.159314i	0.996822	+	0.0796571i	$0.0253825\pi$
$137$			1.86472i			0.159314i	−0.996822	+	0.0796571i	$0.974617\pi$
$138$		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	$0.936383\pi$
$140$	−4.53813	+	5.85648i	−0.383542	+	0.494963i
$141$		0			0
$142$	16.3692	−	28.3524i	1.37368	−	2.37928i
$143$	2.21957	+	4.94533i	0.185610	+	0.413550i
$144$		0			0
$145$		−	1.15207i		−	0.0956741i
$146$	7.78676	+	13.4871i	0.644437	+	1.11620i
$147$		0			0
$148$		−	22.1510i		−	1.82080i
$149$	−5.51106	+	3.18181i	−0.451484	+	0.260664i	−0.708457	−	0.705754i	$-0.750608\pi$
$149$	−5.51106	+	3.18181i	−0.451484	+	0.260664i	0.256973	+	0.966419i	$0.417275\pi$
$150$		0			0
$151$	0.575122	−	0.332047i	0.0468028	−	0.0270216i	−0.476416	−	0.879220i	$-0.658064\pi$
$151$	0.575122	−	0.332047i	0.0468028	−	0.0270216i	0.523219	+	0.852198i	$0.324731\pi$
$152$	−0.0712794	−	0.123460i	−0.00578152	−	0.0100139i
$153$		0			0
$154$	7.24180	+	5.61160i	0.583561	+	0.452196i
$155$	6.66060			0.534992
$156$		0			0
$157$	8.28798	+	14.3552i	0.661453	+	1.14567i	0.980234	+	0.197842i	$0.0633933\pi$
$157$	8.28798	+	14.3552i	0.661453	+	1.14567i	−0.318781	+	0.947828i	$0.603273\pi$
$158$	−23.2562	−	13.4269i	−1.85016	−	1.06819i
$159$		0			0
$160$	−2.24122	+	3.88191i	−0.177184	+	0.306892i
$161$	2.79735	−	20.4963i	0.220462	−	1.61534i
$162$		0			0
$163$	7.83863	−	4.52563i	0.613969	−	0.354475i	−0.160548	−	0.987028i	$-0.551326\pi$
$163$	7.83863	−	4.52563i	0.613969	−	0.354475i	0.774517	+	0.632553i	$0.217993\pi$
$164$	−28.6752	+	16.5557i	−2.23916	+	1.29278i
$165$		0			0
$166$	−26.5710			−2.06231
$167$	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
$172$	−15.3117	+	26.5206i	−1.16750	+	2.02218i
$173$	−9.79352	−	16.9629i	−0.744588	−	1.28966i	−0.950387	−	0.311070i	$-0.899313\pi$
$173$	−9.79352	−	16.9629i	−0.744588	−	1.28966i	0.205799	−	0.978594i	$-0.434021\pi$
$174$		0			0
$175$	10.4874	−	4.28587i	0.792774	−	0.323981i
$176$	−0.407774	−	0.235428i	−0.0307371	−	0.0177461i
$177$		0			0
$178$	−40.3330			−3.02309
$179$	1.44666	−	2.50569i	0.108129	−	0.187284i	−0.806884	−	0.590711i	$-0.798848\pi$
$179$	1.44666	−	2.50569i	0.108129	−	0.187284i	0.915012	+	0.403426i	$0.132181\pi$
$180$		0			0
$181$	−1.36804			−0.101686			−0.0508429	−	0.998707i	$-0.516191\pi$
$181$	−1.36804			−0.101686			−0.0508429	+	0.998707i	$0.516191\pi$
$182$	15.9113	+	15.1522i	1.17942	+	1.12316i
$183$		0			0
$184$			23.5018i			1.73258i
$185$	2.83936	−	4.91791i	0.208754	−	0.361572i
$186$		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
$191$	−0.756625	−	1.31051i	−0.0547475	−	0.0948254i	0.837353	−	0.546663i	$-0.184102\pi$
$191$	−0.756625	−	1.31051i	−0.0547475	−	0.0948254i	−0.892100	+	0.451837i	$0.850769\pi$
$192$		0			0
$193$	−6.02229	−	3.47697i	−0.433494	−	0.250278i	0.267340	−	0.963602i	$-0.413855\pi$
$193$	−6.02229	−	3.47697i	−0.433494	−	0.250278i	−0.700834	+	0.713324i	$0.747189\pi$
$194$	−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
$199$	−6.61529			−0.468945			−0.234473	−	0.972123i	$-0.575336\pi$
$199$	−6.61529			−0.468945			−0.234473	+	0.972123i	$0.575336\pi$
$200$	−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
$205$	−8.48854			−0.592865
$206$	−19.9035	−	11.4913i	−1.38674	−	0.800634i
$207$		0			0
$208$	−0.915555	−	0.661010i	−0.0634823	−	0.0458328i
$209$	−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	$0.743457\pi$
$212$	−4.48132	−	7.76187i	−0.307778	−	0.533088i
$213$		0			0
$214$		−	22.7153i		−	1.55279i
$215$	−6.79892	+	3.92536i	−0.463683	+	0.267707i
$216$		0			0
$217$	−7.86797	−	19.2527i	−0.534113	−	1.30696i
$218$	−13.3653	−	23.1493i	−0.905211	−	1.56787i
$219$		0			0
$220$	−2.10501	−	3.64599i	−0.141920	−	0.245812i
$221$	−6.05530	−	4.37178i	−0.407323	−	0.294078i
$222$		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	$0.152640\pi$
$224$	13.8683	+	1.89276i	0.926616	+	0.126465i
$225$		0			0
$226$	−6.93668	−	4.00490i	−0.461421	−	0.266402i
$227$			1.29581i			0.0860057i	0.999075	+	0.0430029i	$0.0136925\pi$
$227$			1.29581i			0.0860057i	−0.999075	+	0.0430029i	$0.986308\pi$
$228$		0			0
$229$	18.0285	+	10.4088i	1.19136	+	0.687831i	0.958614	−	0.284707i	$-0.0918965\pi$
$229$	18.0285	+	10.4088i	1.19136	+	0.687831i	0.232743	+	0.972538i	$0.425230\pi$
$230$	−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	−0.561565	−	0.827433i	$-0.689800\pi$
$233$	6.65213	−	11.5218i	0.435796	−	0.754820i	0.997360	+	0.0726127i	$0.0231337\pi$
$234$		0			0
$235$	−0.152518	−	0.264169i	−0.00994920	−	0.0172325i
$236$			5.42421i			0.353086i
$237$		0			0
$238$	−12.5069	−	1.70695i	−0.810702	−	0.110645i
$239$			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
$241$		−	0.834153i		−	0.0537325i	−0.999639	−	0.0268663i	$-0.991447\pi$
$241$		−	0.834153i		−	0.0537325i	0.999639	−	0.0268663i	$-0.00855282\pi$
$242$	17.4331	−	10.0650i	1.12064	−	0.647004i
$243$		0			0
$244$	7.47259	+	12.9429i	0.478384	+	0.828585i
$245$	4.15391	+	4.23347i	0.265383	+	0.270467i
$246$		0			0
$247$	−0.170117	−	0.0173651i	−0.0108243	−	0.00110491i
$248$	11.8146	+	20.4634i	0.750225	+	1.29943i
$249$		0			0
$250$	−18.1144			−1.14565
$251$	−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
$254$	31.3163	−	18.0804i	1.96496	−	1.13447i
$255$		0			0
$256$	−17.9721			−1.12326
$257$	6.55188			0.408695			0.204348	−	0.978898i	$-0.434493\pi$
$257$	6.55188			0.408695			0.204348	+	0.978898i	$0.434493\pi$
$258$		0			0
$259$	−17.5695	−	2.39789i	−1.09171	−	0.148998i
$260$	−4.13432	−	9.21148i	−0.256399	−	0.571272i
$261$		0			0
$262$	−5.07682	−	2.93110i	−0.313647	−	0.181084i
$263$	−11.2945	+	19.5627i	−0.696450	+	1.20629i	0.273239	+	0.961946i	$0.411905\pi$
$263$	−11.2945	+	19.5627i	−0.696450	+	1.20629i	−0.969689	+	0.244341i	$0.921428\pi$
$264$		0			0
$265$		−	2.29770i		−	0.141146i
$266$	−0.267537	+	0.109334i	−0.0164037	+	0.00670367i
$267$		0			0
$268$	5.84660	+	3.37553i	0.357138	+	0.206194i
$269$	−16.0013			−0.975617			−0.487808	−	0.872951i	$-0.662203\pi$
$269$	−16.0013			−0.975617			−0.487808	+	0.872951i	$0.662203\pi$
$270$		0			0
$271$			8.75935i			0.532093i	0.963960	+	0.266046i	$0.0857174\pi$
$271$			8.75935i			0.532093i	−0.963960	+	0.266046i	$0.914283\pi$
$272$	0.648750			0.0393363
$273$		0			0
$274$	−4.29496			−0.259468
$275$			6.43771i			0.388209i
$276$		0			0
$277$	19.9183			1.19677			0.598387	−	0.801208i	$-0.295809\pi$
$277$	19.9183			1.19677			0.598387	+	0.801208i	$0.295809\pi$
$278$	−31.1355	−	17.9761i	−1.86739	−	1.07814i
$279$		0			0
$280$	−5.32632	−	4.12731i	−0.318308	−	0.246654i
$281$		−	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
$283$	0.506295	−	0.876929i	0.0300961	−	0.0521280i	−0.850585	−	0.525838i	$-0.823752\pi$
$283$	0.506295	−	0.876929i	0.0300961	−	0.0521280i	0.880681	+	0.473710i	$0.157085\pi$
$284$	40.6838	+	23.4888i	2.41414	+	1.39380i
$285$		0			0
$286$	−11.3904	+	5.11227i	−0.673530	+	0.302295i
$287$	10.0273	+	24.5365i	0.591890	+	1.44834i
$288$		0			0
$289$	−12.7093			−0.747606
$290$	2.65352			0.155820
$291$		0			0
$292$	−19.3531	+	11.1735i	−1.13255	+	0.653879i
$293$	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
$296$	20.1458			1.17095
$297$		0			0
$298$	−7.32857	−	12.6935i	−0.424532	−	0.735312i
$299$	22.8563	+	16.5017i	1.32181	+	0.954319i
$300$		0			0
$301$	19.3778	+	15.0156i	1.11692	+	0.865487i
$302$	0.764792	+	1.32466i	0.0440088	+	0.0762256i
$303$		0			0
$304$	0.0128639	−	0.00742695i	0.000737793	−	0.000425965i
$305$			3.83140i			0.219386i
$306$		0			0
$307$			27.2004i			1.55241i	0.630482	+	0.776204i	$0.282857\pi$
$307$			27.2004i			1.55241i	−0.630482	+	0.776204i	$0.717143\pi$
$308$	−8.05228	+	10.3915i	−0.458821	+	0.592111i
$309$		0			0
$310$			15.3411i			0.871318i
$311$	−13.5505	−	23.4701i	−0.768376	−	1.33087i	−0.938443	−	0.345434i	$-0.887732\pi$
$311$	−13.5505	−	23.4701i	−0.768376	−	1.33087i	0.170067	−	0.985432i	$-0.445602\pi$
$312$		0			0
$313$	11.0392	−	19.1205i	0.623975	−	1.08076i	−0.364763	−	0.931100i	$-0.618850\pi$
$313$	11.0392	−	19.1205i	0.623975	−	1.08076i	0.988738	−	0.149656i	$-0.0478165\pi$
$314$	−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	$-0.269728\pi$
$317$	6.12126	+	3.53411i	0.343804	+	0.198496i	−0.318149	+	0.948041i	$0.603061\pi$
$318$		0			0
$319$		−	2.04419i		−	0.114453i
$320$	−9.40071	−	5.42750i	−0.525516	−	0.303407i
$321$		0			0
$322$	47.2085	+	6.44305i	2.63083	+	0.359057i
$323$	0.0850789	−	0.0491204i	0.00473392	−	0.00273313i
$324$		0			0
$325$	−1.56786	+	15.3595i	−0.0869690	+	0.851992i
$326$	10.4237	+	18.0544i	0.577318	+	0.999943i
$327$		0			0
$328$	−15.0569	−	26.0794i	−0.831381	−	1.43999i
$329$	−0.583427	+	0.752916i	−0.0321654	+	0.0415096i
$330$		0			0
$331$	5.70588	−	3.29429i	0.313623	−	0.181071i	−0.334923	−	0.942245i	$-0.608710\pi$
$331$	5.70588	−	3.29429i	0.313623	−	0.181071i	0.648547	+	0.761175i	$0.275377\pi$
$332$		−	38.1277i		−	2.09253i
$333$		0			0
$334$	3.06059	+	5.30110i	0.167468	+	0.290063i
$335$	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	$0.536693\pi$
$338$	−28.4210	+	9.42313i	−1.54590	+	0.512551i
$339$		0			0
$340$	5.02347	+	2.90030i	0.272436	+	0.157291i
$341$	11.8183			0.639998
$342$		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
$347$	9.09478			0.488233			0.244117	−	0.969746i	$-0.421502\pi$
$347$	9.09478			0.488233			0.244117	+	0.969746i	$0.421502\pi$
$348$		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
$353$	−1.86584	−	1.07724i	−0.0993087	−	0.0573359i	0.449523	−	0.893269i	$-0.351594\pi$
$353$	−1.86584	−	1.07724i	−0.0993087	−	0.0573359i	−0.548832	+	0.835933i	$0.684927\pi$
$354$		0			0
$355$	6.02167	+	10.4298i	0.319597	+	0.553559i
$356$		−	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	$-0.260825\pi$
$359$	7.41107	+	4.27878i	0.391141	+	0.225825i	−0.291513	+	0.956567i	$0.594159\pi$
$360$		0			0
$361$	−9.49888	+	16.4525i	−0.499941	+	0.865923i
$362$		−	3.15096i		−	0.165611i
$363$		0			0
$364$	−21.7424	+	22.8317i	−1.13961	+	1.19670i
$365$	−5.72896			−0.299867
$366$		0			0
$367$	−1.14912	+	1.99033i	−0.0599833	+	0.103894i	−0.894458	−	0.447153i	$-0.852438\pi$
$367$	−1.14912	+	1.99033i	−0.0599833	+	0.103894i	0.834474	+	0.551047i	$0.185771\pi$
$368$	−2.44877			−0.127651
$369$		0			0
$370$	11.3273	+	6.53979i	0.588876	+	0.339988i
$371$	−6.64158	+	2.71420i	−0.344814	+	0.140914i
$372$		0			0
$373$	−5.88418	−	10.1917i	−0.304672	−	0.527707i	0.672517	−	0.740082i	$-0.265213\pi$
$373$	−5.88418	−	10.1917i	−0.304672	−	0.527707i	−0.977188	+	0.212375i	$0.931880\pi$
$374$	3.58636	−	6.21175i	0.185446	−	0.321202i
$375$		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	$0.399129\pi$
$380$	0.132812			0.00681310
$381$		0			0
$382$	3.01846	−	1.74271i	0.154438	−	0.0891647i
$383$	24.4605	−	14.1223i	1.24988	−	0.721616i	0.278791	−	0.960352i	$-0.410066\pi$
$383$	24.4605	−	14.1223i	1.24988	−	0.721616i	0.971084	+	0.238736i	$0.0767331\pi$
$384$		0			0
$385$	−3.11975	+	1.27494i	−0.158997	+	0.0649770i
$386$	8.00839	−	13.8709i	0.407616	−	0.706012i
$387$		0			0
$388$	−1.21997	−	0.704352i	−0.0619347	−	0.0357580i
$389$	−3.84043	−	6.65182i	−0.194717	−	0.337261i	0.752090	−	0.659060i	$-0.229046\pi$
$389$	−3.84043	−	6.65182i	−0.194717	−	0.337261i	−0.946808	+	0.321799i	$0.895712\pi$
$390$		0			0
$391$	−16.1957			−0.819050
$392$	−5.63834	+	20.2714i	−0.284779	+	1.02386i
$393$		0			0
$394$	17.8241	+	30.8722i	0.897964	+	1.55532i
$395$	8.55513	−	4.93931i	0.430455	−	0.248524i
$396$		0			0
$397$	6.45433	−	3.72641i	0.323933	−	0.187023i	−0.329211	−	0.944256i	$-0.606783\pi$
$397$	6.45433	−	3.72641i	0.323933	−	0.187023i	0.653144	+	0.757233i	$0.273449\pi$
$398$		−	15.2368i		−	0.763750i
$399$		0			0
$400$	−0.670563	−	1.16145i	−0.0335282	−	0.0580725i
$401$		−	18.1982i		−	0.908777i	−0.890804	−	0.454389i	$-0.849858\pi$
$401$		−	18.1982i		−	0.908777i	0.890804	−	0.454389i	$-0.150142\pi$
$402$		0			0
$403$	28.1969	+	2.87826i	1.40459	+	0.143376i
$404$	15.9798	−	27.6778i	0.795025	−	1.37702i
$405$		0			0
$406$	−3.13453	−	7.67011i	−0.155564	−	0.380661i
$407$	5.03804	−	8.72615i	0.249727	−	0.432539i
$408$		0			0
$409$		−	29.2825i		−	1.44793i	−0.689838	−	0.723964i	$-0.742318\pi$
$409$		−	29.2825i		−	1.44793i	0.689838	−	0.723964i	$-0.257682\pi$
$410$		−	19.5514i		−	0.965573i
$411$		0			0
$412$	16.4892	−	28.5602i	0.812365	−	1.40706i
$413$	4.30231	+	0.587183i	0.211703	+	0.0288934i
$414$		0			0
$415$	4.88728	−	8.46502i	0.239907	−	0.415531i
$416$	−11.1655	+	15.4651i	−0.547432	+	0.758241i
$417$		0			0
$418$		−	0.164228i		−	0.00803264i
$419$	−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	$0.792759\pi$
$422$	−16.1456	+	9.32165i	−0.785954	+	0.453771i
$423$		0			0
$424$	7.05923	−	4.07565i	0.342826	−	0.197931i
$425$	−4.43497	−	7.68159i	−0.215128	−	0.372612i
$426$		0			0
$427$	11.0748	−	4.52592i	0.535948	−	0.219025i
$428$	32.5950			1.57554
$429$		0			0
$430$	−9.04115	−	15.6597i	−0.436003	−	0.755179i
$431$	18.3327	+	10.5844i	0.883055	+	0.509832i	0.871665	−	0.490103i	$-0.163041\pi$
$431$	18.3327	+	10.5844i	0.883055	+	0.509832i	0.0113906	+	0.999935i	$0.496374\pi$
$432$		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
$436$	33.2178	−	19.1783i	1.59084	−	0.918474i
$437$	−0.321139	+	0.185409i	−0.0153621	+	0.00886934i
$438$		0			0
$439$	12.0384			0.574561			0.287280	−	0.957847i	$-0.407249\pi$
$439$	12.0384			0.574561			0.287280	+	0.957847i	$0.407249\pi$
$440$	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	−0.616388	−	0.787443i	$-0.711405\pi$
$443$	7.86656	−	13.6253i	0.373752	−	0.647357i	0.990139	+	0.140086i	$0.0447379\pi$
$444$		0			0
$445$	7.41855	−	12.8493i	0.351673	−	0.609116i
$446$	18.4930	+	32.0308i	0.875669	+	1.51670i
$447$		0			0
$448$	−4.58363	+	33.5845i	−0.216556	+	1.58672i
$449$	−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
$451$	−15.0617			−0.709230
$452$	5.74676	−	9.95369i	0.270305	−	0.468182i
$453$		0			0
$454$	−2.98459			−0.140074
$455$	−7.75380	+	2.28204i	−0.363504	+	0.106984i
$456$		0			0
$457$		−	30.7958i		−	1.44057i	−0.693679	−	0.720284i	$-0.744011\pi$
$457$		−	30.7958i		−	1.44057i	0.693679	−	0.720284i	$-0.255989\pi$
$458$	−23.9742	+	41.5245i	−1.12024	+	1.94031i
$459$		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	$-0.0125170\pi$
$464$	0.212926	+	0.368799i	0.00988485	+	0.0171211i
$465$		0			0
$466$	26.5378	+	15.3216i	1.22934	+	0.709761i
$467$	−14.1762	+	24.5539i	−0.655996	+	1.13622i	0.325647	+	0.945491i	$0.394418\pi$
$467$	−14.1762	+	24.5539i	−0.655996	+	1.13622i	−0.981643	+	0.190727i	$0.938916\pi$
$468$		0			0
$469$	3.31027	−	4.27192i	0.152854	−	0.197259i
$470$	0.608453	−	0.351290i	0.0280658	−	0.0162038i
$471$		0			0
$472$	−4.93318			−0.227068
$473$	−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
$478$	−30.7837			−1.40801
$479$	−5.44077	−	3.14123i	−0.248595	−	0.143526i	0.370526	−	0.928822i	$-0.379178\pi$
$479$	−5.44077	−	3.14123i	−0.248595	−	0.143526i	−0.619121	+	0.785296i	$0.712511\pi$
$480$		0			0
$481$	14.1453	−	19.5924i	0.644969	−	0.893338i
$482$	1.92128			0.0875117
$483$		0			0
$484$	14.4427	+	25.0154i	0.656484	+	1.13706i
$485$	−0.180570	−	0.312757i	−0.00819927	−	0.0142016i
$486$		0			0
$487$		−	13.0176i		−	0.589883i	−0.955515	−	0.294942i	$-0.904700\pi$
$487$		−	13.0176i		−	0.589883i	0.955515	−	0.294942i	$-0.0953002\pi$
$488$	−11.7712	+	6.79613i	−0.532859	+	0.307647i
$489$		0			0
$490$	−9.75082	+	9.56756i	−0.440497	+	0.432218i
$491$	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
$494$	0.0399964	−	0.391825i	0.00179952	−	0.0176290i
$495$		0			0
$496$	−2.13218	+	1.23102i	−0.0957378	+	0.0552743i
$497$	23.0347	−	29.7264i	1.03325	−	1.33341i
$498$		0			0
$499$	7.92708	+	4.57670i	0.354865	+	0.204881i	0.666826	−	0.745214i	$-0.267652\pi$
$499$	7.92708	+	4.57670i	0.354865	+	0.204881i	−0.311961	+	0.950095i	$0.600986\pi$
$500$		−	25.9929i		−	1.16244i
$501$		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
$509$		−	38.6606i		−	1.71360i	−0.515649	−	0.856800i	$-0.672449\pi$
$509$		−	38.6606i		−	1.71360i	0.515649	−	0.856800i	$-0.327551\pi$
$510$		0			0
$511$	6.76745	+	16.5598i	0.299374	+	0.732562i
$512$		−	3.53972i		−	0.156435i
$513$		0			0
$514$			15.0907i			0.665623i
$515$	7.32179	−	4.22724i	0.322637	−	0.186274i
$516$		0			0
$517$	−0.270623	−	0.468732i	−0.0119020	−	0.0206148i
$518$	5.52298	−	40.4671i	0.242666	−	1.77802i
$519$		0			0
$520$	8.37761	−	3.76006i	0.367383	−	0.164889i
$521$	20.1176	+	34.8446i	0.881366	+	1.52657i	0.849823	+	0.527068i	$0.176709\pi$
$521$	20.1176	+	34.8446i	0.881366	+	1.52657i	0.0315430	+	0.999502i	$0.489958\pi$
$522$		0			0
$523$	−0.732146			−0.0320145			−0.0160073	−	0.999872i	$-0.505095\pi$
$523$	−0.732146			−0.0320145			−0.0160073	+	0.999872i	$0.505095\pi$
$524$	4.20594	−	7.28491i	0.183737	−	0.318243i
$525$		0			0
$526$	−45.0581	−	26.0143i	−1.96463	−	1.13428i
$527$	−14.1018	+	8.14169i	−0.614285	+	0.354658i
$528$		0			0
$529$	38.1321			1.65792
$530$	5.29221			0.229879
$531$		0			0
$532$	−0.156887	−	0.383898i	−0.00680189	−	0.0166441i
$533$	−35.9353	−	3.66817i	−1.55653	−	0.158886i
$534$		0			0
$535$	7.23667	+	4.17809i	0.312868	+	0.180635i
$536$	−3.06996	+	5.31733i	−0.132602	+	0.229674i
$537$		0			0
$538$		−	36.8553i		−	1.58894i
$539$	7.37054	+	7.51171i	0.317472	+	0.323552i
$540$		0			0
$541$	−20.4847	−	11.8268i	−0.880705	−	0.508476i	−0.00981448	−	0.999952i	$-0.503124\pi$
$541$	−20.4847	−	11.8268i	−0.880705	−	0.508476i	−0.870891	+	0.491476i	$0.836457\pi$
$542$	−20.1751			−0.866595
$543$		0			0
$544$		−	10.9584i		−	0.469837i
$545$	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	$0.589271\pi$
$548$		−	6.16298i		−	0.263270i
$549$		0			0
$550$	−14.8278			−0.632258
$551$	0.0558475	+	0.0322436i	0.00237918	+	0.00137362i
$552$		0			0
$553$	−24.3832	−	18.8943i	−1.03688	−	0.803467i
$554$			45.8771i			1.94913i
$555$		0			0
$556$	25.7946	−	44.6775i	1.09393	−	1.89475i
$557$	−5.54845	−	3.20340i	−0.235096	−	0.135732i	0.377825	−	0.925877i	$-0.376672\pi$
$557$	−5.54845	−	3.20340i	−0.235096	−	0.135732i	−0.612921	+	0.790145i	$0.710005\pi$
$558$		0			0
$559$	−30.4787	+	13.6795i	−1.28911	+	0.578582i
$560$	0.430045	−	0.554975i	0.0181727	−	0.0234520i
$561$		0			0
$562$	32.2996			1.36248
$563$	7.32084			0.308537			0.154268	−	0.988029i	$-0.450698\pi$
$563$	7.32084			0.308537			0.154268	+	0.988029i	$0.450698\pi$
$564$		0			0
$565$	2.55176	−	1.47326i	0.107354	−	0.0619806i
$566$	2.01980	+	1.16613i	0.0848986	+	0.0490162i
$567$		0			0
$568$	−21.3625	+	37.0009i	−0.896349	+	1.55252i
$569$	−4.31743			−0.180996			−0.0904981	−	0.995897i	$-0.528846\pi$
$569$	−4.31743			−0.180996			−0.0904981	+	0.995897i	$0.528846\pi$
$570$		0			0
$571$	17.0847	+	29.5916i	0.714974	+	1.23837i	0.962970	+	0.269610i	$0.0868946\pi$
$571$	17.0847	+	29.5916i	0.714974	+	1.23837i	−0.247996	+	0.968761i	$0.579772\pi$
$572$	−7.33577	−	16.3445i	−0.306724	−	0.683398i
$573$		0			0
$574$	−56.5140	+	23.0954i	−2.35885	+	0.963985i
$575$	16.7402	+	28.9949i	0.698115	+	1.20917i
$576$		0			0
$577$	−5.50494	+	3.17828i	−0.229174	+	0.132314i	−0.610191	−	0.792254i	$-0.708907\pi$
$577$	−5.50494	+	3.17828i	−0.229174	+	0.132314i	0.381017	+	0.924568i	$0.375574\pi$
$578$		−	29.2729i		−	1.21759i
$579$		0			0
$580$			3.80763i			0.158103i
$581$	−30.2417	−	4.12740i	−1.25464	−	0.171234i
$582$		0			0
$583$		−	4.07695i		−	0.168850i
$584$	−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
$592$			2.09909i			0.0862719i
$593$	−0.409641	−	0.236506i	−0.0168219	−	0.00971215i	0.491565	−	0.870841i	$-0.336425\pi$
$593$	−0.409641	−	0.236506i	−0.0168219	−	0.00971215i	−0.508387	+	0.861128i	$0.669758\pi$
$594$		0			0
$595$	2.84423	−	3.67049i	0.116602	−	0.150476i
$596$	18.2143	−	10.5160i	0.746086	−	0.430753i
$597$		0			0
$598$	−38.0079	+	52.6442i	−1.55426	+	2.15278i
$599$	−4.81348	−	8.33719i	−0.196673	−	0.340648i	0.750774	−	0.660559i	$-0.229680\pi$
$599$	−4.81348	−	8.33719i	−0.196673	−	0.340648i	−0.947448	+	0.319910i	$0.896347\pi$
$600$		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	$0.517151\pi$
$602$	−34.5850	+	44.6322i	−1.40958	+	1.81907i
$603$		0			0
$604$	−1.90080	+	1.09743i	−0.0773424	+	0.0446537i
$605$			7.40514i			0.301062i
$606$		0			0
$607$	−9.54289	−	16.5288i	−0.387334	−	0.670882i	0.604756	−	0.796411i	$-0.293271\pi$
$607$	−9.54289	−	16.5288i	−0.387334	−	0.670882i	−0.992090	+	0.125529i	$0.959937\pi$
$608$	−0.125453	−	0.217290i	−0.00508777	−	0.00881228i
$609$		0			0
$610$	−8.82474			−0.357303
$611$	−0.531513	−	1.18424i	−0.0215027	−	0.0479092i
$612$		0			0
$613$	−32.9131	−	19.0024i	−1.32935	−	0.767500i	−0.344149	−	0.938915i	$-0.611833\pi$
$613$	−32.9131	−	19.0024i	−1.32935	−	0.767500i	−0.985199	+	0.171415i	$0.945166\pi$
$614$	−62.6498			−2.52834
$615$		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	−0.549739	+	0.835336i	$0.685273\pi$
$619$	−38.5146	+	22.2364i	−1.54803	+	0.893756i	−0.998292	+	0.0584199i	$0.981394\pi$
$620$	−22.0135			−0.884085
$621$		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
$626$	44.0397	+	25.4263i	1.76018	+	1.01624i
$627$		0			0
$628$	−27.3921	−	47.4445i	−1.09306	−	1.89324i
$629$			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
$634$	−8.14001	+	14.0989i	−0.323281	+	0.559939i
$635$			13.3023i			0.527887i
$636$		0			0
$637$	15.7557	+	19.7170i	0.624263	+	0.781215i
$638$	4.70831			0.186404
$639$		0			0
$640$	8.01854	−	13.8885i	0.316961	−	0.548992i
$641$	10.4868			0.414205			0.207102	−	0.978319i	$-0.433597\pi$
$641$	10.4868			0.414205			0.207102	+	0.978319i	$0.433597\pi$
$642$		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	$0.455085\pi$
$644$	−9.24536	+	67.7411i	−0.364318	+	2.66937i
$645$		0			0
$646$	0.113137	+	0.195959i	0.00445133	+	0.00770992i
$647$	13.4337	−	23.2679i	0.528135	−	0.914757i	−0.471327	−	0.881959i	$-0.656225\pi$
$647$	13.4337	−	23.2679i	0.528135	−	0.914757i	0.999462	−	0.0327983i	$-0.0104419\pi$
$648$		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
$653$	4.14161			0.162074			0.0810369	−	0.996711i	$-0.474177\pi$
$653$	4.14161			0.162074			0.0810369	+	0.996711i	$0.474177\pi$
$654$		0			0
$655$	1.86759	−	1.07825i	0.0729726	−	0.0421308i
$656$	2.71734	−	1.56886i	0.106094	−	0.0612536i
$657$		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
$661$	−36.7084	−	21.1936i	−1.42779	−	0.824335i	−0.430844	−	0.902426i	$-0.641784\pi$
$661$	−36.7084	−	21.1936i	−1.42779	−	0.824335i	−0.996946	+	0.0780909i	$0.975118\pi$
$662$	7.58763	+	13.1422i	0.294902	+	0.510785i
$663$		0			0
$664$	34.6762			1.34570
$665$	0.0143772	−	0.105342i	0.000557522	−	0.00408499i
$666$		0			0
$667$	−5.31558	−	9.20685i	−0.205820	−	0.356491i
$668$	−7.60673	+	4.39175i	−0.294313	+	0.169922i
$669$		0			0
$670$	−3.45226	+	1.99317i	−0.133373	+	0.0770027i
$671$			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	$-0.359809\pi$
$674$		−	9.72645i		−	0.374649i
$675$		0			0
$676$	−13.5216	−	40.7823i	−0.520061	−	1.56855i
$677$	16.0830	−	27.8565i	0.618118	−	1.07061i	−0.371711	−	0.928349i	$-0.621229\pi$
$677$	16.0830	−	27.8565i	0.618118	−	1.07061i	0.989829	−	0.142263i	$-0.0454380\pi$
$678$		0			0
$679$	−0.690734	+	0.891396i	−0.0265079	+	0.0342086i
$680$	−2.63775	+	4.56872i	−0.101153	+	0.175202i
$681$		0			0
$682$			27.2207i			1.04234i
$683$			8.60236i			0.329160i	0.986364	+	0.164580i	$0.0526269\pi$
$683$			8.60236i			0.329160i	−0.986364	+	0.164580i	$0.947373\pi$
$684$		0			0
$685$	0.789983	−	1.36829i	0.0301837	−	0.0522797i
$686$	39.1738	+	16.8833i	1.49566	+	0.644606i
$687$		0			0
$688$	1.45097	−	2.51316i	0.0553179	−	0.0958134i
$689$	0.992909	−	9.72704i	0.0378268	−	0.370571i
$690$		0			0
$691$		−	20.4420i		−	0.777651i	−0.921311	−	0.388826i	$-0.872881\pi$
$691$		−	20.4420i		−	0.777651i	0.921311	−	0.388826i	$-0.127119\pi$
$692$	32.3680	+	56.0629i	1.23044	+	2.13119i
$693$		0			0
$694$			20.9477i			0.795164i
$695$	11.4537	−	6.61279i	0.434463	−	0.250837i
$696$		0			0
$697$	17.9719	−	10.3761i	0.680736	−	0.393023i
$698$	10.6187	+	18.3921i	0.401922	+	0.696150i
$699$		0			0
$700$	−34.6613	+	14.1649i	−1.31007	+	0.535385i
$701$	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
$704$	−16.6803	−	9.63036i	−0.628661	−	0.362958i
$705$		0			0
$706$	2.48118	−	4.29753i	0.0933804	−	0.161740i
$707$	−20.2233	−	15.6709i	−0.760576	−	0.589363i
$708$		0			0
$709$	−25.5416	+	14.7464i	−0.959234	+	0.553814i	−0.895937	−	0.444181i	$-0.853495\pi$
$709$	−25.5416	+	14.7464i	−0.959234	+	0.553814i	−0.0632970	+	0.997995i	$0.520162\pi$
$710$	−24.0227	+	13.8695i	−0.901556	+	0.520514i
$711$		0			0
$712$	52.6360			1.97262
$713$	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
$718$	−9.85518	+	17.0697i	−0.367792	+	0.637034i
$719$	4.16576	+	7.21531i	0.155357	+	0.269086i	0.933189	−	0.359386i	$-0.117014\pi$
$719$	4.16576	+	7.21531i	0.155357	+	0.269086i	−0.777832	+	0.628472i	$0.783681\pi$
$720$		0			0
$721$	−20.8680	−	16.1704i	−0.777165	−	0.602218i
$722$	−37.8946	−	21.8784i	−1.41029	−	0.814231i
$723$		0			0
$724$	4.52143			0.168038
$725$	2.91120	−	5.04235i	0.108119	−	0.187268i
$726$		0			0
$727$	9.66141			0.358322			0.179161	−	0.983820i	$-0.442662\pi$
$727$	9.66141			0.358322			0.179161	+	0.983820i	$0.442662\pi$
$728$	−20.7648	−	19.7742i	−0.769595	−	0.732880i
$729$		0			0
$730$		−	13.1953i		−	0.488381i
$731$	9.59645	−	16.6215i	0.354938	−	0.614770i
$732$		0			0
$733$	−12.1398	−	7.00894i	−0.448395	−	0.258881i	0.258757	−	0.965942i	$-0.416687\pi$
$733$	−12.1398	−	7.00894i	−0.448395	−	0.258881i	−0.707152	+	0.707061i	$0.750020\pi$
$734$	−4.58425	−	2.64672i	−0.169208	−	0.0976921i
$735$		0			0
$736$			41.3635i			1.52468i
$737$	1.53547	+	2.65951i	0.0565598	+	0.0979644i
$738$		0			0
$739$	33.6145	+	19.4073i	1.23653	+	0.713910i	0.968383	−	0.249468i	$-0.0802559\pi$
$739$	33.6145	+	19.4073i	1.23653	+	0.713910i	0.268146	+	0.963378i	$0.413589\pi$
$740$	−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
$745$	5.39185			0.197542
$746$	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
$751$	−48.1470			−1.75691			−0.878454	−	0.477827i	$-0.841425\pi$
$751$	−48.1470			−1.75691			−0.878454	+	0.477827i	$0.841425\pi$
$752$	0.0976479	+	0.0563770i	0.00356085	+	0.00205586i
$753$		0			0
$754$	11.2334	+	1.14667i	0.409096	+	0.0417594i
$755$	−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	$0.793277\pi$
$758$	−9.20262	−	15.9394i	−0.334254	−	0.578945i
$759$		0			0
$760$			0.120789i			0.00438147i
$761$	27.6895	−	15.9865i	1.00374	−	0.579511i	0.0943888	−	0.995535i	$-0.469910\pi$
$761$	27.6895	−	15.9865i	1.00374	−	0.579511i	0.909353	+	0.416025i	$0.136577\pi$
$762$		0			0
$763$	−11.6157	−	28.4234i	−0.420517	−	1.02900i
$764$	2.50067	+	4.33129i	0.0904712	+	0.156701i
$765$		0			0
$766$	32.5274	+	56.3391i	1.17526	+	2.03562i
$767$	−3.46382	+	4.79769i	−0.125071	+	0.173234i
$768$		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	$0.249759\pi$
$770$	−2.93653	−	7.18562i	−0.105825	−	0.258952i
$771$		0			0
$772$	19.9039	+	11.4915i	0.716357	+	0.413589i
$773$			37.2771i			1.34076i	0.742016	+	0.670382i	$0.233870\pi$
$773$			37.2771i			1.34076i	−0.742016	+	0.670382i	$0.766130\pi$
$774$		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
$782$		−	37.3029i		−	1.33395i
$783$		0			0
$784$	−2.11218	−	0.587486i	−0.0754349	−	0.0209816i
$785$		−	14.0447i		−	0.501276i
$786$		0			0
$787$		−	14.3486i		−	0.511472i	−0.966747	−	0.255736i	$-0.917682\pi$
$787$		−	14.3486i		−	0.511472i	0.966747	−	0.255736i	$-0.0823178\pi$
$788$	−44.2996	+	25.5764i	−1.57811	+	0.911120i
$789$		0			0
$790$	11.3765	+	19.7047i	0.404759	+	0.701064i
$791$	−7.27285	−	5.63566i	−0.258593	−	0.200381i
$792$		0			0
$793$	−1.65567	+	16.2198i	−0.0587947	+	0.575982i
$794$	8.58291	+	14.8660i	0.304596	+	0.527576i
$795$		0			0
$796$	21.8638			0.774940
$797$	−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
$800$	−19.6187	+	11.3268i	−0.693625	+	0.400464i
$801$		0			0
$802$	41.9154			1.48008
$803$	−10.1652			−0.358724
$804$		0			0
$805$	−10.7358	+	13.8546i	−0.378388	+	0.488312i
$806$	−6.62941	+	64.9450i	−0.233511	+	2.28759i
$807$		0			0
$808$	25.1723	+	14.5332i	0.885558	+	0.511277i
$809$	−21.2768	+	36.8525i	−0.748052	+	1.29566i	0.200703	+	0.979652i	$0.435677\pi$
$809$	−21.2768	+	36.8525i	−0.748052	+	1.29566i	−0.948755	+	0.316013i	$0.897656\pi$
$810$		0			0
$811$			16.3622i			0.574554i	0.957848	+	0.287277i	$0.0927500\pi$
$811$			16.3622i			0.574554i	−0.957848	+	0.287277i	$0.907250\pi$
$812$	11.0061	−	4.49784i	0.386239	−	0.157843i
$813$		0			0
$814$	20.0986	+	11.6040i	0.704457	+	0.406719i
$815$	−7.66906			−0.268636
$816$		0			0
$817$		−	0.439444i		−	0.0153742i
$818$	67.4455			2.35818
$819$		0			0
$820$	28.0549			0.979721
$821$			3.10550i			0.108383i	0.998531	+	0.0541913i	$0.0172581\pi$
$821$			3.10550i			0.108383i	−0.998531	+	0.0541913i	$0.982742\pi$
$822$		0			0
$823$	−49.0164			−1.70860			−0.854301	−	0.519778i	$-0.826015\pi$
$823$	−49.0164			−1.70860			−0.854301	+	0.519778i	$0.826015\pi$
$824$	25.9747	+	14.9965i	0.904873	+	0.522429i
$825$		0			0
$826$	−1.35244	+	9.90937i	−0.0470573	+	0.344791i
$827$			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
$829$	24.6282	−	42.6574i	0.855374	−	1.48155i	−0.0209227	−	0.999781i	$-0.506660\pi$
$829$	24.6282	−	42.6574i	0.855374	−	1.48155i	0.876297	−	0.481771i	$-0.160006\pi$
$830$	19.4972	+	11.2567i	0.676757	+	0.390726i
$831$		0			0
$832$	−37.4514	−	27.0391i	−1.29839	−	0.937411i
$833$	−13.9695	−	3.88551i	−0.484015	−	0.134625i
$834$		0			0
$835$	−2.25177			−0.0779257
$836$	0.235656			0.00815034
$837$		0			0
$838$	41.3684	−	23.8841i	1.42905	−	0.825062i
$839$	−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
$842$	−57.2814			−1.97405
$843$		0			0
$844$	−13.3760	−	23.1678i	−0.460419	−	0.797470i
$845$	2.22553	−	10.7876i	0.0765606	−	0.371105i
$846$		0			0
$847$	21.4049	−	8.74748i	0.735480	−	0.300567i
$848$	0.424662	+	0.735535i	0.0145829	+	0.0252584i
$849$		0			0
$850$	17.6928	−	10.2149i	0.606857	−	0.350369i
$851$		−	52.4024i		−	1.79633i
$852$		0			0
$853$		−	52.4163i		−	1.79470i	−0.441319	−	0.897350i	$-0.645489\pi$
$853$		−	52.4163i		−	1.79470i	0.441319	−	0.897350i	$-0.354511\pi$
$854$	10.4244	+	25.5083i	0.356716	+	0.872875i
$855$		0			0
$856$			29.6443i			1.01322i
$857$	−5.06355	−	8.77032i	−0.172967	−	0.299588i	0.766489	−	0.642258i	$-0.222002\pi$
$857$	−5.06355	−	8.77032i	−0.172967	−	0.299588i	−0.939456	+	0.342670i	$0.888669\pi$
$858$		0			0
$859$	0.255118	−	0.441878i	0.00870452	−	0.0150767i	−0.861640	−	0.507519i	$-0.830563\pi$
$859$	0.255118	−	0.441878i	0.00870452	−	0.0150767i	0.870345	+	0.492443i	$0.163896\pi$
$860$	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	$-0.219889\pi$
$863$	17.7527	+	10.2495i	0.604310	+	0.348898i	−0.166426	+	0.986054i	$0.553223\pi$
$864$		0			0
$865$			16.5959i			0.564279i
$866$	−46.7347	−	26.9823i	−1.58811	−	0.916896i
$867$		0			0
$868$	26.0039	+	63.6310i	0.882631	+	2.15978i
$869$	15.1799	−	8.76412i	0.514943	−	0.297302i
$870$		0			0
$871$	3.01572	+	6.71919i	0.102184	+	0.227671i
$872$	17.4422	+	30.2107i	0.590667	+	1.02306i
$873$		0			0
$874$	−0.427047	−	0.739668i	−0.0144451	−	0.0250196i
$875$	−20.6168	−	2.81379i	−0.696974	−	0.0951235i
$876$		0			0
$877$	−9.77794	+	5.64530i	−0.330178	+	0.190628i	−0.655920	−	0.754830i	$-0.727719\pi$
$877$	−9.77794	+	5.64530i	−0.330178	+	0.190628i	0.325742	+	0.945459i	$0.394386\pi$
$878$			27.7276i			0.935762i
$879$		0			0
$880$	0.199476	+	0.345503i	0.00672435	+	0.0116469i
$881$	−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	$0.656319\pi$
$884$	20.0130	+	14.4489i	0.673109	+	0.485969i
$885$		0			0
$886$	31.3827	+	18.1188i	1.05432	+	0.608713i
$887$	20.6235			0.692470			0.346235	−	0.938148i	$-0.387460\pi$
$887$	20.6235			0.692470			0.346235	+	0.938148i	$0.387460\pi$
$888$		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
$893$	0.0170744			0.000571374
$894$		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
$899$	−9.25671	−	5.34437i	−0.308729	−	0.178245i
$900$		0			0
$901$	2.80863	+	4.86468i	0.0935689	+	0.162066i
$902$		−	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
$907$	20.7315	−	35.9081i	0.688379	−	1.19231i	−0.283982	−	0.958829i	$-0.591656\pi$
$907$	20.7315	−	35.9081i	0.688379	−	1.19231i	0.972362	−	0.233479i	$-0.0750109\pi$
$908$		−	4.28269i		−	0.142126i
$909$		0			0
$910$	−5.25616	−	17.8591i	−0.174240	−	0.592023i
$911$	−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
$913$	8.67180	−	15.0200i	0.286995	−	0.497090i
$914$	70.9310			2.34619
$915$		0			0
$916$	−59.5849	−	34.4014i	−1.96874	−	1.13665i
$917$	−5.32285	−	4.12463i	−0.175776	−	0.136207i
$918$		0			0
$919$	24.3839	+	42.2341i	0.804350	+	1.39318i	0.916729	+	0.399510i	$0.130820\pi$
$919$	24.3839	+	42.2341i	0.804350	+	1.39318i	−0.112379	+	0.993665i	$0.535847\pi$
$920$	9.95645	−	17.2451i	0.328254	−	0.568553i
$921$		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
$926$	3.89675			0.128055
$927$		0			0
$928$	6.22958	−	3.59665i	0.204496	−	0.118066i
$929$	25.4464	−	14.6915i	0.834868	−	0.482012i	−0.0206482	−	0.999787i	$-0.506573\pi$
$929$	25.4464	−	14.6915i	0.834868	−	0.482012i	0.855517	+	0.517775i	$0.173240\pi$
$930$		0			0
$931$	−0.321479	+	0.0828796i	−0.0105360	+	0.00271627i
$932$	−21.9855	+	38.0801i	−0.720160	+	1.24735i
$933$		0			0
$934$	−56.5541	−	32.6515i	−1.85051	−	1.06839i
$935$	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	$0.611558\pi$
$938$	9.83938	+	7.62444i	0.321267	+	0.248947i
$939$		0			0
$940$	0.504079	+	0.873090i	0.0164412	+	0.0284770i
$941$	20.8740	−	12.0516i	0.680474	−	0.392872i	−0.119560	−	0.992827i	$-0.538148\pi$
$941$	20.8740	−	12.0516i	0.680474	−	0.392872i	0.800034	+	0.599955i	$0.204815\pi$
$942$		0			0
$943$	−67.8368	+	39.1656i	−2.20907	+	1.27541i
$944$		−	0.514013i		−	0.0167297i
$945$		0			0
$946$	−16.0423	−	27.7860i	−0.521579	−	0.903402i
$947$		−	3.34046i		−	0.108550i	−0.998526	−	0.0542751i	$-0.982715\pi$
$947$		−	3.34046i		−	0.108550i	0.998526	−	0.0542751i	$-0.0172848\pi$
$948$		0			0
$949$	−24.2529	−	2.47567i	−0.787282	−	0.0803636i
$950$	0.233883	−	0.405097i	0.00758815	−	0.0131431i
$951$		0			0
$952$	16.3220	+	2.22763i	0.528998	+	0.0721980i
$953$	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
$955$			1.28216i			0.0414898i
$956$		−	44.1726i		−	1.42864i
$957$		0			0
$958$	7.23509	−	12.5315i	0.233755	−	0.404876i
$959$	−4.88828	−	0.667156i	−0.157851	−	0.0215436i
$960$		0			0
$961$	15.3981	−	26.6702i	0.496711	−	0.860329i
$962$	45.1266	+	32.5803i	1.45494	+	1.05043i
$963$		0			0
$964$			2.75691i			0.0887939i
$965$	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	$0.723402\pi$
$968$	−22.7509	+	13.1352i	−0.731241	+	0.422182i
$969$		0			0
$970$	0.720362	−	0.415901i	0.0231294	−	0.0133538i
$971$	17.2357	+	29.8532i	0.553121	+	0.958033i	0.998047	+	0.0624662i	$0.0198966\pi$
$971$	17.2357	+	29.8532i	0.553121	+	0.958033i	−0.444926	+	0.895567i	$0.646770\pi$
$972$		0			0
$973$	−32.6444	−	25.2958i	−1.04653	−	0.810948i
$974$	29.9830			0.960717
$975$		0			0
$976$	−0.708122	−	1.22650i	−0.0226664	−	0.0392594i
$977$	−11.5598	−	6.67406i	−0.369831	−	0.213522i	0.303553	−	0.952814i	$-0.401827\pi$
$977$	−11.5598	−	6.67406i	−0.369831	−	0.213522i	−0.673385	+	0.739292i	$0.735160\pi$
$978$		0			0
$979$	13.1632	−	22.7993i	0.420698	−	0.728670i
$980$	−13.7288	−	13.9918i	−0.438551	−	0.446951i
$981$		0			0
$982$	−24.6390	+	14.2253i	−0.786263	+	0.453949i
$983$	10.8551	−	6.26720i	0.346224	−	0.199893i	−0.316797	−	0.948493i	$-0.602607\pi$
$983$	10.8551	−	6.26720i	0.346224	−	0.199893i	0.663021	+	0.748601i	$0.269274\pi$
$984$		0			0
$985$	−13.1137			−0.417838
$986$	−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
$991$	5.20596	−	9.01698i	0.165373	−	0.286434i	−0.771415	−	0.636332i	$-0.780451\pi$
$991$	5.20596	−	9.01698i	0.165373	−	0.286434i	0.936788	+	0.349899i	$0.113784\pi$
$992$	20.7938	+	36.0158i	0.660202	+	1.14350i
$993$		0			0
$994$	68.4677	+	53.0550i	2.17166	+	1.68280i
$995$	4.85414	+	2.80254i	0.153887	+	0.0888464i
$996$		0			0
$997$	5.75270			0.182190			0.0910949	−	0.995842i	$-0.470963\pi$
$997$	5.75270			0.182190			0.0910949	+	0.995842i	$0.470963\pi$
$998$	−10.5414	+	18.2582i	−0.333681	+	0.577953i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.6	✓	12	273.95	odd	6
91.2.k.b.23.1	yes	12	3.2	odd	2
91.2.u.b.30.6	yes	12	39.17	odd	6
91.2.u.b.88.6	yes	12	21.11	odd	6
637.2.k.i.459.6		12	273.17	even	6
637.2.k.i.569.1		12	21.20	even	2
637.2.q.g.491.1		12	21.2	odd	6
637.2.q.g.589.1		12	273.212	odd	6
637.2.q.i.491.1		12	21.5	even	6
637.2.q.i.589.1		12	273.173	even	6
637.2.u.g.30.6		12	273.251	even	6
637.2.u.g.361.6		12	21.17	even	6
819.2.bm.f.478.6		12	1.1	even	1	trivial
819.2.bm.f.550.1		12	91.4	even	6	inner
819.2.do.e.361.1		12	7.4	even	3
819.2.do.e.667.1		12	13.4	even	6
1183.2.e.j.170.2		24	39.11	even	12
1183.2.e.j.170.11		24	39.2	even	12
1183.2.e.j.508.2		24	273.11	even	12
1183.2.e.j.508.11		24	273.158	even	12
8281.2.a.co.1.2		12	273.236	odd	12
8281.2.a.co.1.11		12	273.89	odd	12
8281.2.a.cp.1.2		12	273.2	even	12
8281.2.a.cp.1.11		12	273.128	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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.30327i q^{2} -3.30504 q^{4} +(-0.733776 - 0.423646i) q^{5} +(-0.357777 + 2.62145i) q^{7} -3.00585i q^{8} +O(q^{10})\)	\(q+2.30327i q^{2} -3.30504 q^{4} +(-0.733776 - 0.423646i) q^{5} +(-0.357777 + 2.62145i) q^{7} -3.00585i q^{8} +(0.975769 - 1.69008i) q^{10} +(-1.30198 - 0.751701i) q^{11} +(-2.92329 - 2.11054i) q^{13} +(-6.03790 - 0.824057i) q^{14} +0.313194 q^{16} +2.07140 q^{17} +(0.0410731 - 0.0237136i) q^{19} +(2.42516 + 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} -7.81870 q^{23} +(-2.14105 - 3.70840i) q^{25} +(4.86115 - 6.73311i) q^{26} +(1.18247 - 8.66399i) q^{28} +(0.679854 + 1.17754i) q^{29} +(-6.80787 + 3.93052i) q^{31} -5.29033i q^{32} +4.77099i q^{34} +(1.37309 - 1.77199i) q^{35} +6.70219i q^{37} +(0.0546187 + 0.0946024i) q^{38} +(-1.27341 + 2.20562i) q^{40} +(8.67622 - 5.00922i) q^{41} +(4.63283 - 8.02430i) q^{43} +(4.30311 + 2.48440i) q^{44} -18.0086i q^{46} +(0.311781 + 0.180007i) q^{47} +(-6.74399 - 1.87579i) q^{49} +(8.54144 - 4.93141i) q^{50} +(9.66157 + 6.97543i) q^{52} +(1.35591 + 2.34850i) q^{53} +(0.636910 + 1.10316i) q^{55} +(7.87968 + 1.07542i) q^{56} +(-2.71219 + 1.56588i) q^{58} -1.64120i q^{59} +(-2.26097 - 3.91612i) q^{61} +(-9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(1.25091 + 2.78711i) q^{65} +(-1.76900 - 1.02133i) q^{67} -6.84606 q^{68} +(4.08136 + 3.16260i) q^{70} +(-12.3096 - 7.10697i) q^{71} +(5.85563 - 3.38075i) q^{73} -15.4369 q^{74} +(-0.135748 + 0.0783743i) q^{76} +(2.43637 - 3.14414i) q^{77} +(-5.82952 + 10.0970i) q^{79} +(-0.229814 - 0.132683i) q^{80} +(11.5376 + 19.9837i) q^{82} +11.5362i q^{83} +(-1.51994 - 0.877541i) q^{85} +(18.4821 + 10.6706i) q^{86} +(-2.25950 + 3.91357i) q^{88} +17.5112i q^{89} +(6.57857 - 6.90814i) q^{91} +25.8411 q^{92} +(-0.414604 + 0.718115i) q^{94} -0.0401846 q^{95} +(0.369125 + 0.213115i) q^{97} +(4.32044 - 15.5332i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

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