LMFDB - Embedded newform 819.2.n.d.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, 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 $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.3
Root			$0.756174 - 1.30973i$ of defining polynomial
Character	$\chi$	$=$	819.100
Dual form			819.2.n.d.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.425563 - 0.737096i) q^{2} +(0.637793 - 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +(1.82097 - 1.91940i) q^{7} -2.78793 q^{8} +O(q^{10})$	\(q+(-0.425563 - 0.737096i) q^{2} +(0.637793 - 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +(1.82097 - 1.91940i) q^{7} -2.78793 q^{8} -2.92913 q^{10} +0.897986 q^{11} +(-3.07517 - 1.88237i) q^{13} +(-2.18972 - 0.525403i) q^{14} +(-0.0891447 - 0.154403i) q^{16} +(0.968404 - 1.67733i) q^{17} +1.03804 q^{19} +(-2.19495 - 3.80177i) q^{20} +(-0.382150 - 0.661902i) q^{22} +(2.82506 + 4.89315i) q^{23} +(-3.42189 - 5.92688i) q^{25} +(-0.0788077 + 3.06776i) q^{26} +(-0.958938 - 3.23578i) q^{28} +(-0.917969 + 1.58997i) q^{29} +(4.56692 + 7.91014i) q^{31} +(-2.86381 + 4.96026i) q^{32} -1.64847 q^{34} +(-2.58718 - 8.73000i) q^{35} +(5.30001 + 9.17989i) q^{37} +(-0.441751 - 0.765135i) q^{38} +(-4.79731 + 8.30918i) q^{40} +(-2.66571 + 4.61715i) q^{41} +(1.95732 + 3.39018i) q^{43} +(0.572729 - 0.991996i) q^{44} +(2.40448 - 4.16469i) q^{46} +(3.59565 - 6.22784i) q^{47} +(-0.368167 - 6.99031i) q^{49} +(-2.91246 + 5.04452i) q^{50} +(-4.04076 + 2.19655i) q^{52} +(-4.69324 - 8.12893i) q^{53} +(1.54520 - 2.67637i) q^{55} +(-5.07673 + 5.35115i) q^{56} +1.56261 q^{58} +(-0.255259 + 0.442121i) q^{59} +1.43619 q^{61} +(3.88702 - 6.73252i) q^{62} +4.51834 q^{64} +(-10.9018 + 5.92620i) q^{65} -8.44932 q^{67} +(-1.23528 - 2.13957i) q^{68} +(-5.33385 + 5.62216i) q^{70} +(-1.72419 - 2.98638i) q^{71} +(-5.45026 - 9.44013i) q^{73} +(4.51097 - 7.81324i) q^{74} +(0.662054 - 1.14671i) q^{76} +(1.63520 - 1.72359i) q^{77} +(6.04589 - 10.4718i) q^{79} -0.613579 q^{80} +4.53771 q^{82} -1.51669 q^{83} +(-3.33274 - 5.77248i) q^{85} +(1.66593 - 2.88547i) q^{86} -2.50353 q^{88} +(6.80391 + 11.7847i) q^{89} +(-9.21280 + 2.47475i) q^{91} +7.20722 q^{92} -6.12069 q^{94} +(1.78619 - 3.09378i) q^{95} +(-0.253120 - 0.438417i) q^{97} +(-4.99585 + 3.24619i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8	$ 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29} + 16 q^{31} - 8 q^{32} + 32 q^{34} - 8 q^{35} - 13 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} + 16 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} - 25 q^{52} + 2 q^{53} + 9 q^{55} + 18 q^{56} + 16 q^{58} - 13 q^{59} + 10 q^{61} - 5 q^{62} - 30 q^{64} - 19 q^{65} + 22 q^{67} - 29 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} + 3 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} - 14 q^{80} - 2 q^{82} + 54 q^{83} - q^{85} + 7 q^{86} - 4 q^{89} - 20 q^{91} - 54 q^{92} - 90 q^{94} + 6 q^{95} - 35 q^{97} - 62 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.425563	−	0.737096i	−0.300918	−	0.521206i	0.675426	−	0.737428i	$-0.263960\pi$
$2$	−0.425563	−	0.737096i	−0.300918	−	0.521206i	−0.976344	+	0.216222i	$0.930626\pi$
$3$		0			0
$3$		0			0
$4$	0.637793	−	1.10469i	0.318896	−	0.552345i
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	−0.168276	−	0.985740i	$-0.553820\pi$
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	0.937814	−	0.347139i	$-0.112847\pi$
$6$		0			0
$7$	1.82097	−	1.91940i	0.688260	−	0.725464i
$7$	1.82097	−	1.91940i	0.688260	−	0.725464i
$8$	−2.78793			−0.985684
$9$		0			0
$10$	−2.92913			−0.926272
$11$	0.897986			0.270753			0.135377	−	0.990794i	$-0.456776\pi$
$11$	0.897986			0.270753			0.135377	+	0.990794i	$0.456776\pi$
$12$		0			0
$13$	−3.07517	−	1.88237i	−0.852900	−	0.522075i
$13$	−3.07517	−	1.88237i	−0.852900	−	0.522075i
$14$	−2.18972	−	0.525403i	−0.585226	−	0.140420i
$15$		0			0
$16$	−0.0891447	−	0.154403i	−0.0222862	−	0.0386008i
$17$	0.968404	−	1.67733i	0.234873	−	0.406811i	−0.724363	−	0.689419i	$-0.757866\pi$
$17$	0.968404	−	1.67733i	0.234873	−	0.406811i	0.959236	+	0.282607i	$0.0911994\pi$
$18$		0			0
$19$	1.03804			0.238142			0.119071	−	0.992886i	$-0.462008\pi$
$19$	1.03804			0.238142			0.119071	+	0.992886i	$0.462008\pi$
$20$	−2.19495	−	3.80177i	−0.490806	−	0.850101i
$21$		0			0
$22$	−0.382150	−	0.661902i	−0.0814745	−	0.141118i
$23$	2.82506	+	4.89315i	0.589067	+	1.02029i	0.994355	+	0.106104i	$0.0338378\pi$
$23$	2.82506	+	4.89315i	0.589067	+	1.02029i	−0.405288	+	0.914189i	$0.632829\pi$
$24$		0			0
$25$	−3.42189	−	5.92688i	−0.684378	−	1.18538i
$26$	−0.0788077	+	3.06776i	−0.0154555	+	0.601638i
$27$		0			0
$28$	−0.958938	−	3.23578i	−0.181222	−	0.611505i
$29$	−0.917969	+	1.58997i	−0.170463	+	0.295250i	−0.938582	−	0.345057i	$-0.887860\pi$
$29$	−0.917969	+	1.58997i	−0.170463	+	0.295250i	0.768119	+	0.640307i	$0.221193\pi$
$30$		0			0
$31$	4.56692	+	7.91014i	0.820244	+	1.42070i	0.905501	+	0.424345i	$0.139495\pi$
$31$	4.56692	+	7.91014i	0.820244	+	1.42070i	−0.0852573	+	0.996359i	$0.527171\pi$
$32$	−2.86381	+	4.96026i	−0.506254	+	0.876858i
$33$		0			0
$34$	−1.64847			−0.282710
$35$	−2.58718	−	8.73000i	−0.437313	−	1.47564i
$36$		0			0
$37$	5.30001	+	9.17989i	0.871316	+	1.50916i	0.860636	+	0.509221i	$0.170067\pi$
$37$	5.30001	+	9.17989i	0.871316	+	1.50916i	0.0106808	+	0.999943i	$0.496600\pi$
$38$	−0.441751	−	0.765135i	−0.0716614	−	0.124121i
$39$		0			0
$40$	−4.79731	+	8.30918i	−0.758521	+	1.31380i
$41$	−2.66571	+	4.61715i	−0.416314	+	0.721078i	−0.995565	−	0.0940715i	$-0.970012\pi$
$41$	−2.66571	+	4.61715i	−0.416314	+	0.721078i	0.579251	+	0.815149i	$0.303345\pi$
$42$		0			0
$43$	1.95732	+	3.39018i	0.298489	+	0.516998i	0.975790	−	0.218708i	$-0.0701841\pi$
$43$	1.95732	+	3.39018i	0.298489	+	0.516998i	−0.677302	+	0.735706i	$0.736851\pi$
$44$	0.572729	−	0.991996i	0.0863422	−	0.149549i
$45$		0			0
$46$	2.40448	−	4.16469i	0.354522	−	0.614050i
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	−0.475115	−	0.879924i	$-0.657593\pi$
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	0.999594	−	0.0285004i	$-0.00907317\pi$
$48$		0			0
$49$	−0.368167	−	6.99031i	−0.0525953	−	0.998616i
$50$	−2.91246	+	5.04452i	−0.411883	+	0.713403i
$51$		0			0
$52$	−4.04076	+	2.19655i	−0.560352	+	0.304607i
$53$	−4.69324	−	8.12893i	−0.644666	−	1.11659i	−0.984378	−	0.176065i	$-0.943663\pi$
$53$	−4.69324	−	8.12893i	−0.644666	−	1.11659i	0.339712	−	0.940529i	$-0.389670\pi$
$54$		0			0
$55$	1.54520	−	2.67637i	0.208355	−	0.360881i
$56$	−5.07673	+	5.35115i	−0.678407	+	0.715078i
$57$		0			0
$58$	1.56261			0.205181
$59$	−0.255259	+	0.442121i	−0.0332318	+	0.0575592i	−0.882163	−	0.470944i	$-0.843913\pi$
$59$	−0.255259	+	0.442121i	−0.0332318	+	0.0575592i	0.848931	+	0.528503i	$0.177247\pi$
$60$		0			0
$61$	1.43619			0.183885			0.0919426	−	0.995764i	$-0.470692\pi$
$61$	1.43619			0.183885			0.0919426	+	0.995764i	$0.470692\pi$
$62$	3.88702	−	6.73252i	0.493653	−	0.855031i
$63$		0			0
$64$	4.51834			0.564792
$65$	−10.9018	+	5.92620i	−1.35220	+	0.735055i
$66$		0			0
$67$	−8.44932			−1.03225			−0.516124	−	0.856514i	$-0.672626\pi$
$67$	−8.44932			−1.03225			−0.516124	+	0.856514i	$0.672626\pi$
$68$	−1.23528	−	2.13957i	−0.149800	−	0.259461i
$69$		0			0
$70$	−5.33385	+	5.62216i	−0.637516	+	0.671977i
$71$	−1.72419	−	2.98638i	−0.204623	−	0.354418i	0.745389	−	0.666629i	$-0.232264\pi$
$71$	−1.72419	−	2.98638i	−0.204623	−	0.354418i	−0.950013	+	0.312211i	$0.898930\pi$
$72$		0			0
$73$	−5.45026	−	9.44013i	−0.637905	−	1.10488i	−0.985892	−	0.167384i	$-0.946468\pi$
$73$	−5.45026	−	9.44013i	−0.637905	−	1.10488i	0.347987	−	0.937499i	$-0.386865\pi$
$74$	4.51097	−	7.81324i	0.524390	−	0.908270i
$75$		0			0
$76$	0.662054	−	1.14671i	0.0759428	−	0.131537i
$77$	1.63520	−	1.72359i	0.186349	−	0.196422i
$78$		0			0
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	−0.294699	−	0.955590i	$-0.595219\pi$
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	0.974915	−	0.222578i	$-0.0714472\pi$
$80$	−0.613579			−0.0686002
$81$		0			0
$82$	4.53771			0.501107
$83$	−1.51669			−0.166479			−0.0832393	−	0.996530i	$-0.526527\pi$
$83$	−1.51669			−0.166479			−0.0832393	+	0.996530i	$0.526527\pi$
$84$		0			0
$85$	−3.33274	−	5.77248i	−0.361487	−	0.626113i
$86$	1.66593	−	2.88547i	0.179642	−	0.311148i
$87$		0			0
$88$	−2.50353			−0.266877
$89$	6.80391	+	11.7847i	0.721213	+	1.24918i	0.960514	+	0.278232i	$0.0897484\pi$
$89$	6.80391	+	11.7847i	0.721213	+	1.24918i	−0.239301	+	0.970945i	$0.576918\pi$
$90$		0			0
$91$	−9.21280	+	2.47475i	−0.965763	+	0.259424i
$92$	7.20722			0.751405
$93$		0			0
$94$	−6.12069			−0.631301
$95$	1.78619	−	3.09378i	0.183260	−	0.317415i
$96$		0			0
$97$	−0.253120	−	0.438417i	−0.0257005	−	0.0445145i	0.852889	−	0.522092i	$-0.174848\pi$
$97$	−0.253120	−	0.438417i	−0.0257005	−	0.0445145i	−0.878590	+	0.477578i	$0.841515\pi$
$98$	−4.99585	+	3.24619i	−0.504657	+	0.327915i
$99$		0			0
$100$	−8.72982			−0.872982
$101$	5.98654			0.595683			0.297842	−	0.954615i	$-0.403733\pi$
$101$	5.98654			0.595683			0.297842	+	0.954615i	$0.403733\pi$
$102$		0			0
$103$	2.06651	−	3.57930i	0.203619	−	0.352679i	−0.746073	−	0.665865i	$-0.768063\pi$
$103$	2.06651	−	3.57930i	0.203619	−	0.352679i	0.949692	+	0.313186i	$0.101396\pi$
$104$	8.57338	+	5.24792i	0.840689	+	0.514601i
$105$		0			0
$106$	−3.99454	+	6.91874i	−0.387984	+	0.672008i
$107$	−7.06169	−	12.2312i	−0.682679	−	1.18243i	−0.974160	−	0.225858i	$-0.927481\pi$
$107$	−7.06169	−	12.2312i	−0.682679	−	1.18243i	0.291481	−	0.956577i	$-0.405852\pi$
$108$		0			0
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	0.948934	−	0.315475i	$-0.102164\pi$
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	−0.747677	+	0.664063i	$0.768831\pi$
$110$	−2.63032			−0.250791
$111$		0			0
$112$	−0.458690	−	0.110059i	−0.0433421	−	0.0103996i
$113$	6.88472	+	11.9247i	0.647660	+	1.12178i	0.983680	+	0.179926i	$0.0575857\pi$
$113$	6.88472	+	11.9247i	0.647660	+	1.12178i	−0.336020	+	0.941855i	$0.609081\pi$
$114$		0			0
$115$	19.4448			1.81324
$116$	1.17095	+	2.02814i	0.108720	+	0.188308i
$117$		0			0
$118$	0.434514			0.0400003
$119$	−1.45602	−	4.91310i	−0.133473	−	0.450384i
$120$		0			0
$121$	−10.1936			−0.926693
$122$	−0.611189	−	1.05861i	−0.0553344	−	0.0958420i
$123$		0			0
$124$	11.6510			1.04629
$125$	−6.34531			−0.567542
$126$		0			0
$127$	−0.972482	+	1.68439i	−0.0862938	+	0.149465i	−0.905942	−	0.423402i	$-0.860836\pi$
$127$	−0.972482	+	1.68439i	−0.0862938	+	0.149465i	0.819648	+	0.572868i	$0.194169\pi$
$128$	3.80478	+	6.59007i	0.336298	+	0.582485i
$129$		0			0
$130$	9.00758	+	5.51370i	0.790017	+	0.483584i
$131$	−6.01770	+	10.4230i	−0.525769	+	0.910659i	0.473780	+	0.880643i	$0.342889\pi$
$131$	−6.01770	+	10.4230i	−0.525769	+	0.910659i	−0.999549	+	0.0300158i	$0.990444\pi$
$132$		0			0
$133$	1.89023	−	1.99241i	0.163904	−	0.172764i
$134$	3.59571	+	6.22796i	0.310622	+	0.538014i
$135$		0			0
$136$	−2.69985	+	4.67627i	−0.231510	+	0.400987i
$137$	4.35857	−	7.54927i	0.372378	−	0.644978i	−0.617553	−	0.786529i	$-0.711876\pi$
$137$	4.35857	−	7.54927i	0.372378	−	0.644978i	0.989931	+	0.141552i	$0.0452092\pi$
$138$		0			0
$139$	−2.10625	−	3.64813i	−0.178650	−	0.309430i	0.762769	−	0.646672i	$-0.223840\pi$
$139$	−2.10625	−	3.64813i	−0.178650	−	0.309430i	−0.941418	+	0.337241i	$0.890506\pi$
$140$	−11.2940	−	2.70990i	−0.954519	−	0.229029i
$141$		0			0
$142$	−1.46750	+	2.54178i	−0.123150	+	0.213302i
$143$	−2.76146	−	1.69034i	−0.230925	−	0.141353i
$144$		0			0
$145$	3.15917	+	5.47184i	0.262355	+	0.454412i
$146$	−4.63885	+	8.03473i	−0.383914	+	0.664959i
$147$		0			0
$148$	13.5212			1.11144
$149$	−5.86484			−0.480466			−0.240233	−	0.970715i	$-0.577224\pi$
$149$	−5.86484			−0.480466			−0.240233	+	0.970715i	$0.577224\pi$
$150$		0			0
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	0.973155	+	0.230150i	$0.0739216\pi$
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	−0.287262	+	0.957852i	$0.592745\pi$
$152$	−2.89398			−0.234733
$153$		0			0
$154$	−1.96633	−	0.471805i	−0.158452	−	0.0380191i
$155$	31.4339			2.52483
$156$		0			0
$157$	0.969500	+	1.67922i	0.0773746	+	0.134017i	0.902116	−	0.431493i	$-0.142013\pi$
$157$	0.969500	+	1.67922i	0.0773746	+	0.134017i	−0.824742	+	0.565509i	$0.808680\pi$
$158$	−10.2916			−0.818757
$159$		0			0
$160$	9.85573	+	17.0706i	0.779164	+	1.34955i
$161$	14.5362	+	3.48785i	1.14562	+	0.274881i
$162$		0			0
$163$	−11.8959			−0.931762			−0.465881	−	0.884847i	$-0.654262\pi$
$163$	−11.8959			−0.931762			−0.465881	+	0.884847i	$0.654262\pi$
$164$	3.40035	+	5.88957i	0.265522	+	0.459898i
$165$		0			0
$166$	0.645448	+	1.11795i	0.0500965	+	0.0867696i
$167$	8.28801	−	14.3553i	0.641346	−	1.11084i	−0.343787	−	0.939048i	$-0.611710\pi$
$167$	8.28801	−	14.3553i	0.641346	−	1.11084i	0.985133	−	0.171796i	$-0.0549569\pi$
$168$		0			0
$169$	5.91338	+	11.5772i	0.454875	+	0.890555i
$170$	−2.83658	+	4.91310i	−0.217556	+	0.376818i
$171$		0			0
$172$	4.99346			0.380748
$173$	9.98656			0.759264			0.379632	−	0.925138i	$-0.376051\pi$
$173$	9.98656			0.759264			0.379632	+	0.925138i	$0.376051\pi$
$174$		0			0
$175$	−17.6072	−	4.22469i	−1.33098	−	0.319357i
$176$	−0.0800507	−	0.138652i	−0.00603405	−	0.0104513i
$177$		0			0
$178$	5.79098	−	10.0303i	0.434052	−	0.751801i
$179$	−9.17657			−0.685889			−0.342945	−	0.939356i	$-0.611424\pi$
$179$	−9.17657			−0.685889			−0.342945	+	0.939356i	$0.611424\pi$
$180$		0			0
$181$	6.00489			0.446340			0.223170	−	0.974780i	$-0.428360\pi$
$181$	6.00489			0.446340			0.223170	+	0.974780i	$0.428360\pi$
$182$	5.74475	+	5.73756i	0.425829	+	0.425296i
$183$		0			0
$184$	−7.87609	−	13.6418i	−0.580633	−	1.00569i
$185$	36.4797			2.68204
$186$		0			0
$187$	0.869614	−	1.50622i	0.0635925	−	0.110145i
$188$	−4.58655	−	7.94415i	−0.334509	−	0.579386i
$189$		0			0
$190$	−3.04055			−0.220585
$191$	−1.31612			−0.0952313			−0.0476156	−	0.998866i	$-0.515162\pi$
$191$	−1.31612			−0.0952313			−0.0476156	+	0.998866i	$0.515162\pi$
$192$		0			0
$193$	−16.4254			−1.18233			−0.591163	−	0.806552i	$-0.701331\pi$
$193$	−16.4254			−1.18233			−0.591163	+	0.806552i	$0.701331\pi$
$194$	−0.215437	+	0.373148i	−0.0154675	+	0.0267905i
$195$		0			0
$196$	−7.95694	−	4.05166i	−0.568353	−	0.289404i
$197$	−12.7938	+	22.1594i	−0.911517	+	1.57879i	−0.0995951	+	0.995028i	$0.531755\pi$
$197$	−12.7938	+	22.1594i	−0.911517	+	1.57879i	−0.811922	+	0.583766i	$0.801579\pi$
$198$		0			0
$199$	12.6894	−	21.9787i	0.899528	−	1.55803i	0.0714284	−	0.997446i	$-0.477244\pi$
$199$	12.6894	−	21.9787i	0.899528	−	1.55803i	0.828099	−	0.560582i	$-0.189422\pi$
$200$	9.54000	+	16.5238i	0.674580	+	1.16841i
$201$		0			0
$202$	−2.54765	−	4.41266i	−0.179252	−	0.310473i
$203$	1.38019	+	4.65723i	0.0968704	+	0.326873i
$204$		0			0
$205$	9.17399	+	15.8898i	0.640740	+	1.10979i
$206$	−3.51772			−0.245091
$207$		0			0
$208$	−0.0165082	+	0.642619i	−0.00114464	+	0.0445576i
$209$	0.932145			0.0644778
$210$		0			0
$211$	2.84824	−	4.93330i	0.196081	−	0.339622i	−0.751173	−	0.660105i	$-0.770512\pi$
$211$	2.84824	−	4.93330i	0.196081	−	0.339622i	0.947254	+	0.320483i	$0.103845\pi$
$212$	−11.9733			−0.822327
$213$		0			0
$214$	−6.01038	+	10.4103i	−0.410861	+	0.711633i
$215$	13.4722			0.918794
$216$		0			0
$217$	23.4989	+	5.63836i	1.59521	+	0.382757i
$218$	1.78837	−	3.09755i	0.121124	−	0.209793i
$219$		0			0
$220$	−1.97104	−	3.41393i	−0.132887	−	0.230167i
$221$	−6.13536	+	3.33517i	−0.412709	+	0.224348i
$222$		0			0
$223$	−1.17906	+	2.04219i	−0.0789558	+	0.136755i	−0.902800	−	0.430061i	$-0.858492\pi$
$223$	−1.17906	+	2.04219i	−0.0789558	+	0.136755i	0.823844	+	0.566817i	$0.191825\pi$
$224$	4.30581	+	14.5292i	0.287694	+	0.970776i
$225$		0			0
$226$	5.85976	−	10.1494i	0.389786	−	0.675129i
$227$	13.1463	−	22.7701i	0.872551	−	1.51130i	0.0132022	−	0.999913i	$-0.495797\pi$
$227$	13.1463	−	22.7701i	0.872551	−	1.51130i	0.859349	−	0.511390i	$-0.170869\pi$
$228$		0			0
$229$	−0.0342777	+	0.0593708i	−0.00226514	+	0.00392333i	−0.867156	−	0.498037i	$-0.834054\pi$
$229$	−0.0342777	+	0.0593708i	−0.00226514	+	0.00392333i	0.864891	+	0.501960i	$0.167388\pi$
$230$	−8.27498	−	14.3327i	−0.545636	−	0.945069i
$231$		0			0
$232$	2.55924	−	4.43273i	0.168022	−	0.291023i
$233$	7.33514	−	12.7048i	0.480541	−	0.832322i	−0.519210	−	0.854647i	$-0.673774\pi$
$233$	7.33514	−	12.7048i	0.480541	−	0.832322i	0.999751	+	0.0223253i	$0.00710694\pi$
$234$		0			0
$235$	−12.3743	−	21.4330i	−0.807213	−	1.39813i
$236$	0.325604	+	0.563963i	0.0211950	+	0.0367109i
$237$		0			0
$238$	−3.00180	+	3.16406i	−0.194578	+	0.205096i
$239$	−3.35434			−0.216974			−0.108487	−	0.994098i	$-0.534601\pi$
$239$	−3.35434			−0.216974			−0.108487	+	0.994098i	$0.534601\pi$
$240$		0			0
$241$	4.28989	−	7.43031i	0.276336	−	0.478628i	−0.694135	−	0.719845i	$-0.744213\pi$
$241$	4.28989	−	7.43031i	0.276336	−	0.478628i	0.970471	+	0.241216i	$0.0775464\pi$
$242$	4.33802	+	7.51368i	0.278859	+	0.482998i
$243$		0			0
$244$	0.915991	−	1.58654i	0.0586403	−	0.101568i
$245$	−21.4675	−	10.9312i	−1.37151	−	0.698370i
$246$		0			0
$247$	−3.19215	−	1.95397i	−0.203112	−	0.124328i
$248$	−12.7323	−	22.0530i	−0.808501	−	1.40036i
$249$		0			0
$250$	2.70033	+	4.67711i	0.170784	+	0.295806i
$251$	10.7575	+	18.6326i	0.679010	+	1.17608i	0.975280	+	0.220975i	$0.0709238\pi$
$251$	10.7575	+	18.6326i	0.679010	+	1.17608i	−0.296270	+	0.955104i	$0.595743\pi$
$252$		0			0
$253$	2.53687	+	4.39399i	0.159492	+	0.276248i
$254$	1.65541			0.103870
$255$		0			0
$256$	7.75668	−	13.4350i	0.484793	−	0.839686i
$257$	2.46896	+	4.27636i	0.154010	+	0.266752i	0.932698	−	0.360659i	$-0.117448\pi$
$257$	2.46896	+	4.27636i	0.154010	+	0.266752i	−0.778688	+	0.627411i	$0.784115\pi$
$258$		0			0
$259$	27.2710	+	6.54344i	1.69454	+	0.406590i
$260$	−0.406471	+	15.8228i	−0.0252083	+	0.981288i
$261$		0			0
$262$	10.2436			0.632854
$263$	8.95439			0.552151			0.276076	−	0.961136i	$-0.410966\pi$
$263$	8.95439			0.552151			0.276076	+	0.961136i	$0.410966\pi$
$264$		0			0
$265$	−32.3034			−1.98438
$266$	−2.27301	−	0.545389i	−0.139367	−	0.0334400i
$267$		0			0
$268$	−5.38891	+	9.33387i	−0.329180	+	0.570157i
$269$	−2.41172	+	4.17723i	−0.147045	+	0.254690i	−0.930134	−	0.367220i	$-0.880310\pi$
$269$	−2.41172	+	4.17723i	−0.147045	+	0.254690i	0.783089	+	0.621910i	$0.213643\pi$
$270$		0			0
$271$	3.71072	+	6.42715i	0.225410	+	0.390422i	0.956442	−	0.291921i	$-0.0942945\pi$
$271$	3.71072	+	6.42715i	0.225410	+	0.390422i	−0.731032	+	0.682343i	$0.760961\pi$
$272$	−0.345312			−0.0209376
$273$		0			0
$274$	−7.41938			−0.448221
$275$	−3.07281	−	5.32226i	−0.185297	−	0.320944i
$276$		0			0
$277$	−1.90816	+	3.30503i	−0.114650	+	0.198580i	−0.917640	−	0.397413i	$-0.869908\pi$
$277$	−1.90816	+	3.30503i	−0.114650	+	0.198580i	0.802990	+	0.595993i	$0.203241\pi$
$278$	−1.79268	+	3.10502i	−0.107518	+	0.186226i
$279$		0			0
$280$	7.21288	+	24.3387i	0.431052	+	1.45451i
$281$	−8.54978			−0.510037			−0.255019	−	0.966936i	$-0.582082\pi$
$281$	−8.54978			−0.510037			−0.255019	+	0.966936i	$0.582082\pi$
$282$		0			0
$283$	15.2643			0.907371			0.453686	−	0.891162i	$-0.350109\pi$
$283$	15.2643			0.907371			0.453686	+	0.891162i	$0.350109\pi$
$284$	−4.39870			−0.261015
$285$		0			0
$286$	−0.0707683	+	2.75481i	−0.00418461	+	0.162895i
$287$	4.00797	+	13.5242i	0.236583	+	0.798310i
$288$		0			0
$289$	6.62439	+	11.4738i	0.389670	+	0.674928i
$290$	2.68885	−	4.65723i	0.157895	−	0.273482i
$291$		0			0
$292$	−13.9045			−0.813702
$293$	−2.96982	−	5.14388i	−0.173499	−	0.300509i	0.766142	−	0.642671i	$-0.222174\pi$
$293$	−2.96982	−	5.14388i	−0.173499	−	0.300509i	−0.939641	+	0.342163i	$0.888841\pi$
$294$		0			0
$295$	0.878467	+	1.52155i	0.0511463	+	0.0885881i
$296$	−14.7761	−	25.5929i	−0.858842	−	1.48756i
$297$		0			0
$298$	2.49586	+	4.32295i	0.144581	+	0.250422i
$299$	0.523159	−	20.3651i	0.0302551	−	1.17774i
$300$		0			0
$301$	10.0713	+	2.41653i	0.580501	+	0.139286i
$302$	7.17362	−	12.4251i	0.412796	−	0.714983i
$303$		0			0
$304$	−0.0925356	−	0.160276i	−0.00530728	−	0.00919248i
$305$	2.47131	−	4.28043i	0.141507	−	0.245097i
$306$		0			0
$307$	22.2133			1.26778			0.633891	−	0.773422i	$-0.281457\pi$
$307$	22.2133			1.26778			0.633891	+	0.773422i	$0.281457\pi$
$308$	−0.861114	−	2.90569i	−0.0490665	−	0.165567i
$309$		0			0
$310$	−13.3771	−	23.1698i	−0.759769	−	1.31596i
$311$	4.92130	+	8.52394i	0.279061	+	0.483348i	0.971152	−	0.238463i	$-0.0766435\pi$
$311$	4.92130	+	8.52394i	0.279061	+	0.483348i	−0.692091	+	0.721811i	$0.743310\pi$
$312$		0			0
$313$	10.4563	−	18.1108i	0.591023	−	1.02368i	−0.403072	−	0.915168i	$-0.632058\pi$
$313$	10.4563	−	18.1108i	0.591023	−	1.02368i	0.994095	−	0.108513i	$-0.0346090\pi$
$314$	0.825166	−	1.42923i	0.0465668	−	0.0806561i
$315$		0			0
$316$	−7.71205	−	13.3577i	−0.433837	−	0.751427i
$317$	−12.6801	+	21.9626i	−0.712188	+	1.23355i	0.251847	+	0.967767i	$0.418962\pi$
$317$	−12.6801	+	21.9626i	−0.712188	+	1.23355i	−0.964034	+	0.265778i	$0.914371\pi$
$318$		0			0
$319$	−0.824324	+	1.42777i	−0.0461533	+	0.0799398i
$320$	7.77489	−	13.4665i	0.434629	−	0.752800i
$321$		0			0
$322$	−3.61521	−	12.1989i	−0.201468	−	0.679819i
$323$	1.00524	−	1.74113i	0.0559331	−	0.0968790i
$324$		0			0
$325$	−0.633681	+	24.6674i	−0.0351503	+	1.36830i
$326$	5.06247	+	8.76845i	0.280384	+	0.485640i
$327$		0			0
$328$	7.43183	−	12.8723i	0.410354	−	0.710755i
$329$	−5.40615	−	18.2422i	−0.298051	−	1.00572i
$330$		0			0
$331$	1.78283			0.0979935			0.0489967	−	0.998799i	$-0.484398\pi$
$331$	1.78283			0.0979935			0.0489967	+	0.998799i	$0.484398\pi$
$332$	−0.967335	+	1.67547i	−0.0530894	+	0.0919536i
$333$		0			0
$334$	−14.1083			−0.771971
$335$	−14.5391	+	25.1824i	−0.794354	+	1.37586i
$336$		0			0
$337$	9.56149			0.520848			0.260424	−	0.965494i	$-0.416138\pi$
$337$	9.56149			0.520848			0.260424	+	0.965494i	$0.416138\pi$
$338$	6.01701	−	9.28556i	0.327282	−	0.505068i
$339$		0			0
$340$	−8.50240			−0.461107
$341$	4.10103	+	7.10320i	0.222083	+	0.384660i
$342$		0			0
$343$	−14.0876	−	12.0225i	−0.760659	−	0.649152i
$344$	−5.45689	−	9.45160i	−0.294216	−	0.509596i
$345$		0			0
$346$	−4.24991	−	7.36106i	−0.228477	−	0.395733i
$347$	0.316694	−	0.548531i	0.0170010	−	0.0294467i	−0.857400	−	0.514651i	$-0.827921\pi$
$347$	0.316694	−	0.548531i	0.0170010	−	0.0294467i	0.874401	+	0.485204i	$0.161255\pi$
$348$		0			0
$349$	−15.2994	+	26.4994i	−0.818960	+	1.41848i	0.0874885	+	0.996166i	$0.472116\pi$
$349$	−15.2994	+	26.4994i	−0.818960	+	1.41848i	−0.906449	+	0.422315i	$0.861217\pi$
$350$	4.37895	+	14.7761i	0.234065	+	0.789813i
$351$		0			0
$352$	−2.57166	+	4.45425i	−0.137070	+	0.237412i
$353$	1.10035			0.0585655			0.0292828	−	0.999571i	$-0.490678\pi$
$353$	1.10035			0.0585655			0.0292828	+	0.999571i	$0.490678\pi$
$354$		0			0
$355$	−11.8675			−0.629862
$356$	17.3579			0.919969
$357$		0			0
$358$	3.90521	+	6.76402i	0.206397	+	0.357489i
$359$	−4.88693	+	8.46441i	−0.257922	+	0.446734i	−0.965685	−	0.259716i	$-0.916371\pi$
$359$	−4.88693	+	8.46441i	−0.257922	+	0.446734i	0.707763	+	0.706450i	$0.249705\pi$
$360$		0			0
$361$	−17.9225			−0.943288
$362$	−2.55546	−	4.42618i	−0.134312	−	0.232635i
$363$		0			0
$364$	−3.14203	+	11.7557i	−0.164687	+	0.616164i
$365$	−37.5139			−1.96357
$366$		0			0
$367$	−11.1473			−0.581882			−0.290941	−	0.956741i	$-0.593968\pi$
$367$	−11.1473			−0.581882			−0.290941	+	0.956741i	$0.593968\pi$
$368$	0.503679	−	0.872397i	0.0262561	−	0.0454769i
$369$		0			0
$370$	−15.5244	−	26.8891i	−0.807076	−	1.39790i
$371$	−24.1489	−	5.79432i	−1.25375	−	0.300826i
$372$		0			0
$373$	−30.7301			−1.59115			−0.795573	−	0.605858i	$-0.792830\pi$
$373$	−30.7301			−1.59115			−0.795573	+	0.605858i	$0.792830\pi$
$374$	−1.48030			−0.0765445
$375$		0			0
$376$	−10.0244	+	17.3628i	−0.516970	+	0.895419i
$377$	5.81582	−	3.16147i	0.299530	−	0.162824i
$378$		0			0
$379$	−11.3286	+	19.6217i	−0.581912	+	1.00790i	0.413341	+	0.910576i	$0.364362\pi$
$379$	−11.3286	+	19.6217i	−0.581912	+	1.00790i	−0.995253	+	0.0973246i	$0.968972\pi$
$380$	−2.27844	−	3.94638i	−0.116882	−	0.202445i
$381$		0			0
$382$	0.560093	+	0.970109i	0.0286568	+	0.0496351i
$383$	0.589263			0.0301099			0.0150550	−	0.999887i	$-0.495208\pi$
$383$	0.589263			0.0301099			0.0150550	+	0.999887i	$0.495208\pi$
$384$		0			0
$385$	−2.32325	−	7.83942i	−0.118404	−	0.399534i
$386$	6.99004	+	12.1071i	0.355783	+	0.616235i
$387$		0			0
$388$	−0.645753			−0.0327832
$389$	2.84973	+	4.93587i	0.144487	+	0.250259i	0.929181	−	0.369624i	$-0.120514\pi$
$389$	2.84973	+	4.93587i	0.144487	+	0.250259i	−0.784695	+	0.619883i	$0.787180\pi$
$390$		0			0
$391$	10.9432			0.553422
$392$	1.02643	+	19.4885i	0.0518423	+	0.984319i
$393$		0			0
$394$	21.7782			1.09717
$395$	−20.8068	−	36.0384i	−1.04690	−	1.81329i
$396$		0			0
$397$	−25.5283			−1.28123			−0.640614	−	0.767863i	$-0.721320\pi$
$397$	−25.5283			−1.28123			−0.640614	+	0.767863i	$0.721320\pi$
$398$	−21.6005			−1.08274
$399$		0			0
$400$	−0.610086	+	1.05670i	−0.0305043	+	0.0528350i
$401$	12.7506	+	22.0846i	0.636733	+	1.10285i	0.986145	+	0.165884i	$0.0530478\pi$
$401$	12.7506	+	22.0846i	0.636733	+	1.10285i	−0.349413	+	0.936969i	$0.613619\pi$
$402$		0			0
$403$	0.845724	−	32.9217i	0.0421285	−	1.63995i
$404$	3.81817	−	6.61327i	0.189961	−	0.329022i
$405$		0			0
$406$	2.84547	−	2.99928i	0.141218	−	0.148852i
$407$	4.75934	+	8.24341i	0.235912	+	0.408611i
$408$		0			0
$409$	−0.0734938	+	0.127295i	−0.00363403	+	0.00629433i	−0.867837	−	0.496850i	$-0.834490\pi$
$409$	−0.0734938	+	0.127295i	−0.00363403	+	0.00629433i	0.864203	+	0.503144i	$0.167823\pi$
$410$	7.80822	−	13.5242i	0.385621	−	0.667914i
$411$		0			0
$412$	−2.63601	−	4.56570i	−0.129867	−	0.224936i
$413$	0.383788	+	1.29503i	0.0188850	+	0.0637242i
$414$		0			0
$415$	−2.60983	+	4.52036i	−0.128112	+	0.221896i
$416$	18.1437	−	9.86292i	0.889570	−	0.483569i
$417$		0			0
$418$	−0.396686	−	0.687080i	−0.0194026	−	0.0336062i
$419$	6.84795	−	11.8610i	0.334544	−	0.579447i	−0.648853	−	0.760914i	$-0.724751\pi$
$419$	6.84795	−	11.8610i	0.334544	−	0.579447i	0.983397	+	0.181466i	$0.0580844\pi$
$420$		0			0
$421$	3.44169			0.167738			0.0838688	−	0.996477i	$-0.473272\pi$
$421$	3.44169			0.167738			0.0838688	+	0.996477i	$0.473272\pi$
$422$	−4.84842			−0.236017
$423$		0			0
$424$	13.0844	+	22.6629i	0.635437	+	1.10061i
$425$	−13.2551			−0.642966
$426$		0			0
$427$	2.61525	−	2.75662i	0.126561	−	0.133402i
$428$	−18.0156			−0.870816
$429$		0			0
$430$	−5.73325	−	9.93028i	−0.276482	−	0.478881i
$431$	−22.2910			−1.07372			−0.536861	−	0.843671i	$-0.680390\pi$
$431$	−22.2910			−1.07372			−0.536861	+	0.843671i	$0.680390\pi$
$432$		0			0
$433$	12.9481	+	22.4268i	0.622247	+	1.07776i	0.989066	+	0.147472i	$0.0471136\pi$
$433$	12.9481	+	22.4268i	0.622247	+	1.07776i	−0.366819	+	0.930292i	$0.619553\pi$
$434$	−5.84424	−	19.7204i	−0.280533	−	0.946611i
$435$		0			0
$436$	5.36049			0.256721
$437$	2.93253	+	5.07929i	0.140282	+	0.242975i
$438$		0			0
$439$	13.9919	+	24.2347i	0.667798	+	1.15666i	0.978519	+	0.206159i	$0.0660963\pi$
$439$	13.9919	+	24.2347i	0.667798	+	1.15666i	−0.310721	+	0.950501i	$0.600570\pi$
$440$	−4.30792	+	7.46153i	−0.205372	+	0.355715i
$441$		0			0
$442$	5.06932	+	3.10302i	0.241123	+	0.147596i
$443$	16.6044	−	28.7597i	0.788900	−	1.36642i	−0.137741	−	0.990468i	$-0.543984\pi$
$443$	16.6044	−	28.7597i	0.788900	−	1.36642i	0.926641	−	0.375947i	$-0.122683\pi$
$444$		0			0
$445$	46.8310			2.22000
$446$	2.00706			0.0950370
$447$		0			0
$448$	8.22774	−	8.67249i	0.388724	−	0.409736i
$449$	9.84320	+	17.0489i	0.464529	+	0.804589i	0.999180	−	0.0404845i	$-0.0128901\pi$
$449$	9.84320	+	17.0489i	0.464529	+	0.804589i	−0.534651	+	0.845073i	$0.679557\pi$
$450$		0			0
$451$	−2.39377	+	4.14614i	−0.112718	+	0.195234i
$452$	17.5641			0.826146
$453$		0			0
$454$	−22.3783			−1.05027
$455$	−8.47706	+	31.7163i	−0.397411	+	1.48688i
$456$		0			0
$457$	0.373471	+	0.646871i	0.0174702	+	0.0302593i	0.874628	−	0.484794i	$-0.161105\pi$
$457$	0.373471	+	0.646871i	0.0174702	+	0.0302593i	−0.857158	+	0.515053i	$0.827772\pi$
$458$	0.0583493			0.00272648
$459$		0			0
$460$	12.4017	−	21.4805i	0.578235	−	1.00153i
$461$	−16.5855	−	28.7269i	−0.772464	−	1.33795i	−0.936209	−	0.351445i	$-0.885691\pi$
$461$	−16.5855	−	28.7269i	−0.772464	−	1.33795i	0.163744	−	0.986503i	$-0.447643\pi$
$462$		0			0
$463$	−30.7521			−1.42917			−0.714586	−	0.699548i	$-0.753385\pi$
$463$	−30.7521			−1.42917			−0.714586	+	0.699548i	$0.753385\pi$
$464$	0.327328			0.0151958
$465$		0			0
$466$	−12.4863			−0.578414
$467$	−14.8033	+	25.6400i	−0.685013	+	1.18648i	0.288420	+	0.957504i	$0.406870\pi$
$467$	−14.8033	+	25.6400i	−0.685013	+	1.18648i	−0.973433	+	0.228973i	$0.926463\pi$
$468$		0			0
$469$	−15.3859	+	16.2176i	−0.710456	+	0.748859i
$470$	−10.5321	+	18.2422i	−0.485810	+	0.841448i
$471$		0			0
$472$	0.711644	−	1.23260i	0.0327561	−	0.0567352i
$473$	1.75765	+	3.04434i	0.0808168	+	0.139979i
$474$		0			0
$475$	−3.55205	−	6.15234i	−0.162979	−	0.282289i
$476$	−6.35609	−	1.52509i	−0.291331	−	0.0699024i
$477$		0			0
$478$	1.42748	+	2.47247i	0.0652915	+	0.113088i
$479$	−14.0905			−0.643813			−0.321907	−	0.946771i	$-0.604324\pi$
$479$	−14.0905			−0.643813			−0.321907	+	0.946771i	$0.604324\pi$
$480$		0			0
$481$	0.981481	−	38.2063i	0.0447517	−	1.74206i
$482$	−7.30247			−0.332618
$483$		0			0
$484$	−6.50142	+	11.2608i	−0.295519	+	0.511854i
$485$	−1.74222			−0.0791100
$486$		0			0
$487$	8.39773	−	14.5453i	0.380537	−	0.659110i	−0.610602	−	0.791938i	$-0.709072\pi$
$487$	8.39773	−	14.5453i	0.380537	−	0.659110i	0.991139	+	0.132828i	$0.0424057\pi$
$488$	−4.00400			−0.181253
$489$		0			0
$490$	1.07841	+	20.4755i	0.0487176	+	0.924990i
$491$	10.8345	−	18.7659i	0.488954	−	0.846893i	−0.510965	−	0.859601i	$-0.670712\pi$
$491$	10.8345	−	18.7659i	0.488954	−	0.846893i	0.999919	+	0.0127081i	$0.00404524\pi$
$492$		0			0
$493$	1.77793	+	3.07947i	0.0800740	+	0.138692i
$494$	−0.0818055	+	3.18446i	−0.00368060	+	0.143276i
$495$		0			0
$496$	0.814234	−	1.41029i	0.0365602	−	0.0633241i
$497$	−8.87173	−	2.12870i	−0.397952	−	0.0954851i
$498$		0			0
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	−0.478051	−	0.878332i	$-0.658656\pi$
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	0.999683	−	0.0251622i	$-0.00801023\pi$
$500$	−4.04699	+	7.00960i	−0.180987	+	0.313479i
$501$		0			0
$502$	9.15601	−	15.8587i	0.408653	−	0.707807i
$503$	−21.9415	−	38.0037i	−0.978322	−	1.69450i	−0.668506	−	0.743707i	$-0.733066\pi$
$503$	−21.9415	−	38.0037i	−0.978322	−	1.69450i	−0.309816	−	0.950796i	$-0.600268\pi$
$504$		0			0
$505$	10.3013	−	17.8423i	0.458401	−	0.793974i
$506$	2.15919	−	3.73983i	0.0959879	−	0.166256i
$507$		0			0
$508$	1.24048	+	2.14858i	0.0550376	+	0.0953279i
$509$	9.96210	+	17.2549i	0.441563	+	0.764809i	0.997806	−	0.0662109i	$-0.0210910\pi$
$509$	9.96210	+	17.2549i	0.441563	+	0.764809i	−0.556243	+	0.831020i	$0.687758\pi$
$510$		0			0
$511$	−28.0441	−	6.72894i	−1.24060	−	0.297671i
$512$	2.01529			0.0890641
$513$		0			0
$514$	2.10139	−	3.63972i	0.0926886	−	0.160541i
$515$	−7.11185	−	12.3181i	−0.313386	−	0.542800i
$516$		0			0
$517$	3.22884	−	5.59252i	0.142004	−	0.245959i
$518$	−6.78237	−	22.8860i	−0.298000	−	1.00555i
$519$		0			0
$520$	30.3935	−	16.5219i	1.33284	−	0.724532i
$521$	−8.26204	−	14.3103i	−0.361967	−	0.626944i	0.626318	−	0.779568i	$-0.284561\pi$
$521$	−8.26204	−	14.3103i	−0.361967	−	0.626944i	−0.988284	+	0.152623i	$0.951228\pi$
$522$		0			0
$523$	5.99809	+	10.3890i	0.262278	+	0.454279i	0.966847	−	0.255357i	$-0.0821929\pi$
$523$	5.99809	+	10.3890i	0.262278	+	0.454279i	−0.704569	+	0.709636i	$0.748860\pi$
$524$	7.67609	+	13.2954i	0.335332	+	0.580812i
$525$		0			0
$526$	−3.81065	−	6.60024i	−0.166152	−	0.287784i
$527$	17.6905			0.770611
$528$		0			0
$529$	−4.46197	+	7.72837i	−0.193999	+	0.336016i
$530$	13.7471	+	23.8107i	0.597137	+	1.03427i
$531$		0			0
$532$	−0.995416	−	3.35886i	−0.0431567	−	0.145625i
$533$	16.8887	−	9.18068i	0.731531	−	0.397660i
$534$		0			0
$535$	−48.6053			−2.10139
$536$	23.5561			1.01747
$537$		0			0
$538$	4.10536			0.176995
$539$	−0.330609	−	6.27720i	−0.0142403	−	0.270378i
$540$		0			0
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	0.153739	+	0.988112i	$0.450869\pi$
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	−0.932599	+	0.360914i	$0.882465\pi$
$542$	3.15829	−	5.47031i	0.135660	−	0.234970i
$543$		0			0
$544$	5.54665	+	9.60707i	0.237811	+	0.411900i
$545$	14.4624			0.619500
$546$		0			0
$547$	−7.34857			−0.314202			−0.157101	−	0.987583i	$-0.550215\pi$
$547$	−7.34857			−0.314202			−0.157101	+	0.987583i	$0.550215\pi$
$548$	−5.55973	−	9.62974i	−0.237500	−	0.411362i
$549$		0			0
$550$	−2.61535	+	4.52991i	−0.111519	+	0.193156i
$551$	−0.952888	+	1.65045i	−0.0405944	+	0.0703115i
$552$		0			0
$553$	−9.09016	−	30.6732i	−0.386553	−	1.30436i
$554$	3.24816			0.138001
$555$		0			0
$556$	−5.37340			−0.227883
$557$	−10.8280			−0.458796			−0.229398	−	0.973333i	$-0.573676\pi$
$557$	−10.8280			−0.458796			−0.229398	+	0.973333i	$0.573676\pi$
$558$		0			0
$559$	0.362466	−	14.1098i	0.0153307	−	0.596781i
$560$	−1.11731	+	1.17770i	−0.0472148	+	0.0497670i
$561$		0			0
$562$	3.63847	+	6.30201i	0.153480	+	0.265834i
$563$	−6.92997	+	12.0031i	−0.292064	+	0.505869i	−0.974298	−	0.225265i	$-0.927675\pi$
$563$	−6.92997	+	12.0031i	−0.292064	+	0.505869i	0.682234	+	0.731134i	$0.261009\pi$
$564$		0			0
$565$	47.3873			1.99360
$566$	−6.49594	−	11.2513i	−0.273045	−	0.472927i
$567$		0			0
$568$	4.80692	+	8.32583i	0.201694	+	0.349344i
$569$	13.7060	+	23.7395i	0.574586	+	0.995212i	0.996086	+	0.0883842i	$0.0281703\pi$
$569$	13.7060	+	23.7395i	0.574586	+	0.995212i	−0.421500	+	0.906828i	$0.638496\pi$
$570$		0			0
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	0.868191	−	0.496230i	$-0.165283\pi$
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	−0.863844	+	0.503760i	$0.831950\pi$
$572$	−3.62854	+	1.97247i	−0.151717	+	0.0824732i
$573$		0			0
$574$	8.26302	−	8.70967i	0.344892	−	0.363535i
$575$	19.3341	−	33.4876i	0.806288	−	1.39653i
$576$		0			0
$577$	1.66328	+	2.88089i	0.0692434	+	0.119933i	0.898568	−	0.438833i	$-0.144608\pi$
$577$	1.66328	+	2.88089i	0.0692434	+	0.119933i	−0.829325	+	0.558766i	$0.811275\pi$
$578$	5.63818	−	9.76562i	0.234518	−	0.406196i
$579$		0			0
$580$	8.05959			0.334656
$581$	−2.76184	+	2.91113i	−0.114581	+	0.120774i
$582$		0			0
$583$	−4.21447	−	7.29967i	−0.174545	−	0.302321i
$584$	15.1950	+	26.3185i	0.628772	+	1.08907i
$585$		0			0
$586$	−2.52769	+	4.37809i	−0.104418	+	0.180857i
$587$	−7.54051	+	13.0606i	−0.311230	+	0.539067i	−0.978629	−	0.205634i	$-0.934074\pi$
$587$	−7.54051	+	13.0606i	−0.311230	+	0.539067i	0.667399	+	0.744701i	$0.267408\pi$
$588$		0			0
$589$	4.74064	+	8.21104i	0.195335	+	0.338330i
$590$	0.747686	−	1.29503i	0.0307817	−	0.0533155i
$591$		0			0
$592$	0.944935	−	1.63668i	0.0388366	−	0.0672670i
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	−0.468609	−	0.883405i	$-0.655245\pi$
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	0.999356	−	0.0358751i	$-0.0114218\pi$
$594$		0			0
$595$	−17.1485	−	4.11463i	−0.703020	−	0.168684i
$596$	−3.74055	+	6.47882i	−0.153219	+	0.265383i
$597$		0			0
$598$	−15.2337	+	8.28101i	−0.622952	+	0.338636i
$599$	−17.7734	−	30.7845i	−0.726203	−	1.25782i	−0.958477	−	0.285170i	$-0.907950\pi$
$599$	−17.7734	−	30.7845i	−0.726203	−	1.25782i	0.232274	−	0.972650i	$-0.425383\pi$
$600$		0			0
$601$	13.6474	−	23.6379i	0.556688	−	0.964212i	−0.441082	−	0.897467i	$-0.645405\pi$
$601$	13.6474	−	23.6379i	0.556688	−	0.964212i	0.997770	−	0.0667449i	$-0.0212614\pi$
$602$	−2.50477	−	8.45192i	−0.102087	−	0.344474i
$603$		0			0
$604$	21.5023			0.874915
$605$	−17.5406	+	30.3811i	−0.713125	+	1.23517i
$606$		0			0
$607$	−38.9258			−1.57995			−0.789976	−	0.613138i	$-0.789907\pi$
$607$	−38.9258			−1.57995			−0.789976	+	0.613138i	$0.789907\pi$
$608$	−2.97274	+	5.14894i	−0.120561	+	0.208817i
$609$		0			0
$610$	−4.20679			−0.170328
$611$	−22.7803	+	12.3834i	−0.921593	+	0.500977i
$612$		0			0
$613$	0.886645			0.0358113			0.0179056	−	0.999840i	$-0.494300\pi$
$613$	0.886645			0.0358113			0.0179056	+	0.999840i	$0.494300\pi$
$614$	−9.45317	−	16.3734i	−0.381499	−	0.660775i
$615$		0			0
$616$	−4.55884	+	4.80526i	−0.183681	+	0.193609i
$617$	17.3944	+	30.1280i	0.700272	+	1.21291i	0.968371	+	0.249515i	$0.0802712\pi$
$617$	17.3944	+	30.1280i	0.700272	+	1.21291i	−0.268099	+	0.963391i	$0.586395\pi$
$618$		0			0
$619$	−1.02781	−	1.78021i	−0.0413111	−	0.0715529i	0.844631	−	0.535350i	$-0.179820\pi$
$619$	−1.02781	−	1.78021i	−0.0413111	−	0.0715529i	−0.885942	+	0.463797i	$0.846487\pi$
$620$	20.0483	−	34.7247i	0.805161	−	1.39458i
$621$		0			0
$622$	4.18864	−	7.25494i	0.167949	−	0.290897i
$623$	35.0092	+	8.40016i	1.40262	+	0.336545i
$624$		0			0
$625$	6.19081	−	10.7228i	0.247632	−	0.428912i
$626$	−17.7992			−0.711398
$627$		0			0
$628$	2.47336			0.0986979
$629$	20.5302			0.818593
$630$		0			0
$631$	22.6169	+	39.1736i	0.900363	+	1.55947i	0.827023	+	0.562168i	$0.190033\pi$
$631$	22.6169	+	39.1736i	0.900363	+	1.55947i	0.0733401	+	0.997307i	$0.476634\pi$
$632$	−16.8555	+	29.1946i	−0.670477	+	1.16130i
$633$		0			0
$634$	21.5848			0.857241
$635$	3.34678	+	5.79679i	0.132813	+	0.230038i
$636$		0			0
$637$	−12.0262	+	22.1894i	−0.476494	+	0.879178i
$638$	1.40321			0.0555534
$639$		0			0
$640$	26.1881			1.03518
$641$	−9.53097	+	16.5081i	−0.376451	+	0.652032i	−0.990543	−	0.137202i	$-0.956189\pi$
$641$	−9.53097	+	16.5081i	−0.376451	+	0.652032i	0.614092	+	0.789234i	$0.289522\pi$
$642$		0			0
$643$	5.26755	+	9.12367i	0.207732	+	0.359802i	0.951000	−	0.309192i	$-0.100058\pi$
$643$	5.26755	+	9.12367i	0.207732	+	0.359802i	−0.743268	+	0.668994i	$0.766725\pi$
$644$	13.1241	−	13.8335i	0.517162	−	0.545117i
$645$		0			0
$646$	−1.71117			−0.0673252
$647$	24.1608			0.949860			0.474930	−	0.880024i	$-0.342473\pi$
$647$	24.1608			0.949860			0.474930	+	0.880024i	$0.342473\pi$
$648$		0			0
$649$	−0.229219	+	0.397019i	−0.00899762	+	0.0155843i
$650$	18.4520	−	10.0305i	0.723745	−	0.393427i
$651$		0			0
$652$	−7.58714	+	13.1413i	−0.297135	+	0.514654i
$653$	−16.8445	−	29.1755i	−0.659176	−	1.14173i	−0.980829	−	0.194869i	$-0.937572\pi$
$653$	−16.8445	−	29.1755i	−0.659176	−	1.14173i	0.321653	−	0.946858i	$-0.395762\pi$
$654$		0			0
$655$	20.7098	+	35.8704i	0.809199	+	1.40157i
$656$	0.950537			0.0371122
$657$		0			0
$658$	−11.1456	+	11.7480i	−0.434500	+	0.457986i
$659$	−2.10030	−	3.63782i	−0.0818159	−	0.141709i	0.822214	−	0.569178i	$-0.192739\pi$
$659$	−2.10030	−	3.63782i	−0.0818159	−	0.141709i	−0.904030	+	0.427469i	$0.859405\pi$
$660$		0			0
$661$	17.6726			0.687385			0.343693	−	0.939082i	$-0.388322\pi$
$661$	17.6726			0.687385			0.343693	+	0.939082i	$0.388322\pi$
$662$	−0.758708	−	1.31412i	−0.0294880	−	0.0510748i
$663$		0			0
$664$	4.22844			0.164095
$665$	−2.68559	−	9.06208i	−0.104143	−	0.351413i
$666$		0			0
$667$	−10.3733			−0.401655
$668$	−10.5721	−	18.3114i	−0.409046	−	0.708488i
$669$		0			0
$670$	24.7491			0.956143
$671$	1.28968			0.0497875
$672$		0			0
$673$	10.3052	−	17.8491i	0.397235	−	0.688031i	−0.596149	−	0.802874i	$-0.703303\pi$
$673$	10.3052	−	17.8491i	0.397235	−	0.688031i	0.993384	+	0.114843i	$0.0366366\pi$
$674$	−4.06901	−	7.04774i	−0.156733	−	0.271469i
$675$		0			0
$676$	16.5607	+	0.851419i	0.636952	+	0.0327469i
$677$	−10.6537	+	18.4527i	−0.409455	+	0.709196i	−0.994829	−	0.101567i	$-0.967614\pi$
$677$	−10.6537	+	18.4527i	−0.409455	+	0.709196i	0.585374	+	0.810763i	$0.300948\pi$
$678$		0			0
$679$	−1.30242	−	0.312505i	−0.0499823	−	0.0119928i
$680$	9.29147	+	16.0933i	0.356312	+	0.617150i
$681$		0			0
$682$	3.49049	−	6.04571i	0.133658	−	0.231502i
$683$	−3.34878	+	5.80026i	−0.128138	+	0.221941i	−0.922955	−	0.384908i	$-0.874233\pi$
$683$	−3.34878	+	5.80026i	−0.128138	+	0.221941i	0.794817	+	0.606849i	$0.207567\pi$
$684$		0			0
$685$	−14.9999	−	25.9806i	−0.573118	−	0.992670i
$686$	−2.86655	+	15.5002i	−0.109445	+	0.591801i
$687$		0			0
$688$	0.348970	−	0.604433i	0.0133043	−	0.0230438i
$689$	−0.869117	+	33.8323i	−0.0331107	+	1.28891i
$690$		0			0
$691$	12.4632	+	21.5868i	0.474121	+	0.821202i	0.999561	−	0.0296291i	$-0.00943262\pi$
$691$	12.4632	+	21.5868i	0.474121	+	0.821202i	−0.525440	+	0.850831i	$0.676099\pi$
$692$	6.36936	−	11.0321i	0.242127	−	0.419376i
$693$		0			0
$694$	−0.539093			−0.0204637
$695$	−14.4972			−0.549911
$696$		0			0
$697$	5.16298	+	8.94254i	0.195562	+	0.338723i
$698$	26.0435			0.985761
$699$		0			0
$700$	−15.8967	+	16.7560i	−0.600839	+	0.633317i
$701$	4.94583			0.186801			0.0934007	−	0.995629i	$-0.470226\pi$
$701$	4.94583			0.186801			0.0934007	+	0.995629i	$0.470226\pi$
$702$		0			0
$703$	5.50162	+	9.52908i	0.207497	+	0.359396i
$704$	4.05741			0.152919
$705$		0			0
$706$	−0.468266	−	0.811061i	−0.0176234	−	0.0305247i
$707$	10.9013	−	11.4905i	0.409985	−	0.432147i
$708$		0			0
$709$	−4.64497			−0.174446			−0.0872228	−	0.996189i	$-0.527799\pi$
$709$	−4.64497			−0.174446			−0.0872228	+	0.996189i	$0.527799\pi$
$710$	5.05037	+	8.74749i	0.189537	+	0.328288i
$711$		0			0
$712$	−18.9688	−	32.8550i	−0.710888	−	1.23129i
$713$	−25.8037	+	44.6933i	−0.966356	+	1.67378i
$714$		0			0
$715$	−9.78966	+	5.32165i	−0.366113	+	0.199018i
$716$	−5.85275	+	10.1373i	−0.218728	+	0.378847i
$717$		0			0
$718$	8.31878			0.310454
$719$	−31.7413			−1.18375			−0.591875	−	0.806030i	$-0.701612\pi$
$719$	−31.7413			−1.18375			−0.591875	+	0.806030i	$0.701612\pi$
$720$		0			0
$721$	−3.10705	−	10.4842i	−0.115713	−	0.390453i
$722$	7.62714	+	13.2106i	0.283853	+	0.491647i
$723$		0			0
$724$	3.82987	−	6.63354i	0.142336	−	0.246533i
$725$	12.5647			0.466643
$726$		0			0
$727$	47.8755			1.77560			0.887801	−	0.460227i	$-0.152232\pi$
$727$	47.8755			1.77560			0.887801	+	0.460227i	$0.152232\pi$
$728$	25.6847	−	6.89944i	0.951937	−	0.255710i
$729$		0			0
$730$	15.9645	+	27.6514i	0.590873	+	1.02342i
$731$	7.58192			0.280427
$732$		0			0
$733$	3.80104	−	6.58359i	0.140395	−	0.243171i	−0.787251	−	0.616633i	$-0.788496\pi$
$733$	3.80104	−	6.58359i	0.140395	−	0.243171i	0.927645	+	0.373463i	$0.121830\pi$
$734$	4.74386	+	8.21660i	0.175099	+	0.303280i
$735$		0			0
$736$	−32.3618			−1.19287
$737$	−7.58737			−0.279484
$738$		0			0
$739$	−33.4236			−1.22951			−0.614754	−	0.788719i	$-0.710745\pi$
$739$	−33.4236			−1.22951			−0.614754	+	0.788719i	$0.710745\pi$
$740$	23.2665	−	40.2988i	0.855294	−	1.48141i
$741$		0			0
$742$	6.00589	+	20.2659i	0.220483	+	0.743984i
$743$	−1.46912	+	2.54458i	−0.0538966	+	0.0933517i	−0.891715	−	0.452597i	$-0.850497\pi$
$743$	−1.46912	+	2.54458i	−0.0538966	+	0.0933517i	0.837818	+	0.545949i	$0.183831\pi$
$744$		0			0
$745$	−10.0919	+	17.4796i	−0.369737	+	0.640403i
$746$	13.0776	+	22.6511i	0.478805	+	0.829314i
$747$		0			0
$748$	−1.10927	−	1.92131i	−0.0405588	−	0.0702499i
$749$	−36.3356	−	8.71842i	−1.32767	−	0.318564i
$750$		0			0
$751$	−0.598389	−	1.03644i	−0.0218355	−	0.0378202i	0.854901	−	0.518791i	$-0.173618\pi$
$751$	−0.598389	−	1.03644i	−0.0218355	−	0.0378202i	−0.876737	+	0.480971i	$0.840284\pi$
$752$	−1.28213			−0.0467545
$753$		0			0
$754$	−4.80531	−	2.94141i	−0.174999	−	0.107120i
$755$	58.0123			2.11128
$756$		0			0
$757$	−5.77321	+	9.99950i	−0.209831	+	0.363438i	−0.951661	−	0.307150i	$-0.900625\pi$
$757$	−5.77321	+	9.99950i	−0.209831	+	0.363438i	0.741830	+	0.670588i	$0.233958\pi$
$758$	19.2841			0.700432
$759$		0			0
$760$	−4.97979	+	8.62525i	−0.180636	+	0.312871i
$761$	−34.6497			−1.25605			−0.628026	−	0.778192i	$-0.716137\pi$
$761$	−34.6497			−1.25605			−0.628026	+	0.778192i	$0.716137\pi$
$762$		0			0
$763$	10.8116	+	2.59414i	0.391405	+	0.0939143i
$764$	−0.839413	+	1.45391i	−0.0303689	+	0.0526005i
$765$		0			0
$766$	−0.250768	−	0.434344i	−0.00906063	−	0.0156935i
$767$	1.61720	−	0.879108i	0.0583937	−	0.0317427i
$768$		0			0
$769$	3.27437	−	5.67138i	0.118077	−	0.204515i	−0.800929	−	0.598760i	$-0.795660\pi$
$769$	3.27437	−	5.67138i	0.118077	−	0.204515i	0.919006	+	0.394245i	$0.128994\pi$
$770$	−4.78972	+	5.04862i	−0.172610	+	0.181940i
$771$		0			0
$772$	−10.4760	+	18.1450i	−0.377039	+	0.653051i
$773$	16.9637	−	29.3821i	0.610143	−	1.05680i	−0.381073	−	0.924545i	$-0.624445\pi$
$773$	16.9637	−	29.3821i	0.610143	−	1.05680i	0.991216	−	0.132254i	$-0.0422214\pi$
$774$		0			0
$775$	31.2550	−	54.1352i	1.12271	−	1.94459i
$776$	0.705683	+	1.22228i	0.0253325	+	0.0438772i
$777$		0			0
$778$	2.42547	−	4.20104i	0.0869575	−	0.150615i
$779$	−2.76711	+	4.79278i	−0.0991422	+	0.171719i
$780$		0			0
$781$	−1.54830	−	2.68173i	−0.0554024	−	0.0959598i
$782$	−4.65703	−	8.06620i	−0.166535	−	0.288447i
$783$		0			0
$784$	−1.04651	+	0.679995i	−0.0373752	+	0.0242855i
$785$	6.67303			0.238171
$786$		0			0
$787$	−6.48717	+	11.2361i	−0.231243	+	0.400524i	−0.958174	−	0.286186i	$-0.907612\pi$
$787$	−6.48717	+	11.2361i	−0.231243	+	0.400524i	0.726932	+	0.686710i	$0.240946\pi$
$788$	16.3195	+	28.2662i	0.581359	+	1.00694i
$789$		0			0
$790$	−17.7092	+	30.6732i	−0.630065	+	1.09130i
$791$	35.4251	+	8.49994i	1.25957	+	0.302223i
$792$		0			0
$793$	−4.41653	−	2.70344i	−0.156836	−	0.0960019i
$794$	10.8639	+	18.8168i	0.385545	+	0.667784i
$795$		0			0
$796$	−16.1864	−	28.0357i	−0.573712	−	0.993699i
$797$	2.20956	+	3.82707i	0.0782667	+	0.135562i	0.902502	−	0.430685i	$-0.141728\pi$
$797$	2.20956	+	3.82707i	0.0782667	+	0.135562i	−0.824235	+	0.566247i	$0.808395\pi$
$798$		0			0
$799$	−6.96408	−	12.0621i	−0.246371	−	0.426728i
$800$	39.1985			1.38588
$801$		0			0
$802$	10.8523	−	18.7968i	0.383209	−	0.663737i
$803$	−4.89426	−	8.47711i	−0.172715	−	0.299151i
$804$		0			0
$805$	35.4083	−	37.3223i	1.24798	−	1.31544i
$806$	−24.6264	+	13.3869i	−0.867427	+	0.471532i
$807$		0			0
$808$	−16.6901			−0.587155
$809$	−11.4716			−0.403320			−0.201660	−	0.979456i	$-0.564634\pi$
$809$	−11.4716			−0.403320			−0.201660	+	0.979456i	$0.564634\pi$
$810$		0			0
$811$	23.8664			0.838063			0.419032	−	0.907972i	$-0.362370\pi$
$811$	23.8664			0.838063			0.419032	+	0.907972i	$0.362370\pi$
$812$	6.02506	+	1.44566i	0.211438	+	0.0507328i
$813$		0			0
$814$	4.05079	−	7.01618i	0.141980	−	0.245917i
$815$	−20.4698	+	35.4548i	−0.717026	+	1.24193i
$816$		0			0
$817$	2.03178	+	3.51914i	0.0710829	+	0.123119i
$818$	0.125105			0.00437419
$819$		0			0
$820$	23.4044			0.817318
$821$	15.4847	+	26.8203i	0.540420	+	0.936035i	0.998880	+	0.0473197i	$0.0150679\pi$
$821$	15.4847	+	26.8203i	0.540420	+	0.936035i	−0.458460	+	0.888715i	$0.651599\pi$
$822$		0			0
$823$	4.30678	−	7.45957i	0.150125	−	0.260024i	−0.781148	−	0.624346i	$-0.785366\pi$
$823$	4.30678	−	7.45957i	0.150125	−	0.260024i	0.931273	+	0.364321i	$0.118699\pi$
$824$	−5.76129	+	9.97885i	−0.200704	+	0.347630i
$825$		0			0
$826$	0.791236	−	0.834005i	0.0275306	−	0.0290188i
$827$	−22.9128			−0.796756			−0.398378	−	0.917221i	$-0.630427\pi$
$827$	−22.9128			−0.796756			−0.398378	+	0.917221i	$0.630427\pi$
$828$		0			0
$829$	−42.5611			−1.47821			−0.739104	−	0.673591i	$-0.764751\pi$
$829$	−42.5611			−1.47821			−0.739104	+	0.673591i	$0.764751\pi$
$830$	4.44259			0.154204
$831$		0			0
$832$	−13.8947	−	8.50518i	−0.481711	−	0.294864i
$833$	−12.0816	−	6.15191i	−0.418601	−	0.213151i
$834$		0			0
$835$	−28.5230	−	49.4033i	−0.987080	−	1.70967i
$836$	0.594515	−	1.02973i	0.0205617	−	0.0356140i
$837$		0			0
$838$	−11.6569			−0.402682
$839$	0.920524	+	1.59439i	0.0317800	+	0.0550446i	0.881478	−	0.472225i	$-0.156549\pi$
$839$	0.920524	+	1.59439i	0.0317800	+	0.0550446i	−0.849698	+	0.527270i	$0.823216\pi$
$840$		0			0
$841$	12.8147	+	22.1957i	0.441885	+	0.765367i
$842$	−1.46465	−	2.53686i	−0.0504753	−	0.0874258i
$843$		0			0
$844$	−3.63317	−	6.29284i	−0.125059	−	0.216609i
$845$	44.6802	+	2.29709i	1.53705	+	0.0790224i
$846$		0			0
$847$	−18.5622	+	19.5656i	−0.637806	+	0.672282i
$848$	−0.836755	+	1.44930i	−0.0287343	+	0.0497692i
$849$		0			0
$850$	5.64087	+	9.77027i	0.193480	+	0.335118i
$851$	−29.9457	+	51.8675i	−1.02653	+	1.77800i
$852$		0			0
$853$	−27.0293			−0.925466			−0.462733	−	0.886498i	$-0.653131\pi$
$853$	−27.0293			−0.925466			−0.462733	+	0.886498i	$0.653131\pi$
$854$	−3.14485	−	0.754579i	−0.107614	−	0.0258212i
$855$		0			0
$856$	19.6875	+	34.0998i	0.672906	+	1.16551i
$857$	8.39268	+	14.5365i	0.286688	+	0.496559i	0.973017	−	0.230732i	$-0.0741122\pi$
$857$	8.39268	+	14.5365i	0.286688	+	0.496559i	−0.686329	+	0.727291i	$0.740779\pi$
$858$		0			0
$859$	−25.8058	+	44.6969i	−0.880482	+	1.52504i	−0.0296769	+	0.999560i	$0.509448\pi$
$859$	−25.8058	+	44.6969i	−0.880482	+	1.52504i	−0.850806	+	0.525481i	$0.823886\pi$
$860$	8.59245	−	14.8826i	0.293000	−	0.507491i
$861$		0			0
$862$	9.48624	+	16.4306i	0.323102	+	0.559630i
$863$	10.9807	−	19.0191i	0.373787	−	0.647417i	−0.616358	−	0.787466i	$-0.711393\pi$
$863$	10.9807	−	19.0191i	0.373787	−	0.647417i	0.990145	+	0.140049i	$0.0447259\pi$
$864$		0			0
$865$	17.1843	−	29.7640i	0.584283	−	1.01201i
$866$	11.0205	−	19.0880i	0.374491	−	0.648638i
$867$		0			0
$868$	21.2161	−	22.3629i	0.720120	−	0.759046i
$869$	5.42913	−	9.40352i	0.184170	−	0.318993i
$870$		0			0
$871$	25.9831	+	15.9047i	0.880404	+	0.538911i
$872$	−5.85797	−	10.1463i	−0.198376	−	0.343597i
$873$		0			0
$874$	2.49595	−	4.32311i	0.0844267	−	0.146231i
$875$	−11.5546	+	12.1792i	−0.390617	+	0.411731i
$876$		0			0
$877$	−9.61745			−0.324758			−0.162379	−	0.986728i	$-0.551917\pi$
$877$	−9.61745			−0.324758			−0.162379	+	0.986728i	$0.551917\pi$
$878$	11.9089	−	20.6268i	0.401905	−	0.696120i
$879$		0			0
$880$	−0.550986			−0.0185737
$881$	14.4863	−	25.0910i	0.488055	−	0.845336i	−0.511851	−	0.859075i	$-0.671040\pi$
$881$	14.4863	−	25.0910i	0.488055	−	0.845336i	0.999906	+	0.0137383i	$0.00437318\pi$
$882$		0			0
$883$	6.60727			0.222352			0.111176	−	0.993801i	$-0.464538\pi$
$883$	6.60727			0.222352			0.111176	+	0.993801i	$0.464538\pi$
$884$	−0.228755	+	8.90481i	−0.00769388	+	0.299501i
$885$		0			0
$886$	−28.2649			−0.949578
$887$	−15.7072	−	27.2057i	−0.527397	−	0.913478i	−0.999490	−	0.0319293i	$-0.989835\pi$
$887$	−15.7072	−	27.2057i	−0.527397	−	0.913478i	0.472094	−	0.881548i	$-0.343498\pi$
$888$		0			0
$889$	1.46215	+	4.93379i	0.0490390	+	0.165474i
$890$	−19.9295	−	34.5190i	−0.668039	−	1.15708i
$891$		0			0
$892$	1.50399	+	2.60499i	0.0503574	+	0.0872216i
$893$	3.73242	−	6.46474i	0.124901	−	0.216334i
$894$		0			0
$895$	−15.7905	+	27.3499i	−0.527818	+	0.914208i
$896$	19.5773	+	4.69741i	0.654033	+	0.156930i
$897$		0			0
$898$	8.37780	−	14.5108i	0.279571	−	0.484231i
$899$	−16.7692			−0.559283
$900$		0			0
$901$	−18.1798			−0.605658
$902$	4.07480			0.135676
$903$		0			0
$904$	−19.1942	−	33.2453i	−0.638388	−	1.10572i
$905$	10.3328	−	17.8970i	0.343475	−	0.594917i
$906$		0			0
$907$	9.73642			0.323292			0.161646	−	0.986849i	$-0.448320\pi$
$907$	9.73642			0.323292			0.161646	+	0.986849i	$0.448320\pi$
$908$	−16.7692	−	29.0452i	−0.556507	−	0.963898i
$909$		0			0
$910$	26.9855	−	7.24886i	0.894560	−	0.240297i
$911$	38.4372			1.27348			0.636740	−	0.771078i	$-0.280282\pi$
$911$	38.4372			1.27348			0.636740	+	0.771078i	$0.280282\pi$
$912$		0			0
$913$	−1.36197			−0.0450746
$914$	0.317871	−	0.550568i	0.0105142	−	0.0182112i
$915$		0			0
$916$	0.0437242	+	0.0757325i	0.00144469	+	0.00250227i
$917$	9.04778	+	30.5302i	0.298784	+	1.00820i
$918$		0			0
$919$	54.2804			1.79055			0.895273	−	0.445519i	$-0.146981\pi$
$919$	54.2804			1.79055			0.895273	+	0.445519i	$0.146981\pi$
$920$	−54.2108			−1.78728
$921$		0			0
$922$	−14.1164	+	24.4502i	−0.464897	+	0.805226i
$923$	−0.319293	+	12.4292i	−0.0105097	+	0.409112i
$924$		0			0
$925$	36.2721	−	62.8251i	1.19262	−	2.06568i
$926$	13.0869	+	22.6673i	0.430064	+	0.744892i
$927$		0			0
$928$	−5.25777	−	9.10673i	−0.172595	−	0.298943i
$929$	38.1920			1.25304			0.626519	−	0.779406i	$-0.284479\pi$
$929$	38.1920			1.25304			0.626519	+	0.779406i	$0.284479\pi$
$930$		0			0
$931$	−0.382172	−	7.25622i	−0.0125252	−	0.237813i
$932$	−9.35660	−	16.2061i	−0.306486	−	0.530849i
$933$		0			0
$934$	25.1988			0.824531
$935$	−2.99276	−	5.18361i	−0.0978736	−	0.169522i
$936$		0			0
$937$	−19.0376			−0.621931			−0.310966	−	0.950421i	$-0.600652\pi$
$937$	−19.0376			−0.621931			−0.310966	+	0.950421i	$0.600652\pi$
$938$	18.5016	+	4.43930i	0.604098	+	0.144948i
$939$		0			0
$940$	−31.5691			−1.02967
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	0.946646	+	0.322275i	$0.104448\pi$
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	−0.194224	+	0.980957i	$0.562219\pi$
$942$		0			0
$943$	−30.1232			−0.980948
$944$	0.0910198			0.00296244
$945$		0			0
$946$	1.49598	−	2.59111i	0.0486385	−	0.0842443i
$947$	−4.59687	−	7.96201i	−0.149378	−	0.258730i	0.781620	−	0.623755i	$-0.214394\pi$
$947$	−4.59687	−	7.96201i	−0.149378	−	0.258730i	−0.930998	+	0.365025i	$0.881060\pi$
$948$		0			0
$949$	−1.00930	+	39.2894i	−0.0327634	+	1.27539i
$950$	−3.02324	+	5.23641i	−0.0980869	+	0.169892i
$951$		0			0
$952$	4.05929	+	13.6974i	0.131562	+	0.443936i
$953$	−22.3232	−	38.6648i	−0.723118	−	1.25248i	−0.959744	−	0.280876i	$-0.909375\pi$
$953$	−22.3232	−	38.6648i	−0.723118	−	1.25248i	0.236626	−	0.971601i	$-0.423958\pi$
$954$		0			0
$955$	−2.26470	+	3.92258i	−0.0732841	+	0.126932i
$956$	−2.13937	+	3.70550i	−0.0691923	+	0.119844i
$957$		0			0
$958$	5.99641	+	10.3861i	0.193735	+	0.335559i
$959$	−6.55323	−	22.1128i	−0.211615	−	0.714059i
$960$		0			0
$961$	−26.2136	+	45.4032i	−0.845599	+	1.46462i
$962$	−28.5794	+	15.5357i	−0.921437	+	0.500892i
$963$		0			0
$964$	−5.47212	−	9.47799i	−0.176245	−	0.305266i
$965$	−28.2638	+	48.9544i	−0.909845	+	1.57590i
$966$		0			0
$967$	13.8268			0.444639			0.222320	−	0.974974i	$-0.428637\pi$
$967$	13.8268			0.444639			0.222320	+	0.974974i	$0.428637\pi$
$968$	28.4191			0.913426
$969$		0			0
$970$	0.741422	+	1.28418i	0.0238056	+	0.0412326i
$971$	−7.26873			−0.233265			−0.116632	−	0.993175i	$-0.537210\pi$
$971$	−7.26873			−0.233265			−0.116632	+	0.993175i	$0.537210\pi$
$972$		0			0
$973$	−10.8376	−	2.60039i	−0.347438	−	0.0833648i
$974$	−14.2950			−0.458043
$975$		0			0
$976$	−0.128029	−	0.221752i	−0.00409810	−	0.00709811i
$977$	−42.8101			−1.36962			−0.684808	−	0.728723i	$-0.740114\pi$
$977$	−42.8101			−1.36962			−0.684808	+	0.728723i	$0.740114\pi$
$978$		0			0
$979$	6.10982	+	10.5825i	0.195271	+	0.338219i
$980$	−25.7674	+	16.7431i	−0.823110	+	0.534838i
$981$		0			0
$982$	−18.4430			−0.588541
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	−0.953166	−	0.302448i	$-0.902196\pi$
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	0.214655	−	0.976690i	$-0.431137\pi$
$984$		0			0
$985$	44.0294	+	76.2612i	1.40289	+	2.42988i
$986$	1.51324	−	2.62101i	0.0481914	−	0.0834700i
$987$		0			0
$988$	−4.19446	+	2.28010i	−0.133444	+	0.0725398i
$989$	−11.0591	+	19.1550i	−0.351660	+	0.609092i
$990$		0			0
$991$	−58.2324			−1.84981			−0.924907	−	0.380194i	$-0.875857\pi$
$991$	−58.2324			−1.84981			−0.924907	+	0.380194i	$0.875857\pi$
$992$	−52.3151			−1.66101
$993$		0			0
$994$	2.20642	+	7.44521i	0.0699835	+	0.236148i
$995$	−43.6703	−	75.6392i	−1.38444	−	2.39792i
$996$		0			0
$997$	2.24739	−	3.89260i	0.0711757	−	0.123280i	−0.828241	−	0.560372i	$-0.810658\pi$
$997$	2.24739	−	3.89260i	0.0711757	−	0.123280i	0.899417	+	0.437092i	$0.143992\pi$
$998$	−19.8353			−0.627875
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.d.100.3		12
3.2	odd	2		91.2.g.b.9.4	✓	12
7.4	even	3		819.2.s.d.802.4		12
13.3	even	3		819.2.s.d.289.4		12
21.2	odd	6		637.2.f.k.295.4		12
21.5	even	6		637.2.f.j.295.4		12
21.11	odd	6		91.2.h.b.74.3	yes	12
21.17	even	6		637.2.h.l.165.3		12
21.20	even	2		637.2.g.l.373.4		12
39.17	odd	6		1183.2.e.g.170.3		12
39.29	odd	6		91.2.h.b.16.3	yes	12
39.35	odd	6		1183.2.e.h.170.4		12
91.81	even	3	inner	819.2.n.d.172.3		12
273.68	even	6		637.2.f.j.393.4		12
273.74	odd	6		1183.2.e.h.508.4		12
273.95	odd	6		1183.2.e.g.508.3		12
273.107	odd	6		637.2.f.k.393.4		12
273.146	even	6		637.2.h.l.471.3		12
273.152	even	6		8281.2.a.ca.1.3		6
273.173	even	6		8281.2.a.cf.1.4		6
273.185	even	6		637.2.g.l.263.4		12
273.191	odd	6		8281.2.a.bz.1.3		6
273.212	odd	6		8281.2.a.ce.1.4		6
273.263	odd	6		91.2.g.b.81.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.4	✓	12	3.2	odd	2
91.2.g.b.81.4	yes	12	273.263	odd	6
91.2.h.b.16.3	yes	12	39.29	odd	6
91.2.h.b.74.3	yes	12	21.11	odd	6
637.2.f.j.295.4		12	21.5	even	6
637.2.f.j.393.4		12	273.68	even	6
637.2.f.k.295.4		12	21.2	odd	6
637.2.f.k.393.4		12	273.107	odd	6
637.2.g.l.263.4		12	273.185	even	6
637.2.g.l.373.4		12	21.20	even	2
637.2.h.l.165.3		12	21.17	even	6
637.2.h.l.471.3		12	273.146	even	6
819.2.n.d.100.3		12	1.1	even	1	trivial
819.2.n.d.172.3		12	91.81	even	3	inner
819.2.s.d.289.4		12	13.3	even	3
819.2.s.d.802.4		12	7.4	even	3
1183.2.e.g.170.3		12	39.17	odd	6
1183.2.e.g.508.3		12	273.95	odd	6
1183.2.e.h.170.4		12	39.35	odd	6
1183.2.e.h.508.4		12	273.74	odd	6
8281.2.a.bz.1.3		6	273.191	odd	6
8281.2.a.ca.1.3		6	273.152	even	6
8281.2.a.ce.1.4		6	273.212	odd	6
8281.2.a.cf.1.4		6	273.173	even	6

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.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.425563 - 0.737096i) q^{2} +(0.637793 - 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +(1.82097 - 1.91940i) q^{7} -2.78793 q^{8} +O(q^{10})\)	\(q+(-0.425563 - 0.737096i) q^{2} +(0.637793 - 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +(1.82097 - 1.91940i) q^{7} -2.78793 q^{8} -2.92913 q^{10} +0.897986 q^{11} +(-3.07517 - 1.88237i) q^{13} +(-2.18972 - 0.525403i) q^{14} +(-0.0891447 - 0.154403i) q^{16} +(0.968404 - 1.67733i) q^{17} +1.03804 q^{19} +(-2.19495 - 3.80177i) q^{20} +(-0.382150 - 0.661902i) q^{22} +(2.82506 + 4.89315i) q^{23} +(-3.42189 - 5.92688i) q^{25} +(-0.0788077 + 3.06776i) q^{26} +(-0.958938 - 3.23578i) q^{28} +(-0.917969 + 1.58997i) q^{29} +(4.56692 + 7.91014i) q^{31} +(-2.86381 + 4.96026i) q^{32} -1.64847 q^{34} +(-2.58718 - 8.73000i) q^{35} +(5.30001 + 9.17989i) q^{37} +(-0.441751 - 0.765135i) q^{38} +(-4.79731 + 8.30918i) q^{40} +(-2.66571 + 4.61715i) q^{41} +(1.95732 + 3.39018i) q^{43} +(0.572729 - 0.991996i) q^{44} +(2.40448 - 4.16469i) q^{46} +(3.59565 - 6.22784i) q^{47} +(-0.368167 - 6.99031i) q^{49} +(-2.91246 + 5.04452i) q^{50} +(-4.04076 + 2.19655i) q^{52} +(-4.69324 - 8.12893i) q^{53} +(1.54520 - 2.67637i) q^{55} +(-5.07673 + 5.35115i) q^{56} +1.56261 q^{58} +(-0.255259 + 0.442121i) q^{59} +1.43619 q^{61} +(3.88702 - 6.73252i) q^{62} +4.51834 q^{64} +(-10.9018 + 5.92620i) q^{65} -8.44932 q^{67} +(-1.23528 - 2.13957i) q^{68} +(-5.33385 + 5.62216i) q^{70} +(-1.72419 - 2.98638i) q^{71} +(-5.45026 - 9.44013i) q^{73} +(4.51097 - 7.81324i) q^{74} +(0.662054 - 1.14671i) q^{76} +(1.63520 - 1.72359i) q^{77} +(6.04589 - 10.4718i) q^{79} -0.613579 q^{80} +4.53771 q^{82} -1.51669 q^{83} +(-3.33274 - 5.77248i) q^{85} +(1.66593 - 2.88547i) q^{86} -2.50353 q^{88} +(6.80391 + 11.7847i) q^{89} +(-9.21280 + 2.47475i) q^{91} +7.20722 q^{92} -6.12069 q^{94} +(1.78619 - 3.09378i) q^{95} +(-0.253120 - 0.438417i) q^{97} +(-4.99585 + 3.24619i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8	\( 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29} + 16 q^{31} - 8 q^{32} + 32 q^{34} - 8 q^{35} - 13 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} + 16 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} - 25 q^{52} + 2 q^{53} + 9 q^{55} + 18 q^{56} + 16 q^{58} - 13 q^{59} + 10 q^{61} - 5 q^{62} - 30 q^{64} - 19 q^{65} + 22 q^{67} - 29 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} + 3 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} - 14 q^{80} - 2 q^{82} + 54 q^{83} - q^{85} + 7 q^{86} - 4 q^{89} - 20 q^{91} - 54 q^{92} - 90 q^{94} + 6 q^{95} - 35 q^{97} - 62 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

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