LMFDB - Embedded newform 819.2.do.e.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("819.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			667.2
Root			$0.874681 - 1.11128i$ of defining polynomial
Character	$\chi$	$=$	819.667
Dual form			819.2.do.e.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16500 + 0.672613i) q^{2} +(-0.0951832 + 0.164862i) q^{4} +(3.08979 + 1.78389i) q^{5} +(-2.09638 + 1.61406i) q^{7} -2.94654i q^{8} +O(q^{10})$	\(q+(-1.16500 + 0.672613i) q^{2} +(-0.0951832 + 0.164862i) q^{4} +(3.08979 + 1.78389i) q^{5} +(-2.09638 + 1.61406i) q^{7} -2.94654i q^{8} -4.79947 q^{10} +1.27867i q^{11} +(3.57420 + 0.474474i) q^{13} +(1.35664 - 3.29043i) q^{14} +(1.79151 + 3.10299i) q^{16} +(-3.86960 + 6.70234i) q^{17} -0.943878i q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} +(-0.823637 - 1.42658i) q^{23} +(3.86451 + 6.69354i) q^{25} +(-4.48308 + 1.85129i) q^{26} +(-0.0665578 - 0.499245i) q^{28} +(2.02242 - 3.50293i) q^{29} +(-4.46193 + 2.57610i) q^{31} +(0.929326 + 0.536547i) q^{32} -10.4110i q^{34} +(-9.35667 + 1.24740i) q^{35} +(0.914594 - 0.528041i) q^{37} +(0.634865 + 1.09962i) q^{38} +(5.25629 - 9.10417i) q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} +(-0.210805 - 0.121708i) q^{44} +(1.91908 + 1.10798i) q^{46} +(0.774415 + 0.447109i) q^{47} +(1.78961 - 6.76737i) q^{49} +(-9.00432 - 5.19865i) q^{50} +(-0.418426 + 0.544088i) q^{52} +(-0.0399961 - 0.0692754i) q^{53} +(-2.28101 + 3.95082i) q^{55} +(4.75590 + 6.17706i) q^{56} +5.44122i q^{58} +(-9.68627 - 5.59237i) q^{59} -7.62392 q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(10.1971 + 7.84199i) q^{65} +6.32103i q^{67} +(-0.736641 - 1.27590i) q^{68} +(10.0615 - 7.74664i) q^{70} +(-9.89346 + 5.71199i) q^{71} +(-0.658617 + 0.380253i) q^{73} +(-0.710335 + 1.23034i) q^{74} +(0.155610 + 0.0898413i) q^{76} +(-2.06386 - 2.68058i) q^{77} +(1.42765 - 2.47277i) q^{79} +12.7834i q^{80} -5.64837 q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} +(-4.46270 - 2.57654i) q^{86} +3.76766 q^{88} +(-6.56124 + 3.78813i) q^{89} +(-8.25870 + 4.77430i) q^{91} +0.313586 q^{92} -1.20292 q^{94} +(1.68377 - 2.91638i) q^{95} +(-0.414443 + 0.239279i) q^{97} +(2.46693 + 9.08770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.16500	+	0.672613i	−0.823779	+	0.475609i	−0.851718	−	0.524000i	$-0.824439\pi$
$2$	−1.16500	+	0.672613i	−0.823779	+	0.475609i	0.0279386	+	0.999610i	$0.491106\pi$
$3$		0			0
$3$		0			0
$4$	−0.0951832	+	0.164862i	−0.0475916	+	0.0824311i
$5$	3.08979	+	1.78389i	1.38179	+	0.797779i	0.992372	−	0.123280i	$-0.0393415\pi$
$5$	3.08979	+	1.78389i	1.38179	+	0.797779i	0.389422	+	0.921059i	$0.372675\pi$
$6$		0			0
$7$	−2.09638	+	1.61406i	−0.792357	+	0.610058i
$7$	−2.09638	+	1.61406i	−0.792357	+	0.610058i
$8$		−	2.94654i		−	1.04176i
$9$		0			0
$10$	−4.79947			−1.51772
$11$			1.27867i			0.385534i	0.981245	+	0.192767i	$0.0617462\pi$
$11$			1.27867i			0.385534i	−0.981245	+	0.192767i	$0.938254\pi$
$12$		0			0
$13$	3.57420	+	0.474474i	0.991304	+	0.131595i
$13$	3.57420	+	0.474474i	0.991304	+	0.131595i
$14$	1.35664	−	3.29043i	0.362578	−	0.879406i
$15$		0			0
$16$	1.79151	+	3.10299i	0.447878	+	0.775748i
$17$	−3.86960	+	6.70234i	−0.938515	+	1.62556i	−0.170273	+	0.985397i	$0.554465\pi$
$17$	−3.86960	+	6.70234i	−0.938515	+	1.62556i	−0.768242	+	0.640159i	$0.778868\pi$
$18$		0			0
$19$		−	0.943878i		−	0.216540i	−0.994121	−	0.108270i	$-0.965469\pi$
$19$		−	0.943878i		−	0.216540i	0.994121	−	0.108270i	$-0.0345312\pi$
$20$	−0.588191	+	0.339592i	−0.131524	+	0.0759352i
$21$		0			0
$22$	−0.860052	−	1.48965i	−0.183364	−	0.317595i
$23$	−0.823637	−	1.42658i	−0.171740	−	0.297463i	0.767288	−	0.641303i	$-0.221606\pi$
$23$	−0.823637	−	1.42658i	−0.171740	−	0.297463i	−0.939028	+	0.343840i	$0.888272\pi$
$24$		0			0
$25$	3.86451	+	6.69354i	0.772903	+	1.33871i
$26$	−4.48308	+	1.85129i	−0.879203	+	0.363068i
$27$		0			0
$28$	−0.0665578	−	0.499245i	−0.0125782	−	0.0943485i
$29$	2.02242	−	3.50293i	0.375554	−	0.650478i	−0.614856	−	0.788639i	$-0.710786\pi$
$29$	2.02242	−	3.50293i	0.375554	−	0.650478i	0.990410	+	0.138161i	$0.0441192\pi$
$30$		0			0
$31$	−4.46193	+	2.57610i	−0.801387	+	0.462681i	−0.843956	−	0.536413i	$-0.819779\pi$
$31$	−4.46193	+	2.57610i	−0.801387	+	0.462681i	0.0425691	+	0.999094i	$0.486446\pi$
$32$	0.929326	+	0.536547i	0.164283	+	0.0948490i
$33$		0			0
$34$		−	10.4110i		−	1.78547i
$35$	−9.35667	+	1.24740i	−1.58157	+	0.210849i
$36$		0			0
$37$	0.914594	−	0.528041i	0.150358	−	0.0868094i	−0.422933	−	0.906161i	$-0.639000\pi$
$37$	0.914594	−	0.528041i	0.150358	−	0.0868094i	0.573292	+	0.819351i	$0.305666\pi$
$38$	0.634865	+	1.09962i	0.102989	+	0.178382i
$39$		0			0
$40$	5.25629	−	9.10417i	0.831093	−	1.43950i
$41$	3.63629	+	2.09941i	0.567893	+	0.327873i	0.756307	−	0.654217i	$-0.227002\pi$
$41$	3.63629	+	2.09941i	0.567893	+	0.327873i	−0.188415	+	0.982090i	$0.560335\pi$
$42$		0			0
$43$	1.91532	+	3.31744i	0.292084	+	0.505904i	0.974302	−	0.225244i	$-0.0723180\pi$
$43$	1.91532	+	3.31744i	0.292084	+	0.505904i	−0.682218	+	0.731148i	$0.738985\pi$
$44$	−0.210805	−	0.121708i	−0.0317800	−	0.0183482i
$45$		0			0
$46$	1.91908	+	1.10798i	0.282952	+	0.163363i
$47$	0.774415	+	0.447109i	0.112960	+	0.0652175i	0.555416	−	0.831573i	$-0.312559\pi$
$47$	0.774415	+	0.447109i	0.112960	+	0.0652175i	−0.442456	+	0.896790i	$0.645893\pi$
$48$		0			0
$49$	1.78961	−	6.76737i	0.255658	−	0.966767i
$50$	−9.00432	−	5.19865i	−1.27340	−	0.735200i
$51$		0			0
$52$	−0.418426	+	0.544088i	−0.0580253	+	0.0754514i
$53$	−0.0399961	−	0.0692754i	−0.00549389	−	0.00951570i	0.863265	−	0.504750i	$-0.168415\pi$
$53$	−0.0399961	−	0.0692754i	−0.00549389	−	0.00951570i	−0.868759	+	0.495235i	$0.835082\pi$
$54$		0			0
$55$	−2.28101	+	3.95082i	−0.307571	+	0.532729i
$56$	4.75590	+	6.17706i	0.635533	+	0.825444i
$57$		0			0
$58$			5.44122i			0.714467i
$59$	−9.68627	−	5.59237i	−1.26104	−	0.728064i	−0.287768	−	0.957700i	$-0.592913\pi$
$59$	−9.68627	−	5.59237i	−1.26104	−	0.728064i	−0.973277	+	0.229636i	$0.926246\pi$
$60$		0			0
$61$	−7.62392			−0.976143			−0.488072	−	0.872804i	$-0.662299\pi$
$61$	−7.62392			−0.976143			−0.488072	+	0.872804i	$0.662299\pi$
$62$	3.46543	−	6.00231i	0.440111	−	0.762294i
$63$		0			0
$64$	−8.60961			−1.07620
$65$	10.1971	+	7.84199i	1.26479	+	0.972679i
$66$		0			0
$67$			6.32103i			0.772237i	0.922449	+	0.386119i	$0.126184\pi$
$67$			6.32103i			0.772237i	−0.922449	+	0.386119i	$0.873816\pi$
$68$	−0.736641	−	1.27590i	−0.0893309	−	0.154726i
$69$		0			0
$70$	10.0615	−	7.74664i	1.20258	−	0.925900i
$71$	−9.89346	+	5.71199i	−1.17414	+	0.677889i	−0.954651	−	0.297727i	$-0.903772\pi$
$71$	−9.89346	+	5.71199i	−1.17414	+	0.677889i	−0.219487	+	0.975616i	$0.570438\pi$
$72$		0			0
$73$	−0.658617	+	0.380253i	−0.0770853	+	0.0445052i	−0.538047	−	0.842915i	$-0.680838\pi$
$73$	−0.658617	+	0.380253i	−0.0770853	+	0.0445052i	0.460962	+	0.887420i	$0.347504\pi$
$74$	−0.710335	+	1.23034i	−0.0825747	+	0.143024i
$75$		0			0
$76$	0.155610	+	0.0898413i	0.0178497	+	0.0103055i
$77$	−2.06386	−	2.68058i	−0.235198	−	0.305481i
$78$		0			0
$79$	1.42765	−	2.47277i	0.160624	−	0.278208i	−0.774469	−	0.632612i	$-0.781983\pi$
$79$	1.42765	−	2.47277i	0.160624	−	0.278208i	0.935093	+	0.354404i	$0.115316\pi$
$80$			12.7834i			1.42923i
$81$		0			0
$82$	−5.64837			−0.623758
$83$			2.32483i			0.255183i	0.991827	+	0.127591i	$0.0407246\pi$
$83$			2.32483i			0.255183i	−0.991827	+	0.127591i	$0.959275\pi$
$84$		0			0
$85$	−23.9125	+	13.8059i	−2.59367	+	1.49746i
$86$	−4.46270	−	2.57654i	−0.481226	−	0.277836i
$87$		0			0
$88$	3.76766			0.401634
$89$	−6.56124	+	3.78813i	−0.695490	+	0.401541i	−0.805665	−	0.592371i	$-0.798192\pi$
$89$	−6.56124	+	3.78813i	−0.695490	+	0.401541i	0.110176	+	0.993912i	$0.464859\pi$
$90$		0			0
$91$	−8.25870	+	4.77430i	−0.865747	+	0.500482i
$92$	0.313586			0.0326936
$93$		0			0
$94$	−1.20292			−0.124072
$95$	1.68377	−	2.91638i	0.172751	−	0.299214i
$96$		0			0
$97$	−0.414443	+	0.239279i	−0.0420803	+	0.0242951i	−0.520893	−	0.853622i	$-0.674401\pi$
$97$	−0.414443	+	0.239279i	−0.0420803	+	0.0242951i	0.478812	+	0.877917i	$0.341067\pi$
$98$	2.46693	+	9.08770i	0.249198	+	0.917996i
$99$		0			0
$100$	−1.47135			−0.147135
$101$	2.87836			0.286407			0.143204	−	0.989693i	$-0.454260\pi$
$101$	2.87836			0.286407			0.143204	+	0.989693i	$0.454260\pi$
$102$		0			0
$103$	−5.66755	+	9.81649i	−0.558441	+	0.967248i	0.439186	+	0.898396i	$0.355267\pi$
$103$	−5.66755	+	9.81649i	−0.558441	+	0.967248i	−0.997627	+	0.0688516i	$0.978066\pi$
$104$	1.39806	−	10.5315i	0.137091	−	1.03270i
$105$		0			0
$106$	0.0931910	+	0.0538039i	0.00905151	+	0.00522589i
$107$	−3.28603	−	5.69157i	−0.317673	−	0.550225i	0.662329	−	0.749213i	$-0.269568\pi$
$107$	−3.28603	−	5.69157i	−0.317673	−	0.550225i	−0.980002	+	0.198988i	$0.936235\pi$
$108$		0			0
$109$	5.05684	−	2.91957i	0.484358	−	0.279644i	−0.237873	−	0.971296i	$-0.576450\pi$
$109$	5.05684	−	2.91957i	0.484358	−	0.279644i	0.722231	+	0.691652i	$0.243117\pi$
$110$		−	6.13694i		−	0.585135i
$111$		0			0
$112$	−8.76412	−	3.61343i	−0.828131	−	0.341437i
$113$	3.26617	+	5.65717i	0.307255	+	0.532181i	0.977761	−	0.209723i	$-0.0672562\pi$
$113$	3.26617	+	5.65717i	0.307255	+	0.532181i	−0.670506	+	0.741904i	$0.733923\pi$
$114$		0			0
$115$		−	5.87711i		−	0.548043i
$116$	0.385001	+	0.666841i	0.0357464	+	0.0619146i
$117$		0			0
$118$	15.0460			1.38510
$119$	−2.70585	−	20.2964i	−0.248045	−	1.86057i
$120$		0			0
$121$	9.36500			0.851363
$122$	8.88187	−	5.12795i	0.804127	−	0.464263i
$123$		0			0
$124$		−	0.980805i		−	0.0880789i
$125$			9.73656i			0.870865i
$126$		0			0
$127$	7.35818	−	12.7447i	0.652932	−	1.13091i	−0.329475	−	0.944164i	$-0.606872\pi$
$127$	7.35818	−	12.7447i	0.652932	−	1.13091i	0.982408	−	0.186748i	$-0.0597948\pi$
$128$	8.17154	−	4.71784i	0.722269	−	0.417002i
$129$		0			0
$130$	−17.1542	−	2.27722i	−1.50453	−	0.199726i
$131$	5.59335	−	9.68796i	0.488693	−	0.846441i	−0.511222	−	0.859448i	$-0.670807\pi$
$131$	5.59335	−	9.68796i	0.488693	−	0.846441i	0.999915	+	0.0130074i	$0.00414049\pi$
$132$		0			0
$133$	1.52348	+	1.97873i	0.132102	+	0.171577i
$134$	−4.25161	−	7.36400i	−0.367283	−	0.636153i
$135$		0			0
$136$	19.7487	+	11.4019i	1.69344	+	0.977706i
$137$	15.2687	+	8.81541i	1.30450	+	0.753151i	0.981172	−	0.193137i	$-0.0618662\pi$
$137$	15.2687	+	8.81541i	1.30450	+	0.753151i	0.323324	+	0.946288i	$0.395200\pi$
$138$		0			0
$139$	2.92855	+	5.07240i	0.248396	+	0.430235i	0.963081	−	0.269212i	$-0.0867631\pi$
$139$	2.92855	+	5.07240i	0.248396	+	0.430235i	−0.714685	+	0.699447i	$0.753430\pi$
$140$	0.684948	−	1.66129i	0.0578887	−	0.140405i
$141$		0			0
$142$	7.68392	−	13.3089i	0.644820	−	1.11686i
$143$	−0.606697	+	4.57022i	−0.0507345	+	0.382181i
$144$		0			0
$145$	12.4977	−	7.21554i	1.03788	−	0.599218i
$146$	0.511526	−	0.885989i	0.0423342	−	0.0733250i
$147$		0			0
$148$			0.201043i			0.0165256i
$149$			10.4790i			0.858470i	0.903193	+	0.429235i	$0.141217\pi$
$149$			10.4790i			0.858470i	−0.903193	+	0.429235i	$0.858783\pi$
$150$		0			0
$151$	4.08249	−	2.35703i	0.332229	−	0.191812i	−0.324602	−	0.945851i	$-0.605230\pi$
$151$	4.08249	−	2.35703i	0.332229	−	0.191812i	0.656830	+	0.754039i	$0.271897\pi$
$152$	−2.78117			−0.225583
$153$		0			0
$154$	4.20739	+	1.73470i	0.339041	+	0.139786i
$155$	−18.3819			−1.47647
$156$		0			0
$157$	−4.50105	−	7.79604i	−0.359223	−	0.622192i	0.628608	−	0.777722i	$-0.283625\pi$
$157$	−4.50105	−	7.79604i	−0.359223	−	0.622192i	−0.987831	+	0.155530i	$0.950291\pi$
$158$			3.84103i			0.305576i
$159$		0			0
$160$	1.91428	+	3.31563i	0.151337	+	0.262123i
$161$	4.02925	+	1.66125i	0.317549	+	0.130925i
$162$		0			0
$163$		−	12.0324i		−	0.942449i	−0.882013	−	0.471224i	$-0.843812\pi$
$163$		−	12.0324i		−	0.942449i	0.882013	−	0.471224i	$-0.156188\pi$
$164$	−0.692227	+	0.399657i	−0.0540538	+	0.0312080i
$165$		0			0
$166$	−1.56371	−	2.70842i	−0.121367	−	0.210214i
$167$	16.8199	+	9.71099i	1.30157	+	0.751459i	0.980672	−	0.195657i	$-0.0626838\pi$
$167$	16.8199	+	9.71099i	1.30157	+	0.751459i	0.320893	+	0.947116i	$0.396017\pi$
$168$		0			0
$169$	12.5497	+	3.39173i	0.965365	+	0.260902i
$170$	18.5720	−	32.1677i	1.42441	−	2.46715i
$171$		0			0
$172$	−0.729226			−0.0556030
$173$	14.3795			1.09325			0.546627	−	0.837376i	$-0.315912\pi$
$173$	14.3795			1.09325			0.546627	+	0.837376i	$0.315912\pi$
$174$		0			0
$175$	−18.9053	−	7.79462i	−1.42910	−	0.589218i
$176$	−3.96771	+	2.29076i	−0.299077	+	0.172672i
$177$		0			0
$178$	5.09589	−	8.82635i	0.381953	−	0.661563i
$179$	5.42606			0.405563			0.202781	−	0.979224i	$-0.435002\pi$
$179$	5.42606			0.405563			0.202781	+	0.979224i	$0.435002\pi$
$180$		0			0
$181$	−15.4902			−1.15138			−0.575688	−	0.817669i	$-0.695266\pi$
$181$	−15.4902			−1.15138			−0.575688	+	0.817669i	$0.695266\pi$
$182$	6.41013	−	11.1170i	0.475150	−	0.824044i
$183$		0			0
$184$	−4.20348	+	2.42688i	−0.309885	+	0.178912i
$185$	3.76786			0.277019
$186$		0			0
$187$	−8.57010	−	4.94795i	−0.626707	−	0.361830i
$188$	−0.147423	+	0.0851144i	−0.0107519	+	0.00620761i
$189$		0			0
$190$			4.53011i			0.328649i
$191$	−4.74622			−0.343425			−0.171712	−	0.985147i	$-0.554930\pi$
$191$	−4.74622			−0.343425			−0.171712	+	0.985147i	$0.554930\pi$
$192$		0			0
$193$			21.0391i			1.51443i	0.653166	+	0.757215i	$0.273441\pi$
$193$			21.0391i			1.51443i	−0.653166	+	0.757215i	$0.726559\pi$
$194$	0.321884	−	0.557519i	0.0231099	−	0.0400276i
$195$		0			0
$196$	0.945343	+	0.939178i	0.0675245	+	0.0670842i
$197$	−5.03342	−	2.90604i	−0.358616	−	0.207047i	0.309857	−	0.950783i	$-0.399719\pi$
$197$	−5.03342	−	2.90604i	−0.358616	−	0.207047i	−0.668474	+	0.743736i	$0.733052\pi$
$198$		0			0
$199$	5.30909	−	9.19562i	0.376352	−	0.651860i	−0.614177	−	0.789168i	$-0.710512\pi$
$199$	5.30909	−	9.19562i	0.376352	−	0.651860i	0.990528	+	0.137309i	$0.0438452\pi$
$200$	19.7228	−	11.3869i	1.39461	−	0.805178i
$201$		0			0
$202$	−3.35329	+	1.93602i	−0.235936	+	0.136218i
$203$	1.41420	+	10.6078i	0.0992571	+	0.744520i
$204$		0			0
$205$	7.49023	+	12.9735i	0.523140	+	0.906106i
$206$		−	15.2483i		−	1.06240i
$207$		0			0
$208$	4.93093	+	11.9407i	0.341899	+	0.827941i
$209$	1.20691			0.0834837
$210$		0			0
$211$	2.33275	−	4.04043i	0.160593	−	0.278155i	−0.774489	−	0.632588i	$-0.781993\pi$
$211$	2.33275	−	4.04043i	0.160593	−	0.278155i	0.935081	+	0.354433i	$0.115326\pi$
$212$	0.0152278			0.00104585
$213$		0			0
$214$	7.65645	+	4.42046i	0.523384	+	0.302176i
$215$			13.6669i			0.932074i
$216$		0			0
$217$	5.19592	−	12.6023i	0.352722	−	0.855501i
$218$	−3.92748	+	6.80260i	−0.266003	+	0.460730i
$219$		0			0
$220$	−0.434227	−	0.752104i	−0.0292756	−	0.0507068i
$221$	−17.0108	+	22.1195i	−1.14427	+	1.48792i
$222$		0			0
$223$	20.9798	+	12.1127i	1.40491	+	0.811126i	0.994891	−	0.100950i	$-0.0321883\pi$
$223$	20.9798	+	12.1127i	1.40491	+	0.811126i	0.410020	+	0.912076i	$0.365522\pi$
$224$	−2.81424	+	0.375185i	−0.188034	+	0.0250681i
$225$		0			0
$226$	−7.61017	−	4.39373i	−0.506221	−	0.292267i
$227$	13.3154	+	7.68764i	0.883773	+	0.510247i	0.871901	−	0.489683i	$-0.162887\pi$
$227$	13.3154	+	7.68764i	0.883773	+	0.510247i	0.0118726	+	0.999930i	$0.496221\pi$
$228$		0			0
$229$	14.1608	+	8.17573i	0.935771	+	0.540268i	0.888632	−	0.458621i	$-0.151656\pi$
$229$	14.1608	+	8.17573i	0.935771	+	0.540268i	0.0471389	+	0.998888i	$0.484990\pi$
$230$	3.95302	+	6.84683i	0.260654	+	0.451467i
$231$		0			0
$232$	−10.3215	−	5.95913i	−0.677641	−	0.391236i
$233$	14.5554	−	25.2106i	0.953554	−	1.65160i	0.215911	−	0.976413i	$-0.430728\pi$
$233$	14.5554	−	25.2106i	0.953554	−	1.65160i	0.737643	−	0.675191i	$-0.235939\pi$
$234$		0			0
$235$	1.59518	+	2.76294i	0.104058	+	0.180234i
$236$	1.84394	−	1.06460i	0.120030	−	0.0692995i
$237$		0			0
$238$	16.8040	+	21.8253i	1.08924	+	1.41473i
$239$		−	8.65409i		−	0.559787i	−0.960031	−	0.279893i	$-0.909701\pi$
$239$		−	8.65409i		−	0.559787i	0.960031	−	0.279893i	$-0.0902991\pi$
$240$		0			0
$241$	15.7601	+	9.09909i	1.01520	+	0.586124i	0.912709	−	0.408611i	$-0.133987\pi$
$241$	15.7601	+	9.09909i	1.01520	+	0.586124i	0.102487	+	0.994734i	$0.467320\pi$
$242$	−10.9102	+	6.29902i	−0.701336	+	0.404916i
$243$		0			0
$244$	0.725669	−	1.25690i	0.0464562	−	0.0804645i
$245$	17.6017	−	17.7173i	1.12453	−	1.13191i
$246$		0			0
$247$	0.447846	−	3.37360i	0.0284957	−	0.214657i
$248$	7.59057	+	13.1473i	0.482002	+	0.834851i
$249$		0			0
$250$	−6.54894	−	11.3431i	−0.414191	−	0.717400i
$251$	−7.93598	−	13.7455i	−0.500915	−	0.867610i	−0.999999	−	0.00105678i	$-0.999664\pi$
$251$	−7.93598	−	13.7455i	−0.500915	−	0.867610i	0.499085	−	0.866553i	$-0.333670\pi$
$252$		0			0
$253$	1.82413	−	1.05316i	0.114682	−	0.0662117i
$254$			19.7968i			1.24216i
$255$		0			0
$256$	2.26304	−	3.91971i	0.141440	−	0.244982i
$257$	12.1634	+	21.0676i	0.758730	+	1.31416i	0.943499	+	0.331376i	$0.107513\pi$
$257$	12.1634	+	21.0676i	0.758730	+	1.31416i	−0.184769	+	0.982782i	$0.559154\pi$
$258$		0			0
$259$	−1.06504	+	2.58319i	−0.0661786	+	0.160511i
$260$	−2.26344	+	0.934688i	−0.140372	+	0.0579669i
$261$		0			0
$262$			15.0486i			0.929708i
$263$	−15.4345			−0.951734			−0.475867	−	0.879517i	$-0.657866\pi$
$263$	−15.4345			−0.951734			−0.475867	+	0.879517i	$0.657866\pi$
$264$		0			0
$265$		−	0.285395i		−	0.0175317i
$266$	−3.10577	−	1.28050i	−0.190427	−	0.0785128i
$267$		0			0
$268$	−1.04210	−	0.601656i	−0.0636563	−	0.0367520i
$269$	−6.52035	+	11.2936i	−0.397553	+	0.688582i	−0.993423	−	0.114499i	$-0.963474\pi$
$269$	−6.52035	+	11.2936i	−0.397553	+	0.688582i	0.595870	+	0.803081i	$0.296807\pi$
$270$		0			0
$271$	23.3572	−	13.4853i	1.41885	−	0.819174i	0.422654	−	0.906291i	$-0.361099\pi$
$271$	23.3572	−	13.4853i	1.41885	−	0.819174i	0.996198	+	0.0871168i	$0.0277653\pi$
$272$	−27.7298			−1.68136
$273$		0			0
$274$	−23.7174			−1.43282
$275$	−8.55884	+	4.94145i	−0.516117	+	0.297980i
$276$		0			0
$277$	6.35073	−	10.9998i	0.381578	−	0.660913i	−0.609710	−	0.792625i	$-0.708714\pi$
$277$	6.35073	−	10.9998i	0.381578	−	0.660913i	0.991288	+	0.131712i	$0.0420474\pi$
$278$	−6.82352	−	3.93956i	−0.409248	−	0.236279i
$279$		0			0
$280$	3.67551	+	27.5698i	0.219654	+	1.64761i
$281$		−	26.7216i		−	1.59408i	−0.603930	−	0.797038i	$-0.706399\pi$
$281$		−	26.7216i		−	1.59408i	0.603930	−	0.797038i	$-0.293601\pi$
$282$		0			0
$283$	−14.7423			−0.876336			−0.438168	−	0.898893i	$-0.644373\pi$
$283$	−14.7423			−0.876336			−0.438168	+	0.898893i	$0.644373\pi$
$284$		−	2.17474i		−	0.129047i
$285$		0			0
$286$	−2.36719	−	5.73238i	−0.139975	−	0.338963i
$287$	−11.0116	+	1.46803i	−0.649995	+	0.0866553i
$288$		0			0
$289$	−21.4476	−	37.1483i	−1.26162	−	2.18519i
$290$	−9.70653	+	16.8122i	−0.569987	+	0.987247i
$291$		0			0
$292$		−	0.144775i		−	0.00847230i
$293$	10.0312	−	5.79153i	0.586030	−	0.338345i	−0.177496	−	0.984121i	$-0.556800\pi$
$293$	10.0312	−	5.79153i	0.586030	−	0.338345i	0.763526	+	0.645777i	$0.223466\pi$
$294$		0			0
$295$	−19.9523	−	34.5584i	−1.16167	−	2.01207i
$296$	−1.55589	−	2.69489i	−0.0904344	−	0.156637i
$297$		0			0
$298$	−7.04829	−	12.2080i	−0.408297	−	0.707190i
$299$	−2.26697	−	5.48968i	−0.131102	−	0.317476i
$300$		0			0
$301$	−9.36979	−	3.86315i	−0.540066	−	0.222668i
$302$	−3.17074	+	5.49188i	−0.182455	+	0.316022i
$303$		0			0
$304$	2.92885	−	1.69097i	0.167981	−	0.0969838i
$305$	−23.5563	−	13.6002i	−1.34883	−	0.778746i
$306$		0			0
$307$			29.3335i			1.67415i	0.547086	+	0.837076i	$0.315737\pi$
$307$			29.3335i			1.67415i	−0.547086	+	0.837076i	$0.684263\pi$
$308$	0.638371	−	0.0851055i	0.0363746	−	0.00484934i
$309$		0			0
$310$	21.4149	−	12.3639i	1.21628	−	0.702222i
$311$	0.0753271	+	0.130470i	0.00427141	+	0.00739830i	0.868153	−	0.496296i	$-0.165307\pi$
$311$	0.0753271	+	0.130470i	0.00427141	+	0.00739830i	−0.863882	+	0.503695i	$0.831974\pi$
$312$		0			0
$313$	5.26057	−	9.11157i	0.297345	−	0.515016i	−0.678183	−	0.734893i	$-0.737232\pi$
$313$	5.26057	−	9.11157i	0.297345	−	0.515016i	0.975528	+	0.219877i	$0.0705656\pi$
$314$	10.4874	+	6.05493i	0.591841	+	0.341699i
$315$		0			0
$316$	0.271777	+	0.470732i	0.0152887	+	0.0264808i
$317$	1.30489	+	0.753380i	0.0732901	+	0.0423140i	0.536197	−	0.844093i	$-0.319860\pi$
$317$	1.30489	+	0.753380i	0.0732901	+	0.0423140i	−0.462907	+	0.886407i	$0.653194\pi$
$318$		0			0
$319$	4.47910	+	2.58601i	0.250782	+	0.144789i
$320$	−26.6018	−	15.3586i	−1.48709	−	0.858571i
$321$		0			0
$322$	−5.81145	+	0.774765i	−0.323860	+	0.0431759i
$323$	6.32619	+	3.65243i	0.351999	+	0.203227i
$324$		0			0
$325$	10.6366	+	25.7576i	0.590014	+	1.42878i
$326$	8.09314	+	14.0177i	0.448237	+	0.776370i
$327$		0			0
$328$	6.18600	−	10.7145i	0.341565	−	0.591607i
$329$	−2.34513	+	0.312645i	−0.129291	+	0.0172367i
$330$		0			0
$331$			25.2509i			1.38791i	0.720017	+	0.693957i	$0.244134\pi$
$331$			25.2509i			1.38791i	−0.720017	+	0.693957i	$0.755866\pi$
$332$	−0.383276	−	0.221284i	−0.0210350	−	0.0121446i
$333$		0			0
$334$	−26.1270			−1.42960
$335$	−11.2760	+	19.5306i	−0.616075	+	1.06707i
$336$		0			0
$337$	32.1811			1.75302			0.876509	−	0.481386i	$-0.159866\pi$
$337$	32.1811			1.75302			0.876509	+	0.481386i	$0.159866\pi$
$338$	−16.9018	+	4.48977i	−0.919335	+	0.244211i
$339$		0			0
$340$		−	5.25634i		−	0.285065i
$341$	−3.29398	−	5.70535i	−0.178379	−	0.308962i
$342$		0			0
$343$	7.17127	+	17.0755i	0.387212	+	0.921991i
$344$	9.77495	−	5.64357i	0.527030	−	0.304281i
$345$		0			0
$346$	−16.7521	+	9.67185i	−0.900600	+	0.519962i
$347$	12.3819	−	21.4461i	0.664695	−	1.15128i	−0.314673	−	0.949200i	$-0.601895\pi$
$347$	12.3819	−	21.4461i	0.664695	−	1.15128i	0.979368	−	0.202085i	$-0.0647717\pi$
$348$		0			0
$349$	−10.0075	−	5.77782i	−0.535688	−	0.309280i	0.207642	−	0.978205i	$-0.433421\pi$
$349$	−10.0075	−	5.77782i	−0.535688	−	0.309280i	−0.743330	+	0.668925i	$0.766755\pi$
$350$	27.2674	−	3.63520i	1.45750	−	0.194310i
$351$		0			0
$352$	−0.686067	+	1.18830i	−0.0365675	+	0.0633368i
$353$			20.0884i			1.06920i	0.845106	+	0.534599i	$0.179537\pi$
$353$			20.0884i			1.06920i	−0.845106	+	0.534599i	$0.820463\pi$
$354$		0			0
$355$	−40.7582			−2.16322
$356$		−	1.44227i		−	0.0764399i
$357$		0			0
$358$	−6.32136	+	3.64964i	−0.334094	+	0.192890i
$359$	13.0346	+	7.52551i	0.687938	+	0.397181i	0.802839	−	0.596196i	$-0.203322\pi$
$359$	13.0346	+	7.52551i	0.687938	+	0.397181i	−0.114901	+	0.993377i	$0.536655\pi$
$360$		0			0
$361$	18.1091			0.953110
$362$	18.0461	−	10.4189i	0.948481	−	0.547606i
$363$		0			0
$364$	−0.00101167	−	1.81598i	−5.30260e−5	−	0.0951832i
$365$	−2.71331			−0.142021
$366$		0			0
$367$	9.00355			0.469982			0.234991	−	0.971998i	$-0.424494\pi$
$367$	9.00355			0.469982			0.234991	+	0.971998i	$0.424494\pi$
$368$	2.95112	−	5.11148i	0.153838	−	0.266454i
$369$		0			0
$370$	−4.38956	+	2.53431i	−0.228202	+	0.131753i
$371$	0.195662	+	0.0806711i	0.0101583	+	0.00418823i
$372$		0			0
$373$	−16.1391			−0.835649			−0.417824	−	0.908528i	$-0.637207\pi$
$373$	−16.1391			−0.835649			−0.417824	+	0.908528i	$0.637207\pi$
$374$	13.3122			0.688358
$375$		0			0
$376$	1.31742	−	2.28184i	0.0679409	−	0.117677i
$377$	8.89057	−	11.5606i	0.457888	−	0.595400i
$378$		0			0
$379$	−13.5668	−	7.83277i	−0.696878	−	0.402342i	0.109306	−	0.994008i	$-0.465137\pi$
$379$	−13.5668	−	7.83277i	−0.696878	−	0.402342i	−0.806183	+	0.591666i	$0.798471\pi$
$380$	0.320534	+	0.555181i	0.0164430	+	0.0284802i
$381$		0			0
$382$	5.52935	−	3.19237i	0.282906	−	0.163336i
$383$			24.6328i			1.25868i	0.777131	+	0.629339i	$0.216674\pi$
$383$			24.6328i			1.25868i	−0.777131	+	0.629339i	$0.783326\pi$
$384$		0			0
$385$	−1.59502	−	11.9641i	−0.0812896	−	0.609747i
$386$	−14.1512	−	24.5106i	−0.720277	−	1.24756i
$387$		0			0
$388$		−	0.0911013i		−	0.00462497i
$389$	9.42834	+	16.3304i	0.478036	+	0.827982i	0.999683	−	0.0251791i	$-0.00801560\pi$
$389$	9.42834	+	16.3304i	0.478036	+	0.827982i	−0.521647	+	0.853161i	$0.674682\pi$
$390$		0			0
$391$	12.7486			0.644724
$392$	−19.9403	−	5.27314i	−1.00714	−	0.266334i
$393$		0			0
$394$	7.81857			0.393894
$395$	8.82229	−	5.09355i	0.443897	−	0.256284i
$396$		0			0
$397$			14.5030i			0.727884i	0.931422	+	0.363942i	$0.118569\pi$
$397$			14.5030i			0.727884i	−0.931422	+	0.363942i	$0.881431\pi$
$398$			14.2839i			0.715985i
$399$		0			0
$400$	−13.8467	+	23.9831i	−0.692333	+	1.19916i
$401$	−18.1770	+	10.4945i	−0.907714	+	0.524069i	−0.879695	−	0.475539i	$-0.842253\pi$
$401$	−18.1770	+	10.4945i	−0.907714	+	0.524069i	−0.0280189	+	0.999607i	$0.508920\pi$
$402$		0			0
$403$	−17.1701	+	7.09041i	−0.855304	+	0.353198i
$404$	−0.273971	+	0.474532i	−0.0136306	+	0.0236089i
$405$		0			0
$406$	−8.78247	−	11.4069i	−0.435867	−	0.566113i
$407$	0.675191	+	1.16947i	0.0334680	+	0.0579683i
$408$		0			0
$409$	−18.5568	−	10.7138i	−0.917576	−	0.529763i	−0.0347148	−	0.999397i	$-0.511052\pi$
$409$	−18.5568	−	10.7138i	−0.917576	−	0.529763i	−0.882861	+	0.469635i	$0.844386\pi$
$410$	−17.4522	−	10.0761i	−0.861905	−	0.497621i
$411$		0			0
$412$	−1.07891	−	1.86873i	−0.0531542	−	0.0920657i
$413$	29.3325	−	3.91052i	1.44336	−	0.192424i
$414$		0			0
$415$	−4.14723	+	7.18321i	−0.203580	+	0.352610i
$416$	3.06702	+	2.35866i	0.150373	+	0.115643i
$417$		0			0
$418$	−1.40605	+	0.811784i	−0.0687722	+	0.0397056i
$419$	3.98203	−	6.89708i	0.194535	−	0.336944i	−0.752213	−	0.658920i	$-0.771014\pi$
$419$	3.98203	−	6.89708i	0.194535	−	0.336944i	0.946748	+	0.321976i	$0.104347\pi$
$420$		0			0
$421$		−	2.81786i		−	0.137334i	−0.997640	−	0.0686670i	$-0.978125\pi$
$421$		−	2.81786i		−	0.137334i	0.997640	−	0.0686670i	$-0.0218746\pi$
$422$			6.27614i			0.305518i
$423$		0			0
$424$	−0.204122	+	0.117850i	−0.00991306	+	0.00572331i
$425$	−59.8165			−2.90152
$426$		0			0
$427$	15.9826	−	12.3055i	0.773453	−	0.595504i
$428$	1.25110			0.0604742
$429$		0			0
$430$	−9.19253	−	15.9219i	−0.443303	−	0.767823i
$431$		−	5.73626i		−	0.276306i	−0.990411	−	0.138153i	$-0.955883\pi$
$431$		−	5.73626i		−	0.276306i	0.990411	−	0.138153i	$-0.0441166\pi$
$432$		0			0
$433$	−12.2628	−	21.2398i	−0.589314	−	1.02072i	−0.994322	−	0.106409i	$-0.966065\pi$
$433$	−12.2628	−	21.2398i	−0.589314	−	1.02072i	0.405009	−	0.914313i	$-0.367268\pi$
$434$	2.42324	+	18.1765i	0.116319	+	0.872502i
$435$		0			0
$436$			1.11158i			0.0532349i
$437$	−1.34652	+	0.777413i	−0.0644128	+	0.0371887i
$438$		0			0
$439$	18.3211	+	31.7332i	0.874420	+	1.51454i	0.857379	+	0.514686i	$0.172091\pi$
$439$	18.3211	+	31.7332i	0.874420	+	1.51454i	0.0170416	+	0.999855i	$0.494575\pi$
$440$	11.6412	+	6.72108i	0.554975	+	0.320415i
$441$		0			0
$442$	4.93973	−	37.2108i	0.234959	−	1.76994i
$443$	13.5467	−	23.4635i	0.643622	−	1.11479i	−0.340996	−	0.940065i	$-0.610764\pi$
$443$	13.5467	−	23.4635i	0.643622	−	1.11479i	0.984618	−	0.174721i	$-0.0559022\pi$
$444$		0			0
$445$	−27.0304			−1.28136
$446$	−32.5886			−1.54312
$447$		0			0
$448$	18.0490	−	13.8964i	0.852735	−	0.656545i
$449$	−23.7571	+	13.7162i	−1.12117	+	0.647307i	−0.941699	−	0.336456i	$-0.890772\pi$
$449$	−23.7571	+	13.7162i	−1.12117	+	0.647307i	−0.179470	+	0.983764i	$0.557438\pi$
$450$		0			0
$451$	−2.68446	+	4.64962i	−0.126406	+	0.218942i
$452$	−1.24354			−0.0584911
$453$		0			0
$454$	−20.6832			−0.970712
$455$	−34.0344	+	0.0189604i	−1.59556	+	0.000888877i
$456$		0			0
$457$	−34.3500	+	19.8320i	−1.60682	+	0.927700i	−0.616748	+	0.787161i	$0.711550\pi$
$457$	−34.3500	+	19.8320i	−1.60682	+	0.927700i	−0.990075	+	0.140539i	$0.955116\pi$
$458$	−21.9964			−1.02783
$459$		0			0
$460$	0.968913	+	0.559402i	0.0451758	+	0.0260823i
$461$	4.23988	−	2.44790i	0.197471	−	0.114010i	−0.398004	−	0.917384i	$-0.630297\pi$
$461$	4.23988	−	2.44790i	0.197471	−	0.114010i	0.595475	+	0.803374i	$0.296964\pi$
$462$		0			0
$463$			4.71193i			0.218982i	0.993988	+	0.109491i	$0.0349221\pi$
$463$			4.71193i			0.218982i	−0.993988	+	0.109491i	$0.965078\pi$
$464$	14.4928			0.672810
$465$		0			0
$466$			39.1605i			1.81408i
$467$	−16.0081	+	27.7268i	−0.740765	+	1.28304i	0.211383	+	0.977403i	$0.432203\pi$
$467$	−16.0081	+	27.7268i	−0.740765	+	1.28304i	−0.952147	+	0.305639i	$0.901130\pi$
$468$		0			0
$469$	−10.2025	−	13.2513i	−0.471110	−	0.611887i
$470$	−3.71678	−	2.14588i	−0.171442	−	0.0989822i
$471$		0			0
$472$	−16.4781	+	28.5410i	−0.758467	+	1.31370i
$473$	−4.24191	+	2.44907i	−0.195043	+	0.112608i
$474$		0			0
$475$	6.31788	−	3.64763i	0.289884	−	0.167365i
$476$	3.60366	+	1.48578i	0.165174	+	0.0681008i
$477$		0			0
$478$	5.82086	+	10.0820i	0.266240	+	0.461141i
$479$		−	18.0245i		−	0.823560i	−0.911283	−	0.411780i	$-0.864907\pi$
$479$		−	18.0245i		−	0.823560i	0.911283	−	0.411780i	$-0.135093\pi$
$480$		0			0
$481$	3.51948	−	1.45337i	0.160474	−	0.0662680i
$482$	−24.4807			−1.11506
$483$		0			0
$484$	−0.891390	+	1.54393i	−0.0405177	+	0.0701788i
$485$	−1.70739			−0.0775284
$486$		0			0
$487$	−15.2424	−	8.80020i	−0.690699	−	0.398775i	0.113175	−	0.993575i	$-0.463898\pi$
$487$	−15.2424	−	8.80020i	−0.690699	−	0.398775i	−0.803874	+	0.594800i	$0.797231\pi$
$488$			22.4642i			1.01691i
$489$		0			0
$490$	−8.58915	+	32.4798i	−0.388018	+	1.46729i
$491$	−1.93180	+	3.34598i	−0.0871810	+	0.151002i	−0.906318	−	0.422595i	$-0.861119\pi$
$491$	−1.93180	+	3.34598i	−0.0871810	+	0.151002i	0.819138	+	0.573597i	$0.194453\pi$
$492$		0			0
$493$	15.6519	+	27.1099i	0.704926	+	1.22097i
$494$	1.74739	+	4.23148i	0.0786188	+	0.190383i
$495$		0			0
$496$	−15.9872	−	9.23023i	−0.717848	−	0.414450i
$497$	11.5209	−	27.9432i	0.516784	−	1.25342i
$498$		0			0
$499$	10.9528	+	6.32363i	0.490317	+	0.283084i	0.724706	−	0.689058i	$-0.241976\pi$
$499$	10.9528	+	6.32363i	0.490317	+	0.283084i	−0.234389	+	0.972143i	$0.575309\pi$
$500$	−1.60519	−	0.926757i	−0.0717863	−	0.0414458i
$501$		0			0
$502$	18.4908	+	10.6757i	0.825287	+	0.476480i
$503$	11.0180	+	19.0837i	0.491268	+	0.850902i	0.999949	−	0.0100533i	$-0.00320011\pi$
$503$	11.0180	+	19.0837i	0.491268	+	0.850902i	−0.508681	+	0.860955i	$0.669867\pi$
$504$		0			0
$505$	8.89351	+	5.13467i	0.395756	+	0.228490i
$506$	−1.41674	+	2.45387i	−0.0629818	+	0.109088i
$507$		0			0
$508$	1.40075	+	2.42617i	0.0621482	+	0.107644i
$509$	13.5708	−	7.83509i	0.601514	−	0.347284i	−0.168123	−	0.985766i	$-0.553771\pi$
$509$	13.5708	−	7.83509i	0.601514	−	0.347284i	0.769637	+	0.638482i	$0.220437\pi$
$510$		0			0
$511$	0.766959	−	1.86020i	0.0339283	−	0.0822906i
$512$			24.9600i			1.10309i
$513$		0			0
$514$	−28.3406	−	16.3625i	−1.25005	−	0.721718i
$515$	−35.0230	+	20.2206i	−1.54330	+	0.891025i
$516$		0			0
$517$	−0.571705	+	0.990222i	−0.0251436	+	0.0435499i
$518$	−0.496708	−	3.72577i	−0.0218241	−	0.163701i
$519$		0			0
$520$	23.1067	−	30.0461i	1.01330	−	1.31761i
$521$	−12.6207	−	21.8598i	−0.552925	−	0.957694i	−0.998062	−	0.0622317i	$-0.980178\pi$
$521$	−12.6207	−	21.8598i	−0.552925	−	0.957694i	0.445137	−	0.895463i	$-0.353155\pi$
$522$		0			0
$523$	6.62383	+	11.4728i	0.289640	+	0.501671i	0.973724	−	0.227733i	$-0.0731312\pi$
$523$	6.62383	+	11.4728i	0.289640	+	0.501671i	−0.684084	+	0.729403i	$0.739798\pi$
$524$	1.06479	+	1.84426i	0.0465154	+	0.0805670i
$525$		0			0
$526$	17.9812	−	10.3815i	0.784019	−	0.452654i
$527$		−	39.8738i		−	1.73693i
$528$		0			0
$529$	10.1432	−	17.5686i	0.441011	−	0.763853i
$530$	0.191960	+	0.332485i	0.00833822	+	0.0144422i
$531$		0			0
$532$	−0.471226	+	0.0628224i	−0.0204303	+	0.00272370i
$533$	12.0007	+	9.22903i	0.519807	+	0.399754i
$534$		0			0
$535$		−	23.4477i		−	1.01373i
$536$	18.6252			0.804485
$537$		0			0
$538$		−	17.5427i		−	0.756320i
$539$	8.65325	+	2.28832i	0.372722	+	0.0985649i
$540$		0			0
$541$	12.4737	+	7.20170i	0.536287	+	0.309625i	0.743573	−	0.668655i	$-0.233130\pi$
$541$	12.4737	+	7.20170i	0.536287	+	0.309625i	−0.207286	+	0.978280i	$0.566463\pi$
$542$	−18.1408	+	31.4208i	−0.779214	+	1.34964i
$543$		0			0
$544$	−7.19224	+	4.15244i	−0.308365	+	0.178034i
$545$	20.8328			0.892377
$546$		0			0
$547$	2.00679			0.0858042			0.0429021	−	0.999079i	$-0.486340\pi$
$547$	2.00679			0.0858042			0.0429021	+	0.999079i	$0.486340\pi$
$548$	−2.90665	+	1.67816i	−0.124166	+	0.0716873i
$549$		0			0
$550$	6.64736	−	11.5136i	0.283445	−	0.490940i
$551$	−3.30634	−	1.90892i	−0.140855	−	0.0813226i
$552$		0			0
$553$	0.998300	+	7.48818i	0.0424521	+	0.318430i
$554$			17.0863i			0.725928i
$555$		0			0
$556$	−1.11499			−0.0472863
$557$			8.57916i			0.363511i	0.983344	+	0.181755i	$0.0581779\pi$
$557$			8.57916i			0.363511i	−0.983344	+	0.181755i	$0.941822\pi$
$558$		0			0
$559$	5.27170	+	12.7659i	0.222969	+	0.539942i
$560$	−20.6333	−	26.7989i	−0.871915	−	1.13246i
$561$		0			0
$562$	17.9733	+	31.1306i	0.758157	+	1.31317i
$563$	6.38718	−	11.0629i	0.269188	−	0.466247i	−0.699465	−	0.714667i	$-0.746578\pi$
$563$	6.38718	−	11.0629i	0.269188	−	0.466247i	0.968652	+	0.248421i	$0.0799115\pi$
$564$		0			0
$565$			23.3059i			0.980487i
$566$	17.1747	−	9.91583i	0.721908	−	0.416794i
$567$		0			0
$568$	16.8306	+	29.1515i	0.706196	+	1.22317i
$569$	2.89558	+	5.01530i	0.121389	+	0.210252i	0.920316	−	0.391176i	$-0.127932\pi$
$569$	2.89558	+	5.01530i	0.121389	+	0.210252i	−0.798927	+	0.601429i	$0.794598\pi$
$570$		0			0
$571$	−22.0666	−	38.2204i	−0.923458	−	1.59948i	−0.794023	−	0.607888i	$-0.792017\pi$
$571$	−22.0666	−	38.2204i	−0.923458	−	1.59948i	−0.129435	−	0.991588i	$-0.541316\pi$
$572$	−0.695710	−	0.535030i	−0.0290891	−	0.0223707i
$573$		0			0
$574$	11.8411	−	9.11682i	0.494239	−	0.380529i
$575$	6.36592	−	11.0261i	0.265477	−	0.459820i
$576$		0			0
$577$	−10.3343	+	5.96649i	−0.430221	+	0.248388i	−0.699441	−	0.714691i	$-0.746568\pi$
$577$	−10.3343	+	5.96649i	−0.430221	+	0.248388i	0.269220	+	0.963079i	$0.413234\pi$
$578$	49.9729	+	28.8518i	2.07860	+	1.20008i
$579$		0			0
$580$			2.74719i			0.114071i
$581$	−3.75242	−	4.87372i	−0.155676	−	0.202196i
$582$		0			0
$583$	0.0885805	−	0.0511420i	0.00366863	−	0.00211808i
$584$	1.12043	+	1.94064i	0.0463637	+	0.0803043i
$585$		0			0
$586$	−7.79091	+	13.4943i	−0.321840	+	0.557443i
$587$	−17.6250	−	10.1758i	−0.727462	−	0.420000i	0.0900312	−	0.995939i	$-0.471303\pi$
$587$	−17.6250	−	10.1758i	−0.727462	−	0.420000i	−0.817493	+	0.575939i	$0.804637\pi$
$588$		0			0
$589$	2.43152	+	4.21152i	0.100189	+	0.173533i
$590$	46.4889	+	26.8404i	1.91392	+	1.10500i
$591$		0			0
$592$	3.27701	+	1.89199i	0.134684	+	0.0777601i
$593$	15.7443	+	9.09000i	0.646543	+	0.373282i	0.787130	−	0.616787i	$-0.211566\pi$
$593$	15.7443	+	9.09000i	0.646543	+	0.373282i	−0.140588	+	0.990068i	$0.544899\pi$
$594$		0			0
$595$	27.8460	−	67.5385i	1.14158	−	2.76881i
$596$	−1.72759	−	0.997422i	−0.0707646	−	0.0408560i
$597$		0			0
$598$	6.33344	+	4.87068i	0.258994	+	0.199177i
$599$	−19.1341	−	33.1412i	−0.781797	−	1.35411i	−0.930894	−	0.365290i	$-0.880970\pi$
$599$	−19.1341	−	33.1412i	−0.781797	−	1.35411i	0.149096	−	0.988823i	$-0.452364\pi$
$600$		0			0
$601$	13.4360	−	23.2718i	0.548064	−	0.949275i	−0.450343	−	0.892856i	$-0.648698\pi$
$601$	13.4360	−	23.2718i	0.548064	−	0.949275i	0.998407	−	0.0564195i	$-0.0179684\pi$
$602$	13.5142	−	1.80167i	0.550798	−	0.0734306i
$603$		0			0
$604$			0.897398i			0.0365146i
$605$	28.9358	+	16.7061i	1.17641	+	0.679200i
$606$		0			0
$607$	−9.40209			−0.381619			−0.190810	−	0.981627i	$-0.561111\pi$
$607$	−9.40209			−0.381619			−0.190810	+	0.981627i	$0.561111\pi$
$608$	0.506435	−	0.877171i	0.0205386	−	0.0355740i
$609$		0			0
$610$	36.5908			1.48152
$611$	2.55577	+	1.96549i	0.103395	+	0.0795153i
$612$		0			0
$613$			13.2894i			0.536753i	0.963314	+	0.268376i	$0.0864871\pi$
$613$			13.2894i			0.536753i	−0.963314	+	0.268376i	$0.913513\pi$
$614$	−19.7301	−	34.1735i	−0.796242	−	1.37913i
$615$		0			0
$616$	−7.89843	+	6.08123i	−0.318237	+	0.245020i
$617$	9.72211	−	5.61306i	0.391397	−	0.225973i	−0.291368	−	0.956611i	$-0.594110\pi$
$617$	9.72211	−	5.61306i	0.391397	−	0.225973i	0.682765	+	0.730638i	$0.260777\pi$
$618$		0			0
$619$	8.04109	−	4.64253i	0.323199	−	0.186599i	−0.329619	−	0.944114i	$-0.606920\pi$
$619$	8.04109	−	4.64253i	0.323199	−	0.186599i	0.652817	+	0.757515i	$0.273587\pi$
$620$	1.74965	−	3.03048i	0.0702675	−	0.121707i
$621$		0			0
$622$	−0.175512	−	0.101332i	−0.00703740	−	0.00406304i
$623$	7.64055	−	18.5316i	0.306112	−	0.742453i
$624$		0			0
$625$	1.95363	−	3.38379i	0.0781452	−	0.135351i
$626$			14.1533i			0.565680i
$627$		0			0
$628$	1.71370			0.0683839
$629$			8.17322i			0.325888i
$630$		0			0
$631$	9.00894	−	5.20132i	0.358640	−	0.207061i	−0.309844	−	0.950787i	$-0.600277\pi$
$631$	9.00894	−	5.20132i	0.358640	−	0.207061i	0.668484	+	0.743726i	$0.266943\pi$
$632$	−7.28611	−	4.20664i	−0.289826	−	0.167331i
$633$		0			0
$634$	−2.02693			−0.0804998
$635$	45.4704	−	26.2523i	1.80444	−	1.04179i
$636$		0			0
$637$	9.60734	−	23.3388i	0.380657	−	0.924716i
$638$	−6.95754			−0.275452
$639$		0			0
$640$	33.6644			1.33070
$641$	−7.42955	+	12.8684i	−0.293449	+	0.508269i	−0.974623	−	0.223853i	$-0.928137\pi$
$641$	−7.42955	+	12.8684i	−0.293449	+	0.508269i	0.681174	+	0.732122i	$0.261470\pi$
$642$		0			0
$643$	1.98945	−	1.14861i	0.0784563	−	0.0452968i	−0.460259	−	0.887785i	$-0.652243\pi$
$643$	1.98945	−	1.14861i	0.0784563	−	0.0452968i	0.538715	+	0.842488i	$0.318910\pi$
$644$	−0.657395	+	0.506147i	−0.0259050	+	0.0199450i
$645$		0			0
$646$	−9.82669			−0.386626
$647$	7.99865			0.314459			0.157230	−	0.987562i	$-0.449744\pi$
$647$	7.99865			0.314459			0.157230	+	0.987562i	$0.449744\pi$
$648$		0			0
$649$	7.15081	−	12.3856i	0.280694	−	0.486176i
$650$	−29.7166	−	22.8533i	−1.16558	−	0.896380i
$651$		0			0
$652$	1.98368	+	1.14528i	0.0776871	+	0.0448526i
$653$	1.99222	+	3.45062i	0.0779615	+	0.135033i	0.902370	−	0.430962i	$-0.141826\pi$
$653$	1.99222	+	3.45062i	0.0779615	+	0.135033i	−0.824409	+	0.565995i	$0.808492\pi$
$654$		0			0
$655$	34.5645	−	19.9558i	1.35055	−	0.779738i
$656$			15.0445i			0.587389i
$657$		0			0
$658$	2.52178	−	1.94159i	0.0983094	−	0.0756912i
$659$	−13.7501	−	23.8159i	−0.535629	−	0.927737i	−0.999133	−	0.0416417i	$-0.986741\pi$
$659$	−13.7501	−	23.8159i	−0.535629	−	0.927737i	0.463504	−	0.886095i	$-0.346592\pi$
$660$		0			0
$661$			6.98621i			0.271732i	0.990727	+	0.135866i	$0.0433817\pi$
$661$			6.98621i			0.271732i	−0.990727	+	0.135866i	$0.956618\pi$
$662$	−16.9841	−	29.4173i	−0.660105	−	1.14333i
$663$		0			0
$664$	6.85019			0.265839
$665$	1.17739	+	8.83155i	0.0456574	+	0.342473i
$666$		0			0
$667$	−6.66296			−0.257991
$668$	−3.20195	+	1.84865i	−0.123887	+	0.0715263i
$669$		0			0
$670$		−	30.3376i		−	1.17204i
$671$		−	9.74849i		−	0.376336i
$672$		0			0
$673$	2.72783	−	4.72474i	0.105150	−	0.182125i	−0.808649	−	0.588291i	$-0.799801\pi$
$673$	2.72783	−	4.72474i	0.105150	−	0.182125i	0.913800	+	0.406166i	$0.133134\pi$
$674$	−37.4910	+	21.6455i	−1.44410	+	0.833752i
$675$		0			0
$676$	−1.75369	+	1.74614i	−0.0674497	+	0.0671594i
$677$	16.8961	−	29.2649i	0.649371	−	1.12474i	−0.333903	−	0.942607i	$-0.608366\pi$
$677$	16.8961	−	29.2649i	0.649371	−	1.12474i	0.983273	−	0.182135i	$-0.0583009\pi$
$678$		0			0
$679$	0.482618	−	1.17056i	0.0185212	−	0.0449218i
$680$	40.6795	+	70.4590i	1.55999	+	2.70198i
$681$		0			0
$682$	7.67498	+	4.43115i	0.293890	+	0.169678i
$683$	10.6511	+	6.14942i	0.407553	+	0.235301i	0.689738	−	0.724059i	$-0.257726\pi$
$683$	10.6511	+	6.14942i	0.407553	+	0.235301i	−0.282185	+	0.959360i	$0.591059\pi$
$684$		0			0
$685$	31.4514	+	54.4754i	1.20170	+	2.08140i
$686$	−19.8397	−	15.0695i	−0.757485	−	0.575355i
$687$		0			0
$688$	−6.86265	+	11.8865i	−0.261636	+	0.453167i
$689$	−0.110085	−	0.266581i	−0.00419389	−	0.0101559i
$690$		0			0
$691$	9.60393	−	5.54483i	0.365351	−	0.210935i	−0.306075	−	0.952008i	$-0.599016\pi$
$691$	9.60393	−	5.54483i	0.365351	−	0.210935i	0.671425	+	0.741072i	$0.265682\pi$
$692$	−1.36869	+	2.37064i	−0.0520297	+	0.0901181i
$693$		0			0
$694$			33.3129i			1.26454i
$695$			20.8968i			0.792662i
$696$		0			0
$697$	−28.1419	+	16.2478i	−1.06595	+	0.615428i
$698$	15.5449			0.588385
$699$		0			0
$700$	3.08450	−	2.37485i	0.116583	−	0.0897608i
$701$	−10.6470			−0.402133			−0.201066	−	0.979578i	$-0.564441\pi$
$701$	−10.6470			−0.402133			−0.201066	+	0.979578i	$0.564441\pi$
$702$		0			0
$703$	−0.498406	−	0.863265i	−0.0187977	−	0.0325587i
$704$		−	11.0089i		−	0.414912i
$705$		0			0
$706$	−13.5117	−	23.4030i	−0.508521	−	0.880784i
$707$	−6.03413	+	4.64585i	−0.226937	+	0.174725i
$708$		0			0
$709$		−	40.7069i		−	1.52878i	−0.644754	−	0.764391i	$-0.723040\pi$
$709$		−	40.7069i		−	1.52878i	0.644754	−	0.764391i	$-0.276960\pi$
$710$	47.4833	−	27.4145i	1.78202	−	1.02885i
$711$		0			0
$712$	11.1619	+	19.3329i	0.418309	+	0.724532i
$713$	7.35003	+	4.24354i	0.275261	+	0.158922i
$714$		0			0
$715$	−10.0273	+	13.0387i	−0.375001	+	0.487621i
$716$	−0.516470	+	0.894552i	−0.0193014	+	0.0334310i
$717$		0			0
$718$	−20.2470			−0.755612
$719$	−9.77537			−0.364560			−0.182280	−	0.983247i	$-0.558348\pi$
$719$	−9.77537			−0.364560			−0.182280	+	0.983247i	$0.558348\pi$
$720$		0			0
$721$	−3.96309	−	29.7269i	−0.147593	−	1.10709i
$722$	−21.0971	+	12.1804i	−0.785153	+	0.453308i
$723$		0			0
$724$	1.47441	−	2.55375i	0.0547959	−	0.0949092i
$725$	31.2627			1.16107
$726$		0			0
$727$	−12.2091			−0.452811			−0.226406	−	0.974033i	$-0.572697\pi$
$727$	−12.2091			−0.452811			−0.226406	+	0.974033i	$0.572697\pi$
$728$	14.0677	+	24.3346i	0.521382	+	0.901899i
$729$		0			0
$730$	3.16101	−	1.82501i	0.116994	−	0.0675467i
$731$	−29.6461			−1.09650
$732$		0			0
$733$	19.3256	+	11.1577i	0.713809	+	0.412118i	0.812470	−	0.583003i	$-0.198123\pi$
$733$	19.3256	+	11.1577i	0.713809	+	0.412118i	−0.0986608	+	0.995121i	$0.531456\pi$
$734$	−10.4891	+	6.05591i	−0.387161	+	0.223528i
$735$		0			0
$736$		−	1.76768i		−	0.0651576i
$737$	−8.08253			−0.297724
$738$		0			0
$739$		−	42.3729i		−	1.55871i	−0.626580	−	0.779357i	$-0.715546\pi$
$739$		−	42.3729i		−	1.55871i	0.626580	−	0.779357i	$-0.284454\pi$
$740$	−0.358637	+	0.621178i	−0.0131838	+	0.0228350i
$741$		0			0
$742$	−0.282206	+	0.0376229i	−0.0103601	+	0.00138118i
$743$	26.8296	+	15.4901i	0.984282	+	0.568276i	0.903560	−	0.428461i	$-0.140944\pi$
$743$	26.8296	+	15.4901i	0.984282	+	0.568276i	0.0807220	+	0.996737i	$0.474277\pi$
$744$		0			0
$745$	−18.6933	+	32.3778i	−0.684870	+	1.18623i
$746$	18.8020	−	10.8553i	0.688390	−	0.397442i
$747$		0			0
$748$	1.63146	−	0.941923i	0.0596520	−	0.0344401i
$749$	16.0753	+	6.62783i	0.587379	+	0.242176i
$750$		0			0
$751$	11.2830	+	19.5427i	0.411722	+	0.713123i	0.995078	−	0.0990930i	$-0.0315941\pi$
$751$	11.2830	+	19.5427i	0.411722	+	0.713123i	−0.583356	+	0.812216i	$0.698261\pi$
$752$			3.20400i			0.116838i
$753$		0			0
$754$	−2.58172	+	19.4480i	−0.0940206	+	0.708254i
$755$	16.8187			0.612095
$756$		0			0
$757$	−16.1404	+	27.9560i	−0.586633	+	1.01608i	0.408037	+	0.912965i	$0.366213\pi$
$757$	−16.1404	+	27.9560i	−0.586633	+	1.01608i	−0.994670	+	0.103112i	$0.967120\pi$
$758$	21.0737			0.765431
$759$		0			0
$760$	−8.59323	−	4.96130i	−0.311709	−	0.179965i
$761$		−	29.7517i		−	1.07850i	−0.842147	−	0.539249i	$-0.818708\pi$
$761$		−	29.7517i		−	1.07850i	0.842147	−	0.539249i	$-0.181292\pi$
$762$		0			0
$763$	−5.88869	+	14.2826i	−0.213185	+	0.517064i
$764$	0.451761	−	0.782473i	0.0163441	−	0.0283089i
$765$		0			0
$766$	−16.5684	−	28.6972i	−0.598639	−	1.03687i
$767$	−31.9672	−	24.5841i	−1.15427	−	0.887680i
$768$		0			0
$769$	−36.2090	−	20.9053i	−1.30573	−	0.753863i	−0.324349	−	0.945938i	$-0.605145\pi$
$769$	−36.2090	−	20.9053i	−1.30573	−	0.753863i	−0.981380	+	0.192075i	$0.938478\pi$
$770$	9.90541	+	12.8654i	0.356966	+	0.463635i
$771$		0			0
$772$	−3.46856	−	2.00257i	−0.124836	−	0.0720742i
$773$	−35.8826	−	20.7168i	−1.29061	−	0.745132i	−0.311845	−	0.950133i	$-0.600947\pi$
$773$	−35.8826	−	20.7168i	−1.29061	−	0.745132i	−0.978762	+	0.205001i	$0.934280\pi$
$774$		0			0
$775$	−34.4864	−	19.9107i	−1.23879	−	0.715215i
$776$	0.705044	+	1.22117i	0.0253096	+	0.0438375i
$777$		0			0
$778$	−21.9680	−	12.6832i	−0.787592	−	0.454716i
$779$	1.98159	−	3.43221i	0.0709978	−	0.122972i
$780$		0			0
$781$	−7.30376	−	12.6505i	−0.261349	−	0.452670i
$782$	−14.8521	+	8.57486i	−0.531110	+	0.306637i
$783$		0			0
$784$	24.2052	−	6.57071i	0.864472	−	0.234668i
$785$		−	32.1175i		−	1.14632i
$786$		0			0
$787$	20.6657	+	11.9313i	0.736651	+	0.425306i	0.820851	−	0.571143i	$-0.193500\pi$
$787$	20.6657	+	11.9313i	0.736651	+	0.425306i	−0.0841992	+	0.996449i	$0.526833\pi$
$788$	0.958193	−	0.553213i	0.0341342	−	0.0197074i
$789$		0			0
$790$	−6.85198	+	11.8680i	−0.243782	+	0.422243i
$791$	−15.9781	−	6.58777i	−0.568117	−	0.234234i
$792$		0			0
$793$	−27.2494	−	3.61735i	−0.967654	−	0.128456i
$794$	−9.75490	−	16.8960i	−0.346188	−	0.599616i
$795$		0			0
$796$	1.01067	+	1.75054i	0.0358223	+	0.0620461i
$797$	−25.4115	−	44.0141i	−0.900123	−	1.55906i	−0.827333	−	0.561712i	$-0.810143\pi$
$797$	−25.4115	−	44.0141i	−0.900123	−	1.55906i	−0.0727899	−	0.997347i	$-0.523190\pi$
$798$		0			0
$799$	−5.99335	+	3.46026i	−0.212029	+	0.122415i
$800$			8.29397i			0.293236i
$801$		0			0
$802$	14.1174	−	24.4521i	0.498504	−	0.863434i
$803$	−0.486219	−	0.842156i	−0.0171583	−	0.0297190i
$804$		0			0
$805$	9.48602	+	12.3206i	0.334338	+	0.434246i
$806$	15.2341	−	19.8092i	0.536598	−	0.697748i
$807$		0			0
$808$		−	8.48119i		−	0.298367i
$809$	−4.41176			−0.155109			−0.0775547	−	0.996988i	$-0.524711\pi$
$809$	−4.41176			−0.155109			−0.0775547	+	0.996988i	$0.524711\pi$
$810$		0			0
$811$			17.6493i			0.619750i	0.950777	+	0.309875i	$0.100287\pi$
$811$			17.6493i			0.619750i	−0.950777	+	0.309875i	$0.899713\pi$
$812$	−1.88343	−	0.776535i	−0.0660954	−	0.0272510i
$813$		0			0
$814$	−1.57320	−	0.908285i	−0.0551405	−	0.0318354i
$815$	21.4644	−	37.1775i	0.751866	−	1.30227i
$816$		0			0
$817$	3.13126	−	1.80783i	0.109549	−	0.0632480i
$818$	28.8249			1.00784
$819$		0			0
$820$	−2.85178			−0.0995884
$821$	−3.08342	+	1.78022i	−0.107612	+	0.0621299i	−0.552840	−	0.833287i	$-0.686456\pi$
$821$	−3.08342	+	1.78022i	−0.107612	+	0.0621299i	0.445228	+	0.895417i	$0.353123\pi$
$822$		0			0
$823$	10.9332	−	18.9369i	0.381109	−	0.660100i	−0.610112	−	0.792315i	$-0.708876\pi$
$823$	10.9332	−	18.9369i	0.381109	−	0.660100i	0.991221	+	0.132215i	$0.0422091\pi$
$824$	28.9247	+	16.6997i	1.00764	+	0.581760i
$825$		0			0
$826$	−31.5421	+	24.2852i	−1.09749	+	0.844990i
$827$		−	18.1361i		−	0.630653i	−0.948983	−	0.315327i	$-0.897886\pi$
$827$		−	18.1361i		−	0.630653i	0.948983	−	0.315327i	$-0.102114\pi$
$828$		0			0
$829$	−30.8994			−1.07318			−0.536590	−	0.843843i	$-0.680288\pi$
$829$	−30.8994			−1.07318			−0.536590	+	0.843843i	$0.680288\pi$
$830$		−	11.1579i		−	0.387297i
$831$		0			0
$832$	−30.7724	−	4.08504i	−1.06684	−	0.141623i
$833$	38.4322	+	38.1816i	1.33160	+	1.32291i
$834$		0			0
$835$	34.6466	+	60.0097i	1.19900	+	2.07672i
$836$	−0.114878	+	0.198974i	−0.00397313	+	0.00688165i
$837$		0			0
$838$			10.7135i			0.370090i
$839$	13.3333	−	7.69796i	0.460315	−	0.265763i	−0.251862	−	0.967763i	$-0.581043\pi$
$839$	13.3333	−	7.69796i	0.460315	−	0.265763i	0.712177	+	0.702000i	$0.247709\pi$
$840$		0			0
$841$	6.31965	+	10.9459i	0.217919	+	0.377446i
$842$	1.89533	+	3.28280i	0.0653173	+	0.113133i
$843$		0			0
$844$	0.444076	+	0.769163i	0.0152857	+	0.0264757i
$845$	32.7256	+	32.8671i	1.12579	+	1.13066i
$846$		0			0
$847$	−19.6326	+	15.1157i	−0.674583	+	0.519381i
$848$	0.143307	−	0.248216i	0.00492119	−	0.00852376i
$849$		0			0
$850$	69.6862	−	40.2333i	2.39022	−	1.37999i
$851$	−1.50659	−	0.869829i	−0.0516451	−	0.0298173i
$852$		0			0
$853$		−	23.7772i		−	0.814116i	−0.913402	−	0.407058i	$-0.866555\pi$
$853$		−	23.7772i		−	0.814116i	0.913402	−	0.407058i	$-0.133445\pi$
$854$	−10.3429	+	25.0860i	−0.353928	+	0.858426i
$855$		0			0
$856$	−16.7704	+	9.68242i	−0.573202	+	0.330938i
$857$	15.0525	+	26.0717i	0.514184	+	0.890592i	0.999865	+	0.0164561i	$0.00523837\pi$
$857$	15.0525	+	26.0717i	0.514184	+	0.890592i	−0.485681	+	0.874136i	$0.661428\pi$
$858$		0			0
$859$	7.56717	−	13.1067i	0.258188	−	0.447195i	−0.707568	−	0.706645i	$-0.750208\pi$
$859$	7.56717	−	13.1067i	0.258188	−	0.447195i	0.965757	+	0.259450i	$0.0835411\pi$
$860$	−2.25315	−	1.30086i	−0.0768318	−	0.0443589i
$861$		0			0
$862$	3.85828	+	6.68274i	0.131414	+	0.227615i
$863$	15.8186	+	9.13287i	0.538471	+	0.310886i	0.744459	−	0.667668i	$-0.232707\pi$
$863$	15.8186	+	9.13287i	0.538471	+	0.310886i	−0.205988	+	0.978555i	$0.566041\pi$
$864$		0			0
$865$	44.4296	+	25.6514i	1.51065	+	0.872175i
$866$	28.5724	+	16.4963i	0.970929	+	0.560566i
$867$		0			0
$868$	1.58308	+	2.05614i	0.0537332	+	0.0697899i
$869$	3.16186	+	1.82550i	0.107259	+	0.0619259i
$870$		0			0
$871$	−2.99917	+	22.5926i	−0.101623	+	0.765521i
$872$	−8.60263	−	14.9002i	−0.291322	−	0.504584i
$873$		0			0
$874$	1.04580	−	1.81137i	0.0353746	−	0.0612706i
$875$	−15.7154	−	20.4115i	−0.531278	−	0.690035i
$876$		0			0
$877$			6.99639i			0.236251i	0.992999	+	0.118126i	$0.0376886\pi$
$877$			6.99639i			0.236251i	−0.992999	+	0.118126i	$0.962311\pi$
$878$	−42.6883	−	24.6461i	−1.44066	−	0.831765i
$879$		0			0
$880$	−16.3458			−0.551018
$881$	−12.8873	+	22.3215i	−0.434184	+	0.752029i	−0.997229	−	0.0743977i	$-0.976297\pi$
$881$	−12.8873	+	22.3215i	−0.434184	+	0.752029i	0.563045	+	0.826427i	$0.309630\pi$
$882$		0			0
$883$	−16.4526			−0.553674			−0.276837	−	0.960917i	$-0.589286\pi$
$883$	−16.4526			−0.553674			−0.276837	+	0.960917i	$0.589286\pi$
$884$	−2.02752	−	4.90983i	−0.0681928	−	0.165136i
$885$		0			0
$886$			36.4467i			1.22445i
$887$	27.6227	+	47.8440i	0.927481	+	1.60644i	0.787522	+	0.616286i	$0.211364\pi$
$887$	27.6227	+	47.8440i	0.927481	+	1.60644i	0.139958	+	0.990157i	$0.455303\pi$
$888$		0			0
$889$	5.14527	+	38.5943i	0.172567	+	1.29441i
$890$	31.4904	−	18.1810i	1.05556	−	0.609429i
$891$		0			0
$892$	−3.99385	+	2.30585i	−0.133724	+	0.0772056i
$893$	0.422016	−	0.730953i	0.0141222	−	0.0244604i
$894$		0			0
$895$	16.7654	+	9.67949i	0.560404	+	0.323550i
$896$	−9.51575	+	23.0798i	−0.317899	+	0.771041i
$897$		0			0
$898$	18.4514	−	31.9587i	0.615731	−	1.06648i
$899$			20.8398i			0.695046i
$900$		0			0
$901$	0.619076			0.0206244
$902$		−	7.22241i		−	0.240480i
$903$		0			0
$904$	16.6691	−	9.62388i	0.554405	−	0.320086i
$905$	−47.8614	−	27.6328i	−1.59097	−	0.918544i
$906$		0			0
$907$	−47.8424			−1.58858			−0.794290	−	0.607538i	$-0.792157\pi$
$907$	−47.8424			−1.58858			−0.794290	+	0.607538i	$0.792157\pi$
$908$	−2.53480	+	1.46347i	−0.0841204	+	0.0485669i
$909$		0			0
$910$	39.6373	−	22.9141i	1.31397	−	0.759594i
$911$	23.0711			0.764380			0.382190	−	0.924084i	$-0.375170\pi$
$911$	23.0711			0.764380			0.382190	+	0.924084i	$0.375170\pi$
$912$		0			0
$913$	−2.97269			−0.0983817
$914$	26.6785	−	46.2085i	0.882445	−	1.52844i
$915$		0			0
$916$	−2.69574	+	1.55638i	−0.0890697	+	0.0514244i
$917$	3.91120	+	29.3376i	0.129159	+	0.968814i
$918$		0			0
$919$	−43.4368			−1.43285			−0.716424	−	0.697665i	$-0.754222\pi$
$919$	−43.4368			−1.43285			−0.716424	+	0.697665i	$0.754222\pi$
$920$	−17.3171			−0.570929
$921$		0			0
$922$	−3.29298	+	5.70360i	−0.108448	+	0.187838i
$923$	−38.0714	+	15.7216i	−1.25313	+	0.517482i
$924$		0			0
$925$	7.06892	+	4.08124i	0.232425	+	0.134190i
$926$	−3.16931	−	5.48940i	−0.104150	−	0.180393i
$927$		0			0
$928$	3.75897	−	2.17024i	0.123394	−	0.0712418i
$929$			12.7819i			0.419361i	0.977770	+	0.209680i	$0.0672424\pi$
$929$			12.7819i			0.419361i	−0.977770	+	0.209680i	$0.932758\pi$
$930$		0			0
$931$	−6.38757	−	1.68917i	−0.209344	−	0.0553603i
$932$	2.77085	+	4.79926i	0.0907623	+	0.157205i
$933$		0			0
$934$		−	43.0689i		−	1.40926i
$935$	−17.6532	−	30.5762i	−0.577320	−	0.999948i
$936$		0			0
$937$	16.2533			0.530971			0.265486	−	0.964115i	$-0.414468\pi$
$937$	16.2533			0.530971			0.265486	+	0.964115i	$0.414468\pi$
$938$	20.7989	+	8.57538i	0.679110	+	0.279996i
$939$		0			0
$940$	−0.607339			−0.0198092
$941$	39.1000	−	22.5744i	1.27462	−	0.735905i	0.298770	−	0.954325i	$-0.403424\pi$
$941$	39.1000	−	22.5744i	1.27462	−	0.735905i	0.975855	+	0.218420i	$0.0700904\pi$
$942$		0			0
$943$		−	6.91662i		−	0.225236i
$944$		−	40.0752i		−	1.30434i
$945$		0			0
$946$	3.29455	−	5.70633i	0.107115	−	0.185529i
$947$	−17.1956	+	9.92787i	−0.558781	+	0.322612i	−0.752656	−	0.658414i	$-0.771228\pi$
$947$	−17.1956	+	9.92787i	−0.558781	+	0.322612i	0.193875	+	0.981026i	$0.437894\pi$
$948$		0			0
$949$	−2.53445	+	1.04660i	−0.0822716	+	0.0339741i
$950$	−4.90689	+	8.49898i	−0.159200	+	0.275743i
$951$		0			0
$952$	−59.8042	+	7.97290i	−1.93826	+	0.258403i
$953$	−7.86433	−	13.6214i	−0.254751	−	0.441241i	0.710077	−	0.704124i	$-0.248660\pi$
$953$	−7.86433	−	13.6214i	−0.254751	−	0.441241i	−0.964828	+	0.262883i	$0.915327\pi$
$954$		0			0
$955$	−14.6648	−	8.46673i	−0.474542	−	0.273977i
$956$	1.42673	+	0.823724i	0.0461438	+	0.0266412i
$957$		0			0
$958$	12.1235	+	20.9985i	0.391693	+	0.678432i
$959$	−46.2377	+	6.16426i	−1.49309	+	0.199054i
$960$		0			0
$961$	−2.22744	+	3.85804i	−0.0718529	+	0.124453i
$962$	−3.12264	+	4.06042i	−0.100678	+	0.130913i
$963$		0			0
$964$	−3.00019	+	1.73216i	−0.0966296	+	0.0557891i
$965$	−37.5315	+	65.0064i	−1.20818	+	2.09263i
$966$		0			0
$967$		−	52.1912i		−	1.67835i	−0.543858	−	0.839177i	$-0.683037\pi$
$967$		−	52.1912i		−	1.67835i	0.543858	−	0.839177i	$-0.316963\pi$
$968$		−	27.5943i		−	0.886915i
$969$		0			0
$970$	1.98910	−	1.14841i	0.0638663	−	0.0368732i
$971$	22.4584			0.720724			0.360362	−	0.932813i	$-0.382653\pi$
$971$	22.4584			0.720724			0.360362	+	0.932813i	$0.382653\pi$
$972$		0			0
$973$	−14.3265	−	5.90680i	−0.459287	−	0.189363i
$974$	23.6765			0.758645
$975$		0			0
$976$	−13.6584	−	23.6570i	−0.437193	−	0.757241i
$977$			41.0345i			1.31281i	0.754409	+	0.656405i	$0.227924\pi$
$977$			41.0345i			1.31281i	−0.754409	+	0.656405i	$0.772076\pi$
$978$		0			0
$979$	−4.84378	−	8.38967i	−0.154808	−	0.268135i
$980$	1.24552	+	4.58825i	0.0397866	+	0.146566i
$981$		0			0
$982$		−	5.19742i		−	0.165856i
$983$	−23.2379	+	13.4164i	−0.741173	+	0.427916i	−0.822496	−	0.568772i	$-0.807419\pi$
$983$	−23.2379	+	13.4164i	−0.741173	+	0.427916i	0.0813229	+	0.996688i	$0.474085\pi$
$984$		0			0
$985$	−10.3681	−	17.9581i	−0.330356	−	0.572193i
$986$	−36.4689	−	21.0553i	−1.16141	−	0.670539i
$987$		0			0
$988$	0.513552	+	0.394943i	0.0163383	+	0.0125648i
$989$	3.15506	−	5.46473i	0.100325	−	0.173768i
$990$		0			0
$991$	10.3751			0.329576			0.164788	−	0.986329i	$-0.447306\pi$
$991$	10.3751			0.329576			0.164788	+	0.986329i	$0.447306\pi$
$992$	−5.52879			−0.175539
$993$		0			0
$994$	5.37305	+	40.3029i	0.170423	+	1.27833i
$995$	32.8079	−	18.9417i	1.04008	−	0.600491i
$996$		0			0
$997$	26.9549	−	46.6872i	0.853669	−	1.47860i	−0.0242056	−	0.999707i	$-0.507706\pi$
$997$	26.9549	−	46.6872i	0.853669	−	1.47860i	0.877874	−	0.478891i	$-0.158961\pi$
$998$	−17.0134			−0.538550
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.do.e.667.2		12
3.2	odd	2		91.2.u.b.30.5	yes	12
7.4	even	3		819.2.bm.f.550.2		12
13.10	even	6		819.2.bm.f.478.5		12
21.2	odd	6		637.2.q.g.589.2		12
21.5	even	6		637.2.q.i.589.2		12
21.11	odd	6		91.2.k.b.4.5	✓	12
21.17	even	6		637.2.k.i.459.5		12
21.20	even	2		637.2.u.g.30.5		12
39.20	even	12		1183.2.e.j.170.9		24
39.23	odd	6		91.2.k.b.23.2	yes	12
39.32	even	12		1183.2.e.j.170.4		24
91.88	even	6	inner	819.2.do.e.361.2		12
273.23	odd	6		637.2.q.g.491.2		12
273.32	even	12		1183.2.e.j.508.4		24
273.62	even	6		637.2.k.i.569.2		12
273.101	even	6		637.2.u.g.361.5		12
273.110	odd	12		8281.2.a.co.1.9		12
273.137	even	12		1183.2.e.j.508.9		24
273.149	even	12		8281.2.a.cp.1.9		12
273.179	odd	6		91.2.u.b.88.5	yes	12
273.215	odd	12		8281.2.a.co.1.4		12
273.254	even	12		8281.2.a.cp.1.4		12
273.257	even	6		637.2.q.i.491.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.5	✓	12	21.11	odd	6
91.2.k.b.23.2	yes	12	39.23	odd	6
91.2.u.b.30.5	yes	12	3.2	odd	2
91.2.u.b.88.5	yes	12	273.179	odd	6
637.2.k.i.459.5		12	21.17	even	6
637.2.k.i.569.2		12	273.62	even	6
637.2.q.g.491.2		12	273.23	odd	6
637.2.q.g.589.2		12	21.2	odd	6
637.2.q.i.491.2		12	273.257	even	6
637.2.q.i.589.2		12	21.5	even	6
637.2.u.g.30.5		12	21.20	even	2
637.2.u.g.361.5		12	273.101	even	6
819.2.bm.f.478.5		12	13.10	even	6
819.2.bm.f.550.2		12	7.4	even	3
819.2.do.e.361.2		12	91.88	even	6	inner
819.2.do.e.667.2		12	1.1	even	1	trivial
1183.2.e.j.170.4		24	39.32	even	12
1183.2.e.j.170.9		24	39.20	even	12
1183.2.e.j.508.4		24	273.32	even	12
1183.2.e.j.508.9		24	273.137	even	12
8281.2.a.co.1.4		12	273.215	odd	12
8281.2.a.co.1.9		12	273.110	odd	12
8281.2.a.cp.1.4		12	273.254	even	12
8281.2.a.cp.1.9		12	273.149	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.16500 + 0.672613i) q^{2} +(-0.0951832 + 0.164862i) q^{4} +(3.08979 + 1.78389i) q^{5} +(-2.09638 + 1.61406i) q^{7} -2.94654i q^{8} +O(q^{10})\)	\(q+(-1.16500 + 0.672613i) q^{2} +(-0.0951832 + 0.164862i) q^{4} +(3.08979 + 1.78389i) q^{5} +(-2.09638 + 1.61406i) q^{7} -2.94654i q^{8} -4.79947 q^{10} +1.27867i q^{11} +(3.57420 + 0.474474i) q^{13} +(1.35664 - 3.29043i) q^{14} +(1.79151 + 3.10299i) q^{16} +(-3.86960 + 6.70234i) q^{17} -0.943878i q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} +(-0.823637 - 1.42658i) q^{23} +(3.86451 + 6.69354i) q^{25} +(-4.48308 + 1.85129i) q^{26} +(-0.0665578 - 0.499245i) q^{28} +(2.02242 - 3.50293i) q^{29} +(-4.46193 + 2.57610i) q^{31} +(0.929326 + 0.536547i) q^{32} -10.4110i q^{34} +(-9.35667 + 1.24740i) q^{35} +(0.914594 - 0.528041i) q^{37} +(0.634865 + 1.09962i) q^{38} +(5.25629 - 9.10417i) q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} +(-0.210805 - 0.121708i) q^{44} +(1.91908 + 1.10798i) q^{46} +(0.774415 + 0.447109i) q^{47} +(1.78961 - 6.76737i) q^{49} +(-9.00432 - 5.19865i) q^{50} +(-0.418426 + 0.544088i) q^{52} +(-0.0399961 - 0.0692754i) q^{53} +(-2.28101 + 3.95082i) q^{55} +(4.75590 + 6.17706i) q^{56} +5.44122i q^{58} +(-9.68627 - 5.59237i) q^{59} -7.62392 q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(10.1971 + 7.84199i) q^{65} +6.32103i q^{67} +(-0.736641 - 1.27590i) q^{68} +(10.0615 - 7.74664i) q^{70} +(-9.89346 + 5.71199i) q^{71} +(-0.658617 + 0.380253i) q^{73} +(-0.710335 + 1.23034i) q^{74} +(0.155610 + 0.0898413i) q^{76} +(-2.06386 - 2.68058i) q^{77} +(1.42765 - 2.47277i) q^{79} +12.7834i q^{80} -5.64837 q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} +(-4.46270 - 2.57654i) q^{86} +3.76766 q^{88} +(-6.56124 + 3.78813i) q^{89} +(-8.25870 + 4.77430i) q^{91} +0.313586 q^{92} -1.20292 q^{94} +(1.68377 - 2.91638i) q^{95} +(-0.414443 + 0.239279i) q^{97} +(2.46693 + 9.08770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

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