LMFDB - Embedded newform 819.2.s.d.802.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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, 2]))

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.3
Root			$-0.437442 - 0.757672i$ of defining polynomial
Character	$\chi$	$=$	819.802
Dual form			819.2.s.d.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.268125 q^{2} -1.92811 q^{4} +(-1.28088 - 2.21854i) q^{5} +(1.80416 + 1.93520i) q^{7} -1.05323 q^{8} +O(q^{10})$	\(q+0.268125 q^{2} -1.92811 q^{4} +(-1.28088 - 2.21854i) q^{5} +(1.80416 + 1.93520i) q^{7} -1.05323 q^{8} +(-0.343436 - 0.594848i) q^{10} +(1.97300 + 3.41734i) q^{11} +(-3.15374 + 1.74755i) q^{13} +(0.483741 + 0.518876i) q^{14} +3.57382 q^{16} -0.785100 q^{17} +(3.74764 - 6.49110i) q^{19} +(2.46967 + 4.27760i) q^{20} +(0.529011 + 0.916274i) q^{22} +7.95518 q^{23} +(-0.781294 + 1.35324i) q^{25} +(-0.845598 + 0.468561i) q^{26} +(-3.47862 - 3.73128i) q^{28} +(1.17586 - 2.03666i) q^{29} +(1.27718 - 2.21215i) q^{31} +3.06468 q^{32} -0.210505 q^{34} +(1.98242 - 6.48137i) q^{35} +6.75716 q^{37} +(1.00484 - 1.74043i) q^{38} +(1.34905 + 2.33663i) q^{40} +(-1.21874 + 2.11091i) q^{41} +(1.12473 + 1.94809i) q^{43} +(-3.80416 - 6.58900i) q^{44} +2.13298 q^{46} +(0.658276 + 1.14017i) q^{47} +(-0.490011 + 6.98283i) q^{49} +(-0.209485 + 0.362838i) q^{50} +(6.08076 - 3.36946i) q^{52} +(4.63977 - 8.03632i) q^{53} +(5.05434 - 8.75438i) q^{55} +(-1.90019 - 2.03820i) q^{56} +(0.315279 - 0.546079i) q^{58} +8.96671 q^{59} +(-4.72273 + 8.18002i) q^{61} +(0.342445 - 0.593132i) q^{62} -6.32592 q^{64} +(7.91657 + 4.75832i) q^{65} +(0.676281 + 1.17135i) q^{67} +1.51376 q^{68} +(0.531538 - 1.73782i) q^{70} +(6.15808 + 10.6661i) q^{71} +(-0.384295 + 0.665619i) q^{73} +1.81176 q^{74} +(-7.22585 + 12.5155i) q^{76} +(-3.05363 + 9.98358i) q^{77} +(-3.09642 - 5.36316i) q^{79} +(-4.57763 - 7.92868i) q^{80} +(-0.326774 + 0.565989i) q^{82} +1.07292 q^{83} +(1.00562 + 1.74178i) q^{85} +(0.301568 + 0.522332i) q^{86} +(-2.07801 - 3.59923i) q^{88} -7.66299 q^{89} +(-9.07171 - 2.95027i) q^{91} -15.3384 q^{92} +(0.176501 + 0.305708i) q^{94} -19.2010 q^{95} +(1.18601 + 2.05423i) q^{97} +(-0.131384 + 1.87227i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8	$ 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29} + 16 q^{31} + 16 q^{32} + 32 q^{34} - 20 q^{35} + 26 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} - 32 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} + 41 q^{52} + 2 q^{53} + 9 q^{55} - 9 q^{56} - 8 q^{58} + 26 q^{59} - 5 q^{61} - 5 q^{62} - 30 q^{64} + 5 q^{65} - 11 q^{67} + 58 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} - 6 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} + 7 q^{80} + q^{82} + 54 q^{83} - q^{85} + 7 q^{86} + 8 q^{89} - 23 q^{91} - 54 q^{92} + 45 q^{94} - 12 q^{95} - 35 q^{97} - 20 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^13 + 2 * q^14 - 16 * q^16 + 10 * q^17 - q^19 + q^20 - 5 * q^22 - 2 * q^23 + 7 * q^25 + 16 * q^26 - q^28 - 3 * q^29 + 16 * q^31 + 16 * q^32 + 32 * q^34 - 20 * q^35 + 26 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 - 32 * q^46 + q^47 - 3 * q^49 - 6 * q^50 + 41 * q^52 + 2 * q^53 + 9 * q^55 - 9 * q^56 - 8 * q^58 + 26 * q^59 - 5 * q^61 - 5 * q^62 - 30 * q^64 + 5 * q^65 - 11 * q^67 + 58 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 - 6 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 + 7 * q^80 + q^82 + 54 * q^83 - q^85 + 7 * q^86 + 8 * q^89 - 23 * q^91 - 54 * q^92 + 45 * q^94 - 12 * q^95 - 35 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.268125			0.189593			0.0947966	−	0.995497i	$-0.469780\pi$
$2$	0.268125			0.189593			0.0947966	+	0.995497i	$0.469780\pi$
$3$		0			0
$3$		0			0
$4$	−1.92811			−0.964054
$5$	−1.28088	−	2.21854i	−0.572826	−	0.992163i	−0.996274	−	0.0862431i	$-0.972514\pi$
$5$	−1.28088	−	2.21854i	−0.572826	−	0.992163i	0.423448	−	0.905920i	$-0.360820\pi$
$6$		0			0
$7$	1.80416	+	1.93520i	0.681909	+	0.731437i
$7$	1.80416	+	1.93520i	0.681909	+	0.731437i
$8$	−1.05323			−0.372371
$9$		0			0
$10$	−0.343436	−	0.594848i	−0.108604	−	0.188107i
$11$	1.97300	+	3.41734i	0.594882	+	1.03037i	0.993563	+	0.113277i	$0.0361346\pi$
$11$	1.97300	+	3.41734i	0.594882	+	1.03037i	−0.398681	+	0.917090i	$0.630532\pi$
$12$		0			0
$13$	−3.15374	+	1.74755i	−0.874690	+	0.484682i
$13$	−3.15374	+	1.74755i	−0.874690	+	0.484682i
$14$	0.483741	+	0.518876i	0.129285	+	0.138676i
$15$		0			0
$16$	3.57382			0.893455
$17$	−0.785100			−0.190415			−0.0952073	−	0.995457i	$-0.530351\pi$
$17$	−0.785100			−0.190415			−0.0952073	+	0.995457i	$0.530351\pi$
$18$		0			0
$19$	3.74764	−	6.49110i	0.859767	−	1.48916i	−0.0123849	−	0.999923i	$-0.503942\pi$
$19$	3.74764	−	6.49110i	0.859767	−	1.48916i	0.872151	−	0.489236i	$-0.162724\pi$
$20$	2.46967	+	4.27760i	0.552235	+	0.956500i
$21$		0			0
$22$	0.529011	+	0.916274i	0.112786	+	0.195350i
$23$	7.95518			1.65877			0.829384	−	0.558678i	$-0.188691\pi$
$23$	7.95518			1.65877			0.829384	+	0.558678i	$0.188691\pi$
$24$		0			0
$25$	−0.781294	+	1.35324i	−0.156259	+	0.270648i
$26$	−0.845598	+	0.468561i	−0.165835	+	0.0918924i
$27$		0			0
$28$	−3.47862	−	3.73128i	−0.657397	−	0.705146i
$29$	1.17586	−	2.03666i	0.218353	−	0.378198i	−0.735952	−	0.677034i	$-0.763265\pi$
$29$	1.17586	−	2.03666i	0.218353	−	0.378198i	0.954304	+	0.298836i	$0.0965984\pi$
$30$		0			0
$31$	1.27718	−	2.21215i	0.229389	−	0.397313i	−0.728238	−	0.685324i	$-0.759661\pi$
$31$	1.27718	−	2.21215i	0.229389	−	0.397313i	0.957627	+	0.288011i	$0.0929939\pi$
$32$	3.06468			0.541764
$33$		0			0
$34$	−0.210505			−0.0361013
$35$	1.98242	−	6.48137i	0.335091	−	1.09555i
$36$		0			0
$37$	6.75716			1.11087			0.555435	−	0.831560i	$-0.312552\pi$
$37$	6.75716			1.11087			0.555435	+	0.831560i	$0.312552\pi$
$38$	1.00484	−	1.74043i	0.163006	−	0.282334i
$39$		0			0
$40$	1.34905	+	2.33663i	0.213304	+	0.369453i
$41$	−1.21874	+	2.11091i	−0.190335	+	0.329669i	−0.945361	−	0.326025i	$-0.894291\pi$
$41$	−1.21874	+	2.11091i	−0.190335	+	0.329669i	0.755027	+	0.655694i	$0.227624\pi$
$42$		0			0
$43$	1.12473	+	1.94809i	0.171520	+	0.297081i	0.938951	−	0.344050i	$-0.111799\pi$
$43$	1.12473	+	1.94809i	0.171520	+	0.297081i	−0.767432	+	0.641131i	$0.778466\pi$
$44$	−3.80416	−	6.58900i	−0.573499	−	0.993329i
$45$		0			0
$46$	2.13298			0.314491
$47$	0.658276	+	1.14017i	0.0960195	+	0.166311i	0.910034	−	0.414534i	$-0.136056\pi$
$47$	0.658276	+	1.14017i	0.0960195	+	0.166311i	−0.814014	+	0.580845i	$0.802722\pi$
$48$		0			0
$49$	−0.490011	+	6.98283i	−0.0700016	+	0.997547i
$50$	−0.209485	+	0.362838i	−0.0296256	+	0.0513130i
$51$		0			0
$52$	6.08076	−	3.36946i	0.843249	−	0.467260i
$53$	4.63977	−	8.03632i	0.637321	−	1.10387i	−0.348697	−	0.937236i	$-0.613376\pi$
$53$	4.63977	−	8.03632i	0.637321	−	1.10387i	0.986018	−	0.166637i	$-0.0532909\pi$
$54$		0			0
$55$	5.05434	−	8.75438i	0.681528	−	1.18044i
$56$	−1.90019	−	2.03820i	−0.253923	−	0.272366i
$57$		0			0
$58$	0.315279	−	0.546079i	0.0413981	−	0.0717037i
$59$	8.96671			1.16737			0.583683	−	0.811982i	$-0.301611\pi$
$59$	8.96671			1.16737			0.583683	+	0.811982i	$0.301611\pi$
$60$		0			0
$61$	−4.72273	+	8.18002i	−0.604684	+	1.04734i	0.387417	+	0.921905i	$0.373367\pi$
$61$	−4.72273	+	8.18002i	−0.604684	+	1.04734i	−0.992101	+	0.125439i	$0.959966\pi$
$62$	0.342445	−	0.593132i	0.0434906	−	0.0753279i
$63$		0			0
$64$	−6.32592			−0.790741
$65$	7.91657	+	4.75832i	0.981929	+	0.590197i
$66$		0			0
$67$	0.676281	+	1.17135i	0.0826209	+	0.143104i	0.904375	−	0.426739i	$-0.140338\pi$
$67$	0.676281	+	1.17135i	0.0826209	+	0.143104i	−0.821754	+	0.569842i	$0.807004\pi$
$68$	1.51376			0.183570
$69$		0			0
$70$	0.531538	−	1.73782i	0.0635309	−	0.207709i
$71$	6.15808	+	10.6661i	0.730829	+	1.26583i	0.956529	+	0.291637i	$0.0941998\pi$
$71$	6.15808	+	10.6661i	0.730829	+	1.26583i	−0.225700	+	0.974197i	$0.572467\pi$
$72$		0			0
$73$	−0.384295	+	0.665619i	−0.0449783	+	0.0779048i	−0.887638	−	0.460542i	$-0.847655\pi$
$73$	−0.384295	+	0.665619i	−0.0449783	+	0.0779048i	0.842660	+	0.538446i	$0.180989\pi$
$74$	1.81176			0.210613
$75$		0			0
$76$	−7.22585	+	12.5155i	−0.828862	+	1.43563i
$77$	−3.05363	+	9.98358i	−0.347993	+	1.13773i
$78$		0			0
$79$	−3.09642	−	5.36316i	−0.348375	−	0.603402i	0.637586	−	0.770379i	$-0.279933\pi$
$79$	−3.09642	−	5.36316i	−0.348375	−	0.603402i	−0.985961	+	0.166976i	$0.946600\pi$
$80$	−4.57763	−	7.92868i	−0.511794	−	0.886454i
$81$		0			0
$82$	−0.326774	+	0.565989i	−0.0360861	+	0.0625030i
$83$	1.07292			0.117768			0.0588841	−	0.998265i	$-0.481246\pi$
$83$	1.07292			0.117768			0.0588841	+	0.998265i	$0.481246\pi$
$84$		0			0
$85$	1.00562	+	1.74178i	0.109074	+	0.188922i
$86$	0.301568	+	0.522332i	0.0325190	+	0.0563245i
$87$		0			0
$88$	−2.07801	−	3.59923i	−0.221517	−	0.383679i
$89$	−7.66299			−0.812275			−0.406138	−	0.913812i	$-0.633125\pi$
$89$	−7.66299			−0.812275			−0.406138	+	0.913812i	$0.633125\pi$
$90$		0			0
$91$	−9.07171	−	2.95027i	−0.950973	−	0.309272i
$92$	−15.3384			−1.59914
$93$		0			0
$94$	0.176501	+	0.305708i	0.0182046	+	0.0315314i
$95$	−19.2010			−1.96999
$96$		0			0
$97$	1.18601	+	2.05423i	0.120421	+	0.208575i	0.919934	−	0.392074i	$-0.128242\pi$
$97$	1.18601	+	2.05423i	0.120421	+	0.208575i	−0.799513	+	0.600649i	$0.794909\pi$
$98$	−0.131384	+	1.87227i	−0.0132718	+	0.189128i
$99$		0			0
$100$	1.50642	−	2.60920i	0.150642	−	0.260920i
$101$	−0.398665	−	0.690508i	−0.0396686	−	0.0687081i	0.845509	−	0.533961i	$-0.179297\pi$
$101$	−0.398665	−	0.690508i	−0.0396686	−	0.0687081i	−0.885178	+	0.465252i	$0.845964\pi$
$102$		0			0
$103$	−1.08309	−	1.87597i	−0.106720	−	0.184844i	0.807720	−	0.589567i	$-0.200701\pi$
$103$	−1.08309	−	1.87597i	−0.106720	−	0.184844i	−0.914440	+	0.404722i	$0.867368\pi$
$104$	3.32160	−	1.84056i	0.325710	−	0.180482i
$105$		0			0
$106$	1.24404	−	2.15474i	0.120832	−	0.209287i
$107$	11.5262			1.11428			0.557141	−	0.830418i	$-0.311898\pi$
$107$	11.5262			1.11428			0.557141	+	0.830418i	$0.311898\pi$
$108$		0			0
$109$	−4.03912	+	6.99595i	−0.386877	+	0.670091i	−0.992028	−	0.126020i	$-0.959780\pi$
$109$	−4.03912	+	6.99595i	−0.386877	+	0.670091i	0.605151	+	0.796111i	$0.293113\pi$
$110$	1.35520	−	2.34727i	0.129213	−	0.223803i
$111$		0			0
$112$	6.44775	+	6.91607i	0.609255	+	0.653507i
$113$	4.02067	+	6.96401i	0.378233	+	0.655119i	0.990805	−	0.135296i	$-0.0431984\pi$
$113$	4.02067	+	6.96401i	0.378233	+	0.655119i	−0.612572	+	0.790415i	$0.709865\pi$
$114$		0			0
$115$	−10.1896	−	17.6489i	−0.950186	−	1.64577i
$116$	−2.26719	+	3.92690i	−0.210504	+	0.364603i
$117$		0			0
$118$	2.40420			0.221325
$119$	−1.41645	−	1.51933i	−0.129845	−	0.139276i
$120$		0			0
$121$	−2.28546	+	3.95854i	−0.207769	+	0.359867i
$122$	−1.26628	+	2.19327i	−0.114644	+	0.198569i
$123$		0			0
$124$	−2.46255	+	4.26526i	−0.221143	+	0.383032i
$125$	−8.80581			−0.787615
$126$		0			0
$127$	−0.894023	+	1.54849i	−0.0793317	+	0.137406i	−0.902962	−	0.429721i	$-0.858612\pi$
$127$	−0.894023	+	1.54849i	−0.0793317	+	0.137406i	0.823630	+	0.567127i	$0.191945\pi$
$128$	−7.82550			−0.691683
$129$		0			0
$130$	2.12263	+	1.27583i	0.186167	+	0.111897i
$131$	−3.19545	−	5.53469i	−0.279188	−	0.483568i	0.691995	−	0.721902i	$-0.256732\pi$
$131$	−3.19545	−	5.53469i	−0.279188	−	0.483568i	−0.971183	+	0.238334i	$0.923399\pi$
$132$		0			0
$133$	19.3229	−	4.45855i	1.67551	−	0.386605i
$134$	0.181328	+	0.314069i	0.0156644	+	0.0271315i
$135$		0			0
$136$	0.826887			0.0709050
$137$	−10.0365			−0.857480			−0.428740	−	0.903428i	$-0.641042\pi$
$137$	−10.0365			−0.857480			−0.428740	+	0.903428i	$0.641042\pi$
$138$		0			0
$139$	2.77278	+	4.80260i	0.235184	+	0.407351i	0.959326	−	0.282300i	$-0.0910972\pi$
$139$	2.77278	+	4.80260i	0.235184	+	0.407351i	−0.724142	+	0.689651i	$0.757764\pi$
$140$	−3.82233	+	12.4968i	−0.323046	+	1.05617i
$141$		0			0
$142$	1.65114	+	2.85985i	0.138560	+	0.239993i
$143$	−12.1943	−	7.32949i	−1.01974	−	0.612922i
$144$		0			0
$145$	−6.02455			−0.500312
$146$	−0.103039	+	0.178469i	−0.00852759	+	0.0147702i
$147$		0			0
$148$	−13.0285			−1.07094
$149$	9.23254	−	15.9912i	0.756359	−	1.31005i	−0.188337	−	0.982104i	$-0.560310\pi$
$149$	9.23254	−	15.9912i	0.756359	−	1.31005i	0.944696	−	0.327947i	$-0.106357\pi$
$150$		0			0
$151$	−0.803678	+	1.39201i	−0.0654024	+	0.113280i	−0.896872	−	0.442289i	$-0.854166\pi$
$151$	−0.803678	+	1.39201i	−0.0654024	+	0.113280i	0.831470	+	0.555570i	$0.187500\pi$
$152$	−3.94710	+	6.83658i	−0.320152	+	0.554520i
$153$		0			0
$154$	−0.818755	+	2.67685i	−0.0659771	+	0.215707i
$155$	−6.54366			−0.525600
$156$		0			0
$157$	0.822967	−	1.42542i	0.0656799	−	0.113761i	−0.831315	−	0.555801i	$-0.812412\pi$
$157$	0.822967	−	1.42542i	0.0656799	−	0.113761i	0.896995	+	0.442040i	$0.145745\pi$
$158$	−0.830229	−	1.43800i	−0.0660494	−	0.114401i
$159$		0			0
$160$	−3.92548	−	6.79913i	−0.310337	−	0.537519i
$161$	14.3524	+	15.3949i	1.13113	+	1.21329i
$162$		0			0
$163$	3.27409	−	5.67090i	0.256447	−	0.444179i	−0.708841	−	0.705369i	$-0.750782\pi$
$163$	3.27409	−	5.67090i	0.256447	−	0.444179i	0.965287	+	0.261190i	$0.0841148\pi$
$164$	2.34986	−	4.07007i	0.183493	−	0.317819i
$165$		0			0
$166$	0.287677			0.0223281
$167$	4.77440	−	8.26950i	0.369454	−	0.639913i	−0.620026	−	0.784581i	$-0.712878\pi$
$167$	4.77440	−	8.26950i	0.369454	−	0.639913i	0.989480	+	0.144668i	$0.0462114\pi$
$168$		0			0
$169$	6.89216	−	11.0226i	0.530166	−	0.847894i
$170$	0.269631	+	0.467015i	0.0206798	+	0.0358184i
$171$		0			0
$172$	−2.16860	−	3.75613i	−0.165354	−	0.286402i
$173$	5.56582	−	9.64028i	0.423161	−	0.732937i	−0.573085	−	0.819496i	$-0.694254\pi$
$173$	5.56582	−	9.64028i	0.423161	−	0.732937i	0.996247	+	0.0865588i	$0.0275870\pi$
$174$		0			0
$175$	−4.02837	+	0.929502i	−0.304516	+	0.0702638i
$176$	7.05115	+	12.2130i	0.531501	+	0.920586i
$177$		0			0
$178$	−2.05464			−0.154002
$179$	−6.32173	−	10.9496i	−0.472508	−	0.818409i	0.526997	−	0.849867i	$-0.323318\pi$
$179$	−6.32173	−	10.9496i	−0.472508	−	0.818409i	−0.999505	+	0.0314588i	$0.989985\pi$
$180$		0			0
$181$	14.9158			1.10868			0.554341	−	0.832289i	$-0.312970\pi$
$181$	14.9158			1.10868			0.554341	+	0.832289i	$0.312970\pi$
$182$	−2.43235	−	0.791042i	−0.180298	−	0.0586359i
$183$		0			0
$184$	−8.37859			−0.617678
$185$	−8.65509	−	14.9911i	−0.636335	−	1.10216i
$186$		0			0
$187$	−1.54900	−	2.68295i	−0.113274	−	0.196197i
$188$	−1.26923	−	2.19837i	−0.0925680	−	0.160332i
$189$		0			0
$190$	−5.14829			−0.373496
$191$	−7.06528	+	12.2374i	−0.511226	+	0.885469i	0.488690	+	0.872458i	$0.337475\pi$
$191$	−7.06528	+	12.2374i	−0.511226	+	0.885469i	−0.999915	+	0.0130110i	$0.995858\pi$
$192$		0			0
$193$	−1.94727	−	3.37277i	−0.140167	−	0.242777i	0.787392	−	0.616452i	$-0.211431\pi$
$193$	−1.94727	−	3.37277i	−0.140167	−	0.242777i	−0.927560	+	0.373675i	$0.878097\pi$
$194$	0.317999	+	0.550790i	0.0228310	+	0.0395444i
$195$		0			0
$196$	0.944795	−	13.4637i	0.0674853	−	0.961689i
$197$	−5.85445	+	10.1402i	−0.417112	+	0.722459i	−0.995648	−	0.0931979i	$-0.970291\pi$
$197$	−5.85445	+	10.1402i	−0.417112	+	0.722459i	0.578536	+	0.815657i	$0.303624\pi$
$198$		0			0
$199$	3.49684			0.247884			0.123942	−	0.992289i	$-0.460446\pi$
$199$	3.49684			0.247884			0.123942	+	0.992289i	$0.460446\pi$
$200$	0.822878	−	1.42527i	0.0581863	−	0.100782i
$201$		0			0
$202$	−0.106892	−	0.185143i	−0.00752090	−	0.0130266i
$203$	6.06279	−	1.39892i	0.425524	−	0.0981850i
$204$		0			0
$205$	6.24421			0.436114
$206$	−0.290403	−	0.502994i	−0.0202334	−	0.0350452i
$207$		0			0
$208$	−11.2709	+	6.24542i	−0.781497	+	0.433042i
$209$	29.5764			2.04584
$210$		0			0
$211$	−9.50258	+	16.4589i	−0.654184	+	1.13308i	0.327913	+	0.944708i	$0.393655\pi$
$211$	−9.50258	+	16.4589i	−0.654184	+	1.13308i	−0.982098	+	0.188373i	$0.939679\pi$
$212$	−8.94598	+	15.4949i	−0.614412	+	1.06419i
$213$		0			0
$214$	3.09047			0.211260
$215$	2.88128	−	4.99053i	0.196502	−	0.340351i
$216$		0			0
$217$	6.58519	−	1.51946i	0.447032	−	0.103148i
$218$	−1.08299	+	1.87579i	−0.0733492	+	0.127045i
$219$		0			0
$220$	−9.74533	+	16.8794i	−0.657030	+	1.13801i
$221$	2.47600	−	1.37200i	0.166554	−	0.0922906i
$222$		0			0
$223$	5.98311	−	10.3630i	0.400658	−	0.693961i	−0.593147	−	0.805094i	$-0.702115\pi$
$223$	5.98311	−	10.3630i	0.400658	−	0.693961i	0.993805	+	0.111133i	$0.0354481\pi$
$224$	5.52918	+	5.93078i	0.369434	+	0.396267i
$225$		0			0
$226$	1.07804	+	1.86723i	0.0717104	+	0.124206i
$227$	−15.3842			−1.02108			−0.510542	−	0.859853i	$-0.670555\pi$
$227$	−15.3842			−1.02108			−0.510542	+	0.859853i	$0.670555\pi$
$228$		0			0
$229$	−4.33084	−	7.50123i	−0.286190	−	0.495695i	0.686707	−	0.726934i	$-0.259055\pi$
$229$	−4.33084	−	7.50123i	−0.286190	−	0.495695i	−0.972897	+	0.231239i	$0.925722\pi$
$230$	−2.73209	−	4.73212i	−0.180149	−	0.312027i
$231$		0			0
$232$	−1.23845	+	2.14506i	−0.0813082	+	0.140830i
$233$	10.1253	+	17.5376i	0.663333	+	1.14893i	0.979734	+	0.200301i	$0.0641919\pi$
$233$	10.1253	+	17.5376i	0.663333	+	1.14893i	−0.316402	+	0.948625i	$0.602475\pi$
$234$		0			0
$235$	1.68634	−	2.92083i	0.110005	−	0.190534i
$236$	−17.2888			−1.12540
$237$		0			0
$238$	−0.379785	−	0.407370i	−0.0246178	−	0.0264059i
$239$	−16.5526			−1.07070			−0.535350	−	0.844630i	$-0.679820\pi$
$239$	−16.5526			−1.07070			−0.535350	+	0.844630i	$0.679820\pi$
$240$		0			0
$241$	−16.4008			−1.05647			−0.528233	−	0.849100i	$-0.677145\pi$
$241$	−16.4008			−1.05647			−0.528233	+	0.849100i	$0.677145\pi$
$242$	−0.612791	+	1.06138i	−0.0393917	+	0.0682284i
$243$		0			0
$244$	9.10595	−	15.7720i	0.582949	−	1.00970i
$245$	16.1194	−	7.85704i	1.02983	−	0.501968i
$246$		0			0
$247$	−0.475582	+	27.0204i	−0.0302605	+	1.71927i
$248$	−1.34516	+	2.32989i	−0.0854178	+	0.147948i
$249$		0			0
$250$	−2.36106			−0.149326
$251$	−10.2154	−	17.6935i	−0.644788	−	1.11681i	−0.984350	−	0.176222i	$-0.943612\pi$
$251$	−10.2154	−	17.6935i	−0.644788	−	1.11681i	0.339563	−	0.940583i	$-0.389721\pi$
$252$		0			0
$253$	15.6956	+	27.1855i	0.986772	+	1.70914i
$254$	−0.239710	+	0.415190i	−0.0150407	+	0.0260513i
$255$		0			0
$256$	10.5536			0.659602
$257$	−13.7779			−0.859442			−0.429721	−	0.902962i	$-0.641388\pi$
$257$	−13.7779			−0.859442			−0.429721	+	0.902962i	$0.641388\pi$
$258$		0			0
$259$	12.1910	+	13.0765i	0.757511	+	0.812532i
$260$	−15.2640	−	9.17456i	−0.946633	−	0.568982i
$261$		0			0
$262$	−0.856782	−	1.48399i	−0.0529321	−	0.0916812i
$263$	12.9587	+	22.4451i	0.799065	+	1.38402i	0.920225	+	0.391389i	$0.128005\pi$
$263$	12.9587	+	22.4451i	0.799065	+	1.38402i	−0.121160	+	0.992633i	$0.538662\pi$
$264$		0			0
$265$	−23.7719			−1.46030
$266$	5.18096	−	1.19545i	0.317665	−	0.0732977i
$267$		0			0
$268$	−1.30394	−	2.25850i	−0.0796510	−	0.137960i
$269$	30.0666			1.83319			0.916596	−	0.399814i	$-0.130925\pi$
$269$	30.0666			1.83319			0.916596	+	0.399814i	$0.130925\pi$
$270$		0			0
$271$	14.4505			0.877808			0.438904	−	0.898534i	$-0.355367\pi$
$271$	14.4505			0.877808			0.438904	+	0.898534i	$0.355367\pi$
$272$	−2.80581			−0.170127
$273$		0			0
$274$	−2.69105			−0.162572
$275$	−6.16598			−0.371822
$276$		0			0
$277$	−15.3255			−0.920819			−0.460409	−	0.887707i	$-0.652297\pi$
$277$	−15.3255			−0.920819			−0.460409	+	0.887707i	$0.652297\pi$
$278$	0.743453	+	1.28770i	0.0445894	+	0.0772310i
$279$		0			0
$280$	−2.08794	+	6.82634i	−0.124778	+	0.407952i
$281$	−5.29279			−0.315741			−0.157871	−	0.987460i	$-0.550463\pi$
$281$	−5.29279			−0.315741			−0.157871	+	0.987460i	$0.550463\pi$
$282$		0			0
$283$	15.3923	+	26.6602i	0.914975	+	1.58478i	0.806938	+	0.590636i	$0.201123\pi$
$283$	15.3923	+	26.6602i	0.914975	+	1.58478i	0.108036	+	0.994147i	$0.465544\pi$
$284$	−11.8734	−	20.5654i	−0.704559	−	1.22033i
$285$		0			0
$286$	−3.26960	−	1.96522i	−0.193335	−	0.116206i
$287$	−6.28384	+	1.44992i	−0.370923	+	0.0855864i
$288$		0			0
$289$	−16.3836			−0.963742
$290$	−1.61533			−0.0948557
$291$		0			0
$292$	0.740963	−	1.28339i	0.0433616	−	0.0751044i
$293$	−8.75864	−	15.1704i	−0.511685	−	0.886265i	−0.999908	−	0.0135461i	$-0.995688\pi$
$293$	−8.75864	−	15.1704i	−0.511685	−	0.886265i	0.488223	−	0.872719i	$-0.337645\pi$
$294$		0			0
$295$	−11.4853	−	19.8930i	−0.668697	−	1.15822i
$296$	−7.11681			−0.413656
$297$		0			0
$298$	2.47548	−	4.28765i	0.143400	−	0.248377i
$299$	−25.0886	+	13.9020i	−1.45091	+	0.803976i
$300$		0			0
$301$	−1.74075	+	5.69124i	−0.100335	+	0.328038i
$302$	−0.215486	+	0.373233i	−0.0123998	+	0.0214772i
$303$		0			0
$304$	13.3934	−	23.1980i	0.768163	−	1.33050i
$305$	24.1970			1.38551
$306$		0			0
$307$	−8.63573			−0.492867			−0.246434	−	0.969160i	$-0.579259\pi$
$307$	−8.63573			−0.492867			−0.246434	+	0.969160i	$0.579259\pi$
$308$	5.88773	−	19.2494i	0.335484	−	1.09684i
$309$		0			0
$310$	−1.75452			−0.0996501
$311$	−8.21130	+	14.2224i	−0.465620	+	0.806478i	−0.999229	−	0.0392535i	$-0.987502\pi$
$311$	−8.21130	+	14.2224i	−0.465620	+	0.806478i	0.533609	+	0.845731i	$0.320835\pi$
$312$		0			0
$313$	−5.02308	−	8.70024i	−0.283921	−	0.491766i	0.688426	−	0.725307i	$-0.258302\pi$
$313$	−5.02308	−	8.70024i	−0.283921	−	0.491766i	−0.972347	+	0.233541i	$0.924969\pi$
$314$	0.220658	−	0.382191i	0.0124525	−	0.0215683i
$315$		0			0
$316$	5.97024	+	10.3408i	0.335852	+	0.581713i
$317$	5.07249	+	8.78581i	0.284899	+	0.493460i	0.972585	−	0.232549i	$-0.0747064\pi$
$317$	5.07249	+	8.78581i	0.284899	+	0.493460i	−0.687685	+	0.726009i	$0.741373\pi$
$318$		0			0
$319$	9.27992			0.519576
$320$	8.10273	+	14.0343i	0.452957	+	0.784544i
$321$		0			0
$322$	3.84824	+	4.12775i	0.214454	+	0.230031i
$323$	−2.94227	+	5.09616i	−0.163712	+	0.283558i
$324$		0			0
$325$	0.0991476	−	5.63312i	0.00549972	−	0.312469i
$326$	0.877867	−	1.52051i	0.0486206	−	0.0842133i
$327$		0			0
$328$	1.28360	−	2.22327i	0.0708751	−	0.122759i
$329$	−1.01882	+	3.33094i	−0.0561693	+	0.183641i
$330$		0			0
$331$	−1.15958	+	2.00845i	−0.0637363	+	0.110395i	−0.896133	−	0.443786i	$-0.853635\pi$
$331$	−1.15958	+	2.00845i	−0.0637363	+	0.110395i	0.832396	+	0.554181i	$0.186968\pi$
$332$	−2.06871			−0.113535
$333$		0			0
$334$	1.28014	−	2.21726i	0.0700460	−	0.121323i
$335$	1.73247	−	3.00072i	0.0946547	−	0.163947i
$336$		0			0
$337$	−15.9998			−0.871565			−0.435783	−	0.900052i	$-0.643528\pi$
$337$	−15.9998			−0.871565			−0.435783	+	0.900052i	$0.643528\pi$
$338$	1.84796	−	2.95544i	0.100516	−	0.160755i
$339$		0			0
$340$	−1.93894	−	3.35834i	−0.105154	−	0.182132i
$341$	10.0795			0.545837
$342$		0			0
$343$	−14.3972	+	11.6499i	−0.777378	+	0.629034i
$344$	−1.18459	−	2.05178i	−0.0638690	−	0.110624i
$345$		0			0
$346$	1.49234	−	2.58480i	0.0802285	−	0.138960i
$347$	22.8208			1.22509			0.612543	−	0.790437i	$-0.290147\pi$
$347$	22.8208			1.22509			0.612543	+	0.790437i	$0.290147\pi$
$348$		0			0
$349$	11.3511	−	19.6607i	0.607612	−	1.05241i	−0.384021	−	0.923324i	$-0.625461\pi$
$349$	11.3511	−	19.6607i	0.607612	−	1.05241i	0.991633	−	0.129090i	$-0.0412056\pi$
$350$	−1.08011	+	0.249223i	−0.0577342	+	0.0133215i
$351$		0			0
$352$	6.04662	+	10.4731i	0.322286	+	0.558216i
$353$	−13.6322	−	23.6116i	−0.725568	−	1.25672i	−0.958740	−	0.284286i	$-0.908244\pi$
$353$	−13.6322	−	23.6116i	−0.725568	−	1.25672i	0.233171	−	0.972436i	$-0.425090\pi$
$354$		0			0
$355$	15.7755	−	27.3239i	0.837276	−	1.45020i
$356$	14.7751			0.783077
$357$		0			0
$358$	−1.69502	−	2.93585i	−0.0895844	−	0.155165i
$359$	−7.21309	−	12.4934i	−0.380692	−	0.659378i	0.610469	−	0.792040i	$-0.290981\pi$
$359$	−7.21309	−	12.4934i	−0.380692	−	0.659378i	−0.991161	+	0.132662i	$0.957648\pi$
$360$		0			0
$361$	−18.5895	−	32.1980i	−0.978397	−	1.69463i
$362$	3.99930			0.210199
$363$		0			0
$364$	17.4912	+	5.68844i	0.916790	+	0.298155i
$365$	1.96894			0.103059
$366$		0			0
$367$	5.69586	+	9.86553i	0.297322	+	0.514976i	0.975522	−	0.219901i	$-0.0705733\pi$
$367$	5.69586	+	9.86553i	0.297322	+	0.514976i	−0.678201	+	0.734877i	$0.737240\pi$
$368$	28.4304			1.48204
$369$		0			0
$370$	−2.32065	−	4.01948i	−0.120645	−	0.208963i
$371$	23.9228	−	5.51991i	1.24201	−	0.286580i
$372$		0			0
$373$	15.4815	−	26.8147i	0.801599	−	1.38841i	−0.116964	−	0.993136i	$-0.537316\pi$
$373$	15.4815	−	26.8147i	0.801599	−	1.38841i	0.918563	−	0.395274i	$-0.129351\pi$
$374$	−0.415327	−	0.719367i	−0.0214760	−	0.0371976i
$375$		0			0
$376$	−0.693313	−	1.20085i	−0.0357549	−	0.0619293i
$377$	−0.149219	+	8.47796i	−0.00768518	+	0.436637i
$378$		0			0
$379$	−5.29330	+	9.16826i	−0.271898	+	0.470942i	−0.969348	−	0.245692i	$-0.920985\pi$
$379$	−5.29330	+	9.16826i	−0.271898	+	0.470942i	0.697450	+	0.716634i	$0.254318\pi$
$380$	37.0217			1.89917
$381$		0			0
$382$	−1.89438	+	3.28116i	−0.0969249	+	0.167879i
$383$	15.3758	−	26.6317i	0.785668	−	1.36082i	−0.142931	−	0.989733i	$-0.545653\pi$
$383$	15.3758	−	26.6317i	0.785668	−	1.36082i	0.928599	−	0.371084i	$-0.121014\pi$
$384$		0			0
$385$	26.0603	−	6.01313i	1.32816	−	0.306458i
$386$	−0.522112	−	0.904324i	−0.0265748	−	0.0460289i
$387$		0			0
$388$	−2.28675	−	3.96077i	−0.116092	−	0.201078i
$389$	−8.18978	+	14.1851i	−0.415239	+	0.719214i	−0.995453	−	0.0952492i	$-0.969635\pi$
$389$	−8.18978	+	14.1851i	−0.415239	+	0.719214i	0.580215	+	0.814463i	$0.302969\pi$
$390$		0			0
$391$	−6.24561			−0.315854
$392$	0.516092	−	7.35449i	0.0260666	−	0.371458i
$393$		0			0
$394$	−1.56972	+	2.71884i	−0.0790816	+	0.136973i
$395$	−7.93227	+	13.7391i	−0.399116	+	0.691289i
$396$		0			0
$397$	7.94133	−	13.7548i	0.398564	−	0.690333i	−0.594985	−	0.803737i	$-0.702842\pi$
$397$	7.94133	−	13.7548i	0.398564	−	0.690333i	0.993549	+	0.113404i	$0.0361755\pi$
$398$	0.937591			0.0469972
$399$		0			0
$400$	−2.79221	+	4.83624i	−0.139610	+	0.241812i
$401$	−6.63573			−0.331373			−0.165686	−	0.986178i	$-0.552984\pi$
$401$	−6.63573			−0.331373			−0.165686	+	0.986178i	$0.552984\pi$
$402$		0			0
$403$	−0.162077	+	9.20847i	−0.00807362	+	0.458707i
$404$	0.768670	+	1.33137i	0.0382427	+	0.0662384i
$405$		0			0
$406$	1.62559	−	0.375086i	0.0806765	−	0.0186152i
$407$	13.3319	+	23.0915i	0.660836	+	1.14460i
$408$		0			0
$409$	5.87235			0.290369			0.145184	−	0.989405i	$-0.453622\pi$
$409$	5.87235			0.290369			0.145184	+	0.989405i	$0.453622\pi$
$410$	1.67423			0.0826843
$411$		0			0
$412$	2.08831	+	3.61707i	0.102884	+	0.178200i
$413$	16.1774	+	17.3524i	0.796037	+	0.853855i
$414$		0			0
$415$	−1.37428	−	2.38032i	−0.0674607	−	0.116845i
$416$	−9.66521	+	5.35567i	−0.473876	+	0.262584i
$417$		0			0
$418$	7.93017			0.387877
$419$	−15.0712	+	26.1040i	−0.736274	+	1.27526i	0.217888	+	0.975974i	$0.430083\pi$
$419$	−15.0712	+	26.1040i	−0.736274	+	1.27526i	−0.954162	+	0.299290i	$0.903250\pi$
$420$		0			0
$421$	40.0580			1.95231			0.976153	−	0.217083i	$-0.0696543\pi$
$421$	40.0580			1.95231			0.976153	+	0.217083i	$0.0696543\pi$
$422$	−2.54788	+	4.41306i	−0.124029	+	0.214824i
$423$		0			0
$424$	−4.88672	+	8.46405i	−0.237320	+	0.411051i
$425$	0.613394	−	1.06243i	0.0297540	−	0.0515354i
$426$		0			0
$427$	−24.3506	+	5.61862i	−1.17841	+	0.271904i
$428$	−22.2238			−1.07423
$429$		0			0
$430$	0.772544	−	1.33809i	0.0372554	−	0.0645282i
$431$	−1.95793	−	3.39124i	−0.0943104	−	0.163350i	0.815010	−	0.579447i	$-0.196731\pi$
$431$	−1.95793	−	3.39124i	−0.0943104	−	0.163350i	−0.909321	+	0.416096i	$0.863398\pi$
$432$		0			0
$433$	20.3963	+	35.3274i	0.980182	+	1.69772i	0.661650	+	0.749813i	$0.269856\pi$
$433$	20.3963	+	35.3274i	0.980182	+	1.69772i	0.318532	+	0.947912i	$0.396810\pi$
$434$	1.76566	−	0.407405i	0.0847542	−	0.0195561i
$435$		0			0
$436$	7.78785	−	13.4890i	0.372971	−	0.646004i
$437$	29.8131	−	51.6378i	1.42615	−	2.47017i
$438$		0			0
$439$	−25.5623			−1.22002			−0.610010	−	0.792394i	$-0.708835\pi$
$439$	−25.5623			−1.22002			−0.610010	+	0.792394i	$0.708835\pi$
$440$	−5.32336	+	9.22033i	−0.253781	+	0.439562i
$441$		0			0
$442$	0.663878	−	0.367867i	0.0315775	−	0.0174977i
$443$	−13.7282	−	23.7779i	−0.652247	−	1.12972i	−0.982576	−	0.185859i	$-0.940493\pi$
$443$	−13.7282	−	23.7779i	−0.652247	−	1.12972i	0.330330	−	0.943866i	$-0.392840\pi$
$444$		0			0
$445$	9.81535	+	17.0007i	0.465292	+	0.805910i
$446$	1.60422	−	2.77859i	0.0759621	−	0.131570i
$447$		0			0
$448$	−11.4130	−	12.2419i	−0.539213	−	0.578377i
$449$	−7.40181	−	12.8203i	−0.349313	−	0.605028i	0.636815	−	0.771017i	$-0.280252\pi$
$449$	−7.40181	−	12.8203i	−0.349313	−	0.605028i	−0.986128	+	0.165989i	$0.946918\pi$
$450$		0			0
$451$	−9.61827			−0.452907
$452$	−7.75230	−	13.4274i	−0.364637	−	0.631571i
$453$		0			0
$454$	−4.12489			−0.193590
$455$	5.07444	+	23.9049i	0.237893	+	1.12068i
$456$		0			0
$457$	−0.651951			−0.0304970			−0.0152485	−	0.999884i	$-0.504854\pi$
$457$	−0.651951			−0.0304970			−0.0152485	+	0.999884i	$0.504854\pi$
$458$	−1.16121	−	2.01127i	−0.0542596	−	0.0939805i
$459$		0			0
$460$	19.6467	+	34.0290i	0.916031	+	1.58661i
$461$	6.24774	+	10.8214i	0.290986	+	0.504003i	0.974043	−	0.226362i	$-0.0726833\pi$
$461$	6.24774	+	10.8214i	0.290986	+	0.504003i	−0.683057	+	0.730365i	$0.739350\pi$
$462$		0			0
$463$	−0.309503			−0.0143838			−0.00719190	−	0.999974i	$-0.502289\pi$
$463$	−0.309503			−0.0143838			−0.00719190	+	0.999974i	$0.502289\pi$
$464$	4.20233	−	7.27865i	0.195088	−	0.337903i
$465$		0			0
$466$	2.71486	+	4.70227i	0.125763	+	0.217829i
$467$	12.2387	+	21.1980i	0.566338	+	0.980926i	0.996924	+	0.0783762i	$0.0249735\pi$
$467$	12.2387	+	21.1980i	0.566338	+	0.980926i	−0.430586	+	0.902549i	$0.641693\pi$
$468$		0			0
$469$	−1.04668	+	3.42205i	−0.0483314	+	0.158016i
$470$	0.452151	−	0.783149i	0.0208562	−	0.0361240i
$471$		0			0
$472$	−9.44396			−0.434694
$473$	−4.43818	+	7.68716i	−0.204068	+	0.353456i
$474$		0			0
$475$	5.85601	+	10.1429i	0.268692	+	0.465389i
$476$	2.73106	+	2.92943i	0.125178	+	0.134270i
$477$		0			0
$478$	−4.43817			−0.202997
$479$	4.06925	+	7.04815i	0.185929	+	0.322038i	0.943889	−	0.330262i	$-0.107137\pi$
$479$	4.06925	+	7.04815i	0.185929	+	0.322038i	−0.757960	+	0.652301i	$0.773804\pi$
$480$		0			0
$481$	−21.3103	+	11.8084i	−0.971667	+	0.538419i
$482$	−4.39746			−0.200299
$483$		0			0
$484$	4.40662	−	7.63250i	0.200301	−	0.346932i
$485$	3.03826	−	5.26243i	0.137960	−	0.238954i
$486$		0			0
$487$	4.60960			0.208881			0.104440	−	0.994531i	$-0.466695\pi$
$487$	4.60960			0.208881			0.104440	+	0.994531i	$0.466695\pi$
$488$	4.97410	−	8.61540i	0.225167	−	0.390001i
$489$		0			0
$490$	4.32201	−	2.10667i	0.195248	−	0.0951696i
$491$	6.50947	−	11.2747i	0.293768	−	0.508822i	−0.680929	−	0.732349i	$-0.738424\pi$
$491$	6.50947	−	11.2747i	0.293768	−	0.508822i	0.974698	+	0.223527i	$0.0717572\pi$
$492$		0			0
$493$	−0.923171	+	1.59898i	−0.0415775	+	0.0720144i
$494$	−0.127515	+	7.24485i	−0.00573719	+	0.325961i
$495$		0			0
$496$	4.56443	−	7.90582i	0.204949	−	0.354982i
$497$	−9.53090	+	31.1605i	−0.427519	+	1.39774i
$498$		0			0
$499$	16.1603	+	27.9905i	0.723436	+	1.25303i	0.959614	+	0.281319i	$0.0907717\pi$
$499$	16.1603	+	27.9905i	0.723436	+	1.25303i	−0.236178	+	0.971710i	$0.575895\pi$
$500$	16.9786			0.759304
$501$		0			0
$502$	−2.73900	−	4.74408i	−0.122247	−	0.211739i
$503$	−15.9126	−	27.5615i	−0.709509	−	1.22891i	−0.965039	−	0.262105i	$-0.915583\pi$
$503$	−15.9126	−	27.5615i	−0.709509	−	1.22891i	0.255531	−	0.966801i	$-0.417750\pi$
$504$		0			0
$505$	−1.02128	+	1.76891i	−0.0454465	+	0.0787156i
$506$	4.20838	+	7.28912i	0.187085	+	0.324041i
$507$		0			0
$508$	1.72377	−	2.98566i	0.0764801	−	0.132467i
$509$	−2.25575			−0.0999845			−0.0499922	−	0.998750i	$-0.515920\pi$
$509$	−2.25575			−0.0999845			−0.0499922	+	0.998750i	$0.515920\pi$
$510$		0			0
$511$	−1.98144	+	0.457194i	−0.0876536	+	0.0202251i
$512$	18.4807			0.816739
$513$		0			0
$514$	−3.69420			−0.162944
$515$	−2.77461	+	4.80576i	−0.122264	+	0.211767i
$516$		0			0
$517$	−2.59756	+	4.49911i	−0.114241	+	0.197870i
$518$	3.26871	+	3.50613i	0.143619	+	0.154050i
$519$		0			0
$520$	−8.33793	−	5.01158i	−0.365642	−	0.219773i
$521$	5.38562	−	9.32817i	0.235948	−	0.408675i	−0.723600	−	0.690220i	$-0.757514\pi$
$521$	5.38562	−	9.32817i	0.235948	−	0.408675i	0.959548	+	0.281546i	$0.0908471\pi$
$522$		0			0
$523$	7.40793			0.323926			0.161963	−	0.986797i	$-0.448217\pi$
$523$	7.40793			0.323926			0.161963	+	0.986797i	$0.448217\pi$
$524$	6.16118	+	10.6715i	0.269152	+	0.466186i
$525$		0			0
$526$	3.47454	+	6.01809i	0.151497	+	0.262401i
$527$	−1.00272	+	1.73676i	−0.0436790	+	0.0756543i
$528$		0			0
$529$	40.2848			1.75151
$530$	−6.37385			−0.276862
$531$		0			0
$532$	−37.2567	+	8.59656i	−1.61528	+	0.372708i
$533$	0.154660	−	8.78707i	0.00669906	−	0.380610i
$534$		0			0
$535$	−14.7637	−	25.5715i	−0.638290	−	1.10555i
$536$	−0.712276	−	1.23370i	−0.0307656	−	0.0532876i
$537$		0			0
$538$	8.06161			0.347561
$539$	−24.8295	+	12.1026i	−1.06948	+	0.521296i
$540$		0			0
$541$	−16.2741	−	28.1875i	−0.699676	−	1.21188i	−0.968579	−	0.248708i	$-0.919994\pi$
$541$	−16.2741	−	28.1875i	−0.699676	−	1.21188i	0.268902	−	0.963168i	$-0.413339\pi$
$542$	3.87455			0.166426
$543$		0			0
$544$	−2.40608			−0.103160
$545$	20.6944			0.886453
$546$		0			0
$547$	−13.4997			−0.577206			−0.288603	−	0.957449i	$-0.593191\pi$
$547$	−13.4997			−0.577206			−0.288603	+	0.957449i	$0.593191\pi$
$548$	19.3515			0.826657
$549$		0			0
$550$	−1.65325			−0.0704950
$551$	−8.81342	−	15.2653i	−0.375464	−	0.650323i
$552$		0			0
$553$	4.79235	−	15.6682i	0.203792	−	0.666280i
$554$	−4.10915			−0.174581
$555$		0			0
$556$	−5.34623	−	9.25994i	−0.226731	−	0.392709i
$557$	−14.8851	−	25.7818i	−0.630703	−	1.09241i	−0.987408	−	0.158193i	$-0.949433\pi$
$557$	−14.8851	−	25.7818i	−0.630703	−	1.09241i	0.356705	−	0.934217i	$-0.383900\pi$
$558$		0			0
$559$	−6.95148	−	4.17825i	−0.294016	−	0.176721i
$560$	7.08483	−	23.1632i	0.299389	−	0.978826i
$561$		0			0
$562$	−1.41913			−0.0598624
$563$	−14.1326			−0.595617			−0.297809	−	0.954626i	$-0.596256\pi$
$563$	−14.1326			−0.595617			−0.297809	+	0.954626i	$0.596256\pi$
$564$		0			0
$565$	10.3000	−	17.8401i	0.433324	−	0.750538i
$566$	4.12705	+	7.14826i	0.173473	+	0.300464i
$567$		0			0
$568$	−6.48584	−	11.2338i	−0.272140	−	0.471360i
$569$	24.2540			1.01678			0.508391	−	0.861127i	$-0.330241\pi$
$569$	24.2540			1.01678			0.508391	+	0.861127i	$0.330241\pi$
$570$		0			0
$571$	−0.604159	+	1.04643i	−0.0252832	+	0.0437919i	−0.878390	−	0.477944i	$-0.841382\pi$
$571$	−0.604159	+	1.04643i	−0.0252832	+	0.0437919i	0.853107	+	0.521736i	$0.174715\pi$
$572$	23.5119	+	14.1320i	0.983083	+	0.590891i
$573$		0			0
$574$	−1.68486	+	0.388761i	−0.0703245	+	0.0162266i
$575$	−6.21533	+	10.7653i	−0.259197	+	0.448943i
$576$		0			0
$577$	7.30518	−	12.6529i	0.304119	−	0.526749i	−0.672946	−	0.739692i	$-0.734971\pi$
$577$	7.30518	−	12.6529i	0.304119	−	0.526749i	0.977065	+	0.212943i	$0.0683047\pi$
$578$	−4.39286			−0.182719
$579$		0			0
$580$	11.6160			0.482328
$581$	1.93572	+	2.07632i	0.0803072	+	0.0861401i
$582$		0			0
$583$	36.6171			1.51652
$584$	0.404749	−	0.701046i	0.0167486	−	0.0290095i
$585$		0			0
$586$	−2.34841	−	4.06757i	−0.0970120	−	0.168030i
$587$	10.7548	−	18.6278i	0.443897	−	0.768852i	−0.554078	−	0.832465i	$-0.686929\pi$
$587$	10.7548	−	18.6278i	0.443897	−	0.768852i	0.997975	+	0.0636132i	$0.0202624\pi$
$588$		0			0
$589$	−9.57284	−	16.5806i	−0.394442	−	0.683193i
$590$	−3.07949	−	5.33383i	−0.126780	−	0.219590i
$591$		0			0
$592$	24.1489			0.992512
$593$	−1.32429	−	2.29373i	−0.0543820	−	0.0941923i	0.837553	−	0.546356i	$-0.183986\pi$
$593$	−1.32429	−	2.29373i	−0.0543820	−	0.0941923i	−0.891935	+	0.452164i	$0.850652\pi$
$594$		0			0
$595$	−1.55640	+	5.08852i	−0.0638062	+	0.208609i
$596$	−17.8013	+	30.8328i	−0.729171	+	1.26296i
$597$		0			0
$598$	−6.72688	+	3.72749i	−0.275082	+	0.152428i
$599$	−20.1250	+	34.8576i	−0.822287	+	1.42424i	0.0816889	+	0.996658i	$0.473969\pi$
$599$	−20.1250	+	34.8576i	−0.822287	+	1.42424i	−0.903975	+	0.427584i	$0.859365\pi$
$600$		0			0
$601$	−19.1725	+	33.2077i	−0.782061	+	1.35457i	0.148679	+	0.988886i	$0.452498\pi$
$601$	−19.1725	+	33.2077i	−0.782061	+	1.35457i	−0.930739	+	0.365683i	$0.880835\pi$
$602$	−0.466740	+	1.52597i	−0.0190229	+	0.0621937i
$603$		0			0
$604$	1.54958	−	2.68395i	0.0630515	−	0.109208i
$605$	11.7096			0.476063
$606$		0			0
$607$	−21.2773	+	36.8534i	−0.863620	+	1.49583i	0.00479063	+	0.999989i	$0.498475\pi$
$607$	−21.2773	+	36.8534i	−0.863620	+	1.49583i	−0.868411	+	0.495845i	$0.834858\pi$
$608$	11.4853	−	19.8931i	0.465791	−	0.806773i
$609$		0			0
$610$	6.48782			0.262684
$611$	−4.06853	−	2.44543i	−0.164595	−	0.0989314i
$612$		0			0
$613$	−7.63261	−	13.2201i	−0.308278	−	0.533953i	0.669708	−	0.742625i	$-0.266419\pi$
$613$	−7.63261	−	13.2201i	−0.308278	−	0.533953i	−0.977986	+	0.208672i	$0.933086\pi$
$614$	−2.31546			−0.0934442
$615$		0			0
$616$	3.21616	−	10.5150i	0.129583	−	0.423660i
$617$	6.99061	+	12.1081i	0.281431	+	0.487453i	0.971737	−	0.236064i	$-0.0758575\pi$
$617$	6.99061	+	12.1081i	0.281431	+	0.487453i	−0.690306	+	0.723517i	$0.742524\pi$
$618$		0			0
$619$	4.25792	−	7.37494i	0.171140	−	0.296424i	−0.767678	−	0.640835i	$-0.778588\pi$
$619$	4.25792	−	7.37494i	0.171140	−	0.296424i	0.938819	+	0.344411i	$0.111921\pi$
$620$	12.6169			0.506707
$621$		0			0
$622$	−2.20166	+	3.81338i	−0.0882784	+	0.152903i
$623$	−13.8253	−	14.8294i	−0.553897	−	0.594129i
$624$		0			0
$625$	15.1856	+	26.3023i	0.607425	+	1.05209i
$626$	−1.34682	−	2.33275i	−0.0538296	−	0.0932356i
$627$		0			0
$628$	−1.58677	+	2.74837i	−0.0633190	+	0.109672i
$629$	−5.30504			−0.211526
$630$		0			0
$631$	−18.4146	−	31.8950i	−0.733074	−	1.26972i	−0.955563	−	0.294786i	$-0.904752\pi$
$631$	−18.4146	−	31.8950i	−0.733074	−	1.26972i	0.222490	−	0.974935i	$-0.428582\pi$
$632$	3.26123	+	5.64861i	0.129725	+	0.224690i
$633$		0			0
$634$	1.36006	+	2.35570i	0.0540150	+	0.0935567i
$635$	4.58053			0.181773
$636$		0			0
$637$	−10.6574	−	22.8783i	−0.422263	−	0.906473i
$638$	2.48818			0.0985081
$639$		0			0
$640$	10.0235	+	17.3612i	0.396214	+	0.686263i
$641$	−25.8747			−1.02199			−0.510996	−	0.859583i	$-0.670723\pi$
$641$	−25.8747			−1.02199			−0.510996	+	0.859583i	$0.670723\pi$
$642$		0			0
$643$	−20.2626	−	35.0958i	−0.799078	−	1.38404i	−0.920217	−	0.391408i	$-0.871988\pi$
$643$	−20.2626	−	35.0958i	−0.799078	−	1.38404i	0.121139	−	0.992636i	$-0.461345\pi$
$644$	−27.6730	−	29.6830i	−1.09047	−	1.16967i
$645$		0			0
$646$	−0.788896	+	1.36641i	−0.0310387	+	0.0537606i
$647$	0.892002	+	1.54499i	0.0350682	+	0.0607399i	0.883027	−	0.469322i	$-0.155502\pi$
$647$	0.892002	+	1.54499i	0.0350682	+	0.0607399i	−0.847959	+	0.530062i	$0.822168\pi$
$648$		0			0
$649$	17.6913	+	30.6423i	0.694445	+	1.20281i
$650$	0.0265840	−	1.51038i	0.00104271	−	0.0592420i
$651$		0			0
$652$	−6.31281	+	10.9341i	−0.247229	+	0.428213i
$653$	−12.4042			−0.485414			−0.242707	−	0.970100i	$-0.578035\pi$
$653$	−12.4042			−0.485414			−0.242707	+	0.970100i	$0.578035\pi$
$654$		0			0
$655$	−8.18597	+	14.1785i	−0.319852	+	0.554000i
$656$	−4.35554	+	7.54402i	−0.170055	+	0.294545i
$657$		0			0
$658$	−0.273171	+	0.893110i	−0.0106493	+	0.0348171i
$659$	−0.564336	−	0.977458i	−0.0219834	−	0.0380764i	0.854824	−	0.518917i	$-0.173665\pi$
$659$	−0.564336	−	0.977458i	−0.0219834	−	0.0380764i	−0.876808	+	0.480841i	$0.840331\pi$
$660$		0			0
$661$	14.4627	+	25.0502i	0.562534	+	0.974338i	0.997274	+	0.0737821i	$0.0235069\pi$
$661$	14.4627	+	25.0502i	0.562534	+	0.974338i	−0.434740	+	0.900556i	$0.643160\pi$
$662$	−0.310913	+	0.538517i	−0.0120840	+	0.0209301i
$663$		0			0
$664$	−1.13003			−0.0438535
$665$	−34.6418	−	37.1579i	−1.34335	−	1.44092i
$666$		0			0
$667$	9.35421	−	16.2020i	0.362196	−	0.627342i
$668$	−9.20556	+	15.9445i	−0.356174	+	0.616911i
$669$		0			0
$670$	0.464518	−	0.804568i	0.0179459	−	0.0310832i
$671$	−37.2718			−1.43886
$672$		0			0
$673$	3.54980	−	6.14843i	0.136835	−	0.237005i	−0.789462	−	0.613799i	$-0.789640\pi$
$673$	3.54980	−	6.14843i	0.136835	−	0.237005i	0.926297	+	0.376795i	$0.122974\pi$
$674$	−4.28995			−0.165243
$675$		0			0
$676$	−13.2888	+	21.2528i	−0.511109	+	0.817416i
$677$	−25.2010	−	43.6494i	−0.968552	−	1.67758i	−0.699752	−	0.714386i	$-0.746706\pi$
$677$	−25.2010	−	43.6494i	−0.968552	−	1.67758i	−0.268800	−	0.963196i	$-0.586627\pi$
$678$		0			0
$679$	−1.83559	+	6.00132i	−0.0704436	+	0.230310i
$680$	−1.05914	−	1.83449i	−0.0406162	−	0.0703493i
$681$		0			0
$682$	2.70258			0.103487
$683$	−27.5282			−1.05334			−0.526669	−	0.850070i	$-0.676559\pi$
$683$	−27.5282			−1.05334			−0.526669	+	0.850070i	$0.676559\pi$
$684$		0			0
$685$	12.8556	+	22.2665i	0.491186	+	0.850760i
$686$	−3.86026	+	3.12362i	−0.147386	+	0.119261i
$687$		0			0
$688$	4.01958	+	6.96212i	0.153245	+	0.265428i
$689$	−0.588795	+	33.4527i	−0.0224313	+	1.27445i
$690$		0			0
$691$	−24.3338			−0.925702			−0.462851	−	0.886436i	$-0.653174\pi$
$691$	−24.3338			−0.925702			−0.462851	+	0.886436i	$0.653174\pi$
$692$	−10.7315	+	18.5875i	−0.407950	+	0.706591i
$693$		0			0
$694$	6.11884			0.232268
$695$	7.10319	−	12.3031i	0.269439	−	0.466683i
$696$		0			0
$697$	0.956829	−	1.65728i	0.0362425	−	0.0627738i
$698$	3.04352	−	5.27153i	0.115199	−	0.199531i
$699$		0			0
$700$	7.76714	−	1.79218i	0.293570	−	0.0677381i
$701$	20.5588			0.776495			0.388248	−	0.921555i	$-0.373081\pi$
$701$	20.5588			0.776495			0.388248	+	0.921555i	$0.373081\pi$
$702$		0			0
$703$	25.3234	−	43.8613i	0.955088	−	1.65426i
$704$	−12.4811	−	21.6178i	−0.470397	−	0.814752i
$705$		0			0
$706$	−3.65513	−	6.33088i	−0.137563	−	0.238266i
$707$	0.617017	−	2.01728i	0.0232053	−	0.0758678i
$708$		0			0
$709$	−20.4544	+	35.4281i	−0.768183	+	1.33053i	0.170364	+	0.985381i	$0.445506\pi$
$709$	−20.4544	+	35.4281i	−0.768183	+	1.33053i	−0.938547	+	0.345151i	$0.887828\pi$
$710$	4.22981	−	7.32624i	0.158742	−	0.274949i
$711$		0			0
$712$	8.07085			0.302468
$713$	10.1602	−	17.5980i	0.380503	−	0.659051i
$714$		0			0
$715$	−0.641405	+	36.4418i	−0.0239872	+	1.36284i
$716$	12.1890	+	21.1119i	0.455524	+	0.788990i
$717$		0			0
$718$	−1.93401	−	3.34981i	−0.0721767	−	0.125014i
$719$	−0.599734	+	1.03877i	−0.0223663	+	0.0387396i	−0.876992	−	0.480505i	$-0.840453\pi$
$719$	−0.599734	+	1.03877i	−0.0223663	+	0.0387396i	0.854626	+	0.519245i	$0.173787\pi$
$720$		0			0
$721$	1.67630	−	5.48054i	0.0624289	−	0.204106i
$722$	−4.98433	−	8.63311i	−0.185497	−	0.321291i
$723$		0			0
$724$	−28.7593			−1.06883
$725$	1.83739	+	3.18246i	0.0682390	+	0.118193i
$726$		0			0
$727$	−2.06230			−0.0764865			−0.0382433	−	0.999268i	$-0.512176\pi$
$727$	−2.06230			−0.0764865			−0.0382433	+	0.999268i	$0.512176\pi$
$728$	9.55455	+	3.10730i	0.354115	+	0.115164i
$729$		0			0
$730$	0.527922			0.0195393
$731$	−0.883025	−	1.52944i	−0.0326599	−	0.0565685i
$732$		0			0
$733$	−15.0310	−	26.0345i	−0.555184	−	0.961606i	−0.997889	−	0.0649392i	$-0.979315\pi$
$733$	−15.0310	−	26.0345i	−0.555184	−	0.961606i	0.442706	−	0.896667i	$-0.354019\pi$
$734$	1.52720	+	2.64520i	0.0563702	+	0.0976360i
$735$		0			0
$736$	24.3801			0.898662
$737$	−2.66861	+	4.62216i	−0.0982993	+	0.170259i
$738$		0			0
$739$	−22.1274	−	38.3257i	−0.813969	−	1.40984i	−0.910066	−	0.414464i	$-0.863969\pi$
$739$	−22.1274	−	38.3257i	−0.813969	−	1.40984i	0.0960970	−	0.995372i	$-0.469364\pi$
$740$	16.6880	+	28.9044i	0.613461	+	1.06255i
$741$		0			0
$742$	6.41430	−	1.48003i	0.235476	−	0.0543335i
$743$	−4.31326	+	7.47078i	−0.158238	+	0.274076i	−0.934233	−	0.356662i	$-0.883915\pi$
$743$	−4.31326	+	7.47078i	−0.158238	+	0.274076i	0.775995	+	0.630739i	$0.217248\pi$
$744$		0			0
$745$	−47.3030			−1.73305
$746$	4.15097	−	7.18969i	0.151978	−	0.263233i
$747$		0			0
$748$	2.98665	+	5.17302i	0.109203	+	0.189144i
$749$	20.7952	+	22.3056i	0.759839	+	0.815028i
$750$		0			0
$751$	5.72211			0.208803			0.104401	−	0.994535i	$-0.466707\pi$
$751$	5.72211			0.208803			0.104401	+	0.994535i	$0.466707\pi$
$752$	2.35256	+	4.07476i	0.0857891	+	0.148591i
$753$		0			0
$754$	−0.0400094	+	2.27316i	−0.00145706	+	0.0827835i
$755$	4.11765			0.149857
$756$		0			0
$757$	17.3611	−	30.0703i	0.631000	−	1.09292i	−0.356347	−	0.934354i	$-0.615978\pi$
$757$	17.3611	−	30.0703i	0.631000	−	1.09292i	0.987348	−	0.158571i	$-0.0506887\pi$
$758$	−1.41927	+	2.45824i	−0.0515501	+	0.0892873i
$759$		0			0
$760$	20.2230			0.733566
$761$	−26.5867	+	46.0496i	−0.963768	+	1.66930i	−0.250880	+	0.968018i	$0.580720\pi$
$761$	−26.5867	+	46.0496i	−0.963768	+	1.66930i	−0.712888	+	0.701278i	$0.752613\pi$
$762$		0			0
$763$	−20.8258	+	4.80532i	−0.753944	+	0.173964i
$764$	13.6226	−	23.5951i	0.492849	−	0.853640i
$765$		0			0
$766$	4.12265	−	7.14063i	0.148957	−	0.258002i
$767$	−28.2787	+	15.6697i	−1.02108	+	0.565801i
$768$		0			0
$769$	−2.45578	+	4.25354i	−0.0885578	+	0.153387i	−0.906902	−	0.421342i	$-0.861559\pi$
$769$	−2.45578	+	4.25354i	−0.0885578	+	0.153387i	0.818344	+	0.574729i	$0.194892\pi$
$770$	6.98744	−	1.61227i	0.251810	−	0.0581023i
$771$		0			0
$772$	3.75455	+	6.50306i	0.135129	+	0.234050i
$773$	22.9807			0.826557			0.413279	−	0.910605i	$-0.364384\pi$
$773$	22.9807			0.826557			0.413279	+	0.910605i	$0.364384\pi$
$774$		0			0
$775$	1.99571	+	3.45667i	0.0716881	+	0.124167i
$776$	−1.24913	−	2.16356i	−0.0448413	−	0.0776674i
$777$		0			0
$778$	−2.19589	+	3.80339i	−0.0787264	+	0.136358i
$779$	9.13476	+	15.8219i	0.327287	+	0.566877i
$780$		0			0
$781$	−24.2998	+	42.0885i	−0.869515	+	1.50604i
$782$	−1.67460			−0.0598837
$783$		0			0
$784$	−1.75121	+	24.9554i	−0.0625433	+	0.891264i
$785$	−4.21648			−0.150493
$786$		0			0
$787$	−3.18774			−0.113631			−0.0568154	−	0.998385i	$-0.518095\pi$
$787$	−3.18774			−0.113631			−0.0568154	+	0.998385i	$0.518095\pi$
$788$	11.2880	−	19.5514i	0.402119	−	0.696490i
$789$		0			0
$790$	−2.12684	+	3.68380i	−0.0756696	+	0.131064i
$791$	−6.22283	+	20.3450i	−0.221258	+	0.723385i
$792$		0			0
$793$	0.599323	−	34.0509i	0.0212826	−	1.20918i
$794$	2.12927	−	3.68800i	0.0755650	−	0.130882i
$795$		0			0
$796$	−6.74229			−0.238974
$797$	27.3255	+	47.3291i	0.967918	+	1.67648i	0.701562	+	0.712608i	$0.252486\pi$
$797$	27.3255	+	47.3291i	0.967918	+	1.67648i	0.266355	+	0.963875i	$0.414180\pi$
$798$		0			0
$799$	−0.516813	−	0.895146i	−0.0182835	−	0.0316680i
$800$	−2.39442	+	4.14725i	−0.0846554	+	0.146628i
$801$		0			0
$802$	−1.77921			−0.0628260
$803$	−3.03286			−0.107027
$804$		0			0
$805$	15.7705	−	51.5604i	0.555838	−	1.81727i
$806$	−0.0434569	+	2.46902i	−0.00153070	+	0.0869677i
$807$		0			0
$808$	0.419884	+	0.727260i	0.0147715	+	0.0255849i
$809$	−10.1498	−	17.5799i	−0.356847	−	0.618077i	0.630585	−	0.776120i	$-0.282815\pi$
$809$	−10.1498	−	17.5799i	−0.356847	−	0.618077i	−0.987432	+	0.158043i	$0.949482\pi$
$810$		0			0
$811$	2.43587			0.0855350			0.0427675	−	0.999085i	$-0.486383\pi$
$811$	2.43587			0.0855350			0.0427675	+	0.999085i	$0.486383\pi$
$812$	−11.6897	+	2.69727i	−0.410229	+	0.0946557i
$813$		0			0
$814$	3.57461	+	6.19141i	0.125290	+	0.217009i
$815$	−16.7748			−0.587597
$816$		0			0
$817$	16.8603			0.589867
$818$	1.57452			0.0550519
$819$		0			0
$820$	−12.0395			−0.420438
$821$	−45.3524			−1.58281			−0.791405	−	0.611292i	$-0.790650\pi$
$821$	−45.3524			−1.58281			−0.791405	+	0.611292i	$0.790650\pi$
$822$		0			0
$823$	−2.75742			−0.0961177			−0.0480588	−	0.998845i	$-0.515303\pi$
$823$	−2.75742			−0.0961177			−0.0480588	+	0.998845i	$0.515303\pi$
$824$	1.14074	+	1.97581i	0.0397394	+	0.0688307i
$825$		0			0
$826$	4.33756	+	4.65261i	0.150923	+	0.161885i
$827$	8.64504			0.300618			0.150309	−	0.988639i	$-0.451973\pi$
$827$	8.64504			0.300618			0.150309	+	0.988639i	$0.451973\pi$
$828$		0			0
$829$	14.7871	+	25.6119i	0.513576	+	0.889540i	0.999876	+	0.0157478i	$0.00501289\pi$
$829$	14.7871	+	25.6119i	0.513576	+	0.889540i	−0.486300	+	0.873792i	$0.661654\pi$
$830$	−0.368479	−	0.638224i	−0.0127901	−	0.0221531i
$831$		0			0
$832$	19.9503	−	11.0548i	0.691653	−	0.383258i
$833$	0.384708	−	5.48222i	0.0133293	−	0.189948i
$834$		0			0
$835$	−24.4617			−0.846531
$836$	−57.0264			−1.97230
$837$		0			0
$838$	−4.04096	+	6.99914i	−0.139593	+	0.241781i
$839$	12.6236	+	21.8648i	0.435817	+	0.754857i	0.997362	−	0.0725895i	$-0.0231263\pi$
$839$	12.6236	+	21.8648i	0.435817	+	0.754857i	−0.561545	+	0.827446i	$0.689793\pi$
$840$		0			0
$841$	11.7347	+	20.3251i	0.404644	+	0.700865i
$842$	10.7406			0.370144
$843$		0			0
$844$	18.3220	−	31.7346i	0.630669	−	1.09235i
$845$	−33.2822	−	1.17195i	−1.14494	−	0.0403164i
$846$		0			0
$847$	−11.7839	+	2.71901i	−0.404900	+	0.0934262i
$848$	16.5817	−	28.7204i	0.569418	−	0.986261i
$849$		0			0
$850$	0.164466	−	0.284864i	0.00564115	−	0.00977076i
$851$	53.7544			1.84268
$852$		0			0
$853$	−35.1368			−1.20306			−0.601531	−	0.798850i	$-0.705442\pi$
$853$	−35.1368			−1.20306			−0.601531	+	0.798850i	$0.705442\pi$
$854$	−6.52900	+	1.50649i	−0.223418	+	0.0515511i
$855$		0			0
$856$	−12.1397			−0.414927
$857$	−0.671345	+	1.16280i	−0.0229327	+	0.0397206i	−0.877264	−	0.480008i	$-0.840634\pi$
$857$	−0.671345	+	1.16280i	−0.0229327	+	0.0397206i	0.854331	+	0.519729i	$0.173967\pi$
$858$		0			0
$859$	−2.38386	−	4.12897i	−0.0813363	−	0.140879i	0.822488	−	0.568783i	$-0.192585\pi$
$859$	−2.38386	−	4.12897i	−0.0813363	−	0.140879i	−0.903824	+	0.427904i	$0.859252\pi$
$860$	−5.55542	+	9.62228i	−0.189438	+	0.328117i
$861$		0			0
$862$	−0.524972	−	0.909278i	−0.0178806	−	0.0309701i
$863$	−13.3052	−	23.0453i	−0.452915	−	0.784472i	0.545650	−	0.838013i	$-0.316283\pi$
$863$	−13.3052	−	23.0453i	−0.452915	−	0.784472i	−0.998566	+	0.0535407i	$0.982949\pi$
$864$		0			0
$865$	−28.5165			−0.969591
$866$	5.46875	+	9.47216i	0.185836	+	0.321877i
$867$		0			0
$868$	−12.6970	+	2.92968i	−0.430963	+	0.0994399i
$869$	12.2185	−	21.1630i	0.414484	−	0.717907i
$870$		0			0
$871$	−4.17981	−	2.51231i	−0.141627	−	0.0851264i
$872$	4.25410	−	7.36831i	0.144062	−	0.249523i
$873$		0			0
$874$	7.99364	−	13.8454i	0.270389	−	0.468328i
$875$	−15.8871	−	17.0410i	−0.537082	−	0.576091i
$876$		0			0
$877$	−4.01848	+	6.96022i	−0.135695	+	0.235030i	−0.925863	−	0.377860i	$-0.876660\pi$
$877$	−4.01848	+	6.96022i	−0.135695	+	0.235030i	0.790168	+	0.612890i	$0.209993\pi$
$878$	−6.85389			−0.231307
$879$		0			0
$880$	18.0633	−	31.2866i	0.608915	−	1.05467i
$881$	−27.3349	+	47.3454i	−0.920935	+	1.59511i	−0.122964	+	0.992411i	$0.539240\pi$
$881$	−27.3349	+	47.3454i	−0.920935	+	1.59511i	−0.797971	+	0.602695i	$0.794093\pi$
$882$		0			0
$883$	−8.45085			−0.284394			−0.142197	−	0.989838i	$-0.545417\pi$
$883$	−8.45085			−0.284394			−0.142197	+	0.989838i	$0.545417\pi$
$884$	−4.77400	+	2.64536i	−0.160567	+	0.0889732i
$885$		0			0
$886$	−3.68088	−	6.37547i	−0.123662	−	0.214188i
$887$	10.3557			0.347710			0.173855	−	0.984771i	$-0.444378\pi$
$887$	10.3557			0.347710			0.173855	+	0.984771i	$0.444378\pi$
$888$		0			0
$889$	−4.60961	+	1.06361i	−0.154601	+	0.0356725i
$890$	2.63174	+	4.55831i	0.0882162	+	0.152795i
$891$		0			0
$892$	−11.5361	+	19.9811i	−0.386256	+	0.669016i
$893$	9.86792			0.330217
$894$		0			0
$895$	−16.1947	+	28.0501i	−0.541330	+	0.937611i
$896$	−14.1185	−	15.1439i	−0.471665	−	0.505923i
$897$		0			0
$898$	−1.98461	−	3.43745i	−0.0662274	−	0.114709i
$899$	−3.00359	−	5.20237i	−0.100175	−	0.173509i
$900$		0			0
$901$	−3.64268	+	6.30931i	−0.121355	+	0.210194i
$902$	−2.57890			−0.0858680
$903$		0			0
$904$	−4.23468	−	7.33467i	−0.140843	−	0.243948i
$905$	−19.1053	−	33.0914i	−0.635082	−	1.09999i
$906$		0			0
$907$	−9.24019	−	16.0045i	−0.306815	−	0.531420i	0.670849	−	0.741594i	$-0.265930\pi$
$907$	−9.24019	−	16.0045i	−0.306815	−	0.531420i	−0.977664	+	0.210175i	$0.932597\pi$
$908$	29.6624			0.984380
$909$		0			0
$910$	1.36059	+	6.40951i	0.0451030	+	0.212473i
$911$	26.6282			0.882230			0.441115	−	0.897451i	$-0.354583\pi$
$911$	26.6282			0.882230			0.441115	+	0.897451i	$0.354583\pi$
$912$		0			0
$913$	2.11687	+	3.66653i	0.0700582	+	0.121344i
$914$	−0.174804			−0.00578202
$915$		0			0
$916$	8.35033	+	14.4632i	0.275903	+	0.477877i
$917$	4.94563	−	16.1693i	0.163319	−	0.533958i
$918$		0			0
$919$	5.57467	−	9.65561i	0.183891	−	0.318509i	−0.759311	−	0.650728i	$-0.774464\pi$
$919$	5.57467	−	9.65561i	0.183891	−	0.318509i	0.943202	+	0.332219i	$0.107797\pi$
$920$	10.7319	+	18.5883i	0.353822	+	0.612837i
$921$		0			0
$922$	1.67518	+	2.90149i	0.0551690	+	0.0955555i
$923$	−38.0605	−	22.8766i	−1.25278	−	0.752993i
$924$		0			0
$925$	−5.27933	+	9.14406i	−0.173583	+	0.300655i
$926$	−0.0829855			−0.00272707
$927$		0			0
$928$	3.60365	−	6.24170i	0.118296	−	0.204894i
$929$	3.87255	−	6.70745i	0.127054	−	0.220064i	−0.795480	−	0.605980i	$-0.792781\pi$
$929$	3.87255	−	6.70745i	0.127054	−	0.220064i	0.922534	+	0.385916i	$0.126114\pi$
$930$		0			0
$931$	43.4898	+	29.3498i	1.42532	+	0.961901i
$932$	−19.5227	−	33.8144i	−0.639489	−	1.10763i
$933$		0			0
$934$	3.28149	+	5.68371i	0.107374	+	0.185977i
$935$	−3.96817	+	6.87306i	−0.129773	+	0.224773i
$936$		0			0
$937$	36.4239			1.18992			0.594959	−	0.803756i	$-0.297168\pi$
$937$	36.4239			1.18992			0.594959	+	0.803756i	$0.297168\pi$
$938$	−0.280643	+	0.917537i	−0.00916331	+	0.0299587i
$939$		0			0
$940$	−3.25145	+	5.63168i	−0.106051	+	0.183685i
$941$	−9.89466	+	17.1381i	−0.322557	+	0.558685i	−0.981015	−	0.193933i	$-0.937876\pi$
$941$	−9.89466	+	17.1381i	−0.322557	+	0.558685i	0.658458	+	0.752617i	$0.271209\pi$
$942$		0			0
$943$	−9.69526	+	16.7927i	−0.315721	+	0.546845i
$944$	32.0454			1.04299
$945$		0			0
$946$	−1.18999	+	2.06112i	−0.0386899	+	0.0670129i
$947$	−9.94796			−0.323265			−0.161633	−	0.986851i	$-0.551676\pi$
$947$	−9.94796			−0.323265			−0.161633	+	0.986851i	$0.551676\pi$
$948$		0			0
$949$	0.0487677	−	2.77076i	0.00158307	−	0.0899427i
$950$	1.57014	+	2.71957i	0.0509422	+	0.0882345i
$951$		0			0
$952$	1.49184	+	1.60019i	0.0483507	+	0.0518625i
$953$	0.0105567	+	0.0182847i	0.000341965	+	0.000592300i	0.866196	−	0.499704i	$-0.166558\pi$
$953$	0.0105567	+	0.0182847i	0.000341965	+	0.000592300i	−0.865854	+	0.500296i	$0.833224\pi$
$954$		0			0
$955$	36.1990			1.17137
$956$	31.9152			1.03221
$957$		0			0
$958$	1.09107	+	1.88979i	0.0352508	+	0.0610562i
$959$	−18.1075	−	19.4227i	−0.584723	−	0.627193i
$960$		0			0
$961$	12.2376	+	21.1962i	0.394761	+	0.683747i
$962$	−5.71383	+	3.16614i	−0.184221	+	0.102081i
$963$		0			0
$964$	31.6224			1.01849
$965$	−4.98842	+	8.64020i	−0.160583	+	0.278138i
$966$		0			0
$967$	−19.8102			−0.637053			−0.318526	−	0.947914i	$-0.603188\pi$
$967$	−19.8102			−0.637053			−0.318526	+	0.947914i	$0.603188\pi$
$968$	2.40711	−	4.16923i	0.0773674	−	0.134004i
$969$		0			0
$970$	0.814635	−	1.41099i	0.0261563	−	0.0453041i
$971$	−1.80887	+	3.13305i	−0.0580493	+	0.100544i	−0.893590	−	0.448885i	$-0.851821\pi$
$971$	−1.80887	+	3.13305i	−0.0580493	+	0.100544i	0.835540	+	0.549429i	$0.185155\pi$
$972$		0			0
$973$	−4.29146	+	14.0306i	−0.137578	+	0.449799i
$974$	1.23595			0.0396024
$975$		0			0
$976$	−16.8782	+	29.2339i	−0.540258	+	0.935755i
$977$	1.08085	+	1.87208i	0.0345793	+	0.0598931i	0.882797	−	0.469754i	$-0.155658\pi$
$977$	1.08085	+	1.87208i	0.0345793	+	0.0598931i	−0.848218	+	0.529648i	$0.822324\pi$
$978$		0			0
$979$	−15.1191	−	26.1870i	−0.483208	−	0.836941i
$980$	−31.0799	+	15.1492i	−0.992810	+	0.483924i
$981$		0			0
$982$	1.74535	−	3.02304i	0.0556965	−	0.0964692i
$983$	−15.0545	+	26.0752i	−0.480165	+	0.831671i	−0.999741	−	0.0227535i	$-0.992757\pi$
$983$	−15.0545	+	26.0752i	−0.480165	+	0.831671i	0.519576	+	0.854424i	$0.326090\pi$
$984$		0			0
$985$	29.9953			0.955730
$986$	−0.247525	+	0.428727i	−0.00788281	+	0.0136534i
$987$		0			0
$988$	0.916973	−	52.0983i	0.0291728	−	1.65747i
$989$	8.94742	+	15.4974i	0.284511	+	0.492788i
$990$		0			0
$991$	13.5730	+	23.5092i	0.431161	+	0.746793i	0.996974	−	0.0777408i	$-0.0247706\pi$
$991$	13.5730	+	23.5092i	0.431161	+	0.746793i	−0.565812	+	0.824534i	$0.691437\pi$
$992$	3.91416	−	6.77953i	0.124275	−	0.215250i
$993$		0			0
$994$	−2.55548	+	8.35491i	−0.0810548	+	0.265002i
$995$	−4.47902	−	7.75790i	−0.141995	−	0.245942i
$996$		0			0
$997$	50.8009			1.60888			0.804441	−	0.594033i	$-0.202465\pi$
$997$	50.8009			1.60888			0.804441	+	0.594033i	$0.202465\pi$
$998$	4.33300	+	7.50497i	0.137159	+	0.237566i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.d.802.3		12
3.2	odd	2		91.2.h.b.74.4	yes	12
7.2	even	3		819.2.n.d.100.4		12
13.3	even	3		819.2.n.d.172.4		12
21.2	odd	6		91.2.g.b.9.3	✓	12
21.5	even	6		637.2.g.l.373.3		12
21.11	odd	6		637.2.f.k.295.3		12
21.17	even	6		637.2.f.j.295.3		12
21.20	even	2		637.2.h.l.165.4		12
39.17	odd	6		1183.2.e.g.508.4		12
39.29	odd	6		91.2.g.b.81.3	yes	12
39.35	odd	6		1183.2.e.h.508.3		12
91.16	even	3	inner	819.2.s.d.289.3		12
273.17	even	6		8281.2.a.cf.1.3		6
273.68	even	6		637.2.h.l.471.4		12
273.74	odd	6		8281.2.a.bz.1.4		6
273.95	odd	6		8281.2.a.ce.1.3		6
273.107	odd	6		91.2.h.b.16.4	yes	12
273.146	even	6		637.2.g.l.263.3		12
273.185	even	6		637.2.f.j.393.3		12
273.191	odd	6		1183.2.e.h.170.3		12
273.212	odd	6		1183.2.e.g.170.4		12
273.263	odd	6		637.2.f.k.393.3		12
273.269	even	6		8281.2.a.ca.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.3	✓	12	21.2	odd	6
91.2.g.b.81.3	yes	12	39.29	odd	6
91.2.h.b.16.4	yes	12	273.107	odd	6
91.2.h.b.74.4	yes	12	3.2	odd	2
637.2.f.j.295.3		12	21.17	even	6
637.2.f.j.393.3		12	273.185	even	6
637.2.f.k.295.3		12	21.11	odd	6
637.2.f.k.393.3		12	273.263	odd	6
637.2.g.l.263.3		12	273.146	even	6
637.2.g.l.373.3		12	21.5	even	6
637.2.h.l.165.4		12	21.20	even	2
637.2.h.l.471.4		12	273.68	even	6
819.2.n.d.100.4		12	7.2	even	3
819.2.n.d.172.4		12	13.3	even	3
819.2.s.d.289.3		12	91.16	even	3	inner
819.2.s.d.802.3		12	1.1	even	1	trivial
1183.2.e.g.170.4		12	273.212	odd	6
1183.2.e.g.508.4		12	39.17	odd	6
1183.2.e.h.170.3		12	273.191	odd	6
1183.2.e.h.508.3		12	39.35	odd	6
8281.2.a.bz.1.4		6	273.74	odd	6
8281.2.a.ca.1.4		6	273.269	even	6
8281.2.a.ce.1.3		6	273.95	odd	6
8281.2.a.cf.1.3		6	273.17	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.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.268125 q^{2} -1.92811 q^{4} +(-1.28088 - 2.21854i) q^{5} +(1.80416 + 1.93520i) q^{7} -1.05323 q^{8} +O(q^{10})\)	\(q+0.268125 q^{2} -1.92811 q^{4} +(-1.28088 - 2.21854i) q^{5} +(1.80416 + 1.93520i) q^{7} -1.05323 q^{8} +(-0.343436 - 0.594848i) q^{10} +(1.97300 + 3.41734i) q^{11} +(-3.15374 + 1.74755i) q^{13} +(0.483741 + 0.518876i) q^{14} +3.57382 q^{16} -0.785100 q^{17} +(3.74764 - 6.49110i) q^{19} +(2.46967 + 4.27760i) q^{20} +(0.529011 + 0.916274i) q^{22} +7.95518 q^{23} +(-0.781294 + 1.35324i) q^{25} +(-0.845598 + 0.468561i) q^{26} +(-3.47862 - 3.73128i) q^{28} +(1.17586 - 2.03666i) q^{29} +(1.27718 - 2.21215i) q^{31} +3.06468 q^{32} -0.210505 q^{34} +(1.98242 - 6.48137i) q^{35} +6.75716 q^{37} +(1.00484 - 1.74043i) q^{38} +(1.34905 + 2.33663i) q^{40} +(-1.21874 + 2.11091i) q^{41} +(1.12473 + 1.94809i) q^{43} +(-3.80416 - 6.58900i) q^{44} +2.13298 q^{46} +(0.658276 + 1.14017i) q^{47} +(-0.490011 + 6.98283i) q^{49} +(-0.209485 + 0.362838i) q^{50} +(6.08076 - 3.36946i) q^{52} +(4.63977 - 8.03632i) q^{53} +(5.05434 - 8.75438i) q^{55} +(-1.90019 - 2.03820i) q^{56} +(0.315279 - 0.546079i) q^{58} +8.96671 q^{59} +(-4.72273 + 8.18002i) q^{61} +(0.342445 - 0.593132i) q^{62} -6.32592 q^{64} +(7.91657 + 4.75832i) q^{65} +(0.676281 + 1.17135i) q^{67} +1.51376 q^{68} +(0.531538 - 1.73782i) q^{70} +(6.15808 + 10.6661i) q^{71} +(-0.384295 + 0.665619i) q^{73} +1.81176 q^{74} +(-7.22585 + 12.5155i) q^{76} +(-3.05363 + 9.98358i) q^{77} +(-3.09642 - 5.36316i) q^{79} +(-4.57763 - 7.92868i) q^{80} +(-0.326774 + 0.565989i) q^{82} +1.07292 q^{83} +(1.00562 + 1.74178i) q^{85} +(0.301568 + 0.522332i) q^{86} +(-2.07801 - 3.59923i) q^{88} -7.66299 q^{89} +(-9.07171 - 2.95027i) q^{91} -15.3384 q^{92} +(0.176501 + 0.305708i) q^{94} -19.2010 q^{95} +(1.18601 + 2.05423i) q^{97} +(-0.131384 + 1.87227i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8	\( 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29} + 16 q^{31} + 16 q^{32} + 32 q^{34} - 20 q^{35} + 26 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} - 32 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} + 41 q^{52} + 2 q^{53} + 9 q^{55} - 9 q^{56} - 8 q^{58} + 26 q^{59} - 5 q^{61} - 5 q^{62} - 30 q^{64} + 5 q^{65} - 11 q^{67} + 58 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} - 6 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} + 7 q^{80} + q^{82} + 54 q^{83} - q^{85} + 7 q^{86} + 8 q^{89} - 23 q^{91} - 54 q^{92} + 45 q^{94} - 12 q^{95} - 35 q^{97} - 20 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^13 + 2 * q^14 - 16 * q^16 + 10 * q^17 - q^19 + q^20 - 5 * q^22 - 2 * q^23 + 7 * q^25 + 16 * q^26 - q^28 - 3 * q^29 + 16 * q^31 + 16 * q^32 + 32 * q^34 - 20 * q^35 + 26 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 - 32 * q^46 + q^47 - 3 * q^49 - 6 * q^50 + 41 * q^52 + 2 * q^53 + 9 * q^55 - 9 * q^56 - 8 * q^58 + 26 * q^59 - 5 * q^61 - 5 * q^62 - 30 * q^64 + 5 * q^65 - 11 * q^67 + 58 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 - 6 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 + 7 * q^80 + q^82 + 54 * q^83 - q^85 + 7 * q^86 + 8 * q^89 - 23 * q^91 - 54 * q^92 + 45 * q^94 - 12 * q^95 - 35 * q^97 - 20 * q^98

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