LMFDB - Embedded newform 162.3.f.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, not 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:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	162.17
Dual form			162.3.f.a.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-0.891042 - 0.157115i) q^{5} +(-5.50064 + 4.61559i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})$	\(q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-0.891042 - 0.157115i) q^{5} +(-5.50064 + 4.61559i) q^{7} +(2.44949 - 1.41421i) q^{8} +(0.639781 - 1.10813i) q^{10} +(-7.28314 + 1.28421i) q^{11} +(-18.3634 + 6.68372i) q^{13} +(-3.47317 - 9.54246i) q^{14} +(0.694593 + 3.93923i) q^{16} +(-12.7824 - 7.37992i) q^{17} +(6.58593 + 11.4072i) q^{19} +(1.16317 + 1.38621i) q^{20} +(1.81615 - 10.2999i) q^{22} +(15.0696 - 17.9592i) q^{23} +(-22.7230 - 8.27051i) q^{25} -27.6364i q^{26} +14.3612 q^{28} +(-13.5277 + 37.1670i) q^{29} +(-9.20424 - 7.72327i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(15.9901 - 13.4173i) q^{34} +(5.62648 - 3.24845i) q^{35} +(33.0149 - 57.1836i) q^{37} +(-18.3448 + 3.23469i) q^{38} +(-2.40479 + 0.875273i) q^{40} +(26.1687 + 71.8979i) q^{41} +(9.66961 + 54.8391i) q^{43} +(12.8094 + 7.39550i) q^{44} +(16.5775 + 28.7131i) q^{46} +(0.204653 + 0.243896i) q^{47} +(0.444665 - 2.52182i) q^{49} +(21.9818 - 26.1969i) q^{50} +(36.7267 + 13.3674i) q^{52} -0.264306i q^{53} +6.69135 q^{55} +(-6.94634 + 19.0849i) q^{56} +(-42.8490 - 35.9545i) q^{58} +(62.3379 + 10.9919i) q^{59} +(-42.4660 + 35.6332i) q^{61} +(14.7157 - 8.49608i) q^{62} +(4.00000 - 6.92820i) q^{64} +(17.4126 - 3.07032i) q^{65} +(58.6251 - 21.3378i) q^{67} +(10.0963 + 27.7394i) q^{68} +(1.59548 + 9.04842i) q^{70} +(-57.0927 - 32.9625i) q^{71} +(22.7040 + 39.3244i) q^{73} +(60.0237 + 71.5335i) q^{74} +(4.57454 - 25.9435i) q^{76} +(34.1346 - 40.6800i) q^{77} +(22.8997 + 8.33480i) q^{79} -3.61915i q^{80} -108.205 q^{82} +(28.1190 - 77.2563i) q^{83} +(10.2302 + 8.58412i) q^{85} +(-77.5542 - 13.6749i) q^{86} +(-16.0238 + 13.4456i) q^{88} +(-115.387 + 66.6186i) q^{89} +(70.1610 - 121.522i) q^{91} +(-46.1759 + 8.14205i) q^{92} +(-0.423109 + 0.153999i) q^{94} +(-4.07611 - 11.1990i) q^{95} +(-11.9691 - 67.8800i) q^{97} +(3.13623 + 1.81071i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{5}+O(q^{10}) $ 36 * q - 18 * q^5	$ 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) $ 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.483690	+	1.32893i	−0.241845	+	0.664463i
$2$	−0.483690	+	1.32893i	−0.241845	+	0.664463i
$3$		0			0
$3$		0			0
$4$	−1.53209	−	1.28558i	−0.383022	−	0.321394i
$5$	−0.891042	−	0.157115i	−0.178208	−	0.0314229i	0.0838318	−	0.996480i	$-0.473284\pi$
$5$	−0.891042	−	0.157115i	−0.178208	−	0.0314229i	−0.262040	+	0.965057i	$0.584395\pi$
$6$		0			0
$7$	−5.50064	+	4.61559i	−0.785806	+	0.659370i	−0.944704	−	0.327925i	$-0.893651\pi$
$7$	−5.50064	+	4.61559i	−0.785806	+	0.659370i	0.158897	+	0.987295i	$0.449206\pi$
$8$	2.44949	−	1.41421i	0.306186	−	0.176777i
$9$		0			0
$10$	0.639781	−	1.10813i	0.0639781	−	0.110813i
$11$	−7.28314	+	1.28421i	−0.662104	+	0.116747i	−0.494595	−	0.869124i	$-0.664683\pi$
$11$	−7.28314	+	1.28421i	−0.662104	+	0.116747i	−0.167509	+	0.985871i	$0.553572\pi$
$12$		0			0
$13$	−18.3634	+	6.68372i	−1.41257	+	0.514132i	−0.931882	−	0.362762i	$-0.881834\pi$
$13$	−18.3634	+	6.68372i	−1.41257	+	0.514132i	−0.480684	+	0.876894i	$0.659612\pi$
$14$	−3.47317	−	9.54246i	−0.248084	−	0.681604i
$15$		0			0
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	−12.7824	−	7.37992i	−0.751906	−	0.434113i	0.0744762	−	0.997223i	$-0.476272\pi$
$17$	−12.7824	−	7.37992i	−0.751906	−	0.434113i	−0.826382	+	0.563110i	$0.809605\pi$
$18$		0			0
$19$	6.58593	+	11.4072i	0.346628	+	0.600377i	0.985648	−	0.168813i	$-0.0539933\pi$
$19$	6.58593	+	11.4072i	0.346628	+	0.600377i	−0.639020	+	0.769190i	$0.720660\pi$
$20$	1.16317	+	1.38621i	0.0581586	+	0.0693107i
$21$		0			0
$22$	1.81615	−	10.2999i	0.0825524	−	0.468178i
$23$	15.0696	−	17.9592i	0.655199	−	0.780836i	−0.331489	−	0.943459i	$-0.607551\pi$
$23$	15.0696	−	17.9592i	0.655199	−	0.780836i	0.986688	+	0.162623i	$0.0519954\pi$
$24$		0			0
$25$	−22.7230	−	8.27051i	−0.908922	−	0.330820i
$26$		−	27.6364i		−	1.06294i
$27$		0			0
$28$	14.3612			0.512899
$29$	−13.5277	+	37.1670i	−0.466471	+	1.28162i	0.454067	+	0.890967i	$0.349973\pi$
$29$	−13.5277	+	37.1670i	−0.466471	+	1.28162i	−0.920538	+	0.390652i	$0.872250\pi$
$30$		0			0
$31$	−9.20424	−	7.72327i	−0.296911	−	0.249138i	0.482146	−	0.876091i	$-0.339857\pi$
$31$	−9.20424	−	7.72327i	−0.296911	−	0.249138i	−0.779057	+	0.626953i	$0.784302\pi$
$32$	−5.57091	−	0.982302i	−0.174091	−	0.0306970i
$33$		0			0
$34$	15.9901	−	13.4173i	0.470297	−	0.394626i
$35$	5.62648	−	3.24845i	0.160757	−	0.0928128i
$36$		0			0
$37$	33.0149	−	57.1836i	0.892296	−	1.54550i	0.0551793	−	0.998476i	$-0.482427\pi$
$37$	33.0149	−	57.1836i	0.892296	−	1.54550i	0.837116	−	0.547025i	$-0.184240\pi$
$38$	−18.3448	+	3.23469i	−0.482758	+	0.0851233i
$39$		0			0
$40$	−2.40479	+	0.875273i	−0.0601198	+	0.0218818i
$41$	26.1687	+	71.8979i	0.638261	+	1.75361i	0.657120	+	0.753786i	$0.271774\pi$
$41$	26.1687	+	71.8979i	0.638261	+	1.75361i	−0.0188592	+	0.999822i	$0.506003\pi$
$42$		0			0
$43$	9.66961	+	54.8391i	0.224875	+	1.27533i	0.862925	+	0.505333i	$0.168630\pi$
$43$	9.66961	+	54.8391i	0.224875	+	1.27533i	−0.638050	+	0.769995i	$0.720259\pi$
$44$	12.8094	+	7.39550i	0.291122	+	0.168079i
$45$		0			0
$46$	16.5775	+	28.7131i	0.360380	+	0.624197i
$47$	0.204653	+	0.243896i	0.00435432	+	0.00518928i	0.768217	−	0.640189i	$-0.221144\pi$
$47$	0.204653	+	0.243896i	0.00435432	+	0.00518928i	−0.763863	+	0.645379i	$0.776700\pi$
$48$		0			0
$49$	0.444665	−	2.52182i	0.00907480	−	0.0514657i
$50$	21.9818	−	26.1969i	0.439636	−	0.523938i
$51$		0			0
$52$	36.7267	+	13.3674i	0.706283	+	0.257066i
$53$		−	0.264306i		−	0.00498691i	−0.999997	−	0.00249346i	$-0.999206\pi$
$53$		−	0.264306i		−	0.00498691i	0.999997	−	0.00249346i	$-0.000793693\pi$
$54$		0			0
$55$	6.69135			0.121661
$56$	−6.94634	+	19.0849i	−0.124042	+	0.340802i
$57$		0			0
$58$	−42.8490	−	35.9545i	−0.738775	−	0.619906i
$59$	62.3379	+	10.9919i	1.05657	+	0.186303i	0.674836	−	0.737968i	$-0.264214\pi$
$59$	62.3379	+	10.9919i	1.05657	+	0.186303i	0.381739	+	0.924270i	$0.375325\pi$
$60$		0			0
$61$	−42.4660	+	35.6332i	−0.696164	+	0.584151i	−0.920679	−	0.390320i	$-0.872364\pi$
$61$	−42.4660	+	35.6332i	−0.696164	+	0.584151i	0.224516	+	0.974470i	$0.427920\pi$
$62$	14.7157	−	8.49608i	0.237349	−	0.137034i
$63$		0			0
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	17.4126	−	3.07032i	0.267887	−	0.0472356i
$66$		0			0
$67$	58.6251	−	21.3378i	0.875001	−	0.318474i	0.134810	−	0.990871i	$-0.456957\pi$
$67$	58.6251	−	21.3378i	0.875001	−	0.318474i	0.740191	+	0.672397i	$0.234735\pi$
$68$	10.0963	+	27.7394i	0.148475	+	0.407933i
$69$		0			0
$70$	1.59548	+	9.04842i	0.0227926	+	0.129263i
$71$	−57.0927	−	32.9625i	−0.804122	−	0.464260i	0.0407882	−	0.999168i	$-0.487013\pi$
$71$	−57.0927	−	32.9625i	−0.804122	−	0.464260i	−0.844911	+	0.534908i	$0.820346\pi$
$72$		0			0
$73$	22.7040	+	39.3244i	0.311013	+	0.538691i	0.978582	−	0.205857i	$-0.0659983\pi$
$73$	22.7040	+	39.3244i	0.311013	+	0.538691i	−0.667569	+	0.744548i	$0.732665\pi$
$74$	60.0237	+	71.5335i	0.811131	+	0.966669i
$75$		0			0
$76$	4.57454	−	25.9435i	0.0601913	−	0.341362i
$77$	34.1346	−	40.6800i	0.443306	−	0.528311i
$78$		0			0
$79$	22.8997	+	8.33480i	0.289869	+	0.105504i	0.482862	−	0.875696i	$-0.339597\pi$
$79$	22.8997	+	8.33480i	0.289869	+	0.105504i	−0.192993	+	0.981200i	$0.561819\pi$
$80$		−	3.61915i		−	0.0452394i
$81$		0			0
$82$	−108.205			−1.31957
$83$	28.1190	−	77.2563i	0.338783	−	0.930799i	−0.646957	−	0.762526i	$-0.723959\pi$
$83$	28.1190	−	77.2563i	0.338783	−	0.930799i	0.985740	−	0.168273i	$-0.0538190\pi$
$84$		0			0
$85$	10.2302	+	8.58412i	0.120355	+	0.100990i
$86$	−77.5542	−	13.6749i	−0.901793	−	0.159010i
$87$		0			0
$88$	−16.0238	+	13.4456i	−0.182089	+	0.152791i
$89$	−115.387	+	66.6186i	−1.29648	+	0.748523i	−0.979794	−	0.200007i	$-0.935903\pi$
$89$	−115.387	+	66.6186i	−1.29648	+	0.748523i	−0.316686	+	0.948530i	$0.602570\pi$
$90$		0			0
$91$	70.1610	−	121.522i	0.771000	−	1.33541i
$92$	−46.1759	+	8.14205i	−0.501912	+	0.0885006i
$93$		0			0
$94$	−0.423109	+	0.153999i	−0.00450115	+	0.00163829i
$95$	−4.07611	−	11.1990i	−0.0429064	−	0.117884i
$96$		0			0
$97$	−11.9691	−	67.8800i	−0.123392	−	0.699794i	−0.982250	−	0.187578i	$-0.939936\pi$
$97$	−11.9691	−	67.8800i	−0.123392	−	0.699794i	0.858857	−	0.512215i	$-0.171175\pi$
$98$	3.13623	+	1.81071i	0.0320024	+	0.0184766i
$99$		0			0
$100$	24.1814	+	41.8833i	0.241814	+	0.418833i
$101$	−114.042	−	135.910i	−1.12913	−	1.34564i	−0.930810	−	0.365503i	$-0.880897\pi$
$101$	−114.042	−	135.910i	−1.12913	−	1.34564i	−0.198316	−	0.980138i	$-0.563547\pi$
$102$		0			0
$103$	−2.96634	+	16.8229i	−0.0287994	+	0.163330i	−0.995816	−	0.0913853i	$-0.970871\pi$
$103$	−2.96634	+	16.8229i	−0.0287994	+	0.163330i	0.967016	+	0.254715i	$0.0819816\pi$
$104$	−35.5287	+	42.3414i	−0.341622	+	0.407129i
$105$		0			0
$106$	0.351244	+	0.127842i	0.00331362	+	0.00120606i
$107$		−	29.1810i		−	0.272719i	−0.990659	−	0.136360i	$-0.956460\pi$
$107$		−	29.1810i		−	0.272719i	0.990659	−	0.136360i	$-0.0435403\pi$
$108$		0			0
$109$	−161.118			−1.47814			−0.739071	−	0.673627i	$-0.764735\pi$
$109$	−161.118			−1.47814			−0.739071	+	0.673627i	$0.764735\pi$
$110$	−3.23654	+	8.89231i	−0.0294231	+	0.0808392i
$111$		0			0
$112$	−22.0026	−	18.4624i	−0.196452	−	0.164842i
$113$	−66.6379	−	11.7501i	−0.589716	−	0.103983i	−0.129176	−	0.991622i	$-0.541233\pi$
$113$	−66.6379	−	11.7501i	−0.589716	−	0.103983i	−0.460540	+	0.887639i	$0.652344\pi$
$114$		0			0
$115$	−16.2493	+	13.6348i	−0.141298	+	0.118563i
$116$	68.5065	−	39.5523i	0.590573	−	0.340968i
$117$		0			0
$118$	−44.7596	+	77.5258i	−0.379318	+	0.656998i
$119$	104.374	−	18.4040i	0.877093	−	0.154655i
$120$		0			0
$121$	−62.3079	+	22.6782i	−0.514941	+	0.187423i
$122$	−26.8135	−	73.6695i	−0.219783	−	0.603849i
$123$		0			0
$124$	4.17286	+	23.6655i	0.0336521	+	0.190851i
$125$	38.5370	+	22.2493i	0.308296	+	0.177995i
$126$		0			0
$127$	26.0758	+	45.1647i	0.205322	+	0.355627i	0.950235	−	0.311534i	$-0.100843\pi$
$127$	26.0758	+	45.1647i	0.205322	+	0.355627i	−0.744914	+	0.667161i	$0.767509\pi$
$128$	7.27231	+	8.66680i	0.0568149	+	0.0677094i
$129$		0			0
$130$	−4.34208	+	24.6252i	−0.0334006	+	0.189424i
$131$	−25.4225	+	30.2974i	−0.194065	+	0.231278i	−0.854298	−	0.519783i	$-0.826013\pi$
$131$	−25.4225	+	30.2974i	−0.194065	+	0.231278i	0.660233	+	0.751060i	$0.270457\pi$
$132$		0			0
$133$	−88.8776	−	32.3488i	−0.668253	−	0.243224i
$134$			88.2292i			0.658427i
$135$		0			0
$136$	−41.7472			−0.306964
$137$	14.7144	−	40.4275i	0.107404	−	0.295091i	−0.874335	−	0.485323i	$-0.838702\pi$
$137$	14.7144	−	40.4275i	0.107404	−	0.295091i	0.981739	+	0.190232i	$0.0609241\pi$
$138$		0			0
$139$	184.188	+	154.552i	1.32509	+	1.11188i	0.985198	+	0.171418i	$0.0548349\pi$
$139$	184.188	+	154.552i	1.32509	+	1.11188i	0.339892	+	0.940465i	$0.389610\pi$
$140$	−12.7964	−	2.25635i	−0.0914028	−	0.0161168i
$141$		0			0
$142$	71.4198	−	59.9284i	0.502957	−	0.422031i
$143$	125.160	−	72.2609i	0.875242	−	0.505321i
$144$		0			0
$145$	17.8932	−	30.9919i	0.123401	−	0.213737i
$146$	−63.2409	+	11.1511i	−0.433157	+	0.0763773i
$147$		0			0
$148$	−124.096	+	45.1671i	−0.838484	+	0.305183i
$149$	11.4189	+	31.3731i	0.0766368	+	0.210558i	0.972095	−	0.234588i	$-0.0753741\pi$
$149$	11.4189	+	31.3731i	0.0766368	+	0.210558i	−0.895458	+	0.445146i	$0.853152\pi$
$150$		0			0
$151$	−24.9315	−	141.394i	−0.165110	−	0.936383i	−0.948951	−	0.315422i	$-0.897854\pi$
$151$	−24.9315	−	141.394i	−0.165110	−	0.936383i	0.783842	−	0.620960i	$-0.213257\pi$
$152$	32.2643	+	18.6278i	0.212265	+	0.122551i
$153$		0			0
$154$	37.5502	+	65.0388i	0.243832	+	0.422330i
$155$	6.98792	+	8.32788i	0.0450834	+	0.0537283i
$156$		0			0
$157$	−20.8900	+	118.473i	−0.133057	+	0.754606i	0.843135	+	0.537701i	$0.180707\pi$
$157$	−20.8900	+	118.473i	−0.133057	+	0.754606i	−0.976193	+	0.216905i	$0.930404\pi$
$158$	−22.1527	+	26.4005i	−0.140207	+	0.167092i
$159$		0			0
$160$	4.80958	+	1.75055i	0.0300599	+	0.0109409i
$161$			168.342i			1.04560i
$162$		0			0
$163$	−228.535			−1.40205			−0.701027	−	0.713134i	$-0.747275\pi$
$163$	−228.535			−1.40205			−0.701027	+	0.713134i	$0.747275\pi$
$164$	52.3374	−	143.796i	0.319131	−	0.876804i
$165$		0			0
$166$	89.0671	+	74.7362i	0.536549	+	0.450218i
$167$	−191.370	−	33.7438i	−1.14593	−	0.202059i	−0.431732	−	0.902002i	$-0.642098\pi$
$167$	−191.370	−	33.7438i	−1.14593	−	0.202059i	−0.714199	+	0.699943i	$0.753209\pi$
$168$		0			0
$169$	163.079	−	136.840i	0.964967	−	0.809704i
$170$	−16.3559	+	9.44308i	−0.0962111	+	0.0555475i
$171$		0			0
$172$	55.6851	−	96.4494i	0.323750	−	0.560752i
$173$	120.900	−	21.3179i	0.698841	−	0.123225i	0.187070	−	0.982347i	$-0.440101\pi$
$173$	120.900	−	21.3179i	0.698841	−	0.123225i	0.511771	+	0.859122i	$0.328990\pi$
$174$		0			0
$175$	163.165	−	59.3871i	0.932369	−	0.339355i
$176$	−10.1176	−	27.7980i	−0.0574866	−	0.157943i
$177$		0			0
$178$	−32.7198	−	185.563i	−0.183819	−	1.04249i
$179$	252.003	+	145.494i	1.40784	+	0.812816i	0.995180	−	0.0980700i	$-0.0312669\pi$
$179$	252.003	+	145.494i	1.40784	+	0.812816i	0.412659	+	0.910886i	$0.364600\pi$
$180$		0			0
$181$	111.720	+	193.505i	0.617239	+	1.06909i	0.989987	+	0.141157i	$0.0450821\pi$
$181$	111.720	+	193.505i	0.617239	+	1.06909i	−0.372748	+	0.927932i	$0.621585\pi$
$182$	127.558	+	152.018i	0.700869	+	0.835263i
$183$		0			0
$184$	11.5146	−	65.3026i	0.0625794	−	0.354905i
$185$	−38.4021	+	45.7658i	−0.207579	+	0.247383i
$186$		0			0
$187$	102.573	+	37.3337i	0.548521	+	0.199645i
$188$		−	0.636768i		−	0.00338706i
$189$		0			0
$190$	16.8542			0.0887064
$191$	−100.749	+	276.805i	−0.527481	+	1.44924i	0.334546	+	0.942379i	$0.391417\pi$
$191$	−100.749	+	276.805i	−0.527481	+	1.44924i	−0.862027	+	0.506863i	$0.830805\pi$
$192$		0			0
$193$	−43.1317	−	36.1918i	−0.223480	−	0.187522i	0.524172	−	0.851612i	$-0.324375\pi$
$193$	−43.1317	−	36.1918i	−0.223480	−	0.187522i	−0.747653	+	0.664090i	$0.768819\pi$
$194$	95.9968	+	16.9268i	0.494829	+	0.0872517i
$195$		0			0
$196$	−3.92326	+	3.29200i	−0.0200166	+	0.0167959i
$197$	−146.685	+	84.6884i	−0.744592	+	0.429891i	−0.823737	−	0.566973i	$-0.808115\pi$
$197$	−146.685	+	84.6884i	−0.744592	+	0.429891i	0.0791444	+	0.996863i	$0.474781\pi$
$198$		0			0
$199$	53.4896	−	92.6468i	0.268792	−	0.465562i	−0.699758	−	0.714380i	$-0.746709\pi$
$199$	53.4896	−	92.6468i	0.268792	−	0.465562i	0.968550	+	0.248818i	$0.0800422\pi$
$200$	−67.3561	+	11.8767i	−0.336781	+	0.0593835i
$201$		0			0
$202$	235.775	−	85.8150i	1.16720	−	0.424827i
$203$	−97.1365	−	266.880i	−0.478505	−	1.31468i
$204$		0			0
$205$	−12.0212	−	68.1755i	−0.0586399	−	0.332564i
$206$	−20.9217	−	12.0791i	−0.101561	−	0.0586365i
$207$		0			0
$208$	−39.0838	−	67.6951i	−0.187903	−	0.325457i
$209$	−62.6155	−	74.6222i	−0.299596	−	0.357044i
$210$		0			0
$211$	6.11577	−	34.6843i	0.0289847	−	0.164380i	−0.966880	−	0.255233i	$-0.917848\pi$
$211$	6.11577	−	34.6843i	0.0289847	−	0.164380i	0.995864	+	0.0908522i	$0.0289591\pi$
$212$	−0.339786	+	0.404941i	−0.00160276	+	0.00191010i
$213$		0			0
$214$	38.7793	+	14.1145i	0.181212	+	0.0659557i
$215$		−	50.3832i		−	0.234340i
$216$		0			0
$217$	86.2767			0.397588
$218$	77.9309	−	214.113i	0.357481	−	0.982171i
$219$		0			0
$220$	−10.2517	−	8.60224i	−0.0465989	−	0.0391011i
$221$	284.053	+	50.0862i	1.28531	+	0.226635i
$222$		0			0
$223$	−83.0007	+	69.6459i	−0.372200	+	0.312313i	−0.809631	−	0.586939i	$-0.800333\pi$
$223$	−83.0007	+	69.6459i	−0.372200	+	0.312313i	0.437431	+	0.899252i	$0.355888\pi$
$224$	35.1775	−	20.3097i	0.157042	−	0.0906685i
$225$		0			0
$226$	47.8470	−	82.8735i	0.211713	−	0.366697i
$227$	223.383	−	39.3885i	0.984068	−	0.173518i	0.341613	−	0.939841i	$-0.389027\pi$
$227$	223.383	−	39.3885i	0.984068	−	0.173518i	0.642455	+	0.766323i	$0.277916\pi$
$228$		0			0
$229$	−197.382	+	71.8412i	−0.861930	+	0.313717i	−0.734895	−	0.678181i	$-0.762768\pi$
$229$	−197.382	+	71.8412i	−0.861930	+	0.313717i	−0.127035	+	0.991898i	$0.540546\pi$
$230$	−10.2600	−	28.1891i	−0.0446087	−	0.122561i
$231$		0			0
$232$	19.4261	+	110.171i	0.0837334	+	0.474875i
$233$	−36.1880	−	20.8932i	−0.155313	−	0.0896702i	0.420329	−	0.907372i	$-0.361915\pi$
$233$	−36.1880	−	20.8932i	−0.155313	−	0.0896702i	−0.575642	+	0.817702i	$0.695248\pi$
$234$		0			0
$235$	−0.144035	−	0.249476i	−0.000612914	−	0.00106160i
$236$	−81.3764	−	96.9806i	−0.344815	−	0.410935i
$237$		0			0
$238$	−26.0271	+	147.607i	−0.109358	+	0.620199i
$239$	−239.745	+	285.717i	−1.00312	+	1.19547i	−0.0224583	+	0.999748i	$0.507149\pi$
$239$	−239.745	+	285.717i	−1.00312	+	1.19547i	−0.980660	+	0.195722i	$0.937295\pi$
$240$		0			0
$241$	−109.123	−	39.7174i	−0.452792	−	0.164803i	0.105550	−	0.994414i	$-0.466340\pi$
$241$	−109.123	−	39.7174i	−0.452792	−	0.164803i	−0.558341	+	0.829611i	$0.688562\pi$
$242$		−	93.7718i		−	0.387487i
$243$		0			0
$244$	110.871			0.454388
$245$	−0.792430	+	2.17718i	−0.00323441	+	0.00888647i
$246$		0			0
$247$	−197.182	−	165.455i	−0.798308	−	0.669860i
$248$	−33.4680	−	5.90132i	−0.134952	−	0.0237956i
$249$		0			0
$250$	−48.2077	+	40.4510i	−0.192831	+	0.161804i
$251$	160.201	−	92.4920i	0.638251	−	0.368494i	−0.145690	−	0.989330i	$-0.546540\pi$
$251$	160.201	−	92.4920i	0.638251	−	0.368494i	0.783940	+	0.620836i	$0.213207\pi$
$252$		0			0
$253$	−86.6904	+	150.152i	−0.342650	+	0.593487i
$254$	−72.6331	+	12.8072i	−0.285957	+	0.0504220i
$255$		0			0
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	33.0286	+	90.7454i	0.128516	+	0.353095i	0.987217	−	0.159382i	$-0.0509502\pi$
$257$	33.0286	+	90.7454i	0.128516	+	0.353095i	−0.858701	+	0.512477i	$0.828728\pi$
$258$		0			0
$259$	82.3323	+	466.930i	0.317885	+	1.80282i
$260$	−30.6248	−	17.6813i	−0.117788	−	0.0680048i
$261$		0			0
$262$	−27.9664	−	48.4392i	−0.106742	−	0.184882i
$263$	−8.89610	−	10.6020i	−0.0338255	−	0.0403116i	0.748866	−	0.662721i	$-0.230598\pi$
$263$	−8.89610	−	10.6020i	−0.0338255	−	0.0403116i	−0.782692	+	0.622409i	$0.786154\pi$
$264$		0			0
$265$	−0.0415264	+	0.235508i	−0.000156704	+	0.000888710i
$266$	85.9783	−	102.465i	0.323227	−	0.385207i
$267$		0			0
$268$	−117.250	−	42.6756i	−0.437501	−	0.159237i
$269$			52.5454i			0.195336i	0.995219	+	0.0976680i	$0.0311383\pi$
$269$			52.5454i			0.195336i	−0.995219	+	0.0976680i	$0.968862\pi$
$270$		0			0
$271$	−282.779			−1.04346			−0.521732	−	0.853109i	$-0.674714\pi$
$271$	−282.779			−1.04346			−0.521732	+	0.853109i	$0.674714\pi$
$272$	20.1927	−	55.4789i	0.0742377	−	0.203966i
$273$		0			0
$274$	46.6079	+	39.1087i	0.170102	+	0.142732i
$275$	176.116	+	31.0540i	0.640423	+	0.112924i
$276$		0			0
$277$	62.3862	−	52.3482i	0.225221	−	0.188983i	−0.523194	−	0.852214i	$-0.675260\pi$
$277$	62.3862	−	52.3482i	0.225221	−	0.188983i	0.748415	+	0.663231i	$0.230815\pi$
$278$	−294.477	+	170.017i	−1.05927	+	0.611570i
$279$		0			0
$280$	9.18800	−	15.9141i	0.0328143	−	0.0568360i
$281$	−206.646	+	36.4372i	−0.735393	+	0.129670i	−0.528787	−	0.848754i	$-0.677353\pi$
$281$	−206.646	+	36.4372i	−0.735393	+	0.129670i	−0.206606	+	0.978424i	$0.566242\pi$
$282$		0			0
$283$	60.4622	−	22.0064i	0.213647	−	0.0777612i	−0.232979	−	0.972482i	$-0.574847\pi$
$283$	60.4622	−	22.0064i	0.213647	−	0.0777612i	0.446627	+	0.894720i	$0.352625\pi$
$284$	45.0953	+	123.898i	0.158786	+	0.436262i
$285$		0			0
$286$	35.4911	+	201.280i	0.124095	+	0.703775i
$287$	−475.796	−	274.701i	−1.65783	−	0.957146i
$288$		0			0
$289$	−35.5735	−	61.6150i	−0.123092	−	0.213201i
$290$	32.5312	+	38.7692i	0.112177	+	0.133687i
$291$		0			0
$292$	15.7700	−	89.4362i	0.0540069	−	0.306288i
$293$	88.2641	−	105.189i	0.301243	−	0.359007i	−0.594095	−	0.804395i	$-0.702490\pi$
$293$	88.2641	−	105.189i	0.301243	−	0.359007i	0.895338	+	0.445388i	$0.146934\pi$
$294$		0			0
$295$	−53.8187	−	19.5884i	−0.182436	−	0.0664014i
$296$		−	186.761i		−	0.630948i
$297$		0			0
$298$	−47.2158			−0.158442
$299$	−156.694	+	430.513i	−0.524060	+	1.43984i
$300$		0			0
$301$	−306.304	−	257.019i	−1.01762	−	0.853885i
$302$	199.961	+	35.2585i	0.662123	+	0.116750i
$303$		0			0
$304$	−40.3609	+	33.8668i	−0.132766	+	0.111404i
$305$	43.4375	−	25.0786i	0.142418	−	0.0822250i
$306$		0			0
$307$	−181.401	+	314.195i	−0.590882	+	1.02344i	0.403232	+	0.915098i	$0.367887\pi$
$307$	−181.401	+	314.195i	−0.590882	+	1.02344i	−0.994114	+	0.108340i	$0.965447\pi$
$308$	−104.594	+	18.4428i	−0.339592	+	0.0598792i
$309$		0			0
$310$	−14.4471	+	5.25832i	−0.0466036	+	0.0169623i
$311$	−75.3296	−	206.966i	−0.242217	−	0.665487i	−0.999917	−	0.0128834i	$-0.995899\pi$
$311$	−75.3296	−	206.966i	−0.242217	−	0.665487i	0.757700	−	0.652603i	$-0.226323\pi$
$312$		0			0
$313$	−7.54061	−	42.7650i	−0.0240914	−	0.136629i	0.970390	−	0.241544i	$-0.0776540\pi$
$313$	−7.54061	−	42.7650i	−0.0240914	−	0.136629i	−0.994481	+	0.104915i	$0.966543\pi$
$314$	−147.338	−	85.0655i	−0.469228	−	0.270909i
$315$		0			0
$316$	−24.3693	−	42.2089i	−0.0771181	−	0.133572i
$317$	−78.0234	−	92.9846i	−0.246131	−	0.293327i	0.628808	−	0.777560i	$-0.283543\pi$
$317$	−78.0234	−	92.9846i	−0.246131	−	0.293327i	−0.874939	+	0.484233i	$0.839099\pi$
$318$		0			0
$319$	50.7936	−	288.065i	0.159228	−	0.903024i
$320$	−4.65269	+	5.54486i	−0.0145397	+	0.0173277i
$321$		0			0
$322$	−223.714	−	81.4254i	−0.694765	−	0.252874i
$323$		−	194.415i		−	0.601903i
$324$		0			0
$325$	472.549			1.45400
$326$	110.540	−	303.706i	0.339080	−	0.931613i
$327$		0			0
$328$	165.779	+	139.105i	0.505424	+	0.424101i
$329$	−2.25145	−	0.396991i	−0.00684331	−	0.00120666i
$330$		0			0
$331$	−106.552	+	89.4075i	−0.321908	+	0.270113i	−0.789393	−	0.613888i	$-0.789605\pi$
$331$	−106.552	+	89.4075i	−0.321908	+	0.270113i	0.467485	+	0.884001i	$0.345160\pi$
$332$	−142.400	+	82.2145i	−0.428915	+	0.247634i
$333$		0			0
$334$	137.407	−	237.996i	0.411398	−	0.712562i
$335$	−55.5899	+	9.80199i	−0.165940	+	0.0292597i
$336$		0			0
$337$	−22.7816	+	8.29181i	−0.0676010	+	0.0246048i	−0.375599	−	0.926782i	$-0.622563\pi$
$337$	−22.7816	+	8.29181i	−0.0676010	+	0.0246048i	0.307998	+	0.951387i	$0.400341\pi$
$338$	102.970	+	282.909i	0.304646	+	0.837008i
$339$		0			0
$340$	−4.63798	−	26.3033i	−0.0136411	−	0.0773626i
$341$	76.9541	+	44.4295i	0.225672	+	0.130292i
$342$		0			0
$343$	−166.730	−	288.786i	−0.486095	−	0.841941i
$344$	101.240	+	120.653i	0.294302	+	0.350735i
$345$		0			0
$346$	−30.1480	+	170.978i	−0.0871329	+	0.494155i
$347$	163.919	−	195.352i	0.472390	−	0.562973i	−0.476258	−	0.879306i	$-0.658007\pi$
$347$	163.919	−	195.352i	0.472390	−	0.562973i	0.948648	+	0.316333i	$0.102452\pi$
$348$		0			0
$349$	588.280	+	214.116i	1.68562	+	0.613514i	0.994062	−	0.108811i	$-0.0347042\pi$
$349$	588.280	+	214.116i	1.68562	+	0.613514i	0.691554	+	0.722325i	$0.256926\pi$
$350$			245.559i			0.701596i
$351$		0			0
$352$	41.8352			0.118850
$353$	−45.8606	+	126.001i	−0.129917	+	0.356944i	−0.987547	−	0.157323i	$-0.949714\pi$
$353$	−45.8606	+	126.001i	−0.129917	+	0.356944i	0.857630	+	0.514267i	$0.171936\pi$
$354$		0			0
$355$	45.6931	+	38.3410i	0.128713	+	0.108003i
$356$	262.426	+	46.2728i	0.737152	+	0.129980i
$357$		0			0
$358$	−315.242	+	264.519i	−0.880564	+	0.738881i
$359$	480.602	−	277.476i	1.33872	−	0.772913i	0.352107	−	0.935960i	$-0.385465\pi$
$359$	480.602	−	277.476i	1.33872	−	0.772913i	0.986618	+	0.163047i	$0.0521321\pi$
$360$		0			0
$361$	93.7511	−	162.382i	0.259698	−	0.449811i
$362$	−311.192	+	54.8715i	−0.859646	+	0.151579i
$363$		0			0
$364$	−263.719	+	95.9859i	−0.724503	+	0.263698i
$365$	−14.0517	−	38.6068i	−0.0384979	−	0.105772i
$366$		0			0
$367$	31.4908	+	178.593i	0.0858061	+	0.486630i	0.997180	+	0.0750505i	$0.0239118\pi$
$367$	31.4908	+	178.593i	0.0858061	+	0.486630i	−0.911374	+	0.411580i	$0.864977\pi$
$368$	81.2128	+	46.8882i	0.220687	+	0.127414i
$369$		0			0
$370$	−42.2447	−	73.1699i	−0.114175	−	0.197757i
$371$	1.21993	+	1.45386i	0.00328822	+	0.00391875i
$372$		0			0
$373$	61.7520	−	350.213i	0.165555	−	0.938909i	−0.782935	−	0.622103i	$-0.786278\pi$
$373$	61.7520	−	350.213i	0.165555	−	0.938909i	0.948490	−	0.316806i	$-0.102610\pi$
$374$	−99.2274	+	118.255i	−0.265314	+	0.316189i
$375$		0			0
$376$	0.846217	+	0.307998i	0.00225058	+	0.000819143i
$377$		−	772.925i		−	2.05020i
$378$		0			0
$379$	571.606			1.50819			0.754097	−	0.656763i	$-0.228075\pi$
$379$	571.606			1.50819			0.754097	+	0.656763i	$0.228075\pi$
$380$	−8.15221	+	22.3980i	−0.0214532	+	0.0589421i
$381$		0			0
$382$	−319.123	−	267.776i	−0.835399	−	0.700983i
$383$	−410.213	−	72.3315i	−1.07105	−	0.188855i	−0.389796	−	0.920901i	$-0.627454\pi$
$383$	−410.213	−	72.3315i	−1.07105	−	0.188855i	−0.681255	+	0.732046i	$0.738566\pi$
$384$		0			0
$385$	−36.8067	+	30.8845i	−0.0956019	+	0.0802195i
$386$	68.9586	−	39.8133i	0.178649	−	0.103143i
$387$		0			0
$388$	−68.9271	+	119.385i	−0.177647	+	0.307694i
$389$	181.375	−	31.9812i	0.466259	−	0.0822140i	0.0644168	−	0.997923i	$-0.479481\pi$
$389$	181.375	−	31.9812i	0.466259	−	0.0822140i	0.401842	+	0.915709i	$0.368370\pi$
$390$		0			0
$391$	−325.163	+	118.350i	−0.831620	+	0.302685i
$392$	−2.47719	−	6.80602i	−0.00631936	−	0.0173623i
$393$		0			0
$394$	−41.5948	−	235.896i	−0.105571	−	0.598721i
$395$	−19.0950	−	11.0245i	−0.0483419	−	0.0279102i
$396$		0			0
$397$	145.068	+	251.265i	0.365411	+	0.632910i	0.988842	−	0.148968i	$-0.0475952\pi$
$397$	145.068	+	251.265i	0.365411	+	0.632910i	−0.623431	+	0.781878i	$0.714262\pi$
$398$	97.2483	+	115.896i	0.244343	+	0.291196i
$399$		0			0
$400$	16.7962	−	95.2560i	0.0419905	−	0.238140i
$401$	290.603	−	346.328i	0.724697	−	0.863660i	−0.270381	−	0.962753i	$-0.587150\pi$
$401$	290.603	−	346.328i	0.724697	−	0.863660i	0.995078	+	0.0990934i	$0.0315943\pi$
$402$		0			0
$403$	220.641	+	80.3067i	0.547496	+	0.199272i
$404$			354.835i			0.878305i
$405$		0			0
$406$	401.648			0.989281
$407$	−167.017	+	458.874i	−0.410360	+	1.12745i
$408$		0			0
$409$	226.326	+	189.910i	0.553363	+	0.464327i	0.876078	−	0.482169i	$-0.160151\pi$
$409$	226.326	+	189.910i	0.553363	+	0.464327i	−0.322715	+	0.946496i	$0.604595\pi$
$410$	96.4148	+	17.0005i	0.235158	+	0.0414647i
$411$		0			0
$412$	26.1719	−	21.9608i	0.0635239	−	0.0533029i
$413$	−393.632	+	227.264i	−0.953105	+	0.550276i
$414$		0			0
$415$	−37.1933	+	64.4207i	−0.0896225	+	0.155231i
$416$	108.866	−	19.1960i	0.261697	−	0.0461443i
$417$		0			0
$418$	129.454	−	47.1174i	0.309698	−	0.112721i
$419$	184.754	+	507.608i	0.440941	+	1.21147i	0.938875	+	0.344259i	$0.111870\pi$
$419$	184.754	+	507.608i	0.440941	+	1.21147i	−0.497934	+	0.867215i	$0.665908\pi$
$420$		0			0
$421$	−58.5712	−	332.174i	−0.139124	−	0.789011i	−0.971899	−	0.235399i	$-0.924360\pi$
$421$	−58.5712	−	332.174i	−0.139124	−	0.789011i	0.832775	−	0.553612i	$-0.186751\pi$
$422$	43.1347	+	24.9038i	0.102215	+	0.0590138i
$423$		0			0
$424$	−0.373786	−	0.647416i	−0.000881570	−	0.00152692i
$425$	229.419	+	273.411i	0.539810	+	0.643321i
$426$		0			0
$427$	69.1221	−	392.011i	0.161878	−	0.918058i
$428$	−37.5143	+	44.7078i	−0.0876503	+	0.104458i
$429$		0			0
$430$	66.9555	+	24.3698i	0.155710	+	0.0566740i
$431$			625.633i			1.45158i	0.687914	+	0.725792i	$0.258527\pi$
$431$			625.633i			1.45158i	−0.687914	+	0.725792i	$0.741473\pi$
$432$		0			0
$433$	754.656			1.74286			0.871428	−	0.490524i	$-0.163195\pi$
$433$	754.656			1.74286			0.871428	+	0.490524i	$0.163195\pi$
$434$	−41.7311	+	114.655i	−0.0961546	+	0.264183i
$435$		0			0
$436$	246.846	+	207.129i	0.566161	+	0.475066i
$437$	304.111	+	53.6230i	0.695906	+	0.122707i
$438$		0			0
$439$	130.229	−	109.276i	0.296650	−	0.248919i	−0.482298	−	0.876007i	$-0.660198\pi$
$439$	130.229	−	109.276i	0.296650	−	0.248919i	0.778948	+	0.627088i	$0.215753\pi$
$440$	16.3904	−	9.46300i	0.0372509	−	0.0215068i
$441$		0			0
$442$	−203.954	+	353.260i	−0.461435	+	0.799230i
$443$	−16.3964	+	2.89112i	−0.0370121	+	0.00652623i	−0.192124	−	0.981371i	$-0.561537\pi$
$443$	−16.3964	+	2.89112i	−0.0370121	+	0.00652623i	0.155111	+	0.987897i	$0.450426\pi$
$444$		0			0
$445$	113.281	−	41.2310i	0.254564	−	0.0926539i
$446$	−52.4076	−	143.989i	−0.117506	−	0.322845i
$447$		0			0
$448$	9.97516	+	56.5719i	0.0222660	+	0.126277i
$449$	584.655	+	337.551i	1.30213	+	0.751784i	0.980769	−	0.195174i	$-0.0625272\pi$
$449$	584.655	+	337.551i	1.30213	+	0.751784i	0.321359	+	0.946958i	$0.395860\pi$
$450$		0			0
$451$	−282.923	−	490.037i	−0.627323	−	1.08656i
$452$	86.9896	+	103.670i	0.192455	+	0.229359i
$453$		0			0
$454$	−55.7038	+	315.912i	−0.122696	+	0.695841i
$455$	−81.6094	+	97.2583i	−0.179361	+	0.213754i
$456$		0			0
$457$	−504.675	−	183.687i	−1.10432	−	0.401940i	−0.275414	−	0.961326i	$-0.588815\pi$
$457$	−504.675	−	183.687i	−1.10432	−	0.401940i	−0.828908	+	0.559385i	$0.811037\pi$
$458$		−	297.055i		−	0.648591i
$459$		0			0
$460$	42.4239			0.0922258
$461$	111.541	−	306.457i	0.241955	−	0.664765i	−0.757968	−	0.652292i	$-0.773808\pi$
$461$	111.541	−	306.457i	0.241955	−	0.664765i	0.999922	−	0.0124727i	$-0.00397027\pi$
$462$		0			0
$463$	−170.249	−	142.856i	−0.367708	−	0.308544i	0.440146	−	0.897926i	$-0.354927\pi$
$463$	−170.249	−	142.856i	−0.367708	−	0.308544i	−0.807854	+	0.589382i	$0.799371\pi$
$464$	−155.805	−	27.4727i	−0.335788	−	0.0592084i
$465$		0			0
$466$	45.2692	−	37.9854i	0.0971443	−	0.0815137i
$467$	80.9832	−	46.7556i	0.173411	−	0.100119i	−0.410782	−	0.911734i	$-0.634744\pi$
$467$	80.9832	−	46.7556i	0.173411	−	0.100119i	0.584193	+	0.811614i	$0.301411\pi$
$468$		0			0
$469$	−223.989	+	387.961i	−0.477589	+	0.827208i
$470$	0.401203	−	0.0707429i	0.000853623	−	0.000150517i
$471$		0			0
$472$	168.241	−	61.2347i	0.356443	−	0.129734i
$473$	−140.850	−	386.983i	−0.297781	−	0.818146i
$474$		0			0
$475$	−55.3093	−	313.675i	−0.116441	−	0.660367i
$476$	−183.570	−	105.984i	−0.385652	−	0.222656i
$477$		0			0
$478$	−263.735	−	456.802i	−0.551746	−	0.955653i
$479$	7.97154	+	9.50011i	0.0166420	+	0.0198332i	0.774301	−	0.632817i	$-0.218102\pi$
$479$	7.97154	+	9.50011i	0.0166420	+	0.0198332i	−0.757659	+	0.652650i	$0.773657\pi$
$480$		0			0
$481$	−224.067	+	1270.74i	−0.465835	+	2.64188i
$482$	105.563	−	125.805i	0.219011	−	0.261007i
$483$		0			0
$484$	124.616	+	45.3564i	0.257471	+	0.0937116i
$485$			62.3644i			0.128586i
$486$		0			0
$487$	−551.768			−1.13299			−0.566497	−	0.824064i	$-0.691702\pi$
$487$	−551.768			−1.13299			−0.566497	+	0.824064i	$0.691702\pi$
$488$	−53.6270	+	147.339i	−0.109891	+	0.301924i
$489$		0			0
$490$	−2.51003	−	2.10616i	−0.00512250	−	0.00429829i
$491$	−803.339	−	141.650i	−1.63613	−	0.288494i	−0.721387	−	0.692532i	$-0.756495\pi$
$491$	−803.339	−	141.650i	−1.63613	−	0.288494i	−0.914742	+	0.404038i	$0.867606\pi$
$492$		0			0
$493$	447.205	−	375.250i	0.907110	−	0.761156i
$494$	315.253	−	182.011i	0.638164	−	0.368444i
$495$		0			0
$496$	24.0306	−	41.6221i	0.0484487	−	0.0839156i
$497$	466.188	−	82.2015i	0.938003	−	0.165395i
$498$		0			0
$499$	270.216	−	98.3506i	0.541515	−	0.197095i	−0.0567575	−	0.998388i	$-0.518076\pi$
$499$	270.216	−	98.3506i	0.541515	−	0.197095i	0.598273	+	0.801293i	$0.295854\pi$
$500$	−30.4389	−	83.6302i	−0.0608778	−	0.167260i
$501$		0			0
$502$	45.4276	+	257.633i	0.0904932	+	0.513212i
$503$	22.2054	+	12.8203i	0.0441459	+	0.0254877i	0.521911	−	0.853000i	$-0.325219\pi$
$503$	22.2054	+	12.8203i	0.0441459	+	0.0254877i	−0.477765	+	0.878488i	$0.658553\pi$
$504$		0			0
$505$	80.2626	+	139.019i	0.158936	+	0.275285i
$506$	−157.610	−	187.832i	−0.311482	−	0.371210i
$507$		0			0
$508$	18.1121	−	102.719i	0.0356537	−	0.202202i
$509$	−80.2854	+	95.6804i	−0.157732	+	0.187977i	−0.839123	−	0.543942i	$-0.816931\pi$
$509$	−80.2854	+	95.6804i	−0.157732	+	0.187977i	0.681391	+	0.731920i	$0.261375\pi$
$510$		0			0
$511$	−306.392	−	111.517i	−0.599593	−	0.218234i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−136.570			−0.265699
$515$	5.28627	−	14.5239i	0.0102646	−	0.0282017i
$516$		0			0
$517$	−1.80373	−	1.51351i	−0.00348884	−	0.00292749i
$518$	−660.338	−	116.435i	−1.27478	−	0.224779i
$519$		0			0
$520$	38.3100	−	32.1459i	0.0736730	−	0.0618190i
$521$	−23.1236	+	13.3504i	−0.0443831	+	0.0256246i	−0.522027	−	0.852929i	$-0.674824\pi$
$521$	−23.1236	+	13.3504i	−0.0443831	+	0.0256246i	0.477644	+	0.878553i	$0.341491\pi$
$522$		0			0
$523$	−361.405	+	625.972i	−0.691023	+	1.19689i	0.280480	+	0.959860i	$0.409506\pi$
$523$	−361.405	+	625.972i	−0.691023	+	1.19689i	−0.971503	+	0.237027i	$0.923827\pi$
$524$	77.8991	−	13.7357i	0.148662	−	0.0262132i
$525$		0			0
$526$	18.3922	−	6.69420i	0.0349661	−	0.0127266i
$527$	60.6551	+	166.649i	0.115095	+	0.316221i
$528$		0			0
$529$	−3.58173	−	20.3130i	−0.00677075	−	0.0383988i
$530$	−0.292887	−	0.169098i	−0.000552617	−	0.000319053i
$531$		0			0
$532$	94.5816	+	163.820i	0.177785	+	0.307933i
$533$	−961.091	−	1145.38i	−1.80317	−	2.14894i
$534$		0			0
$535$	−4.58476	+	26.0015i	−0.00856964	+	0.0486009i
$536$	113.425	−	135.175i	0.211614	−	0.252192i
$537$		0			0
$538$	−69.8289	−	25.4157i	−0.129794	−	0.0472410i
$539$			18.9378i			0.0351351i
$540$		0			0
$541$	−181.539			−0.335562			−0.167781	−	0.985824i	$-0.553660\pi$
$541$	−181.539			−0.335562			−0.167781	+	0.985824i	$0.553660\pi$
$542$	136.777	−	375.792i	0.252356	−	0.693343i
$543$		0			0
$544$	63.9603	+	53.6691i	0.117574	+	0.0986564i
$545$	143.562	+	25.3139i	0.263417	+	0.0464476i
$546$		0			0
$547$	−584.502	+	490.456i	−1.06856	+	0.896628i	−0.994921	−	0.100657i	$-0.967906\pi$
$547$	−584.502	+	490.456i	−1.06856	+	0.896628i	−0.0736388	+	0.997285i	$0.523461\pi$
$548$	−74.5163	+	43.0220i	−0.135979	+	0.0785073i
$549$		0			0
$550$	−126.454	+	219.025i	−0.229917	+	0.398227i
$551$	−513.062	+	90.4667i	−0.931147	+	0.164186i
$552$		0			0
$553$	−164.433	+	59.8487i	−0.297347	+	0.108225i
$554$	39.3914	+	108.227i	0.0711036	+	0.195356i
$555$		0			0
$556$	−83.5038	−	473.574i	−0.150187	−	0.851752i
$557$	−154.424	−	89.1568i	−0.277243	−	0.160066i	0.354932	−	0.934892i	$-0.384504\pi$
$557$	−154.424	−	89.1568i	−0.277243	−	0.160066i	−0.632174	+	0.774826i	$0.717837\pi$
$558$		0			0
$559$	−544.096	−	942.401i	−0.973337	−	1.68587i
$560$	16.7045	+	19.9077i	0.0298295	+	0.0355494i
$561$		0			0
$562$	51.5300	−	292.241i	0.0916903	−	0.520002i
$563$	83.6205	−	99.6550i	0.148527	−	0.177007i	−0.686651	−	0.726987i	$-0.740920\pi$
$563$	83.6205	−	99.6550i	0.148527	−	0.177007i	0.835178	+	0.549980i	$0.185365\pi$
$564$		0			0
$565$	57.5311	+	20.9396i	0.101825	+	0.0370612i
$566$			90.9940i			0.160767i
$567$		0			0
$568$	−186.464			−0.328282
$569$	334.788	−	919.824i	0.588380	−	1.61656i	−0.185084	−	0.982723i	$-0.559256\pi$
$569$	334.788	−	919.824i	0.588380	−	1.61656i	0.773465	−	0.633839i	$-0.218522\pi$
$570$		0			0
$571$	353.588	+	296.696i	0.619244	+	0.519607i	0.897566	−	0.440880i	$-0.145334\pi$
$571$	353.588	+	296.696i	0.619244	+	0.519607i	−0.278322	+	0.960488i	$0.589778\pi$
$572$	−284.653	−	50.1919i	−0.497644	−	0.0877481i
$573$		0			0
$574$	595.195	−	499.428i	1.03692	−	0.870083i
$575$	−490.959	+	283.455i	−0.853842	+	0.492966i
$576$		0			0
$577$	−192.832	+	333.994i	−0.334197	+	0.578846i	−0.983330	−	0.181829i	$-0.941798\pi$
$577$	−192.832	+	333.994i	−0.334197	+	0.578846i	0.649133	+	0.760675i	$0.275132\pi$
$578$	99.0883	−	17.4719i	0.171433	−	0.0302283i
$579$		0			0
$580$	−67.2564	+	24.4793i	−0.115959	+	0.0422057i
$581$	201.911	+	554.745i	0.347523	+	0.954811i
$582$		0			0
$583$	0.339426	+	1.92498i	0.000582206	+	0.00330185i
$584$	111.226	+	64.2165i	0.190456	+	0.109960i
$585$		0			0
$586$	97.0961	+	168.175i	0.165693	+	0.286989i
$587$	633.940	+	755.500i	1.07997	+	1.28705i	0.955552	+	0.294823i	$0.0952607\pi$
$587$	633.940	+	755.500i	1.07997	+	1.28705i	0.124414	+	0.992230i	$0.460295\pi$
$588$		0			0
$589$	27.4822	−	155.859i	0.0466590	−	0.264617i
$590$	52.0631	−	62.0464i	0.0882425	−	0.105163i
$591$		0			0
$592$	248.191	+	90.3342i	0.419242	+	0.152592i
$593$			216.884i			0.365741i	0.983137	+	0.182870i	$0.0585388\pi$
$593$			216.884i			0.365741i	−0.983137	+	0.182870i	$0.941461\pi$
$594$		0			0
$595$	−95.8932			−0.161165
$596$	22.8378	−	62.7463i	0.0383184	−	0.105279i
$597$		0			0
$598$	−496.328	−	416.469i	−0.829981	−	0.696436i
$599$	−641.044	−	113.033i	−1.07019	−	0.188703i	−0.389316	−	0.921104i	$-0.627289\pi$
$599$	−641.044	−	113.033i	−1.07019	−	0.188703i	−0.680874	+	0.732401i	$0.738400\pi$
$600$		0			0
$601$	−165.422	+	138.806i	−0.275245	+	0.230958i	−0.769952	−	0.638102i	$-0.779720\pi$
$601$	−165.422	+	138.806i	−0.275245	+	0.230958i	0.494707	+	0.869060i	$0.335275\pi$
$602$	489.716	−	282.737i	0.813481	−	0.469663i
$603$		0			0
$604$	−143.575	+	248.679i	−0.237707	+	0.411721i
$605$	59.0820	−	10.4177i	0.0976562	−	0.0172194i
$606$		0			0
$607$	611.890	−	222.710i	1.00806	−	0.366902i	0.215370	−	0.976532i	$-0.430904\pi$
$607$	611.890	−	222.710i	1.00806	−	0.366902i	0.792686	+	0.609630i	$0.208682\pi$
$608$	−25.4844	−	70.0177i	−0.0419151	−	0.115161i
$609$		0			0
$610$	12.3174	+	69.8554i	0.0201925	+	0.114517i
$611$	−5.38825	−	3.11091i	−0.00881874	−	0.00509150i
$612$		0			0
$613$	−428.616	−	742.385i	−0.699211	−	1.21107i	−0.968740	−	0.248077i	$-0.920201\pi$
$613$	−428.616	−	742.385i	−0.699211	−	1.21107i	0.269529	−	0.962992i	$-0.413132\pi$
$614$	−329.801	−	393.041i	−0.537135	−	0.640132i
$615$		0			0
$616$	26.0821	−	147.919i	0.0423410	−	0.240128i
$617$	−633.317	+	754.757i	−1.02645	+	1.22327i	−0.0519994	+	0.998647i	$0.516559\pi$
$617$	−633.317	+	754.757i	−1.02645	+	1.22327i	−0.974446	+	0.224623i	$0.927885\pi$
$618$		0			0
$619$	83.7604	+	30.4863i	0.135316	+	0.0492509i	0.408790	−	0.912628i	$-0.365951\pi$
$619$	83.7604	+	30.4863i	0.135316	+	0.0492509i	−0.273475	+	0.961879i	$0.588173\pi$
$620$		−	21.7425i		−	0.0350686i
$621$		0			0
$622$	311.479			0.500770
$623$	327.217	−	899.023i	0.525229	−	1.44305i
$624$		0			0
$625$	432.258	+	362.707i	0.691612	+	0.580331i
$626$	60.4788	+	10.6640i	0.0966115	+	0.0170352i
$627$		0			0
$628$	184.311	−	154.656i	0.293490	−	0.246267i
$629$	−844.020	+	487.295i	−1.34184	+	0.774715i
$630$		0			0
$631$	71.5623	−	123.950i	0.113411	−	0.196433i	−0.803733	−	0.594991i	$-0.797156\pi$
$631$	71.5623	−	123.950i	0.113411	−	0.196433i	0.917143	+	0.398557i	$0.130489\pi$
$632$	67.8797	−	11.9690i	0.107405	−	0.0189383i
$633$		0			0
$634$	161.309	−	58.7116i	0.254430	−	0.0926050i
$635$	−16.1386	−	44.3405i	−0.0254152	−	0.0698276i
$636$		0			0
$637$	8.68959	+	49.2811i	0.0136414	+	0.0773644i
$638$	358.248	+	206.835i	0.561518	+	0.324192i
$639$		0			0
$640$	−5.11825	−	8.86507i	−0.00799727	−	0.0138517i
$641$	176.476	+	210.316i	0.275314	+	0.328106i	0.885929	−	0.463821i	$-0.153522\pi$
$641$	176.476	+	210.316i	0.275314	+	0.328106i	−0.610615	+	0.791928i	$0.709078\pi$
$642$		0			0
$643$	−157.474	+	893.080i	−0.244905	+	1.38893i	0.575807	+	0.817585i	$0.304688\pi$
$643$	−157.474	+	893.080i	−0.244905	+	1.38893i	−0.820713	+	0.571341i	$0.806423\pi$
$644$	216.417	−	257.915i	0.336051	−	0.400490i
$645$		0			0
$646$	258.363	+	94.0363i	0.399942	+	0.145567i
$647$			766.329i			1.18443i	0.805779	+	0.592217i	$0.201747\pi$
$647$			766.329i			1.18443i	−0.805779	+	0.592217i	$0.798253\pi$
$648$		0			0
$649$	−468.132			−0.721312
$650$	−228.567	+	627.983i	−0.351642	+	0.966128i
$651$		0			0
$652$	350.136	+	293.799i	0.537018	+	0.450612i
$653$	491.110	+	86.5959i	0.752082	+	0.132612i	0.536532	−	0.843880i	$-0.319734\pi$
$653$	491.110	+	86.5959i	0.752082	+	0.132612i	0.215551	+	0.976493i	$0.430845\pi$
$654$		0			0
$655$	27.4127	−	23.0020i	0.0418514	−	0.0351175i
$656$	−265.046	+	153.024i	−0.404033	+	0.233269i
$657$		0			0
$658$	1.61657	−	2.79999i	0.00245680	−	0.00425530i
$659$	987.874	−	174.189i	1.49905	−	0.264323i	0.636888	−	0.770956i	$-0.280221\pi$
$659$	987.874	−	174.189i	1.49905	−	0.264323i	0.862162	+	0.506633i	$0.169110\pi$
$660$		0			0
$661$	−40.4553	+	14.7245i	−0.0612032	+	0.0222761i	−0.372440	−	0.928056i	$-0.621479\pi$
$661$	−40.4553	+	14.7245i	−0.0612032	+	0.0222761i	0.311237	+	0.950332i	$0.399257\pi$
$662$	−67.2780	−	184.845i	−0.101628	−	0.279222i
$663$		0			0
$664$	−40.3797	−	229.005i	−0.0608129	−	0.344887i
$665$	74.1112	+	42.7881i	0.111445	+	0.0643430i
$666$		0			0
$667$	463.634	+	803.037i	0.695103	+	1.20395i
$668$	249.816	+	297.720i	0.373977	+	0.445688i
$669$		0			0
$670$	13.8621	−	78.6159i	0.0206897	−	0.117337i
$671$	263.525	−	314.057i	0.392735	−	0.468043i
$672$		0			0
$673$	−254.900	−	92.7760i	−0.378752	−	0.137854i	0.145627	−	0.989340i	$-0.453480\pi$
$673$	−254.900	−	92.7760i	−0.378752	−	0.137854i	−0.524379	+	0.851485i	$0.675702\pi$
$674$		−	34.2857i		−	0.0508689i
$675$		0			0
$676$	−425.770			−0.629838
$677$	−332.978	+	914.850i	−0.491844	+	1.35133i	0.407147	+	0.913362i	$0.366524\pi$
$677$	−332.978	+	914.850i	−0.491844	+	1.35133i	−0.898991	+	0.437967i	$0.855699\pi$
$678$		0			0
$679$	379.144	+	318.139i	0.558385	+	0.468541i
$680$	37.1985	+	6.55909i	0.0547036	+	0.00964572i
$681$		0			0
$682$	−96.2654	+	80.7762i	−0.141152	+	0.118440i
$683$	1043.61	−	602.531i	1.52799	−	0.882183i	0.528540	−	0.848908i	$-0.322740\pi$
$683$	1043.61	−	602.531i	1.52799	−	0.882183i	0.999446	−	0.0332748i	$-0.0105936\pi$
$684$		0			0
$685$	−19.4629	+	33.7107i	−0.0284130	+	0.0492127i
$686$	464.421	−	81.8899i	0.676998	−	0.119373i
$687$		0			0
$688$	−209.307	+	76.1817i	−0.304226	+	0.110729i
$689$	1.76655	+	4.85355i	0.00256393	+	0.00704435i
$690$		0			0
$691$	44.6727	+	253.352i	0.0646494	+	0.366645i	0.999919	+	0.0127094i	$0.00404563\pi$
$691$	44.6727	+	253.352i	0.0646494	+	0.366645i	−0.935270	+	0.353935i	$0.884843\pi$
$692$	−212.635	−	122.765i	−0.307275	−	0.177406i
$693$		0			0
$694$	180.322	+	312.326i	0.259829	+	0.450038i
$695$	−139.836	−	166.651i	−0.201204	−	0.239785i
$696$		0			0
$697$	196.102	−	1112.15i	0.281352	−	1.59563i
$698$	−569.090	+	678.215i	−0.815315	+	0.971655i
$699$		0			0
$700$	−326.329	−	118.774i	−0.466185	−	0.169677i
$701$			357.086i			0.509395i	0.967021	+	0.254697i	$0.0819759\pi$
$701$			357.086i			0.509395i	−0.967021	+	0.254697i	$0.918024\pi$
$702$		0			0
$703$	869.736			1.23718
$704$	−20.2353	+	55.5959i	−0.0287433	+	0.0789715i
$705$		0			0
$706$	−145.264	−	121.891i	−0.205756	−	0.172650i
$707$	1254.61	+	221.221i	1.77455	+	0.312901i
$708$		0			0
$709$	137.566	−	115.432i	0.194029	−	0.162809i	−0.540598	−	0.841281i	$-0.681802\pi$
$709$	137.566	−	115.432i	0.194029	−	0.162809i	0.734626	+	0.678472i	$0.237357\pi$
$710$	−73.0537	+	42.1776i	−0.102893	+	0.0594050i
$711$		0			0
$712$	−188.426	+	326.363i	−0.264643	+	0.458375i
$713$	−277.408	+	48.9145i	−0.389072	+	0.0686038i
$714$		0			0
$715$	−122.876	+	44.7231i	−0.171854	+	0.0625498i
$716$	−199.048	−	546.879i	−0.277999	−	0.763797i
$717$		0			0
$718$	136.283	+	772.897i	0.189809	+	1.07646i
$719$	−768.741	−	443.833i	−1.06918	−	0.617292i	−0.141223	−	0.989978i	$-0.545103\pi$
$719$	−768.741	−	443.833i	−1.06918	−	0.617292i	−0.927957	+	0.372686i	$0.878437\pi$
$720$		0			0
$721$	−61.3310	−	106.228i	−0.0850638	−	0.147335i
$722$	170.447	+	203.131i	0.236076	+	0.281344i
$723$		0			0
$724$	77.6001	−	440.092i	0.107182	−	0.607862i
$725$	614.780	−	732.666i	0.847972	−	1.01057i
$726$		0			0
$727$	−822.255	−	299.276i	−1.13103	−	0.411659i	−0.292361	−	0.956308i	$-0.594441\pi$
$727$	−822.255	−	299.276i	−1.13103	−	0.411659i	−0.838664	+	0.544649i	$0.816663\pi$
$728$		−	396.891i		−	0.545179i
$729$		0			0
$730$	58.1023			0.0795922
$731$	281.107	−	772.336i	0.384552	−	1.05655i
$732$		0			0
$733$	22.5932	+	18.9579i	0.0308229	+	0.0258634i	0.658069	−	0.752958i	$-0.271374\pi$
$733$	22.5932	+	18.9579i	0.0308229	+	0.0258634i	−0.627246	+	0.778821i	$0.715818\pi$
$734$	−252.569	−	44.5348i	−0.344100	−	0.0606741i
$735$		0			0
$736$	−101.593	+	85.2464i	−0.138034	+	0.115824i
$737$	−399.572	+	230.693i	−0.542161	+	0.313017i
$738$		0			0
$739$	589.760	−	1021.50i	0.798052	−	1.38227i	−0.122831	−	0.992428i	$-0.539197\pi$
$739$	589.760	−	1021.50i	0.798052	−	1.38227i	0.920883	−	0.389839i	$-0.127469\pi$
$740$	117.671	−	20.7485i	0.159015	−	0.0280386i
$741$		0			0
$742$	−2.52213	+	0.917982i	−0.00339910	+	0.00123717i
$743$	178.261	+	489.768i	0.239921	+	0.659176i	0.999957	+	0.00929571i	$0.00295896\pi$
$743$	178.261	+	489.768i	0.239921	+	0.659176i	−0.760036	+	0.649881i	$0.774819\pi$
$744$		0			0
$745$	−5.24553	−	29.7489i	−0.00704097	−	0.0399313i
$746$	435.539	+	251.458i	0.583832	+	0.337076i
$747$		0			0
$748$	−109.156	−	189.064i	−0.145931	−	0.252760i
$749$	134.687	+	160.514i	0.179823	+	0.214305i
$750$		0			0
$751$	11.9742	−	67.9089i	0.0159443	−	0.0904246i	−0.975797	−	0.218677i	$-0.929826\pi$
$751$	11.9742	−	67.9089i	0.0159443	−	0.0904246i	0.991742	+	0.128253i	$0.0409369\pi$
$752$	−0.818613	+	0.975585i	−0.00108858	+	0.00129732i
$753$		0			0
$754$	1027.16	+	373.856i	1.36228	+	0.495830i
$755$			129.905i			0.172059i
$756$		0			0
$757$	376.111			0.496845			0.248422	−	0.968652i	$-0.420088\pi$
$757$	376.111			0.496845			0.248422	+	0.968652i	$0.420088\pi$
$758$	−276.480	+	759.622i	−0.364749	+	1.00214i
$759$		0			0
$760$	−25.8222	−	21.6674i	−0.0339765	−	0.0285097i
$761$	21.1240	+	3.72472i	0.0277582	+	0.00489451i	0.187510	−	0.982263i	$-0.439958\pi$
$761$	21.1240	+	3.72472i	0.0277582	+	0.00489451i	−0.159752	+	0.987157i	$0.551069\pi$
$762$		0			0
$763$	886.250	−	743.652i	1.16153	−	0.974642i
$764$	510.210	−	294.570i	0.667814	−	0.385563i
$765$		0			0
$766$	294.539	−	510.156i	0.384515	−	0.666000i
$767$	−1218.20	+	214.802i	−1.58827	+	0.280054i
$768$		0			0
$769$	−320.840	+	116.776i	−0.417218	+	0.151855i	−0.542095	−	0.840317i	$-0.682369\pi$
$769$	−320.840	+	116.776i	−0.417218	+	0.151855i	0.124877	+	0.992172i	$0.460146\pi$
$770$	−23.2402	−	63.8520i	−0.0301821	−	0.0829246i
$771$		0			0
$772$	19.5543	+	110.898i	0.0253294	+	0.143650i
$773$	926.077	+	534.671i	1.19803	+	0.691683i	0.960116	−	0.279603i	$-0.0902029\pi$
$773$	926.077	+	534.671i	1.19803	+	0.691683i	0.237914	+	0.971286i	$0.423536\pi$
$774$		0			0
$775$	145.273	+	251.620i	0.187449	+	0.324671i
$776$	−125.315	−	149.344i	−0.161488	−	0.192454i
$777$		0			0
$778$	−45.2283	+	256.502i	−0.0581341	+	0.329695i
$779$	−647.806	+	772.025i	−0.831587	+	0.991047i
$780$		0			0
$781$	458.145	+	166.751i	0.586613	+	0.213510i
$782$		−	489.362i		−	0.625783i
$783$		0			0
$784$	10.2429			0.0130649
$785$	37.2277	−	102.282i	0.0474239	−	0.130296i
$786$		0			0
$787$	−320.568	−	268.988i	−0.407329	−	0.341789i	0.415989	−	0.909369i	$-0.363435\pi$
$787$	−320.568	−	268.988i	−0.407329	−	0.341789i	−0.823318	+	0.567580i	$0.807880\pi$
$788$	333.607	+	58.8240i	0.423360	+	0.0746497i
$789$		0			0
$790$	23.8869	−	20.0434i	0.0302365	−	0.0253715i
$791$	420.785	−	242.940i	0.531966	−	0.307131i
$792$		0			0
$793$	541.656	−	938.176i	0.683047	−	1.18307i
$794$	−404.081	+	71.2504i	−0.508918	+	0.0897360i
$795$		0			0
$796$	−201.055	+	73.1781i	−0.252582	+	0.0919323i
$797$	−53.5729	−	147.190i	−0.0672182	−	0.184681i	0.901536	−	0.432705i	$-0.142441\pi$
$797$	−53.5729	−	147.190i	−0.0672182	−	0.184681i	−0.968754	+	0.248025i	$0.920219\pi$
$798$		0			0
$799$	−0.816024	−	4.62790i	−0.00102131	−	0.00579212i
$800$	118.464	+	68.3952i	0.148080	+	0.0854940i
$801$		0			0
$802$	319.682	+	553.705i	0.398606	+	0.690406i
$803$	−215.857	−	257.249i	−0.268813	−	0.320359i
$804$		0			0
$805$	26.4491	−	150.000i	0.0328560	−	0.186335i
$806$	−213.443	+	254.372i	−0.264818	+	0.315598i
$807$		0			0
$808$	−471.550	−	171.630i	−0.583601	−	0.212413i
$809$		−	1306.60i		−	1.61509i	−0.589809	−	0.807543i	$-0.700797\pi$
$809$		−	1306.60i		−	1.61509i	0.589809	−	0.807543i	$-0.299203\pi$
$810$		0			0
$811$	290.663			0.358401			0.179201	−	0.983813i	$-0.442649\pi$
$811$	290.663			0.358401			0.179201	+	0.983813i	$0.442649\pi$
$812$	−194.273	+	533.761i	−0.239252	+	0.657341i
$813$		0			0
$814$	−529.026	−	443.905i	−0.649909	−	0.545338i
$815$	203.634	+	35.9062i	0.249858	+	0.0440567i
$816$		0			0
$817$	−561.875	+	471.469i	−0.687730	+	0.577074i
$818$	−361.847	+	208.913i	−0.442356	+	0.255394i
$819$		0			0
$820$	−69.2273	+	119.905i	−0.0844235	+	0.146226i
$821$	−837.272	+	147.634i	−1.01982	+	0.179822i	−0.658469	−	0.752608i	$-0.728795\pi$
$821$	−837.272	+	147.634i	−1.01982	+	0.179822i	−0.361351	+	0.932430i	$0.617684\pi$
$822$		0			0
$823$	−93.3532	+	33.9778i	−0.113430	+	0.0412853i	−0.398112	−	0.917337i	$-0.630334\pi$
$823$	−93.3532	+	33.9778i	−0.113430	+	0.0412853i	0.284681	+	0.958622i	$0.408112\pi$
$824$	16.5252	+	45.4027i	0.0200549	+	0.0551003i
$825$		0			0
$826$	−111.621	−	633.033i	−0.135134	−	0.766384i
$827$	−1046.01	−	603.912i	−1.26482	−	0.730245i	−0.290817	−	0.956779i	$-0.593927\pi$
$827$	−1046.01	−	603.912i	−1.26482	−	0.730245i	−0.974003	+	0.226534i	$0.927261\pi$
$828$		0			0
$829$	177.183	+	306.890i	0.213731	+	0.370193i	0.952879	−	0.303350i	$-0.0981050\pi$
$829$	177.183	+	306.890i	0.213731	+	0.370193i	−0.739148	+	0.673543i	$0.764772\pi$
$830$	−67.6204	−	80.5868i	−0.0814703	−	0.0970925i
$831$		0			0
$832$	−27.1473	+	153.960i	−0.0326290	+	0.185048i
$833$	−24.2947	+	28.9533i	−0.0291653	+	0.0347579i
$834$		0			0
$835$	165.217	+	60.1342i	0.197865	+	0.0720171i
$836$			194.825i			0.233044i
$837$		0			0
$838$	−763.937			−0.911619
$839$	28.0929	−	77.1847i	0.0334838	−	0.0919961i	−0.921824	−	0.387608i	$-0.873301\pi$
$839$	28.0929	−	77.1847i	0.0334838	−	0.0919961i	0.955308	+	0.295612i	$0.0955236\pi$
$840$		0			0
$841$	−554.142	−	464.980i	−0.658908	−	0.552890i
$842$	469.764	+	82.8321i	0.557915	+	0.0983755i
$843$		0			0
$844$	−53.9591	+	45.2771i	−0.0639326	+	0.0536458i
$845$	−166.810	+	96.3079i	−0.197409	+	0.113974i
$846$		0			0
$847$	238.060	−	412.332i	0.281063	−	0.486815i
$848$	1.04116	−	0.183585i	0.00122779	−	0.000216492i
$849$		0			0
$850$	−474.311	+	172.635i	−0.558013	+	0.203100i
$851$	−529.451	−	1454.66i	−0.622152	−	1.70935i
$852$		0			0
$853$	40.4872	+	229.614i	0.0474644	+	0.269184i	0.999299	−	0.0374268i	$-0.0119161\pi$
$853$	40.4872	+	229.614i	0.0474644	+	0.269184i	−0.951835	+	0.306611i	$0.900805\pi$
$854$	487.520	+	281.470i	0.570866	+	0.329590i
$855$		0			0
$856$	−41.2681	−	71.4785i	−0.0482104	−	0.0835029i
$857$	918.268	+	1094.35i	1.07149	+	1.27695i	0.959032	+	0.283298i	$0.0914285\pi$
$857$	918.268	+	1094.35i	1.07149	+	1.27695i	0.112460	+	0.993656i	$0.464127\pi$
$858$		0			0
$859$	−167.854	+	951.948i	−0.195406	+	1.10820i	0.716433	+	0.697656i	$0.245774\pi$
$859$	−167.854	+	951.948i	−0.195406	+	1.10820i	−0.911839	+	0.410548i	$0.865337\pi$
$860$	−64.7713	+	77.1915i	−0.0753155	+	0.0897575i
$861$		0			0
$862$	−831.420	−	302.612i	−0.964524	−	0.351058i
$863$		−	1136.46i		−	1.31688i	−0.752635	−	0.658438i	$-0.771218\pi$
$863$		−	1136.46i		−	1.31688i	0.752635	−	0.658438i	$-0.228782\pi$
$864$		0			0
$865$	−111.076			−0.128411
$866$	−365.019	+	1002.88i	−0.421500	+	1.15806i
$867$		0			0
$868$	−132.184	−	110.915i	−0.152285	−	0.127782i
$869$	−177.485	−	31.2954i	−0.204241	−	0.0360131i
$870$		0			0
$871$	−933.938	+	783.667i	−1.07226	+	0.899732i
$872$	−394.656	+	227.855i	−0.452587	+	0.261301i
$873$		0			0
$874$	−218.356	+	378.204i	−0.249836	+	0.432728i
$875$	−314.672	+	55.4852i	−0.359625	+	0.0634116i
$876$		0			0
$877$	58.6484	−	21.3463i	0.0668739	−	0.0243401i	−0.308367	−	0.951268i	$-0.599782\pi$
$877$	58.6484	−	21.3463i	0.0668739	−	0.0243401i	0.375240	+	0.926927i	$0.377560\pi$
$878$	82.2284	+	225.921i	0.0936542	+	0.257313i
$879$		0			0
$880$	4.64776	+	26.3588i	0.00528155	+	0.0299532i
$881$	−759.695	−	438.610i	−0.862310	−	0.497855i	0.00247512	−	0.999997i	$-0.499212\pi$
$881$	−759.695	−	438.610i	−0.862310	−	0.497855i	−0.864785	+	0.502142i	$0.832545\pi$
$882$		0			0
$883$	617.031	+	1068.73i	0.698789	+	1.21034i	0.968887	+	0.247505i	$0.0796108\pi$
$883$	617.031	+	1068.73i	0.698789	+	1.21034i	−0.270097	+	0.962833i	$0.587056\pi$
$884$	−370.805	−	441.908i	−0.419463	−	0.499896i
$885$		0			0
$886$	4.08866	−	23.1880i	0.00461474	−	0.0261715i
$887$	986.184	−	1175.29i	1.11182	−	1.32502i	0.171322	−	0.985215i	$-0.445196\pi$
$887$	986.184	−	1175.29i	1.11182	−	1.32502i	0.940498	−	0.339800i	$-0.110359\pi$
$888$		0			0
$889$	−351.895	−	128.079i	−0.395833	−	0.144071i
$890$			170.485i			0.191557i
$891$		0			0
$892$	216.699			0.242937
$893$	−1.43433	+	3.94079i	−0.00160619	+	0.00441298i
$894$		0			0
$895$	−201.686	−	169.235i	−0.225347	−	0.189089i
$896$	−80.0048	−	14.1070i	−0.0892911	−	0.0157444i
$897$		0			0
$898$	−731.372	+	613.694i	−0.814445	+	0.683401i
$899$	411.562	−	237.616i	0.457800	−	0.264311i
$900$		0			0
$901$	−1.95056	+	3.37847i	−0.00216488	+	0.00374969i
$902$	788.069	−	138.958i	0.873691	−	0.154055i
$903$		0			0
$904$	−179.846	+	65.4586i	−0.198945	+	0.0724099i
$905$	−69.1449	−	189.974i	−0.0764032	−	0.209916i
$906$		0			0
$907$	41.6356	+	236.127i	0.0459048	+	0.260339i	0.999119	−	0.0419552i	$-0.0133587\pi$
$907$	41.6356	+	236.127i	0.0459048	+	0.260339i	−0.953215	+	0.302294i	$0.902248\pi$
$908$	−392.880	−	226.830i	−0.432687	−	0.249812i
$909$		0			0
$910$	−89.7754	−	155.496i	−0.0986543	−	0.170874i
$911$	127.479	+	151.923i	0.139933	+	0.166765i	0.831459	−	0.555586i	$-0.187506\pi$
$911$	127.479	+	151.923i	0.139933	+	0.166765i	−0.691527	+	0.722351i	$0.743062\pi$
$912$		0			0
$913$	−105.581	+	598.780i	−0.115642	+	0.655838i
$914$	488.212	−	581.829i	0.534149	−	0.636574i
$915$		0			0
$916$	394.764	+	143.682i	0.430965	+	0.156858i
$917$		−	283.995i		−	0.309700i
$918$		0			0
$919$	−712.921			−0.775758			−0.387879	−	0.921710i	$-0.626792\pi$
$919$	−712.921			−0.775758			−0.387879	+	0.921710i	$0.626792\pi$
$920$	−20.5200	+	56.3782i	−0.0223043	+	0.0612807i
$921$		0			0
$922$	353.307	+	296.460i	0.383196	+	0.321540i
$923$	1268.73	+	223.711i	1.37457	+	0.242373i
$924$		0			0
$925$	−1223.14	+	1026.33i	−1.32231	+	1.10955i
$926$	272.192	−	157.150i	0.293944	−	0.169709i
$927$		0			0
$928$	111.871	−	193.766i	0.120550	−	0.208799i
$929$	−1269.35	+	223.821i	−1.36636	+	0.240927i	−0.808250	−	0.588839i	$-0.799585\pi$
$929$	−1269.35	+	223.821i	−1.36636	+	0.240927i	−0.558112	+	0.829765i	$0.688474\pi$
$930$		0			0
$931$	31.6954	−	11.5362i	0.0340444	−	0.0123912i
$932$	28.5835	+	78.5326i	0.0306690	+	0.0842624i
$933$		0			0
$934$	22.9641	+	130.236i	0.0245868	+	0.139439i
$935$	−85.5316	−	49.3817i	−0.0914776	−	0.0528146i
$936$		0			0
$937$	101.266	+	175.398i	0.108075	+	0.187191i	0.914990	−	0.403476i	$-0.132198\pi$
$937$	101.266	+	175.398i	0.108075	+	0.187191i	−0.806916	+	0.590667i	$0.798865\pi$
$938$	−407.230	−	485.318i	−0.434147	−	0.517396i
$939$		0			0
$940$	−0.100046	+	0.567387i	−0.000106431	+	0.000603603i
$941$	−672.488	+	801.440i	−0.714652	+	0.851689i	−0.994100	−	0.108472i	$-0.965404\pi$
$941$	−672.488	+	801.440i	−0.714652	+	0.851689i	0.279447	+	0.960161i	$0.409849\pi$
$942$		0			0
$943$	1685.58	+	613.502i	1.78747	+	0.650585i
$944$			253.198i			0.268218i
$945$		0			0
$946$	582.400			0.615644
$947$	−52.6990	+	144.789i	−0.0556484	+	0.152893i	−0.964402	−	0.264440i	$-0.914813\pi$
$947$	−52.6990	+	144.789i	−0.0556484	+	0.152893i	0.908754	+	0.417333i	$0.137035\pi$
$948$		0			0
$949$	−679.755	−	570.382i	−0.716285	−	0.601035i
$950$	443.603	+	78.2191i	0.466950	+	0.0823359i
$951$		0			0
$952$	229.636	−	192.688i	0.241214	−	0.202403i
$953$	23.8079	−	13.7455i	0.0249820	−	0.0144234i	−0.487457	−	0.873147i	$-0.662075\pi$
$953$	23.8079	−	13.7455i	0.0249820	−	0.0144234i	0.512439	+	0.858724i	$0.328742\pi$
$954$		0			0
$955$	133.262	−	230.816i	0.139541	−	0.241692i
$956$	734.622	−	129.534i	0.768433	−	0.135495i
$957$		0			0
$958$	−16.4807	+	5.99848i	−0.0172032	+	0.00626146i
$959$	105.658	+	290.293i	0.110175	+	0.302704i
$960$		0			0
$961$	−141.807	−	804.227i	−0.147562	−	0.836864i
$962$	−1580.35	−	912.414i	−1.64277	−	0.948455i
$963$		0			0
$964$	116.126	+	201.136i	0.120463	+	0.208647i
$965$	32.7459	+	39.0250i	0.0339336	+	0.0404405i
$966$		0			0
$967$	231.642	−	1313.70i	0.239547	−	1.35854i	−0.593277	−	0.804998i	$-0.702166\pi$
$967$	231.642	−	1313.70i	0.239547	−	1.35854i	0.832824	−	0.553538i	$-0.186723\pi$
$968$	−120.551	+	143.667i	−0.124536	+	0.148416i
$969$		0			0
$970$	−82.8777	−	30.1650i	−0.0854409	−	0.0310980i
$971$			1473.78i			1.51780i	0.651209	+	0.758898i	$0.274262\pi$
$971$			1473.78i			1.51780i	−0.651209	+	0.758898i	$0.725738\pi$
$972$		0			0
$973$	−1726.50			−1.77441
$974$	266.884	−	733.259i	0.274009	−	0.752832i
$975$		0			0
$976$	−169.864	−	142.533i	−0.174041	−	0.146038i
$977$	−1321.53	−	233.022i	−1.35264	−	0.238508i	−0.550099	−	0.835099i	$-0.685410\pi$
$977$	−1321.53	−	233.022i	−1.35264	−	0.238508i	−0.802545	+	0.596592i	$0.796521\pi$
$978$		0			0
$979$	754.826	−	633.374i	0.771017	−	0.646960i
$980$	4.01301	−	2.31691i	0.00409491	−	0.00236419i
$981$		0			0
$982$	576.810	−	999.064i	0.587383	−	1.01738i
$983$	990.831	−	174.710i	1.00797	−	0.177732i	0.354797	−	0.934943i	$-0.384550\pi$
$983$	990.831	−	174.710i	1.00797	−	0.177732i	0.653169	+	0.757212i	$0.273439\pi$
$984$		0			0
$985$	144.008	−	52.4146i	0.146201	−	0.0532128i
$986$	282.371	+	775.807i	0.286380	+	0.786823i
$987$		0			0
$988$	89.3951	+	506.985i	0.0904809	+	0.513142i
$989$	1130.58	+	652.744i	1.14316	+	0.660004i
$990$		0			0
$991$	789.470	+	1367.40i	0.796640	+	1.37982i	0.921793	+	0.387683i	$0.126725\pi$
$991$	789.470	+	1367.40i	0.796640	+	1.37982i	−0.125153	+	0.992137i	$0.539942\pi$
$992$	43.6894	+	52.0670i	0.0440418	+	0.0524869i
$993$		0			0
$994$	−116.250	+	659.289i	−0.116952	+	0.663269i
$995$	−62.2177	+	74.1481i	−0.0625303	+	0.0745207i
$996$		0			0
$997$	−432.596	−	157.452i	−0.433897	−	0.157926i	0.115832	−	0.993269i	$-0.463047\pi$
$997$	−432.596	−	157.452i	−0.433897	−	0.157926i	−0.549729	+	0.835343i	$0.685269\pi$
$998$			406.668i			0.407483i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.17.2		36
3.2	odd	2		54.3.f.a.23.6	✓	36
12.11	even	2		432.3.bc.c.401.1		36
27.7	even	9		54.3.f.a.47.6	yes	36
27.13	even	9		1458.3.b.c.1457.9		36
27.14	odd	18		1458.3.b.c.1457.28		36
27.20	odd	18	inner	162.3.f.a.143.2		36
108.7	odd	18		432.3.bc.c.209.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.23.6	✓	36	3.2	odd	2
54.3.f.a.47.6	yes	36	27.7	even	9
162.3.f.a.17.2		36	1.1	even	1	trivial
162.3.f.a.143.2		36	27.20	odd	18	inner
432.3.bc.c.209.1		36	108.7	odd	18
432.3.bc.c.401.1		36	12.11	even	2
1458.3.b.c.1457.9		36	27.13	even	9
1458.3.b.c.1457.28		36	27.14	odd	18

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-0.891042 - 0.157115i) q^{5} +(-5.50064 + 4.61559i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-0.891042 - 0.157115i) q^{5} +(-5.50064 + 4.61559i) q^{7} +(2.44949 - 1.41421i) q^{8} +(0.639781 - 1.10813i) q^{10} +(-7.28314 + 1.28421i) q^{11} +(-18.3634 + 6.68372i) q^{13} +(-3.47317 - 9.54246i) q^{14} +(0.694593 + 3.93923i) q^{16} +(-12.7824 - 7.37992i) q^{17} +(6.58593 + 11.4072i) q^{19} +(1.16317 + 1.38621i) q^{20} +(1.81615 - 10.2999i) q^{22} +(15.0696 - 17.9592i) q^{23} +(-22.7230 - 8.27051i) q^{25} -27.6364i q^{26} +14.3612 q^{28} +(-13.5277 + 37.1670i) q^{29} +(-9.20424 - 7.72327i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(15.9901 - 13.4173i) q^{34} +(5.62648 - 3.24845i) q^{35} +(33.0149 - 57.1836i) q^{37} +(-18.3448 + 3.23469i) q^{38} +(-2.40479 + 0.875273i) q^{40} +(26.1687 + 71.8979i) q^{41} +(9.66961 + 54.8391i) q^{43} +(12.8094 + 7.39550i) q^{44} +(16.5775 + 28.7131i) q^{46} +(0.204653 + 0.243896i) q^{47} +(0.444665 - 2.52182i) q^{49} +(21.9818 - 26.1969i) q^{50} +(36.7267 + 13.3674i) q^{52} -0.264306i q^{53} +6.69135 q^{55} +(-6.94634 + 19.0849i) q^{56} +(-42.8490 - 35.9545i) q^{58} +(62.3379 + 10.9919i) q^{59} +(-42.4660 + 35.6332i) q^{61} +(14.7157 - 8.49608i) q^{62} +(4.00000 - 6.92820i) q^{64} +(17.4126 - 3.07032i) q^{65} +(58.6251 - 21.3378i) q^{67} +(10.0963 + 27.7394i) q^{68} +(1.59548 + 9.04842i) q^{70} +(-57.0927 - 32.9625i) q^{71} +(22.7040 + 39.3244i) q^{73} +(60.0237 + 71.5335i) q^{74} +(4.57454 - 25.9435i) q^{76} +(34.1346 - 40.6800i) q^{77} +(22.8997 + 8.33480i) q^{79} -3.61915i q^{80} -108.205 q^{82} +(28.1190 - 77.2563i) q^{83} +(10.2302 + 8.58412i) q^{85} +(-77.5542 - 13.6749i) q^{86} +(-16.0238 + 13.4456i) q^{88} +(-115.387 + 66.6186i) q^{89} +(70.1610 - 121.522i) q^{91} +(-46.1759 + 8.14205i) q^{92} +(-0.423109 + 0.153999i) q^{94} +(-4.07611 - 11.1990i) q^{95} +(-11.9691 - 67.8800i) q^{97} +(3.13623 + 1.81071i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 36 * q - 18 * q^5	\( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

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