LMFDB - Embedded newform 162.3.f.a.143.2

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			143.2
Character	$\chi$	$=$	162.143
Dual form			162.3.f.a.17.2

$q$-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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

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	−0.262040	−	0.965057i	$-0.584395\pi$
$5$	−0.891042	+	0.157115i	−0.178208	+	0.0314229i	0.0838318	+	0.996480i	$0.473284\pi$
$6$		0			0
$7$	−5.50064	−	4.61559i	−0.785806	−	0.659370i	0.158897	−	0.987295i	$-0.449206\pi$
$7$	−5.50064	−	4.61559i	−0.785806	−	0.659370i	−0.944704	+	0.327925i	$0.893651\pi$
$8$	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	−0.167509	−	0.985871i	$-0.553572\pi$
$11$	−7.28314	−	1.28421i	−0.662104	−	0.116747i	−0.494595	+	0.869124i	$0.664683\pi$
$12$		0			0
$13$	−18.3634	−	6.68372i	−1.41257	−	0.514132i	−0.480684	−	0.876894i	$-0.659612\pi$
$13$	−18.3634	−	6.68372i	−1.41257	−	0.514132i	−0.931882	+	0.362762i	$0.881834\pi$
$14$	−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	−0.826382	−	0.563110i	$-0.809605\pi$
$17$	−12.7824	+	7.37992i	−0.751906	+	0.434113i	0.0744762	+	0.997223i	$0.476272\pi$
$18$		0			0
$19$	6.58593	−	11.4072i	0.346628	−	0.600377i	−0.639020	−	0.769190i	$-0.720660\pi$
$19$	6.58593	−	11.4072i	0.346628	−	0.600377i	0.985648	+	0.168813i	$0.0539933\pi$
$20$	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	0.986688	−	0.162623i	$-0.0519954\pi$
$23$	15.0696	+	17.9592i	0.655199	+	0.780836i	−0.331489	+	0.943459i	$0.607551\pi$
$24$		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	−0.920538	−	0.390652i	$-0.872250\pi$
$29$	−13.5277	−	37.1670i	−0.466471	−	1.28162i	0.454067	−	0.890967i	$-0.349973\pi$
$30$		0			0
$31$	−9.20424	+	7.72327i	−0.296911	+	0.249138i	−0.779057	−	0.626953i	$-0.784302\pi$
$31$	−9.20424	+	7.72327i	−0.296911	+	0.249138i	0.482146	+	0.876091i	$0.339857\pi$
$32$	−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	0.837116	+	0.547025i	$0.184240\pi$
$37$	33.0149	+	57.1836i	0.892296	+	1.54550i	0.0551793	+	0.998476i	$0.482427\pi$
$38$	−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	−0.0188592	−	0.999822i	$-0.506003\pi$
$41$	26.1687	−	71.8979i	0.638261	−	1.75361i	0.657120	−	0.753786i	$-0.271774\pi$
$42$		0			0
$43$	9.66961	−	54.8391i	0.224875	−	1.27533i	−0.638050	−	0.769995i	$-0.720259\pi$
$43$	9.66961	−	54.8391i	0.224875	−	1.27533i	0.862925	−	0.505333i	$-0.168630\pi$
$44$	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	−0.763863	−	0.645379i	$-0.776700\pi$
$47$	0.204653	−	0.243896i	0.00435432	−	0.00518928i	0.768217	+	0.640189i	$0.221144\pi$
$48$		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	$0.000793693\pi$
$53$			0.264306i			0.00498691i	−0.999997	+	0.00249346i	$0.999206\pi$
$54$		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	0.381739	−	0.924270i	$-0.375325\pi$
$59$	62.3379	−	10.9919i	1.05657	−	0.186303i	0.674836	+	0.737968i	$0.264214\pi$
$60$		0			0
$61$	−42.4660	−	35.6332i	−0.696164	−	0.584151i	0.224516	−	0.974470i	$-0.427920\pi$
$61$	−42.4660	−	35.6332i	−0.696164	−	0.584151i	−0.920679	+	0.390320i	$0.872364\pi$
$62$	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	0.740191	−	0.672397i	$-0.234735\pi$
$67$	58.6251	+	21.3378i	0.875001	+	0.318474i	0.134810	+	0.990871i	$0.456957\pi$
$68$	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	−0.844911	−	0.534908i	$-0.820346\pi$
$71$	−57.0927	+	32.9625i	−0.804122	+	0.464260i	0.0407882	+	0.999168i	$0.487013\pi$
$72$		0			0
$73$	22.7040	−	39.3244i	0.311013	−	0.538691i	−0.667569	−	0.744548i	$-0.732665\pi$
$73$	22.7040	−	39.3244i	0.311013	−	0.538691i	0.978582	+	0.205857i	$0.0659983\pi$
$74$	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	−0.192993	−	0.981200i	$-0.561819\pi$
$79$	22.8997	−	8.33480i	0.289869	−	0.105504i	0.482862	+	0.875696i	$0.339597\pi$
$80$			3.61915i			0.0452394i
$81$		0			0
$82$	−108.205			−1.31957
$83$	28.1190	+	77.2563i	0.338783	+	0.930799i	0.985740	+	0.168273i	$0.0538190\pi$
$83$	28.1190	+	77.2563i	0.338783	+	0.930799i	−0.646957	+	0.762526i	$0.723959\pi$
$84$		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	−0.316686	−	0.948530i	$-0.602570\pi$
$89$	−115.387	−	66.6186i	−1.29648	−	0.748523i	−0.979794	+	0.200007i	$0.935903\pi$
$90$		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	0.858857	+	0.512215i	$0.171175\pi$
$97$	−11.9691	+	67.8800i	−0.123392	+	0.699794i	−0.982250	+	0.187578i	$0.939936\pi$
$98$	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	−0.198316	+	0.980138i	$0.563547\pi$
$101$	−114.042	+	135.910i	−1.12913	+	1.34564i	−0.930810	+	0.365503i	$0.880897\pi$
$102$		0			0
$103$	−2.96634	−	16.8229i	−0.0287994	−	0.163330i	0.967016	−	0.254715i	$-0.0819816\pi$
$103$	−2.96634	−	16.8229i	−0.0287994	−	0.163330i	−0.995816	+	0.0913853i	$0.970871\pi$
$104$	−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	$0.0435403\pi$
$107$			29.1810i			0.272719i	−0.990659	+	0.136360i	$0.956460\pi$
$108$		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	−0.460540	−	0.887639i	$-0.652344\pi$
$113$	−66.6379	+	11.7501i	−0.589716	+	0.103983i	−0.129176	+	0.991622i	$0.541233\pi$
$114$		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	−0.744914	−	0.667161i	$-0.767509\pi$
$127$	26.0758	−	45.1647i	0.205322	−	0.355627i	0.950235	+	0.311534i	$0.100843\pi$
$128$	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	0.660233	−	0.751060i	$-0.270457\pi$
$131$	−25.4225	−	30.2974i	−0.194065	−	0.231278i	−0.854298	+	0.519783i	$0.826013\pi$
$132$		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	0.981739	−	0.190232i	$-0.0609241\pi$
$137$	14.7144	+	40.4275i	0.107404	+	0.295091i	−0.874335	+	0.485323i	$0.838702\pi$
$138$		0			0
$139$	184.188	−	154.552i	1.32509	−	1.11188i	0.339892	−	0.940465i	$-0.389610\pi$
$139$	184.188	−	154.552i	1.32509	−	1.11188i	0.985198	−	0.171418i	$-0.0548349\pi$
$140$	−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	−0.895458	−	0.445146i	$-0.853152\pi$
$149$	11.4189	−	31.3731i	0.0766368	−	0.210558i	0.972095	+	0.234588i	$0.0753741\pi$
$150$		0			0
$151$	−24.9315	+	141.394i	−0.165110	+	0.936383i	0.783842	+	0.620960i	$0.213257\pi$
$151$	−24.9315	+	141.394i	−0.165110	+	0.936383i	−0.948951	+	0.315422i	$0.897854\pi$
$152$	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	−0.976193	−	0.216905i	$-0.930404\pi$
$157$	−20.8900	−	118.473i	−0.133057	−	0.754606i	0.843135	−	0.537701i	$-0.180707\pi$
$158$	−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	−0.714199	−	0.699943i	$-0.753209\pi$
$167$	−191.370	+	33.7438i	−1.14593	+	0.202059i	−0.431732	+	0.902002i	$0.642098\pi$
$168$		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	0.511771	−	0.859122i	$-0.328990\pi$
$173$	120.900	+	21.3179i	0.698841	+	0.123225i	0.187070	+	0.982347i	$0.440101\pi$
$174$		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	0.412659	−	0.910886i	$-0.364600\pi$
$179$	252.003	−	145.494i	1.40784	−	0.812816i	0.995180	+	0.0980700i	$0.0312669\pi$
$180$		0			0
$181$	111.720	−	193.505i	0.617239	−	1.06909i	−0.372748	−	0.927932i	$-0.621585\pi$
$181$	111.720	−	193.505i	0.617239	−	1.06909i	0.989987	−	0.141157i	$-0.0450821\pi$
$182$	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	−0.862027	−	0.506863i	$-0.830805\pi$
$191$	−100.749	−	276.805i	−0.527481	−	1.44924i	0.334546	−	0.942379i	$-0.391417\pi$
$192$		0			0
$193$	−43.1317	+	36.1918i	−0.223480	+	0.187522i	−0.747653	−	0.664090i	$-0.768819\pi$
$193$	−43.1317	+	36.1918i	−0.223480	+	0.187522i	0.524172	+	0.851612i	$0.324375\pi$
$194$	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	0.0791444	−	0.996863i	$-0.474781\pi$
$197$	−146.685	−	84.6884i	−0.744592	−	0.429891i	−0.823737	+	0.566973i	$0.808115\pi$
$198$		0			0
$199$	53.4896	+	92.6468i	0.268792	+	0.465562i	0.968550	−	0.248818i	$-0.0800422\pi$
$199$	53.4896	+	92.6468i	0.268792	+	0.465562i	−0.699758	+	0.714380i	$0.746709\pi$
$200$	−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	0.995864	−	0.0908522i	$-0.0289591\pi$
$211$	6.11577	+	34.6843i	0.0289847	+	0.164380i	−0.966880	+	0.255233i	$0.917848\pi$
$212$	−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	0.437431	−	0.899252i	$-0.355888\pi$
$223$	−83.0007	−	69.6459i	−0.372200	−	0.312313i	−0.809631	+	0.586939i	$0.800333\pi$
$224$	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	0.642455	−	0.766323i	$-0.277916\pi$
$227$	223.383	+	39.3885i	0.984068	+	0.173518i	0.341613	+	0.939841i	$0.389027\pi$
$228$		0			0
$229$	−197.382	−	71.8412i	−0.861930	−	0.313717i	−0.127035	−	0.991898i	$-0.540546\pi$
$229$	−197.382	−	71.8412i	−0.861930	−	0.313717i	−0.734895	+	0.678181i	$0.762768\pi$
$230$	−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	−0.575642	−	0.817702i	$-0.695248\pi$
$233$	−36.1880	+	20.8932i	−0.155313	+	0.0896702i	0.420329	+	0.907372i	$0.361915\pi$
$234$		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	−0.980660	−	0.195722i	$-0.937295\pi$
$239$	−239.745	−	285.717i	−1.00312	−	1.19547i	−0.0224583	−	0.999748i	$-0.507149\pi$
$240$		0			0
$241$	−109.123	+	39.7174i	−0.452792	+	0.164803i	−0.558341	−	0.829611i	$-0.688562\pi$
$241$	−109.123	+	39.7174i	−0.452792	+	0.164803i	0.105550	+	0.994414i	$0.466340\pi$
$242$			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	0.783940	−	0.620836i	$-0.213207\pi$
$251$	160.201	+	92.4920i	0.638251	+	0.368494i	−0.145690	+	0.989330i	$0.546540\pi$
$252$		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	−0.858701	−	0.512477i	$-0.828728\pi$
$257$	33.0286	−	90.7454i	0.128516	−	0.353095i	0.987217	+	0.159382i	$0.0509502\pi$
$258$		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	−0.782692	−	0.622409i	$-0.786154\pi$
$263$	−8.89610	+	10.6020i	−0.0338255	+	0.0403116i	0.748866	+	0.662721i	$0.230598\pi$
$264$		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	$-0.968862\pi$
$269$		−	52.5454i		−	0.195336i	0.995219	−	0.0976680i	$-0.0311383\pi$
$270$		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	0.748415	−	0.663231i	$-0.230815\pi$
$277$	62.3862	+	52.3482i	0.225221	+	0.188983i	−0.523194	+	0.852214i	$0.675260\pi$
$278$	−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	−0.206606	−	0.978424i	$-0.566242\pi$
$281$	−206.646	−	36.4372i	−0.735393	−	0.129670i	−0.528787	+	0.848754i	$0.677353\pi$
$282$		0			0
$283$	60.4622	+	22.0064i	0.213647	+	0.0777612i	0.446627	−	0.894720i	$-0.352625\pi$
$283$	60.4622	+	22.0064i	0.213647	+	0.0777612i	−0.232979	+	0.972482i	$0.574847\pi$
$284$	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	0.895338	−	0.445388i	$-0.146934\pi$
$293$	88.2641	+	105.189i	0.301243	+	0.359007i	−0.594095	+	0.804395i	$0.702490\pi$
$294$		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	−0.994114	−	0.108340i	$-0.965447\pi$
$307$	−181.401	−	314.195i	−0.590882	−	1.02344i	0.403232	−	0.915098i	$-0.367887\pi$
$308$	−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	0.757700	+	0.652603i	$0.226323\pi$
$311$	−75.3296	+	206.966i	−0.242217	+	0.665487i	−0.999917	+	0.0128834i	$0.995899\pi$
$312$		0			0
$313$	−7.54061	+	42.7650i	−0.0240914	+	0.136629i	−0.994481	−	0.104915i	$-0.966543\pi$
$313$	−7.54061	+	42.7650i	−0.0240914	+	0.136629i	0.970390	+	0.241544i	$0.0776540\pi$
$314$	−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	−0.874939	−	0.484233i	$-0.839099\pi$
$317$	−78.0234	+	92.9846i	−0.246131	+	0.293327i	0.628808	+	0.777560i	$0.283543\pi$
$318$		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	0.467485	−	0.884001i	$-0.345160\pi$
$331$	−106.552	−	89.4075i	−0.321908	−	0.270113i	−0.789393	+	0.613888i	$0.789605\pi$
$332$	−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	0.307998	−	0.951387i	$-0.400341\pi$
$337$	−22.7816	−	8.29181i	−0.0676010	−	0.0246048i	−0.375599	+	0.926782i	$0.622563\pi$
$338$	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	0.948648	−	0.316333i	$-0.102452\pi$
$347$	163.919	+	195.352i	0.472390	+	0.562973i	−0.476258	+	0.879306i	$0.658007\pi$
$348$		0			0
$349$	588.280	−	214.116i	1.68562	−	0.613514i	0.691554	−	0.722325i	$-0.256926\pi$
$349$	588.280	−	214.116i	1.68562	−	0.613514i	0.994062	+	0.108811i	$0.0347042\pi$
$350$		−	245.559i		−	0.701596i
$351$		0			0
$352$	41.8352			0.118850
$353$	−45.8606	−	126.001i	−0.129917	−	0.356944i	0.857630	−	0.514267i	$-0.171936\pi$
$353$	−45.8606	−	126.001i	−0.129917	−	0.356944i	−0.987547	+	0.157323i	$0.949714\pi$
$354$		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	0.986618	−	0.163047i	$-0.0521321\pi$
$359$	480.602	+	277.476i	1.33872	+	0.772913i	0.352107	+	0.935960i	$0.385465\pi$
$360$		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	−0.911374	−	0.411580i	$-0.864977\pi$
$367$	31.4908	−	178.593i	0.0858061	−	0.486630i	0.997180	−	0.0750505i	$-0.0239118\pi$
$368$	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	0.948490	+	0.316806i	$0.102610\pi$
$373$	61.7520	+	350.213i	0.165555	+	0.938909i	−0.782935	+	0.622103i	$0.786278\pi$
$374$	−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	−0.681255	−	0.732046i	$-0.738566\pi$
$383$	−410.213	+	72.3315i	−1.07105	+	0.188855i	−0.389796	+	0.920901i	$0.627454\pi$
$384$		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	0.401842	−	0.915709i	$-0.368370\pi$
$389$	181.375	+	31.9812i	0.466259	+	0.0822140i	0.0644168	+	0.997923i	$0.479481\pi$
$390$		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	−0.623431	−	0.781878i	$-0.714262\pi$
$397$	145.068	−	251.265i	0.365411	−	0.632910i	0.988842	+	0.148968i	$0.0475952\pi$
$398$	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	0.995078	−	0.0990934i	$-0.0315943\pi$
$401$	290.603	+	346.328i	0.724697	+	0.863660i	−0.270381	+	0.962753i	$0.587150\pi$
$402$		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	−0.322715	−	0.946496i	$-0.604595\pi$
$409$	226.326	−	189.910i	0.553363	−	0.464327i	0.876078	+	0.482169i	$0.160151\pi$
$410$	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	−0.497934	−	0.867215i	$-0.665908\pi$
$419$	184.754	−	507.608i	0.440941	−	1.21147i	0.938875	−	0.344259i	$-0.111870\pi$
$420$		0			0
$421$	−58.5712	+	332.174i	−0.139124	+	0.789011i	0.832775	+	0.553612i	$0.186751\pi$
$421$	−58.5712	+	332.174i	−0.139124	+	0.789011i	−0.971899	+	0.235399i	$0.924360\pi$
$422$	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	$-0.741473\pi$
$431$		−	625.633i		−	1.45158i	0.687914	−	0.725792i	$-0.258527\pi$
$432$		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	0.778948	−	0.627088i	$-0.215753\pi$
$439$	130.229	+	109.276i	0.296650	+	0.248919i	−0.482298	+	0.876007i	$0.660198\pi$
$440$	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	0.155111	−	0.987897i	$-0.450426\pi$
$443$	−16.3964	−	2.89112i	−0.0370121	−	0.00652623i	−0.192124	+	0.981371i	$0.561537\pi$
$444$		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	0.321359	−	0.946958i	$-0.395860\pi$
$449$	584.655	−	337.551i	1.30213	−	0.751784i	0.980769	+	0.195174i	$0.0625272\pi$
$450$		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	−0.828908	−	0.559385i	$-0.811037\pi$
$457$	−504.675	+	183.687i	−1.10432	+	0.401940i	−0.275414	+	0.961326i	$0.588815\pi$
$458$			297.055i			0.648591i
$459$		0			0
$460$	42.4239			0.0922258
$461$	111.541	+	306.457i	0.241955	+	0.664765i	0.999922	+	0.0124727i	$0.00397027\pi$
$461$	111.541	+	306.457i	0.241955	+	0.664765i	−0.757968	+	0.652292i	$0.773808\pi$
$462$		0			0
$463$	−170.249	+	142.856i	−0.367708	+	0.308544i	−0.807854	−	0.589382i	$-0.799371\pi$
$463$	−170.249	+	142.856i	−0.367708	+	0.308544i	0.440146	+	0.897926i	$0.354927\pi$
$464$	−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	0.584193	−	0.811614i	$-0.301411\pi$
$467$	80.9832	+	46.7556i	0.173411	+	0.100119i	−0.410782	+	0.911734i	$0.634744\pi$
$468$		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	−0.757659	−	0.652650i	$-0.773657\pi$
$479$	7.97154	−	9.50011i	0.0166420	−	0.0198332i	0.774301	+	0.632817i	$0.218102\pi$
$480$		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	−0.914742	−	0.404038i	$-0.867606\pi$
$491$	−803.339	+	141.650i	−1.63613	+	0.288494i	−0.721387	+	0.692532i	$0.756495\pi$
$492$		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	0.598273	−	0.801293i	$-0.295854\pi$
$499$	270.216	+	98.3506i	0.541515	+	0.197095i	−0.0567575	+	0.998388i	$0.518076\pi$
$500$	−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	−0.477765	−	0.878488i	$-0.658553\pi$
$503$	22.2054	−	12.8203i	0.0441459	−	0.0254877i	0.521911	+	0.853000i	$0.325219\pi$
$504$		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	0.681391	−	0.731920i	$-0.261375\pi$
$509$	−80.2854	−	95.6804i	−0.157732	−	0.187977i	−0.839123	+	0.543942i	$0.816931\pi$
$510$		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	0.477644	−	0.878553i	$-0.341491\pi$
$521$	−23.1236	−	13.3504i	−0.0443831	−	0.0256246i	−0.522027	+	0.852929i	$0.674824\pi$
$522$		0			0
$523$	−361.405	−	625.972i	−0.691023	−	1.19689i	−0.971503	−	0.237027i	$-0.923827\pi$
$523$	−361.405	−	625.972i	−0.691023	−	1.19689i	0.280480	−	0.959860i	$-0.409506\pi$
$524$	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	−0.0736388	−	0.997285i	$-0.523461\pi$
$547$	−584.502	−	490.456i	−1.06856	−	0.896628i	−0.994921	+	0.100657i	$0.967906\pi$
$548$	−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	−0.632174	−	0.774826i	$-0.717837\pi$
$557$	−154.424	+	89.1568i	−0.277243	+	0.160066i	0.354932	+	0.934892i	$0.384504\pi$
$558$		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	0.835178	−	0.549980i	$-0.185365\pi$
$563$	83.6205	+	99.6550i	0.148527	+	0.177007i	−0.686651	+	0.726987i	$0.740920\pi$
$564$		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	0.773465	+	0.633839i	$0.218522\pi$
$569$	334.788	+	919.824i	0.588380	+	1.61656i	−0.185084	+	0.982723i	$0.559256\pi$
$570$		0			0
$571$	353.588	−	296.696i	0.619244	−	0.519607i	−0.278322	−	0.960488i	$-0.589778\pi$
$571$	353.588	−	296.696i	0.619244	−	0.519607i	0.897566	+	0.440880i	$0.145334\pi$
$572$	−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	0.649133	−	0.760675i	$-0.275132\pi$
$577$	−192.832	−	333.994i	−0.334197	−	0.578846i	−0.983330	+	0.181829i	$0.941798\pi$
$578$	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	0.124414	−	0.992230i	$-0.460295\pi$
$587$	633.940	−	755.500i	1.07997	−	1.28705i	0.955552	−	0.294823i	$-0.0952607\pi$
$588$		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	$-0.941461\pi$
$593$		−	216.884i		−	0.365741i	0.983137	−	0.182870i	$-0.0585388\pi$
$594$		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	−0.680874	−	0.732401i	$-0.738400\pi$
$599$	−641.044	+	113.033i	−1.07019	+	0.188703i	−0.389316	+	0.921104i	$0.627289\pi$
$600$		0			0
$601$	−165.422	−	138.806i	−0.275245	−	0.230958i	0.494707	−	0.869060i	$-0.335275\pi$
$601$	−165.422	−	138.806i	−0.275245	−	0.230958i	−0.769952	+	0.638102i	$0.779720\pi$
$602$	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	0.792686	−	0.609630i	$-0.208682\pi$
$607$	611.890	+	222.710i	1.00806	+	0.366902i	0.215370	+	0.976532i	$0.430904\pi$
$608$	−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	0.269529	+	0.962992i	$0.413132\pi$
$613$	−428.616	+	742.385i	−0.699211	+	1.21107i	−0.968740	+	0.248077i	$0.920201\pi$
$614$	−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	−0.974446	−	0.224623i	$-0.927885\pi$
$617$	−633.317	−	754.757i	−1.02645	−	1.22327i	−0.0519994	−	0.998647i	$-0.516559\pi$
$618$		0			0
$619$	83.7604	−	30.4863i	0.135316	−	0.0492509i	−0.273475	−	0.961879i	$-0.588173\pi$
$619$	83.7604	−	30.4863i	0.135316	−	0.0492509i	0.408790	+	0.912628i	$0.365951\pi$
$620$			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	0.917143	−	0.398557i	$-0.130489\pi$
$631$	71.5623	+	123.950i	0.113411	+	0.196433i	−0.803733	+	0.594991i	$0.797156\pi$
$632$	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	−0.610615	−	0.791928i	$-0.709078\pi$
$641$	176.476	−	210.316i	0.275314	−	0.328106i	0.885929	+	0.463821i	$0.153522\pi$
$642$		0			0
$643$	−157.474	−	893.080i	−0.244905	−	1.38893i	−0.820713	−	0.571341i	$-0.806423\pi$
$643$	−157.474	−	893.080i	−0.244905	−	1.38893i	0.575807	−	0.817585i	$-0.304688\pi$
$644$	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	$-0.798253\pi$
$647$		−	766.329i		−	1.18443i	0.805779	−	0.592217i	$-0.201747\pi$
$648$		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	0.215551	−	0.976493i	$-0.430845\pi$
$653$	491.110	−	86.5959i	0.752082	−	0.132612i	0.536532	+	0.843880i	$0.319734\pi$
$654$		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	0.862162	−	0.506633i	$-0.169110\pi$
$659$	987.874	+	174.189i	1.49905	+	0.264323i	0.636888	+	0.770956i	$0.280221\pi$
$660$		0			0
$661$	−40.4553	−	14.7245i	−0.0612032	−	0.0222761i	0.311237	−	0.950332i	$-0.399257\pi$
$661$	−40.4553	−	14.7245i	−0.0612032	−	0.0222761i	−0.372440	+	0.928056i	$0.621479\pi$
$662$	−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	−0.524379	−	0.851485i	$-0.675702\pi$
$673$	−254.900	+	92.7760i	−0.378752	+	0.137854i	0.145627	+	0.989340i	$0.453480\pi$
$674$			34.2857i			0.0508689i
$675$		0			0
$676$	−425.770			−0.629838
$677$	−332.978	−	914.850i	−0.491844	−	1.35133i	−0.898991	−	0.437967i	$-0.855699\pi$
$677$	−332.978	−	914.850i	−0.491844	−	1.35133i	0.407147	−	0.913362i	$-0.366524\pi$
$678$		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	0.999446	+	0.0332748i	$0.0105936\pi$
$683$	1043.61	+	602.531i	1.52799	+	0.882183i	0.528540	+	0.848908i	$0.322740\pi$
$684$		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	−0.935270	−	0.353935i	$-0.884843\pi$
$691$	44.6727	−	253.352i	0.0646494	−	0.366645i	0.999919	−	0.0127094i	$-0.00404563\pi$
$692$	−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	$-0.918024\pi$
$701$		−	357.086i		−	0.509395i	0.967021	−	0.254697i	$-0.0819759\pi$
$702$		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	0.734626	−	0.678472i	$-0.237357\pi$
$709$	137.566	+	115.432i	0.194029	+	0.162809i	−0.540598	+	0.841281i	$0.681802\pi$
$710$	−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	−0.927957	−	0.372686i	$-0.878437\pi$
$719$	−768.741	+	443.833i	−1.06918	+	0.617292i	−0.141223	+	0.989978i	$0.545103\pi$
$720$		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	−0.838664	−	0.544649i	$-0.816663\pi$
$727$	−822.255	+	299.276i	−1.13103	+	0.411659i	−0.292361	+	0.956308i	$0.594441\pi$
$728$			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	−0.627246	−	0.778821i	$-0.715818\pi$
$733$	22.5932	−	18.9579i	0.0308229	−	0.0258634i	0.658069	+	0.752958i	$0.271374\pi$
$734$	−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	0.920883	+	0.389839i	$0.127469\pi$
$739$	589.760	+	1021.50i	0.798052	+	1.38227i	−0.122831	+	0.992428i	$0.539197\pi$
$740$	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	−0.760036	−	0.649881i	$-0.774819\pi$
$743$	178.261	−	489.768i	0.239921	−	0.659176i	0.999957	−	0.00929571i	$-0.00295896\pi$
$744$		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	0.991742	−	0.128253i	$-0.0409369\pi$
$751$	11.9742	+	67.9089i	0.0159443	+	0.0904246i	−0.975797	+	0.218677i	$0.929826\pi$
$752$	−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	−0.159752	−	0.987157i	$-0.551069\pi$
$761$	21.1240	−	3.72472i	0.0277582	−	0.00489451i	0.187510	+	0.982263i	$0.439958\pi$
$762$		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	0.124877	−	0.992172i	$-0.460146\pi$
$769$	−320.840	−	116.776i	−0.417218	−	0.151855i	−0.542095	+	0.840317i	$0.682369\pi$
$770$	−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	0.237914	−	0.971286i	$-0.423536\pi$
$773$	926.077	−	534.671i	1.19803	−	0.691683i	0.960116	+	0.279603i	$0.0902029\pi$
$774$		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	−0.823318	−	0.567580i	$-0.807880\pi$
$787$	−320.568	+	268.988i	−0.407329	+	0.341789i	0.415989	+	0.909369i	$0.363435\pi$
$788$	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	−0.968754	−	0.248025i	$-0.920219\pi$
$797$	−53.5729	+	147.190i	−0.0672182	+	0.184681i	0.901536	+	0.432705i	$0.142441\pi$
$798$		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	$0.299203\pi$
$809$			1306.60i			1.61509i	−0.589809	+	0.807543i	$0.700797\pi$
$810$		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	−0.361351	−	0.932430i	$-0.617684\pi$
$821$	−837.272	−	147.634i	−1.01982	−	0.179822i	−0.658469	+	0.752608i	$0.728795\pi$
$822$		0			0
$823$	−93.3532	−	33.9778i	−0.113430	−	0.0412853i	0.284681	−	0.958622i	$-0.408112\pi$
$823$	−93.3532	−	33.9778i	−0.113430	−	0.0412853i	−0.398112	+	0.917337i	$0.630334\pi$
$824$	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	−0.974003	−	0.226534i	$-0.927261\pi$
$827$	−1046.01	+	603.912i	−1.26482	+	0.730245i	−0.290817	+	0.956779i	$0.593927\pi$
$828$		0			0
$829$	177.183	−	306.890i	0.213731	−	0.370193i	−0.739148	−	0.673543i	$-0.764772\pi$
$829$	177.183	−	306.890i	0.213731	−	0.370193i	0.952879	+	0.303350i	$0.0981050\pi$
$830$	−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	0.955308	−	0.295612i	$-0.0955236\pi$
$839$	28.0929	+	77.1847i	0.0334838	+	0.0919961i	−0.921824	+	0.387608i	$0.873301\pi$
$840$		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	−0.951835	−	0.306611i	$-0.900805\pi$
$853$	40.4872	−	229.614i	0.0474644	−	0.269184i	0.999299	+	0.0374268i	$0.0119161\pi$
$854$	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	0.112460	−	0.993656i	$-0.464127\pi$
$857$	918.268	−	1094.35i	1.07149	−	1.27695i	0.959032	−	0.283298i	$-0.0914285\pi$
$858$		0			0
$859$	−167.854	−	951.948i	−0.195406	−	1.10820i	−0.911839	−	0.410548i	$-0.865337\pi$
$859$	−167.854	−	951.948i	−0.195406	−	1.10820i	0.716433	−	0.697656i	$-0.245774\pi$
$860$	−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	$0.228782\pi$
$863$			1136.46i			1.31688i	−0.752635	+	0.658438i	$0.771218\pi$
$864$		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	0.375240	−	0.926927i	$-0.377560\pi$
$877$	58.6484	+	21.3463i	0.0668739	+	0.0243401i	−0.308367	+	0.951268i	$0.599782\pi$
$878$	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	−0.864785	−	0.502142i	$-0.832545\pi$
$881$	−759.695	+	438.610i	−0.862310	+	0.497855i	0.00247512	+	0.999997i	$0.499212\pi$
$882$		0			0
$883$	617.031	−	1068.73i	0.698789	−	1.21034i	−0.270097	−	0.962833i	$-0.587056\pi$
$883$	617.031	−	1068.73i	0.698789	−	1.21034i	0.968887	−	0.247505i	$-0.0796108\pi$
$884$	−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	0.940498	+	0.339800i	$0.110359\pi$
$887$	986.184	+	1175.29i	1.11182	+	1.32502i	0.171322	+	0.985215i	$0.445196\pi$
$888$		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	−0.953215	−	0.302294i	$-0.902248\pi$
$907$	41.6356	−	236.127i	0.0459048	−	0.260339i	0.999119	+	0.0419552i	$0.0133587\pi$
$908$	−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	−0.691527	−	0.722351i	$-0.743062\pi$
$911$	127.479	−	151.923i	0.139933	−	0.166765i	0.831459	+	0.555586i	$0.187506\pi$
$912$		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	−0.558112	−	0.829765i	$-0.688474\pi$
$929$	−1269.35	−	223.821i	−1.36636	−	0.240927i	−0.808250	+	0.588839i	$0.799585\pi$
$930$		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	−0.806916	−	0.590667i	$-0.798865\pi$
$937$	101.266	−	175.398i	0.108075	−	0.187191i	0.914990	+	0.403476i	$0.132198\pi$
$938$	−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	0.279447	−	0.960161i	$-0.409849\pi$
$941$	−672.488	−	801.440i	−0.714652	−	0.851689i	−0.994100	+	0.108472i	$0.965404\pi$
$942$		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	0.908754	−	0.417333i	$-0.137035\pi$
$947$	−52.6990	−	144.789i	−0.0556484	−	0.152893i	−0.964402	+	0.264440i	$0.914813\pi$
$948$		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	0.512439	−	0.858724i	$-0.328742\pi$
$953$	23.8079	+	13.7455i	0.0249820	+	0.0144234i	−0.487457	+	0.873147i	$0.662075\pi$
$954$		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	0.832824	+	0.553538i	$0.186723\pi$
$967$	231.642	+	1313.70i	0.239547	+	1.35854i	−0.593277	+	0.804998i	$0.702166\pi$
$968$	−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	$-0.725738\pi$
$971$		−	1473.78i		−	1.51780i	0.651209	−	0.758898i	$-0.274262\pi$
$972$		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	−0.802545	−	0.596592i	$-0.796521\pi$
$977$	−1321.53	+	233.022i	−1.35264	+	0.238508i	−0.550099	+	0.835099i	$0.685410\pi$
$978$		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	0.653169	−	0.757212i	$-0.273439\pi$
$983$	990.831	+	174.710i	1.00797	+	0.177732i	0.354797	+	0.934943i	$0.384550\pi$
$984$		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	−0.125153	−	0.992137i	$-0.539942\pi$
$991$	789.470	−	1367.40i	0.796640	−	1.37982i	0.921793	−	0.387683i	$-0.126725\pi$
$992$	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	−0.549729	−	0.835343i	$-0.685269\pi$
$997$	−432.596	+	157.452i	−0.433897	+	0.157926i	0.115832	+	0.993269i	$0.463047\pi$
$998$		−	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.143.2		36
3.2	odd	2		54.3.f.a.47.6	yes	36
12.11	even	2		432.3.bc.c.209.1		36
27.2	odd	18		1458.3.b.c.1457.9		36
27.4	even	9		54.3.f.a.23.6	✓	36
27.23	odd	18	inner	162.3.f.a.17.2		36
27.25	even	9		1458.3.b.c.1457.28		36
108.31	odd	18		432.3.bc.c.401.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.23.6	✓	36	27.4	even	9
54.3.f.a.47.6	yes	36	3.2	odd	2
162.3.f.a.17.2		36	27.23	odd	18	inner
162.3.f.a.143.2		36	1.1	even	1	trivial
432.3.bc.c.209.1		36	12.11	even	2
432.3.bc.c.401.1		36	108.31	odd	18
1458.3.b.c.1457.9		36	27.2	odd	18
1458.3.b.c.1457.28		36	27.25	even	9

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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