LMFDB - Embedded newform 162.5.f.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,5,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, 5, names="a")

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
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:	$16.7459340196$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	162.17
Dual form			162.5.f.a.143.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-39.1530 - 6.90373i) q^{5} +(-3.77039 + 3.16373i) q^{7} +(19.5959 - 11.3137i) q^{8} +O(q^{10})$	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-39.1530 - 6.90373i) q^{5} +(-3.77039 + 3.16373i) q^{7} +(19.5959 - 11.3137i) q^{8} +(56.2249 - 97.3844i) q^{10} +(-181.112 + 31.9350i) q^{11} +(203.029 - 73.8964i) q^{13} +(-4.76134 - 13.0817i) q^{14} +(11.1135 + 63.0277i) q^{16} +(192.499 + 111.139i) q^{17} +(144.396 + 250.101i) q^{19} +(204.443 + 243.645i) q^{20} +(90.3257 - 512.262i) q^{22} +(611.337 - 728.563i) q^{23} +(897.989 + 326.841i) q^{25} +611.106i q^{26} +39.3752 q^{28} +(-184.883 + 507.961i) q^{29} +(-36.2204 - 30.3925i) q^{31} +(-178.269 - 31.4337i) q^{32} +(-481.611 + 404.120i) q^{34} +(169.464 - 97.8399i) q^{35} +(493.614 - 854.965i) q^{37} +(-804.417 + 141.840i) q^{38} +(-845.346 + 307.681i) q^{40} +(370.924 + 1019.10i) q^{41} +(-203.016 - 1151.36i) q^{43} +(1274.14 + 735.624i) q^{44} +(1345.02 + 2329.64i) q^{46} +(2600.16 + 3098.75i) q^{47} +(-412.723 + 2340.67i) q^{49} +(-1737.39 + 2070.54i) q^{50} +(-1624.23 - 591.171i) q^{52} -3624.45i q^{53} +7311.56 q^{55} +(-38.0907 + 104.653i) q^{56} +(-1171.23 - 982.782i) q^{58} +(4311.09 + 760.161i) q^{59} +(445.569 - 373.877i) q^{61} +(115.818 - 66.8674i) q^{62} +(256.000 - 443.405i) q^{64} +(-8459.35 + 1491.61i) q^{65} +(-871.605 + 317.238i) q^{67} +(-608.190 - 1670.99i) q^{68} +(96.1084 + 545.058i) q^{70} +(-3883.05 - 2241.88i) q^{71} +(-1291.24 - 2236.50i) q^{73} +(1794.86 + 2139.03i) q^{74} +(401.185 - 2275.23i) q^{76} +(581.830 - 693.398i) q^{77} +(-1882.88 - 685.312i) q^{79} -2544.45i q^{80} -3067.45 q^{82} +(2371.25 - 6514.94i) q^{83} +(-6769.64 - 5680.40i) q^{85} +(3256.55 + 574.217i) q^{86} +(-3187.76 + 2674.84i) q^{88} +(6590.17 - 3804.84i) q^{89} +(-531.709 + 920.947i) q^{91} +(-7492.98 + 1321.22i) q^{92} +(-10751.4 + 3913.18i) q^{94} +(-3926.90 - 10789.1i) q^{95} +(1172.65 + 6650.44i) q^{97} +(-5821.89 - 3361.27i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{5}+O(q^{10}) $ 72 * q + 18 * q^5	$ 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) $ 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * 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 $

$2$	−0.967379	+	2.65785i	−0.241845	+	0.664463i
$2$	−0.967379	+	2.65785i	−0.241845	+	0.664463i
$3$		0			0
$3$		0			0
$4$	−6.12836	−	5.14230i	−0.383022	−	0.321394i
$5$	−39.1530	−	6.90373i	−1.56612	−	0.276149i	−0.677756	−	0.735287i	$-0.737047\pi$
$5$	−39.1530	−	6.90373i	−1.56612	−	0.276149i	−0.888365	+	0.459138i	$0.848158\pi$
$6$		0			0
$7$	−3.77039	+	3.16373i	−0.0769467	+	0.0645660i	−0.680450	−	0.732795i	$-0.738216\pi$
$7$	−3.77039	+	3.16373i	−0.0769467	+	0.0645660i	0.603503	+	0.797361i	$0.293771\pi$
$8$	19.5959	−	11.3137i	0.306186	−	0.176777i
$9$		0			0
$10$	56.2249	−	97.3844i	0.562249	−	0.973844i
$11$	−181.112	+	31.9350i	−1.49679	+	0.263925i	−0.861267	−	0.508153i	$-0.830328\pi$
$11$	−181.112	+	31.9350i	−1.49679	+	0.263925i	−0.635528	+	0.772078i	$0.719217\pi$
$12$		0			0
$13$	203.029	−	73.8964i	1.20135	−	0.437257i	0.337657	−	0.941269i	$-0.390366\pi$
$13$	203.029	−	73.8964i	1.20135	−	0.437257i	0.863697	+	0.504012i	$0.168143\pi$
$14$	−4.76134	−	13.0817i	−0.0242925	−	0.0667432i
$15$		0			0
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	192.499	+	111.139i	0.666086	+	0.384565i	0.794592	−	0.607144i	$-0.207685\pi$
$17$	192.499	+	111.139i	0.666086	+	0.384565i	−0.128506	+	0.991709i	$0.541018\pi$
$18$		0			0
$19$	144.396	+	250.101i	0.399989	+	0.692800i	0.993724	−	0.111860i	$-0.0356808\pi$
$19$	144.396	+	250.101i	0.399989	+	0.692800i	−0.593735	+	0.804660i	$0.702347\pi$
$20$	204.443	+	243.645i	0.511106	+	0.609113i
$21$		0			0
$22$	90.3257	−	512.262i	0.186623	−	1.05839i
$23$	611.337	−	728.563i	1.15565	−	1.37725i	0.242231	−	0.970219i	$-0.422121\pi$
$23$	611.337	−	728.563i	1.15565	−	1.37725i	0.913416	−	0.407028i	$-0.133435\pi$
$24$		0			0
$25$	897.989	+	326.841i	1.43678	+	0.522946i
$26$			611.106i			0.904003i
$27$		0			0
$28$	39.3752			0.0502234
$29$	−184.883	+	507.961i	−0.219837	+	0.603996i	−0.999761	−	0.0218779i	$-0.993035\pi$
$29$	−184.883	+	507.961i	−0.219837	+	0.603996i	0.779924	+	0.625874i	$0.215258\pi$
$30$		0			0
$31$	−36.2204	−	30.3925i	−0.0376903	−	0.0316259i	0.623748	−	0.781626i	$-0.285609\pi$
$31$	−36.2204	−	30.3925i	−0.0376903	−	0.0316259i	−0.661438	+	0.750000i	$0.730054\pi$
$32$	−178.269	−	31.4337i	−0.174091	−	0.0306970i
$33$		0			0
$34$	−481.611	+	404.120i	−0.416619	+	0.349585i
$35$	169.464	−	97.8399i	0.138338	−	0.0798693i
$36$		0			0
$37$	493.614	−	854.965i	0.360566	−	0.624518i	−0.627488	−	0.778626i	$-0.715917\pi$
$37$	493.614	−	854.965i	0.360566	−	0.624518i	0.988054	+	0.154108i	$0.0492504\pi$
$38$	−804.417	+	141.840i	−0.557075	+	0.0982274i
$39$		0			0
$40$	−845.346	+	307.681i	−0.528341	+	0.192300i
$41$	370.924	+	1019.10i	0.220656	+	0.606249i	0.999788	−	0.0206124i	$-0.00656159\pi$
$41$	370.924	+	1019.10i	0.220656	+	0.606249i	−0.779131	+	0.626861i	$0.784339\pi$
$42$		0			0
$43$	−203.016	−	1151.36i	−0.109798	−	0.622695i	−0.989195	−	0.146606i	$-0.953165\pi$
$43$	−203.016	−	1151.36i	−0.109798	−	0.622695i	0.879397	−	0.476089i	$-0.157946\pi$
$44$	1274.14	+	735.624i	0.658130	+	0.379971i
$45$		0			0
$46$	1345.02	+	2329.64i	0.635642	+	1.10096i
$47$	2600.16	+	3098.75i	1.17708	+	1.40279i	0.896552	+	0.442938i	$0.146064\pi$
$47$	2600.16	+	3098.75i	1.17708	+	1.40279i	0.280525	+	0.959847i	$0.409492\pi$
$48$		0			0
$49$	−412.723	+	2340.67i	−0.171896	+	0.974871i
$50$	−1737.39	+	2070.54i	−0.694957	+	0.828217i
$51$		0			0
$52$	−1624.23	−	591.171i	−0.600677	−	0.218628i
$53$		−	3624.45i		−	1.29030i	−0.764056	−	0.645150i	$-0.776795\pi$
$53$		−	3624.45i		−	1.29030i	0.764056	−	0.645150i	$-0.223205\pi$
$54$		0			0
$55$	7311.56			2.41704
$56$	−38.0907	+	104.653i	−0.0121463	+	0.0333716i
$57$		0			0
$58$	−1171.23	−	982.782i	−0.348167	−	0.292147i
$59$	4311.09	+	760.161i	1.23846	+	0.218374i	0.754256	−	0.656580i	$-0.227998\pi$
$59$	4311.09	+	760.161i	1.23846	+	0.218374i	0.484206	+	0.874954i	$0.339109\pi$
$60$		0			0
$61$	445.569	−	373.877i	0.119744	−	0.100478i	−0.580949	−	0.813940i	$-0.697318\pi$
$61$	445.569	−	373.877i	0.119744	−	0.100478i	0.700694	+	0.713462i	$0.252874\pi$
$62$	115.818	−	66.8674i	0.0301295	−	0.0173953i
$63$		0			0
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	−8459.35	+	1491.61i	−2.00221	+	0.353044i
$66$		0			0
$67$	−871.605	+	317.238i	−0.194165	+	0.0706702i	−0.437272	−	0.899329i	$-0.644055\pi$
$67$	−871.605	+	317.238i	−0.194165	+	0.0706702i	0.243108	+	0.969999i	$0.421833\pi$
$68$	−608.190	−	1670.99i	−0.131529	−	0.361373i
$69$		0			0
$70$	96.1084	+	545.058i	0.0196140	+	0.111236i
$71$	−3883.05	−	2241.88i	−0.770294	−	0.444730i	0.0626854	−	0.998033i	$-0.480034\pi$
$71$	−3883.05	−	2241.88i	−0.770294	−	0.444730i	−0.832980	+	0.553304i	$0.813367\pi$
$72$		0			0
$73$	−1291.24	−	2236.50i	−0.242305	−	0.419684i	0.719066	−	0.694942i	$-0.244570\pi$
$73$	−1291.24	−	2236.50i	−0.242305	−	0.419684i	−0.961370	+	0.275258i	$0.911237\pi$
$74$	1794.86	+	2139.03i	0.327768	+	0.390619i
$75$		0			0
$76$	401.185	−	2275.23i	0.0694573	−	0.393912i
$77$	581.830	−	693.398i	0.0981329	−	0.116950i
$78$		0			0
$79$	−1882.88	−	685.312i	−0.301695	−	0.109808i	0.186737	−	0.982410i	$-0.440209\pi$
$79$	−1882.88	−	685.312i	−0.301695	−	0.109808i	−0.488432	+	0.872602i	$0.662431\pi$
$80$		−	2544.45i		−	0.397570i
$81$		0			0
$82$	−3067.45			−0.456194
$83$	2371.25	−	6514.94i	0.344207	−	0.945702i	−0.639952	−	0.768415i	$-0.721046\pi$
$83$	2371.25	−	6514.94i	0.344207	−	0.945702i	0.984159	−	0.177287i	$-0.0567321\pi$
$84$		0			0
$85$	−6769.64	−	5680.40i	−0.936974	−	0.786214i
$86$	3256.55	+	574.217i	0.440312	+	0.0776389i
$87$		0			0
$88$	−3187.76	+	2674.84i	−0.411642	+	0.345409i
$89$	6590.17	−	3804.84i	0.831987	−	0.480348i	−0.0225454	−	0.999746i	$-0.507177\pi$
$89$	6590.17	−	3804.84i	0.831987	−	0.480348i	0.854533	+	0.519398i	$0.173844\pi$
$90$		0			0
$91$	−531.709	+	920.947i	−0.0642083	+	0.111212i
$92$	−7492.98	+	1321.22i	−0.885277	+	0.156098i
$93$		0			0
$94$	−10751.4	+	3913.18i	−1.21677	+	0.442868i
$95$	−3926.90	−	10789.1i	−0.435114	−	1.19547i
$96$		0			0
$97$	1172.65	+	6650.44i	0.124631	+	0.706817i	0.981526	+	0.191327i	$0.0612790\pi$
$97$	1172.65	+	6650.44i	0.124631	+	0.706817i	−0.856895	+	0.515490i	$0.827610\pi$
$98$	−5821.89	−	3361.27i	−0.606194	−	0.349986i
$99$		0			0
$100$	−3822.48	−	6620.73i	−0.382248	−	0.662073i
$101$	−5880.72	−	7008.37i	−0.576485	−	0.687028i	0.396464	−	0.918050i	$-0.370237\pi$
$101$	−5880.72	−	7008.37i	−0.576485	−	0.687028i	−0.972948	+	0.231023i	$0.925793\pi$
$102$		0			0
$103$	1733.34	−	9830.28i	0.163384	−	0.926598i	−0.787330	−	0.616531i	$-0.788537\pi$
$103$	1733.34	−	9830.28i	0.163384	−	0.926598i	0.950715	−	0.310067i	$-0.100351\pi$
$104$	3142.49	−	3745.08i	0.290541	−	0.346253i
$105$		0			0
$106$	9633.26	+	3506.22i	0.857357	+	0.312052i
$107$		−	9066.26i		−	0.791882i	−0.918276	−	0.395941i	$-0.870418\pi$
$107$		−	9066.26i		−	0.791882i	0.918276	−	0.395941i	$-0.129582\pi$
$108$		0			0
$109$	13605.2			1.14512			0.572562	−	0.819861i	$-0.305949\pi$
$109$	13605.2			1.14512			0.572562	+	0.819861i	$0.305949\pi$
$110$	−7073.05	+	19433.0i	−0.584549	+	1.60604i
$111$		0			0
$112$	−241.305	−	202.479i	−0.0192367	−	0.0161415i
$113$	21434.2	+	3779.44i	1.67862	+	0.295985i	0.930148	−	0.367186i	$-0.119679\pi$
$113$	21434.2	+	3779.44i	1.67862	+	0.295985i	0.748468	+	0.663171i	$0.230790\pi$
$114$		0			0
$115$	−28965.5	+	24304.9i	−2.19021	+	1.83780i
$116$	3745.11	−	2162.24i	0.278323	−	0.160690i
$117$		0			0
$118$	−6190.85	+	10722.9i	−0.444617	+	0.770099i
$119$	−1077.41	+	189.977i	−0.0760830	+	0.0134155i
$120$		0			0
$121$	18023.7	−	6560.10i	1.23104	−	0.448064i
$122$	562.675	+	1545.94i	0.0378040	+	0.103866i
$123$		0			0
$124$	65.6840	+	372.512i	0.00427185	+	0.0242269i
$125$	−11383.4	−	6572.23i	−0.728540	−	0.420623i
$126$		0			0
$127$	−238.724	−	413.482i	−0.0148009	−	0.0256359i	0.858530	−	0.512763i	$-0.171378\pi$
$127$	−238.724	−	413.482i	−0.0148009	−	0.0256359i	−0.873331	+	0.487127i	$0.838045\pi$
$128$	930.856	+	1109.35i	0.0568149	+	0.0677094i
$129$		0			0
$130$	4218.91	−	23926.7i	0.249640	−	1.41578i
$131$	−6276.63	+	7480.20i	−0.365750	+	0.435884i	−0.917263	−	0.398283i	$-0.869606\pi$
$131$	−6276.63	+	7480.20i	−0.365750	+	0.435884i	0.551513	+	0.834166i	$0.314051\pi$
$132$		0			0
$133$	−1335.68	−	486.148i	−0.0755092	−	0.0274831i
$134$		−	2623.49i		−	0.146106i
$135$		0			0
$136$	5029.59			0.271929
$137$	−2162.94	+	5942.63i	−0.115240	+	0.316620i	−0.983881	−	0.178822i	$-0.942771\pi$
$137$	−2162.94	+	5942.63i	−0.115240	+	0.316620i	0.868641	+	0.495441i	$0.164994\pi$
$138$		0			0
$139$	−19575.0	−	16425.3i	−1.01314	−	0.850129i	−0.0243935	−	0.999702i	$-0.507765\pi$
$139$	−19575.0	−	16425.3i	−1.01314	−	0.850129i	−0.988751	+	0.149574i	$0.952210\pi$
$140$	−1541.66	−	271.836i	−0.0786559	−	0.0138692i
$141$		0			0
$142$	9714.97	−	8151.83i	0.481798	−	0.404276i
$143$	−34411.1	+	19867.3i	−1.68278	+	0.971551i
$144$		0			0
$145$	10745.5	−	18611.8i	0.511084	−	0.885223i
$146$	7193.40	−	1268.39i	0.337465	−	0.0595041i
$147$		0			0
$148$	−7421.53	+	2701.22i	−0.338821	+	0.123321i
$149$	13193.4	+	36248.4i	0.594269	+	1.63274i	0.762497	+	0.646991i	$0.223973\pi$
$149$	13193.4	+	36248.4i	0.594269	+	1.63274i	−0.168229	+	0.985748i	$0.553805\pi$
$150$		0			0
$151$	3880.33	+	22006.5i	0.170183	+	0.965153i	0.943559	+	0.331206i	$0.107455\pi$
$151$	3880.33	+	22006.5i	0.170183	+	0.965153i	−0.773376	+	0.633947i	$0.781434\pi$
$152$	5659.14	+	3267.31i	0.244942	+	0.141417i
$153$		0			0
$154$	1280.10	+	2217.20i	0.0539762	+	0.0934895i
$155$	1208.32	+	1440.02i	0.0502941	+	0.0599382i
$156$		0			0
$157$	−6787.41	+	38493.3i	−0.275363	+	1.56166i	0.462445	+	0.886648i	$0.346972\pi$
$157$	−6787.41	+	38493.3i	−0.275363	+	1.56166i	−0.737807	+	0.675011i	$0.764139\pi$
$158$	3642.92	−	4341.46i	0.145927	−	0.173909i
$159$		0			0
$160$	6762.77	+	2461.45i	0.264171	+	0.0961502i
$161$			4681.08i			0.180590i
$162$		0			0
$163$	19035.9			0.716471			0.358235	−	0.933631i	$-0.383378\pi$
$163$	19035.9			0.716471			0.358235	+	0.933631i	$0.383378\pi$
$164$	2967.39	−	8152.83i	0.110328	−	0.303124i
$165$		0			0
$166$	15021.9	+	12604.8i	0.545139	+	0.457426i
$167$	35958.1	+	6340.38i	1.28933	+	0.227343i	0.775936	−	0.630811i	$-0.217278\pi$
$167$	35958.1	+	6340.38i	1.28933	+	0.227343i	0.513391	+	0.858155i	$0.328389\pi$
$168$		0			0
$169$	13881.0	−	11647.5i	0.486012	−	0.407813i
$170$	21646.5	−	12497.6i	0.749013	−	0.432443i
$171$		0			0
$172$	−4676.50	+	8099.94i	−0.158075	+	0.273794i
$173$	50910.8	−	8976.94i	1.70105	−	0.299941i	0.762990	−	0.646410i	$-0.223730\pi$
$173$	50910.8	−	8976.94i	1.70105	−	0.299941i	0.938062	+	0.346469i	$0.112619\pi$
$174$		0			0
$175$	−4419.81	+	1608.68i	−0.144320	+	0.0525283i
$176$	−4025.57	−	11060.2i	−0.129958	−	0.357056i
$177$		0			0
$178$	3737.50	+	21196.4i	0.117962	+	0.668994i
$179$	−18516.9	−	10690.7i	−0.577913	−	0.333658i	0.182391	−	0.983226i	$-0.441616\pi$
$179$	−18516.9	−	10690.7i	−0.577913	−	0.333658i	−0.760303	+	0.649568i	$0.774950\pi$
$180$		0			0
$181$	−6820.45	−	11813.4i	−0.208188	−	0.360592i	0.742956	−	0.669341i	$-0.233423\pi$
$181$	−6820.45	−	11813.4i	−0.208188	−	0.360592i	−0.951144	+	0.308748i	$0.900090\pi$
$182$	−1933.38	−	2304.11i	−0.0583679	−	0.0695601i
$183$		0			0
$184$	3736.96	−	21193.4i	0.110378	−	0.625985i
$185$	−25228.9	+	30066.7i	−0.737149	+	0.878500i
$186$		0			0
$187$	−38413.1	−	13981.2i	−1.09849	−	0.399818i
$188$		−	32361.1i		−	0.915603i
$189$		0			0
$190$	32474.6			0.899573
$191$	−13501.0	+	37093.7i	−0.370083	+	1.01680i	0.605245	+	0.796039i	$0.293075\pi$
$191$	−13501.0	+	37093.7i	−0.370083	+	1.01680i	−0.975329	+	0.220757i	$0.929147\pi$
$192$		0			0
$193$	37421.0	+	31400.0i	1.00462	+	0.842975i	0.987618	−	0.156880i	$-0.0501437\pi$
$193$	37421.0	+	31400.0i	1.00462	+	0.842975i	0.0170010	+	0.999855i	$0.494588\pi$
$194$	−18810.3	−	3316.76i	−0.499795	−	0.0881274i
$195$		0			0
$196$	14565.7	−	12222.1i	0.379158	−	0.318151i
$197$	12642.8	−	7299.31i	0.325769	−	0.188083i	−0.328192	−	0.944611i	$-0.606439\pi$
$197$	12642.8	−	7299.31i	0.325769	−	0.188083i	0.653961	+	0.756528i	$0.273106\pi$
$198$		0			0
$199$	−4103.40	+	7107.29i	−0.103618	+	0.179472i	−0.913173	−	0.407572i	$-0.866375\pi$
$199$	−4103.40	+	7107.29i	−0.103618	+	0.179472i	0.809554	+	0.587045i	$0.199709\pi$
$200$	21294.7	−	3754.83i	0.532368	−	0.0938708i
$201$		0			0
$202$	24316.1	−	8850.34i	0.595924	−	0.216899i
$203$	−909.973	−	2500.13i	−0.0220819	−	0.0606695i
$204$		0			0
$205$	−7487.15	−	42461.7i	−0.178159	−	1.01039i
$206$	24450.6	+	14116.6i	0.576177	+	0.332656i
$207$		0			0
$208$	6913.88	+	11975.2i	0.159807	+	0.276793i
$209$	−34138.8	−	40685.0i	−0.781548	−	0.931413i
$210$		0			0
$211$	2272.28	−	12886.8i	0.0510384	−	0.289453i	−0.948596	−	0.316489i	$-0.897496\pi$
$211$	2272.28	−	12886.8i	0.0510384	−	0.289453i	0.999634	+	0.0270361i	$0.00860692\pi$
$212$	−18638.0	+	22211.9i	−0.414694	+	0.494214i
$213$		0			0
$214$	24096.8	+	8770.51i	0.526177	+	0.191513i
$215$			46480.9i			1.00554i
$216$		0			0
$217$	232.719			0.00494211
$218$	−13161.4	+	36160.7i	−0.276942	+	0.760893i
$219$		0			0
$220$	−44807.8	−	37598.2i	−0.925781	−	0.776823i
$221$	47295.6	+	8339.49i	0.968359	+	0.170748i
$222$		0			0
$223$	29784.5	−	24992.1i	0.598936	−	0.502567i	−0.292168	−	0.956367i	$-0.594377\pi$
$223$	29784.5	−	24992.1i	0.598936	−	0.502567i	0.891103	+	0.453800i	$0.149932\pi$
$224$	771.592	−	445.479i	0.0153777	−	0.00887833i
$225$		0			0
$226$	−30780.2	+	53312.9i	−0.602636	+	1.04380i
$227$	−66139.5	+	11662.2i	−1.28354	+	0.226323i	−0.773482	−	0.633818i	$-0.781487\pi$
$227$	−66139.5	+	11662.2i	−1.28354	+	0.226323i	−0.510057	+	0.860140i	$0.670376\pi$
$228$		0			0
$229$	11182.5	−	4070.11i	0.213240	−	0.0776132i	−0.233191	−	0.972431i	$-0.574917\pi$
$229$	11182.5	−	4070.11i	0.213240	−	0.0776132i	0.446432	+	0.894818i	$0.352695\pi$
$230$	−36578.3	−	100498.i	−0.691462	−	1.89978i
$231$		0			0
$232$	2123.98	+	12045.7i	0.0394615	+	0.223797i
$233$	37430.6	+	21610.6i	0.689470	+	0.398066i	0.803413	−	0.595422i	$-0.203015\pi$
$233$	37430.6	+	21610.6i	0.689470	+	0.398066i	−0.113944	+	0.993487i	$0.536348\pi$
$234$		0			0
$235$	−80411.2	−	139276.i	−1.45607	−	2.52198i
$236$	−22510.9	−	26827.4i	−0.404174	−	0.481676i
$237$		0			0
$238$	537.335	−	3047.38i	0.00948618	−	0.0537988i
$239$	−6529.01	+	7780.97i	−0.114301	+	0.136219i	−0.820161	−	0.572132i	$-0.806116\pi$
$239$	−6529.01	+	7780.97i	−0.114301	+	0.136219i	0.705860	+	0.708351i	$0.250561\pi$
$240$		0			0
$241$	17483.5	+	6363.46i	0.301019	+	0.109562i	0.488114	−	0.872780i	$-0.337685\pi$
$241$	17483.5	+	6363.46i	0.301019	+	0.109562i	−0.187095	+	0.982342i	$0.559907\pi$
$242$			54250.5i			0.926346i
$243$		0			0
$244$	−4653.19			−0.0781576
$245$	32318.7	−	88794.8i	0.538420	−	1.47930i
$246$		0			0
$247$	47798.1	+	40107.4i	0.783459	+	0.657401i
$248$	−1053.62	−	185.782i	−0.0171310	−	0.00302066i
$249$		0			0
$250$	28480.1	−	23897.6i	0.455682	−	0.382362i
$251$	−39138.9	+	22596.8i	−0.621242	+	0.358674i	−0.777352	−	0.629065i	$-0.783438\pi$
$251$	−39138.9	+	22596.8i	−0.621242	+	0.358674i	0.156110	+	0.987740i	$0.450104\pi$
$252$		0			0
$253$	−87454.0	+	151475.i	−1.36628	+	2.36646i
$254$	1329.91	−	234.499i	0.0206137	−	0.00363474i
$255$		0			0
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	−35299.6	−	96984.9i	−0.534446	−	1.46838i	−0.853728	−	0.520719i	$-0.825664\pi$
$257$	−35299.6	−	96984.9i	−0.534446	−	1.46838i	0.319282	−	0.947660i	$-0.396558\pi$
$258$		0			0
$259$	843.763	+	4785.22i	0.0125783	+	0.0713349i
$260$	59512.2	+	34359.4i	0.880358	+	0.508275i
$261$		0			0
$262$	−13809.4	−	23918.5i	−0.201174	−	0.348443i
$263$	61595.1	+	73406.2i	0.890502	+	1.06126i	0.997751	+	0.0670269i	$0.0213513\pi$
$263$	61595.1	+	73406.2i	0.890502	+	1.06126i	−0.107249	+	0.994232i	$0.534204\pi$
$264$		0			0
$265$	−25022.3	+	141908.i	−0.356315	+	2.02077i
$266$	2584.22	−	3079.75i	0.0365230	−	0.0435264i
$267$		0			0
$268$	6972.84	+	2537.91i	0.0970823	+	0.0353351i
$269$		−	9299.57i		−	0.128516i	−0.997933	−	0.0642581i	$-0.979532\pi$
$269$		−	9299.57i		−	0.128516i	0.997933	−	0.0642581i	$-0.0204681\pi$
$270$		0			0
$271$	83997.0			1.14373			0.571867	−	0.820346i	$-0.306219\pi$
$271$	83997.0			1.14373			0.571867	+	0.820346i	$0.306219\pi$
$272$	−4865.52	+	13367.9i	−0.0657645	+	0.180686i
$273$		0			0
$274$	−13702.3	−	11497.6i	−0.182512	−	0.153146i
$275$	−173074.	−	30517.7i	−2.28859	−	0.403540i
$276$		0			0
$277$	−59511.1	+	49935.8i	−0.775601	+	0.650807i	−0.942137	−	0.335229i	$-0.891186\pi$
$277$	−59511.1	+	49935.8i	−0.775601	+	0.650807i	0.166535	+	0.986035i	$0.446742\pi$
$278$	62592.5	−	36137.8i	0.809903	−	0.467598i
$279$		0			0
$280$	2213.86	−	3834.53i	0.0282381	−	0.0489098i
$281$	1218.12	−	214.787i	0.0154268	−	0.00272017i	−0.165929	−	0.986138i	$-0.553062\pi$
$281$	1218.12	−	214.787i	0.0154268	−	0.00272017i	0.181356	+	0.983417i	$0.441951\pi$
$282$		0			0
$283$	−103425.	+	37643.6i	−1.29138	+	0.470023i	−0.894179	−	0.447710i	$-0.852240\pi$
$283$	−103425.	+	37643.6i	−1.29138	+	0.470023i	−0.397198	+	0.917733i	$0.630017\pi$
$284$	12268.3	+	33706.9i	0.152106	+	0.417909i
$285$		0			0
$286$	−19515.7	−	110679.i	−0.238589	−	1.35311i
$287$	−4622.70	−	2668.92i	−0.0561218	−	0.0324020i
$288$		0			0
$289$	−17056.6	−	29542.9i	−0.204219	−	0.353719i
$290$	39072.5	+	46564.7i	0.464595	+	0.553683i
$291$		0			0
$292$	−3587.55	+	20346.0i	−0.0420758	+	0.238624i
$293$	54136.1	−	64516.9i	0.630597	−	0.751516i	−0.352257	−	0.935903i	$-0.614586\pi$
$293$	54136.1	−	64516.9i	0.630597	−	0.751516i	0.982854	+	0.184387i	$0.0590300\pi$
$294$		0			0
$295$	−163544.	−	59525.2i	−1.87928	−	0.684001i
$296$		−	22338.4i		−	0.254958i
$297$		0			0
$298$	−109106.			−1.22862
$299$	70280.8	−	193095.i	0.786130	−	2.15987i
$300$		0			0
$301$	4408.06	+	3698.80i	0.0486535	+	0.0408252i
$302$	−62243.6	−	10975.2i	−0.682466	−	0.120337i
$303$		0			0
$304$	−14158.5	+	11880.4i	−0.153205	+	0.128554i
$305$	−20026.5	+	11562.3i	−0.215281	+	0.124293i
$306$		0			0
$307$	−11093.3	+	19214.2i	−0.117702	+	0.203867i	−0.918857	−	0.394591i	$-0.870886\pi$
$307$	−11093.3	+	19214.2i	−0.117702	+	0.203867i	0.801154	+	0.598458i	$0.204220\pi$
$308$	−7131.32	+	1257.44i	−0.0751741	+	0.0132552i
$309$		0			0
$310$	−4996.25	+	1818.49i	−0.0519901	+	0.0189228i
$311$	22794.6	+	62627.7i	0.235674	+	0.647509i	0.999996	+	0.00267471i	$0.000851388\pi$
$311$	22794.6	+	62627.7i	0.235674	+	0.647509i	−0.764322	+	0.644834i	$0.776926\pi$
$312$		0			0
$313$	−24431.8	−	138559.i	−0.249383	−	1.41432i	−0.810090	−	0.586306i	$-0.800582\pi$
$313$	−24431.8	−	138559.i	−0.249383	−	1.41432i	0.560707	−	0.828014i	$-0.310529\pi$
$314$	−95743.6	−	55277.6i	−0.971070	−	0.560647i
$315$		0			0
$316$	8014.87	+	13882.2i	0.0802643	+	0.139022i
$317$	11777.8	+	14036.3i	0.117205	+	0.139680i	0.821457	−	0.570271i	$-0.193162\pi$
$317$	11777.8	+	14036.3i	0.117205	+	0.139680i	−0.704252	+	0.709950i	$0.748717\pi$
$318$		0			0
$319$	17262.8	−	97902.1i	0.169640	−	0.962079i
$320$	−13084.3	+	15593.3i	−0.127777	+	0.152278i
$321$		0			0
$322$	−12441.6	−	4528.38i	−0.119995	−	0.0436748i
$323$			64192.2i			0.615286i
$324$		0			0
$325$	206470.			1.95475
$326$	−18414.9	+	50594.7i	−0.173275	+	0.476068i
$327$		0			0
$328$	18798.4	+	15773.8i	0.174733	+	0.146618i
$329$	−19607.3	−	3457.29i	−0.181144	−	0.0319406i
$330$		0			0
$331$	126436.	−	106092.i	1.15402	−	0.968342i	0.154219	−	0.988037i	$-0.450714\pi$
$331$	126436.	−	106092.i	1.15402	−	0.968342i	0.999806	+	0.0196950i	$0.00626952\pi$
$332$	−48033.6	+	27732.2i	−0.435782	+	0.251599i
$333$		0			0
$334$	−51636.9	+	89437.6i	−0.462878	+	0.801729i
$335$	36316.1	−	6403.51i	0.323601	−	0.0570595i
$336$		0			0
$337$	58589.3	−	21324.8i	0.515892	−	0.187769i	−0.0709362	−	0.997481i	$-0.522599\pi$
$337$	58589.3	−	21324.8i	0.515892	−	0.187769i	0.586828	+	0.809712i	$0.300376\pi$
$338$	17529.3	+	48161.2i	0.153437	+	0.421565i
$339$		0			0
$340$	12276.4	+	69623.0i	0.106197	+	0.602275i
$341$	7530.54	+	4347.76i	0.0647616	+	0.0373901i
$342$		0			0
$343$	−11757.9	−	20365.2i	−0.0999401	−	0.173101i
$344$	−17004.5	−	20265.2i	−0.143697	−	0.171251i
$345$		0			0
$346$	−25390.6	+	143997.i	−0.212091	+	1.20283i
$347$	−53805.1	+	64122.4i	−0.446853	+	0.532539i	−0.941706	−	0.336438i	$-0.890778\pi$
$347$	−53805.1	+	64122.4i	−0.446853	+	0.532539i	0.494853	+	0.868977i	$0.335222\pi$
$348$		0			0
$349$	202833.	+	73825.2i	1.66528	+	0.606113i	0.991180	−	0.132524i	$-0.0423082\pi$
$349$	202833.	+	73825.2i	1.66528	+	0.606113i	0.674103	+	0.738637i	$0.264530\pi$
$350$		−	13303.4i		−	0.108599i
$351$		0			0
$352$	33290.6			0.268680
$353$	76213.6	−	209395.i	0.611622	−	1.68042i	−0.114988	−	0.993367i	$-0.536683\pi$
$353$	76213.6	−	209395.i	0.611622	−	1.68042i	0.726610	−	0.687050i	$-0.241095\pi$
$354$		0			0
$355$	136556.	+	114584.i	1.08356	+	0.909216i
$356$	−59952.5	−	10571.2i	−0.473050	−	0.0834116i
$357$		0			0
$358$	46327.3	−	38873.2i	0.361469	−	0.303308i
$359$	68211.7	−	39382.0i	0.529261	−	0.305569i	−0.211454	−	0.977388i	$-0.567820\pi$
$359$	68211.7	−	39382.0i	0.529261	−	0.305569i	0.740715	+	0.671819i	$0.234487\pi$
$360$		0			0
$361$	23460.2	−	40634.2i	0.180018	−	0.311801i
$362$	37996.2	−	6699.75i	0.289950	−	0.0511259i
$363$		0			0
$364$	7994.29	−	2909.68i	0.0603361	−	0.0219605i
$365$	35115.8	+	96480.0i	0.263583	+	0.724188i
$366$		0			0
$367$	3983.82	+	22593.3i	0.0295779	+	0.167745i	0.996019	−	0.0891450i	$-0.0284135\pi$
$367$	3983.82	+	22593.3i	0.0295779	+	0.167745i	−0.966441	+	0.256890i	$0.917302\pi$
$368$	52713.8	+	30434.3i	0.389250	+	0.224733i
$369$		0			0
$370$	−55506.8	−	96140.7i	−0.405455	−	0.702269i
$371$	11466.8	+	13665.6i	0.0833095	+	0.0992844i
$372$		0			0
$373$	29101.5	−	165043.i	0.209170	−	1.18626i	−0.681573	−	0.731750i	$-0.738704\pi$
$373$	29101.5	−	165043.i	0.209170	−	1.18626i	0.890742	−	0.454509i	$-0.150185\pi$
$374$	74320.1	−	88571.2i	0.531328	−	0.633212i
$375$		0			0
$376$	86010.9	+	31305.4i	0.608384	+	0.221434i
$377$			116793.i			0.821738i
$378$		0			0
$379$	−157312.			−1.09518			−0.547589	−	0.836748i	$-0.684454\pi$
$379$	−157312.			−1.09518			−0.547589	+	0.836748i	$0.684454\pi$
$380$	−31415.2	+	86312.6i	−0.217557	+	0.597733i
$381$		0			0
$382$	−85529.0	−	71767.4i	−0.586121	−	0.491813i
$383$	−39148.5	−	6902.93i	−0.266881	−	0.0470583i	0.0386063	−	0.999254i	$-0.487708\pi$
$383$	−39148.5	−	6902.93i	−0.266881	−	0.0470583i	−0.305487	+	0.952196i	$0.598819\pi$
$384$		0			0
$385$	−27567.4	+	23131.8i	−0.185984	+	0.156059i
$386$	−119657.	+	69083.9i	−0.803088	+	0.463663i
$387$		0			0
$388$	27012.1	−	46786.4i	0.179430	−	0.310782i
$389$	−50226.1	+	8856.22i	−0.331918	+	0.0585261i	−0.337124	−	0.941460i	$-0.609454\pi$
$389$	−50226.1	+	8856.22i	−0.331918	+	0.0585261i	0.00520580	+	0.999986i	$0.498343\pi$
$390$		0			0
$391$	198654.	−	72304.1i	1.29940	−	0.472943i
$392$	18393.9	+	50536.9i	0.119702	+	0.328879i
$393$		0			0
$394$	7170.13	+	40663.8i	0.0461886	+	0.261948i
$395$	68989.2	+	39830.9i	0.442168	+	0.255286i
$396$		0			0
$397$	−59351.1	−	102799.i	−0.376571	−	0.652241i	0.613989	−	0.789314i	$-0.289564\pi$
$397$	−59351.1	−	102799.i	−0.376571	−	0.652241i	−0.990561	+	0.137073i	$0.956230\pi$
$398$	−14920.6	−	17781.7i	−0.0941932	−	0.112255i
$399$		0			0
$400$	−10620.3	+	60230.5i	−0.0663767	+	0.376441i
$401$	30668.0	−	36548.7i	0.190720	−	0.227291i	−0.662208	−	0.749320i	$-0.730380\pi$
$401$	30668.0	−	36548.7i	0.190720	−	0.227291i	0.852928	+	0.522029i	$0.174825\pi$
$402$		0			0
$403$	−9599.68	−	3494.00i	−0.0591081	−	0.0215136i
$404$			73190.2i			0.448426i
$405$		0			0
$406$	7525.27			0.0456530
$407$	−62096.3	+	170608.i	−0.374867	+	1.02994i
$408$		0			0
$409$	101089.	+	84823.3i	0.604304	+	0.507071i	0.892826	−	0.450402i	$-0.148719\pi$
$409$	101089.	+	84823.3i	0.604304	+	0.507071i	−0.288522	+	0.957473i	$0.593164\pi$
$410$	120100.	+	21176.9i	0.714455	+	0.125978i
$411$		0			0
$412$	−61172.8	+	51330.1i	−0.360383	+	0.302397i
$413$	−18659.4	+	10773.0i	−0.109395	+	0.0631593i
$414$		0			0
$415$	−137819.	+	238709.i	−0.800225	+	1.38603i
$416$	−38516.6	+	6791.52i	−0.222567	+	0.0392446i
$417$		0			0
$418$	141160.	−	51378.0i	0.807903	−	0.294053i
$419$	−21097.8	−	57965.6i	−0.120173	−	0.330174i	0.864991	−	0.501788i	$-0.167324\pi$
$419$	−21097.8	−	57965.6i	−0.120173	−	0.330174i	−0.985164	+	0.171614i	$0.945102\pi$
$420$		0			0
$421$	24551.8	+	139240.i	0.138522	+	0.785599i	0.972342	+	0.233562i	$0.0750382\pi$
$421$	24551.8	+	139240.i	0.138522	+	0.785599i	−0.833820	+	0.552037i	$0.813851\pi$
$422$	32052.9	+	18505.8i	0.179988	+	0.103916i
$423$		0			0
$424$	−41006.0	−	71024.5i	−0.228095	−	0.395072i
$425$	136537.	+	162718.i	0.755914	+	0.900863i
$426$		0			0
$427$	−497.123	+	2819.32i	−0.00272651	+	0.0154628i
$428$	−46621.4	+	55561.3i	−0.254506	+	0.303309i
$429$		0			0
$430$	−123539.	−	44964.7i	−0.668142	−	0.243184i
$431$		−	181817.i		−	0.978771i	−0.872068	−	0.489385i	$-0.837221\pi$
$431$		−	181817.i		−	0.978771i	0.872068	−	0.489385i	$-0.162779\pi$
$432$		0			0
$433$	229037.			1.22160			0.610800	−	0.791785i	$-0.290848\pi$
$433$	229037.			1.22160			0.610800	+	0.791785i	$0.290848\pi$
$434$	−225.127	+	618.533i	−0.00119522	+	0.00328385i
$435$		0			0
$436$	−83377.7	−	69962.2i	−0.438608	−	0.368036i
$437$	270489.	+	47694.5i	1.41640	+	0.249750i
$438$		0			0
$439$	−119564.	+	100326.i	−0.620398	+	0.520576i	−0.897929	−	0.440141i	$-0.854928\pi$
$439$	−119564.	+	100326.i	−0.620398	+	0.520576i	0.277531	+	0.960717i	$0.410484\pi$
$440$	143277.	−	82720.8i	0.740065	−	0.427277i
$441$		0			0
$442$	−67917.9	+	117637.i	−0.347648	+	0.602144i
$443$	−206819.	+	36467.7i	−1.05386	+	0.185824i	−0.673630	−	0.739069i	$-0.735266\pi$
$443$	−206819.	+	36467.7i	−1.05386	+	0.185824i	−0.380229	+	0.924893i	$0.624155\pi$
$444$		0			0
$445$	−284293.	+	103474.i	−1.43564	+	0.522530i
$446$	37612.5	+	103340.i	0.189088	+	0.519514i
$447$		0			0
$448$	437.595	+	2481.73i	0.00218030	+	0.0123651i
$449$	−52888.9	−	30535.4i	−0.262345	−	0.151465i	0.363059	−	0.931766i	$-0.381732\pi$
$449$	−52888.9	−	30535.4i	−0.262345	−	0.151465i	−0.625404	+	0.780301i	$0.715066\pi$
$450$		0			0
$451$	−99723.8	−	172727.i	−0.490282	−	0.849193i
$452$	−111922.	−	133383.i	−0.547819	−	0.652866i
$453$		0			0
$454$	32985.6	−	187071.i	0.160034	−	0.907600i
$455$	27176.0	−	32387.1i	0.131269	−	0.156440i
$456$		0			0
$457$	318533.	+	115936.i	1.52518	+	0.555121i	0.962436	−	0.271509i	$-0.0875225\pi$
$457$	318533.	+	115936.i	1.52518	+	0.555121i	0.562746	+	0.826630i	$0.309745\pi$
$458$			33658.9i			0.160461i
$459$		0			0
$460$	302494.			1.42956
$461$	−54187.8	+	148880.i	−0.254976	+	0.700541i	0.744482	+	0.667642i	$0.232696\pi$
$461$	−54187.8	+	148880.i	−0.254976	+	0.700541i	−0.999459	+	0.0328993i	$0.989526\pi$
$462$		0			0
$463$	−125857.	−	105607.i	−0.587106	−	0.492640i	0.300166	−	0.953887i	$-0.402958\pi$
$463$	−125857.	−	105607.i	−0.587106	−	0.492640i	−0.887272	+	0.461247i	$0.847402\pi$
$464$	−34070.3	−	6007.51i	−0.158249	−	0.0279035i
$465$		0			0
$466$	−93647.3	+	78579.4i	−0.431244	+	0.361857i
$467$	55470.1	−	32025.7i	0.254346	−	0.146847i	−0.367407	−	0.930060i	$-0.619754\pi$
$467$	55470.1	−	32025.7i	0.254346	−	0.146847i	0.621753	+	0.783214i	$0.286421\pi$
$468$		0			0
$469$	2282.63	−	3953.64i	0.0103775	−	0.0179743i
$470$	447964.	−	78988.1i	2.02790	−	0.357574i
$471$		0			0
$472$	93079.9	−	33878.3i	0.417803	−	0.152068i
$473$	73537.5	+	202043.i	0.328690	+	0.903068i
$474$		0			0
$475$	47922.6	+	271782.i	0.212399	+	1.20458i
$476$	7579.68	+	4376.13i	0.0334531	+	0.0193142i
$477$		0			0
$478$	−14364.6	−	24880.3i	−0.0628693	−	0.108893i
$479$	−141290.	−	168383.i	−0.615802	−	0.733884i	0.364541	−	0.931187i	$-0.381226\pi$
$479$	−141290.	−	168383.i	−0.615802	−	0.733884i	−0.980342	+	0.197304i	$0.936782\pi$
$480$		0			0
$481$	37039.0	−	210059.i	0.160092	−	0.907927i
$482$	−33826.3	+	40312.6i	−0.145600	+	0.173519i
$483$		0			0
$484$	−144190.	−	52480.8i	−0.615522	−	0.224032i
$485$		−	268481.i		−	1.14138i
$486$		0			0
$487$	−193104.			−0.814204			−0.407102	−	0.913383i	$-0.633461\pi$
$487$	−193104.			−0.814204			−0.407102	+	0.913383i	$0.633461\pi$
$488$	4501.40	−	12367.5i	0.0189020	−	0.0519329i
$489$		0			0
$490$	204739.	+	171796.i	0.852724	+	0.715521i
$491$	−45870.0	−	8088.12i	−0.190268	−	0.0335494i	0.0777020	−	0.996977i	$-0.475242\pi$
$491$	−45870.0	−	8088.12i	−0.190268	−	0.0335494i	−0.267970	+	0.963427i	$0.586353\pi$
$492$		0			0
$493$	−92044.1	+	77234.2i	−0.378706	+	0.317772i
$494$	−152838.	+	88241.2i	−0.626294	+	0.361591i
$495$		0			0
$496$	1513.04	−	2620.66i	0.00615015	−	0.0106524i
$497$	21733.3	−	3832.17i	0.0879860	−	0.0155143i
$498$		0			0
$499$	−97499.1	+	35486.8i	−0.391561	+	0.142517i	−0.530295	−	0.847813i	$-0.677919\pi$
$499$	−97499.1	+	35486.8i	−0.391561	+	0.142517i	0.138734	+	0.990330i	$0.455697\pi$
$500$	35965.4	+	98814.0i	0.143861	+	0.395256i
$501$		0			0
$502$	−22196.9	−	125885.i	−0.0880816	−	0.499536i
$503$	−160202.	−	92492.8i	−0.633188	−	0.365571i	0.148798	−	0.988868i	$-0.452460\pi$
$503$	−160202.	−	92492.8i	−0.633188	−	0.365571i	−0.781986	+	0.623297i	$0.785793\pi$
$504$		0			0
$505$	181864.	+	314998.i	0.713122	+	1.23516i
$506$	−317996.	−	378973.i	−1.24200	−	1.48016i
$507$		0			0
$508$	−663.264	+	3761.55i	−0.00257015	+	0.0145761i
$509$	290934.	−	346721.i	1.12294	−	1.33827i	0.188538	−	0.982066i	$-0.439625\pi$
$509$	290934.	−	346721.i	1.12294	−	1.33827i	0.934407	−	0.356208i	$-0.115930\pi$
$510$		0			0
$511$	11944.2	+	4347.32i	0.0457419	+	0.0166487i
$512$		−	11585.2i		−	0.0441942i
$513$		0			0
$514$	291920.			1.10494
$515$	−135731.	+	372919.i	−0.511759	+	1.40605i
$516$		0			0
$517$	−569879.	−	478186.i	−2.13207	−	1.78902i
$518$	−13534.6	−	2386.52i	−0.0504414	−	0.00889418i
$519$		0			0
$520$	−148893.	+	124936.i	−0.550640	+	0.462042i
$521$	−336831.	+	194469.i	−1.24090	+	0.716433i	−0.969277	−	0.245971i	$-0.920893\pi$
$521$	−336831.	+	194469.i	−1.24090	+	0.716433i	−0.271621	+	0.962404i	$0.587560\pi$
$522$		0			0
$523$	85626.7	−	148310.i	0.313044	−	0.542209i	−0.665975	−	0.745974i	$-0.731984\pi$
$523$	85626.7	−	148310.i	0.313044	−	0.542209i	0.979020	+	0.203765i	$0.0653178\pi$
$524$	76930.9	−	13565.0i	0.280181	−	0.0494034i
$525$		0			0
$526$	−254689.	+	92699.1i	−0.920531	+	0.335046i
$527$	−3594.58	−	9876.04i	−0.0129428	−	0.0355600i
$528$		0			0
$529$	−108477.	−	615206.i	−0.387640	−	2.19841i
$530$	−352965.	−	203785.i	−1.25655	−	0.725470i
$531$		0			0
$532$	5685.61	+	9847.77i	0.0200888	+	0.0347948i
$533$	150616.	+	179497.i	0.530173	+	0.631835i
$534$		0			0
$535$	−62591.1	+	354971.i	−0.218678	+	1.24018i
$536$	−13490.8	+	16077.7i	−0.0469577	+	0.0559620i
$537$		0			0
$538$	24716.9	+	8996.21i	0.0853943	+	0.0310810i
$539$		−	437103.i		−	1.50455i
$540$		0			0
$541$	427456.			1.46049			0.730243	−	0.683188i	$-0.239407\pi$
$541$	427456.			1.46049			0.730243	+	0.683188i	$0.239407\pi$
$542$	−81256.9	+	223252.i	−0.276606	+	0.759969i
$543$		0			0
$544$	−30823.1	−	25863.7i	−0.104155	−	0.0873961i
$545$	−532686.	−	93926.8i	−1.79340	−	0.316225i
$546$		0			0
$547$	90572.0	−	75998.9i	0.302705	−	0.253999i	−0.478764	−	0.877943i	$-0.658915\pi$
$547$	90572.0	−	75998.9i	0.302705	−	0.253999i	0.781469	+	0.623944i	$0.214471\pi$
$548$	43814.1	−	25296.1i	0.145899	−	0.0842349i
$549$		0			0
$550$	248540.	−	430484.i	0.821620	−	1.42309i
$551$	−153738.	+	27108.1i	−0.506381	+	0.0892887i
$552$		0			0
$553$	9267.34	−	3373.03i	0.0303043	−	0.0110299i
$554$	−75152.0	−	206479.i	−0.244862	−	0.672753i
$555$		0			0
$556$	35498.3	+	201321.i	0.114831	+	0.651236i
$557$	−330124.	−	190597.i	−1.06406	−	0.614336i	−0.137508	−	0.990501i	$-0.543909\pi$
$557$	−330124.	−	190597.i	−1.06406	−	0.614336i	−0.926553	+	0.376164i	$0.877243\pi$
$558$		0			0
$559$	−126300.	−	218758.i	−0.404184	−	0.700067i
$560$	8049.96	+	9593.57i	0.0256695	+	0.0305917i
$561$		0			0
$562$	−607.510	+	3445.36i	−0.00192345	+	0.0109084i
$563$	33282.4	−	39664.4i	0.105002	−	0.125137i	−0.710984	−	0.703208i	$-0.751750\pi$
$563$	33282.4	−	39664.4i	0.105002	−	0.125137i	0.815986	+	0.578072i	$0.196195\pi$
$564$		0			0
$565$	−813123.	−	295953.i	−2.54718	−	0.927097i
$566$		−	311304.i		−	0.971744i
$567$		0			0
$568$	−101456.			−0.314471
$569$	1926.60	−	5293.30i	0.00595069	−	0.0163494i	−0.936682	−	0.350182i	$-0.886120\pi$
$569$	1926.60	−	5293.30i	0.00595069	−	0.0163494i	0.942632	+	0.333833i	$0.108342\pi$
$570$		0			0
$571$	−251886.	−	211358.i	−0.772560	−	0.648255i	0.168803	−	0.985650i	$-0.446010\pi$
$571$	−251886.	−	211358.i	−0.772560	−	0.648255i	−0.941363	+	0.337395i	$0.890454\pi$
$572$	313047.	+	55198.6i	0.956791	+	0.168708i
$573$		0			0
$574$	11565.5	−	9704.60i	0.0351027	−	0.0294546i
$575$	787099.	−	454432.i	2.38064	−	1.37446i
$576$		0			0
$577$	−183839.	+	318418.i	−0.552186	+	0.956413i	0.445931	+	0.895067i	$0.352873\pi$
$577$	−183839.	+	318418.i	−0.552186	+	0.956413i	−0.998117	+	0.0613461i	$0.980461\pi$
$578$	95020.9	−	16754.8i	0.284422	−	0.0501513i
$579$		0			0
$580$	−161560.	+	58803.1i	−0.480262	+	0.174801i
$581$	11671.0	+	32065.9i	0.0345746	+	0.0949928i
$582$		0			0
$583$	115747.	+	656432.i	0.340543	+	1.93131i
$584$	−50606.1	−	29217.5i	−0.148381	−	0.0856677i
$585$		0			0
$586$	119106.	+	206298.i	0.346848	+	0.600759i
$587$	272661.	+	324945.i	0.791310	+	0.943047i	0.999385	−	0.0350662i	$-0.0111642\pi$
$587$	272661.	+	324945.i	0.791310	+	0.943047i	−0.208075	+	0.978113i	$0.566720\pi$
$588$		0			0
$589$	2371.12	−	13447.3i	0.00683477	−	0.0387619i
$590$	316418.	−	377093.i	0.908986	−	1.08329i
$591$		0			0
$592$	59372.2	+	21609.7i	0.169410	+	0.0616603i
$593$			592801.i			1.68578i	0.538090	+	0.842888i	$0.319146\pi$
$593$			592801.i			1.68578i	−0.538090	+	0.842888i	$0.680854\pi$
$594$		0			0
$595$	43495.4			0.122860
$596$	105547.	−	289988.i	0.297134	−	0.816370i
$597$		0			0
$598$	445230.	+	373592.i	1.24504	+	1.04471i
$599$	−66463.6	−	11719.3i	−0.185238	−	0.0326625i	0.0802595	−	0.996774i	$-0.474425\pi$
$599$	−66463.6	−	11719.3i	−0.185238	−	0.0326625i	−0.265498	+	0.964112i	$0.585536\pi$
$600$		0			0
$601$	−64759.3	+	54339.5i	−0.179289	+	0.150441i	−0.728016	−	0.685561i	$-0.759557\pi$
$601$	−64759.3	+	54339.5i	−0.179289	+	0.150441i	0.548727	+	0.836002i	$0.315113\pi$
$602$	−14095.1	+	8137.82i	−0.0388934	+	0.0224551i
$603$		0			0
$604$	89383.8	−	154817.i	0.245011	−	0.424371i
$605$	−750972.	+	132417.i	−2.05170	+	0.361770i
$606$		0			0
$607$	137246.	−	49953.5i	0.372497	−	0.135578i	−0.148987	−	0.988839i	$-0.547601\pi$
$607$	137246.	−	49953.5i	0.372497	−	0.135578i	0.521483	+	0.853262i	$0.325379\pi$
$608$	−17879.7	−	49124.2i	−0.0483676	−	0.132889i
$609$		0			0
$610$	−11357.7	−	64412.7i	−0.0305232	−	0.173106i
$611$	756894.	+	436993.i	2.02746	+	1.17056i
$612$		0			0
$613$	223284.	+	386738.i	0.594204	+	1.02919i	0.993659	+	0.112439i	$0.0358663\pi$
$613$	223284.	+	386738.i	0.594204	+	1.02919i	−0.399454	+	0.916753i	$0.630800\pi$
$614$	−40337.1	−	48071.9i	−0.106996	−	0.127513i
$615$		0			0
$616$	3556.59	−	20170.4i	0.00937286	−	0.0531561i
$617$	−203553.	+	242585.i	−0.534697	+	0.637227i	−0.963990	−	0.265939i	$-0.914318\pi$
$617$	−203553.	+	242585.i	−0.534697	+	0.637227i	0.429293	+	0.903165i	$0.358763\pi$
$618$		0			0
$619$	156386.	+	56920.0i	0.408148	+	0.148554i	0.537931	−	0.842989i	$-0.319206\pi$
$619$	156386.	+	56920.0i	0.408148	+	0.148554i	−0.129783	+	0.991542i	$0.541428\pi$
$620$		−	15038.5i		−	0.0391219i
$621$		0			0
$622$	−188506.			−0.487242
$623$	−12810.0	+	35195.3i	−0.0330046	+	0.0906793i
$624$		0			0
$625$	−57206.7	−	48002.1i	−0.146449	−	0.122885i
$626$	391905.	+	69103.5i	1.00007	+	0.176340i
$627$		0			0
$628$	239540.	−	200998.i	0.607378	−	0.509650i
$629$	190040.	−	109720.i	0.480335	−	0.277322i
$630$		0			0
$631$	25781.5	−	44654.9i	0.0647515	−	0.112153i	−0.831832	−	0.555027i	$-0.812708\pi$
$631$	25781.5	−	44654.9i	0.0647515	−	0.112153i	0.896584	+	0.442874i	$0.146041\pi$
$632$	−44650.2	+	7873.03i	−0.111786	+	0.0197110i
$633$		0			0
$634$	−48699.9	+	17725.3i	−0.121157	+	0.0440977i
$635$	6492.19	+	17837.2i	0.0161007	+	0.0442362i
$636$		0			0
$637$	89172.3	+	505721.i	0.219761	+	1.24633i
$638$	243510.	+	140590.i	0.598239	+	0.345394i
$639$		0			0
$640$	−28787.2	−	49860.8i	−0.0702811	−	0.121730i
$641$	−54715.0	−	65206.8i	−0.133165	−	0.158700i	0.695341	−	0.718680i	$-0.255253\pi$
$641$	−54715.0	−	65206.8i	−0.133165	−	0.158700i	−0.828506	+	0.559980i	$0.810809\pi$
$642$		0			0
$643$	114445.	−	649048.i	0.276805	−	1.56984i	−0.456366	−	0.889792i	$-0.650849\pi$
$643$	114445.	−	649048.i	0.276805	−	1.56984i	0.733170	−	0.680045i	$-0.238040\pi$
$644$	24071.5	−	28687.3i	0.0580405	−	0.0691700i
$645$		0			0
$646$	−170613.	−	62098.2i	−0.408835	−	0.148804i
$647$			99925.7i			0.238709i	0.992852	+	0.119354i	$0.0380825\pi$
$647$			99925.7i			0.238709i	−0.992852	+	0.119354i	$0.961918\pi$
$648$		0			0
$649$	−805066.			−1.91136
$650$	−199735.	+	548767.i	−0.472745	+	1.29886i
$651$		0			0
$652$	−116659.	−	97888.4i	−0.274424	−	0.230269i
$653$	307372.	+	54198.0i	0.720838	+	0.127103i	0.522020	−	0.852933i	$-0.325179\pi$
$653$	307372.	+	54198.0i	0.720838	+	0.127103i	0.198818	+	0.980036i	$0.436290\pi$
$654$		0			0
$655$	297390.	−	249540.i	0.693177	−	0.581645i
$656$	−60109.5	+	34704.3i	−0.139680	+	0.0806445i
$657$		0			0
$658$	28156.6	−	48768.7i	0.0650322	−	0.112639i
$659$	−387764.	+	68373.3i	−0.892888	+	0.157440i	−0.601224	−	0.799081i	$-0.705320\pi$
$659$	−387764.	+	68373.3i	−0.892888	+	0.157440i	−0.291664	+	0.956521i	$0.594209\pi$
$660$		0			0
$661$	−385642.	+	140362.i	−0.882636	+	0.321253i	−0.743273	−	0.668988i	$-0.766728\pi$
$661$	−385642.	+	140362.i	−0.882636	+	0.321253i	−0.139363	+	0.990241i	$0.544506\pi$
$662$	159667.	+	438680.i	0.364332	+	1.00100i
$663$		0			0
$664$	−27241.4	−	154494.i	−0.0617865	−	0.350409i
$665$	48939.7	+	28255.4i	0.110667	+	0.0638936i
$666$		0			0
$667$	257056.	+	445234.i	0.577798	+	1.00078i
$668$	−187760.	−	223763.i	−0.420774	−	0.501459i
$669$		0			0
$670$	−18111.9	+	102717.i	−0.0403472	+	0.228820i
$671$	−68758.2	+	81942.9i	−0.152714	+	0.181998i
$672$		0			0
$673$	591227.	+	215189.i	1.30534	+	0.475105i	0.898733	−	0.438497i	$-0.144489\pi$
$673$	591227.	+	215189.i	1.30534	+	0.475105i	0.406609	+	0.913602i	$0.366711\pi$
$674$			176351.i			0.388202i
$675$		0			0
$676$	−144963.			−0.317222
$677$	198285.	−	544784.i	0.432626	−	1.18863i	−0.511569	−	0.859242i	$-0.670935\pi$
$677$	198285.	−	544784.i	0.432626	−	1.18863i	0.944195	−	0.329388i	$-0.106842\pi$
$678$		0			0
$679$	−25461.6	−	21364.8i	−0.0552263	−	0.0463404i
$680$	−196924.	−	34722.9i	−0.425873	−	0.0750929i
$681$		0			0
$682$	−18840.6	+	15809.1i	−0.0405066	+	0.0339891i
$683$	−433355.	+	250198.i	−0.928972	+	0.536342i	−0.886486	−	0.462755i	$-0.846861\pi$
$683$	−433355.	+	250198.i	−0.928972	+	0.536342i	−0.0424860	+	0.999097i	$0.513528\pi$
$684$		0			0
$685$	125712.	−	217740.i	0.267914	−	0.464041i
$686$	65502.0	−	11549.8i	0.139189	−	0.0245429i
$687$		0			0
$688$	70311.6	−	25591.3i	0.148542	−	0.0540649i
$689$	−267834.	−	735868.i	−0.564193	−	1.55011i
$690$		0			0
$691$	−21398.5	−	121357.i	−0.0448154	−	0.254161i	0.954166	−	0.299277i	$-0.0967454\pi$
$691$	−21398.5	−	121357.i	−0.0448154	−	0.254161i	−0.998982	+	0.0451160i	$0.985634\pi$
$692$	−358162.	−	206785.i	−0.747940	−	0.431823i
$693$		0			0
$694$	−118378.	−	205037.i	−0.245783	−	0.425709i
$695$	653022.	+	778242.i	1.35194	+	1.61118i
$696$		0			0
$697$	−41860.1	+	237401.i	−0.0861658	+	0.488671i
$698$	−392433.	+	467683.i	−0.805480	+	0.959933i
$699$		0			0
$700$	35358.5	+	12869.4i	0.0721601	+	0.0262641i
$701$			384307.i			0.782064i	0.920377	+	0.391032i	$0.127882\pi$
$701$			384307.i			0.782064i	−0.920377	+	0.391032i	$0.872118\pi$
$702$		0			0
$703$	285103.			0.576888
$704$	−32204.6	+	88481.4i	−0.0649789	+	0.178528i
$705$		0			0
$706$	482814.	+	405129.i	0.968658	+	0.812800i
$707$	44345.2	+	7819.26i	0.0887173	+	0.0156432i
$708$		0			0
$709$	153248.	−	128590.i	0.304861	−	0.255809i	−0.477503	−	0.878630i	$-0.658458\pi$
$709$	153248.	−	128590.i	0.304861	−	0.255809i	0.782364	+	0.622821i	$0.214014\pi$
$710$	−436649.	+	252099.i	−0.866194	+	0.500098i
$711$		0			0
$712$	86093.6	−	149119.i	0.169829	−	0.294152i
$713$	−44285.8	+	7808.78i	−0.0871134	+	0.0153604i
$714$		0			0
$715$	1.48446e6	−	540298.i	2.90372	−	1.05687i
$716$	58503.2	+	160736.i	0.114118	+	0.313536i
$717$		0			0
$718$	38685.1	+	219394.i	0.0750403	+	0.425575i
$719$	217864.	+	125784.i	0.421432	+	0.243314i	0.695690	−	0.718342i	$-0.255099\pi$
$719$	217864.	+	125784.i	0.421432	+	0.243314i	−0.274258	+	0.961656i	$0.588432\pi$
$720$		0			0
$721$	24565.0	+	42547.8i	0.0472548	+	0.0818478i
$722$	85304.8	+	101662.i	0.163644	+	0.195023i
$723$		0			0
$724$	−18949.7	+	107469.i	−0.0361515	+	0.205025i
$725$	−332045.	+	395716.i	−0.631715	+	0.752849i
$726$		0			0
$727$	258027.	+	93914.3i	0.488199	+	0.177690i	0.574379	−	0.818590i	$-0.305244\pi$
$727$	258027.	+	93914.3i	0.488199	+	0.177690i	−0.0861796	+	0.996280i	$0.527466\pi$
$728$			24062.4i			0.0454021i
$729$		0			0
$730$	−290400.			−0.544942
$731$	88881.3	−	244199.i	0.166332	−	0.456993i
$732$		0			0
$733$	331056.	+	277789.i	0.616159	+	0.517019i	0.896594	−	0.442854i	$-0.146034\pi$
$733$	331056.	+	277789.i	0.616159	+	0.517019i	−0.280434	+	0.959873i	$0.590478\pi$
$734$	−63903.6	−	11267.9i	−0.118613	−	0.0209147i
$735$		0			0
$736$	−131884.	+	110664.i	−0.243465	+	0.204291i
$737$	147727.	−	85290.4i	0.271973	−	0.157024i
$738$		0			0
$739$	197706.	−	342437.i	0.362019	−	0.627036i	−0.626274	−	0.779603i	$-0.715421\pi$
$739$	197706.	−	342437.i	0.362019	−	0.627036i	0.988293	+	0.152567i	$0.0487541\pi$
$740$	309224.	−	54524.5i	0.564689	−	0.0995699i
$741$		0			0
$742$	−47413.9	+	17257.2i	−0.0861188	+	0.0313447i
$743$	−263735.	−	724605.i	−0.477738	−	1.31257i	−0.911409	−	0.411502i	$-0.865004\pi$
$743$	−263735.	−	724605.i	−0.477738	−	1.31257i	0.433671	−	0.901071i	$-0.357218\pi$
$744$		0			0
$745$	−266310.	−	1.51032e6i	−0.479816	−	2.72117i
$746$	410508.	+	237007.i	0.737639	+	0.425876i
$747$		0			0
$748$	163514.	+	283214.i	0.292247	+	0.506187i
$749$	28683.2	+	34183.4i	0.0511287	+	0.0609328i
$750$		0			0
$751$	−156730.	+	888862.i	−0.277890	+	1.57599i	0.451739	+	0.892150i	$0.350804\pi$
$751$	−156730.	+	888862.i	−0.277890	+	1.57599i	−0.729629	+	0.683843i	$0.760307\pi$
$752$	−166410.	+	198320.i	−0.294269	+	0.350696i
$753$		0			0
$754$	−310418.	−	112983.i	−0.546015	−	0.198733i
$755$		−	888408.i		−	1.55854i
$756$		0			0
$757$	−64777.5			−0.113040			−0.0565201	−	0.998401i	$-0.518000\pi$
$757$	−64777.5			−0.113040			−0.0565201	+	0.998401i	$0.518000\pi$
$758$	152181.	−	418113.i	0.264863	−	0.727705i
$759$		0			0
$760$	−199016.	−	166994.i	−0.344556	−	0.289117i
$761$	840579.	+	148217.i	1.45147	+	0.255934i	0.843117	−	0.537730i	$-0.180718\pi$
$761$	840579.	+	148217.i	1.45147	+	0.255934i	0.608356	+	0.793664i	$0.291829\pi$
$762$		0			0
$763$	−51297.0	+	43043.3i	−0.0881136	+	0.0739361i
$764$	273486.	−	157897.i	0.468542	−	0.270513i
$765$		0			0
$766$	56218.4	−	97373.1i	0.0958122	−	0.165952i
$767$	931448.	−	164239.i	1.58332	−	0.279181i
$768$		0			0
$769$	−856444.	+	311720.i	−1.44826	+	0.527123i	−0.942104	−	0.335320i	$-0.891156\pi$
$769$	−856444.	+	311720.i	−1.44826	+	0.527123i	−0.506154	+	0.862443i	$0.668933\pi$
$770$	−34812.8	−	95647.4i	−0.0587161	−	0.161321i
$771$		0			0
$772$	−67861.3	−	384860.i	−0.113864	−	0.645756i
$773$	−75468.7	−	43571.9i	−0.126301	−	0.0729201i	0.435518	−	0.900180i	$-0.356565\pi$
$773$	−75468.7	−	43571.9i	−0.126301	−	0.0729201i	−0.561820	+	0.827260i	$0.689898\pi$
$774$		0			0
$775$	−22592.0	−	39130.5i	−0.0376141	−	0.0651496i
$776$	98220.4	+	117054.i	0.163109	+	0.194386i
$777$		0			0
$778$	25049.2	−	142061.i	0.0413842	−	0.234701i
$779$	−201319.	+	239923.i	−0.331749	+	0.395363i
$780$		0			0
$781$	774862.	+	282027.i	1.27035	+	0.462369i
$782$			597938.i			0.977783i
$783$		0			0
$784$	−152114.			−0.247478
$785$	531495.	−	1.46027e6i	0.862502	−	2.36971i
$786$		0			0
$787$	330535.	+	277352.i	0.533664	+	0.447797i	0.869364	−	0.494172i	$-0.164529\pi$
$787$	330535.	+	277352.i	0.533664	+	0.447797i	−0.335701	+	0.941969i	$0.608973\pi$
$788$	−115015.	−	20280.2i	−0.185225	−	0.0326602i
$789$		0			0
$790$	−172603.	+	144831.i	−0.276564	+	0.232065i
$791$	−92772.6	+	53562.3i	−0.148275	+	0.0856064i
$792$		0			0
$793$	62835.2	−	108834.i	0.0999209	−	0.173068i
$794$	330640.	−	58300.7i	0.524462	−	0.0924768i
$795$		0			0
$796$	61694.9	−	22455.1i	0.0973695	−	0.0354396i
$797$	259781.	+	713742.i	0.408969	+	1.12363i	0.957734	+	0.287656i	$0.0928760\pi$
$797$	259781.	+	713742.i	0.408969	+	1.12363i	−0.548765	+	0.835977i	$0.684902\pi$
$798$		0			0
$799$	156135.	+	885487.i	0.244572	+	1.38704i
$800$	−149810.	−	86492.8i	−0.234078	−	0.135145i
$801$		0			0
$802$	67473.4	+	116867.i	0.104902	+	0.181696i
$803$	305282.	+	363821.i	0.473446	+	0.564231i
$804$		0			0
$805$	32316.9	−	183278.i	0.0498698	−	0.282826i
$806$	18573.1	−	22134.5i	0.0285900	−	0.0340722i
$807$		0			0
$808$	−194529.	−	70802.7i	−0.297962	−	0.108449i
$809$		−	20536.7i		−	0.0313786i	−0.999877	−	0.0156893i	$-0.995006\pi$
$809$		−	20536.7i		−	0.0313786i	0.999877	−	0.0156893i	$-0.00499427\pi$
$810$		0			0
$811$	−936475.			−1.42382			−0.711909	−	0.702272i	$-0.752169\pi$
$811$	−936475.			−1.42382			−0.711909	+	0.702272i	$0.752169\pi$
$812$	−7279.78	+	20001.0i	−0.0110410	+	0.0303348i
$813$		0			0
$814$	−393380.	−	330085.i	−0.593696	−	0.498170i
$815$	−745313.	−	131419.i	−1.12208	−	0.197853i
$816$		0			0
$817$	258642.	−	217027.i	0.387486	−	0.325139i
$818$	−323239.	+	186622.i	−0.483078	+	0.278905i
$819$		0			0
$820$	−172467.	+	298722.i	−0.256495	+	0.444262i
$821$	−777509.	+	137096.i	−1.15350	+	0.203394i	−0.717505	−	0.696553i	$-0.754716\pi$
$821$	−777509.	+	137096.i	−1.15350	+	0.203394i	−0.435999	+	0.899947i	$0.643605\pi$
$822$		0			0
$823$	493492.	−	179616.i	0.728585	−	0.265183i	0.0490193	−	0.998798i	$-0.484390\pi$
$823$	493492.	−	179616.i	0.728585	−	0.265183i	0.679566	+	0.733615i	$0.262168\pi$
$824$	−77250.5	−	212244.i	−0.113775	−	0.312594i
$825$		0			0
$826$	−10582.4	−	60015.6i	−0.0155104	−	0.0879638i
$827$	−932150.	−	538177.i	−1.36293	−	0.786890i	−0.372920	−	0.927863i	$-0.621643\pi$
$827$	−932150.	−	538177.i	−1.36293	−	0.786890i	−0.990013	+	0.140973i	$0.954977\pi$
$828$		0			0
$829$	−78556.6	−	136064.i	−0.114307	−	0.197986i	0.803195	−	0.595716i	$-0.203131\pi$
$829$	−78556.6	−	136064.i	−0.114307	−	0.197986i	−0.917503	+	0.397730i	$0.869798\pi$
$830$	−501131.	−	597224.i	−0.727436	−	0.866925i
$831$		0			0
$832$	19209.3	−	108941.i	0.0277501	−	0.157379i
$833$	−339589.	+	404706.i	−0.489399	+	0.583243i
$834$		0			0
$835$	−1.36409e6	−	496490.i	−1.95646	−	0.712094i
$836$			424884.i			0.607937i
$837$		0			0
$838$	174474.			0.248452
$839$	432026.	−	1.18698e6i	0.613743	−	1.68624i	−0.108060	−	0.994144i	$-0.534464\pi$
$839$	432026.	−	1.18698e6i	0.613743	−	1.68624i	0.721802	−	0.692099i	$-0.243314\pi$
$840$		0			0
$841$	317966.	+	266805.i	0.449561	+	0.377226i
$842$	−393831.	−	69443.1i	−0.555502	−	0.0979501i
$843$		0			0
$844$	−80192.9	+	67289.8i	−0.112577	+	0.0944636i
$845$	−623894.	+	360206.i	−0.873771	+	0.504472i
$846$		0			0
$847$	−47202.1	+	81756.4i	−0.0657952	+	0.113961i
$848$	228441.	−	40280.3i	0.317674	−	0.0560146i
$849$		0			0
$850$	−564565.	+	205485.i	−0.781404	+	0.284408i
$851$	−321131.	−	882301.i	−0.443429	−	1.21831i
$852$		0			0
$853$	−117724.	−	667643.i	−0.161795	−	0.917585i	−0.952308	−	0.305139i	$-0.901297\pi$
$853$	−117724.	−	667643.i	−0.161795	−	0.917585i	0.790513	−	0.612446i	$-0.209814\pi$
$854$	−7012.44	−	4048.63i	−0.00961509	−	0.00555127i
$855$		0			0
$856$	−102573.	−	177662.i	−0.139986	−	0.242464i
$857$	−584775.	−	696907.i	−0.796209	−	0.948884i	0.203334	−	0.979109i	$-0.434822\pi$
$857$	−584775.	−	696907.i	−0.796209	−	0.948884i	−0.999543	+	0.0302248i	$0.990378\pi$
$858$		0			0
$859$	86443.6	−	490246.i	0.117151	−	0.664397i	−0.868512	−	0.495669i	$-0.834923\pi$
$859$	86443.6	−	490246.i	0.117151	−	0.664397i	0.985663	−	0.168728i	$-0.0539659\pi$
$860$	239019.	−	284852.i	0.323173	−	0.385143i
$861$		0			0
$862$	483244.	+	175886.i	0.650357	+	0.236711i
$863$			1.06322e6i			1.42759i	0.700355	+	0.713795i	$0.253025\pi$
$863$			1.06322e6i			1.42759i	−0.700355	+	0.713795i	$0.746975\pi$
$864$		0			0
$865$	−2.05528e6			−2.74688
$866$	−221565.	+	608746.i	−0.295438	+	0.811709i
$867$		0			0
$868$	−1426.18	−	1196.71i	−0.00189294	−	0.00158836i
$869$	362898.	+	63988.7i	0.480557	+	0.0847351i
$870$		0			0
$871$	−153518.	+	128817.i	−0.202359	+	0.169800i
$872$	266607.	−	153926.i	0.350621	−	0.202431i
$873$		0			0
$874$	−388430.	+	672781.i	−0.508499	+	0.880746i
$875$	63712.8	−	11234.3i	0.0832167	−	0.0146733i
$876$		0			0
$877$	176659.	−	64298.6i	0.229687	−	0.0835992i	−0.224613	−	0.974448i	$-0.572112\pi$
$877$	176659.	−	64298.6i	0.229687	−	0.0835992i	0.454300	+	0.890849i	$0.349890\pi$
$878$	−150988.	−	414836.i	−0.195863	−	0.538130i
$879$		0			0
$880$	81256.9	+	460831.i	0.104929	+	0.595081i
$881$	153281.	+	88497.0i	0.197486	+	0.114019i	0.595483	−	0.803368i	$-0.296961\pi$
$881$	153281.	+	88497.0i	0.197486	+	0.114019i	−0.397996	+	0.917387i	$0.630294\pi$
$882$		0			0
$883$	163197.	+	282665.i	0.209310	+	0.362535i	0.951497	−	0.307657i	$-0.0995449\pi$
$883$	163197.	+	282665.i	0.209310	+	0.362535i	−0.742187	+	0.670192i	$0.766212\pi$
$884$	−246960.	−	294316.i	−0.316026	−	0.376625i
$885$		0			0
$886$	103146.	−	584972.i	0.131397	−	0.745190i
$887$	484489.	−	577391.i	0.615795	−	0.733876i	−0.364546	−	0.931185i	$-0.618776\pi$
$887$	484489.	−	577391.i	0.615795	−	0.733876i	0.980341	+	0.197309i	$0.0632202\pi$
$888$		0			0
$889$	2208.23	+	803.730i	0.00279409	+	0.00101697i
$890$		−	855706.i		−	1.08030i
$891$		0			0
$892$	−311047.			−0.390927
$893$	−399548.	+	1.09775e6i	−0.501033	+	1.37658i
$894$		0			0
$895$	651186.	+	546410.i	0.812941	+	0.682139i
$896$	−7019.38	−	1237.71i	−0.00874345	−	0.00154171i
$897$		0			0
$898$	132322.	−	111032.i	0.164089	−	0.137687i
$899$	22134.7	−	12779.5i	0.0273877	−	0.0158123i
$900$		0			0
$901$	402819.	−	697703.i	0.496204	−	0.859451i
$902$	555553.	−	97958.9i	0.682829	−	0.120401i
$903$		0			0
$904$	462783.	−	168439.i	0.566292	−	0.206114i
$905$	185485.	+	509616.i	0.226470	+	0.622222i
$906$		0			0
$907$	76295.5	+	432693.i	0.0927437	+	0.525975i	0.995415	+	0.0956457i	$0.0304916\pi$
$907$	76295.5	+	432693.i	0.0927437	+	0.525975i	−0.902672	+	0.430330i	$0.858397\pi$
$908$	465297.	+	268639.i	0.564363	+	0.325835i
$909$		0			0
$910$	59790.6	+	103560.i	0.0722021	+	0.125058i
$911$	217105.	+	258736.i	0.261597	+	0.311759i	0.880816	−	0.473459i	$-0.156995\pi$
$911$	217105.	+	258736.i	0.261597	+	0.311759i	−0.619218	+	0.785219i	$0.712550\pi$
$912$		0			0
$913$	−221407.	+	1.25566e6i	−0.265613	+	1.50637i
$914$	−616284.	+	734459.i	−0.737715	+	0.879174i
$915$		0			0
$916$	−89460.3	−	32560.9i	−0.106620	−	0.0388066i
$917$		−	48060.9i		−	0.0571548i
$918$		0			0
$919$	−882464.			−1.04488			−0.522440	−	0.852676i	$-0.674978\pi$
$919$	−882464.			−1.04488			−0.522440	+	0.852676i	$0.674978\pi$
$920$	−292627.	+	803985.i	−0.345731	+	0.949888i
$921$		0			0
$922$	−343280.	−	288046.i	−0.403819	−	0.338844i
$923$	−954038.	−	168223.i	−1.11986	−	0.197461i
$924$		0			0
$925$	722698.	−	606416.i	0.844643	−	0.708740i
$926$	402439.	−	232348.i	0.469330	−	0.270968i
$927$		0			0
$928$	48926.0	−	84742.3i	0.0568124	−	0.0984020i
$929$	1.21436e6	−	214124.i	1.40707	−	0.248104i	0.582022	−	0.813173i	$-0.302262\pi$
$929$	1.21436e6	−	214124.i	1.40707	−	0.248104i	0.825043	+	0.565069i	$0.191151\pi$
$930$		0			0
$931$	−644998.	+	234760.i	−0.744148	+	0.270848i
$932$	−118260.	−	324917.i	−0.136146	−	0.374059i
$933$		0			0
$934$	31458.9	+	178412.i	0.0360620	+	0.204518i
$935$	1.40747e6	+	812601.i	1.60996	+	0.929510i
$936$		0			0
$937$	373580.	+	647060.i	0.425505	+	0.736996i	0.996467	−	0.0839798i	$-0.0267631\pi$
$937$	373580.	+	647060.i	0.425505	+	0.736996i	−0.570962	+	0.820976i	$0.693430\pi$
$938$	8300.01	+	9891.57i	0.00943351	+	0.0112424i
$939$		0			0
$940$	−223412.	+	1.26703e6i	−0.252843	+	1.43394i
$941$	450253.	−	536590.i	0.508484	−	0.605987i	−0.449334	−	0.893364i	$-0.648339\pi$
$941$	450253.	−	536590.i	0.508484	−	0.605987i	0.957818	+	0.287377i	$0.0927831\pi$
$942$		0			0
$943$	969241.	+	352775.i	1.08995	+	0.396711i
$944$			280166.i			0.314392i
$945$		0			0
$946$	−608138.			−0.679547
$947$	−274783.	+	754961.i	−0.306401	+	0.841830i	0.686950	+	0.726705i	$0.258949\pi$
$947$	−274783.	+	754961.i	−0.306401	+	0.841830i	−0.993351	+	0.115125i	$0.963273\pi$
$948$		0			0
$949$	−427428.	−	358655.i	−0.474603	−	0.398240i
$950$	−768717.	−	135546.i	−0.851764	−	0.150189i
$951$		0			0
$952$	−18963.5	+	15912.3i	−0.0209240	+	0.0175573i
$953$	−41150.2	+	23758.1i	−0.0453091	+	0.0261592i	−0.522483	−	0.852649i	$-0.674994\pi$
$953$	−41150.2	+	23758.1i	−0.0453091	+	0.0261592i	0.477174	+	0.878809i	$0.341661\pi$
$954$		0			0
$955$	784691.	−	1.35912e6i	0.860383	−	1.49023i
$956$	80024.2	−	14110.4i	0.0875599	−	0.0154392i
$957$		0			0
$958$	584218.	−	212638.i	0.636567	−	0.231691i
$959$	−10645.8	−	29249.0i	−0.0115755	−	0.0318034i
$960$		0			0
$961$	−159980.	−	907289.i	−0.173228	−	0.982424i
$962$	522474.	+	301651.i	0.564566	+	0.325952i
$963$		0			0
$964$	−74422.0	−	128903.i	−0.0800843	−	0.138710i
$965$	−1.24837e6	−	1.48775e6i	−1.34057	−	1.59763i
$966$		0			0
$967$	177548.	−	1.00692e6i	0.189873	−	1.07682i	−0.729660	−	0.683810i	$-0.760322\pi$
$967$	177548.	−	1.00692e6i	0.189873	−	1.07682i	0.919533	−	0.393012i	$-0.128567\pi$
$968$	278972.	−	332466.i	0.297722	−	0.354811i
$969$		0			0
$970$	713582.	+	259722.i	0.758403	+	0.276036i
$971$		−	4260.96i		−	0.00451928i	−0.999997	−	0.00225964i	$-0.999281\pi$
$971$		−	4260.96i		−	0.00451928i	0.999997	−	0.00225964i	$-0.000719267\pi$
$972$		0			0
$973$	125771.			0.132848
$974$	186805.	−	513242.i	0.196911	−	0.541009i
$975$		0			0
$976$	28516.4	+	23928.1i	0.0299361	+	0.0251194i
$977$	−216844.	−	38235.5i	−0.227174	−	0.0400570i	0.0589021	−	0.998264i	$-0.481240\pi$
$977$	−216844.	−	38235.5i	−0.227174	−	0.0400570i	−0.286076	+	0.958207i	$0.592351\pi$
$978$		0			0
$979$	−1.07205e6	+	899559.i	−1.11854	+	0.938565i
$980$	−654670.	+	377974.i	−0.681664	+	0.393559i
$981$		0			0
$982$	65870.7	−	114091.i	0.0683077	−	0.118312i
$983$	−295795.	+	52156.6i	−0.306114	+	0.0539762i	−0.324595	−	0.945853i	$-0.605228\pi$
$983$	−295795.	+	52156.6i	−0.306114	+	0.0539762i	0.0184810	+	0.999829i	$0.494117\pi$
$984$		0			0
$985$	−545395.	+	198508.i	−0.562133	+	0.204600i
$986$	−116235.	−	319354.i	−0.119560	−	0.328488i
$987$		0			0
$988$	−86679.6	−	491584.i	−0.0887979	−	0.503598i
$989$	−962953.	−	555961.i	−0.984492	−	0.568397i
$990$		0			0
$991$	141296.	+	244733.i	0.143875	+	0.249198i	0.928952	−	0.370199i	$-0.120711\pi$
$991$	141296.	+	244733.i	0.143875	+	0.249198i	−0.785078	+	0.619397i	$0.787377\pi$
$992$	5501.64	+	6556.59i	0.00559073	+	0.00666277i
$993$		0			0
$994$	−10839.0	+	61471.2i	−0.0109703	+	0.0622155i
$995$	209727.	−	249943.i	0.211840	−	0.252461i
$996$		0			0
$997$	−1.35235e6	−	492214.i	−1.36050	−	0.495181i	−0.444289	−	0.895883i	$-0.646544\pi$
$997$	−1.35235e6	−	492214.i	−1.36050	−	0.495181i	−0.916208	+	0.400703i	$0.868766\pi$
$998$		−	293467.i		−	0.294645i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.17.6		72
3.2	odd	2		54.5.f.a.23.7	✓	72
27.7	even	9		54.5.f.a.47.7	yes	72
27.20	odd	18	inner	162.5.f.a.143.6		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.7	✓	72	3.2	odd	2
54.5.f.a.47.7	yes	72	27.7	even	9
162.5.f.a.17.6		72	1.1	even	1	trivial
162.5.f.a.143.6		72	27.20	odd	18	inner

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-39.1530 - 6.90373i) q^{5} +(-3.77039 + 3.16373i) q^{7} +(19.5959 - 11.3137i) q^{8} +O(q^{10})\)	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-39.1530 - 6.90373i) q^{5} +(-3.77039 + 3.16373i) q^{7} +(19.5959 - 11.3137i) q^{8} +(56.2249 - 97.3844i) q^{10} +(-181.112 + 31.9350i) q^{11} +(203.029 - 73.8964i) q^{13} +(-4.76134 - 13.0817i) q^{14} +(11.1135 + 63.0277i) q^{16} +(192.499 + 111.139i) q^{17} +(144.396 + 250.101i) q^{19} +(204.443 + 243.645i) q^{20} +(90.3257 - 512.262i) q^{22} +(611.337 - 728.563i) q^{23} +(897.989 + 326.841i) q^{25} +611.106i q^{26} +39.3752 q^{28} +(-184.883 + 507.961i) q^{29} +(-36.2204 - 30.3925i) q^{31} +(-178.269 - 31.4337i) q^{32} +(-481.611 + 404.120i) q^{34} +(169.464 - 97.8399i) q^{35} +(493.614 - 854.965i) q^{37} +(-804.417 + 141.840i) q^{38} +(-845.346 + 307.681i) q^{40} +(370.924 + 1019.10i) q^{41} +(-203.016 - 1151.36i) q^{43} +(1274.14 + 735.624i) q^{44} +(1345.02 + 2329.64i) q^{46} +(2600.16 + 3098.75i) q^{47} +(-412.723 + 2340.67i) q^{49} +(-1737.39 + 2070.54i) q^{50} +(-1624.23 - 591.171i) q^{52} -3624.45i q^{53} +7311.56 q^{55} +(-38.0907 + 104.653i) q^{56} +(-1171.23 - 982.782i) q^{58} +(4311.09 + 760.161i) q^{59} +(445.569 - 373.877i) q^{61} +(115.818 - 66.8674i) q^{62} +(256.000 - 443.405i) q^{64} +(-8459.35 + 1491.61i) q^{65} +(-871.605 + 317.238i) q^{67} +(-608.190 - 1670.99i) q^{68} +(96.1084 + 545.058i) q^{70} +(-3883.05 - 2241.88i) q^{71} +(-1291.24 - 2236.50i) q^{73} +(1794.86 + 2139.03i) q^{74} +(401.185 - 2275.23i) q^{76} +(581.830 - 693.398i) q^{77} +(-1882.88 - 685.312i) q^{79} -2544.45i q^{80} -3067.45 q^{82} +(2371.25 - 6514.94i) q^{83} +(-6769.64 - 5680.40i) q^{85} +(3256.55 + 574.217i) q^{86} +(-3187.76 + 2674.84i) q^{88} +(6590.17 - 3804.84i) q^{89} +(-531.709 + 920.947i) q^{91} +(-7492.98 + 1321.22i) q^{92} +(-10751.4 + 3913.18i) q^{94} +(-3926.90 - 10789.1i) q^{95} +(1172.65 + 6650.44i) q^{97} +(-5821.89 - 3361.27i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 72 * q + 18 * q^5	\( 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) \) 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Introduction

L-functions

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