LMFDB - Embedded newform 162.4.e.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, 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:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	162.37
Dual form			162.4.e.a.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53209 + 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-3.45007 + 1.25572i) q^{5} +(0.157049 + 0.890672i) q^{7} +(4.00000 + 6.92820i) q^{8} +O(q^{10})$	\(q+(-1.53209 + 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-3.45007 + 1.25572i) q^{5} +(0.157049 + 0.890672i) q^{7} +(4.00000 + 6.92820i) q^{8} +(3.67149 - 6.35921i) q^{10} +(0.906624 + 0.329984i) q^{11} +(-34.0067 - 28.5350i) q^{13} +(-1.38564 - 1.16269i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(23.7626 - 41.1579i) q^{17} +(-40.7198 - 70.5287i) q^{19} +(2.55019 + 14.4628i) q^{20} +(-1.81325 + 0.659968i) q^{22} +(22.7842 - 129.216i) q^{23} +(-85.4294 + 71.6838i) q^{25} +88.7851 q^{26} +3.61765 q^{28} +(108.416 - 90.9721i) q^{29} +(33.1725 - 188.131i) q^{31} +(30.0702 - 10.9446i) q^{32} +(16.5053 + 93.6062i) q^{34} +(-1.66027 - 2.87567i) q^{35} +(172.744 - 299.201i) q^{37} +(153.056 + 55.7079i) q^{38} +(-22.5002 - 18.8799i) q^{40} +(-268.115 - 224.975i) q^{41} +(-51.5184 - 18.7511i) q^{43} +(1.92962 - 3.34220i) q^{44} +(131.209 + 227.261i) q^{46} +(65.7759 + 373.034i) q^{47} +(321.546 - 117.033i) q^{49} +(38.7305 - 219.652i) q^{50} +(-136.027 + 114.140i) q^{52} -583.296 q^{53} -3.54229 q^{55} +(-5.54256 + 4.65076i) q^{56} +(-49.1520 + 278.755i) q^{58} +(-180.229 + 65.5981i) q^{59} +(94.1572 + 533.992i) q^{61} +(191.033 + 330.879i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(153.158 + 55.7448i) q^{65} +(-543.282 - 455.868i) q^{67} +(-145.625 - 122.194i) q^{68} +(6.24057 + 2.27138i) q^{70} +(-484.577 + 839.312i) q^{71} +(253.463 + 439.011i) q^{73} +(119.987 + 680.478i) q^{74} +(-306.113 + 111.416i) q^{76} +(-0.151523 + 0.859328i) q^{77} +(-716.824 + 601.486i) q^{79} +58.7438 q^{80} +699.998 q^{82} +(704.182 - 590.879i) q^{83} +(-30.2995 + 171.837i) q^{85} +(103.037 - 37.5023i) q^{86} +(1.34030 + 7.60121i) q^{88} +(-17.2388 - 29.8584i) q^{89} +(20.0746 - 34.7702i) q^{91} +(-493.185 - 179.505i) q^{92} +(-580.337 - 486.961i) q^{94} +(229.051 + 192.196i) q^{95} +(509.323 + 185.378i) q^{97} +(-342.182 + 592.677i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−1.53209	+	1.28558i	−0.541675	+	0.454519i
$2$	−1.53209	+	1.28558i	−0.541675	+	0.454519i
$3$		0			0
$3$		0			0
$4$	0.694593	−	3.93923i	0.0868241	−	0.492404i
$5$	−3.45007	+	1.25572i	−0.308584	+	0.112315i	−0.491670	−	0.870782i	$-0.663613\pi$
$5$	−3.45007	+	1.25572i	−0.308584	+	0.112315i	0.183086	+	0.983097i	$0.441391\pi$
$6$		0			0
$7$	0.157049	+	0.890672i	0.00847987	+	0.0480917i	0.988754	−	0.149551i	$-0.0477827\pi$
$7$	0.157049	+	0.890672i	0.00847987	+	0.0480917i	−0.980274	+	0.197642i	$0.936672\pi$
$8$	4.00000	+	6.92820i	0.176777	+	0.306186i
$9$		0			0
$10$	3.67149	−	6.35921i	0.116103	−	0.201096i
$11$	0.906624	+	0.329984i	0.0248507	+	0.00904491i	0.354416	−	0.935088i	$-0.384680\pi$
$11$	0.906624	+	0.329984i	0.0248507	+	0.00904491i	−0.329565	+	0.944133i	$0.606902\pi$
$12$		0			0
$13$	−34.0067	−	28.5350i	−0.725519	−	0.608783i	0.203387	−	0.979099i	$-0.434805\pi$
$13$	−34.0067	−	28.5350i	−0.725519	−	0.608783i	−0.928906	+	0.370315i	$0.879250\pi$
$14$	−1.38564	−	1.16269i	−0.0264520	−	0.0221958i
$15$		0			0
$16$	−15.0351	−	5.47232i	−0.234923	−	0.0855050i
$17$	23.7626	−	41.1579i	0.339016	−	0.587192i	−0.645232	−	0.763987i	$-0.723239\pi$
$17$	23.7626	−	41.1579i	0.339016	−	0.587192i	0.984248	+	0.176794i	$0.0565727\pi$
$18$		0			0
$19$	−40.7198	−	70.5287i	−0.491671	−	0.851600i	0.508283	−	0.861190i	$-0.330281\pi$
$19$	−40.7198	−	70.5287i	−0.491671	−	0.851600i	−0.999954	+	0.00959053i	$0.996947\pi$
$20$	2.55019	+	14.4628i	0.0285120	+	0.161700i
$21$		0			0
$22$	−1.81325	+	0.659968i	−0.0175721	+	0.00639571i
$23$	22.7842	−	129.216i	0.206558	−	1.17145i	−0.688411	−	0.725321i	$-0.741691\pi$
$23$	22.7842	−	129.216i	0.206558	−	1.17145i	0.894969	−	0.446128i	$-0.147198\pi$
$24$		0			0
$25$	−85.4294	+	71.6838i	−0.683435	+	0.573470i
$26$	88.7851			0.669700
$27$		0			0
$28$	3.61765			0.0244168
$29$	108.416	−	90.9721i	0.694221	−	0.582521i	−0.225902	−	0.974150i	$-0.572533\pi$
$29$	108.416	−	90.9721i	0.694221	−	0.582521i	0.920123	+	0.391629i	$0.128088\pi$
$30$		0			0
$31$	33.1725	−	188.131i	0.192192	−	1.08998i	−0.724169	−	0.689623i	$-0.757776\pi$
$31$	33.1725	−	188.131i	0.192192	−	1.08998i	0.916361	−	0.400353i	$-0.131113\pi$
$32$	30.0702	−	10.9446i	0.166116	−	0.0604612i
$33$		0			0
$34$	16.5053	+	93.6062i	0.0832540	+	0.472157i
$35$	−1.66027	−	2.87567i	−0.00801819	−	0.0138879i
$36$		0			0
$37$	172.744	−	299.201i	0.767538	−	1.32941i	−0.171357	−	0.985209i	$-0.554815\pi$
$37$	172.744	−	299.201i	0.767538	−	1.32941i	0.938894	−	0.344205i	$-0.111852\pi$
$38$	153.056	+	55.7079i	0.653395	+	0.237816i
$39$		0			0
$40$	−22.5002	−	18.8799i	−0.0889398	−	0.0746294i
$41$	−268.115	−	224.975i	−1.02128	−	0.856957i	−0.0314931	−	0.999504i	$-0.510026\pi$
$41$	−268.115	−	224.975i	−1.02128	−	0.856957i	−0.989788	+	0.142547i	$0.954471\pi$
$42$		0			0
$43$	−51.5184	−	18.7511i	−0.182709	−	0.0665005i	0.249046	−	0.968492i	$-0.419883\pi$
$43$	−51.5184	−	18.7511i	−0.182709	−	0.0665005i	−0.431754	+	0.901991i	$0.642105\pi$
$44$	1.92962	−	3.34220i	0.00661138	−	0.0114513i
$45$		0			0
$46$	131.209	+	227.261i	0.420559	+	0.728430i
$47$	65.7759	+	373.034i	0.204136	+	1.15771i	0.898793	+	0.438373i	$0.144445\pi$
$47$	65.7759	+	373.034i	0.204136	+	1.15771i	−0.694657	+	0.719341i	$0.744444\pi$
$48$		0			0
$49$	321.546	−	117.033i	0.937452	−	0.341205i
$50$	38.7305	−	219.652i	0.109547	−	0.621269i
$51$		0			0
$52$	−136.027	+	114.140i	−0.362760	+	0.304392i
$53$	−583.296			−1.51173			−0.755867	−	0.654726i	$-0.772784\pi$
$53$	−583.296			−1.51173			−0.755867	+	0.654726i	$0.772784\pi$
$54$		0			0
$55$	−3.54229			−0.00868440
$56$	−5.54256	+	4.65076i	−0.0132260	+	0.0110979i
$57$		0			0
$58$	−49.1520	+	278.755i	−0.111275	+	0.631074i
$59$	−180.229	+	65.5981i	−0.397692	+	0.144748i	−0.533121	−	0.846039i	$-0.678981\pi$
$59$	−180.229	+	65.5981i	−0.397692	+	0.144748i	0.135429	+	0.990787i	$0.456759\pi$
$60$		0			0
$61$	94.1572	+	533.992i	0.197633	+	1.12083i	0.908619	+	0.417625i	$0.137137\pi$
$61$	94.1572	+	533.992i	0.197633	+	1.12083i	−0.710987	+	0.703205i	$0.751751\pi$
$62$	191.033	+	330.879i	0.391309	+	0.677768i
$63$		0			0
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	153.158	+	55.7448i	0.292259	+	0.106374i
$66$		0			0
$67$	−543.282	−	455.868i	−0.990634	−	0.831240i	−0.00497435	−	0.999988i	$-0.501583\pi$
$67$	−543.282	−	455.868i	−0.990634	−	0.831240i	−0.985659	+	0.168747i	$0.946028\pi$
$68$	−145.625	−	122.194i	−0.259701	−	0.217915i
$69$		0			0
$70$	6.24057	+	2.27138i	0.0106556	+	0.00387832i
$71$	−484.577	+	839.312i	−0.809982	+	1.40293i	0.102894	+	0.994692i	$0.467190\pi$
$71$	−484.577	+	839.312i	−0.809982	+	1.40293i	−0.912876	+	0.408237i	$0.866144\pi$
$72$		0			0
$73$	253.463	+	439.011i	0.406378	+	0.703868i	0.994481	−	0.104918i	$-0.0334582\pi$
$73$	253.463	+	439.011i	0.406378	+	0.703868i	−0.588102	+	0.808786i	$0.700125\pi$
$74$	119.987	+	680.478i	0.188489	+	1.06897i
$75$		0			0
$76$	−306.113	+	111.416i	−0.462020	+	0.168162i
$77$	−0.151523	+	0.859328i	−0.000224255	+	0.00127181i
$78$		0			0
$79$	−716.824	+	601.486i	−1.02087	+	0.856614i	−0.989737	−	0.142901i	$-0.954357\pi$
$79$	−716.824	+	601.486i	−1.02087	+	0.856614i	−0.0311359	+	0.999515i	$0.509912\pi$
$80$	58.7438			0.0820970
$81$		0			0
$82$	699.998			0.942706
$83$	704.182	−	590.879i	0.931254	−	0.781415i	−0.0447884	−	0.998996i	$-0.514261\pi$
$83$	704.182	−	590.879i	0.931254	−	0.781415i	0.976042	+	0.217582i	$0.0698169\pi$
$84$		0			0
$85$	−30.2995	+	171.837i	−0.0386640	+	0.219275i
$86$	103.037	−	37.5023i	0.129195	−	0.0470230i
$87$		0			0
$88$	1.34030	+	7.60121i	0.00162359	+	0.00920786i
$89$	−17.2388	−	29.8584i	−0.0205315	−	0.0355616i	0.855577	−	0.517675i	$-0.173203\pi$
$89$	−17.2388	−	29.8584i	−0.0205315	−	0.0355616i	−0.876109	+	0.482114i	$0.839869\pi$
$90$		0			0
$91$	20.0746	−	34.7702i	0.0231251	−	0.0400539i
$92$	−493.185	−	179.505i	−0.558892	−	0.203420i
$93$		0			0
$94$	−580.337	−	486.961i	−0.636779	−	0.534321i
$95$	229.051	+	192.196i	0.247370	+	0.207568i
$96$		0			0
$97$	509.323	+	185.378i	0.533133	+	0.194044i	0.594537	−	0.804069i	$-0.297336\pi$
$97$	509.323	+	185.378i	0.533133	+	0.194044i	−0.0614039	+	0.998113i	$0.519558\pi$
$98$	−342.182	+	592.677i	−0.352710	+	0.610912i
$99$		0			0
$100$	223.040	+	386.317i	0.223040	+	0.386317i
$101$	−47.7079	−	270.565i	−0.0470011	−	0.266557i	0.952247	−	0.305329i	$-0.0987664\pi$
$101$	−47.7079	−	270.565i	−0.0470011	−	0.266557i	−0.999248	+	0.0387722i	$0.987655\pi$
$102$		0			0
$103$	549.879	−	200.139i	0.526031	−	0.191459i	−0.0653345	−	0.997863i	$-0.520811\pi$
$103$	549.879	−	200.139i	0.526031	−	0.191459i	0.591365	+	0.806404i	$0.298589\pi$
$104$	61.6695	−	349.745i	0.0581461	−	0.329763i
$105$		0			0
$106$	893.661	−	749.871i	0.818869	−	0.687112i
$107$	−1048.99			−0.947757			−0.473878	−	0.880590i	$-0.657146\pi$
$107$	−1048.99			−0.947757			−0.473878	+	0.880590i	$0.657146\pi$
$108$		0			0
$109$	971.417			0.853623			0.426812	−	0.904341i	$-0.359637\pi$
$109$	971.417			0.853623			0.426812	+	0.904341i	$0.359637\pi$
$110$	5.42710	−	4.55388i	0.00470412	−	0.00394723i
$111$		0			0
$112$	2.51279	−	14.2507i	0.00211997	−	0.0120229i
$113$	695.954	−	253.306i	0.579379	−	0.210877i	−0.0356727	−	0.999364i	$-0.511357\pi$
$113$	695.954	−	253.306i	0.579379	−	0.210877i	0.615052	+	0.788487i	$0.289135\pi$
$114$		0			0
$115$	83.6520	+	474.414i	0.0678312	+	0.384690i
$116$	−283.055	−	490.266i	−0.226560	−	0.392414i
$117$		0			0
$118$	191.796	−	332.200i	0.149629	−	0.259165i
$119$	40.3901	+	14.7008i	0.0311139	+	0.0113245i
$120$		0			0
$121$	−1018.89	−	854.952i	−0.765509	−	0.642338i
$122$	−830.744	−	697.077i	−0.616492	−	0.517298i
$123$		0			0
$124$	−718.048	−	261.348i	−0.520021	−	0.189272i
$125$	434.191	−	752.040i	0.310682	−	0.538116i
$126$		0			0
$127$	−520.125	−	900.884i	−0.363415	−	0.629453i	0.625106	−	0.780540i	$-0.285056\pi$
$127$	−520.125	−	900.884i	−0.363415	−	0.629453i	−0.988520	+	0.151087i	$0.951722\pi$
$128$	−22.2270	−	126.055i	−0.0153485	−	0.0870455i
$129$		0			0
$130$	−306.315	+	111.490i	−0.206659	+	0.0752175i
$131$	−131.460	+	745.549i	−0.0876775	+	0.497244i	0.909069	+	0.416645i	$0.136794\pi$
$131$	−131.460	+	745.549i	−0.0876775	+	0.497244i	−0.996747	+	0.0805986i	$0.974317\pi$
$132$		0			0
$133$	56.4229	−	47.3444i	0.0367856	−	0.0308668i
$134$	1418.41			0.914417
$135$		0			0
$136$	380.201			0.239720
$137$	2323.34	−	1949.52i	1.44888	−	1.21575i	0.515487	−	0.856898i	$-0.327611\pi$
$137$	2323.34	−	1949.52i	1.44888	−	1.21575i	0.933393	−	0.358857i	$-0.116833\pi$
$138$		0			0
$139$	−164.344	+	932.043i	−0.100284	+	0.568740i	0.892715	+	0.450621i	$0.148797\pi$
$139$	−164.344	+	932.043i	−0.100284	+	0.568740i	−0.992999	+	0.118119i	$0.962314\pi$
$140$	−12.4811	+	4.54276i	−0.00753464	+	0.00274238i
$141$		0			0
$142$	−336.584	−	1908.86i	−0.198912	−	1.12808i
$143$	−21.4152	−	37.0922i	−0.0125233	−	0.0216909i
$144$		0			0
$145$	−259.808	+	450.001i	−0.148799	+	0.257728i
$146$	−952.710	−	346.758i	−0.540047	−	0.196561i
$147$		0			0
$148$	−1058.64	−	888.300i	−0.587968	−	0.493364i
$149$	1765.18	+	1481.16i	0.970531	+	0.814372i	0.982634	−	0.185555i	$-0.0594082\pi$
$149$	1765.18	+	1481.16i	0.970531	+	0.814372i	−0.0121030	+	0.999927i	$0.503853\pi$
$150$		0			0
$151$	−499.712	−	181.880i	−0.269311	−	0.0980212i	0.203835	−	0.979005i	$-0.434659\pi$
$151$	−499.712	−	181.880i	−0.269311	−	0.0980212i	−0.473146	+	0.880984i	$0.656882\pi$
$152$	325.758	−	564.230i	0.173832	−	0.301086i
$153$		0			0
$154$	−0.872585	−	1.51136i	−0.000456590	−	0.000790837i
$155$	121.792	+	690.720i	0.0631136	+	0.357935i
$156$		0			0
$157$	2976.12	−	1083.22i	1.51287	−	0.550639i	0.553514	−	0.832840i	$-0.313287\pi$
$157$	2976.12	−	1083.22i	1.51287	−	0.550639i	0.959355	+	0.282200i	$0.0910643\pi$
$158$	324.981	−	1843.06i	0.163634	−	0.928013i
$159$		0			0
$160$	−90.0008	+	75.5196i	−0.0444699	+	0.0373147i
$161$	118.667			0.0580886
$162$		0			0
$163$	−3338.06			−1.60403			−0.802015	−	0.597304i	$-0.796239\pi$
$163$	−3338.06			−1.60403			−0.802015	+	0.597304i	$0.796239\pi$
$164$	−1072.46	+	899.901i	−0.510641	+	0.428478i
$165$		0			0
$166$	−319.250	+	1810.56i	−0.149269	+	0.846546i
$167$	−141.413	+	51.4702i	−0.0655262	+	0.0238496i	−0.374575	−	0.927197i	$-0.622211\pi$
$167$	−141.413	+	51.4702i	−0.0655262	+	0.0238496i	0.309049	+	0.951046i	$0.399989\pi$
$168$		0			0
$169$	−39.2968	−	222.863i	−0.0178866	−	0.101440i
$170$	−174.488	−	302.222i	−0.0787213	−	0.136349i
$171$		0			0
$172$	−109.649	+	189.918i	−0.0486086	+	0.0841926i
$173$	−3.99229	−	1.45307i	−0.00175450	−	0.000638585i	0.341143	−	0.940012i	$-0.389186\pi$
$173$	−3.99229	−	1.45307i	−0.00175450	−	0.000638585i	−0.342897	+	0.939373i	$0.611408\pi$
$174$		0			0
$175$	−77.2633	−	64.8316i	−0.0333746	−	0.0280046i
$176$	−11.8254	−	9.92268i	−0.00506461	−	0.00424972i
$177$		0			0
$178$	64.7966	+	23.5840i	0.0272849	+	0.00993088i
$179$	303.284	−	525.303i	0.126640	−	0.219346i	−0.795733	−	0.605648i	$-0.792914\pi$
$179$	303.284	−	525.303i	0.126640	−	0.219346i	0.922373	+	0.386301i	$0.126247\pi$
$180$		0			0
$181$	−1154.34	−	1999.38i	−0.474042	−	0.821066i	0.525516	−	0.850784i	$-0.323872\pi$
$181$	−1154.34	−	1999.38i	−0.474042	−	0.821066i	−0.999558	+	0.0297182i	$0.990539\pi$
$182$	13.9437	+	79.0784i	0.00567897	+	0.0322070i
$183$		0			0
$184$	986.369	−	359.009i	0.395196	−	0.143840i
$185$	−220.265	+	1249.18i	−0.0875361	+	0.496442i
$186$		0			0
$187$	35.1252	−	29.4735i	0.0137359	−	0.0115258i
$188$	1515.15			0.587787
$189$		0			0
$190$	−598.009			−0.228338
$191$	−2261.01	+	1897.21i	−0.856548	+	0.718729i	−0.961221	−	0.275778i	$-0.911065\pi$
$191$	−2261.01	+	1897.21i	−0.856548	+	0.718729i	0.104674	+	0.994507i	$0.466620\pi$
$192$		0			0
$193$	−827.740	+	4694.35i	−0.308715	+	1.75081i	0.296765	+	0.954951i	$0.404092\pi$
$193$	−827.740	+	4694.35i	−0.308715	+	1.75081i	−0.605480	+	0.795861i	$0.707019\pi$
$194$	−1018.65	+	370.756i	−0.376982	+	0.137210i
$195$		0			0
$196$	−237.677	−	1347.93i	−0.0866170	−	0.491230i
$197$	−118.634	−	205.480i	−0.0429051	−	0.0743139i	0.843775	−	0.536697i	$-0.180328\pi$
$197$	−118.634	−	205.480i	−0.0429051	−	0.0743139i	−0.886680	+	0.462383i	$0.846995\pi$
$198$		0			0
$199$	−1035.36	+	1793.29i	−0.368816	+	0.638808i	−0.989381	−	0.145347i	$-0.953570\pi$
$199$	−1035.36	+	1793.29i	−0.368816	+	0.638808i	0.620565	+	0.784155i	$0.286903\pi$
$200$	−838.357	−	305.137i	−0.296404	−	0.107882i
$201$		0			0
$202$	420.925	+	353.198i	0.146615	+	0.123024i
$203$	98.0530	+	82.2762i	0.0339013	+	0.0284466i
$204$		0			0
$205$	1207.52	+	439.502i	0.411400	+	0.149737i
$206$	−585.169	+	1013.54i	−0.197916	+	0.342800i
$207$		0			0
$208$	355.140	+	615.121i	0.118387	+	0.205053i
$209$	−13.6442	−	77.3799i	−0.00451573	−	0.0256099i
$210$		0			0
$211$	5063.19	−	1842.85i	1.65197	−	0.601266i	0.662895	−	0.748712i	$-0.269328\pi$
$211$	5063.19	−	1842.85i	1.65197	−	0.601266i	0.989070	+	0.147446i	$0.0471054\pi$
$212$	−405.153	+	2297.74i	−0.131255	+	0.744383i
$213$		0			0
$214$	1607.15	−	1348.56i	0.513376	−	0.430774i
$215$	201.288			0.0638500
$216$		0			0
$217$	172.772			0.0540486
$218$	−1488.30	+	1248.83i	−0.462386	+	0.387988i
$219$		0			0
$220$	−2.46045	+	13.9539i	−0.000754015	+	0.00427623i
$221$	−1982.53	+	721.581i	−0.603435	+	0.219632i
$222$		0			0
$223$	411.818	+	2335.53i	0.123665	+	0.701341i	0.982092	+	0.188404i	$0.0603314\pi$
$223$	411.818	+	2335.53i	0.123665	+	0.701341i	−0.858426	+	0.512937i	$0.828557\pi$
$224$	14.4706	+	25.0638i	0.00431632	+	0.00747609i
$225$		0			0
$226$	−740.619	+	1282.79i	−0.217988	+	0.377566i
$227$	−4404.32	−	1603.04i	−1.28777	−	0.468711i	−0.394778	−	0.918776i	$-0.629179\pi$
$227$	−4404.32	−	1603.04i	−1.28777	−	0.468711i	−0.892996	+	0.450065i	$0.851401\pi$
$228$		0			0
$229$	1581.00	+	1326.62i	0.456225	+	0.382818i	0.841740	−	0.539883i	$-0.181532\pi$
$229$	1581.00	+	1326.62i	0.456225	+	0.382818i	−0.385515	+	0.922702i	$0.625976\pi$
$230$	−738.057	−	619.304i	−0.211592	−	0.177546i
$231$		0			0
$232$	1063.94	+	387.242i	0.301082	+	0.109585i
$233$	3402.02	−	5892.46i	0.956538	−	1.65677i	0.225731	−	0.974190i	$-0.427523\pi$
$233$	3402.02	−	5892.46i	0.956538	−	1.65677i	0.730808	−	0.682583i	$-0.239144\pi$
$234$		0			0
$235$	−695.359	−	1204.40i	−0.193022	−	0.334324i
$236$	133.220	+	755.529i	0.0367453	+	0.208393i
$237$		0			0
$238$	−80.7802	+	29.4016i	−0.0220009	+	0.00800766i
$239$	−600.793	+	3407.26i	−0.162603	+	0.922166i	0.788899	+	0.614523i	$0.210651\pi$
$239$	−600.793	+	3407.26i	−0.162603	+	0.922166i	−0.951502	+	0.307643i	$0.900460\pi$
$240$		0			0
$241$	1330.91	−	1116.76i	0.355732	−	0.298494i	−0.447355	−	0.894356i	$-0.647634\pi$
$241$	1330.91	−	1116.76i	0.355732	−	0.298494i	0.803087	+	0.595862i	$0.203190\pi$
$242$	2660.14			0.706612
$243$		0			0
$244$	2168.92			0.569061
$245$	−962.395	+	807.546i	−0.250960	+	0.210580i
$246$		0			0
$247$	−627.792	+	3560.38i	−0.161722	+	0.917173i
$248$	1436.10	−	522.697i	0.367711	−	0.133836i
$249$		0			0
$250$	301.586	+	1710.38i	0.0762958	+	0.432695i
$251$	1579.71	+	2736.14i	0.397253	+	0.688062i	0.993386	−	0.114823i	$-0.0366302\pi$
$251$	1579.71	+	2736.14i	0.397253	+	0.688062i	−0.596133	+	0.802886i	$0.703297\pi$
$252$		0			0
$253$	63.2958	−	109.632i	0.0157288	−	0.0272430i
$254$	1955.03	+	711.573i	0.482951	+	0.175780i
$255$		0			0
$256$	196.107	+	164.554i	0.0478778	+	0.0401742i
$257$	543.201	+	455.799i	0.131844	+	0.110630i	0.706325	−	0.707888i	$-0.250352\pi$
$257$	543.201	+	455.799i	0.131844	+	0.110630i	−0.574481	+	0.818518i	$0.694796\pi$
$258$		0			0
$259$	293.619	+	106.869i	0.0704425	+	0.0256390i
$260$	325.974	−	564.603i	0.0777540	−	0.134674i
$261$		0			0
$262$	−757.051	−	1311.25i	−0.178514	−	0.309196i
$263$	−605.174	−	3432.11i	−0.141888	−	0.804689i	−0.969813	−	0.243850i	$-0.921590\pi$
$263$	−605.174	−	3432.11i	−0.141888	−	0.804689i	0.827925	−	0.560839i	$-0.189521\pi$
$264$		0			0
$265$	2012.41	−	732.459i	0.466497	−	0.169791i
$266$	−25.5801	+	145.072i	−0.00589630	+	0.0334396i
$267$		0			0
$268$	−2173.13	+	1823.47i	−0.495317	+	0.415620i
$269$	−2793.10			−0.633080			−0.316540	−	0.948579i	$-0.602521\pi$
$269$	−2793.10			−0.633080			−0.316540	+	0.948579i	$0.602521\pi$
$270$		0			0
$271$	−5039.48			−1.12962			−0.564809	−	0.825222i	$-0.691050\pi$
$271$	−5039.48			−1.12962			−0.564809	+	0.825222i	$0.691050\pi$
$272$	−582.501	+	488.777i	−0.129851	+	0.108958i
$273$		0			0
$274$	−1053.32	+	5973.66i	−0.232238	+	1.31709i
$275$	−101.107	+	36.7999i	−0.0221708	+	0.00806951i
$276$		0			0
$277$	−774.796	−	4394.09i	−0.168061	−	0.953123i	−0.945852	−	0.324599i	$-0.894771\pi$
$277$	−774.796	−	4394.09i	−0.168061	−	0.953123i	0.777790	−	0.628524i	$-0.216340\pi$
$278$	−946.421	−	1639.25i	−0.204182	−	0.353654i
$279$		0			0
$280$	13.2822	−	23.0054i	0.00283486	−	0.00491012i
$281$	2873.91	+	1046.02i	0.610119	+	0.222065i	0.628555	−	0.777765i	$-0.283647\pi$
$281$	2873.91	+	1046.02i	0.610119	+	0.222065i	−0.0184366	+	0.999830i	$0.505869\pi$
$282$		0			0
$283$	−4898.87	−	4110.64i	−1.02900	−	0.863436i	−0.0382706	−	0.999267i	$-0.512185\pi$
$283$	−4898.87	−	4110.64i	−1.02900	−	0.863436i	−0.990732	+	0.135832i	$0.956629\pi$
$284$	2969.66	+	2491.84i	0.620482	+	0.520646i
$285$		0			0
$286$	80.4947	+	29.2977i	0.0166425	+	0.00605737i
$287$	158.272	−	274.135i	0.0325522	−	0.0563821i
$288$		0			0
$289$	1327.18	+	2298.75i	0.270137	+	0.467891i
$290$	−180.461	−	1023.45i	−0.0365415	−	0.207237i
$291$		0			0
$292$	1905.42	−	693.516i	0.381871	−	0.138990i
$293$	−188.221	+	1067.45i	−0.0375290	+	0.212837i	−0.997806	−	0.0662126i	$-0.978908\pi$
$293$	−188.221	+	1067.45i	−0.0375290	+	0.212837i	0.960277	+	0.279050i	$0.0900195\pi$
$294$		0			0
$295$	539.431	−	452.636i	0.106464	−	0.0893339i
$296$	2763.90			0.542731
$297$		0			0
$298$	−4608.56			−0.895861
$299$	−4461.98	+	3744.05i	−0.863021	+	0.724160i
$300$		0			0
$301$	8.61019	−	48.8308i	0.00164878	−	0.00935070i
$302$	999.423	−	363.760i	0.190432	−	0.0693114i
$303$		0			0
$304$	226.269	+	1283.24i	0.0426889	+	0.242101i
$305$	−995.395	−	1724.08i	−0.186873	−	0.323673i
$306$		0			0
$307$	2594.82	−	4494.35i	0.482391	−	0.835525i	−0.517405	−	0.855741i	$-0.673102\pi$
$307$	2594.82	−	4494.35i	0.482391	−	0.835525i	0.999796	+	0.0202154i	$0.00643521\pi$
$308$	3.27985	+	1.19377i	0.000606774	+	0.000220848i
$309$		0			0
$310$	−1074.57	−	901.670i	−0.196876	−	0.165198i
$311$	−1343.31	−	1127.17i	−0.244926	−	0.205518i	0.512058	−	0.858951i	$-0.328883\pi$
$311$	−1343.31	−	1127.17i	−0.244926	−	0.205518i	−0.756984	+	0.653434i	$0.773328\pi$
$312$		0			0
$313$	−4429.40	−	1612.17i	−0.799887	−	0.291135i	−0.0904476	−	0.995901i	$-0.528830\pi$
$313$	−4429.40	−	1612.17i	−0.799887	−	0.291135i	−0.709440	+	0.704766i	$0.751052\pi$
$314$	−3167.12	+	5485.62i	−0.569208	+	0.985896i
$315$		0			0
$316$	1871.49	+	3241.52i	0.333164	+	0.577057i
$317$	−923.346	−	5236.56i	−0.163597	−	0.927805i	−0.950499	−	0.310727i	$-0.899427\pi$
$317$	−923.346	−	5236.56i	−0.163597	−	0.927805i	0.786902	−	0.617078i	$-0.211684\pi$
$318$		0			0
$319$	128.312	−	46.7018i	0.0225207	−	0.00819687i
$320$	40.8030	−	231.406i	0.00712800	−	0.0404249i
$321$		0			0
$322$	−181.808	+	152.555i	−0.0314652	+	0.0264024i
$323$	−3870.42			−0.666737
$324$		0			0
$325$	4950.66			0.844965
$326$	5114.20	−	4291.32i	0.868863	−	0.729063i
$327$		0			0
$328$	486.214	−	2757.46i	0.0818496	−	0.464192i
$329$	−321.920	+	117.169i	−0.0539454	+	0.0196345i
$330$		0			0
$331$	−858.688	−	4869.86i	−0.142591	−	0.808676i	−0.969270	−	0.246001i	$-0.920883\pi$
$331$	−858.688	−	4869.86i	−0.142591	−	0.808676i	0.826678	−	0.562675i	$-0.190228\pi$
$332$	−1838.49	−	3184.36i	−0.303916	−	0.526399i
$333$		0			0
$334$	150.489	−	260.654i	0.0246538	−	0.0427017i
$335$	2446.81	+	890.565i	0.399055	+	0.145244i
$336$		0			0
$337$	−4351.14	−	3651.04i	−0.703328	−	0.590162i	0.219390	−	0.975637i	$-0.429593\pi$
$337$	−4351.14	−	3651.04i	−0.703328	−	0.590162i	−0.922718	+	0.385475i	$0.874038\pi$
$338$	346.713	+	290.927i	0.0557950	+	0.0468176i
$339$		0			0
$340$	655.860	+	238.714i	0.104615	+	0.0380767i
$341$	92.1551	−	159.617i	0.0146348	−	0.0253483i
$342$		0			0
$343$	309.843	+	536.664i	0.0487754	+	0.0844815i
$344$	−76.1617	−	431.934i	−0.0119371	−	0.0676986i
$345$		0			0
$346$	7.98458	−	2.90615i	0.00124062	−	0.000451548i
$347$	1588.15	−	9006.84i	0.245695	−	1.39341i	−0.573177	−	0.819432i	$-0.694289\pi$
$347$	1588.15	−	9006.84i	0.245695	−	1.39341i	0.818872	−	0.573976i	$-0.194600\pi$
$348$		0			0
$349$	5900.93	−	4951.46i	0.905070	−	0.759444i	−0.0661050	−	0.997813i	$-0.521057\pi$
$349$	5900.93	−	4951.46i	0.905070	−	0.759444i	0.971175	+	0.238369i	$0.0766128\pi$
$350$	201.720			0.0308069
$351$		0			0
$352$	30.8739			0.00467495
$353$	1964.72	−	1648.60i	0.296237	−	0.248572i	−0.482539	−	0.875875i	$-0.660285\pi$
$353$	1964.72	−	1648.60i	0.296237	−	0.248572i	0.778776	+	0.627302i	$0.215841\pi$
$354$		0			0
$355$	617.882	−	3504.18i	0.0923768	−	0.523895i
$356$	−129.593	+	47.1680i	−0.0192933	+	0.00702219i
$357$		0			0
$358$	210.659	+	1194.70i	0.0310996	+	0.176375i
$359$	6068.18	+	10510.4i	0.892107	+	1.54517i	0.837345	+	0.546675i	$0.184107\pi$
$359$	6068.18	+	10510.4i	0.892107	+	1.54517i	0.0547620	+	0.998499i	$0.482560\pi$
$360$		0			0
$361$	113.301	−	196.243i	0.0165186	−	0.0286110i
$362$	4338.91	+	1579.24i	0.629967	+	0.229289i
$363$		0			0
$364$	−123.024	−	103.229i	−0.0177149	−	0.0148645i
$365$	−1425.74	−	1196.34i	−0.204457	−	0.171560i
$366$		0			0
$367$	845.015	+	307.560i	0.120189	+	0.0437453i	0.401415	−	0.915896i	$-0.368519\pi$
$367$	845.015	+	307.560i	0.120189	+	0.0437453i	−0.281225	+	0.959642i	$0.590741\pi$
$368$	−1049.67	+	1818.09i	−0.148690	+	0.257539i
$369$		0			0
$370$	−1268.45	−	2197.03i	−0.178226	−	0.308697i
$371$	−91.6063	−	519.525i	−0.0128193	−	0.0727019i
$372$		0			0
$373$	−7573.79	+	2756.63i	−1.05136	+	0.382662i	−0.809174	−	0.587569i	$-0.800085\pi$
$373$	−7573.79	+	2756.63i	−1.05136	+	0.382662i	−0.242182	+	0.970231i	$0.577863\pi$
$374$	−15.9245	+	90.3121i	−0.00220170	+	0.0124864i
$375$		0			0
$376$	−2321.35	+	1947.84i	−0.318390	+	0.267161i
$377$	−6282.77			−0.858300
$378$		0			0
$379$	2394.42			0.324520			0.162260	−	0.986748i	$-0.448122\pi$
$379$	2394.42			0.324520			0.162260	+	0.986748i	$0.448122\pi$
$380$	916.203	−	768.785i	0.123685	−	0.103784i
$381$		0			0
$382$	1025.06	−	5813.39i	0.137294	−	0.778635i
$383$	10905.6	−	3969.30i	1.45496	−	0.529560i	0.510985	−	0.859590i	$-0.329281\pi$
$383$	10905.6	−	3969.30i	1.45496	−	0.529560i	0.943971	+	0.330029i	$0.107059\pi$
$384$		0			0
$385$	−0.556314	−	3.15501i	−7.36426e−5	−	0.000417648i
$386$	−4766.77	−	8256.28i	−0.628554	−	1.08869i
$387$		0			0
$388$	1084.02	−	1877.58i	0.141837	−	0.245669i
$389$	9197.18	+	3347.50i	1.19875	+	0.436311i	0.862790	−	0.505563i	$-0.168715\pi$
$389$	9197.18	+	3347.50i	1.19875	+	0.436311i	0.335965	+	0.941874i	$0.390937\pi$
$390$		0			0
$391$	−4776.84	−	4008.25i	−0.617840	−	0.518429i
$392$	2097.01	+	1759.60i	0.270192	+	0.226718i
$393$		0			0
$394$	445.917	+	162.301i	0.0570177	+	0.0207528i
$395$	1717.79	−	2975.30i	0.218814	−	0.378997i
$396$		0			0
$397$	5723.78	+	9913.87i	0.723597	+	1.25331i	0.959549	+	0.281542i	$0.0908460\pi$
$397$	5723.78	+	9913.87i	0.723597	+	1.25331i	−0.235951	+	0.971765i	$0.575821\pi$
$398$	−719.150	−	4078.51i	−0.0905723	−	0.513661i
$399$		0			0
$400$	1676.71	−	610.274i	0.209589	−	0.0762843i
$401$	1642.85	−	9317.09i	0.204589	−	1.16028i	−0.693496	−	0.720460i	$-0.743931\pi$
$401$	1642.85	−	9317.09i	0.204589	−	1.16028i	0.898085	−	0.439822i	$-0.144958\pi$
$402$		0			0
$403$	−6496.39	+	5451.12i	−0.802998	+	0.673795i
$404$	−1098.96			−0.135334
$405$		0			0
$406$	−255.998			−0.0312930
$407$	255.345	−	214.260i	0.0310983	−	0.0260945i
$408$		0			0
$409$	−1213.29	+	6880.93i	−0.146683	+	0.831883i	0.819317	+	0.573341i	$0.194353\pi$
$409$	−1213.29	+	6880.93i	−0.146683	+	0.831883i	−0.966000	+	0.258542i	$0.916758\pi$
$410$	−2415.05	+	879.005i	−0.290904	+	0.105880i
$411$		0			0
$412$	−406.454	−	2305.11i	−0.0486033	−	0.275643i
$413$	−86.7313	−	150.223i	−0.0103336	−	0.0178983i
$414$		0			0
$415$	−1687.50	+	2922.83i	−0.199605	+	0.345726i
$416$	−1334.89	−	485.861i	−0.157328	−	0.0572627i
$417$		0			0
$418$	120.382	+	101.012i	0.0140863	+	0.0118198i
$419$	−5662.58	−	4751.47i	−0.660227	−	0.553996i	0.249928	−	0.968264i	$-0.419593\pi$
$419$	−5662.58	−	4751.47i	−0.660227	−	0.553996i	−0.910155	+	0.414268i	$0.864037\pi$
$420$		0			0
$421$	−926.159	−	337.094i	−0.107217	−	0.0390237i	0.287855	−	0.957674i	$-0.407058\pi$
$421$	−926.159	−	337.094i	−0.107217	−	0.0390237i	−0.395071	+	0.918650i	$0.629280\pi$
$422$	−5388.14	+	9332.53i	−0.621541	+	1.07654i
$423$		0			0
$424$	−2333.18	−	4041.19i	−0.267239	−	0.462872i
$425$	920.337	+	5219.49i	0.105042	+	0.595723i
$426$		0			0
$427$	−460.824	+	167.726i	−0.0522268	+	0.0190090i
$428$	−728.623	+	4132.23i	−0.0822881	+	0.466679i
$429$		0			0
$430$	−308.392	+	258.771i	−0.0345860	+	0.0290211i
$431$	5007.29			0.559612			0.279806	−	0.960057i	$-0.409730\pi$
$431$	5007.29			0.559612			0.279806	+	0.960057i	$0.409730\pi$
$432$		0			0
$433$	16525.3			1.83408			0.917038	−	0.398801i	$-0.130573\pi$
$433$	16525.3			1.83408			0.917038	+	0.398801i	$0.130573\pi$
$434$	−264.702	+	222.112i	−0.0292768	+	0.0245661i
$435$		0			0
$436$	674.739	−	3826.64i	0.0741150	−	0.420327i
$437$	−10041.2	+	3654.69i	−1.09916	+	0.400063i
$438$		0			0
$439$	2889.86	+	16389.2i	0.314181	+	1.78181i	0.576778	+	0.816901i	$0.304310\pi$
$439$	2889.86	+	16389.2i	0.314181	+	1.78181i	−0.262597	+	0.964906i	$0.584579\pi$
$440$	−14.1691	−	24.5417i	−0.00153520	−	0.00265904i
$441$		0			0
$442$	2109.76	−	3654.21i	0.227039	−	0.393242i
$443$	12.2688	+	4.46548i	0.00131582	+	0.000478919i	0.342678	−	0.939453i	$-0.388666\pi$
$443$	12.2688	+	4.46548i	0.00131582	+	0.000478919i	−0.341362	+	0.939932i	$0.610888\pi$
$444$		0			0
$445$	96.9689	+	81.3666i	0.0103298	+	0.00866774i
$446$	−3633.45	−	3048.82i	−0.385759	−	0.323691i
$447$		0			0
$448$	−54.3916	−	19.7969i	−0.00573608	−	0.00208776i
$449$	−5195.91	+	8999.58i	−0.546125	+	0.945917i	0.452410	+	0.891810i	$0.350564\pi$
$449$	−5195.91	+	8999.58i	−0.546125	+	0.945917i	−0.998535	+	0.0541067i	$0.982769\pi$
$450$		0			0
$451$	−168.841	−	292.442i	−0.0176284	−	0.0305333i
$452$	−514.428	−	2917.47i	−0.0535325	−	0.303598i
$453$		0			0
$454$	8808.63	−	3206.08i	0.910594	−	0.331429i
$455$	−25.5970	+	145.168i	−0.00263737	+	0.0149573i
$456$		0			0
$457$	−7838.74	+	6577.49i	−0.802365	+	0.673264i	−0.948772	−	0.315960i	$-0.897673\pi$
$457$	−7838.74	+	6577.49i	−0.802365	+	0.673264i	0.146407	+	0.989224i	$0.453229\pi$
$458$	−4127.70			−0.421124
$459$		0			0
$460$	1926.93			0.195312
$461$	−3914.11	+	3284.33i	−0.395441	+	0.331814i	−0.818728	−	0.574181i	$-0.805321\pi$
$461$	−3914.11	+	3284.33i	−0.395441	+	0.331814i	0.423287	+	0.905996i	$0.360876\pi$
$462$		0			0
$463$	1294.70	−	7342.60i	0.129956	−	0.737019i	−0.848284	−	0.529542i	$-0.822364\pi$
$463$	1294.70	−	7342.60i	0.129956	−	0.737019i	0.978240	−	0.207477i	$-0.0665251\pi$
$464$	−2127.88	+	774.484i	−0.212897	+	0.0774882i
$465$		0			0
$466$	2363.02	+	13401.3i	0.234902	+	1.33220i
$467$	4755.60	+	8236.94i	0.471227	+	0.816189i	0.999458	−	0.0329116i	$-0.0104780\pi$
$467$	4755.60	+	8236.94i	0.471227	+	0.816189i	−0.528231	+	0.849100i	$0.677145\pi$
$468$		0			0
$469$	320.706	−	555.480i	0.0315754	−	0.0546901i
$470$	2613.69	+	951.307i	0.256512	+	0.0933628i
$471$		0			0
$472$	−1175.39	−	986.273i	−0.114623	−	0.0961798i
$473$	−40.5202	−	34.0005i	−0.00393894	−	0.00330517i
$474$		0			0
$475$	8534.43	+	3106.28i	0.824393	+	0.300054i
$476$	85.9645	−	148.895i	0.00827768	−	0.0143374i
$477$		0			0
$478$	−3459.83	−	5992.60i	−0.331064	−	0.573420i
$479$	2814.87	+	15963.9i	0.268506	+	1.52277i	0.758861	+	0.651252i	$0.225756\pi$
$479$	2814.87	+	15963.9i	0.268506	+	1.52277i	−0.490355	+	0.871523i	$0.663133\pi$
$480$		0			0
$481$	−14412.1	+	5245.59i	−1.36619	+	0.497252i
$482$	−603.385	+	3421.96i	−0.0570195	+	0.323374i
$483$		0			0
$484$	−4075.57	+	3419.81i	−0.382754	+	0.321169i
$485$	−1989.98			−0.186310
$486$		0			0
$487$	4480.12			0.416866			0.208433	−	0.978037i	$-0.433164\pi$
$487$	4480.12			0.416866			0.208433	+	0.978037i	$0.433164\pi$
$488$	−3322.98	+	2788.31i	−0.308246	+	0.258649i
$489$		0			0
$490$	436.315	−	2474.46i	0.0402259	−	0.228132i
$491$	−891.793	+	324.586i	−0.0819675	+	0.0298337i	−0.382678	−	0.923882i	$-0.624998\pi$
$491$	−891.793	+	324.586i	−0.0819675	+	0.0298337i	0.300711	+	0.953715i	$0.402776\pi$
$492$		0			0
$493$	−1167.98	−	6623.92i	−0.106700	−	0.605125i
$494$	−3615.31	−	6261.90i	−0.329272	−	0.570316i
$495$		0			0
$496$	−1528.26	+	2647.03i	−0.138349	+	0.239627i
$497$	−823.654	−	299.785i	−0.0743379	−	0.0270568i
$498$		0			0
$499$	12512.6	+	10499.3i	1.12253	+	0.941911i	0.998729	−	0.0503970i	$-0.0160487\pi$
$499$	12512.6	+	10499.3i	1.12253	+	0.941911i	0.123796	+	0.992308i	$0.460493\pi$
$500$	−2660.88	−	2232.74i	−0.237996	−	0.199702i
$501$		0			0
$502$	−5937.77	−	2161.17i	−0.527920	−	0.192147i
$503$	1578.92	−	2734.76i	0.139961	−	0.242420i	−0.787521	−	0.616288i	$-0.788636\pi$
$503$	1578.92	−	2734.76i	0.139961	−	0.242420i	0.927482	+	0.373869i	$0.121969\pi$
$504$		0			0
$505$	504.351	+	873.561i	0.0444422	+	0.0769762i
$506$	43.9648	+	249.337i	0.00386260	+	0.0219059i
$507$		0			0
$508$	−3910.06	+	1423.15i	−0.341498	+	0.124295i
$509$	−1705.09	+	9670.05i	−0.148481	+	0.842078i	0.816025	+	0.578017i	$0.196173\pi$
$509$	−1705.09	+	9670.05i	−0.148481	+	0.842078i	−0.964506	+	0.264061i	$0.914938\pi$
$510$		0			0
$511$	−351.208	+	294.699i	−0.0304042	+	0.0255122i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−1418.20			−0.121700
$515$	−1645.80	+	1380.99i	−0.140821	+	0.118163i
$516$		0			0
$517$	−63.4612	+	359.906i	−0.00539849	+	0.0306164i
$518$	−587.238	+	213.737i	−0.0498104	+	0.0181295i
$519$		0			0
$520$	226.419	+	1284.09i	0.0190945	+	0.108290i
$521$	4370.40	+	7569.76i	0.367506	+	0.636540i	0.989175	−	0.146741i	$-0.0468783\pi$
$521$	4370.40	+	7569.76i	0.367506	+	0.636540i	−0.621669	+	0.783280i	$0.713545\pi$
$522$		0			0
$523$	88.3525	−	153.031i	0.00738697	−	0.0127946i	−0.862308	−	0.506384i	$-0.830982\pi$
$523$	88.3525	−	153.031i	0.00738697	−	0.0127946i	0.869695	+	0.493589i	$0.164315\pi$
$524$	2845.58	+	1035.71i	0.237232	+	0.0863455i
$525$		0			0
$526$	5339.42	+	4480.30i	0.442604	+	0.371389i
$527$	−6954.81	−	5835.77i	−0.574869	−	0.482373i
$528$		0			0
$529$	−4744.34	−	1726.80i	−0.389935	−	0.141925i
$530$	−2141.57	+	3709.30i	−0.175516	+	0.304003i
$531$		0			0
$532$	−147.310	−	255.148i	−0.0120051	−	0.0207934i
$533$	2698.03	+	15301.3i	0.219259	+	1.24348i
$534$		0			0
$535$	3619.10	−	1317.25i	0.292463	−	0.106448i
$536$	985.216	−	5587.44i	0.0793934	−	0.450262i
$537$		0			0
$538$	4279.28	−	3590.74i	0.342924	−	0.287747i
$539$	330.140			0.0263825
$540$		0			0
$541$	−11689.1			−0.928935			−0.464467	−	0.885590i	$-0.653754\pi$
$541$	−11689.1			−0.928935			−0.464467	+	0.885590i	$0.653754\pi$
$542$	7720.93	−	6478.63i	0.611886	−	0.513433i
$543$		0			0
$544$	264.085	−	1497.70i	0.0208135	−	0.118039i
$545$	−3351.46	+	1219.83i	−0.263414	+	0.0958750i
$546$		0			0
$547$	601.729	+	3412.57i	0.0470348	+	0.266748i	0.999252	−	0.0386744i	$-0.0123135\pi$
$547$	601.729	+	3412.57i	0.0470348	+	0.266748i	−0.952217	+	0.305422i	$0.901202\pi$
$548$	−6065.81	−	10506.3i	−0.472844	−	0.818991i
$549$		0			0
$550$	107.596	−	186.361i	0.00834163	−	0.0144481i
$551$	−10830.8	−	3942.10i	−0.837403	−	0.304790i
$552$		0			0
$553$	−648.304	−	543.991i	−0.0498529	−	0.0418316i
$554$	6835.98	+	5736.07i	0.524247	+	0.439896i
$555$		0			0
$556$	3557.38	+	1294.78i	0.271343	+	0.0987607i
$557$	10827.8	−	18754.3i	0.823676	−	1.42665i	−0.0792501	−	0.996855i	$-0.525253\pi$
$557$	10827.8	−	18754.3i	0.823676	−	1.42665i	0.902927	−	0.429795i	$-0.141414\pi$
$558$		0			0
$559$	1216.90	+	2107.74i	0.0920743	+	0.159477i
$560$	9.22569	+	52.3215i	0.000696172	+	0.00394819i
$561$		0			0
$562$	−5747.83	+	2092.04i	−0.431419	+	0.157024i
$563$	4100.12	−	23252.9i	0.306926	−	1.74066i	−0.307371	−	0.951590i	$-0.599449\pi$
$563$	4100.12	−	23252.9i	0.306926	−	1.74066i	0.614297	−	0.789075i	$-0.289440\pi$
$564$		0			0
$565$	−2083.01	+	1747.85i	−0.155102	+	0.130146i
$566$	12790.0			0.949833
$567$		0			0
$568$	−7753.23			−0.572743
$569$	5074.93	−	4258.38i	0.373906	−	0.313744i	−0.436399	−	0.899753i	$-0.643746\pi$
$569$	5074.93	−	4258.38i	0.373906	−	0.313744i	0.810304	+	0.586009i	$0.199302\pi$
$570$		0			0
$571$	3297.98	−	18703.8i	0.241710	−	1.37080i	−0.586301	−	0.810093i	$-0.699417\pi$
$571$	3297.98	−	18703.8i	0.241710	−	1.37080i	0.828011	−	0.560712i	$-0.189472\pi$
$572$	−160.989	+	58.5954i	−0.0117680	+	0.00428321i
$573$		0			0
$574$	109.934	+	623.469i	0.00799403	+	0.0453364i
$575$	7316.23	+	12672.1i	0.530622	+	0.919065i
$576$		0			0
$577$	1013.23	−	1754.97i	0.0731049	−	0.126621i	−0.827156	−	0.561973i	$-0.810043\pi$
$577$	1013.23	−	1754.97i	0.0731049	−	0.126621i	0.900261	+	0.435351i	$0.143376\pi$
$578$	−4988.57	−	1815.69i	−0.358992	−	0.130662i
$579$		0			0
$580$	1592.20	+	1336.01i	0.113987	+	0.0956464i
$581$	636.871	+	534.398i	0.0454765	+	0.0381593i
$582$		0			0
$583$	−528.830	−	192.478i	−0.0375676	−	0.0136735i
$584$	−2027.71	+	3512.09i	−0.143676	+	0.248855i
$585$		0			0
$586$	−1083.92	−	1877.41i	−0.0764102	−	0.132346i
$587$	−4006.99	−	22724.8i	−0.281748	−	1.59788i	−0.716674	−	0.697409i	$-0.754336\pi$
$587$	−4006.99	−	22724.8i	−0.281748	−	1.59788i	0.434925	−	0.900467i	$-0.356775\pi$
$588$		0			0
$589$	−14619.4	+	5321.02i	−1.02272	+	0.372239i
$590$	−244.558	+	1386.96i	−0.0170649	+	0.0967799i
$591$		0			0
$592$	−4234.54	+	3553.20i	−0.293984	+	0.246682i
$593$	−7318.96			−0.506836			−0.253418	−	0.967357i	$-0.581555\pi$
$593$	−7318.96			−0.506836			−0.253418	+	0.967357i	$0.581555\pi$
$594$		0			0
$595$	−157.809			−0.0108732
$596$	7060.72	−	5924.64i	0.485265	−	0.407186i
$597$		0			0
$598$	2022.90	−	11472.4i	0.138332	−	0.784519i
$599$	20482.1	−	7454.88i	1.39712	−	0.508511i	0.469799	−	0.882773i	$-0.344326\pi$
$599$	20482.1	−	7454.88i	1.39712	−	0.508511i	0.927323	+	0.374262i	$0.122104\pi$
$600$		0			0
$601$	−4359.51	−	24724.0i	−0.295887	−	1.67806i	−0.663575	−	0.748110i	$-0.730962\pi$
$601$	−4359.51	−	24724.0i	−0.295887	−	1.67806i	0.367688	−	0.929949i	$-0.380150\pi$
$602$	49.5841	+	85.8822i	0.00335697	+	0.00581444i
$603$		0			0
$604$	−1063.56	+	1842.15i	−0.0716487	+	0.124099i
$605$	4588.83	+	1670.20i	0.308368	+	0.112237i
$606$		0			0
$607$	19739.8	+	16563.6i	1.31995	+	1.10757i	0.986315	+	0.164872i	$0.0527213\pi$
$607$	19739.8	+	16563.6i	1.31995	+	1.10757i	0.333639	+	0.942701i	$0.391723\pi$
$608$	−1996.36	−	1675.15i	−0.133163	−	0.111737i
$609$		0			0
$610$	3741.46	+	1361.78i	0.248340	+	0.0903884i
$611$	8407.69	−	14562.5i	0.556692	−	0.964219i
$612$		0			0
$613$	−5917.72	−	10249.8i	−0.389910	−	0.675343i	0.602527	−	0.798098i	$-0.294160\pi$
$613$	−5917.72	−	10249.8i	−0.389910	−	0.675343i	−0.992437	+	0.122755i	$0.960827\pi$
$614$	1802.34	+	10221.6i	0.118463	+	0.671839i
$615$		0			0
$616$	−6.55969	+	2.38753i	−0.000429054	+	0.000156163i
$617$	−3562.45	+	20203.7i	−0.232445	+	1.31826i	0.615482	+	0.788151i	$0.288961\pi$
$617$	−3562.45	+	20203.7i	−0.232445	+	1.31826i	−0.847927	+	0.530112i	$0.822150\pi$
$618$		0			0
$619$	19061.7	−	15994.6i	1.23773	−	1.03858i	0.240029	−	0.970766i	$-0.422843\pi$
$619$	19061.7	−	15994.6i	1.23773	−	1.03858i	0.997698	−	0.0678106i	$-0.0216014\pi$
$620$	2805.50			0.181728
$621$		0			0
$622$	3507.13			0.226082
$623$	23.8867	−	20.0433i	0.00153612	−	0.00128895i
$624$		0			0
$625$	1867.02	−	10588.4i	0.119490	−	0.677659i
$626$	8858.81	−	3224.34i	0.565606	−	0.205864i
$627$		0			0
$628$	−2199.86	−	12476.0i	−0.139783	−	0.792752i
$629$	−8209.67	−	14219.6i	−0.520415	−	0.901385i
$630$		0			0
$631$	−3468.01	+	6006.78i	−0.218795	+	0.378964i	−0.954440	−	0.298404i	$-0.903546\pi$
$631$	−3468.01	+	6006.78i	−0.218795	+	0.378964i	0.735645	+	0.677367i	$0.236879\pi$
$632$	−7034.52	−	2560.35i	−0.442750	−	0.161148i
$633$		0			0
$634$	8146.64	+	6835.84i	0.510322	+	0.428211i
$635$	2925.73	+	2454.98i	0.182841	+	0.153422i
$636$		0			0
$637$	−14274.2	−	5195.40i	−0.887859	−	0.323154i
$638$	−136.547	+	236.506i	−0.00847327	+	0.0146761i
$639$		0			0
$640$	234.975	+	406.989i	0.0145128	+	0.0251370i
$641$	−609.866	−	3458.72i	−0.0375792	−	0.213122i	0.960236	−	0.279190i	$-0.0900658\pi$
$641$	−609.866	−	3458.72i	−0.0375792	−	0.213122i	−0.997815	+	0.0660675i	$0.978955\pi$
$642$		0			0
$643$	3371.82	−	1227.24i	0.206799	−	0.0752686i	−0.236544	−	0.971621i	$-0.576015\pi$
$643$	3371.82	−	1227.24i	0.206799	−	0.0752686i	0.443343	+	0.896352i	$0.353792\pi$
$644$	82.4252	−	467.457i	0.00504349	−	0.0286031i
$645$		0			0
$646$	5929.83	−	4975.72i	0.361155	−	0.303045i
$647$	−370.905			−0.0225376			−0.0112688	−	0.999937i	$-0.503587\pi$
$647$	−370.905			−0.0225376			−0.0112688	+	0.999937i	$0.503587\pi$
$648$		0			0
$649$	−185.047			−0.0111922
$650$	−7584.86	+	6364.45i	−0.457696	+	0.384053i
$651$		0			0
$652$	−2318.59	+	13149.4i	−0.139268	+	0.789831i
$653$	−14168.9	+	5157.05i	−0.849113	+	0.309052i	−0.729679	−	0.683790i	$-0.760330\pi$
$653$	−14168.9	+	5157.05i	−0.849113	+	0.309052i	−0.119435	+	0.992842i	$0.538108\pi$
$654$		0			0
$655$	−482.656	−	2737.28i	−0.0287923	−	0.163289i
$656$	2799.99	+	4849.73i	0.166648	+	0.288644i
$657$		0			0
$658$	342.581	−	593.367i	0.0202966	−	0.0351548i
$659$	−24318.9	−	8851.34i	−1.43752	−	0.523216i	−0.498446	−	0.866921i	$-0.666096\pi$
$659$	−24318.9	−	8851.34i	−1.43752	−	0.523216i	−0.939078	+	0.343705i	$0.888318\pi$
$660$		0			0
$661$	522.473	+	438.407i	0.0307441	+	0.0257974i	0.658030	−	0.752992i	$-0.271390\pi$
$661$	522.473	+	438.407i	0.0307441	+	0.0257974i	−0.627286	+	0.778789i	$0.715834\pi$
$662$	7576.16	+	6357.15i	0.444797	+	0.373229i
$663$		0			0
$664$	6910.46	+	2515.20i	0.403882	+	0.147001i
$665$	−135.212	+	234.193i	−0.00788463	+	0.0136566i
$666$		0			0
$667$	−9284.84	−	16081.8i	−0.538996	−	0.933569i
$668$	104.528	+	592.810i	0.00605438	+	0.0343361i
$669$		0			0
$670$	−4893.61	+	1781.13i	−0.282174	+	0.102703i
$671$	−90.8437	+	515.200i	−0.00522650	+	0.0296410i
$672$		0			0
$673$	14863.8	−	12472.2i	0.851347	−	0.714365i	−0.108739	−	0.994070i	$-0.534681\pi$
$673$	14863.8	−	12472.2i	0.851347	−	0.714365i	0.960086	+	0.279705i	$0.0902368\pi$
$674$	11360.0			0.649216
$675$		0			0
$676$	−905.204			−0.0515023
$677$	13305.4	−	11164.5i	0.755342	−	0.633807i	−0.181568	−	0.983378i	$-0.558117\pi$
$677$	13305.4	−	11164.5i	0.755342	−	0.633807i	0.936910	+	0.349571i	$0.113673\pi$
$678$		0			0
$679$	−85.1223	+	482.753i	−0.00481104	+	0.0272848i
$680$	−1311.72	+	477.427i	−0.0739738	+	0.0269243i
$681$		0			0
$682$	64.0103	+	363.020i	0.00359396	+	0.0203823i
$683$	−6514.55	−	11283.5i	−0.364967	−	0.632141i	0.623804	−	0.781581i	$-0.285586\pi$
$683$	−6514.55	−	11283.5i	−0.364967	−	0.632141i	−0.988771	+	0.149440i	$0.952253\pi$
$684$		0			0
$685$	−5567.64	+	9643.44i	−0.310553	+	0.537893i
$686$	−1164.63	−	423.891i	−0.0648189	−	0.0235922i
$687$		0			0
$688$	671.970	+	563.850i	0.0372364	+	0.0312450i
$689$	19836.0	+	16644.3i	1.09679	+	0.920318i
$690$		0			0
$691$	17006.4	+	6189.84i	0.936260	+	0.340771i	0.764688	−	0.644401i	$-0.222893\pi$
$691$	17006.4	+	6189.84i	0.936260	+	0.340771i	0.171572	+	0.985172i	$0.445115\pi$
$692$	−8.49701	+	14.7173i	−0.000466774	+	0.000808477i
$693$		0			0
$694$	9145.79	+	15841.0i	0.500244	+	0.866448i
$695$	−603.389	−	3421.99i	−0.0329321	−	0.186767i
$696$		0			0
$697$	−15630.6	+	5689.08i	−0.849429	+	0.309167i
$698$	−2675.26	+	15172.2i	−0.145072	+	0.822744i
$699$		0			0
$700$	−309.053	+	259.327i	−0.0166873	+	0.0140023i
$701$	−3892.41			−0.209721			−0.104860	−	0.994487i	$-0.533440\pi$
$701$	−3892.41			−0.209721			−0.104860	+	0.994487i	$0.533440\pi$
$702$		0			0
$703$	−28136.3			−1.50951
$704$	−47.3015	+	39.6907i	−0.00253231	+	0.00212486i
$705$		0			0
$706$	−890.733	+	5051.60i	−0.0474833	+	0.269291i
$707$	233.492	−	84.9842i	0.0124206	−	0.00452073i
$708$		0			0
$709$	−210.255	−	1192.42i	−0.0111372	−	0.0631624i	0.978733	−	0.205140i	$-0.0657650\pi$
$709$	−210.255	−	1192.42i	−0.0111372	−	0.0631624i	−0.989870	+	0.141978i	$0.954654\pi$
$710$	3558.24	+	6163.05i	0.188082	+	0.325768i
$711$		0			0
$712$	137.910	−	238.867i	0.00725899	−	0.0125729i
$713$	−23553.6	−	8572.81i	−1.23715	−	0.450287i
$714$		0			0
$715$	120.461	+	101.079i	0.00630070	+	0.00528692i
$716$	−1858.63	−	1559.58i	−0.0970116	−	0.0814024i
$717$		0			0
$718$	−22808.9	−	8301.76i	−1.18554	−	0.431503i
$719$	−2309.70	+	4000.52i	−0.119801	+	0.207502i	−0.919689	−	0.392648i	$-0.871559\pi$
$719$	−2309.70	+	4000.52i	−0.119801	+	0.207502i	0.799887	+	0.600150i	$0.204892\pi$
$720$		0			0
$721$	264.617	+	458.329i	0.0136683	+	0.0236742i
$722$	78.6979	+	446.318i	0.00405655	+	0.0230059i
$723$		0			0
$724$	−8677.83	+	3158.47i	−0.445454	+	0.162132i
$725$	−2740.72	+	15543.4i	−0.140397	+	0.796230i
$726$		0			0
$727$	−12806.0	+	10745.5i	−0.653298	+	0.548182i	−0.908070	−	0.418819i	$-0.862444\pi$
$727$	−12806.0	+	10745.5i	−0.653298	+	0.548182i	0.254772	+	0.967001i	$0.418000\pi$
$728$	321.193			0.0163519
$729$		0			0
$730$	3722.35			0.188727
$731$	−1995.97	+	1674.81i	−0.100990	+	0.0847404i
$732$		0			0
$733$	−1284.70	+	7285.89i	−0.0647359	+	0.367136i	0.935180	+	0.354173i	$0.115237\pi$
$733$	−1284.70	+	7285.89i	−0.0647359	+	0.367136i	−0.999916	+	0.0129629i	$0.995874\pi$
$734$	−1690.03	+	615.121i	−0.0849866	+	0.0309326i
$735$		0			0
$736$	−729.095	−	4134.90i	−0.0365147	−	0.207085i
$737$	−342.123	−	592.575i	−0.0170994	−	0.0296171i
$738$		0			0
$739$	1966.48	−	3406.04i	0.0978865	−	0.169544i	−0.812923	−	0.582371i	$-0.802125\pi$
$739$	1966.48	−	3406.04i	0.0978865	−	0.169544i	0.910810	+	0.412827i	$0.135458\pi$
$740$	4767.83	+	1735.35i	0.236850	+	0.0862063i
$741$		0			0
$742$	808.238	+	678.192i	0.0399883	+	0.0335542i
$743$	7690.59	+	6453.17i	0.379731	+	0.318632i	0.812597	−	0.582826i	$-0.198053\pi$
$743$	7690.59	+	6453.17i	0.379731	+	0.318632i	−0.432866	+	0.901458i	$0.642498\pi$
$744$		0			0
$745$	−7949.92	−	2893.54i	−0.390957	−	0.142297i
$746$	8059.86	−	13960.1i	0.395566	−	0.685141i
$747$		0			0
$748$	−91.7053	−	158.838i	−0.00448272	−	0.00776431i
$749$	−164.744	−	934.308i	−0.00803686	−	0.0455793i
$750$		0			0
$751$	−10715.9	+	3900.26i	−0.520677	+	0.189511i	−0.588971	−	0.808154i	$-0.700467\pi$
$751$	−10715.9	+	3900.26i	−0.520677	+	0.189511i	0.0682938	+	0.997665i	$0.478244\pi$
$752$	1052.41	−	5968.54i	0.0510341	−	0.289428i
$753$		0			0
$754$	9625.76	−	8076.97i	0.464920	−	0.390114i
$755$	1952.43			0.0941143
$756$		0			0
$757$	5411.26			0.259809			0.129905	−	0.991527i	$-0.458533\pi$
$757$	5411.26			0.259809			0.129905	+	0.991527i	$0.458533\pi$
$758$	−3668.46	+	3078.20i	−0.175784	+	0.147501i
$759$		0			0
$760$	−415.373	+	2355.70i	−0.0198252	+	0.112434i
$761$	−21528.9	+	7835.88i	−1.02552	+	0.373259i	−0.799374	−	0.600834i	$-0.794835\pi$
$761$	−21528.9	+	7835.88i	−1.02552	+	0.373259i	−0.226147	+	0.974093i	$0.572613\pi$
$762$		0			0
$763$	152.561	+	865.214i	0.00723861	+	0.0410522i
$764$	5903.07	+	10224.4i	0.279536	+	0.484170i
$765$		0			0
$766$	−11605.5	+	20101.2i	−0.547418	+	0.948155i
$767$	8000.84	+	2912.07i	0.376654	+	0.137091i
$768$		0			0
$769$	28524.4	+	23934.9i	1.33760	+	1.12238i	0.982234	+	0.187658i	$0.0600895\pi$
$769$	28524.4	+	23934.9i	1.33760	+	1.12238i	0.355370	+	0.934726i	$0.384355\pi$
$770$	4.90833	+	4.11858i	0.000229719	+	0.000192758i
$771$		0			0
$772$	17917.2	+	6521.32i	0.835302	+	0.304025i
$773$	4729.13	−	8191.08i	0.220045	−	0.381129i	−0.734776	−	0.678309i	$-0.762713\pi$
$773$	4729.13	−	8191.08i	0.220045	−	0.381129i	0.954821	+	0.297180i	$0.0960462\pi$
$774$		0			0
$775$	10652.0	+	18449.8i	0.493718	+	0.855144i
$776$	752.952	+	4270.20i	0.0348317	+	0.197540i
$777$		0			0
$778$	−18394.4	+	6695.00i	−0.847648	+	0.308519i
$779$	−4949.63	+	28070.7i	−0.227649	+	1.29106i
$780$		0			0
$781$	−716.289	+	601.037i	−0.0328180	+	0.0275375i
$782$	12471.4			0.570304
$783$		0			0
$784$	−5474.91			−0.249404
$785$	−8907.62	+	7474.38i	−0.405002	+	0.339837i
$786$		0			0
$787$	5100.06	−	28923.9i	0.231001	−	1.31007i	−0.619874	−	0.784701i	$-0.712816\pi$
$787$	5100.06	−	28923.9i	0.231001	−	1.31007i	0.850875	−	0.525368i	$-0.176072\pi$
$788$	−891.835	+	324.601i	−0.0403176	+	0.0146744i
$789$		0			0
$790$	1193.17	+	6766.78i	0.0537354	+	0.304748i
$791$	334.912	+	580.085i	0.0150545	+	0.0260751i
$792$		0			0
$793$	12035.5	−	20846.1i	0.538956	−	0.933500i
$794$	−21514.4	−	7830.59i	−0.961607	−	0.349996i
$795$		0			0
$796$	6345.03	+	5324.11i	0.282530	+	0.237070i
$797$	17826.4	+	14958.2i	0.792277	+	0.664799i	0.946308	−	0.323267i	$-0.104781\pi$
$797$	17826.4	+	14958.2i	0.792277	+	0.664799i	−0.154031	+	0.988066i	$0.549226\pi$
$798$		0			0
$799$	16916.3	+	6157.03i	0.749006	+	0.272616i
$800$	−1784.32	+	3090.54i	−0.0788567	+	0.136584i
$801$		0			0
$802$	9460.82	+	16386.6i	0.416550	+	0.721486i
$803$	84.9291	+	481.657i	0.00373236	+	0.0211672i
$804$		0			0
$805$	−409.410	+	149.013i	−0.0179252	+	0.00652424i
$806$	2945.22	−	16703.2i	0.128711	−	0.729956i
$807$		0			0
$808$	1683.70	−	1412.79i	0.0733073	−	0.0615121i
$809$	−32362.0			−1.40641			−0.703206	−	0.710986i	$-0.748249\pi$
$809$	−32362.0			−1.40641			−0.703206	+	0.710986i	$0.748249\pi$
$810$		0			0
$811$	−19905.7			−0.861877			−0.430938	−	0.902381i	$-0.641817\pi$
$811$	−19905.7			−0.861877			−0.430938	+	0.902381i	$0.641817\pi$
$812$	392.212	−	329.105i	0.0169507	−	0.0142233i
$813$		0			0
$814$	−115.764	+	656.531i	−0.00498468	+	0.0282695i
$815$	11516.5	−	4191.68i	0.494978	−	0.180157i
$816$		0			0
$817$	775.321	+	4397.07i	0.0332008	+	0.188291i
$818$	−6987.08	−	12102.0i	−0.298652	−	0.517281i
$819$		0			0
$820$	2570.04	−	4451.44i	0.109451	−	0.189574i
$821$	6250.73	+	2275.08i	0.265715	+	0.0967123i	0.471442	−	0.881897i	$-0.343734\pi$
$821$	6250.73	+	2275.08i	0.265715	+	0.0967123i	−0.205727	+	0.978609i	$0.565956\pi$
$822$		0			0
$823$	23462.3	+	19687.2i	0.993734	+	0.833842i	0.986104	−	0.166129i	$-0.0531268\pi$
$823$	23462.3	+	19687.2i	0.993734	+	0.833842i	0.00762996	+	0.999971i	$0.497571\pi$
$824$	3586.12	+	3009.11i	0.151612	+	0.127218i
$825$		0			0
$826$	326.003	+	118.655i	0.0137326	+	0.00499824i
$827$	−18729.4	+	32440.3i	−0.787529	+	1.36404i	0.139948	+	0.990159i	$0.455307\pi$
$827$	−18729.4	+	32440.3i	−0.787529	+	1.36404i	−0.927477	+	0.373881i	$0.878027\pi$
$828$		0			0
$829$	2008.77	+	3479.30i	0.0841588	+	0.145767i	0.905032	−	0.425343i	$-0.139846\pi$
$829$	2008.77	+	3479.30i	0.0841588	+	0.145767i	−0.820874	+	0.571110i	$0.806513\pi$
$830$	−1172.12	−	6647.45i	−0.0490181	−	0.277996i
$831$		0			0
$832$	2669.78	−	971.721i	0.111248	−	0.0404908i
$833$	2823.91	−	16015.2i	0.117458	−	0.666138i
$834$		0			0
$835$	423.253	−	355.152i	0.0175417	−	0.0147192i
$836$	−314.294			−0.0130025
$837$		0			0
$838$	14783.9			0.609430
$839$	−2433.61	+	2042.04i	−0.100140	+	0.0840274i	−0.691483	−	0.722393i	$-0.743042\pi$
$839$	−2433.61	+	2042.04i	−0.100140	+	0.0840274i	0.591343	+	0.806420i	$0.298598\pi$
$840$		0			0
$841$	−756.928	+	4292.75i	−0.0310356	+	0.176012i
$842$	1852.32	−	674.189i	0.0758137	−	0.0275939i
$843$		0			0
$844$	−3742.56	−	21225.1i	−0.152635	−	0.865638i
$845$	415.431	+	719.548i	0.0169127	+	0.0292937i
$846$		0			0
$847$	601.465	−	1041.77i	0.0243997	−	0.0422616i
$848$	8769.90	+	3191.98i	0.355141	+	0.129261i
$849$		0			0
$850$	−8120.08	−	6813.56i	−0.327666	−	0.274945i
$851$	−34725.6	−	29138.3i	−1.39880	−	1.17373i
$852$		0			0
$853$	20329.9	+	7399.49i	0.816042	+	0.297015i	0.716117	−	0.697980i	$-0.245918\pi$
$853$	20329.9	+	7399.49i	0.816042	+	0.297015i	0.0999247	+	0.994995i	$0.468140\pi$
$854$	490.399	−	849.396i	0.0196500	−	0.0340348i
$855$		0			0
$856$	−4195.97	−	7267.64i	−0.167541	−	0.290190i
$857$	−19.1577	−	108.648i	−0.000763609	−	0.00433064i	0.984424	−	0.175813i	$-0.0562554\pi$
$857$	−19.1577	−	108.648i	−0.000763609	−	0.00433064i	−0.985187	+	0.171482i	$0.945144\pi$
$858$		0			0
$859$	37272.7	−	13566.1i	1.48047	−	0.538848i	0.529551	−	0.848278i	$-0.322360\pi$
$859$	37272.7	−	13566.1i	1.48047	−	0.538848i	0.950922	+	0.309430i	$0.100138\pi$
$860$	139.813	−	792.921i	0.00554372	−	0.0314400i
$861$		0			0
$862$	−7671.62	+	6437.25i	−0.303128	+	0.254355i
$863$	34065.7			1.34369			0.671847	−	0.740690i	$-0.265501\pi$
$863$	34065.7			1.34369			0.671847	+	0.740690i	$0.265501\pi$
$864$		0			0
$865$	15.5983			0.000613133
$866$	−25318.2	+	21244.5i	−0.993473	+	0.833623i
$867$		0			0
$868$	120.006	−	680.590i	0.00469272	−	0.0266137i
$869$	−848.371	+	308.782i	−0.0331174	+	0.0120537i
$870$		0			0
$871$	5467.03	+	31005.1i	0.212679	+	1.20616i
$872$	3885.67	+	6730.18i	0.150901	+	0.261368i
$873$		0			0
$874$	10685.6	−	18508.0i	0.413554	−	0.716296i
$875$	738.010	+	268.614i	0.0285135	+	0.0103781i
$876$		0			0
$877$	−13122.7	−	11011.2i	−0.505269	−	0.423971i	0.354191	−	0.935173i	$-0.384756\pi$
$877$	−13122.7	−	11011.2i	−0.505269	−	0.423971i	−0.859461	+	0.511202i	$0.829201\pi$
$878$	−25497.0	−	21394.6i	−0.980050	−	0.822359i
$879$		0			0
$880$	53.2586	+	19.3845i	0.00204017	+	0.000742560i
$881$	3430.34	−	5941.53i	0.131182	−	0.227214i	−0.792951	−	0.609286i	$-0.791456\pi$
$881$	3430.34	−	5941.53i	0.131182	−	0.227214i	0.924132	+	0.382072i	$0.124790\pi$
$882$		0			0
$883$	−12029.6	−	20835.9i	−0.458471	−	0.794094i	0.540410	−	0.841402i	$-0.318269\pi$
$883$	−12029.6	−	20835.9i	−0.458471	−	0.794094i	−0.998880	+	0.0473076i	$0.984936\pi$
$884$	1465.42	+	8310.84i	0.0557552	+	0.316203i
$885$		0			0
$886$	−24.5376	+	8.93096i	−0.000930426	+	0.000338647i
$887$	−4727.10	+	26808.7i	−0.178941	+	1.01482i	0.754555	+	0.656237i	$0.227853\pi$
$887$	−4727.10	+	26808.7i	−0.178941	+	1.01482i	−0.933496	+	0.358588i	$0.883258\pi$
$888$		0			0
$889$	720.706	−	604.744i	0.0271898	−	0.0228149i
$890$	−253.168			−0.00953506
$891$		0			0
$892$	9486.26			0.356080
$893$	23631.2	−	19828.9i	0.885541	−	0.743057i
$894$		0			0
$895$	−386.716	+	2193.17i	−0.0144430	+	0.0819103i
$896$	108.783	−	39.5939i	0.00405602	−	0.00147627i
$897$		0			0
$898$	−3609.04	−	20467.9i	−0.134115	−	0.760604i
$899$	−13518.2	−	23414.2i	−0.501509	−	0.868640i
$900$		0			0
$901$	−13860.6	+	24007.3i	−0.512501	+	0.887678i
$902$	634.635	+	230.988i	0.0234269	+	0.00852669i
$903$		0			0
$904$	4538.77	+	3808.48i	0.166988	+	0.140120i
$905$	6493.24	+	5448.48i	0.238500	+	0.200125i
$906$		0			0
$907$	−43758.5	−	15926.8i	−1.60196	−	0.583065i	−0.622131	−	0.782913i	$-0.713733\pi$
$907$	−43758.5	−	15926.8i	−1.60196	−	0.583065i	−0.979827	+	0.199848i	$0.935955\pi$
$908$	−9373.95	+	16236.2i	−0.342605	+	0.593410i
$909$		0			0
$910$	−147.407	−	255.317i	−0.00536978	−	0.00930073i
$911$	2044.80	+	11596.7i	0.0743659	+	0.421750i	0.999149	+	0.0412545i	$0.0131354\pi$
$911$	2044.80	+	11596.7i	0.0743659	+	0.421750i	−0.924783	+	0.380496i	$0.875753\pi$
$912$		0			0
$913$	833.409	−	303.336i	0.0302101	−	0.0109956i
$914$	3553.80	−	20154.6i	0.128610	−	0.729381i
$915$		0			0
$916$	6324.01	−	5306.47i	0.228113	−	0.191409i
$917$	−684.686			−0.0246568
$918$		0			0
$919$	−3110.56			−0.111652			−0.0558258	−	0.998441i	$-0.517779\pi$
$919$	−3110.56			−0.111652			−0.0558258	+	0.998441i	$0.517779\pi$
$920$	−2952.23	+	2477.21i	−0.105796	+	0.0887732i
$921$		0			0
$922$	1774.51	−	10063.8i	0.0633845	−	0.359471i
$923$	40428.6	−	14714.8i	1.44174	−	0.524749i
$924$		0			0
$925$	6690.46	+	37943.5i	0.237817	+	1.34873i
$926$	7455.88	+	12914.0i	0.264595	+	0.458293i
$927$		0			0
$928$	2264.44	−	3922.12i	0.0801012	−	0.138739i
$929$	48093.6	+	17504.7i	1.69849	+	0.618201i	0.995653	−	0.0931453i	$-0.0296921\pi$
$929$	48093.6	+	17504.7i	1.69849	+	0.618201i	0.702841	+	0.711347i	$0.251914\pi$
$930$		0			0
$931$	−21347.5	−	17912.7i	−0.751488	−	0.630573i
$932$	−20848.8	−	17494.2i	−0.732751	−	0.614851i
$933$		0			0
$934$	−17875.2	−	6506.04i	−0.626226	−	0.227927i
$935$	−84.1738	+	145.793i	−0.00294415	+	0.00509941i
$936$		0			0
$937$	8984.69	+	15561.9i	0.313252	+	0.542568i	0.979064	−	0.203551i	$-0.0652482\pi$
$937$	8984.69	+	15561.9i	0.313252	+	0.542568i	−0.665812	+	0.746119i	$0.731915\pi$
$938$	222.760	+	1263.34i	0.00775414	+	0.0439759i
$939$		0			0
$940$	−5227.39	+	1902.61i	−0.181382	+	0.0660175i
$941$	6679.31	−	37880.3i	0.231392	−	1.31229i	−0.618690	−	0.785635i	$-0.712336\pi$
$941$	6679.31	−	37880.3i	0.231392	−	1.31229i	0.850081	−	0.526651i	$-0.176553\pi$
$942$		0			0
$943$	−35179.1	+	29518.8i	−1.21484	+	1.01937i
$944$	3068.74			0.105804
$945$		0			0
$946$	105.791			0.00363589
$947$	9902.18	−	8308.91i	0.339786	−	0.285114i	−0.456887	−	0.889525i	$-0.651036\pi$
$947$	9902.18	−	8308.91i	0.339786	−	0.285114i	0.796673	+	0.604410i	$0.206591\pi$
$948$		0			0
$949$	3907.74	−	22161.9i	0.133668	−	0.758066i
$950$	−17068.9	+	6212.56i	−0.582934	+	0.212170i
$951$		0			0
$952$	59.7103	+	338.634i	0.00203280	+	0.0115286i
$953$	−2695.20	−	4668.23i	−0.0916120	−	0.158677i	0.816578	−	0.577236i	$-0.195869\pi$
$953$	−2695.20	−	4668.23i	−0.0916120	−	0.158677i	−0.908190	+	0.418559i	$0.862535\pi$
$954$		0			0
$955$	5418.26	−	9384.71i	0.183593	−	0.317992i
$956$	13004.7	+	4733.32i	0.439960	+	0.160132i
$957$		0			0
$958$	−24835.4	−	20839.4i	−0.837574	−	0.702808i
$959$	2101.26	+	1763.16i	0.0707541	+	0.0593697i
$960$		0			0
$961$	−6298.32	−	2292.40i	−0.211417	−	0.0769494i
$962$	15337.1	−	26564.6i	0.514020	−	0.890308i
$963$		0			0
$964$	−3474.75	−	6018.45i	−0.116094	−	0.201080i
$965$	−3039.04	−	17235.3i	−0.101378	−	0.574946i
$966$		0			0
$967$	−19871.6	+	7232.66i	−0.660834	+	0.240524i	−0.650596	−	0.759424i	$-0.725481\pi$
$967$	−19871.6	+	7232.66i	−0.660834	+	0.240524i	−0.0102377	+	0.999948i	$0.503259\pi$
$968$	1847.71	−	10478.9i	0.0613510	−	0.347939i
$969$		0			0
$970$	3048.83	−	2558.27i	0.100920	−	0.0846817i
$971$	−11707.2			−0.386923			−0.193462	−	0.981108i	$-0.561971\pi$
$971$	−11707.2			−0.386923			−0.193462	+	0.981108i	$0.561971\pi$
$972$		0			0
$973$	−855.955			−0.0282021
$974$	−6863.94	+	5759.53i	−0.225806	+	0.189474i
$975$		0			0
$976$	1506.51	−	8543.87i	0.0494082	−	0.280208i
$977$	−32318.6	+	11763.0i	−1.05831	+	0.385192i	−0.811792	−	0.583947i	$-0.801508\pi$
$977$	−32318.6	+	11763.0i	−1.05831	+	0.385192i	−0.246515	+	0.969139i	$0.579285\pi$
$978$		0			0
$979$	−5.77627	−	32.7589i	−0.000188570	−	0.00106944i
$980$	2512.64	+	4352.01i	0.0819012	+	0.141857i
$981$		0			0
$982$	949.026	−	1643.76i	0.0308398	−	0.0534160i
$983$	36830.9	+	13405.4i	1.19504	+	0.434959i	0.861490	−	0.507774i	$-0.169532\pi$
$983$	36830.9	+	13405.4i	1.19504	+	0.434959i	0.333549	+	0.942733i	$0.391754\pi$
$984$		0			0
$985$	667.321	+	559.949i	0.0215864	+	0.0181132i
$986$	10305.0	+	8646.92i	0.332838	+	0.279284i
$987$		0			0
$988$	13589.1	+	4946.03i	0.437578	+	0.159265i
$989$	−3596.75	+	6229.75i	−0.115642	+	0.200298i
$990$		0			0
$991$	−24685.2	−	42756.0i	−0.791272	−	1.37052i	−0.925180	−	0.379530i	$-0.876086\pi$
$991$	−24685.2	−	42756.0i	−0.791272	−	1.37052i	0.133907	−	0.990994i	$-0.457248\pi$
$992$	−1061.52	−	6020.18i	−0.0339751	−	0.192682i
$993$		0			0
$994$	1647.31	−	599.571i	0.0525648	−	0.0191320i
$995$	1320.18	−	7487.10i	0.0420627	−	0.238550i
$996$		0			0
$997$	−21523.9	+	18060.7i	−0.683720	+	0.573709i	−0.917091	−	0.398679i	$-0.869469\pi$
$997$	−21523.9	+	18060.7i	−0.683720	+	0.573709i	0.233371	+	0.972388i	$0.425024\pi$
$998$	−32668.0			−1.03616
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.37.2		24
3.2	odd	2		54.4.e.a.49.4	yes	24
27.4	even	9		1458.4.a.e.1.8		12
27.11	odd	18		54.4.e.a.43.4	✓	24
27.16	even	9	inner	162.4.e.a.127.2		24
27.23	odd	18		1458.4.a.h.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.43.4	✓	24	27.11	odd	18
54.4.e.a.49.4	yes	24	3.2	odd	2
162.4.e.a.37.2		24	1.1	even	1	trivial
162.4.e.a.127.2		24	27.16	even	9	inner
1458.4.a.e.1.8		12	27.4	even	9
1458.4.a.h.1.5		12	27.23	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53209 + 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-3.45007 + 1.25572i) q^{5} +(0.157049 + 0.890672i) q^{7} +(4.00000 + 6.92820i) q^{8} +O(q^{10})\)	\(q+(-1.53209 + 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-3.45007 + 1.25572i) q^{5} +(0.157049 + 0.890672i) q^{7} +(4.00000 + 6.92820i) q^{8} +(3.67149 - 6.35921i) q^{10} +(0.906624 + 0.329984i) q^{11} +(-34.0067 - 28.5350i) q^{13} +(-1.38564 - 1.16269i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(23.7626 - 41.1579i) q^{17} +(-40.7198 - 70.5287i) q^{19} +(2.55019 + 14.4628i) q^{20} +(-1.81325 + 0.659968i) q^{22} +(22.7842 - 129.216i) q^{23} +(-85.4294 + 71.6838i) q^{25} +88.7851 q^{26} +3.61765 q^{28} +(108.416 - 90.9721i) q^{29} +(33.1725 - 188.131i) q^{31} +(30.0702 - 10.9446i) q^{32} +(16.5053 + 93.6062i) q^{34} +(-1.66027 - 2.87567i) q^{35} +(172.744 - 299.201i) q^{37} +(153.056 + 55.7079i) q^{38} +(-22.5002 - 18.8799i) q^{40} +(-268.115 - 224.975i) q^{41} +(-51.5184 - 18.7511i) q^{43} +(1.92962 - 3.34220i) q^{44} +(131.209 + 227.261i) q^{46} +(65.7759 + 373.034i) q^{47} +(321.546 - 117.033i) q^{49} +(38.7305 - 219.652i) q^{50} +(-136.027 + 114.140i) q^{52} -583.296 q^{53} -3.54229 q^{55} +(-5.54256 + 4.65076i) q^{56} +(-49.1520 + 278.755i) q^{58} +(-180.229 + 65.5981i) q^{59} +(94.1572 + 533.992i) q^{61} +(191.033 + 330.879i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(153.158 + 55.7448i) q^{65} +(-543.282 - 455.868i) q^{67} +(-145.625 - 122.194i) q^{68} +(6.24057 + 2.27138i) q^{70} +(-484.577 + 839.312i) q^{71} +(253.463 + 439.011i) q^{73} +(119.987 + 680.478i) q^{74} +(-306.113 + 111.416i) q^{76} +(-0.151523 + 0.859328i) q^{77} +(-716.824 + 601.486i) q^{79} +58.7438 q^{80} +699.998 q^{82} +(704.182 - 590.879i) q^{83} +(-30.2995 + 171.837i) q^{85} +(103.037 - 37.5023i) q^{86} +(1.34030 + 7.60121i) q^{88} +(-17.2388 - 29.8584i) q^{89} +(20.0746 - 34.7702i) q^{91} +(-493.185 - 179.505i) q^{92} +(-580.337 - 486.961i) q^{94} +(229.051 + 192.196i) q^{95} +(509.323 + 185.378i) q^{97} +(-342.182 + 592.677i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Introduction

L-functions

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