LMFDB - Embedded newform 162.4.e.b.91.2

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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			91.2
Character	$\chi$	$=$	162.91
Dual form			162.4.e.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347296 + 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(-6.77242 - 5.68273i) q^{5} +(30.7336 + 11.1861i) q^{7} +(-4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(0.347296 + 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(-6.77242 - 5.68273i) q^{5} +(30.7336 + 11.1861i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(8.84076 - 15.3127i) q^{10} +(25.1908 - 21.1376i) q^{11} +(-11.2582 + 63.8482i) q^{13} +(-11.3587 + 64.4182i) q^{14} +(12.2567 - 10.2846i) q^{16} +(-44.3659 + 76.8440i) q^{17} +(56.0627 + 97.1034i) q^{19} +(33.2304 + 12.0949i) q^{20} +(50.3815 + 42.2751i) q^{22} +(67.4024 - 24.5325i) q^{23} +(-8.13384 - 46.1293i) q^{25} -129.666 q^{26} -130.824 q^{28} +(36.3969 + 206.417i) q^{29} +(9.06899 - 3.30084i) q^{31} +(24.5134 + 20.5692i) q^{32} +(-166.761 - 60.6961i) q^{34} +(-144.573 - 250.408i) q^{35} +(58.8343 - 101.904i) q^{37} +(-171.786 + 144.146i) q^{38} +(-12.2815 + 69.6516i) q^{40} +(1.53490 - 8.70486i) q^{41} +(157.184 - 131.893i) q^{43} +(-65.7684 + 113.914i) q^{44} +(71.7281 + 124.237i) q^{46} +(176.760 + 64.3354i) q^{47} +(556.670 + 467.102i) q^{49} +(88.0321 - 32.0411i) q^{50} +(-45.0326 - 255.393i) q^{52} -52.1118 q^{53} -290.722 q^{55} +(-45.4347 - 257.673i) q^{56} +(-393.922 + 143.376i) q^{58} +(-207.031 - 173.720i) q^{59} +(-215.595 - 78.4700i) q^{61} +(9.65102 + 16.7161i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(439.077 - 368.429i) q^{65} +(36.9619 - 209.621i) q^{67} +(61.6325 - 349.535i) q^{68} +(442.997 - 371.719i) q^{70} +(168.485 - 291.824i) q^{71} +(-589.936 - 1021.80i) q^{73} +(221.145 + 80.4901i) q^{74} +(-343.572 - 288.291i) q^{76} +(1010.65 - 367.846i) q^{77} +(9.64429 + 54.6955i) q^{79} -141.452 q^{80} +17.6783 q^{82} +(201.000 + 1139.93i) q^{83} +(737.148 - 268.300i) q^{85} +(314.367 + 263.786i) q^{86} +(-247.208 - 89.9765i) q^{88} +(-650.056 - 1125.93i) q^{89} +(-1060.22 + 1836.35i) q^{91} +(-219.788 + 184.424i) q^{92} +(-65.3278 + 370.493i) q^{94} +(172.133 - 976.214i) q^{95} +(1129.23 - 947.537i) q^{97} +(-726.681 + 1258.65i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.347296	+	1.96962i	0.122788	+	0.696364i
$2$	0.347296	+	1.96962i	0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−3.75877	+	1.36808i	−0.469846	+	0.171010i
$5$	−6.77242	−	5.68273i	−0.605743	−	0.508279i	0.287543	−	0.957768i	$-0.407162\pi$
$5$	−6.77242	−	5.68273i	−0.605743	−	0.508279i	−0.893286	+	0.449489i	$0.851606\pi$
$6$		0			0
$7$	30.7336	+	11.1861i	1.65946	+	0.603993i	0.990277	−	0.139108i	$-0.0444234\pi$
$7$	30.7336	+	11.1861i	1.65946	+	0.603993i	0.669180	+	0.743101i	$0.266646\pi$
$8$	−4.00000	−	6.92820i	−0.176777	−	0.306186i
$9$		0			0
$10$	8.84076	−	15.3127i	0.279570	−	0.484229i
$11$	25.1908	−	21.1376i	0.690482	−	0.579383i	−0.228566	−	0.973528i	$-0.573404\pi$
$11$	25.1908	−	21.1376i	0.690482	−	0.579383i	0.919048	+	0.394145i	$0.128959\pi$
$12$		0			0
$13$	−11.2582	+	63.8482i	−0.240189	+	1.36218i	0.591218	+	0.806512i	$0.298647\pi$
$13$	−11.2582	+	63.8482i	−0.240189	+	1.36218i	−0.831406	+	0.555665i	$0.812464\pi$
$14$	−11.3587	+	64.4182i	−0.216838	+	1.22975i
$15$		0			0
$16$	12.2567	−	10.2846i	0.191511	−	0.160697i
$17$	−44.3659	+	76.8440i	−0.632960	+	1.09632i	0.353984	+	0.935251i	$0.384827\pi$
$17$	−44.3659	+	76.8440i	−0.632960	+	1.09632i	−0.986944	+	0.161067i	$0.948507\pi$
$18$		0			0
$19$	56.0627	+	97.1034i	0.676930	+	1.17248i	0.975901	+	0.218214i	$0.0700232\pi$
$19$	56.0627	+	97.1034i	0.676930	+	1.17248i	−0.298971	+	0.954262i	$0.596644\pi$
$20$	33.2304	+	12.0949i	0.371527	+	0.135225i
$21$		0			0
$22$	50.3815	+	42.2751i	0.488244	+	0.409686i
$23$	67.4024	−	24.5325i	0.611059	−	0.222407i	−0.0179073	−	0.999840i	$-0.505700\pi$
$23$	67.4024	−	24.5325i	0.611059	−	0.222407i	0.628967	+	0.777432i	$0.283478\pi$
$24$		0			0
$25$	−8.13384	−	46.1293i	−0.0650707	−	0.369034i
$26$	−129.666			−0.978064
$27$		0			0
$28$	−130.824			−0.882979
$29$	36.3969	+	206.417i	0.233060	+	1.32175i	0.846661	+	0.532133i	$0.178609\pi$
$29$	36.3969	+	206.417i	0.233060	+	1.32175i	−0.613601	+	0.789616i	$0.710280\pi$
$30$		0			0
$31$	9.06899	−	3.30084i	0.0525432	−	0.0191242i	−0.315615	−	0.948887i	$-0.602211\pi$
$31$	9.06899	−	3.30084i	0.0525432	−	0.0191242i	0.368158	+	0.929763i	$0.379989\pi$
$32$	24.5134	+	20.5692i	0.135419	+	0.113630i
$33$		0			0
$34$	−166.761	−	60.6961i	−0.841156	−	0.306156i
$35$	−144.573	−	250.408i	−0.698208	−	1.20933i
$36$		0			0
$37$	58.8343	−	101.904i	0.261414	−	0.452782i	−0.705204	−	0.709004i	$-0.749145\pi$
$37$	58.8343	−	101.904i	0.261414	−	0.452782i	0.966618	+	0.256223i	$0.0824780\pi$
$38$	−171.786	+	144.146i	−0.733352	+	0.615355i
$39$		0			0
$40$	−12.2815	+	69.6516i	−0.0485467	+	0.275322i
$41$	1.53490	−	8.70486i	0.00584662	−	0.0331578i	−0.981745	−	0.190202i	$-0.939086\pi$
$41$	1.53490	−	8.70486i	0.00584662	−	0.0331578i	0.987592	+	0.157045i	$0.0501967\pi$
$42$		0			0
$43$	157.184	−	131.893i	0.557448	−	0.467755i	−0.320005	−	0.947416i	$-0.603685\pi$
$43$	157.184	−	131.893i	0.557448	−	0.467755i	0.877454	+	0.479661i	$0.159240\pi$
$44$	−65.7684	+	113.914i	−0.225340	+	0.390300i
$45$		0			0
$46$	71.7281	+	124.237i	0.229907	+	0.398211i
$47$	176.760	+	64.3354i	0.548576	+	0.199665i	0.601414	−	0.798938i	$-0.294604\pi$
$47$	176.760	+	64.3354i	0.548576	+	0.199665i	−0.0528375	+	0.998603i	$0.516827\pi$
$48$		0			0
$49$	556.670	+	467.102i	1.62295	+	1.36181i
$50$	88.0321	−	32.0411i	0.248992	−	0.0906258i
$51$		0			0
$52$	−45.0326	−	255.393i	−0.120094	−	0.681088i
$53$	−52.1118			−0.135058			−0.0675292	−	0.997717i	$-0.521512\pi$
$53$	−52.1118			−0.135058			−0.0675292	+	0.997717i	$0.521512\pi$
$54$		0			0
$55$	−290.722			−0.712743
$56$	−45.4347	−	257.673i	−0.108419	−	0.614875i
$57$		0			0
$58$	−393.922	+	143.376i	−0.891802	+	0.324589i
$59$	−207.031	−	173.720i	−0.456833	−	0.383328i	0.385131	−	0.922862i	$-0.374156\pi$
$59$	−207.031	−	173.720i	−0.456833	−	0.383328i	−0.841964	+	0.539534i	$0.818601\pi$
$60$		0			0
$61$	−215.595	−	78.4700i	−0.452526	−	0.164706i	0.105695	−	0.994399i	$-0.466293\pi$
$61$	−215.595	−	78.4700i	−0.452526	−	0.164706i	−0.558220	+	0.829693i	$0.688516\pi$
$62$	9.65102	+	16.7161i	0.0197690	+	0.0342410i
$63$		0			0
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	439.077	−	368.429i	0.837859	−	0.703047i
$66$		0			0
$67$	36.9619	−	209.621i	0.0673972	−	0.382229i	−0.932387	−	0.361461i	$-0.882278\pi$
$67$	36.9619	−	209.621i	0.0673972	−	0.382229i	0.999784	−	0.0207674i	$-0.00661094\pi$
$68$	61.6325	−	349.535i	0.109912	−	0.623343i
$69$		0			0
$70$	442.997	−	371.719i	0.756404	−	0.634698i
$71$	168.485	−	291.824i	0.281626	−	0.487791i	−0.690159	−	0.723658i	$-0.742459\pi$
$71$	168.485	−	291.824i	0.281626	−	0.487791i	0.971785	+	0.235867i	$0.0757928\pi$
$72$		0			0
$73$	−589.936	−	1021.80i	−0.945846	−	1.63825i	−0.754049	−	0.656818i	$-0.771902\pi$
$73$	−589.936	−	1021.80i	−0.945846	−	1.63825i	−0.191797	−	0.981435i	$-0.561431\pi$
$74$	221.145	+	80.4901i	0.347399	+	0.126443i
$75$		0			0
$76$	−343.572	−	288.291i	−0.518558	−	0.435122i
$77$	1010.65	−	367.846i	1.49577	−	0.544415i
$78$		0			0
$79$	9.64429	+	54.6955i	0.0137350	+	0.0778952i	0.990905	−	0.134565i	$-0.0429636\pi$
$79$	9.64429	+	54.6955i	0.0137350	+	0.0778952i	−0.977170	+	0.212460i	$0.931852\pi$
$80$	−141.452			−0.197685
$81$		0			0
$82$	17.6783			0.0238078
$83$	201.000	+	1139.93i	0.265815	+	1.50751i	0.766705	+	0.641999i	$0.221895\pi$
$83$	201.000	+	1139.93i	0.265815	+	1.50751i	−0.500890	+	0.865511i	$0.666994\pi$
$84$		0			0
$85$	737.148	−	268.300i	0.940647	−	0.342367i
$86$	314.367	+	263.786i	0.394176	+	0.330753i
$87$		0			0
$88$	−247.208	−	89.9765i	−0.299460	−	0.108995i
$89$	−650.056	−	1125.93i	−0.774222	−	1.34099i	−0.935231	−	0.354039i	$-0.884808\pi$
$89$	−650.056	−	1125.93i	−0.774222	−	1.34099i	0.161008	−	0.986953i	$-0.448525\pi$
$90$		0			0
$91$	−1060.22	+	1836.35i	−1.22133	+	2.11540i
$92$	−219.788	+	184.424i	−0.249070	+	0.208995i
$93$		0			0
$94$	−65.3278	+	370.493i	−0.0716814	+	0.406525i
$95$	172.133	−	976.214i	0.185900	−	1.05429i
$96$		0			0
$97$	1129.23	−	947.537i	1.18202	−	0.991833i	0.182057	−	0.983288i	$-0.441724\pi$
$97$	1129.23	−	947.537i	1.18202	−	0.991833i	0.999963	−	0.00854543i	$-0.00272013\pi$
$98$	−726.681	+	1258.65i	−0.749040	+	1.29738i
$99$		0			0
$100$	93.6818	+	162.262i	0.0936818	+	0.162262i
$101$	184.428	+	67.1264i	0.181696	+	0.0661319i	0.431266	−	0.902225i	$-0.358067\pi$
$101$	184.428	+	67.1264i	0.181696	+	0.0661319i	−0.249570	+	0.968357i	$0.580289\pi$
$102$		0			0
$103$	1.17472	+	0.985708i	0.00112377	+	0.000942958i	0.643349	−	0.765573i	$-0.277544\pi$
$103$	1.17472	+	0.985708i	0.00112377	+	0.000942958i	−0.642226	+	0.766516i	$0.721989\pi$
$104$	487.386	−	177.394i	0.459540	−	0.167259i
$105$		0			0
$106$	−18.0982	−	102.640i	−0.0165835	−	0.0940499i
$107$	653.554			0.590481			0.295240	−	0.955423i	$-0.404600\pi$
$107$	653.554			0.590481			0.295240	+	0.955423i	$0.404600\pi$
$108$		0			0
$109$	−655.133			−0.575692			−0.287846	−	0.957677i	$-0.592939\pi$
$109$	−655.133			−0.575692			−0.287846	+	0.957677i	$0.592939\pi$
$110$	−100.967	−	572.610i	−0.0875162	−	0.496329i
$111$		0			0
$112$	491.737	−	178.978i	0.414864	−	0.150998i
$113$	−675.036	−	566.422i	−0.561965	−	0.471544i	0.317004	−	0.948424i	$-0.397323\pi$
$113$	−675.036	−	566.422i	−0.561965	−	0.471544i	−0.878968	+	0.476880i	$0.841768\pi$
$114$		0			0
$115$	−595.888	−	216.886i	−0.483190	−	0.175867i
$116$	−419.203	−	726.081i	−0.335535	−	0.581163i
$117$		0			0
$118$	270.260	−	468.104i	0.210843	−	0.365190i
$119$	−2223.11	+	1865.41i	−1.71254	+	1.43699i
$120$		0			0
$121$	−43.3476	+	245.836i	−0.0325677	+	0.184700i
$122$	79.6806	−	451.891i	0.0591306	−	0.335347i
$123$		0			0
$124$	−29.5724	+	24.8142i	−0.0214168	+	0.0179708i
$125$	−759.602	+	1315.67i	−0.543527	+	0.941417i
$126$		0			0
$127$	−617.248	−	1069.11i	−0.431275	−	0.746990i	0.565708	−	0.824605i	$-0.308603\pi$
$127$	−617.248	−	1069.11i	−0.431275	−	0.746990i	−0.996983	+	0.0776151i	$0.975269\pi$
$128$	−120.281	−	43.7786i	−0.0830579	−	0.0302306i
$129$		0			0
$130$	878.154	+	736.859i	0.592456	+	0.497129i
$131$	−2719.45	+	989.799i	−1.81374	+	0.660146i	−0.817262	+	0.576267i	$0.804509\pi$
$131$	−2719.45	+	989.799i	−1.81374	+	0.660146i	−0.996476	+	0.0838794i	$0.973269\pi$
$132$		0			0
$133$	636.797	+	3611.46i	0.415168	+	2.35453i
$134$	425.710			0.274446
$135$		0			0
$136$	709.854			0.447570
$137$	160.275	+	908.964i	0.0999504	+	0.566847i	0.993118	+	0.117122i	$0.0373668\pi$
$137$	160.275	+	908.964i	0.0999504	+	0.566847i	−0.893167	+	0.449725i	$0.851522\pi$
$138$		0			0
$139$	155.431	−	56.5723i	0.0948453	−	0.0345209i	−0.294162	−	0.955756i	$-0.595040\pi$
$139$	155.431	−	56.5723i	0.0948453	−	0.0345209i	0.389007	+	0.921235i	$0.372818\pi$
$140$	885.994	+	743.438i	0.534859	+	0.448800i
$141$		0			0
$142$	633.296	+	230.501i	0.374261	+	0.136220i
$143$	1065.99	+	1846.35i	0.623377	+	1.07972i
$144$		0			0
$145$	926.519	−	1604.78i	0.530643	−	0.919100i
$146$	1807.67	−	1516.81i	1.02468	−	0.859811i
$147$		0			0
$148$	−81.7318	+	463.524i	−0.0453940	+	0.257442i
$149$	−93.0924	+	527.953i	−0.0511841	+	0.290279i	−0.999646	−	0.0266123i	$-0.991528\pi$
$149$	−93.0924	+	527.953i	−0.0511841	+	0.290279i	0.948462	+	0.316892i	$0.102639\pi$
$150$		0			0
$151$	−368.858	+	309.508i	−0.198790	+	0.166804i	−0.736749	−	0.676167i	$-0.763640\pi$
$151$	−368.858	+	309.508i	−0.198790	+	0.166804i	0.537959	+	0.842971i	$0.319195\pi$
$152$	448.501	−	776.827i	0.239331	−	0.414533i
$153$		0			0
$154$	1075.51	+	1862.84i	0.562773	+	0.974752i
$155$	−80.1768	−	29.1820i	−0.0415481	−	0.0151223i
$156$		0			0
$157$	−714.681	−	599.689i	−0.363298	−	0.304843i	0.442806	−	0.896618i	$-0.353983\pi$
$157$	−714.681	−	599.689i	−0.363298	−	0.304843i	−0.806104	+	0.591774i	$0.798428\pi$
$158$	−104.380	+	37.9911i	−0.0525570	+	0.0191292i
$159$		0			0
$160$	−49.1258	−	278.606i	−0.0242734	−	0.137661i
$161$	2345.94			1.14836
$162$		0			0
$163$	−758.326			−0.364397			−0.182198	−	0.983262i	$-0.558321\pi$
$163$	−758.326			−0.364397			−0.182198	+	0.983262i	$0.558321\pi$
$164$	6.13961	+	34.8195i	0.00292331	+	0.0165789i
$165$		0			0
$166$	−2175.41	+	791.786i	−1.01714	+	0.370208i
$167$	433.558	+	363.798i	0.200897	+	0.168572i	0.737686	−	0.675144i	$-0.235919\pi$
$167$	433.558	+	363.798i	0.200897	+	0.168572i	−0.536789	+	0.843716i	$0.680363\pi$
$168$		0			0
$169$	−1885.34	−	686.208i	−0.858143	−	0.312338i
$170$	784.457	+	1358.72i	0.353912	+	0.612994i
$171$		0			0
$172$	−410.377	+	710.795i	−0.181924	+	0.315102i
$173$	1180.84	−	990.846i	0.518948	−	0.435449i	−0.345317	−	0.938486i	$-0.612229\pi$
$173$	1180.84	−	990.846i	0.518948	−	0.435449i	0.864265	+	0.503037i	$0.167784\pi$
$174$		0			0
$175$	266.025	−	1508.70i	0.114912	−	0.651699i
$176$	91.3645	−	518.154i	0.0391299	−	0.221917i
$177$		0			0
$178$	1991.89	−	1671.39i	0.838754	−	0.703798i
$179$	469.549	−	813.282i	0.196066	−	0.339595i	−0.751184	−	0.660093i	$-0.770517\pi$
$179$	469.549	−	813.282i	0.196066	−	0.339595i	0.947249	+	0.320498i	$0.103850\pi$
$180$		0			0
$181$	1763.10	+	3053.77i	0.724033	+	1.25406i	0.959371	+	0.282148i	$0.0910469\pi$
$181$	1763.10	+	3053.77i	0.724033	+	1.25406i	−0.235338	+	0.971914i	$0.575620\pi$
$182$	−3985.11	−	1450.46i	−1.62305	−	0.590743i
$183$		0			0
$184$	−439.575	−	368.848i	−0.176119	−	0.147782i
$185$	−977.545	+	355.797i	−0.388489	+	0.141399i
$186$		0			0
$187$	506.684	+	2873.55i	0.198141	+	1.12371i
$188$	−752.416			−0.291891
$189$		0			0
$190$	1982.55			0.756995
$191$	−449.430	−	2548.84i	−0.170260	−	0.965591i	−0.943474	−	0.331446i	$-0.892463\pi$
$191$	−449.430	−	2548.84i	−0.170260	−	0.965591i	0.773214	−	0.634145i	$-0.218648\pi$
$192$		0			0
$193$	2515.11	−	915.426i	0.938041	−	0.341419i	0.172649	−	0.984983i	$-0.444767\pi$
$193$	2515.11	−	915.426i	0.938041	−	0.341419i	0.765392	+	0.643565i	$0.222545\pi$
$194$	2258.46	+	1895.07i	0.835815	+	0.701332i
$195$		0			0
$196$	−2731.43	−	994.159i	−0.995419	−	0.362303i
$197$	−2493.45	−	4318.79i	−0.901783	−	1.56193i	−0.825179	−	0.564872i	$-0.808926\pi$
$197$	−2493.45	−	4318.79i	−0.901783	−	1.56193i	−0.0766037	−	0.997062i	$-0.524408\pi$
$198$		0			0
$199$	1725.59	−	2988.81i	0.614693	−	1.06468i	−0.375745	−	0.926723i	$-0.622613\pi$
$199$	1725.59	−	2988.81i	0.614693	−	1.06468i	0.990438	−	0.137957i	$-0.0440535\pi$
$200$	−287.058	+	240.870i	−0.101490	+	0.0851604i
$201$		0			0
$202$	−68.1619	+	386.565i	−0.0237419	+	0.134647i
$203$	−1190.40	+	6751.08i	−0.411574	+	2.33415i
$204$		0			0
$205$	−59.8624	+	50.2305i	−0.0203950	+	0.0171134i
$206$	−1.53349	+	2.65608i	−0.000518656	+	0.000898339i
$207$		0			0
$208$	518.665	+	898.354i	0.172899	+	0.299470i
$209$	3464.79	+	1261.08i	1.14672	+	0.417372i
$210$		0			0
$211$	−2266.83	−	1902.10i	−0.739598	−	0.620597i	0.193131	−	0.981173i	$-0.438136\pi$
$211$	−2266.83	−	1902.10i	−0.739598	−	0.620597i	−0.932730	+	0.360576i	$0.882580\pi$
$212$	195.876	−	71.2931i	0.0634567	−	0.0230964i
$213$		0			0
$214$	226.977	+	1287.25i	0.0725038	+	0.411190i
$215$	−1814.02			−0.575421
$216$		0			0
$217$	315.646			0.0987440
$218$	−227.525	−	1290.36i	−0.0706879	−	0.400891i
$219$		0			0
$220$	1092.76	−	397.730i	0.334880	−	0.121886i
$221$	−4406.87	−	3697.80i	−1.34135	−	1.12553i
$222$		0			0
$223$	−5991.92	−	2180.88i	−1.79932	−	0.654900i	−0.998425	−	0.0560969i	$-0.982134\pi$
$223$	−5991.92	−	2180.88i	−1.79932	−	0.654900i	−0.800897	−	0.598803i	$-0.795643\pi$
$224$	523.296	+	906.375i	0.156090	+	0.270356i
$225$		0			0
$226$	881.196	−	1526.28i	0.259364	−	0.449232i
$227$	1500.20	−	1258.81i	0.438641	−	0.368063i	−0.396560	−	0.918009i	$-0.629796\pi$
$227$	1500.20	−	1258.81i	0.438641	−	0.368063i	0.835201	+	0.549946i	$0.185352\pi$
$228$		0			0
$229$	−7.78875	+	44.1722i	−0.00224758	+	0.0127466i	−0.985911	−	0.167271i	$-0.946504\pi$
$229$	−7.78875	+	44.1722i	−0.00224758	+	0.0127466i	0.983663	+	0.180018i	$0.0576156\pi$
$230$	220.231	−	1248.99i	0.0631375	−	0.358071i
$231$		0			0
$232$	1284.51	−	1077.83i	0.363502	−	0.305014i
$233$	2453.51	−	4249.60i	0.689848	−	1.19485i	−0.282038	−	0.959403i	$-0.591011\pi$
$233$	2453.51	−	4249.60i	0.689848	−	1.19485i	0.971887	−	0.235449i	$-0.0756561\pi$
$234$		0			0
$235$	−831.492	−	1440.19i	−0.230811	−	0.399776i
$236$	1015.84	+	369.737i	0.280194	+	0.101982i
$237$		0			0
$238$	−4446.22	−	3730.82i	−1.21095	−	1.01610i
$239$	4470.63	−	1627.18i	1.20996	−	0.440390i	0.343271	−	0.939236i	$-0.388465\pi$
$239$	4470.63	−	1627.18i	1.20996	−	0.440390i	0.866691	+	0.498846i	$0.166243\pi$
$240$		0			0
$241$	641.593	+	3638.65i	0.171488	+	0.972557i	0.942120	+	0.335276i	$0.108830\pi$
$241$	641.593	+	3638.65i	0.171488	+	0.972557i	−0.770632	+	0.637281i	$0.780059\pi$
$242$	−499.257			−0.132618
$243$		0			0
$244$	917.724			0.240784
$245$	−1115.59	−	6326.82i	−0.290908	−	1.64982i
$246$		0			0
$247$	−6831.04	+	2486.29i	−1.75971	+	0.640482i
$248$	−59.1449	−	49.6285i	−0.0151440	−	0.0127073i
$249$		0			0
$250$	−2855.17	−	1039.20i	−0.722307	−	0.262898i
$251$	3114.71	+	5394.84i	0.783262	+	1.35665i	0.930032	+	0.367479i	$0.119779\pi$
$251$	3114.71	+	5394.84i	0.783262	+	1.35665i	−0.146769	+	0.989171i	$0.546888\pi$
$252$		0			0
$253$	1179.36	−	2042.71i	0.293066	−	0.507606i
$254$	1891.36	−	1587.04i	0.467222	−	0.392046i
$255$		0			0
$256$	44.4539	−	252.111i	0.0108530	−	0.0615505i
$257$	−407.874	+	2313.17i	−0.0989980	+	0.561446i	0.894451	+	0.447167i	$0.147567\pi$
$257$	−407.874	+	2313.17i	−0.0989980	+	0.561446i	−0.993449	+	0.114279i	$0.963544\pi$
$258$		0			0
$259$	2948.10	−	2473.75i	0.707282	−	0.593480i
$260$	−1146.35	+	1985.53i	−0.273437	+	0.473606i
$261$		0			0
$262$	−2893.98	−	5012.52i	−0.682407	−	1.18196i
$263$	−3193.19	−	1162.23i	−0.748672	−	0.272494i	−0.0606249	−	0.998161i	$-0.519309\pi$
$263$	−3193.19	−	1162.23i	−0.748672	−	0.272494i	−0.688047	+	0.725666i	$0.741532\pi$
$264$		0			0
$265$	352.923	+	296.137i	0.0818108	+	0.0686474i
$266$	−6892.03	+	2508.49i	−1.58864	+	0.578216i
$267$		0			0
$268$	147.848	+	838.485i	0.0336986	+	0.191114i
$269$	7858.07			1.78110			0.890548	−	0.454889i	$-0.150321\pi$
$269$	7858.07			1.78110			0.890548	+	0.454889i	$0.150321\pi$
$270$		0			0
$271$	4785.22			1.07263			0.536313	−	0.844019i	$-0.319817\pi$
$271$	4785.22			1.07263			0.536313	+	0.844019i	$0.319817\pi$
$272$	246.530	+	1398.14i	0.0549561	+	0.311672i
$273$		0			0
$274$	−1734.65	+	631.359i	−0.382459	+	0.139204i
$275$	−1179.96	−	990.102i	−0.258742	−	0.217111i
$276$		0			0
$277$	4480.65	+	1630.82i	0.971899	+	0.353742i	0.778686	−	0.627414i	$-0.215887\pi$
$277$	4480.65	+	1630.82i	0.971899	+	0.353742i	0.193214	+	0.981157i	$0.438109\pi$
$278$	165.406	+	286.492i	0.0356849	+	0.0618081i
$279$		0			0
$280$	−1156.58	+	2003.26i	−0.246854	+	0.427563i
$281$	−986.758	+	827.989i	−0.209484	+	0.175778i	−0.741493	−	0.670961i	$-0.765882\pi$
$281$	−986.758	+	827.989i	−0.209484	+	0.175778i	0.532009	+	0.846739i	$0.321437\pi$
$282$		0			0
$283$	353.691	−	2005.88i	0.0742924	−	0.421333i	−0.924865	−	0.380295i	$-0.875822\pi$
$283$	353.691	−	2005.88i	0.0742924	−	0.421333i	0.999158	−	0.0410381i	$-0.0130665\pi$
$284$	−234.057	+	1327.40i	−0.0489039	+	0.277348i
$285$		0			0
$286$	−3266.39	+	2740.83i	−0.675335	+	0.566674i
$287$	144.547	−	250.362i	0.0297293	−	0.0514927i
$288$		0			0
$289$	−1480.17	−	2563.72i	−0.301275	−	0.521824i
$290$	3482.57	+	1267.55i	0.705185	+	0.256666i
$291$		0			0
$292$	3615.34	+	3033.63i	0.724560	+	0.607978i
$293$	1106.94	−	402.891i	0.220709	−	0.0803316i	−0.229299	−	0.973356i	$-0.573643\pi$
$293$	1106.94	−	402.891i	0.220709	−	0.0803316i	0.450008	+	0.893024i	$0.351421\pi$
$294$		0			0
$295$	414.898	+	2353.00i	0.0818857	+	0.464397i
$296$	−941.350			−0.184847
$297$		0			0
$298$	−1072.20			−0.208425
$299$	807.526	+	4579.71i	0.156189	+	0.885791i
$300$		0			0
$301$	6306.18	−	2295.26i	1.20758	−	0.439524i
$302$	−737.716	−	619.017i	−0.140565	−	0.117948i
$303$		0			0
$304$	1685.81	+	613.586i	0.318053	+	0.115762i
$305$	1014.17	+	1756.60i	0.190398	+	0.329779i
$306$		0			0
$307$	−3677.69	+	6369.95i	−0.683704	+	1.18421i	0.290139	+	0.956985i	$0.406299\pi$
$307$	−3677.69	+	6369.95i	−0.683704	+	1.18421i	−0.973842	+	0.227225i	$0.927035\pi$
$308$	−3295.56	+	2765.30i	−0.609681	+	0.511583i
$309$		0			0
$310$	29.6322	−	168.052i	0.00542901	−	0.0307895i
$311$	1236.41	−	7012.01i	0.225435	−	1.27850i	−0.636418	−	0.771344i	$-0.719585\pi$
$311$	1236.41	−	7012.01i	0.225435	−	1.27850i	0.861853	−	0.507159i	$-0.169304\pi$
$312$		0			0
$313$	1276.79	−	1071.35i	0.230570	−	0.193471i	−0.520182	−	0.854055i	$-0.674136\pi$
$313$	1276.79	−	1071.35i	0.230570	−	0.193471i	0.750752	+	0.660585i	$0.229691\pi$
$314$	932.950	−	1615.92i	0.167673	−	0.290419i
$315$		0			0
$316$	−111.079	−	192.394i	−0.0197742	−	0.0342500i
$317$	−4395.81	−	1599.94i	−0.778843	−	0.283476i	−0.0781527	−	0.996941i	$-0.524902\pi$
$317$	−4395.81	−	1599.94i	−0.778843	−	0.283476i	−0.700690	+	0.713466i	$0.747124\pi$
$318$		0			0
$319$	5280.02	+	4430.47i	0.926723	+	0.777613i
$320$	531.686	−	193.518i	0.0928818	−	0.0338062i
$321$		0			0
$322$	814.736	+	4620.60i	0.141005	+	0.799676i
$323$	−9949.09			−1.71388
$324$		0			0
$325$	3036.84			0.518319
$326$	−263.364	−	1493.61i	−0.0447435	−	0.253753i
$327$		0			0
$328$	−66.4487	+	24.1853i	−0.0111860	+	0.00407138i
$329$	4712.80	+	3954.51i	0.789742	+	0.662672i
$330$		0			0
$331$	−1139.25	−	414.654i	−0.189181	−	0.0688563i	0.245692	−	0.969348i	$-0.420985\pi$
$331$	−1139.25	−	414.654i	−0.189181	−	0.0688563i	−0.434874	+	0.900492i	$0.643207\pi$
$332$	−2315.03	−	4009.74i	−0.382691	−	0.662841i
$333$		0			0
$334$	−565.970	+	980.288i	−0.0927200	+	0.160596i
$335$	−1441.54	+	1209.60i	−0.235104	+	0.197276i
$336$		0			0
$337$	263.431	−	1493.99i	0.0425815	−	0.241492i	−0.956087	−	0.293084i	$-0.905318\pi$
$337$	263.431	−	1493.99i	0.0425815	−	0.241492i	0.998668	+	0.0515920i	$0.0164296\pi$
$338$	696.793	−	3951.71i	0.112132	−	0.635931i
$339$		0			0
$340$	−2403.72	+	2016.96i	−0.383411	+	0.321720i
$341$	158.683	−	274.847i	0.0251999	−	0.0436475i
$342$		0			0
$343$	6274.34	+	10867.5i	0.987704	+	1.71075i
$344$	−1542.51	−	561.429i	−0.241764	−	0.0879949i
$345$		0			0
$346$	2361.69	+	1981.69i	0.366951	+	0.307909i
$347$	6778.15	−	2467.04i	1.04862	−	0.381665i	0.240476	−	0.970655i	$-0.422696\pi$
$347$	6778.15	−	2467.04i	1.04862	−	0.381665i	0.808141	+	0.588990i	$0.200474\pi$
$348$		0			0
$349$	−336.433	−	1908.01i	−0.0516013	−	0.292645i	0.948076	−	0.318043i	$-0.103026\pi$
$349$	−336.433	−	1908.01i	−0.0516013	−	0.292645i	−0.999677	+	0.0253981i	$0.991915\pi$
$350$	3063.96			0.467929
$351$		0			0
$352$	1052.29			0.159339
$353$	1659.45	+	9411.22i	0.250209	+	1.41900i	0.808078	+	0.589076i	$0.200508\pi$
$353$	1659.45	+	9411.22i	0.250209	+	1.41900i	−0.557869	+	0.829929i	$0.688381\pi$
$354$		0			0
$355$	−2799.41	+	1018.90i	−0.418527	+	0.152331i
$356$	3983.77	+	3342.78i	0.593089	+	0.497661i
$357$		0			0
$358$	1764.93	+	642.381i	0.260557	+	0.0948348i
$359$	4555.42	+	7890.22i	0.669710	+	1.15997i	0.977985	+	0.208675i	$0.0669150\pi$
$359$	4555.42	+	7890.22i	0.669710	+	1.15997i	−0.308275	+	0.951297i	$0.599752\pi$
$360$		0			0
$361$	−2856.55	+	4947.69i	−0.416467	+	0.721342i
$362$	−5402.44	+	4533.19i	−0.784381	+	0.658174i
$363$		0			0
$364$	1472.84	−	8352.87i	0.212081	−	1.20277i
$365$	−1811.32	+	10272.5i	−0.259750	+	1.47311i
$366$		0			0
$367$	8967.69	−	7524.79i	1.27550	−	1.07027i	0.281656	−	0.959515i	$-0.409116\pi$
$367$	8967.69	−	7524.79i	1.27550	−	1.07027i	0.993847	−	0.110759i	$-0.0353281\pi$
$368$	573.825	−	993.894i	0.0812845	−	0.140789i
$369$		0			0
$370$	−1040.28	−	1801.82i	−0.146167	−	0.253168i
$371$	−1601.58	−	582.928i	−0.224124	−	0.0815744i
$372$		0			0
$373$	440.399	+	369.538i	0.0611340	+	0.0512975i	0.672843	−	0.739786i	$-0.265073\pi$
$373$	440.399	+	369.538i	0.0611340	+	0.0512975i	−0.611709	+	0.791083i	$0.709518\pi$
$374$	−5483.81	+	1995.94i	−0.758185	+	0.275957i
$375$		0			0
$376$	−261.311	−	1481.97i	−0.0358407	−	0.203263i
$377$	−13589.1			−1.85643
$378$		0			0
$379$	−9338.61			−1.26568			−0.632839	−	0.774283i	$-0.718111\pi$
$379$	−9338.61			−1.26568			−0.632839	+	0.774283i	$0.718111\pi$
$380$	688.532	+	3904.86i	0.0929498	+	0.527145i
$381$		0			0
$382$	4864.16	−	1770.41i	0.651497	−	0.237126i
$383$	−9341.95	−	7838.83i	−1.24635	−	1.04581i	−0.997000	−	0.0773960i	$-0.975339\pi$
$383$	−9341.95	−	7838.83i	−1.24635	−	1.04581i	−0.249348	−	0.968414i	$-0.580216\pi$
$384$		0			0
$385$	−8934.91	−	3252.04i	−1.18277	−	0.430492i
$386$	2676.53	+	4635.88i	0.352932	+	0.611296i
$387$		0			0
$388$	−2948.21	+	5106.45i	−0.385755	+	0.668147i
$389$	7022.63	−	5892.69i	0.915325	−	0.768049i	−0.0577995	−	0.998328i	$-0.518408\pi$
$389$	7022.63	−	5892.69i	0.915325	−	0.768049i	0.973125	+	0.230279i	$0.0739640\pi$
$390$		0			0
$391$	−1105.20	+	6267.87i	−0.142947	+	0.810690i
$392$	1009.50	−	5725.13i	0.130069	−	0.737660i
$393$		0			0
$394$	7640.38	−	6411.04i	0.976947	−	0.819755i
$395$	245.505	−	425.227i	0.0312726	−	0.0541658i
$396$		0			0
$397$	−4177.42	−	7235.50i	−0.528107	−	0.914708i	−0.999463	−	0.0327652i	$-0.989569\pi$
$397$	−4177.42	−	7235.50i	−0.528107	−	0.914708i	0.471356	−	0.881943i	$-0.343765\pi$
$398$	6486.10	+	2360.75i	0.816882	+	0.297321i
$399$		0			0
$400$	−574.115	−	481.740i	−0.0717644	−	0.0602175i
$401$	1173.34	−	427.060i	0.146119	−	0.0531829i	−0.267925	−	0.963440i	$-0.586338\pi$
$401$	1173.34	−	427.060i	0.146119	−	0.0531829i	0.414044	+	0.910257i	$0.364116\pi$
$402$		0			0
$403$	108.653	+	616.200i	0.0134302	+	0.0761665i
$404$	−785.057			−0.0966784
$405$		0			0
$406$	−13710.4			−1.67596
$407$	−671.922	−	3810.66i	−0.0818327	−	0.464096i
$408$		0			0
$409$	−2525.85	+	919.333i	−0.305367	+	0.111144i	−0.490159	−	0.871633i	$-0.663061\pi$
$409$	−2525.85	+	919.333i	−0.305367	+	0.111144i	0.184792	+	0.982778i	$0.440839\pi$
$410$	−119.725	−	100.461i	−0.0144214	−	0.0121010i
$411$		0			0
$412$	−5.76403	−	2.09794i	−0.000689256	−	0.000250869i
$413$	−4419.55	−	7654.89i	−0.526567	−	0.912040i
$414$		0			0
$415$	5116.65	−	8862.30i	0.605220	−	1.04827i
$416$	−1589.28	+	1333.57i	−0.187310	+	0.157172i
$417$		0			0
$418$	−1280.54	+	7262.28i	−0.149840	+	0.849784i
$419$	705.457	−	4000.85i	0.0822526	−	0.466477i	−0.915663	−	0.401947i	$-0.868334\pi$
$419$	705.457	−	4000.85i	0.0822526	−	0.466477i	0.997916	−	0.0645310i	$-0.0205551\pi$
$420$		0			0
$421$	−5265.06	+	4417.91i	−0.609509	+	0.511439i	−0.894486	−	0.447095i	$-0.852458\pi$
$421$	−5265.06	+	4417.91i	−0.609509	+	0.511439i	0.284977	+	0.958534i	$0.408014\pi$
$422$	2959.14	−	5125.38i	0.341348	−	0.591232i
$423$		0			0
$424$	208.447	+	361.041i	0.0238752	+	0.0413530i
$425$	3905.62	+	1421.53i	0.445766	+	0.162246i
$426$		0			0
$427$	−5748.22	−	4823.33i	−0.651466	−	0.546645i
$428$	−2456.56	+	894.114i	−0.277435	+	0.100978i
$429$		0			0
$430$	−630.004	−	3572.93i	−0.0706547	−	0.400702i
$431$	2250.85			0.251553			0.125777	−	0.992059i	$-0.459858\pi$
$431$	2250.85			0.251553			0.125777	+	0.992059i	$0.459858\pi$
$432$		0			0
$433$	−9167.13			−1.01742			−0.508712	−	0.860937i	$-0.669878\pi$
$433$	−9167.13			−1.01742			−0.508712	+	0.860937i	$0.669878\pi$
$434$	109.623	+	621.701i	0.0121246	+	0.0687618i
$435$		0			0
$436$	2462.50	−	896.275i	0.270487	−	0.0984491i
$437$	6160.94	+	5169.65i	0.674412	+	0.565899i
$438$		0			0
$439$	12345.3	+	4493.32i	1.34216	+	0.488507i	0.910493	−	0.413525i	$-0.135703\pi$
$439$	12345.3	+	4493.32i	1.34216	+	0.488507i	0.431669	+	0.902032i	$0.357925\pi$
$440$	1162.89	+	2014.18i	0.125996	+	0.218232i
$441$		0			0
$442$	5752.76	−	9964.08i	0.619075	−	1.07227i
$443$	−5056.71	+	4243.08i	−0.542328	+	0.455067i	−0.872333	−	0.488912i	$-0.837394\pi$
$443$	−5056.71	+	4243.08i	−0.542328	+	0.455067i	0.330005	+	0.943979i	$0.392950\pi$
$444$		0			0
$445$	−1995.91	+	11319.4i	−0.212618	+	1.20582i
$446$	2214.52	−	12559.2i	0.235114	−	1.33340i
$447$		0			0
$448$	−1603.47	+	1345.47i	−0.169100	+	0.141892i
$449$	−7906.79	+	13695.0i	−0.831057	+	1.43943i	0.0661436	+	0.997810i	$0.478930\pi$
$449$	−7906.79	+	13695.0i	−0.831057	+	1.43943i	−0.897201	+	0.441623i	$0.854403\pi$
$450$		0			0
$451$	−145.334	−	251.726i	−0.0151741	−	0.0262823i
$452$	3312.22	+	1205.55i	0.344676	+	0.125452i
$453$		0			0
$454$	3000.39	+	2517.63i	0.310166	+	0.260260i
$455$	17615.7	−	6411.59i	1.81503	−	0.660615i
$456$		0			0
$457$	−2175.56	−	12338.2i	−0.222688	−	1.26293i	−0.867056	−	0.498211i	$-0.833990\pi$
$457$	−2175.56	−	12338.2i	−0.222688	−	1.26293i	0.644368	−	0.764716i	$-0.277121\pi$
$458$	−89.7073			−0.00915228
$459$		0			0
$460$	2536.53			0.257100
$461$	26.0435	+	147.700i	0.00263116	+	0.0149221i	0.986095	−	0.166182i	$-0.0531440\pi$
$461$	26.0435	+	147.700i	0.00263116	+	0.0149221i	−0.983464	+	0.181104i	$0.942033\pi$
$462$		0			0
$463$	−4386.19	+	1596.44i	−0.440267	+	0.160244i	−0.552636	−	0.833422i	$-0.686378\pi$
$463$	−4386.19	+	1596.44i	−0.440267	+	0.160244i	0.112369	+	0.993666i	$0.464156\pi$
$464$	2569.03	+	2155.67i	0.257035	+	0.215678i
$465$		0			0
$466$	9222.17	+	3356.60i	0.916757	+	0.333672i
$467$	−3368.83	−	5834.99i	−0.333814	−	0.578182i	0.649443	−	0.760411i	$-0.275002\pi$
$467$	−3368.83	−	5834.99i	−0.333814	−	0.578182i	−0.983256	+	0.182229i	$0.941669\pi$
$468$		0			0
$469$	3480.82	−	6028.95i	0.342706	−	0.593585i
$470$	2547.84	−	2137.89i	0.250049	−	0.209816i
$471$		0			0
$472$	−375.441	+	2129.23i	−0.0366124	+	0.207639i
$473$	1171.69	−	6644.96i	0.113899	−	0.645953i
$474$		0			0
$475$	4023.31	−	3375.95i	0.388636	−	0.326104i
$476$	5804.12	−	10053.0i	0.558890	−	0.968025i
$477$		0			0
$478$	4757.54	+	8240.31i	0.455240	+	0.788500i
$479$	587.130	+	213.698i	0.0560055	+	0.0203843i	0.369871	−	0.929083i	$-0.379402\pi$
$479$	587.130	+	213.698i	0.0560055	+	0.0203843i	−0.313865	+	0.949467i	$0.601624\pi$
$480$		0			0
$481$	5844.02	+	4903.72i	0.553980	+	0.464845i
$482$	−6943.92	+	2527.38i	−0.656197	+	0.238836i
$483$		0			0
$484$	−173.390	−	983.345i	−0.0162838	−	0.0923502i
$485$	−13032.2			−1.22013
$486$		0			0
$487$	2744.63			0.255382			0.127691	−	0.991814i	$-0.459243\pi$
$487$	2744.63			0.255382			0.127691	+	0.991814i	$0.459243\pi$
$488$	318.722	+	1807.56i	0.0295653	+	0.167673i
$489$		0			0
$490$	12074.0	−	4394.56i	1.11315	−	0.405155i
$491$	−4679.07	−	3926.20i	−0.430068	−	0.360870i	0.401910	−	0.915679i	$-0.368347\pi$
$491$	−4679.07	−	3926.20i	−0.430068	−	0.360870i	−0.831977	+	0.554810i	$0.812791\pi$
$492$		0			0
$493$	−17476.7	−	6361.00i	−1.59657	−	0.581106i
$494$	−7269.44	−	12591.0i	−0.662080	−	1.14676i
$495$		0			0
$496$	77.2082	−	133.728i	0.00698941	−	0.0121060i
$497$	8442.52	−	7084.11i	0.761969	−	0.639368i
$498$		0			0
$499$	187.847	−	1065.34i	0.0168521	−	0.0955730i	−0.975222	−	0.221230i	$-0.928993\pi$
$499$	187.847	−	1065.34i	0.0168521	−	0.0955730i	0.992074	+	0.125657i	$0.0401039\pi$
$500$	1055.23	−	5984.50i	0.0943825	−	0.535270i
$501$		0			0
$502$	−9544.03	+	8008.39i	−0.848547	+	0.712016i
$503$	−758.051	+	1312.98i	−0.0671965	+	0.116388i	−0.897666	−	0.440676i	$-0.854739\pi$
$503$	−758.051	+	1312.98i	−0.0671965	+	0.116388i	0.830470	+	0.557064i	$0.188072\pi$
$504$		0			0
$505$	−867.563	−	1502.66i	−0.0764477	−	0.132411i
$506$	4432.95	+	1613.46i	0.389464	+	0.141753i
$507$		0			0
$508$	3782.72	+	3174.08i	0.330376	+	0.277218i
$509$	−823.511	+	299.734i	−0.0717122	+	0.0261011i	−0.377627	−	0.925958i	$-0.623260\pi$
$509$	−823.511	+	299.734i	−0.0717122	+	0.0261011i	0.305915	+	0.952059i	$0.401038\pi$
$510$		0			0
$511$	−6700.88	−	38002.6i	−0.580097	−	3.28989i
$512$	512.000			0.0441942
$513$		0			0
$514$	−4697.71			−0.403126
$515$	−2.35419	−	13.3512i	−0.000201433	−	0.00114238i
$516$		0			0
$517$	5812.61	−	2115.62i	0.494465	−	0.179971i
$518$	5896.20	+	4947.50i	0.500124	+	0.419654i
$519$		0			0
$520$	−4308.86	−	1568.30i	−0.363377	−	0.132258i
$521$	−2682.27	−	4645.83i	−0.225552	−	0.390667i	0.730933	−	0.682449i	$-0.239085\pi$
$521$	−2682.27	−	4645.83i	−0.225552	−	0.390667i	−0.956485	+	0.291782i	$0.905752\pi$
$522$		0			0
$523$	−11069.6	+	19173.2i	−0.925510	+	1.60303i	−0.134770	+	0.990877i	$0.543030\pi$
$523$	−11069.6	+	19173.2i	−0.925510	+	1.60303i	−0.790739	+	0.612153i	$0.790304\pi$
$524$	8867.67	−	7440.86i	0.739286	−	0.620335i
$525$		0			0
$526$	1180.16	−	6693.00i	0.0978275	−	0.554807i
$527$	−148.704	+	843.343i	−0.0122916	+	0.0697089i
$528$		0			0
$529$	−5379.22	+	4513.70i	−0.442116	+	0.370979i
$530$	−460.708	+	797.969i	−0.0377582	+	0.0653992i
$531$		0			0
$532$	−7334.34	−	12703.5i	−0.597714	−	1.03527i
$533$	538.510	+	196.001i	0.0437625	+	0.0159283i
$534$		0			0
$535$	−4426.14	−	3713.97i	−0.357680	−	0.300129i
$536$	−1600.15	+	582.406i	−0.128947	+	0.0469330i
$537$		0			0
$538$	2729.08	+	15477.4i	0.218697	+	1.24029i
$539$	23896.3			1.90963
$540$		0			0
$541$	12985.5			1.03196			0.515980	−	0.856600i	$-0.327428\pi$
$541$	12985.5			1.03196			0.515980	+	0.856600i	$0.327428\pi$
$542$	1661.89	+	9425.05i	0.131705	+	0.746938i
$543$		0			0
$544$	−2668.18	+	971.138i	−0.210289	+	0.0765390i
$545$	4436.84	+	3722.95i	0.348722	+	0.292612i
$546$		0			0
$547$	12290.7	+	4473.44i	0.960714	+	0.349671i	0.774313	−	0.632802i	$-0.218095\pi$
$547$	12290.7	+	4473.44i	0.960714	+	0.349671i	0.186401	+	0.982474i	$0.440318\pi$
$548$	−1845.97	−	3197.32i	−0.143898	−	0.249238i
$549$		0			0
$550$	1540.33	−	2667.92i	0.119418	−	0.206837i
$551$	−18003.3	+	15106.6i	−1.39195	+	1.16799i
$552$		0			0
$553$	−315.426	+	1788.87i	−0.0242555	+	0.137560i
$554$	−1655.98	+	9391.53i	−0.126996	+	0.720231i
$555$		0			0
$556$	−506.834	+	425.285i	−0.0386593	+	0.0324390i
$557$	−2372.21	+	4108.78i	−0.180455	+	0.312558i	−0.942036	−	0.335513i	$-0.891090\pi$
$557$	−2372.21	+	4108.78i	−0.180455	+	0.312558i	0.761580	+	0.648071i	$0.224424\pi$
$558$		0			0
$559$	6651.51	+	11520.8i	0.503272	+	0.871693i
$560$	−4347.33	−	1582.30i	−0.328051	−	0.119401i
$561$		0			0
$562$	−1973.52	−	1655.98i	−0.148128	−	0.124294i
$563$	4452.91	−	1620.73i	0.333335	−	0.121324i	−0.169930	−	0.985456i	$-0.554354\pi$
$563$	4452.91	−	1620.73i	0.333335	−	0.121324i	0.503265	+	0.864132i	$0.332132\pi$
$564$		0			0
$565$	1352.80	+	7672.10i	0.100730	+	0.571270i
$566$	4073.65			0.302524
$567$		0			0
$568$	−2695.76			−0.199140
$569$	−476.154	−	2700.41i	−0.0350816	−	0.198958i	0.962230	−	0.272239i	$-0.0877641\pi$
$569$	−476.154	−	2700.41i	−0.0350816	−	0.198958i	−0.997311	+	0.0732812i	$0.976653\pi$
$570$		0			0
$571$	−21548.7	+	7843.09i	−1.57931	+	0.574822i	−0.975054	−	0.221969i	$-0.928752\pi$
$571$	−21548.7	+	7843.09i	−1.57931	+	0.574822i	−0.604256	+	0.796790i	$0.706529\pi$
$572$	−6532.79	−	5481.66i	−0.477534	−	0.400699i
$573$		0			0
$574$	543.317	+	197.751i	0.0395081	+	0.0143798i
$575$	−1679.90	−	2909.68i	−0.121838	−	0.211030i
$576$		0			0
$577$	−1116.27	+	1933.44i	−0.0805389	+	0.139498i	−0.903482	−	0.428627i	$-0.858997\pi$
$577$	−1116.27	+	1933.44i	−0.0805389	+	0.139498i	0.822943	+	0.568124i	$0.192331\pi$
$578$	4535.49	−	3805.73i	0.326387	−	0.273871i
$579$		0			0
$580$	−1287.11	+	7299.54i	−0.0921451	+	0.522581i
$581$	−6573.90	+	37282.5i	−0.469417	+	2.66220i
$582$		0			0
$583$	−1312.74	+	1101.52i	−0.0932555	+	0.0782506i
$584$	−4719.48	+	8174.39i	−0.334407	+	0.579210i
$585$		0			0
$586$	1177.98	+	2040.31i	0.0830405	+	0.143830i
$587$	6689.40	+	2434.74i	0.470360	+	0.171197i	0.566315	−	0.824189i	$-0.308368\pi$
$587$	6689.40	+	2434.74i	0.470360	+	0.171197i	−0.0959556	+	0.995386i	$0.530591\pi$
$588$		0			0
$589$	828.955	+	695.576i	0.0579907	+	0.0486599i
$590$	−4490.42	+	1634.38i	−0.313335	+	0.114045i
$591$		0			0
$592$	−326.927	−	1854.10i	−0.0226970	−	0.128721i
$593$	−15808.7			−1.09475			−0.547373	−	0.836889i	$-0.684372\pi$
$593$	−15808.7			−1.09475			−0.547373	+	0.836889i	$0.684372\pi$
$594$		0			0
$595$	25656.4			1.76775
$596$	−372.370	−	2111.81i	−0.0255920	−	0.145140i
$597$		0			0
$598$	−8739.82	+	3181.03i	−0.597655	+	0.217529i
$599$	−1763.34	−	1479.61i	−0.120280	−	0.100927i	0.580663	−	0.814144i	$-0.302793\pi$
$599$	−1763.34	−	1479.61i	−0.120280	−	0.100927i	−0.700944	+	0.713216i	$0.747238\pi$
$600$		0			0
$601$	25329.2	+	9219.06i	1.71913	+	0.625713i	0.997764	−	0.0668387i	$-0.0212913\pi$
$601$	25329.2	+	9219.06i	1.71913	+	0.625713i	0.721368	+	0.692552i	$0.243514\pi$
$602$	6710.90	+	11623.6i	0.454345	+	0.786949i
$603$		0			0
$604$	963.019	−	1668.00i	0.0648753	−	0.112367i
$605$	1690.59	−	1418.57i	0.113607	−	0.0953276i
$606$		0			0
$607$	1594.07	−	9040.39i	0.106592	−	0.604511i	−0.883981	−	0.467523i	$-0.845147\pi$
$607$	1594.07	−	9040.39i	0.106592	−	0.604511i	0.990573	−	0.136988i	$-0.0437423\pi$
$608$	−623.052	+	3533.50i	−0.0415593	+	0.235695i
$609$		0			0
$610$	−3107.61	+	2607.59i	−0.206268	+	0.173079i
$611$	−6097.69	+	10561.5i	−0.403741	+	0.699301i
$612$		0			0
$613$	−11466.2	−	19860.1i	−0.755492	−	1.30855i	−0.945129	−	0.326697i	$-0.894064\pi$
$613$	−11466.2	−	19860.1i	−0.755492	−	1.30855i	0.189637	−	0.981854i	$-0.439269\pi$
$614$	−13823.6	−	5031.38i	−0.908591	−	0.330700i
$615$		0			0
$616$	−6591.11	−	5530.60i	−0.431109	−	0.361744i
$617$	−2469.18	+	898.710i	−0.161111	+	0.0586397i	−0.421317	−	0.906914i	$-0.638432\pi$
$617$	−2469.18	+	898.710i	−0.161111	+	0.0586397i	0.260205	+	0.965553i	$0.416210\pi$
$618$		0			0
$619$	−718.987	−	4077.58i	−0.0466859	−	0.264769i	0.952526	−	0.304456i	$-0.0984748\pi$
$619$	−718.987	−	4077.58i	−0.0466859	−	0.264769i	−0.999212	+	0.0396877i	$0.987364\pi$
$620$	341.290			0.0221073
$621$		0			0
$622$	14240.4			0.917985
$623$	−7383.77	−	41875.4i	−0.474839	−	2.69294i
$624$		0			0
$625$	7118.94	−	2591.08i	0.455612	−	0.165829i
$626$	2553.57	+	2142.70i	0.163037	+	0.136805i
$627$		0			0
$628$	3506.74	+	1276.35i	0.222825	+	0.0811018i
$629$	5220.48	+	9042.13i	0.330929	+	0.573185i
$630$		0			0
$631$	−1335.72	+	2313.53i	−0.0842694	+	0.145959i	−0.905080	−	0.425242i	$-0.860189\pi$
$631$	−1335.72	+	2313.53i	−0.0842694	+	0.145959i	0.820810	+	0.571201i	$0.193522\pi$
$632$	340.364	−	285.600i	0.0214224	−	0.0179755i
$633$		0			0
$634$	1624.62	−	9213.70i	0.101770	−	0.577166i
$635$	−1895.18	+	10748.1i	−0.118438	+	0.671693i
$636$		0			0
$637$	−36090.7	+	30283.7i	−2.24484	+	1.88365i
$638$	−6892.58	+	11938.3i	−0.427711	+	0.740818i
$639$		0			0
$640$	565.809	+	980.010i	0.0349462	+	0.0605286i
$641$	−10229.4	−	3723.18i	−0.630321	−	0.229418i	0.00705014	−	0.999975i	$-0.497756\pi$
$641$	−10229.4	−	3723.18i	−0.630321	−	0.229418i	−0.637371	+	0.770557i	$0.719978\pi$
$642$		0			0
$643$	−6343.81	−	5323.08i	−0.389075	−	0.326473i	0.427178	−	0.904168i	$-0.359508\pi$
$643$	−6343.81	−	5323.08i	−0.389075	−	0.326473i	−0.816253	+	0.577695i	$0.803952\pi$
$644$	−8817.84	+	3209.43i	−0.539552	+	0.196381i
$645$		0			0
$646$	−3455.28	−	19595.9i	−0.210443	−	1.19348i
$647$	25662.6			1.55935			0.779677	−	0.626182i	$-0.215383\pi$
$647$	25662.6			1.55935			0.779677	+	0.626182i	$0.215383\pi$
$648$		0			0
$649$	−8887.28			−0.537529
$650$	1054.68	+	5981.41i	0.0636433	+	0.360939i
$651$		0			0
$652$	2850.37	−	1037.45i	0.171211	−	0.0623155i
$653$	−20915.6	−	17550.3i	−1.25343	−	1.05176i	−0.996350	−	0.0853667i	$-0.972794\pi$
$653$	−20915.6	−	17550.3i	−1.25343	−	1.05176i	−0.257084	−	0.966389i	$-0.582762\pi$
$654$		0			0
$655$	24042.0	+	8750.58i	1.43420	+	0.522005i
$656$	−70.7132	−	122.479i	−0.00420867	−	0.00728963i
$657$		0			0
$658$	−6152.13	+	10655.8i	−0.364491	+	0.631316i
$659$	3524.82	−	2957.67i	0.208357	−	0.174832i	−0.532637	−	0.846344i	$-0.678799\pi$
$659$	3524.82	−	2957.67i	0.208357	−	0.174832i	0.740994	+	0.671511i	$0.234355\pi$
$660$		0			0
$661$	−2366.66	+	13422.0i	−0.139262	+	0.789796i	0.832534	+	0.553974i	$0.186889\pi$
$661$	−2366.66	+	13422.0i	−0.139262	+	0.789796i	−0.971796	+	0.235822i	$0.924222\pi$
$662$	421.051	−	2387.90i	0.0247199	−	0.140194i
$663$		0			0
$664$	7093.65	−	5952.28i	0.414589	−	0.347881i
$665$	16210.3	−	28077.1i	0.945275	−	1.63727i
$666$		0			0
$667$	7517.16	+	13020.1i	0.436380	+	0.755833i
$668$	−2127.35	−	774.292i	−0.123218	−	0.0448477i
$669$		0			0
$670$	−2883.09	−	2419.20i	−0.166244	−	0.139495i
$671$	−7089.66	+	2580.43i	−0.407889	+	0.148459i
$672$		0			0
$673$	4239.82	+	24045.2i	0.242843	+	1.37723i	0.825450	+	0.564475i	$0.190921\pi$
$673$	4239.82	+	24045.2i	0.242843	+	1.37723i	−0.582608	+	0.812754i	$0.697968\pi$
$674$	3034.07			0.173395
$675$		0			0
$676$	8025.35			0.456608
$677$	2780.22	+	15767.4i	0.157833	+	0.895113i	0.956150	+	0.292877i	$0.0946125\pi$
$677$	2780.22	+	15767.4i	0.157833	+	0.895113i	−0.798318	+	0.602237i	$0.794276\pi$
$678$		0			0
$679$	45304.6	−	16489.5i	2.56057	−	0.931972i
$680$	−4807.43	−	4033.91i	−0.271113	−	0.227490i
$681$		0			0
$682$	596.453	+	217.091i	0.0334888	+	0.0121889i
$683$	7361.68	+	12750.8i	0.412426	+	0.714343i	0.995154	−	0.0983241i	$-0.0313482\pi$
$683$	7361.68	+	12750.8i	0.412426	+	0.714343i	−0.582728	+	0.812667i	$0.698015\pi$
$684$		0			0
$685$	4079.95	−	7066.68i	0.227572	−	0.394166i
$686$	−19225.7	+	16132.3i	−1.07003	+	0.897861i
$687$		0			0
$688$	570.090	−	3233.14i	0.0315908	−	0.179160i
$689$	586.682	−	3327.24i	0.0324395	−	0.183974i
$690$		0			0
$691$	−8908.09	+	7474.78i	−0.490419	+	0.411511i	−0.854177	−	0.519983i	$-0.825938\pi$
$691$	−8908.09	+	7474.78i	−0.490419	+	0.411511i	0.363757	+	0.931494i	$0.381494\pi$
$692$	−3082.97	+	5339.85i	−0.169360	+	0.293339i
$693$		0			0
$694$	7213.16	+	12493.6i	0.394536	+	0.683356i
$695$	−1374.13	−	500.142i	−0.0749982	−	0.0272971i
$696$		0			0
$697$	600.819	+	504.147i	0.0326509	+	0.0273973i
$698$	3641.20	−	1325.29i	0.197452	−	0.0718666i
$699$		0			0
$700$	1064.10	+	6034.81i	0.0574560	+	0.325849i
$701$	22150.8			1.19347			0.596736	−	0.802438i	$-0.296464\pi$
$701$	22150.8			1.19347			0.596736	+	0.802438i	$0.296464\pi$
$702$		0			0
$703$	13193.6			0.707835
$704$	365.458	+	2072.62i	0.0195649	+	0.110958i
$705$		0			0
$706$	−17960.2	+	6536.96i	−0.957422	+	0.348473i
$707$	4917.25	+	4126.07i	0.261573	+	0.219486i
$708$		0			0
$709$	2755.64	+	1002.97i	0.145966	+	0.0531275i	0.413970	−	0.910290i	$-0.364142\pi$
$709$	2755.64	+	1002.97i	0.145966	+	0.0531275i	−0.268004	+	0.963418i	$0.586364\pi$
$710$	−2979.07	−	5159.90i	−0.157468	−	0.272743i
$711$		0			0
$712$	−5200.45	+	9007.44i	−0.273729	+	0.474112i
$713$	530.294	−	444.969i	0.0278537	−	0.0233720i
$714$		0			0
$715$	3272.99	−	18562.0i	0.171193	−	0.970883i
$716$	−652.290	+	3699.32i	−0.0340464	+	0.193087i
$717$		0			0
$718$	−13958.6	+	11712.7i	−0.725531	+	0.608793i
$719$	2440.27	−	4226.67i	0.126574	−	0.219233i	−0.795773	−	0.605595i	$-0.792935\pi$
$719$	2440.27	−	4226.67i	0.126574	−	0.219233i	0.922347	+	0.386362i	$0.126269\pi$
$720$		0			0
$721$	25.0771	+	43.4349i	0.00129531	+	0.00224355i
$722$	−10737.1	−	3907.99i	−0.553454	−	0.201441i
$723$		0			0
$724$	−10804.9	−	9066.37i	−0.554641	−	0.465399i
$725$	9225.83	−	3357.93i	0.472605	−	0.172014i
$726$		0			0
$727$	2875.21	+	16306.1i	0.146679	+	0.831859i	0.966004	+	0.258529i	$0.0832377\pi$
$727$	2875.21	+	16306.1i	0.146679	+	0.831859i	−0.819324	+	0.573330i	$0.805651\pi$
$728$	16963.5			0.863609
$729$		0			0
$730$	−20861.9			−1.05772
$731$	3161.57	+	17930.2i	0.159966	+	0.907211i
$732$		0			0
$733$	−13406.2	+	4879.47i	−0.675540	+	0.245876i	−0.656931	−	0.753951i	$-0.728146\pi$
$733$	−13406.2	+	4879.47i	−0.675540	+	0.245876i	−0.0186084	+	0.999827i	$0.505924\pi$
$734$	17935.4	+	15049.6i	0.901917	+	0.756798i
$735$		0			0
$736$	2156.88	+	785.039i	0.108021	+	0.0393165i
$737$	−3499.79	−	6061.81i	−0.174920	−	0.302971i
$738$		0			0
$739$	15632.5	−	27076.3i	0.778147	−	1.34779i	−0.154862	−	0.987936i	$-0.549493\pi$
$739$	15632.5	−	27076.3i	0.778147	−	1.34779i	0.933009	−	0.359853i	$-0.117173\pi$
$740$	3187.61	−	2674.72i	0.158350	−	0.132871i
$741$		0			0
$742$	591.920	−	3356.95i	0.0292858	−	0.166088i
$743$	6714.26	−	38078.5i	0.331524	−	1.88017i	−0.127649	−	0.991819i	$-0.540743\pi$
$743$	6714.26	−	38078.5i	0.331524	−	1.88017i	0.459173	−	0.888347i	$-0.348146\pi$
$744$		0			0
$745$	3630.68	−	3046.50i	0.178547	−	0.149819i
$746$	−574.900	+	995.755i	−0.0282152	+	0.0488702i
$747$		0			0
$748$	−5835.75	−	10107.8i	−0.285262	−	0.494089i
$749$	20086.0	+	7310.72i	0.979877	+	0.356646i
$750$		0			0
$751$	−463.046	−	388.542i	−0.0224990	−	0.0188789i	0.631469	−	0.775401i	$-0.282452\pi$
$751$	−463.046	−	388.542i	−0.0224990	−	0.0188789i	−0.653968	+	0.756522i	$0.726897\pi$
$752$	2828.16	−	1029.37i	0.137144	−	0.0499164i
$753$		0			0
$754$	−4719.45	−	26765.4i	−0.227947	−	1.29275i
$755$	4256.91			0.205199
$756$		0			0
$757$	−23421.5			−1.12453			−0.562265	−	0.826957i	$-0.690070\pi$
$757$	−23421.5			−1.12453			−0.562265	+	0.826957i	$0.690070\pi$
$758$	−3243.27	−	18393.5i	−0.155410	−	0.881373i
$759$		0			0
$760$	−7451.94	+	2712.28i	−0.355671	+	0.129454i
$761$	−13187.4	−	11065.6i	−0.628179	−	0.527105i	0.272184	−	0.962245i	$-0.412254\pi$
$761$	−13187.4	−	11065.6i	−0.628179	−	0.527105i	−0.900363	+	0.435141i	$0.856699\pi$
$762$		0			0
$763$	−20134.6	−	7328.39i	−0.955336	−	0.347714i
$764$	5176.33	+	8965.66i	0.245122	+	0.424563i
$765$		0			0
$766$	12195.0	−	21122.4i	0.575228	−	0.996325i
$767$	13422.5	−	11262.8i	0.631887	−	0.530216i
$768$		0			0
$769$	5872.58	−	33305.1i	0.275385	−	1.56178i	−0.462353	−	0.886696i	$-0.652995\pi$
$769$	5872.58	−	33305.1i	0.275385	−	1.56178i	0.737738	−	0.675088i	$-0.235894\pi$
$770$	3302.21	−	18727.8i	0.154550	−	0.876496i
$771$		0			0
$772$	−8201.36	+	6881.76i	−0.382349	+	0.320829i
$773$	−96.0271	+	166.324i	−0.00446812	+	0.00773901i	−0.868251	−	0.496126i	$-0.834756\pi$
$773$	−96.0271	+	166.324i	−0.00446812	+	0.00773901i	0.863783	+	0.503865i	$0.168089\pi$
$774$		0			0
$775$	−226.031	−	391.498i	−0.0104765	−	0.0181458i
$776$	−11081.7	−	4033.39i	−0.512639	−	0.186585i
$777$		0			0
$778$	14045.3	+	11785.4i	0.647233	+	0.543093i
$779$	931.323	−	338.974i	0.0428345	−	0.0155905i
$780$		0			0
$781$	−1924.19	−	10912.6i	−0.0881601	−	0.499980i
$782$	−12729.1			−0.582088
$783$		0			0
$784$	11626.9			0.529651
$785$	1432.25	+	8122.69i	0.0651199	+	0.369313i
$786$		0			0
$787$	−25038.0	+	9113.09i	−1.13406	+	0.412766i	−0.839766	−	0.542948i	$-0.817308\pi$
$787$	−25038.0	+	9113.09i	−1.13406	+	0.412766i	−0.294298	+	0.955714i	$0.595086\pi$
$788$	15280.8	+	12822.1i	0.690806	+	0.579655i
$789$		0			0
$790$	922.796	+	335.870i	0.0415590	+	0.0151262i
$791$	−14410.2	−	24959.2i	−0.647747	−	1.12193i
$792$		0			0
$793$	7437.37	−	12881.9i	0.333050	−	0.576860i
$794$	12800.3	−	10740.8i	0.572125	−	0.480070i
$795$		0			0
$796$	−2397.17	+	13595.0i	−0.106740	+	0.605355i
$797$	−4614.51	+	26170.2i	−0.205087	+	1.16311i	0.692216	+	0.721690i	$0.256634\pi$
$797$	−4614.51	+	26170.2i	−0.205087	+	1.16311i	−0.897303	+	0.441415i	$0.854477\pi$
$798$		0			0
$799$	−12785.9	+	10728.6i	−0.566123	+	0.475034i
$800$	749.454	−	1298.09i	0.0331215	−	0.0573681i
$801$		0			0
$802$	1248.64	+	2162.71i	0.0549763	+	0.0952217i
$803$	−36459.3	−	13270.1i	−1.60227	−	0.583177i
$804$		0			0
$805$	−15887.7	−	13331.3i	−0.695611	−	0.583687i
$806$	−1175.94	+	428.008i	−0.0513906	+	0.0187046i
$807$		0			0
$808$	−272.648	−	1546.26i	−0.0118709	−	0.0673234i
$809$	26773.9			1.16356			0.581780	−	0.813346i	$-0.302357\pi$
$809$	26773.9			1.16356			0.581780	+	0.813346i	$0.302357\pi$
$810$		0			0
$811$	−23654.1			−1.02418			−0.512089	−	0.858932i	$-0.671128\pi$
$811$	−23654.1			−1.02418			−0.512089	+	0.858932i	$0.671128\pi$
$812$	−4761.59	−	27004.3i	−0.205787	−	1.16708i
$813$		0			0
$814$	7272.17	−	2646.85i	0.313132	−	0.113971i
$815$	5135.70	+	4309.37i	0.220731	+	0.185215i
$816$		0			0
$817$	21619.4	+	7868.81i	0.925785	+	0.336958i
$818$	−2687.95	−	4655.66i	−0.114892	−	0.198999i
$819$		0			0
$820$	156.290	−	270.702i	0.00665594	−	0.0115284i
$821$	19653.1	−	16490.9i	0.835442	−	0.701019i	−0.121092	−	0.992641i	$-0.538640\pi$
$821$	19653.1	−	16490.9i	0.835442	−	0.701019i	0.956534	+	0.291622i	$0.0941951\pi$
$822$		0			0
$823$	1872.95	−	10622.0i	0.0793281	−	0.449892i	−0.919109	−	0.394004i	$-0.871090\pi$
$823$	1872.95	−	10622.0i	0.0793281	−	0.449892i	0.998437	−	0.0558884i	$-0.0177991\pi$
$824$	2.13030	−	12.0815i	9.00637e−5	−	0.000510777i
$825$		0			0
$826$	13542.3	−	11363.3i	0.570456	−	0.478670i
$827$	−17533.7	+	30369.3i	−0.737252	+	1.27696i	0.216476	+	0.976288i	$0.430544\pi$
$827$	−17533.7	+	30369.3i	−0.737252	+	1.27696i	−0.953728	+	0.300670i	$0.902790\pi$
$828$		0			0
$829$	2567.23	+	4446.58i	0.107556	+	0.186292i	0.914780	−	0.403954i	$-0.132364\pi$
$829$	2567.23	+	4446.58i	0.107556	+	0.186292i	−0.807224	+	0.590246i	$0.799031\pi$
$830$	19232.3	+	6999.99i	0.804293	+	0.292739i
$831$		0			0
$832$	−3178.56	−	2667.13i	−0.132448	−	0.111137i
$833$	−60591.1	+	22053.4i	−2.52024	+	0.917292i
$834$		0			0
$835$	−868.867	−	4927.59i	−0.0360100	−	0.204223i
$836$	−14748.6			−0.610157
$837$		0			0
$838$	8125.13			0.334938
$839$	−3857.12	−	21874.8i	−0.158716	−	0.900121i	−0.955310	−	0.295607i	$-0.904478\pi$
$839$	−3857.12	−	21874.8i	−0.158716	−	0.900121i	0.796594	−	0.604514i	$-0.206633\pi$
$840$		0			0
$841$	−18365.2	+	6684.37i	−0.753010	+	0.274073i
$842$	−10530.1	−	8835.82i	−0.430988	−	0.361642i
$843$		0			0
$844$	11122.7	+	4048.34i	0.453626	+	0.165106i
$845$	8868.77	+	15361.2i	0.361059	+	0.625373i
$846$		0			0
$847$	−4082.18	+	7070.54i	−0.165602	+	0.286832i
$848$	−638.719	+	535.949i	−0.0258652	+	0.0217035i
$849$		0			0
$850$	−1443.46	+	8186.27i	−0.0582474	+	0.330337i
$851$	1465.62	−	8311.93i	0.0590373	−	0.334817i
$852$		0			0
$853$	17176.2	−	14412.6i	0.689452	−	0.578519i	−0.229299	−	0.973356i	$-0.573643\pi$
$853$	17176.2	−	14412.6i	0.689452	−	0.578519i	0.918751	+	0.394837i	$0.129199\pi$
$854$	7503.77	−	12996.9i	0.300672	−	0.520779i
$855$		0			0
$856$	−2614.21	−	4527.95i	−0.104383	−	0.180797i
$857$	317.702	+	115.634i	0.0126634	+	0.00460909i	0.348344	−	0.937367i	$-0.386744\pi$
$857$	317.702	+	115.634i	0.0126634	+	0.00460909i	−0.335681	+	0.941976i	$0.608966\pi$
$858$		0			0
$859$	12612.5	+	10583.1i	0.500970	+	0.420363i	0.857938	−	0.513753i	$-0.171745\pi$
$859$	12612.5	+	10583.1i	0.500970	+	0.420363i	−0.356969	+	0.934116i	$0.616190\pi$
$860$	6818.50	−	2481.73i	0.270359	−	0.0984028i
$861$		0			0
$862$	781.711	+	4433.30i	0.0308877	+	0.175173i
$863$	19547.2			0.771025			0.385512	−	0.922703i	$-0.374025\pi$
$863$	19547.2			0.771025			0.385512	+	0.922703i	$0.374025\pi$
$864$		0			0
$865$	−13627.9			−0.535679
$866$	−3183.71	−	18055.7i	−0.124927	−	0.708497i
$867$		0			0
$868$	−1186.44	+	431.829i	−0.0463945	+	0.0168862i
$869$	1399.08	+	1173.96i	0.0546150	+	0.0458274i
$870$		0			0
$871$	12967.8	+	4719.90i	0.504475	+	0.183614i
$872$	2620.53	+	4538.90i	0.101769	+	0.176269i
$873$		0			0
$874$	−8042.54	+	13930.1i	−0.311262	+	0.539122i
$875$	−38062.5	+	31938.2i	−1.47057	+	1.23395i
$876$		0			0
$877$	5968.92	−	33851.4i	0.229824	−	1.30340i	−0.623420	−	0.781887i	$-0.714257\pi$
$877$	5968.92	−	33851.4i	0.229824	−	1.30340i	0.853244	−	0.521512i	$-0.174632\pi$
$878$	−4562.64	+	25876.0i	−0.175378	+	0.994616i
$879$		0			0
$880$	−3563.29	+	2989.96i	−0.136498	+	0.114536i
$881$	14913.7	−	25831.2i	0.570322	−	0.987827i	−0.426210	−	0.904624i	$-0.640152\pi$
$881$	14913.7	−	25831.2i	0.570322	−	0.987827i	0.996533	−	0.0832031i	$-0.0265150\pi$
$882$		0			0
$883$	1155.83	+	2001.95i	0.0440506	+	0.0762979i	0.887210	−	0.461366i	$-0.152640\pi$
$883$	1155.83	+	2001.95i	0.0440506	+	0.0762979i	−0.843159	+	0.537664i	$0.819307\pi$
$884$	21623.3	+	7870.24i	0.822704	+	0.299440i
$885$		0			0
$886$	−10113.4	−	8486.16i	−0.383484	−	0.321781i
$887$	−3043.75	+	1107.84i	−0.115219	+	0.0419363i	−0.398986	−	0.916957i	$-0.630638\pi$
$887$	−3043.75	+	1107.84i	−0.115219	+	0.0419363i	0.283767	+	0.958893i	$0.408416\pi$
$888$		0			0
$889$	−7011.12	−	39762.0i	−0.264506	−	1.50009i
$890$	−22988.0			−0.865796
$891$		0			0
$892$	25505.9			0.957399
$893$	3662.45	+	20770.8i	0.137244	+	0.778352i
$894$		0			0
$895$	−7801.65	+	2839.57i	−0.291375	+	0.106052i
$896$	−3206.94	−	2690.94i	−0.119572	−	0.100333i
$897$		0			0
$898$	−29719.8	−	10817.1i	−1.10441	−	0.401974i
$899$	1011.43	+	1751.86i	0.0375231	+	0.0649918i
$900$		0			0
$901$	2311.99	−	4004.48i	0.0854866	−	0.148067i
$902$	445.330	−	373.676i	0.0164389	−	0.0137939i
$903$		0			0
$904$	−1224.15	+	6942.47i	−0.0450381	+	0.255424i
$905$	5413.35	−	30700.6i	0.198835	−	1.12765i
$906$		0			0
$907$	−18974.2	+	15921.2i	−0.694628	+	0.582862i	−0.920240	−	0.391355i	$-0.872006\pi$
$907$	−18974.2	+	15921.2i	−0.694628	+	0.582862i	0.225612	+	0.974217i	$0.427562\pi$
$908$	−3916.73	+	6783.98i	−0.143151	+	0.247945i
$909$		0			0
$910$	18746.2	+	32469.4i	0.682892	+	1.18280i
$911$	38660.3	+	14071.2i	1.40601	+	0.511745i	0.929955	−	0.367672i	$-0.119845\pi$
$911$	38660.3	+	14071.2i	1.40601	+	0.511745i	0.476052	+	0.879417i	$0.342067\pi$
$912$		0			0
$913$	29158.6	+	24467.0i	1.05697	+	0.886900i
$914$	23546.0	−	8570.04i	0.852114	−	0.310144i
$915$		0			0
$916$	−31.1550	−	176.689i	−0.00112379	−	0.00637332i
$917$	−94650.5			−3.40854
$918$		0			0
$919$	−12135.5			−0.435598			−0.217799	−	0.975994i	$-0.569888\pi$
$919$	−12135.5			−0.435598			−0.217799	+	0.975994i	$0.569888\pi$
$920$	880.926	+	4995.98i	0.0315688	+	0.179035i
$921$		0			0
$922$	−281.867	+	102.591i	−0.0100681	+	0.00366450i
$923$	16735.6	+	14042.9i	0.596814	+	0.500787i
$924$		0			0
$925$	−5179.31	−	1885.11i	−0.184102	−	0.0670078i
$926$	−4667.69	−	8084.67i	−0.165648	−	0.286910i
$927$		0			0
$928$	−3353.62	+	5808.65i	−0.118629	+	0.205472i
$929$	2420.11	−	2030.71i	0.0854696	−	0.0717175i	−0.599052	−	0.800710i	$-0.704456\pi$
$929$	2420.11	−	2030.71i	0.0854696	−	0.0717175i	0.684521	+	0.728993i	$0.260011\pi$
$930$		0			0
$931$	−14148.8	+	80241.6i	−0.498074	+	2.82472i
$932$	−3408.38	+	19329.9i	−0.119791	+	0.679368i
$933$		0			0
$934$	10322.7	−	8661.77i	0.361637	−	0.303450i
$935$	12898.1	−	22340.2i	0.451138	−	0.781393i
$936$		0			0
$937$	5312.44	+	9201.42i	0.185219	+	0.320808i	0.943650	−	0.330945i	$-0.107367\pi$
$937$	5312.44	+	9201.42i	0.185219	+	0.320808i	−0.758432	+	0.651753i	$0.774034\pi$
$938$	13083.6	+	4762.04i	0.455431	+	0.165763i
$939$		0			0
$940$	5095.68	+	4275.78i	0.176811	+	0.148362i
$941$	47890.4	−	17430.7i	1.65907	−	0.603851i	0.668850	−	0.743397i	$-0.266787\pi$
$941$	47890.4	−	17430.7i	1.65907	−	0.603851i	0.990216	+	0.139546i	$0.0445644\pi$
$942$		0			0
$943$	−110.096	−	624.383i	−0.00380192	−	0.0215617i
$944$	−4324.16			−0.149088
$945$		0			0
$946$	13494.9			0.463804
$947$	5092.18	+	28879.2i	0.174734	+	0.990968i	0.938450	+	0.345415i	$0.112262\pi$
$947$	5092.18	+	28879.2i	0.174734	+	0.990968i	−0.763715	+	0.645553i	$0.776627\pi$
$948$		0			0
$949$	71881.6	−	26162.7i	2.45877	−	0.894920i
$950$	8046.61	+	6751.91i	0.274807	+	0.230590i
$951$		0			0
$952$	21816.4	+	7940.51i	0.742723	+	0.270329i
$953$	−10556.5	−	18284.4i	−0.358823	−	0.621500i	0.628941	−	0.777453i	$-0.283489\pi$
$953$	−10556.5	−	18284.4i	−0.358823	−	0.621500i	−0.987764	+	0.155953i	$0.950155\pi$
$954$		0			0
$955$	−11440.7	+	19815.8i	−0.387656	+	0.671440i
$956$	−14578.0	+	12232.4i	−0.493185	+	0.413831i
$957$		0			0
$958$	−216.994	+	1230.64i	−0.00731813	+	0.0415032i
$959$	−5241.94	+	29728.5i	−0.176508	+	1.00103i
$960$		0			0
$961$	−22749.9	+	19089.4i	−0.763649	+	0.640778i
$962$	−7628.83	+	13213.5i	−0.255679	+	0.442849i
$963$		0			0
$964$	−7389.57	−	12799.1i	−0.246890	−	0.427626i
$965$	−22235.5	−	8093.07i	−0.741748	−	0.269974i
$966$		0			0
$967$	−12957.9	−	10872.9i	−0.430917	−	0.361582i	0.401381	−	0.915911i	$-0.368530\pi$
$967$	−12957.9	−	10872.9i	−0.430917	−	0.361582i	−0.832298	+	0.554329i	$0.812975\pi$
$968$	1876.59	−	683.024i	0.0623099	−	0.0226790i
$969$		0			0
$970$	−4526.04	−	25668.5i	−0.149817	−	0.849655i
$971$	−8924.35			−0.294950			−0.147475	−	0.989066i	$-0.547115\pi$
$971$	−8924.35			−0.294950			−0.147475	+	0.989066i	$0.547115\pi$
$972$		0			0
$973$	5409.78			0.178242
$974$	953.201	+	5405.87i	0.0313578	+	0.177839i
$975$		0			0
$976$	−3449.51	+	1255.52i	−0.113131	+	0.0411765i
$977$	35119.8	+	29469.0i	1.15003	+	0.964992i	0.999720	−	0.0236466i	$-0.00752764\pi$
$977$	35119.8	+	29469.0i	1.15003	+	0.964992i	0.150312	+	0.988639i	$0.451972\pi$
$978$		0			0
$979$	−40174.8	−	14622.4i	−1.31154	−	0.477360i
$980$	12848.8	+	22254.8i	0.418817	+	0.725413i
$981$		0			0
$982$	6108.09	−	10579.5i	0.198490	−	0.343794i
$983$	−2424.81	+	2034.66i	−0.0786769	+	0.0660177i	−0.681278	−	0.732025i	$-0.738575\pi$
$983$	−2424.81	+	2034.66i	−0.0786769	+	0.0660177i	0.602601	+	0.798043i	$0.294131\pi$
$984$		0			0
$985$	−7655.81	+	43418.3i	−0.247649	+	1.40449i
$986$	6459.13	−	36631.5i	0.208621	−	1.18315i
$987$		0			0
$988$	22274.9	−	18690.8i	0.717265	−	0.601857i
$989$	7358.90	−	12746.0i	0.236602	−	0.409807i
$990$		0			0
$991$	−21465.1	−	37178.6i	−0.688053	−	1.19174i	−0.972467	−	0.233041i	$-0.925132\pi$
$991$	−21465.1	−	37178.6i	−0.688053	−	1.19174i	0.284414	−	0.958702i	$-0.408201\pi$
$992$	290.208	+	105.627i	0.00928841	+	0.00338071i
$993$		0			0
$994$	16885.0	+	14168.2i	0.538793	+	0.452101i
$995$	−28671.1	+	10435.4i	−0.913501	+	0.332487i
$996$		0			0
$997$	4563.32	+	25879.9i	0.144957	+	0.822090i	0.967402	+	0.253246i	$0.0814982\pi$
$997$	4563.32	+	25879.9i	0.144957	+	0.822090i	−0.822445	+	0.568844i	$0.807391\pi$
$998$	2163.54			0.0686229
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.91.2		30
3.2	odd	2		54.4.e.b.13.1	✓	30
27.2	odd	18		54.4.e.b.25.1	yes	30
27.5	odd	18		1458.4.a.i.1.11		15
27.22	even	9		1458.4.a.j.1.5		15
27.25	even	9	inner	162.4.e.b.73.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.13.1	✓	30	3.2	odd	2
54.4.e.b.25.1	yes	30	27.2	odd	18
162.4.e.b.73.2		30	27.25	even	9	inner
162.4.e.b.91.2		30	1.1	even	1	trivial
1458.4.a.i.1.11		15	27.5	odd	18
1458.4.a.j.1.5		15	27.22	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.347296 + 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(-6.77242 - 5.68273i) q^{5} +(30.7336 + 11.1861i) q^{7} +(-4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(0.347296 + 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(-6.77242 - 5.68273i) q^{5} +(30.7336 + 11.1861i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(8.84076 - 15.3127i) q^{10} +(25.1908 - 21.1376i) q^{11} +(-11.2582 + 63.8482i) q^{13} +(-11.3587 + 64.4182i) q^{14} +(12.2567 - 10.2846i) q^{16} +(-44.3659 + 76.8440i) q^{17} +(56.0627 + 97.1034i) q^{19} +(33.2304 + 12.0949i) q^{20} +(50.3815 + 42.2751i) q^{22} +(67.4024 - 24.5325i) q^{23} +(-8.13384 - 46.1293i) q^{25} -129.666 q^{26} -130.824 q^{28} +(36.3969 + 206.417i) q^{29} +(9.06899 - 3.30084i) q^{31} +(24.5134 + 20.5692i) q^{32} +(-166.761 - 60.6961i) q^{34} +(-144.573 - 250.408i) q^{35} +(58.8343 - 101.904i) q^{37} +(-171.786 + 144.146i) q^{38} +(-12.2815 + 69.6516i) q^{40} +(1.53490 - 8.70486i) q^{41} +(157.184 - 131.893i) q^{43} +(-65.7684 + 113.914i) q^{44} +(71.7281 + 124.237i) q^{46} +(176.760 + 64.3354i) q^{47} +(556.670 + 467.102i) q^{49} +(88.0321 - 32.0411i) q^{50} +(-45.0326 - 255.393i) q^{52} -52.1118 q^{53} -290.722 q^{55} +(-45.4347 - 257.673i) q^{56} +(-393.922 + 143.376i) q^{58} +(-207.031 - 173.720i) q^{59} +(-215.595 - 78.4700i) q^{61} +(9.65102 + 16.7161i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(439.077 - 368.429i) q^{65} +(36.9619 - 209.621i) q^{67} +(61.6325 - 349.535i) q^{68} +(442.997 - 371.719i) q^{70} +(168.485 - 291.824i) q^{71} +(-589.936 - 1021.80i) q^{73} +(221.145 + 80.4901i) q^{74} +(-343.572 - 288.291i) q^{76} +(1010.65 - 367.846i) q^{77} +(9.64429 + 54.6955i) q^{79} -141.452 q^{80} +17.6783 q^{82} +(201.000 + 1139.93i) q^{83} +(737.148 - 268.300i) q^{85} +(314.367 + 263.786i) q^{86} +(-247.208 - 89.9765i) q^{88} +(-650.056 - 1125.93i) q^{89} +(-1060.22 + 1836.35i) q^{91} +(-219.788 + 184.424i) q^{92} +(-65.3278 + 370.493i) q^{94} +(172.133 - 976.214i) q^{95} +(1129.23 - 947.537i) q^{97} +(-726.681 + 1258.65i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Introduction

L-functions

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