LMFDB - Embedded newform 225.3.r.b.172.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(28,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("225.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.r (of order $20$, degree $8$, 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:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			172.1
Character	$\chi$	$=$	225.172
Dual form			225.3.r.b.208.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.93190 + 1.49388i) q^{2} +(4.01322 - 5.52372i) q^{4} +(0.890939 + 4.91998i) q^{5} +(4.34391 + 4.34391i) q^{7} +(-1.45557 + 9.19012i) q^{8} +O(q^{10})$	\(q+(-2.93190 + 1.49388i) q^{2} +(4.01322 - 5.52372i) q^{4} +(0.890939 + 4.91998i) q^{5} +(4.34391 + 4.34391i) q^{7} +(-1.45557 + 9.19012i) q^{8} +(-9.96199 - 13.0939i) q^{10} +(4.51369 - 13.8917i) q^{11} +(6.86423 + 3.49750i) q^{13} +(-19.2252 - 6.24664i) q^{14} +(-1.02182 - 3.14483i) q^{16} +(25.6357 + 4.06030i) q^{17} +(-1.24222 - 1.70977i) q^{19} +(30.7522 + 14.8237i) q^{20} +(7.51883 + 47.4720i) q^{22} +(2.15443 + 4.22830i) q^{23} +(-23.4125 + 8.76681i) q^{25} -25.3501 q^{26} +(41.4277 - 6.56150i) q^{28} +(-32.6254 + 44.9050i) q^{29} +(27.1558 - 19.7298i) q^{31} +(-18.6237 - 18.6237i) q^{32} +(-81.2269 + 26.3922i) q^{34} +(-17.5018 + 25.2421i) q^{35} +(-18.7363 + 36.7721i) q^{37} +(6.19627 + 3.15716i) q^{38} +(-46.5120 + 1.02645i) q^{40} +(1.20677 + 3.71404i) q^{41} +(-32.8976 + 32.8976i) q^{43} +(-58.6196 - 80.6829i) q^{44} +(-12.6331 - 9.17851i) q^{46} +(12.8776 + 81.3060i) q^{47} -11.2608i q^{49} +(55.5464 - 60.6787i) q^{50} +(46.8669 - 23.8799i) q^{52} +(81.1884 - 12.8590i) q^{53} +(72.3684 + 9.83061i) q^{55} +(-46.2440 + 33.5982i) q^{56} +(28.5718 - 180.395i) q^{58} +(10.7101 - 3.47991i) q^{59} +(-9.84864 + 30.3110i) q^{61} +(-50.1440 + 98.4132i) q^{62} +(95.0038 + 30.8686i) q^{64} +(-11.0920 + 36.8880i) q^{65} +(-0.351533 - 0.0556774i) q^{67} +(125.310 - 125.310i) q^{68} +(13.6049 - 100.153i) q^{70} +(-88.5525 - 64.3371i) q^{71} +(-20.1163 - 39.4805i) q^{73} -135.802i q^{74} -14.4296 q^{76} +(79.9515 - 40.7373i) q^{77} +(33.1447 - 45.6197i) q^{79} +(14.5621 - 7.82918i) q^{80} +(-9.08644 - 9.08644i) q^{82} +(2.71085 - 17.1156i) q^{83} +(2.86327 + 129.745i) q^{85} +(47.3074 - 145.597i) q^{86} +(121.097 + 61.7018i) q^{88} +(85.2857 + 27.7110i) q^{89} +(14.6248 + 45.0105i) q^{91} +(32.0022 + 5.06865i) q^{92} +(-159.217 - 219.143i) q^{94} +(7.30531 - 7.63503i) q^{95} +(1.37908 + 8.70714i) q^{97} +(16.8223 + 33.0156i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8}+O(q^{10}) $ 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8	$ 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 4 q^{10} + 32 q^{13} + 80 q^{16} + 100 q^{17} - 100 q^{19} + 244 q^{20} - 100 q^{22} + 96 q^{23} - 16 q^{25} + 40 q^{26} + 196 q^{28} - 200 q^{29} - 636 q^{32} + 100 q^{34} - 260 q^{35} - 184 q^{37} + 564 q^{38} - 948 q^{40} - 160 q^{41} - 472 q^{43} + 700 q^{44} + 288 q^{47} - 16 q^{50} + 620 q^{52} - 304 q^{53} + 604 q^{55} + 1272 q^{58} - 800 q^{59} - 240 q^{61} - 1212 q^{62} + 100 q^{64} - 272 q^{65} - 80 q^{67} - 104 q^{68} - 260 q^{70} - 116 q^{73} + 88 q^{77} + 200 q^{79} + 164 q^{80} - 168 q^{82} + 1264 q^{83} - 212 q^{85} - 212 q^{88} + 1500 q^{89} + 1504 q^{92} - 200 q^{94} + 784 q^{95} - 260 q^{97} + 92 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 4 * q^10 + 32 * q^13 + 80 * q^16 + 100 * q^17 - 100 * q^19 + 244 * q^20 - 100 * q^22 + 96 * q^23 - 16 * q^25 + 40 * q^26 + 196 * q^28 - 200 * q^29 - 636 * q^32 + 100 * q^34 - 260 * q^35 - 184 * q^37 + 564 * q^38 - 948 * q^40 - 160 * q^41 - 472 * q^43 + 700 * q^44 + 288 * q^47 - 16 * q^50 + 620 * q^52 - 304 * q^53 + 604 * q^55 + 1272 * q^58 - 800 * q^59 - 240 * q^61 - 1212 * q^62 + 100 * q^64 - 272 * q^65 - 80 * q^67 - 104 * q^68 - 260 * q^70 - 116 * q^73 + 88 * q^77 + 200 * q^79 + 164 * q^80 - 168 * q^82 + 1264 * q^83 - 212 * q^85 - 212 * q^88 + 1500 * q^89 + 1504 * q^92 - 200 * q^94 + 784 * q^95 - 260 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−2.93190	+	1.49388i	−1.46595	+	0.746939i	−0.991099	−	0.133128i	$-0.957498\pi$
$2$	−2.93190	+	1.49388i	−1.46595	+	0.746939i	−0.474850	+	0.880066i	$0.657498\pi$
$3$		0			0
$3$		0			0
$4$	4.01322	−	5.52372i	1.00331	−	1.38093i
$5$	0.890939	+	4.91998i	0.178188	+	0.983996i
$5$	0.890939	+	4.91998i	0.178188	+	0.983996i
$6$		0			0
$7$	4.34391	+	4.34391i	0.620559	+	0.620559i	0.945674	−	0.325115i	$-0.105403\pi$
$7$	4.34391	+	4.34391i	0.620559	+	0.620559i	−0.325115	+	0.945674i	$0.605403\pi$
$8$	−1.45557	+	9.19012i	−0.181946	+	1.14876i
$9$		0			0
$10$	−9.96199	−	13.0939i	−0.996199	−	1.30939i
$11$	4.51369	−	13.8917i	0.410336	−	1.26288i	−0.506021	−	0.862521i	$-0.668884\pi$
$11$	4.51369	−	13.8917i	0.410336	−	1.26288i	0.916357	−	0.400362i	$-0.131116\pi$
$12$		0			0
$13$	6.86423	+	3.49750i	0.528018	+	0.269039i	0.697612	−	0.716475i	$-0.254246\pi$
$13$	6.86423	+	3.49750i	0.528018	+	0.269039i	−0.169595	+	0.985514i	$0.554246\pi$
$14$	−19.2252	−	6.24664i	−1.37323	−	0.446189i
$15$		0			0
$16$	−1.02182	−	3.14483i	−0.0638636	−	0.196552i
$17$	25.6357	+	4.06030i	1.50798	+	0.238841i	0.855039	−	0.518564i	$-0.173533\pi$
$17$	25.6357	+	4.06030i	1.50798	+	0.238841i	0.652945	+	0.757405i	$0.273533\pi$
$18$		0			0
$19$	−1.24222	−	1.70977i	−0.0653802	−	0.0899881i	0.775075	−	0.631870i	$-0.217712\pi$
$19$	−1.24222	−	1.70977i	−0.0653802	−	0.0899881i	−0.840455	+	0.541881i	$0.817712\pi$
$20$	30.7522	+	14.8237i	1.53761	+	0.741184i
$21$		0			0
$22$	7.51883	+	47.4720i	0.341765	+	2.15782i
$23$	2.15443	+	4.22830i	0.0936708	+	0.183839i	0.933088	−	0.359649i	$-0.117103\pi$
$23$	2.15443	+	4.22830i	0.0936708	+	0.183839i	−0.839417	+	0.543488i	$0.817103\pi$
$24$		0			0
$25$	−23.4125	+	8.76681i	−0.936498	+	0.350672i
$26$	−25.3501			−0.975003
$27$		0			0
$28$	41.4277	−	6.56150i	1.47956	−	0.234339i
$29$	−32.6254	+	44.9050i	−1.12501	+	1.54845i	−0.327806	+	0.944745i	$0.606309\pi$
$29$	−32.6254	+	44.9050i	−1.12501	+	1.54845i	−0.797208	+	0.603704i	$0.793691\pi$
$30$		0			0
$31$	27.1558	−	19.7298i	0.875993	−	0.636446i	−0.0561957	−	0.998420i	$-0.517897\pi$
$31$	27.1558	−	19.7298i	0.875993	−	0.636446i	0.932188	+	0.361974i	$0.117897\pi$
$32$	−18.6237	−	18.6237i	−0.581992	−	0.581992i
$33$		0			0
$34$	−81.2269	+	26.3922i	−2.38903	+	0.776242i
$35$	−17.5018	+	25.2421i	−0.500052	+	0.721204i
$36$		0			0
$37$	−18.7363	+	36.7721i	−0.506388	+	0.993842i	0.486375	+	0.873750i	$0.338319\pi$
$37$	−18.7363	+	36.7721i	−0.506388	+	0.993842i	−0.992763	+	0.120092i	$0.961681\pi$
$38$	6.19627	+	3.15716i	0.163060	+	0.0830831i
$39$		0			0
$40$	−46.5120	+	1.02645i	−1.16280	+	0.0256613i
$41$	1.20677	+	3.71404i	0.0294333	+	0.0905864i	0.964694	−	0.263373i	$-0.0848350\pi$
$41$	1.20677	+	3.71404i	0.0294333	+	0.0905864i	−0.935261	+	0.353960i	$0.884835\pi$
$42$		0			0
$43$	−32.8976	+	32.8976i	−0.765060	+	0.765060i	−0.977232	−	0.212172i	$-0.931946\pi$
$43$	−32.8976	+	32.8976i	−0.765060	+	0.765060i	0.212172	+	0.977232i	$0.431946\pi$
$44$	−58.6196	−	80.6829i	−1.33226	−	1.83370i
$45$		0			0
$46$	−12.6331	−	9.17851i	−0.274633	−	0.199533i
$47$	12.8776	+	81.3060i	0.273991	+	1.72991i	0.613837	+	0.789433i	$0.289625\pi$
$47$	12.8776	+	81.3060i	0.273991	+	1.72991i	−0.339846	+	0.940481i	$0.610375\pi$
$48$		0			0
$49$		−	11.2608i		−	0.229813i
$50$	55.5464	−	60.6787i	1.11093	−	1.21357i
$51$		0			0
$52$	46.8669	−	23.8799i	0.901287	−	0.459229i
$53$	81.1884	−	12.8590i	1.53186	−	0.242622i	0.667159	−	0.744916i	$-0.267510\pi$
$53$	81.1884	−	12.8590i	1.53186	−	0.242622i	0.864697	+	0.502293i	$0.167510\pi$
$54$		0			0
$55$	72.3684	+	9.83061i	1.31579	+	0.178738i
$56$	−46.2440	+	33.5982i	−0.825785	+	0.599968i
$57$		0			0
$58$	28.5718	−	180.395i	0.492618	−	3.11026i
$59$	10.7101	−	3.47991i	0.181526	−	0.0589815i	−0.216843	−	0.976206i	$-0.569576\pi$
$59$	10.7101	−	3.47991i	0.181526	−	0.0589815i	0.398370	+	0.917225i	$0.369576\pi$
$60$		0			0
$61$	−9.84864	+	30.3110i	−0.161453	+	0.496902i	−0.998757	−	0.0498356i	$-0.984130\pi$
$61$	−9.84864	+	30.3110i	−0.161453	+	0.496902i	0.837304	+	0.546737i	$0.184130\pi$
$62$	−50.1440	+	98.4132i	−0.808775	+	1.58731i
$63$		0			0
$64$	95.0038	+	30.8686i	1.48443	+	0.482322i
$65$	−11.0920	+	36.8880i	−0.170647	+	0.567507i
$66$		0			0
$67$	−0.351533	−	0.0556774i	−0.00524677	−	0.000831006i	0.153811	−	0.988100i	$-0.450845\pi$
$67$	−0.351533	−	0.0556774i	−0.00524677	−	0.000831006i	−0.159057	+	0.987269i	$0.550845\pi$
$68$	125.310	−	125.310i	1.84279	−	1.84279i
$69$		0			0
$70$	13.6049	−	100.153i	0.194356	−	1.43076i
$71$	−88.5525	−	64.3371i	−1.24722	−	0.906157i	−0.249161	−	0.968462i	$-0.580155\pi$
$71$	−88.5525	−	64.3371i	−1.24722	−	0.906157i	−0.998057	+	0.0623051i	$0.980155\pi$
$72$		0			0
$73$	−20.1163	−	39.4805i	−0.275566	−	0.540828i	0.711198	−	0.702992i	$-0.248153\pi$
$73$	−20.1163	−	39.4805i	−0.275566	−	0.540828i	−0.986764	+	0.162163i	$0.948153\pi$
$74$		−	135.802i		−	1.83516i
$75$		0			0
$76$	−14.4296			−0.189864
$77$	79.9515	−	40.7373i	1.03833	−	0.529056i
$78$		0			0
$79$	33.1447	−	45.6197i	0.419553	−	0.577465i	−0.545963	−	0.837809i	$-0.683836\pi$
$79$	33.1447	−	45.6197i	0.419553	−	0.577465i	0.965516	+	0.260344i	$0.0838361\pi$
$80$	14.5621	−	7.82918i	0.182027	−	0.0978648i
$81$		0			0
$82$	−9.08644	−	9.08644i	−0.110810	−	0.110810i
$83$	2.71085	−	17.1156i	0.0326608	−	0.206212i	−0.965961	−	0.258686i	$-0.916711\pi$
$83$	2.71085	−	17.1156i	0.0326608	−	0.206212i	0.998622	+	0.0524736i	$0.0167105\pi$
$84$		0			0
$85$	2.86327	+	129.745i	0.0336855	+	1.52641i
$86$	47.3074	−	145.597i	0.550087	−	1.69299i
$87$		0			0
$88$	121.097	+	61.7018i	1.37610	+	0.701156i
$89$	85.2857	+	27.7110i	0.958267	+	0.311360i	0.746070	−	0.665867i	$-0.231938\pi$
$89$	85.2857	+	27.7110i	0.958267	+	0.311360i	0.212196	+	0.977227i	$0.431938\pi$
$90$		0			0
$91$	14.6248	+	45.0105i	0.160712	+	0.494621i
$92$	32.0022	+	5.06865i	0.347850	+	0.0550940i
$93$		0			0
$94$	−159.217	−	219.143i	−1.69380	−	2.33131i
$95$	7.30531	−	7.63503i	0.0768981	−	0.0803687i
$96$		0			0
$97$	1.37908	+	8.70714i	0.0142173	+	0.0897643i	0.993777	−	0.111391i	$-0.0355305\pi$
$97$	1.37908	+	8.70714i	0.0142173	+	0.0897643i	−0.979559	+	0.201155i	$0.935531\pi$
$98$	16.8223	+	33.0156i	0.171656	+	0.336894i
$99$		0			0
$100$	−45.5339	+	164.507i	−0.455339	+	1.64507i
$101$	−4.54639			−0.0450138			−0.0225069	−	0.999747i	$-0.507165\pi$
$101$	−4.54639			−0.0450138			−0.0225069	+	0.999747i	$0.507165\pi$
$102$		0			0
$103$	98.1209	−	15.5408i	0.952630	−	0.150882i	0.339273	−	0.940688i	$-0.389819\pi$
$103$	98.1209	−	15.5408i	0.952630	−	0.150882i	0.613357	+	0.789806i	$0.289819\pi$
$104$	−42.1338	+	57.9922i	−0.405133	+	0.557618i
$105$		0			0
$106$	−218.826	+	158.987i	−2.06440	+	1.49987i
$107$	−58.0204	−	58.0204i	−0.542247	−	0.542247i	0.381940	−	0.924187i	$-0.375256\pi$
$107$	−58.0204	−	58.0204i	−0.542247	−	0.542247i	−0.924187	+	0.381940i	$0.875256\pi$
$108$		0			0
$109$	77.8317	−	25.2890i	0.714052	−	0.232010i	0.0706096	−	0.997504i	$-0.477506\pi$
$109$	77.8317	−	25.2890i	0.714052	−	0.232010i	0.643442	+	0.765494i	$0.277506\pi$
$110$	−226.863	+	79.2872i	−2.06239	+	0.720793i
$111$		0			0
$112$	9.22219	−	18.0996i	0.0823410	−	0.161603i
$113$	−168.661	−	85.9369i	−1.49257	−	0.760504i	−0.498262	−	0.867027i	$-0.666028\pi$
$113$	−168.661	−	85.9369i	−1.49257	−	0.760504i	−0.994310	+	0.106523i	$0.966028\pi$
$114$		0			0
$115$	−18.8837	+	14.3669i	−0.164206	+	0.124930i
$116$	117.110	+	360.428i	1.00957	+	3.10713i
$117$		0			0
$118$	−26.2022	+	26.2022i	−0.222053	+	0.222053i
$119$	93.7218	+	128.997i	0.787578	+	1.08401i
$120$		0			0
$121$	−74.7153	−	54.2839i	−0.617482	−	0.448627i
$122$	−16.4057	−	103.581i	−0.134473	−	0.849028i
$123$		0			0
$124$		−	229.181i		−	1.84823i
$125$	−63.9916	−	107.378i	−0.511933	−	0.859025i
$126$		0			0
$127$	−99.6529	+	50.7757i	−0.784668	+	0.399808i	−0.799944	−	0.600075i	$-0.795137\pi$
$127$	−99.6529	+	50.7757i	−0.784668	+	0.399808i	0.0152756	+	0.999883i	$0.495137\pi$
$128$	−220.601	+	34.9397i	−1.72344	+	0.272967i
$129$		0			0
$130$	−22.5854	−	124.722i	−0.173734	−	0.959399i
$131$	84.3598	−	61.2910i	0.643968	−	0.467870i	−0.217243	−	0.976118i	$-0.569706\pi$
$131$	84.3598	−	61.2910i	0.643968	−	0.467870i	0.861211	+	0.508247i	$0.169706\pi$
$132$		0			0
$133$	2.03100	−	12.8232i	0.0152707	−	0.0964152i
$134$	1.11384	−	0.361907i	0.00831221	−	0.00270080i
$135$		0			0
$136$	−74.6293	+	229.685i	−0.548745	+	1.68886i
$137$	−69.3960	+	136.197i	−0.506540	+	0.994141i	0.486198	+	0.873849i	$0.338383\pi$
$137$	−69.3960	+	136.197i	−0.506540	+	0.994141i	−0.992738	+	0.120293i	$0.961617\pi$
$138$		0			0
$139$	149.736	+	48.6523i	1.07724	+	0.350016i	0.793303	−	0.608827i	$-0.208359\pi$
$139$	149.736	+	48.6523i	1.07724	+	0.350016i	0.283937	+	0.958843i	$0.408359\pi$
$140$	69.1920	+	197.977i	0.494228	+	1.41412i
$141$		0			0
$142$	355.739	+	56.3435i	2.50520	+	0.396785i
$143$	79.5693	−	79.5693i	0.556429	−	0.556429i
$144$		0			0
$145$	−249.999	−	120.509i	−1.72413	−	0.831095i
$146$	117.958	+	85.7015i	0.807931	+	0.586996i
$147$		0			0
$148$	127.926	+	251.069i	0.864365	+	1.69641i
$149$			80.4685i			0.540057i	0.962852	+	0.270028i	$0.0870331\pi$
$149$			80.4685i			0.540057i	−0.962852	+	0.270028i	$0.912967\pi$
$150$		0			0
$151$	187.435			1.24129			0.620647	−	0.784090i	$-0.286870\pi$
$151$	187.435			1.24129			0.620647	+	0.784090i	$0.286870\pi$
$152$	17.5212	−	8.92749i	0.115271	−	0.0587335i
$153$		0			0
$154$	−173.553	+	238.875i	−1.12697	+	1.55114i
$155$	121.265	+	116.028i	0.782352	+	0.748567i
$156$		0			0
$157$	−90.0864	−	90.0864i	−0.573798	−	0.573798i	0.359389	−	0.933188i	$-0.382985\pi$
$157$	−90.0864	−	90.0864i	−0.573798	−	0.573798i	−0.933188	+	0.359389i	$0.882985\pi$
$158$	−29.0266	+	183.267i	−0.183712	+	1.15991i
$159$		0			0
$160$	75.0358	−	108.221i	0.468974	−	0.676382i
$161$	−9.00873	+	27.7260i	−0.0559549	+	0.172211i
$162$		0			0
$163$	−30.5160	−	15.5487i	−0.187215	−	0.0953908i	0.357871	−	0.933771i	$-0.383503\pi$
$163$	−30.5160	−	15.5487i	−0.187215	−	0.0953908i	−0.545086	+	0.838380i	$0.683503\pi$
$164$	25.3584	+	8.23943i	0.154624	+	0.0502404i
$165$		0			0
$166$	17.6207	+	54.2310i	0.106149	+	0.326693i
$167$	58.2426	+	9.22473i	0.348758	+	0.0552379i	0.328356	−	0.944554i	$-0.393505\pi$
$167$	58.2426	+	9.22473i	0.348758	+	0.0552379i	0.0204021	+	0.999792i	$0.493505\pi$
$168$		0			0
$169$	−64.4505	−	88.7086i	−0.381364	−	0.524903i
$170$	−202.218	−	376.121i	−1.18951	−	2.21248i
$171$		0			0
$172$	49.6919	+	313.742i	0.288907	+	1.82408i
$173$	−35.3231	−	69.3255i	−0.204180	−	0.400726i	0.766096	−	0.642726i	$-0.222197\pi$
$173$	−35.3231	−	69.3255i	−0.204180	−	0.400726i	−0.970276	+	0.242000i	$0.922197\pi$
$174$		0			0
$175$	−139.784	−	63.6194i	−0.798765	−	0.363539i
$176$	−48.2993			−0.274428
$177$		0			0
$178$	−291.446	+	46.1605i	−1.63734	+	0.259329i
$179$	89.6932	−	123.452i	0.501080	−	0.689677i	−0.481304	−	0.876554i	$-0.659837\pi$
$179$	89.6932	−	123.452i	0.501080	−	0.689677i	0.982383	+	0.186877i	$0.0598366\pi$
$180$		0			0
$181$	−26.4190	+	19.1945i	−0.145961	+	0.106047i	−0.658369	−	0.752695i	$-0.728753\pi$
$181$	−26.4190	+	19.1945i	−0.145961	+	0.106047i	0.512408	+	0.858742i	$0.328753\pi$
$182$	−110.119	−	110.119i	−0.605047	−	0.605047i
$183$		0			0
$184$	−41.9945	+	13.6449i	−0.228231	+	0.0741568i
$185$	−197.611	−	59.4207i	−1.06817	−	0.321193i
$186$		0			0
$187$	172.116	−	337.797i	0.920408	−	1.80640i
$188$	500.792	+	255.166i	2.66379	+	1.35727i
$189$		0			0
$190$	−10.0127	+	33.2984i	−0.0526982	+	0.175255i
$191$	−15.5033	−	47.7143i	−0.0811692	−	0.249813i	0.902234	−	0.431247i	$-0.141926\pi$
$191$	−15.5033	−	47.7143i	−0.0811692	−	0.249813i	−0.983403	+	0.181434i	$0.941926\pi$
$192$		0			0
$193$	49.2763	−	49.2763i	0.255318	−	0.255318i	−0.567829	−	0.823147i	$-0.692216\pi$
$193$	49.2763	−	49.2763i	0.255318	−	0.255318i	0.823147	+	0.567829i	$0.192216\pi$
$194$	−17.0507	−	23.4683i	−0.0878902	−	0.120971i
$195$		0			0
$196$	−62.2017	−	45.1922i	−0.317356	−	0.230572i
$197$	54.5847	+	344.634i	0.277080	+	1.74941i	0.597253	+	0.802053i	$0.296259\pi$
$197$	54.5847	+	344.634i	0.277080	+	1.74941i	−0.320174	+	0.947359i	$0.603741\pi$
$198$		0			0
$199$			39.9002i			0.200504i	0.994962	+	0.100252i	$0.0319648\pi$
$199$			39.9002i			0.200504i	−0.994962	+	0.100252i	$0.968035\pi$
$200$	−46.4895	−	227.924i	−0.232448	−	1.13962i
$201$		0			0
$202$	13.3296	−	6.79175i	0.0659879	−	0.0336225i
$203$	−336.786	+	53.3416i	−1.65904	+	0.262766i
$204$		0			0
$205$	−17.1979	+	9.24625i	−0.0838920	+	0.0451037i
$206$	−264.464	+	192.145i	−1.28381	+	0.932741i
$207$		0			0
$208$	3.98506	−	25.1607i	0.0191589	−	0.120965i
$209$	−29.3587	+	9.53923i	−0.140472	+	0.0456422i
$210$		0			0
$211$	59.1092	−	181.919i	0.280138	−	0.862177i	−0.707676	−	0.706538i	$-0.750256\pi$
$211$	59.1092	−	181.919i	0.280138	−	0.862177i	0.987814	−	0.155640i	$-0.0497439\pi$
$212$	254.797	−	500.068i	1.20187	−	2.35881i
$213$		0			0
$214$	256.785	+	83.4346i	1.19993	+	0.389882i
$215$	−191.165	−	132.546i	−0.889141	−	0.616492i
$216$		0			0
$217$	203.667	+	32.2577i	0.938557	+	0.148653i
$218$	−190.416	+	190.416i	−0.873467	+	0.873467i
$219$		0			0
$220$	344.732	−	360.291i	1.56696	−	1.63769i
$221$	161.769	+	117.532i	0.731985	+	0.531818i
$222$		0			0
$223$	82.3253	+	161.572i	0.369172	+	0.724540i	0.998621	−	0.0525014i	$-0.0167194\pi$
$223$	82.3253	+	161.572i	0.369172	+	0.724540i	−0.629449	+	0.777042i	$0.716719\pi$
$224$		−	161.800i		−	0.722320i
$225$		0			0
$226$	622.875			2.75608
$227$	266.514	−	135.796i	1.17407	−	0.598220i	0.245509	−	0.969394i	$-0.421045\pi$
$227$	266.514	−	135.796i	1.17407	−	0.598220i	0.928563	+	0.371174i	$0.121045\pi$
$228$		0			0
$229$	−128.483	+	176.841i	−0.561060	+	0.772232i	−0.991461	−	0.130405i	$-0.958372\pi$
$229$	−128.483	+	176.841i	−0.561060	+	0.772232i	0.430401	+	0.902638i	$0.358372\pi$
$230$	33.9027	−	70.3323i	0.147403	−	0.305792i
$231$		0			0
$232$	−365.194	−	365.194i	−1.57411	−	1.57411i
$233$	28.5917	−	180.521i	0.122711	−	0.774767i	−0.847194	−	0.531284i	$-0.821710\pi$
$233$	28.5917	−	180.521i	0.122711	−	0.774767i	0.969905	−	0.243484i	$-0.0782902\pi$
$234$		0			0
$235$	−388.551	+	135.796i	−1.65341	+	0.577856i
$236$	23.7598	−	73.1250i	0.100677	−	0.309852i
$237$		0			0
$238$	−467.488	−	238.197i	−1.96424	−	1.00083i
$239$	434.275	+	141.105i	1.81705	+	0.590396i	0.999902	+	0.0139688i	$0.00444655\pi$
$239$	434.275	+	141.105i	1.81705	+	0.590396i	0.817149	+	0.576427i	$0.195553\pi$
$240$		0			0
$241$	−123.592	−	380.378i	−0.512831	−	1.57833i	−0.787194	−	0.616706i	$-0.788467\pi$
$241$	−123.592	−	380.378i	−0.512831	−	1.57833i	0.274363	−	0.961626i	$-0.411533\pi$
$242$	300.151	+	47.5393i	1.24029	+	0.196443i
$243$		0			0
$244$	127.905	+	176.046i	0.524200	+	0.721499i
$245$	55.4031	−	10.0327i	0.226135	−	0.0409499i
$246$		0			0
$247$	−2.54698	−	16.0810i	−0.0103116	−	0.0651051i
$248$	141.792	+	278.283i	0.571743	+	1.12211i
$249$		0			0
$250$	348.027	+	219.226i	1.39211	+	0.876905i
$251$	−153.360			−0.610995			−0.305497	−	0.952193i	$-0.598823\pi$
$251$	−153.360			−0.610995			−0.305497	+	0.952193i	$0.598823\pi$
$252$		0			0
$253$	68.4628	−	10.8434i	0.270604	−	0.0428595i
$254$	216.319	−	297.738i	0.851652	−	1.17220i
$255$		0			0
$256$	271.323	−	197.128i	1.05986	−	0.770030i
$257$	−208.413	−	208.413i	−0.810947	−	0.810947i	0.173829	−	0.984776i	$-0.444386\pi$
$257$	−208.413	−	208.413i	−0.810947	−	0.810947i	−0.984776	+	0.173829i	$0.944386\pi$
$258$		0			0
$259$	−241.124	+	78.3459i	−0.930981	+	0.302494i
$260$	159.244	+	209.309i	0.612478	+	0.805034i
$261$		0			0
$262$	−155.773	+	305.722i	−0.594554	+	1.16688i
$263$	9.36797	+	4.77322i	0.0356197	+	0.0181491i	0.471710	−	0.881754i	$-0.343637\pi$
$263$	9.36797	+	4.77322i	0.0356197	+	0.0181491i	−0.436090	+	0.899903i	$0.643637\pi$
$264$		0			0
$265$	135.600	+	387.989i	0.511698	+	1.46411i
$266$	13.2016	+	40.6305i	0.0496302	+	0.152746i
$267$		0			0
$268$	−1.71833	+	1.71833i	−0.00641167	+	0.00641167i
$269$	−270.816	−	372.747i	−1.00675	−	1.38568i	−0.921089	−	0.389351i	$-0.872699\pi$
$269$	−270.816	−	372.747i	−1.00675	−	1.38568i	−0.0856627	−	0.996324i	$-0.527301\pi$
$270$		0			0
$271$	120.422	+	87.4918i	0.444362	+	0.322848i	0.787366	−	0.616486i	$-0.211444\pi$
$271$	120.422	+	87.4918i	0.444362	+	0.322848i	−0.343004	+	0.939334i	$0.611444\pi$
$272$	−13.4261	−	84.7689i	−0.0493606	−	0.311651i
$273$		0			0
$274$		−	502.986i		−	1.83572i
$275$	16.1095	+	364.810i	0.0585798	+	1.32658i
$276$		0			0
$277$	−229.696	+	117.036i	−0.829229	+	0.422513i	−0.816458	−	0.577405i	$-0.804065\pi$
$277$	−229.696	+	117.036i	−0.829229	+	0.422513i	−0.0127710	+	0.999918i	$0.504065\pi$
$278$	−511.692	+	81.0441i	−1.84062	+	0.291526i
$279$		0			0
$280$	−206.503	−	197.586i	−0.737511	−	0.705663i
$281$	64.5890	−	46.9267i	0.229854	−	0.166999i	−0.466897	−	0.884312i	$-0.654628\pi$
$281$	64.5890	−	46.9267i	0.229854	−	0.166999i	0.696751	+	0.717313i	$0.254628\pi$
$282$		0			0
$283$	5.52224	−	34.8661i	0.0195132	−	0.123202i	−0.976009	−	0.217731i	$-0.930135\pi$
$283$	5.52224	−	34.8661i	0.0195132	−	0.123202i	0.995522	+	0.0945291i	$0.0301345\pi$
$284$	−710.761	+	230.940i	−2.50268	+	0.813170i
$285$		0			0
$286$	−114.422	+	352.156i	−0.400078	+	1.23131i
$287$	−10.8914	+	21.3756i	−0.0379491	+	0.0744793i
$288$		0			0
$289$	365.849	+	118.871i	1.26591	+	0.411320i
$290$	912.998	−	20.1485i	3.14827	−	0.0694775i
$291$		0			0
$292$	−298.810	−	47.3269i	−1.02332	−	0.162078i
$293$	16.7371	−	16.7371i	0.0571231	−	0.0571231i	−0.677968	−	0.735091i	$-0.737139\pi$
$293$	16.7371	−	16.7371i	0.0571231	−	0.0571231i	0.735091	+	0.677968i	$0.237139\pi$
$294$		0			0
$295$	26.6631	+	49.5929i	0.0903834	+	0.168112i
$296$	−310.668	−	225.714i	−1.04955	−	0.762546i
$297$		0			0
$298$	−120.210	−	235.925i	−0.403389	−	0.791696i
$299$			36.5592i			0.122271i
$300$		0			0
$301$	−285.809			−0.949530
$302$	−549.541	+	280.005i	−1.81967	+	0.927170i
$303$		0			0
$304$	−4.10763	+	5.65367i	−0.0135119	+	0.0185976i
$305$	−157.904	−	21.4499i	−0.517718	−	0.0703275i
$306$		0			0
$307$	14.0410	+	14.0410i	0.0457363	+	0.0457363i	0.729605	−	0.683869i	$-0.239704\pi$
$307$	14.0410	+	14.0410i	0.0457363	+	0.0457363i	−0.683869	+	0.729605i	$0.739704\pi$
$308$	95.8413	−	605.118i	0.311173	−	1.96467i
$309$		0			0
$310$	−528.867	−	159.028i	−1.70602	−	0.512992i
$311$	59.5063	−	183.142i	0.191339	−	0.588880i	−0.808661	−	0.588275i	$-0.799807\pi$
$311$	59.5063	−	183.142i	0.191339	−	0.588880i	1.00000		0.000605266i	$-0.000192662\pi$
$312$		0			0
$313$	141.673	+	72.1860i	0.452629	+	0.230626i	0.665416	−	0.746473i	$-0.268254\pi$
$313$	141.673	+	72.1860i	0.452629	+	0.230626i	−0.212787	+	0.977099i	$0.568254\pi$
$314$	398.702	+	129.546i	1.26975	+	0.412567i
$315$		0			0
$316$	−118.974	−	366.164i	−0.376500	−	1.15875i
$317$	−378.338	−	59.9228i	−1.19349	−	0.189031i	−0.472093	−	0.881549i	$-0.656501\pi$
$317$	−378.338	−	59.9228i	−1.19349	−	0.189031i	−0.721401	+	0.692518i	$0.756501\pi$
$318$		0			0
$319$	476.547	+	655.911i	1.49388	+	2.05615i
$320$	−67.2304	+	494.919i	−0.210095	+	1.54662i
$321$		0			0
$322$	−15.0066	−	94.7479i	−0.0466043	−	0.294248i
$323$	−24.9031	−	48.8751i	−0.0770994	−	0.151316i
$324$		0			0
$325$	−191.370	−	21.7076i	−0.588832	−	0.0667928i
$326$	112.698			0.345699
$327$		0			0
$328$	−35.8890	+	5.68426i	−0.109418	+	0.0173301i
$329$	−297.247	+	409.125i	−0.903486	+	1.24354i
$330$		0			0
$331$	−450.680	+	327.439i	−1.36157	+	0.989240i	−0.363229	+	0.931700i	$0.618326\pi$
$331$	−450.680	+	327.439i	−1.36157	+	0.989240i	−0.998343	+	0.0575405i	$0.981674\pi$
$332$	−83.6628	−	83.6628i	−0.251996	−	0.251996i
$333$		0			0
$334$	−184.542	+	59.9614i	−0.552521	+	0.179525i
$335$	−0.0392630	−	1.77914i	−0.000117203	−	0.00531088i
$336$		0			0
$337$	86.1758	−	169.130i	0.255715	−	0.501868i	−0.727084	−	0.686548i	$-0.759125\pi$
$337$	86.1758	−	169.130i	0.255715	−	0.501868i	0.982799	+	0.184680i	$0.0591250\pi$
$338$	321.482	+	163.803i	0.951131	+	0.484625i
$339$		0			0
$340$	728.165	+	504.878i	2.14166	+	1.48494i
$341$	−151.508	−	466.295i	−0.444306	−	1.36743i
$342$		0			0
$343$	261.768	−	261.768i	0.763172	−	0.763172i
$344$	−254.448	−	350.217i	−0.739674	−	1.01807i
$345$		0			0
$346$	207.128	+	150.487i	0.598635	+	0.434934i
$347$	−23.6780	−	149.497i	−0.0682362	−	0.430827i	−0.998030	−	0.0627447i	$-0.980015\pi$
$347$	−23.6780	−	149.497i	−0.0682362	−	0.430827i	0.929793	−	0.368082i	$-0.119985\pi$
$348$		0			0
$349$		−	124.533i		−	0.356829i	−0.983955	−	0.178415i	$-0.942903\pi$
$349$		−	124.533i		−	0.356829i	0.983955	−	0.178415i	$-0.0570968\pi$
$350$	504.872	−	22.2944i	1.44249	−	0.0636982i
$351$		0			0
$352$	−342.777	+	174.654i	−0.973800	+	0.496176i
$353$	367.421	−	58.1938i	1.04085	−	0.164855i	0.387470	−	0.921882i	$-0.373349\pi$
$353$	367.421	−	58.1938i	1.04085	−	0.164855i	0.653383	+	0.757027i	$0.273349\pi$
$354$		0			0
$355$	237.643	−	492.997i	0.669416	−	1.38872i
$356$	495.338	−	359.884i	1.39140	−	1.01091i
$357$		0			0
$358$	−78.5492	+	495.940i	−0.219411	+	1.38531i
$359$	232.340	−	75.4918i	0.647186	−	0.210283i	0.0330130	−	0.999455i	$-0.489490\pi$
$359$	232.340	−	75.4918i	0.647186	−	0.210283i	0.614173	+	0.789171i	$0.289490\pi$
$360$		0			0
$361$	110.175	−	339.084i	0.305194	−	0.939290i
$362$	48.7835	−	95.7430i	0.134761	−	0.264483i
$363$		0			0
$364$	307.318	+	99.8537i	0.844280	+	0.274323i
$365$	176.321	−	134.147i	0.483071	−	0.367525i
$366$		0			0
$367$	−170.553	−	27.0130i	−0.464723	−	0.0736049i	−0.0803176	−	0.996769i	$-0.525593\pi$
$367$	−170.553	−	27.0130i	−0.464723	−	0.0736049i	−0.384405	+	0.923164i	$0.625593\pi$
$368$	11.0959	−	11.0959i	0.0301518	−	0.0301518i
$369$		0			0
$370$	668.143	−	120.991i	1.80579	−	0.327004i
$371$	408.534	+	296.817i	1.10117	+	0.800046i
$372$		0			0
$373$	−17.9357	−	35.2007i	−0.0480849	−	0.0943718i	0.865714	−	0.500539i	$-0.166865\pi$
$373$	−17.9357	−	35.2007i	−0.0480849	−	0.0943718i	−0.913799	+	0.406168i	$0.866865\pi$
$374$			1247.51i			3.33558i
$375$		0			0
$376$	−765.956			−2.03712
$377$	−381.004	+	194.131i	−1.01062	+	0.514937i
$378$		0			0
$379$	−52.2973	+	71.9811i	−0.137988	+	0.189924i	−0.872418	−	0.488760i	$-0.837449\pi$
$379$	−52.2973	+	71.9811i	−0.137988	+	0.189924i	0.734431	+	0.678684i	$0.237449\pi$
$380$	−12.8559	−	70.9936i	−0.0338314	−	0.186825i
$381$		0			0
$382$	116.734	+	116.734i	0.305585	+	0.305585i
$383$	50.0372	−	315.922i	0.130645	−	0.824863i	−0.832134	−	0.554575i	$-0.812881\pi$
$383$	50.0372	−	315.922i	0.130645	−	0.824863i	0.962779	−	0.270288i	$-0.0871190\pi$
$384$		0			0
$385$	271.659	+	357.066i	0.705608	+	0.927443i
$386$	−70.8604	+	218.086i	−0.183576	+	0.564989i
$387$		0			0
$388$	53.6304	+	27.3260i	0.138223	+	0.0704279i
$389$	77.7419	+	25.2599i	0.199851	+	0.0649354i	0.407232	−	0.913325i	$-0.366494\pi$
$389$	77.7419	+	25.2599i	0.199851	+	0.0649354i	−0.207381	+	0.978260i	$0.566494\pi$
$390$		0			0
$391$	38.0621	+	117.143i	0.0973456	+	0.299599i
$392$	103.488	+	16.3909i	0.264001	+	0.0418136i
$393$		0			0
$394$	−674.878	−	928.889i	−1.71289	−	2.35759i
$395$	253.978	+	122.427i	0.642983	+	0.309941i
$396$		0			0
$397$	8.70402	+	54.9550i	0.0219245	+	0.138426i	0.996223	−	0.0868371i	$-0.0276760\pi$
$397$	8.70402	+	54.9550i	0.0219245	+	0.138426i	−0.974298	+	0.225263i	$0.927676\pi$
$398$	−59.6060	−	116.983i	−0.149764	−	0.293928i
$399$		0			0
$400$	51.4934	+	64.6702i	0.128734	+	0.161675i
$401$	−706.598			−1.76209			−0.881045	−	0.473032i	$-0.843160\pi$
$401$	−706.598			−1.76209			−0.881045	+	0.473032i	$0.843160\pi$
$402$		0			0
$403$	255.409	−	40.4527i	0.633768	−	0.100379i
$404$	−18.2457	+	25.1130i	−0.0451626	+	0.0621609i
$405$		0			0
$406$	907.735	−	659.508i	2.23580	−	1.62440i
$407$	426.258	+	426.258i	1.04732	+	1.04732i
$408$		0			0
$409$	225.857	−	73.3853i	0.552217	−	0.179426i	−0.0195993	−	0.999808i	$-0.506239\pi$
$409$	225.857	−	73.3853i	0.552217	−	0.179426i	0.571816	+	0.820382i	$0.306239\pi$
$410$	36.6096	−	52.8006i	0.0892918	−	0.128782i
$411$		0			0
$412$	307.938	−	604.362i	0.747421	−	1.46690i
$413$	61.6400	+	31.4071i	0.149249	+	0.0760463i
$414$		0			0
$415$	86.6238	−	1.91166i	0.208732	−	0.00460640i
$416$	−62.7011	−	192.974i	−0.150724	−	0.463880i
$417$		0			0
$418$	71.8264	−	71.8264i	0.171833	−	0.171833i
$419$	−140.550	−	193.451i	−0.335443	−	0.461697i	0.607661	−	0.794197i	$-0.292108\pi$
$419$	−140.550	−	193.451i	−0.335443	−	0.461697i	−0.943103	+	0.332500i	$0.892108\pi$
$420$		0			0
$421$	−392.951	−	285.496i	−0.933375	−	0.678137i	0.0134415	−	0.999910i	$-0.495721\pi$
$421$	−392.951	−	285.496i	−0.933375	−	0.678137i	−0.946817	+	0.321773i	$0.895721\pi$
$422$	98.4630	+	621.671i	0.233325	+	1.47315i
$423$		0			0
$424$			764.848i			1.80389i
$425$	−635.791	+	129.682i	−1.49598	+	0.305134i
$426$		0			0
$427$	−174.450	+	88.8867i	−0.408548	+	0.208166i
$428$	−553.338	+	87.6401i	−1.29285	+	0.204767i
$429$		0			0
$430$	758.484	+	103.033i	1.76392	+	0.239613i
$431$	224.130	−	162.840i	0.520023	−	0.377819i	−0.296589	−	0.955005i	$-0.595849\pi$
$431$	224.130	−	162.840i	0.520023	−	0.377819i	0.816613	+	0.577186i	$0.195849\pi$
$432$		0			0
$433$	78.8616	−	497.912i	0.182128	−	1.14991i	−0.712026	−	0.702154i	$-0.752222\pi$
$433$	78.8616	−	497.912i	0.182128	−	1.14991i	0.894154	−	0.447760i	$-0.147778\pi$
$434$	−645.320	+	209.677i	−1.48691	+	0.483127i
$435$		0			0
$436$	172.666	−	531.411i	0.396023	−	1.21883i
$437$	4.55316	−	8.93609i	0.0104191	−	0.0204487i
$438$		0			0
$439$	−644.964	−	209.562i	−1.46917	−	0.477361i	−0.538310	−	0.842747i	$-0.680937\pi$
$439$	−644.964	−	209.562i	−1.46917	−	0.477361i	−0.930856	+	0.365385i	$0.880937\pi$
$440$	−195.682	+	650.765i	−0.444732	+	1.47901i
$441$		0			0
$442$	−649.867	−	102.929i	−1.47029	−	0.232871i
$443$	−229.580	+	229.580i	−0.518238	+	0.518238i	−0.917038	−	0.398800i	$-0.869427\pi$
$443$	−229.580	+	229.580i	−0.518238	+	0.518238i	0.398800	+	0.917038i	$0.369427\pi$
$444$		0			0
$445$	−60.3533	+	444.293i	−0.135625	+	0.998412i
$446$	−482.739	−	350.730i	−1.08237	−	0.786391i
$447$		0			0
$448$	278.598	+	546.779i	0.621870	+	1.22049i
$449$		−	72.7747i		−	0.162082i	−0.996711	−	0.0810409i	$-0.974176\pi$
$449$		−	72.7747i		−	0.162082i	0.996711	−	0.0810409i	$-0.0258244\pi$
$450$		0			0
$451$	57.0414			0.126478
$452$	−1151.56	+	586.751i	−2.54771	+	1.29812i
$453$		0			0
$454$	−578.531	+	796.280i	−1.27430	+	1.75392i
$455$	−208.421	+	112.055i	−0.458068	+	0.246275i
$456$		0			0
$457$	209.874	+	209.874i	0.459243	+	0.459243i	0.898407	−	0.439164i	$-0.144725\pi$
$457$	209.874	+	209.874i	0.459243	+	0.459243i	−0.439164	+	0.898407i	$0.644725\pi$
$458$	112.519	−	710.418i	0.245675	−	1.55113i
$459$		0			0
$460$	3.57435	+	161.966i	0.00777032	+	0.352100i
$461$	−41.7392	+	128.460i	−0.0905406	+	0.278655i	−0.986066	−	0.166355i	$-0.946800\pi$
$461$	−41.7392	+	128.460i	−0.0905406	+	0.278655i	0.895525	+	0.445011i	$0.146800\pi$
$462$		0			0
$463$	−657.694	−	335.112i	−1.42051	−	0.723784i	−0.436133	−	0.899882i	$-0.643652\pi$
$463$	−657.694	−	335.112i	−1.42051	−	0.723784i	−0.984373	+	0.176099i	$0.943652\pi$
$464$	174.556	+	56.7167i	0.376198	+	0.122234i
$465$		0			0
$466$	185.848	+	571.981i	0.398815	+	1.22743i
$467$	193.470	+	30.6426i	0.414282	+	0.0656158i	0.360096	−	0.932915i	$-0.382744\pi$
$467$	193.470	+	30.6426i	0.414282	+	0.0656158i	0.0541855	+	0.998531i	$0.482744\pi$
$468$		0			0
$469$	−1.28517	−	1.76889i	−0.00274024	−	0.00377162i
$470$	936.328	−	978.588i	1.99219	−	2.08210i
$471$		0			0
$472$	16.3915	+	103.492i	0.0347278	+	0.219263i
$473$	308.514	+	605.494i	0.652250	+	1.28011i
$474$		0			0
$475$	44.0728	+	29.1397i	0.0927848	+	0.0613467i
$476$	1088.67			2.28712
$477$		0			0
$478$	−1484.04	+	235.049i	−3.10469	+	0.491735i
$479$	84.2910	−	116.017i	0.175973	−	0.242206i	−0.711915	−	0.702265i	$-0.752172\pi$
$479$	84.2910	−	116.017i	0.175973	−	0.242206i	0.887888	+	0.460060i	$0.152172\pi$
$480$		0			0
$481$	−257.221	+	186.882i	−0.534763	+	0.388528i
$482$	930.598	+	930.598i	1.93070	+	1.93070i
$483$		0			0
$484$	−599.698	+	194.854i	−1.23905	+	0.402590i
$485$	−41.6103	+	14.5426i	−0.0857944	+	0.0299847i
$486$		0			0
$487$	152.898	−	300.080i	0.313959	−	0.616180i	−0.679067	−	0.734077i	$-0.737615\pi$
$487$	152.898	−	300.080i	0.313959	−	0.616180i	0.993026	+	0.117897i	$0.0376152\pi$
$488$	−264.226	−	134.630i	−0.541447	−	0.275881i
$489$		0			0
$490$	−147.449	+	112.180i	−0.300916	+	0.228939i
$491$	−196.552	−	604.925i	−0.400310	−	1.23203i	−0.924748	−	0.380579i	$-0.875725\pi$
$491$	−196.552	−	604.925i	−0.400310	−	1.23203i	0.524439	−	0.851448i	$-0.324275\pi$
$492$		0			0
$493$	−1018.70	+	1018.70i	−2.06634	+	2.06634i
$494$	31.4905	+	43.3429i	0.0637459	+	0.0877387i
$495$		0			0
$496$	−89.7953	−	65.2401i	−0.181039	−	0.131532i
$497$	−105.189	−	664.139i	−0.211649	−	1.33630i
$498$		0			0
$499$			220.616i			0.442116i	0.975261	+	0.221058i	$0.0709511\pi$
$499$			220.616i			0.442116i	−0.975261	+	0.221058i	$0.929049\pi$
$500$	−849.940	−	77.4601i	−1.69988	−	0.154920i
$501$		0			0
$502$	449.635	−	229.100i	0.895687	−	0.456375i
$503$	377.227	−	59.7469i	0.749954	−	0.118781i	0.230255	−	0.973130i	$-0.426044\pi$
$503$	377.227	−	59.7469i	0.749954	−	0.118781i	0.519699	+	0.854349i	$0.326044\pi$
$504$		0			0
$505$	−4.05056	−	22.3682i	−0.00802091	−	0.0442934i
$506$	−184.527	+	134.067i	−0.364678	+	0.264954i
$507$		0			0
$508$	−119.458	+	754.229i	−0.235154	+	1.48470i
$509$	54.3299	−	17.6528i	0.106738	−	0.0346814i	−0.255161	−	0.966899i	$-0.582128\pi$
$509$	54.3299	−	17.6528i	0.106738	−	0.0346814i	0.361899	+	0.932217i	$0.382128\pi$
$510$		0			0
$511$	84.1163	−	258.883i	0.164611	−	0.506621i
$512$	−95.4111	+	187.255i	−0.186350	+	0.365732i
$513$		0			0
$514$	922.391	+	299.703i	1.79454	+	0.583080i
$515$	163.880	+	468.907i	0.318214	+	0.910499i
$516$		0			0
$517$	1187.60	+	188.098i	2.29711	+	0.363826i
$518$	589.912	−	589.912i	1.13883	−	1.13883i
$519$		0			0
$520$	−322.860	−	155.630i	−0.620884	−	0.299289i
$521$	−37.2208	−	27.0425i	−0.0714410	−	0.0519050i	0.551492	−	0.834181i	$-0.314059\pi$
$521$	−37.2208	−	27.0425i	−0.0714410	−	0.0519050i	−0.622933	+	0.782276i	$0.714059\pi$
$522$		0			0
$523$	138.623	+	272.063i	0.265053	+	0.520197i	0.984725	−	0.174118i	$-0.0557075\pi$
$523$	138.623	+	272.063i	0.265053	+	0.520197i	−0.719671	+	0.694315i	$0.755707\pi$
$524$		−	711.954i		−	1.35869i
$525$		0			0
$526$	−34.5965			−0.0657729
$527$	776.267	−	395.528i	1.47299	−	0.750527i
$528$		0			0
$529$	297.701	−	409.751i	0.562763	−	0.774576i
$530$	−977.173	−	934.974i	−1.84372	−	1.76410i
$531$		0			0
$532$	−62.6811	−	62.6811i	−0.117822	−	0.117822i
$533$	−4.70635	+	29.7147i	−0.00882992	+	0.0557499i
$534$		0			0
$535$	233.767	−	337.152i	0.436947	−	0.630191i
$536$	1.02336	−	3.14959i	0.00190926	−	0.00587610i
$537$		0			0
$538$	1350.84	+	688.289i	2.51086	+	1.27935i
$539$	−156.432	−	50.8279i	−0.290227	−	0.0943004i
$540$		0			0
$541$	−72.3805	−	222.764i	−0.133790	−	0.411764i	0.861610	−	0.507571i	$-0.169457\pi$
$541$	−72.3805	−	222.764i	−0.133790	−	0.411764i	−0.995400	+	0.0958075i	$0.969457\pi$
$542$	−483.768	−	76.6213i	−0.892560	−	0.141368i
$543$		0			0
$544$	−401.815	−	553.051i	−0.738630	−	1.01664i
$545$	193.765	+	360.399i	0.355532	+	0.661283i
$546$		0			0
$547$	−126.813	−	800.663i	−0.231833	−	1.46374i	−0.779164	−	0.626819i	$-0.784356\pi$
$547$	−126.813	−	800.663i	−0.231833	−	1.46374i	0.547332	−	0.836916i	$-0.315644\pi$
$548$	473.815	+	929.914i	0.864626	+	1.69692i
$549$		0			0
$550$	−592.212	−	1045.52i	−1.07675	−	1.90095i
$551$	117.306			0.212896
$552$		0			0
$553$	342.146	−	54.1906i	0.618708	−	0.0979938i
$554$	498.609	−	686.276i	0.900016	−	1.23877i
$555$		0			0
$556$	869.667	−	631.850i	1.56415	−	1.13642i
$557$	−581.702	−	581.702i	−1.04435	−	1.04435i	−0.998970	−	0.0453787i	$-0.985551\pi$
$557$	−581.702	−	581.702i	−1.04435	−	1.04435i	−0.0453787	−	0.998970i	$-0.514449\pi$
$558$		0			0
$559$	−340.876	+	110.757i	−0.609796	+	0.198135i
$560$	97.2660	+	29.2474i	0.173689	+	0.0522275i
$561$		0			0
$562$	−119.266	+	234.072i	−0.212217	+	0.416499i
$563$	376.119	+	191.642i	0.668062	+	0.340395i	0.754911	−	0.655827i	$-0.227680\pi$
$563$	376.119	+	191.642i	0.668062	+	0.340395i	−0.0868492	+	0.996221i	$0.527680\pi$
$564$		0			0
$565$	272.542	−	906.372i	0.482375	−	1.60420i
$566$	35.8950	+	110.473i	0.0634187	+	0.195183i
$567$		0			0
$568$	720.161	−	720.161i	1.26789	−	1.26789i
$569$	470.636	+	647.774i	0.827128	+	1.13844i	0.988451	+	0.151542i	$0.0484239\pi$
$569$	470.636	+	647.774i	0.827128	+	1.13844i	−0.161323	+	0.986902i	$0.551576\pi$
$570$		0			0
$571$	545.948	+	396.655i	0.956127	+	0.694667i	0.952248	−	0.305326i	$-0.0987653\pi$
$571$	545.948	+	396.655i	0.956127	+	0.694667i	0.00387883	+	0.999992i	$0.498765\pi$
$572$	−120.190	−	758.848i	−0.210122	−	1.32666i
$573$		0			0
$574$		−	78.9414i		−	0.137529i
$575$	−87.5092	−	80.1075i	−0.152190	−	0.139317i
$576$		0			0
$577$	−809.001	+	412.206i	−1.40208	+	0.714396i	−0.981249	−	0.192743i	$-0.938262\pi$
$577$	−809.001	+	412.206i	−1.40208	+	0.714396i	−0.420831	+	0.907139i	$0.638262\pi$
$578$	−1250.21	+	198.014i	−2.16299	+	0.342585i
$579$		0			0
$580$	−1668.96	+	897.298i	−2.87752	+	1.54707i
$581$	86.1245	−	62.5731i	0.148235	−	0.107699i
$582$		0			0
$583$	187.826	−	1185.89i	0.322172	−	2.03411i
$584$	392.111	−	127.405i	0.671423	−	0.218159i
$585$		0			0
$586$	−24.0682	+	74.0745i	−0.0410721	+	0.126407i
$587$	−54.6357	+	107.229i	−0.0930761	+	0.182672i	−0.932851	−	0.360263i	$-0.882687\pi$
$587$	−54.6357	+	107.229i	−0.0930761	+	0.182672i	0.839775	+	0.542935i	$0.182687\pi$
$588$		0			0
$589$	−67.4671	−	21.9214i	−0.114545	−	0.0372180i
$590$	−152.259	−	105.570i	−0.258066	−	0.178932i
$591$		0			0
$592$	134.787	+	21.3482i	0.227681	+	0.0360612i
$593$	−255.390	+	255.390i	−0.430674	+	0.430674i	−0.888858	−	0.458183i	$-0.848500\pi$
$593$	−255.390	+	255.390i	−0.430674	+	0.430674i	0.458183	+	0.888858i	$0.348500\pi$
$594$		0			0
$595$	−551.162	+	576.038i	−0.926323	+	0.968131i
$596$	444.486	+	322.938i	0.745781	+	0.541842i
$597$		0			0
$598$	−54.6149	−	107.188i	−0.0913293	−	0.179244i
$599$		−	546.766i		−	0.912799i	−0.889775	−	0.456399i	$-0.849139\pi$
$599$		−	546.766i		−	0.912799i	0.889775	−	0.456399i	$-0.150861\pi$
$600$		0			0
$601$	−768.536			−1.27876			−0.639381	−	0.768890i	$-0.720809\pi$
$601$	−768.536			−1.27876			−0.639381	+	0.768890i	$0.720809\pi$
$602$	837.962	−	426.963i	1.39196	−	0.709241i
$603$		0			0
$604$	752.219	−	1035.34i	1.24540	−	1.71414i
$605$	200.509	−	415.962i	0.331420	−	0.687540i
$606$		0			0
$607$	−163.485	−	163.485i	−0.269333	−	0.269333i	0.559498	−	0.828832i	$-0.310994\pi$
$607$	−163.485	−	163.485i	−0.269333	−	0.269333i	−0.828832	+	0.559498i	$0.810994\pi$
$608$	−8.70754	+	54.9772i	−0.0143216	+	0.0904231i
$609$		0			0
$610$	495.002	−	173.000i	0.811479	−	0.283607i
$611$	−195.973	+	603.142i	−0.320741	+	0.987140i
$612$		0			0
$613$	530.506	+	270.306i	0.865426	+	0.440957i	0.829572	−	0.558400i	$-0.188585\pi$
$613$	530.506	+	270.306i	0.865426	+	0.440957i	0.0358546	+	0.999357i	$0.488585\pi$
$614$	−62.1425	−	20.1913i	−0.101209	−	0.0328849i
$615$		0			0
$616$	258.006	+	794.060i	0.418840	+	1.28906i
$617$	−319.636	−	50.6254i	−0.518049	−	0.0820509i	−0.108065	−	0.994144i	$-0.534466\pi$
$617$	−319.636	−	50.6254i	−0.518049	−	0.0820509i	−0.409984	+	0.912093i	$0.634466\pi$
$618$		0			0
$619$	6.19820	+	8.53110i	0.0100133	+	0.0137821i	0.813994	−	0.580873i	$-0.197289\pi$
$619$	6.19820	+	8.53110i	0.0100133	+	0.0137821i	−0.803981	+	0.594655i	$0.797289\pi$
$620$	1127.57	−	204.186i	1.81866	−	0.329333i
$621$		0			0
$622$	99.1246	+	625.848i	0.159364	+	1.00619i
$623$	250.100	+	490.848i	0.401444	+	0.787878i
$624$		0			0
$625$	471.286	−	410.505i	0.754058	−	0.656808i
$626$	−523.208			−0.835795
$627$		0			0
$628$	−859.149	+	136.076i	−1.36807	+	0.216681i
$629$	−629.625	+	866.605i	−1.00099	+	1.37775i
$630$		0			0
$631$	−25.4826	+	18.5142i	−0.0403844	+	0.0293410i	−0.607794	−	0.794094i	$-0.707946\pi$
$631$	−25.4826	+	18.5142i	−0.0403844	+	0.0293410i	0.567410	+	0.823435i	$0.307946\pi$
$632$	371.006	+	371.006i	0.587035	+	0.587035i
$633$		0			0
$634$	1198.77	−	389.502i	1.89080	−	0.614357i
$635$	−338.600	−	445.052i	−0.533228	−	0.700870i
$636$		0			0
$637$	39.3848	−	77.2970i	0.0618285	−	0.121345i
$638$	−2377.04	−	1211.16i	−3.72576	−	1.89837i
$639$		0			0
$640$	−368.445	−	1054.22i	−0.575695	−	1.64722i
$641$	347.695	+	1070.09i	0.542425	+	1.66941i	0.727034	+	0.686601i	$0.240898\pi$
$641$	347.695	+	1070.09i	0.542425	+	1.66941i	−0.184609	+	0.982812i	$0.559102\pi$
$642$		0			0
$643$	737.920	−	737.920i	1.14762	−	1.14762i	0.160602	−	0.987019i	$-0.448656\pi$
$643$	737.920	−	737.920i	1.14762	−	1.14762i	0.987019	−	0.160602i	$-0.0513436\pi$
$644$	116.997	+	161.032i	0.181672	+	0.250050i
$645$		0			0
$646$	146.027	+	106.095i	0.226048	+	0.164233i
$647$	−167.580	−	1058.06i	−0.259011	−	1.63533i	−0.683536	−	0.729916i	$-0.739559\pi$
$647$	−167.580	−	1058.06i	−0.259011	−	1.63533i	0.424525	−	0.905416i	$-0.360441\pi$
$648$		0			0
$649$		−	164.488i		−	0.253449i
$650$	593.507	−	222.239i	0.913088	−	0.341907i
$651$		0			0
$652$	−208.354	+	106.162i	−0.319562	+	0.162825i
$653$	375.029	−	59.3987i	0.574317	−	0.0909628i	0.137481	−	0.990504i	$-0.456099\pi$
$653$	375.029	−	59.3987i	0.574317	−	0.0909628i	0.436835	+	0.899542i	$0.356099\pi$
$654$		0			0
$655$	376.710	+	360.442i	0.575130	+	0.550293i
$656$	10.4469	−	7.59015i	0.0159252	−	0.0115704i
$657$		0			0
$658$	260.315	−	1643.56i	0.395615	−	2.49782i
$659$	−329.556	+	107.079i	−0.500085	+	0.162487i	−0.548188	−	0.836355i	$-0.684682\pi$
$659$	−329.556	+	107.079i	−0.500085	+	0.162487i	0.0481033	+	0.998842i	$0.484682\pi$
$660$		0			0
$661$	−246.800	+	759.573i	−0.373374	+	1.14913i	0.571195	+	0.820814i	$0.306480\pi$
$661$	−246.800	+	759.573i	−0.373374	+	1.14913i	−0.944569	+	0.328312i	$0.893520\pi$
$662$	832.197	−	1633.28i	1.25709	−	2.46719i
$663$		0			0
$664$	153.349	+	49.8260i	0.230947	+	0.0750392i
$665$	64.8995	−	1.43224i	0.0975933	−	0.00215374i
$666$		0			0
$667$	−260.161	−	41.2055i	−0.390047	−	0.0617773i
$668$	284.695	−	284.695i	0.426191	−	0.426191i
$669$		0			0
$670$	2.77294	+	5.15761i	0.00413871	+	0.00769793i
$671$	376.618	+	273.629i	0.561279	+	0.407793i
$672$		0			0
$673$	32.9059	+	64.5815i	0.0488944	+	0.0959606i	0.914161	−	0.405352i	$-0.132851\pi$
$673$	32.9059	+	64.5815i	0.0488944	+	0.0959606i	−0.865267	+	0.501312i	$0.832851\pi$
$674$			624.607i			0.926716i
$675$		0			0
$676$	−748.656			−1.10748
$677$	529.170	−	269.626i	0.781640	−	0.398265i	−0.0171675	−	0.999853i	$-0.505465\pi$
$677$	529.170	−	269.626i	0.781640	−	0.398265i	0.798807	+	0.601587i	$0.205465\pi$
$678$		0			0
$679$	−31.8325	+	43.8136i	−0.0468814	+	0.0645267i
$680$	−1196.54	−	162.539i	−1.75961	−	0.239028i
$681$		0			0
$682$	1140.79	+	1140.79i	1.67272	+	1.67272i
$683$	−114.459	+	722.664i	−0.167582	+	1.05807i	0.750264	+	0.661138i	$0.229926\pi$
$683$	−114.459	+	722.664i	−0.167582	+	1.05807i	−0.917847	+	0.396935i	$0.870074\pi$
$684$		0			0
$685$	−731.916	−	220.084i	−1.06849	−	0.321290i
$686$	−376.428	+	1158.53i	−0.548729	+	1.68881i
$687$		0			0
$688$	137.073	+	69.8421i	0.199234	+	0.101515i
$689$	602.270	+	195.689i	0.874122	+	0.284019i
$690$		0			0
$691$	161.872	+	498.191i	0.234257	+	0.720970i	0.997219	+	0.0745265i	$0.0237445\pi$
$691$	161.872	+	498.191i	0.234257	+	0.720970i	−0.762962	+	0.646444i	$0.776255\pi$
$692$	−524.694	−	83.1034i	−0.758229	−	0.120092i
$693$		0			0
$694$	292.751	+	402.938i	0.421832	+	0.580602i
$695$	−105.962	+	780.046i	−0.152464	+	1.12237i
$696$		0			0
$697$	15.8562	+	100.112i	0.0227492	+	0.143633i
$698$	186.038	+	365.119i	0.266530	+	0.523094i
$699$		0			0
$700$	−912.400	+	516.809i	−1.30343	+	0.738299i
$701$	699.523			0.997893			0.498947	−	0.866633i	$-0.333720\pi$
$701$	699.523			0.997893			0.498947	+	0.866633i	$0.333720\pi$
$702$		0			0
$703$	86.1468	−	13.6443i	0.122542	−	0.0194087i
$704$	857.636	−	1180.43i	1.21823	−	1.67675i
$705$		0			0
$706$	−990.308	+	719.501i	−1.40270	+	1.01912i
$707$	−19.7491	−	19.7491i	−0.0279337	−	0.0279337i
$708$		0			0
$709$	145.144	−	47.1600i	0.204716	−	0.0665162i	−0.204864	−	0.978790i	$-0.565675\pi$
$709$	145.144	−	47.1600i	0.204716	−	0.0665162i	0.409580	+	0.912274i	$0.365675\pi$
$710$	39.7327	+	1800.43i	0.0559616	+	2.53581i
$711$		0			0
$712$	−378.807	+	743.451i	−0.532032	+	1.04417i
$713$	141.929	+	72.3163i	0.199059	+	0.101425i
$714$		0			0
$715$	462.371	+	320.588i	0.646673	+	0.448375i
$716$	−321.957	−	990.882i	−0.449661	−	1.38391i
$717$		0			0
$718$	−568.421	+	568.421i	−0.791673	+	0.791673i
$719$	−431.478	−	593.879i	−0.600109	−	0.825979i	0.395610	−	0.918419i	$-0.370533\pi$
$719$	−431.478	−	593.879i	−0.600109	−	0.825979i	−0.995718	+	0.0924401i	$0.970533\pi$
$720$		0			0
$721$	493.737	+	358.721i	0.684794	+	0.497532i
$722$	183.527	+	1158.75i	0.254193	+	1.60491i
$723$		0			0
$724$			222.963i			0.307960i
$725$	370.167	−	1337.36i	0.510575	−	1.84463i
$726$		0			0
$727$	1179.77	−	601.120i	1.62279	−	0.826851i	0.623811	−	0.781575i	$-0.285583\pi$
$727$	1179.77	−	601.120i	1.62279	−	0.826851i	0.998975	−	0.0452756i	$-0.0144166\pi$
$728$	−434.939	+	68.8876i	−0.597444	+	0.0946258i
$729$		0			0
$730$	−316.556	+	656.706i	−0.433639	+	0.899597i
$731$	−976.927	+	709.779i	−1.33643	+	0.970970i
$732$		0			0
$733$	−133.600	+	843.514i	−0.182264	+	1.15077i	0.711651	+	0.702533i	$0.247948\pi$
$733$	−133.600	+	843.514i	−0.182264	+	1.15077i	−0.893915	+	0.448237i	$0.852052\pi$
$734$	540.399	−	175.586i	0.736238	−	0.239218i
$735$		0			0
$736$	38.6233	−	118.870i	0.0524773	−	0.161509i
$737$	−2.36017	+	4.63209i	−0.00320240	+	0.00628506i
$738$		0			0
$739$	32.3337	+	10.5059i	0.0437534	+	0.0142163i	0.330812	−	0.943697i	$-0.392677\pi$
$739$	32.3337	+	10.5059i	0.0437534	+	0.0142163i	−0.287059	+	0.957913i	$0.592677\pi$
$740$	−1121.28	+	853.081i	−1.51524	+	1.15281i
$741$		0			0
$742$	−1641.19	−	259.938i	−2.21184	−	0.350321i
$743$	327.809	−	327.809i	0.441197	−	0.441197i	−0.451217	−	0.892414i	$-0.649010\pi$
$743$	327.809	−	327.809i	0.441197	−	0.441197i	0.892414	+	0.451217i	$0.149010\pi$
$744$		0			0
$745$	−395.904	+	71.6925i	−0.531414	+	0.0962316i
$746$	105.171	+	76.4112i	0.140980	+	0.102428i
$747$		0			0
$748$	−1175.16	−	2306.38i	−1.57107	−	3.08339i
$749$		−	504.071i		−	0.672993i
$750$		0			0
$751$	436.259			0.580905			0.290452	−	0.956889i	$-0.406194\pi$
$751$	436.259			0.580905			0.290452	+	0.956889i	$0.406194\pi$
$752$	242.535	−	123.578i	0.322520	−	0.164332i
$753$		0			0
$754$	827.057	−	1138.35i	1.09689	−	1.50974i
$755$	166.993	+	922.178i	0.221183	+	1.22143i
$756$		0			0
$757$	−667.784	−	667.784i	−0.882145	−	0.882145i	0.111607	−	0.993752i	$-0.464400\pi$
$757$	−667.784	−	667.784i	−0.882145	−	0.882145i	−0.993752	+	0.111607i	$0.964400\pi$
$758$	45.7996	−	289.167i	0.0604216	−	0.381487i
$759$		0			0
$760$	59.5334	+	78.2500i	0.0783334	+	0.102961i
$761$	−265.924	+	818.431i	−0.349440	+	1.07547i	0.609723	+	0.792615i	$0.291281\pi$
$761$	−265.924	+	818.431i	−0.349440	+	1.07547i	−0.959163	+	0.282853i	$0.908719\pi$
$762$		0			0
$763$	447.947	+	228.241i	0.587087	+	0.299136i
$764$	−325.779	−	105.852i	−0.426412	−	0.138550i
$765$		0			0
$766$	325.245	+	1001.00i	0.424602	+	1.30679i
$767$	85.6873	+	13.5715i	0.111717	+	0.0176943i
$768$		0			0
$769$	534.634	+	735.861i	0.695233	+	0.956907i	0.999990	+	0.00447640i	$0.00142489\pi$
$769$	534.634	+	735.861i	0.695233	+	0.956907i	−0.304757	+	0.952430i	$0.598575\pi$
$770$	−1329.89	−	641.055i	−1.72713	−	0.832539i
$771$		0			0
$772$	−74.4320	−	469.945i	−0.0964146	−	0.608738i
$773$	330.014	+	647.689i	0.426926	+	0.837889i	0.999833	+	0.0182691i	$0.00581557\pi$
$773$	330.014	+	647.689i	0.426926	+	0.837889i	−0.572907	+	0.819620i	$0.694184\pi$
$774$		0			0
$775$	−462.816	+	699.993i	−0.597181	+	0.903217i
$776$	−82.0270			−0.105705
$777$		0			0
$778$	−265.666	+	42.0774i	−0.341474	+	0.0540841i
$779$	4.85110	−	6.67697i	0.00622734	−	0.00857120i
$780$		0			0
$781$	−1293.45	+	939.748i	−1.65615	+	1.20326i
$782$	−286.592	−	286.592i	−0.366486	−	0.366486i
$783$		0			0
$784$	−35.4134	+	11.5065i	−0.0451702	+	0.0146767i
$785$	362.962	−	523.485i	0.462372	−	0.666860i
$786$		0			0
$787$	−665.324	+	1305.77i	−0.845393	+	1.65918i	−0.0976189	+	0.995224i	$0.531123\pi$
$787$	−665.324	+	1305.77i	−0.845393	+	1.65918i	−0.747774	+	0.663953i	$0.768877\pi$
$788$	2122.72	+	1081.58i	2.69381	+	1.37257i
$789$		0			0
$790$	−927.529	+	20.4692i	−1.17409	+	0.0259103i
$791$	−359.345	−	1105.95i	−0.454292	−	1.39817i
$792$		0			0
$793$	−173.616	+	173.616i	−0.218936	+	0.218936i
$794$	−107.615	−	148.120i	−0.135536	−	0.186549i
$795$		0			0
$796$	220.398	+	160.128i	0.276882	+	0.201166i
$797$	118.617	+	748.917i	0.148829	+	0.939669i	0.943197	+	0.332233i	$0.107802\pi$
$797$	118.617	+	748.917i	0.148829	+	0.939669i	−0.794368	+	0.607436i	$0.792198\pi$
$798$		0			0
$799$			2136.62i			2.67412i
$800$	599.298	+	272.757i	0.749123	+	0.340946i
$801$		0			0
$802$	2071.68	−	1055.57i	2.58314	−	1.31617i
$803$	−639.250	+	101.247i	−0.796078	+	0.126086i
$804$		0			0
$805$	−144.438	−	19.6206i	−0.179426	−	0.0243734i
$806$	−688.401	+	500.152i	−0.854095	+	0.620536i
$807$		0			0
$808$	6.61760	−	41.7819i	0.00819010	−	0.0517102i
$809$	684.508	−	222.410i	0.846116	−	0.274920i	0.146298	−	0.989241i	$-0.453264\pi$
$809$	684.508	−	222.410i	0.846116	−	0.274920i	0.699818	+	0.714321i	$0.253264\pi$
$810$		0			0
$811$	−27.5305	+	84.7302i	−0.0339464	+	0.104476i	−0.966594	−	0.256312i	$-0.917492\pi$
$811$	−27.5305	+	84.7302i	−0.0339464	+	0.104476i	0.932648	+	0.360789i	$0.117492\pi$
$812$	−1056.95	+	2074.38i	−1.30166	+	2.55466i
$813$		0			0
$814$	−1886.52	−	612.968i	−2.31760	−	0.753032i
$815$	49.3114	−	163.991i	0.0605048	−	0.201216i
$816$		0			0
$817$	97.1136	+	15.3813i	0.118866	+	0.0188265i
$818$	−552.560	+	552.560i	−0.675502	+	0.675502i
$819$		0			0
$820$	−17.9451	+	132.104i	−0.0218843	+	0.161102i
$821$	−543.123	−	394.602i	−0.661538	−	0.480635i	0.205644	−	0.978627i	$-0.434071\pi$
$821$	−543.123	−	394.602i	−0.661538	−	0.480635i	−0.867182	+	0.497991i	$0.834071\pi$
$822$		0			0
$823$	558.523	+	1096.16i	0.678643	+	1.33191i	0.931263	+	0.364347i	$0.118708\pi$
$823$	558.523	+	1096.16i	0.678643	+	1.33191i	−0.252620	+	0.967566i	$0.581292\pi$
$824$			924.364i			1.12180i
$825$		0			0
$826$	−227.641			−0.275594
$827$	−150.479	+	76.6727i	−0.181957	+	0.0927119i	−0.542596	−	0.839994i	$-0.682559\pi$
$827$	−150.479	+	76.6727i	−0.181957	+	0.0927119i	0.360639	+	0.932705i	$0.382559\pi$
$828$		0			0
$829$	637.618	−	877.605i	0.769141	−	1.05863i	−0.227258	−	0.973835i	$-0.572976\pi$
$829$	637.618	−	877.605i	0.769141	−	1.05863i	0.996398	−	0.0847965i	$-0.0270240\pi$
$830$	−251.116	+	135.010i	−0.302550	+	0.162663i
$831$		0			0
$832$	544.165	+	544.165i	0.654045	+	0.654045i
$833$	45.7223	−	288.679i	0.0548888	−	0.346554i
$834$		0			0
$835$	6.50516	+	294.771i	0.00779061	+	0.353020i
$836$	−65.1310	+	200.453i	−0.0779079	+	0.239776i
$837$		0			0
$838$	701.072	+	357.214i	0.836601	+	0.426270i
$839$	−1156.94	−	375.911i	−1.37895	−	0.448047i	−0.476623	−	0.879108i	$-0.658139\pi$
$839$	−1156.94	−	375.911i	−1.37895	−	0.448047i	−0.902323	+	0.431061i	$0.858139\pi$
$840$		0			0
$841$	−692.161	−	2130.25i	−0.823021	−	2.53300i
$842$	1578.59	+	250.024i	1.87481	+	0.296940i
$843$		0			0
$844$	−767.654	−	1056.59i	−0.909543	−	1.25188i
$845$	379.023	−	396.129i	0.448548	−	0.468792i
$846$		0			0
$847$	−88.7525	−	560.361i	−0.104785	−	0.661584i
$848$	−123.399	−	242.184i	−0.145518	−	0.285595i
$849$		0			0
$850$	1670.35	−	1330.01i	1.96511	−	1.56472i
$851$	−195.850			−0.230141
$852$		0			0
$853$	−182.560	+	28.9147i	−0.214021	+	0.0338977i	−0.262524	−	0.964925i	$-0.584555\pi$
$853$	−182.560	+	28.9147i	−0.214021	+	0.0338977i	0.0485029	+	0.998823i	$0.484555\pi$
$854$	378.684	−	521.214i	0.443424	−	0.610320i
$855$		0			0
$856$	617.668	−	448.762i	0.721574	−	0.524254i
$857$	−203.015	−	203.015i	−0.236890	−	0.236890i	0.578671	−	0.815561i	$-0.303572\pi$
$857$	−203.015	−	203.015i	−0.236890	−	0.236890i	−0.815561	+	0.578671i	$0.803572\pi$
$858$		0			0
$859$	−1263.62	+	410.575i	−1.47103	+	0.477968i	−0.931421	−	0.363944i	$-0.881430\pi$
$859$	−1263.62	+	410.575i	−1.47103	+	0.477968i	−0.539614	+	0.841913i	$0.681430\pi$
$860$	−1499.33	+	524.009i	−1.74341	+	0.609313i
$861$		0			0
$862$	−413.864	+	812.253i	−0.480120	+	0.942289i
$863$	−1200.75	−	611.814i	−1.39137	−	0.708938i	−0.412032	−	0.911169i	$-0.635181\pi$
$863$	−1200.75	−	611.814i	−1.39137	−	0.708938i	−0.979338	+	0.202231i	$0.935181\pi$
$864$		0			0
$865$	309.610	−	235.554i	0.357930	−	0.272317i
$866$	512.606	+	1577.64i	0.591924	+	1.82175i
$867$		0			0
$868$	995.543	−	995.543i	1.14694	−	1.14694i
$869$	−484.132	−	666.350i	−0.557113	−	0.766801i
$870$		0			0
$871$	−2.21828	−	1.61167i	−0.00254681	−	0.00185037i
$872$	119.120	+	752.092i	0.136605	+	0.862491i
$873$		0			0
$874$			33.0016i			0.0377592i
$875$	188.467	−	744.416i	0.215391	−	0.850761i
$876$		0			0
$877$	892.419	−	454.710i	1.01758	−	0.518484i	0.136096	−	0.990696i	$-0.456544\pi$
$877$	892.419	−	454.710i	1.01758	−	0.518484i	0.881485	+	0.472212i	$0.156544\pi$
$878$	2204.03	−	349.084i	2.51028	−	0.397590i
$879$		0			0
$880$	−43.0318	−	237.632i	−0.0488997	−	0.270036i
$881$	−610.778	+	443.756i	−0.693278	+	0.503696i	−0.877736	−	0.479145i	$-0.840947\pi$
$881$	−610.778	+	443.756i	−0.693278	+	0.503696i	0.184458	+	0.982840i	$0.440947\pi$
$882$		0			0
$883$	−143.134	+	903.715i	−0.162100	+	1.02346i	0.763735	+	0.645530i	$0.223364\pi$
$883$	−143.134	+	903.715i	−0.162100	+	1.02346i	−0.925835	+	0.377929i	$0.876636\pi$
$884$	1298.43	−	421.884i	1.46881	−	0.477245i
$885$		0			0
$886$	330.140	−	1016.07i	0.372619	−	1.14680i
$887$	−668.313	+	1311.64i	−0.753453	+	1.47874i	0.120494	+	0.992714i	$0.461552\pi$
$887$	−668.313	+	1311.64i	−0.753453	+	1.47874i	−0.873947	+	0.486021i	$0.838448\pi$
$888$		0			0
$889$	−653.449	−	212.318i	−0.735038	−	0.238828i
$890$	−486.770	−	1392.78i	−0.546932	−	1.56492i
$891$		0			0
$892$	1222.87	+	193.684i	1.37093	+	0.217134i
$893$	123.018	−	123.018i	0.137758	−	0.137758i
$894$		0			0
$895$	687.294	+	331.301i	0.767926	+	0.370169i
$896$	−1110.05	−	806.495i	−1.23889	−	0.900106i
$897$		0			0
$898$	108.716	+	213.368i	0.121065	+	0.237604i
$899$			1863.12i			2.07244i
$900$		0			0
$901$	2133.53			2.36796
$902$	−167.240	+	85.2128i	−0.185410	+	0.0944710i
$903$		0			0
$904$	1035.27	−	1424.92i	1.14521	−	1.57624i
$905$	−117.974	−	112.880i	−0.130358	−	0.124729i
$906$		0			0
$907$	−511.441	−	511.441i	−0.563882	−	0.563882i	0.366526	−	0.930408i	$-0.380547\pi$
$907$	−511.441	−	511.441i	−0.563882	−	0.563882i	−0.930408	+	0.366526i	$0.880547\pi$
$908$	319.482	−	2017.13i	0.351853	−	2.22151i
$909$		0			0
$910$	443.672	−	639.890i	0.487552	−	0.703176i
$911$	196.843	−	605.821i	0.216074	−	0.665007i	−0.783002	−	0.622019i	$-0.786312\pi$
$911$	196.843	−	605.821i	0.216074	−	0.665007i	0.999076	−	0.0429874i	$-0.0136875\pi$
$912$		0			0
$913$	−225.530	−	114.913i	−0.247020	−	0.125863i
$914$	−928.856	−	301.803i	−1.01625	−	0.330201i
$915$		0			0
$916$	461.193	+	1419.41i	0.503486	+	1.54957i
$917$	632.694	+	100.209i	0.689961	+	0.109279i
$918$		0			0
$919$	−576.765	−	793.848i	−0.627600	−	0.863818i	0.370278	−	0.928921i	$-0.379262\pi$
$919$	−576.765	−	793.848i	−0.627600	−	0.863818i	−0.997879	+	0.0651032i	$0.979262\pi$
$920$	−104.547	−	194.456i	−0.113638	−	0.211365i
$921$		0			0
$922$	−69.5284	−	438.985i	−0.0754105	−	0.476123i
$923$	−382.826	−	751.338i	−0.414762	−	0.814017i
$924$		0			0
$925$	116.289	−	1025.18i	0.125718	−	1.10831i
$926$	2428.91			2.62301
$927$		0			0
$928$	1443.91	−	228.692i	1.55593	−	0.246436i
$929$	503.341	−	692.790i	0.541810	−	0.745737i	−0.447063	−	0.894503i	$-0.647530\pi$
$929$	503.341	−	692.790i	0.541810	−	0.745737i	0.988873	+	0.148765i	$0.0475299\pi$
$930$		0			0
$931$	−19.2535	+	13.9885i	−0.0206804	+	0.0150252i
$932$	−882.402	−	882.402i	−0.946784	−	0.946784i
$933$		0			0
$934$	−613.010	+	199.179i	−0.656327	+	0.213254i
$935$	1815.30	+	545.852i	1.94150	+	0.583799i
$936$		0			0
$937$	−80.6308	+	158.247i	−0.0860521	+	0.168887i	−0.930022	−	0.367504i	$-0.880213\pi$
$937$	−80.6308	+	158.247i	−0.0860521	+	0.168887i	0.843970	+	0.536390i	$0.180213\pi$
$938$	6.41050	+	3.26631i	0.00683422	+	0.00348221i
$939$		0			0
$940$	−809.239	+	2691.23i	−0.860892	+	2.86301i
$941$	254.617	+	783.630i	0.270581	+	0.832763i	0.990355	+	0.138554i	$0.0442455\pi$
$941$	254.617	+	783.630i	0.270581	+	0.832763i	−0.719774	+	0.694209i	$0.755755\pi$
$942$		0			0
$943$	−13.1042	+	13.1042i	−0.0138963	+	0.0138963i
$944$	−21.8875	−	30.1255i	−0.0231859	−	0.0319126i
$945$		0			0
$946$	−1809.07	−	1314.36i	−1.91233	−	1.38939i
$947$	−34.8644	−	220.125i	−0.0368156	−	0.232444i	0.962419	−	0.271570i	$-0.0875428\pi$
$947$	−34.8644	−	220.125i	−0.0368156	−	0.232444i	−0.999234	+	0.0391254i	$0.987543\pi$
$948$		0			0
$949$		−	341.360i		−	0.359705i
$950$	−172.748	−	19.5953i	−0.181840	−	0.0206266i
$951$		0			0
$952$	−1321.92	+	673.550i	−1.38857	+	0.707510i
$953$	794.568	−	125.847i	0.833754	−	0.132054i	0.275060	−	0.961427i	$-0.411302\pi$
$953$	794.568	−	125.847i	0.833754	−	0.132054i	0.558694	+	0.829374i	$0.311302\pi$
$954$		0			0
$955$	220.941	−	118.787i	0.231352	−	0.124384i
$956$	2522.26	−	1832.53i	2.63835	−	1.91688i
$957$		0			0
$958$	−73.8181	+	466.069i	−0.0770544	+	0.486502i
$959$	−893.080	+	290.179i	−0.931261	+	0.302585i
$960$		0			0
$961$	51.2046	−	157.592i	0.0532826	−	0.163987i
$962$	474.968	−	932.176i	0.493729	−	0.968998i
$963$		0			0
$964$	−2597.11	−	843.851i	−2.69409	−	0.875364i
$965$	286.341	+	198.536i	0.296726	+	0.205737i
$966$		0			0
$967$	193.991	+	30.7251i	0.200611	+	0.0317736i	0.255931	−	0.966695i	$-0.417618\pi$
$967$	193.991	+	30.7251i	0.200611	+	0.0317736i	−0.0553203	+	0.998469i	$0.517618\pi$
$968$	607.629	−	607.629i	0.627716	−	0.627716i
$969$		0			0
$970$	100.272	−	104.798i	0.103374	−	0.108039i
$971$	465.952	+	338.534i	0.479868	+	0.348645i	0.801275	−	0.598297i	$-0.204156\pi$
$971$	465.952	+	338.534i	0.479868	+	0.348645i	−0.321406	+	0.946941i	$0.604156\pi$
$972$		0			0
$973$	439.100	+	861.783i	0.451285	+	0.885697i
$974$			1108.21i			1.13780i
$975$		0			0
$976$	105.387			0.107978
$977$	478.563	−	243.840i	0.489829	−	0.249581i	−0.191588	−	0.981475i	$-0.561364\pi$
$977$	478.563	−	243.840i	0.489829	−	0.249581i	0.681418	+	0.731895i	$0.261364\pi$
$978$		0			0
$979$	769.907	−	1059.69i	0.786422	−	1.08242i
$980$	166.927	−	346.295i	0.170334	−	0.353362i
$981$		0			0
$982$	1479.96	+	1479.96i	1.50708	+	1.50708i
$983$	81.0532	−	511.749i	0.0824549	−	0.520600i	−0.911543	−	0.411204i	$-0.865108\pi$
$983$	81.0532	−	511.749i	0.0824549	−	0.520600i	0.993998	−	0.109396i	$-0.0348916\pi$
$984$		0			0
$985$	−1646.96	+	575.604i	−1.67204	+	0.584369i
$986$	1464.92	−	4508.55i	1.48572	−	4.57257i
$987$		0			0
$988$	−99.0484	−	50.4677i	−0.100251	−	0.0510807i
$989$	−209.976	−	68.2255i	−0.212312	−	0.0689843i
$990$		0			0
$991$	−372.803	−	1147.37i	−0.376189	−	1.15779i	−0.942673	−	0.333717i	$-0.891697\pi$
$991$	−372.803	−	1147.37i	−0.376189	−	1.15779i	0.566485	−	0.824072i	$-0.308303\pi$
$992$	−873.185	−	138.299i	−0.880226	−	0.139414i
$993$		0			0
$994$	1300.55	+	1790.05i	1.30840	+	1.80085i
$995$	−196.308	+	35.5487i	−0.197295	+	0.0357273i
$996$		0			0
$997$	24.0632	+	151.929i	0.0241356	+	0.152386i	0.996813	−	0.0797753i	$-0.0254203\pi$
$997$	24.0632	+	151.929i	0.0241356	+	0.152386i	−0.972677	+	0.232161i	$0.925420\pi$
$998$	−329.573	−	646.824i	−0.330234	−	0.648120i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.r.b.172.1		80
3.2	odd	2		75.3.k.a.22.10	✓	80
15.2	even	4		375.3.k.b.118.10		80
15.8	even	4		375.3.k.c.118.1		80
15.14	odd	2		375.3.k.a.7.1		80
25.8	odd	20	inner	225.3.r.b.208.1		80
75.8	even	20		75.3.k.a.58.10	yes	80
75.17	even	20		375.3.k.a.268.1		80
75.44	odd	10		375.3.k.b.232.10		80
75.56	odd	10		375.3.k.c.232.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.22.10	✓	80	3.2	odd	2
75.3.k.a.58.10	yes	80	75.8	even	20
225.3.r.b.172.1		80	1.1	even	1	trivial
225.3.r.b.208.1		80	25.8	odd	20	inner
375.3.k.a.7.1		80	15.14	odd	2
375.3.k.a.268.1		80	75.17	even	20
375.3.k.b.118.10		80	15.2	even	4
375.3.k.b.232.10		80	75.44	odd	10
375.3.k.c.118.1		80	15.8	even	4
375.3.k.c.232.1		80	75.56	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.93190 + 1.49388i) q^{2} +(4.01322 - 5.52372i) q^{4} +(0.890939 + 4.91998i) q^{5} +(4.34391 + 4.34391i) q^{7} +(-1.45557 + 9.19012i) q^{8} +O(q^{10})\)	\(q+(-2.93190 + 1.49388i) q^{2} +(4.01322 - 5.52372i) q^{4} +(0.890939 + 4.91998i) q^{5} +(4.34391 + 4.34391i) q^{7} +(-1.45557 + 9.19012i) q^{8} +(-9.96199 - 13.0939i) q^{10} +(4.51369 - 13.8917i) q^{11} +(6.86423 + 3.49750i) q^{13} +(-19.2252 - 6.24664i) q^{14} +(-1.02182 - 3.14483i) q^{16} +(25.6357 + 4.06030i) q^{17} +(-1.24222 - 1.70977i) q^{19} +(30.7522 + 14.8237i) q^{20} +(7.51883 + 47.4720i) q^{22} +(2.15443 + 4.22830i) q^{23} +(-23.4125 + 8.76681i) q^{25} -25.3501 q^{26} +(41.4277 - 6.56150i) q^{28} +(-32.6254 + 44.9050i) q^{29} +(27.1558 - 19.7298i) q^{31} +(-18.6237 - 18.6237i) q^{32} +(-81.2269 + 26.3922i) q^{34} +(-17.5018 + 25.2421i) q^{35} +(-18.7363 + 36.7721i) q^{37} +(6.19627 + 3.15716i) q^{38} +(-46.5120 + 1.02645i) q^{40} +(1.20677 + 3.71404i) q^{41} +(-32.8976 + 32.8976i) q^{43} +(-58.6196 - 80.6829i) q^{44} +(-12.6331 - 9.17851i) q^{46} +(12.8776 + 81.3060i) q^{47} -11.2608i q^{49} +(55.5464 - 60.6787i) q^{50} +(46.8669 - 23.8799i) q^{52} +(81.1884 - 12.8590i) q^{53} +(72.3684 + 9.83061i) q^{55} +(-46.2440 + 33.5982i) q^{56} +(28.5718 - 180.395i) q^{58} +(10.7101 - 3.47991i) q^{59} +(-9.84864 + 30.3110i) q^{61} +(-50.1440 + 98.4132i) q^{62} +(95.0038 + 30.8686i) q^{64} +(-11.0920 + 36.8880i) q^{65} +(-0.351533 - 0.0556774i) q^{67} +(125.310 - 125.310i) q^{68} +(13.6049 - 100.153i) q^{70} +(-88.5525 - 64.3371i) q^{71} +(-20.1163 - 39.4805i) q^{73} -135.802i q^{74} -14.4296 q^{76} +(79.9515 - 40.7373i) q^{77} +(33.1447 - 45.6197i) q^{79} +(14.5621 - 7.82918i) q^{80} +(-9.08644 - 9.08644i) q^{82} +(2.71085 - 17.1156i) q^{83} +(2.86327 + 129.745i) q^{85} +(47.3074 - 145.597i) q^{86} +(121.097 + 61.7018i) q^{88} +(85.2857 + 27.7110i) q^{89} +(14.6248 + 45.0105i) q^{91} +(32.0022 + 5.06865i) q^{92} +(-159.217 - 219.143i) q^{94} +(7.30531 - 7.63503i) q^{95} +(1.37908 + 8.70714i) q^{97} +(16.8223 + 33.0156i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8}+O(q^{10}) \) 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8	\( 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 4 q^{10} + 32 q^{13} + 80 q^{16} + 100 q^{17} - 100 q^{19} + 244 q^{20} - 100 q^{22} + 96 q^{23} - 16 q^{25} + 40 q^{26} + 196 q^{28} - 200 q^{29} - 636 q^{32} + 100 q^{34} - 260 q^{35} - 184 q^{37} + 564 q^{38} - 948 q^{40} - 160 q^{41} - 472 q^{43} + 700 q^{44} + 288 q^{47} - 16 q^{50} + 620 q^{52} - 304 q^{53} + 604 q^{55} + 1272 q^{58} - 800 q^{59} - 240 q^{61} - 1212 q^{62} + 100 q^{64} - 272 q^{65} - 80 q^{67} - 104 q^{68} - 260 q^{70} - 116 q^{73} + 88 q^{77} + 200 q^{79} + 164 q^{80} - 168 q^{82} + 1264 q^{83} - 212 q^{85} - 212 q^{88} + 1500 q^{89} + 1504 q^{92} - 200 q^{94} + 784 q^{95} - 260 q^{97} + 92 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 4 * q^10 + 32 * q^13 + 80 * q^16 + 100 * q^17 - 100 * q^19 + 244 * q^20 - 100 * q^22 + 96 * q^23 - 16 * q^25 + 40 * q^26 + 196 * q^28 - 200 * q^29 - 636 * q^32 + 100 * q^34 - 260 * q^35 - 184 * q^37 + 564 * q^38 - 948 * q^40 - 160 * q^41 - 472 * q^43 + 700 * q^44 + 288 * q^47 - 16 * q^50 + 620 * q^52 - 304 * q^53 + 604 * q^55 + 1272 * q^58 - 800 * q^59 - 240 * q^61 - 1212 * q^62 + 100 * q^64 - 272 * q^65 - 80 * q^67 - 104 * q^68 - 260 * q^70 - 116 * q^73 + 88 * q^77 + 200 * q^79 + 164 * q^80 - 168 * q^82 + 1264 * q^83 - 212 * q^85 - 212 * q^88 + 1500 * q^89 + 1504 * q^92 - 200 * q^94 + 784 * q^95 - 260 * q^97 + 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more