LMFDB - Embedded newform 740.4.i.b.581.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,4,Mod(121,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("740.121");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	740.i (of order $3$, degree $2$, 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:	$43.6614134042$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			581.1
Character	$\chi$	$=$	740.581
Dual form			740.4.i.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.92424 + 8.52903i) q^{3} +(2.50000 - 4.33013i) q^{5} +(-5.38226 + 9.32234i) q^{7} +(-34.9962 - 60.6152i) q^{9} +67.4205 q^{11} +(-29.1089 + 50.4181i) q^{13} +(24.6212 + 42.6451i) q^{15} +(63.9807 + 110.818i) q^{17} +(11.5331 - 19.9759i) q^{19} +(-53.0070 - 91.8108i) q^{21} -202.359 q^{23} +(-12.5000 - 21.6506i) q^{25} +423.410 q^{27} -0.613518 q^{29} -148.687 q^{31} +(-331.994 + 575.031i) q^{33} +(26.9113 + 46.6117i) q^{35} +(-102.776 + 200.225i) q^{37} +(-286.678 - 496.541i) q^{39} +(-154.475 + 267.558i) q^{41} +156.304 q^{43} -349.962 q^{45} -354.366 q^{47} +(113.563 + 196.696i) q^{49} -1260.23 q^{51} +(-5.25501 - 9.10195i) q^{53} +(168.551 - 291.939i) q^{55} +(113.583 + 196.732i) q^{57} +(69.7627 + 120.832i) q^{59} +(259.558 - 449.567i) q^{61} +753.435 q^{63} +(145.545 + 252.091i) q^{65} +(397.722 - 688.874i) q^{67} +(996.462 - 1725.92i) q^{69} +(228.250 - 395.340i) q^{71} -512.606 q^{73} +246.212 q^{75} +(-362.874 + 628.517i) q^{77} +(432.633 - 749.342i) q^{79} +(-1140.07 + 1974.66i) q^{81} +(334.459 + 579.300i) q^{83} +639.807 q^{85} +(3.02111 - 5.23271i) q^{87} +(33.2787 + 57.6404i) q^{89} +(-313.343 - 542.726i) q^{91} +(732.170 - 1268.16i) q^{93} +(-57.6654 - 99.8794i) q^{95} +79.4347 q^{97} +(-2359.46 - 4086.71i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{3} + 95 q^{5} - 32 q^{7} - 187 q^{9} - 2 q^{11} + 93 q^{13} + 30 q^{15} + 38 q^{17} - 91 q^{19} - 230 q^{21} - 306 q^{23} - 475 q^{25} + 552 q^{27} + 156 q^{29} - 144 q^{31} - 484 q^{33} + 160 q^{35}+ \cdots + 721 q^{99}+O(q^{100}) $ 38 * q - 6 * q^3 + 95 * q^5 - 32 * q^7 - 187 * q^9 - 2 * q^11 + 93 * q^13 + 30 * q^15 + 38 * q^17 - 91 * q^19 - 230 * q^21 - 306 * q^23 - 475 * q^25 + 552 * q^27 + 156 * q^29 - 144 * q^31 - 484 * q^33 + 160 * q^35 - 231 * q^37 - 590 * q^39 - 236 * q^41 + 228 * q^43 - 1870 * q^45 - 1082 * q^47 - 655 * q^49 - 1560 * q^51 + 2 * q^53 - 5 * q^55 + 598 * q^57 - 285 * q^59 + 1290 * q^61 + 2992 * q^63 - 465 * q^65 + 664 * q^67 - 240 * q^69 + 1614 * q^71 - 400 * q^73 + 300 * q^75 - 1334 * q^77 + 2236 * q^79 - 1759 * q^81 - 922 * q^83 + 380 * q^85 - 1968 * q^87 + 1107 * q^89 + 2456 * q^91 + 2986 * q^93 + 455 * q^95 - 5328 * q^97 + 721 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−4.92424	+	8.52903i	−0.947670	+	1.64141i	−0.197355	+	0.980332i	$0.563235\pi$
$3$	−4.92424	+	8.52903i	−0.947670	+	1.64141i	−0.750315	+	0.661080i	$0.770098\pi$
$4$		0			0
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$	−5.38226	+	9.32234i	−0.290615	+	0.503359i	−0.973955	−	0.226741i	$-0.927193\pi$
$7$	−5.38226	+	9.32234i	−0.290615	+	0.503359i	0.683341	+	0.730100i	$0.260526\pi$
$8$		0			0
$9$	−34.9962	−	60.6152i	−1.29616	−	2.24501i
$10$		0			0
$11$	67.4205			1.84800			0.924002	−	0.382389i	$-0.124898\pi$
$11$	67.4205			1.84800			0.924002	+	0.382389i	$0.124898\pi$
$12$		0			0
$13$	−29.1089	+	50.4181i	−0.621028	+	1.07565i	0.368267	+	0.929720i	$0.379951\pi$
$13$	−29.1089	+	50.4181i	−0.621028	+	1.07565i	−0.989295	+	0.145931i	$0.953382\pi$
$14$		0			0
$15$	24.6212	+	42.6451i	0.423811	+	0.734062i
$16$		0			0
$17$	63.9807	+	110.818i	0.912800	+	1.58102i	0.810090	+	0.586305i	$0.199418\pi$
$17$	63.9807	+	110.818i	0.912800	+	1.58102i	0.102710	+	0.994711i	$0.467249\pi$
$18$		0			0
$19$	11.5331	−	19.9759i	0.139256	−	0.241199i	−0.787959	−	0.615728i	$-0.788862\pi$
$19$	11.5331	−	19.9759i	0.139256	−	0.241199i	0.927215	+	0.374529i	$0.122195\pi$
$20$		0			0
$21$	−53.0070	−	91.8108i	−0.550813	−	0.954037i
$22$		0			0
$23$	−202.359			−1.83455			−0.917276	−	0.398253i	$-0.869617\pi$
$23$	−202.359			−1.83455			−0.917276	+	0.398253i	$0.869617\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$		0			0
$27$	423.410			3.01797
$28$		0			0
$29$	−0.613518			−0.00392853			−0.00196426	−	0.999998i	$-0.500625\pi$
$29$	−0.613518			−0.00392853			−0.00196426	+	0.999998i	$0.500625\pi$
$30$		0			0
$31$	−148.687			−0.861450			−0.430725	−	0.902483i	$-0.641742\pi$
$31$	−148.687			−0.861450			−0.430725	+	0.902483i	$0.641742\pi$
$32$		0			0
$33$	−331.994	+	575.031i	−1.75130	+	3.03334i
$34$		0			0
$35$	26.9113	+	46.6117i	0.129967	+	0.225109i
$36$		0			0
$37$	−102.776	+	200.225i	−0.456656	+	0.889644i
$37$	−102.776	+	200.225i	−0.456656	+	0.889644i
$38$		0			0
$39$	−286.678	−	496.541i	−1.17706	−	2.03872i
$40$		0			0
$41$	−154.475	+	267.558i	−0.588413	+	1.01916i	0.406027	+	0.913861i	$0.366914\pi$
$41$	−154.475	+	267.558i	−0.588413	+	1.01916i	−0.994440	+	0.105300i	$0.966420\pi$
$42$		0			0
$43$	156.304			0.554329			0.277165	−	0.960822i	$-0.410605\pi$
$43$	156.304			0.554329			0.277165	+	0.960822i	$0.410605\pi$
$44$		0			0
$45$	−349.962			−1.15932
$46$		0			0
$47$	−354.366			−1.09978			−0.549889	−	0.835238i	$-0.685330\pi$
$47$	−354.366			−1.09978			−0.549889	+	0.835238i	$0.685330\pi$
$48$		0			0
$49$	113.563	+	196.696i	0.331086	+	0.573458i
$50$		0			0
$51$	−1260.23			−3.46013
$52$		0			0
$53$	−5.25501	−	9.10195i	−0.0136195	−	0.0235896i	0.859135	−	0.511748i	$-0.171002\pi$
$53$	−5.25501	−	9.10195i	−0.0136195	−	0.0235896i	−0.872755	+	0.488159i	$0.837669\pi$
$54$		0			0
$55$	168.551	−	291.939i	0.413226	−	0.715729i
$56$		0			0
$57$	113.583	+	196.732i	0.263938	+	0.457154i
$58$		0			0
$59$	69.7627	+	120.832i	0.153938	+	0.266628i	0.932672	−	0.360726i	$-0.117471\pi$
$59$	69.7627	+	120.832i	0.153938	+	0.266628i	−0.778734	+	0.627354i	$0.784138\pi$
$60$		0			0
$61$	259.558	−	449.567i	0.544803	−	0.943626i	−0.453816	−	0.891095i	$-0.649938\pi$
$61$	259.558	−	449.567i	0.544803	−	0.943626i	0.998619	−	0.0525312i	$-0.0167289\pi$
$62$		0			0
$63$	753.435			1.50673
$64$		0			0
$65$	145.545	+	252.091i	0.277732	+	0.481046i
$66$		0			0
$67$	397.722	−	688.874i	0.725215	−	1.25611i	−0.233670	−	0.972316i	$-0.575074\pi$
$67$	397.722	−	688.874i	0.725215	−	1.25611i	0.958885	−	0.283794i	$-0.0915931\pi$
$68$		0			0
$69$	996.462	−	1725.92i	1.73855	−	3.01126i
$70$		0			0
$71$	228.250	−	395.340i	0.381525	−	0.660820i	−0.609756	−	0.792589i	$-0.708732\pi$
$71$	228.250	−	395.340i	0.381525	−	0.660820i	0.991280	+	0.131769i	$0.0420658\pi$
$72$		0			0
$73$	−512.606			−0.821863			−0.410931	−	0.911666i	$-0.634796\pi$
$73$	−512.606			−0.821863			−0.410931	+	0.911666i	$0.634796\pi$
$74$		0			0
$75$	246.212			0.379068
$76$		0			0
$77$	−362.874	+	628.517i	−0.537057	+	0.930209i
$78$		0			0
$79$	432.633	−	749.342i	0.616139	−	1.06718i	−0.374044	−	0.927411i	$-0.622029\pi$
$79$	432.633	−	749.342i	0.616139	−	1.06718i	0.990184	−	0.139773i	$-0.0446374\pi$
$80$		0			0
$81$	−1140.07	+	1974.66i	−1.56389	+	2.70873i
$82$		0			0
$83$	334.459	+	579.300i	0.442309	+	0.766102i	0.997860	−	0.0653804i	$-0.0208261\pi$
$83$	334.459	+	579.300i	0.442309	+	0.766102i	−0.555551	+	0.831482i	$0.687493\pi$
$84$		0			0
$85$	639.807			0.816434
$86$		0			0
$87$	3.02111	−	5.23271i	0.00372295	−	0.00644834i
$88$		0			0
$89$	33.2787	+	57.6404i	0.0396352	+	0.0686503i	0.885163	−	0.465282i	$-0.154047\pi$
$89$	33.2787	+	57.6404i	0.0396352	+	0.0686503i	−0.845527	+	0.533932i	$0.820714\pi$
$90$		0			0
$91$	−313.343	−	542.726i	−0.360959	−	0.625200i
$92$		0			0
$93$	732.170	−	1268.16i	0.816371	−	1.41400i
$94$		0			0
$95$	−57.6654	−	99.8794i	−0.0622773	−	0.107867i
$96$		0			0
$97$	79.4347			0.0831482			0.0415741	−	0.999135i	$-0.486763\pi$
$97$	79.4347			0.0831482			0.0415741	+	0.999135i	$0.486763\pi$
$98$		0			0
$99$	−2359.46	−	4086.71i	−2.39530	−	4.14878i
$100$		0			0
$101$	−322.547			−0.317768			−0.158884	−	0.987297i	$-0.550790\pi$
$101$	−322.547			−0.317768			−0.158884	+	0.987297i	$0.550790\pi$
$102$		0			0
$103$	−1923.60			−1.84017			−0.920087	−	0.391714i	$-0.871882\pi$
$103$	−1923.60			−1.84017			−0.920087	+	0.391714i	$0.871882\pi$
$104$		0			0
$105$	−530.070			−0.492662
$106$		0			0
$107$	−386.344	+	669.168i	−0.349059	+	0.604588i	−0.986083	−	0.166256i	$-0.946832\pi$
$107$	−386.344	+	669.168i	−0.349059	+	0.604588i	0.637023	+	0.770844i	$0.280165\pi$
$108$		0			0
$109$	388.809	+	673.437i	0.341662	+	0.591776i	0.984742	−	0.174023i	$-0.0556769\pi$
$109$	388.809	+	673.437i	0.341662	+	0.591776i	−0.643079	+	0.765799i	$0.722344\pi$
$110$		0			0
$111$	−1201.63	−	1862.53i	−1.02751	−	1.59265i
$112$		0			0
$113$	−730.243	−	1264.82i	−0.607925	−	1.05296i	−0.991582	−	0.129481i	$-0.958669\pi$
$113$	−730.243	−	1264.82i	−0.607925	−	1.05296i	0.383657	−	0.923476i	$-0.374664\pi$
$114$		0			0
$115$	−505.896	+	876.238i	−0.410218	+	0.710519i
$116$		0			0
$117$	4074.81			3.21980
$118$		0			0
$119$	−1377.44			−1.06109
$120$		0			0
$121$	3214.52			2.41512
$122$		0			0
$123$	−1521.34	−	2635.04i	−1.11524	−	1.93166i
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	232.893	+	403.382i	0.162724	+	0.281846i	0.935845	−	0.352413i	$-0.114639\pi$
$127$	232.893	+	403.382i	0.162724	+	0.281846i	−0.773121	+	0.634259i	$0.781305\pi$
$128$		0			0
$129$	−769.678	+	1333.12i	−0.525321	+	0.909883i
$130$		0			0
$131$	−422.732	−	732.194i	−0.281941	−	0.488337i	0.689922	−	0.723884i	$-0.257645\pi$
$131$	−422.732	−	732.194i	−0.281941	−	0.488337i	−0.971863	+	0.235548i	$0.924312\pi$
$132$		0			0
$133$	124.148	+	215.031i	0.0809398	+	0.140192i
$134$		0			0
$135$	1058.53	−	1833.42i	0.674839	−	1.16886i
$136$		0			0
$137$	−925.231			−0.576991			−0.288496	−	0.957481i	$-0.593155\pi$
$137$	−925.231			−0.576991			−0.288496	+	0.957481i	$0.593155\pi$
$138$		0			0
$139$	670.053	+	1160.57i	0.408872	+	0.708187i	0.994764	−	0.102202i	$-0.0325890\pi$
$139$	670.053	+	1160.57i	0.408872	+	0.708187i	−0.585892	+	0.810389i	$0.699256\pi$
$140$		0			0
$141$	1744.98	−	3022.39i	1.04223	−	1.80519i
$142$		0			0
$143$	−1962.54	+	3399.21i	−1.14766	+	1.98781i
$144$		0			0
$145$	−1.53379	+	2.65661i	−0.000878446	+	0.00152151i
$146$		0			0
$147$	−2236.84			−1.25504
$148$		0			0
$149$	−2620.87			−1.44101			−0.720504	−	0.693451i	$-0.756089\pi$
$149$	−2620.87			−1.44101			−0.720504	+	0.693451i	$0.756089\pi$
$150$		0			0
$151$	749.660	−	1298.45i	0.404017	−	0.699777i	−0.590190	−	0.807264i	$-0.700947\pi$
$151$	749.660	−	1298.45i	0.404017	−	0.699777i	0.994206	+	0.107487i	$0.0342805\pi$
$152$		0			0
$153$	4478.17	−	7756.41i	2.36626	−	4.09849i
$154$		0			0
$155$	−371.717	+	643.833i	−0.192626	+	0.333638i
$156$		0			0
$157$	−1135.64	−	1966.99i	−0.577288	−	0.999891i	−0.995789	−	0.0916753i	$-0.970778\pi$
$157$	−1135.64	−	1966.99i	−0.577288	−	0.999891i	0.418501	−	0.908216i	$-0.362556\pi$
$158$		0			0
$159$	103.508			0.0516270
$160$		0			0
$161$	1089.15	−	1886.46i	0.533147	−	0.923438i
$162$		0			0
$163$	−1880.18	−	3256.56i	−0.903478	−	1.56487i	−0.822947	−	0.568118i	$-0.807672\pi$
$163$	−1880.18	−	3256.56i	−0.903478	−	1.56487i	−0.0805312	−	0.996752i	$-0.525662\pi$
$164$		0			0
$165$	1659.97	+	2875.16i	0.783204	+	1.35655i
$166$		0			0
$167$	1498.22	−	2594.99i	0.694225	−	1.20243i	−0.276216	−	0.961096i	$-0.589081\pi$
$167$	1498.22	−	2594.99i	0.694225	−	1.20243i	0.970441	−	0.241337i	$-0.0775861\pi$
$168$		0			0
$169$	−596.157	−	1032.57i	−0.271350	−	0.469993i
$170$		0			0
$171$	−1614.46			−0.721992
$172$		0			0
$173$	1163.53	+	2015.30i	0.511340	+	0.885667i	0.999914	+	0.0131443i	$0.00418407\pi$
$173$	1163.53	+	2015.30i	0.511340	+	0.885667i	−0.488574	+	0.872523i	$0.662483\pi$
$174$		0			0
$175$	269.113			0.116246
$176$		0			0
$177$	−1374.11			−0.583528
$178$		0			0
$179$	−1128.45			−0.471197			−0.235599	−	0.971850i	$-0.575705\pi$
$179$	−1128.45			−0.471197			−0.235599	+	0.971850i	$0.575705\pi$
$180$		0			0
$181$	−831.265	+	1439.79i	−0.341367	+	0.591265i	−0.984687	−	0.174333i	$-0.944223\pi$
$181$	−831.265	+	1439.79i	−0.341367	+	0.591265i	0.643320	+	0.765598i	$0.277557\pi$
$182$		0			0
$183$	2556.25	+	4427.55i	1.03259	+	1.78849i
$184$		0			0
$185$	610.060	+	945.596i	0.242446	+	0.375792i
$186$		0			0
$187$	4313.61	+	7471.39i	1.68686	+	2.92172i
$188$		0			0
$189$	−2278.90	+	3947.17i	−0.877067	+	1.51912i
$190$		0			0
$191$	−378.648			−0.143445			−0.0717224	−	0.997425i	$-0.522850\pi$
$191$	−378.648			−0.143445			−0.0717224	+	0.997425i	$0.522850\pi$
$192$		0			0
$193$	−1612.63			−0.601449			−0.300724	−	0.953711i	$-0.597228\pi$
$193$	−1612.63			−0.601449			−0.300724	+	0.953711i	$0.597228\pi$
$194$		0			0
$195$	−2866.78			−1.05279
$196$		0			0
$197$	−2029.77	−	3515.67i	−0.734088	−	1.27148i	−0.955122	−	0.296212i	$-0.904276\pi$
$197$	−2029.77	−	3515.67i	−0.734088	−	1.27148i	0.221034	−	0.975266i	$-0.429057\pi$
$198$		0			0
$199$	−2038.30			−0.726087			−0.363044	−	0.931772i	$-0.618262\pi$
$199$	−2038.30			−0.726087			−0.363044	+	0.931772i	$0.618262\pi$
$200$		0			0
$201$	3916.95	+	6784.36i	1.37453	+	2.38075i
$202$		0			0
$203$	3.30211	−	5.71942i	0.00114169	−	0.00197746i
$204$		0			0
$205$	772.375	+	1337.79i	0.263146	+	0.455783i
$206$		0			0
$207$	7081.79	+	12266.0i	2.37787	+	4.11858i
$208$		0			0
$209$	777.566	−	1346.78i	0.257346	−	0.445737i
$210$		0			0
$211$	−5056.25			−1.64970			−0.824849	−	0.565353i	$-0.808740\pi$
$211$	−5056.25			−1.64970			−0.824849	+	0.565353i	$0.808740\pi$
$212$		0			0
$213$	2247.91	+	3893.50i	0.723119	+	1.25248i
$214$		0			0
$215$	390.760	−	676.817i	0.123952	−	0.214691i
$216$		0			0
$217$	800.271	−	1386.11i	0.250350	−	0.433619i
$218$		0			0
$219$	2524.19	−	4372.03i	0.778854	−	1.34902i
$220$		0			0
$221$	−7449.64			−2.26750
$222$		0			0
$223$	905.638			0.271955			0.135978	−	0.990712i	$-0.456582\pi$
$223$	905.638			0.271955			0.135978	+	0.990712i	$0.456582\pi$
$224$		0			0
$225$	−874.906	+	1515.38i	−0.259231	+	0.449002i
$226$		0			0
$227$	−1380.61	+	2391.29i	−0.403676	+	0.699188i	−0.994166	−	0.107857i	$-0.965601\pi$
$227$	−1380.61	+	2391.29i	−0.403676	+	0.699188i	0.590490	+	0.807045i	$0.298934\pi$
$228$		0			0
$229$	−38.4708	+	66.6334i	−0.0111014	+	0.0192282i	−0.871523	−	0.490355i	$-0.836867\pi$
$229$	−38.4708	+	66.6334i	−0.0111014	+	0.0192282i	0.860421	+	0.509583i	$0.170200\pi$
$230$		0			0
$231$	−3573.76	−	6189.93i	−1.01790	−	1.76306i
$232$		0			0
$233$	−899.413			−0.252886			−0.126443	−	0.991974i	$-0.540356\pi$
$233$	−899.413			−0.252886			−0.126443	+	0.991974i	$0.540356\pi$
$234$		0			0
$235$	−885.914	+	1534.45i	−0.245918	+	0.425942i
$236$		0			0
$237$	4260.77	+	7379.87i	1.16779	+	2.02268i
$238$		0			0
$239$	−846.801	−	1466.70i	−0.229184	−	0.396958i	0.728382	−	0.685171i	$-0.240272\pi$
$239$	−846.801	−	1466.70i	−0.229184	−	0.396958i	−0.957567	+	0.288212i	$0.906939\pi$
$240$		0			0
$241$	−1631.60	+	2826.01i	−0.436101	+	0.755349i	−0.997385	−	0.0722744i	$-0.976974\pi$
$241$	−1631.60	+	2826.01i	−0.436101	+	0.755349i	0.561284	+	0.827623i	$0.310308\pi$
$242$		0			0
$243$	−5511.95	−	9546.97i	−1.45511	−	2.52032i
$244$		0			0
$245$	1135.63			0.296133
$246$		0			0
$247$	671.431	+	1162.95i	0.172964	+	0.299582i
$248$		0			0
$249$	−6587.82			−1.67665
$250$		0			0
$251$	914.089			0.229868			0.114934	−	0.993373i	$-0.463334\pi$
$251$	914.089			0.229868			0.114934	+	0.993373i	$0.463334\pi$
$252$		0			0
$253$	−13643.1			−3.39026
$254$		0			0
$255$	−3150.56	+	5456.94i	−0.773709	+	1.34010i
$256$		0			0
$257$	495.075	+	857.495i	0.120163	+	0.208129i	0.919832	−	0.392313i	$-0.128325\pi$
$257$	495.075	+	857.495i	0.120163	+	0.208129i	−0.799669	+	0.600441i	$0.794992\pi$
$258$		0			0
$259$	−1313.40	−	2035.78i	−0.315099	−	0.488405i
$260$		0			0
$261$	21.4708	+	37.1885i	0.00509199	+	0.00881958i
$262$		0			0
$263$	4098.93	−	7099.55i	0.961030	−	1.66455i	0.241106	−	0.970499i	$-0.422490\pi$
$263$	4098.93	−	7099.55i	0.961030	−	1.66455i	0.719924	−	0.694053i	$-0.244177\pi$
$264$		0			0
$265$	−52.5501			−0.0121816
$266$		0			0
$267$	−655.489			−0.150245
$268$		0			0
$269$	1797.50			0.407418			0.203709	−	0.979032i	$-0.434700\pi$
$269$	1797.50			0.407418			0.203709	+	0.979032i	$0.434700\pi$
$270$		0			0
$271$	1459.51	+	2527.94i	0.327154	+	0.566647i	0.981946	−	0.189162i	$-0.0605772\pi$
$271$	1459.51	+	2527.94i	0.327154	+	0.566647i	−0.654792	+	0.755809i	$0.727244\pi$
$272$		0			0
$273$	6171.90			1.36828
$274$		0			0
$275$	−842.756	−	1459.70i	−0.184800	−	0.320084i
$276$		0			0
$277$	737.057	−	1276.62i	0.159875	−	0.276912i	−0.774948	−	0.632025i	$-0.782224\pi$
$277$	737.057	−	1276.62i	0.159875	−	0.276912i	0.934824	+	0.355113i	$0.115557\pi$
$278$		0			0
$279$	5203.48	+	9012.69i	1.11657	+	1.93396i
$280$		0			0
$281$	2906.08	+	5033.47i	0.616947	+	1.06858i	0.990040	+	0.140789i	$0.0449639\pi$
$281$	2906.08	+	5033.47i	0.616947	+	1.06858i	−0.373093	+	0.927794i	$0.621703\pi$
$282$		0			0
$283$	−1691.39	+	2929.58i	−0.355275	+	0.615355i	−0.987165	−	0.159704i	$-0.948946\pi$
$283$	−1691.39	+	2929.58i	−0.355275	+	0.615355i	0.631890	+	0.775058i	$0.282279\pi$
$284$		0			0
$285$	1135.83			0.236073
$286$		0			0
$287$	−1662.85	−	2880.14i	−0.342003	−	0.592366i
$288$		0			0
$289$	−5730.57	+	9925.64i	−1.16641	+	2.02028i
$290$		0			0
$291$	−391.155	+	677.501i	−0.0787970	+	0.136480i
$292$		0			0
$293$	−137.804	+	238.684i	−0.0274765	+	0.0475907i	−0.879437	−	0.476016i	$-0.842080\pi$
$293$	−137.804	+	238.684i	−0.0274765	+	0.0475907i	0.851960	+	0.523607i	$0.175414\pi$
$294$		0			0
$295$	697.627			0.137686
$296$		0			0
$297$	28546.5			5.57723
$298$		0			0
$299$	5890.44	−	10202.5i	1.13931	−	1.97334i
$300$		0			0
$301$	−841.269	+	1457.12i	−0.161096	+	0.279027i
$302$		0			0
$303$	1588.30	−	2751.01i	0.301139	−	0.521589i
$304$		0			0
$305$	−1297.79	−	2247.84i	−0.243643	−	0.422003i
$306$		0			0
$307$	6828.61			1.26948			0.634739	−	0.772727i	$-0.281108\pi$
$307$	6828.61			1.26948			0.634739	+	0.772727i	$0.281108\pi$
$308$		0			0
$309$	9472.26	−	16406.4i	1.74388	−	3.02049i
$310$		0			0
$311$	3855.52	+	6677.96i	0.702979	+	1.21760i	0.967416	+	0.253192i	$0.0814805\pi$
$311$	3855.52	+	6677.96i	0.702979	+	1.21760i	−0.264437	+	0.964403i	$0.585186\pi$
$312$		0			0
$313$	2107.31	+	3649.96i	0.380550	+	0.659132i	0.991141	−	0.132814i	$-0.0424014\pi$
$313$	2107.31	+	3649.96i	0.380550	+	0.659132i	−0.610591	+	0.791946i	$0.709068\pi$
$314$		0			0
$315$	1883.59	−	3262.47i	0.336915	−	0.583553i
$316$		0			0
$317$	90.5951	+	156.915i	0.0160515	+	0.0278020i	0.873940	−	0.486035i	$-0.161557\pi$
$317$	90.5951	+	156.915i	0.0160515	+	0.0278020i	−0.857888	+	0.513837i	$0.828224\pi$
$318$		0			0
$319$	−41.3636			−0.00725993
$320$		0			0
$321$	−3804.90	−	6590.28i	−0.661586	−	1.14590i
$322$		0			0
$323$	2951.58			0.508453
$324$		0			0
$325$	1455.45			0.248411
$326$		0			0
$327$	−7658.35			−1.29513
$328$		0			0
$329$	1907.29	−	3303.52i	0.319611	−	0.553583i
$330$		0			0
$331$	−2584.62	−	4476.69i	−0.429195	−	0.743387i	0.567607	−	0.823299i	$-0.307869\pi$
$331$	−2584.62	−	4476.69i	−0.429195	−	0.743387i	−0.996802	+	0.0799126i	$0.974536\pi$
$332$		0			0
$333$	15733.5	−	777.336i	2.58915	−	0.127921i
$334$		0			0
$335$	−1988.61	−	3444.37i	−0.324326	−	0.561749i
$336$		0			0
$337$	−3188.32	+	5522.33i	−0.515367	+	0.892642i	0.484474	+	0.874806i	$0.339011\pi$
$337$	−3188.32	+	5522.33i	−0.515367	+	0.892642i	−0.999841	+	0.0178363i	$0.994322\pi$
$338$		0			0
$339$	14383.6			2.30445
$340$		0			0
$341$	−10024.5			−1.59196
$342$		0			0
$343$	−6137.12			−0.966103
$344$		0			0
$345$	−4982.31	−	8629.61i	−0.777503	−	1.34667i
$346$		0			0
$347$	11494.3			1.77823			0.889115	−	0.457683i	$-0.151321\pi$
$347$	11494.3			1.77823			0.889115	+	0.457683i	$0.151321\pi$
$348$		0			0
$349$	−1105.40	−	1914.60i	−0.169543	−	0.293657i	0.768716	−	0.639590i	$-0.220896\pi$
$349$	−1105.40	−	1914.60i	−0.169543	−	0.293657i	−0.938259	+	0.345933i	$0.887563\pi$
$350$		0			0
$351$	−12325.0	+	21347.5i	−1.87424	+	3.24629i
$352$		0			0
$353$	3318.06	+	5747.04i	0.500290	+	0.866528i	1.00000		0.000334787i	$0.000106566\pi$
$353$	3318.06	+	5747.04i	0.500290	+	0.866528i	−0.499710	+	0.866193i	$0.666560\pi$
$354$		0			0
$355$	−1141.25	−	1976.70i	−0.170623	−	0.295528i
$356$		0			0
$357$	6782.86	−	11748.3i	1.00557	−	1.74169i
$358$		0			0
$359$	−412.749			−0.0606799			−0.0303399	−	0.999540i	$-0.509659\pi$
$359$	−412.749			−0.0606799			−0.0303399	+	0.999540i	$0.509659\pi$
$360$		0			0
$361$	3163.48	+	5479.30i	0.461215	+	0.798848i
$362$		0			0
$363$	−15829.1	+	27416.7i	−2.28873	+	3.96420i
$364$		0			0
$365$	−1281.51	+	2219.65i	−0.183774	+	0.318306i
$366$		0			0
$367$	2708.28	−	4690.88i	0.385208	−	0.667199i	−0.606590	−	0.795015i	$-0.707463\pi$
$367$	2708.28	−	4690.88i	0.385208	−	0.667199i	0.991798	+	0.127815i	$0.0407964\pi$
$368$		0			0
$369$	21624.2			3.05070
$370$		0			0
$371$	113.135			0.0158321
$372$		0			0
$373$	3109.83	−	5386.38i	0.431692	−	0.747712i	−0.565328	−	0.824866i	$-0.691250\pi$
$373$	3109.83	−	5386.38i	0.431692	−	0.747712i	0.997019	+	0.0771548i	$0.0245836\pi$
$374$		0			0
$375$	615.530	−	1066.13i	0.0847622	−	0.146812i
$376$		0			0
$377$	17.8588	−	30.9324i	0.00243972	−	0.00422573i
$378$		0			0
$379$	4129.13	+	7151.86i	0.559628	+	0.969305i	0.997527	+	0.0702804i	$0.0223894\pi$
$379$	4129.13	+	7151.86i	0.559628	+	0.969305i	−0.437899	+	0.899024i	$0.644277\pi$
$380$		0			0
$381$	−4587.28			−0.616833
$382$		0			0
$383$	441.220	−	764.215i	0.0588650	−	0.101957i	−0.835091	−	0.550112i	$-0.814585\pi$
$383$	441.220	−	764.215i	0.0588650	−	0.101957i	0.893956	+	0.448154i	$0.147919\pi$
$384$		0			0
$385$	1814.37	+	3142.58i	0.240179	+	0.416002i
$386$		0			0
$387$	−5470.05	−	9474.41i	−0.718497	−	1.24447i
$388$		0			0
$389$	−5228.41	+	9055.88i	−0.681468	+	1.18034i	0.293065	+	0.956093i	$0.405325\pi$
$389$	−5228.41	+	9055.88i	−0.681468	+	1.18034i	−0.974533	+	0.224245i	$0.928008\pi$
$390$		0			0
$391$	−12947.0	−	22424.9i	−1.67458	−	2.90046i
$392$		0			0
$393$	8326.54			1.06875
$394$		0			0
$395$	−2163.16	−	3746.71i	−0.275546	−	0.477259i
$396$		0			0
$397$	−10716.4			−1.35476			−0.677378	−	0.735635i	$-0.736884\pi$
$397$	−10716.4			−1.35476			−0.677378	+	0.735635i	$0.736884\pi$
$398$		0			0
$399$	−2445.34			−0.306817
$400$		0			0
$401$	−3285.37			−0.409136			−0.204568	−	0.978852i	$-0.565579\pi$
$401$	−3285.37			−0.409136			−0.204568	+	0.978852i	$0.565579\pi$
$402$		0			0
$403$	4328.11	−	7496.51i	0.534984	−	0.926620i
$404$		0			0
$405$	5700.37	+	9873.32i	0.699391	+	1.21138i
$406$		0			0
$407$	−6929.20	+	13499.3i	−0.843901	+	1.64406i
$408$		0			0
$409$	−4156.86	−	7199.90i	−0.502552	−	0.870445i	−0.999996	−	0.00294885i	$-0.999061\pi$
$409$	−4156.86	−	7199.90i	−0.502552	−	0.870445i	0.497444	−	0.867496i	$-0.334272\pi$
$410$		0			0
$411$	4556.06	−	7891.32i	0.546797	−	0.947081i
$412$		0			0
$413$	−1501.92			−0.178946
$414$		0			0
$415$	3344.59			0.395613
$416$		0			0
$417$	−13198.0			−1.54990
$418$		0			0
$419$	−5990.09	−	10375.1i	−0.698413	−	1.20969i	−0.969016	−	0.246996i	$-0.920556\pi$
$419$	−5990.09	−	10375.1i	−0.698413	−	1.20969i	0.270603	−	0.962691i	$-0.412777\pi$
$420$		0			0
$421$	3956.63			0.458039			0.229019	−	0.973422i	$-0.426448\pi$
$421$	3956.63			0.458039			0.229019	+	0.973422i	$0.426448\pi$
$422$		0			0
$423$	12401.5	+	21480.0i	1.42548	+	2.46901i
$424$		0			0
$425$	1599.52	−	2770.45i	0.182560	−	0.316203i
$426$		0			0
$427$	2794.01	+	4839.37i	0.316655	+	0.548463i
$428$		0			0
$429$	−19328.0	−	33477.1i	−2.17521	−	3.76757i
$430$		0			0
$431$	−3889.78	+	6737.30i	−0.434720	+	0.752956i	−0.997273	−	0.0738047i	$-0.976486\pi$
$431$	−3889.78	+	6737.30i	−0.434720	+	0.752956i	0.562553	+	0.826761i	$0.309819\pi$
$432$		0			0
$433$	−12952.6			−1.43755			−0.718777	−	0.695240i	$-0.755298\pi$
$433$	−12952.6			−1.43755			−0.718777	+	0.695240i	$0.755298\pi$
$434$		0			0
$435$	−15.1055	−	26.1635i	−0.00166495	−	0.00288378i
$436$		0			0
$437$	−2333.82	+	4042.29i	−0.255473	+	0.442492i
$438$		0			0
$439$	−6574.50	+	11387.4i	−0.714770	+	1.23802i	0.248279	+	0.968689i	$0.420135\pi$
$439$	−6574.50	+	11387.4i	−0.714770	+	1.23802i	−0.963048	+	0.269329i	$0.913198\pi$
$440$		0			0
$441$	7948.53	−	13767.3i	0.858279	−	1.48658i
$442$		0			0
$443$	−11968.0			−1.28356			−0.641778	−	0.766890i	$-0.721803\pi$
$443$	−11968.0			−1.28356			−0.641778	+	0.766890i	$0.721803\pi$
$444$		0			0
$445$	332.787			0.0354508
$446$		0			0
$447$	12905.8	−	22353.5i	1.36560	−	2.36529i
$448$		0			0
$449$	−571.111	+	989.194i	−0.0600276	+	0.103971i	−0.894478	−	0.447113i	$-0.852452\pi$
$449$	−571.111	+	989.194i	−0.0600276	+	0.103971i	0.834450	+	0.551084i	$0.185786\pi$
$450$		0			0
$451$	−10414.8	+	18038.9i	−1.08739	+	1.88341i
$452$		0			0
$453$	7383.01	+	12787.8i	0.765749	+	1.32632i
$454$		0			0
$455$	−3133.43			−0.322852
$456$		0			0
$457$	4751.96	−	8230.64i	0.486406	−	0.842479i	−0.513472	−	0.858106i	$-0.671641\pi$
$457$	4751.96	−	8230.64i	0.486406	−	0.842479i	0.999878	+	0.0156269i	$0.00497439\pi$
$458$		0			0
$459$	27090.1	+	46921.4i	2.75481	+	4.77147i
$460$		0			0
$461$	2315.33	+	4010.27i	0.233917	+	0.405156i	0.958957	−	0.283551i	$-0.0915124\pi$
$461$	2315.33	+	4010.27i	0.233917	+	0.405156i	−0.725041	+	0.688706i	$0.758179\pi$
$462$		0			0
$463$	3868.46	−	6700.37i	0.388299	−	0.672554i	−0.603922	−	0.797044i	$-0.706396\pi$
$463$	3868.46	−	6700.37i	0.388299	−	0.672554i	0.992221	+	0.124490i	$0.0397294\pi$
$464$		0			0
$465$	−3660.85	−	6340.78i	−0.365092	−	0.632358i
$466$		0			0
$467$	−18732.3			−1.85616			−0.928082	−	0.372376i	$-0.878543\pi$
$467$	−18732.3			−1.85616			−0.928082	+	0.372376i	$0.878543\pi$
$468$		0			0
$469$	4281.28	+	7415.39i	0.421516	+	0.730087i
$470$		0			0
$471$	22368.7			2.18831
$472$		0			0
$473$	10538.1			1.02440
$474$		0			0
$475$	−576.654			−0.0557025
$476$		0			0
$477$	−367.811	+	637.068i	−0.0353059	+	0.0611516i
$478$		0			0
$479$	−424.222	−	734.775i	−0.0404660	−	0.0700892i	0.845083	−	0.534635i	$-0.179551\pi$
$479$	−424.222	−	734.775i	−0.0404660	−	0.0700892i	−0.885549	+	0.464546i	$0.846218\pi$
$480$		0			0
$481$	−7103.28	−	11010.1i	−0.673350	−	1.04370i
$482$		0			0
$483$	10726.4	+	18578.7i	1.01050	+	1.75023i
$484$		0			0
$485$	198.587	−	343.962i	0.0185925	−	0.0322031i
$486$		0			0
$487$	1260.91			0.117325			0.0586625	−	0.998278i	$-0.481316\pi$
$487$	1260.91			0.117325			0.0586625	+	0.998278i	$0.481316\pi$
$488$		0			0
$489$	37033.8			3.42480
$490$		0			0
$491$	−6703.08			−0.616101			−0.308051	−	0.951370i	$-0.599677\pi$
$491$	−6703.08			−0.616101			−0.308051	+	0.951370i	$0.599677\pi$
$492$		0			0
$493$	−39.2533	−	67.9887i	−0.00358596	−	0.00621107i
$494$		0			0
$495$	−23594.6			−2.14242
$496$		0			0
$497$	2457.00	+	4255.64i	0.221753	+	0.384088i
$498$		0			0
$499$	−9045.86	+	15667.9i	−0.811520	+	1.40559i	0.100281	+	0.994959i	$0.468026\pi$
$499$	−9045.86	+	15667.9i	−0.811520	+	1.40559i	−0.911800	+	0.410634i	$0.865307\pi$
$500$		0			0
$501$	14755.2	+	25556.7i	1.31579	+	2.27902i
$502$		0			0
$503$	−5424.01	−	9394.67i	−0.480805	−	0.832778i	0.518953	−	0.854803i	$-0.326322\pi$
$503$	−5424.01	−	9394.67i	−0.480805	−	0.832778i	−0.999757	+	0.0220247i	$0.992989\pi$
$504$		0			0
$505$	−806.366	+	1396.67i	−0.0710551	+	0.123071i
$506$		0			0
$507$	11742.5			1.02860
$508$		0			0
$509$	9047.57	+	15670.9i	0.787871	+	1.36463i	0.927269	+	0.374397i	$0.122150\pi$
$509$	9047.57	+	15670.9i	0.787871	+	1.36463i	−0.139397	+	0.990237i	$0.544516\pi$
$510$		0			0
$511$	2758.98	−	4778.69i	0.238845	−	0.413692i
$512$		0			0
$513$	4883.22	−	8457.99i	0.420272	−	0.727932i
$514$		0			0
$515$	−4809.00	+	8329.43i	−0.411476	+	0.712696i
$516$		0			0
$517$	−23891.5			−2.03239
$518$		0			0
$519$	−22918.1			−1.93833
$520$		0			0
$521$	2652.28	−	4593.88i	0.223030	−	0.386299i	−0.732697	−	0.680555i	$-0.761739\pi$
$521$	2652.28	−	4593.88i	0.223030	−	0.386299i	0.955727	+	0.294256i	$0.0950719\pi$
$522$		0			0
$523$	−9050.72	+	15676.3i	−0.756712	+	1.31066i	0.187807	+	0.982206i	$0.439862\pi$
$523$	−9050.72	+	15676.3i	−0.756712	+	1.31066i	−0.944519	+	0.328457i	$0.893471\pi$
$524$		0			0
$525$	−1325.18	+	2295.27i	−0.110163	+	0.190807i
$526$		0			0
$527$	−9513.10	−	16477.2i	−0.786332	−	1.36197i
$528$		0			0
$529$	28782.0			2.36558
$530$		0			0
$531$	4882.86	−	8457.36i	0.399055	−	0.691183i
$532$		0			0
$533$	−8993.19	−	15576.7i	−0.730841	−	1.26585i
$534$		0			0
$535$	1931.72	+	3345.84i	0.156104	+	0.270380i
$536$		0			0
$537$	5556.75	−	9624.58i	0.446539	−	0.773429i
$538$		0			0
$539$	7656.44	+	13261.4i	0.611849	+	1.05975i
$540$		0			0
$541$	2424.15			0.192648			0.0963239	−	0.995350i	$-0.469292\pi$
$541$	2424.15			0.192648			0.0963239	+	0.995350i	$0.469292\pi$
$542$		0			0
$543$	−8186.69	−	14179.8i	−0.647006	−	1.12065i
$544$		0			0
$545$	3888.09			0.305592
$546$		0			0
$547$	18982.7			1.48381			0.741903	−	0.670507i	$-0.233923\pi$
$547$	18982.7			1.48381			0.741903	+	0.670507i	$0.233923\pi$
$548$		0			0
$549$	−36334.2			−2.82460
$550$		0			0
$551$	−7.07575	+	12.2556i	−0.000547073	+	0.000947558i
$552$		0			0
$553$	4657.08	+	8066.30i	0.358118	+	0.620279i
$554$		0			0
$555$	−11069.1	+	546.886i	−0.846589	+	0.0418271i
$556$		0			0
$557$	−9360.81	−	16213.4i	−0.712083	−	1.23336i	−0.964074	−	0.265634i	$-0.914419\pi$
$557$	−9360.81	−	16213.4i	−0.712083	−	1.23336i	0.251991	−	0.967730i	$-0.418915\pi$
$558$		0			0
$559$	−4549.84	+	7880.56i	−0.344254	+	0.596265i
$560$		0			0
$561$	−84965.0			−6.39434
$562$		0			0
$563$	4856.49			0.363546			0.181773	−	0.983341i	$-0.441816\pi$
$563$	4856.49			0.363546			0.181773	+	0.983341i	$0.441816\pi$
$564$		0			0
$565$	−7302.43			−0.543744
$566$		0			0
$567$	−12272.3	−	21256.3i	−0.908976	−	1.57439i
$568$		0			0
$569$	14381.9			1.05962			0.529809	−	0.848117i	$-0.322264\pi$
$569$	14381.9			1.05962			0.529809	+	0.848117i	$0.322264\pi$
$570$		0			0
$571$	7299.86	+	12643.7i	0.535008	+	0.926661i	0.999163	+	0.0409072i	$0.0130248\pi$
$571$	7299.86	+	12643.7i	0.535008	+	0.926661i	−0.464155	+	0.885754i	$0.653642\pi$
$572$		0			0
$573$	1864.55	−	3229.50i	0.135938	−	0.235452i
$574$		0			0
$575$	2529.48	+	4381.19i	0.183455	+	0.317754i
$576$		0			0
$577$	−2101.39	−	3639.72i	−0.151616	−	0.262606i	0.780206	−	0.625523i	$-0.215114\pi$
$577$	−2101.39	−	3639.72i	−0.151616	−	0.262606i	−0.931822	+	0.362917i	$0.881781\pi$
$578$		0			0
$579$	7940.97	−	13754.2i	0.569975	−	0.987226i
$580$		0			0
$581$	−7200.58			−0.514166
$582$		0			0
$583$	−354.296	−	613.658i	−0.0251688	−	0.0435937i
$584$		0			0
$585$	10187.0	−	17644.4i	0.719968	−	1.24702i
$586$		0			0
$587$	12504.3	−	21658.1i	0.879231	−	1.52287i	0.0270442	−	0.999634i	$-0.491391\pi$
$587$	12504.3	−	21658.1i	0.879231	−	1.52287i	0.852187	−	0.523238i	$-0.175276\pi$
$588$		0			0
$589$	−1714.82	+	2970.15i	−0.119962	+	0.207781i
$590$		0			0
$591$	39980.4			2.78269
$592$		0			0
$593$	24087.5			1.66805			0.834027	−	0.551724i	$-0.186030\pi$
$593$	24087.5			1.66805			0.834027	+	0.551724i	$0.186030\pi$
$594$		0			0
$595$	−3443.61	+	5964.50i	−0.237267	+	0.410959i
$596$		0			0
$597$	10037.1	−	17384.7i	0.688091	−	1.19181i
$598$		0			0
$599$	−3790.02	+	6564.50i	−0.258524	+	0.447777i	−0.965847	−	0.259114i	$-0.916569\pi$
$599$	−3790.02	+	6564.50i	−0.258524	+	0.447777i	0.707323	+	0.706891i	$0.249903\pi$
$600$		0			0
$601$	−1910.75	−	3309.52i	−0.129686	−	0.224622i	0.793869	−	0.608089i	$-0.208064\pi$
$601$	−1910.75	−	3309.52i	−0.129686	−	0.224622i	−0.923555	+	0.383466i	$0.874730\pi$
$602$		0			0
$603$	−55675.0			−3.75997
$604$		0			0
$605$	8036.30	−	13919.3i	0.540036	−	0.935370i
$606$		0			0
$607$	−2189.84	−	3792.92i	−0.146430	−	0.253624i	0.783476	−	0.621423i	$-0.213445\pi$
$607$	−2189.84	−	3792.92i	−0.146430	−	0.253624i	−0.929906	+	0.367798i	$0.880112\pi$
$608$		0			0
$609$	32.5207	+	56.3276i	0.00216389	+	0.00374796i
$610$		0			0
$611$	10315.2	−	17866.4i	0.682992	−	1.18298i
$612$		0			0
$613$	7921.40	+	13720.3i	0.521929	+	0.904007i	0.999675	+	0.0255091i	$0.00812069\pi$
$613$	7921.40	+	13720.3i	0.521929	+	0.904007i	−0.477746	+	0.878498i	$0.658546\pi$
$614$		0			0
$615$	−15213.4			−0.997503
$616$		0			0
$617$	13143.4	+	22765.0i	0.857589	+	1.48539i	0.874222	+	0.485527i	$0.161372\pi$
$617$	13143.4	+	22765.0i	0.857589	+	1.48539i	−0.0166325	+	0.999862i	$0.505295\pi$
$618$		0			0
$619$	8009.58			0.520084			0.260042	−	0.965597i	$-0.416264\pi$
$619$	8009.58			0.520084			0.260042	+	0.965597i	$0.416264\pi$
$620$		0			0
$621$	−85680.6			−5.53663
$622$		0			0
$623$	−716.458			−0.0460743
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	7657.84	+	13263.8i	0.487758	+	0.844822i
$628$		0			0
$629$	−28764.2	+	1421.14i	−1.82338	+	0.0900868i
$630$		0			0
$631$	−11010.7	−	19071.1i	−0.694659	−	1.20319i	−0.970295	−	0.241923i	$-0.922222\pi$
$631$	−11010.7	−	19071.1i	−0.694659	−	1.20319i	0.275636	−	0.961262i	$-0.411112\pi$
$632$		0			0
$633$	24898.2	−	43124.9i	1.56337	−	2.70783i
$634$		0			0
$635$	2328.93			0.145544
$636$		0			0
$637$	−13222.7			−0.822455
$638$		0			0
$639$	−31951.5			−1.97806
$640$		0			0
$641$	1441.33	+	2496.46i	0.0888129	+	0.153829i	0.907010	−	0.421110i	$-0.138359\pi$
$641$	1441.33	+	2496.46i	0.0888129	+	0.153829i	−0.818197	+	0.574938i	$0.805026\pi$
$642$		0			0
$643$	−2401.72			−0.147301			−0.0736506	−	0.997284i	$-0.523465\pi$
$643$	−2401.72			−0.147301			−0.0736506	+	0.997284i	$0.523465\pi$
$644$		0			0
$645$	3848.39	+	6665.61i	0.234931	+	0.406912i
$646$		0			0
$647$	−1213.51	+	2101.86i	−0.0737372	+	0.127717i	−0.900536	−	0.434781i	$-0.856826\pi$
$647$	−1213.51	+	2101.86i	−0.0737372	+	0.127717i	0.826799	+	0.562497i	$0.190159\pi$
$648$		0			0
$649$	4703.43	+	8146.58i	0.284477	+	0.492729i
$650$		0			0
$651$	7881.45	+	13651.1i	0.474498	+	0.821855i
$652$		0			0
$653$	170.789	−	295.816i	0.0102351	−	0.0177277i	−0.860863	−	0.508838i	$-0.830075\pi$
$653$	170.789	−	295.816i	0.0102351	−	0.0177277i	0.871098	+	0.491110i	$0.163409\pi$
$654$		0			0
$655$	−4227.32			−0.252176
$656$		0			0
$657$	17939.3	+	31071.7i	1.06526	+	1.84509i
$658$		0			0
$659$	−9747.41	+	16883.0i	−0.576184	+	0.997979i	0.419728	+	0.907650i	$0.362125\pi$
$659$	−9747.41	+	16883.0i	−0.576184	+	0.997979i	−0.995912	+	0.0903295i	$0.971208\pi$
$660$		0			0
$661$	−8947.14	+	15496.9i	−0.526480	+	0.911890i	0.473044	+	0.881039i	$0.343155\pi$
$661$	−8947.14	+	15496.9i	−0.526480	+	0.911890i	−0.999524	+	0.0308514i	$0.990178\pi$
$662$		0			0
$663$	36683.8	−	63538.2i	2.14884	−	3.72190i
$664$		0			0
$665$	1241.48			0.0723948
$666$		0			0
$667$	124.151			0.00720709
$668$		0			0
$669$	−4459.57	+	7724.21i	−0.257724	+	0.446390i
$670$		0			0
$671$	17499.5	−	30310.0i	1.00680	−	1.74382i
$672$		0			0
$673$	−2131.91	+	3692.58i	−0.122109	+	0.211498i	−0.920599	−	0.390509i	$-0.872299\pi$
$673$	−2131.91	+	3692.58i	−0.122109	+	0.211498i	0.798490	+	0.602008i	$0.205632\pi$
$674$		0			0
$675$	−5292.63	−	9167.10i	−0.301797	−	0.522728i
$676$		0			0
$677$	33724.5			1.91453			0.957264	−	0.289214i	$-0.0933941\pi$
$677$	33724.5			1.91453			0.957264	+	0.289214i	$0.0933941\pi$
$678$		0			0
$679$	−427.538	+	740.518i	−0.0241641	+	0.0418534i
$680$		0			0
$681$	−13596.9	−	23550.6i	−0.765104	−	1.32520i
$682$		0			0
$683$	−13189.1	−	22844.2i	−0.738896	−	1.27981i	−0.952993	−	0.302993i	$-0.902014\pi$
$683$	−13189.1	−	22844.2i	−0.738896	−	1.27981i	0.214097	−	0.976812i	$-0.431319\pi$
$684$		0			0
$685$	−2313.08	+	4006.37i	−0.129019	+	0.223468i
$686$		0			0
$687$	−378.879	−	656.237i	−0.0210409	−	0.0364440i
$688$		0			0
$689$	611.871			0.0338323
$690$		0			0
$691$	12218.0	+	21162.3i	0.672643	+	1.16505i	0.977152	+	0.212543i	$0.0681745\pi$
$691$	12218.0	+	21162.3i	0.672643	+	1.16505i	−0.304509	+	0.952510i	$0.598492\pi$
$692$		0			0
$693$	50796.9			2.78444
$694$		0			0
$695$	6700.53			0.365706
$696$		0			0
$697$	−39533.7			−2.14841
$698$		0			0
$699$	4428.92	−	7671.12i	0.239653	−	0.415091i
$700$		0			0
$701$	5134.76	+	8893.66i	0.276658	+	0.479185i	0.970552	−	0.240892i	$-0.0774399\pi$
$701$	5134.76	+	8893.66i	0.276658	+	0.479185i	−0.693894	+	0.720077i	$0.744107\pi$
$702$		0			0
$703$	2814.35	+	4362.25i	0.150989	+	0.234033i
$704$		0			0
$705$	−8724.90	−	15112.0i	−0.466098	−	0.807305i
$706$		0			0
$707$	1736.03	−	3006.89i	0.0923481	−	0.159952i
$708$		0			0
$709$	25802.7			1.36677			0.683385	−	0.730058i	$-0.260507\pi$
$709$	25802.7			1.36677			0.683385	+	0.730058i	$0.260507\pi$
$710$		0			0
$711$	−60562.1			−3.19445
$712$		0			0
$713$	30088.1			1.58037
$714$		0			0
$715$	9812.68	+	16996.1i	0.513250	+	0.888974i
$716$		0			0
$717$	16679.4			0.868763
$718$		0			0
$719$	392.354	+	679.578i	0.0203510	+	0.0352489i	0.876022	−	0.482272i	$-0.160188\pi$
$719$	392.354	+	679.578i	0.0203510	+	0.0352489i	−0.855671	+	0.517521i	$0.826855\pi$
$720$		0			0
$721$	10353.3	−	17932.5i	0.534781	−	0.926269i
$722$		0			0
$723$	−16068.7	−	27831.9i	−0.826560	−	1.43164i
$724$		0			0
$725$	7.66897	+	13.2830i	0.000392853	+	0.000680441i
$726$		0			0
$727$	−6688.68	+	11585.1i	−0.341223	+	0.591016i	−0.984660	−	0.174483i	$-0.944175\pi$
$727$	−6688.68	+	11585.1i	−0.341223	+	0.591016i	0.643437	+	0.765499i	$0.277508\pi$
$728$		0			0
$729$	47004.6			2.38808
$730$		0			0
$731$	10000.5	+	17321.3i	0.505992	+	0.876404i
$732$		0			0
$733$	−6136.73	+	10629.1i	−0.309230	+	0.535601i	−0.978194	−	0.207693i	$-0.933405\pi$
$733$	−6136.73	+	10629.1i	−0.309230	+	0.535601i	0.668964	+	0.743294i	$0.266738\pi$
$734$		0			0
$735$	−5592.09	+	9685.79i	−0.280636	+	0.486076i
$736$		0			0
$737$	26814.6	−	46444.2i	1.34020	−	2.32129i
$738$		0			0
$739$	13588.9			0.676424			0.338212	−	0.941070i	$-0.390178\pi$
$739$	13588.9			0.676424			0.338212	+	0.941070i	$0.390178\pi$
$740$		0			0
$741$	−13225.1			−0.655651
$742$		0			0
$743$	−9816.16	+	17002.1i	−0.484684	+	0.839497i	−0.999845	−	0.0175964i	$-0.994399\pi$
$743$	−9816.16	+	17002.1i	−0.484684	+	0.839497i	0.515162	+	0.857093i	$0.327732\pi$
$744$		0			0
$745$	−6552.18	+	11348.7i	−0.322219	+	0.558100i
$746$		0			0
$747$	23409.6	−	40546.6i	1.14660	−	1.98598i
$748$		0			0
$749$	−4158.81	−	7203.27i	−0.202883	−	0.351404i
$750$		0			0
$751$	−28320.4			−1.37607			−0.688033	−	0.725679i	$-0.741526\pi$
$751$	−28320.4			−1.37607			−0.688033	+	0.725679i	$0.741526\pi$
$752$		0			0
$753$	−4501.19	+	7796.29i	−0.217839	+	0.377308i
$754$		0			0
$755$	−3748.30	−	6492.25i	−0.180682	−	0.312950i
$756$		0			0
$757$	−7865.43	−	13623.3i	−0.377641	−	0.654093i	0.613078	−	0.790023i	$-0.289931\pi$
$757$	−7865.43	−	13623.3i	−0.377641	−	0.654093i	−0.990719	+	0.135930i	$0.956598\pi$
$758$		0			0
$759$	67181.9	−	116362.i	3.21284	−	5.56481i
$760$		0			0
$761$	8119.88	+	14064.0i	0.386788	+	0.669936i	0.992015	−	0.126117i	$-0.0402513\pi$
$761$	8119.88	+	14064.0i	0.386788	+	0.669936i	−0.605228	+	0.796052i	$0.706918\pi$
$762$		0			0
$763$	−8370.68			−0.397168
$764$		0			0
$765$	−22390.8	−	38782.1i	−1.05823	−	1.83290i
$766$		0			0
$767$	−8122.86			−0.382398
$768$		0			0
$769$	−8837.84			−0.414435			−0.207218	−	0.978295i	$-0.566441\pi$
$769$	−8837.84			−0.414435			−0.207218	+	0.978295i	$0.566441\pi$
$770$		0			0
$771$	−9751.47			−0.455500
$772$		0			0
$773$	−19849.1	+	34379.7i	−0.923574	+	1.59968i	−0.129737	+	0.991548i	$0.541413\pi$
$773$	−19849.1	+	34379.7i	−0.923574	+	1.59968i	−0.793838	+	0.608129i	$0.791920\pi$
$774$		0			0
$775$	1858.59	+	3219.17i	0.0861450	+	0.149208i
$776$		0			0
$777$	23830.7	−	1177.39i	1.10028	−	0.0543613i
$778$		0			0
$779$	3563.14	+	6171.55i	0.163880	+	0.283849i
$780$		0			0
$781$	15388.7	−	26654.0i	0.705059	−	1.22120i
$782$		0			0
$783$	−259.769			−0.0118562
$784$		0			0
$785$	−11356.4			−0.516342
$786$		0			0
$787$	15643.7			0.708563			0.354281	−	0.935139i	$-0.384726\pi$
$787$	15643.7			0.708563			0.354281	+	0.935139i	$0.384726\pi$
$788$		0			0
$789$	40368.2	+	69919.8i	1.82148	+	3.15489i
$790$		0			0
$791$	15721.4			0.706687
$792$		0			0
$793$	15110.9	+	26172.8i	0.676675	+	1.17204i
$794$		0			0
$795$	258.769	−	448.202i	0.0115442	−	0.0199951i
$796$		0			0
$797$	−5667.63	−	9816.62i	−0.251892	−	0.436289i	0.712155	−	0.702022i	$-0.247719\pi$
$797$	−5667.63	−	9816.62i	−0.251892	−	0.436289i	−0.964047	+	0.265733i	$0.914386\pi$
$798$		0			0
$799$	−22672.6	−	39270.0i	−1.00388	−	1.73877i
$800$		0			0
$801$	2329.26	−	4034.39i	0.102747	−	0.177963i
$802$		0			0
$803$	−34560.1			−1.51880
$804$		0			0
$805$	−5445.73	−	9432.28i	−0.238431	−	0.412974i
$806$		0			0
$807$	−8851.30	+	15330.9i	−0.386097	+	0.668740i
$808$		0			0
$809$	3400.60	−	5890.01i	0.147786	−	0.255972i	−0.782623	−	0.622496i	$-0.786119\pi$
$809$	3400.60	−	5890.01i	0.147786	−	0.255972i	0.930409	+	0.366524i	$0.119452\pi$
$810$		0			0
$811$	9763.27	−	16910.5i	0.422731	−	0.732191i	−0.573475	−	0.819223i	$-0.694405\pi$
$811$	9763.27	−	16910.5i	0.422731	−	0.732191i	0.996206	+	0.0870319i	$0.0277382\pi$
$812$		0			0
$813$	−28747.8			−1.24013
$814$		0			0
$815$	−18801.8			−0.808095
$816$		0			0
$817$	1802.67	−	3122.31i	0.0771938	−	0.133704i
$818$		0			0
$819$	−21931.7	+	37986.7i	−0.935719	+	1.62071i
$820$		0			0
$821$	−14422.9	+	24981.2i	−0.613108	+	1.06193i	0.377605	+	0.925967i	$0.376748\pi$
$821$	−14422.9	+	24981.2i	−0.613108	+	1.06193i	−0.990713	+	0.135968i	$0.956586\pi$
$822$		0			0
$823$	−7717.86	−	13367.7i	−0.326887	−	0.566184i	0.655006	−	0.755624i	$-0.272666\pi$
$823$	−7717.86	−	13367.7i	−0.326887	−	0.566184i	−0.981892	+	0.189440i	$0.939333\pi$
$824$		0			0
$825$	16599.7			0.700519
$826$		0			0
$827$	15951.9	−	27629.6i	0.670741	−	1.16176i	−0.306953	−	0.951725i	$-0.599309\pi$
$827$	15951.9	−	27629.6i	0.670741	−	1.16176i	0.977694	−	0.210033i	$-0.0673572\pi$
$828$		0			0
$829$	1678.49	+	2907.23i	0.0703212	+	0.121800i	0.899042	−	0.437862i	$-0.144264\pi$
$829$	1678.49	+	2907.23i	0.0703212	+	0.121800i	−0.828721	+	0.559662i	$0.810931\pi$
$830$		0			0
$831$	7258.88	+	12572.8i	0.303018	+	0.524842i
$832$		0			0
$833$	−14531.6	+	25169.5i	−0.604432	+	1.04691i
$834$		0			0
$835$	−7491.09	−	12974.9i	−0.310467	−	0.537744i
$836$		0			0
$837$	−62955.5			−2.59983
$838$		0			0
$839$	−13917.1	−	24105.1i	−0.572671	−	0.991895i	−0.996290	−	0.0860545i	$-0.972574\pi$
$839$	−13917.1	−	24105.1i	−0.572671	−	0.991895i	0.423620	−	0.905840i	$-0.360759\pi$
$840$		0			0
$841$	−24388.6			−0.999985
$842$		0			0
$843$	−57240.8			−2.33865
$844$		0			0
$845$	−5961.57			−0.242703
$846$		0			0
$847$	−17301.4	+	29966.8i	−0.701868	+	1.21567i
$848$		0			0
$849$	−16657.6	−	28851.9i	−0.673367	−	1.16631i
$850$		0			0
$851$	20797.6	−	40517.3i	0.837758	−	1.63210i
$852$		0			0
$853$	15689.8	+	27175.5i	0.629787	+	1.09082i	0.987594	+	0.157027i	$0.0501911\pi$
$853$	15689.8	+	27175.5i	0.629787	+	1.09082i	−0.357807	+	0.933795i	$0.616476\pi$
$854$		0			0
$855$	−4036.14	+	6990.80i	−0.161442	+	0.279626i
$856$		0			0
$857$	−13826.9			−0.551131			−0.275566	−	0.961282i	$-0.588865\pi$
$857$	−13826.9			−0.551131			−0.275566	+	0.961282i	$0.588865\pi$
$858$		0			0
$859$	930.659			0.0369659			0.0184829	−	0.999829i	$-0.494116\pi$
$859$	930.659			0.0369659			0.0184829	+	0.999829i	$0.494116\pi$
$860$		0			0
$861$	32753.0			1.29642
$862$		0			0
$863$	24954.6	+	43222.7i	0.984317	+	1.70489i	0.644931	+	0.764241i	$0.276886\pi$
$863$	24954.6	+	43222.7i	0.984317	+	1.70489i	0.339386	+	0.940647i	$0.389781\pi$
$864$		0			0
$865$	11635.3			0.457356
$866$		0			0
$867$	−56437.4	−	97752.4i	−2.21074	−	3.82912i
$868$		0			0
$869$	29168.3	−	50521.0i	1.13863	−	1.97216i
$870$		0			0
$871$	23154.5	+	40104.7i	0.900757	+	1.56016i
$872$		0			0
$873$	−2779.91	−	4814.95i	−0.107773	−	0.186668i
$874$		0			0
$875$	672.782	−	1165.29i	0.0259934	−	0.0450218i
$876$		0			0
$877$	6593.37			0.253868			0.126934	−	0.991911i	$-0.459486\pi$
$877$	6593.37			0.253868			0.126934	+	0.991911i	$0.459486\pi$
$878$		0			0
$879$	−1357.16	−	2350.68i	−0.0520773	−	0.0902006i
$880$		0			0
$881$	22995.6	−	39829.5i	0.879388	−	1.52314i	0.0273737	−	0.999625i	$-0.491286\pi$
$881$	22995.6	−	39829.5i	0.879388	−	1.52314i	0.852014	−	0.523519i	$-0.175381\pi$
$882$		0			0
$883$	−24940.3	+	43198.0i	−0.950520	+	1.64635i	−0.206219	+	0.978506i	$0.566116\pi$
$883$	−24940.3	+	43198.0i	−0.950520	+	1.64635i	−0.744301	+	0.667844i	$0.767217\pi$
$884$		0			0
$885$	−3435.28	+	5950.08i	−0.130481	+	0.226000i
$886$		0			0
$887$	28051.9			1.06188			0.530941	−	0.847409i	$-0.321839\pi$
$887$	28051.9			1.06188			0.530941	+	0.847409i	$0.321839\pi$
$888$		0			0
$889$	−5013.96			−0.189159
$890$		0			0
$891$	−76864.3	+	133133.i	−2.89007	+	5.00574i
$892$		0			0
$893$	−4086.93	+	7078.77i	−0.153151	+	0.265265i
$894$		0			0
$895$	−2821.12	+	4886.33i	−0.105363	+	0.182494i
$896$		0			0
$897$	58011.8	+	100479.i	2.15937	+	3.74014i
$898$		0			0
$899$	91.2220			0.00338423
$900$		0			0
$901$	672.439	−	1164.70i	0.0248637	−	0.0430652i
$902$		0			0
$903$	−8285.21	−	14350.4i	−0.305332	−	0.528850i
$904$		0			0
$905$	4156.32	+	7198.96i	0.152664	+	0.264422i
$906$		0			0
$907$	−16681.9	+	28893.8i	−0.610708	+	1.05778i	0.380413	+	0.924817i	$0.375782\pi$
$907$	−16681.9	+	28893.8i	−0.610708	+	1.05778i	−0.991121	+	0.132961i	$0.957552\pi$
$908$		0			0
$909$	11287.9	+	19551.2i	0.411877	+	0.713392i
$910$		0			0
$911$	35627.6			1.29571			0.647857	−	0.761762i	$-0.275666\pi$
$911$	35627.6			1.29571			0.647857	+	0.761762i	$0.275666\pi$
$912$		0			0
$913$	22549.4	+	39056.7i	0.817389	+	1.41576i
$914$		0			0
$915$	25562.5			0.923574
$916$		0			0
$917$	9101.02			0.327745
$918$		0			0
$919$	−7758.44			−0.278485			−0.139242	−	0.990258i	$-0.544467\pi$
$919$	−7758.44			−0.278485			−0.139242	+	0.990258i	$0.544467\pi$
$920$		0			0
$921$	−33625.7	+	58241.4i	−1.20305	+	2.08374i
$922$		0			0
$923$	13288.2	+	23015.8i	0.473875	+	0.820775i
$924$		0			0
$925$	5619.70	−	277.650i	0.199756	−	0.00986928i
$926$		0			0
$927$	67318.7	+	116599.i	2.38515	+	4.13121i
$928$		0			0
$929$	593.803	−	1028.50i	0.0209710	−	0.0363228i	−0.855349	−	0.518051i	$-0.826658\pi$
$929$	593.803	−	1028.50i	0.0209710	−	0.0363228i	0.876320	+	0.481729i	$0.159991\pi$
$930$		0			0
$931$	5238.91			0.184423
$932$		0			0
$933$	−75942.0			−2.66477
$934$		0			0
$935$	43136.1			1.50877
$936$		0			0
$937$	3025.46	+	5240.26i	0.105483	+	0.182702i	0.913935	−	0.405860i	$-0.133028\pi$
$937$	3025.46	+	5240.26i	0.105483	+	0.182702i	−0.808452	+	0.588562i	$0.799694\pi$
$938$		0			0
$939$	−41507.5			−1.44254
$940$		0			0
$941$	−10439.2	−	18081.2i	−0.361645	−	0.626388i	0.626587	−	0.779352i	$-0.284451\pi$
$941$	−10439.2	−	18081.2i	−0.361645	−	0.626388i	−0.988232	+	0.152964i	$0.951118\pi$
$942$		0			0
$943$	31259.3	−	54142.7i	1.07947	−	1.86970i
$944$		0			0
$945$	11394.5	+	19735.9i	0.392236	+	0.679373i
$946$		0			0
$947$	3931.69	+	6809.89i	0.134913	+	0.233677i	0.925564	−	0.378590i	$-0.123591\pi$
$947$	3931.69	+	6809.89i	0.134913	+	0.233677i	−0.790651	+	0.612267i	$0.790258\pi$
$948$		0			0
$949$	14921.4	−	25844.6i	0.510399	−	0.884037i
$950$		0			0
$951$	−1784.45			−0.0608461
$952$		0			0
$953$	−4971.89	−	8611.56i	−0.168998	−	0.292713i	0.769070	−	0.639165i	$-0.220720\pi$
$953$	−4971.89	−	8611.56i	−0.168998	−	0.292713i	−0.938068	+	0.346451i	$0.887387\pi$
$954$		0			0
$955$	−946.619	+	1639.59i	−0.0320753	+	0.0555560i
$956$		0			0
$957$	203.684	−	352.792i	0.00688002	−	0.0119165i
$958$		0			0
$959$	4979.83	−	8625.32i	0.167682	−	0.290434i
$960$		0			0
$961$	−7683.20			−0.257903
$962$		0			0
$963$	54082.4			1.80974
$964$		0			0
$965$	−4031.57	+	6982.89i	−0.134488	+	0.232940i
$966$		0			0
$967$	8324.68	−	14418.8i	0.276839	−	0.479500i	−0.693758	−	0.720208i	$-0.744046\pi$
$967$	8324.68	−	14418.8i	0.276839	−	0.479500i	0.970598	+	0.240708i	$0.0773797\pi$
$968$		0			0
$969$	−14534.3	+	25174.1i	−0.481846	+	0.834581i
$970$		0			0
$971$	−19137.9	−	33147.9i	−0.632508	−	1.09554i	−0.987037	−	0.160491i	$-0.948692\pi$
$971$	−19137.9	−	33147.9i	−0.632508	−	1.09554i	0.354529	−	0.935045i	$-0.384641\pi$
$972$		0			0
$973$	−14425.6			−0.475296
$974$		0			0
$975$	−7166.96	+	12413.5i	−0.235412	+	0.407745i
$976$		0			0
$977$	4586.75	+	7944.48i	0.150198	+	0.260150i	0.931300	−	0.364253i	$-0.118676\pi$
$977$	4586.75	+	7944.48i	0.150198	+	0.260150i	−0.781102	+	0.624403i	$0.785342\pi$
$978$		0			0
$979$	2243.67	+	3886.14i	0.0732461	+	0.126866i
$980$		0			0
$981$	27213.7	−	47135.5i	0.885695	−	1.53407i
$982$		0			0
$983$	3694.04	+	6398.26i	0.119859	+	0.207602i	0.919712	−	0.392594i	$-0.128422\pi$
$983$	3694.04	+	6398.26i	0.119859	+	0.207602i	−0.799853	+	0.600196i	$0.795089\pi$
$984$		0			0
$985$	−20297.7			−0.656589
$986$		0			0
$987$	18783.9	+	32534.6i	0.605772	+	1.04923i
$988$		0			0
$989$	−31629.5			−1.01695
$990$		0			0
$991$	48377.5			1.55072			0.775359	−	0.631521i	$-0.217569\pi$
$991$	48377.5			1.55072			0.775359	+	0.631521i	$0.217569\pi$
$992$		0			0
$993$	50909.1			1.62694
$994$		0			0
$995$	−5095.75	+	8826.11i	−0.162358	+	0.281212i
$996$		0			0
$997$	2928.94	+	5073.07i	0.0930394	+	0.161149i	0.908789	−	0.417257i	$-0.137008\pi$
$997$	2928.94	+	5073.07i	0.0930394	+	0.161149i	−0.815749	+	0.578406i	$0.803675\pi$
$998$		0			0
$999$	−43516.4	+	84777.3i	−1.37817	+	2.68492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.4.i.b.581.1	yes	38
37.10	even	3	inner	740.4.i.b.121.1	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.4.i.b.121.1	✓	38	37.10	even	3	inner
740.4.i.b.581.1	yes	38	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	740.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.92424 + 8.52903i) q^{3} +(2.50000 - 4.33013i) q^{5} +(-5.38226 + 9.32234i) q^{7} +(-34.9962 - 60.6152i) q^{9} +67.4205 q^{11} +(-29.1089 + 50.4181i) q^{13} +(24.6212 + 42.6451i) q^{15} +(63.9807 + 110.818i) q^{17} +(11.5331 - 19.9759i) q^{19} +(-53.0070 - 91.8108i) q^{21} -202.359 q^{23} +(-12.5000 - 21.6506i) q^{25} +423.410 q^{27} -0.613518 q^{29} -148.687 q^{31} +(-331.994 + 575.031i) q^{33} +(26.9113 + 46.6117i) q^{35} +(-102.776 + 200.225i) q^{37} +(-286.678 - 496.541i) q^{39} +(-154.475 + 267.558i) q^{41} +156.304 q^{43} -349.962 q^{45} -354.366 q^{47} +(113.563 + 196.696i) q^{49} -1260.23 q^{51} +(-5.25501 - 9.10195i) q^{53} +(168.551 - 291.939i) q^{55} +(113.583 + 196.732i) q^{57} +(69.7627 + 120.832i) q^{59} +(259.558 - 449.567i) q^{61} +753.435 q^{63} +(145.545 + 252.091i) q^{65} +(397.722 - 688.874i) q^{67} +(996.462 - 1725.92i) q^{69} +(228.250 - 395.340i) q^{71} -512.606 q^{73} +246.212 q^{75} +(-362.874 + 628.517i) q^{77} +(432.633 - 749.342i) q^{79} +(-1140.07 + 1974.66i) q^{81} +(334.459 + 579.300i) q^{83} +639.807 q^{85} +(3.02111 - 5.23271i) q^{87} +(33.2787 + 57.6404i) q^{89} +(-313.343 - 542.726i) q^{91} +(732.170 - 1268.16i) q^{93} +(-57.6654 - 99.8794i) q^{95} +79.4347 q^{97} +(-2359.46 - 4086.71i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{3} + 95 q^{5} - 32 q^{7} - 187 q^{9} - 2 q^{11} + 93 q^{13} + 30 q^{15} + 38 q^{17} - 91 q^{19} - 230 q^{21} - 306 q^{23} - 475 q^{25} + 552 q^{27} + 156 q^{29} - 144 q^{31} - 484 q^{33} + 160 q^{35}+ \cdots + 721 q^{99}+O(q^{100}) \) 38 * q - 6 * q^3 + 95 * q^5 - 32 * q^7 - 187 * q^9 - 2 * q^11 + 93 * q^13 + 30 * q^15 + 38 * q^17 - 91 * q^19 - 230 * q^21 - 306 * q^23 - 475 * q^25 + 552 * q^27 + 156 * q^29 - 144 * q^31 - 484 * q^33 + 160 * q^35 - 231 * q^37 - 590 * q^39 - 236 * q^41 + 228 * q^43 - 1870 * q^45 - 1082 * q^47 - 655 * q^49 - 1560 * q^51 + 2 * q^53 - 5 * q^55 + 598 * q^57 - 285 * q^59 + 1290 * q^61 + 2992 * q^63 - 465 * q^65 + 664 * q^67 - 240 * q^69 + 1614 * q^71 - 400 * q^73 + 300 * q^75 - 1334 * q^77 + 2236 * q^79 - 1759 * q^81 - 922 * q^83 + 380 * q^85 - 1968 * q^87 + 1107 * q^89 + 2456 * q^91 + 2986 * q^93 + 455 * q^95 - 5328 * q^97 + 721 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more