LMFDB - Embedded newform 304.5.r.d.145.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.19
Character	$\chi$	$=$	304.145
Dual form			304.5.r.d.65.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.1979 - 7.04247i) q^{3} +(0.573898 + 0.994020i) q^{5} +40.4604 q^{7} +(58.6927 - 101.659i) q^{9} +O(q^{10})$	\(q+(12.1979 - 7.04247i) q^{3} +(0.573898 + 0.994020i) q^{5} +40.4604 q^{7} +(58.6927 - 101.659i) q^{9} +186.858 q^{11} +(-39.2276 - 22.6481i) q^{13} +(14.0007 + 8.08331i) q^{15} +(77.4698 + 134.182i) q^{17} +(-350.517 - 86.3650i) q^{19} +(493.532 - 284.941i) q^{21} +(-59.5991 + 103.229i) q^{23} +(311.841 - 540.125i) q^{25} -512.486i q^{27} +(996.645 + 575.413i) q^{29} +258.707i q^{31} +(2279.27 - 1315.94i) q^{33} +(23.2201 + 40.2184i) q^{35} +368.779i q^{37} -637.994 q^{39} +(1631.76 - 942.096i) q^{41} +(-1038.38 - 1798.53i) q^{43} +134.734 q^{45} +(-470.623 + 815.143i) q^{47} -763.957 q^{49} +(1889.94 + 1091.16i) q^{51} +(-3920.29 - 2263.38i) q^{53} +(107.237 + 185.740i) q^{55} +(-4883.80 + 1415.03i) q^{57} +(2009.90 - 1160.42i) q^{59} +(1976.30 - 3423.04i) q^{61} +(2374.73 - 4113.15i) q^{63} -51.9907i q^{65} +(1011.74 + 584.127i) q^{67} +1678.90i q^{69} +(-7767.25 + 4484.42i) q^{71} +(-464.364 - 804.303i) q^{73} -8784.53i q^{75} +7560.33 q^{77} +(-151.768 + 87.6231i) q^{79} +(1144.94 + 1983.10i) q^{81} +3354.26 q^{83} +(-88.9194 + 154.013i) q^{85} +16209.3 q^{87} +(-6301.19 - 3637.99i) q^{89} +(-1587.17 - 916.351i) q^{91} +(1821.93 + 3155.68i) q^{93} +(-115.312 - 397.985i) q^{95} +(3272.67 - 1889.48i) q^{97} +(10967.2 - 18995.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	12.1979	−	7.04247i	1.35532	−	0.782496i	0.366334	−	0.930483i	$-0.380613\pi$
$3$	12.1979	−	7.04247i	1.35532	−	0.782496i	0.988989	+	0.147987i	$0.0472793\pi$
$4$		0			0
$5$	0.573898	+	0.994020i	0.0229559	+	0.0397608i	0.877275	−	0.479988i	$-0.159359\pi$
$5$	0.573898	+	0.994020i	0.0229559	+	0.0397608i	−0.854319	+	0.519749i	$0.826026\pi$
$6$		0			0
$7$	40.4604			0.825722			0.412861	−	0.910794i	$-0.364529\pi$
$7$	40.4604			0.825722			0.412861	+	0.910794i	$0.364529\pi$
$8$		0			0
$9$	58.6927	−	101.659i	0.724601	−	1.25505i
$10$		0			0
$11$	186.858			1.54428			0.772139	−	0.635454i	$-0.219187\pi$
$11$	186.858			1.54428			0.772139	+	0.635454i	$0.219187\pi$
$12$		0			0
$13$	−39.2276	−	22.6481i	−0.232116	−	0.134012i	0.379432	−	0.925220i	$-0.376120\pi$
$13$	−39.2276	−	22.6481i	−0.232116	−	0.134012i	−0.611548	+	0.791207i	$0.709453\pi$
$14$		0			0
$15$	14.0007	+	8.08331i	0.0622254	+	0.0359258i
$16$		0			0
$17$	77.4698	+	134.182i	0.268061	+	0.464296i	0.968361	−	0.249553i	$-0.0802836\pi$
$17$	77.4698	+	134.182i	0.268061	+	0.464296i	−0.700300	+	0.713849i	$0.746950\pi$
$18$		0			0
$19$	−350.517	−	86.3650i	−0.970961	−	0.239238i
$19$	−350.517	−	86.3650i	−0.970961	−	0.239238i
$20$		0			0
$21$	493.532	−	284.941i	1.11912	−	0.646125i
$22$		0			0
$23$	−59.5991	+	103.229i	−0.112664	+	0.195139i	−0.916843	−	0.399247i	$-0.869272\pi$
$23$	−59.5991	+	103.229i	−0.112664	+	0.195139i	0.804180	+	0.594386i	$0.202605\pi$
$24$		0			0
$25$	311.841	−	540.125i	0.498946	−	0.864200i
$26$		0			0
$27$		−	512.486i		−	0.702999i
$28$		0			0
$29$	996.645	+	575.413i	1.18507	+	0.684201i	0.957182	−	0.289486i	$-0.0934843\pi$
$29$	996.645	+	575.413i	1.18507	+	0.684201i	0.227889	+	0.973687i	$0.426818\pi$
$30$		0			0
$31$			258.707i			0.269206i	0.990900	+	0.134603i	$0.0429759\pi$
$31$			258.707i			0.269206i	−0.990900	+	0.134603i	$0.957024\pi$
$32$		0			0
$33$	2279.27	−	1315.94i	2.09300	−	1.20839i
$34$		0			0
$35$	23.2201	+	40.2184i	0.0189552	+	0.0328314i
$36$		0			0
$37$			368.779i			0.269378i	0.990888	+	0.134689i	$0.0430036\pi$
$37$			368.779i			0.269378i	−0.990888	+	0.134689i	$0.956996\pi$
$38$		0			0
$39$	−637.994			−0.419457
$40$		0			0
$41$	1631.76	−	942.096i	0.970707	−	0.560438i	0.0712552	−	0.997458i	$-0.477300\pi$
$41$	1631.76	−	942.096i	0.970707	−	0.560438i	0.899452	+	0.437020i	$0.143966\pi$
$42$		0			0
$43$	−1038.38	−	1798.53i	−0.561592	−	0.972707i	−0.997358	−	0.0726463i	$-0.976856\pi$
$43$	−1038.38	−	1798.53i	−0.561592	−	0.972707i	0.435765	−	0.900060i	$-0.356478\pi$
$44$		0			0
$45$	134.734			0.0665355
$46$		0			0
$47$	−470.623	+	815.143i	−0.213048	+	0.369010i	−0.952667	−	0.304016i	$-0.901672\pi$
$47$	−470.623	+	815.143i	−0.213048	+	0.369010i	0.739619	+	0.673026i	$0.235006\pi$
$48$		0			0
$49$	−763.957			−0.318183
$50$		0			0
$51$	1889.94	+	1091.16i	0.726620	+	0.419514i
$52$		0			0
$53$	−3920.29	−	2263.38i	−1.39562	−	0.805760i	−0.401687	−	0.915777i	$-0.631576\pi$
$53$	−3920.29	−	2263.38i	−1.39562	−	0.805760i	−0.993930	+	0.110017i	$0.964909\pi$
$54$		0			0
$55$	107.237	+	185.740i	0.0354503	+	0.0614017i
$56$		0			0
$57$	−4883.80	+	1415.03i	−1.50317	+	0.435528i
$58$		0			0
$59$	2009.90	−	1160.42i	0.577391	−	0.333357i	−0.182705	−	0.983168i	$-0.558485\pi$
$59$	2009.90	−	1160.42i	0.577391	−	0.333357i	0.760096	+	0.649811i	$0.225152\pi$
$60$		0			0
$61$	1976.30	−	3423.04i	0.531120	−	0.919926i	−0.468221	−	0.883611i	$-0.655105\pi$
$61$	1976.30	−	3423.04i	0.531120	−	0.919926i	0.999340	−	0.0363146i	$-0.0115618\pi$
$62$		0			0
$63$	2374.73	−	4113.15i	0.598319	−	1.03632i
$64$		0			0
$65$		−	51.9907i		−	0.0123055i
$66$		0			0
$67$	1011.74	+	584.127i	0.225381	+	0.130124i	0.608440	−	0.793600i	$-0.291796\pi$
$67$	1011.74	+	584.127i	0.225381	+	0.130124i	−0.383058	+	0.923724i	$0.625129\pi$
$68$		0			0
$69$			1678.90i			0.352636i
$70$		0			0
$71$	−7767.25	+	4484.42i	−1.54081	+	0.889590i	−0.542027	+	0.840361i	$0.682343\pi$
$71$	−7767.25	+	4484.42i	−1.54081	+	0.889590i	−0.998788	+	0.0492285i	$0.984324\pi$
$72$		0			0
$73$	−464.364	−	804.303i	−0.0871391	−	0.150929i	0.819162	−	0.573563i	$-0.194439\pi$
$73$	−464.364	−	804.303i	−0.0871391	−	0.150929i	−0.906301	+	0.422633i	$0.861106\pi$
$74$		0			0
$75$		−	8784.53i		−	1.56169i
$76$		0			0
$77$	7560.33			1.27514
$78$		0			0
$79$	−151.768	+	87.6231i	−0.0243178	+	0.0140399i	−0.512110	−	0.858920i	$-0.671136\pi$
$79$	−151.768	+	87.6231i	−0.0243178	+	0.0140399i	0.487792	+	0.872960i	$0.337803\pi$
$80$		0			0
$81$	1144.94	+	1983.10i	0.174507	+	0.302255i
$82$		0			0
$83$	3354.26			0.486900			0.243450	−	0.969913i	$-0.421721\pi$
$83$	3354.26			0.486900			0.243450	+	0.969913i	$0.421721\pi$
$84$		0			0
$85$	−88.9194	+	154.013i	−0.0123072	+	0.0213167i
$86$		0			0
$87$	16209.3			2.14154
$88$		0			0
$89$	−6301.19	−	3637.99i	−0.795505	−	0.459285i	0.0463923	−	0.998923i	$-0.485228\pi$
$89$	−6301.19	−	3637.99i	−0.795505	−	0.459285i	−0.841897	+	0.539639i	$0.818561\pi$
$90$		0			0
$91$	−1587.17	−	916.351i	−0.191664	−	0.110657i
$92$		0			0
$93$	1821.93	+	3155.68i	0.210653	+	0.364861i
$94$		0			0
$95$	−115.312	−	397.985i	−0.0127770	−	0.0440981i
$96$		0			0
$97$	3272.67	−	1889.48i	0.347823	−	0.200816i	−0.315903	−	0.948792i	$-0.602307\pi$
$97$	3272.67	−	1889.48i	0.347823	−	0.200816i	0.663726	+	0.747976i	$0.268974\pi$
$98$		0			0
$99$	10967.2	−	18995.7i	1.11899	−	1.93814i
$100$		0			0
$101$	−288.891	+	500.374i	−0.0283199	+	0.0490514i	−0.879838	−	0.475274i	$-0.842349\pi$
$101$	−288.891	+	500.374i	−0.0283199	+	0.0490514i	0.851518	+	0.524325i	$0.175682\pi$
$102$		0			0
$103$			18286.7i			1.72369i	0.507169	+	0.861847i	$0.330692\pi$
$103$			18286.7i			1.72369i	−0.507169	+	0.861847i	$0.669308\pi$
$104$		0			0
$105$	566.474	+	327.054i	0.0513809	+	0.0296648i
$106$		0			0
$107$		−	16099.0i		−	1.40615i	−0.711115	−	0.703076i	$-0.751809\pi$
$107$		−	16099.0i		−	1.40615i	0.711115	−	0.703076i	$-0.248191\pi$
$108$		0			0
$109$	1207.26	−	697.015i	0.101613	−	0.0586663i	−0.448332	−	0.893867i	$-0.647982\pi$
$109$	1207.26	−	697.015i	0.101613	−	0.0586663i	0.549945	+	0.835201i	$0.314649\pi$
$110$		0			0
$111$	2597.11	+	4498.34i	0.210788	+	0.365095i
$112$		0			0
$113$		−	11777.1i		−	0.922321i	−0.887317	−	0.461161i	$-0.847433\pi$
$113$		−	11777.1i		−	0.922321i	0.887317	−	0.461161i	$-0.152567\pi$
$114$		0			0
$115$	−136.815			−0.0103452
$116$		0			0
$117$	−4604.75	+	2658.56i	−0.336384	+	0.194211i
$118$		0			0
$119$	3134.46	+	5429.04i	0.221344	+	0.383380i
$120$		0			0
$121$	20274.8			1.38480
$122$		0			0
$123$	13269.4	−	22983.2i	0.877081	−	1.51915i
$124$		0			0
$125$	1433.23			0.0917268
$126$		0			0
$127$	13169.3	+	7603.30i	0.816498	+	0.471405i	0.849207	−	0.528060i	$-0.177080\pi$
$127$	13169.3	+	7603.30i	0.816498	+	0.471405i	−0.0327094	+	0.999465i	$0.510414\pi$
$128$		0			0
$129$	−25332.2	−	14625.6i	−1.52228	−	0.878888i
$130$		0			0
$131$	1846.94	+	3198.99i	0.107624	+	0.186411i	0.914807	−	0.403890i	$-0.132342\pi$
$131$	1846.94	+	3198.99i	0.107624	+	0.186411i	−0.807183	+	0.590301i	$0.799009\pi$
$132$		0			0
$133$	−14182.0	−	3494.36i	−0.801744	−	0.197544i
$134$		0			0
$135$	509.422	−	294.115i	0.0279518	−	0.0161380i
$136$		0			0
$137$	−3285.55	+	5690.74i	−0.175052	+	0.303199i	−0.940179	−	0.340680i	$-0.889343\pi$
$137$	−3285.55	+	5690.74i	−0.175052	+	0.303199i	0.765127	+	0.643879i	$0.222676\pi$
$138$		0			0
$139$	−18070.3	+	31298.6i	−0.935265	+	1.61993i	−0.161104	+	0.986937i	$0.551506\pi$
$139$	−18070.3	+	31298.6i	−0.935265	+	1.61993i	−0.774161	+	0.632989i	$0.781828\pi$
$140$		0			0
$141$			13257.4i			0.666838i
$142$		0			0
$143$	−7329.99	−	4231.97i	−0.358452	−	0.206952i
$144$		0			0
$145$			1320.91i			0.0628258i
$146$		0			0
$147$	−9318.68	+	5380.14i	−0.431241	+	0.248977i
$148$		0			0
$149$	19437.7	+	33667.1i	0.875532	+	1.51647i	0.856194	+	0.516654i	$0.172823\pi$
$149$	19437.7	+	33667.1i	0.875532	+	1.51647i	0.0193380	+	0.999813i	$0.493844\pi$
$150$		0			0
$151$			38005.6i			1.66684i	0.552642	+	0.833419i	$0.313620\pi$
$151$			38005.6i			1.66684i	−0.552642	+	0.833419i	$0.686380\pi$
$152$		0			0
$153$	18187.6			0.776951
$154$		0			0
$155$	−257.160	+	148.471i	−0.0107038	+	0.00617987i
$156$		0			0
$157$	9524.09	+	16496.2i	0.386388	+	0.669244i	0.991961	−	0.126546i	$-0.0403891\pi$
$157$	9524.09	+	16496.2i	0.386388	+	0.669244i	−0.605572	+	0.795790i	$0.707056\pi$
$158$		0			0
$159$	−63759.1			−2.52202
$160$		0			0
$161$	−2411.40	+	4176.67i	−0.0930289	+	0.161131i
$162$		0			0
$163$	−44363.2			−1.66973			−0.834867	−	0.550452i	$-0.814455\pi$
$163$	−44363.2			−1.66973			−0.834867	+	0.550452i	$0.814455\pi$
$164$		0			0
$165$	2616.14	+	1510.43i	0.0960933	+	0.0554795i
$166$		0			0
$167$	−40658.3	−	23474.1i	−1.45786	−	0.841697i	−0.458955	−	0.888459i	$-0.651776\pi$
$167$	−40658.3	−	23474.1i	−1.45786	−	0.841697i	−0.998906	+	0.0467625i	$0.985110\pi$
$168$		0			0
$169$	−13254.6	−	22957.7i	−0.464081	−	0.803813i
$170$		0			0
$171$	−29352.5	+	30564.1i	−1.00381	+	1.04525i
$172$		0			0
$173$	−32262.2	+	18626.6i	−1.07796	+	0.622358i	−0.930344	−	0.366687i	$-0.880492\pi$
$173$	−32262.2	+	18626.6i	−1.07796	+	0.622358i	−0.147612	+	0.989045i	$0.547159\pi$
$174$		0			0
$175$	12617.2	−	21853.7i	0.411991	−	0.713589i
$176$		0			0
$177$	16344.4	−	28309.3i	0.521702	−	0.903614i
$178$		0			0
$179$			47796.9i			1.49174i	0.666090	+	0.745871i	$0.267967\pi$
$179$			47796.9i			1.49174i	−0.666090	+	0.745871i	$0.732033\pi$
$180$		0			0
$181$	14054.6	+	8114.42i	0.429004	+	0.247685i	0.698922	−	0.715198i	$-0.253663\pi$
$181$	14054.6	+	8114.42i	0.429004	+	0.247685i	−0.269918	+	0.962883i	$0.586997\pi$
$182$		0			0
$183$		−	55672.0i		−	1.66240i
$184$		0			0
$185$	−366.574	+	211.641i	−0.0107107	+	0.00618383i
$186$		0			0
$187$	14475.8	+	25072.9i	0.413961	+	0.717002i
$188$		0			0
$189$		−	20735.4i		−	0.580482i
$190$		0			0
$191$	−16561.0			−0.453962			−0.226981	−	0.973899i	$-0.572885\pi$
$191$	−16561.0			−0.453962			−0.226981	+	0.973899i	$0.572885\pi$
$192$		0			0
$193$	−40250.1	+	23238.4i	−1.08057	+	0.623867i	−0.931050	−	0.364892i	$-0.881106\pi$
$193$	−40250.1	+	23238.4i	−1.08057	+	0.623867i	−0.149519	+	0.988759i	$0.547773\pi$
$194$		0			0
$195$	−366.143	−	634.179i	−0.00962901	−	0.0166779i
$196$		0			0
$197$	22998.4			0.592606			0.296303	−	0.955094i	$-0.404246\pi$
$197$	22998.4			0.592606			0.296303	+	0.955094i	$0.404246\pi$
$198$		0			0
$199$	−15737.1	+	27257.4i	−0.397391	+	0.688301i	−0.993403	−	0.114674i	$-0.963417\pi$
$199$	−15737.1	+	27257.4i	−0.397391	+	0.688301i	0.596013	+	0.802975i	$0.296751\pi$
$200$		0			0
$201$	16454.8			0.407286
$202$		0			0
$203$	40324.6	+	23281.4i	0.978540	+	0.564960i
$204$		0			0
$205$	1872.92	+	1081.33i	0.0445669	+	0.0257307i
$206$		0			0
$207$	6996.06	+	12117.5i	0.163272	+	0.282796i
$208$		0			0
$209$	−65496.8	−	16138.0i	−1.49943	−	0.369450i
$210$		0			0
$211$	−17276.6	+	9974.67i	−0.388056	+	0.224044i	−0.681317	−	0.731988i	$-0.738593\pi$
$211$	−17276.6	+	9974.67i	−0.388056	+	0.224044i	0.293261	+	0.956032i	$0.405259\pi$
$212$		0			0
$213$	−63162.8	+	109401.i	−1.39220	+	2.41136i
$214$		0			0
$215$	1191.85	−	2064.35i	0.0257837	−	0.0446587i
$216$		0			0
$217$			10467.4i			0.222289i
$218$		0			0
$219$	−11328.6	−	6540.54i	−0.236203	−	0.136372i
$220$		0			0
$221$		−	7018.17i		−	0.143694i
$222$		0			0
$223$	53668.6	−	30985.6i	1.07922	−	0.623089i	0.148535	−	0.988907i	$-0.452544\pi$
$223$	53668.6	−	30985.6i	1.07922	−	0.623089i	0.930686	+	0.365818i	$0.119211\pi$
$224$		0			0
$225$	−36605.6	−	63402.8i	−0.723074	−	1.25240i
$226$		0			0
$227$			49408.6i			0.958851i	0.877582	+	0.479426i	$0.159155\pi$
$227$			49408.6i			0.958851i	−0.877582	+	0.479426i	$0.840845\pi$
$228$		0			0
$229$	74785.9			1.42610			0.713048	−	0.701115i	$-0.247314\pi$
$229$	74785.9			1.42610			0.713048	+	0.701115i	$0.247314\pi$
$230$		0			0
$231$	92220.3	−	53243.4i	1.72823	−	0.997796i
$232$		0			0
$233$	35107.0	+	60807.2i	0.646669	+	1.12006i	0.983913	+	0.178647i	$0.0571720\pi$
$233$	35107.0	+	60807.2i	0.646669	+	1.12006i	−0.337244	+	0.941417i	$0.609495\pi$
$234$		0			0
$235$	−1080.36			−0.0195628
$236$		0			0
$237$	−1234.17	+	2137.64i	−0.0219724	+	0.0380572i
$238$		0			0
$239$	24919.2			0.436253			0.218126	−	0.975921i	$-0.430005\pi$
$239$	24919.2			0.436253			0.218126	+	0.975921i	$0.430005\pi$
$240$		0			0
$241$	−84538.5	−	48808.3i	−1.45553	−	0.840350i	−0.456742	−	0.889599i	$-0.650984\pi$
$241$	−84538.5	−	48808.3i	−1.45553	−	0.840350i	−0.998786	+	0.0492498i	$0.984317\pi$
$242$		0			0
$243$	63881.7	+	36882.1i	1.08184	+	0.624602i
$244$		0			0
$245$	−438.433	−	759.388i	−0.00730418	−	0.0126512i
$246$		0			0
$247$	11793.9	+	11326.4i	0.193315	+	0.185652i
$248$		0			0
$249$	40914.9	−	23622.2i	0.659908	−	0.380998i
$250$		0			0
$251$	38326.5	−	66383.5i	0.608348	−	1.05369i	−0.383165	−	0.923680i	$-0.625166\pi$
$251$	38326.5	−	66383.5i	0.608348	−	1.05369i	0.991513	−	0.130009i	$-0.0415006\pi$
$252$		0			0
$253$	−11136.5	+	19289.1i	−0.173984	+	0.301349i
$254$		0			0
$255$			2504.85i			0.0385213i
$256$		0			0
$257$	23832.4	+	13759.6i	0.360829	+	0.208325i	0.669444	−	0.742862i	$-0.266532\pi$
$257$	23832.4	+	13759.6i	0.360829	+	0.208325i	−0.308615	+	0.951187i	$0.599866\pi$
$258$		0			0
$259$			14920.9i			0.222432i
$260$		0			0
$261$	116992.	−	67545.1i	1.71741	−	0.991546i
$262$		0			0
$263$	−38708.4	−	67044.8i	−0.559620	−	0.969290i	−0.997528	−	0.0702705i	$-0.977614\pi$
$263$	−38708.4	−	67044.8i	−0.559620	−	0.969290i	0.437908	−	0.899020i	$-0.355720\pi$
$264$		0			0
$265$		−	5195.79i		−	0.0739878i
$266$		0			0
$267$	−102482.			−1.43755
$268$		0			0
$269$	−51407.8	+	29680.3i	−0.710436	+	0.410170i	−0.811222	−	0.584738i	$-0.801197\pi$
$269$	−51407.8	+	29680.3i	−0.710436	+	0.410170i	0.100787	+	0.994908i	$0.467864\pi$
$270$		0			0
$271$	−20166.5	−	34929.5i	−0.274595	−	0.475613i	0.695438	−	0.718586i	$-0.255211\pi$
$271$	−20166.5	−	34929.5i	−0.274595	−	0.475613i	−0.970033	+	0.242974i	$0.921877\pi$
$272$		0			0
$273$	−25813.5			−0.346355
$274$		0			0
$275$	58269.9	−	100926.i	0.770512	−	1.33457i
$276$		0			0
$277$	2011.85			0.0262202			0.0131101	−	0.999914i	$-0.495827\pi$
$277$	2011.85			0.0262202			0.0131101	+	0.999914i	$0.495827\pi$
$278$		0			0
$279$	26299.8	+	15184.2i	0.337866	+	0.195067i
$280$		0			0
$281$	12312.3	+	7108.52i	0.155929	+	0.0900258i	0.575934	−	0.817496i	$-0.304638\pi$
$281$	12312.3	+	7108.52i	0.155929	+	0.0900258i	−0.420005	+	0.907522i	$0.637972\pi$
$282$		0			0
$283$	14325.7	+	24812.8i	0.178872	+	0.309816i	0.941494	−	0.337028i	$-0.109422\pi$
$283$	14325.7	+	24812.8i	0.178872	+	0.309816i	−0.762622	+	0.646844i	$0.776089\pi$
$284$		0			0
$285$	−4209.37	−	4042.51i	−0.0518236	−	0.0497693i
$286$		0			0
$287$	66021.6	−	38117.6i	0.801534	−	0.462766i
$288$		0			0
$289$	29757.4	−	51541.3i	0.356286	−	0.617106i
$290$		0			0
$291$	26613.2	−	46095.4i	0.314276	−	0.544341i
$292$		0			0
$293$			103967.i			1.21105i	0.795826	+	0.605525i	$0.207037\pi$
$293$			103967.i			1.21105i	−0.795826	+	0.605525i	$0.792963\pi$
$294$		0			0
$295$	2306.95	+	1331.92i	0.0265091	+	0.0153050i
$296$		0			0
$297$		−	95762.0i		−	1.08563i
$298$		0			0
$299$	4675.86	−	2699.61i	0.0523021	−	0.0301967i
$300$		0			0
$301$	−42013.4	−	72769.4i	−0.463719	−	0.803185i
$302$		0			0
$303$			8138.02i			0.0886408i
$304$		0			0
$305$	4536.77			0.0487693
$306$		0			0
$307$	−60596.3	+	34985.3i	−0.642939	+	0.371201i	−0.785746	−	0.618550i	$-0.787721\pi$
$307$	−60596.3	+	34985.3i	−0.642939	+	0.371201i	0.142807	+	0.989751i	$0.454387\pi$
$308$		0			0
$309$	128783.	+	223059.i	1.34878	+	2.33616i
$310$		0			0
$311$	−91038.1			−0.941245			−0.470622	−	0.882335i	$-0.655971\pi$
$311$	−91038.1			−0.941245			−0.470622	+	0.882335i	$0.655971\pi$
$312$		0			0
$313$	27779.1	−	48114.8i	0.283550	−	0.491123i	−0.688706	−	0.725040i	$-0.741821\pi$
$313$	27779.1	−	48114.8i	0.283550	−	0.491123i	0.972257	+	0.233917i	$0.0751544\pi$
$314$		0			0
$315$	5451.41			0.0549399
$316$		0			0
$317$	−90317.7	−	52145.0i	−0.898782	−	0.518912i	−0.0219773	−	0.999758i	$-0.506996\pi$
$317$	−90317.7	−	52145.0i	−0.898782	−	0.518912i	−0.876805	+	0.480846i	$0.840330\pi$
$318$		0			0
$319$	186231.	+	107520.i	1.83008	+	1.05660i
$320$		0			0
$321$	−113377.	−	196375.i	−1.10031	−	1.90579i
$322$		0			0
$323$	−15565.9	−	53723.6i	−0.149200	−	0.514944i
$324$		0			0
$325$	−24465.6	+	14125.2i	−0.231627	+	0.133730i
$326$		0			0
$327$	9817.41	−	17004.2i	0.0918124	−	0.159024i
$328$		0			0
$329$	−19041.6	+	32981.0i	−0.175919	+	0.304700i
$330$		0			0
$331$			145784.i			1.33062i	0.746567	+	0.665310i	$0.231701\pi$
$331$			145784.i			1.33062i	−0.746567	+	0.665310i	$0.768299\pi$
$332$		0			0
$333$	37489.6	+	21644.6i	0.338082	+	0.195192i
$334$		0			0
$335$			1340.92i			0.0119485i
$336$		0			0
$337$	165548.	−	95579.4i	1.45769	−	0.841598i	0.458792	−	0.888544i	$-0.348282\pi$
$337$	165548.	−	95579.4i	1.45769	−	0.841598i	0.998897	+	0.0469461i	$0.0149489\pi$
$338$		0			0
$339$	−82940.0	−	143656.i	−0.721713	−	1.25004i
$340$		0			0
$341$			48341.4i			0.415729i
$342$		0			0
$343$	−128055.			−1.08845
$344$		0			0
$345$	−1668.86	+	963.516i	−0.0140211	+	0.00809507i
$346$		0			0
$347$	74915.2	+	129757.i	0.622173	+	1.07764i	0.989080	+	0.147378i	$0.0470833\pi$
$347$	74915.2	+	129757.i	0.622173	+	1.07764i	−0.366907	+	0.930258i	$0.619583\pi$
$348$		0			0
$349$	−161158.			−1.32312			−0.661562	−	0.749890i	$-0.730106\pi$
$349$	−161158.			−1.32312			−0.661562	+	0.749890i	$0.730106\pi$
$350$		0			0
$351$	−11606.8	+	20103.6i	−0.0942106	+	0.163178i
$352$		0			0
$353$	−154042.			−1.23621			−0.618103	−	0.786097i	$-0.712099\pi$
$353$	−154042.			−1.23621			−0.618103	+	0.786097i	$0.712099\pi$
$354$		0			0
$355$	−8915.21	−	5147.20i	−0.0707416	−	0.0408427i
$356$		0			0
$357$	76467.7	+	44148.6i	0.599986	+	0.346402i
$358$		0			0
$359$	−110306.	−	191055.i	−0.855871	−	1.48241i	−0.875834	−	0.482612i	$-0.839688\pi$
$359$	−110306.	−	191055.i	−0.855871	−	1.48241i	0.0199627	−	0.999801i	$-0.493645\pi$
$360$		0			0
$361$	115403.	+	60544.8i	0.885530	+	0.464582i
$362$		0			0
$363$	247310.	−	142785.i	1.87685	−	1.08360i
$364$		0			0
$365$	532.995	−	923.175i	0.00400071	−	0.00692944i
$366$		0			0
$367$	−84590.4	+	146515.i	−0.628042	+	1.08780i	0.359902	+	0.932990i	$0.382810\pi$
$367$	−84590.4	+	146515.i	−0.628042	+	1.08780i	−0.987944	+	0.154811i	$0.950523\pi$
$368$		0			0
$369$		−	221177.i		−	1.62438i
$370$		0			0
$371$	−158616.	−	91577.2i	−1.15239	−	0.665334i
$372$		0			0
$373$			61396.3i			0.441290i	0.975354	+	0.220645i	$0.0708163\pi$
$373$			61396.3i			0.441290i	−0.975354	+	0.220645i	$0.929184\pi$
$374$		0			0
$375$	17482.4	−	10093.5i	0.124320	−	0.0717759i
$376$		0			0
$377$	−26064.0	−	45144.2i	−0.183383	−	0.317628i
$378$		0			0
$379$			105973.i			0.737760i	0.929477	+	0.368880i	$0.120259\pi$
$379$			105973.i			0.737760i	−0.929477	+	0.368880i	$0.879741\pi$
$380$		0			0
$381$	214184.			1.47549
$382$		0			0
$383$	98679.1	−	56972.4i	0.672710	−	0.388389i	−0.124393	−	0.992233i	$-0.539698\pi$
$383$	98679.1	−	56972.4i	0.672710	−	0.388389i	0.797103	+	0.603844i	$0.206365\pi$
$384$		0			0
$385$	4338.86	+	7515.12i	0.0292721	+	0.0507008i
$386$		0			0
$387$	−243782.			−1.62772
$388$		0			0
$389$	135868.	−	235330.i	0.897878	−	1.55517i	0.0676755	−	0.997707i	$-0.478442\pi$
$389$	135868.	−	235330.i	0.897878	−	1.55517i	0.830202	−	0.557462i	$-0.188225\pi$
$390$		0			0
$391$	−18468.5			−0.120803
$392$		0			0
$393$	45057.6	+	26014.0i	0.291731	+	0.168431i
$394$		0			0
$395$	−174.198	−	100.573i	−0.00111648	−	0.000644598i
$396$		0			0
$397$	−7833.57	−	13568.1i	−0.0497026	−	0.0860874i	0.840104	−	0.542426i	$-0.182494\pi$
$397$	−7833.57	−	13568.1i	−0.0497026	−	0.0860874i	−0.889806	+	0.456338i	$0.849161\pi$
$398$		0			0
$399$	−197600.	+	57252.7i	−1.24120	+	0.359625i
$400$		0			0
$401$	130476.	−	75330.3i	0.811412	−	0.468469i	−0.0360341	−	0.999351i	$-0.511473\pi$
$401$	130476.	−	75330.3i	0.811412	−	0.468469i	0.847446	+	0.530882i	$0.178139\pi$
$402$		0			0
$403$	5859.22	−	10148.5i	0.0360769	−	0.0624871i
$404$		0			0
$405$	−1314.16	+	2276.19i	−0.00801194	+	0.0138771i
$406$		0			0
$407$			68909.2i			0.415995i
$408$		0			0
$409$	105798.	+	61082.5i	0.632456	+	0.365149i	0.781703	−	0.623651i	$-0.214351\pi$
$409$	105798.	+	61082.5i	0.632456	+	0.365149i	−0.149246	+	0.988800i	$0.547685\pi$
$410$		0			0
$411$			92553.5i			0.547910i
$412$		0			0
$413$	81321.3	−	46950.9i	0.476765	−	0.275260i
$414$		0			0
$415$	1925.00	+	3334.20i	0.0111772	+	0.0193595i
$416$		0			0
$417$			509037.i			2.92737i
$418$		0			0
$419$	81544.2			0.464478			0.232239	−	0.972659i	$-0.425395\pi$
$419$	81544.2			0.464478			0.232239	+	0.972659i	$0.425395\pi$
$420$		0			0
$421$	215473.	−	124404.i	1.21571	−	0.701889i	0.251711	−	0.967802i	$-0.419007\pi$
$421$	215473.	−	124404.i	1.21571	−	0.701889i	0.963997	+	0.265913i	$0.0856734\pi$
$422$		0			0
$423$	55244.3	+	95685.9i	0.308750	+	0.534770i
$424$		0			0
$425$	96633.1			0.534993
$426$		0			0
$427$	79961.7	−	138498.i	0.438557	−	0.759603i
$428$		0			0
$429$	−119214.			−0.647758
$430$		0			0
$431$	−246145.	−	142112.i	−1.32506	−	0.765024i	−0.340530	−	0.940234i	$-0.610607\pi$
$431$	−246145.	−	142112.i	−1.32506	−	0.765024i	−0.984531	+	0.175209i	$0.943940\pi$
$432$		0			0
$433$	−154155.	−	89001.3i	−0.822207	−	0.474701i	0.0289701	−	0.999580i	$-0.490777\pi$
$433$	−154155.	−	89001.3i	−0.822207	−	0.474701i	−0.851177	+	0.524879i	$0.824111\pi$
$434$		0			0
$435$	9302.49	+	16112.4i	0.0491610	+	0.0851493i
$436$		0			0
$437$	29805.8	−	31036.1i	0.156077	−	0.162519i
$438$		0			0
$439$	47909.6	−	27660.6i	0.248595	−	0.143527i	−0.370526	−	0.928822i	$-0.620822\pi$
$439$	47909.6	−	27660.6i	0.248595	−	0.143527i	0.619121	+	0.785296i	$0.287489\pi$
$440$		0			0
$441$	−44838.7	+	77662.9i	−0.230556	+	0.399334i
$442$		0			0
$443$	171527.	−	297093.i	0.874026	−	1.51386i	0.0162292	−	0.999868i	$-0.494834\pi$
$443$	171527.	−	297093.i	0.874026	−	1.51386i	0.857797	−	0.513989i	$-0.171833\pi$
$444$		0			0
$445$		−	8351.35i		−	0.0421732i
$446$		0			0
$447$	474199.	+	273779.i	2.37326	+	1.37020i
$448$		0			0
$449$		−	327397.i		−	1.62398i	−0.583668	−	0.811992i	$-0.698383\pi$
$449$		−	327397.i		−	1.62398i	0.583668	−	0.811992i	$-0.301617\pi$
$450$		0			0
$451$	304907.	−	176038.i	1.49904	−	0.865472i
$452$		0			0
$453$	267653.	+	463588.i	1.30429	+	2.25910i
$454$		0			0
$455$		−	2103.57i		−	0.0101609i
$456$		0			0
$457$	8764.90			0.0419677			0.0209838	−	0.999780i	$-0.493320\pi$
$457$	8764.90			0.0419677			0.0209838	+	0.999780i	$0.493320\pi$
$458$		0			0
$459$	68766.2	−	39702.2i	0.326400	−	0.188447i
$460$		0			0
$461$	−154049.	−	266820.i	−0.724864	−	1.25550i	−0.959030	−	0.283305i	$-0.908569\pi$
$461$	−154049.	−	266820.i	−0.724864	−	1.25550i	0.234166	−	0.972197i	$-0.424764\pi$
$462$		0			0
$463$	−185202.			−0.863941			−0.431970	−	0.901888i	$-0.642182\pi$
$463$	−185202.			−0.863941			−0.431970	+	0.901888i	$0.642182\pi$
$464$		0			0
$465$	−2091.21	+	3622.08i	−0.00967145	+	0.0167514i
$466$		0			0
$467$	−9553.82			−0.0438070			−0.0219035	−	0.999760i	$-0.506973\pi$
$467$	−9553.82			−0.0438070			−0.0219035	+	0.999760i	$0.506973\pi$
$468$		0			0
$469$	40935.3	+	23634.0i	0.186102	+	0.107446i
$470$		0			0
$471$	232348.	+	134146.i	1.04736	+	0.604695i
$472$		0			0
$473$	−194030.	−	336070.i	−0.867255	−	1.50213i
$474$		0			0
$475$	−155954.	+	162391.i	−0.691207	+	0.719737i
$476$		0			0
$477$	−460185.	+	265688.i	−2.02253	+	1.16771i
$478$		0			0
$479$	24916.1	−	43156.0i	0.108595	−	0.188092i	−0.806606	−	0.591089i	$-0.798698\pi$
$479$	24916.1	−	43156.0i	0.108595	−	0.188092i	0.915201	+	0.402997i	$0.132032\pi$
$480$		0			0
$481$	8352.14	−	14466.3i	0.0361000	−	0.0625271i
$482$		0			0
$483$			67928.9i			0.291179i
$484$		0			0
$485$	3756.36	+	2168.73i	0.0159692	+	0.00921982i
$486$		0			0
$487$			434706.i			1.83290i	0.400154	+	0.916448i	$0.368957\pi$
$487$			434706.i			1.83290i	−0.400154	+	0.916448i	$0.631043\pi$
$488$		0			0
$489$	−541138.	+	312426.i	−2.26303	+	1.30656i
$490$		0			0
$491$	−187587.	−	324909.i	−0.778106	−	1.34772i	−0.933032	−	0.359793i	$-0.882847\pi$
$491$	−187587.	−	324909.i	−0.778106	−	1.34772i	0.154926	−	0.987926i	$-0.450486\pi$
$492$		0			0
$493$			178309.i			0.733632i
$494$		0			0
$495$	25176.2			0.102749
$496$		0			0
$497$	−314266.	+	181441.i	−1.27228	+	0.734554i
$498$		0			0
$499$	201705.	+	349363.i	0.810057	+	1.40306i	0.912824	+	0.408354i	$0.133897\pi$
$499$	201705.	+	349363.i	0.810057	+	1.40306i	−0.102767	+	0.994705i	$0.532770\pi$
$500$		0			0
$501$	−661262.			−2.63450
$502$		0			0
$503$	−13583.9	+	23528.0i	−0.0536893	+	0.0929926i	−0.891621	−	0.452783i	$-0.850431\pi$
$503$	−13583.9	+	23528.0i	−0.0536893	+	0.0929926i	0.837932	+	0.545775i	$0.183765\pi$
$504$		0			0
$505$	−663.175			−0.00260043
$506$		0			0
$507$	−323358.	−	186691.i	−1.25796	−	0.726284i
$508$		0			0
$509$	140269.	+	80984.2i	0.541409	+	0.312583i	0.745650	−	0.666338i	$-0.232139\pi$
$509$	140269.	+	80984.2i	0.541409	+	0.312583i	−0.204241	+	0.978921i	$0.565473\pi$
$510$		0			0
$511$	−18788.4	−	32542.4i	−0.0719527	−	0.124626i
$512$		0			0
$513$	−44260.9	+	179635.i	−0.168184	+	0.682585i
$514$		0			0
$515$	−18177.3	+	10494.7i	−0.0685354	+	0.0395690i
$516$		0			0
$517$	−87939.6	+	152316.i	−0.329006	+	0.569854i
$518$		0			0
$519$	−262354.	+	454410.i	−0.973986	+	1.68699i
$520$		0			0
$521$			28903.6i			0.106482i	0.998582	+	0.0532410i	$0.0169552\pi$
$521$			28903.6i			0.106482i	−0.998582	+	0.0532410i	$0.983045\pi$
$522$		0			0
$523$	52247.7	+	30165.2i	0.191013	+	0.110282i	0.592457	−	0.805602i	$-0.298158\pi$
$523$	52247.7	+	30165.2i	0.191013	+	0.110282i	−0.401443	+	0.915884i	$0.631491\pi$
$524$		0			0
$525$		−	355425.i		−	1.28953i
$526$		0			0
$527$	−34713.7	+	20042.0i	−0.124991	+	0.0721637i
$528$		0			0
$529$	132816.	+	230045.i	0.474614	+	0.822055i
$530$		0			0
$531$		−	272432.i		−	0.966204i
$532$		0			0
$533$	−85346.7			−0.300422
$534$		0			0
$535$	16002.8	−	9239.19i	0.0559097	−	0.0322795i
$536$		0			0
$537$	336608.	+	583023.i	1.16728	+	2.02179i
$538$		0			0
$539$	−142751.			−0.491363
$540$		0			0
$541$	186742.	−	323447.i	0.638041	−	1.10512i	−0.347821	−	0.937561i	$-0.613078\pi$
$541$	186742.	−	323447.i	0.638041	−	1.10512i	0.985862	−	0.167558i	$-0.0535883\pi$
$542$		0			0
$543$	228582.			0.775252
$544$		0			0
$545$	1385.69	+	800.030i	0.00466524	+	0.00269348i
$546$		0			0
$547$	−224139.	−	129407.i	−0.749105	−	0.432496i	0.0762653	−	0.997088i	$-0.475700\pi$
$547$	−224139.	−	129407.i	−0.749105	−	0.432496i	−0.825370	+	0.564592i	$0.809034\pi$
$548$		0			0
$549$	−231988.	−	401816.i	−0.769700	−	1.33316i
$550$		0			0
$551$	−299645.	−	287767.i	−0.986971	−	0.947847i
$552$		0			0
$553$	−6140.58	+	3545.26i	−0.0200798	+	0.0115931i
$554$		0			0
$555$	−2980.96	+	5163.17i	−0.00967764	+	0.0167622i
$556$		0			0
$557$	−101986.	+	176645.i	−0.328724	+	0.569366i	−0.982259	−	0.187530i	$-0.939952\pi$
$557$	−101986.	+	176645.i	−0.328724	+	0.569366i	0.653535	+	0.756896i	$0.273285\pi$
$558$		0			0
$559$			94069.7i			0.301041i
$560$		0			0
$561$	353150.	+	203891.i	1.12210	+	0.647847i
$562$		0			0
$563$			54523.4i			0.172015i	0.996294	+	0.0860075i	$0.0274109\pi$
$563$			54523.4i			0.172015i	−0.996294	+	0.0860075i	$0.972589\pi$
$564$		0			0
$565$	11706.7	−	6758.86i	0.0366722	−	0.0211727i
$566$		0			0
$567$	46324.8	+	80236.8i	0.144094	+	0.249579i
$568$		0			0
$569$		−	25847.2i		−	0.0798343i	−0.999203	−	0.0399172i	$-0.987291\pi$
$569$		−	25847.2i		−	0.0798343i	0.999203	−	0.0399172i	$-0.0127094\pi$
$570$		0			0
$571$	82465.9			0.252931			0.126466	−	0.991971i	$-0.459637\pi$
$571$	82465.9			0.252931			0.126466	+	0.991971i	$0.459637\pi$
$572$		0			0
$573$	−202009.	+	116630.i	−0.615265	+	0.355223i
$574$		0			0
$575$	37170.9	+	64381.9i	0.112426	+	0.194728i
$576$		0			0
$577$	−416746.			−1.25176			−0.625879	−	0.779920i	$-0.715259\pi$
$577$	−416746.			−1.25176			−0.625879	+	0.779920i	$0.715259\pi$
$578$		0			0
$579$	−327312.	+	566921.i	−0.976348	+	1.69108i
$580$		0			0
$581$	135715.			0.402044
$582$		0			0
$583$	−732536.	−	422930.i	−2.15522	−	1.24432i
$584$		0			0
$585$	−5285.31	−	3051.48i	−0.0154440	−	0.00891658i
$586$		0			0
$587$	331740.	+	574591.i	0.962769	+	1.66756i	0.715494	+	0.698619i	$0.246202\pi$
$587$	331740.	+	574591.i	0.962769	+	1.66756i	0.247274	+	0.968946i	$0.420465\pi$
$588$		0			0
$589$	22343.2	−	90681.1i	0.0644043	−	0.261388i
$590$		0			0
$591$	280533.	−	161966.i	0.803173	−	0.463712i
$592$		0			0
$593$	248023.	−	429588.i	0.705313	−	1.22164i	−0.261265	−	0.965267i	$-0.584140\pi$
$593$	248023.	−	429588.i	0.705313	−	1.22164i	0.966578	−	0.256371i	$-0.0825269\pi$
$594$		0			0
$595$	−3597.71	+	6231.43i	−0.0101623	+	0.0176017i
$596$		0			0
$597$			443311.i			1.24383i
$598$		0			0
$599$	−52958.8	−	30575.8i	−0.147599	−	0.0852166i	0.424381	−	0.905483i	$-0.360492\pi$
$599$	−52958.8	−	30575.8i	−0.147599	−	0.0852166i	−0.571981	+	0.820267i	$0.693825\pi$
$600$		0			0
$601$		−	146321.i		−	0.405095i	−0.979272	−	0.202547i	$-0.935078\pi$
$601$		−	146321.i		−	0.405095i	0.979272	−	0.202547i	$-0.0649220\pi$
$602$		0			0
$603$	118763.	−	68568.0i	0.326623	−	0.188576i
$604$		0			0
$605$	11635.7	+	20153.5i	0.0317892	+	0.0550606i
$606$		0			0
$607$		−	425149.i		−	1.15389i	−0.816784	−	0.576944i	$-0.804245\pi$
$607$		−	425149.i		−	1.15389i	0.816784	−	0.576944i	$-0.195755\pi$
$608$		0			0
$609$	655835.			1.76832
$610$		0			0
$611$	36922.9	−	21317.4i	0.0989039	−	0.0571022i
$612$		0			0
$613$	61973.3	+	107341.i	0.164924	+	0.285657i	0.936628	−	0.350325i	$-0.113929\pi$
$613$	61973.3	+	107341.i	0.164924	+	0.285657i	−0.771704	+	0.635981i	$0.780595\pi$
$614$		0			0
$615$	30461.0			0.0805368
$616$		0			0
$617$	87269.4	−	151155.i	0.229241	−	0.397056i	−0.728343	−	0.685213i	$-0.759709\pi$
$617$	87269.4	−	151155.i	0.229241	−	0.397056i	0.957583	+	0.288157i	$0.0930424\pi$
$618$		0			0
$619$	260058.			0.678718			0.339359	−	0.940657i	$-0.389790\pi$
$619$	260058.			0.678718			0.339359	+	0.940657i	$0.389790\pi$
$620$		0			0
$621$	52903.3	+	30543.7i	0.137183	+	0.0792024i
$622$		0			0
$623$	−254949.	−	147195.i	−0.656866	−	0.379242i
$624$		0			0
$625$	−194078.	−	336153.i	−0.496840	−	0.860553i
$626$		0			0
$627$	−912575.	+	264409.i	−2.32131	+	0.672577i
$628$		0			0
$629$	−49483.4	+	28569.2i	−0.125071	+	0.0722100i
$630$		0			0
$631$	293641.	−	508601.i	0.737494	−	1.27738i	−0.216127	−	0.976365i	$-0.569343\pi$
$631$	293641.	−	508601.i	0.737494	−	1.27738i	0.953621	−	0.301011i	$-0.0973241\pi$
$632$		0			0
$633$	−140493.	+	243340.i	−0.350628	+	0.607305i
$634$		0			0
$635$			17454.1i			0.0432861i
$636$		0			0
$637$	29968.2	+	17302.2i	0.0738554	+	0.0426404i
$638$		0			0
$639$			1.05281e6i			2.57839i
$640$		0			0
$641$	−54385.6	+	31399.6i	−0.132363	+	0.0764201i	−0.564720	−	0.825283i	$-0.691016\pi$
$641$	−54385.6	+	31399.6i	−0.132363	+	0.0764201i	0.432356	+	0.901703i	$0.357682\pi$
$642$		0			0
$643$	62613.5	+	108450.i	0.151442	+	0.262305i	0.931758	−	0.363081i	$-0.118275\pi$
$643$	62613.5	+	108450.i	0.151442	+	0.262305i	−0.780316	+	0.625386i	$0.784942\pi$
$644$		0			0
$645$		−	33574.3i		−	0.0807027i
$646$		0			0
$647$	−51109.2			−0.122093			−0.0610465	−	0.998135i	$-0.519444\pi$
$647$	−51109.2			−0.122093			−0.0610465	+	0.998135i	$0.519444\pi$
$648$		0			0
$649$	375565.	−	216833.i	0.891653	−	0.514796i
$650$		0			0
$651$	73716.2	+	127680.i	0.173941	+	0.301274i
$652$		0			0
$653$	−22714.5			−0.0532694			−0.0266347	−	0.999645i	$-0.508479\pi$
$653$	−22714.5			−0.0532694			−0.0266347	+	0.999645i	$0.508479\pi$
$654$		0			0
$655$	−2119.91	+	3671.79i	−0.00494122	+	0.00855845i
$656$		0			0
$657$	−109019.			−0.252564
$658$		0			0
$659$	163916.	+	94636.8i	0.377442	+	0.217916i	0.676705	−	0.736255i	$-0.263407\pi$
$659$	163916.	+	94636.8i	0.377442	+	0.217916i	−0.299263	+	0.954171i	$0.596741\pi$
$660$		0			0
$661$	−320450.	−	185012.i	−0.733428	−	0.423445i	0.0862471	−	0.996274i	$-0.472513\pi$
$661$	−320450.	−	185012.i	−0.733428	−	0.423445i	−0.819675	+	0.572829i	$0.805846\pi$
$662$		0			0
$663$	−49425.2	−	85607.0i	−0.112440	−	0.194752i
$664$		0			0
$665$	−4665.58	−	16102.6i	−0.0105502	−	0.0364128i
$666$		0			0
$667$	−118798.	+	68588.2i	−0.267029	+	0.154169i
$668$		0			0
$669$	436430.	−	755919.i	0.975129	−	1.68897i
$670$		0			0
$671$	369286.	−	639622.i	0.820196	−	1.42062i
$672$		0			0
$673$			370681.i			0.818408i	0.912443	+	0.409204i	$0.134193\pi$
$673$			370681.i			0.818408i	−0.912443	+	0.409204i	$0.865807\pi$
$674$		0			0
$675$	−276807.	−	159814.i	−0.607532	−	0.350759i
$676$		0			0
$677$		−	882351.i		−	1.92515i	−0.271021	−	0.962573i	$-0.587361\pi$
$677$		−	882351.i		−	1.92515i	0.271021	−	0.962573i	$-0.412639\pi$
$678$		0			0
$679$	132414.	−	76449.0i	0.287206	−	0.165818i
$680$		0			0
$681$	347959.	+	602682.i	0.750298	+	1.29955i
$682$		0			0
$683$		−	185354.i		−	0.397338i	−0.980067	−	0.198669i	$-0.936338\pi$
$683$		−	185354.i		−	0.397338i	0.980067	−	0.198669i	$-0.0636619\pi$
$684$		0			0
$685$	−7542.27			−0.0160739
$686$		0			0
$687$	912232.	−	526677.i	1.93282	−	1.11592i
$688$		0			0
$689$	102522.	+	177574.i	0.215964	+	0.374060i
$690$		0			0
$691$	868957.			1.81988			0.909939	−	0.414742i	$-0.136128\pi$
$691$	868957.			1.81988			0.909939	+	0.414742i	$0.136128\pi$
$692$		0			0
$693$	443736.	−	768574.i	0.923972	−	1.60037i
$694$		0			0
$695$	−41481.9			−0.0858794
$696$		0			0
$697$	252824.	+	145968.i	0.520418	+	0.300464i
$698$		0			0
$699$	856465.	+	494480.i	1.75289	+	1.01203i
$700$		0			0
$701$	−72763.9	−	126031.i	−0.148074	−	0.256472i	0.782441	−	0.622724i	$-0.213974\pi$
$701$	−72763.9	−	126031.i	−0.148074	−	0.256472i	−0.930516	+	0.366252i	$0.880641\pi$
$702$		0			0
$703$	31849.6	−	129263.i	0.0644456	−	0.261556i
$704$		0			0
$705$	−13178.1	+	7608.39i	−0.0265140	+	0.0153079i
$706$		0			0
$707$	−11688.6	+	20245.3i	−0.0233843	+	0.0405029i
$708$		0			0
$709$	29091.3	−	50387.6i	0.0578723	−	0.100238i	−0.835638	−	0.549281i	$-0.814902\pi$
$709$	29091.3	−	50387.6i	0.0578723	−	0.100238i	0.893510	+	0.449043i	$0.148235\pi$
$710$		0			0
$711$			20571.3i			0.0406933i
$712$		0			0
$713$	−26706.0	−	15418.7i	−0.0525326	−	0.0303297i
$714$		0			0
$715$		−	9714.87i		−	0.0190031i
$716$		0			0
$717$	303962.	−	175493.i	0.591264	−	0.341366i
$718$		0			0
$719$	−31535.3	−	54620.8i	−0.0610013	−	0.105657i	0.833912	−	0.551898i	$-0.186096\pi$
$719$	−31535.3	−	54620.8i	−0.0610013	−	0.105657i	−0.894913	+	0.446240i	$0.852763\pi$
$720$		0			0
$721$			739886.i			1.42329i
$722$		0			0
$723$	−1.37492e6			−2.63028
$724$		0			0
$725$	621590.	−	358875.i	1.18257	−	0.682759i
$726$		0			0
$727$	−211149.	−	365721.i	−0.399503	−	0.691960i	0.594161	−	0.804346i	$-0.297484\pi$
$727$	−211149.	−	365721.i	−0.399503	−	0.691960i	−0.993665	+	0.112386i	$0.964151\pi$
$728$		0			0
$729$	853484.			1.60598
$730$		0			0
$731$	160887.	−	278664.i	0.301083	−	0.521490i
$732$		0			0
$733$	1.03343e6			1.92341			0.961704	−	0.274088i	$-0.0883761\pi$
$733$	1.03343e6			1.92341			0.961704	+	0.274088i	$0.0883761\pi$
$734$		0			0
$735$	−10695.9	−	6175.30i	−0.0197990	−	0.0114310i
$736$		0			0
$737$	189051.	+	109149.i	0.348052	+	0.200948i
$738$		0			0
$739$	−206143.	−	357050.i	−0.377468	−	0.653793i	0.613225	−	0.789908i	$-0.289872\pi$
$739$	−206143.	−	357050.i	−0.377468	−	0.653793i	−0.990693	+	0.136115i	$0.956538\pi$
$740$		0			0
$741$	223628.	+	55100.3i	0.407276	+	0.100350i
$742$		0			0
$743$	187408.	−	108200.i	0.339477	−	0.195997i	−0.320564	−	0.947227i	$-0.603872\pi$
$743$	187408.	−	108200.i	0.339477	−	0.195997i	0.660041	+	0.751230i	$0.270539\pi$
$744$		0			0
$745$	−22310.5	+	38642.9i	−0.0401973	+	0.0696237i
$746$		0			0
$747$	196870.	−	340990.i	0.352809	−	0.611083i
$748$		0			0
$749$		−	651373.i		−	1.16109i
$750$		0			0
$751$	−454117.	−	262185.i	−0.805170	−	0.464865i	0.0401055	−	0.999195i	$-0.487231\pi$
$751$	−454117.	−	262185.i	−0.805170	−	0.464865i	−0.845276	+	0.534330i	$0.820564\pi$
$752$		0			0
$753$		−	1.07965e6i		−	1.90412i
$754$		0			0
$755$	−37778.3	+	21811.3i	−0.0662748	+	0.0382638i
$756$		0			0
$757$	99637.3	+	172577.i	0.173872	+	0.301155i	0.939770	−	0.341806i	$-0.111039\pi$
$757$	99637.3	+	172577.i	0.173872	+	0.301155i	−0.765898	+	0.642962i	$0.777705\pi$
$758$		0			0
$759$			313715.i			0.544568i
$760$		0			0
$761$	−147864.			−0.255325			−0.127663	−	0.991818i	$-0.540747\pi$
$761$	−147864.			−0.255325			−0.127663	+	0.991818i	$0.540747\pi$
$762$		0			0
$763$	48846.4	−	28201.5i	0.0839042	−	0.0484421i
$764$		0			0
$765$	10437.8	+	18078.9i	0.0178356	+	0.0308922i
$766$		0			0
$767$	−105125.			−0.178696
$768$		0			0
$769$	−558156.	+	966754.i	−0.943850	+	1.63480i	−0.185812	+	0.982585i	$0.559492\pi$
$769$	−558156.	+	966754.i	−0.943850	+	1.63480i	−0.758038	+	0.652210i	$0.773842\pi$
$770$		0			0
$771$	387608.			0.652054
$772$		0			0
$773$	−942990.	−	544435.i	−1.57815	−	0.911145i	−0.995118	−	0.0986946i	$-0.968533\pi$
$773$	−942990.	−	544435.i	−1.57815	−	0.911145i	−0.583031	−	0.812450i	$-0.698133\pi$
$774$		0			0
$775$	139734.	+	80675.5i	0.232648	+	0.134319i
$776$		0			0
$777$	105080.	+	182004.i	0.174052	+	0.301467i
$778$		0			0
$779$	−653323.	+	189294.i	−1.07660	+	0.311933i
$780$		0			0
$781$	−1.45137e6	+	837948.i	−2.37945	+	1.37377i
$782$		0			0
$783$	294891.	−	510767.i	0.480993	−	0.833104i
$784$		0			0
$785$	−10931.7	+	18934.3i	−0.0177398	+	0.0307262i
$786$		0			0
$787$			538607.i			0.869607i	0.900525	+	0.434803i	$0.143182\pi$
$787$			538607.i			0.869607i	−0.900525	+	0.434803i	$0.856818\pi$
$788$		0			0
$789$	−944322.	−	545205.i	−1.51693	−	0.875801i
$790$		0			0
$791$		−	476507.i		−	0.761581i
$792$		0			0
$793$	−155051.	+	89518.7i	−0.246563	+	0.142353i
$794$		0			0
$795$	−36591.2	−	63377.8i	−0.0578952	−	0.100277i
$796$		0			0
$797$			272807.i			0.429476i	0.976672	+	0.214738i	$0.0688897\pi$
$797$			272807.i			0.429476i	−0.976672	+	0.214738i	$0.931110\pi$
$798$		0			0
$799$	−145836.			−0.228440
$800$		0			0
$801$	−739668.	+	427048.i	−1.15285	+	0.665597i
$802$		0			0
$803$	−86770.0	−	150290.i	−0.134567	−	0.233077i
$804$		0			0
$805$	−5535.59			−0.00854225
$806$		0			0
$807$	−418045.	+	724076.i	−0.641913	+	1.11183i
$808$		0			0
$809$	−858266.			−1.31137			−0.655684	−	0.755035i	$-0.727620\pi$
$809$	−858266.			−1.31137			−0.655684	+	0.755035i	$0.727620\pi$
$810$		0			0
$811$	1.09300e6	+	631045.i	1.66180	+	0.959442i	0.971855	+	0.235582i	$0.0756995\pi$
$811$	1.09300e6	+	631045.i	1.66180	+	0.959442i	0.689947	+	0.723860i	$0.257634\pi$
$812$		0			0
$813$	−491980.	−	284045.i	−0.744331	−	0.429740i
$814$		0			0
$815$	−25459.9	−	44097.9i	−0.0383303	−	0.0663899i
$816$		0			0
$817$	208641.	+	720097.i	0.312576	+	1.07881i
$818$		0			0
$819$	−186310.	+	107566.i	−0.277759	+	0.160364i
$820$		0			0
$821$	−312208.	+	540760.i	−0.463188	+	0.802266i	−0.999118	−	0.0419971i	$-0.986628\pi$
$821$	−312208.	+	540760.i	−0.463188	+	0.802266i	0.535929	+	0.844263i	$0.319961\pi$
$822$		0			0
$823$	263726.	−	456786.i	0.389361	−	0.674394i	−0.603002	−	0.797739i	$-0.706029\pi$
$823$	263726.	−	456786.i	0.389361	−	0.674394i	0.992364	+	0.123346i	$0.0393624\pi$
$824$		0			0
$825$		−	1.64146e6i		−	2.41169i
$826$		0			0
$827$	370071.	+	213660.i	0.541095	+	0.312401i	0.745523	−	0.666480i	$-0.232200\pi$
$827$	370071.	+	213660.i	0.541095	+	0.312401i	−0.204428	+	0.978882i	$0.565533\pi$
$828$		0			0
$829$			743120.i			1.08131i	0.841244	+	0.540655i	$0.181824\pi$
$829$			743120.i			1.08131i	−0.841244	+	0.540655i	$0.818176\pi$
$830$		0			0
$831$	24540.4	−	14168.4i	0.0355369	−	0.0205172i
$832$		0			0
$833$	−59183.6	−	102509.i	−0.0852926	−	0.147731i
$834$		0			0
$835$		−	53886.9i		−	0.0772876i
$836$		0			0
$837$	132584.			0.189251
$838$		0			0
$839$	86058.4	−	49685.8i	0.122256	−	0.0705844i	−0.437625	−	0.899158i	$-0.644180\pi$
$839$	86058.4	−	49685.8i	0.122256	−	0.0705844i	0.559881	+	0.828573i	$0.310847\pi$
$840$		0			0
$841$	308560.	+	534442.i	0.436263	+	0.755629i
$842$		0			0
$843$	200246.			0.281779
$844$		0			0
$845$	15213.6	−	26350.7i	0.0213068	−	0.0369045i
$846$		0			0
$847$	820326.			1.14346
$848$		0			0
$849$	349487.	+	201776.i	0.484859	+	0.279934i
$850$		0			0
$851$	−38068.6	−	21978.9i	−0.0525663	−	0.0303492i
$852$		0			0
$853$	−137514.	−	238181.i	−0.188994	−	0.327348i	0.755921	−	0.654663i	$-0.227189\pi$
$853$	−137514.	−	238181.i	−0.188994	−	0.327348i	−0.944915	+	0.327315i	$0.893856\pi$
$854$		0			0
$855$	−47226.7	−	11636.3i	−0.0646034	−	0.0159178i
$856$		0			0
$857$	−621926.	+	359069.i	−0.846793	+	0.488896i	−0.859568	−	0.511022i	$-0.829267\pi$
$857$	−621926.	+	359069.i	−0.846793	+	0.488896i	0.0127744	+	0.999918i	$0.495934\pi$
$858$		0			0
$859$	132725.	−	229887.i	0.179873	−	0.311550i	−0.761964	−	0.647620i	$-0.775765\pi$
$859$	132725.	−	229887.i	0.179873	−	0.311550i	0.941837	+	0.336070i	$0.109098\pi$
$860$		0			0
$861$	536884.	−	929910.i	0.724226	−	1.25440i
$862$		0			0
$863$		−	564408.i		−	0.757829i	−0.925432	−	0.378915i	$-0.876297\pi$
$863$		−	564408.i		−	0.757829i	0.925432	−	0.378915i	$-0.123703\pi$
$864$		0			0
$865$	−37030.4	−	21379.5i	−0.0494909	−	0.0285736i
$866$		0			0
$867$		−	838261.i		−	1.11517i
$868$		0			0
$869$	−28358.9	+	16373.0i	−0.0375535	+	0.0216815i
$870$		0			0
$871$	−26458.7	−	45827.8i	−0.0348765	−	0.0604078i
$872$		0			0
$873$		−	443594.i		−	0.582046i
$874$		0			0
$875$	57989.1			0.0757409
$876$		0			0
$877$	−1.10607e6	+	638589.i	−1.43808	+	0.830276i	−0.997716	−	0.0675432i	$-0.978484\pi$
$877$	−1.10607e6	+	638589.i	−1.43808	+	0.830276i	−0.440364	+	0.897819i	$0.645151\pi$
$878$		0			0
$879$	732187.	+	1.26819e6i	0.947642	+	1.64136i
$880$		0			0
$881$	352450.			0.454093			0.227047	−	0.973884i	$-0.427093\pi$
$881$	352450.			0.454093			0.227047	+	0.973884i	$0.427093\pi$
$882$		0			0
$883$	280106.	−	485158.i	0.359254	−	0.622246i	−0.628583	−	0.777743i	$-0.716365\pi$
$883$	280106.	−	485158.i	0.359254	−	0.622246i	0.987836	+	0.155497i	$0.0496980\pi$
$884$		0			0
$885$	37520.0			0.0479045
$886$		0			0
$887$	−85600.1	−	49421.2i	−0.108799	−	0.0628154i	0.444613	−	0.895723i	$-0.353341\pi$
$887$	−85600.1	−	49421.2i	−0.108799	−	0.0628154i	−0.553412	+	0.832907i	$0.686675\pi$
$888$		0			0
$889$	532835.	+	307632.i	0.674200	+	0.389250i
$890$		0			0
$891$	213941.	+	370557.i	0.269488	+	0.466766i
$892$		0			0
$893$	235361.	−	245076.i	0.295143	−	0.307325i
$894$		0			0
$895$	−47511.1	+	27430.5i	−0.0593129	+	0.0342443i
$896$		0			0
$897$	38023.8	−	65859.2i	0.0472575	−	0.0818525i
$898$		0			0
$899$	−148863.	+	257839.i	−0.184191	+	0.319028i
$900$		0			0
$901$		−	701374.i		−	0.863973i
$902$		0			0
$903$	−1.02495e6	−	591757.i	−1.25698	−	0.725717i
$904$		0			0
$905$			18627.4i			0.0227434i
$906$		0			0
$907$	−2759.65	+	1593.28i	−0.00335458	+	0.00193677i	−0.501676	−	0.865055i	$-0.667283\pi$
$907$	−2759.65	+	1593.28i	−0.00335458	+	0.00193677i	0.498322	+	0.866992i	$0.333950\pi$
$908$		0			0
$909$	33911.6	+	58736.6i	0.0410412	+	0.0710855i
$910$		0			0
$911$			1.10330e6i			1.32940i	0.747110	+	0.664700i	$0.231441\pi$
$911$			1.10330e6i			1.32940i	−0.747110	+	0.664700i	$0.768559\pi$
$912$		0			0
$913$	626769.			0.751910
$914$		0			0
$915$	55339.1	−	31950.0i	0.0660982	−	0.0381618i
$916$		0			0
$917$	74727.9	+	129433.i	0.0888677	+	0.153923i
$918$		0			0
$919$	−1.20279e6			−1.42416			−0.712080	−	0.702099i	$-0.752246\pi$
$919$	−1.20279e6			−1.42416			−0.712080	+	0.702099i	$0.752246\pi$
$920$		0			0
$921$	−492766.	+	853495.i	−0.580927	+	1.00619i
$922$		0			0
$923$	406254.			0.476864
$924$		0			0
$925$	199187.	+	115001.i	0.232797	+	0.134405i
$926$		0			0
$927$	1.85900e6	+	1.07329e6i	2.16332	+	1.24899i
$928$		0			0
$929$	−73687.4	−	127630.i	−0.0853812	−	0.147884i	0.820172	−	0.572116i	$-0.193877\pi$
$929$	−73687.4	−	127630.i	−0.0853812	−	0.147884i	−0.905554	+	0.424232i	$0.860544\pi$
$930$		0			0
$931$	267780.	+	65979.1i	0.308943	+	0.0761215i
$932$		0			0
$933$	−1.11048e6	+	641133.i	−1.27569	+	0.736521i
$934$		0			0
$935$	−16615.3	+	28778.5i	−0.0190057	+	0.0329189i
$936$		0			0
$937$	245311.	−	424891.i	0.279407	−	0.483948i	−0.691830	−	0.722060i	$-0.743195\pi$
$937$	245311.	−	424891.i	0.279407	−	0.483948i	0.971238	+	0.238112i	$0.0765287\pi$
$938$		0			0
$939$		−	782534.i		−	0.887508i
$940$		0			0
$941$	506513.	+	292435.i	0.572020	+	0.330256i	0.757956	−	0.652306i	$-0.226198\pi$
$941$	506513.	+	292435.i	0.572020	+	0.330256i	−0.185936	+	0.982562i	$0.559532\pi$
$942$		0			0
$943$			224592.i			0.252564i
$944$		0			0
$945$	20611.4	−	11900.0i	0.0230804	−	0.0133255i
$946$		0			0
$947$	−544535.	−	943161.i	−0.607191	−	1.05169i	−0.991701	−	0.128565i	$-0.958963\pi$
$947$	−544535.	−	943161.i	−0.607191	−	1.05169i	0.384510	−	0.923121i	$-0.374370\pi$
$948$		0			0
$949$			42067.9i			0.0467109i
$950$		0			0
$951$	−1.46892e6			−1.62419
$952$		0			0
$953$	679298.	−	392193.i	0.747953	−	0.431831i	−0.0770005	−	0.997031i	$-0.524534\pi$
$953$	679298.	−	392193.i	0.747953	−	0.431831i	0.824954	+	0.565200i	$0.191201\pi$
$954$		0			0
$955$	−9504.30	−	16461.9i	−0.0104211	−	0.0180499i
$956$		0			0
$957$	3.02884e6			3.30713
$958$		0			0
$959$	−132935.	+	230249.i	−0.144544	+	0.250358i
$960$		0			0
$961$	856592.			0.927528
$962$		0			0
$963$	−1.63661e6	−	944896.i	−1.76479	−	1.01890i
$964$		0			0
$965$	−46198.9	−	26673.0i	−0.0496109	−	0.0286429i
$966$		0			0
$967$	225659.	+	390852.i	0.241323	+	0.417984i	0.961091	−	0.276230i	$-0.0890853\pi$
$967$	225659.	+	390852.i	0.241323	+	0.417984i	−0.719768	+	0.694214i	$0.755752\pi$
$968$		0			0
$969$	−568218.	−	545693.i	−0.605156	−	0.581167i
$970$		0			0
$971$	−1.03427e6	+	597135.i	−1.09697	+	0.633336i	−0.935423	−	0.353530i	$-0.884981\pi$
$971$	−1.03427e6	+	597135.i	−1.09697	+	0.633336i	−0.161546	+	0.986865i	$0.551648\pi$
$972$		0			0
$973$	−731130.	+	1.26635e6i	−0.772269	+	1.33761i
$974$		0			0
$975$	−198953.	+	344596.i	−0.209286	+	0.362495i
$976$		0			0
$977$		−	471607.i		−	0.494073i	−0.969006	−	0.247037i	$-0.920543\pi$
$977$		−	471607.i		−	0.494073i	0.969006	−	0.247037i	$-0.0794568\pi$
$978$		0			0
$979$	−1.17743e6	−	679787.i	−1.22848	−	0.709263i
$980$		0			0
$981$		−	163639.i		−	0.170039i
$982$		0			0
$983$	−1.00901e6	+	582553.i	−1.04421	+	0.602876i	−0.921024	−	0.389507i	$-0.872645\pi$
$983$	−1.00901e6	+	582553.i	−1.04421	+	0.602876i	−0.123189	+	0.992383i	$0.539312\pi$
$984$		0			0
$985$	13198.8	+	22860.9i	0.0136038	+	0.0235625i
$986$		0			0
$987$			536399.i			0.550623i
$988$		0			0
$989$	247547.			0.253084
$990$		0			0
$991$	−1.32320e6	+	763948.i	−1.34734	+	0.777887i	−0.987872	−	0.155271i	$-0.950375\pi$
$991$	−1.32320e6	+	763948.i	−1.34734	+	0.777887i	−0.359467	+	0.933158i	$0.617042\pi$
$992$		0			0
$993$	1.02668e6	+	1.77826e6i	1.04121	+	1.80342i
$994$		0			0
$995$	−36125.9			−0.0364898
$996$		0			0
$997$	132736.	−	229906.i	0.133536	−	0.231291i	−0.791501	−	0.611168i	$-0.790700\pi$
$997$	132736.	−	229906.i	0.133536	−	0.231291i	0.925037	+	0.379876i	$0.124033\pi$
$998$		0			0
$999$	188994.			0.189373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.145.19		40
4.3	odd	2		152.5.n.a.145.2	yes	40
19.8	odd	6	inner	304.5.r.d.65.19		40
76.27	even	6		152.5.n.a.65.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.2	✓	40	76.27	even	6
152.5.n.a.145.2	yes	40	4.3	odd	2
304.5.r.d.65.19		40	19.8	odd	6	inner
304.5.r.d.145.19		40	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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.1979 - 7.04247i) q^{3} +(0.573898 + 0.994020i) q^{5} +40.4604 q^{7} +(58.6927 - 101.659i) q^{9} +O(q^{10})\)	\(q+(12.1979 - 7.04247i) q^{3} +(0.573898 + 0.994020i) q^{5} +40.4604 q^{7} +(58.6927 - 101.659i) q^{9} +186.858 q^{11} +(-39.2276 - 22.6481i) q^{13} +(14.0007 + 8.08331i) q^{15} +(77.4698 + 134.182i) q^{17} +(-350.517 - 86.3650i) q^{19} +(493.532 - 284.941i) q^{21} +(-59.5991 + 103.229i) q^{23} +(311.841 - 540.125i) q^{25} -512.486i q^{27} +(996.645 + 575.413i) q^{29} +258.707i q^{31} +(2279.27 - 1315.94i) q^{33} +(23.2201 + 40.2184i) q^{35} +368.779i q^{37} -637.994 q^{39} +(1631.76 - 942.096i) q^{41} +(-1038.38 - 1798.53i) q^{43} +134.734 q^{45} +(-470.623 + 815.143i) q^{47} -763.957 q^{49} +(1889.94 + 1091.16i) q^{51} +(-3920.29 - 2263.38i) q^{53} +(107.237 + 185.740i) q^{55} +(-4883.80 + 1415.03i) q^{57} +(2009.90 - 1160.42i) q^{59} +(1976.30 - 3423.04i) q^{61} +(2374.73 - 4113.15i) q^{63} -51.9907i q^{65} +(1011.74 + 584.127i) q^{67} +1678.90i q^{69} +(-7767.25 + 4484.42i) q^{71} +(-464.364 - 804.303i) q^{73} -8784.53i q^{75} +7560.33 q^{77} +(-151.768 + 87.6231i) q^{79} +(1144.94 + 1983.10i) q^{81} +3354.26 q^{83} +(-88.9194 + 154.013i) q^{85} +16209.3 q^{87} +(-6301.19 - 3637.99i) q^{89} +(-1587.17 - 916.351i) q^{91} +(1821.93 + 3155.68i) q^{93} +(-115.312 - 397.985i) q^{95} +(3272.67 - 1889.48i) q^{97} +(10967.2 - 18995.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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