LMFDB - Embedded newform 75.5.c.i.26.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,5,Mod(26,75)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("75.26"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	75.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.75274723129$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 73x^{4} + 1096x^{2} + 180 $ x^6 + 73x^4 + 1096x^2 + 180
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.4
Root			$0.407512i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.5.c.i.26.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.407512i q^{2} +(-3.21297 - 8.40695i) q^{3} +15.8339 q^{4} +(3.42594 - 1.30932i) q^{6} +46.9457 q^{7} +12.9727i q^{8} +(-60.3537 + 54.0225i) q^{9} -200.952i q^{11} +(-50.8739 - 133.115i) q^{12} +22.3321 q^{13} +19.1309i q^{14} +248.056 q^{16} -344.602i q^{17} +(-22.0148 - 24.5949i) q^{18} -59.9990 q^{19} +(-150.835 - 394.670i) q^{21} +81.8903 q^{22} -212.905i q^{23} +(109.061 - 41.6809i) q^{24} +9.10062i q^{26} +(648.079 + 333.818i) q^{27} +743.335 q^{28} +578.043i q^{29} +490.110 q^{31} +308.650i q^{32} +(-1689.39 + 645.652i) q^{33} +140.429 q^{34} +(-955.636 + 855.389i) q^{36} -1936.81 q^{37} -24.4503i q^{38} +(-71.7524 - 187.745i) q^{39} +1638.25i q^{41} +(160.833 - 61.4671i) q^{42} +2160.31 q^{43} -3181.86i q^{44} +86.7615 q^{46} +2282.28i q^{47} +(-796.997 - 2085.40i) q^{48} -197.104 q^{49} +(-2897.05 + 1107.19i) q^{51} +353.606 q^{52} +2626.84i q^{53} +(-136.035 + 264.100i) q^{54} +609.013i q^{56} +(192.775 + 504.409i) q^{57} -235.560 q^{58} +4106.06i q^{59} +4790.63 q^{61} +199.726i q^{62} +(-2833.34 + 2536.12i) q^{63} +3843.12 q^{64} +(-263.111 - 688.448i) q^{66} +1565.70 q^{67} -5456.40i q^{68} +(-1789.88 + 684.058i) q^{69} -5372.27i q^{71} +(-700.819 - 782.951i) q^{72} +4321.67 q^{73} -789.274i q^{74} -950.020 q^{76} -9433.82i q^{77} +(76.5085 - 29.2400i) q^{78} -4801.14 q^{79} +(724.132 - 6520.92i) q^{81} -667.606 q^{82} +3384.94i q^{83} +(-2388.31 - 6249.18i) q^{84} +880.352i q^{86} +(4859.58 - 1857.23i) q^{87} +2606.89 q^{88} +3446.38i q^{89} +1048.40 q^{91} -3371.13i q^{92} +(-1574.71 - 4120.33i) q^{93} -930.059 q^{94} +(2594.80 - 991.681i) q^{96} -5447.68 q^{97} -80.3221i q^{98} +(10855.9 + 12128.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 8 q^{3} - 50 q^{4} - 2 q^{6} - 76 q^{7} + 118 q^{9} + 452 q^{12} + 424 q^{13} + 802 q^{16} - 1160 q^{18} - 244 q^{19} - 876 q^{21} - 340 q^{22} - 786 q^{24} + 352 q^{27} + 3764 q^{28} + 3772 q^{31}+ \cdots + 9680 q^{99}+O(q^{100}) $ 6 * q - 8 * q^3 - 50 * q^4 - 2 * q^6 - 76 * q^7 + 118 * q^9 + 452 * q^12 + 424 * q^13 + 802 * q^16 - 1160 * q^18 - 244 * q^19 - 876 * q^21 - 340 * q^22 - 786 * q^24 + 352 * q^27 + 3764 * q^28 + 3772 * q^31 - 4420 * q^33 + 3124 * q^34 - 7606 * q^36 - 1896 * q^37 - 1336 * q^39 + 1980 * q^42 + 7384 * q^43 + 8196 * q^46 - 14668 * q^48 - 1318 * q^49 - 8492 * q^51 - 8976 * q^52 - 278 * q^54 + 11584 * q^57 + 23740 * q^58 + 6452 * q^61 - 14796 * q^63 + 3174 * q^64 - 12760 * q^66 - 13816 * q^67 + 5472 * q^69 + 2040 * q^72 - 596 * q^73 + 21348 * q^76 + 1400 * q^78 - 16124 * q^79 + 5086 * q^81 + 31240 * q^82 - 14736 * q^84 + 4900 * q^87 - 15660 * q^88 - 11632 * q^91 + 8184 * q^93 + 34924 * q^94 + 14354 * q^96 - 9756 * q^97 + 9680 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.407512i			0.101878i	0.998702	+	0.0509390i	$0.0162214\pi$
$2$			0.407512i			0.101878i	−0.998702	+	0.0509390i	$0.983779\pi$
$3$	−3.21297	−	8.40695i	−0.356996	−	0.934106i
$3$	−3.21297	−	8.40695i	−0.356996	−	0.934106i
$4$	15.8339			0.989621
$5$		0			0
$5$		0			0
$6$	3.42594	−	1.30932i	0.0951649	−	0.0363701i
$7$	46.9457			0.958075			0.479038	−	0.877794i	$-0.340986\pi$
$7$	46.9457			0.958075			0.479038	+	0.877794i	$0.340986\pi$
$8$			12.9727i			0.202699i
$9$	−60.3537	+	54.0225i	−0.745107	+	0.666945i
$10$		0			0
$11$		−	200.952i		−	1.66076i	−0.557198	−	0.830379i	$-0.688124\pi$
$11$		−	200.952i		−	1.66076i	0.557198	−	0.830379i	$-0.311876\pi$
$12$	−50.8739	−	133.115i	−0.353291	−	0.924411i
$13$	22.3321			0.132143			0.0660714	−	0.997815i	$-0.478953\pi$
$13$	22.3321			0.132143			0.0660714	+	0.997815i	$0.478953\pi$
$14$			19.1309i			0.0976068i
$15$		0			0
$16$	248.056			0.968970
$17$		−	344.602i		−	1.19239i	−0.802838	−	0.596197i	$-0.796678\pi$
$17$		−	344.602i		−	1.19239i	0.802838	−	0.596197i	$-0.203322\pi$
$18$	−22.0148	−	24.5949i	−0.0679471	−	0.0759101i
$19$	−59.9990			−0.166202			−0.0831011	−	0.996541i	$-0.526482\pi$
$19$	−59.9990			−0.166202			−0.0831011	+	0.996541i	$0.526482\pi$
$20$		0			0
$21$	−150.835	−	394.670i	−0.342029	−	0.894943i
$22$	81.8903			0.169195
$23$		−	212.905i		−	0.402467i	−0.979543	−	0.201234i	$-0.935505\pi$
$23$		−	212.905i		−	0.402467i	0.979543	−	0.201234i	$-0.0644951\pi$
$24$	109.061	−	41.6809i	0.189342	−	0.0723627i
$25$		0			0
$26$			9.10062i			0.0134625i
$27$	648.079	+	333.818i	0.888998	+	0.457912i
$28$	743.335			0.948131
$29$			578.043i			0.687328i	0.939093	+	0.343664i	$0.111668\pi$
$29$			578.043i			0.687328i	−0.939093	+	0.343664i	$0.888332\pi$
$30$		0			0
$31$	490.110			0.510000			0.255000	−	0.966941i	$-0.417925\pi$
$31$	490.110			0.510000			0.255000	+	0.966941i	$0.417925\pi$
$32$			308.650i			0.301416i
$33$	−1689.39	+	645.652i	−1.55132	+	0.592885i
$34$	140.429			0.121479
$35$		0			0
$36$	−955.636	+	855.389i	−0.737374	+	0.660023i
$37$	−1936.81			−1.41476			−0.707382	−	0.706832i	$-0.750124\pi$
$37$	−1936.81			−1.41476			−0.707382	+	0.706832i	$0.750124\pi$
$38$		−	24.4503i		−	0.0169324i
$39$	−71.7524	−	187.745i	−0.0471745	−	0.123435i
$40$		0			0
$41$			1638.25i			0.974567i	0.873244	+	0.487284i	$0.162012\pi$
$41$			1638.25i			0.974567i	−0.873244	+	0.487284i	$0.837988\pi$
$42$	160.833	−	61.4671i	0.0911751	−	0.0348453i
$43$	2160.31			1.16837			0.584183	−	0.811622i	$-0.301415\pi$
$43$	2160.31			1.16837			0.584183	+	0.811622i	$0.301415\pi$
$44$		−	3181.86i		−	1.64352i
$45$		0			0
$46$	86.7615			0.0410026
$47$			2282.28i			1.03318i	0.856234	+	0.516588i	$0.172798\pi$
$47$			2282.28i			1.03318i	−0.856234	+	0.516588i	$0.827202\pi$
$48$	−796.997	−	2085.40i	−0.345919	−	0.905121i
$49$	−197.104			−0.0820923
$50$		0			0
$51$	−2897.05	+	1107.19i	−1.11382	+	0.425680i
$52$	353.606			0.130771
$53$			2626.84i			0.935151i	0.883953	+	0.467575i	$0.154872\pi$
$53$			2626.84i			0.935151i	−0.883953	+	0.467575i	$0.845128\pi$
$54$	−136.035	+	264.100i	−0.0466512	+	0.0905694i
$55$		0			0
$56$			609.013i			0.194201i
$57$	192.775	+	504.409i	0.0593336	+	0.155250i
$58$	−235.560			−0.0700237
$59$			4106.06i			1.17956i	0.807563	+	0.589782i	$0.200786\pi$
$59$			4106.06i			1.17956i	−0.807563	+	0.589782i	$0.799214\pi$
$60$		0			0
$61$	4790.63			1.28746			0.643729	−	0.765254i	$-0.277386\pi$
$61$	4790.63			1.28746			0.643729	+	0.765254i	$0.277386\pi$
$62$			199.726i			0.0519578i
$63$	−2833.34	+	2536.12i	−0.713868	+	0.638983i
$64$	3843.12			0.938263
$65$		0			0
$66$	−263.111	−	688.448i	−0.0604020	−	0.158046i
$67$	1565.70			0.348785			0.174393	−	0.984676i	$-0.444204\pi$
$67$	1565.70			0.348785			0.174393	+	0.984676i	$0.444204\pi$
$68$		−	5456.40i		−	1.18002i
$69$	−1789.88	+	684.058i	−0.375947	+	0.143679i
$70$		0			0
$71$		−	5372.27i		−	1.06571i	−0.846205	−	0.532857i	$-0.821118\pi$
$71$		−	5372.27i		−	1.06571i	0.846205	−	0.532857i	$-0.178882\pi$
$72$	−700.819	−	782.951i	−0.135189	−	0.151032i
$73$	4321.67			0.810972			0.405486	−	0.914101i	$-0.367102\pi$
$73$	4321.67			0.810972			0.405486	+	0.914101i	$0.367102\pi$
$74$		−	789.274i		−	0.144133i
$75$		0			0
$76$	−950.020			−0.164477
$77$		−	9433.82i		−	1.59113i
$78$	76.5085	−	29.2400i	0.0125754	−	0.00480605i
$79$	−4801.14			−0.769290			−0.384645	−	0.923065i	$-0.625676\pi$
$79$	−4801.14			−0.769290			−0.384645	+	0.923065i	$0.625676\pi$
$80$		0			0
$81$	724.132	−	6520.92i	0.110369	−	0.993891i
$82$	−667.606			−0.0992870
$83$			3384.94i			0.491354i	0.969352	+	0.245677i	$0.0790103\pi$
$83$			3384.94i			0.491354i	−0.969352	+	0.245677i	$0.920990\pi$
$84$	−2388.31	−	6249.18i	−0.338479	−	0.885655i
$85$		0			0
$86$			880.352i			0.119031i
$87$	4859.58	−	1857.23i	0.642037	−	0.245374i
$88$	2606.89			0.336634
$89$			3446.38i			0.435094i	0.976050	+	0.217547i	$0.0698056\pi$
$89$			3446.38i			0.435094i	−0.976050	+	0.217547i	$0.930194\pi$
$90$		0			0
$91$	1048.40			0.126603
$92$		−	3371.13i		−	0.398290i
$93$	−1574.71	−	4120.33i	−0.182068	−	0.476394i
$94$	−930.059			−0.105258
$95$		0			0
$96$	2594.80	−	991.681i	0.281554	−	0.107604i
$97$	−5447.68			−0.578986			−0.289493	−	0.957180i	$-0.593487\pi$
$97$	−5447.68			−0.578986			−0.289493	+	0.957180i	$0.593487\pi$
$98$		−	80.3221i		−	0.00836340i
$99$	10855.9	+	12128.2i	1.10763	+	1.23744i
$100$		0			0
$101$		−	7655.22i		−	0.750438i	−0.926936	−	0.375219i	$-0.877567\pi$
$101$		−	7655.22i		−	0.750438i	0.926936	−	0.375219i	$-0.122433\pi$
$102$	−451.195	−	1180.58i	−0.0433675	−	0.113474i
$103$	−16163.7			−1.52358			−0.761790	−	0.647824i	$-0.775679\pi$
$103$	−16163.7			−1.52358			−0.761790	+	0.647824i	$0.775679\pi$
$104$			289.708i			0.0267852i
$105$		0			0
$106$	−1070.47			−0.0952713
$107$			18944.3i			1.65466i	0.561713	+	0.827332i	$0.310143\pi$
$107$			18944.3i			1.65466i	−0.561713	+	0.827332i	$0.689857\pi$
$108$	10261.6	+	5285.65i	0.879771	+	0.453159i
$109$	−4373.48			−0.368107			−0.184053	−	0.982916i	$-0.558922\pi$
$109$	−4373.48			−0.368107			−0.184053	+	0.982916i	$0.558922\pi$
$110$		0			0
$111$	6222.91	+	16282.7i	0.505065	+	1.32154i
$112$	11645.2			0.928346
$113$		−	1242.99i		−	0.0973443i	−0.998815	−	0.0486722i	$-0.984501\pi$
$113$		−	1242.99i		−	0.0973443i	0.998815	−	0.0486722i	$-0.0154990\pi$
$114$	−205.553	+	78.5581i	−0.0158166	+	0.00604479i
$115$		0			0
$116$			9152.69i			0.680194i
$117$	−1347.83	+	1206.44i	−0.0984605	+	0.0881320i
$118$	−1673.27			−0.120172
$119$		−	16177.6i		−	1.14240i
$120$		0			0
$121$	−25740.6			−1.75812
$122$			1952.24i			0.131164i
$123$	13772.7	−	5263.64i	0.910349	−	0.347917i
$124$	7760.36			0.504706
$125$		0			0
$126$	−1033.50	−	1154.62i	−0.0650984	−	0.0727275i
$127$	−4143.92			−0.256924			−0.128462	−	0.991714i	$-0.541004\pi$
$127$	−4143.92			−0.256924			−0.128462	+	0.991714i	$0.541004\pi$
$128$			6504.51i			0.397004i
$129$	−6941.00	−	18161.6i	−0.417102	−	1.09138i
$130$		0			0
$131$			23414.5i			1.36440i	0.731166	+	0.682200i	$0.238977\pi$
$131$			23414.5i			1.36440i	−0.731166	+	0.682200i	$0.761023\pi$
$132$	−26749.7	+	10223.2i	−1.53522	+	0.586731i
$133$	−2816.69			−0.159234
$134$			638.041i			0.0355336i
$135$		0			0
$136$	4470.42			0.241697
$137$		−	4168.41i		−	0.222090i	−0.993815	−	0.111045i	$-0.964580\pi$
$137$		−	4168.41i		−	0.222090i	0.993815	−	0.111045i	$-0.0354198\pi$
$138$	−278.762	−	729.400i	−0.0146378	−	0.0383008i
$139$	6702.86			0.346921			0.173460	−	0.984841i	$-0.444505\pi$
$139$	6702.86			0.346921			0.173460	+	0.984841i	$0.444505\pi$
$140$		0			0
$141$	19187.1	−	7332.91i	0.965095	−	0.368840i
$142$	2189.26			0.108573
$143$		−	4487.68i		−	0.219457i
$144$	−14971.1	+	13400.6i	−0.721987	+	0.646250i
$145$		0			0
$146$			1761.13i			0.0826203i
$147$	633.287	+	1657.04i	0.0293067	+	0.0766829i
$148$	−30667.3			−1.40008
$149$			7267.97i			0.327371i	0.986513	+	0.163686i	$0.0523383\pi$
$149$			7267.97i			0.327371i	−0.986513	+	0.163686i	$0.947662\pi$
$150$		0			0
$151$	−17022.9			−0.746584			−0.373292	−	0.927714i	$-0.621771\pi$
$151$	−17022.9			−0.746584			−0.373292	+	0.927714i	$0.621771\pi$
$152$		−	778.350i		−	0.0336890i
$153$	18616.3	+	20798.0i	0.795261	+	0.888461i
$154$	3844.40			0.162101
$155$		0			0
$156$	−1136.12	−	2972.74i	−0.0466849	−	0.122154i
$157$	11560.8			0.469017			0.234509	−	0.972114i	$-0.424652\pi$
$157$	11560.8			0.469017			0.234509	+	0.972114i	$0.424652\pi$
$158$		−	1956.52i		−	0.0783738i
$159$	22083.7	−	8439.95i	0.873530	−	0.333845i
$160$		0			0
$161$		−	9994.98i		−	0.385594i
$162$	2657.35	+	295.093i	0.101256	+	0.0112442i
$163$	6066.12			0.228316			0.114158	−	0.993463i	$-0.463583\pi$
$163$	6066.12			0.228316			0.114158	+	0.993463i	$0.463583\pi$
$164$			25939.9i			0.964452i
$165$		0			0
$166$	−1379.40			−0.0500582
$167$		−	6974.71i		−	0.250088i	−0.992151	−	0.125044i	$-0.960093\pi$
$167$		−	6974.71i		−	0.250088i	0.992151	−	0.125044i	$-0.0399073\pi$
$168$	5119.94	−	1956.74i	0.181404	−	0.0693289i
$169$	−28062.3			−0.982538
$170$		0			0
$171$	3621.16	−	3241.30i	0.123838	−	0.110848i
$172$	34206.2			1.15624
$173$		−	27868.0i		−	0.931135i	−0.885012	−	0.465568i	$-0.845850\pi$
$173$		−	27868.0i		−	0.931135i	0.885012	−	0.465568i	$-0.154150\pi$
$174$	756.845	+	1980.34i	0.0249982	+	0.0654095i
$175$		0			0
$176$		−	49847.4i		−	1.60923i
$177$	34519.4	−	13192.6i	1.10184	−	0.421100i
$178$	−1404.44			−0.0443266
$179$		−	22242.5i		−	0.694189i	−0.937830	−	0.347095i	$-0.887168\pi$
$179$		−	22242.5i		−	0.694189i	0.937830	−	0.347095i	$-0.112832\pi$
$180$		0			0
$181$	33471.7			1.02169			0.510847	−	0.859672i	$-0.329332\pi$
$181$	33471.7			1.02169			0.510847	+	0.859672i	$0.329332\pi$
$182$			427.235i			0.0128980i
$183$	−15392.1	−	40274.6i	−0.459618	−	1.20262i
$184$	2761.96			0.0815796
$185$		0			0
$186$	1679.08	−	641.712i	0.0485341	−	0.0185487i
$187$	−69248.4			−1.98028
$188$			36137.5i			1.02245i
$189$	30424.5	+	15671.3i	0.851726	+	0.438714i
$190$		0			0
$191$			602.154i			0.0165060i	0.999966	+	0.00825298i	$0.00262704\pi$
$191$			602.154i			0.0165060i	−0.999966	+	0.00825298i	$0.997373\pi$
$192$	−12347.8	−	32309.0i	−0.334956	−	0.876437i
$193$	27201.4			0.730259			0.365130	−	0.930957i	$-0.381025\pi$
$193$	27201.4			0.730259			0.365130	+	0.930957i	$0.381025\pi$
$194$		−	2220.00i		−	0.0589860i
$195$		0			0
$196$	−3120.92			−0.0812402
$197$		−	61640.6i		−	1.58831i	−0.607717	−	0.794154i	$-0.707915\pi$
$197$		−	61640.6i		−	1.58831i	0.607717	−	0.794154i	$-0.292085\pi$
$198$	−4942.38	+	4423.92i	−0.126068	+	0.112844i
$199$	−10712.4			−0.270507			−0.135254	−	0.990811i	$-0.543185\pi$
$199$	−10712.4			−0.270507			−0.135254	+	0.990811i	$0.543185\pi$
$200$		0			0
$201$	−5030.53	−	13162.7i	−0.124515	−	0.325802i
$202$	3119.60			0.0764532
$203$			27136.6i			0.658512i
$204$	−45871.7	+	17531.2i	−1.10226	+	0.421262i
$205$		0			0
$206$		−	6586.89i		−	0.155219i
$207$	11501.7	+	12849.6i	0.268424	+	0.299881i
$208$	5539.63			0.128042
$209$			12056.9i			0.276022i
$210$		0			0
$211$	19405.1			0.435865			0.217933	−	0.975964i	$-0.430069\pi$
$211$	19405.1			0.435865			0.217933	+	0.975964i	$0.430069\pi$
$212$			41593.2i			0.925445i
$213$	−45164.4	+	17260.9i	−0.995490	+	0.380456i
$214$	−7720.02			−0.168574
$215$		0			0
$216$	−4330.52	+	8407.35i	−0.0928182	+	0.180199i
$217$	23008.5			0.488618
$218$		−	1782.25i		−	0.0375020i
$219$	−13885.4	−	36332.1i	−0.289514	−	0.757534i
$220$		0			0
$221$		−	7695.70i		−	0.157566i
$222$	−6635.39	+	2535.91i	−0.134636	+	0.0514551i
$223$	60220.2			1.21097			0.605484	−	0.795857i	$-0.292979\pi$
$223$	60220.2			1.21097			0.605484	+	0.795857i	$0.292979\pi$
$224$			14489.8i			0.288779i
$225$		0			0
$226$	506.534			0.00991725
$227$			52638.3i			1.02153i	0.859721	+	0.510764i	$0.170637\pi$
$227$			52638.3i			1.02153i	−0.859721	+	0.510764i	$0.829363\pi$
$228$	3052.38	+	7986.77i	0.0587177	+	0.153639i
$229$	54102.0			1.03167			0.515837	−	0.856687i	$-0.327481\pi$
$229$	54102.0			1.03167			0.515837	+	0.856687i	$0.327481\pi$
$230$		0			0
$231$	−79309.7	+	30310.6i	−1.48629	+	0.568028i
$232$	−7498.79			−0.139321
$233$		−	82178.1i		−	1.51372i	−0.653580	−	0.756858i	$-0.726734\pi$
$233$		−	82178.1i		−	1.51372i	0.653580	−	0.756858i	$-0.273266\pi$
$234$	−491.638	−	549.256i	−0.00897871	−	0.0100310i
$235$		0			0
$236$			65015.1i			1.16732i
$237$	15425.9	+	40362.9i	0.274634	+	0.718598i
$238$	6592.56			0.116386
$239$		−	44047.8i		−	0.771132i	−0.922680	−	0.385566i	$-0.874006\pi$
$239$		−	44047.8i		−	0.771132i	0.922680	−	0.385566i	$-0.125994\pi$
$240$		0			0
$241$	11775.6			0.202744			0.101372	−	0.994849i	$-0.467677\pi$
$241$	11775.6			0.202744			0.101372	+	0.994849i	$0.467677\pi$
$242$		−	10489.6i		−	0.179114i
$243$	−57147.6	+	14863.8i	−0.967800	+	0.251719i
$244$	75854.5			1.27410
$245$		0			0
$246$	2145.00	+	5612.53i	0.0354451	+	0.0927446i
$247$	−1339.91			−0.0219624
$248$			6358.05i			0.103376i
$249$	28457.0	−	10875.7i	0.458977	−	0.175412i
$250$		0			0
$251$			114693.i			1.82050i	0.414061	+	0.910249i	$0.364110\pi$
$251$			114693.i			1.82050i	−0.414061	+	0.910249i	$0.635890\pi$
$252$	−44863.0	+	40156.8i	−0.706459	+	0.632351i
$253$	−42783.7			−0.668401
$254$		−	1688.70i		−	0.0261749i
$255$		0			0
$256$	58839.3			0.897817
$257$			44360.2i			0.671626i	0.941929	+	0.335813i	$0.109011\pi$
$257$			44360.2i			0.671626i	−0.941929	+	0.335813i	$0.890989\pi$
$258$	7401.08	−	2828.54i	0.111187	−	0.0424936i
$259$	−90924.9			−1.35545
$260$		0			0
$261$	−31227.3	−	34887.0i	−0.458410	−	0.512133i
$262$	−9541.68			−0.139002
$263$			61162.6i			0.884249i	0.896954	+	0.442124i	$0.145775\pi$
$263$			61162.6i			0.884249i	−0.896954	+	0.442124i	$0.854225\pi$
$264$	−8375.86	−	21916.0i	−0.120177	−	0.314451i
$265$		0			0
$266$		−	1147.84i		−	0.0162225i
$267$	28973.6	−	11073.1i	0.406424	−	0.155327i
$268$	24791.1			0.345165
$269$			54930.0i			0.759110i	0.925169	+	0.379555i	$0.123923\pi$
$269$			54930.0i			0.759110i	−0.925169	+	0.379555i	$0.876077\pi$
$270$		0			0
$271$	−48199.5			−0.656302			−0.328151	−	0.944625i	$-0.606425\pi$
$271$	−48199.5			−0.656302			−0.328151	+	0.944625i	$0.606425\pi$
$272$		−	85480.7i		−	1.15539i
$273$	−3368.47	−	8813.82i	−0.0451967	−	0.118260i
$274$	1698.68			0.0226261
$275$		0			0
$276$	−28340.9	+	10831.3i	−0.372045	+	0.142188i
$277$	−101493.			−1.32275			−0.661375	−	0.750056i	$-0.730027\pi$
$277$	−101493.			−1.32275			−0.661375	+	0.750056i	$0.730027\pi$
$278$			2731.50i			0.0353436i
$279$	−29579.9	+	26477.0i	−0.380004	+	0.340142i
$280$		0			0
$281$		−	120902.i		−	1.53117i	−0.643337	−	0.765583i	$-0.722451\pi$
$281$		−	120902.i		−	1.53117i	0.643337	−	0.765583i	$-0.277549\pi$
$282$	2988.25	+	7818.96i	0.0375767	+	0.0983220i
$283$	111286.			1.38953			0.694767	−	0.719235i	$-0.255507\pi$
$283$	111286.			1.38953			0.694767	+	0.719235i	$0.255507\pi$
$284$		−	85064.1i		−	1.05465i
$285$		0			0
$286$	1828.79			0.0223579
$287$			76908.6i			0.933708i
$288$	−16674.0	−	18628.1i	−0.201028	−	0.224587i
$289$	−35229.5			−0.421804
$290$		0			0
$291$	17503.2	+	45798.4i	0.206696	+	0.540834i
$292$	68429.1			0.802555
$293$			64072.7i			0.746342i	0.927763	+	0.373171i	$0.121730\pi$
$293$			64072.7i			0.746342i	−0.927763	+	0.373171i	$0.878270\pi$
$294$	−675.264	+	258.072i	−0.00781230	+	0.00298570i
$295$		0			0
$296$		−	25125.7i		−	0.286771i
$297$	67081.3	−	130233.i	0.760481	−	1.47641i
$298$	−2961.79			−0.0333520
$299$		−	4754.63i		−	0.0531832i
$300$		0			0
$301$	101417.			1.11938
$302$		−	6937.02i		−	0.0760605i
$303$	−64357.1	+	24596.0i	−0.700989	+	0.267904i
$304$	−14883.1			−0.161045
$305$		0			0
$306$	−8475.44	+	7586.36i	−0.0905147	+	0.0810197i
$307$	−33666.4			−0.357207			−0.178604	−	0.983921i	$-0.557158\pi$
$307$	−33666.4			−0.357207			−0.178604	+	0.983921i	$0.557158\pi$
$308$		−	149374.i		−	1.57462i
$309$	51933.3	+	135887.i	0.543913	+	1.42318i
$310$		0			0
$311$		−	58424.9i		−	0.604056i	−0.953299	−	0.302028i	$-0.902336\pi$
$311$		−	58424.9i		−	0.604056i	0.953299	−	0.302028i	$-0.0976636\pi$
$312$	2435.57	−	930.824i	0.0250202	−	0.00956221i
$313$	−40228.4			−0.410624			−0.205312	−	0.978697i	$-0.565821\pi$
$313$	−40228.4			−0.410624			−0.205312	+	0.978697i	$0.565821\pi$
$314$			4711.17i			0.0477826i
$315$		0			0
$316$	−76020.9			−0.761305
$317$		−	114181.i		−	1.13625i	−0.822943	−	0.568124i	$-0.807669\pi$
$317$		−	114181.i		−	1.13625i	0.822943	−	0.568124i	$-0.192331\pi$
$318$	3439.38	+	8999.38i	0.0340115	+	0.0889935i
$319$	116159.			1.14149
$320$		0			0
$321$	159263.	−	60867.3i	1.54563	−	0.590709i
$322$	4073.08			0.0392836
$323$			20675.8i			0.198178i
$324$	11465.9	−	103252.i	0.109224	−	0.983575i
$325$		0			0
$326$			2472.02i			0.0232604i
$327$	14051.8	+	36767.6i	0.131413	+	0.343851i
$328$	−21252.5			−0.197544
$329$			107143.i			0.989860i
$330$		0			0
$331$	479.214			0.00437395			0.00218698	−	0.999998i	$-0.499304\pi$
$331$	479.214			0.00437395			0.00218698	+	0.999998i	$0.499304\pi$
$332$			53596.9i			0.486254i
$333$	116894.	−	104631.i	1.05415	−	0.943569i
$334$	2842.28			0.0254785
$335$		0			0
$336$	−37415.6	−	97900.4i	−0.331416	−	0.867174i
$337$	139642.			1.22958			0.614790	−	0.788691i	$-0.289241\pi$
$337$	139642.			1.22958			0.614790	+	0.788691i	$0.289241\pi$
$338$		−	11435.7i		−	0.100099i
$339$	−10449.8	+	3993.69i	−0.0909299	+	0.0347516i
$340$		0			0
$341$		−	98488.4i		−	0.846986i
$342$	1320.87	+	1475.67i	0.0112929	+	0.0126164i
$343$	−121970.			−1.03673
$344$			28025.1i			0.236826i
$345$		0			0
$346$	11356.5			0.0948623
$347$		−	131835.i		−	1.09489i	−0.836842	−	0.547445i	$-0.815600\pi$
$347$		−	131835.i		−	1.09489i	0.836842	−	0.547445i	$-0.184400\pi$
$348$	76946.3	−	29407.3i	0.635373	−	0.242827i
$349$	−238053.			−1.95444			−0.977221	−	0.212222i	$-0.931930\pi$
$349$	−238053.			−1.95444			−0.977221	+	0.212222i	$0.931930\pi$
$350$		0			0
$351$	14473.0	+	7454.86i	0.117475	+	0.0605098i
$352$	62023.7			0.500579
$353$			181533.i			1.45682i	0.685142	+	0.728410i	$0.259740\pi$
$353$			181533.i			1.45682i	−0.685142	+	0.728410i	$0.740260\pi$
$354$	5376.16	+	14067.1i	0.0429008	+	0.112253i
$355$		0			0
$356$			54569.8i			0.430578i
$357$	−136004.	+	51978.0i	−1.06713	+	0.407834i
$358$	9064.10			0.0707227
$359$			32567.2i			0.252692i	0.991986	+	0.126346i	$0.0403249\pi$
$359$			32567.2i			0.252692i	−0.991986	+	0.126346i	$0.959675\pi$
$360$		0			0
$361$	−126721.			−0.972377
$362$			13640.1i			0.104088i
$363$	82703.8	+	216400.i	0.627643	+	1.64227i
$364$	16600.2			0.125289
$365$		0			0
$366$	16412.4	−	6272.49i	0.122521	−	0.0468250i
$367$	−117190.			−0.870076			−0.435038	−	0.900412i	$-0.643265\pi$
$367$	−117190.			−0.870076			−0.435038	+	0.900412i	$0.643265\pi$
$368$		−	52812.5i		−	0.389979i
$369$	−88502.3	−	98874.2i	−0.649983	−	0.726157i
$370$		0			0
$371$			123319.i			0.895945i
$372$	−24933.8	−	65241.0i	−0.180178	−	0.471449i
$373$	−155803.			−1.11984			−0.559922	−	0.828546i	$-0.689169\pi$
$373$	−155803.			−1.11984			−0.559922	+	0.828546i	$0.689169\pi$
$374$		−	28219.6i		−	0.201747i
$375$		0			0
$376$	−29607.4			−0.209423
$377$			12908.9i			0.0908255i
$378$	−6386.25	+	12398.4i	−0.0446953	+	0.0867722i
$379$	174237.			1.21301			0.606503	−	0.795082i	$-0.292572\pi$
$379$	174237.			1.21301			0.606503	+	0.795082i	$0.292572\pi$
$380$		0			0
$381$	13314.3	+	34837.8i	0.0917209	+	0.239994i
$382$	−245.385			−0.00168160
$383$		−	252899.i		−	1.72405i	−0.506869	−	0.862023i	$-0.669197\pi$
$383$		−	252899.i		−	1.72405i	0.506869	−	0.862023i	$-0.330803\pi$
$384$	54683.1	−	20898.8i	0.370844	−	0.141729i
$385$		0			0
$386$			11084.9i			0.0743974i
$387$	−130383.	+	116705.i	−0.870558	+	0.779235i
$388$	−86258.2			−0.572977
$389$		−	125454.i		−	0.829058i	−0.910036	−	0.414529i	$-0.863946\pi$
$389$		−	125454.i		−	0.829058i	0.910036	−	0.414529i	$-0.136054\pi$
$390$		0			0
$391$	−73367.5			−0.479900
$392$		−	2556.97i		−	0.0166400i
$393$	196844.	−	75229.9i	1.27449	−	0.487086i
$394$	25119.3			0.161814
$395$		0			0
$396$	171892.	+	192037.i	1.09614	+	1.22460i
$397$	225399.			1.43012			0.715059	−	0.699064i	$-0.246400\pi$
$397$	225399.			1.43012			0.715059	+	0.699064i	$0.246400\pi$
$398$		−	4365.42i		−	0.0275588i
$399$	9049.94	+	23679.8i	0.0568460	+	0.148742i
$400$		0			0
$401$			128670.i			0.800184i	0.916475	+	0.400092i	$0.131022\pi$
$401$			128670.i			0.800184i	−0.916475	+	0.400092i	$0.868978\pi$
$402$	5363.98	−	2050.00i	0.0331921	−	0.0126854i
$403$	10945.2			0.0673928
$404$		−	121212.i		−	0.742649i
$405$		0			0
$406$	−11058.5			−0.0670879
$407$			389206.i			2.34958i
$408$	−14363.3	−	37582.6i	−0.0862849	−	0.225770i
$409$	105708.			0.631917			0.315958	−	0.948773i	$-0.397674\pi$
$409$	105708.			0.631917			0.315958	+	0.948773i	$0.397674\pi$
$410$		0			0
$411$	−35043.6	+	13393.0i	−0.207456	+	0.0792854i
$412$	−255934.			−1.50777
$413$			192762.i			1.13011i
$414$	−5236.37	+	4687.08i	−0.0305513	+	0.0273465i
$415$		0			0
$416$			6892.80i			0.0398299i
$417$	−21536.1	−	56350.6i	−0.123850	−	0.324061i
$418$	−4913.34			−0.0281206
$419$			157919.i			0.899512i	0.893151	+	0.449756i	$0.148489\pi$
$419$			157919.i			0.899512i	−0.893151	+	0.449756i	$0.851511\pi$
$420$		0			0
$421$	−245033.			−1.38248			−0.691242	−	0.722623i	$-0.742936\pi$
$421$	−245033.			−1.38248			−0.691242	+	0.722623i	$0.742936\pi$
$422$			7907.84i			0.0444051i
$423$	−123295.	−	137744.i	−0.689071	−	0.769826i
$424$	−34077.2			−0.189554
$425$		0			0
$426$	−7034.04	−	18405.0i	−0.0387602	−	0.101419i
$427$	224899.			1.23348
$428$			299962.i			1.63749i
$429$	−37727.7	+	14418.8i	−0.204996	+	0.0783455i
$430$		0			0
$431$			61385.4i			0.330454i	0.986256	+	0.165227i	$0.0528356\pi$
$431$			61385.4i			0.330454i	−0.986256	+	0.165227i	$0.947164\pi$
$432$	160760.	+	82805.6i	0.861412	+	0.443703i
$433$	−25262.9			−0.134743			−0.0673716	−	0.997728i	$-0.521461\pi$
$433$	−25262.9			−0.134743			−0.0673716	+	0.997728i	$0.521461\pi$
$434$			9376.26i			0.0497795i
$435$		0			0
$436$	−69249.3			−0.364286
$437$			12774.1i			0.0668909i
$438$	14805.8	−	5658.47i	0.0771761	−	0.0294952i
$439$	−207087.			−1.07455			−0.537273	−	0.843409i	$-0.680545\pi$
$439$	−207087.			−1.07455			−0.537273	+	0.843409i	$0.680545\pi$
$440$		0			0
$441$	11895.9	−	10648.0i	0.0611675	−	0.0547510i
$442$	3136.09			0.0160525
$443$		−	132568.i		−	0.675508i	−0.941234	−	0.337754i	$-0.890333\pi$
$443$		−	132568.i		−	0.675508i	0.941234	−	0.337754i	$-0.109667\pi$
$444$	98533.2	+	257819.i	0.499823	+	1.30782i
$445$		0			0
$446$			24540.5i			0.123371i
$447$	61101.5	−	23351.8i	0.305799	−	0.116870i
$448$	180418.			0.898926
$449$		−	200739.i		−	0.995726i	−0.867256	−	0.497863i	$-0.834118\pi$
$449$		−	200739.i		−	0.995726i	0.867256	−	0.497863i	$-0.165882\pi$
$450$		0			0
$451$	329209.			1.61852
$452$		−	19681.4i		−	0.0963340i
$453$	54693.9	+	143110.i	0.266528	+	0.697388i
$454$	−21450.8			−0.104071
$455$		0			0
$456$	−6543.55	+	2500.81i	−0.0314691	+	0.0120268i
$457$	−396196.			−1.89705			−0.948523	−	0.316709i	$-0.897422\pi$
$457$	−396196.			−1.89705			−0.948523	+	0.316709i	$0.897422\pi$
$458$			22047.2i			0.105105i
$459$	115034.	−	223329.i	0.546011	−	1.06004i
$460$		0			0
$461$		−	182217.i		−	0.857405i	−0.903446	−	0.428702i	$-0.858971\pi$
$461$		−	182217.i		−	0.857405i	0.903446	−	0.428702i	$-0.141029\pi$
$462$	−12351.9	−	32319.7i	−0.0578696	−	0.151420i
$463$	−181212.			−0.845329			−0.422665	−	0.906286i	$-0.638905\pi$
$463$	−181212.			−0.845329			−0.422665	+	0.906286i	$0.638905\pi$
$464$			143387.i			0.666001i
$465$		0			0
$466$	33488.6			0.154214
$467$		−	370180.i		−	1.69738i	−0.528889	−	0.848691i	$-0.677391\pi$
$467$		−	370180.i		−	1.69738i	0.528889	−	0.848691i	$-0.322609\pi$
$468$	−21341.4	+	19102.7i	−0.0974386	+	0.0872172i
$469$	73502.7			0.334162
$470$		0			0
$471$	−37144.5	−	97191.1i	−0.167437	−	0.438112i
$472$	−53266.8			−0.239096
$473$		−	434118.i		−	1.94037i
$474$	−16448.4	+	6286.24i	−0.0732094	+	0.0279792i
$475$		0			0
$476$		−	256155.i		−	1.13055i
$477$	−141908.	−	158539.i	−0.623694	−	0.696787i
$478$	17950.0			0.0785615
$479$			13652.2i			0.0595020i	0.999557	+	0.0297510i	$0.00947143\pi$
$479$			13652.2i			0.0595020i	−0.999557	+	0.0297510i	$0.990529\pi$
$480$		0			0
$481$	−43253.1			−0.186951
$482$			4798.68i			0.0206551i
$483$	−84027.3	+	32113.6i	−0.360185	+	0.137656i
$484$	−407575.			−1.73987
$485$		0			0
$486$	−6057.16	−	23288.4i	−0.0256446	−	0.0985976i
$487$	193653.			0.816521			0.408260	−	0.912865i	$-0.366136\pi$
$487$	193653.			0.816521			0.408260	+	0.912865i	$0.366136\pi$
$488$			62147.5i			0.260966i
$489$	−19490.2	−	50997.6i	−0.0815079	−	0.213271i
$490$		0			0
$491$			26447.9i			0.109705i	0.998494	+	0.0548527i	$0.0174689\pi$
$491$			26447.9i			0.109705i	−0.998494	+	0.0548527i	$0.982531\pi$
$492$	218075.	−	83344.1i	0.900900	−	0.344306i
$493$	199195.			0.819566
$494$		−	546.028i		−	0.00223749i
$495$		0			0
$496$	121575.			0.494175
$497$		−	252205.i		−	1.02103i
$498$	4431.98	+	11596.6i	0.0178706	+	0.0467597i
$499$	365043.			1.46603			0.733015	−	0.680213i	$-0.238113\pi$
$499$	365043.			1.46603			0.733015	+	0.680213i	$0.238113\pi$
$500$		0			0
$501$	−58636.1	+	22409.5i	−0.233609	+	0.0892806i
$502$	−46738.9			−0.185469
$503$			85439.2i			0.337693i	0.985642	+	0.168846i	$0.0540041\pi$
$503$			85439.2i			0.337693i	−0.985642	+	0.168846i	$0.945996\pi$
$504$	−32900.4	−	36756.2i	−0.129521	−	0.144700i
$505$		0			0
$506$		−	17434.9i		−	0.0680954i
$507$	90163.2	+	235918.i	0.350763	+	0.917795i
$508$	−65614.6			−0.254257
$509$			28412.1i			0.109665i	0.998496	+	0.0548325i	$0.0174625\pi$
$509$			28412.1i			0.109665i	−0.998496	+	0.0548325i	$0.982538\pi$
$510$		0			0
$511$	202884.			0.776972
$512$			128050.i			0.488472i
$513$	−38884.1	−	20028.7i	−0.147753	−	0.0761059i
$514$	−18077.3			−0.0684239
$515$		0			0
$516$	−109903.	−	287570.i	−0.412773	−	1.08005i
$517$	458629.			1.71586
$518$		−	37053.0i		−	0.138091i
$519$	−234285.	+	89538.8i	−0.869779	+	0.332412i
$520$		0			0
$521$			2801.47i			0.0103208i	0.999987	+	0.00516038i	$0.00164261\pi$
$521$			2801.47i			0.0103208i	−0.999987	+	0.00516038i	$0.998357\pi$
$522$	14216.9	−	12725.5i	0.0521751	−	0.0467019i
$523$	524249.			1.91661			0.958306	−	0.285743i	$-0.0922405\pi$
$523$	524249.			1.91661			0.958306	+	0.285743i	$0.0922405\pi$
$524$			370743.i			1.35024i
$525$		0			0
$526$	−24924.5			−0.0900855
$527$		−	168893.i		−	0.608121i
$528$	−419065.	+	160158.i	−1.50319	+	0.574488i
$529$	234512.			0.838020
$530$		0			0
$531$	−221820.	−	247816.i	−0.786704	−	0.878901i
$532$	−44599.3			−0.157581
$533$			36585.6i			0.128782i
$534$	4512.43	+	11807.1i	0.0158244	+	0.0414057i
$535$		0			0
$536$			20311.3i			0.0706983i
$537$	−186992.	+	71464.5i	−0.648446	+	0.247823i
$538$	−22384.6			−0.0773367
$539$			39608.3i			0.136335i
$540$		0			0
$541$	300315.			1.02608			0.513042	−	0.858364i	$-0.328519\pi$
$541$	300315.			1.02608			0.513042	+	0.858364i	$0.328519\pi$
$542$		−	19641.9i		−	0.0668628i
$543$	−107544.	−	281395.i	−0.364741	−	0.954370i
$544$	106361.			0.359406
$545$		0			0
$546$	3591.74	−	1372.69i	0.0120481	−	0.00460455i
$547$	−255317.			−0.853307			−0.426653	−	0.904415i	$-0.640308\pi$
$547$	−255317.			−0.853307			−0.426653	+	0.904415i	$0.640308\pi$
$548$		−	66002.4i		−	0.219785i
$549$	−289132.	+	258802.i	−0.959294	+	0.858663i
$550$		0			0
$551$		−	34682.0i		−	0.114235i
$552$	−8874.09	−	23219.7i	−0.0291236	−	0.0762040i
$553$	−225393.			−0.737037
$554$		−	41359.7i		−	0.134759i
$555$		0			0
$556$	106133.			0.343320
$557$			517752.i			1.66883i	0.551138	+	0.834414i	$0.314194\pi$
$557$			517752.i			1.66883i	−0.551138	+	0.834414i	$0.685806\pi$
$558$	−10789.7	−	12054.2i	−0.0346530	−	0.0387141i
$559$	48244.3			0.154391
$560$		0			0
$561$	222493.	+	582168.i	0.706953	+	1.84979i
$562$	49269.2			0.155992
$563$			353826.i			1.11628i	0.829747	+	0.558139i	$0.188485\pi$
$563$			353826.i			1.11628i	−0.829747	+	0.558139i	$0.811515\pi$
$564$	303807.	−	116109.i	0.955078	−	0.365012i
$565$		0			0
$566$			45350.6i			0.141563i
$567$	33994.9	−	306129.i	0.105742	−	0.952222i
$568$	69692.9			0.216019
$569$		−	570557.i		−	1.76228i	−0.472857	−	0.881139i	$-0.656777\pi$
$569$		−	570557.i		−	1.76228i	0.472857	−	0.881139i	$-0.343223\pi$
$570$		0			0
$571$	−108185.			−0.331815			−0.165908	−	0.986141i	$-0.553055\pi$
$571$	−108185.			−0.331815			−0.165908	+	0.986141i	$0.553055\pi$
$572$		−	71057.7i		−	0.217180i
$573$	5062.28	−	1934.70i	0.0154183	−	0.00589257i
$574$	−31341.2			−0.0951244
$575$		0			0
$576$	−231947.	+	207615.i	−0.699106	+	0.625769i
$577$	−161728.			−0.485772			−0.242886	−	0.970055i	$-0.578094\pi$
$577$	−161728.			−0.485772			−0.242886	+	0.970055i	$0.578094\pi$
$578$		−	14356.4i		−	0.0429725i
$579$	−87397.3	−	228681.i	−0.260700	−	0.682139i
$580$		0			0
$581$			158908.i			0.470754i
$582$	−18663.4	+	7132.78i	−0.0550992	+	0.0210578i
$583$	527868.			1.55306
$584$			56063.8i			0.164383i
$585$		0			0
$586$	−26110.4			−0.0760359
$587$			61507.6i			0.178506i	0.996009	+	0.0892529i	$0.0284479\pi$
$587$			61507.6i			0.178506i	−0.996009	+	0.0892529i	$0.971552\pi$
$588$	10027.4	+	26237.5i	0.0290025	+	0.0758870i
$589$	−29406.1			−0.0847630
$590$		0			0
$591$	−518210.	+	198049.i	−1.48365	+	0.567020i
$592$	−480438.			−1.37086
$593$		−	204770.i		−	0.582313i	−0.956675	−	0.291157i	$-0.905960\pi$
$593$		−	204770.i		−	0.582313i	0.956675	−	0.291157i	$-0.0940400\pi$
$594$	53071.4	+	27336.4i	0.150414	+	0.0774764i
$595$		0			0
$596$			115081.i			0.323974i
$597$	34418.5	+	90058.3i	0.0965702	+	0.252683i
$598$	1937.57			0.00541820
$599$		−	460558.i		−	1.28360i	−0.766871	−	0.641801i	$-0.778188\pi$
$599$		−	460558.i		−	1.28360i	0.766871	−	0.641801i	$-0.221812\pi$
$600$		0			0
$601$	−273581.			−0.757419			−0.378710	−	0.925516i	$-0.623632\pi$
$601$	−273581.			−0.757419			−0.378710	+	0.925516i	$0.623632\pi$
$602$			41328.7i			0.114040i
$603$	−94495.5	+	84582.9i	−0.259882	+	0.232620i
$604$	−269539.			−0.738835
$605$		0			0
$606$	−10023.2	−	26226.3i	−0.0272935	−	0.0714154i
$607$	−6868.44			−0.0186415			−0.00932074	−	0.999957i	$-0.502967\pi$
$607$	−6868.44			−0.0186415			−0.00932074	+	0.999957i	$0.502967\pi$
$608$		−	18518.7i		−	0.0500959i
$609$	228136.	−	87189.1i	0.615120	−	0.235086i
$610$		0			0
$611$			50968.3i			0.136527i
$612$	294769.	+	329314.i	0.787007	+	0.879240i
$613$	−189461.			−0.504196			−0.252098	−	0.967702i	$-0.581121\pi$
$613$	−189461.			−0.504196			−0.252098	+	0.967702i	$0.581121\pi$
$614$		−	13719.5i		−	0.0363916i
$615$		0			0
$616$	122382.			0.322520
$617$			510628.i			1.34132i	0.741763	+	0.670662i	$0.233990\pi$
$617$			510628.i			1.34132i	−0.741763	+	0.670662i	$0.766010\pi$
$618$	−55375.7	+	21163.5i	−0.144991	+	0.0554128i
$619$	−466167.			−1.21663			−0.608317	−	0.793694i	$-0.708155\pi$
$619$	−466167.			−1.21663			−0.608317	+	0.793694i	$0.708155\pi$
$620$		0			0
$621$	71071.5	−	137979.i	0.184295	−	0.357793i
$622$	23808.9			0.0615400
$623$			161793.i			0.416853i
$624$	−17798.6	−	46571.4i	−0.0457107	−	0.119605i
$625$		0			0
$626$		−	16393.6i		−	0.0418336i
$627$	101362.	−	38738.4i	0.257833	−	0.0985388i
$628$	183053.			0.464149
$629$			667429.i			1.68696i
$630$		0			0
$631$	144471.			0.362847			0.181423	−	0.983405i	$-0.441930\pi$
$631$	144471.			0.362847			0.181423	+	0.983405i	$0.441930\pi$
$632$		−	62283.8i		−	0.155934i
$633$	−62348.1	−	163138.i	−0.155602	−	0.407144i
$634$	46530.0			0.115759
$635$		0			0
$636$	349672.	−	133638.i	0.864463	−	0.330380i
$637$	−4401.74			−0.0108479
$638$			47336.1i			0.116292i
$639$	290223.	+	324236.i	0.710773	+	0.794071i
$640$		0			0
$641$			536191.i			1.30498i	0.757798	+	0.652490i	$0.226275\pi$
$641$			536191.i			1.30498i	−0.757798	+	0.652490i	$0.773725\pi$
$642$	24804.2	+	64901.8i	0.0601803	+	0.157466i
$643$	−382957.			−0.926250			−0.463125	−	0.886293i	$-0.653272\pi$
$643$	−382957.			−0.926250			−0.463125	+	0.886293i	$0.653272\pi$
$644$		−	158260.i		−	0.381592i
$645$		0			0
$646$	−8425.63			−0.0201900
$647$		−	320474.i		−	0.765570i	−0.923838	−	0.382785i	$-0.874965\pi$
$647$		−	320474.i		−	0.765570i	0.923838	−	0.382785i	$-0.125035\pi$
$648$	84594.0	+	9393.96i	0.201460	+	0.0223717i
$649$	825120.			1.95897
$650$		0			0
$651$	−73925.7	−	193432.i	−0.174435	−	0.456421i
$652$	96050.5			0.225946
$653$			227576.i			0.533703i	0.963738	+	0.266851i	$0.0859833\pi$
$653$			227576.i			0.533703i	−0.963738	+	0.266851i	$0.914017\pi$
$654$	−14983.2	+	5726.30i	−0.0350308	+	0.0133881i
$655$		0			0
$656$			406378.i			0.944327i
$657$	−260829.	+	233468.i	−0.604261	+	0.540874i
$658$	−43662.3			−0.100845
$659$			531408.i			1.22365i	0.790993	+	0.611825i	$0.209564\pi$
$659$			531408.i			1.22365i	−0.790993	+	0.611825i	$0.790436\pi$
$660$		0			0
$661$	−251100.			−0.574704			−0.287352	−	0.957825i	$-0.592775\pi$
$661$	−251100.			−0.574704			−0.287352	+	0.957825i	$0.592775\pi$
$662$			195.286i			0.000445610i
$663$	−64697.3	+	24726.0i	−0.147184	+	0.0562506i
$664$	−43911.9			−0.0995969
$665$		0			0
$666$	42638.6	+	47635.6i	0.0961290	+	0.107395i
$667$	123068.			0.276627
$668$		−	110437.i		−	0.247493i
$669$	−193486.	−	506269.i	−0.432311	−	1.13117i
$670$		0			0
$671$		−	962686.i		−	2.13816i
$672$	121815.	−	46555.1i	0.269750	−	0.103093i
$673$	−532133.			−1.17487			−0.587435	−	0.809271i	$-0.699862\pi$
$673$	−532133.			−1.17487			−0.587435	+	0.809271i	$0.699862\pi$
$674$			56905.9i			0.125267i
$675$		0			0
$676$	−444336.			−0.972340
$677$		−	73112.8i		−	0.159520i	−0.996814	−	0.0797602i	$-0.974585\pi$
$677$		−	73112.8i		−	0.159520i	0.996814	−	0.0797602i	$-0.0254154\pi$
$678$	−1627.48	−	4258.40i	−0.00354042	−	0.00926376i
$679$	−255745.			−0.554712
$680$		0			0
$681$	442528.	−	169125.i	0.954216	−	0.364682i
$682$	40135.2			0.0862893
$683$		−	674426.i		−	1.44575i	−0.690979	−	0.722875i	$-0.742820\pi$
$683$		−	674426.i		−	1.44575i	0.690979	−	0.722875i	$-0.257180\pi$
$684$	57337.2	−	51322.5i	0.122553	−	0.109697i
$685$		0			0
$686$		−	49704.2i		−	0.105620i
$687$	−173828.	−	454833.i	−0.368304	−	0.963692i
$688$	535878.			1.13211
$689$			58662.9i			0.123573i
$690$		0			0
$691$	617153.			1.29252			0.646259	−	0.763118i	$-0.276333\pi$
$691$	617153.			1.29252			0.646259	+	0.763118i	$0.276333\pi$
$692$		−	441259.i		−	0.921471i
$693$	509639.	+	569366.i	1.06120	+	1.18556i
$694$	53724.2			0.111545
$695$		0			0
$696$	24093.4	+	63042.0i	0.0497369	+	0.130140i
$697$	564543.			1.16207
$698$		−	97009.6i		−	0.199115i
$699$	−690867.	+	264036.i	−1.41397	+	0.540391i
$700$		0			0
$701$		−	154788.i		−	0.314993i	−0.987520	−	0.157496i	$-0.949658\pi$
$701$		−	154788.i		−	0.314993i	0.987520	−	0.157496i	$-0.0503422\pi$
$702$	−3037.95	+	5897.92i	−0.00616462	+	0.0119681i
$703$	116207.			0.235137
$704$		−	772283.i		−	1.55823i
$705$		0			0
$706$	−73976.9			−0.148418
$707$		−	359379.i		−	0.718976i
$708$	546579.	−	208891.i	1.09040	−	0.416729i
$709$	−480282.			−0.955440			−0.477720	−	0.878512i	$-0.658537\pi$
$709$	−480282.			−0.955440			−0.477720	+	0.878512i	$0.658537\pi$
$710$		0			0
$711$	289766.	−	259370.i	0.573203	−	0.513074i
$712$	−44708.9			−0.0881931
$713$		−	104347.i		−	0.205258i
$714$	−21181.7	−	55423.3i	−0.0415493	−	0.108717i
$715$		0			0
$716$		−	352187.i		−	0.686984i
$717$	−370308.	+	141524.i	−0.720319	+	0.275291i
$718$	−13271.5			−0.0257437
$719$		−	99977.2i		−	0.193394i	−0.995314	−	0.0966971i	$-0.969172\pi$
$719$		−	99977.2i		−	0.193394i	0.995314	−	0.0966971i	$-0.0308278\pi$
$720$		0			0
$721$	−758814.			−1.45970
$722$		−	51640.4i		−	0.0990639i
$723$	−37834.5	−	98996.5i	−0.0723788	−	0.189384i
$724$	529989.			1.01109
$725$		0			0
$726$	−88185.8	+	33702.8i	−0.167311	+	0.0639430i
$727$	182930.			0.346112			0.173056	−	0.984912i	$-0.444636\pi$
$727$	182930.			0.346112			0.173056	+	0.984912i	$0.444636\pi$
$728$			13600.6i			0.0256622i
$729$	308572.	+	432681.i	0.580633	+	0.814165i
$730$		0			0
$731$		−	744446.i		−	1.39315i
$732$	−243718.	−	637705.i	−0.454847	−	1.19014i
$733$	−671761.			−1.25028			−0.625139	−	0.780513i	$-0.714958\pi$
$733$	−671761.			−1.25028			−0.625139	+	0.780513i	$0.714958\pi$
$734$		−	47756.2i		−	0.0886417i
$735$		0			0
$736$	65713.1			0.121310
$737$		−	314630.i		−	0.579248i
$738$	40292.5	−	36065.8i	0.0739795	−	0.0662190i
$739$	−209903.			−0.384353			−0.192176	−	0.981360i	$-0.561555\pi$
$739$	−209903.			−0.384353			−0.192176	+	0.981360i	$0.561555\pi$
$740$		0			0
$741$	4305.07	+	11264.5i	0.00784051	+	0.0205152i
$742$	−50253.9			−0.0912771
$743$			980505.i			1.77612i	0.459728	+	0.888060i	$0.347947\pi$
$743$			980505.i			1.77612i	−0.459728	+	0.888060i	$0.652053\pi$
$744$	53451.9	−	20428.2i	0.0965644	−	0.0369050i
$745$		0			0
$746$		−	63491.5i		−	0.114087i
$747$	−182863.	−	204294.i	−0.327706	−	0.366112i
$748$	−1.09647e6			−1.95973
$749$			889351.i			1.58529i
$750$		0			0
$751$	642018.			1.13833			0.569164	−	0.822224i	$-0.307267\pi$
$751$	642018.			1.13833			0.569164	+	0.822224i	$0.307267\pi$
$752$			566135.i			1.00112i
$753$	964220.	−	368506.i	1.70054	−	0.649911i
$754$	−5260.55			−0.00925312
$755$		0			0
$756$	481740.	+	248138.i	0.842886	+	0.434160i
$757$	315426.			0.550434			0.275217	−	0.961382i	$-0.411250\pi$
$757$	315426.			0.550434			0.275217	+	0.961382i	$0.411250\pi$
$758$			71003.8i			0.123579i
$759$	137463.	+	359680.i	0.238617	+	0.624357i
$760$		0			0
$761$			843657.i			1.45679i	0.685158	+	0.728394i	$0.259733\pi$
$761$			843657.i			1.45679i	−0.685158	+	0.728394i	$0.740267\pi$
$762$	−14196.8	+	5425.74i	−0.0244501	+	0.00934435i
$763$	−205316.			−0.352674
$764$			9534.47i			0.0163347i
$765$		0			0
$766$	103059.			0.175643
$767$			91697.1i			0.155871i
$768$	−189049.	−	494659.i	−0.320517	−	0.838656i
$769$	−326397.			−0.551942			−0.275971	−	0.961166i	$-0.588999\pi$
$769$	−326397.			−0.551942			−0.275971	+	0.961166i	$0.588999\pi$
$770$		0			0
$771$	372934.	−	142528.i	0.627369	−	0.239768i
$772$	430706.			0.722680
$773$			702706.i			1.17602i	0.808853	+	0.588010i	$0.200089\pi$
$773$			702706.i			1.17602i	−0.808853	+	0.588010i	$0.799911\pi$
$774$	−47558.8	−	53132.5i	−0.0793870	−	0.0886907i
$775$		0			0
$776$		−	70671.2i		−	0.117360i
$777$	292139.	+	764401.i	0.483891	+	1.26613i
$778$	51124.0			0.0844628
$779$		−	98293.2i		−	0.161975i
$780$		0			0
$781$	−1.07957e6			−1.76989
$782$		−	29898.2i		−	0.0488913i
$783$	−192961.	+	374618.i	−0.314736	+	0.611033i
$784$	−48892.8			−0.0795450
$785$		0			0
$786$	30657.1	+	80216.5i	0.0496234	+	0.129843i
$787$	−447743.			−0.722902			−0.361451	−	0.932391i	$-0.617718\pi$
$787$	−447743.			−0.722902			−0.361451	+	0.932391i	$0.617718\pi$
$788$		−	976013.i		−	1.57182i
$789$	514191.	−	196513.i	0.825982	−	0.315674i
$790$		0			0
$791$		−	58353.0i		−	0.0932632i
$792$	−157335.	+	140831.i	−0.250828	+	0.224516i
$793$	106985.			0.170128
$794$			91853.0i			0.145698i
$795$		0			0
$796$	−169619.			−0.267700
$797$			662789.i			1.04342i	0.853123	+	0.521710i	$0.174706\pi$
$797$			662789.i			1.04342i	−0.853123	+	0.521710i	$0.825294\pi$
$798$	−9649.81	+	3687.96i	−0.0151535	+	0.00579136i
$799$	786480.			1.23195
$800$		0			0
$801$	−186182.	−	208002.i	−0.290184	−	0.324192i
$802$	−52434.7			−0.0815212
$803$		−	868448.i		−	1.34683i
$804$	−79653.1	−	208418.i	−0.123223	−	0.322421i
$805$		0			0
$806$			4460.30i			0.00686585i
$807$	461794.	−	176488.i	0.709089	−	0.271000i
$808$	99309.0			0.152113
$809$		−	1.20479e6i		−	1.84084i	−0.390936	−	0.920418i	$-0.627848\pi$
$809$		−	1.20479e6i		−	1.84084i	0.390936	−	0.920418i	$-0.372152\pi$
$810$		0			0
$811$	−380108.			−0.577917			−0.288958	−	0.957342i	$-0.593309\pi$
$811$	−380108.			−0.577917			−0.288958	+	0.957342i	$0.593309\pi$
$812$			429679.i			0.651677i
$813$	154863.	+	405210.i	0.234297	+	0.613055i
$814$	−158606.			−0.239371
$815$		0			0
$816$	−718632.	+	274647.i	−1.07926	+	0.412472i
$817$	−129616.			−0.194185
$818$			43077.2i			0.0643785i
$819$	−63274.6	+	56637.1i	−0.0943326	+	0.0844370i
$820$		0			0
$821$			1.16909e6i			1.73444i	0.497923	+	0.867221i	$0.334096\pi$
$821$			1.16909e6i			1.73444i	−0.497923	+	0.867221i	$0.665904\pi$
$822$	−5457.80	−	14280.7i	−0.00807745	−	0.0211352i
$823$	1.04796e6			1.54719			0.773594	−	0.633681i	$-0.218457\pi$
$823$	1.04796e6			1.54719			0.773594	+	0.633681i	$0.218457\pi$
$824$		−	209687.i		−	0.308828i
$825$		0			0
$826$	−78552.8			−0.115133
$827$			9106.01i			0.0133143i	0.999978	+	0.00665713i	$0.00211905\pi$
$827$			9106.01i			0.0133143i	−0.999978	+	0.00665713i	$0.997881\pi$
$828$	182117.	+	203460.i	0.265638	+	0.296769i
$829$	−715146.			−1.04060			−0.520302	−	0.853982i	$-0.674181\pi$
$829$	−715146.			−1.04060			−0.520302	+	0.853982i	$0.674181\pi$
$830$		0			0
$831$	326094.	+	853249.i	0.472217	+	1.23559i
$832$	85825.2			0.123985
$833$			67922.3i			0.0978863i
$834$	22963.6	−	8776.22i	0.0330147	−	0.0126176i
$835$		0			0
$836$			190908.i			0.273157i
$837$	317630.	+	163607.i	0.453388	+	0.233535i
$838$	−64354.1			−0.0916406
$839$			242894.i			0.345059i	0.985004	+	0.172529i	$0.0551940\pi$
$839$			242894.i			0.345059i	−0.985004	+	0.172529i	$0.944806\pi$
$840$		0			0
$841$	373147.			0.527580
$842$		−	99853.9i		−	0.140845i
$843$	−1.01642e6	+	388456.i	−1.43027	+	0.546621i
$844$	307260.			0.431341
$845$		0			0
$846$	56132.5	−	50244.1i	0.0784284	−	0.0702012i
$847$	−1.20841e6			−1.68441
$848$			651604.i			0.906133i
$849$	−357560.	−	935580.i	−0.496059	−	1.29797i
$850$		0			0
$851$			412357.i			0.569396i
$852$	−715130.	+	273308.i	−0.985158	+	0.376507i
$853$	−861767.			−1.18438			−0.592191	−	0.805797i	$-0.701737\pi$
$853$	−861767.			−1.18438			−0.592191	+	0.805797i	$0.701737\pi$
$854$			91649.3i			0.125665i
$855$		0			0
$856$	−245758.			−0.335398
$857$		−	525214.i		−	0.715113i	−0.933891	−	0.357557i	$-0.883610\pi$
$857$		−	525214.i		−	0.715113i	0.933891	−	0.357557i	$-0.116390\pi$
$858$	−5875.83	−	15374.5i	−0.00798169	−	0.0208846i
$859$	66206.8			0.0897256			0.0448628	−	0.998993i	$-0.485715\pi$
$859$	66206.8			0.0897256			0.0448628	+	0.998993i	$0.485715\pi$
$860$		0			0
$861$	646567.	−	247105.i	0.872182	−	0.333331i
$862$	−25015.3			−0.0336660
$863$		−	5062.88i		−	0.00679792i	−0.999994	−	0.00339896i	$-0.998918\pi$
$863$		−	5062.88i		−	0.00679792i	0.999994	−	0.00339896i	$-0.00108192\pi$
$864$	−103033.	+	200029.i	−0.138022	+	0.267958i
$865$		0			0
$866$		−	10294.9i		−	0.0137274i
$867$	113191.	+	296172.i	0.150582	+	0.394009i
$868$	364316.			0.483546
$869$			964797.i			1.27760i
$870$		0			0
$871$	34965.3			0.0460894
$872$		−	56735.9i		−	0.0746148i
$873$	328788.	−	294298.i	0.431407	−	0.386152i
$874$	−5205.60			−0.00681472
$875$		0			0
$876$	−219860.	−	575280.i	−0.286509	−	0.749672i
$877$	−1.24871e6			−1.62354			−0.811772	−	0.583975i	$-0.801497\pi$
$877$	−1.24871e6			−1.62354			−0.811772	+	0.583975i	$0.801497\pi$
$878$		−	84390.7i		−	0.109473i
$879$	538656.	−	205864.i	0.697162	−	0.266441i
$880$		0			0
$881$		−	112260.i		−	0.144635i	−0.997382	−	0.0723173i	$-0.976961\pi$
$881$		−	112260.i		−	0.144635i	0.997382	−	0.0723173i	$-0.0230394\pi$
$882$	4339.20	+	4847.73i	0.00557793	+	0.00623163i
$883$	329416.			0.422496			0.211248	−	0.977432i	$-0.432247\pi$
$883$	329416.			0.422496			0.211248	+	0.977432i	$0.432247\pi$
$884$		−	121853.i		−	0.155931i
$885$		0			0
$886$	54023.0			0.0688194
$887$		−	152778.i		−	0.194185i	−0.995275	−	0.0970923i	$-0.969046\pi$
$887$		−	152778.i		−	0.194185i	0.995275	−	0.0970923i	$-0.0309542\pi$
$888$	−211231.	+	80728.1i	−0.267874	+	0.102376i
$889$	−194539.			−0.246152
$890$		0			0
$891$	−1.31039e6	−	145516.i	−1.65061	−	0.183296i
$892$	953523.			1.19840
$893$		−	136935.i		−	0.171716i
$894$	9516.13	+	24899.6i	0.0119065	+	0.0311543i
$895$		0			0
$896$			305359.i			0.380360i
$897$	−39971.9	+	15276.5i	−0.0496787	+	0.0189862i
$898$	81803.8			0.101443
$899$			283304.i			0.350537i
$900$		0			0
$901$	905213.			1.11507
$902$			134157.i			0.164892i
$903$	−325850.	−	852609.i	−0.399615	−	1.04562i
$904$	16125.0			0.0197316
$905$		0			0
$906$	−58319.2	+	22288.4i	−0.0710486	+	0.0271533i
$907$	1.26534e6			1.53813			0.769067	−	0.639169i	$-0.220721\pi$
$907$	1.26534e6			1.53813			0.769067	+	0.639169i	$0.220721\pi$
$908$			833472.i			1.01093i
$909$	413554.	+	462021.i	0.500501	+	0.559157i
$910$		0			0
$911$		−	702340.i		−	0.846274i	−0.906066	−	0.423137i	$-0.860929\pi$
$911$		−	702340.i		−	0.846274i	0.906066	−	0.423137i	$-0.139071\pi$
$912$	47819.0	+	125122.i	0.0574925	+	0.150433i
$913$	680210.			0.816021
$914$		−	161455.i		−	0.193267i
$915$		0			0
$916$	856648.			1.02097
$917$			1.09921e6i			1.30720i
$918$	91009.4	+	46877.9i	0.107994	+	0.0556266i
$919$	266756.			0.315851			0.157926	−	0.987451i	$-0.449519\pi$
$919$	266756.			0.315851			0.157926	+	0.987451i	$0.449519\pi$
$920$		0			0
$921$	108169.	+	283032.i	0.127522	+	0.333670i
$922$	74255.5			0.0873507
$923$		−	119974.i		−	0.140827i
$924$	−1.25578e6	+	479935.i	−1.47086	+	0.562133i
$925$		0			0
$926$		−	73846.3i		−	0.0861205i
$927$	975536.	−	873202.i	1.13523	−	1.01614i
$928$	−178413.			−0.207171
$929$		−	1.29140e6i		−	1.49634i	−0.663509	−	0.748169i	$-0.730933\pi$
$929$		−	1.29140e6i		−	1.49634i	0.663509	−	0.748169i	$-0.269067\pi$
$930$		0			0
$931$	11826.0			0.0136439
$932$		−	1.30120e6i		−	1.49800i
$933$	−491175.	+	187717.i	−0.564252	+	0.215646i
$934$	150853.			0.172926
$935$		0			0
$936$	−15650.8	−	17485.0i	−0.0178642	−	0.0199578i
$937$	399820.			0.455392			0.227696	−	0.973732i	$-0.426881\pi$
$937$	399820.			0.455392			0.227696	+	0.973732i	$0.426881\pi$
$938$			29953.2i			0.0340438i
$939$	129253.	+	338199.i	0.146591	+	0.383566i
$940$		0			0
$941$		−	1.22439e6i		−	1.38274i	−0.722499	−	0.691372i	$-0.757007\pi$
$941$		−	1.22439e6i		−	1.38274i	0.722499	−	0.691372i	$-0.242993\pi$
$942$	39606.6	−	15136.8i	0.0446340	−	0.0170582i
$943$	348791.			0.392231
$944$			1.01853e6i			1.14296i
$945$		0			0
$946$	176908.			0.197682
$947$			699832.i			0.780358i	0.920739	+	0.390179i	$0.127587\pi$
$947$			699832.i			0.780358i	−0.920739	+	0.390179i	$0.872413\pi$
$948$	244253.	+	639104.i	0.271783	+	0.711140i
$949$	96512.2			0.107164
$950$		0			0
$951$	−959910.	+	366858.i	−1.06138	+	0.405637i
$952$	209867.			0.231564
$953$		−	1.25288e6i		−	1.37950i	−0.724045	−	0.689752i	$-0.757719\pi$
$953$		−	1.25288e6i		−	1.37950i	0.724045	−	0.689752i	$-0.242281\pi$
$954$	64606.7	−	57829.4i	0.0709874	−	0.0635407i
$955$		0			0
$956$		−	697451.i		−	0.763128i
$957$	−373214.	−	976541.i	−0.407507	−	1.06627i
$958$	−5563.43			−0.00606194
$959$		−	195689.i		−	0.212779i
$960$		0			0
$961$	−683314.			−0.739900
$962$		−	17626.2i		−	0.0190462i
$963$	−1.02342e6	−	1.14336e6i	−1.10357	−	1.23290i
$964$	186453.			0.200639
$965$		0			0
$966$	−13086.7	−	34242.2i	−0.0140241	−	0.0366950i
$967$	−580972.			−0.621301			−0.310651	−	0.950524i	$-0.600547\pi$
$967$	−580972.			−0.621301			−0.310651	+	0.950524i	$0.600547\pi$
$968$		−	333926.i		−	0.356369i
$969$	173820.	−	66430.6i	0.185120	−	0.0707490i
$970$		0			0
$971$		−	648131.i		−	0.687423i	−0.939075	−	0.343712i	$-0.888316\pi$
$971$		−	648131.i		−	0.687423i	0.939075	−	0.343712i	$-0.111684\pi$
$972$	−904872.	+	235352.i	−0.957755	+	0.249106i
$973$	314670.			0.332376
$974$			78916.2i			0.0831856i
$975$		0			0
$976$	1.18835e6			1.24751
$977$		−	1.48636e6i		−	1.55717i	−0.627539	−	0.778585i	$-0.715938\pi$
$977$		−	1.48636e6i		−	1.55717i	0.627539	−	0.778585i	$-0.284062\pi$
$978$	20782.1	−	7942.51i	0.0217276	−	0.00830386i
$979$	692557.			0.722587
$980$		0			0
$981$	263955.	−	236266.i	0.274279	−	0.245507i
$982$	−10777.8			−0.0111766
$983$			992676.i			1.02731i	0.857998	+	0.513654i	$0.171708\pi$
$983$			992676.i			1.02731i	−0.857998	+	0.513654i	$0.828292\pi$
$984$	68283.7	+	178669.i	0.0705223	+	0.184527i
$985$		0			0
$986$			81174.3i			0.0834958i
$987$	900749.	−	344248.i	0.924634	−	0.353376i
$988$	−21216.0			−0.0217345
$989$		−	459941.i		−	0.470229i
$990$		0			0
$991$	1.60928e6			1.63864			0.819322	−	0.573334i	$-0.194350\pi$
$991$	1.60928e6			1.63864			0.819322	+	0.573334i	$0.194350\pi$
$992$			151272.i			0.153722i
$993$	−1539.70	−	4028.73i	−0.00156148	−	0.00408573i
$994$	102777.			0.104021
$995$		0			0
$996$	450587.	−	172205.i	0.454213	−	0.173591i
$997$	−375625.			−0.377889			−0.188945	−	0.981988i	$-0.560507\pi$
$997$	−375625.			−0.377889			−0.188945	+	0.981988i	$0.560507\pi$
$998$			148759.i			0.149356i
$999$	−1.25521e6	−	646542.i	−1.25772	−	0.647837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.5.c.i.26.4		6
3.2	odd	2	inner	75.5.c.i.26.3		6
5.2	odd	4		75.5.d.d.74.6		12
5.3	odd	4		75.5.d.d.74.7		12
5.4	even	2		15.5.c.a.11.3	✓	6
15.2	even	4		75.5.d.d.74.8		12
15.8	even	4		75.5.d.d.74.5		12
15.14	odd	2		15.5.c.a.11.4	yes	6
20.19	odd	2		240.5.l.d.161.3		6
60.59	even	2		240.5.l.d.161.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.5.c.a.11.3	✓	6	5.4	even	2
15.5.c.a.11.4	yes	6	15.14	odd	2
75.5.c.i.26.3		6	3.2	odd	2	inner
75.5.c.i.26.4		6	1.1	even	1	trivial
75.5.d.d.74.5		12	15.8	even	4
75.5.d.d.74.6		12	5.2	odd	4
75.5.d.d.74.7		12	5.3	odd	4
75.5.d.d.74.8		12	15.2	even	4
240.5.l.d.161.3		6	20.19	odd	2
240.5.l.d.161.4		6	60.59	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.407512i q^{2} +(-3.21297 - 8.40695i) q^{3} +15.8339 q^{4} +(3.42594 - 1.30932i) q^{6} +46.9457 q^{7} +12.9727i q^{8} +(-60.3537 + 54.0225i) q^{9} -200.952i q^{11} +(-50.8739 - 133.115i) q^{12} +22.3321 q^{13} +19.1309i q^{14} +248.056 q^{16} -344.602i q^{17} +(-22.0148 - 24.5949i) q^{18} -59.9990 q^{19} +(-150.835 - 394.670i) q^{21} +81.8903 q^{22} -212.905i q^{23} +(109.061 - 41.6809i) q^{24} +9.10062i q^{26} +(648.079 + 333.818i) q^{27} +743.335 q^{28} +578.043i q^{29} +490.110 q^{31} +308.650i q^{32} +(-1689.39 + 645.652i) q^{33} +140.429 q^{34} +(-955.636 + 855.389i) q^{36} -1936.81 q^{37} -24.4503i q^{38} +(-71.7524 - 187.745i) q^{39} +1638.25i q^{41} +(160.833 - 61.4671i) q^{42} +2160.31 q^{43} -3181.86i q^{44} +86.7615 q^{46} +2282.28i q^{47} +(-796.997 - 2085.40i) q^{48} -197.104 q^{49} +(-2897.05 + 1107.19i) q^{51} +353.606 q^{52} +2626.84i q^{53} +(-136.035 + 264.100i) q^{54} +609.013i q^{56} +(192.775 + 504.409i) q^{57} -235.560 q^{58} +4106.06i q^{59} +4790.63 q^{61} +199.726i q^{62} +(-2833.34 + 2536.12i) q^{63} +3843.12 q^{64} +(-263.111 - 688.448i) q^{66} +1565.70 q^{67} -5456.40i q^{68} +(-1789.88 + 684.058i) q^{69} -5372.27i q^{71} +(-700.819 - 782.951i) q^{72} +4321.67 q^{73} -789.274i q^{74} -950.020 q^{76} -9433.82i q^{77} +(76.5085 - 29.2400i) q^{78} -4801.14 q^{79} +(724.132 - 6520.92i) q^{81} -667.606 q^{82} +3384.94i q^{83} +(-2388.31 - 6249.18i) q^{84} +880.352i q^{86} +(4859.58 - 1857.23i) q^{87} +2606.89 q^{88} +3446.38i q^{89} +1048.40 q^{91} -3371.13i q^{92} +(-1574.71 - 4120.33i) q^{93} -930.059 q^{94} +(2594.80 - 991.681i) q^{96} -5447.68 q^{97} -80.3221i q^{98} +(10855.9 + 12128.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 8 q^{3} - 50 q^{4} - 2 q^{6} - 76 q^{7} + 118 q^{9} + 452 q^{12} + 424 q^{13} + 802 q^{16} - 1160 q^{18} - 244 q^{19} - 876 q^{21} - 340 q^{22} - 786 q^{24} + 352 q^{27} + 3764 q^{28} + 3772 q^{31}+ \cdots + 9680 q^{99}+O(q^{100}) \) 6 * q - 8 * q^3 - 50 * q^4 - 2 * q^6 - 76 * q^7 + 118 * q^9 + 452 * q^12 + 424 * q^13 + 802 * q^16 - 1160 * q^18 - 244 * q^19 - 876 * q^21 - 340 * q^22 - 786 * q^24 + 352 * q^27 + 3764 * q^28 + 3772 * q^31 - 4420 * q^33 + 3124 * q^34 - 7606 * q^36 - 1896 * q^37 - 1336 * q^39 + 1980 * q^42 + 7384 * q^43 + 8196 * q^46 - 14668 * q^48 - 1318 * q^49 - 8492 * q^51 - 8976 * q^52 - 278 * q^54 + 11584 * q^57 + 23740 * q^58 + 6452 * q^61 - 14796 * q^63 + 3174 * q^64 - 12760 * q^66 - 13816 * q^67 + 5472 * q^69 + 2040 * q^72 - 596 * q^73 + 21348 * q^76 + 1400 * q^78 - 16124 * q^79 + 5086 * q^81 + 31240 * q^82 - 14736 * q^84 + 4900 * q^87 - 15660 * q^88 - 11632 * q^91 + 8184 * q^93 + 34924 * q^94 + 14354 * q^96 - 9756 * q^97 + 9680 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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