LMFDB - Embedded newform 75.5.c.d.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,5,Mod(26,75)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$7.75274723129$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-35}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 9 $ x^2 - x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.2
Root			$0.500000 - 2.95804i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.5.c.d.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.91608i q^{2} +(-1.50000 - 8.87412i) q^{3} -19.0000 q^{4} +(52.5000 - 8.87412i) q^{6} +72.0000 q^{7} -17.7482i q^{8} +(-76.5000 + 26.6224i) q^{9} +O(q^{10})$	\(q+5.91608i q^{2} +(-1.50000 - 8.87412i) q^{3} -19.0000 q^{4} +(52.5000 - 8.87412i) q^{6} +72.0000 q^{7} -17.7482i q^{8} +(-76.5000 + 26.6224i) q^{9} +183.398i q^{11} +(28.5000 + 168.608i) q^{12} +202.000 q^{13} +425.958i q^{14} -199.000 q^{16} +76.9090i q^{17} +(-157.500 - 452.580i) q^{18} +367.000 q^{19} +(-108.000 - 638.937i) q^{21} -1085.00 q^{22} +35.4965i q^{23} +(-157.500 + 26.6224i) q^{24} +1195.05i q^{26} +(351.000 + 638.937i) q^{27} -1368.00 q^{28} +366.797i q^{29} -318.000 q^{31} -1461.27i q^{32} +(1627.50 - 275.098i) q^{33} -455.000 q^{34} +(1453.50 - 505.825i) q^{36} +752.000 q^{37} +2171.20i q^{38} +(-303.000 - 1792.57i) q^{39} -1603.26i q^{41} +(3780.00 - 638.937i) q^{42} +982.000 q^{43} -3484.57i q^{44} -210.000 q^{46} +1195.05i q^{47} +(298.500 + 1765.95i) q^{48} +2783.00 q^{49} +(682.500 - 115.364i) q^{51} -3838.00 q^{52} -2354.60i q^{53} +(-3780.00 + 2076.54i) q^{54} -1277.87i q^{56} +(-550.500 - 3256.80i) q^{57} -2170.00 q^{58} +23.6643i q^{59} -3728.00 q^{61} -1881.31i q^{62} +(-5508.00 + 1916.81i) q^{63} +5461.00 q^{64} +(1627.50 + 9628.42i) q^{66} -7443.00 q^{67} -1461.27i q^{68} +(315.000 - 53.2447i) q^{69} -6732.50i q^{71} +(472.500 + 1357.74i) q^{72} +397.000 q^{73} +4448.89i q^{74} -6973.00 q^{76} +13204.7i q^{77} +(10605.0 - 1792.57i) q^{78} -6108.00 q^{79} +(5143.50 - 4073.22i) q^{81} +9485.00 q^{82} -13293.4i q^{83} +(2052.00 + 12139.8i) q^{84} +5809.59i q^{86} +(3255.00 - 550.195i) q^{87} +3255.00 q^{88} +4738.78i q^{89} +14544.0 q^{91} -674.433i q^{92} +(477.000 + 2821.97i) q^{93} -7070.00 q^{94} +(-12967.5 + 2191.91i) q^{96} +8042.00 q^{97} +16464.5i q^{98} +(-4882.50 - 14030.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} - 38 q^{4} + 105 q^{6} + 144 q^{7} - 153 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 - 38 * q^4 + 105 * q^6 + 144 * q^7 - 153 * q^9	$ 2 q - 3 q^{3} - 38 q^{4} + 105 q^{6} + 144 q^{7} - 153 q^{9} + 57 q^{12} + 404 q^{13} - 398 q^{16} - 315 q^{18} + 734 q^{19} - 216 q^{21} - 2170 q^{22} - 315 q^{24} + 702 q^{27} - 2736 q^{28} - 636 q^{31} + 3255 q^{33} - 910 q^{34} + 2907 q^{36} + 1504 q^{37} - 606 q^{39} + 7560 q^{42} + 1964 q^{43} - 420 q^{46} + 597 q^{48} + 5566 q^{49} + 1365 q^{51} - 7676 q^{52} - 7560 q^{54} - 1101 q^{57} - 4340 q^{58} - 7456 q^{61} - 11016 q^{63} + 10922 q^{64} + 3255 q^{66} - 14886 q^{67} + 630 q^{69} + 945 q^{72} + 794 q^{73} - 13946 q^{76} + 21210 q^{78} - 12216 q^{79} + 10287 q^{81} + 18970 q^{82} + 4104 q^{84} + 6510 q^{87} + 6510 q^{88} + 29088 q^{91} + 954 q^{93} - 14140 q^{94} - 25935 q^{96} + 16084 q^{97} - 9765 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 - 38 * q^4 + 105 * q^6 + 144 * q^7 - 153 * q^9 + 57 * q^12 + 404 * q^13 - 398 * q^16 - 315 * q^18 + 734 * q^19 - 216 * q^21 - 2170 * q^22 - 315 * q^24 + 702 * q^27 - 2736 * q^28 - 636 * q^31 + 3255 * q^33 - 910 * q^34 + 2907 * q^36 + 1504 * q^37 - 606 * q^39 + 7560 * q^42 + 1964 * q^43 - 420 * q^46 + 597 * q^48 + 5566 * q^49 + 1365 * q^51 - 7676 * q^52 - 7560 * q^54 - 1101 * q^57 - 4340 * q^58 - 7456 * q^61 - 11016 * q^63 + 10922 * q^64 + 3255 * q^66 - 14886 * q^67 + 630 * q^69 + 945 * q^72 + 794 * q^73 - 13946 * q^76 + 21210 * q^78 - 12216 * q^79 + 10287 * q^81 + 18970 * q^82 + 4104 * q^84 + 6510 * q^87 + 6510 * q^88 + 29088 * q^91 + 954 * q^93 - 14140 * q^94 - 25935 * q^96 + 16084 * q^97 - 9765 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$			5.91608i			1.47902i	0.673146	+	0.739510i	$0.264943\pi$
$2$			5.91608i			1.47902i	−0.673146	+	0.739510i	$0.735057\pi$
$3$	−1.50000	−	8.87412i	−0.166667	−	0.986013i
$3$	−1.50000	−	8.87412i	−0.166667	−	0.986013i
$4$	−19.0000			−1.18750
$5$		0			0
$5$		0			0
$6$	52.5000	−	8.87412i	1.45833	−	0.246503i
$7$	72.0000			1.46939			0.734694	−	0.678399i	$-0.237326\pi$
$7$	72.0000			1.46939			0.734694	+	0.678399i	$0.237326\pi$
$8$		−	17.7482i		−	0.277316i
$9$	−76.5000	+	26.6224i	−0.944444	+	0.328671i
$10$		0			0
$11$			183.398i			1.51569i	0.652435	+	0.757845i	$0.273748\pi$
$11$			183.398i			1.51569i	−0.652435	+	0.757845i	$0.726252\pi$
$12$	28.5000	+	168.608i	0.197917	+	1.17089i
$13$	202.000			1.19527			0.597633	−	0.801770i	$-0.296108\pi$
$13$	202.000			1.19527			0.597633	+	0.801770i	$0.296108\pi$
$14$			425.958i			2.17325i
$15$		0			0
$16$	−199.000			−0.777344
$17$			76.9090i			0.266121i	0.991108	+	0.133061i	$0.0424805\pi$
$17$			76.9090i			0.266121i	−0.991108	+	0.133061i	$0.957520\pi$
$18$	−157.500	−	452.580i	−0.486111	−	1.39685i
$19$	367.000			1.01662			0.508310	−	0.861174i	$-0.330270\pi$
$19$	367.000			1.01662			0.508310	+	0.861174i	$0.330270\pi$
$20$		0			0
$21$	−108.000	−	638.937i	−0.244898	−	1.44884i
$22$	−1085.00			−2.24174
$23$			35.4965i			0.0671011i	0.999437	+	0.0335505i	$0.0106815\pi$
$23$			35.4965i			0.0671011i	−0.999437	+	0.0335505i	$0.989319\pi$
$24$	−157.500	+	26.6224i	−0.273438	+	0.0462194i
$25$		0			0
$26$			1195.05i			1.76782i
$27$	351.000	+	638.937i	0.481481	+	0.876456i
$28$	−1368.00			−1.74490
$29$			366.797i			0.436144i	0.975933	+	0.218072i	$0.0699767\pi$
$29$			366.797i			0.436144i	−0.975933	+	0.218072i	$0.930023\pi$
$30$		0			0
$31$	−318.000			−0.330905			−0.165453	−	0.986218i	$-0.552909\pi$
$31$	−318.000			−0.330905			−0.165453	+	0.986218i	$0.552909\pi$
$32$		−	1461.27i		−	1.42702i
$33$	1627.50	−	275.098i	1.49449	−	0.252615i
$34$	−455.000			−0.393599
$35$		0			0
$36$	1453.50	−	505.825i	1.12153	−	0.390297i
$37$	752.000			0.549306			0.274653	−	0.961543i	$-0.411437\pi$
$37$	752.000			0.549306			0.274653	+	0.961543i	$0.411437\pi$
$38$			2171.20i			1.50360i
$39$	−303.000	−	1792.57i	−0.199211	−	1.17855i
$40$		0			0
$41$		−	1603.26i		−	0.953752i	−0.878970	−	0.476876i	$-0.841769\pi$
$41$		−	1603.26i		−	0.953752i	0.878970	−	0.476876i	$-0.158231\pi$
$42$	3780.00	−	638.937i	2.14286	−	0.362209i
$43$	982.000			0.531098			0.265549	−	0.964097i	$-0.414447\pi$
$43$	982.000			0.531098			0.265549	+	0.964097i	$0.414447\pi$
$44$		−	3484.57i		−	1.79988i
$45$		0			0
$46$	−210.000			−0.0992439
$47$			1195.05i			0.540991i	0.962721	+	0.270495i	$0.0871874\pi$
$47$			1195.05i			0.540991i	−0.962721	+	0.270495i	$0.912813\pi$
$48$	298.500	+	1765.95i	0.129557	+	0.766471i
$49$	2783.00			1.15910
$50$		0			0
$51$	682.500	−	115.364i	0.262399	−	0.0443535i
$52$	−3838.00			−1.41938
$53$		−	2354.60i		−	0.838234i	−0.907932	−	0.419117i	$-0.862340\pi$
$53$		−	2354.60i		−	0.838234i	0.907932	−	0.419117i	$-0.137660\pi$
$54$	−3780.00	+	2076.54i	−1.29630	+	0.712121i
$55$		0			0
$56$		−	1277.87i		−	0.407485i
$57$	−550.500	−	3256.80i	−0.169437	−	1.00240i
$58$	−2170.00			−0.645065
$59$			23.6643i			0.00679814i	0.999994	+	0.00339907i	$0.00108196\pi$
$59$			23.6643i			0.00679814i	−0.999994	+	0.00339907i	$0.998918\pi$
$60$		0			0
$61$	−3728.00			−1.00188			−0.500941	−	0.865482i	$-0.667012\pi$
$61$	−3728.00			−1.00188			−0.500941	+	0.865482i	$0.667012\pi$
$62$		−	1881.31i		−	0.489416i
$63$	−5508.00	+	1916.81i	−1.38776	+	0.482945i
$64$	5461.00			1.33325
$65$		0			0
$66$	1627.50	+	9628.42i	0.373623	+	2.21038i
$67$	−7443.00			−1.65805			−0.829027	−	0.559209i	$-0.811105\pi$
$67$	−7443.00			−1.65805			−0.829027	+	0.559209i	$0.811105\pi$
$68$		−	1461.27i		−	0.316019i
$69$	315.000	−	53.2447i	0.0661626	−	0.0111835i
$70$		0			0
$71$		−	6732.50i		−	1.33555i	−0.744364	−	0.667774i	$-0.767247\pi$
$71$		−	6732.50i		−	1.33555i	0.744364	−	0.667774i	$-0.232753\pi$
$72$	472.500	+	1357.74i	0.0911458	+	0.261910i
$73$	397.000			0.0744980			0.0372490	−	0.999306i	$-0.488141\pi$
$73$	397.000			0.0744980			0.0372490	+	0.999306i	$0.488141\pi$
$74$			4448.89i			0.812435i
$75$		0			0
$76$	−6973.00			−1.20724
$77$			13204.7i			2.22714i
$78$	10605.0	−	1792.57i	1.74310	−	0.294637i
$79$	−6108.00			−0.978689			−0.489345	−	0.872090i	$-0.662764\pi$
$79$	−6108.00			−0.978689			−0.489345	+	0.872090i	$0.662764\pi$
$80$		0			0
$81$	5143.50	−	4073.22i	0.783951	−	0.620823i
$82$	9485.00			1.41062
$83$		−	13293.4i		−	1.92966i	−0.262874	−	0.964830i	$-0.584670\pi$
$83$		−	13293.4i		−	1.92966i	0.262874	−	0.964830i	$-0.415330\pi$
$84$	2052.00	+	12139.8i	0.290816	+	1.72049i
$85$		0			0
$86$			5809.59i			0.785504i
$87$	3255.00	−	550.195i	0.430044	−	0.0726906i
$88$	3255.00			0.420325
$89$			4738.78i			0.598255i	0.954213	+	0.299128i	$0.0966956\pi$
$89$			4738.78i			0.598255i	−0.954213	+	0.299128i	$0.903304\pi$
$90$		0			0
$91$	14544.0			1.75631
$92$		−	674.433i		−	0.0796825i
$93$	477.000	+	2821.97i	0.0551509	+	0.326277i
$94$	−7070.00			−0.800136
$95$		0			0
$96$	−12967.5	+	2191.91i	−1.40706	+	0.237837i
$97$	8042.00			0.854714			0.427357	−	0.904083i	$-0.359445\pi$
$97$	8042.00			0.854714			0.427357	+	0.904083i	$0.359445\pi$
$98$			16464.5i			1.71433i
$99$	−4882.50	−	14030.0i	−0.498163	−	1.43148i
$100$		0			0
$101$			10648.9i			1.04391i	0.852972	+	0.521956i	$0.174797\pi$
$101$			10648.9i			1.04391i	−0.852972	+	0.521956i	$0.825203\pi$
$102$	682.500	+	4037.72i	0.0655998	+	0.388093i
$103$	−6598.00			−0.621925			−0.310962	−	0.950422i	$-0.600651\pi$
$103$	−6598.00			−0.621925			−0.310962	+	0.950422i	$0.600651\pi$
$104$		−	3585.14i		−	0.331467i
$105$		0			0
$106$	13930.0			1.23977
$107$		−	12867.5i		−	1.12389i	−0.827173	−	0.561947i	$-0.810052\pi$
$107$		−	12867.5i		−	1.12389i	0.827173	−	0.561947i	$-0.189948\pi$
$108$	−6669.00	−	12139.8i	−0.571759	−	1.04079i
$109$	−4048.00			−0.340712			−0.170356	−	0.985383i	$-0.554492\pi$
$109$	−4048.00			−0.340712			−0.170356	+	0.985383i	$0.554492\pi$
$110$		0			0
$111$	−1128.00	−	6673.34i	−0.0915510	−	0.541623i
$112$	−14328.0			−1.14222
$113$			2242.19i			0.175597i	0.996138	+	0.0877983i	$0.0279831\pi$
$113$			2242.19i			0.175597i	−0.996138	+	0.0877983i	$0.972017\pi$
$114$	19267.5	−	3256.80i	1.48257	−	0.250600i
$115$		0			0
$116$		−	6969.14i		−	0.517921i
$117$	−15453.0	+	5377.72i	−1.12886	+	0.392849i
$118$	−140.000			−0.0100546
$119$			5537.45i			0.391035i
$120$		0			0
$121$	−18994.0			−1.29732
$122$		−	22055.1i		−	1.48180i
$123$	−14227.5	+	2404.89i	−0.940412	+	0.158959i
$124$	6042.00			0.392950
$125$		0			0
$126$	−11340.0	−	32585.8i	−0.714286	−	2.05252i
$127$	13222.0			0.819766			0.409883	−	0.912138i	$-0.365570\pi$
$127$	13222.0			0.819766			0.409883	+	0.912138i	$0.365570\pi$
$128$			8927.36i			0.544883i
$129$	−1473.00	−	8714.39i	−0.0885163	−	0.523670i
$130$		0			0
$131$			12707.7i			0.740501i	0.928932	+	0.370251i	$0.120728\pi$
$131$			12707.7i			0.740501i	−0.928932	+	0.370251i	$0.879272\pi$
$132$	−30922.5	+	5226.86i	−1.77471	+	0.299980i
$133$	26424.0			1.49381
$134$		−	44033.4i		−	2.45229i
$135$		0			0
$136$	1365.00			0.0737997
$137$			5022.75i			0.267609i	0.991008	+	0.133804i	$0.0427194\pi$
$137$			5022.75i			0.267609i	−0.991008	+	0.133804i	$0.957281\pi$
$138$	315.000	+	1863.57i	0.0165406	+	0.0978558i
$139$	30197.0			1.56291			0.781455	−	0.623961i	$-0.214478\pi$
$139$	30197.0			1.56291			0.781455	+	0.623961i	$0.214478\pi$
$140$		0			0
$141$	10605.0	−	1792.57i	0.533424	−	0.0901651i
$142$	39830.0			1.97530
$143$			37046.5i			1.81165i
$144$	15223.5	−	5297.85i	0.734158	−	0.255490i
$145$		0			0
$146$			2348.68i			0.110184i
$147$	−4174.50	−	24696.7i	−0.193183	−	1.14289i
$148$	−14288.0			−0.652301
$149$			35082.4i			1.58021i	0.612968	+	0.790107i	$0.289975\pi$
$149$			35082.4i			1.58021i	−0.612968	+	0.790107i	$0.710025\pi$
$150$		0			0
$151$	−6428.00			−0.281917			−0.140959	−	0.990015i	$-0.545018\pi$
$151$	−6428.00			−0.281917			−0.140959	+	0.990015i	$0.545018\pi$
$152$		−	6513.60i		−	0.281925i
$153$	−2047.50	−	5883.54i	−0.0874664	−	0.251337i
$154$	−78120.0			−3.29398
$155$		0			0
$156$	5757.00	+	34058.9i	0.236563	+	1.39953i
$157$	15902.0			0.645138			0.322569	−	0.946546i	$-0.395454\pi$
$157$	15902.0			0.645138			0.322569	+	0.946546i	$0.395454\pi$
$158$		−	36135.4i		−	1.44750i
$159$	−20895.0	+	3531.90i	−0.826510	+	0.139706i
$160$		0			0
$161$			2555.75i			0.0985975i
$162$	24097.5	+	30429.4i	0.918210	+	1.15948i
$163$	32147.0			1.20994			0.604972	−	0.796247i	$-0.293184\pi$
$163$	32147.0			1.20994			0.604972	+	0.796247i	$0.293184\pi$
$164$			30461.9i			1.13258i
$165$		0			0
$166$	78645.0			2.85401
$167$			12885.2i			0.462018i	0.972952	+	0.231009i	$0.0742027\pi$
$167$			12885.2i			0.462018i	−0.972952	+	0.231009i	$0.925797\pi$
$168$	−11340.0	+	1916.81i	−0.401786	+	0.0679142i
$169$	12243.0			0.428661
$170$		0			0
$171$	−28075.5	+	9770.41i	−0.960142	+	0.334134i
$172$	−18658.0			−0.630679
$173$		−	47352.3i		−	1.58215i	−0.611716	−	0.791077i	$-0.709521\pi$
$173$		−	47352.3i		−	1.58215i	0.611716	−	0.791077i	$-0.290479\pi$
$174$	3255.00	+	19256.8i	0.107511	+	0.636043i
$175$		0			0
$176$		−	36496.3i		−	1.17821i
$177$	210.000	−	35.4965i	0.00670305	−	0.00113302i
$178$	−28035.0			−0.884831
$179$		−	55510.6i		−	1.73249i	−0.499623	−	0.866243i	$-0.666528\pi$
$179$		−	55510.6i		−	1.73249i	0.499623	−	0.866243i	$-0.333472\pi$
$180$		0			0
$181$	−13858.0			−0.423003			−0.211501	−	0.977378i	$-0.567835\pi$
$181$	−13858.0			−0.423003			−0.211501	+	0.977378i	$0.567835\pi$
$182$			86043.5i			2.59762i
$183$	5592.00	+	33082.7i	0.166980	+	0.987868i
$184$	630.000			0.0186082
$185$		0			0
$186$	−16695.0	+	2821.97i	−0.482570	+	0.0815693i
$187$	−14105.0			−0.403357
$188$		−	22705.9i		−	0.642426i
$189$	25272.0	+	46003.4i	0.707483	+	1.28785i
$190$		0			0
$191$			4697.37i			0.128762i	0.997925	+	0.0643810i	$0.0205073\pi$
$191$			4697.37i			0.128762i	−0.997925	+	0.0643810i	$0.979493\pi$
$192$	−8191.50	−	48461.6i	−0.222209	−	1.31460i
$193$	−12673.0			−0.340224			−0.170112	−	0.985425i	$-0.554413\pi$
$193$	−12673.0			−0.340224			−0.170112	+	0.985425i	$0.554413\pi$
$194$			47577.1i			1.26414i
$195$		0			0
$196$	−52877.0			−1.37643
$197$		−	43057.2i		−	1.10947i	−0.832029	−	0.554733i	$-0.812821\pi$
$197$		−	43057.2i		−	1.10947i	0.832029	−	0.554733i	$-0.187179\pi$
$198$	83002.5	−	28885.3i	2.11719	−	0.736794i
$199$	22972.0			0.580086			0.290043	−	0.957014i	$-0.406330\pi$
$199$	22972.0			0.580086			0.290043	+	0.957014i	$0.406330\pi$
$200$		0			0
$201$	11164.5	+	66050.1i	0.276342	+	1.63486i
$202$	−63000.0			−1.54397
$203$			26409.4i			0.640864i
$204$	−12967.5	+	2191.91i	−0.311599	+	0.0526698i
$205$		0			0
$206$		−	39034.3i		−	0.919839i
$207$	−945.000	−	2715.48i	−0.0220542	−	0.0633733i
$208$	−40198.0			−0.929133
$209$			67307.2i			1.54088i
$210$		0			0
$211$	−63043.0			−1.41603			−0.708014	−	0.706198i	$-0.750409\pi$
$211$	−63043.0			−1.41603			−0.708014	+	0.706198i	$0.750409\pi$
$212$			44737.4i			0.995403i
$213$	−59745.0	+	10098.7i	−1.31687	+	0.222591i
$214$	76125.0			1.66226
$215$		0			0
$216$	11340.0	−	6229.63i	0.243056	−	0.133523i
$217$	−22896.0			−0.486228
$218$		−	23948.3i		−	0.503920i
$219$	−595.500	−	3523.03i	−0.0124163	−	0.0734560i
$220$		0			0
$221$			15535.6i			0.318086i
$222$	39480.0	−	6673.34i	0.801071	−	0.135406i
$223$	43532.0			0.875385			0.437692	−	0.899125i	$-0.355796\pi$
$223$	43532.0			0.875385			0.437692	+	0.899125i	$0.355796\pi$
$224$		−	105212.i		−	2.09685i
$225$		0			0
$226$	−13265.0			−0.259711
$227$		−	40134.7i		−	0.778876i	−0.921053	−	0.389438i	$-0.872669\pi$
$227$		−	40134.7i		−	0.778876i	0.921053	−	0.389438i	$-0.127331\pi$
$228$	10459.5	+	61879.2i	0.201206	+	1.19035i
$229$	−86748.0			−1.65420			−0.827101	−	0.562053i	$-0.810012\pi$
$229$	−86748.0			−1.65420			−0.827101	+	0.562053i	$0.810012\pi$
$230$		0			0
$231$	117180.	−	19807.0i	2.19599	−	0.371189i
$232$	6510.00			0.120950
$233$			32585.8i			0.600228i	0.953903	+	0.300114i	$0.0970247\pi$
$233$			32585.8i			0.600228i	−0.953903	+	0.300114i	$0.902975\pi$
$234$	−31815.0	−	91421.2i	−0.581032	−	1.66961i
$235$		0			0
$236$		−	449.622i		−	0.00807279i
$237$	9162.00	+	54203.1i	0.163115	+	0.965001i
$238$	−32760.0			−0.578349
$239$		−	99118.0i		−	1.73523i	−0.497238	−	0.867614i	$-0.665652\pi$
$239$		−	99118.0i		−	1.73523i	0.497238	−	0.867614i	$-0.334348\pi$
$240$		0			0
$241$	55627.0			0.957749			0.478874	−	0.877883i	$-0.341045\pi$
$241$	55627.0			0.957749			0.478874	+	0.877883i	$0.341045\pi$
$242$		−	112370.i		−	1.91876i
$243$	−43861.5	−	39534.2i	−0.742798	−	0.669515i
$244$	70832.0			1.18973
$245$		0			0
$246$	−14227.5	−	84171.0i	−0.235103	−	1.39089i
$247$	74134.0			1.21513
$248$			5643.94i			0.0917654i
$249$	−117968.	+	19940.1i	−1.90267	+	0.321610i
$250$		0			0
$251$		−	50493.7i		−	0.801475i	−0.916193	−	0.400738i	$-0.868754\pi$
$251$		−	50493.7i		−	0.801475i	0.916193	−	0.400738i	$-0.131246\pi$
$252$	104652.	−	36419.4i	1.64796	−	0.573498i
$253$	−6510.00			−0.101704
$254$			78222.4i			1.21245i
$255$		0			0
$256$	34561.0			0.527359
$257$			64248.6i			0.972742i	0.873752	+	0.486371i	$0.161680\pi$
$257$			64248.6i			0.972742i	−0.873752	+	0.486371i	$0.838320\pi$
$258$	51555.0	−	8714.39i	0.774518	−	0.130917i
$259$	54144.0			0.807144
$260$		0			0
$261$	−9765.00	−	28060.0i	−0.143348	−	0.411914i
$262$	−75180.0			−1.09522
$263$			87404.2i			1.26363i	0.775118	+	0.631816i	$0.217690\pi$
$263$			87404.2i			1.26363i	−0.775118	+	0.631816i	$0.782310\pi$
$264$	−4882.50	−	28885.3i	−0.0700542	−	0.414446i
$265$		0			0
$266$			156326.i			2.20937i
$267$	42052.5	−	7108.17i	0.589888	−	0.0997092i
$268$	141417.			1.96894
$269$		−	72957.1i		−	1.00824i	−0.863634	−	0.504119i	$-0.831817\pi$
$269$		−	72957.1i		−	1.00824i	0.863634	−	0.504119i	$-0.168183\pi$
$270$		0			0
$271$	−2498.00			−0.0340137			−0.0170068	−	0.999855i	$-0.505414\pi$
$271$	−2498.00			−0.0340137			−0.0170068	+	0.999855i	$0.505414\pi$
$272$		−	15304.9i		−	0.206868i
$273$	−21816.0	−	129065.i	−0.292718	−	1.73174i
$274$	−29715.0			−0.395799
$275$		0			0
$276$	−5985.00	+	1011.65i	−0.0785681	+	0.0132804i
$277$	−50178.0			−0.653964			−0.326982	−	0.945031i	$-0.606032\pi$
$277$	−50178.0			−0.653964			−0.326982	+	0.945031i	$0.606032\pi$
$278$			178648.i			2.31158i
$279$	24327.0	−	8465.91i	0.312522	−	0.108759i
$280$		0			0
$281$			57433.3i			0.727363i	0.931523	+	0.363681i	$0.118480\pi$
$281$			57433.3i			0.727363i	−0.931523	+	0.363681i	$0.881520\pi$
$282$	10605.0	+	62740.0i	0.133356	+	0.788945i
$283$	−83463.0			−1.04213			−0.521064	−	0.853518i	$-0.674465\pi$
$283$	−83463.0			−1.04213			−0.521064	+	0.853518i	$0.674465\pi$
$284$			127917.i			1.58596i
$285$		0			0
$286$	−219170.			−2.67947
$287$		−	115435.i		−	1.40143i
$288$	38902.5	+	111787.i	0.469021	+	1.34774i
$289$	77606.0			0.929179
$290$		0			0
$291$	−12063.0	−	71365.7i	−0.142452	−	0.842759i
$292$	−7543.00			−0.0884664
$293$		−	115719.i		−	1.34793i	−0.738763	−	0.673965i	$-0.764590\pi$
$293$		−	115719.i		−	1.34793i	0.738763	−	0.673965i	$-0.235410\pi$
$294$	146108.	−	24696.7i	1.69035	−	0.285722i
$295$		0			0
$296$		−	13346.7i		−	0.152331i
$297$	−117180.	+	64372.9i	−1.32844	+	0.729777i
$298$	−207550.			−2.33717
$299$			7170.29i			0.0802037i
$300$		0			0
$301$	70704.0			0.780389
$302$		−	38028.6i		−	0.416962i
$303$	94500.0	−	15973.4i	1.02931	−	0.173985i
$304$	−73033.0			−0.790264
$305$		0			0
$306$	34807.5	−	12113.2i	0.371732	−	0.129364i
$307$	−123443.			−1.30975			−0.654877	−	0.755736i	$-0.727280\pi$
$307$	−123443.			−1.30975			−0.654877	+	0.755736i	$0.727280\pi$
$308$		−	250889.i		−	2.64472i
$309$	9897.00	+	58551.4i	0.103654	+	0.613226i
$310$		0			0
$311$		−	117280.i		−	1.21256i	−0.795250	−	0.606282i	$-0.792660\pi$
$311$		−	117280.i		−	1.21256i	0.795250	−	0.606282i	$-0.207340\pi$
$312$	−31815.0	+	5377.72i	−0.326831	+	0.0552445i
$313$	51542.0			0.526105			0.263053	−	0.964781i	$-0.415271\pi$
$313$	51542.0			0.526105			0.263053	+	0.964781i	$0.415271\pi$
$314$			94077.5i			0.954172i
$315$		0			0
$316$	116052.			1.16219
$317$			138484.i			1.37810i	0.724715	+	0.689049i	$0.241971\pi$
$317$			138484.i			1.37810i	−0.724715	+	0.689049i	$0.758029\pi$
$318$	−20895.0	−	123616.i	−0.206628	−	1.22242i
$319$	−67270.0			−0.661059
$320$		0			0
$321$	−114188.	+	19301.2i	−1.10818	+	0.187316i
$322$	−15120.0			−0.145828
$323$			28225.6i			0.270544i
$324$	−97726.5	+	77391.2i	−0.930941	+	0.737228i
$325$		0			0
$326$			190184.i			1.78953i
$327$	6072.00	+	35922.4i	0.0567853	+	0.335947i
$328$	−28455.0			−0.264491
$329$			86043.5i			0.794925i
$330$		0			0
$331$	−129483.			−1.18183			−0.590917	−	0.806732i	$-0.701234\pi$
$331$	−129483.			−1.18183			−0.590917	+	0.806732i	$0.701234\pi$
$332$			252575.i			2.29147i
$333$	−57528.0	+	20020.0i	−0.518789	+	0.180541i
$334$	−76230.0			−0.683334
$335$		0			0
$336$	21492.0	+	127148.i	0.190370	+	1.12624i
$337$	142417.			1.25401			0.627006	−	0.779014i	$-0.284280\pi$
$337$	142417.			1.25401			0.627006	+	0.779014i	$0.284280\pi$
$338$			72430.6i			0.633999i
$339$	19897.5	−	3363.29i	0.173141	−	0.0292661i
$340$		0			0
$341$		−	58320.7i		−	0.501550i
$342$	−57802.5	−	166097.i	−0.494191	−	1.42007i
$343$	27504.0			0.233780
$344$		−	17428.8i		−	0.147282i
$345$		0			0
$346$	280140.			2.34004
$347$		−	75566.1i		−	0.627578i	−0.949493	−	0.313789i	$-0.898401\pi$
$347$		−	75566.1i		−	0.627578i	0.949493	−	0.313789i	$-0.101599\pi$
$348$	−61845.0	+	10453.7i	−0.510677	+	0.0863201i
$349$	109132.			0.895986			0.447993	−	0.894037i	$-0.352139\pi$
$349$	109132.			0.895986			0.447993	+	0.894037i	$0.352139\pi$
$350$		0			0
$351$	70902.0	+	129065.i	0.575499	+	1.04760i
$352$	267995.			2.16292
$353$		−	14127.6i		−	0.113375i	−0.998392	−	0.0566877i	$-0.981946\pi$
$353$		−	14127.6i		−	0.113375i	0.998392	−	0.0566877i	$-0.0180539\pi$
$354$	210.000	+	1242.38i	0.00167576	+	0.00991395i
$355$		0			0
$356$		−	90036.8i		−	0.710428i
$357$	49140.0	−	8306.18i	0.385566	−	0.0651725i
$358$	328405.			2.56238
$359$		−	155333.i		−	1.20524i	−0.798028	−	0.602620i	$-0.794123\pi$
$359$		−	155333.i		−	1.20524i	0.798028	−	0.602620i	$-0.205877\pi$
$360$		0			0
$361$	4368.00			0.0335172
$362$		−	81985.0i		−	0.625630i
$363$	28491.0	+	168555.i	0.216219	+	1.27917i
$364$	−276336.			−2.08562
$365$		0			0
$366$	−195720.	+	33082.7i	−1.46108	+	0.246967i
$367$	138492.			1.02824			0.514118	−	0.857720i	$-0.328119\pi$
$367$	138492.			1.02824			0.514118	+	0.857720i	$0.328119\pi$
$368$		−	7063.80i		−	0.0521606i
$369$	42682.5	+	122649.i	0.313471	+	0.900766i
$370$		0			0
$371$		−	169531.i		−	1.23169i
$372$	−9063.00	−	53617.4i	−0.0654917	−	0.387454i
$373$	225802.			1.62297			0.811484	−	0.584374i	$-0.198660\pi$
$373$	225802.			1.62297			0.811484	+	0.584374i	$0.198660\pi$
$374$		−	83446.3i		−	0.596573i
$375$		0			0
$376$	21210.0			0.150025
$377$			74093.0i			0.521308i
$378$	−272160.	+	149511.i	−1.90476	+	1.04638i
$379$	75067.0			0.522601			0.261301	−	0.965257i	$-0.415849\pi$
$379$	75067.0			0.522601			0.261301	+	0.965257i	$0.415849\pi$
$380$		0			0
$381$	−19833.0	−	117334.i	−0.136628	−	0.808300i
$382$	−27790.0			−0.190442
$383$		−	212695.i		−	1.44997i	−0.688764	−	0.724986i	$-0.741846\pi$
$383$		−	212695.i		−	1.44997i	0.688764	−	0.724986i	$-0.258154\pi$
$384$	79222.5	−	13391.0i	0.537262	−	0.0908138i
$385$		0			0
$386$		−	74974.5i		−	0.503198i
$387$	−75123.0	+	26143.2i	−0.501592	+	0.174557i
$388$	−152798.			−1.01497
$389$		−	9548.55i		−	0.0631013i	−0.999502	−	0.0315507i	$-0.989955\pi$
$389$		−	9548.55i		−	0.0631013i	0.999502	−	0.0315507i	$-0.0100446\pi$
$390$		0			0
$391$	−2730.00			−0.0178570
$392$		−	49393.4i		−	0.321437i
$393$	112770.	−	19061.6i	0.730144	−	0.123417i
$394$	254730.			1.64092
$395$		0			0
$396$	92767.5	+	266570.i	0.591569	+	1.69989i
$397$	−16148.0			−0.102456			−0.0512280	−	0.998687i	$-0.516314\pi$
$397$	−16148.0			−0.102456			−0.0512280	+	0.998687i	$0.516314\pi$
$398$			135904.i			0.857959i
$399$	−39636.0	−	234490.i	−0.248968	−	1.47292i
$400$		0			0
$401$		−	80665.7i		−	0.501650i	−0.968033	−	0.250825i	$-0.919298\pi$
$401$		−	80665.7i		−	0.501650i	0.968033	−	0.250825i	$-0.0807018\pi$
$402$	−390758.	+	66050.1i	−2.41799	+	0.408716i
$403$	−64236.0			−0.395520
$404$		−	202330.i		−	1.23965i
$405$		0			0
$406$	−156240.			−0.947851
$407$			137916.i			0.832578i
$408$	−2047.50	−	12113.2i	−0.0123000	−	0.0727675i
$409$	−145483.			−0.869692			−0.434846	−	0.900505i	$-0.643197\pi$
$409$	−145483.			−0.869692			−0.434846	+	0.900505i	$0.643197\pi$
$410$		0			0
$411$	44572.5	−	7534.13i	0.263866	−	0.0446015i
$412$	125362.			0.738536
$413$			1703.83i			0.00998910i
$414$	16065.0	−	5590.70i	0.0937303	−	0.0326186i
$415$		0			0
$416$		−	295177.i		−	1.70567i
$417$	−45295.5	−	267972.i	−0.260485	−	1.54105i
$418$	−398195.			−2.27899
$419$		−	49559.0i		−	0.282289i	−0.989989	−	0.141145i	$-0.954922\pi$
$419$		−	49559.0i		−	0.282289i	0.989989	−	0.141145i	$-0.0450783\pi$
$420$		0			0
$421$	−23108.0			−0.130376			−0.0651881	−	0.997873i	$-0.520765\pi$
$421$	−23108.0			−0.130376			−0.0651881	+	0.997873i	$0.520765\pi$
$422$		−	372967.i		−	2.09433i
$423$	−31815.0	−	91421.2i	−0.177808	−	0.510936i
$424$	−41790.0			−0.232456
$425$		0			0
$426$	−59745.0	−	353456.i	−0.329217	−	1.94767i
$427$	−268416.			−1.47215
$428$			244482.i			1.33463i
$429$	328755.	−	55569.7i	1.78631	−	0.301942i
$430$		0			0
$431$			361993.i			1.94870i	0.225031	+	0.974352i	$0.427752\pi$
$431$			361993.i			1.94870i	−0.225031	+	0.974352i	$0.572248\pi$
$432$	−69849.0	−	127148.i	−0.374277	−	0.681308i
$433$	−70943.0			−0.378385			−0.189192	−	0.981940i	$-0.560587\pi$
$433$	−70943.0			−0.378385			−0.189192	+	0.981940i	$0.560587\pi$
$434$		−	135455.i		−	0.719141i
$435$		0			0
$436$	76912.0			0.404596
$437$			13027.2i			0.0682163i
$438$	20842.5	−	3523.03i	0.108643	−	0.0183640i
$439$	−135818.			−0.704739			−0.352369	−	0.935861i	$-0.614624\pi$
$439$	−135818.			−0.704739			−0.352369	+	0.935861i	$0.614624\pi$
$440$		0			0
$441$	−212900.	+	74090.0i	−1.09471	+	0.380963i
$442$	−91910.0			−0.470455
$443$			252291.i			1.28557i	0.766048	+	0.642783i	$0.222220\pi$
$443$			252291.i			1.28557i	−0.766048	+	0.642783i	$0.777780\pi$
$444$	21432.0	+	126793.i	0.108717	+	0.643177i
$445$		0			0
$446$			257539.i			1.29471i
$447$	311325.	−	52623.5i	1.55811	−	0.263369i
$448$	393192.			1.95906
$449$			381025.i			1.89000i	0.327076	+	0.944998i	$0.393937\pi$
$449$			381025.i			1.89000i	−0.327076	+	0.944998i	$0.606063\pi$
$450$		0			0
$451$	294035.			1.44559
$452$		−	42601.7i		−	0.208521i
$453$	9642.00	+	57042.8i	0.0469862	+	0.277974i
$454$	237440.			1.15197
$455$		0			0
$456$	−57802.5	+	9770.41i	−0.277982	+	0.0469876i
$457$	256357.			1.22748			0.613738	−	0.789510i	$-0.289665\pi$
$457$	256357.			1.22748			0.613738	+	0.789510i	$0.289665\pi$
$458$		−	513208.i		−	2.44660i
$459$	−49140.0	+	26995.1i	−0.233244	+	0.128132i
$460$		0			0
$461$			189764.i			0.892920i	0.894804	+	0.446460i	$0.147315\pi$
$461$			189764.i			0.892920i	−0.894804	+	0.446460i	$0.852685\pi$
$462$	117180.	+	693246.i	0.548996	+	3.24791i
$463$	−339648.			−1.58441			−0.792204	−	0.610256i	$-0.791066\pi$
$463$	−339648.			−1.58441			−0.792204	+	0.610256i	$0.791066\pi$
$464$		−	72992.6i		−	0.339034i
$465$		0			0
$466$	−192780.			−0.887749
$467$			57196.7i			0.262263i	0.991365	+	0.131131i	$0.0418610\pi$
$467$			57196.7i			0.262263i	−0.991365	+	0.131131i	$0.958139\pi$
$468$	293607.	−	102177.i	1.34052	−	0.466509i
$469$	−535896.			−2.43632
$470$		0			0
$471$	−23853.0	−	141116.i	−0.107523	−	0.636114i
$472$	420.000			0.00188523
$473$			180097.i			0.804980i
$474$	−320670.	+	54203.1i	−1.42726	+	0.241250i
$475$		0			0
$476$		−	105212.i		−	0.464354i
$477$	62685.0	+	180127.i	0.275503	+	0.791666i
$478$	586390.			2.56644
$479$			211807.i			0.923146i	0.887102	+	0.461573i	$0.152715\pi$
$479$			211807.i			0.923146i	−0.887102	+	0.461573i	$0.847285\pi$
$480$		0			0
$481$	151904.			0.656567
$482$			329094.i			1.41653i
$483$	22680.0	−	3833.62i	0.0972185	−	0.0164329i
$484$	360886.			1.54056
$485$		0			0
$486$	233888.	−	259488.i	0.990226	−	1.09861i
$487$	−149278.			−0.629416			−0.314708	−	0.949189i	$-0.601907\pi$
$487$	−149278.			−0.629416			−0.314708	+	0.949189i	$0.601907\pi$
$488$			66165.4i			0.277838i
$489$	−48220.5	−	285276.i	−0.201657	−	1.19302i
$490$		0			0
$491$			104265.i			0.432489i	0.976339	+	0.216245i	$0.0693809\pi$
$491$			104265.i			0.432489i	−0.976339	+	0.216245i	$0.930619\pi$
$492$	270322.	−	45692.8i	1.11674	−	0.188763i
$493$	−28210.0			−0.116067
$494$			438583.i			1.79720i
$495$		0			0
$496$	63282.0			0.257227
$497$		−	484740.i		−	1.96244i
$498$	−117968.	−	697905.i	−0.475668	−	2.81409i
$499$	251002.			1.00804			0.504018	−	0.863693i	$-0.331854\pi$
$499$	251002.			1.00804			0.504018	+	0.863693i	$0.331854\pi$
$500$		0			0
$501$	114345.	−	19327.8i	0.455556	−	0.0770030i
$502$	298725.			1.18540
$503$		−	127953.i		−	0.505725i	−0.967502	−	0.252862i	$-0.918628\pi$
$503$		−	127953.i		−	0.505725i	0.967502	−	0.252862i	$-0.0813720\pi$
$504$	34020.0	+	97757.3i	0.133929	+	0.384847i
$505$		0			0
$506$		−	38513.7i		−	0.150423i
$507$	−18364.5	−	108646.i	−0.0714436	−	0.422666i
$508$	−251218.			−0.973472
$509$			7300.44i			0.0281782i	0.999901	+	0.0140891i	$0.00448485\pi$
$509$			7300.44i			0.0281782i	−0.999901	+	0.0140891i	$0.995515\pi$
$510$		0			0
$511$	28584.0			0.109466
$512$			347303.i			1.32486i
$513$	128817.	+	234490.i	0.489484	+	0.891023i
$514$	−380100.			−1.43870
$515$		0			0
$516$	27987.0	+	165573.i	0.105113	+	0.621858i
$517$	−219170.			−0.819974
$518$			320320.i			1.19378i
$519$	−420210.	+	71028.5i	−1.56003	+	0.263692i
$520$		0			0
$521$			464572.i			1.71150i	0.517387	+	0.855751i	$0.326905\pi$
$521$			464572.i			1.71150i	−0.517387	+	0.855751i	$0.673095\pi$
$522$	166005.	−	57770.5i	0.609228	−	0.212014i
$523$	−371153.			−1.35691			−0.678453	−	0.734644i	$-0.737349\pi$
$523$	−371153.			−1.35691			−0.678453	+	0.734644i	$0.737349\pi$
$524$		−	241447.i		−	0.879345i
$525$		0			0
$526$	−517090.			−1.86894
$527$		−	24457.1i		−	0.0880609i
$528$	−323872.	+	54744.4i	−1.16173	+	0.196369i
$529$	278581.			0.995497
$530$		0			0
$531$	−630.000	−	1810.32i	−0.00223435	−	0.00642046i
$532$	−502056.			−1.77390
$533$		−	323858.i		−	1.13999i
$534$	42052.5	+	248786.i	0.147472	+	0.872456i
$535$		0			0
$536$			132100.i			0.459805i
$537$	−492608.	+	83265.9i	−1.70825	+	0.288748i
$538$	431620.			1.49120
$539$			510398.i			1.75684i
$540$		0			0
$541$	−317328.			−1.08421			−0.542106	−	0.840310i	$-0.682373\pi$
$541$	−317328.			−1.08421			−0.542106	+	0.840310i	$0.682373\pi$
$542$		−	14778.4i		−	0.0503069i
$543$	20787.0	+	122978.i	0.0705005	+	0.417087i
$544$	112385.			0.379761
$545$		0			0
$546$	763560.	−	129065.i	2.56128	−	0.432936i
$547$	−321473.			−1.07441			−0.537205	−	0.843452i	$-0.680520\pi$
$547$	−321473.			−1.07441			−0.537205	+	0.843452i	$0.680520\pi$
$548$		−	95432.3i		−	0.317786i
$549$	285192.	−	99248.2i	0.946221	−	0.329289i
$550$		0			0
$551$			134614.i			0.443393i
$552$	−945.000	−	5590.70i	−0.00310137	−	0.0183480i
$553$	−439776.			−1.43807
$554$		−	296857.i		−	0.967226i
$555$		0			0
$556$	−573743.			−1.85596
$557$			302962.i			0.976514i	0.872700	+	0.488257i	$0.162367\pi$
$557$			302962.i			0.976514i	−0.872700	+	0.488257i	$0.837633\pi$
$558$	50085.0	+	143920.i	0.160857	+	0.462226i
$559$	198364.			0.634803
$560$		0			0
$561$	21157.5	+	125169.i	0.0672262	+	0.397716i
$562$	−339780.			−1.07578
$563$		−	306903.i		−	0.968242i	−0.875001	−	0.484121i	$-0.839140\pi$
$563$		−	306903.i		−	0.968242i	0.875001	−	0.484121i	$-0.160860\pi$
$564$	−201495.	+	34058.9i	−0.633441	+	0.107071i
$565$		0			0
$566$		−	493774.i		−	1.54133i
$567$	370332.	−	293272.i	1.15193	−	0.912230i
$568$	−119490.			−0.370369
$569$		−	604310.i		−	1.86653i	−0.359188	−	0.933265i	$-0.616946\pi$
$569$		−	604310.i		−	1.86653i	0.359188	−	0.933265i	$-0.383054\pi$
$570$		0			0
$571$	−207958.			−0.637828			−0.318914	−	0.947784i	$-0.603318\pi$
$571$	−207958.			−0.637828			−0.318914	+	0.947784i	$0.603318\pi$
$572$		−	703883.i		−	2.15134i
$573$	41685.0	−	7046.05i	0.126961	−	0.0214603i
$574$	682920.			2.07275
$575$		0			0
$576$	−417766.	+	145385.i	−1.25918	+	0.438201i
$577$	384857.			1.15597			0.577987	−	0.816046i	$-0.303839\pi$
$577$	384857.			1.15597			0.577987	+	0.816046i	$0.303839\pi$
$578$			459123.i			1.37427i
$579$	19009.5	+	112462.i	0.0567040	+	0.335465i
$580$		0			0
$581$		−	957127.i		−	2.83542i
$582$	422205.	−	71365.7i	1.24646	−	0.210690i
$583$	431830.			1.27050
$584$		−	7046.05i		−	0.0206595i
$585$		0			0
$586$	684600.			1.99362
$587$		−	47334.6i		−	0.137373i	−0.997638	−	0.0686866i	$-0.978119\pi$
$587$		−	47334.6i		−	0.137373i	0.997638	−	0.0686866i	$-0.0218809\pi$
$588$	79315.5	+	469237.i	0.229405	+	1.35718i
$589$	−116706.			−0.336405
$590$		0			0
$591$	−382095.	+	64585.8i	−1.09395	+	0.184911i
$592$	−149648.			−0.427000
$593$			397945.i			1.13165i	0.824524	+	0.565827i	$0.191443\pi$
$593$			397945.i			1.13165i	−0.824524	+	0.565827i	$0.808557\pi$
$594$	−380835.	−	693246.i	−1.07935	−	1.96478i
$595$		0			0
$596$		−	666565.i		−	1.87651i
$597$	−34458.0	−	203856.i	−0.0966811	−	0.571973i
$598$	−42420.0			−0.118623
$599$		−	85073.2i		−	0.237104i	−0.992948	−	0.118552i	$-0.962175\pi$
$599$		−	85073.2i		−	0.237104i	0.992948	−	0.118552i	$-0.0378253\pi$
$600$		0			0
$601$	411977.			1.14058			0.570288	−	0.821445i	$-0.306832\pi$
$601$	411977.			1.14058			0.570288	+	0.821445i	$0.306832\pi$
$602$			418291.i			1.15421i
$603$	569390.	−	198150.i	1.56594	−	0.544954i
$604$	122132.			0.334777
$605$		0			0
$606$	94500.0	+	559070.i	0.257328	+	1.52237i
$607$	−329228.			−0.893551			−0.446776	−	0.894646i	$-0.647428\pi$
$607$	−329228.			−0.893551			−0.446776	+	0.894646i	$0.647428\pi$
$608$		−	536287.i		−	1.45074i
$609$	234360.	−	39614.1i	0.631901	−	0.106811i
$610$		0			0
$611$			241400.i			0.646628i
$612$	38902.5	+	111787.i	0.103866	+	0.298462i
$613$	−109658.			−0.291823			−0.145911	−	0.989298i	$-0.546611\pi$
$613$	−109658.			−0.291823			−0.145911	+	0.989298i	$0.546611\pi$
$614$		−	730299.i		−	1.93715i
$615$		0			0
$616$	234360.			0.617621
$617$			130201.i			0.342014i	0.985270	+	0.171007i	$0.0547021\pi$
$617$			130201.i			0.342014i	−0.985270	+	0.171007i	$0.945298\pi$
$618$	−346395.	+	58551.4i	−0.906974	+	0.153307i
$619$	−497458.			−1.29830			−0.649150	−	0.760660i	$-0.724875\pi$
$619$	−497458.			−1.29830			−0.649150	+	0.760660i	$0.724875\pi$
$620$		0			0
$621$	−22680.0	+	12459.3i	−0.0588112	+	0.0323079i
$622$	693840.			1.79341
$623$			341192.i			0.879069i
$624$	60297.0	+	356722.i	0.154855	+	0.916137i
$625$		0			0
$626$			304927.i			0.778120i
$627$	597292.	−	100961.i	1.51933	−	0.256814i
$628$	−302138.			−0.766101
$629$			57835.6i			0.146182i
$630$		0			0
$631$	45142.0			0.113376			0.0566881	−	0.998392i	$-0.481946\pi$
$631$	45142.0			0.113376			0.0566881	+	0.998392i	$0.481946\pi$
$632$			108406.i			0.271406i
$633$	94564.5	+	559451.i	0.236005	+	1.39622i
$634$	−819280.			−2.03823
$635$		0			0
$636$	397005.	−	67106.1i	0.981481	−	0.165901i
$637$	562166.			1.38543
$638$		−	397975.i		−	0.977719i
$639$	179235.	+	515036.i	0.438956	+	1.26135i
$640$		0			0
$641$			317126.i			0.771818i	0.922537	+	0.385909i	$0.126112\pi$
$641$			317126.i			0.771818i	−0.922537	+	0.385909i	$0.873888\pi$
$642$	−114188.	−	675542.i	−0.277044	−	1.63901i
$643$	283422.			0.685507			0.342753	−	0.939425i	$-0.388641\pi$
$643$	283422.			0.685507			0.342753	+	0.939425i	$0.388641\pi$
$644$		−	48559.2i		−	0.117085i
$645$		0			0
$646$	−166985.			−0.400140
$647$			449693.i			1.07426i	0.843501	+	0.537128i	$0.180491\pi$
$647$			449693.i			1.07426i	−0.843501	+	0.537128i	$0.819509\pi$
$648$	−72292.5	−	91288.1i	−0.172164	−	0.217402i
$649$	−4340.00			−0.0103039
$650$		0			0
$651$	34344.0	+	203182.i	0.0810380	+	0.479427i
$652$	−610793.			−1.43681
$653$			176607.i			0.414172i	0.978323	+	0.207086i	$0.0663980\pi$
$653$			176607.i			0.414172i	−0.978323	+	0.207086i	$0.933602\pi$
$654$	−212520.	+	35922.4i	−0.496872	+	0.0839867i
$655$		0			0
$656$			319048.i			0.741393i
$657$	−30370.5	+	10569.1i	−0.0703593	+	0.0244853i
$658$	−509040.			−1.17571
$659$		−	52777.3i		−	0.121528i	−0.998152	−	0.0607641i	$-0.980646\pi$
$659$		−	52777.3i		−	0.121528i	0.998152	−	0.0607641i	$-0.0193537\pi$
$660$		0			0
$661$	549022.			1.25657			0.628285	−	0.777983i	$-0.283757\pi$
$661$	549022.			1.25657			0.628285	+	0.777983i	$0.283757\pi$
$662$		−	766032.i		−	1.74796i
$663$	137865.	−	23303.4i	0.313637	−	0.0530143i
$664$	−235935.			−0.535126
$665$		0			0
$666$	−118440.	−	340340.i	−0.267024	−	0.767299i
$667$	−13020.0			−0.0292657
$668$		−	244819.i		−	0.548646i
$669$	−65298.0	−	386308.i	−0.145897	−	0.863141i
$670$		0			0
$671$		−	683710.i		−	1.51854i
$672$	−933660.	+	157817.i	−2.06752	+	0.349475i
$673$	150702.			0.332728			0.166364	−	0.986064i	$-0.446797\pi$
$673$	150702.			0.332728			0.166364	+	0.986064i	$0.446797\pi$
$674$			842550.i			1.85471i
$675$		0			0
$676$	−232617.			−0.509035
$677$		−	536849.i		−	1.17132i	−0.810558	−	0.585659i	$-0.800836\pi$
$677$		−	536849.i		−	1.17132i	0.810558	−	0.585659i	$-0.199164\pi$
$678$	19897.5	+	117715.i	0.0432852	+	0.256079i
$679$	579024.			1.25591
$680$		0			0
$681$	−356160.	+	60202.0i	−0.767982	+	0.129813i
$682$	345030.			0.741802
$683$		−	545563.i		−	1.16951i	−0.811210	−	0.584755i	$-0.801191\pi$
$683$		−	545563.i		−	1.16951i	0.811210	−	0.584755i	$-0.198809\pi$
$684$	533434.	−	185638.i	1.14017	−	0.396784i
$685$		0			0
$686$			162716.i			0.345765i
$687$	130122.	+	769812.i	0.275700	+	1.63107i
$688$	−195418.			−0.412846
$689$		−	475629.i		−	1.00191i
$690$		0			0
$691$	−789233.			−1.65291			−0.826455	−	0.563003i	$-0.809646\pi$
$691$	−789233.			−1.65291			−0.826455	+	0.563003i	$0.809646\pi$
$692$			899694.i			1.87881i
$693$	−351540.	−	1.01016e6i	−0.731995	−	2.10341i
$694$	447055.			0.928201
$695$		0			0
$696$	−9765.00	−	57770.5i	−0.0201583	−	0.119258i
$697$	123305.			0.253814
$698$			645634.i			1.32518i
$699$	289170.	−	48878.7i	0.591833	−	0.100038i
$700$		0			0
$701$		−	492750.i		−	1.00275i	−0.865231	−	0.501373i	$-0.832828\pi$
$701$		−	492750.i		−	1.00275i	0.865231	−	0.501373i	$-0.167172\pi$
$702$	−763560.	+	419462.i	−1.54942	+	0.851174i
$703$	275984.			0.558436
$704$			1.00154e6i			2.02080i
$705$		0			0
$706$	83580.0			0.167685
$707$			766724.i			1.53391i
$708$	−3990.00	+	674.433i	−0.00795988	+	0.00134546i
$709$	−461528.			−0.918133			−0.459066	−	0.888402i	$-0.651816\pi$
$709$	−461528.			−0.918133			−0.459066	+	0.888402i	$0.651816\pi$
$710$		0			0
$711$	467262.	−	162609.i	0.924318	−	0.321667i
$712$	84105.0			0.165906
$713$		−	11287.9i		−	0.0222041i
$714$	49140.0	+	290716.i	0.0963915	+	0.570260i
$715$		0			0
$716$			1.05470e6i			2.05733i
$717$	−879585.	+	148677.i	−1.71096	+	0.289205i
$718$	918960.			1.78257
$719$			749615.i			1.45004i	0.688727	+	0.725020i	$0.258170\pi$
$719$			749615.i			1.45004i	−0.688727	+	0.725020i	$0.741830\pi$
$720$		0			0
$721$	−475056.			−0.913849
$722$			25841.4i			0.0495727i
$723$	−83440.5	−	493641.i	−0.159625	−	0.944353i
$724$	263302.			0.502316
$725$		0			0
$726$	−997185.	+	168555.i	−1.89192	+	0.319793i
$727$	−639178.			−1.20935			−0.604676	−	0.796471i	$-0.706698\pi$
$727$	−639178.			−1.20935			−0.604676	+	0.796471i	$0.706698\pi$
$728$		−	258130.i		−	0.487053i
$729$	−285039.	+	448534.i	−0.536351	+	0.843995i
$730$		0			0
$731$			75524.7i			0.141336i
$732$	−106248.	−	628572.i	−0.198289	−	1.17309i
$733$	488162.			0.908565			0.454283	−	0.890858i	$-0.349896\pi$
$733$	488162.			0.908565			0.454283	+	0.890858i	$0.349896\pi$
$734$			819330.i			1.52078i
$735$		0			0
$736$	51870.0			0.0957548
$737$		−	1.36503e6i		−	2.51309i
$738$	−725602.	+	252513.i	−1.33225	+	0.463630i
$739$	315082.			0.576945			0.288473	−	0.957488i	$-0.406853\pi$
$739$	315082.			0.576945			0.288473	+	0.957488i	$0.406853\pi$
$740$		0			0
$741$	−111201.	−	657874.i	−0.202522	−	1.19814i
$742$	1.00296e6			1.82170
$743$		−	135892.i		−	0.246160i	−0.992397	−	0.123080i	$-0.960723\pi$
$743$		−	135892.i		−	0.246160i	0.992397	−	0.123080i	$-0.0392772\pi$
$744$	50085.0	−	8465.91i	0.0904819	−	0.0152942i
$745$		0			0
$746$			1.33586e6i			2.40040i
$747$	353902.	+	1.01695e6i	0.634224	+	1.82246i
$748$	267995.			0.478987
$749$		−	926458.i		−	1.65144i
$750$		0			0
$751$	424882.			0.753336			0.376668	−	0.926348i	$-0.377070\pi$
$751$	424882.			0.753336			0.376668	+	0.926348i	$0.377070\pi$
$752$		−	237815.i		−	0.420536i
$753$	−448088.	+	75740.6i	−0.790265	+	0.133579i
$754$	−438340.			−0.771025
$755$		0			0
$756$	−480168.	−	874065.i	−0.840136	−	1.52933i
$757$	−44528.0			−0.0777037			−0.0388518	−	0.999245i	$-0.512370\pi$
$757$	−44528.0			−0.0777037			−0.0388518	+	0.999245i	$0.512370\pi$
$758$			444102.i			0.772938i
$759$	9765.00	+	57770.5i	0.0169507	+	0.100282i
$760$		0			0
$761$			259426.i			0.447965i	0.974593	+	0.223983i	$0.0719059\pi$
$761$			259426.i			0.447965i	−0.974593	+	0.223983i	$0.928094\pi$
$762$	694155.	−	117334.i	1.19549	−	0.202075i
$763$	−291456.			−0.500638
$764$		−	89250.0i		−	0.152905i
$765$		0			0
$766$	1.25832e6			2.14454
$767$			4780.19i			0.00812559i
$768$	−51841.5	−	306698.i	−0.0878932	−	0.519983i
$769$	−791593.			−1.33860			−0.669298	−	0.742994i	$-0.733405\pi$
$769$	−791593.			−1.33860			−0.669298	+	0.742994i	$0.733405\pi$
$770$		0			0
$771$	570150.	−	96372.9i	0.959136	−	0.162124i
$772$	240787.			0.404016
$773$			254190.i			0.425402i	0.977117	+	0.212701i	$0.0682261\pi$
$773$			254190.i			0.425402i	−0.977117	+	0.212701i	$0.931774\pi$
$774$	−154665.	−	444434.i	−0.258173	−	0.741865i
$775$		0			0
$776$		−	142731.i		−	0.237026i
$777$	−81216.0	−	480480.i	−0.134524	−	0.795854i
$778$	56490.0			0.0933281
$779$		−	588396.i		−	0.969604i
$780$		0			0
$781$	1.23473e6			2.02428
$782$		−	16150.9i		−	0.0264109i
$783$	−234360.	+	128746.i	−0.382261	+	0.209995i
$784$	−553817.			−0.901019
$785$		0			0
$786$	112770.	+	667156.i	0.182536	+	1.07990i
$787$	662422.			1.06951			0.534756	−	0.845007i	$-0.320404\pi$
$787$	662422.			1.06951			0.534756	+	0.845007i	$0.320404\pi$
$788$			818087.i			1.31749i
$789$	775635.	−	131106.i	1.24596	−	0.210605i
$790$		0			0
$791$			161438.i			0.258020i
$792$	−249008.	+	86655.8i	−0.396974	+	0.138149i
$793$	−753056.			−1.19751
$794$		−	95532.9i		−	0.151535i
$795$		0			0
$796$	−436468.			−0.688853
$797$			1.06065e6i			1.66976i	0.550432	+	0.834880i	$0.314463\pi$
$797$			1.06065e6i			1.66976i	−0.550432	+	0.834880i	$0.685537\pi$
$798$	1.38726e6	−	234490.i	2.17847	−	0.368229i
$799$	−91910.0			−0.143969
$800$		0			0
$801$	−126158.	−	362517.i	−0.196629	−	0.565019i
$802$	477225.			0.741950
$803$			72809.2i			0.112916i
$804$	−212126.	−	1.25495e6i	−0.328156	−	1.94140i
$805$		0			0
$806$		−	380025.i		−	0.584982i
$807$	−647430.	+	109436.i	−0.994136	+	0.168040i
$808$	189000.			0.289494
$809$		−	336246.i		−	0.513760i	−0.966443	−	0.256880i	$-0.917305\pi$
$809$		−	336246.i		−	0.513760i	0.966443	−	0.256880i	$-0.0826946\pi$
$810$		0			0
$811$	−605298.			−0.920296			−0.460148	−	0.887842i	$-0.652204\pi$
$811$	−605298.			−0.920296			−0.460148	+	0.887842i	$0.652204\pi$
$812$		−	501778.i		−	0.761026i
$813$	3747.00	+	22167.6i	0.00566895	+	0.0335380i
$814$	−815920.			−1.23140
$815$		0			0
$816$	−135818.	+	22957.3i	−0.203974	+	0.0344779i
$817$	360394.			0.539925
$818$		−	860689.i		−	1.28629i
$819$	−1.11262e6	+	387196.i	−1.65874	+	0.577248i
$820$		0			0
$821$		−	795228.i		−	1.17979i	−0.807480	−	0.589896i	$-0.799169\pi$
$821$		−	795228.i		−	1.17979i	0.807480	−	0.589896i	$-0.200831\pi$
$822$	44572.5	+	263694.i	0.0659665	+	0.390263i
$823$	−550468.			−0.812704			−0.406352	−	0.913717i	$-0.633199\pi$
$823$	−550468.			−0.812704			−0.406352	+	0.913717i	$0.633199\pi$
$824$			117103.i			0.172470i
$825$		0			0
$826$	−10080.0			−0.0147741
$827$		−	964256.i		−	1.40988i	−0.709268	−	0.704939i	$-0.750975\pi$
$827$		−	964256.i		−	1.40988i	0.709268	−	0.704939i	$-0.249025\pi$
$828$	17955.0	+	51594.1i	0.0261894	+	0.0752557i
$829$	558402.			0.812527			0.406264	−	0.913756i	$-0.366831\pi$
$829$	558402.			0.812527			0.406264	+	0.913756i	$0.366831\pi$
$830$		0			0
$831$	75267.0	+	445286.i	0.108994	+	0.644817i
$832$	1.10312e6			1.59359
$833$			214038.i			0.308461i
$834$	1.58534e6	−	267972.i	2.27924	−	0.385263i
$835$		0			0
$836$		−	1.27884e6i		−	1.82980i
$837$	−111618.	−	203182.i	−0.159325	−	0.290024i
$838$	293195.			0.417512
$839$			738658.i			1.04935i	0.851303	+	0.524674i	$0.175813\pi$
$839$			738658.i			1.04935i	−0.851303	+	0.524674i	$0.824187\pi$
$840$		0			0
$841$	572741.			0.809779
$842$		−	136709.i		−	0.192829i
$843$	509670.	−	86150.0i	0.717189	−	0.121227i
$844$	1.19782e6			1.68153
$845$		0			0
$846$	540855.	−	188220.i	0.755684	−	0.262982i
$847$	−1.36757e6			−1.90626
$848$			468565.i			0.651596i
$849$	125194.	+	740661.i	0.173688	+	1.02755i
$850$		0			0
$851$			26693.4i			0.0368590i
$852$	1.13516e6	−	191876.i	1.56378	−	0.264327i
$853$	−347058.			−0.476984			−0.238492	−	0.971144i	$-0.576653\pi$
$853$	−347058.			−0.476984			−0.238492	+	0.971144i	$0.576653\pi$
$854$		−	1.58797e6i		−	2.17734i
$855$		0			0
$856$	−228375.			−0.311674
$857$		−	51144.5i		−	0.0696366i	−0.999394	−	0.0348183i	$-0.988915\pi$
$857$		−	51144.5i		−	0.0696366i	0.999394	−	0.0348183i	$-0.0110852\pi$
$858$	328755.	+	1.94494e6i	0.446578	+	2.64199i
$859$	−181733.			−0.246290			−0.123145	−	0.992389i	$-0.539298\pi$
$859$	−181733.			−0.246290			−0.123145	+	0.992389i	$0.539298\pi$
$860$		0			0
$861$	−1.02438e6	+	173152.i	−1.38183	+	0.233572i
$862$	−2.14158e6			−2.88217
$863$			121126.i			0.162635i	0.996688	+	0.0813177i	$0.0259128\pi$
$863$			121126.i			0.162635i	−0.996688	+	0.0813177i	$0.974087\pi$
$864$	933660.	−	512906.i	1.25072	−	0.687085i
$865$		0			0
$866$		−	419704.i		−	0.559639i
$867$	−116409.	−	688685.i	−0.154863	−	0.916183i
$868$	435024.			0.577396
$869$		−	1.12020e6i		−	1.48339i
$870$		0			0
$871$	−1.50349e6			−1.98181
$872$			71844.9i			0.0944850i
$873$	−615213.	+	214097.i	−0.807229	+	0.280920i
$874$	−77070.0			−0.100893
$875$		0			0
$876$	11314.5	+	66937.5i	0.0147444	+	0.0872291i
$877$	310152.			0.403251			0.201625	−	0.979463i	$-0.435378\pi$
$877$	310152.			0.403251			0.201625	+	0.979463i	$0.435378\pi$
$878$		−	803510.i		−	1.04232i
$879$	−1.02690e6	+	173578.i	−1.32908	+	0.224655i
$880$		0			0
$881$			838592.i			1.08044i	0.841525	+	0.540218i	$0.181658\pi$
$881$			838592.i			1.08044i	−0.841525	+	0.540218i	$0.818342\pi$
$882$	−438322.	−	1.25953e6i	−0.563452	−	1.61909i
$883$	−434533.			−0.557316			−0.278658	−	0.960390i	$-0.589890\pi$
$883$	−434533.			−0.557316			−0.278658	+	0.960390i	$0.589890\pi$
$884$		−	295177.i		−	0.377727i
$885$		0			0
$886$	−1.49258e6			−1.90138
$887$		−	310097.i		−	0.394140i	−0.980389	−	0.197070i	$-0.936857\pi$
$887$		−	310097.i		−	0.394140i	0.980389	−	0.197070i	$-0.0631426\pi$
$888$	−118440.	+	20020.0i	−0.150201	+	0.0253886i
$889$	951984.			1.20455
$890$		0			0
$891$	747022.	+	943310.i	0.940975	+	1.18823i
$892$	−827108.			−1.03952
$893$			438583.i			0.549982i
$894$	311325.	+	1.84182e6i	0.389528	+	2.30448i
$895$		0			0
$896$			642770.i			0.800645i
$897$	63630.0	−	10755.4i	0.0790819	−	0.0133673i
$898$	−2.25418e6			−2.79534
$899$		−	116641.i		−	0.144322i
$900$		0			0
$901$	181090.			0.223072
$902$			1.73953e6i			2.13806i
$903$	−106056.	−	627436.i	−0.130065	−	0.769474i
$904$	39795.0			0.0486958
$905$		0			0
$906$	−337470.	+	57042.8i	−0.411130	+	0.0694936i
$907$	465582.			0.565955			0.282977	−	0.959127i	$-0.408678\pi$
$907$	465582.			0.565955			0.282977	+	0.959127i	$0.408678\pi$
$908$			762559.i			0.924915i
$909$	−283500.	−	814644.i	−0.343104	−	0.985917i
$910$		0			0
$911$		−	408470.i		−	0.492179i	−0.969247	−	0.246090i	$-0.920854\pi$
$911$		−	408470.i		−	0.492179i	0.969247	−	0.246090i	$-0.0791457\pi$
$912$	109550.	+	648104.i	0.131711	+	0.779210i
$913$	2.43800e6			2.92477
$914$			1.51663e6i			1.81546i
$915$		0			0
$916$	1.64821e6			1.96436
$917$			914957.i			1.08808i
$918$	−159705.	−	290716.i	−0.189510	−	0.344972i
$919$	1.01978e6			1.20747			0.603735	−	0.797185i	$-0.293679\pi$
$919$	1.01978e6			1.20747			0.603735	+	0.797185i	$0.293679\pi$
$920$		0			0
$921$	185164.	+	1.09545e6i	0.218292	+	1.29143i
$922$	−1.12266e6			−1.32065
$923$		−	1.35996e6i		−	1.59634i
$924$	−2.22642e6	+	376334.i	−2.60773	+	0.440787i
$925$		0			0
$926$		−	2.00938e6i		−	2.34337i
$927$	504747.	−	175654.i	0.587373	−	0.204409i
$928$	535990.			0.622387
$929$			1.29404e6i			1.49939i	0.661783	+	0.749696i	$0.269800\pi$
$929$			1.29404e6i			1.49939i	−0.661783	+	0.749696i	$0.730200\pi$
$930$		0			0
$931$	1.02136e6			1.17837
$932$		−	619130.i		−	0.712771i
$933$	−1.04076e6	+	175921.i	−1.19560	+	0.202094i
$934$	−338380.			−0.387892
$935$		0			0
$936$	95445.0	+	274264.i	0.108944	+	0.313052i
$937$	−141573.			−0.161251			−0.0806253	−	0.996744i	$-0.525692\pi$
$937$	−141573.			−0.161251			−0.0806253	+	0.996744i	$0.525692\pi$
$938$		−	3.17040e6i		−	3.60337i
$939$	−77313.0	−	457390.i	−0.0876842	−	0.518747i
$940$		0			0
$941$		−	1.68139e6i		−	1.89884i	−0.314011	−	0.949419i	$-0.601673\pi$
$941$		−	1.68139e6i		−	1.89884i	0.314011	−	0.949419i	$-0.398327\pi$
$942$	834855.	−	141116.i	0.940826	−	0.159029i
$943$	56910.0			0.0639978
$944$		−	4709.20i		−	0.00528449i
$945$		0			0
$946$	−1.06547e6			−1.19058
$947$			507671.i			0.566086i	0.959107	+	0.283043i	$0.0913438\pi$
$947$			507671.i			0.566086i	−0.959107	+	0.283043i	$0.908656\pi$
$948$	−174078.	−	1.02986e6i	−0.193699	−	1.14594i
$949$	80194.0			0.0890450
$950$		0			0
$951$	1.22892e6	−	207725.i	1.35882	−	0.229683i
$952$	98280.0			0.108440
$953$			716183.i			0.788566i	0.918989	+	0.394283i	$0.129007\pi$
$953$			716183.i			0.788566i	−0.918989	+	0.394283i	$0.870993\pi$
$954$	−1.06564e6	+	370849.i	−1.17089	+	0.407475i
$955$		0			0
$956$			1.88324e6i			2.06058i
$957$	100905.	+	596962.i	0.110176	+	0.651813i
$958$	−1.25307e6			−1.36535
$959$			361638.i			0.393221i
$960$		0			0
$961$	−822397.			−0.890502
$962$			898676.i			0.971076i
$963$	342562.	+	984362.i	0.369392	+	1.06146i
$964$	−1.05691e6			−1.13733
$965$		0			0
$966$	22680.0	+	134177.i	0.0243046	+	0.143788i
$967$	1.04943e6			1.12228			0.561140	−	0.827721i	$-0.310363\pi$
$967$	1.04943e6			1.12228			0.561140	+	0.827721i	$0.310363\pi$
$968$			337110.i			0.359767i
$969$	250478.	−	42338.4i	0.266760	−	0.0450907i
$970$		0			0
$971$			789246.i			0.837094i	0.908195	+	0.418547i	$0.137460\pi$
$971$			789246.i			0.837094i	−0.908195	+	0.418547i	$0.862540\pi$
$972$	833368.	+	751150.i	0.882073	+	0.795049i
$973$	2.17418e6			2.29652
$974$		−	883141.i		−	0.930919i
$975$		0			0
$976$	741872.			0.778806
$977$		−	493928.i		−	0.517457i	−0.965950	−	0.258728i	$-0.916697\pi$
$977$		−	493928.i		−	0.517457i	0.965950	−	0.258728i	$-0.0833035\pi$
$978$	1.68772e6	−	285276.i	1.76450	−	0.298255i
$979$	−869085.			−0.906769
$980$		0			0
$981$	309672.	−	107767.i	0.321784	−	0.111982i
$982$	−616840.			−0.639661
$983$			363768.i			0.376459i	0.982125	+	0.188229i	$0.0602748\pi$
$983$			363768.i			0.376459i	−0.982125	+	0.188229i	$0.939725\pi$
$984$	42682.5	+	252513.i	0.0440818	+	0.260792i
$985$		0			0
$986$		−	166893.i		−	0.171666i
$987$	763560.	−	129065.i	0.783807	−	0.132487i
$988$	−1.40855e6			−1.44297
$989$			34857.5i			0.0356372i
$990$		0			0
$991$	−1.70055e6			−1.73158			−0.865788	−	0.500411i	$-0.833182\pi$
$991$	−1.70055e6			−1.73158			−0.865788	+	0.500411i	$0.833182\pi$
$992$			464684.i			0.472210i
$993$	194224.	+	1.14905e6i	0.196972	+	1.16530i
$994$	2.86776e6			2.90249
$995$		0			0
$996$	2.24138e6	−	378863.i	2.25942	−	0.381912i
$997$	1.61785e6			1.62760			0.813801	−	0.581143i	$-0.197394\pi$
$997$	1.61785e6			1.62760			0.813801	+	0.581143i	$0.197394\pi$
$998$			1.48495e6i			1.49091i
$999$	263952.	+	480480.i	0.264481	+	0.481443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.5.c.d.26.2	yes	2
3.2	odd	2	inner	75.5.c.d.26.1	✓	2
5.2	odd	4		75.5.d.c.74.2		4
5.3	odd	4		75.5.d.c.74.3		4
5.4	even	2		75.5.c.f.26.1	yes	2
15.2	even	4		75.5.d.c.74.4		4
15.8	even	4		75.5.d.c.74.1		4
15.14	odd	2		75.5.c.f.26.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.5.c.d.26.1	✓	2	3.2	odd	2	inner
75.5.c.d.26.2	yes	2	1.1	even	1	trivial
75.5.c.f.26.1	yes	2	5.4	even	2
75.5.c.f.26.2	yes	2	15.14	odd	2
75.5.d.c.74.1		4	15.8	even	4
75.5.d.c.74.2		4	5.2	odd	4
75.5.d.c.74.3		4	5.3	odd	4
75.5.d.c.74.4		4	15.2	even	4

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

\(f(q)\)	\(=\)	\(q+5.91608i q^{2} +(-1.50000 - 8.87412i) q^{3} -19.0000 q^{4} +(52.5000 - 8.87412i) q^{6} +72.0000 q^{7} -17.7482i q^{8} +(-76.5000 + 26.6224i) q^{9} +O(q^{10})\)	\(q+5.91608i q^{2} +(-1.50000 - 8.87412i) q^{3} -19.0000 q^{4} +(52.5000 - 8.87412i) q^{6} +72.0000 q^{7} -17.7482i q^{8} +(-76.5000 + 26.6224i) q^{9} +183.398i q^{11} +(28.5000 + 168.608i) q^{12} +202.000 q^{13} +425.958i q^{14} -199.000 q^{16} +76.9090i q^{17} +(-157.500 - 452.580i) q^{18} +367.000 q^{19} +(-108.000 - 638.937i) q^{21} -1085.00 q^{22} +35.4965i q^{23} +(-157.500 + 26.6224i) q^{24} +1195.05i q^{26} +(351.000 + 638.937i) q^{27} -1368.00 q^{28} +366.797i q^{29} -318.000 q^{31} -1461.27i q^{32} +(1627.50 - 275.098i) q^{33} -455.000 q^{34} +(1453.50 - 505.825i) q^{36} +752.000 q^{37} +2171.20i q^{38} +(-303.000 - 1792.57i) q^{39} -1603.26i q^{41} +(3780.00 - 638.937i) q^{42} +982.000 q^{43} -3484.57i q^{44} -210.000 q^{46} +1195.05i q^{47} +(298.500 + 1765.95i) q^{48} +2783.00 q^{49} +(682.500 - 115.364i) q^{51} -3838.00 q^{52} -2354.60i q^{53} +(-3780.00 + 2076.54i) q^{54} -1277.87i q^{56} +(-550.500 - 3256.80i) q^{57} -2170.00 q^{58} +23.6643i q^{59} -3728.00 q^{61} -1881.31i q^{62} +(-5508.00 + 1916.81i) q^{63} +5461.00 q^{64} +(1627.50 + 9628.42i) q^{66} -7443.00 q^{67} -1461.27i q^{68} +(315.000 - 53.2447i) q^{69} -6732.50i q^{71} +(472.500 + 1357.74i) q^{72} +397.000 q^{73} +4448.89i q^{74} -6973.00 q^{76} +13204.7i q^{77} +(10605.0 - 1792.57i) q^{78} -6108.00 q^{79} +(5143.50 - 4073.22i) q^{81} +9485.00 q^{82} -13293.4i q^{83} +(2052.00 + 12139.8i) q^{84} +5809.59i q^{86} +(3255.00 - 550.195i) q^{87} +3255.00 q^{88} +4738.78i q^{89} +14544.0 q^{91} -674.433i q^{92} +(477.000 + 2821.97i) q^{93} -7070.00 q^{94} +(-12967.5 + 2191.91i) q^{96} +8042.00 q^{97} +16464.5i q^{98} +(-4882.50 - 14030.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} - 38 q^{4} + 105 q^{6} + 144 q^{7} - 153 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 - 38 * q^4 + 105 * q^6 + 144 * q^7 - 153 * q^9	\( 2 q - 3 q^{3} - 38 q^{4} + 105 q^{6} + 144 q^{7} - 153 q^{9} + 57 q^{12} + 404 q^{13} - 398 q^{16} - 315 q^{18} + 734 q^{19} - 216 q^{21} - 2170 q^{22} - 315 q^{24} + 702 q^{27} - 2736 q^{28} - 636 q^{31} + 3255 q^{33} - 910 q^{34} + 2907 q^{36} + 1504 q^{37} - 606 q^{39} + 7560 q^{42} + 1964 q^{43} - 420 q^{46} + 597 q^{48} + 5566 q^{49} + 1365 q^{51} - 7676 q^{52} - 7560 q^{54} - 1101 q^{57} - 4340 q^{58} - 7456 q^{61} - 11016 q^{63} + 10922 q^{64} + 3255 q^{66} - 14886 q^{67} + 630 q^{69} + 945 q^{72} + 794 q^{73} - 13946 q^{76} + 21210 q^{78} - 12216 q^{79} + 10287 q^{81} + 18970 q^{82} + 4104 q^{84} + 6510 q^{87} + 6510 q^{88} + 29088 q^{91} + 954 q^{93} - 14140 q^{94} - 25935 q^{96} + 16084 q^{97} - 9765 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 - 38 * q^4 + 105 * q^6 + 144 * q^7 - 153 * q^9 + 57 * q^12 + 404 * q^13 - 398 * q^16 - 315 * q^18 + 734 * q^19 - 216 * q^21 - 2170 * q^22 - 315 * q^24 + 702 * q^27 - 2736 * q^28 - 636 * q^31 + 3255 * q^33 - 910 * q^34 + 2907 * q^36 + 1504 * q^37 - 606 * q^39 + 7560 * q^42 + 1964 * q^43 - 420 * q^46 + 597 * q^48 + 5566 * q^49 + 1365 * q^51 - 7676 * q^52 - 7560 * q^54 - 1101 * q^57 - 4340 * q^58 - 7456 * q^61 - 11016 * q^63 + 10922 * q^64 + 3255 * q^66 - 14886 * q^67 + 630 * q^69 + 945 * q^72 + 794 * q^73 - 13946 * q^76 + 21210 * q^78 - 12216 * q^79 + 10287 * q^81 + 18970 * q^82 + 4104 * q^84 + 6510 * q^87 + 6510 * q^88 + 29088 * q^91 + 954 * q^93 - 14140 * q^94 - 25935 * q^96 + 16084 * q^97 - 9765 * q^99

Introduction

L-functions

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