LMFDB - Embedded newform 74.4.b.a.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(73,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("74.73");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.b (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:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 212x^{8} + 15052x^{6} + 392769x^{4} + 2690496x^{2} + 2985984 $ x^10 + 212x^8 + 15052x^6 + 392769x^4 + 2690496x^2 + 2985984
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.5
Root			$-8.84166i$ of defining polynomial
Character	$\chi$	$=$	74.73
Dual form			74.4.b.a.73.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +9.84166 q^{3} -4.00000 q^{4} -14.4069i q^{5} -19.6833i q^{6} -22.1853 q^{7} +8.00000i q^{8} +69.8583 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +9.84166 q^{3} -4.00000 q^{4} -14.4069i q^{5} -19.6833i q^{6} -22.1853 q^{7} +8.00000i q^{8} +69.8583 q^{9} -28.8138 q^{10} +21.0485 q^{11} -39.3667 q^{12} +77.2971i q^{13} +44.3707i q^{14} -141.788i q^{15} +16.0000 q^{16} -73.4632i q^{17} -139.717i q^{18} +68.5271i q^{19} +57.6276i q^{20} -218.341 q^{21} -42.0971i q^{22} -25.3645i q^{23} +78.7333i q^{24} -82.5590 q^{25} +154.594 q^{26} +421.797 q^{27} +88.7413 q^{28} +268.373i q^{29} -283.576 q^{30} -86.5385i q^{31} -32.0000i q^{32} +207.153 q^{33} -146.926 q^{34} +319.622i q^{35} -279.433 q^{36} +(-219.871 + 48.0609i) q^{37} +137.054 q^{38} +760.732i q^{39} +115.255 q^{40} +5.19294 q^{41} +436.681i q^{42} -125.781i q^{43} -84.1942 q^{44} -1006.44i q^{45} -50.7289 q^{46} -181.217 q^{47} +157.467 q^{48} +149.189 q^{49} +165.118i q^{50} -723.000i q^{51} -309.188i q^{52} +63.1517 q^{53} -843.595i q^{54} -303.244i q^{55} -177.483i q^{56} +674.421i q^{57} +536.746 q^{58} -207.923i q^{59} +567.152i q^{60} +299.467i q^{61} -173.077 q^{62} -1549.83 q^{63} -64.0000 q^{64} +1113.61 q^{65} -414.305i q^{66} -142.495 q^{67} +293.853i q^{68} -249.629i q^{69} +639.244 q^{70} -501.281 q^{71} +558.867i q^{72} +200.110 q^{73} +(96.1218 + 439.742i) q^{74} -812.518 q^{75} -274.108i q^{76} -466.969 q^{77} +1521.46 q^{78} -1074.72i q^{79} -230.511i q^{80} +2265.01 q^{81} -10.3859i q^{82} -1120.84 q^{83} +873.362 q^{84} -1058.38 q^{85} -251.563 q^{86} +2641.24i q^{87} +168.388i q^{88} +154.822i q^{89} -2012.89 q^{90} -1714.86i q^{91} +101.458i q^{92} -851.683i q^{93} +362.435i q^{94} +987.263 q^{95} -314.933i q^{96} -829.017i q^{97} -298.378i q^{98} +1470.42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9}+O(q^{10}) $ 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9	$ 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9} + 76 q^{10} - 50 q^{11} - 56 q^{12} + 160 q^{16} - 312 q^{21} - 700 q^{25} + 492 q^{26} + 848 q^{27} + 16 q^{28} - 240 q^{30} - 508 q^{33} - 568 q^{34} - 688 q^{36} + 82 q^{37} + 336 q^{38} - 304 q^{40} - 1194 q^{41} + 200 q^{44} + 60 q^{46} + 464 q^{47} + 224 q^{48} + 2382 q^{49} - 692 q^{53} + 1108 q^{58} - 1700 q^{62} + 2300 q^{63} - 640 q^{64} + 604 q^{65} + 1114 q^{67} + 1880 q^{70} - 1460 q^{71} + 2082 q^{73} + 968 q^{74} - 5160 q^{75} - 6096 q^{77} + 1004 q^{78} + 4978 q^{81} - 1364 q^{83} + 1248 q^{84} + 104 q^{85} + 1400 q^{86} - 2600 q^{90} + 5084 q^{95} + 508 q^{99}+O(q^{100}) $ 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9 + 76 * q^10 - 50 * q^11 - 56 * q^12 + 160 * q^16 - 312 * q^21 - 700 * q^25 + 492 * q^26 + 848 * q^27 + 16 * q^28 - 240 * q^30 - 508 * q^33 - 568 * q^34 - 688 * q^36 + 82 * q^37 + 336 * q^38 - 304 * q^40 - 1194 * q^41 + 200 * q^44 + 60 * q^46 + 464 * q^47 + 224 * q^48 + 2382 * q^49 - 692 * q^53 + 1108 * q^58 - 1700 * q^62 + 2300 * q^63 - 640 * q^64 + 604 * q^65 + 1114 * q^67 + 1880 * q^70 - 1460 * q^71 + 2082 * q^73 + 968 * q^74 - 5160 * q^75 - 6096 * q^77 + 1004 * q^78 + 4978 * q^81 - 1364 * q^83 + 1248 * q^84 + 104 * q^85 + 1400 * q^86 - 2600 * q^90 + 5084 * q^95 + 508 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$-1$

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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$	9.84166			1.89403			0.947015	−	0.321191i	$-0.104083\pi$
$3$	9.84166			1.89403			0.947015	+	0.321191i	$0.104083\pi$
$4$	−4.00000			−0.500000
$5$		−	14.4069i		−	1.28859i	−0.764776	−	0.644297i	$-0.777150\pi$
$5$		−	14.4069i		−	1.28859i	0.764776	−	0.644297i	$-0.222850\pi$
$6$		−	19.6833i		−	1.33928i
$7$	−22.1853			−1.19790			−0.598948	−	0.800788i	$-0.704414\pi$
$7$	−22.1853			−1.19790			−0.598948	+	0.800788i	$0.704414\pi$
$8$			8.00000i			0.353553i
$9$	69.8583			2.58735
$10$	−28.8138			−0.911173
$11$	21.0485			0.576943			0.288472	−	0.957488i	$-0.406853\pi$
$11$	21.0485			0.576943			0.288472	+	0.957488i	$0.406853\pi$
$12$	−39.3667			−0.947015
$13$			77.2971i			1.64910i	0.565786	+	0.824552i	$0.308573\pi$
$13$			77.2971i			1.64910i	−0.565786	+	0.824552i	$0.691427\pi$
$14$			44.3707i			0.847040i
$15$		−	141.788i		−	2.44063i
$16$	16.0000			0.250000
$17$		−	73.4632i		−	1.04808i	−0.851692	−	0.524042i	$-0.824423\pi$
$17$		−	73.4632i		−	1.04808i	0.851692	−	0.524042i	$-0.175577\pi$
$18$		−	139.717i		−	1.82953i
$19$			68.5271i			0.827431i	0.910406	+	0.413716i	$0.135769\pi$
$19$			68.5271i			0.827431i	−0.910406	+	0.413716i	$0.864231\pi$
$20$			57.6276i			0.644297i
$21$	−218.341			−2.26885
$22$		−	42.0971i		−	0.407960i
$23$		−	25.3645i		−	0.229950i	−0.993368	−	0.114975i	$-0.963321\pi$
$23$		−	25.3645i		−	0.229950i	0.993368	−	0.114975i	$-0.0366789\pi$
$24$			78.7333i			0.669640i
$25$	−82.5590			−0.660472
$26$	154.594			1.16609
$27$	421.797			3.00648
$28$	88.7413			0.598948
$29$			268.373i			1.71847i	0.511582	+	0.859235i	$0.329060\pi$
$29$			268.373i			1.71847i	−0.511582	+	0.859235i	$0.670940\pi$
$30$	−283.576			−1.72579
$31$		−	86.5385i		−	0.501380i	−0.968067	−	0.250690i	$-0.919343\pi$
$31$		−	86.5385i		−	0.501380i	0.968067	−	0.250690i	$-0.0806575\pi$
$32$		−	32.0000i		−	0.176777i
$33$	207.153			1.09275
$34$	−146.926			−0.741108
$35$			319.622i			1.54360i
$36$	−279.433			−1.29367
$37$	−219.871	+	48.0609i	−0.976933	+	0.213545i
$37$	−219.871	+	48.0609i	−0.976933	+	0.213545i
$38$	137.054			0.585082
$39$			760.732i			3.12345i
$40$	115.255			0.455586
$41$	5.19294			0.0197805			0.00989025	−	0.999951i	$-0.496852\pi$
$41$	5.19294			0.0197805			0.00989025	+	0.999951i	$0.496852\pi$
$42$			436.681i			1.60432i
$43$		−	125.781i		−	0.446081i	−0.974809	−	0.223040i	$-0.928402\pi$
$43$		−	125.781i		−	0.446081i	0.974809	−	0.223040i	$-0.0715982\pi$
$44$	−84.1942			−0.288472
$45$		−	1006.44i		−	3.33404i
$46$	−50.7289			−0.162599
$47$	−181.217			−0.562410			−0.281205	−	0.959648i	$-0.590734\pi$
$47$	−181.217			−0.562410			−0.281205	+	0.959648i	$0.590734\pi$
$48$	157.467			0.473507
$49$	149.189			0.434953
$50$			165.118i			0.467024i
$51$		−	723.000i		−	1.98510i
$52$		−	309.188i		−	0.824552i
$53$	63.1517			0.163671			0.0818354	−	0.996646i	$-0.473922\pi$
$53$	63.1517			0.163671			0.0818354	+	0.996646i	$0.473922\pi$
$54$		−	843.595i		−	2.12590i
$55$		−	303.244i		−	0.743445i
$56$		−	177.483i		−	0.423520i
$57$			674.421i			1.56718i
$58$	536.746			1.21514
$59$		−	207.923i		−	0.458802i	−0.973332	−	0.229401i	$-0.926323\pi$
$59$		−	207.923i		−	0.458802i	0.973332	−	0.229401i	$-0.0736767\pi$
$60$			567.152i			1.22032i
$61$			299.467i			0.628570i	0.949329	+	0.314285i	$0.101765\pi$
$61$			299.467i			0.628570i	−0.949329	+	0.314285i	$0.898235\pi$
$62$	−173.077			−0.354529
$63$	−1549.83			−3.09937
$64$	−64.0000			−0.125000
$65$	1113.61			2.12503
$66$		−	414.305i		−	0.772689i
$67$	−142.495			−0.259828			−0.129914	−	0.991525i	$-0.541470\pi$
$67$	−142.495			−0.259828			−0.129914	+	0.991525i	$0.541470\pi$
$68$			293.853i			0.524042i
$69$		−	249.629i		−	0.435533i
$70$	639.244			1.09149
$71$	−501.281			−0.837903			−0.418952	−	0.908009i	$-0.637602\pi$
$71$	−501.281			−0.837903			−0.418952	+	0.908009i	$0.637602\pi$
$72$			558.867i			0.914765i
$73$	200.110			0.320837			0.160418	−	0.987049i	$-0.448716\pi$
$73$	200.110			0.320837			0.160418	+	0.987049i	$0.448716\pi$
$74$	96.1218	+	439.742i	0.150999	+	0.690796i
$75$	−812.518			−1.25095
$76$		−	274.108i		−	0.413716i
$77$	−466.969			−0.691117
$78$	1521.46			2.20861
$79$		−	1074.72i		−	1.53057i	−0.643690	−	0.765286i	$-0.722597\pi$
$79$		−	1074.72i		−	1.53057i	0.643690	−	0.765286i	$-0.277403\pi$
$80$		−	230.511i		−	0.322148i
$81$	2265.01			3.10701
$82$		−	10.3859i		−	0.0139869i
$83$	−1120.84			−1.48227			−0.741136	−	0.671355i	$-0.765712\pi$
$83$	−1120.84			−1.48227			−0.741136	+	0.671355i	$0.765712\pi$
$84$	873.362			1.13442
$85$	−1058.38			−1.35055
$86$	−251.563			−0.315427
$87$			2641.24i			3.25483i
$88$			168.388i			0.203980i
$89$			154.822i			0.184395i	0.995741	+	0.0921975i	$0.0293891\pi$
$89$			154.822i			0.184395i	−0.995741	+	0.0921975i	$0.970611\pi$
$90$	−2012.89			−2.35752
$91$		−	1714.86i		−	1.97546i
$92$			101.458i			0.114975i
$93$		−	851.683i		−	0.949628i
$94$			362.435i			0.397684i
$95$	987.263			1.06622
$96$		−	314.933i		−	0.334820i
$97$		−	829.017i		−	0.867773i	−0.900968	−	0.433886i	$-0.857142\pi$
$97$		−	829.017i		−	0.867773i	0.900968	−	0.433886i	$-0.142858\pi$
$98$		−	298.378i		−	0.307559i
$99$	1470.42			1.49275
$100$	330.236			0.330236
$101$	1707.47			1.68217			0.841086	−	0.540901i	$-0.181917\pi$
$101$	1707.47			1.68217			0.841086	+	0.540901i	$0.181917\pi$
$102$	−1446.00			−1.40368
$103$		−	590.822i		−	0.565199i	−0.959238	−	0.282599i	$-0.908803\pi$
$103$		−	590.822i		−	0.565199i	0.959238	−	0.282599i	$-0.0911967\pi$
$104$	−618.377			−0.583047
$105$			3145.61i			2.92362i
$106$		−	126.303i		−	0.115733i
$107$	−611.387			−0.552383			−0.276192	−	0.961103i	$-0.589072\pi$
$107$	−611.387			−0.552383			−0.276192	+	0.961103i	$0.589072\pi$
$108$	−1687.19			−1.50324
$109$		−	473.624i		−	0.416192i	−0.978108	−	0.208096i	$-0.933273\pi$
$109$		−	473.624i		−	0.416192i	0.978108	−	0.208096i	$-0.0667266\pi$
$110$	−606.489			−0.525695
$111$	−2163.89	+	472.999i	−1.85034	+	0.404460i
$112$	−354.965			−0.299474
$113$		−	372.997i		−	0.310519i	−0.987874	−	0.155259i	$-0.950379\pi$
$113$		−	372.997i		−	0.310519i	0.987874	−	0.155259i	$-0.0496213\pi$
$114$	1348.84			1.10816
$115$	−365.424			−0.296312
$116$		−	1073.49i		−	0.859235i
$117$			5399.85i			4.26680i
$118$	−415.847			−0.324422
$119$			1629.81i			1.25550i
$120$	1134.30			0.862894
$121$	−887.959			−0.667137
$122$	598.933			0.444466
$123$	51.1071			0.0374648
$124$			346.154i			0.250690i
$125$		−	611.443i		−	0.437513i
$126$			3099.66i			2.19159i
$127$	2470.83			1.72639			0.863193	−	0.504874i	$-0.168461\pi$
$127$	2470.83			1.72639			0.863193	+	0.504874i	$0.168461\pi$
$128$			128.000i			0.0883883i
$129$		−	1237.90i		−	0.844890i
$130$		−	2227.22i		−	1.50262i
$131$			545.589i			0.363880i	0.983310	+	0.181940i	$0.0582377\pi$
$131$			545.589i			0.363880i	−0.983310	+	0.181940i	$0.941762\pi$
$132$	−828.611			−0.546373
$133$		−	1520.30i		−	0.991176i
$134$			284.989i			0.183726i
$135$		−	6076.80i		−	3.87413i
$136$	587.706			0.370554
$137$	1391.97			0.868059			0.434029	−	0.900899i	$-0.357091\pi$
$137$	1391.97			0.868059			0.434029	+	0.900899i	$0.357091\pi$
$138$	−499.257			−0.307968
$139$	−1428.62			−0.871758			−0.435879	−	0.900005i	$-0.643562\pi$
$139$	−1428.62			−0.871758			−0.435879	+	0.900005i	$0.643562\pi$
$140$		−	1278.49i		−	0.771800i
$141$	−1783.48			−1.06522
$142$			1002.56i			0.592487i
$143$			1626.99i			0.951440i
$144$	1117.73			0.646837
$145$	3866.43			2.21441
$146$		−	400.219i		−	0.226866i
$147$	1468.27			0.823814
$148$	879.483	−	192.244i	0.488467	−	0.106772i
$149$	1451.78			0.798217			0.399109	−	0.916904i	$-0.369320\pi$
$149$	1451.78			0.798217			0.399109	+	0.916904i	$0.369320\pi$
$150$			1625.04i			0.884558i
$151$	−688.505			−0.371058			−0.185529	−	0.982639i	$-0.559400\pi$
$151$	−688.505			−0.371058			−0.185529	+	0.982639i	$0.559400\pi$
$152$	−548.217			−0.292541
$153$		−	5132.02i		−	2.71176i
$154$			933.938i			0.488694i
$155$	−1246.75			−0.646075
$156$		−	3042.93i		−	1.56173i
$157$	−150.958			−0.0767375			−0.0383688	−	0.999264i	$-0.512216\pi$
$157$	−150.958			−0.0767375			−0.0383688	+	0.999264i	$0.512216\pi$
$158$	−2149.44			−1.08228
$159$	621.518			0.309997
$160$	−461.021			−0.227793
$161$			562.719i			0.275456i
$162$		−	4530.03i		−	2.19699i
$163$			2160.65i			1.03825i	0.854698	+	0.519125i	$0.173742\pi$
$163$			2160.65i			1.03825i	−0.854698	+	0.519125i	$0.826258\pi$
$164$	−20.7717			−0.00989025
$165$		−	2984.43i		−	1.40811i
$166$			2241.69i			1.04812i
$167$		−	2678.84i		−	1.24129i	−0.784093	−	0.620643i	$-0.786872\pi$
$167$		−	2678.84i		−	1.24129i	0.784093	−	0.620643i	$-0.213128\pi$
$168$		−	1746.72i		−	0.802159i
$169$	−3777.84			−1.71955
$170$			2116.76i			0.954987i
$171$			4787.19i			2.14085i
$172$			503.125i			0.223040i
$173$	−3865.32			−1.69870			−0.849349	−	0.527832i	$-0.823005\pi$
$173$	−3865.32			−1.69870			−0.849349	+	0.527832i	$0.823005\pi$
$174$	5282.47			2.30151
$175$	1831.60			0.791177
$176$	336.777			0.144236
$177$		−	2046.31i		−	0.868984i
$178$	309.645			0.130387
$179$			3443.78i			1.43799i	0.695015	+	0.718995i	$0.255398\pi$
$179$			3443.78i			1.43799i	−0.695015	+	0.718995i	$0.744602\pi$
$180$			4025.77i			1.66702i
$181$	3574.80			1.46803			0.734013	−	0.679135i	$-0.237645\pi$
$181$	3574.80			1.46803			0.734013	+	0.679135i	$0.237645\pi$
$182$	−3429.72			−1.39686
$183$			2947.25i			1.19053i
$184$	202.916			0.0812997
$185$	692.409	+	3167.66i	0.275172	+	1.25887i
$186$	−1703.37			−0.671488
$187$		−	1546.29i		−	0.604685i
$188$	724.869			0.281205
$189$	−9357.72			−3.60145
$190$		−	1974.53i		−	0.753933i
$191$		−	2114.39i		−	0.801004i	−0.916296	−	0.400502i	$-0.868836\pi$
$191$		−	2114.39i		−	0.801004i	0.916296	−	0.400502i	$-0.131164\pi$
$192$	−629.866			−0.236754
$193$			2989.74i			1.11506i	0.830158	+	0.557528i	$0.188250\pi$
$193$			2989.74i			1.11506i	−0.830158	+	0.557528i	$0.811750\pi$
$194$	−1658.03			−0.613608
$195$	10959.8			4.02486
$196$	−596.756			−0.217477
$197$	372.423			0.134691			0.0673453	−	0.997730i	$-0.478547\pi$
$197$	372.423			0.134691			0.0673453	+	0.997730i	$0.478547\pi$
$198$		−	2940.83i		−	1.05553i
$199$			2535.61i			0.903239i	0.892211	+	0.451619i	$0.149154\pi$
$199$			2535.61i			0.903239i	−0.892211	+	0.451619i	$0.850846\pi$
$200$		−	660.472i		−	0.233512i
$201$	−1402.39			−0.492123
$202$		−	3414.94i		−	1.18948i
$203$		−	5953.94i		−	2.05855i
$204$			2892.00i			0.992552i
$205$		−	74.8142i		−	0.0254890i
$206$	−1181.64			−0.399656
$207$		−	1771.92i		−	0.594961i
$208$			1236.75i			0.412276i
$209$			1442.40i			0.477381i
$210$	6291.23			2.06731
$211$	−1790.51			−0.584189			−0.292094	−	0.956389i	$-0.594352\pi$
$211$	−1790.51			−0.584189			−0.292094	+	0.956389i	$0.594352\pi$
$212$	−252.607			−0.0818354
$213$	−4933.44			−1.58701
$214$			1222.77i			0.390594i
$215$	−1812.12			−0.574816
$216$			3374.38i			1.06295i
$217$			1919.89i			0.600601i
$218$	−947.247			−0.294292
$219$	1969.41			0.607674
$220$			1212.98i			0.371722i
$221$	5678.49			1.72840
$222$	945.998	+	4327.79i	0.285997	+	1.30839i
$223$	−3997.76			−1.20049			−0.600247	−	0.799815i	$-0.704931\pi$
$223$	−3997.76			−1.20049			−0.600247	+	0.799815i	$0.704931\pi$
$224$			709.931i			0.211760i
$225$	−5767.44			−1.70887
$226$	−745.994			−0.219570
$227$			2597.05i			0.759350i	0.925120	+	0.379675i	$0.123964\pi$
$227$			2597.05i			0.759350i	−0.925120	+	0.379675i	$0.876036\pi$
$228$		−	2697.68i		−	0.783589i
$229$	1306.55			0.377026			0.188513	−	0.982071i	$-0.439633\pi$
$229$	1306.55			0.377026			0.188513	+	0.982071i	$0.439633\pi$
$230$			730.847i			0.209525i
$231$	−4595.75			−1.30900
$232$	−2146.98			−0.607571
$233$	6146.47			1.72819			0.864095	−	0.503328i	$-0.167891\pi$
$233$	6146.47			1.72819			0.864095	+	0.503328i	$0.167891\pi$
$234$	10799.7			3.01709
$235$			2610.78i			0.724718i
$236$			831.693i			0.229401i
$237$		−	10577.0i		−	2.89895i
$238$	3259.61			0.887770
$239$		−	3584.56i		−	0.970149i	−0.874473	−	0.485075i	$-0.838792\pi$
$239$		−	3584.56i		−	0.970149i	0.874473	−	0.485075i	$-0.161208\pi$
$240$		−	2268.61i		−	0.610158i
$241$			6404.30i			1.71177i	0.517163	+	0.855887i	$0.326988\pi$
$241$			6404.30i			1.71177i	−0.517163	+	0.855887i	$0.673012\pi$
$242$			1775.92i			0.471737i
$243$	10903.0			2.87829
$244$		−	1197.87i		−	0.314285i
$245$		−	2149.35i		−	0.560478i
$246$		−	102.214i		−	0.0264916i
$247$	−5296.95			−1.36452
$248$	692.308			0.177265
$249$	−11031.0			−2.80746
$250$	−1222.89			−0.309369
$251$			5373.87i			1.35138i	0.737187	+	0.675689i	$0.236154\pi$
$251$			5373.87i			1.35138i	−0.737187	+	0.675689i	$0.763846\pi$
$252$	6199.32			1.54969
$253$		−	533.885i		−	0.132668i
$254$		−	4941.67i		−	1.22074i
$255$	−10416.2			−2.55799
$256$	256.000			0.0625000
$257$			600.536i			0.145760i	0.997341	+	0.0728802i	$0.0232191\pi$
$257$			600.536i			0.145760i	−0.997341	+	0.0728802i	$0.976781\pi$
$258$	−2475.79			−0.597427
$259$	4877.91	−	1066.25i	1.17026	−	0.255804i
$260$	−4454.45			−1.06251
$261$			18748.1i			4.44627i
$262$	1091.18			0.257302
$263$	4800.19			1.12545			0.562723	−	0.826645i	$-0.309754\pi$
$263$	4800.19			1.12545			0.562723	+	0.826645i	$0.309754\pi$
$264$			1657.22i			0.386344i
$265$		−	909.821i		−	0.210905i
$266$	−3040.59			−0.700867
$267$			1523.71i			0.349249i
$268$	569.979			0.129914
$269$	4244.38			0.962024			0.481012	−	0.876714i	$-0.340269\pi$
$269$	4244.38			0.962024			0.481012	+	0.876714i	$0.340269\pi$
$270$	−12153.6			−2.73942
$271$	−4601.98			−1.03155			−0.515775	−	0.856724i	$-0.672496\pi$
$271$	−4601.98			−1.03155			−0.515775	+	0.856724i	$0.672496\pi$
$272$		−	1175.41i		−	0.262021i
$273$		−	16877.1i		−	3.74157i
$274$		−	2783.94i		−	0.613810i
$275$	−1737.75			−0.381055
$276$			998.515i			0.217766i
$277$			963.179i			0.208924i	0.994529	+	0.104462i	$0.0333120\pi$
$277$			963.179i			0.208924i	−0.994529	+	0.104462i	$0.966688\pi$
$278$			2857.25i			0.616426i
$279$		−	6045.44i		−	1.29724i
$280$	−2556.98			−0.545745
$281$		−	1662.13i		−	0.352864i	−0.984313	−	0.176432i	$-0.943545\pi$
$281$		−	1662.13i		−	0.352864i	0.984313	−	0.176432i	$-0.0564555\pi$
$282$			3566.96i			0.753225i
$283$		−	8665.09i		−	1.82009i	−0.414508	−	0.910046i	$-0.636046\pi$
$283$		−	8665.09i		−	1.82009i	0.414508	−	0.910046i	$-0.363954\pi$
$284$	2005.12			0.418952
$285$	9716.32			2.01946
$286$	3253.98			0.672769
$287$	−115.207			−0.0236950
$288$		−	2235.47i		−	0.457383i
$289$	−483.841			−0.0984818
$290$		−	7732.85i		−	1.56582i
$291$		−	8158.91i		−	1.64359i
$292$	−800.439			−0.160418
$293$	−1416.99			−0.282531			−0.141265	−	0.989972i	$-0.545117\pi$
$293$	−1416.99			−0.282531			−0.141265	+	0.989972i	$0.545117\pi$
$294$		−	2936.54i		−	0.582525i
$295$	−2995.53			−0.591209
$296$	−384.487	−	1758.97i	−0.0754995	−	0.345398i
$297$	8878.22			1.73457
$298$		−	2903.56i		−	0.564425i
$299$	1960.60			0.379212
$300$	3250.07			0.625477
$301$			2790.50i			0.534358i
$302$			1377.01i			0.262377i
$303$	16804.3			3.18608
$304$			1096.43i			0.206858i
$305$	4314.39			0.809971
$306$	−10264.0			−1.91750
$307$	−1514.03			−0.281466			−0.140733	−	0.990048i	$-0.544946\pi$
$307$	−1514.03			−0.281466			−0.140733	+	0.990048i	$0.544946\pi$
$308$	1867.88			0.345559
$309$		−	5814.67i		−	1.07050i
$310$			2493.50i			0.456844i
$311$		−	5907.78i		−	1.07717i	−0.842572	−	0.538584i	$-0.818959\pi$
$311$		−	5907.78i		−	1.07717i	0.842572	−	0.538584i	$-0.181041\pi$
$312$	−6085.86			−1.10431
$313$			7146.95i			1.29064i	0.763914	+	0.645318i	$0.223275\pi$
$313$			7146.95i			1.29064i	−0.763914	+	0.645318i	$0.776725\pi$
$314$			301.917i			0.0542616i
$315$			22328.3i			3.99383i
$316$			4298.87i			0.765286i
$317$	3884.11			0.688181			0.344091	−	0.938936i	$-0.388187\pi$
$317$	3884.11			0.688181			0.344091	+	0.938936i	$0.388187\pi$
$318$		−	1243.04i		−	0.219201i
$319$			5648.86i			0.991459i
$320$			922.042i			0.161074i
$321$	−6017.06			−1.04623
$322$	1125.44			0.194777
$323$	5034.22			0.867218
$324$	−9060.05			−1.55351
$325$		−	6381.57i		−	1.08919i
$326$	4321.29			0.734154
$327$		−	4661.24i		−	0.788279i
$328$			41.5435i			0.00699346i
$329$	4020.37			0.673708
$330$	−5968.86			−0.995681
$331$		−	8342.34i		−	1.38531i	−0.721271	−	0.692653i	$-0.756442\pi$
$331$		−	8342.34i		−	1.38531i	0.721271	−	0.692653i	$-0.243558\pi$
$332$	4483.37			0.741136
$333$	−15359.8	+	3357.45i	−2.52766	+	0.552514i
$334$	−5357.68			−0.877721
$335$			2052.91i			0.334813i
$336$	−3493.45			−0.567212
$337$	−6977.10			−1.12779			−0.563897	−	0.825845i	$-0.690699\pi$
$337$	−6977.10			−1.12779			−0.563897	+	0.825845i	$0.690699\pi$
$338$			7555.69i			1.21590i
$339$		−	3670.91i		−	0.588131i
$340$	4233.51			0.675277
$341$		−	1821.51i		−	0.289268i
$342$	9574.38			1.51381
$343$	4299.76			0.676867
$344$	1006.25			0.157713
$345$	−3596.38			−0.561224
$346$			7730.64i			1.20116i
$347$			2837.72i			0.439010i	0.975611	+	0.219505i	$0.0704443\pi$
$347$			2837.72i			0.439010i	−0.975611	+	0.219505i	$0.929556\pi$
$348$		−	10564.9i		−	1.62742i
$349$	4227.80			0.648449			0.324225	−	0.945980i	$-0.394897\pi$
$349$	4227.80			0.648449			0.324225	+	0.945980i	$0.394897\pi$
$350$		−	3663.20i		−	0.559446i
$351$			32603.7i			4.95800i
$352$		−	673.553i		−	0.101990i
$353$		−	10892.5i		−	1.64235i	−0.570674	−	0.821177i	$-0.693318\pi$
$353$		−	10892.5i		−	1.64235i	0.570674	−	0.821177i	$-0.306682\pi$
$354$	−4092.62			−0.614465
$355$			7221.91i			1.07972i
$356$		−	619.290i		−	0.0921975i
$357$			16040.0i			2.37795i
$358$	6887.56			1.01681
$359$	−3963.21			−0.582647			−0.291323	−	0.956625i	$-0.594096\pi$
$359$	−3963.21			−0.582647			−0.291323	+	0.956625i	$0.594096\pi$
$360$	8051.54			1.17876
$361$	2163.04			0.315358
$362$		−	7149.60i		−	1.03805i
$363$	−8738.99			−1.26358
$364$			6859.45i			0.987728i
$365$		−	2882.96i		−	0.413428i
$366$	5894.50			0.841832
$367$	3964.31			0.563857			0.281929	−	0.959435i	$-0.409026\pi$
$367$	3964.31			0.563857			0.281929	+	0.959435i	$0.409026\pi$
$368$		−	405.832i		−	0.0574876i
$369$	362.770			0.0511790
$370$	6335.32	−	1384.82i	0.890155	−	0.194576i
$371$	−1401.04			−0.196061
$372$			3406.73i			0.474814i
$373$	−8481.59			−1.17737			−0.588686	−	0.808362i	$-0.700355\pi$
$373$	−8481.59			−1.17737			−0.588686	+	0.808362i	$0.700355\pi$
$374$	−3092.59			−0.427577
$375$		−	6017.62i		−	0.828663i
$376$		−	1449.74i		−	0.198842i
$377$	−20744.5			−2.83394
$378$			18715.4i			2.54661i
$379$	−4497.99			−0.609620			−0.304810	−	0.952413i	$-0.598593\pi$
$379$	−4497.99			−0.609620			−0.304810	+	0.952413i	$0.598593\pi$
$380$	−3949.05			−0.533111
$381$	24317.1			3.26982
$382$	−4228.77			−0.566395
$383$		−	11367.2i		−	1.51654i	−0.651940	−	0.758270i	$-0.726045\pi$
$383$		−	11367.2i		−	1.51654i	0.651940	−	0.758270i	$-0.273955\pi$
$384$			1259.73i			0.167410i
$385$			6727.58i			0.890569i
$386$	5979.47			0.788464
$387$		−	8786.87i		−	1.15417i
$388$			3316.07i			0.433886i
$389$			961.576i			0.125331i	0.998035	+	0.0626656i	$0.0199602\pi$
$389$			961.576i			0.125331i	−0.998035	+	0.0626656i	$0.980040\pi$
$390$		−	21919.6i		−	2.84601i
$391$	−1863.36			−0.241007
$392$			1193.51i			0.153779i
$393$			5369.50i			0.689200i
$394$		−	744.846i		−	0.0952407i
$395$	−15483.4			−1.97229
$396$	−5881.66			−0.746376
$397$	7023.92			0.887961			0.443981	−	0.896036i	$-0.353566\pi$
$397$	7023.92			0.887961			0.443981	+	0.896036i	$0.353566\pi$
$398$	5071.22			0.638686
$399$		−	14962.2i		−	1.87732i
$400$	−1320.94			−0.165118
$401$			737.767i			0.0918761i	0.998944	+	0.0459380i	$0.0146277\pi$
$401$			737.767i			0.0918761i	−0.998944	+	0.0459380i	$0.985372\pi$
$402$			2804.77i			0.347983i
$403$	6689.18			0.826828
$404$	−6829.87			−0.841086
$405$		−	32631.8i		−	4.00368i
$406$	−11907.9			−1.45561
$407$	−4627.96	+	1011.61i	−0.563635	+	0.123203i
$408$	5784.00			0.701840
$409$		−	14335.2i		−	1.73308i	−0.499108	−	0.866540i	$-0.666339\pi$
$409$		−	14335.2i		−	1.73308i	0.499108	−	0.866540i	$-0.333661\pi$
$410$	−149.628			−0.0180235
$411$	13699.3			1.64413
$412$			2363.29i			0.282599i
$413$			4612.85i			0.549597i
$414$	−3543.84			−0.420701
$415$			16147.9i			1.91004i
$416$	2473.51			0.291523
$417$	−14060.0			−1.65113
$418$	2884.79			0.337559
$419$	2654.25			0.309472			0.154736	−	0.987956i	$-0.450547\pi$
$419$	2654.25			0.309472			0.154736	+	0.987956i	$0.450547\pi$
$420$		−	12582.5i		−	1.46181i
$421$			10432.8i			1.20776i	0.797076	+	0.603879i	$0.206379\pi$
$421$			10432.8i			1.20776i	−0.797076	+	0.603879i	$0.793621\pi$
$422$			3581.02i			0.413084i
$423$	−12659.5			−1.45515
$424$			505.214i			0.0578664i
$425$			6065.05i			0.692231i
$426$			9866.88i			1.12219i
$427$		−	6643.77i		−	0.752961i
$428$	2445.55			0.276192
$429$			16012.3i			1.80205i
$430$			3624.24i			0.406457i
$431$		−	4327.43i		−	0.483631i	−0.970322	−	0.241816i	$-0.922257\pi$
$431$		−	4327.43i		−	0.483631i	0.970322	−	0.241816i	$-0.0777429\pi$
$432$	6748.76			0.751620
$433$	−12628.7			−1.40161			−0.700806	−	0.713352i	$-0.747176\pi$
$433$	−12628.7			−1.40161			−0.700806	+	0.713352i	$0.747176\pi$
$434$	3839.77			0.424689
$435$	38052.1			4.19415
$436$			1894.49i			0.208096i
$437$	1738.15			0.190268
$438$		−	3938.83i		−	0.429690i
$439$			10832.8i			1.17773i	0.808233	+	0.588863i	$0.200424\pi$
$439$			10832.8i			1.17773i	−0.808233	+	0.588863i	$0.799576\pi$
$440$	2425.96			0.262847
$441$	10422.1			1.12538
$442$		−	11357.0i		−	1.22216i
$443$	2693.56			0.288883			0.144441	−	0.989513i	$-0.453862\pi$
$443$	2693.56			0.288883			0.144441	+	0.989513i	$0.453862\pi$
$444$	8655.58	−	1892.00i	0.925170	−	0.202230i
$445$	2230.51			0.237610
$446$			7995.53i			0.848877i
$447$	14287.9			1.51185
$448$	1419.86			0.149737
$449$			14667.5i			1.54166i	0.637043	+	0.770828i	$0.280157\pi$
$449$			14667.5i			1.54166i	−0.637043	+	0.770828i	$0.719843\pi$
$450$			11534.9i			1.20835i
$451$	109.304			0.0114122
$452$			1491.99i			0.155259i
$453$	−6776.03			−0.702794
$454$	5194.11			0.536942
$455$	−24705.9			−2.54556
$456$	−5395.36			−0.554081
$457$		−	15692.6i		−	1.60628i	−0.595792	−	0.803139i	$-0.703162\pi$
$457$		−	15692.6i		−	1.60628i	0.595792	−	0.803139i	$-0.296838\pi$
$458$		−	2613.09i		−	0.266598i
$459$		−	30986.6i		−	3.15105i
$460$	1461.69			0.148156
$461$			3361.86i			0.339648i	0.985474	+	0.169824i	$0.0543199\pi$
$461$			3361.86i			0.339648i	−0.985474	+	0.169824i	$0.945680\pi$
$462$			9191.50i			0.925600i
$463$		−	7999.37i		−	0.802942i	−0.915872	−	0.401471i	$-0.868499\pi$
$463$		−	7999.37i		−	0.802942i	0.915872	−	0.401471i	$-0.131501\pi$
$464$			4293.97i			0.429617i
$465$	−12270.1			−1.22368
$466$		−	12292.9i		−	1.22202i
$467$			14838.8i			1.47036i	0.677871	+	0.735181i	$0.262903\pi$
$467$			14838.8i			1.47036i	−0.677871	+	0.735181i	$0.737097\pi$
$468$		−	21599.4i		−	2.13340i
$469$	3161.29			0.311247
$470$	5221.56			0.512453
$471$	−1485.68			−0.145343
$472$	1663.39			0.162211
$473$		−	2647.51i		−	0.257363i
$474$	−21154.0			−2.04987
$475$		−	5657.53i		−	0.546495i
$476$		−	6519.22i		−	0.627748i
$477$	4411.67			0.423473
$478$	−7169.11			−0.685999
$479$			497.525i			0.0474583i	0.999718	+	0.0237291i	$0.00755393\pi$
$479$			497.525i			0.0474583i	−0.999718	+	0.0237291i	$0.992446\pi$
$480$	−4537.21			−0.431447
$481$	−3714.97	−	16995.4i	−0.352158	−	1.61107i
$482$	12808.6			1.21041
$483$			5538.09i			0.521723i
$484$	3551.84			0.333568
$485$	−11943.6			−1.11821
$486$		−	21805.9i		−	2.03526i
$487$			11080.2i			1.03099i	0.856894	+	0.515493i	$0.172391\pi$
$487$			11080.2i			1.03099i	−0.856894	+	0.515493i	$0.827609\pi$
$488$	−2395.73			−0.222233
$489$			21264.4i			1.96648i
$490$	−4298.71			−0.396318
$491$	10616.2			0.975767			0.487883	−	0.872909i	$-0.337769\pi$
$491$	10616.2			0.975767			0.487883	+	0.872909i	$0.337769\pi$
$492$	−204.429			−0.0187324
$493$	19715.5			1.80110
$494$			10593.9i			0.964862i
$495$		−	21184.2i		−	1.92355i
$496$		−	1384.62i		−	0.125345i
$497$	11121.1			1.00372
$498$			22061.9i			1.98518i
$499$			11183.2i			1.00327i	0.865080	+	0.501633i	$0.167267\pi$
$499$			11183.2i			1.00327i	−0.865080	+	0.501633i	$0.832733\pi$
$500$			2445.77i			0.218757i
$501$		−	26364.2i		−	2.35103i
$502$	10747.7			0.955568
$503$			302.455i			0.0268107i	0.999910	+	0.0134053i	$0.00426718\pi$
$503$			302.455i			0.0268107i	−0.999910	+	0.0134053i	$0.995733\pi$
$504$		−	12398.6i		−	1.09579i
$505$		−	24599.3i		−	2.16764i
$506$	−1067.77			−0.0938106
$507$	−37180.3			−3.25687
$508$	−9883.33			−0.863193
$509$	−3716.93			−0.323674			−0.161837	−	0.986818i	$-0.551742\pi$
$509$	−3716.93			−0.323674			−0.161837	+	0.986818i	$0.551742\pi$
$510$			20832.4i			1.80877i
$511$	−4439.50			−0.384329
$512$		−	512.000i		−	0.0441942i
$513$			28904.5i			2.48765i
$514$	1201.07			0.103068
$515$	−8511.92			−0.728311
$516$			4951.59i			0.422445i
$517$	−3814.36			−0.324479
$518$	−2132.49	−	9755.81i	−0.180881	−	0.827502i
$519$	−38041.2			−3.21738
$520$			8908.90i			0.751310i
$521$	19893.8			1.67287			0.836434	−	0.548068i	$-0.184636\pi$
$521$	19893.8			1.67287			0.836434	+	0.548068i	$0.184636\pi$
$522$	37496.2			3.14399
$523$		−	3531.75i		−	0.295282i	−0.989041	−	0.147641i	$-0.952832\pi$
$523$		−	3531.75i		−	0.295282i	0.989041	−	0.147641i	$-0.0471681\pi$
$524$		−	2182.36i		−	0.181940i
$525$	18026.0			1.49851
$526$		−	9600.38i		−	0.795811i
$527$	−6357.40			−0.525489
$528$	3314.44			0.273187
$529$	11523.6			0.947123
$530$	−1819.64			−0.149132
$531$		−	14525.2i		−	1.18708i
$532$			6081.18i			0.495588i
$533$			401.399i			0.0326201i
$534$	3047.42			0.246957
$535$			8808.19i			0.711797i
$536$		−	1139.96i		−	0.0918632i
$537$			33892.5i			2.72360i
$538$		−	8488.76i		−	0.680254i
$539$	3140.21			0.250943
$540$			24307.2i			1.93706i
$541$			5187.42i			0.412245i	0.978526	+	0.206123i	$0.0660846\pi$
$541$			5187.42i			0.412245i	−0.978526	+	0.206123i	$0.933915\pi$
$542$			9203.96i			0.729417i
$543$	35182.0			2.78048
$544$	−2350.82			−0.185277
$545$	−6823.45			−0.536302
$546$	−33754.2			−2.64569
$547$		−	3326.02i		−	0.259983i	−0.991515	−	0.129991i	$-0.958505\pi$
$547$		−	3326.02i		−	0.259983i	0.991515	−	0.129991i	$-0.0414949\pi$
$548$	−5567.88			−0.434029
$549$			20920.2i			1.62633i
$550$			3475.49i			0.269446i
$551$	−18390.8			−1.42192
$552$	1997.03			0.153984
$553$			23843.0i			1.83347i
$554$	1926.36			0.147731
$555$	6814.45	+	31175.0i	0.521185	+	2.38434i
$556$	5714.50			0.435879
$557$			1609.39i			0.122427i	0.998125	+	0.0612136i	$0.0194971\pi$
$557$			1609.39i			0.122427i	−0.998125	+	0.0612136i	$0.980503\pi$
$558$	−12090.9			−0.917289
$559$	9722.53			0.735634
$560$			5113.95i			0.385900i
$561$		−	15218.1i		−	1.14529i
$562$	−3324.27			−0.249512
$563$			1475.11i			0.110424i	0.998475	+	0.0552119i	$0.0175834\pi$
$563$			1475.11i			0.110424i	−0.998475	+	0.0552119i	$0.982417\pi$
$564$	7133.92			0.532610
$565$	−5373.73			−0.400132
$566$	−17330.2			−1.28700
$567$	−50250.1			−3.72188
$568$		−	4010.25i		−	0.296244i
$569$		−	2760.89i		−	0.203414i	−0.994814	−	0.101707i	$-0.967570\pi$
$569$		−	2760.89i		−	0.203414i	0.994814	−	0.101707i	$-0.0324304\pi$
$570$		−	19432.6i		−	1.42797i
$571$	−3576.89			−0.262151			−0.131075	−	0.991372i	$-0.541843\pi$
$571$	−3576.89			−0.262151			−0.131075	+	0.991372i	$0.541843\pi$
$572$		−	6507.97i		−	0.475720i
$573$		−	20809.1i		−	1.51712i
$574$			230.414i			0.0167549i
$575$			2094.07i			0.151876i
$576$	−4470.93			−0.323418
$577$		−	16503.5i		−	1.19073i	−0.803457	−	0.595363i	$-0.797008\pi$
$577$		−	16503.5i		−	1.19073i	0.803457	−	0.595363i	$-0.202992\pi$
$578$			967.682i			0.0696371i
$579$			29424.0i			2.11195i
$580$	−15465.7			−1.10720
$581$	24866.3			1.77561
$582$	−16317.8			−1.16219
$583$	1329.25			0.0944287
$584$			1600.88i			0.113433i
$585$	77795.1			5.49818
$586$			2833.98i			0.199779i
$587$		−	6174.61i		−	0.434163i	−0.976154	−	0.217081i	$-0.930346\pi$
$587$		−	6174.61i		−	0.434163i	0.976154	−	0.217081i	$-0.0696537\pi$
$588$	−5873.07			−0.411907
$589$	5930.23			0.414857
$590$			5991.07i			0.418048i
$591$	3665.26			0.255108
$592$	−3517.93	+	768.974i	−0.244233	+	0.0533862i
$593$	24639.5			1.70628			0.853139	−	0.521683i	$-0.174696\pi$
$593$	24639.5			1.70628			0.853139	+	0.521683i	$0.174696\pi$
$594$		−	17756.4i		−	1.22652i
$595$	23480.5			1.61782
$596$	−5807.12			−0.399109
$597$			24954.6i			1.71076i
$598$		−	3921.20i		−	0.268144i
$599$	−518.259			−0.0353514			−0.0176757	−	0.999844i	$-0.505627\pi$
$599$	−518.259			−0.0353514			−0.0176757	+	0.999844i	$0.505627\pi$
$600$		−	6500.15i		−	0.442279i
$601$	11558.4			0.784491			0.392245	−	0.919861i	$-0.371698\pi$
$601$	11558.4			0.784491			0.392245	+	0.919861i	$0.371698\pi$
$602$	5581.00			0.377848
$603$	−9954.45			−0.672266
$604$	2754.02			0.185529
$605$			12792.7i			0.859668i
$606$		−	33608.6i		−	2.25290i
$607$		−	12793.4i		−	0.855467i	−0.903905	−	0.427734i	$-0.859312\pi$
$607$		−	12793.4i		−	0.855467i	0.903905	−	0.427734i	$-0.140688\pi$
$608$	2192.87			0.146271
$609$		−	58596.7i		−	3.89895i
$610$		−	8628.77i		−	0.572736i
$611$		−	14007.6i		−	0.927473i
$612$			20528.1i			1.35588i
$613$	−13773.5			−0.907514			−0.453757	−	0.891125i	$-0.649917\pi$
$613$	−13773.5			−0.907514			−0.453757	+	0.891125i	$0.649917\pi$
$614$			3028.05i			0.199026i
$615$		−	736.296i		−	0.0482769i
$616$		−	3735.75i		−	0.244347i
$617$	−1836.66			−0.119840			−0.0599200	−	0.998203i	$-0.519085\pi$
$617$	−1836.66			−0.119840			−0.0599200	+	0.998203i	$0.519085\pi$
$618$	−11629.3			−0.756960
$619$	3482.55			0.226131			0.113066	−	0.993588i	$-0.463933\pi$
$619$	3482.55			0.226131			0.113066	+	0.993588i	$0.463933\pi$
$620$	4987.01			0.323037
$621$		−	10698.7i		−	0.691341i
$622$	−11815.6			−0.761673
$623$		−	3434.79i		−	0.220886i
$624$			12171.7i			0.780863i
$625$	−19128.9			−1.22425
$626$	14293.9			0.912618
$627$			14195.6i			0.904173i
$628$	603.833			0.0383688
$629$	3530.71	+	16152.4i	0.223813	+	1.02391i
$630$	44656.5			2.82406
$631$			4264.73i			0.269059i	0.990910	+	0.134530i	$0.0429523\pi$
$631$			4264.73i			0.269059i	−0.990910	+	0.134530i	$0.957048\pi$
$632$	8597.75			0.541139
$633$	−17621.6			−1.10647
$634$		−	7768.22i		−	0.486618i
$635$		−	35597.1i		−	2.22461i
$636$	−2486.07			−0.154999
$637$			11531.9i			0.717284i
$638$	11297.7			0.701067
$639$	−35018.7			−2.16795
$640$	1844.08			0.113897
$641$	−8120.69			−0.500387			−0.250193	−	0.968196i	$-0.580494\pi$
$641$	−8120.69			−0.500387			−0.250193	+	0.968196i	$0.580494\pi$
$642$			12034.1i			0.739796i
$643$		−	20091.8i		−	1.23226i	−0.787643	−	0.616131i	$-0.788699\pi$
$643$		−	20091.8i		−	1.23226i	0.787643	−	0.616131i	$-0.211301\pi$
$644$		−	2250.88i		−	0.137728i
$645$	−17834.3			−1.08872
$646$		−	10068.4i		−	0.613216i
$647$		−	18981.4i		−	1.15338i	−0.816963	−	0.576690i	$-0.804344\pi$
$647$		−	18981.4i		−	1.15338i	0.816963	−	0.576690i	$-0.195656\pi$
$648$			18120.1i			1.09850i
$649$		−	4376.48i		−	0.264703i
$650$	−12763.1			−0.770172
$651$			18894.9i			1.13756i
$652$		−	8642.58i		−	0.519125i
$653$		−	18483.7i		−	1.10769i	−0.832620	−	0.553845i	$-0.813160\pi$
$653$		−	18483.7i		−	1.10769i	0.832620	−	0.553845i	$-0.186840\pi$
$654$	−9322.49			−0.557398
$655$	7860.25			0.468894
$656$	83.0870			0.00494512
$657$	13979.3			0.830115
$658$		−	8040.73i		−	0.476384i
$659$	−8332.40			−0.492540			−0.246270	−	0.969201i	$-0.579205\pi$
$659$	−8332.40			−0.492540			−0.246270	+	0.969201i	$0.579205\pi$
$660$			11937.7i			0.704053i
$661$		−	19179.2i		−	1.12857i	−0.825581	−	0.564283i	$-0.809153\pi$
$661$		−	19179.2i		−	1.12857i	0.825581	−	0.564283i	$-0.190847\pi$
$662$	−16684.7			−0.979560
$663$	55885.8			3.27364
$664$		−	8966.74i		−	0.524062i
$665$	−21902.8			−1.27722
$666$	6714.91	+	30719.6i	0.390687	+	1.78733i
$667$	6807.14			0.395163
$668$			10715.4i			0.620643i
$669$	−39344.7			−2.27377
$670$	4105.82			0.236749
$671$			6303.33i			0.362649i
$672$			6986.90i			0.401080i
$673$	−21596.9			−1.23700			−0.618498	−	0.785786i	$-0.712259\pi$
$673$	−21596.9			−1.23700			−0.618498	+	0.785786i	$0.712259\pi$
$674$			13954.2i			0.797471i
$675$	−34823.2			−1.98570
$676$	15111.4			0.859773
$677$	−15545.8			−0.882529			−0.441264	−	0.897377i	$-0.645470\pi$
$677$	−15545.8			−0.882529			−0.441264	+	0.897377i	$0.645470\pi$
$678$	−7341.82			−0.415872
$679$			18392.0i			1.03950i
$680$		−	8467.02i		−	0.477493i
$681$			25559.3i			1.43823i
$682$	−3643.02			−0.204543
$683$			13726.4i			0.768998i	0.923126	+	0.384499i	$0.125626\pi$
$683$			13726.4i			0.768998i	−0.923126	+	0.384499i	$0.874374\pi$
$684$		−	19148.8i		−	1.07043i
$685$		−	20054.0i		−	1.11857i
$686$		−	8599.52i		−	0.478617i
$687$	12858.6			0.714099
$688$		−	2012.50i		−	0.111520i
$689$			4881.44i			0.269910i
$690$			7192.75i			0.396846i
$691$	25886.8			1.42515			0.712575	−	0.701596i	$-0.247529\pi$
$691$	25886.8			1.42515			0.712575	+	0.701596i	$0.247529\pi$
$692$	15461.3			0.849349
$693$	−32621.7			−1.78816
$694$	5675.43			0.310427
$695$			20582.1i			1.12334i
$696$	−21129.9			−1.15076
$697$		−	381.490i		−	0.0207316i
$698$		−	8455.60i		−	0.458523i
$699$	60491.5			3.27324
$700$	−7326.40			−0.395588
$701$			34952.1i			1.88320i	0.336734	+	0.941600i	$0.390678\pi$
$701$			34952.1i			1.88320i	−0.336734	+	0.941600i	$0.609322\pi$
$702$	65207.4			3.50584
$703$	−3293.47	−	15067.1i	−0.176694	−	0.808345i
$704$	−1347.11			−0.0721179
$705$			25694.4i			1.37264i
$706$	−21785.1			−1.16132
$707$	−37880.7			−2.01507
$708$			8185.25i			0.434492i
$709$			3226.87i			0.170928i	0.996341	+	0.0854638i	$0.0272372\pi$
$709$			3226.87i			0.170928i	−0.996341	+	0.0854638i	$0.972763\pi$
$710$	14443.8			0.763475
$711$		−	75078.0i		−	3.96012i
$712$	−1238.58			−0.0651934
$713$	−2195.00			−0.115292
$714$	32080.0			1.68146
$715$	23439.9			1.22602
$716$		−	13775.1i		−	0.718995i
$717$		−	35278.0i		−	1.83749i
$718$			7926.42i			0.411993i
$719$	−3017.38			−0.156508			−0.0782540	−	0.996933i	$-0.524935\pi$
$719$	−3017.38			−0.156508			−0.0782540	+	0.996933i	$0.524935\pi$
$720$		−	16103.1i		−	0.833509i
$721$			13107.6i			0.677049i
$722$		−	4326.08i		−	0.222992i
$723$			63029.0i			3.24215i
$724$	−14299.2			−0.734013
$725$		−	22156.6i		−	1.13500i
$726$			17478.0i			0.893483i
$727$		−	32779.7i		−	1.67226i	−0.548533	−	0.836129i	$-0.684814\pi$
$727$		−	32779.7i		−	1.67226i	0.548533	−	0.836129i	$-0.315186\pi$
$728$	13718.9			0.698429
$729$	46148.0			2.34456
$730$	−5765.93			−0.292338
$731$	−9240.30			−0.467530
$732$		−	11789.0i		−	0.595265i
$733$	4189.77			0.211122			0.105561	−	0.994413i	$-0.466336\pi$
$733$	4189.77			0.211122			0.105561	+	0.994413i	$0.466336\pi$
$734$		−	7928.63i		−	0.398707i
$735$		−	21153.2i		−	1.06156i
$736$	−811.663			−0.0406499
$737$	−2999.31			−0.149906
$738$		−	725.540i		−	0.0361890i
$739$	−18584.7			−0.925103			−0.462551	−	0.886592i	$-0.653066\pi$
$739$	−18584.7			−0.925103			−0.462551	+	0.886592i	$0.653066\pi$
$740$	−2769.63	−	12670.6i	−0.137586	−	0.629435i
$741$	−52130.8			−2.58444
$742$			2802.08i			0.138636i
$743$	29757.5			1.46931			0.734654	−	0.678442i	$-0.237345\pi$
$743$	29757.5			1.46931			0.734654	+	0.678442i	$0.237345\pi$
$744$	6813.46			0.335744
$745$		−	20915.6i		−	1.02858i
$746$			16963.2i			0.832528i
$747$	−78300.2			−3.83515
$748$			6185.17i			0.302343i
$749$	13563.8			0.661697
$750$	−12035.2			−0.585953
$751$	32071.4			1.55833			0.779163	−	0.626821i	$-0.215644\pi$
$751$	32071.4			1.55833			0.779163	+	0.626821i	$0.215644\pi$
$752$	−2899.48			−0.140602
$753$			52887.8i			2.55955i
$754$			41488.9i			2.00390i
$755$			9919.22i			0.478142i
$756$	37430.9			1.80072
$757$		−	7855.68i		−	0.377173i	−0.982057	−	0.188586i	$-0.939609\pi$
$757$		−	7855.68i		−	0.377173i	0.982057	−	0.188586i	$-0.0603905\pi$
$758$			8995.97i			0.431067i
$759$		−	5254.32i		−	0.251278i
$760$			7898.11i			0.376966i
$761$	28177.5			1.34222			0.671112	−	0.741356i	$-0.265817\pi$
$761$	28177.5			1.34222			0.671112	+	0.741356i	$0.265817\pi$
$762$		−	48634.2i		−	2.31212i
$763$			10507.5i			0.498554i
$764$			8457.55i			0.400502i
$765$	−73936.5			−3.49435
$766$	−22734.3			−1.07236
$767$	16071.9			0.756612
$768$	2519.47			0.118377
$769$			16097.1i			0.754847i	0.926041	+	0.377423i	$0.123190\pi$
$769$			16097.1i			0.754847i	−0.926041	+	0.377423i	$0.876810\pi$
$770$	13455.2			0.629728
$771$			5910.27i			0.276074i
$772$		−	11958.9i		−	0.557528i
$773$	−4818.75			−0.224215			−0.112108	−	0.993696i	$-0.535760\pi$
$773$	−4818.75			−0.224215			−0.112108	+	0.993696i	$0.535760\pi$
$774$	−17573.7			−0.816118
$775$			7144.54i			0.331147i
$776$	6632.14			0.306804
$777$	48006.7	−	10493.6i	2.21651	−	0.484501i
$778$	1923.15			0.0886226
$779$			355.857i			0.0163670i
$780$	−43839.2			−2.01243
$781$	−10551.2			−0.483422
$782$			3726.71i			0.170418i
$783$			113199.i			5.16654i
$784$	2387.02			0.108738
$785$			2174.84i			0.0988834i
$786$	10739.0			0.487338
$787$	18562.0			0.840740			0.420370	−	0.907353i	$-0.361900\pi$
$787$	18562.0			0.840740			0.420370	+	0.907353i	$0.361900\pi$
$788$	−1489.69			−0.0673453
$789$	47241.9			2.13163
$790$			30966.7i			1.39462i
$791$			8275.06i			0.371969i
$792$			11763.3i			0.527767i
$793$	−23147.9			−1.03658
$794$		−	14047.8i		−	0.627883i
$795$		−	8954.15i		−	0.399460i
$796$		−	10142.4i		−	0.451619i
$797$		−	28589.3i		−	1.27062i	−0.772256	−	0.635311i	$-0.780872\pi$
$797$		−	28589.3i		−	1.27062i	0.772256	−	0.635311i	$-0.219128\pi$
$798$	−29924.5			−1.32746
$799$			13312.8i			0.589453i
$800$			2641.89i			0.116756i
$801$			10815.6i			0.477093i
$802$	1475.53			0.0649662
$803$	4212.02			0.185104
$804$	5609.54			0.246061
$805$	8107.05			0.354951
$806$		−	13378.4i		−	0.584656i
$807$	41771.8			1.82210
$808$			13659.7i			0.594738i
$809$			14616.0i			0.635194i	0.948226	+	0.317597i	$0.102876\pi$
$809$			14616.0i			0.635194i	−0.948226	+	0.317597i	$0.897124\pi$
$810$	−65263.7			−2.83103
$811$	−19534.6			−0.845810			−0.422905	−	0.906174i	$-0.638990\pi$
$811$	−19534.6			−0.845810			−0.422905	+	0.906174i	$0.638990\pi$
$812$			23815.8i			1.02927i
$813$	−45291.1			−1.95379
$814$	2023.22	+	9255.92i	0.0871178	+	0.398550i
$815$	31128.2			1.33788
$816$		−	11568.0i		−	0.496276i
$817$	8619.43			0.369101
$818$	−28670.4			−1.22547
$819$		−	119797.i		−	5.11119i
$820$			299.257i			0.0127445i
$821$	1516.60			0.0644699			0.0322350	−	0.999480i	$-0.489738\pi$
$821$	1516.60			0.0644699			0.0322350	+	0.999480i	$0.489738\pi$
$822$		−	27398.6i		−	1.16257i
$823$	9819.74			0.415911			0.207955	−	0.978138i	$-0.433319\pi$
$823$	9819.74			0.415911			0.207955	+	0.978138i	$0.433319\pi$
$824$	4726.58			0.199828
$825$	−17102.3			−0.721729
$826$	9225.70			0.388624
$827$			25737.2i			1.08219i	0.840962	+	0.541095i	$0.181990\pi$
$827$			25737.2i			1.08219i	−0.840962	+	0.541095i	$0.818010\pi$
$828$			7087.68i			0.297481i
$829$			23449.7i			0.982439i	0.871036	+	0.491219i	$0.163449\pi$
$829$			23449.7i			0.982439i	−0.871036	+	0.491219i	$0.836551\pi$
$830$	32295.8			1.35061
$831$			9479.28i			0.395707i
$832$		−	4947.02i		−	0.206138i
$833$		−	10959.9i		−	0.455868i
$834$			28120.1i			1.16753i
$835$	−38593.8			−1.59951
$836$		−	5769.58i		−	0.238690i
$837$		−	36501.7i		−	1.50739i
$838$		−	5308.50i		−	0.218829i
$839$	3444.39			0.141733			0.0708663	−	0.997486i	$-0.477424\pi$
$839$	3444.39			0.141733			0.0708663	+	0.997486i	$0.477424\pi$
$840$	−25164.9			−1.03366
$841$	−47635.1			−1.95314
$842$	20865.7			0.854013
$843$		−	16358.2i		−	0.668334i
$844$	7162.04			0.292094
$845$			54427.0i			2.21580i
$846$			25319.1i			1.02895i
$847$	19699.7			0.799160
$848$	1010.43			0.0409177
$849$		−	85278.9i		−	3.44731i
$850$	12130.1			0.489481
$851$	1219.04	+	5576.91i	0.0491047	+	0.224646i
$852$	19733.8			0.793507
$853$			31154.2i			1.25053i	0.780414	+	0.625263i	$0.215008\pi$
$853$			31154.2i			1.25053i	−0.780414	+	0.625263i	$0.784992\pi$
$854$	−13287.5			−0.532424
$855$	68968.6			2.75869
$856$		−	4891.09i		−	0.195297i
$857$		−	26707.6i		−	1.06454i	−0.846574	−	0.532271i	$-0.821339\pi$
$857$		−	26707.6i		−	1.06454i	0.846574	−	0.532271i	$-0.178661\pi$
$858$	32024.6			1.27424
$859$			23459.5i			0.931815i	0.884834	+	0.465907i	$0.154272\pi$
$859$			23459.5i			0.931815i	−0.884834	+	0.465907i	$0.845728\pi$
$860$	7248.48			0.287408
$861$	−1133.83			−0.0448790
$862$	−8654.87			−0.341979
$863$	−37956.6			−1.49717			−0.748586	−	0.663038i	$-0.769267\pi$
$863$	−37956.6			−1.49717			−0.748586	+	0.663038i	$0.769267\pi$
$864$		−	13497.5i		−	0.531476i
$865$			55687.3i			2.18893i
$866$			25257.4i			0.991089i
$867$	−4761.80			−0.186527
$868$		−	7679.54i		−	0.300300i
$869$		−	22621.3i		−	0.883053i
$870$		−	76104.1i		−	2.96571i
$871$		−	11014.4i		−	0.428484i
$872$	3788.99			0.147146
$873$		−	57913.8i		−	2.24523i
$874$		−	3476.31i		−	0.134540i
$875$			13565.1i			0.524095i
$876$	−7877.65			−0.303837
$877$	−20729.7			−0.798167			−0.399084	−	0.916915i	$-0.630672\pi$
$877$	−20729.7			−0.798167			−0.399084	+	0.916915i	$0.630672\pi$
$878$	21665.6			0.832778
$879$	−13945.5			−0.535121
$880$		−	4851.91i		−	0.185861i
$881$	14112.8			0.539697			0.269848	−	0.962903i	$-0.413026\pi$
$881$	14112.8			0.539697			0.269848	+	0.962903i	$0.413026\pi$
$882$		−	20844.2i		−	0.795760i
$883$		−	24704.1i		−	0.941515i	−0.882263	−	0.470757i	$-0.843981\pi$
$883$		−	24704.1i		−	0.941515i	0.882263	−	0.470757i	$-0.156019\pi$
$884$	−22714.0			−0.864201
$885$	−29481.0			−1.11977
$886$		−	5387.13i		−	0.204271i
$887$	−48858.2			−1.84949			−0.924745	−	0.380587i	$-0.875722\pi$
$887$	−48858.2			−1.84949			−0.924745	+	0.380587i	$0.875722\pi$
$888$	−3783.99	−	17311.2i	−0.142998	−	0.654194i
$889$	−54816.3			−2.06803
$890$		−	4461.03i		−	0.168016i
$891$	47675.2			1.79257
$892$	15991.1			0.600247
$893$		−	12418.3i		−	0.465355i
$894$		−	28575.8i		−	1.06904i
$895$	49614.2			1.85298
$896$		−	2839.72i		−	0.105880i
$897$	19295.6			0.718239
$898$	29335.1			1.09012
$899$	23224.6			0.861606
$900$	23069.7			0.854435
$901$		−	4639.33i		−	0.171541i
$902$		−	218.607i		−	0.00806966i
$903$			27463.2i			1.01209i
$904$	2983.98			0.109785
$905$		−	51501.8i		−	1.89169i
$906$			13552.1i			0.496951i
$907$		−	37195.3i		−	1.36169i	−0.732430	−	0.680843i	$-0.761614\pi$
$907$		−	37195.3i		−	1.36169i	0.732430	−	0.680843i	$-0.238386\pi$
$908$		−	10388.2i		−	0.379675i
$909$	119281.			4.35236
$910$			49411.7i			1.79998i
$911$			14592.8i			0.530714i	0.964150	+	0.265357i	$0.0854898\pi$
$911$			14592.8i			0.530714i	−0.964150	+	0.265357i	$0.914510\pi$
$912$			10790.7i			0.391795i
$913$	−23592.1			−0.855186
$914$	−31385.2			−1.13581
$915$	42460.7			1.53411
$916$	−5226.19			−0.188513
$917$		−	12104.1i		−	0.435891i
$918$	−61973.2			−2.22813
$919$			47274.0i			1.69687i	0.529298	+	0.848436i	$0.322456\pi$
$919$			47274.0i			1.69687i	−0.529298	+	0.848436i	$0.677544\pi$
$920$		−	2923.39i		−	0.104762i
$921$	−14900.5			−0.533105
$922$	6723.73			0.240167
$923$		−	38747.6i		−	1.38179i
$924$	18383.0			0.654498
$925$	18152.3	−	3967.86i	0.645237	−	0.141040i
$926$	−15998.7			−0.567766
$927$		−	41273.9i		−	1.46236i
$928$	8587.94			0.303785
$929$	−19431.4			−0.686248			−0.343124	−	0.939290i	$-0.611485\pi$
$929$	−19431.4			−0.686248			−0.343124	+	0.939290i	$0.611485\pi$
$930$			24540.2i			0.865275i
$931$			10223.5i			0.359894i
$932$	−24585.9			−0.864095
$933$		−	58142.3i		−	2.04019i
$934$	29677.6			1.03970
$935$	−22277.3			−0.779193
$936$	−43198.8			−1.50854
$937$	21182.4			0.738527			0.369263	−	0.929325i	$-0.379610\pi$
$937$	21182.4			0.738527			0.369263	+	0.929325i	$0.379610\pi$
$938$		−	6322.59i		−	0.220085i
$939$			70337.8i			2.44450i
$940$		−	10443.1i		−	0.362359i
$941$	19258.4			0.667168			0.333584	−	0.942720i	$-0.391742\pi$
$941$	19258.4			0.667168			0.333584	+	0.942720i	$0.391742\pi$
$942$			2971.36i			0.102773i
$943$		−	131.716i		−	0.00454853i
$944$		−	3326.77i		−	0.114700i
$945$			134816.i			4.64080i
$946$	−5295.03			−0.181983
$947$			9721.23i			0.333577i	0.985993	+	0.166789i	$0.0533397\pi$
$947$			9721.23i			0.333577i	−0.985993	+	0.166789i	$0.946660\pi$
$948$			42308.1i			1.44947i
$949$			15467.9i			0.529093i
$950$	−11315.1			−0.386431
$951$	38226.1			1.30344
$952$	−13038.4			−0.443885
$953$	−52356.7			−1.77964			−0.889821	−	0.456309i	$-0.849171\pi$
$953$	−52356.7			−1.77964			−0.889821	+	0.456309i	$0.849171\pi$
$954$		−	8823.35i		−	0.299441i
$955$	−30461.8			−1.03217
$956$			14338.2i			0.485075i
$957$			55594.2i			1.87785i
$958$	995.051			0.0335581
$959$	−30881.3			−1.03984
$960$			9074.43i			0.305079i
$961$	22302.1			0.748618
$962$	−33990.8	+	7429.93i	−1.13920	+	0.249013i
$963$	−42710.5			−1.42921
$964$		−	25617.2i		−	0.855887i
$965$	43072.9			1.43685
$966$	11076.2			0.368914
$967$			37212.3i			1.23750i	0.785586	+	0.618752i	$0.212362\pi$
$967$			37212.3i			1.23750i	−0.785586	+	0.618752i	$0.787638\pi$
$968$		−	7103.67i		−	0.235868i
$969$	49545.1			1.64254
$970$			23887.2i			0.790691i
$971$	−18075.3			−0.597389			−0.298695	−	0.954349i	$-0.596551\pi$
$971$	−18075.3			−0.597389			−0.298695	+	0.954349i	$0.596551\pi$
$972$	−43611.9			−1.43915
$973$	31694.5			1.04427
$974$	22160.3			0.729017
$975$		−	62805.3i		−	2.06295i
$976$			4791.46i			0.157142i
$977$			28601.5i			0.936585i	0.883574	+	0.468292i	$0.155131\pi$
$977$			28601.5i			0.936585i	−0.883574	+	0.468292i	$0.844869\pi$
$978$	42528.7			1.39051
$979$			3258.79i			0.106385i
$980$			8597.41i			0.280239i
$981$		−	33086.6i		−	1.07683i
$982$		−	21232.4i		−	0.689971i
$983$	13727.7			0.445417			0.222708	−	0.974885i	$-0.428510\pi$
$983$	13727.7			0.445417			0.222708	+	0.974885i	$0.428510\pi$
$984$			408.857i			0.0132458i
$985$		−	5365.47i		−	0.173561i
$986$		−	39431.1i		−	1.27357i
$987$	39567.1			1.27602
$988$	21187.8			0.682260
$989$	−3190.38			−0.102576
$990$	−42368.3			−1.36015
$991$		−	6755.17i		−	0.216534i	−0.994122	−	0.108267i	$-0.965470\pi$
$991$		−	6755.17i		−	0.216534i	0.994122	−	0.108267i	$-0.0345301\pi$
$992$	−2769.23			−0.0886323
$993$		−	82102.5i		−	2.62381i
$994$		−	22242.2i		−	0.709738i
$995$	36530.3			1.16391
$996$	44123.8			1.40373
$997$			61499.1i			1.95356i	0.214252	+	0.976778i	$0.431269\pi$
$997$			61499.1i			1.95356i	−0.214252	+	0.976778i	$0.568731\pi$
$998$	22366.5			0.709416
$999$	−92740.9	+	20272.0i	−2.93713	+	0.642018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.b.a.73.5	✓	10
3.2	odd	2		666.4.c.d.73.10		10
4.3	odd	2		592.4.g.d.369.1		10
37.36	even	2	inner	74.4.b.a.73.10	yes	10
111.110	odd	2		666.4.c.d.73.1		10
148.147	odd	2		592.4.g.d.369.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.b.a.73.5	✓	10	1.1	even	1	trivial
74.4.b.a.73.10	yes	10	37.36	even	2	inner
592.4.g.d.369.1		10	4.3	odd	2
592.4.g.d.369.2		10	148.147	odd	2
666.4.c.d.73.1		10	111.110	odd	2
666.4.c.d.73.10		10	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +9.84166 q^{3} -4.00000 q^{4} -14.4069i q^{5} -19.6833i q^{6} -22.1853 q^{7} +8.00000i q^{8} +69.8583 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +9.84166 q^{3} -4.00000 q^{4} -14.4069i q^{5} -19.6833i q^{6} -22.1853 q^{7} +8.00000i q^{8} +69.8583 q^{9} -28.8138 q^{10} +21.0485 q^{11} -39.3667 q^{12} +77.2971i q^{13} +44.3707i q^{14} -141.788i q^{15} +16.0000 q^{16} -73.4632i q^{17} -139.717i q^{18} +68.5271i q^{19} +57.6276i q^{20} -218.341 q^{21} -42.0971i q^{22} -25.3645i q^{23} +78.7333i q^{24} -82.5590 q^{25} +154.594 q^{26} +421.797 q^{27} +88.7413 q^{28} +268.373i q^{29} -283.576 q^{30} -86.5385i q^{31} -32.0000i q^{32} +207.153 q^{33} -146.926 q^{34} +319.622i q^{35} -279.433 q^{36} +(-219.871 + 48.0609i) q^{37} +137.054 q^{38} +760.732i q^{39} +115.255 q^{40} +5.19294 q^{41} +436.681i q^{42} -125.781i q^{43} -84.1942 q^{44} -1006.44i q^{45} -50.7289 q^{46} -181.217 q^{47} +157.467 q^{48} +149.189 q^{49} +165.118i q^{50} -723.000i q^{51} -309.188i q^{52} +63.1517 q^{53} -843.595i q^{54} -303.244i q^{55} -177.483i q^{56} +674.421i q^{57} +536.746 q^{58} -207.923i q^{59} +567.152i q^{60} +299.467i q^{61} -173.077 q^{62} -1549.83 q^{63} -64.0000 q^{64} +1113.61 q^{65} -414.305i q^{66} -142.495 q^{67} +293.853i q^{68} -249.629i q^{69} +639.244 q^{70} -501.281 q^{71} +558.867i q^{72} +200.110 q^{73} +(96.1218 + 439.742i) q^{74} -812.518 q^{75} -274.108i q^{76} -466.969 q^{77} +1521.46 q^{78} -1074.72i q^{79} -230.511i q^{80} +2265.01 q^{81} -10.3859i q^{82} -1120.84 q^{83} +873.362 q^{84} -1058.38 q^{85} -251.563 q^{86} +2641.24i q^{87} +168.388i q^{88} +154.822i q^{89} -2012.89 q^{90} -1714.86i q^{91} +101.458i q^{92} -851.683i q^{93} +362.435i q^{94} +987.263 q^{95} -314.933i q^{96} -829.017i q^{97} -298.378i q^{98} +1470.42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9}+O(q^{10}) \) 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9	\( 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9} + 76 q^{10} - 50 q^{11} - 56 q^{12} + 160 q^{16} - 312 q^{21} - 700 q^{25} + 492 q^{26} + 848 q^{27} + 16 q^{28} - 240 q^{30} - 508 q^{33} - 568 q^{34} - 688 q^{36} + 82 q^{37} + 336 q^{38} - 304 q^{40} - 1194 q^{41} + 200 q^{44} + 60 q^{46} + 464 q^{47} + 224 q^{48} + 2382 q^{49} - 692 q^{53} + 1108 q^{58} - 1700 q^{62} + 2300 q^{63} - 640 q^{64} + 604 q^{65} + 1114 q^{67} + 1880 q^{70} - 1460 q^{71} + 2082 q^{73} + 968 q^{74} - 5160 q^{75} - 6096 q^{77} + 1004 q^{78} + 4978 q^{81} - 1364 q^{83} + 1248 q^{84} + 104 q^{85} + 1400 q^{86} - 2600 q^{90} + 5084 q^{95} + 508 q^{99}+O(q^{100}) \) 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9 + 76 * q^10 - 50 * q^11 - 56 * q^12 + 160 * q^16 - 312 * q^21 - 700 * q^25 + 492 * q^26 + 848 * q^27 + 16 * q^28 - 240 * q^30 - 508 * q^33 - 568 * q^34 - 688 * q^36 + 82 * q^37 + 336 * q^38 - 304 * q^40 - 1194 * q^41 + 200 * q^44 + 60 * q^46 + 464 * q^47 + 224 * q^48 + 2382 * q^49 - 692 * q^53 + 1108 * q^58 - 1700 * q^62 + 2300 * q^63 - 640 * q^64 + 604 * q^65 + 1114 * q^67 + 1880 * q^70 - 1460 * q^71 + 2082 * q^73 + 968 * q^74 - 5160 * q^75 - 6096 * q^77 + 1004 * q^78 + 4978 * q^81 - 1364 * q^83 + 1248 * q^84 + 104 * q^85 + 1400 * q^86 - 2600 * q^90 + 5084 * q^95 + 508 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more