LMFDB - Embedded newform 74.4.b.a.73.9

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			73.9
Root			$6.35485i$ of defining polynomial
Character	$\chi$	$=$	74.73
Dual form			74.4.b.a.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +7.35485 q^{3} -4.00000 q^{4} -16.2134i q^{5} +14.7097i q^{6} +31.9123 q^{7} -8.00000i q^{8} +27.0938 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +7.35485 q^{3} -4.00000 q^{4} -16.2134i q^{5} +14.7097i q^{6} +31.9123 q^{7} -8.00000i q^{8} +27.0938 q^{9} +32.4267 q^{10} -58.7236 q^{11} -29.4194 q^{12} +35.5821i q^{13} +63.8247i q^{14} -119.247i q^{15} +16.0000 q^{16} +109.863i q^{17} +54.1875i q^{18} +2.05339i q^{19} +64.8535i q^{20} +234.710 q^{21} -117.447i q^{22} -86.8518i q^{23} -58.8388i q^{24} -137.873 q^{25} -71.1642 q^{26} +0.689538 q^{27} -127.649 q^{28} -50.6218i q^{29} +238.494 q^{30} +252.387i q^{31} +32.0000i q^{32} -431.903 q^{33} -219.727 q^{34} -517.406i q^{35} -108.375 q^{36} +(-69.2512 - 214.143i) q^{37} -4.10677 q^{38} +261.701i q^{39} -129.707 q^{40} +9.98305 q^{41} +469.421i q^{42} -300.612i q^{43} +234.894 q^{44} -439.281i q^{45} +173.704 q^{46} -118.674 q^{47} +117.678 q^{48} +675.397 q^{49} -275.746i q^{50} +808.028i q^{51} -142.328i q^{52} -250.064 q^{53} +1.37908i q^{54} +952.107i q^{55} -255.299i q^{56} +15.1023i q^{57} +101.244 q^{58} +122.157i q^{59} +476.987i q^{60} +560.246i q^{61} -504.773 q^{62} +864.625 q^{63} -64.0000 q^{64} +576.906 q^{65} -863.806i q^{66} -214.924 q^{67} -439.453i q^{68} -638.781i q^{69} +1034.81 q^{70} -147.924 q^{71} -216.750i q^{72} +478.233 q^{73} +(428.286 - 138.502i) q^{74} -1014.04 q^{75} -8.21354i q^{76} -1874.01 q^{77} -523.402 q^{78} -18.4237i q^{79} -259.414i q^{80} -726.460 q^{81} +19.9661i q^{82} +1186.47 q^{83} -938.841 q^{84} +1781.25 q^{85} +601.224 q^{86} -372.315i q^{87} +469.789i q^{88} -558.821i q^{89} +878.562 q^{90} +1135.51i q^{91} +347.407i q^{92} +1856.26i q^{93} -237.347i q^{94} +33.2923 q^{95} +235.355i q^{96} -1290.66i q^{97} +1350.79i q^{98} -1591.04 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	7.35485			1.41544			0.707720	−	0.706493i	$-0.249724\pi$
$3$	7.35485			1.41544			0.707720	+	0.706493i	$0.249724\pi$
$4$	−4.00000			−0.500000
$5$		−	16.2134i		−	1.45017i	−0.688661	−	0.725084i	$-0.741801\pi$
$5$		−	16.2134i		−	1.45017i	0.688661	−	0.725084i	$-0.258199\pi$
$6$			14.7097i			1.00087i
$7$	31.9123			1.72310			0.861552	−	0.507669i	$-0.169493\pi$
$7$	31.9123			1.72310			0.861552	+	0.507669i	$0.169493\pi$
$8$		−	8.00000i		−	0.353553i
$9$	27.0938			1.00347
$10$	32.4267			1.02542
$11$	−58.7236			−1.60962			−0.804810	−	0.593532i	$-0.797733\pi$
$11$	−58.7236			−1.60962			−0.804810	+	0.593532i	$0.797733\pi$
$12$	−29.4194			−0.707720
$13$			35.5821i			0.759131i	0.925165	+	0.379565i	$0.123926\pi$
$13$			35.5821i			0.759131i	−0.925165	+	0.379565i	$0.876074\pi$
$14$			63.8247i			1.21842i
$15$		−	119.247i		−	2.05263i
$16$	16.0000			0.250000
$17$			109.863i			1.56740i	0.621140	+	0.783699i	$0.286670\pi$
$17$			109.863i			1.56740i	−0.621140	+	0.783699i	$0.713330\pi$
$18$			54.1875i			0.709562i
$19$			2.05339i			0.0247936i	0.999923	+	0.0123968i	$0.00394613\pi$
$19$			2.05339i			0.0247936i	−0.999923	+	0.0123968i	$0.996054\pi$
$20$			64.8535i			0.725084i
$21$	234.710			2.43895
$22$		−	117.447i		−	1.13817i
$23$		−	86.8518i		−	0.787385i	−0.919242	−	0.393692i	$-0.871198\pi$
$23$		−	86.8518i		−	0.787385i	0.919242	−	0.393692i	$-0.128802\pi$
$24$		−	58.8388i		−	0.500434i
$25$	−137.873			−1.10299
$26$	−71.1642			−0.536786
$27$	0.689538			0.00491488
$28$	−127.649			−0.861552
$29$		−	50.6218i		−	0.324146i	−0.986779	−	0.162073i	$-0.948182\pi$
$29$		−	50.6218i		−	0.324146i	0.986779	−	0.162073i	$-0.0518180\pi$
$30$	238.494			1.45143
$31$			252.387i			1.46226i	0.682240	+	0.731128i	$0.261006\pi$
$31$			252.387i			1.46226i	−0.682240	+	0.731128i	$0.738994\pi$
$32$			32.0000i			0.176777i
$33$	−431.903			−2.27832
$34$	−219.727			−1.10832
$35$		−	517.406i		−	2.49879i
$36$	−108.375			−0.501736
$37$	−69.2512	−	214.143i	−0.307698	−	0.951484i
$37$	−69.2512	−	214.143i	−0.307698	−	0.951484i
$38$	−4.10677			−0.0175317
$39$			261.701i			1.07450i
$40$	−129.707			−0.512712
$41$	9.98305			0.0380266			0.0190133	−	0.999819i	$-0.493948\pi$
$41$	9.98305			0.0380266			0.0190133	+	0.999819i	$0.493948\pi$
$42$			469.421i			1.72460i
$43$		−	300.612i		−	1.06611i	−0.846079	−	0.533057i	$-0.821043\pi$
$43$		−	300.612i		−	1.06611i	0.846079	−	0.533057i	$-0.178957\pi$
$44$	234.894			0.804810
$45$		−	439.281i		−	1.45520i
$46$	173.704			0.556765
$47$	−118.674			−0.368305			−0.184153	−	0.982898i	$-0.558954\pi$
$47$	−118.674			−0.368305			−0.184153	+	0.982898i	$0.558954\pi$
$48$	117.678			0.353860
$49$	675.397			1.96909
$50$		−	275.746i		−	0.779929i
$51$			808.028i			2.21856i
$52$		−	142.328i		−	0.379565i
$53$	−250.064			−0.648094			−0.324047	−	0.946041i	$-0.605044\pi$
$53$	−250.064			−0.648094			−0.324047	+	0.946041i	$0.605044\pi$
$54$			1.37908i			0.00347534i
$55$			952.107i			2.33422i
$56$		−	255.299i		−	0.609209i
$57$			15.1023i			0.0350939i
$58$	101.244			0.229206
$59$			122.157i			0.269550i	0.990876	+	0.134775i	$0.0430312\pi$
$59$			122.157i			0.269550i	−0.990876	+	0.134775i	$0.956969\pi$
$60$			476.987i			1.02631i
$61$			560.246i			1.17594i	0.808884	+	0.587968i	$0.200072\pi$
$61$			560.246i			1.17594i	−0.808884	+	0.587968i	$0.799928\pi$
$62$	−504.773			−1.03397
$63$	864.625			1.72909
$64$	−64.0000			−0.125000
$65$	576.906			1.10087
$66$		−	863.806i		−	1.61102i
$67$	−214.924			−0.391897			−0.195949	−	0.980614i	$-0.562779\pi$
$67$	−214.924			−0.391897			−0.195949	+	0.980614i	$0.562779\pi$
$68$		−	439.453i		−	0.783699i
$69$		−	638.781i		−	1.11450i
$70$	1034.81			1.76691
$71$	−147.924			−0.247258			−0.123629	−	0.992328i	$-0.539453\pi$
$71$	−147.924			−0.247258			−0.123629	+	0.992328i	$0.539453\pi$
$72$		−	216.750i		−	0.354781i
$73$	478.233			0.766752			0.383376	−	0.923592i	$-0.374761\pi$
$73$	478.233			0.766752			0.383376	+	0.923592i	$0.374761\pi$
$74$	428.286	−	138.502i	0.672801	−	0.217575i
$75$	−1014.04			−1.56121
$76$		−	8.21354i		−	0.0123968i
$77$	−1874.01			−2.77354
$78$	−523.402			−0.759789
$79$		−	18.4237i		−	0.0262384i	−0.999914	−	0.0131192i	$-0.995824\pi$
$79$		−	18.4237i		−	0.0262384i	0.999914	−	0.0131192i	$-0.00417609\pi$
$80$		−	259.414i		−	0.362542i
$81$	−726.460			−0.996516
$82$			19.9661i			0.0268889i
$83$	1186.47			1.56906			0.784528	−	0.620093i	$-0.212905\pi$
$83$	1186.47			1.56906			0.784528	+	0.620093i	$0.212905\pi$
$84$	−938.841			−1.21948
$85$	1781.25			2.27299
$86$	601.224			0.753857
$87$		−	372.315i		−	0.458809i
$88$			469.789i			0.569087i
$89$		−	558.821i		−	0.665561i	−0.943004	−	0.332781i	$-0.892013\pi$
$89$		−	558.821i		−	0.665561i	0.943004	−	0.332781i	$-0.107987\pi$
$90$	878.562			1.02898
$91$			1135.51i			1.30806i
$92$			347.407i			0.393692i
$93$			1856.26i			2.06974i
$94$		−	237.347i		−	0.260431i
$95$	33.2923			0.0359549
$96$			235.355i			0.250217i
$97$		−	1290.66i		−	1.35100i	−0.737362	−	0.675498i	$-0.763929\pi$
$97$		−	1290.66i		−	1.35100i	0.737362	−	0.675498i	$-0.236071\pi$
$98$			1350.79i			1.39236i
$99$	−1591.04			−1.61521
$100$	551.493			0.551493
$101$	913.925			0.900385			0.450193	−	0.892931i	$-0.351355\pi$
$101$	913.925			0.900385			0.450193	+	0.892931i	$0.351355\pi$
$102$	−1616.06			−1.56876
$103$			1424.92i			1.36312i	0.731762	+	0.681561i	$0.238698\pi$
$103$			1424.92i			1.36312i	−0.731762	+	0.681561i	$0.761302\pi$
$104$	284.657			0.268393
$105$		−	3805.44i		−	3.53689i
$106$		−	500.128i		−	0.458271i
$107$	−1517.85			−1.37137			−0.685683	−	0.727900i	$-0.740497\pi$
$107$	−1517.85			−1.37137			−0.685683	+	0.727900i	$0.740497\pi$
$108$	−2.75815			−0.00245744
$109$		−	952.637i		−	0.837120i	−0.908189	−	0.418560i	$-0.862535\pi$
$109$		−	952.637i		−	0.837120i	0.908189	−	0.418560i	$-0.137465\pi$
$110$	−1904.21			−1.65054
$111$	−509.332	−	1574.99i	−0.435529	−	1.34677i
$112$	510.597			0.430776
$113$		−	328.173i		−	0.273203i	−0.990626	−	0.136601i	$-0.956382\pi$
$113$		−	328.173i		−	0.273203i	0.990626	−	0.136601i	$-0.0436179\pi$
$114$	−30.2047			−0.0248151
$115$	−1408.16			−1.14184
$116$			202.487i			0.162073i
$117$			964.053i			0.761767i
$118$	−244.314			−0.190601
$119$			3506.00i			2.70079i
$120$	−953.974			−0.725713
$121$	2117.46			1.59088
$122$	−1120.49			−0.831513
$123$	73.4238			0.0538244
$124$		−	1009.55i		−	0.731128i
$125$			208.718i			0.149346i
$126$			1729.25i			1.22265i
$127$	−2.16135			−0.00151015			−0.000755074	−	1.00000i	$-0.500240\pi$
$127$	−2.16135			−0.00151015			−0.000755074		1.00000i	$0.500240\pi$
$128$		−	128.000i		−	0.0883883i
$129$		−	2210.96i		−	1.50902i
$130$			1153.81i			0.778430i
$131$		−	967.219i		−	0.645086i	−0.946555	−	0.322543i	$-0.895462\pi$
$131$		−	967.219i		−	0.645086i	0.946555	−	0.322543i	$-0.104538\pi$
$132$	1727.61			1.13916
$133$			65.5283i			0.0427220i
$134$		−	429.848i		−	0.277113i
$135$		−	11.1797i		−	0.00712739i
$136$	878.907			0.554159
$137$	422.497			0.263477			0.131739	−	0.991284i	$-0.457944\pi$
$137$	422.497			0.263477			0.131739	+	0.991284i	$0.457944\pi$
$138$	1277.56			0.788068
$139$	−1112.04			−0.678576			−0.339288	−	0.940683i	$-0.610186\pi$
$139$	−1112.04			−0.678576			−0.339288	+	0.940683i	$0.610186\pi$
$140$			2069.63i			1.24939i
$141$	−872.827			−0.521314
$142$		−	295.848i		−	0.174838i
$143$		−	2089.51i		−	1.22191i
$144$	433.500			0.250868
$145$	−820.749			−0.470066
$146$			956.466i			0.542176i
$147$	4967.44			2.78713
$148$	277.005	+	856.572i	0.153849	+	0.475742i
$149$	−1013.74			−0.557372			−0.278686	−	0.960382i	$-0.589899\pi$
$149$	−1013.74			−0.557372			−0.278686	+	0.960382i	$0.589899\pi$
$150$		−	2028.07i		−	1.10394i
$151$	3271.35			1.76304			0.881519	−	0.472149i	$-0.156522\pi$
$151$	3271.35			1.76304			0.881519	+	0.472149i	$0.156522\pi$
$152$	16.4271			0.00876587
$153$			2976.61i			1.57284i
$154$		−	3748.01i		−	1.96119i
$155$	4092.04			2.12052
$156$		−	1046.80i		−	0.537252i
$157$	−1408.87			−0.716179			−0.358090	−	0.933687i	$-0.616572\pi$
$157$	−1408.87			−0.716179			−0.358090	+	0.933687i	$0.616572\pi$
$158$	36.8475			0.0185533
$159$	−1839.18			−0.917338
$160$	518.828			0.256356
$161$		−	2771.64i		−	1.35675i
$162$		−	1452.92i		−	0.704643i
$163$		−	284.776i		−	0.136843i	−0.997657	−	0.0684215i	$-0.978204\pi$
$163$		−	284.776i		−	0.136843i	0.997657	−	0.0684215i	$-0.0217963\pi$
$164$	−39.9322			−0.0190133
$165$			7002.60i			3.30395i
$166$			2372.93i			1.10949i
$167$		−	371.643i		−	0.172207i	−0.996286	−	0.0861036i	$-0.972558\pi$
$167$		−	371.643i		−	0.172207i	0.996286	−	0.0861036i	$-0.0274416\pi$
$168$		−	1877.68i		−	0.862300i
$169$	930.914			0.423721
$170$			3562.51i			1.60725i
$171$			55.6339i			0.0248797i
$172$			1202.45i			0.533057i
$173$	1375.73			0.604596			0.302298	−	0.953213i	$-0.402246\pi$
$173$	1375.73			0.604596			0.302298	+	0.953213i	$0.402246\pi$
$174$	744.631			0.324427
$175$	−4399.86			−1.90056
$176$	−939.577			−0.402405
$177$			898.445i			0.381532i
$178$	1117.64			0.470623
$179$		−	1584.94i		−	0.661810i	−0.943664	−	0.330905i	$-0.892646\pi$
$179$		−	1584.94i		−	0.661810i	0.943664	−	0.330905i	$-0.107354\pi$
$180$			1757.12i			0.727601i
$181$	−353.895			−0.145330			−0.0726651	−	0.997356i	$-0.523150\pi$
$181$	−353.895			−0.145330			−0.0726651	+	0.997356i	$0.523150\pi$
$182$	−2271.02			−0.924939
$183$			4120.52i			1.66447i
$184$	−694.814			−0.278382
$185$	−3471.98	+	1122.80i	−1.37981	+	0.446214i
$186$	−3712.53			−1.46353
$187$		−	6451.57i		−	2.52292i
$188$	474.695			0.184153
$189$	22.0048			0.00846884
$190$			66.5846i			0.0254240i
$191$		−	4397.81i		−	1.66604i	−0.553241	−	0.833021i	$-0.686609\pi$
$191$		−	4397.81i		−	1.66604i	0.553241	−	0.833021i	$-0.313391\pi$
$192$	−470.710			−0.176930
$193$			22.1015i			0.00824301i	0.999992	+	0.00412150i	$0.00131192\pi$
$193$			22.1015i			0.00824301i	−0.999992	+	0.00412150i	$0.998688\pi$
$194$	2581.32			0.955298
$195$	4243.05			1.55821
$196$	−2701.59			−0.984544
$197$	645.035			0.233283			0.116642	−	0.993174i	$-0.462787\pi$
$197$	645.035			0.233283			0.116642	+	0.993174i	$0.462787\pi$
$198$		−	3182.08i		−	1.14213i
$199$			3703.02i			1.31909i	0.751663	+	0.659547i	$0.229252\pi$
$199$			3703.02i			1.31909i	−0.751663	+	0.659547i	$0.770748\pi$
$200$			1102.99i			0.389964i
$201$	−1580.73			−0.554707
$202$			1827.85i			0.636669i
$203$		−	1615.46i		−	0.558537i
$204$		−	3232.11i		−	1.10928i
$205$		−	161.859i		−	0.0551449i
$206$	−2849.84			−0.963872
$207$		−	2353.14i		−	0.790119i
$208$			569.314i			0.189783i
$209$		−	120.582i		−	0.0399083i
$210$	7610.89			2.50096
$211$	−1249.18			−0.407569			−0.203784	−	0.979016i	$-0.565324\pi$
$211$	−1249.18			−0.407569			−0.203784	+	0.979016i	$0.565324\pi$
$212$	1000.26			0.324047
$213$	−1087.96			−0.349980
$214$		−	3035.70i		−	0.969703i
$215$	−4873.93			−1.54604
$216$		−	5.51630i		−	0.00173767i
$217$			8054.25i			2.51962i
$218$	1905.27			0.591933
$219$	3517.33			1.08529
$220$		−	3808.43i		−	1.16711i
$221$	−3909.17			−1.18986
$222$	3149.98	−	1018.66i	0.952310	−	0.307965i
$223$	5344.34			1.60486			0.802430	−	0.596746i	$-0.203540\pi$
$223$	5344.34			1.60486			0.802430	+	0.596746i	$0.203540\pi$
$224$			1021.19i			0.304605i
$225$	−3735.50			−1.10682
$226$	656.346			0.193183
$227$			2179.96i			0.637397i	0.947856	+	0.318698i	$0.103246\pi$
$227$			2179.96i			0.637397i	−0.947856	+	0.318698i	$0.896754\pi$
$228$		−	60.4093i		−	0.0175470i
$229$	1267.57			0.365780			0.182890	−	0.983133i	$-0.441455\pi$
$229$	1267.57			0.365780			0.182890	+	0.983133i	$0.441455\pi$
$230$		−	2816.32i		−	0.807402i
$231$	−13783.0			−3.92579
$232$	−404.974			−0.114603
$233$	4339.75			1.22020			0.610100	−	0.792324i	$-0.291129\pi$
$233$	4339.75			1.22020			0.610100	+	0.792324i	$0.291129\pi$
$234$	−1928.11			−0.538650
$235$			1924.10i			0.534104i
$236$		−	488.627i		−	0.134775i
$237$		−	135.504i		−	0.0371389i
$238$	−7011.99			−1.90975
$239$			3534.28i			0.956543i	0.878212	+	0.478271i	$0.158736\pi$
$239$			3534.28i			0.956543i	−0.878212	+	0.478271i	$0.841264\pi$
$240$		−	1907.95i		−	0.513157i
$241$		−	2502.73i		−	0.668942i	−0.942406	−	0.334471i	$-0.891442\pi$
$241$		−	2502.73i		−	0.668942i	0.942406	−	0.334471i	$-0.108558\pi$
$242$			4234.92i			1.12492i
$243$	−5361.62			−1.41542
$244$		−	2240.98i		−	0.587968i
$245$		−	10950.5i		−	2.85551i
$246$			146.848i			0.0380596i
$247$	−73.0637			−0.0188216
$248$	2019.09			0.516986
$249$	8726.28			2.22091
$250$	−417.436			−0.105604
$251$			7268.41i			1.82780i	0.405938	+	0.913901i	$0.366945\pi$
$251$			7268.41i			1.82780i	−0.405938	+	0.913901i	$0.633055\pi$
$252$	−3458.50			−0.864544
$253$			5100.25i			1.26739i
$254$		−	4.32270i		−	0.00106784i
$255$	13100.9			3.21728
$256$	256.000			0.0625000
$257$		−	4668.81i		−	1.13320i	−0.823993	−	0.566600i	$-0.808259\pi$
$257$		−	4668.81i		−	1.13320i	0.823993	−	0.566600i	$-0.191741\pi$
$258$	4421.91			1.06704
$259$	−2209.97	−	6833.81i	−0.530196	−	1.63951i
$260$	−2307.62			−0.550433
$261$		−	1371.53i		−	0.325271i
$262$	1934.44			0.456145
$263$	−2973.86			−0.697247			−0.348624	−	0.937263i	$-0.613351\pi$
$263$	−2973.86			−0.697247			−0.348624	+	0.937263i	$0.613351\pi$
$264$			3455.22i			0.805509i
$265$			4054.38i			0.939844i
$266$	−131.057			−0.0302090
$267$		−	4110.04i		−	0.942062i
$268$	859.695			0.195949
$269$	736.769			0.166995			0.0834974	−	0.996508i	$-0.473391\pi$
$269$	736.769			0.166995			0.0834974	+	0.996508i	$0.473391\pi$
$270$	22.3595			0.00503983
$271$	−5575.43			−1.24975			−0.624877	−	0.780724i	$-0.714851\pi$
$271$	−5575.43			−1.24975			−0.624877	+	0.780724i	$0.714851\pi$
$272$			1757.81i			0.391850i
$273$			8351.49i			1.85148i
$274$			844.995i			0.186307i
$275$	8096.41			1.77539
$276$			2555.13i			0.557248i
$277$			578.140i			0.125405i	0.998032	+	0.0627023i	$0.0199719\pi$
$277$			578.140i			0.125405i	−0.998032	+	0.0627023i	$0.980028\pi$
$278$		−	2224.08i		−	0.479826i
$279$			6838.10i			1.46733i
$280$	−4139.25			−0.883456
$281$			5580.82i			1.18478i	0.805651	+	0.592391i	$0.201816\pi$
$281$			5580.82i			1.18478i	−0.805651	+	0.592391i	$0.798184\pi$
$282$		−	1745.65i		−	0.368625i
$283$		−	2600.59i		−	0.546251i	−0.961978	−	0.273126i	$-0.911942\pi$
$283$		−	2600.59i		−	0.546251i	0.961978	−	0.273126i	$-0.0880575\pi$
$284$	591.696			0.123629
$285$	244.860			0.0508920
$286$	4179.02			0.864022
$287$	318.583			0.0655238
$288$			867.000i			0.177391i
$289$	−7156.96			−1.45674
$290$		−	1641.50i		−	0.332387i
$291$		−	9492.60i		−	1.91225i
$292$	−1912.93			−0.383376
$293$	7282.66			1.45207			0.726037	−	0.687656i	$-0.241360\pi$
$293$	7282.66			1.45207			0.726037	+	0.687656i	$0.241360\pi$
$294$			9934.89i			1.97080i
$295$	1980.57			0.390893
$296$	−1713.14	+	554.010i	−0.336400	+	0.108788i
$297$	−40.4921			−0.00791108
$298$		−	2027.47i		−	0.394122i
$299$	3090.37			0.597728
$300$	4056.14			0.780605
$301$		−	9593.24i		−	1.83703i
$302$			6542.70i			1.24666i
$303$	6721.78			1.27444
$304$			32.8542i			0.00619841i
$305$	9083.47			1.70530
$306$	−5953.22			−1.11217
$307$	−4336.87			−0.806249			−0.403125	−	0.915145i	$-0.632076\pi$
$307$	−4336.87			−0.806249			−0.403125	+	0.915145i	$0.632076\pi$
$308$	7496.03			1.38677
$309$			10480.1i			1.92942i
$310$			8184.07i			1.49943i
$311$			3897.48i			0.710629i	0.934747	+	0.355315i	$0.115626\pi$
$311$			3897.48i			0.710629i	−0.934747	+	0.355315i	$0.884374\pi$
$312$	2093.61			0.379895
$313$		−	7615.34i		−	1.37522i	−0.726079	−	0.687611i	$-0.758660\pi$
$313$		−	7615.34i		−	1.37522i	0.726079	−	0.687611i	$-0.241340\pi$
$314$		−	2817.74i		−	0.506415i
$315$		−	14018.5i		−	2.50747i
$316$			73.6950i			0.0131192i
$317$	6011.47			1.06510			0.532552	−	0.846398i	$-0.321233\pi$
$317$	6011.47			1.06510			0.532552	+	0.846398i	$0.321233\pi$
$318$		−	3678.37i		−	0.648656i
$319$			2972.69i			0.521752i
$320$			1037.66i			0.181271i
$321$	−11163.6			−1.94109
$322$	5543.29			0.959364
$323$	−225.592			−0.0388615
$324$	2905.84			0.498258
$325$		−	4905.82i		−	0.837310i
$326$	569.552			0.0967625
$327$		−	7006.50i		−	1.18489i
$328$		−	79.8644i		−	0.0134444i
$329$	−3787.16			−0.634628
$330$	−14005.2			−2.33624
$331$			4655.05i			0.773006i	0.922288	+	0.386503i	$0.126317\pi$
$331$			4655.05i			0.773006i	−0.922288	+	0.386503i	$0.873683\pi$
$332$	−4745.87			−0.784528
$333$	−1876.28	−	5801.94i	−0.308767	−	0.954788i
$334$	743.286			0.121769
$335$			3484.64i			0.568317i
$336$	3755.37			0.609738
$337$	−8059.64			−1.30278			−0.651389	−	0.758744i	$-0.725814\pi$
$337$	−8059.64			−1.30278			−0.651389	+	0.758744i	$0.725814\pi$
$338$			1861.83i			0.299616i
$339$		−	2413.66i		−	0.386702i
$340$	−7125.02			−1.13650
$341$		−	14821.0i		−	2.35368i
$342$	−111.268			−0.0175926
$343$	10607.6			1.66984
$344$	−2404.90			−0.376928
$345$	−10356.8			−1.61621
$346$			2751.47i			0.427514i
$347$		−	1762.77i		−	0.272710i	−0.990660	−	0.136355i	$-0.956461\pi$
$347$		−	1762.77i		−	0.272710i	0.990660	−	0.136355i	$-0.0435388\pi$
$348$			1489.26i			0.229405i
$349$	−4805.93			−0.737122			−0.368561	−	0.929603i	$-0.620149\pi$
$349$	−4805.93			−0.737122			−0.368561	+	0.929603i	$0.620149\pi$
$350$		−	8799.71i		−	1.34390i
$351$			24.5352i			0.00373103i
$352$		−	1879.15i		−	0.284543i
$353$			9014.20i			1.35914i	0.733609	+	0.679571i	$0.237834\pi$
$353$			9014.20i			1.35914i	−0.733609	+	0.679571i	$0.762166\pi$
$354$	−1796.89			−0.269784
$355$			2398.35i			0.358566i
$356$			2235.29i			0.332781i
$357$			25786.1i			3.82281i
$358$	3169.88			0.467970
$359$	−13255.0			−1.94867			−0.974333	−	0.225110i	$-0.927726\pi$
$359$	−13255.0			−1.94867			−0.974333	+	0.225110i	$0.927726\pi$
$360$	−3514.25			−0.514492
$361$	6854.78			0.999385
$362$		−	707.789i		−	0.102764i
$363$	15573.6			2.25179
$364$		−	4542.03i		−	0.654031i
$365$		−	7753.76i		−	1.11192i
$366$	−8241.04			−1.17696
$367$	−9390.22			−1.33560			−0.667801	−	0.744340i	$-0.732764\pi$
$367$	−9390.22			−1.33560			−0.667801	+	0.744340i	$0.732764\pi$
$368$		−	1389.63i		−	0.196846i
$369$	270.478			0.0381586
$370$	−2245.59	−	6943.96i	−0.315521	−	0.975674i
$371$	−7980.13			−1.11673
$372$		−	7425.06i		−	1.03487i
$373$	−4461.14			−0.619273			−0.309637	−	0.950855i	$-0.600207\pi$
$373$	−4461.14			−0.619273			−0.309637	+	0.950855i	$0.600207\pi$
$374$	12903.1			1.78397
$375$			1535.09i			0.211391i
$376$			949.390i			0.130216i
$377$	1801.23			0.246069
$378$			44.0095i			0.00598838i
$379$	−6368.92			−0.863191			−0.431596	−	0.902067i	$-0.642049\pi$
$379$	−6368.92			−0.863191			−0.431596	+	0.902067i	$0.642049\pi$
$380$	−133.169			−0.0179775
$381$	−15.8964			−0.00213752
$382$	8795.61			1.17807
$383$			6198.26i			0.826935i	0.910519	+	0.413468i	$0.135682\pi$
$383$			6198.26i			0.826935i	−0.910519	+	0.413468i	$0.864318\pi$
$384$		−	941.420i		−	0.125108i
$385$			30384.0i			4.02210i
$386$	−44.2030			−0.00582868
$387$		−	8144.71i		−	1.06982i
$388$			5162.64i			0.675498i
$389$		−	10478.0i		−	1.36569i	−0.730563	−	0.682845i	$-0.760742\pi$
$389$		−	10478.0i		−	1.36569i	0.730563	−	0.682845i	$-0.239258\pi$
$390$			8486.10i			1.10182i
$391$	9541.83			1.23415
$392$		−	5403.18i		−	0.696178i
$393$		−	7113.74i		−	0.913081i
$394$			1290.07i			0.164956i
$395$	−298.711			−0.0380501
$396$	6364.17			0.807605
$397$	8366.33			1.05767			0.528834	−	0.848726i	$-0.322630\pi$
$397$	8366.33			1.05767			0.528834	+	0.848726i	$0.322630\pi$
$398$	−7406.03			−0.932741
$399$			481.951i			0.0604705i
$400$	−2205.97			−0.275746
$401$		−	3068.80i		−	0.382166i	−0.981574	−	0.191083i	$-0.938800\pi$
$401$		−	3068.80i		−	0.382166i	0.981574	−	0.191083i	$-0.0611999\pi$
$402$		−	3161.46i		−	0.392237i
$403$	−8980.44			−1.11004
$404$	−3655.70			−0.450193
$405$			11778.4i			1.44511i
$406$	3230.92			0.394945
$407$	4066.68	+	12575.2i	0.495277	+	1.53153i
$408$	6464.22			0.784379
$409$		−	4350.87i		−	0.526006i	−0.964795	−	0.263003i	$-0.915287\pi$
$409$		−	4350.87i		−	0.526006i	0.964795	−	0.263003i	$-0.0847129\pi$
$410$	323.718			0.0389934
$411$	3107.40			0.372937
$412$		−	5699.68i		−	0.681561i
$413$			3898.31i			0.464463i
$414$	4706.28			0.558698
$415$		−	19236.6i		−	2.27539i
$416$	−1138.63			−0.134197
$417$	−8178.89			−0.960484
$418$	241.164			0.0282194
$419$	14272.1			1.66405			0.832027	−	0.554734i	$-0.187180\pi$
$419$	14272.1			1.66405			0.832027	+	0.554734i	$0.187180\pi$
$420$			15221.8i			1.76844i
$421$		−	9642.07i		−	1.11621i	−0.829769	−	0.558107i	$-0.811528\pi$
$421$		−	9642.07i		−	1.11621i	0.829769	−	0.558107i	$-0.188472\pi$
$422$		−	2498.36i		−	0.288195i
$423$	−3215.32			−0.369584
$424$			2000.51i			0.229136i
$425$		−	15147.2i		−	1.72882i
$426$		−	2175.92i		−	0.247473i
$427$			17878.8i			2.02626i
$428$	6071.41			0.685683
$429$		−	15368.0i		−	1.72954i
$430$		−	9747.87i		−	1.09322i
$431$		−	2093.54i		−	0.233973i	−0.993133	−	0.116987i	$-0.962677\pi$
$431$		−	2093.54i		−	0.233973i	0.993133	−	0.116987i	$-0.0373235\pi$
$432$	11.0326			0.00122872
$433$	−4492.12			−0.498563			−0.249281	−	0.968431i	$-0.580194\pi$
$433$	−4492.12			−0.498563			−0.249281	+	0.968431i	$0.580194\pi$
$434$	−16108.5			−1.78164
$435$	−6036.48			−0.665350
$436$			3810.55i			0.418560i
$437$	178.340			0.0195221
$438$			7034.66i			0.767418i
$439$			8447.86i			0.918438i	0.888323	+	0.459219i	$0.151871\pi$
$439$			8447.86i			0.918438i	−0.888323	+	0.459219i	$0.848129\pi$
$440$	7616.85			0.825271
$441$	18299.0			1.97593
$442$		−	7818.34i		−	0.841358i
$443$	−14701.9			−1.57677			−0.788385	−	0.615182i	$-0.789082\pi$
$443$	−14701.9			−1.57677			−0.788385	+	0.615182i	$0.789082\pi$
$444$	2037.33	+	6299.96i	0.217764	+	0.673385i
$445$	−9060.37			−0.965175
$446$			10688.7i			1.13481i
$447$	−7455.87			−0.788928
$448$	−2042.39			−0.215388
$449$			15397.1i			1.61834i	0.587575	+	0.809170i	$0.300083\pi$
$449$			15397.1i			1.61834i	−0.587575	+	0.809170i	$0.699917\pi$
$450$		−	7471.01i		−	0.782637i
$451$	−586.240			−0.0612084
$452$			1312.69i			0.136601i
$453$	24060.3			2.49547
$454$	−4359.92			−0.450707
$455$	18410.4			1.89691
$456$	120.819			0.0124076
$457$		−	3679.81i		−	0.376661i	−0.982106	−	0.188330i	$-0.939692\pi$
$457$		−	3679.81i		−	0.376661i	0.982106	−	0.188330i	$-0.0603076\pi$
$458$			2535.15i			0.258646i
$459$			75.7550i			0.00770357i
$460$	5632.64			0.570920
$461$			9091.60i			0.918520i	0.888302	+	0.459260i	$0.151885\pi$
$461$			9091.60i			0.918520i	−0.888302	+	0.459260i	$0.848115\pi$
$462$		−	27566.1i		−	2.77595i
$463$		−	8572.38i		−	0.860458i	−0.902720	−	0.430229i	$-0.858433\pi$
$463$		−	8572.38i		−	0.860458i	0.902720	−	0.430229i	$-0.141567\pi$
$464$		−	809.948i		−	0.0810364i
$465$	30096.3			3.00147
$466$			8679.51i			0.862812i
$467$			1125.97i			0.111571i	0.998443	+	0.0557854i	$0.0177663\pi$
$467$			1125.97i			0.111571i	−0.998443	+	0.0557854i	$0.982234\pi$
$468$		−	3856.21i		−	0.380883i
$469$	−6858.72			−0.675280
$470$	−3848.20			−0.377669
$471$	−10362.0			−1.01371
$472$	977.255			0.0953004
$473$			17653.0i			1.71604i
$474$	271.008			0.0262612
$475$		−	283.107i		−	0.0273470i
$476$		−	14024.0i		−	1.35040i
$477$	−6775.18			−0.650344
$478$	−7068.56			−0.676378
$479$			15247.5i			1.45444i	0.686403	+	0.727221i	$0.259189\pi$
$479$			15247.5i			1.45444i	−0.686403	+	0.727221i	$0.740811\pi$
$480$	3815.90			0.362856
$481$	7619.66	−	2464.10i	0.722301	−	0.233583i
$482$	5005.46			0.473014
$483$		−	20385.0i		−	1.92039i
$484$	−8469.83			−0.795439
$485$	−20925.9			−1.95917
$486$		−	10723.2i		−	1.00086i
$487$			4951.28i			0.460706i	0.973107	+	0.230353i	$0.0739880\pi$
$487$			4951.28i			0.460706i	−0.973107	+	0.230353i	$0.926012\pi$
$488$	4481.97			0.415756
$489$		−	2094.48i		−	0.193693i
$490$	21900.9			2.01915
$491$	−10245.4			−0.941687			−0.470844	−	0.882217i	$-0.656050\pi$
$491$	−10245.4			−0.941687			−0.470844	+	0.882217i	$0.656050\pi$
$492$	−293.695			−0.0269122
$493$	5561.48			0.508066
$494$		−	146.127i		−	0.0133089i
$495$			25796.1i			2.34232i
$496$			4038.19i			0.365564i
$497$	−4720.60			−0.426052
$498$			17452.6i			1.57042i
$499$		−	148.769i		−	0.0133463i	−0.999978	−	0.00667317i	$-0.997876\pi$
$499$		−	148.769i		−	0.0133463i	0.999978	−	0.00667317i	$-0.00212415\pi$
$500$		−	834.872i		−	0.0746732i
$501$		−	2733.38i		−	0.243749i
$502$	−14536.8			−1.29245
$503$		−	1628.99i		−	0.144400i	−0.997390	−	0.0722000i	$-0.976998\pi$
$503$		−	1628.99i		−	0.144400i	0.997390	−	0.0722000i	$-0.0230020\pi$
$504$		−	6917.00i		−	0.611325i
$505$		−	14817.8i		−	1.30571i
$506$	−10200.5			−0.896180
$507$	6846.73			0.599752
$508$	8.64540			0.000755074
$509$	17175.5			1.49566			0.747828	−	0.663893i	$-0.231097\pi$
$509$	17175.5			1.49566			0.747828	+	0.663893i	$0.231097\pi$
$510$			26201.7i			2.27496i
$511$	15261.5			1.32119
$512$			512.000i			0.0441942i
$513$			1.41589i			0.000121858i
$514$	9337.61			0.801293
$515$	23102.7			1.97675
$516$			8843.82i			0.754511i
$517$	6968.94			0.592831
$518$	13667.6	−	4419.94i	1.15931	−	0.374905i
$519$	10118.3			0.855770
$520$		−	4615.24i		−	0.389215i
$521$	−21284.3			−1.78979			−0.894894	−	0.446278i	$-0.852749\pi$
$521$	−21284.3			−1.78979			−0.894894	+	0.446278i	$0.852749\pi$
$522$	2743.07			0.230002
$523$		−	17971.0i		−	1.50252i	−0.660007	−	0.751259i	$-0.729447\pi$
$523$		−	17971.0i		−	1.50252i	0.660007	−	0.751259i	$-0.270553\pi$
$524$			3868.87i			0.322543i
$525$	−32360.3			−2.69013
$526$		−	5947.72i		−	0.493028i
$527$	−27728.0			−2.29194
$528$	−6910.45			−0.569581
$529$	4623.77			0.380025
$530$	−8108.76			−0.664570
$531$			3309.69i			0.270486i
$532$		−	262.113i		−	0.0213610i
$533$			355.218i			0.0288672i
$534$	8220.09			0.666139
$535$			24609.5i			1.98871i
$536$			1719.39i			0.138557i
$537$		−	11657.0i		−	0.936752i
$538$			1473.54i			0.118083i
$539$	−39661.8			−3.16949
$540$			44.7189i			0.00356370i
$541$			7596.52i			0.603697i	0.953356	+	0.301848i	$0.0976037\pi$
$541$			7596.52i			0.603697i	−0.953356	+	0.301848i	$0.902396\pi$
$542$		−	11150.9i		−	0.883709i
$543$	−2602.84			−0.205706
$544$	−3515.63			−0.277080
$545$	−15445.4			−1.21396
$546$	−16703.0			−1.30920
$547$		−	23894.0i		−	1.86770i	−0.357666	−	0.933850i	$-0.616427\pi$
$547$		−	23894.0i		−	1.86770i	0.357666	−	0.933850i	$-0.383573\pi$
$548$	−1689.99			−0.131739
$549$			15179.2i			1.18002i
$550$			16192.8i			1.25539i
$551$	103.946			0.00803675
$552$	−5110.25			−0.394034
$553$		−	587.945i		−	0.0452115i
$554$	−1156.28			−0.0886744
$555$	−25535.9	+	8257.99i	−1.95304	+	0.631589i
$556$	4448.16			0.339288
$557$		−	3586.21i		−	0.272806i	−0.990653	−	0.136403i	$-0.956446\pi$
$557$		−	3586.21i		−	0.272806i	0.990653	−	0.136403i	$-0.0435541\pi$
$558$	−13676.2			−1.03756
$559$	10696.4			0.809320
$560$		−	8278.50i		−	0.624697i
$561$		−	47450.3i		−	3.57104i
$562$	−11161.6			−0.837767
$563$		−	3283.20i		−	0.245774i	−0.992421	−	0.122887i	$-0.960785\pi$
$563$		−	3283.20i		−	0.245774i	0.992421	−	0.122887i	$-0.0392152\pi$
$564$	3491.31			0.260657
$565$	−5320.78			−0.396190
$566$	5201.18			0.386258
$567$	−23183.0			−1.71710
$568$			1183.39i			0.0874191i
$569$		−	6746.56i		−	0.497066i	−0.968623	−	0.248533i	$-0.920052\pi$
$569$		−	6746.56i		−	0.497066i	0.968623	−	0.248533i	$-0.0799485\pi$
$570$			489.719i			0.0359861i
$571$	24363.3			1.78559			0.892795	−	0.450464i	$-0.148741\pi$
$571$	24363.3			1.78559			0.892795	+	0.450464i	$0.148741\pi$
$572$			8358.03i			0.610956i
$573$		−	32345.2i		−	2.35818i
$574$			637.165i			0.0463323i
$575$			11974.5i			0.868474i
$576$	−1734.00			−0.125434
$577$		−	23205.4i		−	1.67427i	−0.546997	−	0.837134i	$-0.684229\pi$
$577$		−	23205.4i		−	1.67427i	0.546997	−	0.837134i	$-0.315771\pi$
$578$		−	14313.9i		−	1.03007i
$579$			162.553i			0.0116675i
$580$	3283.00			0.235033
$581$	37862.9			2.70365
$582$	18985.2			1.35217
$583$	14684.7			1.04318
$584$		−	3825.86i		−	0.271088i
$585$	15630.5			1.10469
$586$			14565.3i			1.02677i
$587$			24871.4i			1.74881i	0.485193	+	0.874407i	$0.338750\pi$
$587$			24871.4i			1.74881i	−0.485193	+	0.874407i	$0.661250\pi$
$588$	−19869.8			−1.39356
$589$	−518.247			−0.0362547
$590$			3961.15i			0.276403i
$591$	4744.13			0.330199
$592$	−1108.02	−	3426.29i	−0.0769245	−	0.237871i
$593$	−12787.4			−0.885523			−0.442761	−	0.896640i	$-0.646001\pi$
$593$	−12787.4			−0.885523			−0.442761	+	0.896640i	$0.646001\pi$
$594$		−	80.9843i		−	0.00559398i
$595$	56844.0			3.91660
$596$	4054.94			0.278686
$597$			27235.1i			1.86710i
$598$			6180.74i			0.422657i
$599$	−7554.28			−0.515291			−0.257646	−	0.966239i	$-0.582947\pi$
$599$	−7554.28			−0.515291			−0.257646	+	0.966239i	$0.582947\pi$
$600$			8112.29i			0.551971i
$601$	7666.74			0.520354			0.260177	−	0.965561i	$-0.416219\pi$
$601$	7666.74			0.520354			0.260177	+	0.965561i	$0.416219\pi$
$602$	19186.5			1.29897
$603$	−5823.09			−0.393258
$604$	−13085.4			−0.881519
$605$		−	34331.1i		−	2.30704i
$606$			13443.6i			0.901167i
$607$			29020.0i			1.94050i	0.242100	+	0.970251i	$0.422164\pi$
$607$			29020.0i			1.94050i	−0.242100	+	0.970251i	$0.577836\pi$
$608$	−65.7083			−0.00438293
$609$		−	11881.5i		−	0.790576i
$610$			18166.9i			1.20583i
$611$		−	4222.66i		−	0.279592i
$612$		−	11906.4i		−	0.786421i
$613$	−1075.59			−0.0708692			−0.0354346	−	0.999372i	$-0.511282\pi$
$613$	−1075.59			−0.0708692			−0.0354346	+	0.999372i	$0.511282\pi$
$614$		−	8673.75i		−	0.570104i
$615$		−	1190.45i		−	0.0780544i
$616$			14992.1i			0.980596i
$617$	2079.21			0.135666			0.0678329	−	0.997697i	$-0.478392\pi$
$617$	2079.21			0.135666			0.0678329	+	0.997697i	$0.478392\pi$
$618$	−20960.1			−1.36430
$619$	2651.13			0.172145			0.0860727	−	0.996289i	$-0.472568\pi$
$619$	2651.13			0.172145			0.0860727	+	0.996289i	$0.472568\pi$
$620$	−16368.1			−1.06026
$621$		−	59.8876i		−	0.00386990i
$622$	−7794.95			−0.502491
$623$		−	17833.3i		−	1.14683i
$624$			4187.21i			0.268626i
$625$	−13850.1			−0.886408
$626$	15230.7			0.972429
$627$		−	886.863i		−	0.0564879i
$628$	5635.48			0.358090
$629$	23526.5	−	7608.17i	1.49135	−	0.482286i
$630$	28037.0			1.77305
$631$		−	16751.7i		−	1.05686i	−0.848978	−	0.528428i	$-0.822782\pi$
$631$		−	16751.7i		−	1.05686i	0.848978	−	0.528428i	$-0.177218\pi$
$632$	−147.390			−0.00927667
$633$	−9187.52			−0.576890
$634$			12022.9i			0.753142i
$635$			35.0427i			0.00218997i
$636$	7356.73			0.458669
$637$			24032.1i			1.49480i
$638$	−5945.38			−0.368934
$639$	−4007.82			−0.248117
$640$	−2075.31			−0.128178
$641$	24669.9			1.52013			0.760063	−	0.649849i	$-0.225168\pi$
$641$	24669.9			1.52013			0.760063	+	0.649849i	$0.225168\pi$
$642$		−	22327.1i		−	1.37256i
$643$			14373.3i			0.881537i	0.897621	+	0.440769i	$0.145294\pi$
$643$			14373.3i			0.881537i	−0.897621	+	0.440769i	$0.854706\pi$
$644$			11086.6i			0.678373i
$645$	−35847.0			−2.18833
$646$		−	451.184i		−	0.0274792i
$647$			12519.7i			0.760744i	0.924834	+	0.380372i	$0.124204\pi$
$647$			12519.7i			0.760744i	−0.924834	+	0.380372i	$0.875796\pi$
$648$			5811.68i			0.352321i
$649$		−	7173.49i		−	0.433874i
$650$	9811.64			0.592068
$651$			59237.7i			3.56637i
$652$			1139.10i			0.0684215i
$653$			29079.0i			1.74265i	0.490710	+	0.871323i	$0.336737\pi$
$653$			29079.0i			1.74265i	−0.490710	+	0.871323i	$0.663263\pi$
$654$	14013.0			0.837846
$655$	−15681.9			−0.935483
$656$	159.729			0.00950665
$657$	12957.1			0.769415
$658$		−	7574.31i		−	0.448750i
$659$	−1522.32			−0.0899868			−0.0449934	−	0.998987i	$-0.514327\pi$
$659$	−1522.32			−0.0899868			−0.0449934	+	0.998987i	$0.514327\pi$
$660$		−	28010.4i		−	1.65197i
$661$			6630.41i			0.390156i	0.980788	+	0.195078i	$0.0624960\pi$
$661$			6630.41i			0.390156i	−0.980788	+	0.195078i	$0.937504\pi$
$662$	−9310.11			−0.546598
$663$	−28751.3			−1.68418
$664$		−	9491.73i		−	0.554745i
$665$	1062.43			0.0619541
$666$	11603.9	−	3752.55i	0.675137	−	0.218331i
$667$	−4396.59			−0.255227
$668$			1486.57i			0.0861036i
$669$	39306.8			2.27158
$670$	−6969.27			−0.401861
$671$		−	32899.6i		−	1.89281i
$672$			7510.73i			0.431150i
$673$	−1772.58			−0.101527			−0.0507636	−	0.998711i	$-0.516166\pi$
$673$	−1772.58			−0.101527			−0.0507636	+	0.998711i	$0.516166\pi$
$674$		−	16119.3i		−	0.921204i
$675$	−95.0688			−0.00542104
$676$	−3723.66			−0.211860
$677$	−9712.68			−0.551386			−0.275693	−	0.961246i	$-0.588907\pi$
$677$	−9712.68			−0.551386			−0.275693	+	0.961246i	$0.588907\pi$
$678$	4827.32			0.273440
$679$		−	41188.0i		−	2.32791i
$680$		−	14250.0i		−	0.803624i
$681$			16033.3i			0.902197i
$682$	29642.1			1.66430
$683$			12231.5i			0.685250i	0.939472	+	0.342625i	$0.111316\pi$
$683$			12231.5i			0.685250i	−0.939472	+	0.342625i	$0.888684\pi$
$684$		−	222.536i		−	0.0124399i
$685$		−	6850.10i		−	0.382086i
$686$			21215.2i			1.18076i
$687$	9322.81			0.517740
$688$		−	4809.79i		−	0.266529i
$689$		−	8897.81i		−	0.491988i
$690$		−	20713.6i		−	1.14283i
$691$	−16265.8			−0.895485			−0.447743	−	0.894162i	$-0.647772\pi$
$691$	−16265.8			−0.895485			−0.447743	+	0.894162i	$0.647772\pi$
$692$	−5502.93			−0.302298
$693$	−50773.9			−2.78317
$694$	3525.53			0.192835
$695$			18029.9i			0.984049i
$696$	−2978.52			−0.162214
$697$			1096.77i			0.0596029i
$698$		−	9611.87i		−	0.521224i
$699$	31918.2			1.72712
$700$	17599.4			0.950280
$701$		−	8125.30i		−	0.437786i	−0.975749	−	0.218893i	$-0.929755\pi$
$701$		−	8125.30i		−	0.437786i	0.975749	−	0.218893i	$-0.0702446\pi$
$702$	−49.0704			−0.00263824
$703$	439.718	−	142.199i	0.0235907	−	0.00762895i
$704$	3758.31			0.201203
$705$			14151.5i			0.755993i
$706$	−18028.4			−0.961059
$707$	29165.5			1.55146
$708$		−	3593.78i		−	0.190766i
$709$			26830.0i			1.42119i	0.703603	+	0.710593i	$0.251573\pi$
$709$			26830.0i			1.42119i	−0.703603	+	0.710593i	$0.748427\pi$
$710$	−4796.69			−0.253545
$711$		−	499.168i		−	0.0263295i
$712$	−4470.57			−0.235311
$713$	21920.2			1.15136
$714$	−51572.1			−2.70314
$715$	−33878.0			−1.77198
$716$			6339.76i			0.330905i
$717$			25994.1i			1.35393i
$718$		−	26510.0i		−	1.37792i
$719$	−24401.8			−1.26570			−0.632848	−	0.774276i	$-0.718114\pi$
$719$	−24401.8			−1.26570			−0.632848	+	0.774276i	$0.718114\pi$
$720$		−	7028.49i		−	0.363801i
$721$			45472.5i			2.34880i
$722$			13709.6i			0.706672i
$723$		−	18407.2i		−	0.946848i
$724$	1415.58			0.0726651
$725$			6979.39i			0.357528i
$726$			31147.2i			1.59226i
$727$			13278.3i			0.677396i	0.940895	+	0.338698i	$0.109986\pi$
$727$			13278.3i			0.677396i	−0.940895	+	0.338698i	$0.890014\pi$
$728$	9084.06			0.462469
$729$	−19819.5			−1.00693
$730$	15507.5			0.786246
$731$	33026.3			1.67103
$732$		−	16482.1i		−	0.832234i
$733$	39550.6			1.99295			0.996477	−	0.0838666i	$-0.0267270\pi$
$733$	39550.6			1.99295			0.996477	+	0.0838666i	$0.0267270\pi$
$734$		−	18780.4i		−	0.944413i
$735$		−	80539.0i		−	4.04180i
$736$	2779.26			0.139191
$737$	12621.1			0.630806
$738$			540.957i			0.0269822i
$739$	−24896.5			−1.23929			−0.619643	−	0.784884i	$-0.712722\pi$
$739$	−24896.5			−1.23929			−0.619643	+	0.784884i	$0.712722\pi$
$740$	13887.9	−	4491.18i	0.689906	−	0.223107i
$741$	−537.373			−0.0266409
$742$		−	15960.3i		−	0.789649i
$743$	8026.80			0.396332			0.198166	−	0.980168i	$-0.436501\pi$
$743$	8026.80			0.396332			0.198166	+	0.980168i	$0.436501\pi$
$744$	14850.1			0.731763
$745$			16436.1i			0.808283i
$746$		−	8922.28i		−	0.437892i
$747$	32145.8			1.57450
$748$			25806.3i			1.26146i
$749$	−48438.2			−2.36301
$750$	−3070.18			−0.149476
$751$	−7202.61			−0.349969			−0.174985	−	0.984571i	$-0.555988\pi$
$751$	−7202.61			−0.349969			−0.174985	+	0.984571i	$0.555988\pi$
$752$	−1898.78			−0.0920763
$753$			53458.1i			2.58714i
$754$			3602.46i			0.173997i
$755$		−	53039.6i		−	2.55670i
$756$	−88.0191			−0.00423442
$757$			4093.73i			0.196551i	0.995159	+	0.0982756i	$0.0313327\pi$
$757$			4093.73i			0.196551i	−0.995159	+	0.0982756i	$0.968667\pi$
$758$		−	12737.8i		−	0.610368i
$759$			37511.5i			1.79392i
$760$		−	266.338i		−	0.0127120i
$761$	−33493.0			−1.59543			−0.797713	−	0.603038i	$-0.793957\pi$
$761$	−33493.0			−1.59543			−0.797713	+	0.603038i	$0.793957\pi$
$762$		−	31.7928i		−	0.00151146i
$763$		−	30400.9i		−	1.44244i
$764$			17591.2i			0.833021i
$765$	48260.9			2.28088
$766$	−12396.5			−0.584731
$767$	−4346.60			−0.204624
$768$	1882.84			0.0884650
$769$		−	6697.33i		−	0.314060i	−0.987594	−	0.157030i	$-0.949808\pi$
$769$		−	6697.33i		−	0.314060i	0.987594	−	0.157030i	$-0.0501919\pi$
$770$	−60767.9			−2.84406
$771$		−	34338.4i		−	1.60398i
$772$		−	88.4060i		−	0.00412150i
$773$	−1791.74			−0.0833692			−0.0416846	−	0.999131i	$-0.513272\pi$
$773$	−1791.74			−0.0833692			−0.0416846	+	0.999131i	$0.513272\pi$
$774$	16289.4			0.756474
$775$		−	34797.3i		−	1.61285i
$776$	−10325.3			−0.477649
$777$	−16254.0	−	50261.6i	−0.750461	−	2.32062i
$778$	20955.9			0.965689
$779$			20.4990i			0.000942817i
$780$	−16972.2			−0.779106
$781$	8686.63			0.397992
$782$			19083.7i			0.872673i
$783$		−	34.9056i		−	0.00159314i
$784$	10806.4			0.492272
$785$			22842.5i			1.03858i
$786$	14227.5			0.645646
$787$	−3527.23			−0.159761			−0.0798806	−	0.996804i	$-0.525454\pi$
$787$	−3527.23			−0.159761			−0.0798806	+	0.996804i	$0.525454\pi$
$788$	−2580.14			−0.116642
$789$	−21872.3			−0.986912
$790$		−	597.422i		−	0.0269055i
$791$		−	10472.8i		−	0.470757i
$792$			12728.3i			0.571063i
$793$	−19934.7			−0.892689
$794$			16732.7i			0.747884i
$795$			29819.4i			1.33029i
$796$		−	14812.1i		−	0.659547i
$797$		−	27148.7i		−	1.20659i	−0.797517	−	0.603297i	$-0.793853\pi$
$797$		−	27148.7i		−	1.20659i	0.797517	−	0.603297i	$-0.206147\pi$
$798$	−963.901			−0.0427591
$799$		−	13037.9i		−	0.577281i
$800$		−	4411.94i		−	0.194982i
$801$		−	15140.6i		−	0.667872i
$802$	6137.59			0.270232
$803$	−28083.5			−1.23418
$804$	6322.92			0.277354
$805$	−44937.7			−1.96751
$806$		−	17960.9i		−	0.784920i
$807$	5418.82			0.236371
$808$		−	7311.40i		−	0.318334i
$809$			3989.97i			0.173399i	0.996234	+	0.0866997i	$0.0276320\pi$
$809$			3989.97i			0.173399i	−0.996234	+	0.0866997i	$0.972368\pi$
$810$	−23556.7			−1.02185
$811$	−17909.3			−0.775438			−0.387719	−	0.921778i	$-0.626737\pi$
$811$	−17909.3			−0.775438			−0.387719	+	0.921778i	$0.626737\pi$
$812$			6461.84i			0.279268i
$813$	−41006.4			−1.76895
$814$	−25150.5	+	8133.36i	−1.08295	+	0.350214i
$815$	−4617.18			−0.198445
$816$			12928.4i			0.554640i
$817$	617.273			0.0264328
$818$	8701.73			0.371943
$819$			30765.2i			1.31260i
$820$			647.435i			0.0275725i
$821$	−11382.5			−0.483862			−0.241931	−	0.970293i	$-0.577781\pi$
$821$	−11382.5			−0.483862			−0.241931	+	0.970293i	$0.577781\pi$
$822$			6214.81i			0.263706i
$823$	−7645.96			−0.323841			−0.161921	−	0.986804i	$-0.551769\pi$
$823$	−7645.96			−0.323841			−0.161921	+	0.986804i	$0.551769\pi$
$824$	11399.4			0.481936
$825$	59547.8			2.51296
$826$	−7796.62			−0.328425
$827$			44324.9i			1.86376i	0.362769	+	0.931879i	$0.381831\pi$
$827$			44324.9i			1.86376i	−0.362769	+	0.931879i	$0.618169\pi$
$828$			9412.56i			0.395059i
$829$		−	7032.14i		−	0.294616i	−0.989091	−	0.147308i	$-0.952939\pi$
$829$		−	7032.14i		−	0.294616i	0.989091	−	0.147308i	$-0.0470608\pi$
$830$	38473.2			1.60895
$831$			4252.13i			0.177503i
$832$		−	2277.25i		−	0.0948913i
$833$			74201.4i			3.08635i
$834$		−	16357.8i		−	0.679165i
$835$	−6025.58			−0.249729
$836$			482.328i			0.0199542i
$837$			174.030i			0.00718681i
$838$			28544.3i			1.17666i
$839$	30443.8			1.25273			0.626363	−	0.779532i	$-0.284543\pi$
$839$	30443.8			1.25273			0.626363	+	0.779532i	$0.284543\pi$
$840$	−30443.6			−1.25048
$841$	21826.4			0.894930
$842$	19284.1			0.789282
$843$			41046.1i			1.67699i
$844$	4996.72			0.203784
$845$		−	15093.3i		−	0.614466i
$846$		−	6430.63i		−	0.261335i
$847$	67573.1			2.74125
$848$	−4001.03			−0.162023
$849$		−	19127.0i		−	0.773187i
$850$	30294.4			1.22246
$851$	−18598.7	+	6014.59i	−0.749184	+	0.242277i
$852$	4351.83			0.174990
$853$			31565.3i			1.26703i	0.773732	+	0.633514i	$0.218388\pi$
$853$			31565.3i			1.26703i	−0.773732	+	0.633514i	$0.781612\pi$
$854$	−35757.5			−1.43278
$855$	902.013			0.0360798
$856$			12142.8i			0.484851i
$857$		−	11526.4i		−	0.459433i	−0.973258	−	0.229717i	$-0.926220\pi$
$857$		−	11526.4i		−	0.459433i	0.973258	−	0.229717i	$-0.0737799\pi$
$858$	30736.0			1.22297
$859$		−	36604.8i		−	1.45395i	−0.686666	−	0.726973i	$-0.740927\pi$
$859$		−	36604.8i		−	1.45395i	0.686666	−	0.726973i	$-0.259073\pi$
$860$	19495.7			0.773022
$861$	2343.13			0.0927451
$862$	4187.09			0.165444
$863$	30919.9			1.21961			0.609806	−	0.792551i	$-0.291247\pi$
$863$	30919.9			1.21961			0.609806	+	0.792551i	$0.291247\pi$
$864$			22.0652i			0.000868836i
$865$		−	22305.3i		−	0.876765i
$866$		−	8984.25i		−	0.352537i
$867$	−52638.3			−2.06193
$868$		−	32217.0i		−	1.25981i
$869$			1081.91i			0.0422339i
$870$		−	12073.0i		−	0.470474i
$871$		−	7647.44i		−	0.297501i
$872$	−7621.09			−0.295966
$873$		−	34968.8i		−	1.35569i
$874$			356.680i			0.0138042i
$875$			6660.68i			0.257339i
$876$	−14069.3			−0.542646
$877$	48183.7			1.85524			0.927622	−	0.373520i	$-0.121849\pi$
$877$	48183.7			1.85524			0.927622	+	0.373520i	$0.121849\pi$
$878$	−16895.7			−0.649434
$879$	53562.9			2.05532
$880$			15233.7i			0.583555i
$881$	2870.31			0.109765			0.0548826	−	0.998493i	$-0.482522\pi$
$881$	2870.31			0.109765			0.0548826	+	0.998493i	$0.482522\pi$
$882$			36598.1i			1.39719i
$883$			15632.4i			0.595777i	0.954601	+	0.297888i	$0.0962823\pi$
$883$			15632.4i			0.595777i	−0.954601	+	0.297888i	$0.903718\pi$
$884$	15636.7			0.594930
$885$	14566.8			0.553286
$886$		−	29403.8i		−	1.11494i
$887$	23561.9			0.891918			0.445959	−	0.895054i	$-0.352863\pi$
$887$	23561.9			0.891918			0.445959	+	0.895054i	$0.352863\pi$
$888$	−12599.9	+	4074.66i	−0.476155	+	0.153983i
$889$	−68.9737			−0.00260214
$890$		−	18120.7i		−	0.682482i
$891$	42660.3			1.60401
$892$	−21377.4			−0.802430
$893$		−	243.683i		−	0.00913162i
$894$		−	14911.7i		−	0.557856i
$895$	−25697.2			−0.959735
$896$		−	4084.78i		−	0.152302i
$897$	22729.2			0.846048
$898$	−30794.2			−1.14434
$899$	12776.3			0.473984
$900$	14942.0			0.553408
$901$		−	27472.9i		−	1.01582i
$902$		−	1172.48i		−	0.0432809i
$903$		−	70556.8i		−	2.60020i
$904$	−2625.38			−0.0965917
$905$			5737.82i			0.210753i
$906$			48120.5i			1.76457i
$907$		−	19657.3i		−	0.719635i	−0.933023	−	0.359817i	$-0.882839\pi$
$907$		−	19657.3i		−	0.719635i	0.933023	−	0.359817i	$-0.117161\pi$
$908$		−	8719.84i		−	0.318698i
$909$	24761.7			0.903512
$910$			36820.8i			1.34132i
$911$			38877.1i			1.41389i	0.707268	+	0.706946i	$0.249928\pi$
$911$			38877.1i			1.41389i	−0.707268	+	0.706946i	$0.750072\pi$
$912$			241.637i			0.00877348i
$913$	−69673.6			−2.52558
$914$	7359.61			0.266339
$915$	66807.5			2.41376
$916$	−5070.30			−0.182890
$917$		−	30866.2i		−	1.11155i
$918$	−151.510			−0.00544725
$919$		−	17060.0i		−	0.612358i	−0.951974	−	0.306179i	$-0.900949\pi$
$919$		−	17060.0i		−	0.612358i	0.951974	−	0.306179i	$-0.0990507\pi$
$920$			11265.3i			0.403701i
$921$	−31897.0			−1.14120
$922$	−18183.2			−0.649492
$923$		−	5263.45i		−	0.187701i
$924$	55132.1			1.96289
$925$	9547.89	+	29524.6i	0.339387	+	1.04947i
$926$	17144.8			0.608436
$927$			38606.4i			1.36785i
$928$	1619.90			0.0573014
$929$	−4918.14			−0.173691			−0.0868455	−	0.996222i	$-0.527679\pi$
$929$	−4918.14			−0.173691			−0.0868455	+	0.996222i	$0.527679\pi$
$930$			60192.6i			2.12236i
$931$			1386.85i			0.0488208i
$932$	−17359.0			−0.610100
$933$			28665.3i			1.00585i
$934$	−2251.94			−0.0788925
$935$	−104602.			−3.65865
$936$	7712.42			0.269325
$937$	−8486.92			−0.295897			−0.147949	−	0.988995i	$-0.547267\pi$
$937$	−8486.92			−0.295897			−0.147949	+	0.988995i	$0.547267\pi$
$938$		−	13717.4i		−	0.477495i
$939$		−	56009.6i		−	1.94654i
$940$		−	7696.40i		−	0.267052i
$941$	43879.9			1.52013			0.760067	−	0.649845i	$-0.225166\pi$
$941$	43879.9			1.52013			0.760067	+	0.649845i	$0.225166\pi$
$942$		−	20724.1i		−	0.716801i
$943$		−	867.046i		−	0.0299416i
$944$			1954.51i			0.0673876i
$945$		−	356.771i		−	0.0122812i
$946$	−35306.0			−1.21342
$947$			7695.01i			0.264049i	0.991246	+	0.132024i	$0.0421477\pi$
$947$			7695.01i			0.264049i	−0.991246	+	0.132024i	$0.957852\pi$
$948$			542.015i			0.0185694i
$949$			17016.5i			0.582065i
$950$	566.214			0.0193373
$951$	44213.4			1.50759
$952$	28048.0			0.954874
$953$	4682.63			0.159166			0.0795830	−	0.996828i	$-0.474641\pi$
$953$	4682.63			0.159166			0.0795830	+	0.996828i	$0.474641\pi$
$954$		−	13550.4i		−	0.459863i
$955$	−71303.2			−2.41604
$956$		−	14137.1i		−	0.478271i
$957$			21863.7i			0.738508i
$958$	−30495.1			−1.02845
$959$	13482.9			0.453999
$960$			7631.79i			0.256578i
$961$	−33908.0			−1.13820
$962$	4928.21	+	15239.3i	0.165168	+	0.510744i
$963$	−41124.3			−1.37613
$964$			10010.9i			0.334471i
$965$	358.340			0.0119537
$966$	40770.0			1.35792
$967$			33949.2i			1.12899i	0.825437	+	0.564494i	$0.190929\pi$
$967$			33949.2i			1.12899i	−0.825437	+	0.564494i	$0.809071\pi$
$968$		−	16939.7i		−	0.562460i
$969$	−1659.19			−0.0550061
$970$		−	41851.9i		−	1.38534i
$971$	12661.0			0.418445			0.209222	−	0.977868i	$-0.432907\pi$
$971$	12661.0			0.418445			0.209222	+	0.977868i	$0.432907\pi$
$972$	21446.5			0.707712
$973$	−35487.8			−1.16926
$974$	−9902.55			−0.325768
$975$		−	36081.5i		−	1.18516i
$976$			8963.93i			0.293984i
$977$		−	35517.4i		−	1.16305i	−0.813528	−	0.581525i	$-0.802456\pi$
$977$		−	35517.4i		−	1.16305i	0.813528	−	0.581525i	$-0.197544\pi$
$978$	4188.97			0.136962
$979$			32816.0i			1.07130i
$980$			43801.9i			1.42775i
$981$		−	25810.5i		−	0.840026i
$982$		−	20490.8i		−	0.665873i
$983$	48342.4			1.56855			0.784275	−	0.620414i	$-0.213035\pi$
$983$	48342.4			1.56855			0.784275	+	0.620414i	$0.213035\pi$
$984$		−	587.390i		−	0.0190298i
$985$		−	10458.2i		−	0.338300i
$986$			11123.0i			0.359257i
$987$	−27853.9			−0.898278
$988$	292.255			0.00941080
$989$	−26108.7			−0.839442
$990$	−51592.3			−1.65627
$991$		−	20556.2i		−	0.658920i	−0.944170	−	0.329460i	$-0.893133\pi$
$991$		−	20556.2i		−	0.658920i	0.944170	−	0.329460i	$-0.106867\pi$
$992$	−8076.37			−0.258493
$993$			34237.2i			1.09414i
$994$		−	9441.20i		−	0.301264i
$995$	60038.4			1.91291
$996$	−34905.1			−1.11045
$997$		−	31217.1i		−	0.991629i	−0.868428	−	0.495815i	$-0.834870\pi$
$997$		−	31217.1i		−	0.991629i	0.868428	−	0.495815i	$-0.165130\pi$
$998$	297.538			0.00943728
$999$	−47.7514	−	147.660i	−0.00151230	−	0.00467643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.b.a.73.9	yes	10
3.2	odd	2		666.4.c.d.73.4		10
4.3	odd	2		592.4.g.d.369.3		10
37.36	even	2	inner	74.4.b.a.73.4	✓	10
111.110	odd	2		666.4.c.d.73.7		10
148.147	odd	2		592.4.g.d.369.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.b.a.73.4	✓	10	37.36	even	2	inner
74.4.b.a.73.9	yes	10	1.1	even	1	trivial
592.4.g.d.369.3		10	4.3	odd	2
592.4.g.d.369.4		10	148.147	odd	2
666.4.c.d.73.4		10	3.2	odd	2
666.4.c.d.73.7		10	111.110	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)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +7.35485 q^{3} -4.00000 q^{4} -16.2134i q^{5} +14.7097i q^{6} +31.9123 q^{7} -8.00000i q^{8} +27.0938 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +7.35485 q^{3} -4.00000 q^{4} -16.2134i q^{5} +14.7097i q^{6} +31.9123 q^{7} -8.00000i q^{8} +27.0938 q^{9} +32.4267 q^{10} -58.7236 q^{11} -29.4194 q^{12} +35.5821i q^{13} +63.8247i q^{14} -119.247i q^{15} +16.0000 q^{16} +109.863i q^{17} +54.1875i q^{18} +2.05339i q^{19} +64.8535i q^{20} +234.710 q^{21} -117.447i q^{22} -86.8518i q^{23} -58.8388i q^{24} -137.873 q^{25} -71.1642 q^{26} +0.689538 q^{27} -127.649 q^{28} -50.6218i q^{29} +238.494 q^{30} +252.387i q^{31} +32.0000i q^{32} -431.903 q^{33} -219.727 q^{34} -517.406i q^{35} -108.375 q^{36} +(-69.2512 - 214.143i) q^{37} -4.10677 q^{38} +261.701i q^{39} -129.707 q^{40} +9.98305 q^{41} +469.421i q^{42} -300.612i q^{43} +234.894 q^{44} -439.281i q^{45} +173.704 q^{46} -118.674 q^{47} +117.678 q^{48} +675.397 q^{49} -275.746i q^{50} +808.028i q^{51} -142.328i q^{52} -250.064 q^{53} +1.37908i q^{54} +952.107i q^{55} -255.299i q^{56} +15.1023i q^{57} +101.244 q^{58} +122.157i q^{59} +476.987i q^{60} +560.246i q^{61} -504.773 q^{62} +864.625 q^{63} -64.0000 q^{64} +576.906 q^{65} -863.806i q^{66} -214.924 q^{67} -439.453i q^{68} -638.781i q^{69} +1034.81 q^{70} -147.924 q^{71} -216.750i q^{72} +478.233 q^{73} +(428.286 - 138.502i) q^{74} -1014.04 q^{75} -8.21354i q^{76} -1874.01 q^{77} -523.402 q^{78} -18.4237i q^{79} -259.414i q^{80} -726.460 q^{81} +19.9661i q^{82} +1186.47 q^{83} -938.841 q^{84} +1781.25 q^{85} +601.224 q^{86} -372.315i q^{87} +469.789i q^{88} -558.821i q^{89} +878.562 q^{90} +1135.51i q^{91} +347.407i q^{92} +1856.26i q^{93} -237.347i q^{94} +33.2923 q^{95} +235.355i q^{96} -1290.66i q^{97} +1350.79i q^{98} -1591.04 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9}+O(q^{10}) \) 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

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