LMFDB - Embedded newform 27.4.e.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, 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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	27.13
Dual form			27.4.e.a.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0518956 - 0.294314i) q^{2} +(-2.82128 + 4.36353i) q^{3} +(7.43361 - 2.70561i) q^{4} +(15.3604 + 12.8889i) q^{5} +(1.43066 + 0.603897i) q^{6} +(-20.1945 - 7.35018i) q^{7} +(-2.37749 - 4.11794i) q^{8} +(-11.0807 - 24.6215i) q^{9} +O(q^{10})$	\(q+(-0.0518956 - 0.294314i) q^{2} +(-2.82128 + 4.36353i) q^{3} +(7.43361 - 2.70561i) q^{4} +(15.3604 + 12.8889i) q^{5} +(1.43066 + 0.603897i) q^{6} +(-20.1945 - 7.35018i) q^{7} +(-2.37749 - 4.11794i) q^{8} +(-11.0807 - 24.6215i) q^{9} +(2.99626 - 5.18968i) q^{10} +(0.558890 - 0.468965i) q^{11} +(-9.16632 + 40.0701i) q^{12} +(5.34792 - 30.3295i) q^{13} +(-1.11526 + 6.32496i) q^{14} +(-99.5773 + 30.6623i) q^{15} +(47.3909 - 39.7657i) q^{16} +(0.666388 - 1.15422i) q^{17} +(-6.67142 + 4.53896i) q^{18} +(-34.7473 - 60.1840i) q^{19} +(149.056 + 54.2519i) q^{20} +(89.0470 - 67.3821i) q^{21} +(-0.167027 - 0.140152i) q^{22} +(-110.791 + 40.3246i) q^{23} +(24.6763 + 1.24362i) q^{24} +(48.1122 + 272.858i) q^{25} -9.20396 q^{26} +(138.698 + 21.1133i) q^{27} -170.005 q^{28} +(-15.9844 - 90.6519i) q^{29} +(14.1920 + 27.7158i) q^{30} +(175.726 - 63.9590i) q^{31} +(-43.3032 - 36.3357i) q^{32} +(0.469551 + 3.76182i) q^{33} +(-0.374285 - 0.136229i) q^{34} +(-215.460 - 373.187i) q^{35} +(-148.986 - 153.047i) q^{36} +(-74.3188 + 128.724i) q^{37} +(-15.9098 + 13.3499i) q^{38} +(117.256 + 108.904i) q^{39} +(16.5565 - 93.8966i) q^{40} +(-55.1187 + 312.593i) q^{41} +(-24.4527 - 22.7110i) q^{42} +(-220.661 + 185.157i) q^{43} +(2.88574 - 4.99824i) q^{44} +(147.140 - 521.015i) q^{45} +(17.6177 + 30.5147i) q^{46} +(19.8826 + 7.23668i) q^{47} +(39.8154 + 318.982i) q^{48} +(91.0377 + 76.3897i) q^{49} +(77.8093 - 28.3203i) q^{50} +(3.15639 + 6.16418i) q^{51} +(-42.3057 - 239.928i) q^{52} +136.732 q^{53} +(-0.983887 - 41.9166i) q^{54} +14.6293 q^{55} +(17.7446 + 100.634i) q^{56} +(360.646 + 18.1757i) q^{57} +(-25.8506 + 9.40886i) q^{58} +(36.7754 + 30.8583i) q^{59} +(-657.259 + 497.349i) q^{60} +(509.543 + 185.458i) q^{61} +(-27.9435 - 48.3995i) q^{62} +(42.7965 + 578.663i) q^{63} +(239.011 - 413.979i) q^{64} +(473.062 - 396.946i) q^{65} +(1.08279 - 0.333417i) q^{66} +(-15.9741 + 90.5935i) q^{67} +(1.83080 - 10.3830i) q^{68} +(136.615 - 597.206i) q^{69} +(-98.6529 + 82.7796i) q^{70} +(-531.589 + 920.739i) q^{71} +(-75.0455 + 104.167i) q^{72} +(-342.332 - 592.936i) q^{73} +(41.7421 + 15.1929i) q^{74} +(-1326.36 - 559.871i) q^{75} +(-421.132 - 353.372i) q^{76} +(-14.7335 + 5.36254i) q^{77} +(25.9670 - 40.1617i) q^{78} +(-116.266 - 659.375i) q^{79} +1240.48 q^{80} +(-483.436 + 545.647i) q^{81} +94.8612 q^{82} +(96.8709 + 549.382i) q^{83} +(479.631 - 741.819i) q^{84} +(25.1126 - 9.14025i) q^{85} +(65.9457 + 55.3350i) q^{86} +(440.658 + 186.007i) q^{87} +(-3.25992 - 1.18652i) q^{88} +(-269.288 - 466.421i) q^{89} +(-160.978 - 16.2671i) q^{90} +(-330.926 + 573.181i) q^{91} +(-714.474 + 599.515i) q^{92} +(-216.686 + 947.232i) q^{93} +(1.09804 - 6.22729i) q^{94} +(241.975 - 1372.31i) q^{95} +(280.723 - 86.4413i) q^{96} +(226.888 - 190.381i) q^{97} +(17.7581 - 30.7580i) q^{98} +(-17.7395 - 8.56426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0518956	−	0.294314i	−0.0183479	−	0.104056i	0.974259	−	0.225434i	$-0.0723799\pi$
$2$	−0.0518956	−	0.294314i	−0.0183479	−	0.104056i	−0.992606	+	0.121378i	$0.961269\pi$
$3$	−2.82128	+	4.36353i	−0.542956	+	0.839761i
$3$	−2.82128	+	4.36353i	−0.542956	+	0.839761i
$4$	7.43361	−	2.70561i	0.929202	−	0.338202i
$5$	15.3604	+	12.8889i	1.37388	+	1.15282i	0.971416	+	0.237385i	$0.0762902\pi$
$5$	15.3604	+	12.8889i	1.37388	+	1.15282i	0.402463	+	0.915436i	$0.368154\pi$
$6$	1.43066	+	0.603897i	0.0973441	+	0.0410900i
$7$	−20.1945	−	7.35018i	−1.09040	−	0.396872i	−0.266630	−	0.963799i	$-0.585910\pi$
$7$	−20.1945	−	7.35018i	−1.09040	−	0.396872i	−0.823768	+	0.566927i	$0.808132\pi$
$8$	−2.37749	−	4.11794i	−0.105071	−	0.181989i
$9$	−11.0807	−	24.6215i	−0.410397	−	0.911907i
$10$	2.99626	−	5.18968i	0.0947501	−	0.164112i
$11$	0.558890	−	0.468965i	0.0153193	−	0.0128544i	−0.635096	−	0.772433i	$-0.719039\pi$
$11$	0.558890	−	0.468965i	0.0153193	−	0.0128544i	0.650415	+	0.759579i	$0.274595\pi$
$12$	−9.16632	+	40.0701i	−0.220507	+	0.963936i
$13$	5.34792	−	30.3295i	0.114096	−	0.647069i	−0.873098	−	0.487545i	$-0.837893\pi$
$13$	5.34792	−	30.3295i	0.114096	−	0.647069i	0.987194	−	0.159525i	$-0.0509962\pi$
$14$	−1.11526	+	6.32496i	−0.0212904	+	0.120744i
$15$	−99.5773	+	30.6623i	−1.71405	+	0.527798i
$16$	47.3909	−	39.7657i	0.740483	−	0.621339i
$17$	0.666388	−	1.15422i	0.00950722	−	0.0164670i	−0.861233	−	0.508211i	$-0.830307\pi$
$17$	0.666388	−	1.15422i	0.00950722	−	0.0164670i	0.870740	+	0.491744i	$0.163640\pi$
$18$	−6.67142	+	4.53896i	−0.0873594	+	0.0594357i
$19$	−34.7473	−	60.1840i	−0.419556	−	0.726693i	0.576338	−	0.817211i	$-0.304481\pi$
$19$	−34.7473	−	60.1840i	−0.419556	−	0.726693i	−0.995895	+	0.0905182i	$0.971148\pi$
$20$	149.056	+	54.2519i	1.66650	+	0.606555i
$21$	89.0470	−	67.3821i	0.925317	−	0.700189i
$22$	−0.167027	−	0.140152i	−0.00161865	−	0.00135821i
$23$	−110.791	+	40.3246i	−1.00441	+	0.365577i	−0.791285	−	0.611447i	$-0.790588\pi$
$23$	−110.791	+	40.3246i	−1.00441	+	0.365577i	−0.213129	+	0.977024i	$0.568365\pi$
$24$	24.6763	+	1.24362i	0.209876	+	0.0105772i
$25$	48.1122	+	272.858i	0.384898	+	2.18286i
$26$	−9.20396			−0.0694248
$27$	138.698	+	21.1133i	0.988611	+	0.150491i
$28$	−170.005			−1.14742
$29$	−15.9844	−	90.6519i	−0.102353	−	0.580470i	−0.992245	−	0.124299i	$-0.960332\pi$
$29$	−15.9844	−	90.6519i	−0.102353	−	0.580470i	0.889892	−	0.456171i	$-0.150779\pi$
$30$	14.1920	+	27.7158i	0.0863696	+	0.168673i
$31$	175.726	−	63.9590i	1.01811	−	0.370561i	0.221566	−	0.975145i	$-0.428883\pi$
$31$	175.726	−	63.9590i	1.01811	−	0.370561i	0.796541	+	0.604585i	$0.206661\pi$
$32$	−43.3032	−	36.3357i	−0.239219	−	0.200728i
$33$	0.469551	+	3.76182i	0.00247692	+	0.0198439i
$34$	−0.374285	−	0.136229i	−0.00188792	−	0.000687148i
$35$	−215.460	−	373.187i	−1.04055	−	1.80229i
$36$	−148.986	−	153.047i	−0.689750	−	0.708549i
$37$	−74.3188	+	128.724i	−0.330214	+	0.571948i	−0.982554	−	0.185979i	$-0.940454\pi$
$37$	−74.3188	+	128.724i	−0.330214	+	0.571948i	0.652339	+	0.757927i	$0.273788\pi$
$38$	−15.9098	+	13.3499i	−0.0679187	+	0.0569906i
$39$	117.256	+	108.904i	0.481435	+	0.447144i
$40$	16.5565	−	93.8966i	0.0654453	−	0.371159i
$41$	−55.1187	+	312.593i	−0.209953	+	1.19070i	0.679499	+	0.733677i	$0.262197\pi$
$41$	−55.1187	+	312.593i	−0.209953	+	1.19070i	−0.889452	+	0.457028i	$0.848914\pi$
$42$	−24.4527	−	22.7110i	−0.0898364	−	0.0834377i
$43$	−220.661	+	185.157i	−0.782571	+	0.656655i	−0.943895	−	0.330246i	$-0.892868\pi$
$43$	−220.661	+	185.157i	−0.782571	+	0.656655i	0.161324	+	0.986902i	$0.448424\pi$
$44$	2.88574	−	4.99824i	0.00988730	−	0.0171253i
$45$	147.140	−	521.015i	0.487431	−	1.72596i
$46$	17.6177	+	30.5147i	0.0564692	+	0.0978076i
$47$	19.8826	+	7.23668i	0.0617059	+	0.0224591i	0.372689	−	0.927956i	$-0.378436\pi$
$47$	19.8826	+	7.23668i	0.0617059	+	0.0224591i	−0.310983	+	0.950416i	$0.600658\pi$
$48$	39.8154	+	318.982i	0.119726	+	0.959189i
$49$	91.0377	+	76.3897i	0.265416	+	0.222711i
$50$	77.8093	−	28.3203i	0.220078	−	0.0801018i
$51$	3.15639	+	6.16418i	0.00866633	+	0.0169247i
$52$	−42.3057	−	239.928i	−0.112822	−	0.639845i
$53$	136.732			0.354369			0.177184	−	0.984178i	$-0.443301\pi$
$53$	136.732			0.354369			0.177184	+	0.984178i	$0.443301\pi$
$54$	−0.983887	−	41.9166i	−0.00247945	−	0.105632i
$55$	14.6293			0.0358656
$56$	17.7446	+	100.634i	0.0423432	+	0.240140i
$57$	360.646	+	18.1757i	0.838049	+	0.0422356i
$58$	−25.8506	+	9.40886i	−0.0585234	+	0.0213008i
$59$	36.7754	+	30.8583i	0.0811484	+	0.0680916i	0.682460	−	0.730923i	$-0.260910\pi$
$59$	36.7754	+	30.8583i	0.0811484	+	0.0680916i	−0.601311	+	0.799015i	$0.705355\pi$
$60$	−657.259	+	497.349i	−1.41420	+	1.07013i
$61$	509.543	+	185.458i	1.06951	+	0.389271i	0.815994	−	0.578060i	$-0.196190\pi$
$61$	509.543	+	185.458i	1.06951	+	0.389271i	0.253518	+	0.967331i	$0.418412\pi$
$62$	−27.9435	−	48.3995i	−0.0572391	−	0.0991410i
$63$	42.7965	+	578.663i	0.0855849	+	1.15722i
$64$	239.011	−	413.979i	0.466818	−	0.808553i
$65$	473.062	−	396.946i	0.902709	−	0.757463i
$66$	1.08279	−	0.333417i	0.00201943	−	0.000621831i
$67$	−15.9741	+	90.5935i	−0.0291275	+	0.165190i	−0.995902	−	0.0904411i	$-0.971172\pi$
$67$	−15.9741	+	90.5935i	−0.0291275	+	0.165190i	0.966774	+	0.255632i	$0.0822834\pi$
$68$	1.83080	−	10.3830i	0.00326496	−	0.0185165i
$69$	136.615	−	597.206i	0.238356	−	1.04196i
$70$	−98.6529	+	82.7796i	−0.168447	+	0.141344i
$71$	−531.589	+	920.739i	−0.888563	+	1.53904i	−0.0469890	+	0.998895i	$0.514963\pi$
$71$	−531.589	+	920.739i	−0.888563	+	1.53904i	−0.841574	+	0.540141i	$0.818371\pi$
$72$	−75.0455	+	104.167i	−0.122836	+	0.170503i
$73$	−342.332	−	592.936i	−0.548862	−	0.950657i	−0.998353	−	0.0573721i	$-0.981728\pi$
$73$	−342.332	−	592.936i	−0.548862	−	0.950657i	0.449491	−	0.893285i	$-0.351605\pi$
$74$	41.7421	+	15.1929i	0.0655733	+	0.0238667i
$75$	−1326.36	−	559.871i	−2.04207	−	0.861978i
$76$	−421.132	−	353.372i	−0.635621	−	0.533350i
$77$	−14.7335	+	5.36254i	−0.0218056	+	0.00793660i
$78$	25.9670	−	40.1617i	0.0376946	−	0.0583002i
$79$	−116.266	−	659.375i	−0.165581	−	0.939056i	−0.948463	−	0.316887i	$-0.897363\pi$
$79$	−116.266	−	659.375i	−0.165581	−	0.939056i	0.782882	−	0.622170i	$-0.213749\pi$
$80$	1240.48			1.73363
$81$	−483.436	+	545.647i	−0.663149	+	0.748487i
$82$	94.8612			0.127752
$83$	96.8709	+	549.382i	0.128108	+	0.726537i	0.979413	+	0.201866i	$0.0647005\pi$
$83$	96.8709	+	549.382i	0.128108	+	0.726537i	−0.851305	+	0.524671i	$0.824188\pi$
$84$	479.631	−	741.819i	0.623001	−	0.963561i
$85$	25.1126	−	9.14025i	0.0320453	−	0.0116635i
$86$	65.9457	+	55.3350i	0.0826873	+	0.0693829i
$87$	440.658	+	186.007i	0.543029	+	0.229218i
$88$	−3.25992	−	1.18652i	−0.00394897	−	0.00143731i
$89$	−269.288	−	466.421i	−0.320724	−	0.555511i	0.659913	−	0.751342i	$-0.270593\pi$
$89$	−269.288	−	466.421i	−0.320724	−	0.555511i	−0.980638	+	0.195831i	$0.937260\pi$
$90$	−160.978	−	16.2671i	−0.188540	−	0.0190523i
$91$	−330.926	+	573.181i	−0.381214	+	0.660282i
$92$	−714.474	+	599.515i	−0.809664	+	0.679389i
$93$	−216.686	+	947.232i	−0.241605	+	1.05616i
$94$	1.09804	−	6.22729i	0.00120483	−	0.00683294i
$95$	241.975	−	1372.31i	0.261327	−	1.48206i
$96$	280.723	−	86.4413i	0.298449	−	0.0918998i
$97$	226.888	−	190.381i	0.237494	−	0.199281i	−0.516271	−	0.856426i	$-0.672680\pi$
$97$	226.888	−	190.381i	0.237494	−	0.199281i	0.753765	+	0.657144i	$0.228236\pi$
$98$	17.7581	−	30.7580i	0.0183045	−	0.0317044i
$99$	−17.7395	−	8.56426i	−0.0180090	−	0.00869434i
$100$	1095.90	+	1898.15i	1.09590	+	1.89815i
$101$	−1607.63	−	585.129i	−1.58381	−	0.576460i	−0.607783	−	0.794103i	$-0.707941\pi$
$101$	−1607.63	−	585.129i	−1.58381	−	0.576460i	−0.976028	+	0.217643i	$0.930163\pi$
$102$	1.65040	−	1.24886i	0.00160210	−	0.00121231i
$103$	507.261	+	425.643i	0.485262	+	0.407183i	0.852325	−	0.523013i	$-0.175192\pi$
$103$	507.261	+	425.643i	0.485262	+	0.407183i	−0.367063	+	0.930196i	$0.619637\pi$
$104$	−137.610	+	50.0859i	−0.129748	+	0.0472243i
$105$	2236.28	+	112.703i	2.07847	+	0.104750i
$106$	−7.09577	−	40.2421i	−0.00650191	−	0.0368742i
$107$	877.064			0.792421			0.396210	−	0.918160i	$-0.370325\pi$
$107$	877.064			0.792421			0.396210	+	0.918160i	$0.370325\pi$
$108$	1088.15	−	218.316i	0.969516	−	0.194514i
$109$	1106.66			0.972464			0.486232	−	0.873830i	$-0.338371\pi$
$109$	1106.66			0.972464			0.486232	+	0.873830i	$0.338371\pi$
$110$	−0.759194	−	4.30560i	−0.000658057	−	0.00373203i
$111$	−352.016	−	687.459i	−0.301008	−	0.587844i
$112$	−1249.32	+	454.715i	−1.05401	+	0.383630i
$113$	512.305	+	429.875i	0.426492	+	0.357870i	0.830626	−	0.556830i	$-0.187983\pi$
$113$	512.305	+	429.875i	0.426492	+	0.357870i	−0.404134	+	0.914700i	$0.632427\pi$
$114$	−13.3666	−	107.087i	−0.0109815	−	0.0879789i
$115$	−2221.54	−	808.574i	−1.80139	−	0.655651i
$116$	−364.091	−	630.623i	−0.291422	−	0.504758i
$117$	−806.017	+	204.399i	−0.636892	+	0.161510i
$118$	7.17355	−	12.4249i	0.00559643	−	0.00969330i
$119$	−21.9410	+	18.4107i	−0.0169020	+	0.0141824i
$120$	363.010	+	337.154i	0.276151	+	0.256482i
$121$	−231.033	+	1310.25i	−0.173579	+	0.984414i
$122$	28.1401	−	159.590i	0.0208826	−	0.118431i
$123$	−1208.50	−	1122.43i	−0.885912	−	0.822811i
$124$	1133.23	−	950.894i	0.820703	−	0.688651i
$125$	−1524.60	+	2640.68i	−1.09091	+	1.88952i
$126$	168.088	−	42.6257i	0.118845	−	0.0301381i
$127$	−451.431	−	781.902i	−0.315418	−	0.546319i	0.664109	−	0.747636i	$-0.268811\pi$
$127$	−451.431	−	781.902i	−0.315418	−	0.546319i	−0.979526	+	0.201317i	$0.935478\pi$
$128$	−559.198	−	203.531i	−0.386145	−	0.140545i
$129$	−185.388	−	1485.24i	−0.126531	−	1.01371i
$130$	−141.377	−	118.629i	−0.0953812	−	0.0800344i
$131$	1798.84	−	654.724i	1.19973	−	0.436668i	0.336603	−	0.941647i	$-0.390722\pi$
$131$	1798.84	−	654.724i	1.19973	−	0.436668i	0.863132	+	0.504979i	$0.168500\pi$
$132$	13.6685	+	26.6935i	0.00901279	+	0.0176013i
$133$	259.339	+	1470.78i	0.169079	+	0.958895i
$134$	27.4920			0.0177235
$135$	1858.34	+	2111.98i	1.18474	+	1.34645i
$136$	−6.33733			−0.00399574
$137$	−458.731	−	2601.59i	−0.286073	−	1.62240i	−0.701427	−	0.712741i	$-0.747454\pi$
$137$	−458.731	−	2601.59i	−0.286073	−	1.62240i	0.415354	−	0.909660i	$-0.363658\pi$
$138$	−182.856	−	9.21550i	−0.112795	−	0.00568460i
$139$	−155.790	+	56.7028i	−0.0950641	+	0.0346005i	−0.389114	−	0.921189i	$-0.627219\pi$
$139$	−155.790	+	56.7028i	−0.0950641	+	0.0346005i	0.294050	+	0.955790i	$0.404997\pi$
$140$	−2611.34	−	2191.18i	−1.57642	−	1.32277i
$141$	−87.6720	+	66.3416i	−0.0523639	+	0.0396239i
$142$	298.574	+	108.672i	0.176449	+	0.0642222i
$143$	−11.2346	−	19.4589i	−0.00656982	−	0.0113793i
$144$	−1504.22	−	726.203i	−0.870495	−	0.420256i
$145$	922.879	−	1598.47i	0.528558	−	0.915490i
$146$	−156.744	+	131.524i	−0.0888510	+	0.0745548i
$147$	−590.172	+	181.728i	−0.331133	+	0.101964i
$148$	−204.180	+	1157.96i	−0.113402	+	0.643134i
$149$	−238.886	+	1354.79i	−0.131344	+	0.744890i	0.845992	+	0.533196i	$0.179009\pi$
$149$	−238.886	+	1354.79i	−0.131344	+	0.744890i	−0.977336	+	0.211694i	$0.932102\pi$
$150$	−95.9459	+	419.422i	−0.0522263	+	0.228305i
$151$	286.970	−	240.797i	0.154658	−	0.129773i	−0.562175	−	0.827018i	$-0.690035\pi$
$151$	286.970	−	240.797i	0.154658	−	0.129773i	0.716833	+	0.697245i	$0.245591\pi$
$152$	−165.223	+	286.174i	−0.0881666	+	0.152709i
$153$	−35.8026	−	3.61791i	−0.0189181	−	0.00191171i
$154$	2.34288	+	4.05798i	0.00122594	+	0.00212339i
$155$	3523.59	+	1282.48i	1.82595	+	0.664590i
$156$	1166.29	+	492.302i	0.598575	+	0.252665i
$157$	−404.609	−	339.507i	−0.205677	−	0.172584i	0.534131	−	0.845402i	$-0.320639\pi$
$157$	−404.609	−	339.507i	−0.205677	−	0.172584i	−0.739808	+	0.672818i	$0.765084\pi$
$158$	−188.030	+	68.4373i	−0.0946763	+	0.0344593i
$159$	−385.759	+	596.633i	−0.192407	+	0.297585i
$160$	−196.828	−	1116.26i	−0.0972537	−	0.551553i
$161$	2533.76			1.24030
$162$	185.680	+	113.965i	0.0900519	+	0.0552714i
$163$	−714.227			−0.343206			−0.171603	−	0.985166i	$-0.554895\pi$
$163$	−714.227			−0.343206			−0.171603	+	0.985166i	$0.554895\pi$
$164$	436.026	+	2472.83i	0.207609	+	1.17741i
$165$	−41.2733	+	63.8351i	−0.0194735	+	0.0301185i
$166$	156.664	−	57.0210i	0.0732499	−	0.0266608i
$167$	2819.79	+	2366.08i	1.30660	+	1.09637i	0.988965	+	0.148152i	$0.0473325\pi$
$167$	2819.79	+	2366.08i	1.30660	+	1.09637i	0.317633	+	0.948214i	$0.397112\pi$
$168$	−489.184	−	206.490i	−0.224651	−	0.0948275i
$169$	1173.22	+	427.018i	0.534012	+	0.194364i
$170$	−3.99334	−	6.91667i	−0.00180162	−	0.00312050i
$171$	−1096.80	+	1522.41i	−0.490492	+	0.680829i
$172$	−1139.35	+	1973.41i	−0.505084	+	0.874832i
$173$	−1535.44	+	1288.39i	−0.674783	+	0.566211i	−0.914477	−	0.404638i	$-0.867398\pi$
$173$	−1535.44	+	1288.39i	−0.674783	+	0.566211i	0.239693	+	0.970849i	$0.422953\pi$
$174$	31.8762	−	139.345i	0.0138881	−	0.0607110i
$175$	1033.96	−	5863.86i	0.446627	−	2.53295i
$176$	7.83762	−	44.4493i	0.00335672	−	0.0190369i
$177$	−238.405	+	73.4106i	−0.101241	+	0.0311745i
$178$	−123.299	+	103.461i	−0.0519196	+	0.0435657i
$179$	1440.88	−	2495.68i	0.601657	−	1.04210i	−0.390913	−	0.920428i	$-0.627841\pi$
$179$	1440.88	−	2495.68i	0.601657	−	1.04210i	0.992570	−	0.121673i	$-0.0388259\pi$
$180$	−315.882	−	4271.13i	−0.130803	−	1.76862i
$181$	−454.319	−	786.904i	−0.186571	−	0.323150i	0.757534	−	0.652796i	$-0.226404\pi$
$181$	−454.319	−	786.904i	−0.186571	−	0.323150i	−0.944105	+	0.329646i	$0.893071\pi$
$182$	185.869	+	67.6508i	0.0757007	+	0.0275528i
$183$	−2246.82	+	1700.17i	−0.907593	+	0.686777i
$184$	429.459	+	360.359i	0.172066	+	0.144380i
$185$	−2800.68	+	1019.37i	−1.11303	+	0.405109i
$186$	290.029	+	14.6167i	0.114333	+	0.00576210i
$187$	−0.168850	−	0.957594i	−6.60294e−5	−	0.000374472i
$188$	167.379			0.0649329
$189$	−2645.75	−	1445.83i	−1.01825	−	0.556448i
$190$	−416.447			−0.159012
$191$	−195.023	−	1106.03i	−0.0738816	−	0.419003i	−0.999207	−	0.0398281i	$-0.987319\pi$
$191$	−195.023	−	1106.03i	−0.0738816	−	0.419003i	0.925325	−	0.379175i	$-0.123792\pi$
$192$	1132.09	+	2210.88i	0.425529	+	0.831024i
$193$	3274.01	−	1191.64i	1.22108	−	0.444437i	0.350547	−	0.936545i	$-0.385996\pi$
$193$	3274.01	−	1191.64i	1.22108	−	0.444437i	0.870534	+	0.492108i	$0.163774\pi$
$194$	−67.8065	−	56.8964i	−0.0250939	−	0.0210563i
$195$	397.442	+	3184.11i	0.145956	+	1.16933i
$196$	883.420	+	321.539i	0.321946	+	0.117179i
$197$	−2109.35	−	3653.50i	−0.762867	−	1.32132i	−0.941367	−	0.337384i	$-0.890458\pi$
$197$	−2109.35	−	3653.50i	−0.762867	−	1.32132i	0.178500	−	0.983940i	$-0.442875\pi$
$198$	−1.59998	+	5.66544i	−0.000574271	+	0.00203346i
$199$	205.179	−	355.380i	0.0730892	−	0.126594i	−0.827165	−	0.561960i	$-0.810048\pi$
$199$	205.179	−	355.380i	0.0730892	−	0.126594i	0.900254	+	0.435366i	$0.143381\pi$
$200$	1009.23	−	846.841i	0.356815	−	0.299404i
$201$	−350.240	−	325.293i	−0.122906	−	0.114151i
$202$	−88.7831	+	503.514i	−0.0309245	+	0.175382i
$203$	−343.512	+	1948.15i	−0.118768	+	0.673564i
$204$	40.1412	+	37.2821i	0.0137767	+	0.0127954i
$205$	−4875.64	+	4091.15i	−1.66112	+	1.39385i
$206$	98.9482	−	171.383i	0.0334663	−	0.0579653i
$207$	2220.49	+	2281.01i	0.745580	+	0.765901i
$208$	−952.633	−	1650.01i	−0.317563	−	0.550036i
$209$	−47.6441	−	17.3410i	−0.0157685	−	0.00573926i
$210$	−82.8831	−	664.019i	−0.0272356	−	0.218199i
$211$	479.610	+	402.440i	0.156482	+	0.131304i	0.717667	−	0.696386i	$-0.245210\pi$
$211$	479.610	+	402.440i	0.156482	+	0.131304i	−0.561185	+	0.827690i	$0.689654\pi$
$212$	1016.41	−	369.943i	0.329280	−	0.119848i
$213$	−2517.90	−	4917.27i	−0.809972	−	1.58181i
$214$	−45.5158	−	258.133i	−0.0145392	−	0.0824560i
$215$	−5775.93			−1.83216
$216$	−242.811	−	621.348i	−0.0764870	−	0.195728i
$217$	−4018.80			−1.25721
$218$	−57.4306	−	325.705i	−0.0178426	−	0.101191i
$219$	3553.11	+	179.068i	1.09633	+	0.0552525i
$220$	108.748	−	39.5811i	0.0333264	−	0.0121298i
$221$	−31.4431	−	26.3839i	−0.00957055	−	0.00803065i
$222$	−184.061	+	139.279i	−0.0556458	+	0.0421073i
$223$	4262.62	+	1551.47i	1.28003	+	0.465891i	0.890441	−	0.455099i	$-0.150396\pi$
$223$	4262.62	+	1551.47i	1.28003	+	0.465891i	0.389585	+	0.920990i	$0.372618\pi$
$224$	607.411	+	1052.07i	0.181180	+	0.313813i
$225$	6185.06	−	4208.06i	1.83261	−	1.24683i
$226$	99.9321	−	173.087i	0.0294132	−	0.0509452i
$227$	5004.32	−	4199.12i	1.46321	−	1.22778i	0.541035	−	0.841000i	$-0.318033\pi$
$227$	5004.32	−	4199.12i	1.46321	−	1.22778i	0.922173	−	0.386777i	$-0.126412\pi$
$228$	2730.08	−	840.659i	0.793001	−	0.244184i
$229$	−934.579	+	5300.26i	−0.269689	+	1.52948i	0.485654	+	0.874151i	$0.338582\pi$
$229$	−934.579	+	5300.26i	−0.269689	+	1.52948i	−0.755343	+	0.655330i	$0.772530\pi$
$230$	−122.687	+	695.792i	−0.0351728	+	0.199475i
$231$	18.1677	−	79.4191i	0.00517466	−	0.0226208i
$232$	−335.296	+	281.347i	−0.0948847	+	0.0796178i
$233$	−1042.34	+	1805.39i	−0.293074	+	0.507619i	−0.974535	−	0.224235i	$-0.928012\pi$
$233$	−1042.34	+	1805.39i	−0.293074	+	0.507619i	0.681461	+	0.731854i	$0.261345\pi$
$234$	101.986	+	226.615i	0.0284917	+	0.0633090i
$235$	212.132	+	367.424i	0.0588851	+	0.101992i
$236$	356.865	+	129.888i	0.0984319	+	0.0358263i
$237$	3205.22	+	1352.96i	0.878486	+	0.370818i
$238$	6.55719	+	5.50213i	0.00178588	+	0.00149853i
$239$	−4469.26	+	1626.68i	−1.20959	+	0.440256i	−0.866562	−	0.499069i	$-0.833675\pi$
$239$	−4469.26	+	1626.68i	−1.20959	+	0.440256i	−0.343030	+	0.939324i	$0.611453\pi$
$240$	−3499.75	+	5412.88i	−0.941284	+	1.45583i
$241$	400.465	+	2271.15i	0.107038	+	0.607043i	0.990387	+	0.138327i	$0.0441724\pi$
$241$	400.465	+	2271.15i	0.107038	+	0.607043i	−0.883349	+	0.468717i	$0.844717\pi$
$242$	397.617			0.105619
$243$	−1017.04	−	3648.91i	−0.268489	−	0.963283i
$244$	4289.52			1.12544
$245$	413.797	+	2346.76i	0.107904	+	0.611954i
$246$	−267.630	+	413.929i	−0.0693638	+	0.107281i
$247$	−2011.18	+	732.010i	−0.518090	+	0.188569i
$248$	−681.166	−	571.567i	−0.174412	−	0.146349i
$249$	−2670.54	−	1127.27i	−0.679674	−	0.286898i
$250$	856.311	+	311.672i	0.216631	+	0.0788474i
$251$	994.592	+	1722.68i	0.250112	+	0.433207i	0.963556	−	0.267505i	$-0.0861992\pi$
$251$	994.592	+	1722.68i	0.250112	+	0.433207i	−0.713444	+	0.700712i	$0.752866\pi$
$252$	1883.77	+	4185.77i	0.470898	+	1.04634i
$253$	−43.0092	+	74.4941i	−0.0106876	+	0.0185115i
$254$	−206.698	+	173.440i	−0.0510605	+	0.0428448i
$255$	−30.9662	+	135.367i	−0.00760461	+	0.0332431i
$256$	633.179	−	3590.93i	0.154585	−	0.876693i
$257$	1088.91	−	6175.49i	0.264296	−	1.49890i	−0.506737	−	0.862101i	$-0.669148\pi$
$257$	1088.91	−	6175.49i	0.264296	−	1.49890i	0.771033	−	0.636796i	$-0.219741\pi$
$258$	−427.507	+	131.640i	−0.103161	+	0.0317657i
$259$	2446.97	−	2053.25i	0.587056	−	0.492598i
$260$	2442.58	−	4230.67i	0.582624	−	1.00913i
$261$	−2054.87	+	1398.05i	−0.487330	+	0.331559i
$262$	−286.046	−	495.447i	−0.0674504	−	0.116828i
$263$	−2301.62	−	837.722i	−0.539635	−	0.196411i	0.0578002	−	0.998328i	$-0.481591\pi$
$263$	−2301.62	−	837.722i	−0.539635	−	0.196411i	−0.597435	+	0.801917i	$0.703814\pi$
$264$	14.3746	−	10.8773i	0.00335111	−	0.00253579i
$265$	2100.26	+	1762.33i	0.486860	+	0.408524i
$266$	419.414	−	152.654i	0.0966764	−	0.0351873i
$267$	2794.98	+	140.860i	0.640636	+	0.0322865i
$268$	126.366	+	716.657i	0.0288023	+	0.163346i
$269$	−4739.75			−1.07430			−0.537152	−	0.843485i	$-0.680500\pi$
$269$	−4739.75			−1.07430			−0.537152	+	0.843485i	$0.680500\pi$
$270$	525.147	−	656.538i	0.118368	−	0.147984i
$271$	−4368.84			−0.979292			−0.489646	−	0.871921i	$-0.662874\pi$
$271$	−4368.84			−0.979292			−0.489646	+	0.871921i	$0.662874\pi$
$272$	−14.3175	−	81.1988i	−0.00319165	−	0.0181007i
$273$	−1567.45	−	3061.11i	−0.347496	−	0.678633i
$274$	−741.880	+	270.022i	−0.163571	+	0.0595352i
$275$	154.850	+	129.935i	0.0339557	+	0.0284922i
$276$	−600.264	−	4809.03i	−0.130912	−	1.04880i
$277$	−7253.15	−	2639.93i	−1.57328	−	0.572628i	−0.599553	−	0.800335i	$-0.704655\pi$
$277$	−7253.15	−	2639.93i	−1.57328	−	0.572628i	−0.973730	+	0.227707i	$0.926877\pi$
$278$	24.7732	+	42.9085i	0.00534461	+	0.00925713i
$279$	−3521.94	−	3617.93i	−0.755745	−	0.776342i
$280$	−1024.51	+	1774.50i	−0.218664	+	0.378738i
$281$	−2877.77	+	2414.74i	−0.610937	+	0.512637i	−0.894940	−	0.446186i	$-0.852782\pi$
$281$	−2877.77	+	2414.74i	−0.610937	+	0.512637i	0.284003	+	0.958823i	$0.408337\pi$
$282$	24.0751	+	22.3603i	0.00508386	+	0.00472176i
$283$	404.252	−	2292.63i	0.0849127	−	0.481564i	−0.912463	−	0.409160i	$-0.865822\pi$
$283$	404.252	−	2292.63i	0.0849127	−	0.481564i	0.997375	−	0.0724041i	$-0.0230671\pi$
$284$	−1460.46	+	8282.69i	−0.305150	+	1.73059i
$285$	5305.42	+	4927.53i	1.10269	+	1.02415i
$286$	−5.14400	+	4.31633i	−0.00106354	+	0.000892413i
$287$	3410.71	−	5907.52i	0.701491	−	1.21502i
$288$	−414.809	+	1468.82i	−0.0848711	+	0.300524i
$289$	2455.61	+	4253.24i	0.499819	+	0.865712i
$290$	−518.347	−	188.663i	−0.104960	−	0.0382023i
$291$	190.619	+	1527.15i	0.0383997	+	0.307640i
$292$	−4149.02	−	3481.44i	−0.831517	−	0.697726i
$293$	4551.16	−	1656.49i	0.907446	−	0.330283i	0.154214	−	0.988038i	$-0.450716\pi$
$293$	4551.16	−	1656.49i	0.907446	−	0.330283i	0.753233	+	0.657754i	$0.228493\pi$
$294$	84.1126	+	164.265i	0.0166855	+	0.0325855i
$295$	167.157	+	947.992i	0.0329906	+	0.187099i
$296$	706.769			0.138784
$297$	87.4186	−	53.2446i	0.0170793	−	0.0104026i
$298$	411.131			0.0799201
$299$	630.526	+	3575.89i	0.121954	+	0.691636i
$300$	−11374.5	−	573.244i	−2.18901	−	0.110321i
$301$	5817.08	−	2117.24i	1.11392	−	0.405435i
$302$	−85.7624	−	71.9632i	−0.0163413	−	0.0137120i
$303$	7088.80	−	5364.11i	1.34403	−	1.01703i
$304$	−4039.96	−	1470.43i	−0.762197	−	0.277417i
$305$	5436.43	+	9416.18i	1.02062	+	1.76777i
$306$	0.793193	+	10.7250i	0.000148182	+	0.00200362i
$307$	1240.46	−	2148.54i	0.230608	−	0.399425i	−0.727379	−	0.686236i	$-0.759262\pi$
$307$	1240.46	−	2148.54i	0.230608	−	0.399425i	0.957987	+	0.286811i	$0.0925951\pi$
$308$	−95.0139	+	79.7261i	−0.0175777	+	0.0147494i
$309$	−3288.43	+	1012.59i	−0.605412	+	0.186421i
$310$	194.594	−	1103.60i	0.0356523	−	0.202194i
$311$	280.294	−	1589.63i	0.0511062	−	0.289838i	−0.948534	−	0.316677i	$-0.897433\pi$
$311$	280.294	−	1589.63i	0.0511062	−	0.289838i	0.999640	+	0.0268390i	$0.00854414\pi$
$312$	169.685	−	741.770i	0.0307902	−	0.134598i
$313$	7636.44	−	6407.73i	1.37903	−	1.15715i	0.409463	−	0.912327i	$-0.365716\pi$
$313$	7636.44	−	6407.73i	1.37903	−	1.15715i	0.969569	−	0.244819i	$-0.0787284\pi$
$314$	−78.9245	+	136.701i	−0.0141846	+	0.0245685i
$315$	−6800.97	+	9440.11i	−1.21648	+	1.68854i
$316$	−2648.29	−	4586.97i	−0.471449	−	0.816573i
$317$	−1915.29	−	697.110i	−0.339349	−	0.123513i	0.166724	−	0.986004i	$-0.446681\pi$
$317$	−1915.29	−	697.110i	−0.339349	−	0.123513i	−0.506073	+	0.862491i	$0.668903\pi$
$318$	195.617	+	82.5719i	0.0344957	+	0.0145610i
$319$	−51.4461	−	43.1684i	−0.00902955	−	0.00757669i
$320$	9007.06	−	3278.30i	1.57347	−	0.572696i
$321$	−2474.45	+	3827.09i	−0.430250	+	0.665444i
$322$	−131.491	−	745.721i	−0.0227568	−	0.129060i
$323$	−92.6206			−0.0159553
$324$	−2117.36	+	5364.12i	−0.363060	+	0.919774i
$325$	8532.96			1.45638
$326$	37.0652	+	210.207i	0.00629709	+	0.0357126i
$327$	−3122.20	+	4828.93i	−0.528006	+	0.816637i
$328$	1418.28	−	516.213i	0.238755	−	0.0868997i
$329$	−348.328	−	292.282i	−0.0583706	−	0.0489788i
$330$	20.9295	+	8.83456i	0.00349131	+	0.00147372i
$331$	1140.34	+	415.048i	0.189361	+	0.0689218i	0.434960	−	0.900450i	$-0.356762\pi$
$331$	1140.34	+	415.048i	0.189361	+	0.0689218i	−0.245599	+	0.969371i	$0.578985\pi$
$332$	2206.52	+	3821.80i	0.364754	+	0.631773i
$333$	3992.88	+	403.487i	0.657082	+	0.0663993i
$334$	550.038	−	952.694i	0.0901100	−	0.156075i
$335$	−1413.02	+	1185.67i	−0.230453	+	0.193373i
$336$	1540.52	−	6734.31i	0.250126	−	1.09341i
$337$	−1476.83	+	8375.55i	−0.238719	+	1.35384i	0.595919	+	0.803044i	$0.296788\pi$
$337$	−1476.83	+	8375.55i	−0.238719	+	1.35384i	−0.834638	+	0.550798i	$0.814323\pi$
$338$	64.7926	−	367.457i	0.0104268	−	0.0591332i
$339$	−3321.13	+	1022.66i	−0.532092	+	0.163844i
$340$	161.948	−	135.890i	0.0258319	−	0.0216755i
$341$	68.2171	−	118.155i	0.0108333	−	0.0187639i
$342$	504.987	+	243.797i	0.0798437	+	0.0385468i
$343$	2408.64	+	4171.89i	0.379167	+	0.656737i
$344$	1287.09	+	468.461i	0.201730	+	0.0734236i
$345$	9795.82	−	7412.52i	1.52867	−	1.15674i
$346$	458.874	+	385.041i	0.0712984	+	0.0598264i
$347$	−6218.74	+	2263.44i	−0.962073	+	0.350166i	−0.774846	−	0.632151i	$-0.782172\pi$
$347$	−6218.74	+	2263.44i	−0.962073	+	0.350166i	−0.187228	+	0.982317i	$0.559950\pi$
$348$	3778.94	+	190.449i	0.582105	+	0.0293367i
$349$	−910.076	−	5161.30i	−0.139585	−	0.791628i	−0.971556	−	0.236809i	$-0.923899\pi$
$349$	−910.076	−	5161.30i	−0.139585	−	0.791628i	0.831971	−	0.554819i	$-0.187213\pi$
$350$	−1779.48			−0.271763
$351$	1382.10	−	4093.75i	0.210174	−	0.622530i
$352$	−41.2419			−0.00624489
$353$	−852.154	−	4832.81i	−0.128486	−	0.728681i	−0.979176	−	0.203013i	$-0.934927\pi$
$353$	−852.154	−	4832.81i	−0.128486	−	0.728681i	0.850690	−	0.525668i	$-0.176184\pi$
$354$	33.9780	+	66.3563i	0.00510144	+	0.00996270i
$355$	−20032.8	+	7291.33i	−2.99501	+	1.09010i
$356$	−3263.74	−	2738.60i	−0.485892	−	0.407712i
$357$	−18.4337	−	147.682i	−0.00273282	−	0.0218940i
$358$	−809.291	−	294.558i	−0.119476	−	0.0434856i
$359$	4501.47	+	7796.77i	0.661779	+	1.14623i	0.980148	+	0.198267i	$0.0635314\pi$
$359$	4501.47	+	7796.77i	0.661779	+	1.14623i	−0.318369	+	0.947967i	$0.603135\pi$
$360$	−2495.33	+	632.795i	−0.365321	+	0.0926423i
$361$	1014.75	−	1757.61i	0.147945	−	0.256248i
$362$	−208.020	+	174.549i	−0.0302025	+	0.0253429i
$363$	−5065.52	−	4704.72i	−0.732427	−	0.680258i
$364$	−909.170	+	5156.16i	−0.130916	+	0.742462i
$365$	2383.95	−	13520.1i	0.341868	−	1.93883i
$366$	616.985	+	573.039i	0.0881156	+	0.0818394i
$367$	−668.599	+	561.021i	−0.0950970	+	0.0797958i	−0.689097	−	0.724669i	$-0.741992\pi$
$367$	−668.599	+	561.021i	−0.0950970	+	0.0797958i	0.594000	+	0.804465i	$0.297548\pi$
$368$	−3646.95	+	6316.70i	−0.516604	+	0.894785i
$369$	8307.27	−	2106.65i	1.17198	−	0.297203i
$370$	445.357	+	771.381i	0.0625757	+	0.108384i
$371$	−2761.22	−	1005.00i	−0.386403	−	0.140639i
$372$	952.082	+	7627.62i	0.132697	+	1.06310i
$373$	−4820.94	−	4045.25i	−0.669219	−	0.561541i	0.243615	−	0.969872i	$-0.421667\pi$
$373$	−4820.94	−	4045.25i	−0.669219	−	0.561541i	−0.912834	+	0.408331i	$0.866111\pi$
$374$	−0.273071	+	0.0993898i	−3.77545e−5	+	1.37415e-5i
$375$	−7221.36	−	14102.7i	−0.994425	−	1.94203i
$376$	−17.4706	−	99.0805i	−0.00239621	−	0.0135896i
$377$	−2834.91			−0.387282
$378$	−288.226	+	853.715i	−0.0392189	+	0.116165i
$379$	2956.76			0.400734			0.200367	−	0.979721i	$-0.435786\pi$
$379$	2956.76			0.400734			0.200367	+	0.979721i	$0.435786\pi$
$380$	−1914.19	−	10855.9i	−0.258410	−	1.46552i
$381$	4685.46	+	236.136i	0.630036	+	0.0317522i
$382$	−315.400	+	114.796i	−0.0422442	+	0.0153756i
$383$	2545.77	+	2136.16i	0.339642	+	0.284993i	0.796615	−	0.604487i	$-0.206622\pi$
$383$	2545.77	+	2136.16i	0.339642	+	0.284993i	−0.456973	+	0.889481i	$0.651066\pi$
$384$	2465.77	−	1865.85i	0.327684	−	0.247960i
$385$	−295.430	−	107.528i	−0.0391078	−	0.0142341i
$386$	−520.625	−	901.748i	−0.0686505	−	0.118906i
$387$	7003.93	+	3381.34i	0.919973	+	0.444143i
$388$	1171.50	−	2029.09i	0.153283	−	0.265494i
$389$	−7165.62	+	6012.67i	−0.933962	+	0.783687i	−0.976524	−	0.215406i	$-0.930892\pi$
$389$	−7165.62	+	6012.67i	−0.933962	+	0.783687i	0.0425622	+	0.999094i	$0.486448\pi$
$390$	916.505	−	282.214i	0.118998	−	0.0366423i
$391$	−27.2864	+	154.749i	−0.00352924	+	0.0200153i
$392$	98.1266	−	556.503i	0.0126432	−	0.0717032i
$393$	−2218.13	+	9696.44i	−0.284707	+	1.24458i
$394$	−965.811	+	810.412i	−0.123495	+	0.103624i
$395$	6712.75	−	11626.8i	0.855076	−	1.48103i
$396$	−155.040	−	15.6671i	−0.0196744	−	0.00198813i
$397$	2036.76	+	3527.77i	0.257486	+	0.445979i	0.965568	−	0.260152i	$-0.0837725\pi$
$397$	2036.76	+	3527.77i	0.257486	+	0.445979i	−0.708082	+	0.706130i	$0.750439\pi$
$398$	−115.241	−	41.9444i	−0.0145139	−	0.00528262i
$399$	−7149.47	−	3017.87i	−0.897045	−	0.378652i
$400$	13130.5	+	11017.8i	1.64131	+	1.37722i
$401$	−3662.12	+	1332.90i	−0.456054	+	0.165990i	−0.559824	−	0.828611i	$-0.689131\pi$
$401$	−3662.12	+	1332.90i	−0.456054	+	0.165990i	0.103771	+	0.994601i	$0.466909\pi$
$402$	−77.5627	+	119.962i	−0.00962307	+	0.0148835i
$403$	−1000.08	−	5671.74i	−0.123617	−	0.701066i
$404$	−13533.6			−1.66664
$405$	−14458.6	+	2150.40i	−1.77396	+	0.263838i
$406$	591.197			0.0722675
$407$	18.8309	+	106.795i	0.00229340	+	0.0130065i
$408$	17.8794	−	27.6531i	0.00216952	−	0.00335547i
$409$	10586.9	−	3853.30i	1.27992	−	0.465852i	0.389513	−	0.921021i	$-0.372643\pi$
$409$	10586.9	−	3853.30i	1.27992	−	0.465852i	0.890405	+	0.455169i	$0.150421\pi$
$410$	1457.11	+	1222.66i	0.175516	+	0.147275i
$411$	12646.3	+	5338.14i	1.51775	+	0.640660i
$412$	4922.41	+	1791.61i	0.588616	+	0.214239i
$413$	−515.846	−	893.472i	−0.0614604	−	0.106452i
$414$	556.101	−	771.898i	0.0660167	−	0.0916346i
$415$	−5592.97	+	9687.31i	−0.661562	+	1.14586i
$416$	−1333.63	+	1119.05i	−0.157179	+	0.131889i
$417$	192.103	−	839.767i	0.0225595	−	0.0986176i
$418$	−2.63120	+	14.9223i	−0.000307886	+	0.00174611i
$419$	−1041.24	+	5905.18i	−0.121403	+	0.688513i	0.861976	+	0.506949i	$0.169227\pi$
$419$	−1041.24	+	5905.18i	−0.121403	+	0.688513i	−0.983379	+	0.181563i	$0.941884\pi$
$420$	16928.6	−	5212.73i	1.96674	−	0.605607i
$421$	−12007.1	+	10075.2i	−1.39000	+	1.16635i	−0.424666	+	0.905350i	$0.639608\pi$
$421$	−12007.1	+	10075.2i	−1.39000	+	1.16635i	−0.965338	+	0.261002i	$0.915947\pi$
$422$	93.5544	−	162.041i	0.0107918	−	0.0186920i
$423$	−42.1356	−	569.727i	−0.00484327	−	0.0654872i
$424$	−325.079	−	563.053i	−0.0372340	−	0.0644912i
$425$	346.999	+	126.297i	0.0396045	+	0.0144149i
$426$	−1316.55	+	996.240i	−0.149735	+	0.113305i
$427$	−8926.78	−	7490.46i	−1.01170	−	0.848920i
$428$	6519.76	−	2373.00i	0.736319	−	0.267998i
$429$	116.605	+	5.87662i	0.0131230	+	0.000661365i
$430$	299.745	+	1699.94i	0.0336163	+	0.190647i
$431$	8999.40			1.00577			0.502884	−	0.864354i	$-0.332272\pi$
$431$	8999.40			1.00577			0.502884	+	0.864354i	$0.332272\pi$
$432$	7412.62	−	4514.86i	0.825556	−	0.502827i
$433$	−1029.94			−0.114309			−0.0571547	−	0.998365i	$-0.518203\pi$
$433$	−1029.94			−0.114309			−0.0571547	+	0.998365i	$0.518203\pi$
$434$	208.558	+	1182.79i	0.0230671	+	0.130820i
$435$	4371.28	+	8536.75i	0.481808	+	0.940933i
$436$	8226.47	−	2994.19i	0.903615	−	0.328889i
$437$	6276.58	+	5266.68i	0.687070	+	0.576520i
$438$	−131.688	−	1055.02i	−0.0143660	−	0.115094i
$439$	9405.91	+	3423.47i	1.02260	+	0.372194i	0.798257	−	0.602317i	$-0.205756\pi$
$439$	9405.91	+	3423.47i	1.02260	+	0.372194i	0.224338	+	0.974511i	$0.427978\pi$
$440$	−34.7809	−	60.2423i	−0.00376845	−	0.00652714i
$441$	872.066	−	3087.94i	0.0941655	−	0.333434i
$442$	−6.13341	+	10.6234i	−0.000660037	+	0.00114322i
$443$	864.666	−	725.541i	0.0927348	−	0.0778138i	−0.595242	−	0.803547i	$-0.702944\pi$
$443$	864.666	−	725.541i	0.0927348	−	0.0778138i	0.687976	+	0.725733i	$0.258499\pi$
$444$	−4476.75	−	4157.88i	−0.478507	−	0.444424i
$445$	1875.28	−	10635.3i	0.199768	−	1.13294i
$446$	235.408	−	1335.06i	0.0249930	−	0.141742i
$447$	−5237.69	−	4864.63i	−0.554215	−	0.514741i
$448$	−7869.52	+	6603.31i	−0.829910	+	0.696377i
$449$	2633.36	−	4561.12i	0.276784	−	0.479405i	−0.693799	−	0.720168i	$-0.744065\pi$
$449$	2633.36	−	4561.12i	0.276784	−	0.479405i	0.970584	+	0.240764i	$0.0773979\pi$
$450$	−1559.47	−	1601.97i	−0.163365	−	0.167817i
$451$	115.790	+	200.554i	0.0120894	+	0.0209395i
$452$	4971.36	+	1809.43i	0.517329	+	0.188293i
$453$	241.097	+	1931.56i	0.0250061	+	0.200337i
$454$	−1495.56	−	1254.93i	−0.154604	−	0.129728i
$455$	−12470.9	+	4539.02i	−1.28493	+	0.467676i
$456$	−782.588	−	1528.33i	−0.0803685	−	0.156953i
$457$	−1736.03	−	9845.54i	−0.177699	−	1.00778i	−0.934983	−	0.354693i	$-0.884585\pi$
$457$	−1736.03	−	9845.54i	−0.177699	−	1.00778i	0.757284	−	0.653085i	$-0.226526\pi$
$458$	1608.44			0.164100
$459$	116.796	−	146.018i	0.0118771	−	0.0148487i
$460$	−18701.7			−1.89559
$461$	2367.89	+	13429.0i	0.239227	+	1.35672i	0.833526	+	0.552480i	$0.186318\pi$
$461$	2367.89	+	13429.0i	0.239227	+	1.35672i	−0.594299	+	0.804244i	$0.702570\pi$
$462$	−24.3170	−	1.22552i	−0.00244877	−	0.000123412i
$463$	−3631.88	+	1321.90i	−0.364552	+	0.132686i	−0.517800	−	0.855502i	$-0.673249\pi$
$463$	−3631.88	+	1321.90i	−0.364552	+	0.132686i	0.153248	+	0.988188i	$0.451027\pi$
$464$	−4362.35	−	3660.45i	−0.436459	−	0.366233i
$465$	−15537.2	+	11757.0i	−1.54951	+	1.17251i
$466$	585.446	+	213.085i	0.0581980	+	0.0211823i
$467$	−6854.86	−	11873.0i	−0.679240	−	1.17648i	−0.975210	−	0.221281i	$-0.928976\pi$
$467$	−6854.86	−	11873.0i	−0.679240	−	1.17648i	0.295970	−	0.955197i	$-0.404357\pi$
$468$	−5438.60	+	3700.20i	−0.537178	+	0.365474i
$469$	988.467	−	1712.07i	0.0973202	−	0.168563i
$470$	97.1295	−	81.5013i	0.00953245	−	0.00799867i
$471$	2622.97	−	807.675i	0.256603	−	0.0790142i
$472$	39.6390	−	224.804i	0.00386554	−	0.0219226i
$473$	−36.4935	+	206.965i	−0.00354751	+	0.0201189i
$474$	231.858	−	1013.55i	0.0224675	−	0.0982153i
$475$	14749.9	−	12376.7i	1.42479	−	1.19554i
$476$	−113.289	+	196.222i	−0.0109088	+	0.0188946i
$477$	−1515.08	−	3366.54i	−0.145432	−	0.323152i
$478$	710.690	+	1230.95i	0.0680046	+	0.117787i
$479$	6613.84	+	2407.24i	0.630885	+	0.229623i	0.637617	−	0.770354i	$-0.279920\pi$
$479$	6613.84	+	2407.24i	0.630885	+	0.229623i	−0.00673130	+	0.999977i	$0.502143\pi$
$480$	5426.16	+	2290.44i	0.515977	+	0.217799i
$481$	3506.69	+	2942.46i	0.332414	+	0.278929i
$482$	647.649	−	235.725i	0.0612025	−	0.0222759i
$483$	−7148.45	+	11056.1i	−0.673428	+	1.04155i
$484$	1827.63	+	10365.0i	0.171641	+	0.973424i
$485$	5938.91			0.556024
$486$	−1021.15	+	488.691i	−0.0953090	+	0.0456120i
$487$	9484.84			0.882544			0.441272	−	0.897373i	$-0.354527\pi$
$487$	9484.84			0.882544			0.441272	+	0.897373i	$0.354527\pi$
$488$	−447.728	−	2539.19i	−0.0415321	−	0.235540i
$489$	2015.04	−	3116.55i	0.186346	−	0.288211i
$490$	669.210	−	243.573i	0.0616976	−	0.0224561i
$491$	−10315.0	−	8655.29i	−0.948082	−	0.795535i	0.0308914	−	0.999523i	$-0.490165\pi$
$491$	−10315.0	−	8655.29i	−0.948082	−	0.795535i	−0.978974	+	0.203987i	$0.934610\pi$
$492$	−12020.4	−	5073.94i	−1.10147	−	0.464941i
$493$	−115.284	−	41.9599i	−0.0105317	−	0.00383322i
$494$	319.812	+	553.931i	0.0291276	+	0.0504505i
$495$	−162.103	−	360.194i	−0.0147191	−	0.0327061i
$496$	5784.44	−	10018.9i	0.523647	−	0.906984i
$497$	17502.7	−	14686.5i	1.57969	−	1.32552i
$498$	−193.181	+	844.480i	−0.0173828	+	0.0759880i
$499$	2059.98	−	11682.7i	0.184804	−	1.04808i	−0.741402	−	0.671061i	$-0.765839\pi$
$499$	2059.98	−	11682.7i	0.184804	−	1.04808i	0.926206	−	0.377017i	$-0.123050\pi$
$500$	−4188.61	+	23754.8i	−0.374641	+	2.12469i
$501$	−18279.9	+	5628.83i	−1.63011	+	0.501951i
$502$	455.396	−	382.123i	0.0404887	−	0.0339740i
$503$	−7063.42	+	12234.2i	−0.626128	+	1.08449i	0.362194	+	0.932103i	$0.382028\pi$
$503$	−7063.42	+	12234.2i	−0.626128	+	1.08449i	−0.988322	+	0.152383i	$0.951305\pi$
$504$	2281.15	−	1552.00i	0.201608	−	0.137166i
$505$	−17152.2	−	29708.4i	−1.51141	−	2.61784i
$506$	24.1567	+	8.79231i	0.00212232	+	0.000772462i
$507$	−5173.30	+	3914.65i	−0.453165	+	0.342911i
$508$	−5471.29	−	4590.96i	−0.477853	−	0.400966i
$509$	11523.9	−	4194.36i	1.00351	−	0.365249i	0.212576	−	0.977145i	$-0.431815\pi$
$509$	11523.9	−	4194.36i	1.00351	−	0.365249i	0.790939	+	0.611895i	$0.209593\pi$
$510$	41.4474	+	2.08885i	0.00359867	+	0.000181364i
$511$	2555.02	+	14490.2i	0.221189	+	1.25442i
$512$	−5850.41			−0.504988
$513$	−3548.71	−	9081.05i	−0.305418	−	0.781556i
$514$	−1874.04			−0.160818
$515$	2305.67	+	13076.1i	0.197282	+	1.11884i
$516$	−5396.60	−	10539.1i	−0.460411	−	0.899146i
$517$	14.5060	−	5.27974i	0.00123399	−	0.000449134i
$518$	−731.289	−	613.624i	−0.0620290	−	0.0520485i
$519$	−1290.00	−	10334.9i	−0.109103	−	0.874084i
$520$	−2759.30	−	1004.30i	−0.232699	−	0.0846954i
$521$	5683.84	+	9844.69i	0.477953	+	0.827839i	0.999681	−	0.0252735i	$-0.00804566\pi$
$521$	5683.84	+	9844.69i	0.477953	+	0.827839i	−0.521728	+	0.853112i	$0.674712\pi$
$522$	518.104	+	532.224i	0.0434421	+	0.0446261i
$523$	−1568.15	+	2716.12i	−0.131110	+	0.227089i	−0.924105	−	0.382139i	$-0.875187\pi$
$523$	−1568.15	+	2716.12i	−0.131110	+	0.227089i	0.792995	+	0.609229i	$0.208521\pi$
$524$	11600.4	−	9733.93i	0.967114	−	0.811505i
$525$	22670.0	+	21055.3i	1.88457	+	1.75034i
$526$	−127.110	+	720.875i	−0.0105366	+	0.0597559i
$527$	43.2790	−	245.448i	0.00357735	−	0.0202882i
$528$	171.844	+	159.604i	0.0141639	+	0.0131551i
$529$	1328.10	−	1114.41i	0.109156	−	0.0915929i
$530$	409.684	−	709.593i	0.0335765	−	0.0581562i
$531$	352.278	−	1247.40i	0.0287902	−	0.101944i
$532$	5907.19	+	10231.6i	0.481408	+	0.833824i
$533$	9186.05	+	3343.45i	0.746514	+	0.271709i
$534$	−103.590	−	829.912i	−0.00839470	−	0.0672543i
$535$	13472.1	+	11304.4i	1.08869	+	0.913519i
$536$	411.037	−	149.605i	0.0331233	−	0.0120559i
$537$	6824.83	+	13328.4i	0.548442	+	1.07106i
$538$	245.972	+	1394.98i	0.0197112	+	0.111788i
$539$	86.7042			0.00692878
$540$	19528.4	+	10671.7i	1.55624	+	0.850440i
$541$	−8742.14			−0.694739			−0.347370	−	0.937728i	$-0.612925\pi$
$541$	−8742.14			−0.694739			−0.347370	+	0.937728i	$0.612925\pi$
$542$	226.724	+	1285.81i	0.0179679	+	0.101901i
$543$	4715.44	+	237.646i	0.372668	+	0.0187815i
$544$	−70.7961	+	25.7677i	−0.00557970	+	0.00203084i
$545$	16998.7	+	14263.6i	1.33605	+	1.12108i
$546$	−819.585	+	620.182i	−0.0642399	+	0.0486105i
$547$	−11271.8	−	4102.58i	−0.881070	−	0.320683i	−0.138428	−	0.990372i	$-0.544205\pi$
$547$	−11271.8	−	4102.58i	−0.881070	−	0.320683i	−0.742642	+	0.669689i	$0.766427\pi$
$548$	−10448.9	−	18098.1i	−0.814518	−	1.41079i
$549$	−1079.83	−	14600.7i	−0.0839455	−	1.13505i
$550$	30.2057	−	52.3177i	0.00234177	−	0.00405607i
$551$	−4900.38	+	4111.91i	−0.378881	+	0.317919i
$552$	−2784.06	+	857.280i	−0.214669	+	0.0661019i
$553$	−2498.60	+	14170.3i	−0.192136	+	1.08966i
$554$	−400.563	+	2271.71i	−0.0307190	+	0.174216i
$555$	3453.50	−	15096.8i	0.264131	−	1.15463i
$556$	−1004.66	+	843.013i	−0.0766317	+	0.0643017i
$557$	−3246.34	+	5622.82i	−0.246951	+	0.427732i	−0.962678	−	0.270648i	$-0.912762\pi$
$557$	−3246.34	+	5622.82i	−0.246951	+	0.427732i	0.715727	+	0.698380i	$0.246095\pi$
$558$	−882.035	+	1224.31i	−0.0669167	+	0.0928839i
$559$	4435.65	+	7682.77i	0.335613	+	0.581299i
$560$	−25050.9	−	9117.77i	−1.89034	−	0.688029i
$561$	4.65486	+	1.96486i	0.000350318	+	0.000147873i
$562$	860.035	+	721.655i	0.0645523	+	0.0541658i
$563$	−13930.6	+	5070.33i	−1.04282	+	0.379554i	−0.805947	−	0.591988i	$-0.798343\pi$
$563$	−13930.6	+	5070.33i	−1.04282	+	0.379554i	−0.236869	+	0.971542i	$0.576121\pi$
$564$	−472.225	+	730.364i	−0.0352558	+	0.0545281i
$565$	2328.60	+	13206.1i	0.173389	+	0.983339i
$566$	−695.733			−0.0516675
$567$	13773.3	−	7465.71i	1.02015	−	0.552963i
$568$	5055.39			0.373450
$569$	−4263.28	−	24178.3i	−0.314106	−	1.78138i	−0.577191	−	0.816609i	$-0.695851\pi$
$569$	−4263.28	−	24178.3i	−0.314106	−	1.78138i	0.263086	−	0.964772i	$-0.415260\pi$
$570$	1174.92	−	1817.18i	0.0863366	−	0.133532i
$571$	17820.6	−	6486.18i	1.30608	−	0.475374i	0.407107	−	0.913381i	$-0.366538\pi$
$571$	17820.6	−	6486.18i	1.30608	−	0.475374i	0.898972	+	0.438007i	$0.144316\pi$
$572$	−136.162	−	114.253i	−0.00995317	−	0.00835170i
$573$	5376.41	+	2269.44i	0.391977	+	0.165458i
$574$	−1915.67	−	697.247i	−0.139301	−	0.0507013i
$575$	−16333.3	−	28290.1i	−1.18460	−	2.05179i
$576$	−12841.2	−	1297.62i	−0.928906	−	0.0938675i
$577$	−6169.28	+	10685.5i	−0.445114	+	0.770960i	−0.998060	−	0.0622571i	$-0.980170\pi$
$577$	−6169.28	+	10685.5i	−0.445114	+	0.770960i	0.552946	+	0.833217i	$0.313503\pi$
$578$	1124.36	−	943.447i	0.0809118	−	0.0678931i
$579$	−4037.16	+	17648.2i	−0.289773	+	1.26673i
$580$	2535.47	−	14379.4i	0.181517	−	1.02943i
$581$	2081.80	−	11806.5i	0.148654	−	0.843057i
$582$	439.570	−	135.354i	0.0313072	−	0.00964024i
$583$	76.4181	−	64.1224i	0.00542867	−	0.00455519i
$584$	−1627.78	+	2819.40i	−0.115339	+	0.199774i
$585$	−15015.3	−	7249.04i	−1.06120	−	0.512327i
$586$	−723.714	−	1253.51i	−0.0510176	−	0.0883651i
$587$	7668.07	+	2790.95i	0.539174	+	0.196243i	0.597230	−	0.802070i	$-0.296268\pi$
$587$	7668.07	+	2790.95i	0.539174	+	0.196243i	−0.0580560	+	0.998313i	$0.518490\pi$
$588$	−3895.42	+	2947.67i	−0.273205	+	0.206735i
$589$	−9955.31	−	8353.50i	−0.696437	−	0.584380i
$590$	270.333	−	98.3932i	0.0188635	−	0.00686574i
$591$	21893.2	+	1103.36i	1.52380	+	0.0767957i
$592$	1596.76	+	9055.68i	0.110856	+	0.628693i
$593$	14782.8			1.02371			0.511853	−	0.859073i	$-0.328959\pi$
$593$	14782.8			1.02371			0.511853	+	0.859073i	$0.328959\pi$
$594$	−20.2073	−	22.9654i	−0.00139582	−	0.00158633i
$595$	−574.319			−0.0395710
$596$	1889.75	+	10717.3i	0.129878	+	0.736574i
$597$	971.843	+	1897.93i	0.0666246	+	0.130113i
$598$	1019.72	−	371.146i	0.0697312	−	0.0253801i
$599$	−6243.55	−	5238.96i	−0.425884	−	0.357359i	0.404512	−	0.914533i	$-0.367441\pi$
$599$	−6243.55	−	5238.96i	−0.425884	−	0.357359i	−0.830396	+	0.557174i	$0.811886\pi$
$600$	847.899	+	6792.96i	0.0576922	+	0.462203i
$601$	−9208.27	−	3351.54i	−0.624980	−	0.227474i	0.0100647	−	0.999949i	$-0.496796\pi$
$601$	−9208.27	−	3351.54i	−0.624980	−	0.227474i	−0.635045	+	0.772475i	$0.719018\pi$
$602$	−925.016	−	1602.17i	−0.0626259	−	0.108471i
$603$	2407.55	−	610.535i	0.162592	−	0.0412320i
$604$	1481.72	−	2566.42i	0.0998186	−	0.172891i
$605$	−20436.6	+	17148.3i	−1.37333	+	1.15236i
$606$	−1946.61	−	1807.96i	−0.130488	−	0.121194i
$607$	−1060.08	+	6012.04i	−0.0708855	+	0.402012i	0.928633	+	0.370998i	$0.120984\pi$
$607$	−1060.08	+	6012.04i	−0.0708855	+	0.402012i	−0.999519	+	0.0310132i	$0.990127\pi$
$608$	−682.161	+	3868.73i	−0.0455021	+	0.258055i
$609$	−7531.67	−	6995.22i	−0.501147	−	0.465453i
$610$	2489.19	−	2088.68i	0.165220	−	0.138636i
$611$	325.816	−	564.330i	0.0215730	−	0.0373655i
$612$	−275.931	+	69.9739i	−0.0182253	+	0.00462177i
$613$	6792.35	+	11764.7i	0.447537	+	0.775158i	0.998225	−	0.0595537i	$-0.0189678\pi$
$613$	6792.35	+	11764.7i	0.447537	+	0.775158i	−0.550688	+	0.834711i	$0.685634\pi$
$614$	−696.720	−	253.585i	−0.0457937	−	0.0166675i
$615$	−4096.26	−	32817.3i	−0.268581	−	2.15174i
$616$	57.1113	+	47.9221i	0.00373552	+	0.00313447i
$617$	−15876.2	+	5778.46i	−1.03590	+	0.377037i	−0.803325	−	0.595541i	$-0.796938\pi$
$617$	−15876.2	+	5778.46i	−1.03590	+	0.377037i	−0.232576	+	0.972578i	$0.574715\pi$
$618$	468.675	+	915.284i	0.0305062	+	0.0595763i
$619$	−2305.23	−	13073.6i	−0.149685	−	0.848907i	−0.963485	−	0.267762i	$-0.913716\pi$
$619$	−2305.23	−	13073.6i	−0.149685	−	0.848907i	0.813800	−	0.581145i	$-0.197395\pi$
$620$	29662.9			1.92144
$621$	−16217.9	+	3253.80i	−1.04799	+	0.210258i
$622$	−482.396			−0.0310970
$623$	2009.85	+	11398.4i	0.129250	+	0.733015i
$624$	9887.50	+	498.306i	0.634322	+	0.0319682i
$625$	−24909.3	+	9066.24i	−1.59419	+	0.580240i
$626$	−2282.19	−	1914.98i	−0.145710	−	0.122265i
$627$	210.086	−	158.972i	0.0133812	−	0.0101256i
$628$	−3926.28	−	1429.05i	−0.249484	−	0.0908046i
$629$	99.0503	+	171.560i	0.00627884	+	0.0108753i
$630$	3131.30	+	1511.73i	0.198022	+	0.0956009i
$631$	−8328.78	+	14425.9i	−0.525457	+	0.910119i	0.474103	+	0.880469i	$0.342772\pi$
$631$	−8328.78	+	14425.9i	−0.525457	+	0.910119i	−0.999560	+	0.0296493i	$0.990561\pi$
$632$	−2438.84	+	2046.43i	−0.153500	+	0.128802i
$633$	−3109.17	+	957.390i	−0.195227	+	0.0601151i
$634$	−105.774	+	599.876i	−0.00662592	+	0.0375774i
$635$	3143.70	−	17828.8i	0.196463	−	1.11420i
$636$	−1253.33	+	5478.85i	−0.0781410	+	0.341589i
$637$	2803.73	−	2352.61i	0.174392	−	0.146332i
$638$	−10.0353	+	17.3816i	−0.000622726	+	0.00107859i
$639$	28560.3	+	2886.07i	1.76812	+	0.178672i
$640$	−5966.22	−	10333.8i	−0.368493	−	0.638248i
$641$	−15060.7	−	5481.65i	−0.928022	−	0.337772i	−0.166597	−	0.986025i	$-0.553278\pi$
$641$	−15060.7	−	5481.65i	−0.928022	−	0.337772i	−0.761425	+	0.648253i	$0.775500\pi$
$642$	1254.78	+	529.657i	0.0771375	+	0.0325606i
$643$	3341.80	+	2804.10i	0.204957	+	0.171980i	0.739489	−	0.673169i	$-0.235067\pi$
$643$	3341.80	+	2804.10i	0.204957	+	0.171980i	−0.534531	+	0.845149i	$0.679512\pi$
$644$	18835.0	−	6855.37i	1.15249	−	0.419471i
$645$	16295.5	−	25203.4i	0.994785	−	1.53858i
$646$	4.80660	+	27.2596i	0.000292745	+	0.00166024i
$647$	−10839.2			−0.658628			−0.329314	−	0.944220i	$-0.606817\pi$
$647$	−10839.2			−0.658628			−0.329314	+	0.944220i	$0.606817\pi$
$648$	3396.31	+	693.486i	0.205894	+	0.0420412i
$649$	35.0249			0.00211841
$650$	−442.823	−	2511.37i	−0.0267215	−	0.151545i
$651$	11338.2	−	17536.1i	0.682609	−	1.05575i
$652$	−5309.29	+	1932.42i	−0.318908	+	0.116073i
$653$	−11232.4	−	9425.09i	−0.673135	−	0.564827i	0.240856	−	0.970561i	$-0.422572\pi$
$653$	−11232.4	−	9425.09i	−0.673135	−	0.564827i	−0.913992	+	0.405733i	$0.867016\pi$
$654$	1583.25	+	668.307i	0.0946637	+	0.0399585i
$655$	36069.6	+	13128.3i	2.15169	+	0.783151i
$656$	9818.37	+	17005.9i	0.584364	+	1.01215i
$657$	−10805.7	+	14998.9i	−0.641660	+	0.890658i
$658$	−67.9460	+	117.686i	−0.00402555	+	0.00697246i
$659$	10953.7	−	9191.24i	0.647489	−	0.543308i	−0.258819	−	0.965926i	$-0.583333\pi$
$659$	10953.7	−	9191.24i	0.647489	−	0.543308i	0.906308	+	0.422618i	$0.138889\pi$
$660$	−134.096	+	586.195i	−0.00790863	+	0.0345721i
$661$	−313.393	+	1777.34i	−0.0184411	+	0.104585i	−0.992639	−	0.121111i	$-0.961354\pi$
$661$	−313.393	+	1777.34i	−0.0184411	+	0.104585i	0.974198	+	0.225696i	$0.0724654\pi$
$662$	62.9763	−	357.156i	0.00369735	−	0.0209687i
$663$	203.837	−	62.7663i	0.0119402	−	0.00367668i
$664$	2032.01	−	1705.06i	0.118761	−	0.0996524i
$665$	−14973.3	+	25934.5i	−0.873140	+	1.51232i
$666$	−88.4607	−	1196.10i	−0.00514682	−	0.0695916i
$667$	5426.43	+	9398.85i	0.315011	+	0.545614i
$668$	27362.9	+	9959.29i	1.58489	+	0.576851i
$669$	−18795.9	+	14222.9i	−1.08624	+	0.821957i
$670$	422.289	+	354.342i	0.0243499	+	0.0204320i
$671$	371.752	−	135.307i	0.0213880	−	0.00778458i
$672$	−6304.40	−	317.726i	−0.361901	−	0.0182389i
$673$	−75.6114	−	428.813i	−0.00433076	−	0.0245610i	0.982566	−	0.185915i	$-0.0595250\pi$
$673$	−75.6114	−	428.813i	−0.00433076	−	0.0245610i	−0.986897	+	0.161354i	$0.948414\pi$
$674$	2541.69			0.145255
$675$	912.159	+	38860.8i	0.0520134	+	2.21593i
$676$	9876.64			0.561939
$677$	−4269.07	−	24211.1i	−0.242354	−	1.37446i	−0.826559	−	0.562851i	$-0.809705\pi$
$677$	−4269.07	−	24211.1i	−0.242354	−	1.37446i	0.584205	−	0.811606i	$-0.301406\pi$
$678$	473.335	+	924.385i	0.0268117	+	0.0523611i
$679$	−5981.21	+	2176.98i	−0.338053	+	0.123041i
$680$	−97.3441	−	81.6814i	−0.00548967	−	0.00460638i
$681$	4204.37	+	33683.4i	0.236581	+	1.89537i
$682$	−38.3150	−	13.9455i	−0.00215126	−	0.000782994i
$683$	−953.659	−	1651.79i	−0.0534271	−	0.0925385i	0.838075	−	0.545555i	$-0.183681\pi$
$683$	−953.659	−	1651.79i	−0.0534271	−	0.0925385i	−0.891502	+	0.453017i	$0.850348\pi$
$684$	−4034.10	+	14284.5i	−0.225508	+	0.798512i
$685$	26485.4	−	45874.1i	1.47731	−	2.55877i
$686$	1102.85	−	925.400i	0.0613804	−	0.0515043i
$687$	−20491.1	−	19031.6i	−1.13797	−	1.05692i
$688$	−3094.45	+	17549.5i	−0.171475	+	0.972484i
$689$	731.230	−	4147.01i	0.0404320	−	0.229301i
$690$	−2689.97	−	2498.38i	−0.148414	−	0.137843i
$691$	−9024.11	+	7572.13i	−0.496807	+	0.416870i	−0.856458	−	0.516216i	$-0.827340\pi$
$691$	−9024.11	+	7572.13i	−0.496807	+	0.416870i	0.359652	+	0.933087i	$0.382896\pi$
$692$	−7928.00	+	13731.7i	−0.435517	+	0.754337i
$693$	295.291	+	303.339i	0.0161864	+	0.0166276i
$694$	988.887	+	1712.80i	0.0540888	+	0.0936846i
$695$	−3123.83	−	1136.98i	−0.170495	−	0.0620550i
$696$	−281.698	−	2256.83i	−0.0153416	−	0.122909i
$697$	324.070	+	271.927i	0.0176113	+	0.0147776i
$698$	−1471.82	+	535.697i	−0.0798124	+	0.0290493i
$699$	−4937.13	−	9641.82i	−0.267152	−	0.521727i
$700$	−8179.30	−	46387.1i	−0.441641	−	2.50467i
$701$	24949.8			1.34428			0.672141	−	0.740423i	$-0.265375\pi$
$701$	24949.8			1.34428			0.672141	+	0.740423i	$0.265375\pi$
$702$	−1276.57	−	194.326i	−0.0686341	−	0.0104478i
$703$	10329.5			0.554174
$704$	−60.5607	−	343.457i	−0.00324214	−	0.0183871i
$705$	−2201.75	−	110.963i	−0.117621	−	0.00592780i
$706$	−1378.14	+	501.603i	−0.0734661	+	0.0267395i
$707$	28164.4	+	23632.7i	1.49820	+	1.25714i
$708$	−1573.59	+	1190.74i	−0.0835297	+	0.0632071i
$709$	−12350.5	−	4495.22i	−0.654208	−	0.238112i	−0.00647435	−	0.999979i	$-0.502061\pi$
$709$	−12350.5	−	4495.22i	−0.654208	−	0.238112i	−0.647734	+	0.761867i	$0.724283\pi$
$710$	3185.56	+	5517.55i	0.168383	+	0.291648i
$711$	−14946.5	+	10169.0i	−0.788378	+	0.536380i
$712$	−1280.46	+	2217.82i	−0.0673979	+	0.116737i
$713$	−16889.7	+	14172.2i	−0.887133	+	0.744393i
$714$	−42.5084	+	13.0894i	−0.00222806	+	0.000686075i
$715$	78.2360	−	443.699i	0.00409211	−	0.0232075i
$716$	3958.61	−	22450.4i	0.206620	−	1.17180i
$717$	5511.01	−	24091.1i	0.287047	−	1.25481i
$718$	2061.10	−	1729.47i	0.107130	−	0.0898929i
$719$	−8434.31	+	14608.6i	−0.437478	+	0.757734i	−0.997494	−	0.0707477i	$-0.977461\pi$
$719$	−8434.31	+	14608.6i	−0.437478	+	0.757734i	0.560016	+	0.828481i	$0.310795\pi$
$720$	−13745.4	−	30542.5i	−0.711474	−	1.58091i
$721$	−7115.32	−	12324.1i	−0.367529	−	0.636579i
$722$	−569.950	−	207.445i	−0.0293786	−	0.0106929i
$723$	−11040.0	−	4660.11i	−0.567888	−	0.239712i
$724$	−5506.29	−	4620.33i	−0.282651	−	0.237173i
$725$	23966.1	−	8722.93i	1.22769	−	0.446844i
$726$	−1121.79	+	1735.01i	−0.0573464	+	0.0886946i
$727$	−5594.68	−	31729.0i	−0.285413	−	1.61866i	−0.703806	−	0.710392i	$-0.748518\pi$
$727$	−5594.68	−	31729.0i	−0.285413	−	1.61866i	0.418393	−	0.908266i	$-0.362594\pi$
$728$	3147.10			0.160219
$729$	18791.5	+	5856.75i	0.954705	+	0.297554i
$730$	−4102.86			−0.208019
$731$	66.6653	+	378.078i	0.00337306	+	0.0191296i
$732$	−12102.0	+	18717.4i	−0.611067	+	0.945104i
$733$	16319.0	−	5939.64i	0.822315	−	0.299298i	0.103614	−	0.994618i	$-0.466959\pi$
$733$	16319.0	−	5939.64i	0.822315	−	0.299298i	0.718701	+	0.695319i	$0.244737\pi$
$734$	199.814	+	167.664i	0.0100481	+	0.00843132i
$735$	−11407.6	−	4815.26i	−0.572483	−	0.241651i
$736$	6262.83	+	2279.48i	0.313656	+	0.114162i
$737$	33.5574	+	58.1231i	0.00167721	+	0.00290501i
$738$	−1051.13	−	2335.62i	−0.0524290	−	0.116498i
$739$	−14926.7	+	25853.8i	−0.743014	+	1.28694i	0.208103	+	0.978107i	$0.433271\pi$
$739$	−14926.7	+	25853.8i	−0.743014	+	1.28694i	−0.951117	+	0.308831i	$0.900062\pi$
$740$	−18061.2	+	15155.1i	−0.897219	+	0.752856i
$741$	2479.97	−	10841.0i	0.122947	−	0.537457i
$742$	−152.492	+	864.823i	−0.00754467	+	0.0427880i
$743$	−3365.15	+	19084.7i	−0.166158	+	0.942328i	0.781705	+	0.623649i	$0.214350\pi$
$743$	−3365.15	+	19084.7i	−0.166158	+	0.942328i	−0.947863	+	0.318679i	$0.896761\pi$
$744$	4415.81	−	1359.74i	0.217596	−	0.0670031i
$745$	−21131.2	+	17731.2i	−1.03918	+	0.871972i
$746$	−940.389	+	1628.80i	−0.0461529	+	0.0799392i
$747$	12453.2	−	8472.65i	0.609959	−	0.414991i
$748$	−3.84604	−	6.66154i	−0.000188002	−	0.000325628i
$749$	−17711.8	−	6446.58i	−0.864054	−	0.314490i
$750$	−3775.88	+	2857.22i	−0.183834	+	0.139108i
$751$	−19081.1	−	16010.9i	−0.927136	−	0.777960i	0.0481647	−	0.998839i	$-0.484663\pi$
$751$	−19081.1	−	16010.9i	−0.927136	−	0.777960i	−0.975301	+	0.220880i	$0.929107\pi$
$752$	1230.03	−	447.693i	0.0596469	−	0.0217097i
$753$	−10323.0	−	520.254i	−0.499590	−	0.0251781i
$754$	147.119	+	834.356i	0.00710580	+	0.0402990i
$755$	7511.60			0.362086
$756$	−23579.3	−	3589.35i	−1.13436	−	0.172677i
$757$	30693.0			1.47366			0.736828	−	0.676081i	$-0.236323\pi$
$757$	30693.0			1.47366			0.736828	+	0.676081i	$0.236323\pi$
$758$	−153.443	−	870.216i	−0.00735262	−	0.0416988i
$759$	−203.716	−	397.841i	−0.00974231	−	0.0190260i
$760$	−6226.37	+	2266.21i	−0.297177	+	0.108163i
$761$	−3563.33	−	2989.99i	−0.169738	−	0.142427i	0.553962	−	0.832542i	$-0.313115\pi$
$761$	−3563.33	−	2989.99i	−0.169738	−	0.142427i	−0.723700	+	0.690115i	$0.757560\pi$
$762$	−173.657	−	1391.25i	−0.00825580	−	0.0661415i
$763$	−22348.4	−	8134.13i	−1.06037	−	0.385944i
$764$	−4442.22	−	7694.15i	−0.210358	−	0.364352i
$765$	−503.312	−	517.030i	−0.0237873	−	0.0244356i
$766$	496.587	−	860.114i	0.0234235	−	0.0405708i
$767$	1132.59	−	950.355i	0.0533187	−	0.0447397i
$768$	13882.8	+	12893.9i	0.652280	+	0.605820i
$769$	−749.236	+	4249.13i	−0.0351341	+	0.199255i	−0.997322	−	0.0731296i	$-0.976701\pi$
$769$	−749.236	+	4249.13i	−0.0351341	+	0.199255i	0.962188	+	0.272385i	$0.0878124\pi$
$770$	−16.3154	+	92.5295i	−0.000763595	+	0.00433056i
$771$	23874.8	+	22174.3i	1.11521	+	1.03578i
$772$	21113.6	−	17716.4i	0.984321	−	0.825943i
$773$	9214.98	−	15960.8i	0.428771	−	0.742653i	−0.567994	−	0.823033i	$-0.692280\pi$
$773$	9214.98	−	15960.8i	0.428771	−	0.742653i	0.996764	+	0.0803804i	$0.0256135\pi$
$774$	631.706	−	2236.83i	0.0293362	−	0.103878i
$775$	25906.3	+	44871.1i	1.20075	+	2.07976i
$776$	−1323.40	−	481.679i	−0.0612208	−	0.0222826i
$777$	2055.82	+	16470.2i	0.0949190	+	0.760446i
$778$	2141.48	+	1796.91i	0.0986835	+	0.0828053i
$779$	20728.4	−	7544.51i	0.953364	−	0.346996i
$780$	11569.4	+	22594.2i	0.531092	+	1.03718i
$781$	134.694	+	763.889i	0.00617124	+	0.0349988i
$782$	46.9608			0.00214746
$783$	−303.047	−	12910.7i	−0.0138315	−	0.589262i
$784$	7352.05			0.334915
$785$	−1839.08	−	10430.0i	−0.0836174	−	0.474218i
$786$	2968.91	+	149.626i	0.134730	+	0.00679005i
$787$	−10601.7	+	3858.70i	−0.480189	+	0.174775i	−0.570763	−	0.821115i	$-0.693352\pi$
$787$	−10601.7	+	3858.70i	−0.480189	+	0.174775i	0.0905732	+	0.995890i	$0.471130\pi$
$788$	−25565.0	−	21451.6i	−1.15573	−	0.969774i
$789$	10148.9	−	7679.73i	0.457937	−	0.346522i
$790$	−3770.30	−	1372.28i	−0.169799	−	0.0618018i
$791$	−7186.07	−	12446.6i	−0.323018	−	0.559483i
$792$	6.90849	+	93.4117i	0.000309953	+	0.00419096i
$793$	8349.86	−	14462.4i	0.373912	−	0.647634i
$794$	932.575	−	782.523i	0.0416824	−	0.0349757i
$795$	−13615.4	+	4192.51i	−0.607406	+	0.187035i
$796$	563.699	−	3196.89i	0.0251002	−	0.142350i
$797$	−4560.92	+	25866.2i	−0.202705	+	1.14960i	0.698305	+	0.715800i	$0.253938\pi$
$797$	−4560.92	+	25866.2i	−0.202705	+	1.14960i	−0.901010	+	0.433798i	$0.857173\pi$
$798$	−517.176	+	2260.80i	−0.0229421	+	0.100290i
$799$	21.6022	−	18.1264i	0.000956486	−	0.000802587i
$800$	7831.08	−	13563.8i	0.346088	−	0.599442i
$801$	−8500.07	+	11798.5i	−0.374950	+	0.520451i
$802$	582.340	+	1008.64i	0.0256398	+	0.0444095i
$803$	−469.392	−	170.845i	−0.0206283	−	0.00750808i
$804$	−3483.67	−	1470.49i	−0.152810	−	0.0645028i
$805$	38919.6	+	32657.4i	1.70402	+	1.42984i
$806$	−1617.37	+	588.676i	−0.0706819	+	0.0257261i
$807$	13372.2	−	20682.0i	0.583301	−	0.902159i
$808$	1412.60	+	8011.25i	0.0615038	+	0.348805i
$809$	−4965.48			−0.215793			−0.107897	−	0.994162i	$-0.534412\pi$
$809$	−4965.48			−0.215793			−0.107897	+	0.994162i	$0.534412\pi$
$810$	1383.23	+	4143.78i	0.0600022	+	0.179750i
$811$	−37019.4			−1.60287			−0.801434	−	0.598083i	$-0.795929\pi$
$811$	−37019.4			−1.60287			−0.801434	+	0.598083i	$0.795929\pi$
$812$	2717.42	+	15411.2i	0.117442	+	0.666045i
$813$	12325.7	−	19063.5i	0.531713	−	0.822371i
$814$	30.4542	−	11.0844i	0.00131133	−	0.000477284i
$815$	−10970.8	−	9205.62i	−0.471523	−	0.395655i
$816$	394.707	+	166.610i	0.0169332	+	0.00714769i
$817$	18810.9	+	6846.60i	0.805519	+	0.293185i
$818$	−1683.49	−	2915.90i	−0.0719584	−	0.124636i
$819$	17779.5	+	1796.64i	0.758565	+	0.0766542i
$820$	−25174.6	+	43603.6i	−1.07211	+	1.85696i
$821$	1124.67	−	943.710i	0.0478091	−	0.0401166i	−0.618570	−	0.785730i	$-0.712288\pi$
$821$	1124.67	−	943.710i	0.0478091	−	0.0401166i	0.666379	+	0.745613i	$0.267843\pi$
$822$	914.805	−	3999.02i	0.0388169	−	0.169686i
$823$	1879.65	−	10660.1i	0.0796120	−	0.451502i	−0.918778	−	0.394775i	$-0.870823\pi$
$823$	1879.65	−	10660.1i	0.0796120	−	0.451502i	0.998390	−	0.0567267i	$-0.0180664\pi$
$824$	546.761	−	3100.83i	0.0231157	−	0.131095i
$825$	−1003.85	+	309.110i	−0.0423632	+	0.0130446i
$826$	−236.192	+	198.188i	−0.00994934	+	0.00834849i
$827$	−4931.39	+	8541.41i	−0.207353	+	0.359146i	−0.950880	−	0.309560i	$-0.899818\pi$
$827$	−4931.39	+	8541.41i	−0.207353	+	0.359146i	0.743527	+	0.668706i	$0.233152\pi$
$828$	22677.8	+	10948.4i	0.951823	+	0.459520i
$829$	−18383.5	−	31841.1i	−0.770185	−	1.33400i	−0.937461	−	0.348090i	$-0.886830\pi$
$829$	−18383.5	−	31841.1i	−0.770185	−	1.33400i	0.167276	−	0.985910i	$-0.446503\pi$
$830$	3141.37	+	1143.36i	0.131372	+	0.0478154i
$831$	31982.6	−	24201.3i	1.33509	−	1.01027i
$832$	−11277.6	−	9463.02i	−0.469928	−	0.394316i
$833$	148.837	−	54.1721i	0.00619074	−	0.00225325i
$834$	−257.125	−	12.9584i	−0.0106757	−	0.000538027i
$835$	12816.9	+	72688.1i	0.531193	+	3.01255i
$836$	−401.086			−0.0165931
$837$	25723.3	−	5160.86i	1.06228	−	0.213125i
$838$	1792.01			0.0738713
$839$	2194.15	+	12443.7i	0.0902867	+	0.512042i	0.996090	+	0.0883432i	$0.0281572\pi$
$839$	2194.15	+	12443.7i	0.0902867	+	0.512042i	−0.905803	+	0.423698i	$0.860732\pi$
$840$	−4852.64	−	9476.82i	−0.199324	−	0.389264i
$841$	14955.9	−	5443.50i	0.613223	−	0.223195i
$842$	3588.39	+	3011.01i	0.146869	+	0.123238i
$843$	−2417.75	−	19369.9i	−0.0987804	−	0.791381i
$844$	4654.08	+	1693.95i	0.189810	+	0.0690854i
$845$	12517.4	+	21680.8i	0.509600	+	0.882653i
$846$	−165.492	+	41.9674i	−0.00672546	+	0.00170552i
$847$	14296.2	−	24761.8i	0.579957	−	1.00451i
$848$	6479.84	−	5437.23i	0.262404	−	0.220183i
$849$	8863.43	+	8232.12i	0.358295	+	0.332775i
$850$	19.1634	−	108.681i	0.000773294	−	0.00438557i
$851$	3043.11	−	17258.3i	0.122581	−	0.695191i
$852$	−32021.4	−	29740.6i	−1.28760	−	1.19589i
$853$	−3006.58	+	2522.82i	−0.120684	+	0.101266i	−0.701132	−	0.713031i	$-0.747322\pi$
$853$	−3006.58	+	2522.82i	−0.120684	+	0.101266i	0.580448	+	0.814297i	$0.302877\pi$
$854$	−1741.29	+	3016.00i	−0.0697725	+	0.120850i
$855$	−36469.5	+	9248.36i	−1.45875	+	0.369927i
$856$	−2085.21	−	3611.70i	−0.0832607	−	0.144212i
$857$	7537.41	+	2743.39i	0.300435	+	0.109349i	0.487839	−	0.872933i	$-0.337785\pi$
$857$	7537.41	+	2743.39i	0.300435	+	0.109349i	−0.187404	+	0.982283i	$0.560007\pi$
$858$	−4.32173	−	34.6236i	−0.000171960	−	0.00137766i
$859$	−15033.6	−	12614.7i	−0.597136	−	0.501057i	0.293388	−	0.955994i	$-0.405217\pi$
$859$	−15033.6	−	12614.7i	−0.597136	−	0.501057i	−0.890524	+	0.454937i	$0.849662\pi$
$860$	−42936.0	+	15627.4i	−1.70245	+	0.619641i
$861$	16155.0	+	31549.5i	0.639445	+	1.24879i
$862$	−467.029	−	2648.65i	−0.0184537	−	0.104656i
$863$	−37409.0			−1.47557			−0.737785	−	0.675036i	$-0.764128\pi$
$863$	−37409.0			−1.47557			−0.737785	+	0.675036i	$0.764128\pi$
$864$	−5238.92	−	5953.98i	−0.206287	−	0.234443i
$865$	−40191.0			−1.57981
$866$	53.4496	+	303.128i	0.00209733	+	0.0118946i
$867$	−25487.1	−	1284.49i	−0.998371	−	0.0503154i
$868$	−29874.2	+	10873.3i	−1.16820	+	0.425190i
$869$	−374.203	−	313.994i	−0.0146076	−	0.0122572i
$870$	2285.64	−	1729.55i	0.0890695	−	0.0673991i
$871$	2662.23	+	968.973i	0.103566	+	0.0376951i
$872$	−2631.07	−	4557.15i	−0.102178	−	0.176978i
$873$	−7201.55	−	3476.75i	−0.279193	−	0.134788i
$874$	1224.33	−	2120.61i	0.0473841	−	0.0820716i
$875$	50197.9	−	42121.1i	1.93943	−	1.62737i
$876$	26896.9	−	8282.22i	1.03740	−	0.319441i
$877$	−2545.12	+	14434.1i	−0.0979963	+	0.555764i	0.895792	+	0.444474i	$0.146609\pi$
$877$	−2545.12	+	14434.1i	−0.0979963	+	0.555764i	−0.993788	+	0.111290i	$0.964502\pi$
$878$	519.452	−	2945.96i	0.0199666	−	0.113236i
$879$	−5612.00	+	24532.5i	−0.215345	+	0.941368i
$880$	693.294	−	581.742i	0.0265579	−	0.0222847i
$881$	4025.18	−	6971.82i	0.153929	−	0.266613i	−0.778739	−	0.627348i	$-0.784141\pi$
$881$	4025.18	−	6971.82i	0.153929	−	0.266613i	0.932669	+	0.360734i	$0.117474\pi$
$882$	−954.081	−	96.4115i	−0.0364235	−	0.00368066i
$883$	−21299.5	−	36891.7i	−0.811760	−	1.40601i	−0.911631	−	0.411009i	$-0.865177\pi$
$883$	−21299.5	−	36891.7i	−0.811760	−	1.40601i	0.0998716	−	0.995000i	$-0.468157\pi$
$884$	−305.121	−	111.055i	−0.0116090	−	0.00422531i
$885$	−4608.18	−	1945.16i	−0.175031	−	0.0738824i
$886$	−258.410	−	216.831i	−0.00979846	−	0.00822189i
$887$	−47598.1	+	17324.3i	−1.80179	+	0.655797i	−0.803631	+	0.595129i	$0.797101\pi$
$887$	−47598.1	+	17324.3i	−1.80179	+	0.655797i	−0.998158	+	0.0606688i	$0.980677\pi$
$888$	−1994.00	+	3084.01i	−0.0753538	+	0.116546i
$889$	3369.29	+	19108.2i	0.127112	+	0.720886i
$890$	−3227.43			−0.121555
$891$	−14.2983	+	531.671i	−0.000537612	+	0.0199906i
$892$	35884.3			1.34697
$893$	−255.334	−	1448.07i	−0.00956823	−	0.0542641i
$894$	−1159.92	+	1793.98i	−0.0433931	+	0.0671138i
$895$	54299.2	−	19763.3i	2.02796	−	0.738117i
$896$	9796.70	+	8220.41i	0.365273	+	0.306501i
$897$	−17382.4	−	7337.29i	−0.647025	−	0.273116i
$898$	−1479.06	−	538.335i	−0.0549633	−	0.0200050i
$899$	−8606.88	−	14907.5i	−0.319305	−	0.553053i
$900$	34591.9	−	48015.4i	1.28118	−	1.77835i
$901$	91.1164	−	157.818i	0.00336906	−	0.00583539i
$902$	53.0170	−	44.4866i	0.00195707	−	0.00164217i
$903$	−7172.98	+	31356.3i	−0.264343	+	1.15556i
$904$	552.197	−	3131.67i	0.0203162	−	0.115219i
$905$	3163.81	−	17942.9i	0.116208	−	0.659051i
$906$	555.973	−	171.198i	0.0203874	−	0.00627778i
$907$	25852.9	−	21693.2i	0.946452	−	0.794167i	−0.0322446	−	0.999480i	$-0.510266\pi$
$907$	25852.9	−	21693.2i	0.946452	−	0.794167i	0.978696	+	0.205313i	$0.0658211\pi$
$908$	25839.0	−	44754.4i	0.944379	−	1.63571i
$909$	3406.91	+	46065.8i	0.124313	+	1.68087i
$910$	1983.08	+	3434.80i	0.0722401	+	0.125124i
$911$	−28530.0	−	10384.1i	−1.03759	−	0.377651i	−0.233622	−	0.972327i	$-0.575058\pi$
$911$	−28530.0	−	10384.1i	−1.03759	−	0.377651i	−0.803965	+	0.594677i	$0.797280\pi$
$912$	17814.1	−	13480.0i	0.646804	−	0.489438i
$913$	311.781	+	261.616i	0.0113017	+	0.00948325i
$914$	−2807.59	+	1021.88i	−0.101605	+	0.0369812i
$915$	−56425.5	−	2843.70i	−2.03865	−	0.102743i
$916$	7393.16	+	41928.7i	0.266678	+	1.51241i
$917$	−41138.9			−1.48149
$918$	−49.0365	−	26.7971i	−0.00176301	−	0.000963438i
$919$	−30740.1			−1.10340			−0.551699	−	0.834043i	$-0.686020\pi$
$919$	−30740.1			−1.10340			−0.551699	+	0.834043i	$0.686020\pi$
$920$	1952.03	+	11070.5i	0.0699529	+	0.396722i
$921$	5875.51	+	11474.4i	0.210211	+	0.410526i
$922$	3829.46	−	1393.81i	0.136786	−	0.0497860i
$923$	25082.7	+	21046.9i	0.894482	+	0.750560i
$924$	−79.8258	−	639.526i	−0.00284207	−	0.0227693i
$925$	−38699.0	−	14085.3i	−1.37558	−	0.500672i
$926$	577.532	+	1000.31i	0.0204955	+	0.0354993i
$927$	4859.15	−	17206.0i	0.172163	−	0.609620i
$928$	−2601.73	+	4506.32i	−0.0920322	+	0.159404i
$929$	14376.5	−	12063.3i	0.507727	−	0.426034i	−0.352601	−	0.935774i	$-0.614703\pi$
$929$	14376.5	−	12063.3i	0.507727	−	0.426034i	0.860329	+	0.509740i	$0.170258\pi$
$930$	4266.58	+	3962.68i	0.150437	+	0.139722i
$931$	1434.13	−	8133.35i	0.0504852	−	0.286316i
$932$	−2863.69	+	16240.8i	−0.100647	+	0.570799i
$933$	6145.59	+	5707.86i	0.215646	+	0.200286i
$934$	−3138.65	+	2633.64i	−0.109957	+	0.0922648i
$935$	9.74876	−	16.8853i	0.000340982	−	0.000590599i
$936$	2758.00	+	2833.17i	0.0963121	+	0.0989371i
$937$	18847.5	+	32644.8i	0.657119	+	1.13816i	0.981358	+	0.192188i	$0.0615584\pi$
$937$	18847.5	+	32644.8i	0.657119	+	1.13816i	−0.324239	+	0.945975i	$0.605108\pi$
$938$	−555.185	−	202.071i	−0.0193256	−	0.00703396i
$939$	6415.74	+	51399.8i	0.222971	+	1.78634i
$940$	2571.02	+	2157.34i	0.0892100	+	0.0748561i
$941$	34661.8	−	12615.9i	1.20079	−	0.437052i	0.337290	−	0.941401i	$-0.390490\pi$
$941$	34661.8	−	12615.9i	1.20079	−	0.437052i	0.863500	+	0.504349i	$0.168268\pi$
$942$	−373.831	−	730.062i	−0.0129300	−	0.0252513i
$943$	−6498.56	−	36855.2i	−0.224414	−	1.27271i
$944$	2969.92			0.102397
$945$	−22004.7	−	56309.5i	−0.757474	−	1.93836i
$946$	62.8066			0.00215858
$947$	4455.71	+	25269.6i	0.152895	+	0.867108i	0.960685	+	0.277639i	$0.0895519\pi$
$947$	4455.71	+	25269.6i	0.152895	+	0.867108i	−0.807791	+	0.589469i	$0.799337\pi$
$948$	27486.9	+	1385.27i	0.941702	+	0.0474594i
$949$	−19814.3	+	7211.80i	−0.677764	+	0.246686i
$950$	−4408.09	−	3698.82i	−0.150544	−	0.126322i
$951$	8445.44	−	6390.69i	0.287973	−	0.217910i
$952$	127.979	+	46.5805i	0.00435695	+	0.00158580i
$953$	12102.3	+	20961.9i	0.411367	+	0.712509i	0.995040	−	0.0994802i	$-0.0317180\pi$
$953$	12102.3	+	20961.9i	0.411367	+	0.712509i	−0.583672	+	0.811989i	$0.698385\pi$
$954$	−912.195	+	620.620i	−0.0309575	+	0.0210622i
$955$	11259.9	−	19502.8i	0.381531	−	0.660832i
$956$	−28821.6	+	24184.2i	−0.975060	+	0.818172i
$957$	333.510	−	102.696i	0.0112653	−	0.00346885i
$958$	365.257	−	2071.47i	0.0123183	−	0.0698604i
$959$	−9858.35	+	55909.5i	−0.331953	+	1.88260i
$960$	−11106.5	+	48551.5i	−0.373397	+	1.63229i
$961$	3967.65	−	3329.25i	0.133183	−	0.111754i
$962$	684.027	−	1184.77i	0.0229251	−	0.0397074i
$963$	−9718.50	−	21594.6i	−0.325207	−	0.722614i
$964$	9121.75	+	15799.3i	0.304763	+	0.527865i
$965$	65649.3	+	23894.4i	2.18997	+	0.797085i
$966$	3624.95	+	1530.13i	0.120736	+	0.0509638i
$967$	5011.54	+	4205.18i	0.166660	+	0.139844i	0.722303	−	0.691576i	$-0.243083\pi$
$967$	5011.54	+	4205.18i	0.166660	+	0.139844i	−0.555643	+	0.831421i	$0.687528\pi$
$968$	5944.83	−	2163.74i	0.197390	−	0.0718442i
$969$	261.309	−	404.152i	0.00866301	−	0.0133986i
$970$	−308.203	−	1747.91i	−0.0102019	−	0.0578576i
$971$	35553.5			1.17504			0.587521	−	0.809209i	$-0.300104\pi$
$971$	35553.5			1.17504			0.587521	+	0.809209i	$0.300104\pi$
$972$	−17432.8	−	24372.9i	−0.575264	−	0.804280i
$973$	3562.86			0.117390
$974$	−492.221	−	2791.53i	−0.0161928	−	0.0918339i
$975$	−24073.9	+	37233.8i	−0.790751	+	1.22301i
$976$	31522.6	−	11473.3i	1.03382	−	0.376281i
$977$	34259.6	+	28747.2i	1.12187	+	0.941357i	0.998697	−	0.0510292i	$-0.0162502\pi$
$977$	34259.6	+	28747.2i	1.12187	+	0.941357i	0.123168	+	0.992386i	$0.460695\pi$
$978$	−1021.82	−	431.320i	−0.0334091	−	0.0141023i
$979$	−369.237	−	134.391i	−0.0120540	−	0.00438730i
$980$	9425.42	+	16325.3i	0.307229	+	0.532136i
$981$	−12262.6	−	27247.6i	−0.399096	−	0.886797i
$982$	−2012.08	+	3485.02i	−0.0653848	+	0.113250i
$983$	9990.01	−	8382.61i	0.324142	−	0.271988i	−0.466166	−	0.884697i	$-0.654365\pi$
$983$	9990.01	−	8382.61i	0.324142	−	0.271988i	0.790308	+	0.612710i	$0.209921\pi$
$984$	−1748.87	+	7645.10i	−0.0566586	+	0.247680i
$985$	14689.2	−	83306.5i	0.475164	−	2.69479i
$986$	−6.36668	+	36.1072i	−0.000205635	+	0.00116622i
$987$	2258.11	−	695.327i	0.0728231	−	0.0224240i
$988$	−12969.8	+	10883.0i	−0.417636	+	0.350438i
$989$	16980.9	−	29411.8i	0.545967	−	0.945643i
$990$	−97.5979	+	66.4016i	−0.00313320	+	0.00213170i
$991$	−28777.1	−	49843.4i	−0.922436	−	1.59771i	−0.795634	−	0.605778i	$-0.792862\pi$
$991$	−28777.1	−	49843.4i	−0.922436	−	1.59771i	−0.126802	−	0.991928i	$-0.540471\pi$
$992$	−9933.50	−	3615.50i	−0.317932	−	0.115718i
$993$	−5028.28	+	3804.91i	−0.160693	+	0.121596i
$994$	−5230.78	−	4389.14i	−0.166912	−	0.140056i
$995$	7732.11	−	2814.26i	0.246356	−	0.0896663i
$996$	−22901.7	−	1154.19i	−0.728584	−	0.0367188i
$997$	−3423.94	−	19418.2i	−0.108764	−	0.616830i	−0.989650	−	0.143502i	$-0.954164\pi$
$997$	−3423.94	−	19418.2i	−0.108764	−	0.616830i	0.880886	−	0.473328i	$-0.156947\pi$
$998$	−3545.30			−0.112449
$999$	−13025.7	+	16284.7i	−0.412527	+	0.515740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.13.4	✓	48
3.2	odd	2		81.4.e.a.10.5		48
9.2	odd	6		243.4.e.b.109.5		48
9.4	even	3		243.4.e.d.190.5		48
9.5	odd	6		243.4.e.a.190.4		48
9.7	even	3		243.4.e.c.109.4		48
27.2	odd	18		81.4.e.a.73.5		48
27.5	odd	18		729.4.a.c.1.14		24
27.7	even	9		243.4.e.c.136.4		48
27.11	odd	18		243.4.e.a.55.4		48
27.16	even	9		243.4.e.d.55.5		48
27.20	odd	18		243.4.e.b.136.5		48
27.22	even	9		729.4.a.d.1.11		24
27.25	even	9	inner	27.4.e.a.25.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.4	✓	48	1.1	even	1	trivial
27.4.e.a.25.4	yes	48	27.25	even	9	inner
81.4.e.a.10.5		48	3.2	odd	2
81.4.e.a.73.5		48	27.2	odd	18
243.4.e.a.55.4		48	27.11	odd	18
243.4.e.a.190.4		48	9.5	odd	6
243.4.e.b.109.5		48	9.2	odd	6
243.4.e.b.136.5		48	27.20	odd	18
243.4.e.c.109.4		48	9.7	even	3
243.4.e.c.136.4		48	27.7	even	9
243.4.e.d.55.5		48	27.16	even	9
243.4.e.d.190.5		48	9.4	even	3
729.4.a.c.1.14		24	27.5	odd	18
729.4.a.d.1.11		24	27.22	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0518956 - 0.294314i) q^{2} +(-2.82128 + 4.36353i) q^{3} +(7.43361 - 2.70561i) q^{4} +(15.3604 + 12.8889i) q^{5} +(1.43066 + 0.603897i) q^{6} +(-20.1945 - 7.35018i) q^{7} +(-2.37749 - 4.11794i) q^{8} +(-11.0807 - 24.6215i) q^{9} +O(q^{10})\)	\(q+(-0.0518956 - 0.294314i) q^{2} +(-2.82128 + 4.36353i) q^{3} +(7.43361 - 2.70561i) q^{4} +(15.3604 + 12.8889i) q^{5} +(1.43066 + 0.603897i) q^{6} +(-20.1945 - 7.35018i) q^{7} +(-2.37749 - 4.11794i) q^{8} +(-11.0807 - 24.6215i) q^{9} +(2.99626 - 5.18968i) q^{10} +(0.558890 - 0.468965i) q^{11} +(-9.16632 + 40.0701i) q^{12} +(5.34792 - 30.3295i) q^{13} +(-1.11526 + 6.32496i) q^{14} +(-99.5773 + 30.6623i) q^{15} +(47.3909 - 39.7657i) q^{16} +(0.666388 - 1.15422i) q^{17} +(-6.67142 + 4.53896i) q^{18} +(-34.7473 - 60.1840i) q^{19} +(149.056 + 54.2519i) q^{20} +(89.0470 - 67.3821i) q^{21} +(-0.167027 - 0.140152i) q^{22} +(-110.791 + 40.3246i) q^{23} +(24.6763 + 1.24362i) q^{24} +(48.1122 + 272.858i) q^{25} -9.20396 q^{26} +(138.698 + 21.1133i) q^{27} -170.005 q^{28} +(-15.9844 - 90.6519i) q^{29} +(14.1920 + 27.7158i) q^{30} +(175.726 - 63.9590i) q^{31} +(-43.3032 - 36.3357i) q^{32} +(0.469551 + 3.76182i) q^{33} +(-0.374285 - 0.136229i) q^{34} +(-215.460 - 373.187i) q^{35} +(-148.986 - 153.047i) q^{36} +(-74.3188 + 128.724i) q^{37} +(-15.9098 + 13.3499i) q^{38} +(117.256 + 108.904i) q^{39} +(16.5565 - 93.8966i) q^{40} +(-55.1187 + 312.593i) q^{41} +(-24.4527 - 22.7110i) q^{42} +(-220.661 + 185.157i) q^{43} +(2.88574 - 4.99824i) q^{44} +(147.140 - 521.015i) q^{45} +(17.6177 + 30.5147i) q^{46} +(19.8826 + 7.23668i) q^{47} +(39.8154 + 318.982i) q^{48} +(91.0377 + 76.3897i) q^{49} +(77.8093 - 28.3203i) q^{50} +(3.15639 + 6.16418i) q^{51} +(-42.3057 - 239.928i) q^{52} +136.732 q^{53} +(-0.983887 - 41.9166i) q^{54} +14.6293 q^{55} +(17.7446 + 100.634i) q^{56} +(360.646 + 18.1757i) q^{57} +(-25.8506 + 9.40886i) q^{58} +(36.7754 + 30.8583i) q^{59} +(-657.259 + 497.349i) q^{60} +(509.543 + 185.458i) q^{61} +(-27.9435 - 48.3995i) q^{62} +(42.7965 + 578.663i) q^{63} +(239.011 - 413.979i) q^{64} +(473.062 - 396.946i) q^{65} +(1.08279 - 0.333417i) q^{66} +(-15.9741 + 90.5935i) q^{67} +(1.83080 - 10.3830i) q^{68} +(136.615 - 597.206i) q^{69} +(-98.6529 + 82.7796i) q^{70} +(-531.589 + 920.739i) q^{71} +(-75.0455 + 104.167i) q^{72} +(-342.332 - 592.936i) q^{73} +(41.7421 + 15.1929i) q^{74} +(-1326.36 - 559.871i) q^{75} +(-421.132 - 353.372i) q^{76} +(-14.7335 + 5.36254i) q^{77} +(25.9670 - 40.1617i) q^{78} +(-116.266 - 659.375i) q^{79} +1240.48 q^{80} +(-483.436 + 545.647i) q^{81} +94.8612 q^{82} +(96.8709 + 549.382i) q^{83} +(479.631 - 741.819i) q^{84} +(25.1126 - 9.14025i) q^{85} +(65.9457 + 55.3350i) q^{86} +(440.658 + 186.007i) q^{87} +(-3.25992 - 1.18652i) q^{88} +(-269.288 - 466.421i) q^{89} +(-160.978 - 16.2671i) q^{90} +(-330.926 + 573.181i) q^{91} +(-714.474 + 599.515i) q^{92} +(-216.686 + 947.232i) q^{93} +(1.09804 - 6.22729i) q^{94} +(241.975 - 1372.31i) q^{95} +(280.723 - 86.4413i) q^{96} +(226.888 - 190.381i) q^{97} +(17.7581 - 30.7580i) q^{98} +(-17.7395 - 8.56426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

Modular forms

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Database

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