LMFDB - Embedded newform 27.4.e.a.25.4

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			25.4
Character	$\chi$	$=$	27.25
Dual form			27.4.e.a.13.4

$q$-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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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	−0.992606	−	0.121378i	$-0.961269\pi$
$2$	−0.0518956	+	0.294314i	−0.0183479	+	0.104056i	0.974259	+	0.225434i	$0.0723799\pi$
$3$	−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	0.402463	−	0.915436i	$-0.368154\pi$
$5$	15.3604	−	12.8889i	1.37388	−	1.15282i	0.971416	−	0.237385i	$-0.0762902\pi$
$6$	1.43066	−	0.603897i	0.0973441	−	0.0410900i
$7$	−20.1945	+	7.35018i	−1.09040	+	0.396872i	−0.823768	−	0.566927i	$-0.808132\pi$
$7$	−20.1945	+	7.35018i	−1.09040	+	0.396872i	−0.266630	+	0.963799i	$0.585910\pi$
$8$	−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	0.650415	−	0.759579i	$-0.274595\pi$
$11$	0.558890	+	0.468965i	0.0153193	+	0.0128544i	−0.635096	+	0.772433i	$0.719039\pi$
$12$	−9.16632	−	40.0701i	−0.220507	−	0.963936i
$13$	5.34792	+	30.3295i	0.114096	+	0.647069i	0.987194	+	0.159525i	$0.0509962\pi$
$13$	5.34792	+	30.3295i	0.114096	+	0.647069i	−0.873098	+	0.487545i	$0.837893\pi$
$14$	−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	0.870740	−	0.491744i	$-0.163640\pi$
$17$	0.666388	+	1.15422i	0.00950722	+	0.0164670i	−0.861233	+	0.508211i	$0.830307\pi$
$18$	−6.67142	−	4.53896i	−0.0873594	−	0.0594357i
$19$	−34.7473	+	60.1840i	−0.419556	+	0.726693i	−0.995895	−	0.0905182i	$-0.971148\pi$
$19$	−34.7473	+	60.1840i	−0.419556	+	0.726693i	0.576338	+	0.817211i	$0.304481\pi$
$20$	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	−0.213129	−	0.977024i	$-0.568365\pi$
$23$	−110.791	−	40.3246i	−1.00441	−	0.365577i	−0.791285	+	0.611447i	$0.790588\pi$
$24$	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	0.889892	+	0.456171i	$0.150779\pi$
$29$	−15.9844	+	90.6519i	−0.102353	+	0.580470i	−0.992245	+	0.124299i	$0.960332\pi$
$30$	14.1920	−	27.7158i	0.0863696	−	0.168673i
$31$	175.726	+	63.9590i	1.01811	+	0.370561i	0.796541	−	0.604585i	$-0.206661\pi$
$31$	175.726	+	63.9590i	1.01811	+	0.370561i	0.221566	+	0.975145i	$0.428883\pi$
$32$	−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	0.652339	−	0.757927i	$-0.273788\pi$
$37$	−74.3188	−	128.724i	−0.330214	−	0.571948i	−0.982554	+	0.185979i	$0.940454\pi$
$38$	−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	−0.889452	−	0.457028i	$-0.848914\pi$
$41$	−55.1187	−	312.593i	−0.209953	−	1.19070i	0.679499	−	0.733677i	$-0.262197\pi$
$42$	−24.4527	+	22.7110i	−0.0898364	+	0.0834377i
$43$	−220.661	−	185.157i	−0.782571	−	0.656655i	0.161324	−	0.986902i	$-0.448424\pi$
$43$	−220.661	−	185.157i	−0.782571	−	0.656655i	−0.943895	+	0.330246i	$0.892868\pi$
$44$	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	−0.310983	−	0.950416i	$-0.600658\pi$
$47$	19.8826	−	7.23668i	0.0617059	−	0.0224591i	0.372689	+	0.927956i	$0.378436\pi$
$48$	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	−0.601311	−	0.799015i	$-0.705355\pi$
$59$	36.7754	−	30.8583i	0.0811484	−	0.0680916i	0.682460	+	0.730923i	$0.260910\pi$
$60$	−657.259	−	497.349i	−1.41420	−	1.07013i
$61$	509.543	−	185.458i	1.06951	−	0.389271i	0.253518	−	0.967331i	$-0.418412\pi$
$61$	509.543	−	185.458i	1.06951	−	0.389271i	0.815994	+	0.578060i	$0.196190\pi$
$62$	−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	0.966774	−	0.255632i	$-0.0822834\pi$
$67$	−15.9741	−	90.5935i	−0.0291275	−	0.165190i	−0.995902	+	0.0904411i	$0.971172\pi$
$68$	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	−0.841574	−	0.540141i	$-0.818371\pi$
$71$	−531.589	−	920.739i	−0.888563	−	1.53904i	−0.0469890	−	0.998895i	$-0.514963\pi$
$72$	−75.0455	−	104.167i	−0.122836	−	0.170503i
$73$	−342.332	+	592.936i	−0.548862	+	0.950657i	0.449491	+	0.893285i	$0.351605\pi$
$73$	−342.332	+	592.936i	−0.548862	+	0.950657i	−0.998353	+	0.0573721i	$0.981728\pi$
$74$	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	0.782882	+	0.622170i	$0.213749\pi$
$79$	−116.266	+	659.375i	−0.165581	+	0.939056i	−0.948463	+	0.316887i	$0.897363\pi$
$80$	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	−0.851305	−	0.524671i	$-0.824188\pi$
$83$	96.8709	−	549.382i	0.128108	−	0.726537i	0.979413	−	0.201866i	$-0.0647005\pi$
$84$	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	−0.980638	−	0.195831i	$-0.937260\pi$
$89$	−269.288	+	466.421i	−0.320724	+	0.555511i	0.659913	+	0.751342i	$0.270593\pi$
$90$	−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	0.753765	−	0.657144i	$-0.228236\pi$
$97$	226.888	+	190.381i	0.237494	+	0.199281i	−0.516271	+	0.856426i	$0.672680\pi$
$98$	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	−0.976028	−	0.217643i	$-0.930163\pi$
$101$	−1607.63	+	585.129i	−1.58381	+	0.576460i	−0.607783	+	0.794103i	$0.707941\pi$
$102$	1.65040	+	1.24886i	0.00160210	+	0.00121231i
$103$	507.261	−	425.643i	0.485262	−	0.407183i	−0.367063	−	0.930196i	$-0.619637\pi$
$103$	507.261	−	425.643i	0.485262	−	0.407183i	0.852325	+	0.523013i	$0.175192\pi$
$104$	−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	−0.404134	−	0.914700i	$-0.632427\pi$
$113$	512.305	−	429.875i	0.426492	−	0.357870i	0.830626	+	0.556830i	$0.187983\pi$
$114$	−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	−0.979526	−	0.201317i	$-0.935478\pi$
$127$	−451.431	+	781.902i	−0.315418	+	0.546319i	0.664109	+	0.747636i	$0.268811\pi$
$128$	−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	0.863132	−	0.504979i	$-0.168500\pi$
$131$	1798.84	+	654.724i	1.19973	+	0.436668i	0.336603	+	0.941647i	$0.390722\pi$
$132$	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	0.415354	+	0.909660i	$0.363658\pi$
$137$	−458.731	+	2601.59i	−0.286073	+	1.62240i	−0.701427	+	0.712741i	$0.747454\pi$
$138$	−182.856	+	9.21550i	−0.112795	+	0.00568460i
$139$	−155.790	−	56.7028i	−0.0950641	−	0.0346005i	0.294050	−	0.955790i	$-0.404997\pi$
$139$	−155.790	−	56.7028i	−0.0950641	−	0.0346005i	−0.389114	+	0.921189i	$0.627219\pi$
$140$	−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	−0.977336	−	0.211694i	$-0.932102\pi$
$149$	−238.886	−	1354.79i	−0.131344	−	0.744890i	0.845992	−	0.533196i	$-0.179009\pi$
$150$	−95.9459	−	419.422i	−0.0522263	−	0.228305i
$151$	286.970	+	240.797i	0.154658	+	0.129773i	0.716833	−	0.697245i	$-0.245591\pi$
$151$	286.970	+	240.797i	0.154658	+	0.129773i	−0.562175	+	0.827018i	$0.690035\pi$
$152$	−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	−0.739808	−	0.672818i	$-0.765084\pi$
$157$	−404.609	+	339.507i	−0.205677	+	0.172584i	0.534131	+	0.845402i	$0.320639\pi$
$158$	−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	0.317633	−	0.948214i	$-0.397112\pi$
$167$	2819.79	−	2366.08i	1.30660	−	1.09637i	0.988965	−	0.148152i	$-0.0473325\pi$
$168$	−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	0.239693	−	0.970849i	$-0.422953\pi$
$173$	−1535.44	−	1288.39i	−0.674783	−	0.566211i	−0.914477	+	0.404638i	$0.867398\pi$
$174$	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	0.992570	+	0.121673i	$0.0388259\pi$
$179$	1440.88	+	2495.68i	0.601657	+	1.04210i	−0.390913	+	0.920428i	$0.627841\pi$
$180$	−315.882	+	4271.13i	−0.130803	+	1.76862i
$181$	−454.319	+	786.904i	−0.186571	+	0.323150i	−0.944105	−	0.329646i	$-0.893071\pi$
$181$	−454.319	+	786.904i	−0.186571	+	0.323150i	0.757534	+	0.652796i	$0.226404\pi$
$182$	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	0.925325	+	0.379175i	$0.123792\pi$
$191$	−195.023	+	1106.03i	−0.0738816	+	0.419003i	−0.999207	+	0.0398281i	$0.987319\pi$
$192$	1132.09	−	2210.88i	0.425529	−	0.831024i
$193$	3274.01	+	1191.64i	1.22108	+	0.444437i	0.870534	−	0.492108i	$-0.163774\pi$
$193$	3274.01	+	1191.64i	1.22108	+	0.444437i	0.350547	+	0.936545i	$0.385996\pi$
$194$	−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	0.178500	+	0.983940i	$0.442875\pi$
$197$	−2109.35	+	3653.50i	−0.762867	+	1.32132i	−0.941367	+	0.337384i	$0.890458\pi$
$198$	−1.59998	−	5.66544i	−0.000574271	−	0.00203346i
$199$	205.179	+	355.380i	0.0730892	+	0.126594i	0.900254	−	0.435366i	$-0.143381\pi$
$199$	205.179	+	355.380i	0.0730892	+	0.126594i	−0.827165	+	0.561960i	$0.810048\pi$
$200$	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	−0.561185	−	0.827690i	$-0.689654\pi$
$211$	479.610	−	402.440i	0.156482	−	0.131304i	0.717667	+	0.696386i	$0.245210\pi$
$212$	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	0.389585	−	0.920990i	$-0.372618\pi$
$223$	4262.62	−	1551.47i	1.28003	−	0.465891i	0.890441	+	0.455099i	$0.150396\pi$
$224$	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	0.922173	+	0.386777i	$0.126412\pi$
$227$	5004.32	+	4199.12i	1.46321	+	1.22778i	0.541035	+	0.841000i	$0.318033\pi$
$228$	2730.08	+	840.659i	0.793001	+	0.244184i
$229$	−934.579	−	5300.26i	−0.269689	−	1.52948i	−0.755343	−	0.655330i	$-0.772530\pi$
$229$	−934.579	−	5300.26i	−0.269689	−	1.52948i	0.485654	−	0.874151i	$-0.338582\pi$
$230$	−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	0.681461	−	0.731854i	$-0.261345\pi$
$233$	−1042.34	−	1805.39i	−0.293074	−	0.507619i	−0.974535	+	0.224235i	$0.928012\pi$
$234$	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	−0.343030	−	0.939324i	$-0.611453\pi$
$239$	−4469.26	−	1626.68i	−1.20959	−	0.440256i	−0.866562	+	0.499069i	$0.833675\pi$
$240$	−3499.75	−	5412.88i	−0.941284	−	1.45583i
$241$	400.465	−	2271.15i	0.107038	−	0.607043i	−0.883349	−	0.468717i	$-0.844717\pi$
$241$	400.465	−	2271.15i	0.107038	−	0.607043i	0.990387	−	0.138327i	$-0.0441724\pi$
$242$	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	−0.713444	−	0.700712i	$-0.752866\pi$
$251$	994.592	−	1722.68i	0.250112	−	0.433207i	0.963556	+	0.267505i	$0.0861992\pi$
$252$	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	0.771033	+	0.636796i	$0.219741\pi$
$257$	1088.91	+	6175.49i	0.264296	+	1.49890i	−0.506737	+	0.862101i	$0.669148\pi$
$258$	−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	−0.597435	−	0.801917i	$-0.703814\pi$
$263$	−2301.62	+	837.722i	−0.539635	+	0.196411i	0.0578002	+	0.998328i	$0.481591\pi$
$264$	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	−0.973730	−	0.227707i	$-0.926877\pi$
$277$	−7253.15	+	2639.93i	−1.57328	+	0.572628i	−0.599553	+	0.800335i	$0.704655\pi$
$278$	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	0.284003	−	0.958823i	$-0.408337\pi$
$281$	−2877.77	−	2414.74i	−0.610937	−	0.512637i	−0.894940	+	0.446186i	$0.852782\pi$
$282$	24.0751	−	22.3603i	0.00508386	−	0.00472176i
$283$	404.252	+	2292.63i	0.0849127	+	0.481564i	0.997375	+	0.0724041i	$0.0230671\pi$
$283$	404.252	+	2292.63i	0.0849127	+	0.481564i	−0.912463	+	0.409160i	$0.865822\pi$
$284$	−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	0.753233	−	0.657754i	$-0.228493\pi$
$293$	4551.16	+	1656.49i	0.907446	+	0.330283i	0.154214	+	0.988038i	$0.450716\pi$
$294$	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	0.957987	−	0.286811i	$-0.0925951\pi$
$307$	1240.46	+	2148.54i	0.230608	+	0.399425i	−0.727379	+	0.686236i	$0.759262\pi$
$308$	−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	0.999640	−	0.0268390i	$-0.00854414\pi$
$311$	280.294	+	1589.63i	0.0511062	+	0.289838i	−0.948534	+	0.316677i	$0.897433\pi$
$312$	169.685	+	741.770i	0.0307902	+	0.134598i
$313$	7636.44	+	6407.73i	1.37903	+	1.15715i	0.969569	+	0.244819i	$0.0787284\pi$
$313$	7636.44	+	6407.73i	1.37903	+	1.15715i	0.409463	+	0.912327i	$0.365716\pi$
$314$	−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	−0.506073	−	0.862491i	$-0.668903\pi$
$317$	−1915.29	+	697.110i	−0.339349	+	0.123513i	0.166724	+	0.986004i	$0.446681\pi$
$318$	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	−0.245599	−	0.969371i	$-0.578985\pi$
$331$	1140.34	−	415.048i	0.189361	−	0.0689218i	0.434960	+	0.900450i	$0.356762\pi$
$332$	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	−0.834638	−	0.550798i	$-0.814323\pi$
$337$	−1476.83	−	8375.55i	−0.238719	−	1.35384i	0.595919	−	0.803044i	$-0.296788\pi$
$338$	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	−0.187228	−	0.982317i	$-0.559950\pi$
$347$	−6218.74	−	2263.44i	−0.962073	−	0.350166i	−0.774846	+	0.632151i	$0.782172\pi$
$348$	3778.94	−	190.449i	0.582105	−	0.0293367i
$349$	−910.076	+	5161.30i	−0.139585	+	0.791628i	0.831971	+	0.554819i	$0.187213\pi$
$349$	−910.076	+	5161.30i	−0.139585	+	0.791628i	−0.971556	+	0.236809i	$0.923899\pi$
$350$	−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	0.850690	+	0.525668i	$0.176184\pi$
$353$	−852.154	+	4832.81i	−0.128486	+	0.728681i	−0.979176	+	0.203013i	$0.934927\pi$
$354$	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	−0.318369	−	0.947967i	$-0.603135\pi$
$359$	4501.47	−	7796.77i	0.661779	−	1.14623i	0.980148	−	0.198267i	$-0.0635314\pi$
$360$	−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	0.594000	−	0.804465i	$-0.297548\pi$
$367$	−668.599	−	561.021i	−0.0950970	−	0.0797958i	−0.689097	+	0.724669i	$0.741992\pi$
$368$	−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	−0.912834	−	0.408331i	$-0.866111\pi$
$373$	−4820.94	+	4045.25i	−0.669219	+	0.561541i	0.243615	+	0.969872i	$0.421667\pi$
$374$	−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	−0.456973	−	0.889481i	$-0.651066\pi$
$383$	2545.77	−	2136.16i	0.339642	−	0.284993i	0.796615	+	0.604487i	$0.206622\pi$
$384$	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	0.0425622	−	0.999094i	$-0.486448\pi$
$389$	−7165.62	−	6012.67i	−0.933962	−	0.783687i	−0.976524	+	0.215406i	$0.930892\pi$
$390$	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	−0.708082	−	0.706130i	$-0.750439\pi$
$397$	2036.76	−	3527.77i	0.257486	−	0.445979i	0.965568	+	0.260152i	$0.0837725\pi$
$398$	−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	0.103771	−	0.994601i	$-0.466909\pi$
$401$	−3662.12	−	1332.90i	−0.456054	−	0.165990i	−0.559824	+	0.828611i	$0.689131\pi$
$402$	−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	0.890405	−	0.455169i	$-0.150421\pi$
$409$	10586.9	+	3853.30i	1.27992	+	0.465852i	0.389513	+	0.921021i	$0.372643\pi$
$410$	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	−0.983379	−	0.181563i	$-0.941884\pi$
$419$	−1041.24	−	5905.18i	−0.121403	−	0.688513i	0.861976	−	0.506949i	$-0.169227\pi$
$420$	16928.6	+	5212.73i	1.96674	+	0.605607i
$421$	−12007.1	−	10075.2i	−1.39000	−	1.16635i	−0.965338	−	0.261002i	$-0.915947\pi$
$421$	−12007.1	−	10075.2i	−1.39000	−	1.16635i	−0.424666	−	0.905350i	$-0.639608\pi$
$422$	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	0.224338	−	0.974511i	$-0.427978\pi$
$439$	9405.91	−	3423.47i	1.02260	−	0.372194i	0.798257	+	0.602317i	$0.205756\pi$
$440$	−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	0.687976	−	0.725733i	$-0.258499\pi$
$443$	864.666	+	725.541i	0.0927348	+	0.0778138i	−0.595242	+	0.803547i	$0.702944\pi$
$444$	−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	0.970584	−	0.240764i	$-0.0773979\pi$
$449$	2633.36	+	4561.12i	0.276784	+	0.479405i	−0.693799	+	0.720168i	$0.744065\pi$
$450$	−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	0.757284	+	0.653085i	$0.226526\pi$
$457$	−1736.03	+	9845.54i	−0.177699	+	1.00778i	−0.934983	+	0.354693i	$0.884585\pi$
$458$	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	−0.594299	−	0.804244i	$-0.702570\pi$
$461$	2367.89	−	13429.0i	0.239227	−	1.35672i	0.833526	−	0.552480i	$-0.186318\pi$
$462$	−24.3170	+	1.22552i	−0.00244877	+	0.000123412i
$463$	−3631.88	−	1321.90i	−0.364552	−	0.132686i	0.153248	−	0.988188i	$-0.451027\pi$
$463$	−3631.88	−	1321.90i	−0.364552	−	0.132686i	−0.517800	+	0.855502i	$0.673249\pi$
$464$	−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	0.295970	+	0.955197i	$0.404357\pi$
$467$	−6854.86	+	11873.0i	−0.679240	+	1.17648i	−0.975210	+	0.221281i	$0.928976\pi$
$468$	−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	−0.00673130	−	0.999977i	$-0.502143\pi$
$479$	6613.84	−	2407.24i	0.630885	−	0.229623i	0.637617	+	0.770354i	$0.279920\pi$
$480$	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	−0.978974	−	0.203987i	$-0.934610\pi$
$491$	−10315.0	+	8655.29i	−0.948082	+	0.795535i	0.0308914	+	0.999523i	$0.490165\pi$
$492$	−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	0.926206	+	0.377017i	$0.123050\pi$
$499$	2059.98	+	11682.7i	0.184804	+	1.04808i	−0.741402	+	0.671061i	$0.765839\pi$
$500$	−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	−0.988322	−	0.152383i	$-0.951305\pi$
$503$	−7063.42	−	12234.2i	−0.626128	−	1.08449i	0.362194	−	0.932103i	$-0.382028\pi$
$504$	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	0.790939	−	0.611895i	$-0.209593\pi$
$509$	11523.9	+	4194.36i	1.00351	+	0.365249i	0.212576	+	0.977145i	$0.431815\pi$
$510$	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	−0.521728	−	0.853112i	$-0.674712\pi$
$521$	5683.84	−	9844.69i	0.477953	−	0.827839i	0.999681	+	0.0252735i	$0.00804566\pi$
$522$	518.104	−	532.224i	0.0434421	−	0.0446261i
$523$	−1568.15	−	2716.12i	−0.131110	−	0.227089i	0.792995	−	0.609229i	$-0.208521\pi$
$523$	−1568.15	−	2716.12i	−0.131110	−	0.227089i	−0.924105	+	0.382139i	$0.875187\pi$
$524$	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	−0.742642	−	0.669689i	$-0.766427\pi$
$547$	−11271.8	+	4102.58i	−0.881070	+	0.320683i	−0.138428	+	0.990372i	$0.544205\pi$
$548$	−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	0.715727	−	0.698380i	$-0.246095\pi$
$557$	−3246.34	−	5622.82i	−0.246951	−	0.427732i	−0.962678	+	0.270648i	$0.912762\pi$
$558$	−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	−0.236869	−	0.971542i	$-0.576121\pi$
$563$	−13930.6	−	5070.33i	−1.04282	−	0.379554i	−0.805947	+	0.591988i	$0.798343\pi$
$564$	−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	0.263086	+	0.964772i	$0.415260\pi$
$569$	−4263.28	+	24178.3i	−0.314106	+	1.78138i	−0.577191	+	0.816609i	$0.695851\pi$
$570$	1174.92	+	1817.18i	0.0863366	+	0.133532i
$571$	17820.6	+	6486.18i	1.30608	+	0.475374i	0.898972	−	0.438007i	$-0.144316\pi$
$571$	17820.6	+	6486.18i	1.30608	+	0.475374i	0.407107	+	0.913381i	$0.366538\pi$
$572$	−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	0.552946	−	0.833217i	$-0.313503\pi$
$577$	−6169.28	−	10685.5i	−0.445114	−	0.770960i	−0.998060	+	0.0622571i	$0.980170\pi$
$578$	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	−0.0580560	−	0.998313i	$-0.518490\pi$
$587$	7668.07	−	2790.95i	0.539174	−	0.196243i	0.597230	+	0.802070i	$0.296268\pi$
$588$	−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	−0.830396	−	0.557174i	$-0.811886\pi$
$599$	−6243.55	+	5238.96i	−0.425884	+	0.357359i	0.404512	+	0.914533i	$0.367441\pi$
$600$	847.899	−	6792.96i	0.0576922	−	0.462203i
$601$	−9208.27	+	3351.54i	−0.624980	+	0.227474i	−0.635045	−	0.772475i	$-0.719018\pi$
$601$	−9208.27	+	3351.54i	−0.624980	+	0.227474i	0.0100647	+	0.999949i	$0.496796\pi$
$602$	−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	−0.999519	−	0.0310132i	$-0.990127\pi$
$607$	−1060.08	−	6012.04i	−0.0708855	−	0.402012i	0.928633	−	0.370998i	$-0.120984\pi$
$608$	−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	−0.550688	−	0.834711i	$-0.685634\pi$
$613$	6792.35	−	11764.7i	0.447537	−	0.775158i	0.998225	+	0.0595537i	$0.0189678\pi$
$614$	−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	−0.232576	−	0.972578i	$-0.574715\pi$
$617$	−15876.2	−	5778.46i	−1.03590	−	0.377037i	−0.803325	+	0.595541i	$0.796938\pi$
$618$	468.675	−	915.284i	0.0305062	−	0.0595763i
$619$	−2305.23	+	13073.6i	−0.149685	+	0.848907i	0.813800	+	0.581145i	$0.197395\pi$
$619$	−2305.23	+	13073.6i	−0.149685	+	0.848907i	−0.963485	+	0.267762i	$0.913716\pi$
$620$	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	−0.999560	−	0.0296493i	$-0.990561\pi$
$631$	−8328.78	−	14425.9i	−0.525457	−	0.910119i	0.474103	−	0.880469i	$-0.342772\pi$
$632$	−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	−0.761425	−	0.648253i	$-0.775500\pi$
$641$	−15060.7	+	5481.65i	−0.928022	+	0.337772i	−0.166597	+	0.986025i	$0.553278\pi$
$642$	1254.78	−	529.657i	0.0771375	−	0.0325606i
$643$	3341.80	−	2804.10i	0.204957	−	0.171980i	−0.534531	−	0.845149i	$-0.679512\pi$
$643$	3341.80	−	2804.10i	0.204957	−	0.171980i	0.739489	+	0.673169i	$0.235067\pi$
$644$	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	−0.913992	−	0.405733i	$-0.867016\pi$
$653$	−11232.4	+	9425.09i	−0.673135	+	0.564827i	0.240856	+	0.970561i	$0.422572\pi$
$654$	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	0.906308	−	0.422618i	$-0.138889\pi$
$659$	10953.7	+	9191.24i	0.647489	+	0.543308i	−0.258819	+	0.965926i	$0.583333\pi$
$660$	−134.096	−	586.195i	−0.00790863	−	0.0345721i
$661$	−313.393	−	1777.34i	−0.0184411	−	0.104585i	0.974198	−	0.225696i	$-0.0724654\pi$
$661$	−313.393	−	1777.34i	−0.0184411	−	0.104585i	−0.992639	+	0.121111i	$0.961354\pi$
$662$	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	−0.986897	−	0.161354i	$-0.948414\pi$
$673$	−75.6114	+	428.813i	−0.00433076	+	0.0245610i	0.982566	+	0.185915i	$0.0595250\pi$
$674$	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	0.584205	+	0.811606i	$0.301406\pi$
$677$	−4269.07	+	24211.1i	−0.242354	+	1.37446i	−0.826559	+	0.562851i	$0.809705\pi$
$678$	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	−0.891502	−	0.453017i	$-0.850348\pi$
$683$	−953.659	+	1651.79i	−0.0534271	+	0.0925385i	0.838075	+	0.545555i	$0.183681\pi$
$684$	−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	0.359652	−	0.933087i	$-0.382896\pi$
$691$	−9024.11	−	7572.13i	−0.496807	−	0.416870i	−0.856458	+	0.516216i	$0.827340\pi$
$692$	−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	−0.647734	−	0.761867i	$-0.724283\pi$
$709$	−12350.5	+	4495.22i	−0.654208	+	0.238112i	−0.00647435	+	0.999979i	$0.502061\pi$
$710$	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	0.560016	−	0.828481i	$-0.310795\pi$
$719$	−8434.31	−	14608.6i	−0.437478	−	0.757734i	−0.997494	+	0.0707477i	$0.977461\pi$
$720$	−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	0.418393	+	0.908266i	$0.362594\pi$
$727$	−5594.68	+	31729.0i	−0.285413	+	1.61866i	−0.703806	+	0.710392i	$0.748518\pi$
$728$	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	0.718701	−	0.695319i	$-0.244737\pi$
$733$	16319.0	+	5939.64i	0.822315	+	0.299298i	0.103614	+	0.994618i	$0.466959\pi$
$734$	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	−0.951117	−	0.308831i	$-0.900062\pi$
$739$	−14926.7	−	25853.8i	−0.743014	−	1.28694i	0.208103	−	0.978107i	$-0.433271\pi$
$740$	−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	−0.947863	−	0.318679i	$-0.896761\pi$
$743$	−3365.15	−	19084.7i	−0.166158	−	0.942328i	0.781705	−	0.623649i	$-0.214350\pi$
$744$	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	−0.975301	−	0.220880i	$-0.929107\pi$
$751$	−19081.1	+	16010.9i	−0.927136	+	0.777960i	0.0481647	+	0.998839i	$0.484663\pi$
$752$	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	−0.723700	−	0.690115i	$-0.757560\pi$
$761$	−3563.33	+	2989.99i	−0.169738	+	0.142427i	0.553962	+	0.832542i	$0.313115\pi$
$762$	−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	0.962188	−	0.272385i	$-0.0878124\pi$
$769$	−749.236	−	4249.13i	−0.0351341	−	0.199255i	−0.997322	+	0.0731296i	$0.976701\pi$
$770$	−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	0.996764	−	0.0803804i	$-0.0256135\pi$
$773$	9214.98	+	15960.8i	0.428771	+	0.742653i	−0.567994	+	0.823033i	$0.692280\pi$
$774$	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	0.0905732	−	0.995890i	$-0.471130\pi$
$787$	−10601.7	−	3858.70i	−0.480189	−	0.174775i	−0.570763	+	0.821115i	$0.693352\pi$
$788$	−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	−0.901010	−	0.433798i	$-0.857173\pi$
$797$	−4560.92	−	25866.2i	−0.202705	−	1.14960i	0.698305	−	0.715800i	$-0.253938\pi$
$798$	−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	0.666379	−	0.745613i	$-0.267843\pi$
$821$	1124.67	+	943.710i	0.0478091	+	0.0401166i	−0.618570	+	0.785730i	$0.712288\pi$
$822$	914.805	+	3999.02i	0.0388169	+	0.169686i
$823$	1879.65	+	10660.1i	0.0796120	+	0.451502i	0.998390	+	0.0567267i	$0.0180664\pi$
$823$	1879.65	+	10660.1i	0.0796120	+	0.451502i	−0.918778	+	0.394775i	$0.870823\pi$
$824$	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	0.743527	−	0.668706i	$-0.233152\pi$
$827$	−4931.39	−	8541.41i	−0.207353	−	0.359146i	−0.950880	+	0.309560i	$0.899818\pi$
$828$	22677.8	−	10948.4i	0.951823	−	0.459520i
$829$	−18383.5	+	31841.1i	−0.770185	+	1.33400i	0.167276	+	0.985910i	$0.446503\pi$
$829$	−18383.5	+	31841.1i	−0.770185	+	1.33400i	−0.937461	+	0.348090i	$0.886830\pi$
$830$	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	−0.905803	−	0.423698i	$-0.860732\pi$
$839$	2194.15	−	12443.7i	0.0902867	−	0.512042i	0.996090	−	0.0883432i	$-0.0281572\pi$
$840$	−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	0.580448	−	0.814297i	$-0.302877\pi$
$853$	−3006.58	−	2522.82i	−0.120684	−	0.101266i	−0.701132	+	0.713031i	$0.747322\pi$
$854$	−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	−0.187404	−	0.982283i	$-0.560007\pi$
$857$	7537.41	−	2743.39i	0.300435	−	0.109349i	0.487839	+	0.872933i	$0.337785\pi$
$858$	−4.32173	+	34.6236i	−0.000171960	+	0.00137766i
$859$	−15033.6	+	12614.7i	−0.597136	+	0.501057i	−0.890524	−	0.454937i	$-0.849662\pi$
$859$	−15033.6	+	12614.7i	−0.597136	+	0.501057i	0.293388	+	0.955994i	$0.405217\pi$
$860$	−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	−0.993788	−	0.111290i	$-0.964502\pi$
$877$	−2545.12	−	14434.1i	−0.0979963	−	0.555764i	0.895792	−	0.444474i	$-0.146609\pi$
$878$	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	0.932669	−	0.360734i	$-0.117474\pi$
$881$	4025.18	+	6971.82i	0.153929	+	0.266613i	−0.778739	+	0.627348i	$0.784141\pi$
$882$	−954.081	+	96.4115i	−0.0364235	+	0.00368066i
$883$	−21299.5	+	36891.7i	−0.811760	+	1.40601i	0.0998716	+	0.995000i	$0.468157\pi$
$883$	−21299.5	+	36891.7i	−0.811760	+	1.40601i	−0.911631	+	0.411009i	$0.865177\pi$
$884$	−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	−0.998158	−	0.0606688i	$-0.980677\pi$
$887$	−47598.1	−	17324.3i	−1.80179	−	0.655797i	−0.803631	−	0.595129i	$-0.797101\pi$
$888$	−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	0.978696	−	0.205313i	$-0.0658211\pi$
$907$	25852.9	+	21693.2i	0.946452	+	0.794167i	−0.0322446	+	0.999480i	$0.510266\pi$
$908$	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	−0.803965	−	0.594677i	$-0.797280\pi$
$911$	−28530.0	+	10384.1i	−1.03759	+	0.377651i	−0.233622	+	0.972327i	$0.575058\pi$
$912$	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	0.860329	−	0.509740i	$-0.170258\pi$
$929$	14376.5	+	12063.3i	0.507727	+	0.426034i	−0.352601	+	0.935774i	$0.614703\pi$
$930$	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	−0.324239	−	0.945975i	$-0.605108\pi$
$937$	18847.5	−	32644.8i	0.657119	−	1.13816i	0.981358	−	0.192188i	$-0.0615584\pi$
$938$	−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	0.863500	−	0.504349i	$-0.168268\pi$
$941$	34661.8	+	12615.9i	1.20079	+	0.437052i	0.337290	+	0.941401i	$0.390490\pi$
$942$	−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	−0.807791	−	0.589469i	$-0.799337\pi$
$947$	4455.71	−	25269.6i	0.152895	−	0.867108i	0.960685	−	0.277639i	$-0.0895519\pi$
$948$	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	−0.583672	−	0.811989i	$-0.698385\pi$
$953$	12102.3	−	20961.9i	0.411367	−	0.712509i	0.995040	+	0.0994802i	$0.0317180\pi$
$954$	−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	−0.555643	−	0.831421i	$-0.687528\pi$
$967$	5011.54	−	4205.18i	0.166660	−	0.139844i	0.722303	+	0.691576i	$0.243083\pi$
$968$	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	0.123168	−	0.992386i	$-0.460695\pi$
$977$	34259.6	−	28747.2i	1.12187	−	0.941357i	0.998697	+	0.0510292i	$0.0162502\pi$
$978$	−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	0.790308	−	0.612710i	$-0.209921\pi$
$983$	9990.01	+	8382.61i	0.324142	+	0.271988i	−0.466166	+	0.884697i	$0.654365\pi$
$984$	−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	−0.126802	+	0.991928i	$0.540471\pi$
$991$	−28777.1	+	49843.4i	−0.922436	+	1.59771i	−0.795634	+	0.605778i	$0.792862\pi$
$992$	−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	0.880886	+	0.473328i	$0.156947\pi$
$997$	−3423.94	+	19418.2i	−0.108764	+	0.616830i	−0.989650	+	0.143502i	$0.954164\pi$
$998$	−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.25.4	yes	48
3.2	odd	2		81.4.e.a.73.5		48
9.2	odd	6		243.4.e.a.55.4		48
9.4	even	3		243.4.e.c.136.4		48
9.5	odd	6		243.4.e.b.136.5		48
9.7	even	3		243.4.e.d.55.5		48
27.4	even	9		243.4.e.c.109.4		48
27.5	odd	18		243.4.e.a.190.4		48
27.11	odd	18		729.4.a.c.1.14		24
27.13	even	9	inner	27.4.e.a.13.4	✓	48
27.14	odd	18		81.4.e.a.10.5		48
27.16	even	9		729.4.a.d.1.11		24
27.22	even	9		243.4.e.d.190.5		48
27.23	odd	18		243.4.e.b.109.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.4	✓	48	27.13	even	9	inner
27.4.e.a.25.4	yes	48	1.1	even	1	trivial
81.4.e.a.10.5		48	27.14	odd	18
81.4.e.a.73.5		48	3.2	odd	2
243.4.e.a.55.4		48	9.2	odd	6
243.4.e.a.190.4		48	27.5	odd	18
243.4.e.b.109.5		48	27.23	odd	18
243.4.e.b.136.5		48	9.5	odd	6
243.4.e.c.109.4		48	27.4	even	9
243.4.e.c.136.4		48	9.4	even	3
243.4.e.d.55.5		48	9.7	even	3
243.4.e.d.190.5		48	27.22	even	9
729.4.a.c.1.14		24	27.11	odd	18
729.4.a.d.1.11		24	27.16	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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