LMFDB - Embedded newform 27.4.e.a.4.4

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			4.4
Character	$\chi$	$=$	27.4
Dual form			27.4.e.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.982993 - 0.357780i) q^{2} +(-5.19600 - 0.0395600i) q^{3} +(-5.29009 - 4.43891i) q^{4} +(2.68017 - 15.2000i) q^{5} +(5.09348 + 1.89791i) q^{6} +(-18.0349 + 15.1331i) q^{7} +(7.79628 + 13.5036i) q^{8} +(26.9969 + 0.411107i) q^{9} +O(q^{10})$	\(q+(-0.982993 - 0.357780i) q^{2} +(-5.19600 - 0.0395600i) q^{3} +(-5.29009 - 4.43891i) q^{4} +(2.68017 - 15.2000i) q^{5} +(5.09348 + 1.89791i) q^{6} +(-18.0349 + 15.1331i) q^{7} +(7.79628 + 13.5036i) q^{8} +(26.9969 + 0.411107i) q^{9} +(-8.07284 + 13.9826i) q^{10} +(-7.09896 - 40.2602i) q^{11} +(27.3117 + 23.2739i) q^{12} +(11.9280 - 4.34143i) q^{13} +(23.1425 - 8.42319i) q^{14} +(-14.5275 + 78.8731i) q^{15} +(6.76093 + 38.3432i) q^{16} +(23.8240 - 41.2643i) q^{17} +(-26.3907 - 10.0631i) q^{18} +(-67.6602 - 117.191i) q^{19} +(-81.6496 + 68.5122i) q^{20} +(94.3081 - 77.9181i) q^{21} +(-7.42608 + 42.1154i) q^{22} +(36.2326 + 30.4028i) q^{23} +(-39.9753 - 70.4729i) q^{24} +(-106.394 - 38.7244i) q^{25} -13.2784 q^{26} +(-140.260 - 3.20411i) q^{27} +162.581 q^{28} +(-118.886 - 43.2708i) q^{29} +(42.4996 - 72.3341i) q^{30} +(158.028 + 132.602i) q^{31} +(28.7334 - 162.955i) q^{32} +(35.2935 + 209.473i) q^{33} +(-38.1824 + 32.0388i) q^{34} +(181.686 + 314.689i) q^{35} +(-140.991 - 122.011i) q^{36} +(93.6104 - 162.138i) q^{37} +(24.5809 + 139.405i) q^{38} +(-62.1496 + 22.0862i) q^{39} +(226.149 - 82.3116i) q^{40} +(-41.7814 + 15.2072i) q^{41} +(-120.582 + 42.8514i) q^{42} +(41.2948 + 234.195i) q^{43} +(-141.157 + 244.492i) q^{44} +(78.6049 - 409.250i) q^{45} +(-24.7389 - 42.8490i) q^{46} +(83.8400 - 70.3501i) q^{47} +(-33.6130 - 199.499i) q^{48} +(36.6864 - 208.059i) q^{49} +(90.7302 + 76.1317i) q^{50} +(-125.422 + 213.467i) q^{51} +(-82.3713 - 29.9807i) q^{52} +11.6792 q^{53} +(136.728 + 53.3317i) q^{54} -630.981 q^{55} +(-344.956 - 125.554i) q^{56} +(346.927 + 611.601i) q^{57} +(101.382 + 85.0698i) q^{58} +(126.168 - 715.536i) q^{59} +(426.962 - 352.759i) q^{60} +(-45.5286 + 38.2030i) q^{61} +(-107.899 - 186.886i) q^{62} +(-493.108 + 401.132i) q^{63} +(69.1916 - 119.843i) q^{64} +(-34.0207 - 192.941i) q^{65} +(40.2520 - 218.538i) q^{66} +(-290.347 + 105.678i) q^{67} +(-309.199 + 112.539i) q^{68} +(-187.062 - 159.406i) q^{69} +(-66.0065 - 374.341i) q^{70} +(130.821 - 226.589i) q^{71} +(204.924 + 367.759i) q^{72} +(186.795 + 323.539i) q^{73} +(-150.028 + 125.889i) q^{74} +(551.294 + 205.421i) q^{75} +(-162.272 + 920.288i) q^{76} +(737.290 + 618.660i) q^{77} +(68.9947 + 0.525293i) q^{78} +(-128.935 - 46.9287i) q^{79} +600.936 q^{80} +(728.662 + 22.1972i) q^{81} +46.5117 q^{82} +(1033.80 + 376.273i) q^{83} +(-844.769 - 6.43168i) q^{84} +(-563.365 - 472.719i) q^{85} +(43.1977 - 244.986i) q^{86} +(616.018 + 229.538i) q^{87} +(488.311 - 409.741i) q^{88} +(-716.067 - 1240.26i) q^{89} +(-223.690 + 374.167i) q^{90} +(-149.421 + 258.805i) q^{91} +(-56.7185 - 321.667i) q^{92} +(-815.870 - 695.250i) q^{93} +(-107.584 + 39.1574i) q^{94} +(-1962.64 + 714.343i) q^{95} +(-155.746 + 845.580i) q^{96} +(137.698 + 780.924i) q^{97} +(-110.502 + 191.395i) q^{98} +(-175.098 - 1089.82i) 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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.982993	−	0.357780i	−0.347541	−	0.126494i	0.162351	−	0.986733i	$-0.448092\pi$
$2$	−0.982993	−	0.357780i	−0.347541	−	0.126494i	−0.509892	+	0.860239i	$0.670315\pi$
$3$	−5.19600	−	0.0395600i	−0.999971	−	0.00761332i
$3$	−5.19600	−	0.0395600i	−0.999971	−	0.00761332i
$4$	−5.29009	−	4.43891i	−0.661261	−	0.554864i
$5$	2.68017	−	15.2000i	0.239721	−	1.35953i	−0.592717	−	0.805410i	$-0.701945\pi$
$5$	2.68017	−	15.2000i	0.239721	−	1.35953i	0.832439	−	0.554117i	$-0.186944\pi$
$6$	5.09348	+	1.89791i	0.346568	+	0.129137i
$7$	−18.0349	+	15.1331i	−0.973794	+	0.817110i	−0.983142	−	0.182846i	$-0.941469\pi$
$7$	−18.0349	+	15.1331i	−0.973794	+	0.817110i	0.00934778	+	0.999956i	$0.497024\pi$
$8$	7.79628	+	13.5036i	0.344550	+	0.596779i
$9$	26.9969	+	0.411107i	0.999884	+	0.0152262i
$10$	−8.07284	+	13.9826i	−0.255286	+	0.442168i
$11$	−7.09896	−	40.2602i	−0.194583	−	1.10354i	−0.913011	−	0.407935i	$-0.866249\pi$
$11$	−7.09896	−	40.2602i	−0.194583	−	1.10354i	0.718427	−	0.695602i	$-0.244862\pi$
$12$	27.3117	+	23.2739i	0.657017	+	0.559882i
$13$	11.9280	−	4.34143i	0.254479	−	0.0926228i	−0.211631	−	0.977350i	$-0.567877\pi$
$13$	11.9280	−	4.34143i	0.254479	−	0.0926228i	0.466110	+	0.884727i	$0.345655\pi$
$14$	23.1425	−	8.42319i	0.441793	−	0.160799i
$15$	−14.5275	+	78.8731i	−0.250065	+	1.35766i
$16$	6.76093	+	38.3432i	0.105640	+	0.599112i
$17$	23.8240	−	41.2643i	0.339892	−	0.588710i	−0.644520	−	0.764587i	$-0.722943\pi$
$17$	23.8240	−	41.2643i	0.339892	−	0.588710i	0.984412	+	0.175877i	$0.0562762\pi$
$18$	−26.3907	−	10.0631i	−0.345574	−	0.131771i
$19$	−67.6602	−	117.191i	−0.816964	−	1.41502i	−0.907909	−	0.419168i	$-0.862322\pi$
$19$	−67.6602	−	117.191i	−0.816964	−	1.41502i	0.0909443	−	0.995856i	$-0.471011\pi$
$20$	−81.6496	+	68.5122i	−0.912871	+	0.765989i
$21$	94.3081	−	77.9181i	0.979986	−	0.809672i
$22$	−7.42608	+	42.1154i	−0.0719657	+	0.408138i
$23$	36.2326	+	30.4028i	0.328479	+	0.275627i	0.792080	−	0.610418i	$-0.208998\pi$
$23$	36.2326	+	30.4028i	0.328479	+	0.275627i	−0.463601	+	0.886044i	$0.653443\pi$
$24$	−39.9753	−	70.4729i	−0.339997	−	0.599385i
$25$	−106.394	−	38.7244i	−0.851156	−	0.309795i
$26$	−13.2784			−0.100158
$27$	−140.260	−	3.20411i	−0.999739	−	0.0228382i
$28$	162.581			1.09732
$29$	−118.886	−	43.2708i	−0.761258	−	0.277075i	−0.0679230	−	0.997691i	$-0.521637\pi$
$29$	−118.886	−	43.2708i	−0.761258	−	0.277075i	−0.693335	+	0.720615i	$0.743859\pi$
$30$	42.4996	−	72.3341i	0.258645	−	0.440211i
$31$	158.028	+	132.602i	0.915572	+	0.768256i	0.973171	−	0.230083i	$-0.0738999\pi$
$31$	158.028	+	132.602i	0.915572	+	0.768256i	−0.0575985	+	0.998340i	$0.518344\pi$
$32$	28.7334	−	162.955i	0.158731	−	0.900210i
$33$	35.2935	+	209.473i	0.186176	+	1.10499i
$34$	−38.1824	+	32.0388i	−0.192595	+	0.161606i
$35$	181.686	+	314.689i	0.877444	+	1.51978i
$36$	−140.991	−	122.011i	−0.652736	−	0.564868i
$37$	93.6104	−	162.138i	0.415931	−	0.720414i	−0.579594	−	0.814905i	$-0.696789\pi$
$37$	93.6104	−	162.138i	0.415931	−	0.720414i	0.995526	+	0.0944909i	$0.0301223\pi$
$38$	24.5809	+	139.405i	0.104936	+	0.595120i
$39$	−62.1496	+	22.0862i	−0.255177	+	0.0906827i
$40$	226.149	−	82.3116i	0.893933	−	0.325365i
$41$	−41.7814	+	15.2072i	−0.159150	+	0.0579260i	−0.420367	−	0.907354i	$-0.638099\pi$
$41$	−41.7814	+	15.2072i	−0.159150	+	0.0579260i	0.261216	+	0.965280i	$0.415876\pi$
$42$	−120.582	+	42.8514i	−0.443004	+	0.157431i
$43$	41.2948	+	234.195i	0.146451	+	0.830566i	0.966191	+	0.257829i	$0.0830072\pi$
$43$	41.2948	+	234.195i	0.146451	+	0.830566i	−0.819739	+	0.572737i	$0.805882\pi$
$44$	−141.157	+	244.492i	−0.483642	+	0.837693i
$45$	78.6049	−	409.250i	0.260394	−	1.35572i
$46$	−24.7389	−	42.8490i	−0.0792946	−	0.137342i
$47$	83.8400	−	70.3501i	0.260198	−	0.218332i	−0.503351	−	0.864082i	$-0.667900\pi$
$47$	83.8400	−	70.3501i	0.260198	−	0.218332i	0.763549	+	0.645750i	$0.223455\pi$
$48$	−33.6130	−	199.499i	−0.101075	−	0.599899i
$49$	36.6864	−	208.059i	0.106957	−	0.606585i
$50$	90.7302	+	76.1317i	0.256624	+	0.215333i
$51$	−125.422	+	213.467i	−0.344364	+	0.586105i
$52$	−82.3713	−	29.9807i	−0.219670	−	0.0799534i
$53$	11.6792			0.0302692			0.0151346	−	0.999885i	$-0.495182\pi$
$53$	11.6792			0.0302692			0.0151346	+	0.999885i	$0.495182\pi$
$54$	136.728	+	53.3317i	0.344561	+	0.134399i
$55$	−630.981			−1.54693
$56$	−344.956	−	125.554i	−0.823155	−	0.299604i
$57$	346.927	+	611.601i	0.806168	+	1.42120i
$58$	101.382	+	85.0698i	0.229520	+	0.192590i
$59$	126.168	−	715.536i	0.278402	−	1.57890i	−0.449542	−	0.893259i	$-0.648413\pi$
$59$	126.168	−	715.536i	0.278402	−	1.57890i	0.727944	−	0.685636i	$-0.240476\pi$
$60$	426.962	−	352.759i	0.918676	−	0.759017i
$61$	−45.5286	+	38.2030i	−0.0955629	+	0.0801868i	−0.689317	−	0.724459i	$-0.742089\pi$
$61$	−45.5286	+	38.2030i	−0.0955629	+	0.0801868i	0.593755	+	0.804646i	$0.297645\pi$
$62$	−107.899	−	186.886i	−0.221018	−	0.382815i
$63$	−493.108	+	401.132i	−0.986122	+	0.802188i
$64$	69.1916	−	119.843i	0.135140	−	0.234069i
$65$	−34.0207	−	192.941i	−0.0649192	−	0.368175i
$66$	40.2520	−	218.538i	0.0750709	−	0.407578i
$67$	−290.347	+	105.678i	−0.529426	+	0.192695i	−0.592882	−	0.805289i	$-0.702010\pi$
$67$	−290.347	+	105.678i	−0.529426	+	0.192695i	0.0634560	+	0.997985i	$0.479788\pi$
$68$	−309.199	+	112.539i	−0.551411	+	0.200697i
$69$	−187.062	−	159.406i	−0.326371	−	0.278120i
$70$	−66.0065	−	374.341i	−0.112704	−	0.639176i
$71$	130.821	−	226.589i	0.218671	−	0.378749i	−0.735731	−	0.677274i	$-0.763161\pi$
$71$	130.821	−	226.589i	0.218671	−	0.378749i	0.954402	+	0.298525i	$0.0964946\pi$
$72$	204.924	+	367.759i	0.335424	+	0.601956i
$73$	186.795	+	323.539i	0.299490	+	0.518731i	0.976019	−	0.217684i	$-0.0698502\pi$
$73$	186.795	+	323.539i	0.299490	+	0.518731i	−0.676530	+	0.736415i	$0.736517\pi$
$74$	−150.028	+	125.889i	−0.235681	+	0.197760i
$75$	551.294	+	205.421i	0.848772	+	0.316266i
$76$	−162.272	+	920.288i	−0.244919	+	1.38900i
$77$	737.290	+	618.660i	1.09120	+	0.915622i
$78$	68.9947	+	0.525293i	0.100155	+	0.000762535i
$79$	−128.935	−	46.9287i	−0.183625	−	0.0668340i	0.248571	−	0.968614i	$-0.420039\pi$
$79$	−128.935	−	46.9287i	−0.183625	−	0.0668340i	−0.432196	+	0.901780i	$0.642261\pi$
$80$	600.936			0.839833
$81$	728.662	+	22.1972i	0.999536	+	0.0304489i
$82$	46.5117			0.0626385
$83$	1033.80	+	376.273i	1.36716	+	0.497606i	0.918261	−	0.395975i	$-0.129593\pi$
$83$	1033.80	+	376.273i	1.36716	+	0.497606i	0.448901	+	0.893581i	$0.351816\pi$
$84$	−844.769	−	6.43168i	−1.09728	−	0.00835422i
$85$	−563.365	−	472.719i	−0.718888	−	0.603219i
$86$	43.1977	−	244.986i	0.0541642	−	0.307181i
$87$	616.018	+	229.538i	0.759127	+	0.282863i
$88$	488.311	−	409.741i	0.591524	−	0.496347i
$89$	−716.067	−	1240.26i	−0.852842	−	1.47717i	−0.878632	−	0.477499i	$-0.841543\pi$
$89$	−716.067	−	1240.26i	−0.852842	−	1.47717i	0.0257897	−	0.999667i	$-0.491790\pi$
$90$	−223.690	+	374.167i	−0.261989	+	0.438229i
$91$	−149.421	+	258.805i	−0.172127	+	0.298133i
$92$	−56.7185	−	321.667i	−0.0642751	−	0.364522i
$93$	−815.870	−	695.250i	−0.909697	−	0.775205i
$94$	−107.584	+	39.1574i	−0.118047	+	0.0429657i
$95$	−1962.64	+	714.343i	−2.11961	+	0.771474i
$96$	−155.746	+	845.580i	−0.165580	+	0.898976i
$97$	137.698	+	780.924i	0.144135	+	0.817431i	0.968057	+	0.250728i	$0.0806701\pi$
$97$	137.698	+	780.924i	0.144135	+	0.817431i	−0.823922	+	0.566703i	$0.808219\pi$
$98$	−110.502	+	191.395i	−0.113902	+	0.197284i
$99$	−175.098	−	1089.82i	−0.177758	−	1.10637i
$100$	390.942	+	677.131i	0.390942	+	0.677131i
$101$	647.510	−	543.325i	0.637917	−	0.535276i	−0.265461	−	0.964122i	$-0.585524\pi$
$101$	647.510	−	543.325i	0.637917	−	0.535276i	0.903378	+	0.428846i	$0.141080\pi$
$102$	199.663	−	164.963i	0.193820	−	0.160135i
$103$	293.566	−	1664.89i	0.280834	−	1.59269i	−0.438964	−	0.898505i	$-0.644654\pi$
$103$	293.566	−	1664.89i	0.280834	−	1.59269i	0.719798	−	0.694184i	$-0.244234\pi$
$104$	151.619	+	127.223i	0.142956	+	0.119955i
$105$	−931.592	−	1642.31i	−0.865848	−	1.52641i
$106$	−11.4806	−	4.17860i	−0.0105198	−	0.00382889i
$107$	−1055.10			−0.953275			−0.476638	−	0.879100i	$-0.658145\pi$
$107$	−1055.10			−0.953275			−0.476638	+	0.879100i	$0.658145\pi$
$108$	727.762	+	639.549i	0.648416	+	0.569821i
$109$	1352.76			1.18873			0.594363	−	0.804197i	$-0.297404\pi$
$109$	1352.76			1.18873			0.594363	+	0.804197i	$0.297404\pi$
$110$	620.250	+	225.752i	0.537623	+	0.195679i
$111$	−492.814	+	838.766i	−0.421404	+	0.717227i
$112$	−702.183	−	589.202i	−0.592412	−	0.497092i
$113$	−185.962	+	1054.64i	−0.154813	+	0.877986i	0.804144	+	0.594434i	$0.202624\pi$
$113$	−185.962	+	1054.64i	−0.154813	+	0.877986i	−0.958957	+	0.283552i	$0.908487\pi$
$114$	−122.208	−	725.323i	−0.100402	−	0.595901i
$115$	559.231	−	469.250i	0.453466	−	0.380503i
$116$	436.840	+	756.628i	0.349651	+	0.605614i
$117$	323.803	−	112.301i	0.255860	−	0.0887374i
$118$	−380.027	+	658.226i	−0.296477	+	0.513514i
$119$	194.793	+	1104.73i	0.150056	+	0.851011i
$120$	−1178.33	+	418.745i	−0.896384	+	0.318550i
$121$	−319.758	+	116.382i	−0.240239	+	0.0874399i
$122$	58.4226	−	21.2641i	0.0433552	−	0.0157800i
$123$	217.698	−	77.3638i	0.159587	−	0.0567126i
$124$	−247.378	−	1402.95i	−0.179155	−	1.01604i
$125$	90.8887	−	157.424i	0.0650347	−	0.112643i
$126$	628.238	−	217.886i	0.444190	−	0.154054i
$127$	−390.223	−	675.886i	−0.272651	−	0.472245i	0.696889	−	0.717179i	$-0.254567\pi$
$127$	−390.223	−	675.886i	−0.272651	−	0.472245i	−0.969540	+	0.244934i	$0.921234\pi$
$128$	−1124.95	+	943.943i	−0.776814	+	0.651825i
$129$	−205.303	−	1218.51i	−0.140124	−	0.831657i
$130$	−35.5884	+	201.832i	−0.0240100	+	0.136168i
$131$	1968.87	+	1652.07i	1.31313	+	1.10185i	0.987712	+	0.156282i	$0.0499509\pi$
$131$	1968.87	+	1652.07i	1.31313	+	1.10185i	0.325422	+	0.945569i	$0.394494\pi$
$132$	743.126	−	1264.79i	0.490006	−	0.833987i
$133$	2993.71	+	1089.62i	1.95178	+	0.710392i
$134$	323.219			0.208372
$135$	−424.621	+	2123.35i	−0.270708	+	1.35370i
$136$	742.954			0.468439
$137$	−1381.39	−	502.786i	−0.861463	−	0.313547i	−0.126758	−	0.991934i	$-0.540457\pi$
$137$	−1381.39	−	502.786i	−0.861463	−	0.313547i	−0.734705	+	0.678387i	$0.762679\pi$
$138$	126.848	+	223.622i	0.0782467	+	0.137942i
$139$	1104.10	+	926.448i	0.673729	+	0.565326i	0.914166	−	0.405339i	$-0.132846\pi$
$139$	1104.10	+	926.448i	0.673729	+	0.565326i	−0.240438	+	0.970665i	$0.577291\pi$
$140$	435.743	−	2471.22i	0.263050	−	1.49183i
$141$	−438.416	+	362.223i	−0.261853	+	0.216345i
$142$	−209.666	+	175.930i	−0.123907	+	0.103970i
$143$	−259.463	−	449.404i	−0.151730	−	0.262804i
$144$	166.761	+	1037.92i	0.0965052	+	0.600651i
$145$	−976.348	+	1691.08i	−0.559181	+	0.968530i
$146$	−67.8627	−	384.869i	−0.0384682	−	0.218164i
$147$	−198.853	+	1079.62i	−0.111572	+	0.605753i
$148$	−1214.92	+	442.196i	−0.674771	+	0.245596i
$149$	−2536.57	+	923.237i	−1.39466	+	0.507614i	−0.926588	−	0.376077i	$-0.877273\pi$
$149$	−2536.57	+	923.237i	−1.39466	+	0.507614i	−0.468070	+	0.883691i	$0.655051\pi$
$150$	−468.423	−	399.170i	−0.254977	−	0.217280i
$151$	−178.841	−	1014.26i	−0.0963835	−	0.546618i	−0.994315	−	0.106482i	$-0.966041\pi$
$151$	−178.841	−	1014.26i	−0.0963835	−	0.546618i	0.897931	−	0.440136i	$-0.145070\pi$
$152$	1055.00	−	1827.31i	0.562971	−	0.975094i
$153$	660.137	−	1104.21i	0.348816	−	0.583466i
$154$	−503.407	−	871.927i	−0.263414	−	0.456246i
$155$	2439.08	−	2046.63i	1.26395	−	1.06058i
$156$	426.816	+	159.038i	0.219055	+	0.0816235i
$157$	−170.059	+	964.451i	−0.0864469	+	0.490265i	0.910588	+	0.413315i	$0.135629\pi$
$157$	−170.059	+	964.451i	−0.0864469	+	0.490265i	−0.997035	+	0.0769498i	$0.975482\pi$
$158$	109.953	+	92.2612i	0.0553630	+	0.0464551i
$159$	−60.6854	−	0.462030i	−0.0302683	−	0.000230449i
$160$	−2399.91	−	873.495i	−1.18581	−	0.431599i
$161$	−1113.54			−0.545088
$162$	−708.328	−	282.521i	−0.343528	−	0.137018i
$163$	−2890.61			−1.38902			−0.694509	−	0.719484i	$-0.744379\pi$
$163$	−2890.61			−1.38902			−0.694509	+	0.719484i	$0.744379\pi$
$164$	288.531	+	105.017i	0.137381	+	0.0500026i
$165$	3278.58	+	24.9616i	1.54689	+	0.0117773i
$166$	−881.597	−	739.748i	−0.412200	−	0.345877i
$167$	198.680	−	1126.77i	0.0920620	−	0.522110i	−0.903546	−	0.428491i	$-0.859045\pi$
$167$	198.680	−	1126.77i	0.0920620	−	0.522110i	0.995608	−	0.0936188i	$-0.0298435\pi$
$168$	1787.42	+	666.023i	0.820850	+	0.305862i
$169$	−1559.57	+	1308.64i	−0.709864	+	0.595646i
$170$	384.654	+	666.240i	0.173539	+	0.300578i
$171$	−1778.44	−	3191.61i	−0.795324	−	1.42730i
$172$	821.115	−	1422.21i	0.364008	−	0.630481i
$173$	126.482	+	717.312i	0.0555850	+	0.315238i	0.999905	−	0.0137904i	$-0.00438977\pi$
$173$	126.482	+	717.312i	0.0555850	+	0.315238i	−0.944320	+	0.329029i	$0.893279\pi$
$174$	−523.417	−	446.034i	−0.228047	−	0.194332i
$175$	2504.83	−	911.685i	1.08199	−	0.393811i
$176$	1495.71	−	544.393i	0.640587	−	0.233154i
$177$	−683.877	+	3712.93i	−0.290414	+	1.57673i
$178$	260.147	+	1475.37i	0.109544	+	0.621255i
$179$	−525.620	+	910.400i	−0.219479	+	0.380148i	−0.954649	−	0.297735i	$-0.903769\pi$
$179$	−525.620	+	910.400i	−0.219479	+	0.380148i	0.735170	+	0.677883i	$0.237102\pi$
$180$	−2232.45	+	1816.05i	−0.924428	+	0.752001i
$181$	521.671	+	903.561i	0.214229	+	0.371056i	0.953034	−	0.302864i	$-0.0979427\pi$
$181$	521.671	+	903.561i	0.214229	+	0.371056i	−0.738805	+	0.673920i	$0.764609\pi$
$182$	239.475	−	200.943i	0.0975334	−	0.0818402i
$183$	238.078	−	196.702i	0.0961706	−	0.0794569i
$184$	−128.066	+	726.298i	−0.0513106	+	0.290997i
$185$	−2213.60	−	1857.43i	−0.879715	−	0.738169i
$186$	553.248	+	975.328i	0.218098	+	0.384487i
$187$	−1830.44	−	666.224i	−0.715801	−	0.260530i
$188$	−755.798			−0.293204
$189$	2578.06	−	2064.77i	0.992201	−	0.794657i
$190$	2184.84			0.834237
$191$	342.587	+	124.692i	0.129784	+	0.0472375i	0.406096	−	0.913831i	$-0.366890\pi$
$191$	342.587	+	124.692i	0.129784	+	0.0472375i	−0.276312	+	0.961068i	$0.589112\pi$
$192$	−364.261	+	619.970i	−0.136918	+	0.233034i
$193$	627.855	+	526.833i	0.234166	+	0.196489i	0.752318	−	0.658800i	$-0.228936\pi$
$193$	627.855	+	526.833i	0.234166	+	0.196489i	−0.518152	+	0.855288i	$0.673380\pi$
$194$	144.043	−	816.909i	0.0533077	−	0.302323i
$195$	169.139	+	1003.87i	0.0621143	+	0.368659i
$196$	−1117.63	+	937.801i	−0.407299	+	0.341764i
$197$	1084.39	+	1878.22i	0.392180	+	0.679276i	0.992737	−	0.120306i	$-0.0383876\pi$
$197$	1084.39	+	1878.22i	0.392180	+	0.679276i	−0.600557	+	0.799582i	$0.705054\pi$
$198$	−217.795	+	1133.93i	−0.0781717	+	0.406995i
$199$	2026.30	−	3509.66i	0.721813	−	1.25022i	−0.238459	−	0.971153i	$-0.576642\pi$
$199$	2026.30	−	3509.66i	0.721813	−	1.25022i	0.960272	−	0.279065i	$-0.0900244\pi$
$200$	−306.564	−	1738.61i	−0.108387	−	0.614692i
$201$	1512.82	−	537.615i	0.530878	−	0.188659i
$202$	−830.889	+	302.419i	−0.289412	+	0.105337i
$203$	2798.91	−	1018.72i	0.967709	−	0.352217i
$204$	1611.05	−	572.523i	0.552923	−	0.196493i
$205$	119.168	+	675.835i	0.0406002	+	0.230255i
$206$	−884.239	+	1531.55i	−0.299067	+	0.518000i
$207$	965.668	+	835.675i	0.324244	+	0.280596i
$208$	247.109	+	428.005i	0.0823745	+	0.142677i
$209$	−4237.82	+	3555.95i	−1.40256	+	1.17689i
$210$	328.161	+	1947.69i	0.107835	+	0.640016i
$211$	−9.81661	+	55.6728i	−0.00320286	+	0.0181643i	−0.986367	−	0.164559i	$-0.947380\pi$
$211$	−9.81661	+	55.6728i	−0.00320286	+	0.0181643i	0.983164	+	0.182723i	$0.0584911\pi$
$212$	−61.7842	−	51.8431i	−0.0200158	−	0.0167953i
$213$	−688.711	+	1172.18i	−0.221548	+	0.377073i
$214$	1037.16	+	377.494i	0.331302	+	0.120584i
$215$	3670.43			1.16428
$216$	−1050.24	−	1918.98i	−0.330831	−	0.604492i
$217$	−4856.70			−1.51933
$218$	−1329.76	−	483.992i	−0.413131	−	0.150367i
$219$	−957.790	−	1688.50i	−0.295532	−	0.520997i
$220$	3337.94	+	2800.87i	1.02293	+	0.858338i
$221$	105.026	−	595.631i	0.0319674	−	0.181296i
$222$	784.527	−	648.182i	0.237180	−	0.195960i
$223$	282.857	−	237.345i	0.0849395	−	0.0712727i	−0.599329	−	0.800503i	$-0.704566\pi$
$223$	282.857	−	237.345i	0.0849395	−	0.0712727i	0.684269	+	0.729230i	$0.260122\pi$
$224$	1947.81	+	3373.71i	0.580999	+	1.00632i
$225$	−2856.40	−	1089.18i	−0.846340	−	0.322719i
$226$	560.130	−	970.173i	0.164864	−	0.285553i
$227$	−373.816	−	2120.01i	−0.109300	−	0.619869i	−0.989416	−	0.145110i	$-0.953646\pi$
$227$	−373.816	−	2120.01i	−0.109300	−	0.619869i	0.880116	−	0.474759i	$-0.157465\pi$
$228$	879.570	−	4775.40i	0.255487	−	1.38710i
$229$	3772.34	−	1373.02i	1.08857	−	0.396208i	0.265480	−	0.964116i	$-0.414470\pi$
$229$	3772.34	−	1373.02i	1.08857	−	0.396208i	0.823092	+	0.567909i	$0.192247\pi$
$230$	−717.609	+	261.188i	−0.205729	+	0.0748793i
$231$	−3806.49	−	3243.73i	−1.08419	−	0.923903i
$232$	−342.556	−	1942.73i	−0.0969391	−	0.549769i
$233$	−881.056	+	1526.03i	−0.247725	+	0.429072i	−0.962894	−	0.269879i	$-0.913016\pi$
$233$	−881.056	+	1526.03i	−0.247725	+	0.429072i	0.715169	+	0.698951i	$0.246350\pi$
$234$	−358.476	−	5.45885i	−0.100147	−	0.00152503i
$235$	−844.615	−	1462.92i	−0.234454	−	0.406086i
$236$	−3843.64	+	3225.20i	−1.06017	+	0.889587i
$237$	668.093	+	248.942i	0.183111	+	0.0682301i
$238$	203.770	−	1155.63i	0.0554975	−	0.314742i
$239$	2444.98	+	2051.58i	0.661726	+	0.555254i	0.910604	−	0.413281i	$-0.135617\pi$
$239$	2444.98	+	2051.58i	0.661726	+	0.555254i	−0.248878	+	0.968535i	$0.580062\pi$
$240$	−3122.46	−	23.7730i	−0.839809	−	0.00639392i
$241$	2116.26	+	770.257i	0.565646	+	0.205878i	0.608984	−	0.793182i	$-0.291577\pi$
$241$	2116.26	+	770.257i	0.565646	+	0.205878i	−0.0433387	+	0.999060i	$0.513799\pi$
$242$	355.960			0.0945535
$243$	−3785.25	−	144.163i	−0.999276	−	0.0380578i
$244$	410.430			0.107685
$245$	−3064.16	−	1115.26i	−0.799029	−	0.290823i
$246$	−241.675	−	1.84000i	−0.0626367	−	0.000476887i
$247$	−1315.83	−	1104.11i	−0.338964	−	0.284425i
$248$	−558.559	+	3167.75i	−0.143018	+	0.811097i
$249$	−5356.75	−	1996.01i	−1.36333	−	0.508001i
$250$	−145.666	+	122.228i	−0.0368509	+	0.0309216i
$251$	−2815.86	−	4877.20i	−0.708108	−	1.22648i	−0.965558	−	0.260188i	$-0.916215\pi$
$251$	−2815.86	−	4877.20i	−0.708108	−	1.22648i	0.257449	−	0.966292i	$-0.417118\pi$
$252$	4389.17	+	66.8381i	1.09719	+	0.0167079i
$253$	966.808	−	1674.56i	0.240248	−	0.416121i
$254$	141.768	+	804.005i	0.0350209	+	0.198613i
$255$	2908.54	+	2478.54i	0.714275	+	0.608674i
$256$	403.238	−	146.767i	0.0984467	−	0.0358317i
$257$	6307.99	−	2295.92i	1.53106	−	0.557259i	0.567176	−	0.823596i	$-0.308036\pi$
$257$	6307.99	−	2295.92i	1.53106	−	0.557259i	0.963880	+	0.266338i	$0.0858136\pi$
$258$	−234.147	+	1271.24i	−0.0565013	+	0.306759i
$259$	765.393	+	4340.76i	0.183626	+	1.04140i
$260$	−676.475	+	1171.69i	−0.161358	+	0.279481i
$261$	−3191.75	−	1217.05i	−0.756951	−	0.288634i
$262$	−1344.30	−	2328.40i	−0.316990	−	0.549042i
$263$	4224.56	−	3544.82i	0.990484	−	0.831115i	0.00484607	−	0.999988i	$-0.498457\pi$
$263$	4224.56	−	3544.82i	0.990484	−	0.831115i	0.985638	+	0.168874i	$0.0540130\pi$
$264$	−2553.47	+	2109.70i	−0.595285	+	0.491829i
$265$	31.3023	−	177.524i	0.00725617	−	0.0411518i
$266$	−2552.95	−	2142.18i	−0.588464	−	0.493780i
$267$	3671.62	+	6472.75i	0.841572	+	1.48362i
$268$	2005.06	+	729.780i	0.457008	+	0.166337i
$269$	813.037			0.184282			0.0921408	−	0.995746i	$-0.470629\pi$
$269$	813.037			0.184282			0.0921408	+	0.995746i	$0.470629\pi$
$270$	1177.09	−	1935.32i	0.265317	−	0.436222i
$271$	5803.74			1.30093			0.650465	−	0.759536i	$-0.274574\pi$
$271$	5803.74			1.30093			0.650465	+	0.759536i	$0.274574\pi$
$272$	1743.28	+	634.501i	0.388609	+	0.141442i
$273$	786.630	−	1338.84i	0.174392	−	0.296814i
$274$	1178.01	+	988.471i	0.259731	+	0.217941i
$275$	−803.763	+	4558.37i	−0.176250	+	0.999563i
$276$	281.984	+	1673.62i	0.0614980	+	0.365001i
$277$	−2413.49	+	2025.16i	−0.523511	+	0.439278i	−0.865854	−	0.500297i	$-0.833224\pi$
$277$	−2413.49	+	2025.16i	−0.523511	+	0.439278i	0.342343	+	0.939575i	$0.388780\pi$
$278$	−753.856	−	1305.72i	−0.162638	−	0.281697i
$279$	4211.76	+	3644.79i	0.903769	+	0.782108i
$280$	−2832.95	+	4906.82i	−0.604647	+	1.04728i
$281$	1128.17	+	6398.19i	0.239506	+	1.35831i	0.832913	+	0.553404i	$0.186671\pi$
$281$	1128.17	+	6398.19i	0.239506	+	1.35831i	−0.593407	+	0.804903i	$0.702217\pi$
$282$	560.556	−	199.206i	0.118371	−	0.0420657i
$283$	−5039.70	+	1834.30i	−1.05858	+	0.385293i	−0.811896	−	0.583802i	$-0.801564\pi$
$283$	−5039.70	+	1834.30i	−1.05858	+	0.385293i	−0.246688	+	0.969095i	$0.579342\pi$
$284$	−1697.86	+	617.972i	−0.354752	+	0.129119i
$285$	10226.1	−	3634.08i	2.12542	−	0.755314i
$286$	94.2629	+	534.592i	0.0194891	+	0.110528i
$287$	523.393	−	906.543i	0.107648	−	0.186451i
$288$	842.705	−	4387.47i	0.172420	−	0.897689i
$289$	1321.34	+	2288.62i	0.268947	+	0.465830i
$290$	1564.78	−	1313.01i	0.316852	−	0.265870i
$291$	−684.586	−	4063.13i	−0.137908	−	0.818505i
$292$	447.997	−	2540.72i	0.0897844	−	0.509193i
$293$	−6595.63	−	5534.39i	−1.31509	−	1.10349i	−0.987322	−	0.158731i	$-0.949260\pi$
$293$	−6595.63	−	5534.39i	−1.31509	−	1.10349i	−0.327766	−	0.944759i	$-0.606296\pi$
$294$	581.739	−	990.116i	0.115400	−	0.196411i
$295$	−10538.0	−	3835.51i	−2.07981	−	0.756990i
$296$	2919.25			0.573237
$297$	866.699	+	5669.62i	0.169330	+	1.10769i
$298$	2823.75			0.548911
$299$	564.174	+	205.342i	0.109120	+	0.0397166i
$300$	−2004.55	−	3533.84i	−0.385775	−	0.680088i
$301$	−4288.84	−	3598.76i	−0.821277	−	0.689133i
$302$	−187.082	+	1061.00i	−0.0356469	+	0.202164i
$303$	−3385.96	+	2797.50i	−0.641974	+	0.530404i
$304$	4036.03	−	3386.63i	0.761454	−	0.638936i
$305$	458.661	+	794.424i	0.0861077	+	0.149143i
$306$	−1043.98	+	849.251i	−0.195033	+	0.158655i
$307$	−1613.24	+	2794.22i	−0.299911	+	0.519461i	−0.976115	−	0.217253i	$-0.930290\pi$
$307$	−1613.24	+	2794.22i	−0.299911	+	0.519461i	0.676204	+	0.736714i	$0.263624\pi$
$308$	−1154.15	−	6545.53i	−0.213520	−	1.21093i
$309$	−1591.23	+	8639.18i	−0.292951	+	1.59050i
$310$	−3129.85	+	1139.17i	−0.573431	+	0.208712i
$311$	336.079	−	122.323i	0.0612775	−	0.0223032i	−0.311200	−	0.950345i	$-0.600731\pi$
$311$	336.079	−	122.323i	0.0612775	−	0.0223032i	0.372477	+	0.928041i	$0.378509\pi$
$312$	−782.779	−	667.050i	−0.142039	−	0.121039i
$313$	−1107.26	−	6279.59i	−0.199955	−	1.13400i	−0.905183	−	0.425023i	$-0.860266\pi$
$313$	−1107.26	−	6279.59i	−0.199955	−	1.13400i	0.705227	−	0.708981i	$-0.250845\pi$
$314$	512.228	−	887.206i	0.0920596	−	0.159452i
$315$	4775.58	+	8570.32i	0.854202	+	1.53296i
$316$	473.768	+	820.590i	0.0843402	+	0.146082i
$317$	6742.70	−	5657.79i	1.19466	−	1.00244i	0.194895	−	0.980824i	$-0.437563\pi$
$317$	6742.70	−	5657.79i	1.19466	−	1.00244i	0.999766	−	0.0216156i	$-0.00688099\pi$
$318$	59.4880	+	22.1662i	0.0104903	+	0.00390887i
$319$	−898.127	+	5093.53i	−0.157635	+	0.893991i
$320$	−1636.17	−	1372.91i	−0.285828	−	0.239838i
$321$	5482.31	+	41.7397i	0.953248	+	0.00725759i
$322$	1094.60	+	398.403i	0.189440	+	0.0689506i
$323$	−6447.74			−1.11072
$324$	−3756.15	−	3351.89i	−0.644059	−	0.574741i
$325$	−1437.19			−0.245296
$326$	2841.45	+	1034.20i	0.482740	+	0.175703i
$327$	−7028.96	−	53.5152i	−1.18869	−	0.00905015i
$328$	−531.091	−	445.638i	−0.0894043	−	0.0750191i
$329$	−447.432	+	2537.52i	−0.0749780	+	0.425221i
$330$	−3213.89	−	1197.55i	−0.536117	−	0.199766i
$331$	4268.76	−	3581.91i	0.708858	−	0.594803i	−0.215420	−	0.976521i	$-0.569112\pi$
$331$	4268.76	−	3581.91i	0.708858	−	0.594803i	0.924279	+	0.381719i	$0.124668\pi$
$332$	−3798.66	−	6579.47i	−0.627947	−	1.08764i
$333$	2593.84	−	4338.74i	0.426852	−	0.713998i
$334$	−598.439	+	1036.53i	−0.0980393	+	0.169809i
$335$	828.120	+	4696.50i	0.135060	+	0.765962i
$336$	3625.24	+	3089.27i	0.588610	+	0.501588i
$337$	276.634	−	100.686i	0.0447157	−	0.0162752i	−0.319565	−	0.947564i	$-0.603537\pi$
$337$	276.634	−	100.686i	0.0447157	−	0.0162752i	0.364281	+	0.931289i	$0.381315\pi$
$338$	2001.25	−	728.396i	0.322052	−	0.117218i
$339$	1007.98	−	5472.57i	0.161493	−	0.876782i
$340$	881.891	+	5001.45i	0.140668	+	0.797770i
$341$	4216.73	−	7303.59i	0.669644	−	1.15986i
$342$	606.298	+	3773.62i	0.0958621	+	0.596649i
$343$	−1550.67	−	2685.84i	−0.244106	−	0.422804i
$344$	−2840.51	+	2383.47i	−0.445204	+	0.373571i
$345$	−2924.33	+	2416.10i	−0.456349	+	0.377039i
$346$	132.310	−	750.366i	0.0205578	−	0.116589i
$347$	230.707	+	193.586i	0.0356917	+	0.0299489i	0.660459	−	0.750862i	$-0.270362\pi$
$347$	230.707	+	193.586i	0.0356917	+	0.0299489i	−0.624767	+	0.780811i	$0.714806\pi$
$348$	−2239.89	−	3948.72i	−0.345030	−	0.608258i
$349$	7527.49	+	2739.78i	1.15455	+	0.420221i	0.847147	−	0.531359i	$-0.178319\pi$
$349$	7527.49	+	2739.78i	1.15455	+	0.420221i	0.307401	+	0.951580i	$0.400541\pi$
$350$	−2788.42			−0.425849
$351$	−1686.92	+	570.709i	−0.256528	+	0.0867868i
$352$	−6764.60			−1.02430
$353$	−1832.30	−	666.904i	−0.276271	−	0.100555i	0.200169	−	0.979761i	$-0.435851\pi$
$353$	−1832.30	−	666.904i	−0.276271	−	0.100555i	−0.476440	+	0.879207i	$0.658073\pi$
$354$	2000.66	−	3405.11i	0.300378	−	0.511242i
$355$	−3093.53	−	2595.78i	−0.462500	−	0.388083i
$356$	−1717.37	+	9739.67i	−0.255675	+	1.45000i
$357$	−968.444	−	5747.88i	−0.143573	−	0.852129i
$358$	842.404	−	706.861i	0.124364	−	0.104354i
$359$	1524.21	+	2640.01i	0.224080	+	0.388119i	0.956043	−	0.293226i	$-0.0947289\pi$
$359$	1524.21	+	2640.01i	0.224080	+	0.388119i	−0.731963	+	0.681345i	$0.761396\pi$
$360$	6139.16	−	2129.18i	0.898783	−	0.311716i
$361$	−5726.32	+	9918.27i	−0.834862	+	1.44602i
$362$	−189.523	−	1074.84i	−0.0275169	−	0.156056i
$363$	1666.07	−	592.074i	0.240898	−	0.0856083i
$364$	1939.26	−	705.833i	0.279244	−	0.101637i
$365$	5418.43	−	1972.15i	0.777024	−	0.282813i
$366$	−304.405	+	108.177i	−0.0434741	+	0.0154495i
$367$	213.215	+	1209.20i	0.0303262	+	0.171988i	0.996209	−	0.0869907i	$-0.0277250\pi$
$367$	213.215	+	1209.20i	0.0303262	+	0.171988i	−0.965883	+	0.258979i	$0.916614\pi$
$368$	−920.772	+	1594.82i	−0.130431	+	0.225913i
$369$	−1134.22	+	393.370i	−0.160014	+	0.0554960i
$370$	1511.40	+	2617.83i	0.212363	+	0.367823i
$371$	−210.634	+	176.743i	−0.0294760	+	0.0247333i
$372$	1229.87	+	7299.51i	0.171414	+	1.01737i
$373$	13.3473	−	75.6964i	0.00185281	−	0.0105078i	−0.983867	−	0.178900i	$-0.942746\pi$
$373$	13.3473	−	75.6964i	0.00185281	−	0.0105078i	0.985720	+	0.168392i	$0.0538574\pi$
$374$	1560.94	+	1309.79i	0.215814	+	0.181090i
$375$	−478.486	+	814.379i	−0.0658904	+	0.112145i
$376$	1603.62	+	583.669i	0.219947	+	0.0800543i
$377$	−1605.92			−0.219388
$378$	−3272.95	+	1107.28i	−0.445350	+	0.150668i
$379$	4538.70			0.615138			0.307569	−	0.951526i	$-0.400485\pi$
$379$	4538.70			0.615138			0.307569	+	0.951526i	$0.400485\pi$
$380$	13553.4	+	4933.05i	1.82968	+	0.665948i
$381$	2000.86	+	3527.34i	0.269048	+	0.474307i
$382$	−292.149	−	245.142i	−0.0391299	−	0.0328339i
$383$	−1582.94	+	8977.31i	−0.211187	+	1.19770i	0.676215	+	0.736704i	$0.263619\pi$
$383$	−1582.94	+	8977.31i	−0.211187	+	1.19770i	−0.887402	+	0.460996i	$0.847492\pi$
$384$	5882.57	−	4860.23i	0.781754	−	0.645892i
$385$	11379.7	−	9548.69i	1.50640	−	1.26402i
$386$	−428.687	−	742.508i	−0.0565275	−	0.0979084i
$387$	1018.55	+	6339.50i	0.133788	+	0.832700i
$388$	2738.02	−	4742.38i	0.358252	−	0.620511i
$389$	41.7951	+	237.032i	0.00544755	+	0.0308946i	0.987410	−	0.158180i	$-0.0505625\pi$
$389$	41.7951	+	237.032i	0.00544755	+	0.0308946i	−0.981963	+	0.189074i	$0.939451\pi$
$390$	192.902	−	1047.31i	0.0250460	−	0.135981i
$391$	2117.75	−	770.800i	0.273912	−	0.0996957i
$392$	3095.55	−	1126.69i	0.398849	−	0.145169i
$393$	−10164.9	−	8662.07i	−1.30471	−	1.11182i
$394$	−393.958	−	2234.25i	−0.0503739	−	0.285685i
$395$	−1058.88	+	1834.04i	−0.134882	+	0.233622i
$396$	−3911.32	+	6542.48i	−0.496341	+	0.830232i
$397$	5249.73	+	9092.81i	0.663669	+	1.14951i	0.979644	+	0.200741i	$0.0643350\pi$
$397$	5249.73	+	9092.81i	0.663669	+	1.14951i	−0.315975	+	0.948767i	$0.602332\pi$
$398$	−3247.53	+	2725.00i	−0.409005	+	0.343196i
$399$	−15512.2	−	5780.10i	−1.94632	−	0.725231i
$400$	765.491	−	4341.31i	0.0956863	−	0.542664i
$401$	−11889.8	−	9976.74i	−1.48067	−	1.24243i	−0.905464	−	0.424423i	$-0.860477\pi$
$401$	−11889.8	−	9976.74i	−1.48067	−	1.24243i	−0.575207	−	0.818008i	$-0.695079\pi$
$402$	−1679.44	−	12.7865i	−0.208366	−	0.00158640i
$403$	2460.64	+	895.601i	0.304152	+	0.110702i
$404$	−5837.16			−0.718835
$405$	2290.33	−	11016.2i	0.281006	−	1.35160i
$406$	−3115.79			−0.380872
$407$	−7192.25	−	2617.76i	−0.875937	−	0.318815i
$408$	−3860.39	−	29.3912i	−0.468426	−	0.00356638i
$409$	4365.10	+	3662.76i	0.527727	+	0.442816i	0.867316	−	0.497758i	$-0.165843\pi$
$409$	4365.10	+	3662.76i	0.527727	+	0.442816i	−0.339588	+	0.940574i	$0.610288\pi$
$410$	124.659	−	706.977i	0.0150158	−	0.0851588i
$411$	7157.83	+	2667.13i	0.859051	+	0.320096i
$412$	−8943.30	+	7504.32i	−1.06943	+	0.897358i
$413$	8552.83	+	14813.9i	1.01903	+	1.76500i
$414$	−650.257	−	1166.96i	−0.0771942	−	0.138534i
$415$	8490.10	−	14705.3i	1.00425	−	1.73941i
$416$	−364.728	−	2068.48i	−0.0429862	−	0.243787i
$417$	−5700.24	−	4857.50i	−0.669405	−	0.570439i
$418$	5437.99	−	1979.27i	0.636318	−	0.231601i
$419$	−8940.47	+	3254.06i	−1.04241	+	0.379407i	−0.805794	−	0.592196i	$-0.798261\pi$
$419$	−8940.47	+	3254.06i	−1.04241	+	0.379407i	−0.236617	+	0.971603i	$0.576039\pi$
$420$	−2361.88	+	12823.2i	−0.274400	+	1.48979i
$421$	−1986.28	−	11264.7i	−0.229941	−	1.30406i	−0.853010	−	0.521894i	$-0.825226\pi$
$421$	−1986.28	−	11264.7i	−0.229941	−	1.30406i	0.623069	−	0.782167i	$-0.285885\pi$
$422$	29.5683	−	51.2138i	0.00341081	−	0.00590770i
$423$	2292.34	−	1864.77i	0.263492	−	0.214345i
$424$	91.0547	+	157.711i	0.0104293	+	0.0180640i
$425$	−4132.68	+	3467.73i	−0.471681	+	0.395787i
$426$	1096.38	−	905.840i	0.124695	−	0.103024i
$427$	242.974	−	1377.98i	0.0275371	−	0.156171i
$428$	5581.57	+	4683.50i	0.630364	+	0.528938i
$429$	1330.39	+	2345.37i	0.149725	+	0.263952i
$430$	−3608.01	−	1313.21i	−0.404636	−	0.147276i
$431$	6855.26			0.766139			0.383070	−	0.923719i	$-0.374867\pi$
$431$	6855.26			0.766139			0.383070	+	0.923719i	$0.374867\pi$
$432$	−825.430	−	5399.66i	−0.0919294	−	0.601368i
$433$	4284.51			0.475521			0.237760	−	0.971324i	$-0.423587\pi$
$433$	4284.51			0.475521			0.237760	+	0.971324i	$0.423587\pi$
$434$	4774.10	+	1737.63i	0.528028	+	0.192187i
$435$	5140.01	−	8748.25i	0.566539	−	0.964245i
$436$	−7156.23	−	6004.79i	−0.786058	−	0.659581i
$437$	1111.42	−	6303.19i	0.121663	−	0.689983i
$438$	337.389	+	2002.46i	0.0368061	+	0.218451i
$439$	−10557.0	+	8858.38i	−1.14774	+	0.963070i	−0.999664	−	0.0259060i	$-0.991753\pi$
$439$	−10557.0	+	8858.38i	−1.14774	+	0.963070i	−0.148077	+	0.988976i	$0.547309\pi$
$440$	−4919.30	−	8520.49i	−0.532997	−	0.923178i
$441$	1075.95	−	5601.85i	0.116181	−	0.604886i
$442$	−316.345	+	547.925i	−0.0340429	+	0.0589641i
$443$	−410.540	−	2328.29i	−0.0440301	−	0.249707i	0.954846	−	0.297100i	$-0.0960196\pi$
$443$	−410.540	−	2328.29i	−0.0440301	−	0.249707i	−0.998876	+	0.0473935i	$0.984909\pi$
$444$	6330.24	−	2249.59i	0.676621	−	0.240452i
$445$	−20771.2	+	7560.09i	−2.21269	+	0.805354i
$446$	−362.964	+	132.108i	−0.0385355	+	0.0140258i
$447$	13216.6	−	4696.79i	1.39848	−	0.496982i
$448$	565.736	+	3208.45i	0.0596619	+	0.338359i
$449$	−967.587	+	1675.91i	−0.101700	+	0.176149i	−0.912385	−	0.409333i	$-0.865761\pi$
$449$	−967.587	+	1675.91i	−0.101700	+	0.176149i	0.810685	+	0.585482i	$0.199095\pi$
$450$	2418.13	+	2092.62i	0.253315	+	0.219215i
$451$	908.850	+	1574.17i	0.0948915	+	0.164357i
$452$	5665.22	−	4753.68i	0.589534	−	0.494678i
$453$	889.136	+	5277.17i	0.0922191	+	0.547336i
$454$	−391.041	+	2217.70i	−0.0404239	+	0.229255i
$455$	3533.35	+	2964.84i	0.364057	+	0.305480i
$456$	−5554.05	+	9452.96i	−0.570378	+	0.970780i
$457$	−4776.95	−	1738.67i	−0.488964	−	0.177968i	0.0857600	−	0.996316i	$-0.472668\pi$
$457$	−4776.95	−	1738.67i	−0.488964	−	0.177968i	−0.574724	+	0.818348i	$0.694890\pi$
$458$	−4199.42			−0.428441
$459$	−3473.75	+	5711.38i	−0.353248	+	0.580794i
$460$	−5041.34			−0.510986
$461$	−7307.48	−	2659.71i	−0.738272	−	0.268709i	−0.0546099	−	0.998508i	$-0.517392\pi$
$461$	−7307.48	−	2659.71i	−0.738272	−	0.268709i	−0.683662	+	0.729799i	$0.739614\pi$
$462$	2581.21	+	4550.45i	0.259932	+	0.458238i
$463$	12156.4	+	10200.5i	1.22021	+	1.02388i	0.998814	+	0.0486955i	$0.0155064\pi$
$463$	12156.4	+	10200.5i	1.22021	+	1.02388i	0.221398	+	0.975184i	$0.428938\pi$
$464$	855.362	−	4851.00i	0.0855801	−	0.485349i
$465$	−12754.4	+	10537.8i	−1.27199	+	1.05092i
$466$	1412.06	−	1184.86i	0.140370	−	0.117784i
$467$	−3439.99	−	5958.24i	−0.340865	−	0.590395i	0.643729	−	0.765254i	$-0.277387\pi$
$467$	−3439.99	−	5958.24i	−0.340865	−	0.590395i	−0.984594	+	0.174858i	$0.944053\pi$
$468$	−2211.44	−	843.249i	−0.218427	−	0.0832889i
$469$	3637.15	−	6299.74i	0.358098	−	0.620245i
$470$	306.848	+	1740.22i	0.0301146	+	0.170788i
$471$	921.779	−	5004.56i	0.0901770	−	0.489593i
$472$	10645.9	−	3874.80i	1.03817	−	0.377865i
$473$	9135.57	−	3325.08i	0.888063	−	0.323229i
$474$	−567.664	−	483.739i	−0.0550077	−	0.0468752i
$475$	2660.52	+	15088.6i	0.256996	+	1.45750i
$476$	3873.32	−	6708.78i	0.372969	−	0.646001i
$477$	315.303	+	4.80142i	0.0302657	+	0.000460885i
$478$	−1669.38	−	2891.46i	−0.159740	−	0.276678i
$479$	−943.013	+	791.282i	−0.0899528	+	0.0754793i	−0.686655	−	0.726983i	$-0.740922\pi$
$479$	−943.013	+	791.282i	−0.0899528	+	0.0754793i	0.596702	+	0.802463i	$0.296477\pi$
$480$	12435.4	+	4633.62i	1.18249	+	0.440615i
$481$	412.673	−	2340.38i	0.0391191	−	0.221855i
$482$	−1804.69	−	1514.32i	−0.170542	−	0.143102i
$483$	5785.95	+	44.0516i	0.545073	+	0.00414993i
$484$	2208.16	+	803.704i	0.207378	+	0.0754794i
$485$	12239.1			1.14587
$486$	3669.30	+	1496.00i	0.342475	+	0.139629i
$487$	−5337.59			−0.496652			−0.248326	−	0.968677i	$-0.579880\pi$
$487$	−5337.59			−0.496652			−0.248326	+	0.968677i	$0.579880\pi$
$488$	−870.830	−	316.956i	−0.0807800	−	0.0294015i
$489$	15019.6	+	114.352i	1.38898	+	0.0105750i
$490$	2613.03	+	2192.59i	0.240908	+	0.202146i
$491$	1031.86	−	5851.97i	0.0948415	−	0.537873i	−0.899954	−	0.435984i	$-0.856400\pi$
$491$	1031.86	−	5851.97i	0.0948415	−	0.537873i	0.994796	−	0.101889i	$-0.0324886\pi$
$492$	−1495.05	−	557.081i	−0.136996	−	0.0510470i
$493$	−4617.87	+	3874.85i	−0.421862	+	0.353985i
$494$	898.421	+	1556.11i	0.0818256	+	0.141726i
$495$	−17034.5	−	259.401i	−1.54676	−	0.0235539i
$496$	−4015.95	+	6955.82i	−0.363551	+	0.629689i
$497$	1069.64	+	6066.24i	0.0965393	+	0.547501i
$498$	4551.52	+	3878.61i	0.409555	+	0.349005i
$499$	11278.9	−	4105.19i	1.01185	−	0.368284i	0.217708	−	0.976014i	$-0.430142\pi$
$499$	11278.9	−	4105.19i	1.01185	−	0.368284i	0.794144	+	0.607730i	$0.207920\pi$
$500$	−1179.60	+	429.339i	−0.105507	+	0.0384013i
$501$	−1076.92	+	5846.86i	−0.0960343	+	0.521394i
$502$	1023.00	+	5801.72i	0.0909536	+	0.515823i
$503$	−2465.92	+	4271.10i	−0.218588	+	0.378606i	−0.954377	−	0.298605i	$-0.903479\pi$
$503$	−2465.92	+	4271.10i	−0.218588	+	0.378606i	0.735788	+	0.677212i	$0.236812\pi$
$504$	−9261.11	−	3531.37i	−0.818497	−	0.312103i
$505$	−6523.10	−	11298.3i	−0.574800	−	0.995583i
$506$	−1549.49	+	1300.18i	−0.136133	+	0.114229i
$507$	8155.30	−	6737.97i	0.714378	−	0.590225i
$508$	−935.883	+	5307.66i	−0.0817384	+	0.463561i
$509$	10406.5	+	8732.10i	0.906209	+	0.760400i	0.971394	−	0.237474i	$-0.0763193\pi$
$509$	10406.5	+	8732.10i	0.906209	+	0.760400i	−0.0651850	+	0.997873i	$0.520764\pi$
$510$	−1972.31	−	3477.00i	−0.171246	−	0.301891i
$511$	−8264.99	−	3008.21i	−0.715502	−	0.260421i
$512$	11299.2			0.975312
$513$	9114.50	+	16653.9i	0.784435	+	1.43331i
$514$	−7022.14			−0.602594
$515$	−24519.5	−	8924.39i	−2.09798	−	0.763603i
$516$	−4322.78	+	7357.34i	−0.368798	+	0.627692i
$517$	−3427.49	−	2876.00i	−0.291568	−	0.244655i
$518$	800.662	−	4540.78i	0.0679133	−	0.385155i
$519$	−628.821	−	3732.16i	−0.0531834	−	0.315652i
$520$	2340.15	−	1963.62i	0.197351	−	0.165597i
$521$	2801.92	+	4853.07i	0.235613	+	0.408094i	0.959451	−	0.281877i	$-0.0909569\pi$
$521$	2801.92	+	4853.07i	0.235613	+	0.408094i	−0.723838	+	0.689970i	$0.757624\pi$
$522$	2702.03	+	2338.30i	0.226561	+	0.196062i
$523$	−3114.24	+	5394.02i	−0.260375	+	0.450983i	−0.966342	−	0.257262i	$-0.917180\pi$
$523$	−3114.24	+	5394.02i	−0.260375	+	0.450983i	0.705967	+	0.708245i	$0.250513\pi$
$524$	−3082.06	−	17479.2i	−0.256947	−	1.45722i
$525$	−13051.2	+	4638.03i	−1.08495	+	0.385562i
$526$	−5420.98	+	1973.07i	−0.449365	+	0.163555i
$527$	9236.58	−	3361.84i	0.763476	−	0.277882i
$528$	−7793.24	+	2769.50i	−0.642343	+	0.228271i
$529$	−1724.30	−	9779.01i	−0.141720	−	0.803732i
$530$	−94.2847	+	163.306i	−0.00772729	+	0.0133841i
$531$	3700.31	−	19265.4i	0.302410	−	1.57447i
$532$	−11000.2	−	19053.0i	−0.896468	−	1.55273i
$533$	−432.347	+	362.783i	−0.0351352	+	0.0294819i
$534$	−1293.36	−	7676.30i	−0.104811	−	0.622071i
$535$	−2827.85	+	16037.5i	−0.228520	+	1.29600i
$536$	−3690.65	−	3096.83i	−0.297410	−	0.249557i
$537$	2767.14	−	4709.65i	0.222366	−	0.378466i
$538$	−799.210	−	290.889i	−0.0640453	−	0.0233106i
$539$	−8636.92			−0.690202
$540$	11671.7	−	9347.87i	0.930126	−	0.744941i
$541$	15860.5			1.26044			0.630219	−	0.776418i	$-0.282965\pi$
$541$	15860.5			1.26044			0.630219	+	0.776418i	$0.282965\pi$
$542$	−5705.04	−	2076.46i	−0.452126	−	0.164560i
$543$	−2674.86	−	4715.54i	−0.211398	−	0.372676i
$544$	−6039.70	−	5067.91i	−0.476011	−	0.399421i
$545$	3625.63	−	20562.0i	0.284963	−	1.61611i
$546$	−1252.26	+	1034.63i	−0.0981536	+	0.0810953i
$547$	−11583.9	+	9720.02i	−0.905467	+	0.759777i	−0.971251	−	0.238057i	$-0.923490\pi$
$547$	−11583.9	+	9720.02i	−0.905467	+	0.759777i	0.0657839	+	0.997834i	$0.479045\pi$
$548$	5075.87	+	8791.66i	0.395676	+	0.685331i
$549$	−1244.83	+	1012.64i	−0.0967728	+	0.0787225i
$550$	2420.99	−	4193.27i	0.187693	−	0.325094i
$551$	2972.88	+	16860.0i	0.229853	+	1.30356i
$552$	694.163	−	3768.78i	0.0535245	−	0.290598i
$553$	3035.52	−	1104.84i	0.233424	−	0.0849593i
$554$	3097.01	−	1127.22i	0.237508	−	0.0864457i
$555$	11428.4	+	9738.80i	0.874070	+	0.744845i
$556$	−1728.35	−	9801.98i	−0.131832	−	0.747655i
$557$	−13032.6	+	22573.2i	−0.991402	+	1.71716i	−0.382378	+	0.924006i	$0.624895\pi$
$557$	−13032.6	+	22573.2i	−0.991402	+	1.71716i	−0.609024	+	0.793152i	$0.708439\pi$
$558$	−2836.10	−	5089.69i	−0.215164	−	0.386136i
$559$	1509.30	+	2614.19i	0.114198	+	0.197797i
$560$	−10837.8	+	9094.01i	−0.817824	+	0.686236i
$561$	9484.59	+	3534.11i	0.713796	+	0.265972i
$562$	1180.16	−	6693.02i	0.0885802	−	0.502363i
$563$	−6443.37	−	5406.63i	−0.482337	−	0.404728i	0.368934	−	0.929456i	$-0.379723\pi$
$563$	−6443.37	−	5406.63i	−0.482337	−	0.404728i	−0.851270	+	0.524727i	$0.824167\pi$
$564$	3927.13	+	29.8994i	0.293195	+	0.00223225i
$565$	15532.1	+	5653.24i	1.15653	+	0.420944i
$566$	5610.27			0.416638
$567$	−13477.3	+	10626.6i	−0.998222	+	0.787080i
$568$	4079.68			0.301372
$569$	2859.32	+	1040.71i	0.210666	+	0.0766762i	0.445198	−	0.895432i	$-0.353133\pi$
$569$	2859.32	+	1040.71i	0.210666	+	0.0766762i	−0.234532	+	0.972109i	$0.575356\pi$
$570$	−11352.4	−	86.4322i	−0.834213	−	0.00635131i
$571$	15411.5	+	12931.8i	1.12951	+	0.947776i	0.999046	−	0.0436768i	$-0.0139072\pi$
$571$	15411.5	+	12931.8i	1.12951	+	0.947776i	0.130469	+	0.991452i	$0.458352\pi$
$572$	−622.279	+	3529.12i	−0.0454874	+	0.257972i
$573$	−1775.15	−	661.450i	−0.129421	−	0.0482242i
$574$	−838.835	+	703.866i	−0.0609970	+	0.0511826i
$575$	−2677.62	−	4637.77i	−0.194199	−	0.336363i
$576$	1917.23	−	3206.95i	0.138688	−	0.231984i
$577$	−1827.40	+	3165.16i	−0.131847	+	0.228366i	−0.924389	−	0.381452i	$-0.875424\pi$
$577$	−1827.40	+	3165.16i	−0.131847	+	0.228366i	0.792541	+	0.609818i	$0.208757\pi$
$578$	−480.041	−	2722.45i	−0.0345451	−	0.195915i
$579$	−3241.50	−	2762.26i	−0.232663	−	0.198266i
$580$	12671.5	−	4612.06i	0.907167	−	0.330182i
$581$	−24338.7	+	8858.56i	−1.73793	+	0.632556i
$582$	−780.765	+	4238.96i	−0.0556078	+	0.301908i
$583$	−82.9105	−	470.209i	−0.00588988	−	0.0334032i
$584$	−2912.62	+	5044.81i	−0.206379	+	0.357458i
$585$	−839.133	−	5222.79i	−0.0593058	−	0.369121i
$586$	4503.36	+	7800.05i	0.317461	+	0.549859i
$587$	11835.8	−	9931.44i	0.832226	−	0.698321i	−0.123575	−	0.992335i	$-0.539436\pi$
$587$	11835.8	−	9931.44i	0.832226	−	0.698321i	0.955801	+	0.294014i	$0.0949914\pi$
$588$	5844.30	−	4828.60i	0.409889	−	0.338654i
$589$	4847.47	−	27491.4i	0.339111	−	1.92320i
$590$	8986.49	+	7540.56i	0.627064	+	0.526169i
$591$	−5560.18	−	9802.12i	−0.386997	−	0.682242i
$592$	6849.78	+	2493.12i	0.475548	+	0.173085i
$593$	11806.2			0.817573			0.408787	−	0.912630i	$-0.365952\pi$
$593$	11806.2			0.817573			0.408787	+	0.912630i	$0.365952\pi$
$594$	1176.52	−	5883.29i	0.0812680	−	0.406388i
$595$	17313.9			1.19294
$596$	17516.9	+	6375.61i	1.20389	+	0.438180i
$597$	−10667.5	+	18156.0i	−0.731311	+	1.24469i
$598$	−481.112	−	403.701i	−0.0328999	−	0.0276063i
$599$	1878.61	−	10654.1i	0.128143	−	0.726736i	−0.851248	−	0.524763i	$-0.824154\pi$
$599$	1878.61	−	10654.1i	0.128143	−	0.726736i	0.979391	−	0.201972i	$-0.0647351\pi$
$600$	1524.13	+	9045.95i	0.103704	+	0.615499i
$601$	−3054.52	+	2563.05i	−0.207315	+	0.173958i	−0.740533	−	0.672020i	$-0.765427\pi$
$601$	−3054.52	+	2563.05i	−0.207315	+	0.173958i	0.533218	+	0.845978i	$0.320983\pi$
$602$	2928.33	+	5072.02i	0.198256	+	0.343389i
$603$	−7881.91	+	2733.60i	−0.532299	+	0.184612i
$604$	−3556.12	+	6159.38i	−0.239564	+	0.414937i
$605$	912.006	+	5172.24i	0.0612865	+	0.347573i
$606$	4329.26	−	1538.50i	0.290205	−	0.103131i
$607$	5912.85	−	2152.10i	0.395379	−	0.143906i	−0.136676	−	0.990616i	$-0.543642\pi$
$607$	5912.85	−	2152.10i	0.395379	−	0.143906i	0.532056	+	0.846709i	$0.321420\pi$
$608$	−21041.0	+	7658.31i	−1.40350	+	0.510831i
$609$	−14583.4	+	5182.55i	−0.970363	+	0.344840i
$610$	−166.631	−	945.013i	−0.0110602	−	0.0627254i
$611$	694.622	−	1203.12i	0.0459925	−	0.0796613i
$612$	−8393.68	+	2911.10i	−0.554403	+	0.192278i
$613$	−3112.72	−	5391.39i	−0.205093	−	0.355231i	0.745070	−	0.666987i	$-0.232416\pi$
$613$	−3112.72	−	5391.39i	−0.205093	−	0.355231i	−0.950162	+	0.311756i	$0.899083\pi$
$614$	2585.52	−	2169.51i	0.169940	−	0.142597i
$615$	−592.461	−	3516.35i	−0.0388460	−	0.230558i
$616$	−2605.99	+	14779.3i	−0.170452	+	0.966680i
$617$	21021.0	+	17638.7i	1.37159	+	1.15090i	0.972208	+	0.234120i	$0.0752210\pi$
$617$	21021.0	+	17638.7i	1.37159	+	1.15090i	0.399386	+	0.916783i	$0.369223\pi$
$618$	4655.10	−	7922.94i	0.303002	−	0.515708i
$619$	−11484.7	−	4180.09i	−0.745733	−	0.271425i	−0.0589242	−	0.998262i	$-0.518767\pi$
$619$	−11484.7	−	4180.09i	−0.745733	−	0.271425i	−0.686809	+	0.726838i	$0.740989\pi$
$620$	−21987.8			−1.42428
$621$	−4984.55	−	4380.37i	−0.322099	−	0.283057i
$622$	−374.128			−0.0241176
$623$	31683.2	+	11531.8i	2.03750	+	0.741589i
$624$	−1267.05	−	2233.69i	−0.0812859	−	0.143300i
$625$	−12990.9	−	10900.7i	−0.831420	−	0.697644i
$626$	−1158.28	+	6568.95i	−0.0739525	+	0.419406i
$627$	22160.4	−	18309.1i	1.41148	−	1.16618i
$628$	5180.74	−	4347.16i	0.329194	−	0.276227i
$629$	−4460.34	−	7725.54i	−0.282743	−	0.489726i
$630$	−1628.07	−	10133.2i	−0.102959	−	0.640818i
$631$	5283.88	−	9151.94i	0.333356	−	0.577390i	−0.649811	−	0.760095i	$-0.725152\pi$
$631$	5283.88	−	9151.94i	0.333356	−	0.577390i	0.983168	+	0.182705i	$0.0584855\pi$
$632$	−371.513	−	2106.96i	−0.0233829	−	0.132611i
$633$	53.2096	−	288.888i	0.00334106	−	0.0181394i
$634$	−8652.27	+	3149.17i	−0.541996	+	0.197271i
$635$	−11319.3	+	4119.89i	−0.707391	+	0.257469i
$636$	318.980	+	271.821i	0.0198874	+	0.0169472i
$637$	−465.679	−	2640.99i	−0.0289652	−	0.164270i
$638$	2705.22	−	4685.58i	0.167869	−	0.290758i
$639$	3624.92	−	6063.41i	0.224412	−	0.375376i
$640$	11332.9	+	19629.1i	0.699954	+	1.21236i
$641$	−13412.3	+	11254.3i	−0.826452	+	0.693475i	−0.954473	−	0.298296i	$-0.903582\pi$
$641$	−13412.3	+	11254.3i	−0.826452	+	0.693475i	0.128022	+	0.991771i	$0.459137\pi$
$642$	−5374.14	−	2002.49i	−0.330374	−	0.123103i
$643$	−2166.26	+	12285.5i	−0.132860	+	0.753487i	0.843466	+	0.537183i	$0.180511\pi$
$643$	−2166.26	+	12285.5i	−0.132860	+	0.753487i	−0.976326	+	0.216304i	$0.930600\pi$
$644$	5890.72	+	4942.90i	0.360446	+	0.302450i
$645$	−19071.6	−	145.202i	−1.16425	−	0.00886407i
$646$	6338.09	+	2306.88i	0.386020	+	0.140500i
$647$	−13857.5			−0.842029			−0.421015	−	0.907054i	$-0.638326\pi$
$647$	−13857.5			−0.842029			−0.421015	+	0.907054i	$0.638326\pi$
$648$	5381.11	+	10012.6i	0.326219	+	0.606993i
$649$	−29703.3			−1.79654
$650$	1412.75	+	514.199i	0.0852502	+	0.0310285i
$651$	25235.4	+	192.131i	1.51928	+	0.0115671i
$652$	15291.6	+	12831.2i	0.918504	+	0.770716i
$653$	1267.79	−	7190.01i	0.0759763	−	0.430883i	−0.922965	−	0.384884i	$-0.874242\pi$
$653$	1267.79	−	7190.01i	0.0759763	−	0.430883i	0.998941	−	0.0459996i	$-0.0146473\pi$
$654$	6890.27	+	2567.43i	0.411974	+	0.153508i
$655$	30388.4	−	25498.9i	1.81278	−	1.52111i
$656$	−865.574	−	1499.22i	−0.0515167	−	0.0892296i
$657$	4909.88	+	8811.34i	0.291557	+	0.523231i
$658$	1347.70	−	2334.28i	0.0798460	−	0.138297i
$659$	−3817.86	−	21652.1i	−0.225679	−	1.27989i	−0.861382	−	0.507957i	$-0.830401\pi$
$659$	−3817.86	−	21652.1i	−0.225679	−	1.27989i	0.635703	−	0.771934i	$-0.280710\pi$
$660$	−17233.2	−	14685.4i	−1.01636	−	0.866101i
$661$	−23240.8	+	8458.96i	−1.36757	+	0.497754i	−0.918386	−	0.395686i	$-0.870507\pi$
$661$	−23240.8	+	8458.96i	−1.36757	+	0.497754i	−0.449183	+	0.893440i	$0.648285\pi$
$662$	−5477.70	+	1993.72i	−0.321596	+	0.117052i
$663$	−569.277	+	3090.74i	−0.0333467	+	0.181048i
$664$	2978.79	+	16893.5i	0.174095	+	0.987344i
$665$	24585.8	−	42583.9i	1.43368	−	2.48321i
$666$	−4102.05	+	3336.92i	−0.238665	+	0.194149i
$667$	−2991.98	−	5182.26i	−0.173688	−	0.300837i
$668$	−6052.68	+	5078.80i	−0.350577	+	0.294169i
$669$	−1479.11	+	1222.06i	−0.0854796	+	0.0706240i
$670$	866.280	−	4912.92i	0.0499512	−	0.283287i
$671$	1861.27	+	1561.79i	0.107084	+	0.0898542i
$672$	−9987.38	−	17606.9i	−0.573321	−	1.01071i
$673$	−5162.27	−	1878.91i	−0.295678	−	0.107618i	0.189922	−	0.981799i	$-0.439176\pi$
$673$	−5162.27	−	1878.91i	−0.295678	−	0.107618i	−0.485600	+	0.874181i	$0.661399\pi$
$674$	−307.953			−0.0175992
$675$	14798.8	+	5772.37i	0.843859	+	0.329153i
$676$	14059.2			0.799908
$677$	−21448.3	−	7806.53i	−1.21761	−	0.443175i	−0.348275	−	0.937392i	$-0.613232\pi$
$677$	−21448.3	−	7806.53i	−1.21761	−	0.443175i	−0.869338	+	0.494217i	$0.835455\pi$
$678$	−2948.82	+	5018.86i	−0.167033	+	0.284290i
$679$	−14301.2	−	12000.1i	−0.808289	−	0.678235i
$680$	1991.24	−	11292.9i	0.112295	−	0.636856i
$681$	1858.48	+	11030.4i	0.104577	+	0.620683i
$682$	−6758.10	+	5670.72i	−0.379444	+	0.318392i
$683$	−8593.28	−	14884.0i	−0.481424	−	0.833851i	0.518349	−	0.855169i	$-0.326547\pi$
$683$	−8593.28	−	14884.0i	−0.481424	−	0.833851i	−0.999773	+	0.0213186i	$0.993214\pi$
$684$	−4759.16	+	24778.2i	−0.266040	+	1.38511i
$685$	−11344.7	+	19649.6i	−0.632787	+	1.09602i
$686$	563.359	+	3194.97i	0.0313544	+	0.177820i
$687$	−19655.4	+	6984.97i	−1.09156	+	0.387909i
$688$	−8700.57	+	3166.75i	−0.482131	+	0.175481i
$689$	139.310	−	50.7047i	0.00770288	−	0.00280362i
$690$	3739.03	−	1328.75i	0.206293	−	0.0733109i
$691$	−4152.63	−	23550.7i	−0.228616	−	1.29654i	−0.855651	−	0.517553i	$-0.826843\pi$
$691$	−4152.63	−	23550.7i	−0.228616	−	1.29654i	0.627035	−	0.778991i	$-0.284268\pi$
$692$	2514.99	−	4356.08i	0.138158	−	0.239297i
$693$	19650.2	+	17005.0i	1.07713	+	0.932130i
$694$	−157.522	−	272.837i	−0.00861595	−	0.0149233i
$695$	17041.2	−	14299.2i	0.930083	−	0.780432i
$696$	1703.07	+	10108.0i	0.0927507	+	0.550491i
$697$	−367.885	+	2086.38i	−0.0199923	+	0.113382i
$698$	−6419.23	−	5386.37i	−0.348097	−	0.292088i
$699$	4638.34	−	7894.42i	0.250984	−	0.427174i
$700$	−17297.7	−	6295.84i	−0.933987	−	0.339943i
$701$	9600.52			0.517270			0.258635	−	0.965975i	$-0.416727\pi$
$701$	9600.52			0.517270			0.258635	+	0.965975i	$0.416727\pi$
$702$	1862.42	+	42.5455i	0.100132	+	0.00228743i
$703$	−25334.8			−1.35920
$704$	−5316.11	−	1934.91i	−0.284600	−	0.103586i
$705$	4330.75	+	7634.73i	0.231355	+	0.407859i
$706$	1562.54	+	1311.13i	0.0832959	+	0.0698936i
$707$	−3455.59	+	19597.6i	−0.183820	+	1.04250i
$708$	20099.1	−	16606.1i	1.06691	−	0.881489i
$709$	6827.53	−	5728.98i	0.361655	−	0.303464i	−0.443795	−	0.896128i	$-0.646368\pi$
$709$	6827.53	−	5728.98i	0.361655	−	0.303464i	0.805450	+	0.592664i	$0.201924\pi$
$710$	2112.20	+	3658.43i	0.111647	+	0.193378i
$711$	−3461.56	−	1319.93i	−0.182586	−	0.0696222i
$712$	11165.3	−	19338.9i	0.587694	−	1.01792i
$713$	1694.33	+	9609.00i	0.0889944	+	0.504713i
$714$	−1104.50	+	5996.62i	−0.0578922	+	0.314311i
$715$	−7526.33	+	2739.36i	−0.393663	+	0.143282i
$716$	6821.76	−	2482.92i	0.356063	−	0.129596i
$717$	−12623.0	−	10756.7i	−0.657480	−	0.560276i
$718$	−553.746	−	3140.45i	−0.0287822	−	0.163232i
$719$	−9627.06	+	16674.6i	−0.499345	+	0.864890i	−1.00000		0.000756651i	$-0.999759\pi$
$719$	−9627.06	+	16674.6i	−0.499345	+	0.864890i	0.500655	+	0.865647i	$0.333092\pi$
$720$	16223.4	+	247.049i	0.839736	+	0.0127875i
$721$	19900.6	+	34468.8i	1.02793	+	1.78042i
$722$	9177.49	−	7700.83i	0.473062	−	0.396946i
$723$	−10965.6	−	4085.98i	−0.564062	−	0.210179i
$724$	1251.14	−	7095.57i	0.0642241	−	0.364233i
$725$	10973.1	+	9207.55i	0.562113	+	0.471669i
$726$	−1849.57	−	14.0817i	−0.0945508	−	0.000719866i
$727$	23401.7	+	8517.51i	1.19384	+	0.434521i	0.861069	−	0.508488i	$-0.169795\pi$
$727$	23401.7	+	8517.51i	1.19384	+	0.434521i	0.332768	+	0.943009i	$0.392017\pi$
$728$	−4659.71			−0.237226
$729$	19662.5	+	898.813i	0.998957	+	0.0456645i
$730$	−6031.88			−0.305822
$731$	10647.7	+	3875.44i	0.538740	+	0.196085i
$732$	−2132.59	−	16.2366i	−0.107682	−	0.000819838i
$733$	−22459.9	−	18846.1i	−1.13175	−	0.949655i	−0.132617	−	0.991167i	$-0.542338\pi$
$733$	−22459.9	−	18846.1i	−1.13175	−	0.949655i	−0.999138	+	0.0415124i	$0.986782\pi$
$734$	223.039	−	1264.92i	0.0112160	−	0.0636090i
$735$	15877.3	+	5916.13i	0.796792	+	0.296898i
$736$	5995.38	−	5030.72i	0.300262	−	0.251950i
$737$	6315.77	+	10939.2i	0.315664	+	0.546746i
$738$	1255.67	+	19.1213i	0.0626313	+	0.000953746i
$739$	−10452.2	+	18103.8i	−0.520287	+	0.901163i	0.479435	+	0.877577i	$0.340842\pi$
$739$	−10452.2	+	18103.8i	−0.520287	+	0.901163i	−0.999722	+	0.0235855i	$0.992492\pi$
$740$	3465.17	+	19652.0i	0.172138	+	0.976244i
$741$	6793.36	+	5789.01i	0.336789	+	0.286997i
$742$	270.287	−	98.3765i	0.0133727	−	0.00486727i
$743$	−14435.9	+	5254.24i	−0.712788	+	0.259434i	−0.672861	−	0.739769i	$-0.734935\pi$
$743$	−14435.9	+	5254.24i	−0.712788	+	0.259434i	−0.0399271	+	0.999203i	$0.512713\pi$
$744$	3027.59	−	16437.5i	0.149189	−	0.809985i
$745$	7234.74	+	41030.3i	0.355786	+	2.01776i
$746$	−40.2030	+	69.6336i	−0.00197310	+	0.00341752i
$747$	27754.7	+	10583.2i	1.35943	+	0.518365i
$748$	6725.85	+	11649.5i	0.328772	+	0.569450i
$749$	19028.7	−	15966.9i	0.928293	−	0.778931i
$750$	761.717	−	629.337i	0.0370853	−	0.0306402i
$751$	4371.61	−	24792.6i	0.212413	−	1.20465i	−0.672927	−	0.739709i	$-0.734963\pi$
$751$	4371.61	−	24792.6i	0.212413	−	1.20465i	0.885340	−	0.464945i	$-0.153926\pi$
$752$	3264.28	+	2739.06i	0.158293	+	0.132823i
$753$	14438.2	+	25453.4i	0.698750	+	1.23184i
$754$	1578.61	+	574.568i	0.0762462	+	0.0277513i
$755$	−15896.1			−0.766247
$756$	−22803.5	−	520.926i	−1.09703	−	0.0250607i
$757$	8319.25			0.399430			0.199715	−	0.979854i	$-0.435998\pi$
$757$	8319.25			0.399430			0.199715	+	0.979854i	$0.435998\pi$
$758$	−4461.51	−	1623.86i	−0.213785	−	0.0778115i
$759$	−5089.78	+	8662.77i	−0.243409	+	0.414280i
$760$	−24947.5	−	20933.4i	−1.19071	−	0.999125i
$761$	3537.36	−	20061.4i	0.168501	−	0.955616i	−0.776880	−	0.629648i	$-0.783199\pi$
$761$	3537.36	−	20061.4i	0.168501	−	0.955616i	0.945381	−	0.325967i	$-0.105690\pi$
$762$	−704.819	−	4183.22i	−0.0335078	−	0.198874i
$763$	−24397.0	+	20471.5i	−1.15757	+	0.971320i
$764$	−1258.82	−	2180.34i	−0.0596107	−	0.103249i
$765$	−15014.7	−	12993.5i	−0.709620	−	0.614095i
$766$	4767.93	−	8258.29i	0.224898	−	0.389536i
$767$	−1601.52	−	9082.66i	−0.0753943	−	0.427582i
$768$	−2101.03	+	746.647i	−0.0987167	+	0.0350811i
$769$	23981.8	−	8728.66i	1.12458	−	0.409315i	0.288261	−	0.957552i	$-0.406923\pi$
$769$	23981.8	−	8728.66i	1.12458	−	0.409315i	0.836323	+	0.548236i	$0.184701\pi$
$770$	−14602.5	+	5314.87i	−0.683425	+	0.248746i
$771$	−32867.1	+	11680.1i	−1.53525	+	0.545586i
$772$	−982.844	−	5573.99i	−0.0458204	−	0.259860i
$773$	16102.9	−	27891.1i	0.749264	−	1.29776i	−0.198911	−	0.980018i	$-0.563741\pi$
$773$	16102.9	−	27891.1i	0.749264	−	1.29776i	0.948176	−	0.317747i	$-0.102926\pi$
$774$	1266.92	−	6596.10i	0.0588352	−	0.306320i
$775$	−11678.4	−	20227.6i	−0.541292	−	0.937546i
$776$	−9471.72	+	7947.72i	−0.438164	+	0.367663i
$777$	−3805.26	−	22584.9i	−0.175693	−	1.04276i
$778$	43.7210	−	247.954i	0.00201475	−	0.0114262i
$779$	4609.09	+	3867.48i	0.211987	+	0.177878i
$780$	3561.32	−	6061.34i	0.163482	−	0.278244i
$781$	−10051.2	−	3658.34i	−0.460513	−	0.167613i
$782$	−2357.52			−0.107806
$783$	16536.2	+	6450.06i	0.754732	+	0.294389i
$784$	8225.67			0.374711
$785$	14203.9	+	5169.78i	0.645805	+	0.235054i
$786$	6892.89	+	12151.6i	0.312800	+	0.551440i
$787$	27349.4	+	22948.9i	1.23876	+	1.03944i	0.997620	+	0.0689492i	$0.0219646\pi$
$787$	27349.4	+	22948.9i	1.23876	+	1.03944i	0.241137	+	0.970491i	$0.422480\pi$
$788$	2600.72	−	14749.4i	0.117572	−	0.666785i
$789$	−22091.0	+	18251.8i	−0.996783	+	0.823550i
$790$	1697.06	−	1424.00i	0.0764287	−	0.0641313i
$791$	−12606.2	−	21834.6i	−0.566656	−	0.981477i
$792$	13351.3	−	10861.0i	0.599013	−	0.487283i
$793$	−377.209	+	653.345i	−0.0168916	+	0.0292572i
$794$	−1907.23	−	10816.4i	−0.0852455	−	0.483451i
$795$	−169.670	+	921.178i	−0.00756927	+	0.0410954i
$796$	−26298.4	+	9571.83i	−1.17101	+	0.426212i
$797$	−13323.9	+	4849.50i	−0.592166	+	0.215531i	−0.620682	−	0.784063i	$-0.713144\pi$
$797$	−13323.9	+	4849.50i	−0.592166	+	0.215531i	0.0285161	+	0.999593i	$0.490922\pi$
$798$	13180.4	+	11231.8i	0.584688	+	0.498246i
$799$	−905.548	−	5135.62i	−0.0400951	−	0.227391i
$800$	−9367.43	+	16224.9i	−0.413986	+	0.717045i
$801$	−18821.7	−	33777.7i	−0.830252	−	1.48998i
$802$	8118.13	+	14061.0i	0.357433	+	0.619092i
$803$	11699.7	−	9817.21i	0.514164	−	0.431435i
$804$	−10389.4	−	3871.26i	−0.455729	−	0.169812i
$805$	−2984.47	+	16925.8i	−0.130669	+	0.741062i
$806$	−2098.37	−	1760.74i	−0.0917020	−	0.0769471i
$807$	−4224.54	−	32.1637i	−0.184276	−	0.00140299i
$808$	12385.0	+	4507.77i	0.539236	+	0.196266i
$809$	−8931.80			−0.388165			−0.194082	−	0.980985i	$-0.562173\pi$
$809$	−8931.80			−0.388165			−0.194082	+	0.980985i	$0.562173\pi$
$810$	−6192.74	+	10009.4i	−0.268631	+	0.434189i
$811$	8984.05			0.388992			0.194496	−	0.980903i	$-0.437693\pi$
$811$	8984.05			0.388992			0.194496	+	0.980903i	$0.437693\pi$
$812$	−19328.5	−	7034.99i	−0.835341	−	0.304039i
$813$	−30156.3	−	229.596i	−1.30089	−	0.00990440i
$814$	6133.35	+	5146.49i	0.264095	+	0.221602i
$815$	−7747.32	+	43937.2i	−0.332977	+	1.88841i
$816$	−9032.97	−	3365.83i	−0.387521	−	0.144397i
$817$	24651.5	−	20685.0i	1.05563	−	0.885775i
$818$	−2980.41	−	5162.22i	−0.127393	−	0.220651i
$819$	−4140.29	+	6925.49i	−0.176647	+	0.295478i
$820$	2369.56	−	4104.20i	0.100913	−	0.174786i
$821$	3734.89	+	21181.6i	0.158768	+	0.900418i	0.955260	+	0.295768i	$0.0955756\pi$
$821$	3734.89	+	21181.6i	0.158768	+	0.900418i	−0.796492	+	0.604649i	$0.793313\pi$
$822$	−6081.86	−	5182.70i	−0.258065	−	0.219912i
$823$	19406.3	−	7063.32i	0.821945	−	0.299164i	0.103397	−	0.994640i	$-0.467029\pi$
$823$	19406.3	−	7063.32i	0.821945	−	0.299164i	0.718549	+	0.695477i	$0.244807\pi$
$824$	24770.7	−	9015.80i	1.04724	−	0.381166i
$825$	4356.68	−	23653.5i	0.183855	−	0.998192i
$826$	−3107.24	−	17622.0i	−0.130890	−	0.742311i
$827$	−16373.8	+	28360.2i	−0.688479	+	1.19248i	0.283851	+	0.958868i	$0.408388\pi$
$827$	−16373.8	+	28360.2i	−0.688479	+	1.19248i	−0.972330	+	0.233612i	$0.924945\pi$
$828$	−1398.98	−	8707.31i	−0.0587174	−	0.365459i
$829$	−12512.4	−	21672.1i	−0.524214	−	0.907965i	−0.999603	−	0.0281890i	$-0.991026\pi$
$829$	−12512.4	−	21672.1i	−0.524214	−	0.907965i	0.475389	−	0.879776i	$-0.342307\pi$
$830$	−13607.0	+	11417.6i	−0.569042	+	0.477483i
$831$	12620.6	−	10427.2i	0.526840	−	0.435279i
$832$	305.025	−	1729.88i	0.0127101	−	0.0720828i
$833$	−7711.39	−	6470.62i	−0.320749	−	0.269140i
$834$	3865.38	+	6814.33i	0.160488	+	0.282927i
$835$	−16594.4	−	6039.88i	−0.687753	−	0.250322i
$836$	38202.9			1.58047
$837$	−21740.1	−	19105.0i	−0.897788	−	0.788966i
$838$	9952.66			0.410273
$839$	9961.74	+	3625.78i	0.409913	+	0.149196i	0.538742	−	0.842471i	$-0.318900\pi$
$839$	9961.74	+	3625.78i	0.409913	+	0.149196i	−0.128829	+	0.991667i	$0.541122\pi$
$840$	14914.1	−	25383.8i	0.612603	−	1.04265i
$841$	−6421.65	−	5388.41i	−0.263301	−	0.220936i
$842$	−2077.80	+	11783.8i	−0.0850426	+	0.482300i
$843$	−5608.88	−	33289.7i	−0.229158	−	1.36009i
$844$	299.057	−	250.939i	0.0121967	−	0.0102342i
$845$	15711.3	+	27212.8i	0.639628	+	1.10787i
$846$	−2920.53	+	1012.90i	−0.118688	+	0.0411633i
$847$	4005.59	−	6937.88i	0.162495	−	0.281450i
$848$	78.9626	+	447.819i	0.00319763	+	0.0181346i
$849$	26258.9	−	9331.67i	1.06149	−	0.377223i
$850$	5303.08	−	1930.16i	0.213993	−	0.0778871i
$851$	8321.19	−	3028.67i	0.335190	−	0.121999i
$852$	8846.55	−	3143.82i	0.355725	−	0.126415i
$853$	226.264	+	1283.21i	0.00908223	+	0.0515079i	0.989012	−	0.147835i	$-0.0472304\pi$
$853$	226.264	+	1283.21i	0.00908223	+	0.0515079i	−0.979930	+	0.199343i	$0.936119\pi$
$854$	−731.855	+	1267.61i	−0.0293250	+	0.0507924i
$855$	−53278.8	+	18478.2i	−2.13111	+	0.739111i
$856$	−8225.87	−	14247.6i	−0.328451	−	0.568894i
$857$	−26073.7	+	21878.4i	−1.03928	+	0.872057i	−0.991926	−	0.126821i	$-0.959523\pi$
$857$	−26073.7	+	21878.4i	−1.03928	+	0.872057i	−0.0473515	+	0.998878i	$0.515078\pi$
$858$	−468.642	−	2781.47i	−0.0186471	−	0.110673i
$859$	−8389.96	+	47581.8i	−0.333250	+	1.88995i	0.110620	+	0.993863i	$0.464716\pi$
$859$	−8389.96	+	47581.8i	−0.333250	+	1.88995i	−0.443870	+	0.896091i	$0.646395\pi$
$860$	−19416.9	−	16292.7i	−0.769896	−	0.646019i
$861$	−2755.41	+	4689.69i	−0.109064	+	0.185626i
$862$	−6738.67	−	2452.68i	−0.266265	−	0.0969124i
$863$	12693.0			0.500667			0.250334	−	0.968160i	$-0.419460\pi$
$863$	12693.0			0.500667			0.250334	+	0.968160i	$0.419460\pi$
$864$	−4552.27	+	22764.0i	−0.179249	+	0.896350i
$865$	11242.1			0.441900
$866$	−4211.65	−	1532.91i	−0.165263	−	0.0601507i
$867$	−6775.13	−	11944.0i	−0.265393	−	0.467864i
$868$	25692.4	+	21558.5i	1.00467	+	0.843020i
$869$	−974.050	+	5524.11i	−0.0380235	+	0.215642i
$870$	−8182.54	+	6760.48i	−0.318867	+	0.263450i
$871$	−3004.46	+	2521.05i	−0.116880	+	0.0980739i
$872$	10546.5	+	18267.1i	0.409576	+	0.709407i
$873$	3396.37	+	21139.1i	0.131672	+	0.819531i
$874$	−3347.68	+	5798.35i	−0.129562	+	0.224408i
$875$	743.139	+	4214.55i	0.0287117	+	0.162832i
$876$	−2428.30	+	13183.9i	−0.0936585	+	0.508494i
$877$	40269.1	−	14656.8i	1.55050	−	0.564337i	0.581968	−	0.813212i	$-0.302283\pi$
$877$	40269.1	−	14656.8i	1.55050	−	0.564337i	0.968536	+	0.248874i	$0.0800606\pi$
$878$	13546.8	−	4930.64i	0.520710	−	0.189523i
$879$	34052.0	+	29017.6i	1.30665	+	1.11347i
$880$	−4266.02	−	24193.8i	−0.163418	−	0.926787i
$881$	3622.67	−	6274.64i	0.138537	−	0.239952i	−0.788406	−	0.615155i	$-0.789093\pi$
$881$	3622.67	−	6274.64i	0.138537	−	0.239952i	0.926943	+	0.375202i	$0.122427\pi$
$882$	−3061.89	+	5121.63i	−0.116892	+	0.195526i
$883$	−7736.23	−	13399.5i	−0.294841	−	0.510680i	0.680107	−	0.733113i	$-0.261933\pi$
$883$	−7736.23	−	13399.5i	−0.294841	−	0.510680i	−0.974948	+	0.222433i	$0.928600\pi$
$884$	−3199.55	+	2684.74i	−0.121733	+	0.102147i
$885$	54603.6	+	20346.2i	2.07399	+	0.772802i
$886$	−429.457	+	2435.57i	−0.0162843	+	0.0923529i
$887$	13150.9	+	11034.9i	0.497816	+	0.417717i	0.856818	−	0.515620i	$-0.172438\pi$
$887$	13150.9	+	11034.9i	0.497816	+	0.417717i	−0.359001	+	0.933337i	$0.616883\pi$
$888$	−15168.4	−	115.486i	−0.573221	−	0.00436424i
$889$	17265.9	+	6284.26i	0.651382	+	0.237084i
$890$	23122.8			0.870874
$891$	−4279.08	−	29493.7i	−0.160892	−	1.10895i
$892$	−2549.89			−0.0957138
$893$	−13917.0	−	5065.38i	−0.521518	−	0.189817i
$894$	−14672.2	−	111.707i	−0.548895	−	0.00417903i
$895$	12429.3	+	10429.4i	0.464208	+	0.389517i
$896$	6003.56	−	34047.9i	0.223845	−	1.26949i
$897$	−2923.32	−	1089.28i	−0.108815	−	0.0405462i
$898$	1550.74	−	1301.22i	0.0576267	−	0.0483546i
$899$	−13049.5	−	22602.4i	−0.484122	−	0.838524i
$900$	10275.8	+	18441.1i	0.380586	+	0.683005i
$901$	278.246	−	481.936i	0.0102883	−	0.0178198i
$902$	−330.185	−	1872.57i	−0.0121884	−	0.0691239i
$903$	22142.4	+	18868.8i	0.816007	+	0.695366i
$904$	−15691.2	+	5711.15i	−0.577304	+	0.210122i
$905$	15132.3	−	5507.70i	0.555816	−	0.202301i
$906$	1014.05	−	5505.54i	0.0371851	−	0.201887i
$907$	8410.06	+	47695.8i	0.307885	+	1.74610i	0.609605	+	0.792705i	$0.291328\pi$
$907$	8410.06	+	47695.8i	0.307885	+	1.74610i	−0.301721	+	0.953396i	$0.597561\pi$
$908$	−7433.03	+	12874.4i	−0.271667	+	0.470541i
$909$	17704.1	−	14401.9i	0.645994	−	0.525501i
$910$	−2412.50	−	4178.58i	−0.0878832	−	0.152218i
$911$	−11165.9	+	9369.33i	−0.406086	+	0.340746i	−0.822840	−	0.568273i	$-0.807612\pi$
$911$	−11165.9	+	9369.33i	−0.406086	+	0.340746i	0.416755	+	0.909019i	$0.363167\pi$
$912$	−21105.2	+	17437.3i	−0.766296	+	0.633120i
$913$	7809.91	−	44292.2i	0.283100	−	1.60554i
$914$	4073.65	+	3418.20i	0.147423	+	0.123702i
$915$	−2351.78	−	4145.97i	−0.0849697	−	0.149794i
$916$	−26050.7	−	9481.67i	−0.939671	−	0.342012i
$917$	−60509.3			−2.17906
$918$	5458.10	−	4371.41i	0.196235	−	0.157166i
$919$	9736.26			0.349477			0.174739	−	0.984615i	$-0.444092\pi$
$919$	9736.26			0.349477			0.174739	+	0.984615i	$0.444092\pi$
$920$	10696.5	+	3893.20i	0.383318	+	0.139516i
$921$	8492.96	−	14455.0i	0.303857	−	0.517163i
$922$	6231.62	+	5228.95i	0.222589	+	0.186775i
$923$	576.713	−	3270.70i	0.0205664	−	0.116638i
$924$	5738.04	+	34056.2i	0.204294	+	1.21252i
$925$	−16238.3	+	13625.6i	−0.577203	+	0.484331i
$926$	−8300.18	−	14376.3i	−0.294558	−	0.510190i
$927$	8609.81	−	44826.2i	0.305052	−	1.58823i
$928$	−10467.2	+	18129.7i	−0.370262	+	0.641312i
$929$	−5747.46	−	32595.5i	−0.202980	−	1.15116i	−0.900587	−	0.434675i	$-0.856863\pi$
$929$	−5747.46	−	32595.5i	−0.202980	−	1.15116i	0.697608	−	0.716480i	$-0.254248\pi$
$930$	16307.8	−	5795.32i	0.575003	−	0.204340i
$931$	−26864.8	+	9777.99i	−0.945713	+	0.344211i
$932$	11434.8	−	4161.92i	0.401887	−	0.146275i
$933$	−1751.11	+	622.294i	−0.0614455	+	0.0218360i
$934$	1249.75	+	7087.68i	0.0437827	+	0.248304i
$935$	−15032.5	+	26037.0i	−0.525791	+	0.910696i
$936$	4040.93	+	3496.96i	0.141113	+	0.122117i
$937$	−25368.3	−	43939.2i	−0.884468	−	1.53194i	−0.846322	−	0.532671i	$-0.821188\pi$
$937$	−25368.3	−	43939.2i	−0.884468	−	1.53194i	−0.0381458	−	0.999272i	$-0.512145\pi$
$938$	−5829.22	+	4891.30i	−0.202911	+	0.170263i
$939$	5504.91	+	32672.5i	0.191316	+	1.13549i
$940$	−2025.67	+	11488.1i	−0.0702872	+	0.398618i
$941$	−31154.7	−	26141.9i	−1.07929	−	0.905634i	−0.0834307	−	0.996514i	$-0.526588\pi$
$941$	−31154.7	−	26141.9i	−1.07929	−	0.905634i	−0.995862	+	0.0908796i	$0.971032\pi$
$942$	−2696.64	+	4589.66i	−0.0932709	+	0.158746i
$943$	−1976.19	−	719.275i	−0.0682435	−	0.0248386i
$944$	28288.9			0.975345
$945$	−24474.9	−	44720.3i	−0.842506	−	1.53942i
$946$	−10169.9			−0.349525
$947$	−14836.1	−	5399.91i	−0.509091	−	0.185294i	0.0746875	−	0.997207i	$-0.476204\pi$
$947$	−14836.1	−	5399.91i	−0.509091	−	0.185294i	−0.583778	+	0.811913i	$0.698426\pi$
$948$	−2429.24	−	4282.53i	−0.0832256	−	0.146719i
$949$	3632.72	+	3048.21i	0.124260	+	0.104267i
$950$	2783.12	−	15783.9i	0.0950487	−	0.539048i
$951$	−35258.9	+	29131.2i	−1.20226	+	0.993315i
$952$	−13399.1	+	11243.2i	−0.456163	+	0.382766i
$953$	15908.4	+	27554.1i	0.540737	+	0.936585i	0.998862	+	0.0476966i	$0.0151881\pi$
$953$	15908.4	+	27554.1i	0.540737	+	0.936585i	−0.458124	+	0.888888i	$0.651479\pi$
$954$	−308.223	−	117.529i	−0.0104603	−	0.00398862i
$955$	2813.50	−	4873.12i	0.0953326	−	0.165121i
$956$	−3827.37	−	21706.1i	−0.129483	−	0.734336i
$957$	4868.17	−	26430.5i	0.164436	−	0.892765i
$958$	1210.08	−	440.433i	0.0408099	−	0.0148536i
$959$	32522.0	−	11837.0i	1.09509	−	0.398580i
$960$	8447.24	+	7198.38i	0.283993	+	0.242007i
$961$	2216.65	+	12571.2i	0.0744067	+	0.421981i
$962$	−1243.00	+	2152.94i	−0.0416589	+	0.0721553i
$963$	−28484.4	−	433.759i	−0.953165	−	0.0145147i
$964$	−7776.12	−	13468.6i	−0.259805	−	0.449995i
$965$	9690.61	−	8131.39i	0.323266	−	0.271252i
$966$	−5671.79	−	2113.40i	−0.188910	−	0.0703909i
$967$	8384.70	−	47552.0i	0.278835	−	1.58135i	−0.447673	−	0.894197i	$-0.647747\pi$
$967$	8384.70	−	47552.0i	0.278835	−	1.58135i	0.726509	−	0.687157i	$-0.241142\pi$
$968$	−4064.50	−	3410.52i	−0.134957	−	0.113242i
$969$	33502.5	+	255.072i	1.11069	+	0.00845625i
$970$	−12030.9	−	4378.90i	−0.398237	−	0.144946i
$971$	42267.3			1.39693			0.698467	−	0.715642i	$-0.253866\pi$
$971$	42267.3			1.39693			0.698467	+	0.715642i	$0.253866\pi$
$972$	19384.4	+	17565.0i	0.639665	+	0.579628i
$973$	−33932.3			−1.11801
$974$	5246.82	+	1909.69i	0.172607	+	0.0628237i
$975$	7467.65	+	56.8552i	0.245288	+	0.00186751i
$976$	−1772.64	−	1487.42i	−0.0581361	−	0.0487820i
$977$	1433.16	−	8127.85i	0.0469302	−	0.266154i	−0.952310	−	0.305133i	$-0.901299\pi$
$977$	1433.16	−	8127.85i	0.0469302	−	0.266154i	0.999240	+	0.0389782i	$0.0124103\pi$
$978$	−14723.3	−	5486.13i	−0.481389	−	0.179373i
$979$	−44850.0	+	37633.6i	−1.46416	+	1.22858i
$980$	11259.1	+	19501.4i	0.367000	+	0.635662i
$981$	36520.4	+	556.131i	1.18859	+	0.0180998i
$982$	−3108.03	+	5383.27i	−0.100999	+	0.174936i
$983$	−3785.72	−	21469.9i	−0.122834	−	0.696625i	−0.982571	−	0.185888i	$-0.940484\pi$
$983$	−3785.72	−	21469.9i	−0.122834	−	0.696625i	0.859737	−	0.510737i	$-0.170627\pi$
$984$	2741.92	+	2336.55i	0.0888306	+	0.0756976i
$985$	31455.2	−	11448.8i	1.01751	−	0.370343i
$986$	5925.68	−	2156.77i	0.191391	−	0.0696608i
$987$	2425.24	−	13167.2i	0.0782131	−	0.424638i
$988$	2059.80	+	11681.7i	0.0663267	+	0.376158i
$989$	−5623.94	+	9740.96i	−0.180820	+	0.313189i
$990$	16652.0	+	6349.60i	0.534581	+	0.203842i
$991$	24238.0	+	41981.4i	0.776938	+	1.34570i	0.933699	+	0.358059i	$0.116561\pi$
$991$	24238.0	+	41981.4i	0.776938	+	1.34570i	−0.156761	+	0.987637i	$0.550105\pi$
$992$	26148.9	−	21941.5i	0.836922	−	0.702261i
$993$	−22322.2	+	18442.8i	−0.713366	+	0.589389i
$994$	1118.93	−	6345.77i	0.0357046	−	0.202491i
$995$	−47915.9	−	40206.2i	−1.52667	−	1.28103i
$996$	19477.6	+	34337.2i	0.619649	+	1.09239i
$997$	3758.13	+	1367.85i	0.119379	+	0.0434505i	0.401019	−	0.916070i	$-0.368656\pi$
$997$	3758.13	+	1367.85i	0.119379	+	0.0434505i	−0.281640	+	0.959520i	$0.590878\pi$
$998$	−12555.9			−0.398245
$999$	−13649.3	+	22441.5i	−0.432276	+	0.710727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.4.4	✓	48
3.2	odd	2		81.4.e.a.64.5		48
9.2	odd	6		243.4.e.b.28.4		48
9.4	even	3		243.4.e.d.109.5		48
9.5	odd	6		243.4.e.a.109.4		48
9.7	even	3		243.4.e.c.28.5		48
27.2	odd	18		243.4.e.a.136.4		48
27.7	even	9	inner	27.4.e.a.7.4	yes	48
27.11	odd	18		243.4.e.b.217.4		48
27.13	even	9		729.4.a.d.1.15		24
27.14	odd	18		729.4.a.c.1.10		24
27.16	even	9		243.4.e.c.217.5		48
27.20	odd	18		81.4.e.a.19.5		48
27.25	even	9		243.4.e.d.136.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.4.4	✓	48	1.1	even	1	trivial
27.4.e.a.7.4	yes	48	27.7	even	9	inner
81.4.e.a.19.5		48	27.20	odd	18
81.4.e.a.64.5		48	3.2	odd	2
243.4.e.a.109.4		48	9.5	odd	6
243.4.e.a.136.4		48	27.2	odd	18
243.4.e.b.28.4		48	9.2	odd	6
243.4.e.b.217.4		48	27.11	odd	18
243.4.e.c.28.5		48	9.7	even	3
243.4.e.c.217.5		48	27.16	even	9
243.4.e.d.109.5		48	9.4	even	3
243.4.e.d.136.5		48	27.25	even	9
729.4.a.c.1.10		24	27.14	odd	18
729.4.a.d.1.15		24	27.13	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)

\(f(q)\)	\(=\)	\(q+(-0.982993 - 0.357780i) q^{2} +(-5.19600 - 0.0395600i) q^{3} +(-5.29009 - 4.43891i) q^{4} +(2.68017 - 15.2000i) q^{5} +(5.09348 + 1.89791i) q^{6} +(-18.0349 + 15.1331i) q^{7} +(7.79628 + 13.5036i) q^{8} +(26.9969 + 0.411107i) q^{9} +O(q^{10})\)	\(q+(-0.982993 - 0.357780i) q^{2} +(-5.19600 - 0.0395600i) q^{3} +(-5.29009 - 4.43891i) q^{4} +(2.68017 - 15.2000i) q^{5} +(5.09348 + 1.89791i) q^{6} +(-18.0349 + 15.1331i) q^{7} +(7.79628 + 13.5036i) q^{8} +(26.9969 + 0.411107i) q^{9} +(-8.07284 + 13.9826i) q^{10} +(-7.09896 - 40.2602i) q^{11} +(27.3117 + 23.2739i) q^{12} +(11.9280 - 4.34143i) q^{13} +(23.1425 - 8.42319i) q^{14} +(-14.5275 + 78.8731i) q^{15} +(6.76093 + 38.3432i) q^{16} +(23.8240 - 41.2643i) q^{17} +(-26.3907 - 10.0631i) q^{18} +(-67.6602 - 117.191i) q^{19} +(-81.6496 + 68.5122i) q^{20} +(94.3081 - 77.9181i) q^{21} +(-7.42608 + 42.1154i) q^{22} +(36.2326 + 30.4028i) q^{23} +(-39.9753 - 70.4729i) q^{24} +(-106.394 - 38.7244i) q^{25} -13.2784 q^{26} +(-140.260 - 3.20411i) q^{27} +162.581 q^{28} +(-118.886 - 43.2708i) q^{29} +(42.4996 - 72.3341i) q^{30} +(158.028 + 132.602i) q^{31} +(28.7334 - 162.955i) q^{32} +(35.2935 + 209.473i) q^{33} +(-38.1824 + 32.0388i) q^{34} +(181.686 + 314.689i) q^{35} +(-140.991 - 122.011i) q^{36} +(93.6104 - 162.138i) q^{37} +(24.5809 + 139.405i) q^{38} +(-62.1496 + 22.0862i) q^{39} +(226.149 - 82.3116i) q^{40} +(-41.7814 + 15.2072i) q^{41} +(-120.582 + 42.8514i) q^{42} +(41.2948 + 234.195i) q^{43} +(-141.157 + 244.492i) q^{44} +(78.6049 - 409.250i) q^{45} +(-24.7389 - 42.8490i) q^{46} +(83.8400 - 70.3501i) q^{47} +(-33.6130 - 199.499i) q^{48} +(36.6864 - 208.059i) q^{49} +(90.7302 + 76.1317i) q^{50} +(-125.422 + 213.467i) q^{51} +(-82.3713 - 29.9807i) q^{52} +11.6792 q^{53} +(136.728 + 53.3317i) q^{54} -630.981 q^{55} +(-344.956 - 125.554i) q^{56} +(346.927 + 611.601i) q^{57} +(101.382 + 85.0698i) q^{58} +(126.168 - 715.536i) q^{59} +(426.962 - 352.759i) q^{60} +(-45.5286 + 38.2030i) q^{61} +(-107.899 - 186.886i) q^{62} +(-493.108 + 401.132i) q^{63} +(69.1916 - 119.843i) q^{64} +(-34.0207 - 192.941i) q^{65} +(40.2520 - 218.538i) q^{66} +(-290.347 + 105.678i) q^{67} +(-309.199 + 112.539i) q^{68} +(-187.062 - 159.406i) q^{69} +(-66.0065 - 374.341i) q^{70} +(130.821 - 226.589i) q^{71} +(204.924 + 367.759i) q^{72} +(186.795 + 323.539i) q^{73} +(-150.028 + 125.889i) q^{74} +(551.294 + 205.421i) q^{75} +(-162.272 + 920.288i) q^{76} +(737.290 + 618.660i) q^{77} +(68.9947 + 0.525293i) q^{78} +(-128.935 - 46.9287i) q^{79} +600.936 q^{80} +(728.662 + 22.1972i) q^{81} +46.5117 q^{82} +(1033.80 + 376.273i) q^{83} +(-844.769 - 6.43168i) q^{84} +(-563.365 - 472.719i) q^{85} +(43.1977 - 244.986i) q^{86} +(616.018 + 229.538i) q^{87} +(488.311 - 409.741i) q^{88} +(-716.067 - 1240.26i) q^{89} +(-223.690 + 374.167i) q^{90} +(-149.421 + 258.805i) q^{91} +(-56.7185 - 321.667i) q^{92} +(-815.870 - 695.250i) q^{93} +(-107.584 + 39.1574i) q^{94} +(-1962.64 + 714.343i) q^{95} +(-155.746 + 845.580i) q^{96} +(137.698 + 780.924i) q^{97} +(-110.502 + 191.395i) q^{98} +(-175.098 - 1089.82i) 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

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