LMFDB - Embedded newform 27.4.e.a.7.4

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			7.4
Character	$\chi$	$=$	27.7
Dual form			27.4.e.a.4.4

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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	−0.509892	−	0.860239i	$-0.670315\pi$
$2$	−0.982993	+	0.357780i	−0.347541	+	0.126494i	0.162351	+	0.986733i	$0.448092\pi$
$3$	−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	0.832439	+	0.554117i	$0.186944\pi$
$5$	2.68017	+	15.2000i	0.239721	+	1.35953i	−0.592717	+	0.805410i	$0.701945\pi$
$6$	5.09348	−	1.89791i	0.346568	−	0.129137i
$7$	−18.0349	−	15.1331i	−0.973794	−	0.817110i	0.00934778	−	0.999956i	$-0.497024\pi$
$7$	−18.0349	−	15.1331i	−0.973794	−	0.817110i	−0.983142	+	0.182846i	$0.941469\pi$
$8$	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	0.718427	+	0.695602i	$0.244862\pi$
$11$	−7.09896	+	40.2602i	−0.194583	+	1.10354i	−0.913011	+	0.407935i	$0.866249\pi$
$12$	27.3117	−	23.2739i	0.657017	−	0.559882i
$13$	11.9280	+	4.34143i	0.254479	+	0.0926228i	0.466110	−	0.884727i	$-0.345655\pi$
$13$	11.9280	+	4.34143i	0.254479	+	0.0926228i	−0.211631	+	0.977350i	$0.567877\pi$
$14$	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	0.984412	−	0.175877i	$-0.0562762\pi$
$17$	23.8240	+	41.2643i	0.339892	+	0.588710i	−0.644520	+	0.764587i	$0.722943\pi$
$18$	−26.3907	+	10.0631i	−0.345574	+	0.131771i
$19$	−67.6602	+	117.191i	−0.816964	+	1.41502i	0.0909443	+	0.995856i	$0.471011\pi$
$19$	−67.6602	+	117.191i	−0.816964	+	1.41502i	−0.907909	+	0.419168i	$0.862322\pi$
$20$	−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	−0.463601	−	0.886044i	$-0.653443\pi$
$23$	36.2326	−	30.4028i	0.328479	−	0.275627i	0.792080	+	0.610418i	$0.208998\pi$
$24$	−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	−0.693335	−	0.720615i	$-0.743859\pi$
$29$	−118.886	+	43.2708i	−0.761258	+	0.277075i	−0.0679230	+	0.997691i	$0.521637\pi$
$30$	42.4996	+	72.3341i	0.258645	+	0.440211i
$31$	158.028	−	132.602i	0.915572	−	0.768256i	−0.0575985	−	0.998340i	$-0.518344\pi$
$31$	158.028	−	132.602i	0.915572	−	0.768256i	0.973171	+	0.230083i	$0.0738999\pi$
$32$	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	0.995526	−	0.0944909i	$-0.0301223\pi$
$37$	93.6104	+	162.138i	0.415931	+	0.720414i	−0.579594	+	0.814905i	$0.696789\pi$
$38$	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	0.261216	−	0.965280i	$-0.415876\pi$
$41$	−41.7814	−	15.2072i	−0.159150	−	0.0579260i	−0.420367	+	0.907354i	$0.638099\pi$
$42$	−120.582	−	42.8514i	−0.443004	−	0.157431i
$43$	41.2948	−	234.195i	0.146451	−	0.830566i	−0.819739	−	0.572737i	$-0.805882\pi$
$43$	41.2948	−	234.195i	0.146451	−	0.830566i	0.966191	−	0.257829i	$-0.0830072\pi$
$44$	−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	0.763549	−	0.645750i	$-0.223455\pi$
$47$	83.8400	+	70.3501i	0.260198	+	0.218332i	−0.503351	+	0.864082i	$0.667900\pi$
$48$	−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	0.727944	+	0.685636i	$0.240476\pi$
$59$	126.168	+	715.536i	0.278402	+	1.57890i	−0.449542	+	0.893259i	$0.648413\pi$
$60$	426.962	+	352.759i	0.918676	+	0.759017i
$61$	−45.5286	−	38.2030i	−0.0955629	−	0.0801868i	0.593755	−	0.804646i	$-0.297645\pi$
$61$	−45.5286	−	38.2030i	−0.0955629	−	0.0801868i	−0.689317	+	0.724459i	$0.742089\pi$
$62$	−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	0.0634560	−	0.997985i	$-0.479788\pi$
$67$	−290.347	−	105.678i	−0.529426	−	0.192695i	−0.592882	+	0.805289i	$0.702010\pi$
$68$	−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	0.954402	−	0.298525i	$-0.0964946\pi$
$71$	130.821	+	226.589i	0.218671	+	0.378749i	−0.735731	+	0.677274i	$0.763161\pi$
$72$	204.924	−	367.759i	0.335424	−	0.601956i
$73$	186.795	−	323.539i	0.299490	−	0.518731i	−0.676530	−	0.736415i	$-0.736517\pi$
$73$	186.795	−	323.539i	0.299490	−	0.518731i	0.976019	+	0.217684i	$0.0698502\pi$
$74$	−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	−0.432196	−	0.901780i	$-0.642261\pi$
$79$	−128.935	+	46.9287i	−0.183625	+	0.0668340i	0.248571	+	0.968614i	$0.420039\pi$
$80$	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	0.448901	−	0.893581i	$-0.351816\pi$
$83$	1033.80	−	376.273i	1.36716	−	0.497606i	0.918261	+	0.395975i	$0.129593\pi$
$84$	−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	0.0257897	+	0.999667i	$0.491790\pi$
$89$	−716.067	+	1240.26i	−0.852842	+	1.47717i	−0.878632	+	0.477499i	$0.841543\pi$
$90$	−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	−0.823922	−	0.566703i	$-0.808219\pi$
$97$	137.698	−	780.924i	0.144135	−	0.817431i	0.968057	−	0.250728i	$-0.0806701\pi$
$98$	−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	0.903378	−	0.428846i	$-0.141080\pi$
$101$	647.510	+	543.325i	0.637917	+	0.535276i	−0.265461	+	0.964122i	$0.585524\pi$
$102$	199.663	+	164.963i	0.193820	+	0.160135i
$103$	293.566	+	1664.89i	0.280834	+	1.59269i	0.719798	+	0.694184i	$0.244234\pi$
$103$	293.566	+	1664.89i	0.280834	+	1.59269i	−0.438964	+	0.898505i	$0.644654\pi$
$104$	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	−0.958957	−	0.283552i	$-0.908487\pi$
$113$	−185.962	−	1054.64i	−0.154813	−	0.877986i	0.804144	−	0.594434i	$-0.202624\pi$
$114$	−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	−0.969540	−	0.244934i	$-0.921234\pi$
$127$	−390.223	+	675.886i	−0.272651	+	0.472245i	0.696889	+	0.717179i	$0.254567\pi$
$128$	−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	0.325422	−	0.945569i	$-0.394494\pi$
$131$	1968.87	−	1652.07i	1.31313	−	1.10185i	0.987712	−	0.156282i	$-0.0499509\pi$
$132$	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	−0.734705	−	0.678387i	$-0.762679\pi$
$137$	−1381.39	+	502.786i	−0.861463	+	0.313547i	−0.126758	+	0.991934i	$0.540457\pi$
$138$	126.848	−	223.622i	0.0782467	−	0.137942i
$139$	1104.10	−	926.448i	0.673729	−	0.565326i	−0.240438	−	0.970665i	$-0.577291\pi$
$139$	1104.10	−	926.448i	0.673729	−	0.565326i	0.914166	+	0.405339i	$0.132846\pi$
$140$	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	−0.468070	−	0.883691i	$-0.655051\pi$
$149$	−2536.57	−	923.237i	−1.39466	−	0.507614i	−0.926588	+	0.376077i	$0.877273\pi$
$150$	−468.423	+	399.170i	−0.254977	+	0.217280i
$151$	−178.841	+	1014.26i	−0.0963835	+	0.546618i	0.897931	+	0.440136i	$0.145070\pi$
$151$	−178.841	+	1014.26i	−0.0963835	+	0.546618i	−0.994315	+	0.106482i	$0.966041\pi$
$152$	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	−0.997035	−	0.0769498i	$-0.975482\pi$
$157$	−170.059	−	964.451i	−0.0864469	−	0.490265i	0.910588	−	0.413315i	$-0.135629\pi$
$158$	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	0.995608	+	0.0936188i	$0.0298435\pi$
$167$	198.680	+	1126.77i	0.0920620	+	0.522110i	−0.903546	+	0.428491i	$0.859045\pi$
$168$	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	−0.944320	−	0.329029i	$-0.893279\pi$
$173$	126.482	−	717.312i	0.0555850	−	0.315238i	0.999905	+	0.0137904i	$0.00438977\pi$
$174$	−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	0.735170	−	0.677883i	$-0.237102\pi$
$179$	−525.620	−	910.400i	−0.219479	−	0.380148i	−0.954649	+	0.297735i	$0.903769\pi$
$180$	−2232.45	−	1816.05i	−0.924428	−	0.752001i
$181$	521.671	−	903.561i	0.214229	−	0.371056i	−0.738805	−	0.673920i	$-0.764609\pi$
$181$	521.671	−	903.561i	0.214229	−	0.371056i	0.953034	+	0.302864i	$0.0979427\pi$
$182$	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	−0.276312	−	0.961068i	$-0.589112\pi$
$191$	342.587	−	124.692i	0.129784	−	0.0472375i	0.406096	+	0.913831i	$0.366890\pi$
$192$	−364.261	−	619.970i	−0.136918	−	0.233034i
$193$	627.855	−	526.833i	0.234166	−	0.196489i	−0.518152	−	0.855288i	$-0.673380\pi$
$193$	627.855	−	526.833i	0.234166	−	0.196489i	0.752318	+	0.658800i	$0.228936\pi$
$194$	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	−0.600557	−	0.799582i	$-0.705054\pi$
$197$	1084.39	−	1878.22i	0.392180	−	0.679276i	0.992737	+	0.120306i	$0.0383876\pi$
$198$	−217.795	−	1133.93i	−0.0781717	−	0.406995i
$199$	2026.30	+	3509.66i	0.721813	+	1.25022i	0.960272	+	0.279065i	$0.0900244\pi$
$199$	2026.30	+	3509.66i	0.721813	+	1.25022i	−0.238459	+	0.971153i	$0.576642\pi$
$200$	−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	0.983164	−	0.182723i	$-0.0584911\pi$
$211$	−9.81661	−	55.6728i	−0.00320286	−	0.0181643i	−0.986367	+	0.164559i	$0.947380\pi$
$212$	−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	0.684269	−	0.729230i	$-0.260122\pi$
$223$	282.857	+	237.345i	0.0849395	+	0.0712727i	−0.599329	+	0.800503i	$0.704566\pi$
$224$	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	0.880116	+	0.474759i	$0.157465\pi$
$227$	−373.816	+	2120.01i	−0.109300	+	0.619869i	−0.989416	+	0.145110i	$0.953646\pi$
$228$	879.570	+	4775.40i	0.255487	+	1.38710i
$229$	3772.34	+	1373.02i	1.08857	+	0.396208i	0.823092	−	0.567909i	$-0.192247\pi$
$229$	3772.34	+	1373.02i	1.08857	+	0.396208i	0.265480	+	0.964116i	$0.414470\pi$
$230$	−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	0.715169	−	0.698951i	$-0.246350\pi$
$233$	−881.056	−	1526.03i	−0.247725	−	0.429072i	−0.962894	+	0.269879i	$0.913016\pi$
$234$	−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	−0.248878	−	0.968535i	$-0.580062\pi$
$239$	2444.98	−	2051.58i	0.661726	−	0.555254i	0.910604	+	0.413281i	$0.135617\pi$
$240$	−3122.46	+	23.7730i	−0.839809	+	0.00639392i
$241$	2116.26	−	770.257i	0.565646	−	0.205878i	−0.0433387	−	0.999060i	$-0.513799\pi$
$241$	2116.26	−	770.257i	0.565646	−	0.205878i	0.608984	+	0.793182i	$0.291577\pi$
$242$	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	0.257449	+	0.966292i	$0.417118\pi$
$251$	−2815.86	+	4877.20i	−0.708108	+	1.22648i	−0.965558	+	0.260188i	$0.916215\pi$
$252$	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	0.963880	−	0.266338i	$-0.0858136\pi$
$257$	6307.99	+	2295.92i	1.53106	+	0.557259i	0.567176	+	0.823596i	$0.308036\pi$
$258$	−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	0.985638	−	0.168874i	$-0.0540130\pi$
$263$	4224.56	+	3544.82i	0.990484	+	0.831115i	0.00484607	+	0.999988i	$0.498457\pi$
$264$	−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	0.342343	−	0.939575i	$-0.388780\pi$
$277$	−2413.49	−	2025.16i	−0.523511	−	0.439278i	−0.865854	+	0.500297i	$0.833224\pi$
$278$	−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	−0.593407	−	0.804903i	$-0.702217\pi$
$281$	1128.17	−	6398.19i	0.239506	−	1.35831i	0.832913	−	0.553404i	$-0.186671\pi$
$282$	560.556	+	199.206i	0.118371	+	0.0420657i
$283$	−5039.70	−	1834.30i	−1.05858	−	0.385293i	−0.246688	−	0.969095i	$-0.579342\pi$
$283$	−5039.70	−	1834.30i	−1.05858	−	0.385293i	−0.811896	+	0.583802i	$0.801564\pi$
$284$	−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	−0.327766	+	0.944759i	$0.606296\pi$
$293$	−6595.63	+	5534.39i	−1.31509	+	1.10349i	−0.987322	+	0.158731i	$0.949260\pi$
$294$	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	0.676204	−	0.736714i	$-0.263624\pi$
$307$	−1613.24	−	2794.22i	−0.299911	−	0.519461i	−0.976115	+	0.217253i	$0.930290\pi$
$308$	−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	0.372477	−	0.928041i	$-0.378509\pi$
$311$	336.079	+	122.323i	0.0612775	+	0.0223032i	−0.311200	+	0.950345i	$0.600731\pi$
$312$	−782.779	+	667.050i	−0.142039	+	0.121039i
$313$	−1107.26	+	6279.59i	−0.199955	+	1.13400i	0.705227	+	0.708981i	$0.250845\pi$
$313$	−1107.26	+	6279.59i	−0.199955	+	1.13400i	−0.905183	+	0.425023i	$0.860266\pi$
$314$	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	0.999766	+	0.0216156i	$0.00688099\pi$
$317$	6742.70	+	5657.79i	1.19466	+	1.00244i	0.194895	+	0.980824i	$0.437563\pi$
$318$	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	0.924279	−	0.381719i	$-0.124668\pi$
$331$	4268.76	+	3581.91i	0.708858	+	0.594803i	−0.215420	+	0.976521i	$0.569112\pi$
$332$	−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	0.364281	−	0.931289i	$-0.381315\pi$
$337$	276.634	+	100.686i	0.0447157	+	0.0162752i	−0.319565	+	0.947564i	$0.603537\pi$
$338$	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	−0.624767	−	0.780811i	$-0.714806\pi$
$347$	230.707	−	193.586i	0.0356917	−	0.0299489i	0.660459	+	0.750862i	$0.270362\pi$
$348$	−2239.89	+	3948.72i	−0.345030	+	0.608258i
$349$	7527.49	−	2739.78i	1.15455	−	0.420221i	0.307401	−	0.951580i	$-0.400541\pi$
$349$	7527.49	−	2739.78i	1.15455	−	0.420221i	0.847147	+	0.531359i	$0.178319\pi$
$350$	−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	−0.476440	−	0.879207i	$-0.658073\pi$
$353$	−1832.30	+	666.904i	−0.276271	+	0.100555i	0.200169	+	0.979761i	$0.435851\pi$
$354$	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	−0.731963	−	0.681345i	$-0.761396\pi$
$359$	1524.21	−	2640.01i	0.224080	−	0.388119i	0.956043	+	0.293226i	$0.0947289\pi$
$360$	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	−0.965883	−	0.258979i	$-0.916614\pi$
$367$	213.215	−	1209.20i	0.0303262	−	0.171988i	0.996209	+	0.0869907i	$0.0277250\pi$
$368$	−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	0.985720	−	0.168392i	$-0.0538574\pi$
$373$	13.3473	+	75.6964i	0.00185281	+	0.0105078i	−0.983867	+	0.178900i	$0.942746\pi$
$374$	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	−0.887402	−	0.460996i	$-0.847492\pi$
$383$	−1582.94	−	8977.31i	−0.211187	−	1.19770i	0.676215	−	0.736704i	$-0.263619\pi$
$384$	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	−0.981963	−	0.189074i	$-0.939451\pi$
$389$	41.7951	−	237.032i	0.00544755	−	0.0308946i	0.987410	+	0.158180i	$0.0505625\pi$
$390$	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	−0.315975	−	0.948767i	$-0.602332\pi$
$397$	5249.73	−	9092.81i	0.663669	−	1.14951i	0.979644	−	0.200741i	$-0.0643350\pi$
$398$	−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	−0.575207	+	0.818008i	$0.695079\pi$
$401$	−11889.8	+	9976.74i	−1.48067	+	1.24243i	−0.905464	+	0.424423i	$0.860477\pi$
$402$	−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	−0.339588	−	0.940574i	$-0.610288\pi$
$409$	4365.10	−	3662.76i	0.527727	−	0.442816i	0.867316	+	0.497758i	$0.165843\pi$
$410$	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	−0.236617	−	0.971603i	$-0.576039\pi$
$419$	−8940.47	−	3254.06i	−1.04241	−	0.379407i	−0.805794	+	0.592196i	$0.798261\pi$
$420$	−2361.88	−	12823.2i	−0.274400	−	1.48979i
$421$	−1986.28	+	11264.7i	−0.229941	+	1.30406i	0.623069	+	0.782167i	$0.285885\pi$
$421$	−1986.28	+	11264.7i	−0.229941	+	1.30406i	−0.853010	+	0.521894i	$0.825226\pi$
$422$	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	−0.148077	−	0.988976i	$-0.547309\pi$
$439$	−10557.0	−	8858.38i	−1.14774	−	0.963070i	−0.999664	+	0.0259060i	$0.991753\pi$
$440$	−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	−0.998876	−	0.0473935i	$-0.984909\pi$
$443$	−410.540	+	2328.29i	−0.0440301	+	0.249707i	0.954846	+	0.297100i	$0.0960196\pi$
$444$	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	0.810685	−	0.585482i	$-0.199095\pi$
$449$	−967.587	−	1675.91i	−0.101700	−	0.176149i	−0.912385	+	0.409333i	$0.865761\pi$
$450$	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	−0.574724	−	0.818348i	$-0.694890\pi$
$457$	−4776.95	+	1738.67i	−0.488964	+	0.177968i	0.0857600	+	0.996316i	$0.472668\pi$
$458$	−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	−0.683662	−	0.729799i	$-0.739614\pi$
$461$	−7307.48	+	2659.71i	−0.738272	+	0.268709i	−0.0546099	+	0.998508i	$0.517392\pi$
$462$	2581.21	−	4550.45i	0.259932	−	0.458238i
$463$	12156.4	−	10200.5i	1.22021	−	1.02388i	0.221398	−	0.975184i	$-0.428938\pi$
$463$	12156.4	−	10200.5i	1.22021	−	1.02388i	0.998814	−	0.0486955i	$-0.0155064\pi$
$464$	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	−0.984594	−	0.174858i	$-0.944053\pi$
$467$	−3439.99	+	5958.24i	−0.340865	+	0.590395i	0.643729	+	0.765254i	$0.277387\pi$
$468$	−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	0.596702	−	0.802463i	$-0.296477\pi$
$479$	−943.013	−	791.282i	−0.0899528	−	0.0754793i	−0.686655	+	0.726983i	$0.740922\pi$
$480$	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	0.994796	+	0.101889i	$0.0324886\pi$
$491$	1031.86	+	5851.97i	0.0948415	+	0.537873i	−0.899954	+	0.435984i	$0.856400\pi$
$492$	−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	0.794144	−	0.607730i	$-0.207920\pi$
$499$	11278.9	+	4105.19i	1.01185	+	0.368284i	0.217708	+	0.976014i	$0.430142\pi$
$500$	−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	0.735788	−	0.677212i	$-0.236812\pi$
$503$	−2465.92	−	4271.10i	−0.218588	−	0.378606i	−0.954377	+	0.298605i	$0.903479\pi$
$504$	−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	−0.0651850	−	0.997873i	$-0.520764\pi$
$509$	10406.5	−	8732.10i	0.906209	−	0.760400i	0.971394	+	0.237474i	$0.0763193\pi$
$510$	−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	−0.723838	−	0.689970i	$-0.757624\pi$
$521$	2801.92	−	4853.07i	0.235613	−	0.408094i	0.959451	+	0.281877i	$0.0909569\pi$
$522$	2702.03	−	2338.30i	0.226561	−	0.196062i
$523$	−3114.24	−	5394.02i	−0.260375	−	0.450983i	0.705967	−	0.708245i	$-0.250513\pi$
$523$	−3114.24	−	5394.02i	−0.260375	−	0.450983i	−0.966342	+	0.257262i	$0.917180\pi$
$524$	−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	0.0657839	−	0.997834i	$-0.479045\pi$
$547$	−11583.9	−	9720.02i	−0.905467	−	0.759777i	−0.971251	+	0.238057i	$0.923490\pi$
$548$	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	−0.609024	−	0.793152i	$-0.708439\pi$
$557$	−13032.6	−	22573.2i	−0.991402	−	1.71716i	−0.382378	−	0.924006i	$-0.624895\pi$
$558$	−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	−0.851270	−	0.524727i	$-0.824167\pi$
$563$	−6443.37	+	5406.63i	−0.482337	+	0.404728i	0.368934	+	0.929456i	$0.379723\pi$
$564$	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	−0.234532	−	0.972109i	$-0.575356\pi$
$569$	2859.32	−	1040.71i	0.210666	−	0.0766762i	0.445198	+	0.895432i	$0.353133\pi$
$570$	−11352.4	+	86.4322i	−0.834213	+	0.00635131i
$571$	15411.5	−	12931.8i	1.12951	−	0.947776i	0.130469	−	0.991452i	$-0.458352\pi$
$571$	15411.5	−	12931.8i	1.12951	−	0.947776i	0.999046	+	0.0436768i	$0.0139072\pi$
$572$	−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	0.792541	−	0.609818i	$-0.208757\pi$
$577$	−1827.40	−	3165.16i	−0.131847	−	0.228366i	−0.924389	+	0.381452i	$0.875424\pi$
$578$	−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	0.955801	−	0.294014i	$-0.0949914\pi$
$587$	11835.8	+	9931.44i	0.832226	+	0.698321i	−0.123575	+	0.992335i	$0.539436\pi$
$588$	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	0.979391	+	0.201972i	$0.0647351\pi$
$599$	1878.61	+	10654.1i	0.128143	+	0.726736i	−0.851248	+	0.524763i	$0.824154\pi$
$600$	1524.13	−	9045.95i	0.103704	−	0.615499i
$601$	−3054.52	−	2563.05i	−0.207315	−	0.173958i	0.533218	−	0.845978i	$-0.320983\pi$
$601$	−3054.52	−	2563.05i	−0.207315	−	0.173958i	−0.740533	+	0.672020i	$0.765427\pi$
$602$	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	0.532056	−	0.846709i	$-0.321420\pi$
$607$	5912.85	+	2152.10i	0.395379	+	0.143906i	−0.136676	+	0.990616i	$0.543642\pi$
$608$	−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	−0.950162	−	0.311756i	$-0.899083\pi$
$613$	−3112.72	+	5391.39i	−0.205093	+	0.355231i	0.745070	+	0.666987i	$0.232416\pi$
$614$	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	0.399386	−	0.916783i	$-0.369223\pi$
$617$	21021.0	−	17638.7i	1.37159	−	1.15090i	0.972208	−	0.234120i	$-0.0752210\pi$
$618$	4655.10	+	7922.94i	0.303002	+	0.515708i
$619$	−11484.7	+	4180.09i	−0.745733	+	0.271425i	−0.686809	−	0.726838i	$-0.740989\pi$
$619$	−11484.7	+	4180.09i	−0.745733	+	0.271425i	−0.0589242	+	0.998262i	$0.518767\pi$
$620$	−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	0.983168	−	0.182705i	$-0.0584855\pi$
$631$	5283.88	+	9151.94i	0.333356	+	0.577390i	−0.649811	+	0.760095i	$0.725152\pi$
$632$	−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	0.128022	−	0.991771i	$-0.459137\pi$
$641$	−13412.3	−	11254.3i	−0.826452	−	0.693475i	−0.954473	+	0.298296i	$0.903582\pi$
$642$	−5374.14	+	2002.49i	−0.330374	+	0.123103i
$643$	−2166.26	−	12285.5i	−0.132860	−	0.753487i	−0.976326	−	0.216304i	$-0.930600\pi$
$643$	−2166.26	−	12285.5i	−0.132860	−	0.753487i	0.843466	−	0.537183i	$-0.180511\pi$
$644$	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	0.998941	+	0.0459996i	$0.0146473\pi$
$653$	1267.79	+	7190.01i	0.0759763	+	0.430883i	−0.922965	+	0.384884i	$0.874242\pi$
$654$	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	0.635703	+	0.771934i	$0.280710\pi$
$659$	−3817.86	+	21652.1i	−0.225679	+	1.27989i	−0.861382	+	0.507957i	$0.830401\pi$
$660$	−17233.2	+	14685.4i	−1.01636	+	0.866101i
$661$	−23240.8	−	8458.96i	−1.36757	−	0.497754i	−0.449183	−	0.893440i	$-0.648285\pi$
$661$	−23240.8	−	8458.96i	−1.36757	−	0.497754i	−0.918386	+	0.395686i	$0.870507\pi$
$662$	−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	−0.485600	−	0.874181i	$-0.661399\pi$
$673$	−5162.27	+	1878.91i	−0.295678	+	0.107618i	0.189922	+	0.981799i	$0.439176\pi$
$674$	−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	−0.869338	−	0.494217i	$-0.835455\pi$
$677$	−21448.3	+	7806.53i	−1.21761	+	0.443175i	−0.348275	+	0.937392i	$0.613232\pi$
$678$	−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	−0.999773	−	0.0213186i	$-0.993214\pi$
$683$	−8593.28	+	14884.0i	−0.481424	+	0.833851i	0.518349	+	0.855169i	$0.326547\pi$
$684$	−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	0.627035	+	0.778991i	$0.284268\pi$
$691$	−4152.63	+	23550.7i	−0.228616	+	1.29654i	−0.855651	+	0.517553i	$0.826843\pi$
$692$	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	0.805450	−	0.592664i	$-0.201924\pi$
$709$	6827.53	+	5728.98i	0.361655	+	0.303464i	−0.443795	+	0.896128i	$0.646368\pi$
$710$	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	0.500655	−	0.865647i	$-0.333092\pi$
$719$	−9627.06	−	16674.6i	−0.499345	−	0.864890i	−1.00000		0.000756651i	$0.999759\pi$
$720$	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	0.332768	−	0.943009i	$-0.392017\pi$
$727$	23401.7	−	8517.51i	1.19384	−	0.434521i	0.861069	+	0.508488i	$0.169795\pi$
$728$	−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	−0.999138	−	0.0415124i	$-0.986782\pi$
$733$	−22459.9	+	18846.1i	−1.13175	+	0.949655i	−0.132617	+	0.991167i	$0.542338\pi$
$734$	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	−0.999722	−	0.0235855i	$-0.992492\pi$
$739$	−10452.2	−	18103.8i	−0.520287	−	0.901163i	0.479435	−	0.877577i	$-0.340842\pi$
$740$	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	−0.0399271	−	0.999203i	$-0.512713\pi$
$743$	−14435.9	−	5254.24i	−0.712788	−	0.259434i	−0.672861	+	0.739769i	$0.734935\pi$
$744$	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	0.885340	+	0.464945i	$0.153926\pi$
$751$	4371.61	+	24792.6i	0.212413	+	1.20465i	−0.672927	+	0.739709i	$0.734963\pi$
$752$	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	0.945381	+	0.325967i	$0.105690\pi$
$761$	3537.36	+	20061.4i	0.168501	+	0.955616i	−0.776880	+	0.629648i	$0.783199\pi$
$762$	−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	0.836323	−	0.548236i	$-0.184701\pi$
$769$	23981.8	+	8728.66i	1.12458	+	0.409315i	0.288261	+	0.957552i	$0.406923\pi$
$770$	−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	0.948176	+	0.317747i	$0.102926\pi$
$773$	16102.9	+	27891.1i	0.749264	+	1.29776i	−0.198911	+	0.980018i	$0.563741\pi$
$774$	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	0.241137	−	0.970491i	$-0.422480\pi$
$787$	27349.4	−	22948.9i	1.23876	−	1.03944i	0.997620	−	0.0689492i	$-0.0219646\pi$
$788$	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	0.0285161	−	0.999593i	$-0.490922\pi$
$797$	−13323.9	−	4849.50i	−0.592166	−	0.215531i	−0.620682	+	0.784063i	$0.713144\pi$
$798$	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	−0.796492	−	0.604649i	$-0.793313\pi$
$821$	3734.89	−	21181.6i	0.158768	−	0.900418i	0.955260	−	0.295768i	$-0.0955756\pi$
$822$	−6081.86	+	5182.70i	−0.258065	+	0.219912i
$823$	19406.3	+	7063.32i	0.821945	+	0.299164i	0.718549	−	0.695477i	$-0.244807\pi$
$823$	19406.3	+	7063.32i	0.821945	+	0.299164i	0.103397	+	0.994640i	$0.467029\pi$
$824$	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	−0.972330	−	0.233612i	$-0.924945\pi$
$827$	−16373.8	−	28360.2i	−0.688479	−	1.19248i	0.283851	−	0.958868i	$-0.408388\pi$
$828$	−1398.98	+	8707.31i	−0.0587174	+	0.365459i
$829$	−12512.4	+	21672.1i	−0.524214	+	0.907965i	0.475389	+	0.879776i	$0.342307\pi$
$829$	−12512.4	+	21672.1i	−0.524214	+	0.907965i	−0.999603	+	0.0281890i	$0.991026\pi$
$830$	−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	−0.128829	−	0.991667i	$-0.541122\pi$
$839$	9961.74	−	3625.78i	0.409913	−	0.149196i	0.538742	+	0.842471i	$0.318900\pi$
$840$	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	−0.979930	−	0.199343i	$-0.936119\pi$
$853$	226.264	−	1283.21i	0.00908223	−	0.0515079i	0.989012	+	0.147835i	$0.0472304\pi$
$854$	−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	−0.0473515	−	0.998878i	$-0.515078\pi$
$857$	−26073.7	−	21878.4i	−1.03928	−	0.872057i	−0.991926	+	0.126821i	$0.959523\pi$
$858$	−468.642	+	2781.47i	−0.0186471	+	0.110673i
$859$	−8389.96	−	47581.8i	−0.333250	−	1.88995i	−0.443870	−	0.896091i	$-0.646395\pi$
$859$	−8389.96	−	47581.8i	−0.333250	−	1.88995i	0.110620	−	0.993863i	$-0.464716\pi$
$860$	−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	0.968536	−	0.248874i	$-0.0800606\pi$
$877$	40269.1	+	14656.8i	1.55050	+	0.564337i	0.581968	+	0.813212i	$0.302283\pi$
$878$	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	0.926943	−	0.375202i	$-0.122427\pi$
$881$	3622.67	+	6274.64i	0.138537	+	0.239952i	−0.788406	+	0.615155i	$0.789093\pi$
$882$	−3061.89	−	5121.63i	−0.116892	−	0.195526i
$883$	−7736.23	+	13399.5i	−0.294841	+	0.510680i	−0.974948	−	0.222433i	$-0.928600\pi$
$883$	−7736.23	+	13399.5i	−0.294841	+	0.510680i	0.680107	+	0.733113i	$0.261933\pi$
$884$	−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	−0.359001	−	0.933337i	$-0.616883\pi$
$887$	13150.9	−	11034.9i	0.497816	−	0.417717i	0.856818	+	0.515620i	$0.172438\pi$
$888$	−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	−0.301721	−	0.953396i	$-0.597561\pi$
$907$	8410.06	−	47695.8i	0.307885	−	1.74610i	0.609605	−	0.792705i	$-0.291328\pi$
$908$	−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	0.416755	−	0.909019i	$-0.363167\pi$
$911$	−11165.9	−	9369.33i	−0.406086	−	0.340746i	−0.822840	+	0.568273i	$0.807612\pi$
$912$	−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	0.697608	+	0.716480i	$0.254248\pi$
$929$	−5747.46	+	32595.5i	−0.202980	+	1.15116i	−0.900587	+	0.434675i	$0.856863\pi$
$930$	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	−0.0381458	+	0.999272i	$0.512145\pi$
$937$	−25368.3	+	43939.2i	−0.884468	+	1.53194i	−0.846322	+	0.532671i	$0.821188\pi$
$938$	−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	−0.995862	−	0.0908796i	$-0.971032\pi$
$941$	−31154.7	+	26141.9i	−1.07929	+	0.905634i	−0.0834307	+	0.996514i	$0.526588\pi$
$942$	−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	−0.583778	−	0.811913i	$-0.698426\pi$
$947$	−14836.1	+	5399.91i	−0.509091	+	0.185294i	0.0746875	+	0.997207i	$0.476204\pi$
$948$	−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	−0.458124	−	0.888888i	$-0.651479\pi$
$953$	15908.4	−	27554.1i	0.540737	−	0.936585i	0.998862	−	0.0476966i	$-0.0151881\pi$
$954$	−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	0.726509	+	0.687157i	$0.241142\pi$
$967$	8384.70	+	47552.0i	0.278835	+	1.58135i	−0.447673	+	0.894197i	$0.647747\pi$
$968$	−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	0.999240	−	0.0389782i	$-0.0124103\pi$
$977$	1433.16	+	8127.85i	0.0469302	+	0.266154i	−0.952310	+	0.305133i	$0.901299\pi$
$978$	−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	0.859737	+	0.510737i	$0.170627\pi$
$983$	−3785.72	+	21469.9i	−0.122834	+	0.696625i	−0.982571	+	0.185888i	$0.940484\pi$
$984$	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	−0.156761	−	0.987637i	$-0.550105\pi$
$991$	24238.0	−	41981.4i	0.776938	−	1.34570i	0.933699	−	0.358059i	$-0.116561\pi$
$992$	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	−0.281640	−	0.959520i	$-0.590878\pi$
$997$	3758.13	−	1367.85i	0.119379	−	0.0434505i	0.401019	+	0.916070i	$0.368656\pi$
$998$	−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.7.4	yes	48
3.2	odd	2		81.4.e.a.19.5		48
9.2	odd	6		243.4.e.a.136.4		48
9.4	even	3		243.4.e.c.217.5		48
9.5	odd	6		243.4.e.b.217.4		48
9.7	even	3		243.4.e.d.136.5		48
27.2	odd	18		729.4.a.c.1.10		24
27.4	even	9	inner	27.4.e.a.4.4	✓	48
27.5	odd	18		243.4.e.b.28.4		48
27.13	even	9		243.4.e.d.109.5		48
27.14	odd	18		243.4.e.a.109.4		48
27.22	even	9		243.4.e.c.28.5		48
27.23	odd	18		81.4.e.a.64.5		48
27.25	even	9		729.4.a.d.1.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.4.4	✓	48	27.4	even	9	inner
27.4.e.a.7.4	yes	48	1.1	even	1	trivial
81.4.e.a.19.5		48	3.2	odd	2
81.4.e.a.64.5		48	27.23	odd	18
243.4.e.a.109.4		48	27.14	odd	18
243.4.e.a.136.4		48	9.2	odd	6
243.4.e.b.28.4		48	27.5	odd	18
243.4.e.b.217.4		48	9.5	odd	6
243.4.e.c.28.5		48	27.22	even	9
243.4.e.c.217.5		48	9.4	even	3
243.4.e.d.109.5		48	27.13	even	9
243.4.e.d.136.5		48	9.7	even	3
729.4.a.c.1.10		24	27.2	odd	18
729.4.a.d.1.15		24	27.25	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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