LMFDB - Embedded newform 13.5.f.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,5,Mod(2,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("13.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, 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:	$1.34380952009$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + \cdots + 3779136 $ x^16 + 152x^14 + 9190x^12 + 285720x^10 + 4862025x^8 + 43573680x^6 + 169417008x^4 + 100636992*x^2 + 3779136
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.1
Root			$4.89748i$ of defining polynomial
Character	$\chi$	$=$	13.7
Dual form			13.5.f.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.34141 + 1.69918i) q^{2} +(7.28678 - 12.6211i) q^{3} +(23.4699 - 13.5504i) q^{4} +(-20.2793 - 20.2793i) q^{5} +(-24.7631 + 92.4170i) q^{6} +(21.3318 + 5.71584i) q^{7} +(-51.5321 + 51.5321i) q^{8} +(-65.6944 - 113.786i) q^{9} +O(q^{10})$	\(q+(-6.34141 + 1.69918i) q^{2} +(7.28678 - 12.6211i) q^{3} +(23.4699 - 13.5504i) q^{4} +(-20.2793 - 20.2793i) q^{5} +(-24.7631 + 92.4170i) q^{6} +(21.3318 + 5.71584i) q^{7} +(-51.5321 + 51.5321i) q^{8} +(-65.6944 - 113.786i) q^{9} +(163.058 + 94.1415i) q^{10} +(19.8619 + 74.1257i) q^{11} -394.954i q^{12} +(162.185 + 47.5081i) q^{13} -144.986 q^{14} +(-403.718 + 108.176i) q^{15} +(22.4185 - 38.8299i) q^{16} +(119.941 - 69.2480i) q^{17} +(609.938 + 609.938i) q^{18} +(57.8912 - 216.053i) q^{19} +(-750.746 - 201.162i) q^{20} +(227.580 - 227.580i) q^{21} +(-251.905 - 436.312i) q^{22} +(491.603 + 283.827i) q^{23} +(274.887 + 1025.89i) q^{24} +197.503i q^{25} +(-1109.21 - 25.6875i) q^{26} -734.346 q^{27} +(578.107 - 154.903i) q^{28} +(-406.589 + 704.232i) q^{29} +(2376.33 - 1371.98i) q^{30} +(-666.232 - 666.232i) q^{31} +(225.607 - 841.977i) q^{32} +(1080.28 + 289.459i) q^{33} +(-642.931 + 642.931i) q^{34} +(-316.681 - 548.508i) q^{35} +(-3083.68 - 1780.37i) q^{36} +(429.906 + 1604.43i) q^{37} +1468.45i q^{38} +(1781.41 - 1700.77i) q^{39} +2090.07 q^{40} +(907.358 - 243.126i) q^{41} +(-1056.48 + 1829.88i) q^{42} +(-2118.01 + 1222.83i) q^{43} +(1470.59 + 1470.59i) q^{44} +(-975.267 + 3639.75i) q^{45} +(-3599.73 - 964.545i) q^{46} +(908.134 - 908.134i) q^{47} +(-326.717 - 565.890i) q^{48} +(-1656.95 - 956.642i) q^{49} +(-335.593 - 1252.45i) q^{50} -2018.38i q^{51} +(4450.22 - 1082.65i) q^{52} +2101.44 q^{53} +(4656.79 - 1247.78i) q^{54} +(1100.43 - 1906.01i) q^{55} +(-1393.82 + 804.723i) q^{56} +(-2304.98 - 2304.98i) q^{57} +(1381.73 - 5156.69i) q^{58} +(-3417.07 - 915.600i) q^{59} +(-8009.41 + 8009.41i) q^{60} +(2816.09 + 4877.60i) q^{61} +(5356.90 + 3092.81i) q^{62} +(-750.998 - 2802.76i) q^{63} +6440.06i q^{64} +(-2325.57 - 4252.44i) q^{65} -7342.31 q^{66} +(-3279.23 + 878.668i) q^{67} +(1876.67 - 3250.49i) q^{68} +(7164.41 - 4136.38i) q^{69} +(2940.22 + 2940.22i) q^{70} +(-1904.53 + 7107.80i) q^{71} +(9249.01 + 2478.26i) q^{72} +(4192.40 - 4192.40i) q^{73} +(-5452.42 - 9443.87i) q^{74} +(2492.71 + 1439.16i) q^{75} +(-1568.89 - 5855.19i) q^{76} +1694.76i q^{77} +(-8406.75 + 13812.2i) q^{78} -3957.00 q^{79} +(-1242.08 + 332.813i) q^{80} +(-29.7681 + 51.5598i) q^{81} +(-5340.82 + 3083.52i) q^{82} +(1386.98 + 1386.98i) q^{83} +(2257.49 - 8425.08i) q^{84} +(-3836.63 - 1028.02i) q^{85} +(11353.4 - 11353.4i) q^{86} +(5925.45 + 10263.2i) q^{87} +(-4843.38 - 2796.32i) q^{88} +(2395.70 + 8940.86i) q^{89} -24738.3i q^{90} +(3188.15 + 1940.46i) q^{91} +15383.8 q^{92} +(-13263.3 + 3553.88i) q^{93} +(-4215.77 + 7301.93i) q^{94} +(-5555.41 + 3207.42i) q^{95} +(-8982.71 - 8982.71i) q^{96} +(751.041 - 2802.92i) q^{97} +(12132.9 + 3251.01i) q^{98} +(7129.65 - 7129.65i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9} - 486 q^{10} - 100 q^{11} + 294 q^{13} + 808 q^{14} + 346 q^{15} + 230 q^{16} + 984 q^{17} + 2434 q^{18} - 1498 q^{19} - 3962 q^{20} - 1076 q^{21} - 1524 q^{22} - 1014 q^{23} - 2142 q^{24} + 614 q^{26} + 3352 q^{27} + 5764 q^{28} + 814 q^{29} + 9162 q^{30} + 4060 q^{31} - 4996 q^{32} - 5636 q^{33} - 2502 q^{34} - 4892 q^{35} - 15750 q^{36} - 1790 q^{37} + 6982 q^{39} + 18816 q^{40} + 4280 q^{41} - 1204 q^{42} - 1368 q^{43} + 10736 q^{44} - 6806 q^{45} - 15246 q^{46} + 1484 q^{47} - 3002 q^{48} - 11820 q^{49} - 13574 q^{50} + 1432 q^{52} + 7204 q^{53} + 13240 q^{54} + 6936 q^{55} + 8124 q^{56} + 12736 q^{57} + 3030 q^{58} - 2380 q^{59} - 6472 q^{60} - 162 q^{61} + 19614 q^{62} + 12004 q^{63} - 5248 q^{65} - 23872 q^{66} - 14854 q^{67} - 6444 q^{68} + 2412 q^{69} - 34524 q^{70} - 8050 q^{71} + 15420 q^{72} - 15448 q^{73} - 2882 q^{74} + 8280 q^{75} + 10622 q^{76} - 11672 q^{78} - 17064 q^{79} + 2564 q^{80} + 2128 q^{81} - 5346 q^{82} + 12788 q^{83} + 25948 q^{84} + 35382 q^{85} + 67260 q^{86} + 29342 q^{87} + 40836 q^{88} + 20492 q^{89} + 8996 q^{91} - 49884 q^{92} - 78920 q^{93} - 30606 q^{94} - 98574 q^{95} - 94664 q^{96} + 50944 q^{97} + 61484 q^{98} - 21632 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9 - 486 * q^10 - 100 * q^11 + 294 * q^13 + 808 * q^14 + 346 * q^15 + 230 * q^16 + 984 * q^17 + 2434 * q^18 - 1498 * q^19 - 3962 * q^20 - 1076 * q^21 - 1524 * q^22 - 1014 * q^23 - 2142 * q^24 + 614 * q^26 + 3352 * q^27 + 5764 * q^28 + 814 * q^29 + 9162 * q^30 + 4060 * q^31 - 4996 * q^32 - 5636 * q^33 - 2502 * q^34 - 4892 * q^35 - 15750 * q^36 - 1790 * q^37 + 6982 * q^39 + 18816 * q^40 + 4280 * q^41 - 1204 * q^42 - 1368 * q^43 + 10736 * q^44 - 6806 * q^45 - 15246 * q^46 + 1484 * q^47 - 3002 * q^48 - 11820 * q^49 - 13574 * q^50 + 1432 * q^52 + 7204 * q^53 + 13240 * q^54 + 6936 * q^55 + 8124 * q^56 + 12736 * q^57 + 3030 * q^58 - 2380 * q^59 - 6472 * q^60 - 162 * q^61 + 19614 * q^62 + 12004 * q^63 - 5248 * q^65 - 23872 * q^66 - 14854 * q^67 - 6444 * q^68 + 2412 * q^69 - 34524 * q^70 - 8050 * q^71 + 15420 * q^72 - 15448 * q^73 - 2882 * q^74 + 8280 * q^75 + 10622 * q^76 - 11672 * q^78 - 17064 * q^79 + 2564 * q^80 + 2128 * q^81 - 5346 * q^82 + 12788 * q^83 + 25948 * q^84 + 35382 * q^85 + 67260 * q^86 + 29342 * q^87 + 40836 * q^88 + 20492 * q^89 + 8996 * q^91 - 49884 * q^92 - 78920 * q^93 - 30606 * q^94 - 98574 * q^95 - 94664 * q^96 + 50944 * q^97 + 61484 * q^98 - 21632 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−6.34141	+	1.69918i	−1.58535	+	0.424794i	−0.940578	−	0.339578i	$-0.889716\pi$
$2$	−6.34141	+	1.69918i	−1.58535	+	0.424794i	−0.644775	+	0.764372i	$0.723049\pi$
$3$	7.28678	−	12.6211i	0.809643	−	1.40234i	−0.103469	−	0.994633i	$-0.532994\pi$
$3$	7.28678	−	12.6211i	0.809643	−	1.40234i	0.913112	−	0.407710i	$-0.133672\pi$
$4$	23.4699	−	13.5504i	1.46687	−	0.846897i
$5$	−20.2793	−	20.2793i	−0.811174	−	0.811174i	0.173636	−	0.984810i	$-0.444448\pi$
$5$	−20.2793	−	20.2793i	−0.811174	−	0.811174i	−0.984810	+	0.173636i	$0.944448\pi$
$6$	−24.7631	+	92.4170i	−0.687863	+	2.56714i
$7$	21.3318	+	5.71584i	0.435343	+	0.116650i	0.469833	−	0.882755i	$-0.344314\pi$
$7$	21.3318	+	5.71584i	0.435343	+	0.116650i	−0.0344902	+	0.999405i	$0.510981\pi$
$8$	−51.5321	+	51.5321i	−0.805189	+	0.805189i
$9$	−65.6944	−	113.786i	−0.811042	−	1.40477i
$10$	163.058	+	94.1415i	1.63058	+	0.941415i
$11$	19.8619	+	74.1257i	0.164148	+	0.612609i	0.998147	+	0.0608433i	$0.0193790\pi$
$11$	19.8619	+	74.1257i	0.164148	+	0.612609i	−0.833999	+	0.551765i	$0.813954\pi$
$12$		−	394.954i		−	2.74274i
$13$	162.185	+	47.5081i	0.959675	+	0.281113i
$13$	162.185	+	47.5081i	0.959675	+	0.281113i
$14$	−144.986			−0.739724
$15$	−403.718	+	108.176i	−1.79430	+	0.480782i
$16$	22.4185	−	38.8299i	0.0875721	−	0.151679i
$17$	119.941	−	69.2480i	0.415021	−	0.239612i	−0.277924	−	0.960603i	$-0.589646\pi$
$17$	119.941	−	69.2480i	0.415021	−	0.239612i	0.692945	+	0.720991i	$0.256313\pi$
$18$	609.938	+	609.938i	1.88252	+	1.88252i
$19$	57.8912	−	216.053i	0.160364	−	0.598485i	−0.838223	−	0.545328i	$-0.816405\pi$
$19$	57.8912	−	216.053i	0.160364	−	0.598485i	0.998586	−	0.0531568i	$-0.0169283\pi$
$20$	−750.746	−	201.162i	−1.87687	−	0.502905i
$21$	227.580	−	227.580i	0.516055	−	0.516055i
$22$	−251.905	−	436.312i	−0.520465	−	0.901472i
$23$	491.603	+	283.827i	0.929307	+	0.536535i	0.886592	−	0.462552i	$-0.153066\pi$
$23$	491.603	+	283.827i	0.929307	+	0.536535i	0.0427144	+	0.999087i	$0.486399\pi$
$24$	274.887	+	1025.89i	0.477235	+	1.78107i
$25$			197.503i			0.316005i
$26$	−1109.21	−	25.6875i	−1.64084	−	0.0379993i
$27$	−734.346			−1.00733
$28$	578.107	−	154.903i	0.737381	−	0.197581i
$29$	−406.589	+	704.232i	−0.483458	+	0.837375i	−0.999820	−	0.0189964i	$-0.993953\pi$
$29$	−406.589	+	704.232i	−0.483458	+	0.837375i	0.516361	+	0.856371i	$0.327286\pi$
$30$	2376.33	−	1371.98i	2.64037	−	1.52442i
$31$	−666.232	−	666.232i	−0.693270	−	0.693270i	0.269680	−	0.962950i	$-0.413082\pi$
$31$	−666.232	−	666.232i	−0.693270	−	0.693270i	−0.962950	+	0.269680i	$0.913082\pi$
$32$	225.607	−	841.977i	0.220319	−	0.822243i
$33$	1080.28	+	289.459i	0.991988	+	0.265802i
$34$	−642.931	+	642.931i	−0.556169	+	0.556169i
$35$	−316.681	−	548.508i	−0.258515	−	0.447762i
$36$	−3083.68	−	1780.37i	−2.37939	−	1.37374i
$37$	429.906	+	1604.43i	0.314029	+	1.17197i	0.924890	+	0.380235i	$0.124157\pi$
$37$	429.906	+	1604.43i	0.314029	+	1.17197i	−0.610861	+	0.791738i	$0.709177\pi$
$38$			1468.45i			1.01693i
$39$	1781.41	−	1700.77i	1.17121	−	1.11819i
$40$	2090.07			1.30630
$41$	907.358	−	243.126i	0.539773	−	0.144632i	0.0213753	−	0.999772i	$-0.493195\pi$
$41$	907.358	−	243.126i	0.539773	−	0.144632i	0.518397	+	0.855140i	$0.326529\pi$
$42$	−1056.48	+	1829.88i	−0.598912	+	1.03735i
$43$	−2118.01	+	1222.83i	−1.14549	+	0.661349i	−0.947784	−	0.318912i	$-0.896683\pi$
$43$	−2118.01	+	1222.83i	−1.14549	+	0.661349i	−0.197706	+	0.980261i	$0.563349\pi$
$44$	1470.59	+	1470.59i	0.759600	+	0.759600i
$45$	−975.267	+	3639.75i	−0.481613	+	1.79741i
$46$	−3599.73	−	964.545i	−1.70120	−	0.455834i
$47$	908.134	−	908.134i	0.411106	−	0.411106i	−0.471018	−	0.882124i	$-0.656113\pi$
$47$	908.134	−	908.134i	0.411106	−	0.411106i	0.882124	+	0.471018i	$0.156113\pi$
$48$	−326.717	−	565.890i	−0.141804	−	0.245612i
$49$	−1656.95	−	956.642i	−0.690109	−	0.398435i
$50$	−335.593	−	1252.45i	−0.134237	−	0.500980i
$51$		−	2018.38i		−	0.776002i
$52$	4450.22	−	1082.65i	1.64579	−	0.400390i
$53$	2101.44			0.748110			0.374055	−	0.927407i	$-0.377967\pi$
$53$	2101.44			0.748110			0.374055	+	0.927407i	$0.377967\pi$
$54$	4656.79	−	1247.78i	1.59698	−	0.427909i
$55$	1100.43	−	1906.01i	0.363780	−	0.630085i
$56$	−1393.82	+	804.723i	−0.444458	+	0.256608i
$57$	−2304.98	−	2304.98i	−0.709444	−	0.709444i
$58$	1381.73	−	5156.69i	0.410741	−	1.53290i
$59$	−3417.07	−	915.600i	−0.981634	−	0.263028i	−0.267901	−	0.963446i	$-0.586330\pi$
$59$	−3417.07	−	915.600i	−0.981634	−	0.263028i	−0.713733	+	0.700418i	$0.752997\pi$
$60$	−8009.41	+	8009.41i	−2.22483	+	2.22483i
$61$	2816.09	+	4877.60i	0.756809	+	1.31083i	0.944470	+	0.328598i	$0.106576\pi$
$61$	2816.09	+	4877.60i	0.756809	+	1.31083i	−0.187661	+	0.982234i	$0.560091\pi$
$62$	5356.90	+	3092.81i	1.39357	+	0.804580i
$63$	−750.998	−	2802.76i	−0.189216	−	0.706163i
$64$			6440.06i			1.57228i
$65$	−2325.57	−	4252.44i	−0.550431	−	1.00649i
$66$	−7342.31			−1.68556
$67$	−3279.23	+	878.668i	−0.730504	+	0.195738i	−0.604854	−	0.796337i	$-0.706768\pi$
$67$	−3279.23	+	878.668i	−0.730504	+	0.195738i	−0.125650	+	0.992075i	$0.540102\pi$
$68$	1876.67	−	3250.49i	0.405854	−	0.702960i
$69$	7164.41	−	4136.38i	1.50481	−	0.868804i
$70$	2940.22	+	2940.22i	0.600045	+	0.600045i
$71$	−1904.53	+	7107.80i	−0.377808	+	1.41000i	0.471390	+	0.881925i	$0.343752\pi$
$71$	−1904.53	+	7107.80i	−0.377808	+	1.41000i	−0.849198	+	0.528074i	$0.822914\pi$
$72$	9249.01	+	2478.26i	1.78414	+	0.478060i
$73$	4192.40	−	4192.40i	0.786714	−	0.786714i	−0.194240	−	0.980954i	$-0.562224\pi$
$73$	4192.40	−	4192.40i	0.786714	−	0.786714i	0.980954	+	0.194240i	$0.0622240\pi$
$74$	−5452.42	−	9443.87i	−0.995694	−	1.72459i
$75$	2492.71	+	1439.16i	0.443148	+	0.255851i
$76$	−1568.89	−	5855.19i	−0.271623	−	1.01371i
$77$			1694.76i			0.285843i
$78$	−8406.75	+	13812.2i	−1.38178	+	2.27025i
$79$	−3957.00			−0.634033			−0.317016	−	0.948420i	$-0.602681\pi$
$79$	−3957.00			−0.634033			−0.317016	+	0.948420i	$0.602681\pi$
$80$	−1242.08	+	332.813i	−0.194074	+	0.0520021i
$81$	−29.7681	+	51.5598i	−0.00453713	+	0.00785853i
$82$	−5340.82	+	3083.52i	−0.794292	+	0.458584i
$83$	1386.98	+	1386.98i	0.201333	+	0.201333i	0.800571	−	0.599238i	$-0.204530\pi$
$83$	1386.98	+	1386.98i	0.201333	+	0.201333i	−0.599238	+	0.800571i	$0.704530\pi$
$84$	2257.49	−	8425.08i	0.319940	−	1.19403i
$85$	−3836.63	−	1028.02i	−0.531021	−	0.142287i
$86$	11353.4	−	11353.4i	1.53507	−	1.53507i
$87$	5925.45	+	10263.2i	0.782857	+	1.35595i
$88$	−4843.38	−	2796.32i	−0.625436	−	0.361096i
$89$	2395.70	+	8940.86i	0.302449	+	1.12875i	0.935119	+	0.354333i	$0.115292\pi$
$89$	2395.70	+	8940.86i	0.302449	+	1.12875i	−0.632670	+	0.774421i	$0.718041\pi$
$90$		−	24738.3i		−	3.05411i
$91$	3188.15	+	1940.46i	0.384996	+	0.234326i
$92$	15383.8			1.81756
$93$	−13263.3	+	3553.88i	−1.53350	+	0.410901i
$94$	−4215.77	+	7301.93i	−0.477113	+	0.826384i
$95$	−5555.41	+	3207.42i	−0.615558	+	0.355393i
$96$	−8982.71	−	8982.71i	−0.974686	−	0.974686i
$97$	751.041	−	2802.92i	0.0798215	−	0.297898i	−0.914462	−	0.404672i	$-0.867386\pi$
$97$	751.041	−	2802.92i	0.0798215	−	0.297898i	0.994283	+	0.106774i	$0.0340522\pi$
$98$	12132.9	+	3251.01i	1.26332	+	0.338505i
$99$	7129.65	−	7129.65i	0.727441	−	0.727441i
$100$	2676.24	+	4635.38i	0.267624	+	0.463538i
$101$	2484.93	+	1434.67i	0.243596	+	0.140640i	0.616829	−	0.787098i	$-0.288417\pi$
$101$	2484.93	+	1434.67i	0.243596	+	0.140640i	−0.373232	+	0.927738i	$0.621751\pi$
$102$	3429.58	+	12799.4i	0.329641	+	1.23024i
$103$		−	5465.63i		−	0.515188i	−0.966253	−	0.257594i	$-0.917070\pi$
$103$		−	5465.63i		−	0.515188i	0.966253	−	0.257594i	$-0.0829298\pi$
$104$	−10805.9	+	5909.54i	−0.999068	+	0.546370i
$105$	−9230.36			−0.837221
$106$	−13326.1	+	3570.72i	−1.18602	+	0.317793i
$107$	−293.203	+	507.843i	−0.0256095	+	0.0443570i	−0.878546	−	0.477658i	$-0.841486\pi$
$107$	−293.203	+	507.843i	−0.0256095	+	0.0443570i	0.852937	+	0.522015i	$0.174819\pi$
$108$	−17235.0	+	9950.64i	−1.47762	+	0.853107i
$109$	5258.17	+	5258.17i	0.442570	+	0.442570i	0.892875	−	0.450305i	$-0.148685\pi$
$109$	5258.17	+	5258.17i	0.442570	+	0.442570i	−0.450305	+	0.892875i	$0.648685\pi$
$110$	−3739.66	+	13956.6i	−0.309063	+	1.15344i
$111$	23382.3	+	6265.26i	1.89776	+	0.508503i
$112$	700.172	−	700.172i	0.0558173	−	0.0558173i
$113$	−10187.3	−	17645.0i	−0.797818	−	1.38186i	−0.921034	−	0.389481i	$-0.872654\pi$
$113$	−10187.3	−	17645.0i	−0.797818	−	1.38186i	0.123217	−	0.992380i	$-0.460679\pi$
$114$	18533.4	+	10700.3i	1.42609	+	0.823351i
$115$	−4213.56	−	15725.2i	−0.318606	−	1.18905i
$116$			22037.7i			1.63776i
$117$	−5248.89	−	21575.4i	−0.383439	−	1.57611i
$118$	23224.8			1.66797
$119$	2954.37	−	791.621i	0.208627	−	0.0559015i
$120$	15229.9	−	26379.0i	1.05763	−	1.83187i
$121$	7579.36	−	4375.95i	0.517681	−	0.298883i
$122$	−26145.9	−	26145.9i	−1.75664	−	1.75664i
$123$	3543.21	−	13223.4i	0.234200	−	0.874046i
$124$	−24664.1	−	6608.72i	−1.60406	−	0.429808i
$125$	−8669.35	+	8669.35i	−0.554838	+	0.554838i
$126$	9524.77	+	16497.4i	0.599948	+	1.03914i
$127$	−3968.07	−	2290.97i	−0.246021	−	0.142040i	0.371920	−	0.928265i	$-0.378700\pi$
$127$	−3968.07	−	2290.97i	−0.246021	−	0.142040i	−0.617941	+	0.786225i	$0.712033\pi$
$128$	−7333.08	−	27367.4i	−0.447576	−	1.67038i
$129$			35642.1i			2.14183i
$130$	21973.1	+	23014.9i	1.30018	+	1.36183i
$131$	−28273.1			−1.64752			−0.823759	−	0.566940i	$-0.808127\pi$
$131$	−28273.1			−1.64752			−0.823759	+	0.566940i	$0.808127\pi$
$132$	29276.2	−	7844.54i	1.68022	−	0.450215i
$133$	2469.85	−	4277.90i	0.139626	−	0.241840i
$134$	19301.9	−	11144.0i	1.07496	−	0.620627i
$135$	14892.0	+	14892.0i	0.817122	+	0.817122i
$136$	−2612.32	+	9749.30i	−0.141237	+	0.527103i
$137$	−7065.68	−	1893.24i	−0.376455	−	0.100871i	0.0656300	−	0.997844i	$-0.479094\pi$
$137$	−7065.68	−	1893.24i	−0.376455	−	0.100871i	−0.442085	+	0.896973i	$0.645761\pi$
$138$	−38404.1	+	38404.1i	−2.01660	+	2.01660i
$139$	10399.9	+	18013.2i	0.538269	+	0.932310i	0.998997	+	0.0447683i	$0.0142550\pi$
$139$	10399.9	+	18013.2i	0.538269	+	0.932310i	−0.460728	+	0.887541i	$0.652412\pi$
$140$	−14865.0	−	8582.29i	−0.758417	−	0.437872i
$141$	−4844.25	−	18079.0i	−0.243662	−	0.909361i
$142$		−	48309.6i		−	2.39584i
$143$	−300.265	+	12965.7i	−0.0146836	+	0.634049i
$144$	−5891.07			−0.284099
$145$	22526.7	−	6036.01i	1.07142	−	0.287087i
$146$	−19462.1	+	33709.4i	−0.913028	+	1.58141i
$147$	−24147.7	+	13941.7i	−1.11748	+	0.645179i
$148$	31830.4	+	31830.4i	1.45318	+	1.45318i
$149$	56.0657	−	209.240i	0.00252537	−	0.00942480i	−0.964652	−	0.263528i	$-0.915114\pi$
$149$	56.0657	−	209.240i	0.00252537	−	0.00942480i	0.967177	+	0.254104i	$0.0817804\pi$
$150$	−18252.7	−	4890.79i	−0.811230	−	0.217368i
$151$	21275.9	−	21275.9i	0.933114	−	0.933114i	−0.0647854	−	0.997899i	$-0.520636\pi$
$151$	21275.9	−	21275.9i	0.933114	−	0.933114i	0.997899	+	0.0647854i	$0.0206363\pi$
$152$	8150.41	+	14116.9i	0.352770	+	0.611016i
$153$	−15758.9	−	9098.41i	−0.673199	−	0.388672i
$154$	−2879.70	−	10747.2i	−0.121424	−	0.453162i
$155$			27021.5i			1.12472i
$156$	18763.5	−	64055.6i	0.771019	−	2.63213i
$157$	−15748.9			−0.638926			−0.319463	−	0.947599i	$-0.603502\pi$
$157$	−15748.9			−0.638926			−0.319463	+	0.947599i	$0.603502\pi$
$158$	25093.0	−	6723.64i	1.00517	−	0.269333i
$159$	15312.7	−	26522.5i	0.605702	−	1.04911i
$160$	−21649.9	+	12499.6i	−0.845699	+	0.488265i
$161$	8864.47	+	8864.47i	0.341980	+	0.341980i
$162$	101.162	−	377.543i	0.00385469	−	0.0143859i
$163$	2761.28	+	739.883i	0.103929	+	0.0278476i	0.310409	−	0.950603i	$-0.399534\pi$
$163$	2761.28	+	739.883i	0.103929	+	0.0278476i	−0.206480	+	0.978451i	$0.566201\pi$
$164$	18001.2	−	18001.2i	0.669288	−	0.669288i
$165$	−16037.2	−	27777.3i	−0.589063	−	1.02029i
$166$	−11152.2	−	6438.70i	−0.404709	−	0.233659i
$167$	6856.78	+	25589.9i	0.245860	+	0.917561i	0.972949	+	0.231019i	$0.0742058\pi$
$167$	6856.78	+	25589.9i	0.245860	+	0.917561i	−0.727090	+	0.686543i	$0.759127\pi$
$168$			23455.4i			0.831044i
$169$	24047.0	+	15410.2i	0.841951	+	0.539554i
$170$	26076.4			0.902299
$171$	−28387.0	+	7606.27i	−0.970793	+	0.260123i
$172$	−33139.7	+	57399.6i	−1.12019	+	1.94023i
$173$	45826.6	−	26458.0i	1.53118	−	0.884026i	0.531869	−	0.846826i	$-0.321490\pi$
$173$	45826.6	−	26458.0i	1.53118	−	0.884026i	0.999308	−	0.0371990i	$-0.0118436\pi$
$174$	−55014.6	−	55014.6i	−1.81710	−	1.81710i
$175$	−1128.90	+	4213.10i	−0.0368620	+	0.137571i
$176$	3323.57	+	890.547i	0.107295	+	0.0287496i
$177$	−36455.3	+	36455.3i	−1.16363	+	1.16363i
$178$	−30384.2	−	52627.0i	−0.958976	−	1.66100i
$179$	−33039.9	−	19075.6i	−1.03118	−	0.595349i	−0.113854	−	0.993497i	$-0.536320\pi$
$179$	−33039.9	−	19075.6i	−1.03118	−	0.595349i	−0.917321	+	0.398148i	$0.869653\pi$
$180$	26430.4	+	98639.7i	0.815754	+	3.04444i
$181$		−	23773.2i		−	0.725656i	−0.931856	−	0.362828i	$-0.881811\pi$
$181$		−	23773.2i		−	0.725656i	0.931856	−	0.362828i	$-0.118189\pi$
$182$	−23514.6	−	6888.01i	−0.709895	−	0.207946i
$183$	82080.9			2.45098
$184$	−39959.6	+	10707.1i	−1.18028	+	0.316255i
$185$	23818.6	−	41255.0i	0.695941	−	1.20541i
$186$	78069.1	−	45073.2i	2.25659	−	1.30285i
$187$	7515.31	+	7515.31i	0.214913	+	0.214913i
$188$	9008.27	−	33619.3i	0.254874	−	0.951204i
$189$	−15664.9	−	4197.40i	−0.438535	−	0.117505i
$190$	29779.2	−	29779.2i	0.824908	−	0.824908i
$191$	7556.32	+	13087.9i	0.207130	+	0.358760i	0.950809	−	0.309777i	$-0.100254\pi$
$191$	7556.32	+	13087.9i	0.207130	+	0.358760i	−0.743679	+	0.668537i	$0.766921\pi$
$192$	81280.5	+	46927.3i	2.20487	+	1.27298i
$193$	15078.6	+	56274.0i	0.404805	+	1.51075i	0.804415	+	0.594067i	$0.202479\pi$
$193$	15078.6	+	56274.0i	0.404805	+	1.51075i	−0.399610	+	0.916685i	$0.630855\pi$
$194$			19050.6i			0.506181i
$195$	−70616.3	−	1635.36i	−1.85710	−	0.0430076i
$196$	−51851.3			−1.34973
$197$	−24810.2	+	6647.88i	−0.639291	+	0.171297i	−0.563882	−	0.825855i	$-0.690693\pi$
$197$	−24810.2	+	6647.88i	−0.639291	+	0.171297i	−0.0754087	+	0.997153i	$0.524026\pi$
$198$	−33097.5	+	57326.6i	−0.844239	+	1.46226i
$199$	−57761.4	+	33348.6i	−1.45859	+	0.842115i	−0.998942	−	0.0459886i	$-0.985356\pi$
$199$	−57761.4	+	33348.6i	−1.45859	+	0.842115i	−0.459644	+	0.888103i	$0.652023\pi$
$200$	−10177.8	−	10177.8i	−0.254444	−	0.254444i
$201$	−12805.3	+	47790.1i	−0.316956	+	1.18289i
$202$	−18195.7	−	4875.52i	−0.445929	−	0.119486i
$203$	−12698.5	+	12698.5i	−0.308150	+	0.308150i
$204$	−27349.8	−	47371.2i	−0.657193	−	1.13829i
$205$	−23331.1	−	13470.2i	−0.555171	−	0.320528i
$206$	9287.08	+	34659.8i	0.218849	+	0.816756i
$207$		−	74583.5i		−	1.74061i
$208$	5480.67	−	5232.57i	0.126680	−	0.120945i
$209$	17164.9			0.392960
$210$	58533.5	−	15684.0i	1.32729	−	0.355646i
$211$	14547.1	−	25196.3i	0.326747	−	0.565942i	−0.655117	−	0.755527i	$-0.727381\pi$
$211$	14547.1	−	25196.3i	0.326747	−	0.565942i	0.981864	+	0.189585i	$0.0607142\pi$
$212$	49320.6	−	28475.3i	1.09738	−	0.633572i
$213$	75830.3	+	75830.3i	1.67141	+	1.67141i
$214$	996.408	−	3718.65i	0.0217575	−	0.0812002i
$215$	67750.2	+	18153.6i	1.46566	+	0.392723i
$216$	37842.4	−	37842.4i	0.811093	−	0.811093i
$217$	−10403.9	−	18020.0i	−0.220940	−	0.382680i
$218$	−42278.8	−	24409.7i	−0.889631	−	0.513628i
$219$	−22363.5	−	83461.7i	−0.466285	−	1.74020i
$220$		−	59645.0i		−	1.23234i
$221$	22742.5	−	5532.81i	0.465643	−	0.113282i
$222$	−158922.			−3.22462
$223$	−20898.8	+	5599.80i	−0.420253	+	0.112606i	−0.462747	−	0.886490i	$-0.653136\pi$
$223$	−20898.8	+	5599.80i	−0.420253	+	0.112606i	0.0424944	+	0.999097i	$0.486470\pi$
$224$	9625.21	−	16671.4i	0.191829	−	0.332257i
$225$	22473.1	−	12974.9i	0.443914	−	0.256294i
$226$	94584.0	+	94584.0i	1.85183	+	1.85183i
$227$	18887.8	−	70490.2i	0.366547	−	1.36797i	−0.498765	−	0.866737i	$-0.666213\pi$
$227$	18887.8	−	70490.2i	0.366547	−	1.36797i	0.865312	−	0.501234i	$-0.167120\pi$
$228$	−85331.0	−	22864.4i	−1.64149	−	0.439835i
$229$	13183.8	−	13183.8i	0.251403	−	0.251403i	−0.570143	−	0.821546i	$-0.693112\pi$
$229$	13183.8	−	13183.8i	0.251403	−	0.251403i	0.821546	+	0.570143i	$0.193112\pi$
$230$	53439.8	+	92560.5i	1.01020	+	1.74973i
$231$	21389.7	+	12349.4i	0.400849	+	0.231430i
$232$	−15338.2	−	57242.9i	−0.284969	−	1.06352i
$233$			2695.47i			0.0496503i	0.999692	+	0.0248251i	$0.00790290\pi$
$233$			2695.47i			0.0496503i	−0.999692	+	0.0248251i	$0.992097\pi$
$234$	69945.8	+	127900.i	1.27741	+	2.33581i
$235$	−36832.7			−0.666957
$236$	−92604.9	+	24813.4i	−1.66269	+	0.445515i
$237$	−28833.8	+	49941.6i	−0.513340	+	0.889131i
$238$	−17389.8	+	10040.0i	−0.307001	+	0.177247i
$239$	−60150.4	−	60150.4i	−1.05303	−	1.05303i	−0.998513	−	0.0545214i	$-0.982637\pi$
$239$	−60150.4	−	60150.4i	−1.05303	−	1.05303i	−0.0545214	−	0.998513i	$-0.517363\pi$
$240$	−4850.28	+	18101.5i	−0.0842062	+	0.314262i
$241$	−50325.8	−	13484.7i	−0.866475	−	0.232171i	−0.201912	−	0.979404i	$-0.564716\pi$
$241$	−50325.8	−	13484.7i	−0.866475	−	0.232171i	−0.664563	+	0.747232i	$0.731382\pi$
$242$	−40628.3	+	40628.3i	−0.693743	+	0.693743i
$243$	−29307.2	−	50761.5i	−0.496319	−	0.859651i
$244$	132187.	+	76317.9i	2.22028	+	1.28188i
$245$	14201.8	+	53002.0i	0.236599	+	0.882998i
$246$			89875.8i			1.48516i
$247$	19653.4	−	32290.3i	0.322139	−	0.529271i
$248$	68664.7			1.11643
$249$	27611.9	−	7398.58i	0.445346	−	0.119330i
$250$	40245.2	−	69706.7i	0.643923	−	1.11531i
$251$	−32906.3	+	18998.4i	−0.522313	+	0.301558i	−0.737881	−	0.674931i	$-0.764173\pi$
$251$	−32906.3	+	18998.4i	−0.522313	+	0.301558i	0.215567	+	0.976489i	$0.430840\pi$
$252$	−55604.2	−	55604.2i	−0.875602	−	0.875602i
$253$	−11274.7	+	42077.8i	−0.176142	+	0.657373i
$254$	29055.9	+	7785.51i	0.450368	+	0.120676i
$255$	−40931.4	+	40931.4i	−0.629472	+	0.629472i
$256$	41483.7	+	71851.9i	0.632991	+	1.09637i
$257$	3349.07	+	1933.59i	0.0507058	+	0.0292750i	0.525139	−	0.851017i	$-0.324013\pi$
$257$	3349.07	+	1933.59i	0.0507058	+	0.0292750i	−0.474433	+	0.880292i	$0.657347\pi$
$258$	−60562.3	−	226021.i	−0.909835	−	3.39555i
$259$			36682.7i			0.546841i
$260$	−112203.	−	68292.0i	−1.65981	−	1.01024i
$261$	106842.			1.56842
$262$	179291.	−	48040.9i	2.61190	−	0.699856i
$263$	−1730.83	+	2997.89i	−0.0250232	+	0.0433415i	−0.878266	−	0.478173i	$-0.841299\pi$
$263$	−1730.83	+	2997.89i	−0.0250232	+	0.0433415i	0.853243	+	0.521514i	$0.174633\pi$
$264$	−70585.3	+	40752.4i	−1.01276	+	0.584717i
$265$	−42615.8	−	42615.8i	−0.606847	−	0.606847i
$266$	−8393.42	+	31324.7i	−0.118625	+	0.442714i
$267$	130300.	+	34913.9i	1.82778	+	0.489751i
$268$	−65057.0	+	65057.0i	−0.905783	+	0.905783i
$269$	−35350.0	−	61227.9i	−0.488522	−	0.846146i	0.511390	−	0.859348i	$-0.329131\pi$
$269$	−35350.0	−	61227.9i	−0.488522	−	0.846146i	−0.999913	+	0.0132029i	$0.995797\pi$
$270$	−119741.	−	69132.4i	−1.64253	−	0.948318i
$271$	−3225.01	−	12035.9i	−0.0439129	−	0.163885i	0.940487	−	0.339829i	$-0.110369\pi$
$271$	−3225.01	−	12035.9i	−0.0439129	−	0.163885i	−0.984400	+	0.175944i	$0.943702\pi$
$272$		−	6209.73i		−	0.0839334i
$273$	47722.0	−	26098.2i	0.640315	−	0.350175i
$274$	48023.3			0.639663
$275$	−14640.1	+	3922.79i	−0.193588	+	0.0518717i
$276$	112099.	−	194161.i	1.47157	−	2.54884i
$277$	−49200.6	+	28406.0i	−0.641225	+	0.370212i	−0.785086	−	0.619386i	$-0.787381\pi$
$277$	−49200.6	+	28406.0i	−0.641225	+	0.370212i	0.143861	+	0.989598i	$0.454048\pi$
$278$	−96557.6	−	96557.6i	−1.24939	−	1.24939i
$279$	−32040.2	+	119576.i	−0.411611	+	1.53615i
$280$	44585.0	+	11946.5i	0.568687	+	0.152379i
$281$	28752.4	−	28752.4i	0.364135	−	0.364135i	−0.501198	−	0.865333i	$-0.667107\pi$
$281$	28752.4	−	28752.4i	0.364135	−	0.364135i	0.865333	+	0.501198i	$0.167107\pi$
$282$	61438.8	+	106415.i	0.772582	+	1.33815i
$283$	35550.4	+	20525.0i	0.443886	+	0.256278i	0.705245	−	0.708964i	$-0.250837\pi$
$283$	35550.4	+	20525.0i	0.443886	+	0.256278i	−0.261358	+	0.965242i	$0.584170\pi$
$284$	51614.1	+	192626.i	0.639929	+	2.38825i
$285$			93487.0i			1.15096i
$286$	−20126.9	−	82730.9i	−0.246062	−	1.01143i
$287$	20745.2			0.251857
$288$	−110626.	+	29642.3i	−1.33375	+	0.357377i
$289$	−32169.9	+	55720.0i	−0.385172	+	0.667137i
$290$	−132595.	+	76553.7i	−1.57663	+	0.910270i
$291$	−29903.2	−	29903.2i	−0.353128	−	0.353128i
$292$	41586.7	−	155204.i	0.487741	−	1.82027i
$293$	−16479.2	−	4415.59i	−0.191956	−	0.0514344i	0.161560	−	0.986863i	$-0.448347\pi$
$293$	−16479.2	−	4415.59i	−0.191956	−	0.0514344i	−0.353516	+	0.935428i	$0.615014\pi$
$294$	129441.	−	129441.i	1.49754	−	1.49754i
$295$	50728.1	+	87863.7i	0.582914	+	1.00964i
$296$	−104834.	−	60525.7i	−1.19651	−	0.690806i
$297$	−14585.5	−	54433.8i	−0.165352	−	0.617101i
$298$			1422.14i			0.0160144i
$299$	66246.6	+	69387.7i	0.741005	+	0.776140i
$300$	78004.7			0.866719
$301$	−52170.5	+	13979.1i	−0.575827	+	0.154293i
$302$	−98767.9	+	171071.i	−1.08293	+	1.87570i
$303$	36214.2	−	20908.3i	0.394452	−	0.227737i
$304$	−7091.49	−	7091.49i	−0.0767344	−	0.0767344i
$305$	41806.2	−	156023.i	0.449409	−	1.67722i
$306$	115394.	+	30919.6i	1.23236	+	0.330211i
$307$	−33947.8	+	33947.8i	−0.360193	+	0.360193i	−0.863884	−	0.503691i	$-0.831975\pi$
$307$	−33947.8	+	33947.8i	−0.360193	+	0.360193i	0.503691	+	0.863884i	$0.331975\pi$
$308$	22964.6	+	39775.9i	0.242079	+	0.419294i
$309$	−68982.2	−	39826.9i	−0.722471	−	0.417119i
$310$	−45914.3	−	171354.i	−0.477776	−	1.78308i
$311$		−	30532.2i		−	0.315673i	−0.987465	−	0.157836i	$-0.949548\pi$
$311$		−	30532.2i		−	0.315673i	0.987465	−	0.157836i	$-0.0504518\pi$
$312$	−4155.64	+	179444.i	−0.0426903	+	1.84340i
$313$	−10587.5			−0.108070			−0.0540350	−	0.998539i	$-0.517208\pi$
$313$	−10587.5			−0.108070			−0.0540350	+	0.998539i	$0.517208\pi$
$314$	99870.1	−	26760.1i	1.01292	−	0.271412i
$315$	−41608.4	+	72067.9i	−0.419334	+	0.726308i
$316$	−92870.3	+	53618.7i	−0.930043	+	0.536960i
$317$	14491.7	+	14491.7i	0.144212	+	0.144212i	0.775527	−	0.631315i	$-0.217484\pi$
$317$	14491.7	+	14491.7i	0.144212	+	0.144212i	−0.631315	+	0.775527i	$0.717484\pi$
$318$	−52038.1	+	194209.i	−0.514597	+	1.92050i
$319$	−60277.3	−	16151.3i	−0.592342	−	0.158717i
$320$	130600.	−	130600.i	1.27539	−	1.27539i
$321$	4273.02	+	7401.09i	0.0414691	+	0.0718266i
$322$	−71275.6	−	41151.0i	−0.687431	−	0.396888i
$323$	−8017.70	−	29922.5i	−0.0768502	−	0.286809i
$324$			1613.47i			0.0153699i
$325$	−9383.01	+	32032.1i	−0.0888332	+	0.303262i
$326$	−18767.6			−0.176593
$327$	104679.	−	28048.7i	0.978958	−	0.262311i
$328$	−34229.3	+	59286.8i	−0.318163	+	0.551075i
$329$	24562.9	−	14181.4i	0.226928	−	0.131017i
$330$	148897.	+	148897.i	1.36728	+	1.36728i
$331$	9079.85	−	33886.5i	0.0828749	−	0.309293i	−0.912028	−	0.410127i	$-0.865484\pi$
$331$	9079.85	−	33886.5i	0.0828749	−	0.309293i	0.994903	+	0.100834i	$0.0321510\pi$
$332$	51346.5	+	13758.2i	0.465838	+	0.124821i
$333$	154319.	−	154319.i	1.39166	−	1.39166i
$334$	−86963.4	−	150625.i	−0.779549	−	1.35022i
$335$	84319.5	+	48681.9i	0.751343	+	0.433788i
$336$	−3734.92	−	13938.9i	−0.0330829	−	0.123467i
$337$		−	68997.6i		−	0.607539i	−0.952746	−	0.303769i	$-0.901755\pi$
$337$		−	68997.6i		−	0.607539i	0.952746	−	0.303769i	$-0.0982452\pi$
$338$	−178676.	−	56862.4i	−1.56399	−	0.497728i
$339$	−296932.			−2.58379
$340$	−103975.	+	27860.1i	−0.899440	+	0.241004i
$341$	36152.3	−	62617.5i	0.310904	−	0.538502i
$342$	167089.	−	96468.9i	1.42855	−	0.824774i
$343$	−67371.7	−	67371.7i	−0.572650	−	0.572650i
$344$	46130.4	−	172161.i	0.389825	−	1.45485i
$345$	−229173.	−	61406.6i	−1.92542	−	0.515913i
$346$	−245649.	+	245649.i	−2.05193	+	2.05193i
$347$	67786.7	+	117410.i	0.562971	+	0.975094i	0.997235	+	0.0743084i	$0.0236749\pi$
$347$	67786.7	+	117410.i	0.562971	+	0.975094i	−0.434265	+	0.900785i	$0.642992\pi$
$348$	278139.	+	160584.i	2.29670	+	1.32600i
$349$	35819.2	+	133679.i	0.294080	+	1.09752i	0.941945	+	0.335767i	$0.108995\pi$
$349$	35819.2	+	133679.i	0.294080	+	1.09752i	−0.647865	+	0.761755i	$0.724338\pi$
$350$		−	28635.2i		−	0.233757i
$351$	−119100.	−	34887.4i	−0.966712	−	0.283174i
$352$	66893.1			0.539878
$353$	38151.7	−	10222.7i	0.306171	−	0.0820383i	−0.102462	−	0.994737i	$-0.532672\pi$
$353$	38151.7	−	10222.7i	0.306171	−	0.0820383i	0.408633	+	0.912699i	$0.366005\pi$
$354$	169234.	−	293122.i	1.35046	−	2.33906i
$355$	182764.	−	105519.i	1.45022	−	0.837286i
$356$	177379.	+	177379.i	1.39959	+	1.39959i
$357$	11536.7	−	43055.7i	0.0905204	−	0.337827i
$358$	241932.	+	64825.6i	1.88768	+	0.505802i
$359$	−17939.3	+	17939.3i	−0.139193	+	0.139193i	−0.773270	−	0.634077i	$-0.781380\pi$
$359$	−17939.3	+	17939.3i	−0.139193	+	0.139193i	0.634077	+	0.773270i	$0.281380\pi$
$360$	−137306.	−	237821.i	−1.05946	−	1.83504i
$361$	69533.8	+	40145.3i	0.533558	+	0.308050i
$362$	40394.9	+	150756.i	0.308255	+	1.15042i
$363$		−	127546.i		−	0.967954i
$364$	101119.	+	2341.77i	0.763189	+	0.0176743i
$365$	−170038.			−1.27632
$366$	−520508.	+	139470.i	−3.88567	+	1.04116i
$367$	109265.	−	189253.i	0.811242	−	1.40511i	−0.100753	−	0.994911i	$-0.532125\pi$
$367$	109265.	−	189253.i	0.811242	−	1.40511i	0.911995	−	0.410201i	$-0.134541\pi$
$368$	22042.0	−	12725.9i	0.162763	−	0.0939711i
$369$	−87272.7	−	87272.7i	−0.640952	−	0.640952i
$370$	−80943.9	+	302087.i	−0.591263	+	2.20662i
$371$	44827.5	+	12011.5i	0.325684	+	0.0872669i
$372$	−263131.	+	263131.i	−1.90146	+	1.90146i
$373$	97162.0	+	168290.i	0.698359	+	1.20959i	0.969035	+	0.246923i	$0.0794195\pi$
$373$	97162.0	+	168290.i	0.698359	+	1.20959i	−0.270676	+	0.962671i	$0.587247\pi$
$374$	−60427.5	−	34887.8i	−0.432008	−	0.249420i
$375$	46244.9	+	172588.i	0.328852	+	1.22729i
$376$			93596.0i			0.662036i
$377$	−99399.3	+	94899.6i	−0.699360	+	0.667701i
$378$	106470.			0.745149
$379$	188740.	−	50572.7i	1.31397	−	0.352077i	0.467254	−	0.884123i	$-0.345244\pi$
$379$	188740.	−	50572.7i	1.31397	−	0.352077i	0.846715	+	0.532047i	$0.178577\pi$
$380$	−86923.3	+	150556.i	−0.601962	+	1.04263i
$381$	−57829.0	+	33387.6i	−0.398378	+	0.230004i
$382$	−70156.4	−	70156.4i	−0.480774	−	0.480774i
$383$	−31354.7	+	117017.i	−0.213749	+	0.797723i	0.772854	+	0.634584i	$0.218829\pi$
$383$	−31354.7	+	117017.i	−0.213749	+	0.797723i	−0.986603	+	0.163139i	$0.947838\pi$
$384$	−398841.	−	106869.i	−2.70481	−	0.724753i
$385$	34368.6	−	34368.6i	0.231868	−	0.231868i
$386$	−191239.	−	331236.i	−1.28352	−	2.22312i
$387$	278283.	+	160667.i	1.85808	+	1.07276i
$388$	−20353.7	−	75961.2i	−0.135201	−	0.504578i
$389$		−	3999.65i		−	0.0264316i	−0.999913	−	0.0132158i	$-0.995793\pi$
$389$		−	3999.65i		−	0.0264316i	0.999913	−	0.0132158i	$-0.00420684\pi$
$390$	450586.	−	109619.i	2.96243	−	0.720704i
$391$	78617.8			0.514242
$392$	134684.	−	36088.5i	0.876483	−	0.234853i
$393$	−206020.	+	356837.i	−1.33390	+	2.31038i
$394$	146036.	−	84313.9i	0.940736	−	0.543134i
$395$	80245.3	+	80245.3i	0.514311	+	0.514311i
$396$	70722.9	−	263942.i	0.450993	−	1.68313i
$397$	−177669.	−	47606.1i	−1.12727	−	0.302052i	−0.353450	−	0.935453i	$-0.614992\pi$
$397$	−177669.	−	47606.1i	−1.12727	−	0.302052i	−0.773824	+	0.633401i	$0.781658\pi$
$398$	309624.	−	309624.i	1.95465	−	1.95465i
$399$	−35994.5	−	62344.3i	−0.226095	−	0.391608i
$400$	7669.04	+	4427.72i	0.0479315	+	0.0276733i
$401$	−80819.4	−	301622.i	−0.502605	−	1.87575i	−0.482399	−	0.875951i	$-0.660235\pi$
$401$	−80819.4	−	301622.i	−0.502605	−	1.87575i	−0.0202056	−	0.999796i	$-0.506432\pi$
$402$		−	324815.i		−	2.00995i
$403$	−76401.4	−	139704.i	−0.470426	−	0.860200i
$404$	77761.3			0.476432
$405$	1649.28	−	441.922i	0.0100550	−	0.00269424i
$406$	58949.6	−	102104.i	0.357626	−	0.619426i
$407$	−110391.	+	63734.1i	−0.666413	+	0.384754i
$408$	104011.	+	104011.i	0.624828	+	0.624828i
$409$	−42559.5	+	158834.i	−0.254419	+	0.949505i	0.713994	+	0.700152i	$0.246885\pi$
$409$	−42559.5	+	158834.i	−0.254419	+	0.949505i	−0.968413	+	0.249353i	$0.919782\pi$
$410$	170840.	+	45776.4i	1.01630	+	0.272317i
$411$	−75380.9	+	75380.9i	−0.446249	+	0.446249i
$412$	−74061.3	−	128278.i	−0.436312	−	0.755714i
$413$	−67658.8	−	39062.8i	−0.396665	−	0.229015i
$414$	126730.	+	472965.i	0.739402	+	2.75948i
$415$		−	56254.2i		−	0.326632i
$416$	76590.8	−	125838.i	0.442578	−	0.727151i
$417$	303127.			1.74322
$418$	−108850.	+	29166.2i	−0.622981	+	0.166927i
$419$	−133921.	+	231958.i	−0.762817	+	1.32124i	0.178577	+	0.983926i	$0.442851\pi$
$419$	−133921.	+	231958.i	−0.762817	+	1.32124i	−0.941393	+	0.337311i	$0.890483\pi$
$420$	−216636.	+	125075.i	−1.22809	+	0.709040i
$421$	−10736.2	−	10736.2i	−0.0605743	−	0.0605743i	0.676171	−	0.736745i	$-0.263638\pi$
$421$	−10736.2	−	10736.2i	−0.0605743	−	0.0605743i	−0.736745	+	0.676171i	$0.763638\pi$
$422$	−49436.2	+	184498.i	−0.277600	+	1.03602i
$423$	−162992.	−	43673.7i	−0.910933	−	0.244084i
$424$	−108292.	+	108292.i	−0.602370	+	0.602370i
$425$	13676.7	+	23688.8i	0.0757188	+	0.131149i
$426$	−609720.	−	352022.i	−3.35978	−	1.93977i
$427$	32192.6	+	120144.i	0.176563	+	0.658943i
$428$			15892.0i			0.0867545i
$429$	161453.	+	98267.7i	0.877266	+	0.533945i
$430$	−460478.			−2.49042
$431$	73459.2	−	19683.3i	0.395450	−	0.105960i	−0.0556136	−	0.998452i	$-0.517711\pi$
$431$	73459.2	−	19683.3i	0.395450	−	0.105960i	0.451063	+	0.892492i	$0.351045\pi$
$432$	−16462.9	+	28514.6i	−0.0882142	+	0.152792i
$433$	287163.	−	165794.i	1.53163	−	0.884286i	0.532341	−	0.846530i	$-0.321312\pi$
$433$	287163.	−	165794.i	1.53163	−	0.884286i	0.999287	−	0.0377562i	$-0.0120210\pi$
$434$	96594.3	+	96594.3i	0.512828	+	0.512828i
$435$	87966.3	−	328295.i	0.464876	−	1.73494i
$436$	194659.	+	52158.7i	1.02400	+	0.274381i
$437$	89781.3	−	89781.3i	0.470135	−	0.470135i
$438$	283632.	+	491266.i	1.47845	+	2.56076i
$439$	−230242.	−	132931.i	−1.19469	−	0.689756i	−0.235326	−	0.971917i	$-0.575616\pi$
$439$	−230242.	−	132931.i	−1.19469	−	0.689756i	−0.959367	+	0.282160i	$0.908949\pi$
$440$	41512.9	+	154928.i	0.214426	+	0.800248i
$441$			251384.i			1.29259i
$442$	−134818.	+	73729.3i	−0.690087	+	0.377395i
$443$	422.417			0.00215246			0.00107623	−	0.999999i	$-0.499657\pi$
$443$	422.417			0.00215246			0.00107623	+	0.999999i	$0.499657\pi$
$444$	633676.	−	169793.i	3.21441	−	0.861299i
$445$	132732.	−	229898.i	0.670277	−	1.16095i
$446$	123013.	−	71021.3i	0.618415	−	0.357042i
$447$	−2232.30	−	2232.30i	−0.0111722	−	0.0111722i
$448$	−36810.3	+	137378.i	−0.183406	+	0.684481i
$449$	136854.	+	36669.8i	0.678834	+	0.181893i	0.581731	−	0.813381i	$-0.302376\pi$
$449$	136854.	+	36669.8i	0.678834	+	0.181893i	0.0971032	+	0.995274i	$0.469042\pi$
$450$	−120465.	+	120465.i	−0.594888	+	0.594888i
$451$	36043.7	+	62429.6i	0.177205	+	0.306928i
$452$	−478191.	−	276084.i	−2.34059	−	1.35134i
$453$	−113492.	−	423558.i	−0.553056	−	2.06403i
$454$			479101.i			2.32442i
$455$	−25302.4	−	104005.i	−0.122219	−	0.502378i
$456$	237561.			1.14247
$457$	−134308.	+	35987.8i	−0.643088	+	0.172315i	−0.565602	−	0.824679i	$-0.691356\pi$
$457$	−134308.	+	35987.8i	−0.643088	+	0.172315i	−0.0774862	+	0.996993i	$0.524689\pi$
$458$	−61202.4	+	106006.i	−0.291768	+	0.505357i
$459$	−88078.1	+	50851.9i	−0.418064	+	0.241369i
$460$	−311974.	−	311974.i	−1.47436	−	1.47436i
$461$	4115.18	−	15358.1i	0.0193636	−	0.0722660i	−0.955568	−	0.294771i	$-0.904757\pi$
$461$	4115.18	−	15358.1i	0.0193636	−	0.0722660i	0.974932	+	0.222505i	$0.0714233\pi$
$462$	−156625.	−	41967.5i	−0.733798	−	0.196621i
$463$	−146640.	+	146640.i	−0.684055	+	0.684055i	−0.960911	−	0.276856i	$-0.910707\pi$
$463$	−146640.	+	146640.i	−0.684055	+	0.684055i	0.276856	+	0.960911i	$0.410707\pi$
$464$	18230.2	+	31575.6i	0.0846749	+	0.146661i
$465$	341040.	+	196900.i	1.57725	+	0.910625i
$466$	−4580.07	−	17093.1i	−0.0210912	−	0.0787132i
$467$			229929.i			1.05429i	0.849775	+	0.527146i	$0.176738\pi$
$467$			229929.i			1.05429i	−0.849775	+	0.527146i	$0.823262\pi$
$468$	−415545.	−	435249.i	−1.89726	−	1.98722i
$469$	−74974.3			−0.340852
$470$	233571.	−	62585.3i	1.05736	−	0.283319i
$471$	−114759.	+	198768.i	−0.517301	+	0.895992i
$472$	223271.	−	128906.i	1.00219	−	0.578613i
$473$	−132711.	−	132711.i	−0.593178	−	0.593178i
$474$	97987.4	−	365694.i	0.436127	−	1.62765i
$475$	42671.2	+	11433.7i	0.189124	+	0.0506758i
$476$	58612.0	−	58612.0i	0.258686	−	0.258686i
$477$	−138053.	−	239115.i	−0.606749	−	1.05092i
$478$	483644.	+	279232.i	2.11675	+	1.22211i
$479$	36794.2	+	137318.i	0.160364	+	0.598488i	0.998586	+	0.0531586i	$0.0169289\pi$
$479$	36794.2	+	137318.i	0.160364	+	0.598488i	−0.838222	+	0.545330i	$0.816404\pi$
$480$			364327.i			1.58128i
$481$	−6499.15	+	280639.i	−0.0280910	+	1.21299i
$482$	342049.			1.47229
$483$	176473.	−	47285.7i	0.756455	−	0.202692i
$484$	118591.	−	205406.i	0.506246	−	0.876844i
$485$	−72072.0	+	41610.8i	−0.306396	+	0.176898i
$486$	272102.	+	272102.i	1.15202	+	1.15202i
$487$	66412.1	−	247853.i	0.280020	−	1.04505i	−0.672382	−	0.740204i	$-0.734729\pi$
$487$	66412.1	−	247853.i	0.280020	−	1.04505i	0.952402	−	0.304845i	$-0.0986045\pi$
$488$	−396472.	−	106234.i	−1.66484	−	0.446093i
$489$	29459.0	−	29459.0i	0.123197	−	0.123197i
$490$	−180119.	−	311976.i	−0.750185	−	1.29936i
$491$	−246510.	−	142323.i	−1.02252	−	0.590352i	−0.107687	−	0.994185i	$-0.534344\pi$
$491$	−246510.	−	142323.i	−1.02252	−	0.590352i	−0.914833	+	0.403833i	$0.867678\pi$
$492$	−96023.5	−	358365.i	−0.396686	−	1.48045i
$493$			112622.i			0.463370i
$494$	−69763.2	+	238160.i	−0.285873	+	0.975923i
$495$	−289169.			−1.18016
$496$	−40805.6	+	10933.8i	−0.165866	+	0.0444436i
$497$	−81254.1	+	140736.i	−0.328952	+	0.569762i
$498$	−162527.	+	93834.9i	−0.655339	+	0.378360i
$499$	−119045.	−	119045.i	−0.478089	−	0.478089i	0.426431	−	0.904520i	$-0.359771\pi$
$499$	−119045.	−	119045.i	−0.478089	−	0.478089i	−0.904520	+	0.426431i	$0.859771\pi$
$500$	−85996.0	+	320942.i	−0.343984	+	1.28377i
$501$	372936.	+	99927.8i	1.48579	+	0.398117i
$502$	176390.	−	176390.i	0.699951	−	0.699951i
$503$	−7841.79	−	13582.4i	−0.0309941	−	0.0536834i	0.850112	−	0.526601i	$-0.176534\pi$
$503$	−7841.79	−	13582.4i	−0.0309941	−	0.0536834i	−0.881106	+	0.472918i	$0.843201\pi$
$504$	183133.	+	105732.i	0.720949	+	0.416240i
$505$	−21298.4	−	79486.9i	−0.0835151	−	0.311683i
$506$		−	285990.i		−	1.11699i
$507$	369718.	−	191208.i	1.43832	−	0.743857i
$508$	−124174.			−0.481174
$509$	−339655.	+	91010.2i	−1.31100	+	0.351281i	−0.845598	−	0.533820i	$-0.820756\pi$
$509$	−339655.	+	91010.2i	−1.31100	+	0.351281i	−0.465400	+	0.885101i	$0.654089\pi$
$510$	190013.	−	329113.i	0.730539	−	1.26533i
$511$	113395.	−	65468.4i	0.434261	−	0.250720i
$512$	−64604.8	−	64604.8i	−0.246448	−	0.246448i
$513$	−42512.2	+	158658.i	−0.161539	+	0.602873i
$514$	−24523.3	−	6571.00i	−0.0928225	−	0.0248717i
$515$	−110839.	+	110839.i	−0.417907	+	0.417907i
$516$	482963.	+	836517.i	1.81391	+	3.14178i
$517$	85353.3	+	49278.7i	0.319330	+	0.184365i
$518$	−62330.3	−	232620.i	−0.232295	−	0.866937i
$519$		−	771175.i		−	2.86298i
$520$	338979.	+	99295.4i	1.25362	+	0.367217i
$521$	393166.			1.44844			0.724220	−	0.689569i	$-0.242200\pi$
$521$	393166.			1.44844			0.724220	+	0.689569i	$0.242200\pi$
$522$	−677532.	+	181544.i	−2.48650	+	0.666256i
$523$	−105537.	+	182796.i	−0.385836	+	0.668287i	−0.991885	−	0.127140i	$-0.959420\pi$
$523$	−105537.	+	182796.i	−0.385836	+	0.668287i	0.606049	+	0.795427i	$0.292754\pi$
$524$	−663566.	+	383110.i	−2.41669	+	1.39528i
$525$	44947.9	+	44947.9i	0.163076	+	0.163076i
$526$	5881.98	−	21951.8i	0.0212595	−	0.0793414i
$527$	−126044.	−	33773.3i	−0.453837	−	0.121605i
$528$	35457.8	−	35457.8i	0.127187	−	0.127187i
$529$	21195.3	+	36711.4i	0.0757406	+	0.131187i
$530$	342656.	+	197833.i	1.21985	+	0.704282i
$531$	120300.	+	448965.i	0.426654	+	1.59229i
$532$		−	133869.i		−	0.472996i
$533$	158710.	+	3675.48i	0.558664	+	0.0129378i
$534$	−885612.			−3.10571
$535$	16244.7	−	4352.75i	0.0567550	−	0.0152075i
$536$	123706.	−	214265.i	0.430588	−	0.745800i
$537$	−481509.	+	277999.i	−1.66977	+	0.964041i
$538$	328206.	+	328206.i	1.13392	+	1.13392i
$539$	38001.5	−	141823.i	0.130805	−	0.488169i
$540$	551307.	+	147722.i	1.89063	+	0.506592i
$541$	−153707.	+	153707.i	−0.525169	+	0.525169i	−0.919128	−	0.393959i	$-0.871105\pi$
$541$	−153707.	+	153707.i	−0.525169	+	0.525169i	0.393959	+	0.919128i	$0.371105\pi$
$542$	40902.2	+	70844.6i	0.139235	+	0.241162i
$543$	−300044.	−	173230.i	−1.01762	−	0.587522i
$544$	−31245.7	−	116610.i	−0.105582	−	0.394039i
$545$		−	213265.i		−	0.718002i
$546$	−258280.	+	246588.i	−0.866373	+	0.827153i
$547$	555728.			1.85732			0.928662	−	0.370926i	$-0.120960\pi$
$547$	555728.			1.85732			0.928662	+	0.370926i	$0.120960\pi$
$548$	−191485.	+	51308.2i	−0.637637	+	0.170854i
$549$	370002.	−	640863.i	1.22761	−	2.12628i
$550$	86173.2	−	49752.1i	0.284870	−	0.164470i
$551$	128614.	+	128614.i	0.423627	+	0.423627i
$552$	−156041.	+	582353.i	−0.512107	+	1.91121i
$553$	−84409.9	−	22617.6i	−0.276022	−	0.0739598i
$554$	263734.	−	263734.i	0.859305	−	0.859305i
$555$	−347122.	−	601232.i	−1.12693	−	1.95190i
$556$	488169.	+	281845.i	1.57914	+	0.911717i
$557$	5258.75	+	19625.9i	0.0169501	+	0.0632586i	0.973883	−	0.227051i	$-0.0729084\pi$
$557$	5258.75	+	19625.9i	0.0169501	+	0.0632586i	−0.956933	+	0.290310i	$0.906242\pi$
$558$		−	812721.i		−	2.61019i
$559$	−401604.	+	97702.8i	−1.28521	+	0.312668i
$560$	−28398.0			−0.0905550
$561$	149614.	−	40088.9i	0.475385	−	0.127379i
$562$	−133476.	+	231187.i	−0.422600	+	0.731964i
$563$	172856.	−	99798.3i	0.545340	−	0.314852i	−0.201901	−	0.979406i	$-0.564712\pi$
$563$	172856.	−	99798.3i	0.545340	−	0.314852i	0.747240	+	0.664554i	$0.231378\pi$
$564$	−358671.	−	358671.i	−1.12756	−	1.12756i
$565$	−151236.	+	564421.i	−0.473760	+	1.76810i
$566$	−260315.	−	69751.3i	−0.812582	−	0.217731i
$567$	−929.715	+	929.715i	−0.00289190	+	0.00289190i
$568$	−268136.	−	464424.i	−0.831108	−	1.43952i
$569$	281029.	+	162252.i	0.868015	+	0.501149i	0.866688	−	0.498850i	$-0.166244\pi$
$569$	281029.	+	162252.i	0.868015	+	0.501149i	0.00132689	+	0.999999i	$0.499578\pi$
$570$	−158851.	−	592840.i	−0.488923	−	1.82468i
$571$		−	478957.i		−	1.46901i	−0.678605	−	0.734504i	$-0.737415\pi$
$571$		−	478957.i		−	1.46901i	0.678605	−	0.734504i	$-0.262585\pi$
$572$	168642.	+	308372.i	0.515436	+	0.942502i
$573$	220245.			0.670806
$574$	−131554.	+	35249.8i	−0.399283	+	0.106988i
$575$	−56056.8	+	97093.3i	−0.169548	+	0.293666i
$576$	732789.	−	423076.i	2.20869	−	1.27519i
$577$	−178299.	−	178299.i	−0.535547	−	0.535547i	0.386671	−	0.922218i	$-0.373625\pi$
$577$	−178299.	−	178299.i	−0.535547	−	0.535547i	−0.922218	+	0.386671i	$0.873625\pi$
$578$	109325.	−	408006.i	0.327237	−	1.22127i
$579$	820113.	+	219749.i	2.44634	+	0.655495i
$580$	446909.	−	446909.i	1.32851	−	1.32851i
$581$	21659.1	+	37514.6i	0.0641635	+	0.111134i
$582$	240440.	+	138818.i	0.709839	+	0.409826i
$583$	41738.6	+	155771.i	0.122801	+	0.458299i
$584$			432086.i			1.26691i
$585$	−331091.	+	543979.i	−0.967466	+	1.58954i
$586$	112004.			0.326167
$587$	−208395.	+	55839.4i	−0.604800	+	0.162056i	−0.548209	−	0.836342i	$-0.684690\pi$
$587$	−208395.	+	55839.4i	−0.604800	+	0.162056i	−0.0565918	+	0.998397i	$0.518023\pi$
$588$	−377829.	+	654420.i	−1.09280	+	1.89279i
$589$	−182511.	+	105372.i	−0.526087	+	0.303736i
$590$	−470984.	−	470984.i	−1.35301	−	1.35301i
$591$	−96883.4	+	361574.i	−0.277379	+	1.03519i
$592$	71937.7	+	19275.7i	0.205264	+	0.0550004i
$593$	−151916.	+	151916.i	−0.432011	+	0.432011i	−0.889312	−	0.457301i	$-0.848816\pi$
$593$	−151916.	+	151916.i	−0.432011	+	0.432011i	0.457301	+	0.889312i	$0.348816\pi$
$594$	184985.	+	320404.i	0.524282	+	0.908082i
$595$	−75966.2	−	43859.1i	−0.214579	−	0.123887i
$596$	−1519.42	−	5670.55i	−0.00427745	−	0.0159637i
$597$			972016.i			2.72725i
$598$	−537999.	−	327451.i	−1.50445	−	0.915681i
$599$	−544593.			−1.51781			−0.758907	−	0.651199i	$-0.774266\pi$
$599$	−544593.			−1.51781			−0.758907	+	0.651199i	$0.774266\pi$
$600$	−202617.	+	54291.2i	−0.562826	+	0.150809i
$601$	317137.	−	549298.i	0.878008	−	1.52075i	0.0244843	−	0.999700i	$-0.492206\pi$
$601$	317137.	−	549298.i	0.878008	−	1.52075i	0.853524	−	0.521054i	$-0.174461\pi$
$602$	307082.	−	177294.i	0.847347	−	0.489216i
$603$	315407.	+	315407.i	0.867436	+	0.867436i
$604$	211048.	−	787640.i	0.578504	−	2.15901i
$605$	−242446.	−	64963.1i	−0.662375	−	0.177483i
$606$	−194123.	+	194123.i	−0.528604	+	0.528604i
$607$	95785.7	+	165906.i	0.259970	+	0.450281i	0.966234	−	0.257668i	$-0.0829540\pi$
$607$	95785.7	+	165906.i	0.259970	+	0.450281i	−0.706264	+	0.707949i	$0.749621\pi$
$608$	−168851.	−	97486.2i	−0.456769	−	0.263716i
$609$	67737.8	+	252801.i	0.182640	+	0.681623i
$610$			1.06044e6i			2.84989i
$611$	190429.	−	104142.i	0.510096	−	0.278961i
$612$	−493147.			−1.31666
$613$	−184028.	+	49310.1i	−0.489736	+	0.131224i	−0.495233	−	0.868760i	$-0.664917\pi$
$613$	−184028.	+	49310.1i	−0.489736	+	0.131224i	0.00549620	+	0.999985i	$0.498250\pi$
$614$	157594.	−	272960.i	0.418025	−	0.724041i
$615$	−340017.	+	196309.i	−0.898980	+	0.519026i
$616$	−87334.6	−	87334.6i	−0.230157	−	0.230157i
$617$	179296.	−	669141.i	0.470977	−	1.75771i	−0.165294	−	0.986244i	$-0.552857\pi$
$617$	179296.	−	669141.i	0.470977	−	1.75771i	0.636271	−	0.771465i	$-0.280476\pi$
$618$	505118.	+	135346.i	1.32256	+	0.354379i
$619$	−103746.	+	103746.i	−0.270763	+	0.270763i	−0.829407	−	0.558644i	$-0.811322\pi$
$619$	−103746.	+	103746.i	−0.270763	+	0.270763i	0.558644	+	0.829407i	$0.311322\pi$
$620$	366151.	+	634192.i	0.952526	+	1.64982i
$621$	−361007.	−	208427.i	−0.936121	−	0.540470i
$622$	51879.6	+	193617.i	0.134096	+	0.500453i
$623$			204418.i			0.526676i
$624$	−26104.2	−	107301.i	−0.0670412	−	0.275571i
$625$	475057.			1.21615
$626$	67139.8	−	17990.1i	0.171329	−	0.0459075i
$627$	125077.	−	216640.i	0.318158	−	0.551065i
$628$	−369625.	+	213403.i	−0.937220	+	0.541104i
$629$	162667.	+	162667.i	0.411148	+	0.411148i
$630$	141400.	−	527712.i	0.356261	−	1.32958i
$631$	−484445.	−	129807.i	−1.21671	−	0.326015i	−0.407316	−	0.913287i	$-0.633535\pi$
$631$	−484445.	−	129807.i	−1.21671	−	0.326015i	−0.809389	+	0.587272i	$0.800202\pi$
$632$	203912.	−	203912.i	0.510516	−	0.510516i
$633$	−212003.	−	367200.i	−0.529097	−	0.916422i
$634$	−116522.	−	67274.1i	−0.289888	−	0.167367i
$635$	34010.6	+	126929.i	0.0843464	+	0.314785i
$636$		−	829973.i		−	2.05187i
$637$	−223285.	−	233872.i	−0.550275	−	0.576366i
$638$	409687.			1.00649
$639$	933886.	−	250234.i	2.28714	−	0.612837i
$640$	−406284.	+	703704.i	−0.991903	+	1.71803i
$641$	411467.	−	237561.i	1.00143	−	0.578174i	0.0927567	−	0.995689i	$-0.470432\pi$
$641$	411467.	−	237561.i	1.00143	−	0.578174i	0.908670	+	0.417515i	$0.137099\pi$
$642$	−39672.7	−	39672.7i	−0.0962547	−	0.0962547i
$643$	−73868.4	+	275681.i	−0.178664	+	0.666783i	0.817235	+	0.576305i	$0.195506\pi$
$643$	−73868.4	+	275681.i	−0.178664	+	0.666783i	−0.995898	+	0.0904777i	$0.971161\pi$
$644$	328165.	+	87931.5i	0.791262	+	0.212018i
$645$	722799.	−	722799.i	1.73739	−	1.73739i
$646$	101687.	+	176127.i	0.243669	+	0.422048i
$647$	−90764.9	−	52403.1i	−0.216825	−	0.125184i	0.387654	−	0.921805i	$-0.373285\pi$
$647$	−90764.9	−	52403.1i	−0.216825	−	0.125184i	−0.604479	+	0.796621i	$0.706619\pi$
$648$	−1122.97	−	4191.00i	−0.00267436	−	0.00998085i
$649$		−	271478.i		−	0.644533i
$650$	5073.37	−	219072.i	0.0120080	−	0.518514i
$651$	−303243.			−0.715531
$652$	74832.6	−	20051.3i	0.176034	−	0.0471681i
$653$	95438.9	−	165305.i	0.223820	−	0.387668i	−0.732145	−	0.681149i	$-0.761481\pi$
$653$	95438.9	−	165305.i	0.223820	−	0.387668i	0.955965	+	0.293481i	$0.0948139\pi$
$654$	−616153.	+	355736.i	−1.44057	+	0.831711i
$655$	573359.	+	573359.i	1.33642	+	1.33642i
$656$	10901.0	−	40683.1i	0.0253314	−	0.0945381i
$657$	−752454.	−	201620.i	−1.74321	−	0.467091i
$658$	−131667.	+	131667.i	−0.304105	+	0.304105i
$659$	184755.	+	320004.i	0.425426	+	0.736860i	0.996460	−	0.0840664i	$-0.0267908\pi$
$659$	184755.	+	320004.i	0.425426	+	0.736860i	−0.571034	+	0.820927i	$0.693457\pi$
$660$	−752785.	−	434620.i	−1.72816	−	0.997751i
$661$	−167346.	−	624543.i	−0.383011	−	1.42942i	−0.841278	−	0.540603i	$-0.818196\pi$
$661$	−167346.	−	624543.i	−0.383011	−	1.42942i	0.458266	−	0.888815i	$-0.348471\pi$
$662$			230316.i			0.525544i
$663$	95889.4	−	327351.i	0.218144	−	0.744709i
$664$	−142948.			−0.324222
$665$	−136840.	+	36666.2i	−0.309435	+	0.0829129i
$666$	−716387.	+	1.24082e6i	−1.61510	+	2.79744i
$667$	−399760.	+	230802.i	−0.898562	+	0.518785i
$668$	507680.	+	507680.i	1.13772	+	1.13772i
$669$	−81609.1	+	304569.i	−0.182342	+	0.680509i
$670$	−617424.	−	165438.i	−1.37541	−	0.368541i
$671$	−305623.	+	305623.i	−0.678798	+	0.678798i
$672$	−140274.	−	242961.i	−0.310626	−	0.538020i
$673$	−438672.	−	253268.i	−0.968523	−	0.559177i	−0.0697375	−	0.997565i	$-0.522216\pi$
$673$	−438672.	−	253268.i	−0.968523	−	0.559177i	−0.898786	+	0.438388i	$0.855549\pi$
$674$	117239.	+	437542.i	0.258079	+	0.963163i
$675$		−	145036.i		−	0.318323i
$676$	773193.	+	35831.1i	1.69198	+	0.0784092i
$677$	125231.			0.273234			0.136617	−	0.990624i	$-0.456377\pi$
$677$	125231.			0.273234			0.136617	+	0.990624i	$0.456377\pi$
$678$	1.88297e6	−	504539.i	4.09622	−	1.09758i
$679$	32042.1	−	55498.6i	0.0694995	−	0.120377i
$680$	250686.	−	144733.i	0.542140	−	0.313005i
$681$	−752031.	−	752031.i	−1.62159	−	1.62159i
$682$	−122858.	+	458513.i	−0.264141	+	0.985786i
$683$	236156.	+	63277.9i	0.506242	+	0.135647i	0.502896	−	0.864347i	$-0.332268\pi$
$683$	236156.	+	63277.9i	0.506242	+	0.135647i	0.00334667	+	0.999994i	$0.498935\pi$
$684$	−563172.	+	563172.i	−1.20373	+	1.20373i
$685$	104894.	+	181681.i	0.223547	+	0.387194i
$686$	541708.	+	312755.i	1.15111	+	0.664594i
$687$	−70326.4	−	262462.i	−0.149006	−	0.556100i
$688$			109656.i			0.231663i
$689$	340822.	+	99835.5i	0.717942	+	0.210303i
$690$	1.55762e6			3.27162
$691$	−483617.	+	129585.i	−1.01285	+	0.271393i	−0.726820	−	0.686827i	$-0.759003\pi$
$691$	−483617.	+	129585.i	−1.01285	+	0.271393i	−0.286031	+	0.958220i	$0.592336\pi$
$692$	717030.	−	1.24193e6i	1.49736	−	2.59350i
$693$	192840.	−	111336.i	0.401542	−	0.231831i
$694$	−629364.	−	629364.i	−1.30672	−	1.30672i
$695$	154392.	−	576198.i	0.319635	−	1.19289i
$696$	−834233.	−	223532.i	−1.72214	−	0.461447i
$697$	91993.4	−	91993.4i	0.189361	−	0.189361i
$698$	−454289.	−	786852.i	−0.932441	−	1.61504i
$699$	34019.7	+	19641.3i	0.0696267	+	0.0401990i
$700$	30593.9	+	114178.i	0.0624366	+	0.233016i
$701$			790148.i			1.60795i	0.594663	+	0.803975i	$0.297285\pi$
$701$			790148.i			1.60795i	−0.594663	+	0.803975i	$0.702715\pi$
$702$	814541.	+	18863.5i	1.65287	+	0.0382779i
$703$	371530.			0.751767
$704$	−477374.	+	127912.i	−0.963192	+	0.258087i
$705$	−268392.	+	464869.i	−0.539997	+	0.935302i
$706$	−224565.	+	129653.i	−0.450540	+	0.260119i
$707$	44807.6	+	44807.6i	0.0896423	+	0.0896423i
$708$	−361620.	+	1.34958e6i	−0.721416	+	2.69236i
$709$	863561.	+	231390.i	1.71791	+	0.460313i	0.977342	−	0.211668i	$-0.0678895\pi$
$709$	863561.	+	231390.i	1.71791	+	0.460313i	0.740569	+	0.671981i	$0.234556\pi$
$710$	−979688.	+	979688.i	−1.94344	+	1.94344i
$711$	259953.	+	450251.i	0.514227	+	0.890668i
$712$	−584197.	−	337286.i	−1.15239	−	0.665332i
$713$	−138427.	−	516617.i	−0.272296	−	1.01622i
$714$			292637.i			0.574027i
$715$	269024.	−	256846.i	0.526235	−	0.502413i
$716$	−1.03392e6			−2.01680
$717$	−1.19747e6	+	320860.i	−2.32930	+	0.624133i
$718$	83278.6	−	144243.i	0.161542	−	0.279798i
$719$	689802.	−	398258.i	1.33434	−	0.770382i	0.348380	−	0.937354i	$-0.386732\pi$
$719$	689802.	−	398258.i	1.33434	−	0.770382i	0.985962	+	0.166971i	$0.0533987\pi$
$720$	119467.	+	119467.i	0.230453	+	0.230453i
$721$	31240.7	−	116592.i	0.0600966	−	0.224284i
$722$	−509156.	−	136428.i	−0.976735	−	0.261715i
$723$	−536905.	+	536905.i	−1.02712	+	1.02712i
$724$	−322136.	−	557955.i	−0.614556	−	1.06444i
$725$	−139088.	−	80302.6i	−0.264615	−	0.152775i
$726$	216724.	+	808823.i	0.411181	+	1.53455i
$727$		−	60581.5i		−	0.114623i	−0.998356	−	0.0573114i	$-0.981747\pi$
$727$		−	60581.5i		−	0.114623i	0.998356	−	0.0573114i	$-0.0182528\pi$
$728$	−264288.	+	64296.2i	−0.498671	+	0.121317i
$729$	−859042.			−1.61644
$730$	1.07828e6	−	288925.i	2.02342	−	0.542175i
$731$	−169358.	+	293336.i	−0.316935	+	0.548947i
$732$	1.92643e6	−	1.11222e6i	3.59526	−	2.07573i
$733$	572778.	+	572778.i	1.06605	+	1.06605i	0.997658	+	0.0683928i	$0.0217871\pi$
$733$	572778.	+	572778.i	1.06605	+	1.06605i	0.0683928	+	0.997658i	$0.478213\pi$
$734$	−371322.	+	1.38579e6i	−0.689222	+	2.57221i
$735$	772428.	+	206971.i	1.42983	+	0.383121i
$736$	349885.	−	349885.i	0.645907	−	0.645907i
$737$	−130264.	−	225623.i	−0.239822	−	0.415383i
$738$	701724.	+	405140.i	1.28841	+	0.743863i
$739$	40364.3	+	150642.i	0.0739110	+	0.275839i	0.992984	−	0.118247i	$-0.0377276\pi$
$739$	40364.3	+	150642.i	0.0739110	+	0.275839i	−0.919073	+	0.394087i	$0.871061\pi$
$740$		−	1.29100e6i		−	2.35756i
$741$	−264328.	−	483339.i	−0.481401	−	0.880269i
$742$	−304680.			−0.553395
$743$	96406.5	−	25832.0i	0.174634	−	0.0467930i	−0.170442	−	0.985368i	$-0.554520\pi$
$743$	96406.5	−	25832.0i	0.174634	−	0.0467930i	0.345076	+	0.938575i	$0.387853\pi$
$744$	500345.	−	866622.i	0.903906	−	1.56561i
$745$	−5380.23	+	3106.27i	−0.00969366	+	0.00559664i
$746$	−902098.	−	902098.i	−1.62097	−	1.62097i
$747$	66702.3	−	248937.i	0.119536	−	0.446116i
$748$	278219.	+	74548.5i	0.497259	+	0.133240i
$749$	−9157.31	+	9157.31i	−0.0163232	+	0.0163232i
$750$	−586516.	−	1.01587e6i	−1.04269	−	1.80600i
$751$	521537.	+	301110.i	0.924710	+	0.533882i	0.885135	−	0.465335i	$-0.154066\pi$
$751$	521537.	+	301110.i	0.924710	+	0.533882i	0.0395753	+	0.999217i	$0.487399\pi$
$752$	−14903.8	−	55621.7i	−0.0263549	−	0.0983578i
$753$			553750.i			0.976616i
$754$	469081.	−	770695.i	0.825097	−	1.35563i
$755$	−862924.			−1.51383
$756$	−424530.	+	113753.i	−0.742788	+	0.199030i
$757$	−96392.8	+	166957.i	−0.168210	+	0.291349i	−0.937791	−	0.347201i	$-0.887132\pi$
$757$	−96392.8	+	166957.i	−0.168210	+	0.291349i	0.769580	+	0.638550i	$0.220465\pi$
$758$	−1.11094e6	+	641404.i	−1.93354	+	1.11633i
$759$	448910.	+	448910.i	0.779249	+	0.779249i
$760$	120997.	−	451567.i	0.209482	−	0.781799i
$761$	86176.8	+	23091.0i	0.148806	+	0.0398725i	0.332453	−	0.943120i	$-0.392124\pi$
$761$	86176.8	+	23091.0i	0.148806	+	0.0398725i	−0.183647	+	0.982992i	$0.558790\pi$
$762$	309986.	−	309986.i	0.533866	−	0.533866i
$763$	82111.4	+	142221.i	0.141044	+	0.244295i
$764$	354692.	+	204782.i	0.607666	+	0.350836i
$765$	135071.	+	504090.i	0.230801	+	0.861361i
$766$		−	795331.i		−	1.35547i
$767$	−510699.	−	310835.i	−0.868109	−	0.528371i
$768$	1.20913e6			2.04999
$769$	1.06047e6	−	284153.i	1.79327	−	0.480507i	0.800379	−	0.599494i	$-0.204632\pi$
$769$	1.06047e6	−	284153.i	1.79327	−	0.480507i	0.992896	+	0.118988i	$0.0379650\pi$
$770$	−159547.	+	276344.i	−0.269097	+	0.466089i
$771$	48807.9	−	28179.2i	0.0821072	−	0.0474046i
$772$	1.11643e6	+	1.11643e6i	1.87325	+	1.87325i
$773$	−25594.4	+	95519.7i	−0.0428338	+	0.159858i	−0.984030	−	0.178003i	$-0.943036\pi$
$773$	−25594.4	+	95519.7i	−0.0428338	+	0.159858i	0.941196	+	0.337860i	$0.109703\pi$
$774$	−2.03771e6	−	546003.i	−3.40142	−	0.911408i
$775$	131583.	−	131583.i	0.219077	−	0.219077i
$776$	105738.	+	183143.i	0.175593	+	0.304136i
$777$	462975.	+	267299.i	0.766859	+	0.442746i
$778$	6796.11	+	25363.4i	0.0112280	+	0.0419034i
$779$		−	210112.i		−	0.346239i
$780$	−1.67952e6	+	918494.i	−2.76055	+	1.50969i
$781$	−564698.			−0.925794
$782$	−498548.	+	133586.i	−0.815255	+	0.218447i
$783$	298576.	−	517150.i	0.487003	−	0.843515i
$784$	−74292.6	+	42892.9i	−0.120869	+	0.0697835i
$785$	319377.	+	319377.i	0.518280	+	0.518280i
$786$	700128.	−	2.61291e6i	1.13327	−	4.22941i
$787$	−562536.	−	150731.i	−0.908241	−	0.243362i	−0.225689	−	0.974199i	$-0.572463\pi$
$787$	−562536.	−	150731.i	−0.908241	−	0.243362i	−0.682552	+	0.730837i	$0.739130\pi$
$788$	−492213.	+	492213.i	−0.792684	+	0.792684i
$789$	25224.4	+	43690.0i	0.0405198	+	0.0701823i
$790$	−645219.	−	372518.i	−1.03384	−	0.596888i
$791$	−116458.	−	434629.i	−0.186131	−	0.694649i
$792$			734812.i			1.17146i
$793$	225001.	+	924861.i	0.357799	+	1.47072i
$794$	1.20756e6			1.91544
$795$	−848390.	+	227326.i	−1.34234	+	0.359678i
$796$	−903770.	+	1.56538e6i	−1.42637	+	2.47054i
$797$	432314.	−	249597.i	0.680586	−	0.392936i	−0.119490	−	0.992835i	$-0.538126\pi$
$797$	432314.	−	249597.i	0.680586	−	0.392936i	0.800076	+	0.599899i	$0.204793\pi$
$798$	334190.	+	334190.i	0.524793	+	0.524793i
$799$	46036.1	−	171809.i	0.0721115	−	0.269124i
$800$	166293.	+	44558.2i	0.259833	+	0.0696221i
$801$	859962.	−	859962.i	1.34034	−	1.34034i
$802$	1.02502e6	+	1.77538e6i	1.59361	+	2.76022i
$803$	394034.	+	227495.i	0.611086	+	0.352810i
$804$	347033.	+	1.29515e6i	0.536857	+	2.00358i
$805$		−	359531.i		−	0.554811i
$806$	721875.	+	756103.i	1.11120	+	1.16389i
$807$	−1.03035e6			−1.58211
$808$	−201985.	+	54121.7i	−0.309383	+	0.0828990i
$809$	−434066.	+	751824.i	−0.663222	+	1.14873i	0.316542	+	0.948578i	$0.397478\pi$
$809$	−434066.	+	751824.i	−0.663222	+	1.14873i	−0.979764	+	0.200155i	$0.935855\pi$
$810$	−9707.84	+	5604.82i	−0.0147963	+	0.00854264i
$811$	−607624.	−	607624.i	−0.923833	−	0.923833i	0.0734651	−	0.997298i	$-0.476594\pi$
$811$	−607624.	−	607624.i	−0.923833	−	0.923833i	−0.997298	+	0.0734651i	$0.976594\pi$
$812$	−125964.	+	470103.i	−0.191044	+	0.712986i
$813$	−175406.	−	46999.8i	−0.265377	−	0.0711075i
$814$	591737.	−	591737.i	0.893059	−	0.893059i
$815$	−40992.6	−	71001.3i	−0.0617149	−	0.106893i
$816$	−78373.5	−	45249.0i	−0.117703	−	0.0679561i
$817$	141583.	+	528394.i	0.212113	+	0.791615i
$818$		−	1.07955e6i		−	1.61338i
$819$	11353.3	−	490244.i	0.0169260	−	0.730878i
$820$	−730103.			−1.08582
$821$	−255430.	+	68442.2i	−0.378953	+	0.101540i	−0.443267	−	0.896390i	$-0.646181\pi$
$821$	−255430.	+	68442.2i	−0.378953	+	0.101540i	0.0643141	+	0.997930i	$0.479514\pi$
$822$	349936.	−	606106.i	0.517898	−	0.897026i
$823$	−558509.	+	322455.i	−0.824575	+	0.476069i	−0.851992	−	0.523555i	$-0.824605\pi$
$823$	−558509.	+	322455.i	−0.824575	+	0.476069i	0.0274163	+	0.999624i	$0.491272\pi$
$824$	281656.	+	281656.i	0.414824	+	0.414824i
$825$	−57169.1	+	213358.i	−0.0839950	+	0.313474i
$826$	495427.	+	132749.i	0.726138	+	0.194568i
$827$	820167.	−	820167.i	1.19920	−	1.19920i	0.224792	−	0.974407i	$-0.427830\pi$
$827$	820167.	−	820167.i	1.19920	−	1.19920i	0.974407	−	0.224792i	$-0.0721702\pi$
$828$	−1.01063e6	−	1.75047e6i	−1.47412	−	2.55325i
$829$	−1.17667e6	−	679351.i	−1.71217	−	0.988519i	−0.931631	−	0.363406i	$-0.881614\pi$
$829$	−1.17667e6	−	679351.i	−1.71217	−	0.988519i	−0.780535	−	0.625113i	$-0.785053\pi$
$830$	95585.8	+	356731.i	0.138751	+	0.517827i
$831$			827953.i			1.19896i
$832$	−305955.	+	1.04448e6i	−0.441988	+	1.50888i
$833$	−264982.			−0.381879
$834$	−1.92225e6	+	515067.i	−2.76362	+	0.740511i
$835$	379895.	−	657997.i	0.544867	−	0.943737i
$836$	402859.	−	232591.i	0.576421	−	0.332797i
$837$	489245.	+	489245.i	0.698353	+	0.698353i
$838$	455110.	−	1.69849e6i	0.648080	−	2.41867i
$839$	490865.	+	131527.i	0.697330	+	0.186849i	0.590034	−	0.807378i	$-0.299114\pi$
$839$	490865.	+	131527.i	0.697330	+	0.186849i	0.107295	+	0.994227i	$0.465781\pi$
$840$	475660.	−	475660.i	0.674121	−	0.674121i
$841$	23012.0	+	39858.0i	0.0325359	+	0.0563538i
$842$	86325.7	+	49840.2i	0.121763	+	0.0703000i
$843$	−153374.	−	572400.i	−0.215823	−	0.805461i
$844$		−	788474.i		−	1.10688i
$845$	−175148.	−	800165.i	−0.245296	−	1.12064i
$846$	1.10781e6			1.54784
$847$	186694.	−	50024.4i	0.260233	−	0.0697293i
$848$	47111.1	−	81598.8i	0.0655136	−	0.113473i
$849$	518096.	−	299123.i	0.718778	−	0.414987i
$850$	−126981.	−	126981.i	−0.175752	−	0.175752i
$851$	−244038.	+	910762.i	−0.336975	+	1.25761i
$852$	2.80725e6	+	752202.i	3.86725	+	1.03623i
$853$	572753.	−	572753.i	0.787171	−	0.787171i	−0.193859	−	0.981029i	$-0.562100\pi$
$853$	572753.	−	572753.i	0.787171	−	0.787171i	0.981029	+	0.193859i	$0.0621003\pi$
$854$	−408293.	−	707184.i	−0.559830	−	0.969654i
$855$	729919.	+	421419.i	0.998487	+	0.576477i
$856$	−11060.8	−	41279.6i	−0.0150953	−	0.0563362i
$857$			68607.9i			0.0934141i	0.998909	+	0.0467071i	$0.0148727\pi$
$857$			68607.9i			0.0934141i	−0.998909	+	0.0467071i	$0.985127\pi$
$858$	−1.19081e6	−	348819.i	−1.61759	−	0.473834i
$859$	507339.			0.687563			0.343781	−	0.939050i	$-0.388292\pi$
$859$	507339.			0.687563			0.343781	+	0.939050i	$0.388292\pi$
$860$	1.83608e6	−	491975.i	2.48253	−	0.665191i
$861$	151166.	−	261827.i	0.203915	−	0.353190i
$862$	−432389.	+	249640.i	−0.581916	+	0.335970i
$863$	−722013.	−	722013.i	−0.969445	−	0.969445i	0.0301019	−	0.999547i	$-0.490417\pi$
$863$	−722013.	−	722013.i	−0.969445	−	0.969445i	−0.999547	+	0.0301019i	$0.990417\pi$
$864$	−165674.	+	618302.i	−0.221935	+	0.828272i
$865$	−1.46588e6	−	392782.i	−1.95915	−	0.524952i
$866$	−1.53931e6	+	1.53931e6i	−2.05253	+	2.05253i
$867$	468831.	+	812039.i	0.623703	+	1.08029i
$868$	−488355.	−	281952.i	−0.648181	−	0.374227i
$869$	−78593.5	−	293315.i	−0.104075	−	0.388414i
$870$			2.23132e6i			2.94797i
$871$	−573586.	−	13283.4i	−0.756071	−	0.0175094i
$872$	−541929.			−0.712705
$873$	−368273.	+	98678.4i	−0.483216	+	0.129477i
$874$	−416786.	+	721894.i	−0.545620	+	0.945041i
$875$	−234485.	+	135380.i	−0.306267	+	0.176823i
$876$	−1.65581e6	−	1.65581e6i	−2.15775	−	2.15775i
$877$	−238238.	+	889116.i	−0.309750	+	1.15600i	0.619028	+	0.785369i	$0.287527\pi$
$877$	−238238.	+	889116.i	−0.309750	+	1.15600i	−0.928779	+	0.370635i	$0.879140\pi$
$878$	1.68593e6	+	451745.i	2.18701	+	0.586009i
$879$	−175810.	+	175810.i	−0.227544	+	0.227544i
$880$	−49340.0	−	85459.4i	−0.0637139	−	0.110356i
$881$	789311.	+	455709.i	1.01694	+	0.587132i	0.913217	−	0.407474i	$-0.133590\pi$
$881$	789311.	+	455709.i	1.01694	+	0.587132i	0.103725	+	0.994606i	$0.466924\pi$
$882$	−427146.	−	1.59413e6i	−0.549084	−	2.04921i
$883$		−	761482.i		−	0.976648i	−0.872662	−	0.488324i	$-0.837608\pi$
$883$		−	761482.i		−	0.976648i	0.872662	−	0.488324i	$-0.162392\pi$
$884$	458792.	−	438023.i	0.587099	−	0.560522i
$885$	1.47858e6			1.88781
$886$	−2678.72	+	717.761i	−0.00341240	+	0.000914351i
$887$	221118.	−	382987.i	0.281045	−	0.486785i	−0.690597	−	0.723240i	$-0.742652\pi$
$887$	221118.	−	382987.i	0.281045	−	0.486785i	0.971642	+	0.236455i	$0.0759856\pi$
$888$	−1.52780e6	+	882075.i	−1.93749	+	1.11861i
$889$	−71551.3	−	71551.3i	−0.0905345	−	0.0905345i
$890$	−451069.	+	1.68341e6i	−0.569460	+	2.12525i
$891$	−4413.16	−	1182.50i	−0.00555897	−	0.00148952i
$892$	−414612.	+	414612.i	−0.521090	+	0.521090i
$893$	−143632.	−	248778.i	−0.180114	−	0.311967i
$894$	17949.0	+	10362.8i	0.0224577	+	0.0129659i
$895$	283187.	+	1.05687e6i	0.353531	+	1.31939i
$896$		−	625712.i		−	0.779396i
$897$	1.35847e6	−	330491.i	1.68836	−	0.410747i
$898$	−930154.			−1.15346
$899$	740064.	−	198300.i	0.915693	−	0.245359i
$900$	351628.	−	609038.i	0.434109	−	0.751899i
$901$	252049.	−	145521.i	0.310481	−	0.179256i
$902$	−334647.	−	334647.i	−0.411314	−	0.411314i
$903$	−203725.	+	760311.i	−0.249844	+	0.932429i
$904$	1.43426e6	+	384308.i	1.75505	+	0.470265i
$905$	−482105.	+	482105.i	−0.588633	+	0.588633i
$906$	1.43940e6	+	2.49311e6i	1.75358	+	3.03729i
$907$	−1.15076e6	−	664392.i	−1.39885	−	0.807625i	−0.404575	−	0.914505i	$-0.632581\pi$
$907$	−1.15076e6	−	664392.i	−1.39885	−	0.807625i	−0.994272	+	0.106880i	$0.965914\pi$
$908$	−511873.	−	1.91033e6i	−0.620855	−	2.31706i
$909$		−	377000.i		−	0.456261i
$910$	337175.	+	616544.i	0.407167	+	0.744528i
$911$	−77944.7			−0.0939183			−0.0469591	−	0.998897i	$-0.514953\pi$
$911$	−77944.7			−0.0939183			−0.0469591	+	0.998897i	$0.514953\pi$
$912$	−141176.	+	37828.1i	−0.169735	+	0.0454805i
$913$	−75262.9	+	130359.i	−0.0902900	+	0.156387i
$914$	790554.	−	456427.i	0.946323	−	0.546360i
$915$	−1.66455e6	−	1.66455e6i	−1.98817	−	1.98817i
$916$	130778.	−	488069.i	0.155863	−	0.581688i
$917$	−603116.	−	161604.i	−0.717236	−	0.192183i
$918$	472133.	−	472133.i	0.560247	−	0.560247i
$919$	221789.	+	384149.i	0.262608	+	0.454851i	0.966934	−	0.255026i	$-0.0820840\pi$
$919$	221789.	+	384149.i	0.262608	+	0.454851i	−0.704326	+	0.709877i	$0.748751\pi$
$920$	1.02749e6	+	593220.i	1.21395	+	0.700874i
$921$	181088.	+	675829.i	0.213486	+	0.796741i
$922$			104384.i			0.122793i
$923$	−646564.	+	1.06230e6i	−0.758942	+	1.24693i
$924$	669353.			0.783991
$925$	−316880.	+	84907.9i	−0.370350	+	0.0992349i
$926$	680739.	−	1.17907e6i	0.793887	−	1.37505i
$927$	−621913.	+	359062.i	−0.723720	+	0.417840i
$928$	501218.	+	501218.i	0.582010	+	0.582010i
$929$	53117.1	−	198236.i	0.0615464	−	0.229694i	−0.928301	−	0.371830i	$-0.878730\pi$
$929$	53117.1	−	198236.i	0.0615464	−	0.229694i	0.989847	+	0.142136i	$0.0453970\pi$
$930$	−2.49725e6	−	669135.i	−2.88732	−	0.773656i
$931$	−302608.	+	302608.i	−0.349126	+	0.349126i
$932$	36524.5	+	63262.3i	0.0420487	+	0.0728305i
$933$	−385349.	−	222481.i	−0.442681	−	0.255582i
$934$	−390691.	−	1.45808e6i	−0.447857	−	1.67142i
$935$		−	304811.i		−	0.348664i
$936$	1.38231e6	+	841340.i	1.57781	+	0.960329i
$937$	774009.			0.881590			0.440795	−	0.897608i	$-0.354697\pi$
$937$	774009.			0.881590			0.440795	+	0.897608i	$0.354697\pi$
$938$	475443.	−	127394.i	0.540372	−	0.144792i
$939$	−77149.0	+	133626.i	−0.0874982	+	0.151551i
$940$	−864460.	+	499096.i	−0.978338	+	0.564844i
$941$	828766.	+	828766.i	0.935950	+	0.935950i	0.998069	−	0.0621190i	$-0.0197858\pi$
$941$	828766.	+	828766.i	0.935950	+	0.935950i	−0.0621190	+	0.998069i	$0.519786\pi$
$942$	389990.	−	1.45546e6i	0.439493	−	1.64021i
$943$	515066.	+	138011.i	0.579214	+	0.155200i
$944$	−112158.	+	112158.i	−0.125860	+	0.125860i
$945$	232554.	+	402795.i	0.260411	+	0.451045i
$946$	1.06708e6	+	616077.i	1.19238	+	0.688418i
$947$	−17653.9	−	65885.2i	−0.0196852	−	0.0734663i	0.955384	−	0.295365i	$-0.0954412\pi$
$947$	−17653.9	−	65885.2i	−0.0196852	−	0.0734663i	−0.975070	+	0.221899i	$0.928775\pi$
$948$			1.56283e6i			1.73898i
$949$	879118.	−	480772.i	0.976145	−	0.533834i
$950$	−290024.			−0.321356
$951$	288500.	−	77303.2i	0.318995	−	0.0854745i
$952$	−111451.	+	193039.i	−0.122973	+	0.212995i
$953$	−1.43168e6	+	826582.i	−1.57638	+	0.910123i	−0.581020	+	0.813889i	$0.697346\pi$
$953$	−1.43168e6	+	826582.i	−1.57638	+	0.910123i	−0.995359	+	0.0962331i	$0.969321\pi$
$954$	1.28175e6	+	1.28175e6i	1.40834	+	1.40834i
$955$	112177.	−	418652.i	0.122998	−	0.459035i
$956$	−2.22678e6	−	596664.i	−2.43647	−	0.652851i
$957$	−643074.	+	643074.i	−0.702161	+	0.702161i
$958$	−466654.	−	808269.i	−0.508469	−	0.880693i
$959$	−139902.	−	80772.6i	−0.152120	−	0.0878267i
$960$	−696660.	−	2.59997e6i	−0.755924	−	2.82115i
$961$		−	35790.5i		−	0.0387544i
$962$	−435641.	−	1.79069e6i	−0.470737	−	1.93495i
$963$	77047.3			0.0830816
$964$	−1.36386e6	+	365446.i	−1.46763	+	0.393250i
$965$	835416.	−	1.44698e6i	0.897115	−	1.55385i
$966$	−1.03874e6	+	599716.i	−1.11315	+	0.642675i
$967$	264009.	+	264009.i	0.282335	+	0.282335i	0.834040	−	0.551704i	$-0.186022\pi$
$967$	264009.	+	264009.i	0.282335	+	0.282335i	−0.551704	+	0.834040i	$0.686022\pi$
$968$	−165079.	+	616082.i	−0.176173	+	0.657488i
$969$	−436077.	−	116847.i	−0.464425	−	0.124442i
$970$	386334.	−	386334.i	0.410601	−	0.410601i
$971$	−82653.0	−	143159.i	−0.0876637	−	0.151838i	0.818859	−	0.573994i	$-0.194607\pi$
$971$	−82653.0	−	143159.i	−0.0876637	−	0.151838i	−0.906523	+	0.422156i	$0.861273\pi$
$972$	−1.37567e6	−	794245.i	−1.45607	−	0.840663i
$973$	118888.	+	443697.i	0.125578	+	0.468663i
$974$			1.68458e6i			1.77572i
$975$	335908.	+	351835.i	0.353354	+	0.370109i
$976$	252529.			0.265101
$977$	1.60136e6	−	429084.i	1.67765	−	0.449525i	0.710492	−	0.703705i	$-0.248473\pi$
$977$	1.60136e6	−	429084.i	1.67765	−	0.449525i	0.967157	+	0.254181i	$0.0818058\pi$
$978$	−136755.	+	236867.i	−0.142977	+	0.247644i
$979$	−615164.	+	355165.i	−0.641838	+	0.370566i
$980$	1.05151e6	+	1.05151e6i	1.09487	+	1.09487i
$981$	252874.	−	943740.i	0.262764	−	0.980650i
$982$	1.80505e6	+	483662.i	1.87183	+	0.501556i
$983$	1.27109e6	−	1.27109e6i	1.31544	−	1.31544i	0.398089	−	0.917347i	$-0.369674\pi$
$983$	1.27109e6	−	1.27109e6i	1.31544	−	1.31544i	0.917347	−	0.398089i	$-0.130326\pi$
$984$	498843.	+	864021.i	0.515197	+	0.892347i
$985$	637950.	+	368321.i	0.657528	+	0.379624i
$986$	−191364.	−	714181.i	−0.196837	−	0.734606i
$987$		−	413347.i		−	0.424307i
$988$	23717.9	−	1.02416e6i	0.0242976	−	1.04919i
$989$	−1.38830e6			−1.41935
$990$	1.83374e6	−	491350.i	1.87097	−	0.501326i
$991$	−21120.3	+	36581.5i	−0.0215057	+	0.0372490i	−0.876578	−	0.481260i	$-0.840179\pi$
$991$	−21120.3	+	36581.5i	−0.0215057	+	0.0372490i	0.855072	+	0.518509i	$0.173513\pi$
$992$	−711259.	+	410645.i	−0.722777	+	0.417295i
$993$	−361521.	−	361521.i	−0.366636	−	0.366636i
$994$	276130.	−	1.03053e6i	0.279474	−	1.04301i
$995$	1.84765e6	+	495077.i	1.86627	+	0.500065i
$996$	547795.	−	547795.i	0.552203	−	0.552203i
$997$	92901.4	+	160910.i	0.0934613	+	0.161880i	0.908965	−	0.416872i	$-0.136874\pi$
$997$	92901.4	+	160910.i	0.0934613	+	0.161880i	−0.815504	+	0.578751i	$0.803540\pi$
$998$	957189.	+	552633.i	0.961029	+	0.554850i
$999$	−315699.	−	1.17821e6i	−0.316332	−	1.18057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.5.f.a.7.1	yes	16
3.2	odd	2		117.5.bd.c.46.4		16
13.2	odd	12	inner	13.5.f.a.2.1	✓	16
13.4	even	6		169.5.d.c.99.1		16
13.6	odd	12		169.5.d.d.70.8		16
13.7	odd	12		169.5.d.c.70.1		16
13.9	even	3		169.5.d.d.99.8		16
39.2	even	12		117.5.bd.c.28.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.2.1	✓	16	13.2	odd	12	inner
13.5.f.a.7.1	yes	16	1.1	even	1	trivial
117.5.bd.c.28.4		16	39.2	even	12
117.5.bd.c.46.4		16	3.2	odd	2
169.5.d.c.70.1		16	13.7	odd	12
169.5.d.c.99.1		16	13.4	even	6
169.5.d.d.70.8		16	13.6	odd	12
169.5.d.d.99.8		16	13.9	even	3

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.34141 + 1.69918i) q^{2} +(7.28678 - 12.6211i) q^{3} +(23.4699 - 13.5504i) q^{4} +(-20.2793 - 20.2793i) q^{5} +(-24.7631 + 92.4170i) q^{6} +(21.3318 + 5.71584i) q^{7} +(-51.5321 + 51.5321i) q^{8} +(-65.6944 - 113.786i) q^{9} +O(q^{10})\)	\(q+(-6.34141 + 1.69918i) q^{2} +(7.28678 - 12.6211i) q^{3} +(23.4699 - 13.5504i) q^{4} +(-20.2793 - 20.2793i) q^{5} +(-24.7631 + 92.4170i) q^{6} +(21.3318 + 5.71584i) q^{7} +(-51.5321 + 51.5321i) q^{8} +(-65.6944 - 113.786i) q^{9} +(163.058 + 94.1415i) q^{10} +(19.8619 + 74.1257i) q^{11} -394.954i q^{12} +(162.185 + 47.5081i) q^{13} -144.986 q^{14} +(-403.718 + 108.176i) q^{15} +(22.4185 - 38.8299i) q^{16} +(119.941 - 69.2480i) q^{17} +(609.938 + 609.938i) q^{18} +(57.8912 - 216.053i) q^{19} +(-750.746 - 201.162i) q^{20} +(227.580 - 227.580i) q^{21} +(-251.905 - 436.312i) q^{22} +(491.603 + 283.827i) q^{23} +(274.887 + 1025.89i) q^{24} +197.503i q^{25} +(-1109.21 - 25.6875i) q^{26} -734.346 q^{27} +(578.107 - 154.903i) q^{28} +(-406.589 + 704.232i) q^{29} +(2376.33 - 1371.98i) q^{30} +(-666.232 - 666.232i) q^{31} +(225.607 - 841.977i) q^{32} +(1080.28 + 289.459i) q^{33} +(-642.931 + 642.931i) q^{34} +(-316.681 - 548.508i) q^{35} +(-3083.68 - 1780.37i) q^{36} +(429.906 + 1604.43i) q^{37} +1468.45i q^{38} +(1781.41 - 1700.77i) q^{39} +2090.07 q^{40} +(907.358 - 243.126i) q^{41} +(-1056.48 + 1829.88i) q^{42} +(-2118.01 + 1222.83i) q^{43} +(1470.59 + 1470.59i) q^{44} +(-975.267 + 3639.75i) q^{45} +(-3599.73 - 964.545i) q^{46} +(908.134 - 908.134i) q^{47} +(-326.717 - 565.890i) q^{48} +(-1656.95 - 956.642i) q^{49} +(-335.593 - 1252.45i) q^{50} -2018.38i q^{51} +(4450.22 - 1082.65i) q^{52} +2101.44 q^{53} +(4656.79 - 1247.78i) q^{54} +(1100.43 - 1906.01i) q^{55} +(-1393.82 + 804.723i) q^{56} +(-2304.98 - 2304.98i) q^{57} +(1381.73 - 5156.69i) q^{58} +(-3417.07 - 915.600i) q^{59} +(-8009.41 + 8009.41i) q^{60} +(2816.09 + 4877.60i) q^{61} +(5356.90 + 3092.81i) q^{62} +(-750.998 - 2802.76i) q^{63} +6440.06i q^{64} +(-2325.57 - 4252.44i) q^{65} -7342.31 q^{66} +(-3279.23 + 878.668i) q^{67} +(1876.67 - 3250.49i) q^{68} +(7164.41 - 4136.38i) q^{69} +(2940.22 + 2940.22i) q^{70} +(-1904.53 + 7107.80i) q^{71} +(9249.01 + 2478.26i) q^{72} +(4192.40 - 4192.40i) q^{73} +(-5452.42 - 9443.87i) q^{74} +(2492.71 + 1439.16i) q^{75} +(-1568.89 - 5855.19i) q^{76} +1694.76i q^{77} +(-8406.75 + 13812.2i) q^{78} -3957.00 q^{79} +(-1242.08 + 332.813i) q^{80} +(-29.7681 + 51.5598i) q^{81} +(-5340.82 + 3083.52i) q^{82} +(1386.98 + 1386.98i) q^{83} +(2257.49 - 8425.08i) q^{84} +(-3836.63 - 1028.02i) q^{85} +(11353.4 - 11353.4i) q^{86} +(5925.45 + 10263.2i) q^{87} +(-4843.38 - 2796.32i) q^{88} +(2395.70 + 8940.86i) q^{89} -24738.3i q^{90} +(3188.15 + 1940.46i) q^{91} +15383.8 q^{92} +(-13263.3 + 3553.88i) q^{93} +(-4215.77 + 7301.93i) q^{94} +(-5555.41 + 3207.42i) q^{95} +(-8982.71 - 8982.71i) q^{96} +(751.041 - 2802.92i) q^{97} +(12132.9 + 3251.01i) q^{98} +(7129.65 - 7129.65i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9} - 486 q^{10} - 100 q^{11} + 294 q^{13} + 808 q^{14} + 346 q^{15} + 230 q^{16} + 984 q^{17} + 2434 q^{18} - 1498 q^{19} - 3962 q^{20} - 1076 q^{21} - 1524 q^{22} - 1014 q^{23} - 2142 q^{24} + 614 q^{26} + 3352 q^{27} + 5764 q^{28} + 814 q^{29} + 9162 q^{30} + 4060 q^{31} - 4996 q^{32} - 5636 q^{33} - 2502 q^{34} - 4892 q^{35} - 15750 q^{36} - 1790 q^{37} + 6982 q^{39} + 18816 q^{40} + 4280 q^{41} - 1204 q^{42} - 1368 q^{43} + 10736 q^{44} - 6806 q^{45} - 15246 q^{46} + 1484 q^{47} - 3002 q^{48} - 11820 q^{49} - 13574 q^{50} + 1432 q^{52} + 7204 q^{53} + 13240 q^{54} + 6936 q^{55} + 8124 q^{56} + 12736 q^{57} + 3030 q^{58} - 2380 q^{59} - 6472 q^{60} - 162 q^{61} + 19614 q^{62} + 12004 q^{63} - 5248 q^{65} - 23872 q^{66} - 14854 q^{67} - 6444 q^{68} + 2412 q^{69} - 34524 q^{70} - 8050 q^{71} + 15420 q^{72} - 15448 q^{73} - 2882 q^{74} + 8280 q^{75} + 10622 q^{76} - 11672 q^{78} - 17064 q^{79} + 2564 q^{80} + 2128 q^{81} - 5346 q^{82} + 12788 q^{83} + 25948 q^{84} + 35382 q^{85} + 67260 q^{86} + 29342 q^{87} + 40836 q^{88} + 20492 q^{89} + 8996 q^{91} - 49884 q^{92} - 78920 q^{93} - 30606 q^{94} - 98574 q^{95} - 94664 q^{96} + 50944 q^{97} + 61484 q^{98} - 21632 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9 - 486 * q^10 - 100 * q^11 + 294 * q^13 + 808 * q^14 + 346 * q^15 + 230 * q^16 + 984 * q^17 + 2434 * q^18 - 1498 * q^19 - 3962 * q^20 - 1076 * q^21 - 1524 * q^22 - 1014 * q^23 - 2142 * q^24 + 614 * q^26 + 3352 * q^27 + 5764 * q^28 + 814 * q^29 + 9162 * q^30 + 4060 * q^31 - 4996 * q^32 - 5636 * q^33 - 2502 * q^34 - 4892 * q^35 - 15750 * q^36 - 1790 * q^37 + 6982 * q^39 + 18816 * q^40 + 4280 * q^41 - 1204 * q^42 - 1368 * q^43 + 10736 * q^44 - 6806 * q^45 - 15246 * q^46 + 1484 * q^47 - 3002 * q^48 - 11820 * q^49 - 13574 * q^50 + 1432 * q^52 + 7204 * q^53 + 13240 * q^54 + 6936 * q^55 + 8124 * q^56 + 12736 * q^57 + 3030 * q^58 - 2380 * q^59 - 6472 * q^60 - 162 * q^61 + 19614 * q^62 + 12004 * q^63 - 5248 * q^65 - 23872 * q^66 - 14854 * q^67 - 6444 * q^68 + 2412 * q^69 - 34524 * q^70 - 8050 * q^71 + 15420 * q^72 - 15448 * q^73 - 2882 * q^74 + 8280 * q^75 + 10622 * q^76 - 11672 * q^78 - 17064 * q^79 + 2564 * q^80 + 2128 * q^81 - 5346 * q^82 + 12788 * q^83 + 25948 * q^84 + 35382 * q^85 + 67260 * q^86 + 29342 * q^87 + 40836 * q^88 + 20492 * q^89 + 8996 * q^91 - 49884 * q^92 - 78920 * q^93 - 30606 * q^94 - 98574 * q^95 - 94664 * q^96 + 50944 * q^97 + 61484 * q^98 - 21632 * q^99

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