LMFDB - Embedded newform 26.5.f.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,5,Mod(7,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("26.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	26.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:	$2.68761904018$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.120336834816.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 46x^{5} + 445x^{4} + 68x^{3} + 32x^{2} + 1136x + 20164 $ x^8 - 2x^7 + 2x^6 + 46x^5 + 445x^4 + 68x^3 + 32x^2 + 1136*x + 20164
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.2
Root			$-2.16680 - 2.16680i$ of defining polynomial
Character	$\chi$	$=$	26.11
Dual form			26.5.f.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.732051 - 2.73205i) q^{2} +(5.99273 + 10.3797i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(27.8195 + 27.8195i) q^{5} +(32.7449 - 8.77397i) q^{6} +(-17.9912 - 67.1439i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-31.3257 + 54.2577i) q^{9} +O(q^{10})$	\(q+(0.732051 - 2.73205i) q^{2} +(5.99273 + 10.3797i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(27.8195 + 27.8195i) q^{5} +(32.7449 - 8.77397i) q^{6} +(-17.9912 - 67.1439i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-31.3257 + 54.2577i) q^{9} +(96.3695 - 55.6389i) q^{10} +(80.7257 + 21.6304i) q^{11} -95.8837i q^{12} +(-167.015 - 25.8273i) q^{13} -196.611 q^{14} +(-122.044 + 455.473i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-360.998 - 208.422i) q^{17} +(125.303 + 125.303i) q^{18} +(-5.11994 + 1.37188i) q^{19} +(-81.4611 - 304.017i) q^{20} +(589.119 - 589.119i) q^{21} +(118.191 - 204.712i) q^{22} +(400.168 - 231.037i) q^{23} +(-261.959 - 70.1918i) q^{24} +922.846i q^{25} +(-192.825 + 437.386i) q^{26} +219.917 q^{27} +(-143.929 + 537.152i) q^{28} +(-459.437 - 795.768i) q^{29} +(1155.03 + 666.859i) q^{30} +(67.6743 + 67.6743i) q^{31} +(174.851 - 46.8513i) q^{32} +(259.250 + 967.535i) q^{33} +(-833.689 + 833.689i) q^{34} +(1367.40 - 2368.41i) q^{35} +(434.061 - 250.605i) q^{36} +(-210.920 - 56.5158i) q^{37} +14.9922i q^{38} +(-732.796 - 1888.34i) q^{39} -890.223 q^{40} +(-761.848 + 2843.26i) q^{41} +(-1178.24 - 2040.77i) q^{42} +(1219.10 + 703.847i) q^{43} +(-472.762 - 472.762i) q^{44} +(-2380.88 + 637.956i) q^{45} +(-338.262 - 1262.41i) q^{46} +(-1373.25 + 1373.25i) q^{47} +(-383.535 + 664.302i) q^{48} +(-2105.30 + 1215.50i) q^{49} +(2521.26 + 675.570i) q^{50} -4996.07i q^{51} +(1053.80 + 846.996i) q^{52} +2519.79 q^{53} +(160.990 - 600.824i) q^{54} +(1644.00 + 2847.49i) q^{55} +(1362.16 + 786.444i) q^{56} +(-44.9222 - 44.9222i) q^{57} +(-2510.41 + 672.662i) q^{58} +(141.861 + 529.433i) q^{59} +(2667.43 - 2667.43i) q^{60} +(-1352.81 + 2343.14i) q^{61} +(234.431 - 135.349i) q^{62} +(4206.66 + 1127.17i) q^{63} -512.000i q^{64} +(-3927.76 - 5364.77i) q^{65} +2833.14 q^{66} +(-887.915 + 3313.75i) q^{67} +(1667.38 + 2887.98i) q^{68} +(4796.20 + 2769.09i) q^{69} +(-5469.62 - 5469.62i) q^{70} +(6794.09 - 1820.47i) q^{71} +(-366.912 - 1369.33i) q^{72} +(1208.41 - 1208.41i) q^{73} +(-308.808 + 534.871i) q^{74} +(-9578.88 + 5530.37i) q^{75} +(40.9595 + 10.9751i) q^{76} -5809.40i q^{77} +(-5695.49 + 619.672i) q^{78} -3300.68 q^{79} +(-651.689 + 2432.13i) q^{80} +(3855.28 + 6677.55i) q^{81} +(7210.21 + 4162.81i) q^{82} +(-1803.48 - 1803.48i) q^{83} +(-6438.01 + 1725.06i) q^{84} +(-4244.57 - 15841.0i) q^{85} +(2815.39 - 2815.39i) q^{86} +(5506.56 - 9537.65i) q^{87} +(-1637.70 + 945.525i) q^{88} +(-3985.42 - 1067.89i) q^{89} +6971.71i q^{90} +(1270.65 + 11678.7i) q^{91} -3696.59 q^{92} +(-296.886 + 1107.99i) q^{93} +(2746.51 + 4757.09i) q^{94} +(-180.599 - 104.269i) q^{95} +(1534.14 + 1534.14i) q^{96} +(-14270.6 + 3823.79i) q^{97} +(1779.61 + 6641.59i) q^{98} +(-3702.40 + 3702.40i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9	\( 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9} + 132 q^{10} + 192 q^{11} - 78 q^{13} - 344 q^{14} + 132 q^{15} + 256 q^{16} - 870 q^{17} - 360 q^{18} - 218 q^{19} - 144 q^{20} + 1914 q^{21} + 948 q^{22} + 264 q^{23} - 288 q^{24} - 520 q^{26} - 2268 q^{27} - 736 q^{28} - 252 q^{29} + 1728 q^{30} - 3376 q^{31} + 512 q^{32} + 1698 q^{33} + 1080 q^{34} + 6474 q^{35} + 2016 q^{36} + 2552 q^{37} - 5928 q^{39} - 960 q^{40} - 8472 q^{41} - 3828 q^{42} + 7290 q^{43} - 3792 q^{44} - 6282 q^{45} - 540 q^{46} + 4848 q^{47} + 9678 q^{49} + 2524 q^{50} - 832 q^{52} - 6840 q^{53} + 2268 q^{54} + 294 q^{55} + 4320 q^{56} - 4434 q^{57} - 7008 q^{58} - 4632 q^{59} + 9024 q^{60} + 8670 q^{61} + 3936 q^{62} + 8100 q^{63} - 2808 q^{65} - 984 q^{66} - 12446 q^{67} - 2160 q^{68} + 19206 q^{69} - 25896 q^{70} - 4554 q^{71} - 5472 q^{72} + 19294 q^{73} + 10112 q^{74} - 25992 q^{75} + 1744 q^{76} - 8580 q^{78} - 11328 q^{79} - 1152 q^{80} + 6048 q^{81} + 42672 q^{82} + 10344 q^{83} - 8592 q^{84} - 23178 q^{85} + 13536 q^{86} + 18372 q^{87} + 1440 q^{88} - 2538 q^{89} + 1456 q^{91} + 96 q^{92} - 162 q^{93} - 9696 q^{94} + 26568 q^{95} - 64282 q^{97} - 31676 q^{98} + 9504 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9 + 132 * q^10 + 192 * q^11 - 78 * q^13 - 344 * q^14 + 132 * q^15 + 256 * q^16 - 870 * q^17 - 360 * q^18 - 218 * q^19 - 144 * q^20 + 1914 * q^21 + 948 * q^22 + 264 * q^23 - 288 * q^24 - 520 * q^26 - 2268 * q^27 - 736 * q^28 - 252 * q^29 + 1728 * q^30 - 3376 * q^31 + 512 * q^32 + 1698 * q^33 + 1080 * q^34 + 6474 * q^35 + 2016 * q^36 + 2552 * q^37 - 5928 * q^39 - 960 * q^40 - 8472 * q^41 - 3828 * q^42 + 7290 * q^43 - 3792 * q^44 - 6282 * q^45 - 540 * q^46 + 4848 * q^47 + 9678 * q^49 + 2524 * q^50 - 832 * q^52 - 6840 * q^53 + 2268 * q^54 + 294 * q^55 + 4320 * q^56 - 4434 * q^57 - 7008 * q^58 - 4632 * q^59 + 9024 * q^60 + 8670 * q^61 + 3936 * q^62 + 8100 * q^63 - 2808 * q^65 - 984 * q^66 - 12446 * q^67 - 2160 * q^68 + 19206 * q^69 - 25896 * q^70 - 4554 * q^71 - 5472 * q^72 + 19294 * q^73 + 10112 * q^74 - 25992 * q^75 + 1744 * q^76 - 8580 * q^78 - 11328 * q^79 - 1152 * q^80 + 6048 * q^81 + 42672 * q^82 + 10344 * q^83 - 8592 * q^84 - 23178 * q^85 + 13536 * q^86 + 18372 * q^87 + 1440 * q^88 - 2538 * q^89 + 1456 * q^91 + 96 * q^92 - 162 * q^93 - 9696 * q^94 + 26568 * q^95 - 64282 * q^97 - 31676 * q^98 + 9504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.732051	−	2.73205i	0.183013	−	0.683013i
$2$	0.732051	−	2.73205i	0.183013	−	0.683013i
$3$	5.99273	+	10.3797i	0.665859	+	1.15330i	0.979052	+	0.203612i	$0.0652682\pi$
$3$	5.99273	+	10.3797i	0.665859	+	1.15330i	−0.313192	+	0.949690i	$0.601398\pi$
$4$	−6.92820	−	4.00000i	−0.433013	−	0.250000i
$5$	27.8195	+	27.8195i	1.11278	+	1.11278i	0.992773	+	0.120006i	$0.0382913\pi$
$5$	27.8195	+	27.8195i	1.11278	+	1.11278i	0.120006	+	0.992773i	$0.461709\pi$
$6$	32.7449	−	8.77397i	0.909581	−	0.243721i
$7$	−17.9912	−	67.1439i	−0.367167	−	1.37028i	−0.864460	−	0.502702i	$-0.832339\pi$
$7$	−17.9912	−	67.1439i	−0.367167	−	1.37028i	0.497293	−	0.867583i	$-0.334327\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	−31.3257	+	54.2577i	−0.386737	+	0.669848i
$10$	96.3695	−	55.6389i	0.963695	−	0.556389i
$11$	80.7257	+	21.6304i	0.667154	+	0.178763i	0.576473	−	0.817116i	$-0.304429\pi$
$11$	80.7257	+	21.6304i	0.667154	+	0.178763i	0.0906817	+	0.995880i	$0.471095\pi$
$12$		−	95.8837i		−	0.665859i
$13$	−167.015	−	25.8273i	−0.988253	−	0.152824i
$13$	−167.015	−	25.8273i	−0.988253	−	0.152824i
$14$	−196.611			−1.00312
$15$	−122.044	+	455.473i	−0.542416	+	2.02432i
$16$	32.0000	+	55.4256i	0.125000	+	0.216506i
$17$	−360.998	−	208.422i	−1.24913	−	0.721184i	−0.278192	−	0.960526i	$-0.589735\pi$
$17$	−360.998	−	208.422i	−1.24913	−	0.721184i	−0.970935	+	0.239342i	$0.923068\pi$
$18$	125.303	+	125.303i	0.386737	+	0.386737i
$19$	−5.11994	+	1.37188i	−0.0141827	+	0.00380023i	−0.265903	−	0.964000i	$-0.585670\pi$
$19$	−5.11994	+	1.37188i	−0.0141827	+	0.00380023i	0.251721	+	0.967800i	$0.419004\pi$
$20$	−81.4611	−	304.017i	−0.203653	−	0.760042i
$21$	589.119	−	589.119i	1.33587	−	1.33587i
$22$	118.191	−	204.712i	0.244195	−	0.422959i
$23$	400.168	−	231.037i	0.756461	−	0.436743i	−0.0715624	−	0.997436i	$-0.522799\pi$
$23$	400.168	−	231.037i	0.756461	−	0.436743i	0.828024	+	0.560693i	$0.189465\pi$
$24$	−261.959	−	70.1918i	−0.454790	−	0.121861i
$25$			922.846i			1.47655i
$26$	−192.825	+	437.386i	−0.285244	+	0.647021i
$27$	219.917			0.301669
$28$	−143.929	+	537.152i	−0.183583	+	0.685142i
$29$	−459.437	−	795.768i	−0.546298	−	0.946216i	−0.998524	−	0.0543128i	$-0.982703\pi$
$29$	−459.437	−	795.768i	−0.546298	−	0.946216i	0.452226	−	0.891904i	$-0.350630\pi$
$30$	1155.03	+	666.859i	1.28337	+	0.740954i
$31$	67.6743	+	67.6743i	0.0704208	+	0.0704208i	0.741440	−	0.671019i	$-0.234143\pi$
$31$	67.6743	+	67.6743i	0.0704208	+	0.0704208i	−0.671019	+	0.741440i	$0.734143\pi$
$32$	174.851	−	46.8513i	0.170753	−	0.0457532i
$33$	259.250	+	967.535i	0.238063	+	0.888462i
$34$	−833.689	+	833.689i	−0.721184	+	0.721184i
$35$	1367.40	−	2368.41i	1.11625	−	1.93340i
$36$	434.061	−	250.605i	0.334924	−	0.193368i
$37$	−210.920	−	56.5158i	−0.154069	−	0.0412826i	0.180960	−	0.983490i	$-0.442079\pi$
$37$	−210.920	−	56.5158i	−0.154069	−	0.0412826i	−0.335029	+	0.942208i	$0.608746\pi$
$38$			14.9922i			0.0103824i
$39$	−732.796	−	1888.34i	−0.481785	−	1.24151i
$40$	−890.223			−0.556389
$41$	−761.848	+	2843.26i	−0.453211	+	1.69141i	0.240083	+	0.970752i	$0.422825\pi$
$41$	−761.848	+	2843.26i	−0.453211	+	1.69141i	−0.693294	+	0.720655i	$0.743841\pi$
$42$	−1178.24	−	2040.77i	−0.667935	−	1.15690i
$43$	1219.10	+	703.847i	0.659328	+	0.380663i	0.792021	−	0.610494i	$-0.209029\pi$
$43$	1219.10	+	703.847i	0.659328	+	0.380663i	−0.132693	+	0.991157i	$0.542362\pi$
$44$	−472.762	−	472.762i	−0.244195	−	0.244195i
$45$	−2380.88	+	637.956i	−1.17575	+	0.315040i
$46$	−338.262	−	1262.41i	−0.159859	−	0.596602i
$47$	−1373.25	+	1373.25i	−0.621664	+	0.621664i	−0.945957	−	0.324293i	$-0.894874\pi$
$47$	−1373.25	+	1373.25i	−0.621664	+	0.621664i	0.324293	+	0.945957i	$0.394874\pi$
$48$	−383.535	+	664.302i	−0.166465	+	0.288325i
$49$	−2105.30	+	1215.50i	−0.876843	+	0.506246i
$50$	2521.26	+	675.570i	1.00850	+	0.270228i
$51$		−	4996.07i		−	1.92083i
$52$	1053.80	+	846.996i	0.389720	+	0.313238i
$53$	2519.79			0.897040			0.448520	−	0.893773i	$-0.351951\pi$
$53$	2519.79			0.897040			0.448520	+	0.893773i	$0.351951\pi$
$54$	160.990	−	600.824i	0.0552093	−	0.206044i
$55$	1644.00	+	2847.49i	0.543471	+	0.941320i
$56$	1362.16	+	786.444i	0.434363	+	0.250779i
$57$	−44.9222	−	44.9222i	−0.0138265	−	0.0138265i
$58$	−2510.41	+	672.662i	−0.746257	+	0.199959i
$59$	141.861	+	529.433i	0.0407530	+	0.152092i	0.983304	−	0.181970i	$-0.0582473\pi$
$59$	141.861	+	529.433i	0.0407530	+	0.152092i	−0.942551	+	0.334062i	$0.891581\pi$
$60$	2667.43	−	2667.43i	0.740954	−	0.740954i
$61$	−1352.81	+	2343.14i	−0.363562	+	0.629707i	−0.988544	−	0.150932i	$-0.951773\pi$
$61$	−1352.81	+	2343.14i	−0.363562	+	0.629707i	0.624983	+	0.780639i	$0.285106\pi$
$62$	234.431	−	135.349i	0.0609862	−	0.0352104i
$63$	4206.66	+	1127.17i	1.05988	+	0.283994i
$64$		−	512.000i		−	0.125000i
$65$	−3927.76	−	5364.77i	−0.929648	−	1.26977i
$66$	2833.14			0.650399
$67$	−887.915	+	3313.75i	−0.197798	+	0.738192i	0.793727	+	0.608275i	$0.208138\pi$
$67$	−887.915	+	3313.75i	−0.197798	+	0.738192i	−0.991525	+	0.129918i	$0.958529\pi$
$68$	1667.38	+	2887.98i	0.360592	+	0.624564i
$69$	4796.20	+	2769.09i	1.00739	+	0.581619i
$70$	−5469.62	−	5469.62i	−1.11625	−	1.11625i
$71$	6794.09	−	1820.47i	1.34777	−	0.361133i	0.488456	−	0.872589i	$-0.337560\pi$
$71$	6794.09	−	1820.47i	1.34777	−	0.361133i	0.859310	+	0.511456i	$0.170894\pi$
$72$	−366.912	−	1369.33i	−0.0707778	−	0.264146i
$73$	1208.41	−	1208.41i	0.226762	−	0.226762i	−0.584577	−	0.811338i	$-0.698739\pi$
$73$	1208.41	−	1208.41i	0.226762	−	0.226762i	0.811338	+	0.584577i	$0.198739\pi$
$74$	−308.808	+	534.871i	−0.0563930	+	0.0976756i
$75$	−9578.88	+	5530.37i	−1.70291	+	0.983177i
$76$	40.9595	+	10.9751i	0.00709133	+	0.00190012i
$77$		−	5809.40i		−	0.979827i
$78$	−5695.49	+	619.672i	−0.936143	+	0.101853i
$79$	−3300.68			−0.528870			−0.264435	−	0.964403i	$-0.585186\pi$
$79$	−3300.68			−0.528870			−0.264435	+	0.964403i	$0.585186\pi$
$80$	−651.689	+	2432.13i	−0.101826	+	0.380021i
$81$	3855.28	+	6677.55i	0.587606	+	1.01776i
$82$	7210.21	+	4162.81i	1.07231	+	0.619098i
$83$	−1803.48	−	1803.48i	−0.261791	−	0.261791i	0.563991	−	0.825781i	$-0.309265\pi$
$83$	−1803.48	−	1803.48i	−0.261791	−	0.261791i	−0.825781	+	0.563991i	$0.809265\pi$
$84$	−6438.01	+	1725.06i	−0.912417	+	0.244481i
$85$	−4244.57	−	15841.0i	−0.587484	−	2.19252i
$86$	2815.39	−	2815.39i	0.380663	−	0.380663i
$87$	5506.56	−	9537.65i	0.727515	−	1.26009i
$88$	−1637.70	+	945.525i	−0.211479	+	0.122098i
$89$	−3985.42	−	1067.89i	−0.503146	−	0.134818i	−0.00168638	−	0.999999i	$-0.500537\pi$
$89$	−3985.42	−	1067.89i	−0.503146	−	0.134818i	−0.501460	+	0.865181i	$0.667203\pi$
$90$			6971.71i			0.860705i
$91$	1270.65	+	11678.7i	0.153441	+	1.41030i
$92$	−3696.59			−0.436743
$93$	−296.886	+	1107.99i	−0.0343261	+	0.128107i
$94$	2746.51	+	4757.09i	0.310832	+	0.538376i
$95$	−180.599	−	104.269i	−0.0200110	−	0.0115534i
$96$	1534.14	+	1534.14i	0.166465	+	0.166465i
$97$	−14270.6	+	3823.79i	−1.51669	+	0.406397i	−0.918652	−	0.395067i	$-0.870721\pi$
$97$	−14270.6	+	3823.79i	−1.51669	+	0.406397i	−0.598042	+	0.801465i	$0.704055\pi$
$98$	1779.61	+	6641.59i	0.185299	+	0.691544i
$99$	−3702.40	+	3702.40i	−0.377758	+	0.377758i
$100$	3691.38	−	6393.66i	0.369138	−	0.639366i
$101$	−1008.33	+	582.159i	−0.0988460	+	0.0570688i	−0.548608	−	0.836080i	$-0.684842\pi$
$101$	−1008.33	+	582.159i	−0.0988460	+	0.0570688i	0.449762	+	0.893148i	$0.351509\pi$
$102$	−13649.5	−	3657.38i	−1.31195	−	0.351536i
$103$		−	13334.2i		−	1.25688i	−0.777860	−	0.628438i	$-0.783695\pi$
$103$		−	13334.2i		−	1.25688i	0.777860	−	0.628438i	$-0.216305\pi$
$104$	3085.47	−	2259.00i	0.285269	−	0.208857i
$105$	32778.0			2.97306
$106$	1844.61	−	6884.18i	0.164170	−	0.612690i
$107$	−8150.17	−	14116.5i	−0.711868	−	1.23299i	−0.964155	−	0.265339i	$-0.914516\pi$
$107$	−8150.17	−	14116.5i	−0.711868	−	1.23299i	0.252288	−	0.967652i	$-0.418817\pi$
$108$	−1523.63	−	879.667i	−0.130627	−	0.0754173i
$109$	14940.7	+	14940.7i	1.25753	+	1.25753i	0.952269	+	0.305259i	$0.0987430\pi$
$109$	14940.7	+	14940.7i	1.25753	+	1.25753i	0.305259	+	0.952269i	$0.401257\pi$
$110$	8982.98	−	2406.98i	0.742395	−	0.198924i
$111$	−677.368	−	2527.97i	−0.0549767	−	0.205176i
$112$	3145.78	−	3145.78i	0.250779	−	0.250779i
$113$	−1470.05	+	2546.19i	−0.115126	+	0.199404i	−0.917830	−	0.396973i	$-0.870061\pi$
$113$	−1470.05	+	2546.19i	−0.115126	+	0.199404i	0.802704	+	0.596378i	$0.203394\pi$
$114$	−155.615	+	89.8444i	−0.0119741	+	0.00691324i
$115$	17559.8	+	4705.13i	1.32777	+	0.355776i
$116$			7350.99i			0.546298i
$117$	6633.18	−	8252.78i	0.484563	−	0.602877i
$118$	1550.29			0.111339
$119$	−7499.52	+	27988.6i	−0.529589	+	1.97645i
$120$	−5334.87	−	9240.26i	−0.370477	−	0.641685i
$121$	−6630.72	−	3828.25i	−0.452887	−	0.261474i
$122$	5411.25	+	5411.25i	0.363562	+	0.363562i
$123$	−34077.7	+	9131.10i	−2.25248	+	0.603550i
$124$	−198.164	−	739.559i	−0.0128879	−	0.0480983i
$125$	−8285.92	+	8285.92i	−0.530299	+	0.530299i
$126$	6158.98	−	10667.7i	0.387943	−	0.671936i
$127$	25605.7	−	14783.4i	1.58755	−	0.916575i	0.593846	−	0.804579i	$-0.297609\pi$
$127$	25605.7	−	14783.4i	1.58755	−	0.916575i	0.993709	−	0.111996i	$-0.0357245\pi$
$128$	−1398.81	−	374.810i	−0.0853766	−	0.0228766i
$129$			16871.9i			1.01387i
$130$	−17532.1	+	6803.57i	−1.03740	+	0.402578i
$131$	−16053.2			−0.935446			−0.467723	−	0.883875i	$-0.654925\pi$
$131$	−16053.2			−0.935446			−0.467723	+	0.883875i	$0.654925\pi$
$132$	2074.00	−	7740.28i	0.119031	−	0.444231i
$133$	184.227	+	319.091i	0.0104148	+	0.0180390i
$134$	8403.32	+	4851.66i	0.467995	+	0.270197i
$135$	6117.97	+	6117.97i	0.335691	+	0.335691i
$136$	9110.72	−	2441.21i	0.492578	−	0.131986i
$137$	−2823.71	−	10538.2i	−0.150446	−	0.561471i	−0.999452	−	0.0330889i	$-0.989466\pi$
$137$	−2823.71	−	10538.2i	−0.150446	−	0.561471i	0.849007	−	0.528382i	$-0.177201\pi$
$138$	11076.4	−	11076.4i	0.581619	−	0.581619i
$139$	−6792.57	+	11765.1i	−0.351564	+	0.608927i	−0.986524	−	0.163618i	$-0.947683\pi$
$139$	−6792.57	+	11765.1i	−0.351564	+	0.608927i	0.634959	+	0.772545i	$0.281017\pi$
$140$	−18947.3	+	10939.2i	−0.966700	+	0.558124i
$141$	−22483.5	−	6024.45i	−1.13091	−	0.303025i
$142$		−	19894.5i		−	0.986633i
$143$	−12923.7	−	5697.52i	−0.631998	−	0.278621i
$144$	−4009.69			−0.193368
$145$	9356.55	−	34919.1i	0.445020	−	1.66084i
$146$	−2416.83	−	4186.07i	−0.113381	−	0.196381i
$147$	−25233.0	−	14568.3i	−1.16771	−	0.674177i
$148$	1235.23	+	1235.23i	0.0563930	+	0.0563930i
$149$	25835.3	−	6922.53i	1.16370	−	0.311812i	0.375256	−	0.926921i	$-0.377555\pi$
$149$	25835.3	−	6922.53i	1.16370	−	0.311812i	0.788442	+	0.615109i	$0.210888\pi$
$150$	8097.02	+	30218.5i	0.359868	+	1.34304i
$151$	−10548.8	+	10548.8i	−0.462645	+	0.462645i	−0.899521	−	0.436877i	$-0.856085\pi$
$151$	−10548.8	+	10548.8i	−0.462645	+	0.462645i	0.436877	+	0.899521i	$0.356085\pi$
$152$	59.9689	−	103.869i	0.00259561	−	0.00449573i
$153$	22617.0	−	13057.9i	0.966167	−	0.557817i
$154$	−15871.6	−	4252.77i	−0.669235	−	0.179321i
$155$			3765.33i			0.156725i
$156$	−2476.41	+	16014.0i	−0.101759	+	0.658038i
$157$	4252.07			0.172505			0.0862524	−	0.996273i	$-0.472511\pi$
$157$	4252.07			0.172505			0.0862524	+	0.996273i	$0.472511\pi$
$158$	−2416.27	+	9017.63i	−0.0967900	+	0.361225i
$159$	15100.4	+	26154.7i	0.597302	+	1.03456i
$160$	6167.65	+	3560.89i	0.240924	+	0.139097i
$161$	−22712.2	−	22712.2i	−0.876210	−	0.876210i
$162$	21065.7	−	5644.53i	0.802685	−	0.215079i
$163$	3526.07	+	13159.5i	0.132714	+	0.495295i	0.999997	−	0.00252066i	$-0.000802351\pi$
$163$	3526.07	+	13159.5i	0.132714	+	0.495295i	−0.867283	+	0.497815i	$0.834136\pi$
$164$	16651.3	−	16651.3i	0.619098	−	0.619098i
$165$	−19704.1	+	34128.5i	−0.723750	+	1.25357i
$166$	−6247.42	+	3606.95i	−0.226717	+	0.130895i
$167$	37945.5	+	10167.5i	1.36059	+	0.364569i	0.864033	−	0.503435i	$-0.167931\pi$
$167$	37945.5	+	10167.5i	1.36059	+	0.364569i	0.496557	+	0.868004i	$0.334597\pi$
$168$			18851.8i			0.667935i
$169$	27226.9	+	8627.07i	0.953290	+	0.302058i
$170$	−46385.6			−1.60504
$171$	85.9505	−	320.771i	0.00293938	−	0.0109699i
$172$	−5630.77	−	9752.79i	−0.190332	−	0.329664i
$173$	−5.64764	−	3.26067i	−0.000188701	−	0.000108947i	0.499906	−	0.866080i	$-0.333368\pi$
$173$	−5.64764	−	3.26067i	−0.000188701	−	0.000108947i	−0.500094	+	0.865971i	$0.666701\pi$
$174$	−22026.3	−	22026.3i	−0.727515	−	0.727515i
$175$	61963.5	−	16603.1i	2.02330	−	0.542141i
$176$	1384.34	+	5166.44i	0.0446909	+	0.166789i
$177$	−4645.23	+	4645.23i	−0.148272	+	0.148272i
$178$	−5835.06	+	10106.6i	−0.184164	+	0.318982i
$179$	21948.1	−	12671.7i	0.684999	−	0.395485i	−0.116737	−	0.993163i	$-0.537243\pi$
$179$	21948.1	−	12671.7i	0.684999	−	0.395485i	0.801736	+	0.597678i	$0.203910\pi$
$180$	19047.1	+	5103.65i	0.587873	+	0.157520i
$181$		−	13510.0i		−	0.412380i	−0.978512	−	0.206190i	$-0.933894\pi$
$181$		−	13510.0i		−	0.412380i	0.978512	−	0.206190i	$-0.0661065\pi$
$182$	32837.0	+	5077.93i	0.991335	+	0.153301i
$183$	−32428.2			−0.968323
$184$	−2706.09	+	10099.3i	−0.0799295	+	0.298301i
$185$	−4295.44	−	7439.92i	−0.125506	−	0.217383i
$186$	2809.76	+	1622.22i	0.0812164	+	0.0468903i
$187$	−24633.5	−	24633.5i	−0.704439	−	0.704439i
$188$	15007.2	−	4021.17i	0.424604	−	0.113772i
$189$	−3956.56	−	14766.1i	−0.110763	−	0.413373i
$190$	−417.076	+	417.076i	−0.0115534	+	0.0115534i
$191$	6499.62	−	11257.7i	0.178165	−	0.308590i	−0.763087	−	0.646295i	$-0.776317\pi$
$191$	6499.62	−	11257.7i	0.178165	−	0.308590i	0.941252	+	0.337705i	$0.109651\pi$
$192$	5314.42	−	3068.28i	0.144163	−	0.0832324i
$193$	16565.1	+	4438.60i	0.444712	+	0.119160i	0.474224	−	0.880404i	$-0.342729\pi$
$193$	16565.1	+	4438.60i	0.444712	+	0.119160i	−0.0295118	+	0.999564i	$0.509395\pi$
$194$			41787.2i			1.11030i
$195$	32146.7	−	72918.7i	0.845410	−	1.91765i
$196$	19447.9			0.506246
$197$	128.053	−	477.902i	0.00329958	−	0.0123142i	−0.964256	−	0.264971i	$-0.914638\pi$
$197$	128.053	−	477.902i	0.00329958	−	0.0123142i	0.967556	+	0.252657i	$0.0813043\pi$
$198$	7404.80	+	12825.5i	0.188879	+	0.327148i
$199$	−48621.7	−	28071.8i	−1.22779	−	0.708865i	−0.261223	−	0.965278i	$-0.584126\pi$
$199$	−48621.7	−	28071.8i	−1.22779	−	0.708865i	−0.966567	+	0.256413i	$0.917459\pi$
$200$	−14765.5	−	14765.5i	−0.369138	−	0.369138i
$201$	−39716.8	+	10642.1i	−0.983064	+	0.263411i
$202$	852.339	+	3180.97i	0.0208886	+	0.0779574i
$203$	−45165.2	+	45165.2i	−1.09600	+	1.09600i
$204$	−19984.3	+	34613.8i	−0.480207	+	0.831743i
$205$	−100292.	+	57903.7i	−2.38649	+	1.37784i
$206$	−36429.7	−	9761.31i	−0.858462	−	0.230024i
$207$			28949.6i			0.675619i
$208$	−3912.98	−	10083.4i	−0.0904443	−	0.233066i
$209$	−442.985			−0.0101414
$210$	23995.1	−	89551.0i	0.544107	−	2.03064i
$211$	−5285.33	−	9154.47i	−0.118716	−	0.205621i	0.800543	−	0.599275i	$-0.204544\pi$
$211$	−5285.33	−	9154.47i	−0.118716	−	0.205621i	−0.919259	+	0.393653i	$0.871211\pi$
$212$	−17457.6	−	10079.1i	−0.388430	−	0.224260i
$213$	59611.1	+	59611.1i	1.31392	+	1.31392i
$214$	−44533.4	+	11932.7i	−0.972429	+	0.260562i
$215$	14334.0	+	53495.3i	0.310093	+	1.15728i
$216$	−3518.67	+	3518.67i	−0.0754173	+	0.0754173i
$217$	3326.38	−	5761.46i	0.0706403	−	0.122353i
$218$	51756.1	−	29881.4i	1.08905	−	0.628764i
$219$	19784.7	+	5301.29i	0.412516	+	0.110533i
$220$		−	26304.0i		−	0.543471i
$221$	54909.0	+	44133.2i	1.12424	+	0.903609i
$222$	−7402.42			−0.150199
$223$	9982.04	−	37253.5i	0.200729	−	0.749130i	−0.789980	−	0.613132i	$-0.789909\pi$
$223$	9982.04	−	37253.5i	0.200729	−	0.749130i	0.990709	−	0.135998i	$-0.0434240\pi$
$224$	−6291.56	−	10897.3i	−0.125390	−	0.217181i
$225$	−50071.5	−	28908.8i	−0.989066	−	0.571038i
$226$	5880.18	+	5880.18i	0.115126	+	0.115126i
$227$	58036.5	−	15550.8i	1.12629	−	0.301788i	0.352863	−	0.935675i	$-0.385208\pi$
$227$	58036.5	−	15550.8i	1.12629	−	0.301788i	0.773426	+	0.633887i	$0.218542\pi$
$228$	131.541	+	490.919i	0.00253042	+	0.00944366i
$229$	−28796.6	+	28796.6i	−0.549124	+	0.549124i	−0.926188	−	0.377063i	$-0.876934\pi$
$229$	−28796.6	+	28796.6i	−0.549124	+	0.549124i	0.377063	+	0.926188i	$0.376934\pi$
$230$	25709.3	−	44529.9i	0.485999	−	0.841774i
$231$	60299.9	−	34814.2i	1.13004	−	0.652427i
$232$	20083.3	+	5381.30i	0.373129	+	0.0999795i
$233$		−	54456.8i		−	1.00309i	−0.865131	−	0.501546i	$-0.832765\pi$
$233$		−	54456.8i		−	1.00309i	0.865131	−	0.501546i	$-0.167235\pi$
$234$	−17691.2	−	24163.6i	−0.323091	−	0.441297i
$235$	−76406.4			−1.38355
$236$	1134.89	−	4235.46i	0.0203765	−	0.0760461i
$237$	−19780.1	−	34260.1i	−0.352153	−	0.609947i
$238$	70976.2	+	40978.1i	1.25302	+	0.723433i
$239$	32089.5	+	32089.5i	0.561782	+	0.561782i	0.929813	−	0.368031i	$-0.119968\pi$
$239$	32089.5	+	32089.5i	0.561782	+	0.561782i	−0.368031	+	0.929813i	$0.619968\pi$
$240$	−29150.3	+	7810.79i	−0.506081	+	0.135604i
$241$	25400.5	+	94796.1i	0.437330	+	1.63214i	0.735429	+	0.677601i	$0.236980\pi$
$241$	25400.5	+	94796.1i	0.437330	+	1.63214i	−0.298100	+	0.954535i	$0.596353\pi$
$242$	−15313.0	+	15313.0i	−0.261474	+	0.261474i
$243$	−37300.7	+	64606.8i	−0.631691	+	1.09412i
$244$	18745.1	−	10822.5i	0.314854	−	0.181781i
$245$	−92382.8	−	24753.9i	−1.53907	−	0.412393i
$246$			99786.5i			1.64893i
$247$	890.538	−	96.8910i	0.0145968	−	0.00158814i
$248$	−2165.58			−0.0352104
$249$	7911.82	−	29527.3i	0.127608	−	0.476239i
$250$	16571.8	+	28703.3i	0.265149	+	0.459252i
$251$	25747.4	+	14865.3i	0.408683	+	0.235953i	0.690224	−	0.723596i	$-0.257512\pi$
$251$	25747.4	+	14865.3i	0.408683	+	0.235953i	−0.281541	+	0.959549i	$0.590846\pi$
$252$	−24635.9	−	24635.9i	−0.387943	−	0.387943i
$253$	37301.3	−	9994.84i	0.582750	−	0.156147i
$254$	−21644.5	−	80778.2i	−0.335490	−	1.25206i
$255$	138988.	−	138988.i	2.13746	−	2.13746i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−11116.9	+	6418.37i	−0.168314	+	0.0971759i	−0.581790	−	0.813339i	$-0.697648\pi$
$257$	−11116.9	+	6418.37i	−0.168314	+	0.0971759i	0.413477	+	0.910515i	$0.364314\pi$
$258$	46094.8	+	12351.1i	0.692488	+	0.185552i
$259$			15178.8i			0.226275i
$260$	5753.28	+	52879.2i	0.0851077	+	0.782237i
$261$	57568.7			0.845095
$262$	−11751.7	+	43858.1i	−0.171198	+	0.638921i
$263$	−29925.0	−	51831.6i	−0.432636	−	0.749347i	0.564463	−	0.825458i	$-0.309083\pi$
$263$	−29925.0	−	51831.6i	−0.432636	−	0.749347i	−0.997099	+	0.0761107i	$0.975750\pi$
$264$	−19628.6	−	11332.6i	−0.281631	−	0.162600i
$265$	70099.1	+	70099.1i	0.998207	+	0.998207i
$266$	1006.64	−	269.728i	0.0142269	−	0.00381208i
$267$	−12799.2	−	47767.1i	−0.179539	−	0.670049i
$268$	19406.6	−	19406.6i	0.270197	−	0.270197i
$269$	40328.9	−	69851.6i	0.557329	−	0.965321i	−0.440390	−	0.897807i	$-0.645160\pi$
$269$	40328.9	−	69851.6i	0.557329	−	0.965321i	0.997718	−	0.0675147i	$-0.0215070\pi$
$270$	21193.3	−	12235.9i	0.290717	−	0.167846i
$271$	−74687.8	−	20012.5i	−1.01698	−	0.272498i	−0.288435	−	0.957500i	$-0.593135\pi$
$271$	−74687.8	−	20012.5i	−1.01698	−	0.272498i	−0.728542	+	0.685002i	$0.759802\pi$
$272$		−	26678.0i		−	0.360592i
$273$	−113607.	+	83176.3i	−1.52433	+	1.11603i
$274$	−30858.1			−0.411025
$275$	−19961.5	+	74497.4i	−0.263954	+	0.985089i
$276$	−22152.7	−	38369.6i	−0.290809	−	0.503697i
$277$	−47587.3	−	27474.5i	−0.620200	−	0.358073i	0.156747	−	0.987639i	$-0.449899\pi$
$277$	−47587.3	−	27474.5i	−0.620200	−	0.358073i	−0.776947	+	0.629566i	$0.783233\pi$
$278$	27170.3	+	27170.3i	0.351564	+	0.351564i
$279$	−5791.80	+	1551.91i	−0.0744055	+	0.0199369i
$280$	16016.2	+	59773.1i	0.204288	+	0.762412i
$281$	−24920.8	+	24920.8i	−0.315609	+	0.315609i	−0.847078	−	0.531469i	$-0.821640\pi$
$281$	−24920.8	+	24920.8i	−0.315609	+	0.315609i	0.531469	+	0.847078i	$0.321640\pi$
$282$	−32918.2	+	57016.0i	−0.413940	+	0.716966i
$283$	−35284.1	+	20371.3i	−0.440561	+	0.254358i	−0.703836	−	0.710363i	$-0.748531\pi$
$283$	−35284.1	+	20371.3i	−0.440561	+	0.254358i	0.263274	+	0.964721i	$0.415198\pi$
$284$	−54352.7	−	14563.8i	−0.673883	−	0.180566i
$285$		−	2499.43i		−	0.0307716i
$286$	−25026.7	+	31137.4i	−0.305965	+	0.380672i
$287$	204614.			2.48411
$288$	−2935.30	+	10954.7i	−0.0353889	+	0.132073i
$289$	45119.1	+	78148.6i	0.540213	+	0.935676i
$290$	−88551.4	−	51125.2i	−1.05293	−	0.607909i
$291$	−125210.	−	125210.i	−1.47860	−	1.47860i
$292$	−13205.8	+	3538.48i	−0.154881	+	0.0415003i
$293$	−31609.2	−	117967.i	−0.368195	−	1.37412i	−0.863037	−	0.505140i	$-0.831441\pi$
$293$	−31609.2	−	117967.i	−0.368195	−	1.37412i	0.494842	−	0.868983i	$-0.335226\pi$
$294$	−58273.1	+	58273.1i	−0.674177	+	0.674177i
$295$	−10782.0	+	18675.0i	−0.123896	+	0.214594i
$296$	4278.97	−	2470.47i	0.0488378	−	0.0281965i
$297$	17752.9	+	4756.89i	0.201260	+	0.0539274i
$298$		−	75650.9i		−	0.851886i
$299$	−72801.1	+	28251.4i	−0.814320	+	0.316007i
$300$	88485.9			0.983177
$301$	25326.0	−	94518.1i	0.279534	−	1.04323i
$302$	21097.5	+	36542.0i	0.231322	+	0.400662i
$303$	−12085.3	−	6977.44i	−0.131635	−	0.0759995i
$304$	−239.876	−	239.876i	−0.00259561	−	0.00259561i
$305$	−102819.	+	27550.4i	−1.10529	+	0.296161i
$306$	−19118.1	−	71349.9i	−0.204175	−	0.761992i
$307$	−16827.4	+	16827.4i	−0.178542	+	0.178542i	−0.790720	−	0.612178i	$-0.790294\pi$
$307$	−16827.4	+	16827.4i	−0.178542	+	0.178542i	0.612178	+	0.790720i	$0.290294\pi$
$308$	−23237.6	+	40248.7i	−0.244957	+	0.424278i
$309$	138405.	−	79908.3i	1.44956	−	0.836902i
$310$	10287.1	+	2756.41i	0.107045	+	0.0286827i
$311$			91661.6i			0.947691i	0.880608	+	0.473845i	$0.157134\pi$
$311$			91661.6i			0.947691i	−0.880608	+	0.473845i	$0.842866\pi$
$312$	41938.2	+	18488.8i	0.430825	+	0.189932i
$313$	−97693.4			−0.997186			−0.498593	−	0.866836i	$-0.666150\pi$
$313$	−97693.4			−0.997186			−0.498593	+	0.866836i	$0.666150\pi$
$314$	3112.73	−	11616.9i	0.0315706	−	0.117823i
$315$	85669.8	+	148384.i	0.863389	+	1.49543i
$316$	22867.8	+	13202.7i	0.229008	+	0.132218i
$317$	13766.4	+	13766.4i	0.136994	+	0.136994i	0.772278	−	0.635284i	$-0.219117\pi$
$317$	13766.4	+	13766.4i	0.136994	+	0.136994i	−0.635284	+	0.772278i	$0.719117\pi$
$318$	82510.1	−	22108.5i	0.815930	−	0.218628i
$319$	−19875.6	−	74176.7i	−0.195316	−	0.728931i
$320$	14243.6	−	14243.6i	0.139097	−	0.139097i
$321$	97683.6	−	169193.i	0.948007	−	1.64200i
$322$	−78677.5	+	45424.5i	−0.758820	+	0.438105i
$323$	2134.22	+	571.862i	0.0204566	+	0.00548134i
$324$		−	61684.5i		−	0.587606i
$325$	23834.6	−	154129.i	0.225653	−	1.45921i
$326$	38533.7			0.362581
$327$	−65544.6	+	244616.i	−0.612973	+	2.28765i
$328$	−33302.5	−	57681.7i	−0.309549	−	0.536155i
$329$	116912.	+	67499.3i	1.08011	+	0.623602i
$330$	78816.4	+	78816.4i	0.723750	+	0.723750i
$331$	51623.0	−	13832.4i	0.471181	−	0.126253i	−0.0154123	−	0.999881i	$-0.504906\pi$
$331$	51623.0	−	13832.4i	0.471181	−	0.126253i	0.486593	+	0.873629i	$0.338239\pi$
$332$	5280.94	+	19708.7i	0.0479110	+	0.178806i
$333$	9673.63	−	9673.63i	0.0872370	−	0.0872370i
$334$	55556.1	−	96225.9i	0.498011	−	0.862580i
$335$	−116888.	+	67485.3i	−1.04155	+	0.601339i
$336$	51504.1	+	13800.5i	0.456208	+	0.122241i
$337$		−	13090.4i		−	0.115264i	−0.998338	−	0.0576319i	$-0.981645\pi$
$337$		−	13090.4i		−	0.115264i	0.998338	−	0.0576319i	$-0.0183550\pi$
$338$	43501.1	−	68069.8i	0.380773	−	0.595829i
$339$	−35238.4			−0.306631
$340$	−33956.6	+	126728.i	−0.293742	+	1.09626i
$341$	3999.24	+	6926.88i	0.0343929	+	0.0595702i
$342$	−813.444	−	469.642i	−0.00695465	−	0.00401527i
$343$	1474.16	+	1474.16i	0.0125301	+	0.0125301i
$344$	−30767.1	+	8244.03i	−0.259998	+	0.0696663i
$345$	56393.2	+	210462.i	0.473793	+	1.76822i
$346$	−13.0427	+	13.0427i	−0.000108947	+	0.000108947i
$347$	−30899.4	+	53519.3i	−0.256620	+	0.444479i	−0.965334	−	0.261016i	$-0.915942\pi$
$347$	−30899.4	+	53519.3i	−0.256620	+	0.444479i	0.708714	+	0.705496i	$0.249276\pi$
$348$	−76301.2	+	44052.5i	−0.630047	+	0.363758i
$349$	179397.	+	48069.3i	1.47287	+	0.394654i	0.903914	−	0.427714i	$-0.140681\pi$
$349$	179397.	+	48069.3i	1.47287	+	0.394654i	0.568955	+	0.822368i	$0.307348\pi$
$350$		−	181442.i		−	1.48116i
$351$	−36729.4	−	5679.85i	−0.298126	−	0.0461023i
$352$	15128.4			0.122098
$353$	50160.6	−	187202.i	0.402544	−	1.50231i	−0.405997	−	0.913874i	$-0.633076\pi$
$353$	50160.6	−	187202.i	0.402544	−	1.50231i	0.808541	−	0.588440i	$-0.200258\pi$
$354$	9290.45	+	16091.5i	0.0741362	+	0.128408i
$355$	239652.	+	138363.i	1.90163	+	1.09790i
$356$	23340.2	+	23340.2i	0.184164	+	0.184164i
$357$	−335456.	+	89885.2i	−2.63208	+	0.705264i
$358$	−18552.7	−	69239.6i	−0.144757	−	0.540242i
$359$	−24773.9	+	24773.9i	−0.192223	+	0.192223i	−0.796656	−	0.604433i	$-0.793400\pi$
$359$	−24773.9	+	24773.9i	−0.192223	+	0.192223i	0.604433	+	0.796656i	$0.293400\pi$
$360$	27886.8	−	48301.4i	0.215176	−	0.372696i
$361$	−112837.	+	65146.5i	−0.865839	+	0.499892i
$362$	−36909.9	−	9889.99i	−0.281661	−	0.0754708i
$363$		−	91766.6i		−	0.696420i
$364$	37911.5	−	85995.0i	0.286133	−	0.649038i
$365$	67234.9			0.504671
$366$	−23739.1	+	88595.4i	−0.177215	+	0.661377i
$367$	−84338.1	−	146078.i	−0.626169	−	1.08456i	−0.988314	−	0.152434i	$-0.951289\pi$
$367$	−84338.1	−	146078.i	−0.626169	−	1.08456i	0.362145	−	0.932122i	$-0.382045\pi$
$368$	25610.8	+	14786.4i	0.189115	+	0.109186i
$369$	−130403.	−	130403.i	−0.957712	−	0.957712i
$370$	−23470.7	+	6288.96i	−0.171444	+	0.0459383i
$371$	−45333.9	−	169188.i	−0.329363	−	1.22920i
$372$	6488.87	−	6488.87i	0.0468903	−	0.0468903i
$373$	−52351.4	+	90675.2i	−0.376279	+	0.651735i	−0.990518	−	0.137386i	$-0.956130\pi$
$373$	−52351.4	+	90675.2i	−0.376279	+	0.651735i	0.614238	+	0.789121i	$0.289463\pi$
$374$	−85333.1	+	49267.1i	−0.610062	+	0.352220i
$375$	−135661.	−	36350.2i	−0.964699	−	0.258490i
$376$		−	43944.2i		−	0.310832i
$377$	56180.3	+	144771.i	0.395276	+	1.01859i
$378$	−43238.1			−0.302610
$379$	45936.4	−	171437.i	0.319800	−	1.19351i	−0.599637	−	0.800272i	$-0.704689\pi$
$379$	45936.4	−	171437.i	0.319800	−	1.19351i	0.919437	−	0.393237i	$-0.128645\pi$
$380$	834.152	+	1444.79i	0.00577668	+	0.0100055i
$381$	306896.	+	177186.i	2.11418	+	1.22062i
$382$	−25998.5	−	25998.5i	−0.178165	−	0.178165i
$383$	−27637.5	+	7405.45i	−0.188409	+	0.0504840i	−0.351790	−	0.936079i	$-0.614427\pi$
$383$	−27637.5	+	7405.45i	−0.188409	+	0.0504840i	0.163381	+	0.986563i	$0.447760\pi$
$384$	−4492.27	−	16765.4i	−0.0304652	−	0.113698i
$385$	161614.	−	161614.i	1.09033	−	1.09033i
$386$	24253.0	−	42007.4i	0.162776	−	0.281936i
$387$	−76378.2	+	44097.0i	−0.509973	+	0.294433i
$388$	114165.	+	30590.3i	0.758347	+	0.203199i
$389$			139258.i			0.920283i	0.887846	+	0.460141i	$0.152201\pi$
$389$			139258.i			0.920283i	−0.887846	+	0.460141i	$0.847799\pi$
$390$	−175685.	−	141207.i	−1.15506	−	0.928380i
$391$	−192613.			−1.25989
$392$	14236.9	−	53132.7i	0.0926494	−	0.345772i
$393$	−96202.4	−	166627.i	−0.622875	−	1.07885i
$394$	−1211.91	−	699.696i	−0.00780689	−	0.00450731i
$395$	−91823.2	−	91823.2i	−0.588516	−	0.588516i
$396$	40460.6	−	10841.4i	0.258013	−	0.0691344i
$397$	9441.85	+	35237.5i	0.0599068	+	0.223575i	0.989389	−	0.145292i	$-0.0464123\pi$
$397$	9441.85	+	35237.5i	0.0599068	+	0.223575i	−0.929482	+	0.368868i	$0.879746\pi$
$398$	−112287.	+	112287.i	−0.708865	+	0.708865i
$399$	−2208.05	+	3824.46i	−0.0138696	+	0.0240228i
$400$	−51149.3	+	29531.1i	−0.319683	+	0.184569i
$401$	129712.	+	34756.2i	0.806662	+	0.216144i	0.638507	−	0.769616i	$-0.279552\pi$
$401$	129712.	+	34756.2i	0.806662	+	0.216144i	0.168155	+	0.985761i	$0.446219\pi$
$402$			116299.i			0.719653i
$403$	−9554.78	−	13050.5i	−0.0588316	−	0.0803555i
$404$	9314.54			0.0570688
$405$	−78513.9	+	293018.i	−0.478670	+	1.78642i
$406$	90330.4	+	156457.i	0.548002	+	0.949167i
$407$	−15804.2	−	9124.55i	−0.0954077	−	0.0550837i
$408$	79937.2	+	79937.2i	0.480207	+	0.480207i
$409$	−11087.2	+	2970.81i	−0.0662789	+	0.0177594i	−0.291806	−	0.956477i	$-0.594256\pi$
$409$	−11087.2	+	2970.81i	−0.0662789	+	0.0177594i	0.225527	+	0.974237i	$0.427590\pi$
$410$	84776.8	+	316391.i	0.504324	+	1.88216i
$411$	92462.3	−	92462.3i	0.547370	−	0.547370i
$412$	−53336.8	+	92382.0i	−0.314219	+	0.544243i
$413$	32996.0	−	19050.2i	0.193446	−	0.111686i
$414$	79091.7	+	21192.6i	0.461456	+	0.123647i
$415$		−	100343.i		−	0.582630i
$416$	−30412.8	+	3308.92i	−0.175740	+	0.0191205i
$417$	−162824.			−0.936369
$418$	−324.288	+	1210.26i	−0.00185600	+	0.00692669i
$419$	111910.	+	193833.i	0.637441	+	1.10408i	0.985992	+	0.166790i	$0.0533403\pi$
$419$	111910.	+	193833.i	0.637441	+	1.10408i	−0.348551	+	0.937290i	$0.613326\pi$
$420$	−227092.	−	131112.i	−1.28737	−	0.743264i
$421$	−231747.	−	231747.i	−1.30753	−	1.30753i	−0.923195	−	0.384333i	$-0.874432\pi$
$421$	−231747.	−	231747.i	−1.30753	−	1.30753i	−0.384333	−	0.923195i	$-0.625568\pi$
$422$	−28879.6	+	7738.27i	−0.162168	+	0.0434529i
$423$	−31491.5	−	117528.i	−0.176000	−	0.656840i
$424$	−40316.6	+	40316.6i	−0.224260	+	0.224260i
$425$	192342.	−	333145.i	1.06487	−	1.84440i
$426$	206499.	−	119222.i	1.13789	−	0.656959i
$427$	181666.	+	48677.3i	0.996365	+	0.266975i
$428$			130403.i			0.711868i
$429$	−18309.8	−	168288.i	−0.0994879	−	0.914407i
$430$	156645.			0.847189
$431$	−75260.8	+	280877.i	−0.405149	+	1.51204i	0.398632	+	0.917111i	$0.369485\pi$
$431$	−75260.8	+	280877.i	−0.405149	+	1.51204i	−0.803781	+	0.594925i	$0.797182\pi$
$432$	7037.34	+	12189.0i	0.0377087	+	0.0653133i
$433$	192477.	+	111127.i	1.02660	+	0.592710i	0.916010	−	0.401156i	$-0.131392\pi$
$433$	192477.	+	111127.i	1.02660	+	0.592710i	0.110593	+	0.993866i	$0.464725\pi$
$434$	−13305.5	−	13305.5i	−0.0706403	−	0.0706403i
$435$	418522.	−	112143.i	2.21177	−	0.592642i
$436$	−43749.4	−	163275.i	−0.230144	−	0.858908i
$437$	−1731.88	+	1731.88i	−0.00906891	+	0.00906891i
$438$	28966.8	−	50172.0i	0.150991	−	0.261525i
$439$	262958.	−	151819.i	1.36445	−	0.787765i	0.374237	−	0.927333i	$-0.377905\pi$
$439$	262958.	−	151819.i	1.36445	−	0.787765i	0.990213	+	0.139568i	$0.0445713\pi$
$440$	−71863.9	−	19255.9i	−0.371198	−	0.0994621i
$441$		−	152305.i		−	0.783135i
$442$	160770.	−	117706.i	0.822927	−	0.602498i
$443$	103827.			0.529060			0.264530	−	0.964377i	$-0.414783\pi$
$443$	103827.			0.529060			0.264530	+	0.964377i	$0.414783\pi$
$444$	−5418.95	+	20223.8i	−0.0274884	+	0.102588i
$445$	−81164.2	−	140580.i	−0.409868	−	0.709913i
$446$	−94471.0	−	54542.9i	−0.474929	−	0.274201i
$447$	226678.	+	226678.i	1.13447	+	1.13447i
$448$	−34377.7	+	9211.48i	−0.171286	+	0.0458958i
$449$	−4110.93	−	15342.2i	−0.0203914	−	0.0761018i	0.954980	−	0.296669i	$-0.0958758\pi$
$449$	−4110.93	−	15342.2i	−0.0203914	−	0.0761018i	−0.975372	+	0.220567i	$0.929209\pi$
$450$	−115635.	+	115635.i	−0.571038	+	0.571038i
$451$	−123001.	+	213045.i	−0.604724	+	1.04741i
$452$	20369.5	−	11760.4i	0.0997021	−	0.0575631i
$453$	−172709.	−	46277.3i	−0.841625	−	0.225513i
$454$		−	169943.i		−	0.824500i
$455$	−289546.	+	360244.i	−1.39861	+	1.74010i
$456$	1437.51			0.00691324
$457$	−59485.3	+	222002.i	−0.284824	+	1.06298i	0.664143	+	0.747606i	$0.268797\pi$
$457$	−59485.3	+	222002.i	−0.284824	+	1.06298i	−0.948968	+	0.315374i	$0.897870\pi$
$458$	57593.3	+	99754.5i	0.274562	+	0.475556i
$459$	−79389.5	−	45835.6i	−0.376823	−	0.217559i
$460$	−102837.	−	102837.i	−0.485999	−	0.485999i
$461$	50918.9	−	13643.7i	0.239595	−	0.0641992i	−0.137023	−	0.990568i	$-0.543754\pi$
$461$	50918.9	−	13643.7i	0.239595	−	0.0641992i	0.376618	+	0.926369i	$0.377087\pi$
$462$	−50971.5	−	190228.i	−0.238805	−	0.891232i
$463$	−137439.	+	137439.i	−0.641134	+	0.641134i	−0.950834	−	0.309700i	$-0.899771\pi$
$463$	−137439.	+	137439.i	−0.641134	+	0.641134i	0.309700	+	0.950834i	$0.399771\pi$
$464$	29404.0	−	50929.1i	0.136575	−	0.236554i
$465$	−39083.1	+	22564.6i	−0.180752	+	0.104357i
$466$	−148779.	−	39865.2i	−0.685124	−	0.183579i
$467$		−	49120.0i		−	0.225229i	−0.993639	−	0.112615i	$-0.964077\pi$
$467$		−	49120.0i		−	0.225229i	0.993639	−	0.112615i	$-0.0359225\pi$
$468$	−78967.1	+	30644.2i	−0.360541	+	0.139913i
$469$	238473.			1.08416
$470$	−55933.4	+	208746.i	−0.253207	+	0.944981i
$471$	25481.5	+	44135.3i	0.114864	+	0.198950i
$472$	−10740.7	−	6201.15i	−0.0482113	−	0.0278348i
$473$	83188.1	+	83188.1i	0.371825	+	0.371825i
$474$	−108080.	+	28960.1i	−0.481050	+	0.128897i
$475$	−1266.04	−	4724.92i	−0.00561125	−	0.0209415i
$476$	163912.	−	163912.i	0.723433	−	0.723433i
$477$	−78934.0	+	136718.i	−0.346918	+	0.600880i
$478$	111161.	−	64179.1i	0.486517	−	0.280891i
$479$	−358446.	−	96045.3i	−1.56226	−	0.418606i	−0.628880	−	0.777502i	$-0.716486\pi$
$479$	−358446.	−	96045.3i	−1.56226	−	0.418606i	−0.933377	+	0.358897i	$0.883153\pi$
$480$			85357.9i			0.370477i
$481$	33767.1	+	14886.5i	0.145950	+	0.0643430i
$482$	277582.			1.19481
$483$	99638.2	−	371855.i	0.427102	−	1.59397i
$484$	30626.0	+	53045.7i	0.130737	+	0.226443i
$485$	−503376.	−	290624.i	−2.13998	−	1.23552i
$486$	149203.	+	149203.i	0.631691	+	0.631691i
$487$	72062.9	−	19309.2i	0.303846	−	0.0814154i	−0.103675	−	0.994611i	$-0.533060\pi$
$487$	72062.9	−	19309.2i	0.303846	−	0.0814154i	0.407521	+	0.913196i	$0.366393\pi$
$488$	−15845.2	−	59135.2i	−0.0665364	−	0.248317i
$489$	−115461.	+	115461.i	−0.482856	+	0.482856i
$490$	−135258.	+	234273.i	−0.563339	+	0.975732i
$491$	−14995.9	+	8657.91i	−0.0622029	+	0.0359129i	−0.530779	−	0.847510i	$-0.678101\pi$
$491$	−14995.9	+	8657.91i	−0.0622029	+	0.0359129i	0.468576	+	0.883423i	$0.344767\pi$
$492$	272622.	+	73048.8i	1.12624	+	0.301775i
$493$			383027.i			1.57593i
$494$	387.208	−	2503.93i	0.00158669	−	0.0102605i
$495$	−205998.			−0.840721
$496$	−1585.31	+	5916.47i	−0.00644395	+	0.0240491i
$497$	−244467.	−	423429.i	−0.989709	−	1.71423i
$498$	−74878.3	−	43231.0i	−0.301924	−	0.174316i
$499$	−76303.8	−	76303.8i	−0.306440	−	0.306440i	0.537087	−	0.843527i	$-0.319525\pi$
$499$	−76303.8	−	76303.8i	−0.306440	−	0.306440i	−0.843527	+	0.537087i	$0.819525\pi$
$500$	90550.2	−	24262.9i	0.362201	−	0.0970514i
$501$	121862.	+	454795.i	0.485503	+	1.81192i
$502$	59461.1	−	59461.1i	0.235953	−	0.235953i
$503$	166203.	−	287872.i	0.656906	−	1.13779i	−0.324507	−	0.945883i	$-0.605198\pi$
$503$	166203.	−	287872.i	0.656906	−	1.13779i	0.981412	−	0.191910i	$-0.0614683\pi$
$504$	−85341.3	+	49271.8i	−0.335968	+	0.193971i
$505$	−44246.5	−	11855.8i	−0.173499	−	0.0464888i
$506$		−	109226.i		−	0.426603i
$507$	73617.0	+	334307.i	0.286393	+	1.30056i
$508$	−236535.			−0.916575
$509$	37963.3	−	141681.i	0.146531	−	0.546860i	−0.853152	−	0.521663i	$-0.825312\pi$
$509$	37963.3	−	141681.i	0.146531	−	0.546860i	0.999682	−	0.0251974i	$-0.00802144\pi$
$510$	−277976.	−	481469.i	−1.06873	−	1.85109i
$511$	−102878.	−	59396.9i	−0.393988	−	0.227469i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	−1125.96	+	301.701i	−0.00427847	+	0.00114641i
$514$	9397.15	+	35070.6i	0.0355688	+	0.132745i
$515$	370950.	−	370950.i	1.39862	−	1.39862i
$516$	67487.4	−	116892.i	0.253468	−	0.439020i
$517$	−140561.	+	81152.9i	−0.525876	+	0.303615i
$518$	41469.2	+	11111.6i	0.154549	+	0.0414113i
$519$		−	78.1612i		−	0.000290173i
$520$	148680.	+	22992.0i	0.549854	+	0.0850297i
$521$	−510268.			−1.87985			−0.939923	−	0.341385i	$-0.889104\pi$
$521$	−510268.			−1.87985			−0.939923	+	0.341385i	$0.889104\pi$
$522$	42143.2	−	157281.i	0.154663	−	0.577210i
$523$	265595.	+	460024.i	0.970993	+	1.68181i	0.692570	+	0.721351i	$0.256478\pi$
$523$	265595.	+	460024.i	0.970993	+	1.68181i	0.278423	+	0.960458i	$0.410188\pi$
$524$	111220.	+	64212.7i	0.405060	+	0.233861i
$525$	543666.	+	543666.i	1.97248	+	1.97248i
$526$	−163513.	+	43813.2i	−0.590992	+	0.158356i
$527$	−10325.5	−	38535.1i	−0.0371782	−	0.138751i
$528$	−45330.2	+	45330.2i	−0.162600	+	0.162600i
$529$	−33164.2	+	57442.0i	−0.118511	+	0.205267i
$530$	242830.	−	140198.i	0.864473	−	0.499104i
$531$	−33169.7	−	8887.79i	−0.117639	−	0.0315213i
$532$		−	2947.64i		−	0.0104148i
$533$	200673.	−	455189.i	0.706375	−	1.60228i
$534$	−139872.			−0.490510
$535$	165980.	−	619447.i	0.579895	−	2.16420i
$536$	−38813.3	−	67226.6i	−0.135099	−	0.233998i
$537$	263058.	+	151876.i	0.912226	+	0.526674i
$538$	−161315.	−	161315.i	−0.557329	−	0.557329i
$539$	−196243.	+	52583.3i	−0.675488	+	0.180996i
$540$	−17914.7	−	66858.4i	−0.0614357	−	0.229281i
$541$	−266982.	+	266982.i	−0.912194	+	0.912194i	−0.996445	−	0.0842501i	$-0.973151\pi$
$541$	−266982.	+	266982.i	−0.912194	+	0.912194i	0.0842501	+	0.996445i	$0.473151\pi$
$542$	−109350.	+	189401.i	−0.372239	+	0.644737i
$543$	140230.	−	80961.7i	0.475599	−	0.274587i
$544$	−72885.8	−	19529.7i	−0.246289	−	0.0659929i
$545$			831284.i			2.79870i
$546$	144076.	+	371269.i	0.483288	+	1.24538i
$547$	412153.			1.37748			0.688738	−	0.725010i	$-0.258165\pi$
$547$	412153.			1.37748			0.688738	+	0.725010i	$0.258165\pi$
$548$	−22589.7	+	84306.0i	−0.0752228	+	0.280735i
$549$	−84755.5	−	146801.i	−0.281205	−	0.487062i
$550$	188918.	+	109072.i	0.624522	+	0.360568i
$551$	3443.99	+	3443.99i	0.0113438	+	0.0113438i
$552$	−121045.	+	32433.8i	−0.397253	+	0.106444i
$553$	59383.1	+	221621.i	0.194184	+	0.724703i
$554$	−109898.	+	109898.i	−0.358073	+	0.358073i
$555$	51482.8	−	89170.9i	0.167139	−	0.289492i
$556$	94120.7	−	54340.6i	0.304464	−	0.175782i
$557$	−201918.	−	54103.8i	−0.650826	−	0.174388i	−0.0817239	−	0.996655i	$-0.526043\pi$
$557$	−201918.	−	54103.8i	−0.650826	−	0.174388i	−0.569102	+	0.822267i	$0.692709\pi$
$558$			16959.6i			0.0544686i
$559$	−185429.	−	149039.i	−0.593409	−	0.476953i
$560$	175028.			0.558124
$561$	108067.	−	403311.i	0.343374	−	1.28149i
$562$	49841.5	+	86328.1i	0.157804	+	0.273325i
$563$	−184885.	−	106744.i	−0.583291	−	0.336763i	0.179149	−	0.983822i	$-0.442666\pi$
$563$	−184885.	−	106744.i	−0.583291	−	0.336763i	−0.762440	+	0.647059i	$0.775999\pi$
$564$	131673.	+	131673.i	0.413940	+	0.413940i
$565$	−111730.	+	29937.9i	−0.350003	+	0.0937830i
$566$	29825.6	+	111311.i	0.0931016	+	0.347460i
$567$	378996.	−	378996.i	1.17888	−	1.17888i
$568$	−79577.9	+	137833.i	−0.246658	+	0.427225i
$569$	372690.	−	215173.i	1.15113	−	0.664603i	0.201965	−	0.979393i	$-0.435267\pi$
$569$	372690.	−	215173.i	1.15113	−	0.664603i	0.949162	+	0.314789i	$0.101934\pi$
$570$	−6828.56	−	1829.71i	−0.0210174	−	0.00563160i
$571$		−	413840.i		−	1.26929i	−0.772805	−	0.634644i	$-0.781147\pi$
$571$		−	413840.i		−	1.26929i	0.772805	−	0.634644i	$-0.218853\pi$
$572$	66748.2	+	91168.5i	0.204008	+	0.278646i
$573$	155802.			0.474530
$574$	149788.	−	559016.i	0.454624	−	1.69668i
$575$	213212.	+	369294.i	0.644875	+	1.11696i
$576$	27779.9	+	16038.8i	0.0837310	+	0.0483421i
$577$	−349122.	−	349122.i	−1.04864	−	1.04864i	−0.998755	−	0.0498841i	$-0.984115\pi$
$577$	−349122.	−	349122.i	−1.04864	−	1.04864i	−0.0498841	−	0.998755i	$-0.515885\pi$
$578$	246535.	−	66059.0i	0.737944	−	0.197732i
$579$	53198.7	+	198540.i	0.158688	+	0.592232i
$580$	−204501.	+	204501.i	−0.607909	+	0.607909i
$581$	−88645.8	+	153539.i	−0.262607	+	0.454848i
$582$	−433739.	+	250419.i	−1.28051	+	0.739302i
$583$	203411.	+	54503.9i	0.598464	+	0.160358i
$584$			38669.2i			0.113381i
$585$	414120.	−	45056.4i	1.21008	−	0.131657i
$586$	−345432.			−1.00593
$587$	2053.10	−	7662.26i	0.00595845	−	0.0222372i	−0.962883	−	0.269921i	$-0.913003\pi$
$587$	2053.10	−	7662.26i	0.00595845	−	0.0222372i	0.968841	+	0.247683i	$0.0796692\pi$
$588$	116546.	+	201864.i	0.337088	+	0.583854i
$589$	−439.330	−	253.647i	−0.00126637	−	0.000731139i
$590$	43128.2	+	43128.2i	0.123896	+	0.123896i
$591$	5727.87	−	1534.78i	0.0163990	−	0.00439411i
$592$	−3617.01	−	13498.9i	−0.0103206	−	0.0385171i
$593$	−135707.	+	135707.i	−0.385917	+	0.385917i	−0.873228	−	0.487312i	$-0.837978\pi$
$593$	−135707.	+	135707.i	−0.385917	+	0.385917i	0.487312	+	0.873228i	$0.337978\pi$
$594$	25992.1	−	45019.6i	0.0736663	−	0.127594i
$595$	−987260.	+	569995.i	−2.78867	+	1.61004i
$596$	−206682.	−	55380.3i	−0.581849	−	0.155906i
$597$		−	672907.i		−	1.88802i
$598$	23890.1	+	219578.i	0.0668061	+	0.614025i
$599$	43856.1			0.122230			0.0611149	−	0.998131i	$-0.480534\pi$
$599$	43856.1			0.122230			0.0611149	+	0.998131i	$0.480534\pi$
$600$	64776.2	−	241748.i	0.179934	−	0.671522i
$601$	119682.	+	207295.i	0.331345	+	0.573906i	0.982776	−	0.184802i	$-0.0591643\pi$
$601$	119682.	+	207295.i	0.331345	+	0.573906i	−0.651431	+	0.758708i	$0.725831\pi$
$602$	−239688.	−	138384.i	−0.661384	−	0.381850i
$603$	−151982.	−	151982.i	−0.417981	−	0.417981i
$604$	115279.	−	30888.9i	0.315992	−	0.0846699i
$605$	−77963.2	−	290963.i	−0.213000	−	0.794926i
$606$	−27909.8	+	27909.8i	−0.0759995	+	0.0759995i
$607$	−356643.	+	617723.i	−0.967957	+	1.67655i	−0.266506	+	0.963833i	$0.585869\pi$
$607$	−356643.	+	617723.i	−0.967957	+	1.67655i	−0.701451	+	0.712718i	$0.747464\pi$
$608$	−830.954	+	479.751i	−0.00224786	+	0.00129780i
$609$	−739465.	−	198139.i	−1.99381	−	0.534239i
$610$			301076.i			0.809127i
$611$	264821.	−	193886.i	0.709366	−	0.519356i
$612$	−208927.			−0.557817
$613$	−9464.09	+	35320.5i	−0.0251859	+	0.0939952i	−0.977375	−	0.211515i	$-0.932160\pi$
$613$	−9464.09	+	35320.5i	−0.0251859	+	0.0939952i	0.952189	+	0.305510i	$0.0988270\pi$
$614$	33654.8	+	58291.9i	0.0892711	+	0.154622i
$615$	−1.20205e6	−	694002.i	−3.17813	−	1.83489i
$616$	92950.3	+	92950.3i	0.244957	+	0.244957i
$617$	470065.	−	125953.i	1.23477	−	0.330856i	0.418337	−	0.908292i	$-0.362613\pi$
$617$	470065.	−	125953.i	1.23477	−	0.330856i	0.816436	+	0.577436i	$0.195947\pi$
$618$	−116994.	−	436627.i	−0.306327	−	1.14323i
$619$	−112057.	+	112057.i	−0.292453	+	0.292453i	−0.838049	−	0.545596i	$-0.816303\pi$
$619$	−112057.	+	112057.i	−0.292453	+	0.292453i	0.545596	+	0.838049i	$0.316303\pi$
$620$	15061.3	−	26087.0i	0.0391814	−	0.0678641i
$621$	88003.7	−	50809.0i	0.228201	−	0.131752i
$622$	250424.	+	67100.9i	0.647285	+	0.173439i
$623$			286809.i			0.738954i
$624$	81213.1	−	101043.i	0.208572	−	0.259499i
$625$	115759.			0.296343
$626$	−71516.5	+	266903.i	−0.182498	+	0.681091i
$627$	−2654.69	−	4598.06i	−0.00675273	−	0.0116961i
$628$	−29459.2	−	17008.3i	−0.0746968	−	0.0431262i
$629$	64362.5	+	64362.5i	0.162679	+	0.162679i
$630$	468108.	−	125429.i	1.17941	−	0.316022i
$631$	21643.7	+	80775.4i	0.0543592	+	0.202871i	0.987765	−	0.155952i	$-0.0498446\pi$
$631$	21643.7	+	80775.4i	0.0543592	+	0.202871i	−0.933405	+	0.358824i	$0.883178\pi$
$632$	52810.9	−	52810.9i	0.132218	−	0.132218i
$633$	63347.2	−	109721.i	0.158096	−	0.273830i
$634$	47688.1	−	27532.7i	0.118640	−	0.0684969i
$635$	1.12360e6	+	301069.i	2.78654	+	0.746652i
$636$		−	241606.i		−	0.597302i
$637$	383009.	−	148632.i	0.943910	−	0.366296i
$638$	−217204.			−0.533614
$639$	−114055.	+	425659.i	−0.279327	+	1.04246i
$640$	−28487.1	−	49341.2i	−0.0695487	−	0.120462i
$641$	169553.	+	97891.6i	0.412658	+	0.238248i	0.691931	−	0.721964i	$-0.256760\pi$
$641$	169553.	+	97891.6i	0.412658	+	0.238248i	−0.279273	+	0.960212i	$0.590094\pi$
$642$	−390734.	−	390734.i	−0.948007	−	0.948007i
$643$	329998.	−	88422.7i	0.798159	−	0.213866i	0.163383	−	0.986563i	$-0.447759\pi$
$643$	329998.	−	88422.7i	0.798159	−	0.213866i	0.634776	+	0.772697i	$0.281093\pi$
$644$	66506.0	+	248204.i	0.160358	+	0.598462i
$645$	−469366.	+	469366.i	−1.12822	+	1.12822i
$646$	3124.71	−	5412.16i	0.00748764	−	0.0129690i
$647$	673893.	−	389073.i	1.60984	−	0.929441i	0.620435	−	0.784258i	$-0.286956\pi$
$647$	673893.	−	389073.i	1.60984	−	0.929441i	0.989405	−	0.145184i	$-0.0463773\pi$
$648$	−168525.	−	45156.2i	−0.401342	−	0.107539i
$649$			45807.3i			0.108754i
$650$	−403640.	−	177948.i	−0.955361	−	0.421178i
$651$	79736.5			0.188146
$652$	28208.6	−	105276.i	0.0663569	−	0.247647i
$653$	−271347.	−	469988.i	−0.636355	−	1.10220i	−0.986226	−	0.165401i	$-0.947108\pi$
$653$	−271347.	−	469988.i	−0.636355	−	1.10220i	0.349872	−	0.936798i	$-0.386225\pi$
$654$	620321.	+	358142.i	1.45031	+	0.837337i
$655$	−446591.	−	446591.i	−1.04094	−	1.04094i
$656$	−181968.	+	48758.3i	−0.422852	+	0.113303i
$657$	27711.3	+	103420.i	0.0641988	+	0.239593i
$658$	269997.	−	269997.i	0.623602	−	0.623602i
$659$	−388417.	+	672759.i	−0.894392	+	1.54913i	−0.0598363	+	0.998208i	$0.519058\pi$
$659$	−388417.	+	672759.i	−0.894392	+	1.54913i	−0.834556	+	0.550924i	$0.814275\pi$
$660$	273028.	−	157633.i	0.626786	−	0.361875i
$661$	629744.	+	168739.i	1.44132	+	0.386201i	0.892996	−	0.450064i	$-0.148599\pi$
$661$	629744.	+	168739.i	1.44132	+	0.386201i	0.548325	+	0.836265i	$0.315265\pi$
$662$		−	151163.i		−	0.344928i
$663$	−129035.	+	834418.i	−0.293549	+	1.89826i
$664$	57711.2			0.130895
$665$	−3751.84	+	14002.1i	−0.00848401	+	0.0316628i
$666$	−19347.3	−	33510.4i	−0.0436185	−	0.0755495i
$667$	−367704.	−	212294.i	−0.826507	−	0.477184i
$668$	−222224.	−	222224.i	−0.498011	−	0.498011i
$669$	446500.	−	119639.i	0.997630	−	0.267314i
$670$	98805.3	+	368747.i	0.220105	+	0.821445i
$671$	−159890.	+	159890.i	−0.355120	+	0.355120i
$672$	75407.2	−	130609.i	0.166984	−	0.289224i
$673$	−636182.	+	367300.i	−1.40460	+	0.810944i	−0.994860	−	0.101260i	$-0.967713\pi$
$673$	−636182.	+	367300.i	−1.40460	+	0.810944i	−0.409736	+	0.912204i	$0.634379\pi$
$674$	−35763.6	−	9582.83i	−0.0787266	−	0.0210947i
$675$			202949.i			0.445431i
$676$	−154125.	−	168678.i	−0.337272	−	0.369117i
$677$	−275668.			−0.601464			−0.300732	−	0.953709i	$-0.597231\pi$
$677$	−275668.			−0.601464			−0.300732	+	0.953709i	$0.597231\pi$
$678$	−25796.3	+	96273.0i	−0.0561174	+	0.209433i
$679$	513489.	+	889388.i	1.11376	+	1.92909i
$680$	321369.	+	185542.i	0.695001	+	0.401259i
$681$	509210.	+	509210.i	1.09800	+	1.09800i
$682$	21852.2	−	5855.29i	0.0469815	−	0.0125887i
$683$	−7318.40	−	27312.6i	−0.0156883	−	0.0585493i	0.957638	−	0.287975i	$-0.0929819\pi$
$683$	−7318.40	−	27312.6i	−0.0156883	−	0.0585493i	−0.973326	+	0.229425i	$0.926315\pi$
$684$	−1878.57	+	1878.57i	−0.00401527	+	0.00401527i
$685$	214614.	−	371723.i	0.457380	−	0.792206i
$686$	5106.62	−	2948.31i	0.0108514	−	0.00626506i
$687$	−471471.	−	126330.i	−0.998946	−	0.267667i
$688$			90092.4i			0.190332i
$689$	−420842.	−	65079.2i	−0.886503	−	0.137089i
$690$	616276.			1.29443
$691$	84945.6	−	317021.i	0.177904	−	0.663945i	−0.818135	−	0.575026i	$-0.804992\pi$
$691$	84945.6	−	317021.i	0.177904	−	0.663945i	0.996039	−	0.0889195i	$-0.0283414\pi$
$692$	26.0853	+	45.1811i	5.44734e−5	+	9.43506e-5i
$693$	315204.	+	181983.i	0.656335	+	0.378935i
$694$	123598.	+	123598.i	0.256620	+	0.256620i
$695$	−516264.	+	138333.i	−1.06881	+	0.286388i
$696$	64497.3	+	240707.i	0.133145	+	0.496902i
$697$	867623.	−	867623.i	1.78593	−	1.78593i
$698$	262655.	−	454932.i	0.539108	−	0.933762i
$699$	565247.	−	326345.i	1.15687	−	0.667918i
$700$	−495708.	−	132825.i	−1.01165	−	0.271071i
$701$		−	645341.i		−	1.31327i	−0.754209	−	0.656634i	$-0.771980\pi$
$701$		−	645341.i		−	1.31327i	0.754209	−	0.656634i	$-0.228020\pi$
$702$	−42405.4	+	96188.6i	−0.0860492	+	0.195186i
$703$	1157.43			0.00234199
$704$	11074.8	−	41331.5i	0.0223454	−	0.0833943i
$705$	−457883.	−	793077.i	−0.921248	−	1.59565i
$706$	−474725.	−	274083.i	−0.952429	−	0.549885i
$707$	57229.4	+	57229.4i	0.114493	+	0.114493i
$708$	50764.0	−	13602.2i	0.101272	−	0.0271357i
$709$	−24512.2	−	91480.9i	−0.0487630	−	0.181986i	0.937249	−	0.348661i	$-0.113364\pi$
$709$	−24512.2	−	91480.9i	−0.0487630	−	0.181986i	−0.986012	+	0.166675i	$0.946697\pi$
$710$	553454.	−	553454.i	1.09790	−	1.09790i
$711$	103396.	−	179087.i	0.204534	−	0.354263i
$712$	80853.0	−	46680.5i	0.159491	−	0.0920821i
$713$	42716.4	+	11445.8i	0.0840264	+	0.0225148i
$714$			982284.i			1.92682i
$715$	−201029.	−	518033.i	−0.393231	−	1.01332i
$716$	−202748.			−0.395485
$717$	−140776.	+	525385.i	−0.273837	+	1.02197i
$718$	49547.9	+	85819.4i	0.0961117	+	0.166470i
$719$	578090.	+	333760.i	1.11825	+	0.645620i	0.940953	−	0.338538i	$-0.109932\pi$
$719$	578090.	+	333760.i	1.11825	+	0.645620i	0.177294	+	0.984158i	$0.443266\pi$
$720$	−111547.	−	111547.i	−0.215176	−	0.215176i
$721$	−895310.	+	239898.i	−1.72228	+	0.461483i
$722$	95381.0	+	355967.i	0.182973	+	0.682865i
$723$	−831738.	+	831738.i	−1.59115	+	1.59115i
$724$	−54039.9	+	93599.9i	−0.103095	+	0.178566i
$725$	734371.	−	423989.i	1.39714	−	0.806639i
$726$	−250711.	−	67177.8i	−0.475664	−	0.127454i
$727$		−	208700.i		−	0.394870i	−0.980316	−	0.197435i	$-0.936739\pi$
$727$		−	208700.i		−	0.394870i	0.980316	−	0.197435i	$-0.0632611\pi$
$728$	−207190.	−	166529.i	−0.390935	−	0.314215i
$729$	−269577.			−0.507257
$730$	49219.3	−	183689.i	0.0923613	−	0.344697i
$731$	−293395.	−	508174.i	−0.549057	−	0.950994i
$732$	224669.	+	129713.i	0.419296	+	0.242081i
$733$	351672.	+	351672.i	0.654530	+	0.654530i	0.954080	−	0.299550i	$-0.0968367\pi$
$733$	351672.	+	351672.i	0.654530	+	0.654530i	−0.299550	+	0.954080i	$0.596837\pi$
$734$	−460832.	+	123479.i	−0.855363	+	0.229194i
$735$	−296687.	−	1.10725e6i	−0.549191	−	2.04961i
$736$	59145.5	−	59145.5i	0.109186	−	0.109186i
$737$	−143355.	+	248298.i	−0.263924	+	0.457129i
$738$	−451729.	+	260806.i	−0.829403	+	0.478856i
$739$	−478959.	−	128337.i	−0.877021	−	0.234997i	−0.207899	−	0.978150i	$-0.566663\pi$
$739$	−478959.	−	128337.i	−0.877021	−	0.234997i	−0.669121	+	0.743153i	$0.733329\pi$
$740$			68727.0i			0.125506i
$741$	6342.46	+	8662.90i	0.0115510	+	0.0157771i
$742$	−495418.			−0.899837
$743$	−226822.	+	846512.i	−0.410873	+	1.53340i	0.382087	+	0.924126i	$0.375206\pi$
$743$	−226822.	+	846512.i	−0.410873	+	1.53340i	−0.792960	+	0.609274i	$0.791461\pi$
$744$	−12977.7	−	22478.1i	−0.0234452	−	0.0406082i
$745$	911304.	+	526142.i	1.64192	+	0.947960i
$746$	209405.	+	209405.i	0.376279	+	0.376279i
$747$	154348.	−	41357.3i	0.276604	−	0.0741158i
$748$	72132.0	+	269200.i	0.128921	+	0.481141i
$749$	−801207.	+	801207.i	−1.42817	+	1.42817i
$750$	−198621.	+	344022.i	−0.353104	+	0.611595i
$751$	221726.	−	128013.i	0.393130	−	0.226974i	−0.290386	−	0.956910i	$-0.593784\pi$
$751$	221726.	−	128013.i	0.393130	−	0.226974i	0.683515	+	0.729936i	$0.260450\pi$
$752$	−120058.	−	32169.4i	−0.212302	−	0.0568862i
$753$			356335.i			0.628446i
$754$	436649.	−	47507.6i	0.768050	−	0.0835642i
$755$	−586922.			−1.02964
$756$	−31652.5	+	118129.i	−0.0553814	+	0.206686i
$757$	−481695.	−	834321.i	−0.840583	−	1.45593i	−0.889402	−	0.457125i	$-0.848879\pi$
$757$	−481695.	−	834321.i	−0.840583	−	1.45593i	0.0488193	−	0.998808i	$-0.484454\pi$
$758$	−434746.	−	251001.i	−0.756654	−	0.436855i
$759$	327280.	+	327280.i	0.568115	+	0.568115i
$760$	4557.89	−	1221.28i	0.00789109	−	0.00211441i
$761$	101166.	+	377555.i	0.174688	+	0.651946i	0.996605	+	0.0823372i	$0.0262384\pi$
$761$	101166.	+	377555.i	0.174688	+	0.651946i	−0.821916	+	0.569608i	$0.807095\pi$
$762$	708746.	−	708746.i	1.22062	−	1.22062i
$763$	734377.	−	1.27198e6i	1.26145	−	2.18489i
$764$	−90061.4	+	51997.0i	−0.154295	+	0.0890823i
$765$	992458.	+	265928.i	1.69586	+	0.454404i
$766$			80928.3i			0.137925i
$767$	−10019.1	−	92087.0i	−0.0170309	−	0.156534i
$768$	−49092.5			−0.0832324
$769$	−48645.7	+	181548.i	−0.0822606	+	0.307001i	−0.994781	−	0.102030i	$-0.967466\pi$
$769$	−48645.7	+	181548.i	−0.0822606	+	0.307001i	0.912521	+	0.409030i	$0.134133\pi$
$770$	−323229.	−	559848.i	−0.545166	−	0.944255i
$771$	−133242.	−	76927.1i	−0.224146	−	0.129411i
$772$	−97011.9	−	97011.9i	−0.162776	−	0.162776i
$773$	−508697.	+	136305.i	−0.851335	+	0.228115i	−0.658000	−	0.753018i	$-0.728597\pi$
$773$	−508697.	+	136305.i	−0.851335	+	0.228115i	−0.193335	+	0.981133i	$0.561931\pi$
$774$	64562.4	+	240950.i	0.107770	+	0.402203i
$775$	−62453.0	+	62453.0i	−0.103980	+	0.103980i
$776$	167149.	−	289510.i	0.277574	−	0.480773i
$777$	−157551.	+	90962.4i	−0.260964	+	0.150668i
$778$	380460.	+	101944.i	0.628565	+	0.168423i
$779$		−	15602.5i		−	0.0257110i
$780$	−514394.	+	376609.i	−0.845486	+	0.619015i
$781$	587835.			0.963725
$782$	−141003.	+	526229.i	−0.230576	+	0.860520i
$783$	−101038.	−	175003.i	−0.164801	−	0.285444i
$784$	−134739.	−	77791.7i	−0.219211	−	0.126561i
$785$	118290.	+	118290.i	0.191960	+	0.191960i
$786$	−525660.	+	140850.i	−0.850863	+	0.227988i
$787$	−100095.	−	373559.i	−0.161608	−	0.603129i	−0.998449	−	0.0556824i	$-0.982267\pi$
$787$	−100095.	−	373559.i	−0.161608	−	0.603129i	0.836841	−	0.547447i	$-0.184400\pi$
$788$	−2798.79	+	2798.79i	−0.00450731	+	0.00450731i
$789$	358665.	−	621226.i	0.576149	−	0.997920i
$790$	−318085.	+	183646.i	−0.509670	+	0.294258i
$791$	197409.	+	52895.7i	0.315511	+	0.0845409i
$792$		−	118477.i		−	0.188879i
$793$	286457.	−	356400.i	0.455525	−	0.566749i
$794$	103182.			0.163668
$795$	−307524.	+	1.14769e6i	−0.486569	+	1.81590i
$796$	224574.	+	388974.i	0.354433	+	0.613895i
$797$	−726468.	−	419426.i	−1.14367	−	0.660297i	−0.196331	−	0.980538i	$-0.562903\pi$
$797$	−726468.	−	419426.i	−1.14367	−	0.660297i	−0.947336	+	0.320241i	$0.896236\pi$
$798$	8832.21	+	8832.21i	0.0138696	+	0.0138696i
$799$	781959.	−	209525.i	1.22487	−	0.328203i
$800$	43236.5	+	161361.i	0.0675570	+	0.252126i
$801$	182787.	−	182787.i	0.284892	−	0.284892i
$802$	189912.	−	328936.i	0.295259	−	0.511403i
$803$	123688.	−	71411.6i	0.191822	−	0.110748i
$804$	317734.	+	85136.6i	0.491532	+	0.131706i
$805$		−	1.26368e6i		−	1.95006i
$806$	−42649.1	+	16550.5i	−0.0656508	+	0.0254766i
$807$	966720.			1.48441
$808$	6818.72	−	25447.8i	0.0104443	−	0.0389787i
$809$	280234.	+	485380.i	0.428178	+	0.741626i	0.996711	−	0.0810342i	$-0.0258223\pi$
$809$	280234.	+	485380.i	0.428178	+	0.741626i	−0.568533	+	0.822660i	$0.692489\pi$
$810$	743063.	+	429008.i	1.13255	+	0.653876i
$811$	2176.16	+	2176.16i	0.00330863	+	0.00330863i	0.708759	−	0.705451i	$-0.249255\pi$
$811$	2176.16	+	2176.16i	0.00330863	+	0.00330863i	−0.705451	+	0.708759i	$0.749255\pi$
$812$	493574.	−	132253.i	0.748584	−	0.200582i
$813$	−239859.	−	895168.i	−0.362891	−	1.35433i
$814$	−36498.2	+	36498.2i	−0.0550837	+	0.0550837i
$815$	−267996.	+	464184.i	−0.403472	+	0.698835i
$816$	276910.	−	159874.i	0.415871	−	0.240103i
$817$	−7207.31	−	1931.19i	−0.0107976	−	0.00289322i
$818$			32465.6i			0.0485195i
$819$	−673463.	−	296901.i	−1.00403	−	0.442633i
$820$	926458.			1.37784
$821$	29085.6	−	108549.i	0.0431511	−	0.161042i	−0.940988	−	0.338439i	$-0.890101\pi$
$821$	29085.6	−	108549.i	0.0431511	−	0.161042i	0.984139	+	0.177397i	$0.0567677\pi$
$822$	−184925.	−	320299.i	−0.273685	−	0.474036i
$823$	564321.	+	325811.i	0.833157	+	0.481023i	0.854932	−	0.518739i	$-0.173599\pi$
$823$	564321.	+	325811.i	0.833157	+	0.481023i	−0.0217754	+	0.999763i	$0.506932\pi$
$824$	213347.	+	213347.i	0.314219	+	0.314219i
$825$	−892886.	+	239248.i	−1.31186	+	0.351512i
$826$	−27891.5	−	104092.i	−0.0408800	−	0.152566i
$827$	458846.	−	458846.i	0.670897	−	0.670897i	−0.287026	−	0.957923i	$-0.592667\pi$
$827$	458846.	−	458846.i	0.670897	−	0.670897i	0.957923	+	0.287026i	$0.0926665\pi$
$828$	115798.	−	200569.i	0.168905	−	0.292551i
$829$	−1.05721e6	+	610378.i	−1.53833	+	0.888157i	−0.539396	+	0.842052i	$0.681347\pi$
$829$	−1.05721e6	+	610378.i	−1.53833	+	0.888157i	−0.998937	+	0.0461047i	$0.985319\pi$
$830$	−274143.	−	73456.5i	−0.397944	−	0.106629i
$831$		−	658590.i		−	0.953703i
$832$	−13223.6	+	85511.6i	−0.0191030	+	0.123532i
$833$	1.01334e6			1.46038
$834$	−119196.	+	444844.i	−0.171367	+	0.639552i
$835$	772770.	+	1.33848e6i	1.10835	+	1.91972i
$836$	3069.09	+	1771.94i	0.00439134	+	0.00253534i
$837$	14882.7	+	14882.7i	0.0212438	+	0.0212438i
$838$	611486.	−	163847.i	0.870760	−	0.233320i
$839$	−222798.	−	831494.i	−0.316510	−	1.18123i	−0.922575	−	0.385817i	$-0.873919\pi$
$839$	−222798.	−	831494.i	−0.316510	−	1.18123i	0.606065	−	0.795415i	$-0.292747\pi$
$840$	−524447.	+	524447.i	−0.743264	+	0.743264i
$841$	−68523.8	+	118687.i	−0.0968835	+	0.167807i
$842$	−802797.	+	463495.i	−1.13235	+	0.653764i
$843$	−408014.	−	109327.i	−0.574143	−	0.153841i
$844$			84565.3i			0.118716i
$845$	517438.	+	997439.i	0.724677	+	1.39692i
$846$	−344145.			−0.480840
$847$	−137749.	+	514087.i	−0.192009	+	0.716588i
$848$	80633.1	+	139661.i	0.112130	+	0.194215i
$849$	−422897.	−	244159.i	−0.586704	−	0.338733i
$850$	−769366.	−	769366.i	−1.06487	−	1.06487i
$851$	−97460.7	+	26114.5i	−0.134577	+	0.0360597i
$852$	−174553.	−	651442.i	−0.240464	−	0.897422i
$853$	−835615.	+	835615.i	−1.14844	+	1.14844i	−0.161579	+	0.986860i	$0.551659\pi$
$853$	−835615.	+	835615.i	−1.14844	+	1.14844i	−0.986860	+	0.161579i	$0.948341\pi$
$854$	265978.	−	460687.i	0.364695	−	0.631670i
$855$	11314.8	−	6532.60i	0.0154780	−	0.00893621i
$856$	356267.	+	95461.4i	0.486215	+	0.130281i
$857$			1.00820e6i			1.37273i	0.727256	+	0.686366i	$0.240795\pi$
$857$			1.00820e6i			1.37273i	−0.727256	+	0.686366i	$0.759205\pi$
$858$	−473176.	−	73172.2i	−0.642759	−	0.0993966i
$859$	−766118.			−1.03827			−0.519134	−	0.854693i	$-0.673745\pi$
$859$	−766118.			−1.03827			−0.519134	+	0.854693i	$0.673745\pi$
$860$	114672.	−	427963.i	0.155046	−	0.578641i
$861$	1.22620e6	+	2.12383e6i	1.65407	+	2.86493i
$862$	712276.	+	411233.i	0.958592	+	0.553444i
$863$	−205886.	−	205886.i	−0.276442	−	0.276442i	0.555245	−	0.831687i	$-0.312625\pi$
$863$	−205886.	−	205886.i	−0.276442	−	0.276442i	−0.831687	+	0.555245i	$0.812625\pi$
$864$	38452.7	−	10303.4i	0.0515110	−	0.0138023i
$865$	−66.4044	−	247.824i	−8.87492e−5	−	0.000331216i
$866$	444506.	−	444506.i	0.592710	−	0.592710i
$867$	−540773.	+	936647.i	−0.719411	+	1.24606i
$868$	−46091.7	+	26611.1i	−0.0611763	+	0.0353202i
$869$	−266450.	−	71395.0i	−0.352838	−	0.0945427i
$870$		−	1.22552e6i		−	1.61913i
$871$	233880.	−	530512.i	0.308288	−	0.699293i
$872$	−478102.			−0.628764
$873$	239566.	−	894071.i	0.314337	−	1.17312i
$874$	3463.76	+	5999.41i	0.00453446	+	0.00785391i
$875$	705423.	+	407276.i	0.921368	+	0.531952i
$876$	−115867.	−	115867.i	−0.150991	−	0.150991i
$877$	−1.21310e6	+	325049.i	−1.57724	+	0.422619i	−0.938069	−	0.346449i	$-0.887387\pi$
$877$	−1.21310e6	+	325049.i	−1.57724	+	0.422619i	−0.639167	+	0.769068i	$0.720721\pi$
$878$	−222278.	−	829554.i	−0.288342	−	1.07611i
$879$	1.03504e6	−	1.03504e6i	1.33961	−	1.33961i
$880$	−105216.	+	182239.i	−0.135868	+	0.235330i
$881$	325424.	−	187884.i	0.419274	−	0.242068i	−0.275493	−	0.961303i	$-0.588841\pi$
$881$	325424.	−	187884.i	0.419274	−	0.242068i	0.694767	+	0.719235i	$0.255508\pi$
$882$	−416105.	−	111495.i	−0.534891	−	0.143324i
$883$			420890.i			0.539818i	0.962886	+	0.269909i	$0.0869936\pi$
$883$			420890.i			0.539818i	−0.962886	+	0.269909i	$0.913006\pi$
$884$	−203888.	−	525400.i	−0.260908	−	0.672334i
$885$	−258456.			−0.329989
$886$	76007.0	−	283662.i	0.0968247	−	0.361355i
$887$	−520909.	−	902240.i	−0.662086	−	1.14677i	−0.980067	−	0.198669i	$-0.936338\pi$
$887$	−520909.	−	902240.i	−0.662086	−	1.14677i	0.317981	−	0.948097i	$-0.396995\pi$
$888$	51285.5	+	29609.7i	0.0650382	+	0.0375498i
$889$	−1.45329e6	−	1.45329e6i	−1.83887	−	1.83887i
$890$	−443489.	+	118833.i	−0.559890	+	0.150022i
$891$	166782.	+	622441.i	0.210085	+	0.784048i
$892$	−218171.	+	218171.i	−0.274201	+	0.274201i
$893$	5147.04	−	8914.93i	0.00645438	−	0.0111793i
$894$	785235.	−	453355.i	0.982481	−	0.567236i
$895$	963104.	+	258063.i	1.20234	+	0.322166i
$896$			100665.i			0.125390i
$897$	−729519.	−	586351.i	−0.906675	−	0.728741i
$898$	−44925.1			−0.0557104
$899$	22761.0	−	84945.2i	0.0281625	−	0.105104i
$900$	231270.	+	400572.i	0.285519	+	0.494533i
$901$	−909637.	−	525179.i	−1.12052	−	0.646931i
$902$	492006.	+	492006.i	0.604724	+	0.604724i
$903$	1.13284e6	−	303544.i	1.38929	−	0.372260i
$904$	−17218.4	−	64259.8i	−0.0210695	−	0.0786326i
$905$	375840.	−	375840.i	0.458888	−	0.458888i
$906$	−252864.	+	437973.i	−0.308056	+	0.533569i
$907$	−976545.	+	563808.i	−1.18707	+	0.685357i	−0.957640	−	0.287967i	$-0.907021\pi$
$907$	−976545.	+	563808.i	−1.18707	+	0.685357i	−0.229433	+	0.973324i	$0.573687\pi$
$908$	−464292.	−	124407.i	−0.563144	−	0.150894i
$909$		−	72946.1i		−	0.0882824i
$910$	772242.	+	1.05477e6i	0.932547	+	1.27373i
$911$	621926.			0.749380			0.374690	−	0.927150i	$-0.377749\pi$
$911$	621926.			0.749380			0.374690	+	0.927150i	$0.377749\pi$
$912$	1052.33	−	3927.35i	0.00126521	−	0.00472183i
$913$	−106577.	−	184597.i	−0.127856	−	0.221453i
$914$	562975.	+	325034.i	0.673902	+	0.389077i
$915$	−902135.	−	902135.i	−1.07753	−	1.07753i
$916$	314695.	−	84322.4i	0.375059	−	0.100497i
$917$	288815.	+	1.07787e6i	0.343464	+	1.28183i
$918$	−183342.	+	183342.i	−0.217559	+	0.217559i
$919$	−106064.	+	183708.i	−0.125584	+	0.217518i	−0.921961	−	0.387282i	$-0.873414\pi$
$919$	−106064.	+	183708.i	−0.125584	+	0.217518i	0.796377	+	0.604801i	$0.206747\pi$
$920$	−356239.	+	205675.i	−0.420887	+	0.242999i
$921$	−275506.	−	73821.7i	−0.324797	−	0.0870291i
$922$		−	149101.i		−	0.175396i
$923$	−1.18173e6	+	128573.i	−1.38712	+	0.150920i
$924$	−557027.			−0.652427
$925$	52155.4	−	194647.i	0.0609559	−	0.227491i
$926$	274879.	+	476104.i	0.320567	+	0.555239i
$927$	723482.	+	417703.i	0.841916	+	0.486080i
$928$	−117616.	−	117616.i	−0.136575	−	0.136575i
$929$	−449582.	+	120465.i	−0.520928	+	0.139582i	−0.509696	−	0.860355i	$-0.670242\pi$
$929$	−449582.	+	120465.i	−0.520928	+	0.139582i	−0.0112322	+	0.999937i	$0.503575\pi$
$930$	33036.9	+	123295.i	0.0381973	+	0.142554i
$931$	9111.50	−	9111.50i	0.0105121	−	0.0105121i
$932$	−217827.	+	377288.i	−0.250773	+	0.434351i
$933$	−951421.	+	549303.i	−1.09297	+	0.631028i
$934$	−134198.	−	35958.3i	−0.153834	−	0.0412198i
$935$		−	1.37058e6i		−	1.56777i
$936$	25913.6	+	238175.i	0.0295785	+	0.271860i
$937$	860175.			0.979733			0.489867	−	0.871797i	$-0.337045\pi$
$937$	860175.			0.979733			0.489867	+	0.871797i	$0.337045\pi$
$938$	174574.	−	651519.i	0.198415	−	0.740494i
$939$	−585450.	−	1.01403e6i	−0.663986	−	1.15006i
$940$	529359.	+	305626.i	0.599094	+	0.345887i
$941$	976348.	+	976348.i	1.10262	+	1.10262i	0.994094	+	0.108525i	$0.0346128\pi$
$941$	976348.	+	976348.i	1.10262	+	1.10262i	0.108525	+	0.994094i	$0.465387\pi$
$942$	139234.	−	37307.5i	0.156907	−	0.0420431i
$943$	352030.	+	1.31380e6i	0.395874	+	1.47742i
$944$	−24804.6	+	24804.6i	−0.0278348	+	0.0278348i
$945$	300715.	−	520854.i	0.336738	−	0.583247i
$946$	288172.	−	166376.i	0.322010	−	0.185913i
$947$	102024.	+	27337.3i	0.113763	+	0.0304828i	0.315252	−	0.949008i	$-0.397911\pi$
$947$	102024.	+	27337.3i	0.113763	+	0.0304828i	−0.201488	+	0.979491i	$0.564578\pi$
$948$			316482.i			0.352153i
$949$	−233033.	+	170613.i	−0.258753	+	0.189443i
$950$	−13835.5			−0.0153302
$951$	−60392.8	+	225389.i	−0.0667766	+	0.249214i
$952$	−327825.	−	567809.i	−0.361716	−	0.626511i
$953$	1.04127e6	+	601175.i	1.14650	+	0.661935i	0.948033	−	0.318172i	$-0.103069\pi$
$953$	1.04127e6	+	601175.i	1.14650	+	0.661935i	0.198471	+	0.980107i	$0.436402\pi$
$954$	315736.	+	315736.i	0.346918	+	0.346918i
$955$	493998.	−	132366.i	0.541650	−	0.145135i
$956$	−93964.7	−	350681.i	−0.102813	−	0.383704i
$957$	650824.	−	650824.i	0.710624	−	0.710624i
$958$	−524801.	+	908982.i	−0.571826	+	0.990431i
$959$	−656778.	+	379191.i	−0.714136	+	0.412307i
$960$	233202.	+	62486.3i	0.253040	+	0.0678020i
$961$		−	914361.i		−	0.990082i
$962$	65389.8	−	81355.8i	0.0706578	−	0.0879100i
$963$	1.02124e6			1.10122
$964$	203204.	−	758369.i	0.218665	−	0.816068i
$965$	337353.	+	584312.i	0.362268	+	0.627466i
$966$	−942986.	−	544433.i	−1.01053	−	0.583432i
$967$	641718.	+	641718.i	0.686264	+	0.686264i	0.961404	−	0.275140i	$-0.0887241\pi$
$967$	641718.	+	641718.i	0.686264	+	0.686264i	−0.275140	+	0.961404i	$0.588724\pi$
$968$	167343.	−	44839.5i	0.178590	−	0.0478531i
$969$	6854.04	+	25579.6i	0.00729960	+	0.0272425i
$970$	−1.16250e6	+	1.16250e6i	−1.23552	+	1.23552i
$971$	130271.	−	225636.i	0.138168	−	0.239315i	−0.788635	−	0.614862i	$-0.789212\pi$
$971$	130271.	−	225636.i	0.138168	−	0.239315i	0.926803	+	0.375547i	$0.122545\pi$
$972$	516854.	−	298406.i	0.547061	−	0.315846i
$973$	912160.	+	244413.i	0.963486	+	0.258165i
$974$		−	211015.i		−	0.222431i
$975$	1.74265e6	−	676257.i	1.83316	−	0.711382i
$976$	−173160.			−0.181781
$977$	439458.	−	1.64008e6i	0.460392	−	1.71821i	−0.211340	−	0.977413i	$-0.567783\pi$
$977$	439458.	−	1.64008e6i	0.460392	−	1.71821i	0.671732	−	0.740794i	$-0.265551\pi$
$978$	230922.	+	399968.i	0.241428	+	0.418165i
$979$	−298627.	−	172412.i	−0.311576	−	0.179888i
$980$	541031.	+	541031.i	0.563339	+	0.563339i
$981$	−1.27867e6	+	342620.i	−1.32869	+	0.356020i
$982$	12676.1	+	47307.7i	0.0131450	+	0.0490579i
$983$	156188.	−	156188.i	0.161637	−	0.161637i	−0.621655	−	0.783291i	$-0.713539\pi$
$983$	156188.	−	156188.i	0.161637	−	0.161637i	0.783291	+	0.621655i	$0.213539\pi$
$984$	399146.	−	691341.i	0.412232	−	0.714007i
$985$	16857.3	−	9732.59i	0.0173747	−	0.0100313i
$986$	1.04645e6	+	280395.i	1.07638	+	0.288414i
$987$			1.61802e6i			1.66092i
$988$	−6557.40	−	2890.87i	−0.00671765	−	0.00296152i
$989$	650459.			0.665009
$990$	−150801.	+	562796.i	−0.153863	+	0.574223i
$991$	−220476.	−	381876.i	−0.224499	−	0.388844i	0.731670	−	0.681659i	$-0.238741\pi$
$991$	−220476.	−	381876.i	−0.224499	−	0.388844i	−0.956169	+	0.292815i	$0.905408\pi$
$992$	15003.6	+	8662.32i	0.0152465	+	0.00880259i
$993$	452939.	+	452939.i	0.459347	+	0.459347i
$994$	−1.33579e6	+	357925.i	−1.35197	+	0.362259i
$995$	−571689.	−	2.13357e6i	−0.577449	−	2.15507i
$996$	−172924.	+	172924.i	−0.174316	+	0.174316i
$997$	426938.	−	739479.i	0.429511	−	0.743935i	−0.567319	−	0.823498i	$-0.692019\pi$
$997$	426938.	−	739479.i	0.429511	−	0.743935i	0.996830	+	0.0795630i	$0.0253525\pi$
$998$	−264324.	+	152608.i	−0.265385	+	0.153220i
$999$	−46384.8	−	12428.8i	−0.0464777	−	0.0124537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.f.a.11.2	✓	8
3.2	odd	2		234.5.bb.c.37.1		8
13.2	odd	12		338.5.d.h.239.1		8
13.3	even	3		338.5.d.h.99.1		8
13.6	odd	12	inner	26.5.f.a.19.2	yes	8
13.10	even	6		338.5.d.e.99.1		8
13.11	odd	12		338.5.d.e.239.1		8
39.32	even	12		234.5.bb.c.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.f.a.11.2	✓	8	1.1	even	1	trivial
26.5.f.a.19.2	yes	8	13.6	odd	12	inner
234.5.bb.c.19.1		8	39.32	even	12
234.5.bb.c.37.1		8	3.2	odd	2
338.5.d.e.99.1		8	13.10	even	6
338.5.d.e.239.1		8	13.11	odd	12
338.5.d.h.99.1		8	13.3	even	3
338.5.d.h.239.1		8	13.2	odd	12

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.732051 - 2.73205i) q^{2} +(5.99273 + 10.3797i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(27.8195 + 27.8195i) q^{5} +(32.7449 - 8.77397i) q^{6} +(-17.9912 - 67.1439i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-31.3257 + 54.2577i) q^{9} +O(q^{10})\)	\(q+(0.732051 - 2.73205i) q^{2} +(5.99273 + 10.3797i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(27.8195 + 27.8195i) q^{5} +(32.7449 - 8.77397i) q^{6} +(-17.9912 - 67.1439i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-31.3257 + 54.2577i) q^{9} +(96.3695 - 55.6389i) q^{10} +(80.7257 + 21.6304i) q^{11} -95.8837i q^{12} +(-167.015 - 25.8273i) q^{13} -196.611 q^{14} +(-122.044 + 455.473i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-360.998 - 208.422i) q^{17} +(125.303 + 125.303i) q^{18} +(-5.11994 + 1.37188i) q^{19} +(-81.4611 - 304.017i) q^{20} +(589.119 - 589.119i) q^{21} +(118.191 - 204.712i) q^{22} +(400.168 - 231.037i) q^{23} +(-261.959 - 70.1918i) q^{24} +922.846i q^{25} +(-192.825 + 437.386i) q^{26} +219.917 q^{27} +(-143.929 + 537.152i) q^{28} +(-459.437 - 795.768i) q^{29} +(1155.03 + 666.859i) q^{30} +(67.6743 + 67.6743i) q^{31} +(174.851 - 46.8513i) q^{32} +(259.250 + 967.535i) q^{33} +(-833.689 + 833.689i) q^{34} +(1367.40 - 2368.41i) q^{35} +(434.061 - 250.605i) q^{36} +(-210.920 - 56.5158i) q^{37} +14.9922i q^{38} +(-732.796 - 1888.34i) q^{39} -890.223 q^{40} +(-761.848 + 2843.26i) q^{41} +(-1178.24 - 2040.77i) q^{42} +(1219.10 + 703.847i) q^{43} +(-472.762 - 472.762i) q^{44} +(-2380.88 + 637.956i) q^{45} +(-338.262 - 1262.41i) q^{46} +(-1373.25 + 1373.25i) q^{47} +(-383.535 + 664.302i) q^{48} +(-2105.30 + 1215.50i) q^{49} +(2521.26 + 675.570i) q^{50} -4996.07i q^{51} +(1053.80 + 846.996i) q^{52} +2519.79 q^{53} +(160.990 - 600.824i) q^{54} +(1644.00 + 2847.49i) q^{55} +(1362.16 + 786.444i) q^{56} +(-44.9222 - 44.9222i) q^{57} +(-2510.41 + 672.662i) q^{58} +(141.861 + 529.433i) q^{59} +(2667.43 - 2667.43i) q^{60} +(-1352.81 + 2343.14i) q^{61} +(234.431 - 135.349i) q^{62} +(4206.66 + 1127.17i) q^{63} -512.000i q^{64} +(-3927.76 - 5364.77i) q^{65} +2833.14 q^{66} +(-887.915 + 3313.75i) q^{67} +(1667.38 + 2887.98i) q^{68} +(4796.20 + 2769.09i) q^{69} +(-5469.62 - 5469.62i) q^{70} +(6794.09 - 1820.47i) q^{71} +(-366.912 - 1369.33i) q^{72} +(1208.41 - 1208.41i) q^{73} +(-308.808 + 534.871i) q^{74} +(-9578.88 + 5530.37i) q^{75} +(40.9595 + 10.9751i) q^{76} -5809.40i q^{77} +(-5695.49 + 619.672i) q^{78} -3300.68 q^{79} +(-651.689 + 2432.13i) q^{80} +(3855.28 + 6677.55i) q^{81} +(7210.21 + 4162.81i) q^{82} +(-1803.48 - 1803.48i) q^{83} +(-6438.01 + 1725.06i) q^{84} +(-4244.57 - 15841.0i) q^{85} +(2815.39 - 2815.39i) q^{86} +(5506.56 - 9537.65i) q^{87} +(-1637.70 + 945.525i) q^{88} +(-3985.42 - 1067.89i) q^{89} +6971.71i q^{90} +(1270.65 + 11678.7i) q^{91} -3696.59 q^{92} +(-296.886 + 1107.99i) q^{93} +(2746.51 + 4757.09i) q^{94} +(-180.599 - 104.269i) q^{95} +(1534.14 + 1534.14i) q^{96} +(-14270.6 + 3823.79i) q^{97} +(1779.61 + 6641.59i) q^{98} +(-3702.40 + 3702.40i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9	\( 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9} + 132 q^{10} + 192 q^{11} - 78 q^{13} - 344 q^{14} + 132 q^{15} + 256 q^{16} - 870 q^{17} - 360 q^{18} - 218 q^{19} - 144 q^{20} + 1914 q^{21} + 948 q^{22} + 264 q^{23} - 288 q^{24} - 520 q^{26} - 2268 q^{27} - 736 q^{28} - 252 q^{29} + 1728 q^{30} - 3376 q^{31} + 512 q^{32} + 1698 q^{33} + 1080 q^{34} + 6474 q^{35} + 2016 q^{36} + 2552 q^{37} - 5928 q^{39} - 960 q^{40} - 8472 q^{41} - 3828 q^{42} + 7290 q^{43} - 3792 q^{44} - 6282 q^{45} - 540 q^{46} + 4848 q^{47} + 9678 q^{49} + 2524 q^{50} - 832 q^{52} - 6840 q^{53} + 2268 q^{54} + 294 q^{55} + 4320 q^{56} - 4434 q^{57} - 7008 q^{58} - 4632 q^{59} + 9024 q^{60} + 8670 q^{61} + 3936 q^{62} + 8100 q^{63} - 2808 q^{65} - 984 q^{66} - 12446 q^{67} - 2160 q^{68} + 19206 q^{69} - 25896 q^{70} - 4554 q^{71} - 5472 q^{72} + 19294 q^{73} + 10112 q^{74} - 25992 q^{75} + 1744 q^{76} - 8580 q^{78} - 11328 q^{79} - 1152 q^{80} + 6048 q^{81} + 42672 q^{82} + 10344 q^{83} - 8592 q^{84} - 23178 q^{85} + 13536 q^{86} + 18372 q^{87} + 1440 q^{88} - 2538 q^{89} + 1456 q^{91} + 96 q^{92} - 162 q^{93} - 9696 q^{94} + 26568 q^{95} - 64282 q^{97} - 31676 q^{98} + 9504 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9 + 132 * q^10 + 192 * q^11 - 78 * q^13 - 344 * q^14 + 132 * q^15 + 256 * q^16 - 870 * q^17 - 360 * q^18 - 218 * q^19 - 144 * q^20 + 1914 * q^21 + 948 * q^22 + 264 * q^23 - 288 * q^24 - 520 * q^26 - 2268 * q^27 - 736 * q^28 - 252 * q^29 + 1728 * q^30 - 3376 * q^31 + 512 * q^32 + 1698 * q^33 + 1080 * q^34 + 6474 * q^35 + 2016 * q^36 + 2552 * q^37 - 5928 * q^39 - 960 * q^40 - 8472 * q^41 - 3828 * q^42 + 7290 * q^43 - 3792 * q^44 - 6282 * q^45 - 540 * q^46 + 4848 * q^47 + 9678 * q^49 + 2524 * q^50 - 832 * q^52 - 6840 * q^53 + 2268 * q^54 + 294 * q^55 + 4320 * q^56 - 4434 * q^57 - 7008 * q^58 - 4632 * q^59 + 9024 * q^60 + 8670 * q^61 + 3936 * q^62 + 8100 * q^63 - 2808 * q^65 - 984 * q^66 - 12446 * q^67 - 2160 * q^68 + 19206 * q^69 - 25896 * q^70 - 4554 * q^71 - 5472 * q^72 + 19294 * q^73 + 10112 * q^74 - 25992 * q^75 + 1744 * q^76 - 8580 * q^78 - 11328 * q^79 - 1152 * q^80 + 6048 * q^81 + 42672 * q^82 + 10344 * q^83 - 8592 * q^84 - 23178 * q^85 + 13536 * q^86 + 18372 * q^87 + 1440 * q^88 - 2538 * q^89 + 1456 * q^91 + 96 * q^92 - 162 * q^93 - 9696 * q^94 + 26568 * q^95 - 64282 * q^97 - 31676 * q^98 + 9504 * q^99

Introduction

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