LMFDB - Embedded newform 26.5.f.a.19.2

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			19.2
Root			$-2.16680 + 2.16680i$ of defining polynomial
Character	$\chi$	$=$	26.19
Dual form			26.5.f.a.11.2

$q$-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 $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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	−0.313192	−	0.949690i	$-0.601398\pi$
$3$	5.99273	−	10.3797i	0.665859	−	1.15330i	0.979052	−	0.203612i	$-0.0652682\pi$
$4$	−6.92820	+	4.00000i	−0.433013	+	0.250000i
$5$	27.8195	−	27.8195i	1.11278	−	1.11278i	0.120006	−	0.992773i	$-0.461709\pi$
$5$	27.8195	−	27.8195i	1.11278	−	1.11278i	0.992773	−	0.120006i	$-0.0382913\pi$
$6$	32.7449	+	8.77397i	0.909581	+	0.243721i
$7$	−17.9912	+	67.1439i	−0.367167	+	1.37028i	0.497293	+	0.867583i	$0.334327\pi$
$7$	−17.9912	+	67.1439i	−0.367167	+	1.37028i	−0.864460	+	0.502702i	$0.832339\pi$
$8$	−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	0.0906817	−	0.995880i	$-0.471095\pi$
$11$	80.7257	−	21.6304i	0.667154	−	0.178763i	0.576473	+	0.817116i	$0.304429\pi$
$12$			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	−0.970935	−	0.239342i	$-0.923068\pi$
$17$	−360.998	+	208.422i	−1.24913	+	0.721184i	−0.278192	+	0.960526i	$0.589735\pi$
$18$	125.303	−	125.303i	0.386737	−	0.386737i
$19$	−5.11994	−	1.37188i	−0.0141827	−	0.00380023i	0.251721	−	0.967800i	$-0.419004\pi$
$19$	−5.11994	−	1.37188i	−0.0141827	−	0.00380023i	−0.265903	+	0.964000i	$0.585670\pi$
$20$	−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	0.828024	−	0.560693i	$-0.189465\pi$
$23$	400.168	+	231.037i	0.756461	+	0.436743i	−0.0715624	+	0.997436i	$0.522799\pi$
$24$	−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	0.452226	+	0.891904i	$0.350630\pi$
$29$	−459.437	+	795.768i	−0.546298	+	0.946216i	−0.998524	+	0.0543128i	$0.982703\pi$
$30$	1155.03	−	666.859i	1.28337	−	0.740954i
$31$	67.6743	−	67.6743i	0.0704208	−	0.0704208i	−0.671019	−	0.741440i	$-0.734143\pi$
$31$	67.6743	−	67.6743i	0.0704208	−	0.0704208i	0.741440	+	0.671019i	$0.234143\pi$
$32$	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	−0.335029	−	0.942208i	$-0.608746\pi$
$37$	−210.920	+	56.5158i	−0.154069	+	0.0412826i	0.180960	+	0.983490i	$0.442079\pi$
$38$		−	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	−0.693294	−	0.720655i	$-0.743841\pi$
$41$	−761.848	−	2843.26i	−0.453211	−	1.69141i	0.240083	−	0.970752i	$-0.422825\pi$
$42$	−1178.24	+	2040.77i	−0.667935	+	1.15690i
$43$	1219.10	−	703.847i	0.659328	−	0.380663i	−0.132693	−	0.991157i	$-0.542362\pi$
$43$	1219.10	−	703.847i	0.659328	−	0.380663i	0.792021	+	0.610494i	$0.209029\pi$
$44$	−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	0.324293	−	0.945957i	$-0.394874\pi$
$47$	−1373.25	−	1373.25i	−0.621664	−	0.621664i	−0.945957	+	0.324293i	$0.894874\pi$
$48$	−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	−0.942551	−	0.334062i	$-0.891581\pi$
$59$	141.861	−	529.433i	0.0407530	−	0.152092i	0.983304	+	0.181970i	$0.0582473\pi$
$60$	2667.43	+	2667.43i	0.740954	+	0.740954i
$61$	−1352.81	−	2343.14i	−0.363562	−	0.629707i	0.624983	−	0.780639i	$-0.285106\pi$
$61$	−1352.81	−	2343.14i	−0.363562	−	0.629707i	−0.988544	+	0.150932i	$0.951773\pi$
$62$	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	−0.991525	−	0.129918i	$-0.958529\pi$
$67$	−887.915	−	3313.75i	−0.197798	−	0.738192i	0.793727	−	0.608275i	$-0.208138\pi$
$68$	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	0.859310	−	0.511456i	$-0.170894\pi$
$71$	6794.09	+	1820.47i	1.34777	+	0.361133i	0.488456	+	0.872589i	$0.337560\pi$
$72$	−366.912	+	1369.33i	−0.0707778	+	0.264146i
$73$	1208.41	+	1208.41i	0.226762	+	0.226762i	0.811338	−	0.584577i	$-0.198739\pi$
$73$	1208.41	+	1208.41i	0.226762	+	0.226762i	−0.584577	+	0.811338i	$0.698739\pi$
$74$	−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	−0.825781	−	0.563991i	$-0.809265\pi$
$83$	−1803.48	+	1803.48i	−0.261791	+	0.261791i	0.563991	+	0.825781i	$0.309265\pi$
$84$	−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	−0.501460	−	0.865181i	$-0.667203\pi$
$89$	−3985.42	+	1067.89i	−0.503146	+	0.134818i	−0.00168638	+	0.999999i	$0.500537\pi$
$90$		−	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	−0.598042	−	0.801465i	$-0.704055\pi$
$97$	−14270.6	−	3823.79i	−1.51669	−	0.406397i	−0.918652	+	0.395067i	$0.870721\pi$
$98$	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	0.449762	−	0.893148i	$-0.351509\pi$
$101$	−1008.33	−	582.159i	−0.0988460	−	0.0570688i	−0.548608	+	0.836080i	$0.684842\pi$
$102$	−13649.5	+	3657.38i	−1.31195	+	0.351536i
$103$			13334.2i			1.25688i	0.777860	+	0.628438i	$0.216305\pi$
$103$			13334.2i			1.25688i	−0.777860	+	0.628438i	$0.783695\pi$
$104$	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	0.252288	+	0.967652i	$0.418817\pi$
$107$	−8150.17	+	14116.5i	−0.711868	+	1.23299i	−0.964155	+	0.265339i	$0.914516\pi$
$108$	−1523.63	+	879.667i	−0.130627	+	0.0754173i
$109$	14940.7	−	14940.7i	1.25753	−	1.25753i	0.305259	−	0.952269i	$-0.401257\pi$
$109$	14940.7	−	14940.7i	1.25753	−	1.25753i	0.952269	−	0.305259i	$-0.0987430\pi$
$110$	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	0.802704	−	0.596378i	$-0.203394\pi$
$113$	−1470.05	−	2546.19i	−0.115126	−	0.199404i	−0.917830	+	0.396973i	$0.870061\pi$
$114$	−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	0.993709	+	0.111996i	$0.0357245\pi$
$127$	25605.7	+	14783.4i	1.58755	+	0.916575i	0.593846	+	0.804579i	$0.297609\pi$
$128$	−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	0.849007	+	0.528382i	$0.177201\pi$
$137$	−2823.71	+	10538.2i	−0.150446	+	0.561471i	−0.999452	+	0.0330889i	$0.989466\pi$
$138$	11076.4	+	11076.4i	0.581619	+	0.581619i
$139$	−6792.57	−	11765.1i	−0.351564	−	0.608927i	0.634959	−	0.772545i	$-0.281017\pi$
$139$	−6792.57	−	11765.1i	−0.351564	−	0.608927i	−0.986524	+	0.163618i	$0.947683\pi$
$140$	−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	0.788442	−	0.615109i	$-0.210888\pi$
$149$	25835.3	+	6922.53i	1.16370	+	0.311812i	0.375256	+	0.926921i	$0.377555\pi$
$150$	8097.02	−	30218.5i	0.359868	−	1.34304i
$151$	−10548.8	−	10548.8i	−0.462645	−	0.462645i	0.436877	−	0.899521i	$-0.356085\pi$
$151$	−10548.8	−	10548.8i	−0.462645	−	0.462645i	−0.899521	+	0.436877i	$0.856085\pi$
$152$	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	−0.867283	−	0.497815i	$-0.834136\pi$
$163$	3526.07	−	13159.5i	0.132714	−	0.495295i	0.999997	+	0.00252066i	$0.000802351\pi$
$164$	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	0.496557	−	0.868004i	$-0.334597\pi$
$167$	37945.5	−	10167.5i	1.36059	−	0.364569i	0.864033	+	0.503435i	$0.167931\pi$
$168$		−	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	−0.500094	−	0.865971i	$-0.666701\pi$
$173$	−5.64764	+	3.26067i	−0.000188701	+	0.000108947i	0.499906	+	0.866080i	$0.333368\pi$
$174$	−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	0.801736	−	0.597678i	$-0.203910\pi$
$179$	21948.1	+	12671.7i	0.684999	+	0.395485i	−0.116737	+	0.993163i	$0.537243\pi$
$180$	19047.1	−	5103.65i	0.587873	−	0.157520i
$181$			13510.0i			0.412380i	0.978512	+	0.206190i	$0.0661065\pi$
$181$			13510.0i			0.412380i	−0.978512	+	0.206190i	$0.933894\pi$
$182$	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	0.941252	−	0.337705i	$-0.109651\pi$
$191$	6499.62	+	11257.7i	0.178165	+	0.308590i	−0.763087	+	0.646295i	$0.776317\pi$
$192$	5314.42	+	3068.28i	0.144163	+	0.0832324i
$193$	16565.1	−	4438.60i	0.444712	−	0.119160i	−0.0295118	−	0.999564i	$-0.509395\pi$
$193$	16565.1	−	4438.60i	0.444712	−	0.119160i	0.474224	+	0.880404i	$0.342729\pi$
$194$		−	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	0.967556	−	0.252657i	$-0.0813043\pi$
$197$	128.053	+	477.902i	0.00329958	+	0.0123142i	−0.964256	+	0.264971i	$0.914638\pi$
$198$	7404.80	−	12825.5i	0.188879	−	0.327148i
$199$	−48621.7	+	28071.8i	−1.22779	+	0.708865i	−0.966567	−	0.256413i	$-0.917459\pi$
$199$	−48621.7	+	28071.8i	−1.22779	+	0.708865i	−0.261223	+	0.965278i	$0.584126\pi$
$200$	−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	−0.919259	−	0.393653i	$-0.871211\pi$
$211$	−5285.33	+	9154.47i	−0.118716	+	0.205621i	0.800543	+	0.599275i	$0.204544\pi$
$212$	−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	0.990709	+	0.135998i	$0.0434240\pi$
$223$	9982.04	+	37253.5i	0.200729	+	0.749130i	−0.789980	+	0.613132i	$0.789909\pi$
$224$	−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	0.773426	−	0.633887i	$-0.218542\pi$
$227$	58036.5	+	15550.8i	1.12629	+	0.301788i	0.352863	+	0.935675i	$0.385208\pi$
$228$	131.541	−	490.919i	0.00253042	−	0.00944366i
$229$	−28796.6	−	28796.6i	−0.549124	−	0.549124i	0.377063	−	0.926188i	$-0.376934\pi$
$229$	−28796.6	−	28796.6i	−0.549124	−	0.549124i	−0.926188	+	0.377063i	$0.876934\pi$
$230$	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	$0.167235\pi$
$233$			54456.8i			1.00309i	−0.865131	+	0.501546i	$0.832765\pi$
$234$	−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	−0.368031	−	0.929813i	$-0.619968\pi$
$239$	32089.5	−	32089.5i	0.561782	−	0.561782i	0.929813	+	0.368031i	$0.119968\pi$
$240$	−29150.3	−	7810.79i	−0.506081	−	0.135604i
$241$	25400.5	−	94796.1i	0.437330	−	1.63214i	−0.298100	−	0.954535i	$-0.596353\pi$
$241$	25400.5	−	94796.1i	0.437330	−	1.63214i	0.735429	−	0.677601i	$-0.236980\pi$
$242$	−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	−0.281541	−	0.959549i	$-0.590846\pi$
$251$	25747.4	−	14865.3i	0.408683	−	0.235953i	0.690224	+	0.723596i	$0.257512\pi$
$252$	−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	0.413477	−	0.910515i	$-0.364314\pi$
$257$	−11116.9	−	6418.37i	−0.168314	−	0.0971759i	−0.581790	+	0.813339i	$0.697648\pi$
$258$	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	−0.997099	−	0.0761107i	$-0.975750\pi$
$263$	−29925.0	+	51831.6i	−0.432636	+	0.749347i	0.564463	+	0.825458i	$0.309083\pi$
$264$	−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	0.997718	+	0.0675147i	$0.0215070\pi$
$269$	40328.9	+	69851.6i	0.557329	+	0.965321i	−0.440390	+	0.897807i	$0.645160\pi$
$270$	21193.3	+	12235.9i	0.290717	+	0.167846i
$271$	−74687.8	+	20012.5i	−1.01698	+	0.272498i	−0.728542	−	0.685002i	$-0.759802\pi$
$271$	−74687.8	+	20012.5i	−1.01698	+	0.272498i	−0.288435	+	0.957500i	$0.593135\pi$
$272$			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	−0.776947	−	0.629566i	$-0.783233\pi$
$277$	−47587.3	+	27474.5i	−0.620200	+	0.358073i	0.156747	+	0.987639i	$0.449899\pi$
$278$	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	0.531469	−	0.847078i	$-0.321640\pi$
$281$	−24920.8	−	24920.8i	−0.315609	−	0.315609i	−0.847078	+	0.531469i	$0.821640\pi$
$282$	−32918.2	−	57016.0i	−0.413940	−	0.716966i
$283$	−35284.1	−	20371.3i	−0.440561	−	0.254358i	0.263274	−	0.964721i	$-0.415198\pi$
$283$	−35284.1	−	20371.3i	−0.440561	−	0.254358i	−0.703836	+	0.710363i	$0.748531\pi$
$284$	−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	0.494842	+	0.868983i	$0.335226\pi$
$293$	−31609.2	+	117967.i	−0.368195	+	1.37412i	−0.863037	+	0.505140i	$0.831441\pi$
$294$	−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	0.612178	−	0.790720i	$-0.290294\pi$
$307$	−16827.4	−	16827.4i	−0.178542	−	0.178542i	−0.790720	+	0.612178i	$0.790294\pi$
$308$	−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	$-0.842866\pi$
$311$		−	91661.6i		−	0.947691i	0.880608	−	0.473845i	$-0.157134\pi$
$312$	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	−0.635284	−	0.772278i	$-0.719117\pi$
$317$	13766.4	−	13766.4i	0.136994	−	0.136994i	0.772278	+	0.635284i	$0.219117\pi$
$318$	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	0.486593	−	0.873629i	$-0.338239\pi$
$331$	51623.0	+	13832.4i	0.471181	+	0.126253i	−0.0154123	+	0.999881i	$0.504906\pi$
$332$	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	$0.0183550\pi$
$337$			13090.4i			0.115264i	−0.998338	+	0.0576319i	$0.981645\pi$
$338$	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	0.708714	−	0.705496i	$-0.249276\pi$
$347$	−30899.4	−	53519.3i	−0.256620	−	0.444479i	−0.965334	+	0.261016i	$0.915942\pi$
$348$	−76301.2	−	44052.5i	−0.630047	−	0.363758i
$349$	179397.	−	48069.3i	1.47287	−	0.394654i	0.568955	−	0.822368i	$-0.307348\pi$
$349$	179397.	−	48069.3i	1.47287	−	0.394654i	0.903914	+	0.427714i	$0.140681\pi$
$350$			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	0.808541	+	0.588440i	$0.200258\pi$
$353$	50160.6	+	187202.i	0.402544	+	1.50231i	−0.405997	+	0.913874i	$0.633076\pi$
$354$	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	0.604433	−	0.796656i	$-0.293400\pi$
$359$	−24773.9	−	24773.9i	−0.192223	−	0.192223i	−0.796656	+	0.604433i	$0.793400\pi$
$360$	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	0.362145	+	0.932122i	$0.382045\pi$
$367$	−84338.1	+	146078.i	−0.626169	+	1.08456i	−0.988314	+	0.152434i	$0.951289\pi$
$368$	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	0.614238	−	0.789121i	$-0.289463\pi$
$373$	−52351.4	−	90675.2i	−0.376279	−	0.651735i	−0.990518	+	0.137386i	$0.956130\pi$
$374$	−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	0.919437	+	0.393237i	$0.128645\pi$
$379$	45936.4	+	171437.i	0.319800	+	1.19351i	−0.599637	+	0.800272i	$0.704689\pi$
$380$	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	0.163381	−	0.986563i	$-0.447760\pi$
$383$	−27637.5	−	7405.45i	−0.188409	−	0.0504840i	−0.351790	+	0.936079i	$0.614427\pi$
$384$	−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	$-0.847799\pi$
$389$		−	139258.i		−	0.920283i	0.887846	−	0.460141i	$-0.152201\pi$
$390$	−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	−0.929482	−	0.368868i	$-0.879746\pi$
$397$	9441.85	−	35237.5i	0.0599068	−	0.223575i	0.989389	+	0.145292i	$0.0464123\pi$
$398$	−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	0.168155	−	0.985761i	$-0.446219\pi$
$401$	129712.	−	34756.2i	0.806662	−	0.216144i	0.638507	+	0.769616i	$0.279552\pi$
$402$		−	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	0.225527	−	0.974237i	$-0.427590\pi$
$409$	−11087.2	−	2970.81i	−0.0662789	−	0.0177594i	−0.291806	+	0.956477i	$0.594256\pi$
$410$	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	−0.348551	−	0.937290i	$-0.613326\pi$
$419$	111910.	−	193833.i	0.637441	−	1.10408i	0.985992	−	0.166790i	$-0.0533403\pi$
$420$	−227092.	+	131112.i	−1.28737	+	0.743264i
$421$	−231747.	+	231747.i	−1.30753	+	1.30753i	−0.384333	+	0.923195i	$0.625568\pi$
$421$	−231747.	+	231747.i	−1.30753	+	1.30753i	−0.923195	+	0.384333i	$0.874432\pi$
$422$	−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	−0.803781	−	0.594925i	$-0.797182\pi$
$431$	−75260.8	−	280877.i	−0.405149	−	1.51204i	0.398632	−	0.917111i	$-0.369485\pi$
$432$	7037.34	−	12189.0i	0.0377087	−	0.0653133i
$433$	192477.	−	111127.i	1.02660	−	0.592710i	0.110593	−	0.993866i	$-0.464725\pi$
$433$	192477.	−	111127.i	1.02660	−	0.592710i	0.916010	+	0.401156i	$0.131392\pi$
$434$	−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	0.990213	−	0.139568i	$-0.0445713\pi$
$439$	262958.	+	151819.i	1.36445	+	0.787765i	0.374237	+	0.927333i	$0.377905\pi$
$440$	−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	−0.975372	−	0.220567i	$-0.929209\pi$
$449$	−4110.93	+	15342.2i	−0.0203914	+	0.0761018i	0.954980	+	0.296669i	$0.0958758\pi$
$450$	−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	−0.948968	−	0.315374i	$-0.897870\pi$
$457$	−59485.3	−	222002.i	−0.284824	−	1.06298i	0.664143	−	0.747606i	$-0.268797\pi$
$458$	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	0.376618	−	0.926369i	$-0.377087\pi$
$461$	50918.9	+	13643.7i	0.239595	+	0.0641992i	−0.137023	+	0.990568i	$0.543754\pi$
$462$	−50971.5	+	190228.i	−0.238805	+	0.891232i
$463$	−137439.	−	137439.i	−0.641134	−	0.641134i	0.309700	−	0.950834i	$-0.399771\pi$
$463$	−137439.	−	137439.i	−0.641134	−	0.641134i	−0.950834	+	0.309700i	$0.899771\pi$
$464$	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	$0.0359225\pi$
$467$			49120.0i			0.225229i	−0.993639	+	0.112615i	$0.964077\pi$
$468$	−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	−0.933377	−	0.358897i	$-0.883153\pi$
$479$	−358446.	+	96045.3i	−1.56226	+	0.418606i	−0.628880	+	0.777502i	$0.716486\pi$
$480$		−	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	0.407521	−	0.913196i	$-0.366393\pi$
$487$	72062.9	+	19309.2i	0.303846	+	0.0814154i	−0.103675	+	0.994611i	$0.533060\pi$
$488$	−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	0.468576	−	0.883423i	$-0.344767\pi$
$491$	−14995.9	−	8657.91i	−0.0622029	−	0.0359129i	−0.530779	+	0.847510i	$0.678101\pi$
$492$	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	−0.843527	−	0.537087i	$-0.819525\pi$
$499$	−76303.8	+	76303.8i	−0.306440	+	0.306440i	0.537087	+	0.843527i	$0.319525\pi$
$500$	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	0.981412	+	0.191910i	$0.0614683\pi$
$503$	166203.	+	287872.i	0.656906	+	1.13779i	−0.324507	+	0.945883i	$0.605198\pi$
$504$	−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	0.999682	+	0.0251974i	$0.00802144\pi$
$509$	37963.3	+	141681.i	0.146531	+	0.546860i	−0.853152	+	0.521663i	$0.825312\pi$
$510$	−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	0.278423	−	0.960458i	$-0.410188\pi$
$523$	265595.	−	460024.i	0.970993	−	1.68181i	0.692570	−	0.721351i	$-0.256478\pi$
$524$	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	0.0842501	−	0.996445i	$-0.473151\pi$
$541$	−266982.	−	266982.i	−0.912194	−	0.912194i	−0.996445	+	0.0842501i	$0.973151\pi$
$542$	−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	−0.569102	−	0.822267i	$-0.692709\pi$
$557$	−201918.	+	54103.8i	−0.650826	+	0.174388i	−0.0817239	+	0.996655i	$0.526043\pi$
$558$		−	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	−0.762440	−	0.647059i	$-0.775999\pi$
$563$	−184885.	+	106744.i	−0.583291	+	0.336763i	0.179149	+	0.983822i	$0.442666\pi$
$564$	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	0.949162	−	0.314789i	$-0.101934\pi$
$569$	372690.	+	215173.i	1.15113	+	0.664603i	0.201965	+	0.979393i	$0.435267\pi$
$570$	−6828.56	+	1829.71i	−0.0210174	+	0.00563160i
$571$			413840.i			1.26929i	0.772805	+	0.634644i	$0.218853\pi$
$571$			413840.i			1.26929i	−0.772805	+	0.634644i	$0.781147\pi$
$572$	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	−0.0498841	+	0.998755i	$0.515885\pi$
$577$	−349122.	+	349122.i	−1.04864	+	1.04864i	−0.998755	+	0.0498841i	$0.984115\pi$
$578$	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	0.968841	−	0.247683i	$-0.0796692\pi$
$587$	2053.10	+	7662.26i	0.00595845	+	0.0222372i	−0.962883	+	0.269921i	$0.913003\pi$
$588$	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	0.487312	−	0.873228i	$-0.337978\pi$
$593$	−135707.	−	135707.i	−0.385917	−	0.385917i	−0.873228	+	0.487312i	$0.837978\pi$
$594$	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	−0.651431	−	0.758708i	$-0.725831\pi$
$601$	119682.	−	207295.i	0.331345	−	0.573906i	0.982776	+	0.184802i	$0.0591643\pi$
$602$	−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	−0.701451	−	0.712718i	$-0.747464\pi$
$607$	−356643.	−	617723.i	−0.967957	−	1.67655i	−0.266506	−	0.963833i	$-0.585869\pi$
$608$	−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	0.952189	−	0.305510i	$-0.0988270\pi$
$613$	−9464.09	−	35320.5i	−0.0251859	−	0.0939952i	−0.977375	+	0.211515i	$0.932160\pi$
$614$	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	0.816436	−	0.577436i	$-0.195947\pi$
$617$	470065.	+	125953.i	1.23477	+	0.330856i	0.418337	+	0.908292i	$0.362613\pi$
$618$	−116994.	+	436627.i	−0.306327	+	1.14323i
$619$	−112057.	−	112057.i	−0.292453	−	0.292453i	0.545596	−	0.838049i	$-0.316303\pi$
$619$	−112057.	−	112057.i	−0.292453	−	0.292453i	−0.838049	+	0.545596i	$0.816303\pi$
$620$	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	−0.933405	−	0.358824i	$-0.883178\pi$
$631$	21643.7	−	80775.4i	0.0543592	−	0.202871i	0.987765	+	0.155952i	$0.0498446\pi$
$632$	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	−0.279273	−	0.960212i	$-0.590094\pi$
$641$	169553.	−	97891.6i	0.412658	−	0.238248i	0.691931	+	0.721964i	$0.256760\pi$
$642$	−390734.	+	390734.i	−0.948007	+	0.948007i
$643$	329998.	+	88422.7i	0.798159	+	0.213866i	0.634776	−	0.772697i	$-0.281093\pi$
$643$	329998.	+	88422.7i	0.798159	+	0.213866i	0.163383	+	0.986563i	$0.447759\pi$
$644$	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	0.989405	+	0.145184i	$0.0463773\pi$
$647$	673893.	+	389073.i	1.60984	+	0.929441i	0.620435	+	0.784258i	$0.286956\pi$
$648$	−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	0.349872	+	0.936798i	$0.386225\pi$
$653$	−271347.	+	469988.i	−0.636355	+	1.10220i	−0.986226	+	0.165401i	$0.947108\pi$
$654$	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	−0.834556	−	0.550924i	$-0.814275\pi$
$659$	−388417.	−	672759.i	−0.894392	−	1.54913i	−0.0598363	−	0.998208i	$-0.519058\pi$
$660$	273028.	+	157633.i	0.626786	+	0.361875i
$661$	629744.	−	168739.i	1.44132	−	0.386201i	0.548325	−	0.836265i	$-0.315265\pi$
$661$	629744.	−	168739.i	1.44132	−	0.386201i	0.892996	+	0.450064i	$0.148599\pi$
$662$			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	−0.409736	−	0.912204i	$-0.634379\pi$
$673$	−636182.	−	367300.i	−1.40460	−	0.810944i	−0.994860	+	0.101260i	$0.967713\pi$
$674$	−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	−0.973326	−	0.229425i	$-0.926315\pi$
$683$	−7318.40	+	27312.6i	−0.0156883	+	0.0585493i	0.957638	+	0.287975i	$0.0929819\pi$
$684$	−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	0.996039	+	0.0889195i	$0.0283414\pi$
$691$	84945.6	+	317021.i	0.177904	+	0.663945i	−0.818135	+	0.575026i	$0.804992\pi$
$692$	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	$0.228020\pi$
$701$			645341.i			1.31327i	−0.754209	+	0.656634i	$0.771980\pi$
$702$	−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	−0.986012	−	0.166675i	$-0.946697\pi$
$709$	−24512.2	+	91480.9i	−0.0487630	+	0.181986i	0.937249	+	0.348661i	$0.113364\pi$
$710$	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	0.177294	−	0.984158i	$-0.443266\pi$
$719$	578090.	−	333760.i	1.11825	−	0.645620i	0.940953	+	0.338538i	$0.109932\pi$
$720$	−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	$0.0632611\pi$
$727$			208700.i			0.394870i	−0.980316	+	0.197435i	$0.936739\pi$
$728$	−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	−0.299550	−	0.954080i	$-0.596837\pi$
$733$	351672.	−	351672.i	0.654530	−	0.654530i	0.954080	+	0.299550i	$0.0968367\pi$
$734$	−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	−0.669121	−	0.743153i	$-0.733329\pi$
$739$	−478959.	+	128337.i	−0.877021	+	0.234997i	−0.207899	+	0.978150i	$0.566663\pi$
$740$		−	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	−0.792960	−	0.609274i	$-0.791461\pi$
$743$	−226822.	−	846512.i	−0.410873	−	1.53340i	0.382087	−	0.924126i	$-0.375206\pi$
$744$	−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	0.683515	−	0.729936i	$-0.260450\pi$
$751$	221726.	+	128013.i	0.393130	+	0.226974i	−0.290386	+	0.956910i	$0.593784\pi$
$752$	−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	0.0488193	+	0.998808i	$0.484454\pi$
$757$	−481695.	+	834321.i	−0.840583	+	1.45593i	−0.889402	+	0.457125i	$0.848879\pi$
$758$	−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	−0.821916	−	0.569608i	$-0.807095\pi$
$761$	101166.	−	377555.i	0.174688	−	0.651946i	0.996605	−	0.0823372i	$-0.0262384\pi$
$762$	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	0.912521	−	0.409030i	$-0.134133\pi$
$769$	−48645.7	−	181548.i	−0.0822606	−	0.307001i	−0.994781	+	0.102030i	$0.967466\pi$
$770$	−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	−0.193335	−	0.981133i	$-0.561931\pi$
$773$	−508697.	−	136305.i	−0.851335	−	0.228115i	−0.658000	+	0.753018i	$0.728597\pi$
$774$	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	0.836841	+	0.547447i	$0.184400\pi$
$787$	−100095.	+	373559.i	−0.161608	+	0.603129i	−0.998449	+	0.0556824i	$0.982267\pi$
$788$	−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	−0.947336	−	0.320241i	$-0.896236\pi$
$797$	−726468.	+	419426.i	−1.14367	+	0.660297i	−0.196331	+	0.980538i	$0.562903\pi$
$798$	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	−0.568533	−	0.822660i	$-0.692489\pi$
$809$	280234.	−	485380.i	0.428178	−	0.741626i	0.996711	+	0.0810342i	$0.0258223\pi$
$810$	743063.	−	429008.i	1.13255	−	0.653876i
$811$	2176.16	−	2176.16i	0.00330863	−	0.00330863i	−0.705451	−	0.708759i	$-0.749255\pi$
$811$	2176.16	−	2176.16i	0.00330863	−	0.00330863i	0.708759	+	0.705451i	$0.249255\pi$
$812$	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	0.984139	−	0.177397i	$-0.0567677\pi$
$821$	29085.6	+	108549.i	0.0431511	+	0.161042i	−0.940988	+	0.338439i	$0.890101\pi$
$822$	−184925.	+	320299.i	−0.273685	+	0.474036i
$823$	564321.	−	325811.i	0.833157	−	0.481023i	−0.0217754	−	0.999763i	$-0.506932\pi$
$823$	564321.	−	325811.i	0.833157	−	0.481023i	0.854932	+	0.518739i	$0.173599\pi$
$824$	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	0.957923	−	0.287026i	$-0.0926665\pi$
$827$	458846.	+	458846.i	0.670897	+	0.670897i	−0.287026	+	0.957923i	$0.592667\pi$
$828$	115798.	+	200569.i	0.168905	+	0.292551i
$829$	−1.05721e6	−	610378.i	−1.53833	−	0.888157i	−0.998937	−	0.0461047i	$-0.985319\pi$
$829$	−1.05721e6	−	610378.i	−1.53833	−	0.888157i	−0.539396	−	0.842052i	$-0.681347\pi$
$830$	−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	0.606065	+	0.795415i	$0.292747\pi$
$839$	−222798.	+	831494.i	−0.316510	+	1.18123i	−0.922575	+	0.385817i	$0.873919\pi$
$840$	−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	−0.986860	−	0.161579i	$-0.948341\pi$
$853$	−835615.	−	835615.i	−1.14844	−	1.14844i	−0.161579	−	0.986860i	$-0.551659\pi$
$854$	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	$-0.759205\pi$
$857$		−	1.00820e6i		−	1.37273i	0.727256	−	0.686366i	$-0.240795\pi$
$858$	−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	−0.831687	−	0.555245i	$-0.812625\pi$
$863$	−205886.	+	205886.i	−0.276442	+	0.276442i	0.555245	+	0.831687i	$0.312625\pi$
$864$	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	−0.639167	−	0.769068i	$-0.720721\pi$
$877$	−1.21310e6	−	325049.i	−1.57724	−	0.422619i	−0.938069	+	0.346449i	$0.887387\pi$
$878$	−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	0.694767	−	0.719235i	$-0.255508\pi$
$881$	325424.	+	187884.i	0.419274	+	0.242068i	−0.275493	+	0.961303i	$0.588841\pi$
$882$	−416105.	+	111495.i	−0.534891	+	0.143324i
$883$		−	420890.i		−	0.539818i	−0.962886	−	0.269909i	$-0.913006\pi$
$883$		−	420890.i		−	0.539818i	0.962886	−	0.269909i	$-0.0869936\pi$
$884$	−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	0.317981	+	0.948097i	$0.396995\pi$
$887$	−520909.	+	902240.i	−0.662086	+	1.14677i	−0.980067	+	0.198669i	$0.936338\pi$
$888$	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	−0.229433	−	0.973324i	$-0.573687\pi$
$907$	−976545.	−	563808.i	−1.18707	−	0.685357i	−0.957640	+	0.287967i	$0.907021\pi$
$908$	−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	0.796377	−	0.604801i	$-0.206747\pi$
$919$	−106064.	−	183708.i	−0.125584	−	0.217518i	−0.921961	+	0.387282i	$0.873414\pi$
$920$	−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	−0.0112322	−	0.999937i	$-0.503575\pi$
$929$	−449582.	−	120465.i	−0.520928	−	0.139582i	−0.509696	+	0.860355i	$0.670242\pi$
$930$	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	0.108525	−	0.994094i	$-0.465387\pi$
$941$	976348.	−	976348.i	1.10262	−	1.10262i	0.994094	−	0.108525i	$-0.0346128\pi$
$942$	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	−0.201488	−	0.979491i	$-0.564578\pi$
$947$	102024.	−	27337.3i	0.113763	−	0.0304828i	0.315252	+	0.949008i	$0.397911\pi$
$948$		−	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	0.198471	−	0.980107i	$-0.436402\pi$
$953$	1.04127e6	−	601175.i	1.14650	−	0.661935i	0.948033	+	0.318172i	$0.103069\pi$
$954$	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	−0.275140	−	0.961404i	$-0.588724\pi$
$967$	641718.	−	641718.i	0.686264	−	0.686264i	0.961404	+	0.275140i	$0.0887241\pi$
$968$	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	0.926803	−	0.375547i	$-0.122545\pi$
$971$	130271.	+	225636.i	0.138168	+	0.239315i	−0.788635	+	0.614862i	$0.789212\pi$
$972$	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	0.671732	+	0.740794i	$0.265551\pi$
$977$	439458.	+	1.64008e6i	0.460392	+	1.71821i	−0.211340	+	0.977413i	$0.567783\pi$
$978$	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	0.783291	−	0.621655i	$-0.213539\pi$
$983$	156188.	+	156188.i	0.161637	+	0.161637i	−0.621655	+	0.783291i	$0.713539\pi$
$984$	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	−0.956169	−	0.292815i	$-0.905408\pi$
$991$	−220476.	+	381876.i	−0.224499	+	0.388844i	0.731670	+	0.681659i	$0.238741\pi$
$992$	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	0.996830	−	0.0795630i	$-0.0253525\pi$
$997$	426938.	+	739479.i	0.429511	+	0.743935i	−0.567319	+	0.823498i	$0.692019\pi$
$998$	−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.19.2	yes	8
3.2	odd	2		234.5.bb.c.19.1		8
13.4	even	6		338.5.d.e.239.1		8
13.6	odd	12		338.5.d.e.99.1		8
13.7	odd	12		338.5.d.h.99.1		8
13.9	even	3		338.5.d.h.239.1		8
13.11	odd	12	inner	26.5.f.a.11.2	✓	8
39.11	even	12		234.5.bb.c.37.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.f.a.11.2	✓	8	13.11	odd	12	inner
26.5.f.a.19.2	yes	8	1.1	even	1	trivial
234.5.bb.c.19.1		8	3.2	odd	2
234.5.bb.c.37.1		8	39.11	even	12
338.5.d.e.99.1		8	13.6	odd	12
338.5.d.e.239.1		8	13.4	even	6
338.5.d.h.99.1		8	13.7	odd	12
338.5.d.h.239.1		8	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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
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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