LMFDB - Embedded newform 17.6.c.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,6,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	17.c (of order $4$, degree $2$, 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:	$2.72652493682$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 248x^{10} + 21830x^{8} + 802540x^{6} + 10668257x^{4} + 7196228x^{2} + 1183744 $ x^12 + 248x^10 + 21830x^8 + 802540x^6 + 10668257x^4 + 7196228*x^2 + 1183744
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Root			$-9.15858i$ of defining polynomial
Character	$\chi$	$=$	17.13
Dual form			17.6.c.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.15858i q^{2} +(-6.93554 - 6.93554i) q^{3} -34.5625 q^{4} +(-2.80390 - 2.80390i) q^{5} +(-56.5842 + 56.5842i) q^{6} +(-29.5355 + 29.5355i) q^{7} +20.9060i q^{8} -146.796i q^{9} +O(q^{10})$	\(q-8.15858i q^{2} +(-6.93554 - 6.93554i) q^{3} -34.5625 q^{4} +(-2.80390 - 2.80390i) q^{5} +(-56.5842 + 56.5842i) q^{6} +(-29.5355 + 29.5355i) q^{7} +20.9060i q^{8} -146.796i q^{9} +(-22.8759 + 22.8759i) q^{10} +(342.349 - 342.349i) q^{11} +(239.709 + 239.709i) q^{12} +349.268 q^{13} +(240.968 + 240.968i) q^{14} +38.8932i q^{15} -935.435 q^{16} +(952.835 + 715.515i) q^{17} -1197.65 q^{18} +475.851i q^{19} +(96.9098 + 96.9098i) q^{20} +409.690 q^{21} +(-2793.08 - 2793.08i) q^{22} +(-431.238 + 431.238i) q^{23} +(144.995 - 144.995i) q^{24} -3109.28i q^{25} -2849.53i q^{26} +(-2703.45 + 2703.45i) q^{27} +(1020.82 - 1020.82i) q^{28} +(5786.84 + 5786.84i) q^{29} +317.313 q^{30} +(2115.60 + 2115.60i) q^{31} +8300.82i q^{32} -4748.75 q^{33} +(5837.59 - 7773.78i) q^{34} +165.629 q^{35} +5073.65i q^{36} +(-2236.90 - 2236.90i) q^{37} +3882.27 q^{38} +(-2422.36 - 2422.36i) q^{39} +(58.6185 - 58.6185i) q^{40} +(12080.0 - 12080.0i) q^{41} -3342.49i q^{42} -12660.7i q^{43} +(-11832.4 + 11832.4i) q^{44} +(-411.603 + 411.603i) q^{45} +(3518.29 + 3518.29i) q^{46} -24837.1 q^{47} +(6487.75 + 6487.75i) q^{48} +15062.3i q^{49} -25367.3 q^{50} +(-1645.94 - 11570.9i) q^{51} -12071.6 q^{52} +4528.13i q^{53} +(22056.3 + 22056.3i) q^{54} -1919.83 q^{55} +(-617.470 - 617.470i) q^{56} +(3300.28 - 3300.28i) q^{57} +(47212.4 - 47212.4i) q^{58} +7867.78i q^{59} -1344.24i q^{60} +(-3131.15 + 3131.15i) q^{61} +(17260.3 - 17260.3i) q^{62} +(4335.71 + 4335.71i) q^{63} +37789.0 q^{64} +(-979.314 - 979.314i) q^{65} +38743.1i q^{66} -45839.0 q^{67} +(-32932.3 - 24730.0i) q^{68} +5981.74 q^{69} -1351.30i q^{70} +(15936.7 + 15936.7i) q^{71} +3068.93 q^{72} +(27476.6 + 27476.6i) q^{73} +(-18250.0 + 18250.0i) q^{74} +(-21564.5 + 21564.5i) q^{75} -16446.6i q^{76} +20222.9i q^{77} +(-19763.1 + 19763.1i) q^{78} +(31019.9 - 31019.9i) q^{79} +(2622.87 + 2622.87i) q^{80} +1828.24 q^{81} +(-98555.6 - 98555.6i) q^{82} -8092.24i q^{83} -14159.9 q^{84} +(-665.421 - 4677.89i) q^{85} -103293. q^{86} -80269.7i q^{87} +(7157.15 + 7157.15i) q^{88} +127902. q^{89} +(3358.10 + 3358.10i) q^{90} +(-10315.8 + 10315.8i) q^{91} +(14904.7 - 14904.7i) q^{92} -29345.7i q^{93} +202636. i q^{94} +(1334.24 - 1334.24i) q^{95} +(57570.7 - 57570.7i) q^{96} +(27814.4 + 27814.4i) q^{97} +122887. q^{98} +(-50255.6 - 50255.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7}+O(q^{10}) $ 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7	\( 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7} - 334 q^{10} - 504 q^{11} + 1722 q^{12} + 1600 q^{13} - 2364 q^{14} + 2564 q^{16} + 2432 q^{17} - 6052 q^{18} - 4218 q^{20} + 7144 q^{21} - 2590 q^{22} - 2728 q^{23} - 7246 q^{24} - 3024 q^{27} + 26164 q^{28} - 992 q^{29} + 18072 q^{30} - 14680 q^{31} - 96 q^{33} - 20962 q^{34} - 43744 q^{35} + 33552 q^{37} + 9024 q^{38} + 2720 q^{39} + 30922 q^{40} + 20716 q^{41} - 13682 q^{44} + 44848 q^{45} + 4416 q^{46} + 32032 q^{47} - 144770 q^{48} - 42636 q^{50} - 83368 q^{51} - 132556 q^{52} + 80728 q^{54} + 81040 q^{55} + 122460 q^{56} + 36840 q^{57} + 165766 q^{58} - 143200 q^{61} + 222580 q^{62} + 7592 q^{63} + 18428 q^{64} - 175016 q^{65} - 83648 q^{67} - 231150 q^{68} - 341160 q^{69} + 116088 q^{71} + 347100 q^{72} + 83892 q^{73} - 79282 q^{74} + 245864 q^{75} - 128572 q^{78} + 291672 q^{79} + 195426 q^{80} + 387028 q^{81} - 452240 q^{82} - 798600 q^{84} - 200704 q^{85} - 736076 q^{86} + 431258 q^{88} + 456424 q^{89} - 65406 q^{90} + 36224 q^{91} + 476504 q^{92} - 413488 q^{95} + 884318 q^{96} + 356284 q^{97} + 444704 q^{98} - 640440 q^{99}+O(q^{100}) \) 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7 - 334 * q^10 - 504 * q^11 + 1722 * q^12 + 1600 * q^13 - 2364 * q^14 + 2564 * q^16 + 2432 * q^17 - 6052 * q^18 - 4218 * q^20 + 7144 * q^21 - 2590 * q^22 - 2728 * q^23 - 7246 * q^24 - 3024 * q^27 + 26164 * q^28 - 992 * q^29 + 18072 * q^30 - 14680 * q^31 - 96 * q^33 - 20962 * q^34 - 43744 * q^35 + 33552 * q^37 + 9024 * q^38 + 2720 * q^39 + 30922 * q^40 + 20716 * q^41 - 13682 * q^44 + 44848 * q^45 + 4416 * q^46 + 32032 * q^47 - 144770 * q^48 - 42636 * q^50 - 83368 * q^51 - 132556 * q^52 + 80728 * q^54 + 81040 * q^55 + 122460 * q^56 + 36840 * q^57 + 165766 * q^58 - 143200 * q^61 + 222580 * q^62 + 7592 * q^63 + 18428 * q^64 - 175016 * q^65 - 83648 * q^67 - 231150 * q^68 - 341160 * q^69 + 116088 * q^71 + 347100 * q^72 + 83892 * q^73 - 79282 * q^74 + 245864 * q^75 - 128572 * q^78 + 291672 * q^79 + 195426 * q^80 + 387028 * q^81 - 452240 * q^82 - 798600 * q^84 - 200704 * q^85 - 736076 * q^86 + 431258 * q^88 + 456424 * q^89 - 65406 * q^90 + 36224 * q^91 + 476504 * q^92 - 413488 * q^95 + 884318 * q^96 + 356284 * q^97 + 444704 * q^98 - 640440 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	8.15858i		−	1.44225i	−0.692806	−	0.721124i	$-0.743626\pi$
$2$		−	8.15858i		−	1.44225i	0.692806	−	0.721124i	$-0.256374\pi$
$3$	−6.93554	−	6.93554i	−0.444915	−	0.444915i	0.448745	−	0.893660i	$-0.351871\pi$
$3$	−6.93554	−	6.93554i	−0.444915	−	0.444915i	−0.893660	+	0.448745i	$0.851871\pi$
$4$	−34.5625			−1.08008
$5$	−2.80390	−	2.80390i	−0.0501577	−	0.0501577i	0.681583	−	0.731741i	$-0.261292\pi$
$5$	−2.80390	−	2.80390i	−0.0501577	−	0.0501577i	−0.731741	+	0.681583i	$0.761292\pi$
$6$	−56.5842	+	56.5842i	−0.641678	+	0.641678i
$7$	−29.5355	+	29.5355i	−0.227824	+	0.227824i	−0.811783	−	0.583959i	$-0.801503\pi$
$7$	−29.5355	+	29.5355i	−0.227824	+	0.227824i	0.583959	+	0.811783i	$0.301503\pi$
$8$			20.9060i			0.115491i
$9$		−	146.796i		−	0.604101i
$10$	−22.8759	+	22.8759i	−0.0723399	+	0.0723399i
$11$	342.349	−	342.349i	0.853075	−	0.853075i	−0.137436	−	0.990511i	$-0.543886\pi$
$11$	342.349	−	342.349i	0.853075	−	0.853075i	0.990511	+	0.137436i	$0.0438861\pi$
$12$	239.709	+	239.709i	0.480543	+	0.480543i
$13$	349.268			0.573193			0.286596	−	0.958051i	$-0.407476\pi$
$13$	349.268			0.573193			0.286596	+	0.958051i	$0.407476\pi$
$14$	240.968	+	240.968i	0.328579	+	0.328579i
$15$			38.8932i			0.0446319i
$16$	−935.435			−0.913511
$17$	952.835	+	715.515i	0.799642	+	0.600477i
$17$	952.835	+	715.515i	0.799642	+	0.600477i
$18$	−1197.65			−0.871263
$19$			475.851i			0.302403i	0.988503	+	0.151202i	$0.0483143\pi$
$19$			475.851i			0.302403i	−0.988503	+	0.151202i	$0.951686\pi$
$20$	96.9098	+	96.9098i	0.0541742	+	0.0541742i
$21$	409.690			0.202725
$22$	−2793.08	−	2793.08i	−1.23034	−	1.23034i
$23$	−431.238	+	431.238i	−0.169980	+	0.169980i	−0.786971	−	0.616991i	$-0.788352\pi$
$23$	−431.238	+	431.238i	−0.169980	+	0.169980i	0.616991	+	0.786971i	$0.288352\pi$
$24$	144.995	−	144.995i	0.0513835	−	0.0513835i
$25$		−	3109.28i		−	0.994968i
$26$		−	2849.53i		−	0.826685i
$27$	−2703.45	+	2703.45i	−0.713689	+	0.713689i
$28$	1020.82	−	1020.82i	0.246067	−	0.246067i
$29$	5786.84	+	5786.84i	1.27775	+	1.27775i	0.941924	+	0.335827i	$0.109016\pi$
$29$	5786.84	+	5786.84i	1.27775	+	1.27775i	0.335827	+	0.941924i	$0.390984\pi$
$30$	317.313			0.0643702
$31$	2115.60	+	2115.60i	0.395394	+	0.395394i	0.876605	−	0.481211i	$-0.159803\pi$
$31$	2115.60	+	2115.60i	0.395394	+	0.395394i	−0.481211	+	0.876605i	$0.659803\pi$
$32$			8300.82i			1.43300i
$33$	−4748.75			−0.759092
$34$	5837.59	−	7773.78i	0.866037	−	1.15328i
$35$	165.629			0.0228543
$36$			5073.65i			0.652475i
$37$	−2236.90	−	2236.90i	−0.268623	−	0.268623i	0.559922	−	0.828545i	$-0.310831\pi$
$37$	−2236.90	−	2236.90i	−0.268623	−	0.268623i	−0.828545	+	0.559922i	$0.810831\pi$
$38$	3882.27			0.436140
$39$	−2422.36	−	2422.36i	−0.255022	−	0.255022i
$40$	58.6185	−	58.6185i	0.00579275	−	0.00579275i
$41$	12080.0	−	12080.0i	1.12229	−	1.12229i	0.130899	−	0.991396i	$-0.458214\pi$
$41$	12080.0	−	12080.0i	1.12229	−	1.12229i	0.991396	−	0.130899i	$-0.0417864\pi$
$42$		−	3342.49i		−	0.292379i
$43$		−	12660.7i		−	1.04420i	−0.852883	−	0.522102i	$-0.825148\pi$
$43$		−	12660.7i		−	1.04420i	0.852883	−	0.522102i	$-0.174852\pi$
$44$	−11832.4	+	11832.4i	−0.921386	+	0.921386i
$45$	−411.603	+	411.603i	−0.0303003	+	0.0303003i
$46$	3518.29	+	3518.29i	0.245153	+	0.245153i
$47$	−24837.1			−1.64005			−0.820024	−	0.572330i	$-0.806040\pi$
$47$	−24837.1			−1.64005			−0.820024	+	0.572330i	$0.806040\pi$
$48$	6487.75	+	6487.75i	0.406435	+	0.406435i
$49$			15062.3i			0.896192i
$50$	−25367.3			−1.43499
$51$	−1645.94	−	11570.9i	−0.0886112	−	0.622934i
$52$	−12071.6			−0.619092
$53$			4528.13i			0.221426i	0.993852	+	0.110713i	$0.0353135\pi$
$53$			4528.13i			0.221426i	−0.993852	+	0.110713i	$0.964687\pi$
$54$	22056.3	+	22056.3i	1.02932	+	1.02932i
$55$	−1919.83			−0.0855766
$56$	−617.470	−	617.470i	−0.0263115	−	0.0263115i
$57$	3300.28	−	3300.28i	0.134544	−	0.134544i
$58$	47212.4	−	47212.4i	1.84283	−	1.84283i
$59$			7867.78i			0.294254i	0.989118	+	0.147127i	$0.0470026\pi$
$59$			7867.78i			0.294254i	−0.989118	+	0.147127i	$0.952997\pi$
$60$		−	1344.24i		−	0.0482059i
$61$	−3131.15	+	3131.15i	−0.107741	+	0.107741i	−0.758922	−	0.651181i	$-0.774274\pi$
$61$	−3131.15	+	3131.15i	−0.107741	+	0.107741i	0.651181	+	0.758922i	$0.274274\pi$
$62$	17260.3	−	17260.3i	0.570256	−	0.570256i
$63$	4335.71	+	4335.71i	0.137629	+	0.137629i
$64$	37789.0			1.15323
$65$	−979.314	−	979.314i	−0.0287500	−	0.0287500i
$66$			38743.1i			1.09480i
$67$	−45839.0			−1.24752			−0.623761	−	0.781615i	$-0.714396\pi$
$67$	−45839.0			−1.24752			−0.623761	+	0.781615i	$0.714396\pi$
$68$	−32932.3	−	24730.0i	−0.863674	−	0.648562i
$69$	5981.74			0.151253
$70$		−	1351.30i		−	0.0329615i
$71$	15936.7	+	15936.7i	0.375191	+	0.375191i	0.869364	−	0.494173i	$-0.164529\pi$
$71$	15936.7	+	15936.7i	0.375191	+	0.375191i	−0.494173	+	0.869364i	$0.664529\pi$
$72$	3068.93			0.0697679
$73$	27476.6	+	27476.6i	0.603471	+	0.603471i	0.941232	−	0.337761i	$-0.109670\pi$
$73$	27476.6	+	27476.6i	0.603471	+	0.603471i	−0.337761	+	0.941232i	$0.609670\pi$
$74$	−18250.0	+	18250.0i	−0.387420	+	0.387420i
$75$	−21564.5	+	21564.5i	−0.442677	+	0.442677i
$76$		−	16446.6i		−	0.326619i
$77$			20222.9i			0.388702i
$78$	−19763.1	+	19763.1i	−0.367805	+	0.367805i
$79$	31019.9	−	31019.9i	0.559206	−	0.559206i	−0.369875	−	0.929081i	$-0.620600\pi$
$79$	31019.9	−	31019.9i	0.559206	−	0.559206i	0.929081	+	0.369875i	$0.120600\pi$
$80$	2622.87	+	2622.87i	0.0458196	+	0.0458196i
$81$	1828.24			0.0309615
$82$	−98555.6	−	98555.6i	−1.61863	−	1.61863i
$83$		−	8092.24i		−	0.128936i	−0.997920	−	0.0644679i	$-0.979465\pi$
$83$		−	8092.24i		−	0.128936i	0.997920	−	0.0644679i	$-0.0205350\pi$
$84$	−14159.9			−0.218958
$85$	−665.421	−	4677.89i	−0.00998963	−	0.0702268i
$86$	−103293.			−1.50600
$87$		−	80269.7i		−	1.13698i
$88$	7157.15	+	7157.15i	0.0985221	+	0.0985221i
$89$	127902.			1.71160			0.855802	−	0.517304i	$-0.173064\pi$
$89$	127902.			1.71160			0.855802	+	0.517304i	$0.173064\pi$
$90$	3358.10	+	3358.10i	0.0437006	+	0.0437006i
$91$	−10315.8	+	10315.8i	−0.130587	+	0.130587i
$92$	14904.7	−	14904.7i	0.183591	−	0.183591i
$93$		−	29345.7i		−	0.351834i
$94$			202636.i			2.36535i
$95$	1334.24	−	1334.24i	0.0151679	−	0.0151679i
$96$	57570.7	−	57570.7i	0.637563	−	0.637563i
$97$	27814.4	+	27814.4i	0.300151	+	0.300151i	0.841073	−	0.540922i	$-0.181924\pi$
$97$	27814.4	+	27814.4i	0.300151	+	0.300151i	−0.540922	+	0.841073i	$0.681924\pi$
$98$	122887.			1.29253
$99$	−50255.6	−	50255.6i	−0.515343	−	0.515343i
$100$			107464.i			1.07464i
$101$	135528.			1.32199			0.660993	−	0.750392i	$-0.270135\pi$
$101$	135528.			1.32199			0.660993	+	0.750392i	$0.270135\pi$
$102$	−94402.3	+	13428.5i	−0.898425	+	0.127799i
$103$	−140742.			−1.30716			−0.653581	−	0.756857i	$-0.726734\pi$
$103$	−140742.			−1.30716			−0.653581	+	0.756857i	$0.726734\pi$
$104$			7301.81i			0.0661983i
$105$	−1148.73	−	1148.73i	−0.0101682	−	0.0101682i
$106$	36943.1			0.319351
$107$	65354.3	+	65354.3i	0.551842	+	0.551842i	0.926972	−	0.375130i	$-0.122402\pi$
$107$	65354.3	+	65354.3i	0.551842	+	0.551842i	−0.375130	+	0.926972i	$0.622402\pi$
$108$	93437.9	−	93437.9i	0.770839	−	0.770839i
$109$	−120320.	+	120320.i	−0.969996	+	0.969996i	−0.999563	−	0.0295671i	$-0.990587\pi$
$109$	−120320.	+	120320.i	−0.969996	+	0.969996i	0.0295671	+	0.999563i	$0.490587\pi$
$110$			15663.1i			0.123423i
$111$			31028.3i			0.239029i
$112$	27628.6	−	27628.6i	0.208120	−	0.208120i
$113$	114452.	−	114452.i	0.843194	−	0.843194i	−0.146079	−	0.989273i	$-0.546665\pi$
$113$	114452.	−	114452.i	0.843194	−	0.843194i	0.989273	+	0.146079i	$0.0466653\pi$
$114$	−26925.6	−	26925.6i	−0.194045	−	0.194045i
$115$	2418.30			0.0170516
$116$	−200007.	−	200007.i	−1.38007	−	1.38007i
$117$		−	51271.3i		−	0.346266i
$118$	64190.0			0.424387
$119$	−49275.6	+	7009.36i	−0.318981	+	0.0453744i
$120$	−813.102			−0.00515456
$121$		−	73354.4i		−	0.455473i
$122$	25545.7	+	25545.7i	0.155389	+	0.155389i
$123$	−167563.			−0.998652
$124$	−73120.5	−	73120.5i	−0.427056	−	0.427056i
$125$	−17480.3	+	17480.3i	−0.100063	+	0.100063i
$126$	35373.2	−	35373.2i	0.198495	−	0.198495i
$127$			281722.i			1.54993i	0.632006	+	0.774964i	$0.282232\pi$
$127$			281722.i			1.54993i	−0.632006	+	0.774964i	$0.717768\pi$
$128$		−	42678.3i		−	0.230241i
$129$	−87808.7	+	87808.7i	−0.464583	+	0.464583i
$130$	−7989.81	+	7989.81i	−0.0414647	+	0.0414647i
$131$	−164951.	−	164951.i	−0.839800	−	0.839800i	0.149033	−	0.988832i	$-0.452384\pi$
$131$	−164951.	−	164951.i	−0.839800	−	0.839800i	−0.988832	+	0.149033i	$0.952384\pi$
$132$	164128.			0.819878
$133$	−14054.5	−	14054.5i	−0.0688947	−	0.0688947i
$134$			373981.i			1.79923i
$135$	15160.4			0.0715940
$136$	−14958.6	+	19920.0i	−0.0693495	+	0.0923511i
$137$	−73243.4			−0.333401			−0.166701	−	0.986008i	$-0.553311\pi$
$137$	−73243.4			−0.333401			−0.166701	+	0.986008i	$0.553311\pi$
$138$		−	48802.5i		−	0.218145i
$139$	59206.5	+	59206.5i	0.259916	+	0.259916i	0.825020	−	0.565104i	$-0.191164\pi$
$139$	59206.5	+	59206.5i	0.259916	+	0.259916i	−0.565104	+	0.825020i	$0.691164\pi$
$140$	−5724.56			−0.0246844
$141$	172259.	+	172259.i	0.729682	+	0.729682i
$142$	130021.	−	130021.i	0.541118	−	0.541118i
$143$	119572.	−	119572.i	0.488976	−	0.488976i
$144$			137319.i			0.551853i
$145$		−	32451.4i		−	0.128178i
$146$	224170.	−	224170.i	0.870354	−	0.870354i
$147$	104465.	−	104465.i	0.398730	−	0.398730i
$148$	77312.9	+	77312.9i	0.290133	+	0.290133i
$149$	−450295.			−1.66162			−0.830809	−	0.556558i	$-0.812122\pi$
$149$	−450295.			−1.66162			−0.830809	+	0.556558i	$0.812122\pi$
$150$	175936.	+	175936.i	0.638449	+	0.638449i
$151$		−	345710.i		−	1.23387i	−0.787013	−	0.616936i	$-0.788374\pi$
$151$		−	345710.i		−	1.23387i	0.787013	−	0.616936i	$-0.211626\pi$
$152$	−9948.14			−0.0349247
$153$	105035.	−	139873.i	0.362749	−	0.483064i
$154$	164990.			0.560604
$155$		−	11863.9i		−	0.0396641i
$156$	83722.9	+	83722.9i	0.275443	+	0.275443i
$157$	256238.			0.829649			0.414824	−	0.909901i	$-0.363843\pi$
$157$	256238.			0.829649			0.414824	+	0.909901i	$0.363843\pi$
$158$	−253078.	−	253078.i	−0.806514	−	0.806514i
$159$	31405.0	−	31405.0i	0.0985159	−	0.0985159i
$160$	23274.7	−	23274.7i	0.0718760	−	0.0718760i
$161$		−	25473.7i		−	0.0774510i
$162$		−	14915.9i		−	0.0446541i
$163$	−251500.	+	251500.i	−0.741428	+	0.741428i	−0.972853	−	0.231425i	$-0.925661\pi$
$163$	−251500.	+	251500.i	−0.741428	+	0.741428i	0.231425	+	0.972853i	$0.425661\pi$
$164$	−417514.	+	417514.i	−1.21216	+	1.21216i
$165$	13315.0	+	13315.0i	0.0380743	+	0.0380743i
$166$	−66021.2			−0.185957
$167$	408378.	+	408378.i	1.13311	+	1.13311i	0.989658	+	0.143450i	$0.0458195\pi$
$167$	408378.	+	408378.i	1.13311	+	1.13311i	0.143450	+	0.989658i	$0.454180\pi$
$168$			8564.98i			0.0234128i
$169$	−249305.			−0.671450
$170$	−38165.0	+	5428.89i	−0.101284	+	0.0144075i
$171$	69853.2			0.182682
$172$			437584.i			1.12782i
$173$	−371315.	−	371315.i	−0.943251	−	0.943251i	0.0552231	−	0.998474i	$-0.482413\pi$
$173$	−371315.	−	371315.i	−0.943251	−	0.943251i	−0.998474	+	0.0552231i	$0.982413\pi$
$174$	−654887.			−1.63981
$175$	91834.1	+	91834.1i	0.226678	+	0.226678i
$176$	−320245.	+	320245.i	−0.779293	+	0.779293i
$177$	54567.3	−	54567.3i	0.130918	−	0.130918i
$178$		−	1.04350e6i		−	2.46856i
$179$		−	415392.i		−	0.969004i	−0.874790	−	0.484502i	$-0.839001\pi$
$179$		−	415392.i		−	0.969004i	0.874790	−	0.484502i	$-0.160999\pi$
$180$	14226.0	−	14226.0i	0.0327267	−	0.0327267i
$181$	−106859.	+	106859.i	−0.242445	+	0.242445i	−0.817861	−	0.575416i	$-0.804840\pi$
$181$	−106859.	+	106859.i	−0.242445	+	0.242445i	0.575416	+	0.817861i	$0.304840\pi$
$182$	84162.4	+	84162.4i	0.188339	+	0.188339i
$183$	43432.5			0.0958709
$184$	−9015.48	−	9015.48i	−0.0196311	−	0.0196311i
$185$			12544.1i			0.0269470i
$186$	−239419.			−0.507431
$187$	571158.	−	81246.1i	1.19441	−	0.169902i
$188$	858431.			1.77138
$189$		−	159696.i		−	0.325191i
$190$	−10885.5	−	10885.5i	−0.0218758	−	0.0218758i
$191$	688796.			1.36618			0.683089	−	0.730335i	$-0.260636\pi$
$191$	688796.			1.36618			0.683089	+	0.730335i	$0.260636\pi$
$192$	−262087.	−	262087.i	−0.513089	−	0.513089i
$193$	−353389.	+	353389.i	−0.682904	+	0.682904i	−0.960653	−	0.277750i	$-0.910411\pi$
$193$	−353389.	+	353389.i	−0.682904	+	0.682904i	0.277750	+	0.960653i	$0.410411\pi$
$194$	226926.	−	226926.i	0.432892	−	0.432892i
$195$			13584.1i			0.0255827i
$196$		−	520590.i		−	0.967957i
$197$	−186250.	+	186250.i	−0.341926	+	0.341926i	−0.857091	−	0.515165i	$-0.827731\pi$
$197$	−186250.	+	186250.i	−0.341926	+	0.341926i	0.515165	+	0.857091i	$0.327731\pi$
$198$	−410014.	+	410014.i	−0.743252	+	0.743252i
$199$	674776.	+	674776.i	1.20789	+	1.20789i	0.971709	+	0.236179i	$0.0758953\pi$
$199$	674776.	+	674776.i	1.20789	+	1.20789i	0.236179	+	0.971709i	$0.424105\pi$
$200$	65002.6			0.114909
$201$	317918.	+	317918.i	0.555041	+	0.555041i
$202$		−	1.10572e6i		−	1.90663i
$203$	−341834.			−0.582205
$204$	56887.7	+	399919.i	0.0957069	+	0.672817i
$205$	−67742.2			−0.112584
$206$			1.14825e6i			1.88525i
$207$	63304.3	+	63304.3i	0.102685	+	0.102685i
$208$	−326718.			−0.523618
$209$	162907.	+	162907.i	0.257973	+	0.257973i
$210$	−9372.01	+	9372.01i	−0.0146651	+	0.0146651i
$211$	−533704.	+	533704.i	−0.825266	+	0.825266i	−0.986858	−	0.161592i	$-0.948337\pi$
$211$	−533704.	+	533704.i	−0.825266	+	0.825266i	0.161592	+	0.986858i	$0.448337\pi$
$212$		−	156503.i		−	0.239157i
$213$		−	221059.i		−	0.333856i
$214$	533199.	−	533199.i	0.795893	−	0.795893i
$215$	−35499.3	+	35499.3i	−0.0523750	+	0.0523750i
$216$	−56518.4	−	56518.4i	−0.0824243	−	0.0824243i
$217$	−124971.			−0.180161
$218$	981637.	+	981637.i	1.39897	+	1.39897i
$219$		−	381131.i		−	0.536987i
$220$	66353.9			0.0924293
$221$	332795.	+	249907.i	0.458349	+	0.344189i
$222$	253147.			0.344738
$223$		−	895942.i		−	1.20647i	−0.797562	−	0.603237i	$-0.793877\pi$
$223$		−	895942.i		−	1.20647i	0.797562	−	0.603237i	$-0.206123\pi$
$224$	−245169.	−	245169.i	−0.326472	−	0.326472i
$225$	−456431.			−0.601061
$226$	−933767.	−	933767.i	−1.21609	−	1.21609i
$227$	−75871.4	+	75871.4i	−0.0977268	+	0.0977268i	−0.754280	−	0.656553i	$-0.772014\pi$
$227$	−75871.4	+	75871.4i	−0.0977268	+	0.0977268i	0.656553	+	0.754280i	$0.272014\pi$
$228$	−114066.	+	114066.i	−0.145318	+	0.145318i
$229$		−	325768.i		−	0.410506i	−0.978709	−	0.205253i	$-0.934198\pi$
$229$		−	325768.i		−	0.410506i	0.978709	−	0.205253i	$-0.0658017\pi$
$230$		−	19729.9i		−	0.0245926i
$231$	140257.	−	140257.i	0.172939	−	0.172939i
$232$	−120980.	+	120980.i	−0.147568	+	0.147568i
$233$	−928410.	−	928410.i	−1.12034	−	1.12034i	−0.991690	−	0.128651i	$-0.958935\pi$
$233$	−928410.	−	928410.i	−1.12034	−	1.12034i	−0.128651	−	0.991690i	$-0.541065\pi$
$234$	−418301.			−0.499401
$235$	69640.8	+	69640.8i	0.0822611	+	0.0822611i
$236$		−	271930.i		−	0.317817i
$237$	−430279.			−0.497599
$238$	57186.4	+	402019.i	0.0654411	+	0.460049i
$239$	47770.2			0.0540956			0.0270478	−	0.999634i	$-0.491389\pi$
$239$	47770.2			0.0540956			0.0270478	+	0.999634i	$0.491389\pi$
$240$		−	36382.0i		−	0.0407717i
$241$	−337272.	−	337272.i	−0.374057	−	0.374057i	0.494895	−	0.868953i	$-0.335206\pi$
$241$	−337272.	−	337272.i	−0.374057	−	0.374057i	−0.868953	+	0.494895i	$0.835206\pi$
$242$	−598468.			−0.656905
$243$	644259.	+	644259.i	0.699914	+	0.699914i
$244$	108220.	−	108220.i	0.116368	−	0.116368i
$245$	42233.2	−	42233.2i	0.0449510	−	0.0449510i
$246$			1.36707e6i			1.44030i
$247$			166199.i			0.173335i
$248$	−44228.9	+	44228.9i	−0.0456643	+	0.0456643i
$249$	−56124.0	+	56124.0i	−0.0573655	+	0.0573655i
$250$	142614.	+	142614.i	0.144316	+	0.144316i
$251$	−737831.			−0.739218			−0.369609	−	0.929187i	$-0.620508\pi$
$251$	−737831.			−0.739218			−0.369609	+	0.929187i	$0.620508\pi$
$252$	−149853.	−	149853.i	−0.148650	−	0.148650i
$253$			295268.i			0.290011i
$254$	2.29845e6			2.23538
$255$	−27828.7	+	37058.8i	−0.0268004	+	0.0356895i
$256$	861053.			0.821164
$257$		−	351624.i		−	0.332082i	−0.986119	−	0.166041i	$-0.946902\pi$
$257$		−	351624.i		−	0.332082i	0.986119	−	0.166041i	$-0.0530984\pi$
$258$	716394.	+	716394.i	0.670043	+	0.670043i
$259$	132136.			0.122397
$260$	33847.5	+	33847.5i	0.0310523	+	0.0310523i
$261$	849487.	−	849487.i	0.771890	−	0.771890i
$262$	−1.34576e6	+	1.34576e6i	−1.21120	+	1.21120i
$263$			920581.i			0.820678i	0.911933	+	0.410339i	$0.134590\pi$
$263$			920581.i			0.820678i	−0.911933	+	0.410339i	$0.865410\pi$
$264$		−	99277.5i		−	0.0876680i
$265$	12696.4	−	12696.4i	0.0111062	−	0.0111062i
$266$	−114665.	+	114665.i	−0.0993632	+	0.0993632i
$267$	−887072.	−	887072.i	−0.761519	−	0.761519i
$268$	1.58431e6			1.34742
$269$	−621482.	−	621482.i	−0.523658	−	0.523658i	0.395016	−	0.918674i	$-0.370739\pi$
$269$	−621482.	−	621482.i	−0.523658	−	0.523658i	−0.918674	+	0.395016i	$0.870739\pi$
$270$		−	123688.i		−	0.103256i
$271$	1.37855e6			1.14025			0.570125	−	0.821558i	$-0.306895\pi$
$271$	1.37855e6			1.14025			0.570125	+	0.821558i	$0.306895\pi$
$272$	−891315.	−	669318.i	−0.730481	−	0.548543i
$273$	143092.			0.116200
$274$			597563.i			0.480847i
$275$	−1.06446e6	−	1.06446e6i	−0.848782	−	0.848782i
$276$	−206744.			−0.163365
$277$	914915.	+	914915.i	0.716442	+	0.716442i	0.967875	−	0.251433i	$-0.0809017\pi$
$277$	914915.	+	914915.i	0.716442	+	0.716442i	−0.251433	+	0.967875i	$0.580902\pi$
$278$	483041.	−	483041.i	0.374862	−	0.374862i
$279$	310563.	−	310563.i	0.238858	−	0.238858i
$280$			3462.65i			0.00263945i
$281$		−	483431.i		−	0.365232i	−0.983184	−	0.182616i	$-0.941543\pi$
$281$		−	483431.i		−	0.365232i	0.983184	−	0.182616i	$-0.0584565\pi$
$282$	1.40539e6	−	1.40539e6i	1.05238	−	1.05238i
$283$	−1.00145e6	+	1.00145e6i	−0.743299	+	0.743299i	−0.973211	−	0.229912i	$-0.926156\pi$
$283$	−1.00145e6	+	1.00145e6i	−0.743299	+	0.743299i	0.229912	+	0.973211i	$0.426156\pi$
$284$	−550811.	−	550811.i	−0.405235	−	0.405235i
$285$	−18507.3			−0.0134968
$286$	−975534.	−	975534.i	−0.705224	−	0.705224i
$287$			713578.i			0.511371i
$288$	1.21853e6			0.865676
$289$	395932.	+	1.36354e6i	0.278854	+	0.960334i
$290$	−264758.			−0.184865
$291$		−	385816.i		−	0.267084i
$292$	−949660.	−	949660.i	−0.651795	−	0.651795i
$293$	36005.1			0.0245016			0.0122508	−	0.999925i	$-0.496100\pi$
$293$	36005.1			0.0245016			0.0122508	+	0.999925i	$0.496100\pi$
$294$	−852288.	−	852288.i	−0.575067	−	0.575067i
$295$	22060.5	−	22060.5i	0.0147591	−	0.0147591i
$296$	46764.7	−	46764.7i	0.0310234	−	0.0310234i
$297$			1.85105e6i			1.21766i
$298$			3.67377e6i			2.39646i
$299$	−150618.	+	150618.i	−0.0974312	+	0.0974312i
$300$	745323.	−	745323.i	0.478125	−	0.478125i
$301$	373940.	+	373940.i	0.237895	+	0.237895i
$302$	−2.82051e6			−1.77955
$303$	−939963.	−	939963.i	−0.588172	−	0.588172i
$304$		−	445127.i		−	0.276249i
$305$	17558.9			0.0108080
$306$	−1.14116e6	−	856938.i	−0.696698	−	0.523174i
$307$	−2.80505e6			−1.69862			−0.849308	−	0.527898i	$-0.822980\pi$
$307$	−2.80505e6			−1.69862			−0.849308	+	0.527898i	$0.822980\pi$
$308$		−	698953.i		−	0.419828i
$309$	976119.	+	976119.i	0.581576	+	0.581576i
$310$	−96792.6			−0.0572055
$311$	969743.	+	969743.i	0.568533	+	0.568533i	0.931717	−	0.363185i	$-0.118311\pi$
$311$	969743.	+	969743.i	0.568533	+	0.568533i	−0.363185	+	0.931717i	$0.618311\pi$
$312$	50642.0	−	50642.0i	0.0294526	−	0.0294526i
$313$	−912002.	+	912002.i	−0.526181	+	0.526181i	−0.919431	−	0.393251i	$-0.871351\pi$
$313$	−912002.	+	912002.i	−0.526181	+	0.526181i	0.393251	+	0.919431i	$0.371351\pi$
$314$		−	2.09054e6i		−	1.19656i
$315$		−	24313.8i		−	0.0138063i
$316$	−1.07212e6	+	1.07212e6i	−0.603986	+	0.603986i
$317$	510921.	−	510921.i	0.285565	−	0.285565i	−0.549758	−	0.835324i	$-0.685280\pi$
$317$	510921.	−	510921.i	0.285565	−	0.285565i	0.835324	+	0.549758i	$0.185280\pi$
$318$	−256221.	−	256221.i	−0.142084	−	0.142084i
$319$	3.96223e6			2.18003
$320$	−105957.	−	105957.i	−0.0578433	−	0.0578433i
$321$		−	906535.i		−	0.491046i
$322$	−207829.			−0.111704
$323$	−340478.	+	453407.i	−0.181586	+	0.241814i
$324$	−63188.6			−0.0334408
$325$		−	1.08597e6i		−	0.570308i
$326$	2.05188e6	+	2.05188e6i	1.06932	+	1.06932i
$327$	1.66896e6			0.863132
$328$	252545.	+	252545.i	0.129614	+	0.129614i
$329$	733577.	−	733577.i	0.373642	−	0.373642i
$330$	108632.	−	108632.i	0.0549126	−	0.0549126i
$331$		−	2.25124e6i		−	1.12941i	−0.825293	−	0.564704i	$-0.808990\pi$
$331$		−	2.25124e6i		−	1.12941i	0.825293	−	0.564704i	$-0.191010\pi$
$332$			279688.i			0.139260i
$333$	−328369.	+	328369.i	−0.162275	+	0.162275i
$334$	3.33178e6	−	3.33178e6i	1.63422	−	1.63422i
$335$	128528.	+	128528.i	0.0625729	+	0.0625729i
$336$	−383238.			−0.185191
$337$	−143276.	−	143276.i	−0.0687226	−	0.0687226i	0.671910	−	0.740633i	$-0.265474\pi$
$337$	−143276.	−	143276.i	−0.0687226	−	0.0687226i	−0.740633	+	0.671910i	$0.765474\pi$
$338$			2.03397e6i			0.968397i
$339$	−1.58757e6			−0.750300
$340$	22998.6	+	161679.i	0.0107896	+	0.0758503i
$341$	1.44855e6			0.674601
$342$		−	569903.i		−	0.263473i
$343$	−941276.	−	941276.i	−0.431998	−	0.431998i
$344$	264684.			0.120596
$345$	−16772.2	−	16772.2i	−0.00758653	−	0.00758653i
$346$	−3.02940e6	+	3.02940e6i	−1.36040	+	1.36040i
$347$	977159.	−	977159.i	0.435654	−	0.435654i	−0.454892	−	0.890546i	$-0.650322\pi$
$347$	977159.	−	977159.i	0.435654	−	0.435654i	0.890546	+	0.454892i	$0.150322\pi$
$348$			2.77432e6i			1.22803i
$349$		−	301593.i		−	0.132543i	−0.997802	−	0.0662716i	$-0.978890\pi$
$349$		−	301593.i		−	0.132543i	0.997802	−	0.0662716i	$-0.0211104\pi$
$350$	749236.	−	749236.i	0.326925	−	0.326925i
$351$	−944229.	+	944229.i	−0.409081	+	0.409081i
$352$	2.84177e6	+	2.84177e6i	1.22246	+	1.22246i
$353$	3.11209e6			1.32928			0.664638	−	0.747166i	$-0.268586\pi$
$353$	3.11209e6			1.32928			0.664638	+	0.747166i	$0.268586\pi$
$354$	−445192.	−	445192.i	−0.188816	−	0.188816i
$355$		−	89369.8i		−	0.0376374i
$356$	−4.42062e6			−1.84866
$357$	390367.	+	293139.i	0.162107	+	0.121732i
$358$	−3.38901e6			−1.39754
$359$			1.40745e6i			0.576364i	0.957576	+	0.288182i	$0.0930507\pi$
$359$			1.40745e6i			0.576364i	−0.957576	+	0.288182i	$0.906949\pi$
$360$	−8604.98	−	8604.98i	−0.00349940	−	0.00349940i
$361$	2.24967e6			0.908552
$362$	871815.	+	871815.i	0.349666	+	0.349666i
$363$	−508753.	+	508753.i	−0.202647	+	0.202647i
$364$	356540.	−	356540.i	0.141044	−	0.141044i
$365$		−	154084.i		−	0.0605375i
$366$		−	354347.i		−	0.138269i
$367$	−1.42079e6	+	1.42079e6i	−0.550637	+	0.550637i	−0.926625	−	0.375988i	$-0.877303\pi$
$367$	−1.42079e6	+	1.42079e6i	−0.550637	+	0.550637i	0.375988	+	0.926625i	$0.377303\pi$
$368$	403395.	−	403395.i	0.155279	−	0.155279i
$369$	−1.77330e6	−	1.77330e6i	−0.677979	−	0.677979i
$370$	102342.			0.0388643
$371$	−133741.	−	133741.i	−0.0504462	−	0.0504462i
$372$			1.01426e6i			0.380007i
$373$	−3.63918e6			−1.35435			−0.677176	−	0.735821i	$-0.736796\pi$
$373$	−3.63918e6			−1.35435			−0.677176	+	0.735821i	$0.736796\pi$
$374$	−662853.	−	4.65984e6i	−0.245041	−	1.72263i
$375$	242471.			0.0890392
$376$		−	519245.i		−	0.189410i
$377$	2.02116e6	+	2.02116e6i	0.732397	+	0.732397i
$378$	−1.30289e6			−0.469006
$379$	−3.49826e6	−	3.49826e6i	−1.25099	−	1.25099i	−0.955276	−	0.295714i	$-0.904442\pi$
$379$	−3.49826e6	−	3.49826e6i	−1.25099	−	1.25099i	−0.295714	−	0.955276i	$-0.595558\pi$
$380$	−46114.6	+	46114.6i	−0.0163825	+	0.0163825i
$381$	1.95389e6	−	1.95389e6i	0.689586	−	0.689586i
$382$		−	5.61960e6i		−	1.97037i
$383$		−	3.25067e6i		−	1.13234i	−0.824290	−	0.566168i	$-0.808425\pi$
$383$		−	3.25067e6i		−	1.13234i	0.824290	−	0.566168i	$-0.191575\pi$
$384$	−295997.	+	295997.i	−0.102438	+	0.102438i
$385$	56703.0	−	56703.0i	0.0194964	−	0.0194964i
$386$	2.88315e6	+	2.88315e6i	0.984916	+	0.984916i
$387$	−1.85854e6			−0.630805
$388$	−961334.	−	961334.i	−0.324187	−	0.324187i
$389$			2.98999e6i			1.00184i	0.865495	+	0.500918i	$0.167004\pi$
$389$			2.98999e6i			1.00184i	−0.865495	+	0.500918i	$0.832996\pi$
$390$	110827.			0.0368965
$391$	−719457.	+	102341.i	−0.237992	+	0.0338539i
$392$	−314893.			−0.103502
$393$			2.28804e6i			0.747279i
$394$	1.51954e6	+	1.51954e6i	0.493141	+	0.493141i
$395$	−173953.			−0.0560971
$396$	1.73696e6	+	1.73696e6i	0.556610	+	0.556610i
$397$	560630.	−	560630.i	0.178525	−	0.178525i	−0.612187	−	0.790713i	$-0.709710\pi$
$397$	560630.	−	560630.i	0.178525	−	0.178525i	0.790713	+	0.612187i	$0.209710\pi$
$398$	5.50522e6	−	5.50522e6i	1.74207	−	1.74207i
$399$			194951.i			0.0613046i
$400$			2.90853e6i			0.908914i
$401$	−4.31468e6	+	4.31468e6i	−1.33995	+	1.33995i	−0.443845	+	0.896103i	$0.646386\pi$
$401$	−4.31468e6	+	4.31468e6i	−1.33995	+	1.33995i	−0.896103	+	0.443845i	$0.853614\pi$
$402$	2.59376e6	−	2.59376e6i	0.800507	−	0.800507i
$403$	738913.	+	738913.i	0.226637	+	0.226637i
$404$	−4.68419e6			−1.42785
$405$	−5126.22	−	5126.22i	−0.00155296	−	0.00155296i
$406$			2.78888e6i			0.839683i
$407$	−1.53160e6			−0.458311
$408$	241902.	−	34410.1i	0.0719430	−	0.0102338i
$409$	265441.			0.0784621			0.0392310	−	0.999230i	$-0.487509\pi$
$409$	265441.			0.0784621			0.0392310	+	0.999230i	$0.487509\pi$
$410$			552681.i			0.162373i
$411$	507983.	+	507983.i	0.148335	+	0.148335i
$412$	4.86437e6			1.41183
$413$	−232379.	−	232379.i	−0.0670381	−	0.0670381i
$414$	516473.	−	516473.i	0.148097	−	0.148097i
$415$	−22689.8	+	22689.8i	−0.00646712	+	0.00646712i
$416$			2.89921e6i			0.821384i
$417$		−	821258.i		−	0.231281i
$418$	1.32909e6	−	1.32909e6i	0.372060	−	0.372060i
$419$	−4.90492e6	+	4.90492e6i	−1.36489	+	1.36489i	−0.497318	+	0.867568i	$0.665682\pi$
$419$	−4.90492e6	+	4.90492e6i	−1.36489	+	1.36489i	−0.867568	+	0.497318i	$0.834318\pi$
$420$	39702.9	+	39702.9i	0.0109825	+	0.0109825i
$421$	1.86452e6			0.512698			0.256349	−	0.966584i	$-0.417480\pi$
$421$	1.86452e6			0.512698			0.256349	+	0.966584i	$0.417480\pi$
$422$	4.35427e6	+	4.35427e6i	1.19024	+	1.19024i
$423$			3.64600e6i			0.990754i
$424$	−94665.2			−0.0255726
$425$	2.22474e6	−	2.96263e6i	0.597456	−	0.795618i
$426$	−1.80353e6			−0.481503
$427$		−	184960.i		−	0.0490918i
$428$	−2.25881e6	−	2.25881e6i	−0.596032	−	0.596032i
$429$	−1.65859e6			−0.435106
$430$	289624.	+	289624.i	0.0755376	+	0.0755376i
$431$	3.55946e6	−	3.55946e6i	0.922976	−	0.922976i	−0.0742627	−	0.997239i	$-0.523660\pi$
$431$	3.55946e6	−	3.55946e6i	0.922976	−	0.922976i	0.997239	+	0.0742627i	$0.0236603\pi$
$432$	2.52890e6	−	2.52890e6i	0.651963	−	0.651963i
$433$		−	3.59151e6i		−	0.920571i	−0.887771	−	0.460285i	$-0.847747\pi$
$433$		−	3.59151e6i		−	0.920571i	0.887771	−	0.460285i	$-0.152253\pi$
$434$			1.01959e6i			0.259836i
$435$	−225068.	+	225068.i	−0.0570284	+	0.0570284i
$436$	4.15854e6	−	4.15854e6i	1.04767	−	1.04767i
$437$	−205205.	−	205205.i	−0.0514025	−	0.0514025i
$438$	−3.10949e6			−0.774468
$439$	−806958.	−	806958.i	−0.199843	−	0.199843i	0.600090	−	0.799933i	$-0.295132\pi$
$439$	−806958.	−	806958.i	−0.199843	−	0.199843i	−0.799933	+	0.600090i	$0.795132\pi$
$440$		−	40135.9i		−	0.00988329i
$441$	2.21109e6			0.541391
$442$	2.03888e6	−	2.71513e6i	0.496406	−	0.661052i
$443$	−74003.4			−0.0179161			−0.00895803	−	0.999960i	$-0.502851\pi$
$443$	−74003.4			−0.0179161			−0.00895803	+	0.999960i	$0.502851\pi$
$444$		−	1.07241e6i		−	0.258169i
$445$	−358626.	−	358626.i	−0.0858502	−	0.0858502i
$446$	−7.30961e6			−1.74003
$447$	3.12304e6	+	3.12304e6i	0.739279	+	0.739279i
$448$	−1.11612e6	+	1.11612e6i	−0.262733	+	0.262733i
$449$	2.22608e6	−	2.22608e6i	0.521104	−	0.521104i	−0.396801	−	0.917905i	$-0.629880\pi$
$449$	2.22608e6	−	2.22608e6i	0.521104	−	0.521104i	0.917905	+	0.396801i	$0.129880\pi$
$450$			3.72383e6i			0.866879i
$451$		−	8.27114e6i		−	1.91480i
$452$	−3.95575e6	+	3.95575e6i	−0.910715	+	0.910715i
$453$	−2.39769e6	+	2.39769e6i	−0.548968	+	0.548968i
$454$	619003.	+	619003.i	0.140946	+	0.140946i
$455$	57849.1			0.0130999
$456$	68995.8	+	68995.8i	0.0155385	+	0.0155385i
$457$		−	1.89711e6i		−	0.424914i	−0.977170	−	0.212457i	$-0.931853\pi$
$457$		−	1.89711e6i		−	0.424914i	0.977170	−	0.212457i	$-0.0681466\pi$
$458$	−2.65780e6			−0.592051
$459$	−4.51030e6	+	641582.i	−0.999250	+	0.142141i
$460$	−83582.4			−0.0184171
$461$			1.55538e6i			0.340866i	0.985369	+	0.170433i	$0.0545167\pi$
$461$			1.55538e6i			0.340866i	−0.985369	+	0.170433i	$0.945483\pi$
$462$	−1.14430e6	−	1.14430e6i	−0.249421	−	0.249421i
$463$	4.99293e6			1.08244			0.541219	−	0.840882i	$-0.317963\pi$
$463$	4.99293e6			1.08244			0.541219	+	0.840882i	$0.317963\pi$
$464$	−5.41321e6	−	5.41321e6i	−1.16724	−	1.16724i
$465$	−82282.6	+	82282.6i	−0.0176472	+	0.0176472i
$466$	−7.57451e6	+	7.57451e6i	−1.61581	+	1.61581i
$467$			5.33394e6i			1.13176i	0.824487	+	0.565882i	$0.191464\pi$
$467$			5.33394e6i			1.13176i	−0.824487	+	0.565882i	$0.808536\pi$
$468$			1.77206e6i			0.373994i
$469$	1.35388e6	−	1.35388e6i	0.284215	−	0.284215i
$470$	568170.	−	568170.i	0.118641	−	0.118641i
$471$	−1.77715e6	−	1.77715e6i	−0.369123	−	0.369123i
$472$	−164484.			−0.0339836
$473$	−4.33437e6	−	4.33437e6i	−0.890785	−	0.890785i
$474$			3.51047e6i			0.717661i
$475$	1.47955e6			0.300882
$476$	1.70309e6	−	242261.i	0.344524	−	0.0490078i
$477$	664713.			0.133764
$478$		−	389737.i		−	0.0780193i
$479$	4.16657e6	+	4.16657e6i	0.829737	+	0.829737i	0.987480	−	0.157743i	$-0.0504219\pi$
$479$	4.16657e6	+	4.16657e6i	0.829737	+	0.829737i	−0.157743	+	0.987480i	$0.550422\pi$
$480$	−322845.			−0.0639575
$481$	−781279.	−	781279.i	−0.153973	−	0.153973i
$482$	−2.75166e6	+	2.75166e6i	−0.539483	+	0.539483i
$483$	−176674.	+	176674.i	−0.0344591	+	0.0344591i
$484$			2.53531e6i			0.491946i
$485$		−	155978.i		−	0.0301098i
$486$	5.25624e6	−	5.25624e6i	1.00945	−	1.00945i
$487$	3.66403e6	−	3.66403e6i	0.700061	−	0.700061i	−0.264362	−	0.964424i	$-0.585161\pi$
$487$	3.66403e6	−	3.66403e6i	0.700061	−	0.700061i	0.964424	+	0.264362i	$0.0851614\pi$
$488$	−65459.9	−	65459.9i	−0.0124430	−	0.0124430i
$489$	3.48858e6			0.659745
$490$	−344563.	−	344563.i	−0.0648304	−	0.0648304i
$491$		−	1.02225e6i		−	0.191361i	−0.995412	−	0.0956806i	$-0.969497\pi$
$491$		−	1.02225e6i		−	0.191361i	0.995412	−	0.0956806i	$-0.0305028\pi$
$492$	5.79138e6			1.07862
$493$	1.37333e6	+	9.65447e6i	0.254482	+	1.78900i
$494$	1.35595e6			0.249992
$495$			281824.i			0.0516969i
$496$	−1.97901e6	−	1.97901e6i	−0.361197	−	0.361197i
$497$	−941396.			−0.170955
$498$	457893.	+	457893.i	0.0827352	+	0.0827352i
$499$	325286.	−	325286.i	0.0584809	−	0.0584809i	−0.677261	−	0.735742i	$-0.736833\pi$
$499$	325286.	−	325286.i	0.0584809	−	0.0584809i	0.735742	+	0.677261i	$0.236833\pi$
$500$	604162.	−	604162.i	0.108076	−	0.108076i
$501$		−	5.66464e6i		−	1.00827i
$502$			6.01966e6i			1.06614i
$503$	3.75015e6	−	3.75015e6i	0.660889	−	0.660889i	−0.294701	−	0.955590i	$-0.595220\pi$
$503$	3.75015e6	−	3.75015e6i	0.660889	−	0.660889i	0.955590	+	0.294701i	$0.0952200\pi$
$504$	−90642.5	+	90642.5i	−0.0158948	+	0.0158948i
$505$	−380008.	−	380008.i	−0.0663078	−	0.0663078i
$506$	2.40897e6			0.418268
$507$	1.72906e6	+	1.72906e6i	0.298738	+	0.298738i
$508$		−	9.73700e6i		−	1.67404i
$509$	40443.9			0.00691925			0.00345962	−	0.999994i	$-0.498899\pi$
$509$	40443.9			0.00691925			0.00345962	+	0.999994i	$0.498899\pi$
$510$	302347.	+	227042.i	0.0514731	+	0.0386529i
$511$	−1.62307e6			−0.274970
$512$		−	8.39068e6i		−	1.41456i
$513$	−1.28644e6	−	1.28644e6i	−0.215822	−	0.215822i
$514$	−2.86875e6			−0.478944
$515$	394626.	+	394626.i	0.0655643	+	0.0655643i
$516$	3.03488e6	−	3.03488e6i	0.501785	−	0.501785i
$517$	−8.50295e6	+	8.50295e6i	−1.39908	+	1.39908i
$518$		−	1.07804e6i		−	0.176527i
$519$			5.15054e6i			0.839334i
$520$	20473.6	−	20473.6i	0.00332036	−	0.00332036i
$521$	−2.21433e6	+	2.21433e6i	−0.357395	+	0.357395i	−0.862852	−	0.505457i	$-0.831324\pi$
$521$	−2.21433e6	+	2.21433e6i	−0.357395	+	0.357395i	0.505457	+	0.862852i	$0.331324\pi$
$522$	−6.93061e6	−	6.93061e6i	−1.11326	−	1.11326i
$523$	7.86611e6			1.25749			0.628747	−	0.777610i	$-0.283568\pi$
$523$	7.86611e6			1.25749			0.628747	+	0.777610i	$0.283568\pi$
$524$	5.70110e6	+	5.70110e6i	0.907048	+	0.907048i
$525$		−	1.27384e6i		−	0.201705i
$526$	7.51064e6			1.18362
$527$	502074.	+	3.52957e6i	0.0787483	+	0.553599i
$528$	4.44215e6			0.693439
$529$			6.06441e6i			0.942214i
$530$	−103585.	−	103585.i	−0.0160179	−	0.0160179i
$531$	1.15496e6			0.177759
$532$	485758.	+	485758.i	0.0744116	+	0.0744116i
$533$	4.21916e6	−	4.21916e6i	0.643291	−	0.643291i
$534$	−7.23725e6	+	7.23725e6i	−1.09830	+	1.09830i
$535$		−	366494.i		−	0.0553583i
$536$		−	958311.i		−	0.144077i
$537$	−2.88097e6	+	2.88097e6i	−0.431125	+	0.431125i
$538$	−5.07041e6	+	5.07041e6i	−0.755245	+	0.755245i
$539$	5.15656e6	+	5.15656e6i	0.764519	+	0.764519i
$540$	−523982.			−0.0773271
$541$	−6.31807e6	−	6.31807e6i	−0.928093	−	0.928093i	0.0694900	−	0.997583i	$-0.477863\pi$
$541$	−6.31807e6	−	6.31807e6i	−0.928093	−	0.928093i	−0.997583	+	0.0694900i	$0.977863\pi$
$542$		−	1.12470e7i		−	1.64452i
$543$	1.48225e6			0.215735
$544$	−5.93936e6	+	7.90931e6i	−0.860484	+	1.14589i
$545$	674728.			0.0973056
$546$		−	1.16742e6i		−	0.167590i
$547$	−4.21726e6	−	4.21726e6i	−0.602645	−	0.602645i	0.338368	−	0.941014i	$-0.390125\pi$
$547$	−4.21726e6	−	4.21726e6i	−0.602645	−	0.602645i	−0.941014	+	0.338368i	$0.890125\pi$
$548$	2.53147e6			0.360099
$549$	459642.	+	459642.i	0.0650862	+	0.0650862i
$550$	−8.68446e6	+	8.68446e6i	−1.22415	+	1.22415i
$551$	−2.75367e6	+	2.75367e6i	−0.386396	+	0.386396i
$552$			125054.i			0.0174683i
$553$			1.83238e6i			0.254801i
$554$	7.46441e6	−	7.46441e6i	1.03329	−	1.03329i
$555$	87000.2	−	87000.2i	0.0119891	−	0.0119891i
$556$	−2.04632e6	−	2.04632e6i	−0.280729	−	0.280729i
$557$	−1.17521e7			−1.60501			−0.802505	−	0.596645i	$-0.796500\pi$
$557$	−1.17521e7			−1.60501			−0.802505	+	0.596645i	$0.796500\pi$
$558$	−2.53376e6	−	2.53376e6i	−0.344492	−	0.344492i
$559$		−	4.42197e6i		−	0.598530i
$560$	−154936.			−0.0208776
$561$	−4.52478e6	−	3.39780e6i	−0.607002	−	0.455818i
$562$	−3.94411e6			−0.526755
$563$		−	2.82797e6i		−	0.376014i	−0.982168	−	0.188007i	$-0.939797\pi$
$563$		−	2.82797e6i		−	0.376014i	0.982168	−	0.188007i	$-0.0602027\pi$
$564$	−5.95369e6	−	5.95369e6i	−0.788113	−	0.788113i
$565$	−641825.			−0.0845854
$566$	8.17042e6	+	8.17042e6i	1.07202	+	1.07202i
$567$	−53998.2	+	53998.2i	−0.00705377	+	0.00705377i
$568$	−333173.	+	333173.i	−0.0433310	+	0.0433310i
$569$		−	1.43168e6i		−	0.185381i	−0.995695	−	0.0926906i	$-0.970453\pi$
$569$		−	1.43168e6i		−	0.185381i	0.995695	−	0.0926906i	$-0.0295468\pi$
$570$			150994.i			0.0194658i
$571$	4.14722e6	−	4.14722e6i	0.532313	−	0.532313i	−0.388947	−	0.921260i	$-0.627161\pi$
$571$	4.14722e6	−	4.14722e6i	0.532313	−	0.532313i	0.921260	+	0.388947i	$0.127161\pi$
$572$	−4.13269e6	+	4.13269e6i	−0.528132	+	0.528132i
$573$	−4.77717e6	−	4.77717e6i	−0.607833	−	0.607833i
$574$	5.82178e6			0.737524
$575$	1.34084e6	+	1.34084e6i	0.169125	+	0.169125i
$576$		−	5.54729e6i		−	0.696666i
$577$	6.69500e6			0.837165			0.418583	−	0.908179i	$-0.362527\pi$
$577$	6.69500e6			0.837165			0.418583	+	0.908179i	$0.362527\pi$
$578$	1.11245e7	−	3.23025e6i	1.38504	−	0.402176i
$579$	4.90189e6			0.607669
$580$			1.12160e6i			0.138442i
$581$	239008.	+	239008.i	0.0293747	+	0.0293747i
$582$	−3.14771e6			−0.385201
$583$	1.55020e6	+	1.55020e6i	0.188893	+	0.188893i
$584$	−574427.	+	574427.i	−0.0696952	+	0.0696952i
$585$	−143760.	+	143760.i	−0.0173679	+	0.0173679i
$586$		−	293751.i		−	0.0353374i
$587$		−	3.43925e6i		−	0.411973i	−0.978555	−	0.205986i	$-0.933960\pi$
$587$		−	3.43925e6i		−	0.411973i	0.978555	−	0.205986i	$-0.0660403\pi$
$588$	−3.61058e6	+	3.61058e6i	−0.430659	+	0.430659i
$589$	−1.00671e6	+	1.00671e6i	−0.119568	+	0.119568i
$590$	−179982.	−	179982.i	−0.0212863	−	0.0212863i
$591$	2.58349e6			0.304256
$592$	2.09248e6	+	2.09248e6i	0.245390	+	0.245390i
$593$		−	440645.i		−	0.0514579i	−0.999669	−	0.0257289i	$-0.991809\pi$
$593$		−	440645.i		−	0.0514579i	0.999669	−	0.0257289i	$-0.00819068\pi$
$594$	1.51019e7			1.75617
$595$	157818.	+	118510.i	0.0182752	+	0.0137235i
$596$	1.55633e7			1.79467
$597$		−	9.35988e6i		−	1.07482i
$598$	1.22883e6	+	1.22883e6i	0.140520	+	0.140520i
$599$	−8.26911e6			−0.941655			−0.470827	−	0.882225i	$-0.656045\pi$
$599$	−8.26911e6			−0.941655			−0.470827	+	0.882225i	$0.656045\pi$
$600$	−450828.	−	450828.i	−0.0511250	−	0.0511250i
$601$	−4.45959e6	+	4.45959e6i	−0.503627	+	0.503627i	−0.912563	−	0.408936i	$-0.865900\pi$
$601$	−4.45959e6	+	4.45959e6i	−0.503627	+	0.503627i	0.408936	+	0.912563i	$0.365900\pi$
$602$	3.05082e6	−	3.05082e6i	0.343103	−	0.343103i
$603$			6.72900e6i			0.753629i
$604$			1.19486e7i			1.33268i
$605$	−205679.	+	205679.i	−0.0228455	+	0.0228455i
$606$	−7.66876e6	+	7.66876e6i	−0.848289	+	0.848289i
$607$	−2.12756e6	−	2.12756e6i	−0.234374	−	0.234374i	0.580142	−	0.814516i	$-0.302997\pi$
$607$	−2.12756e6	−	2.12756e6i	−0.234374	−	0.234374i	−0.814516	+	0.580142i	$0.802997\pi$
$608$	−3.94995e6			−0.433344
$609$	2.37081e6	+	2.37081e6i	0.259032	+	0.259032i
$610$		−	143256.i		−	0.0155879i
$611$	−8.67481e6			−0.940063
$612$	−3.63027e6	+	4.83435e6i	−0.391797	+	0.521746i
$613$	9.15609e6			0.984145			0.492072	−	0.870554i	$-0.336240\pi$
$613$	9.15609e6			0.984145			0.492072	+	0.870554i	$0.336240\pi$
$614$			2.28853e7i			2.44982i
$615$	469829.	+	469829.i	0.0500901	+	0.0500901i
$616$	−422780.			−0.0448914
$617$	−2.48240e6	−	2.48240e6i	−0.262518	−	0.262518i	0.563558	−	0.826076i	$-0.309432\pi$
$617$	−2.48240e6	−	2.48240e6i	−0.262518	−	0.262518i	−0.826076	+	0.563558i	$0.809432\pi$
$618$	7.96375e6	−	7.96375e6i	0.838776	−	0.838776i
$619$	1.89432e6	−	1.89432e6i	0.198713	−	0.198713i	−0.600735	−	0.799448i	$-0.705125\pi$
$619$	1.89432e6	−	1.89432e6i	0.198713	−	0.198713i	0.799448	+	0.600735i	$0.205125\pi$
$620$			410045.i			0.0428403i
$621$		−	2.33166e6i		−	0.242626i
$622$	7.91172e6	−	7.91172e6i	0.819965	−	0.819965i
$623$	−3.77766e6	+	3.77766e6i	−0.389944	+	0.389944i
$624$	2.26596e6	+	2.26596e6i	0.232965	+	0.232965i
$625$	−9.61846e6			−0.984931
$626$	7.44064e6	+	7.44064e6i	0.758883	+	0.758883i
$627$		−	2.25970e6i		−	0.229552i
$628$	−8.85621e6			−0.896084
$629$	−530861.	−	3.73194e6i	−0.0535000	−	0.376104i
$630$	−198366.			−0.0199121
$631$		−	4.44077e6i		−	0.444002i	−0.975046	−	0.222001i	$-0.928741\pi$
$631$		−	4.44077e6i		−	0.444002i	0.975046	−	0.222001i	$-0.0712589\pi$
$632$	648502.	+	648502.i	0.0645831	+	0.0645831i
$633$	7.40305e6			0.734347
$634$	−4.16839e6	−	4.16839e6i	−0.411856	−	0.411856i
$635$	789921.	−	789921.i	0.0777409	−	0.0777409i
$636$	−1.08544e6	+	1.08544e6i	−0.106405	+	0.106405i
$637$			5.26078e6i			0.513691i
$638$		−	3.23262e7i		−	3.14415i
$639$	2.33945e6	−	2.33945e6i	0.226653	−	0.226653i
$640$	−119666.	+	119666.i	−0.0115483	+	0.0115483i
$641$	−4.47092e6	−	4.47092e6i	−0.429786	−	0.429786i	0.458770	−	0.888555i	$-0.348290\pi$
$641$	−4.47092e6	−	4.47092e6i	−0.429786	−	0.429786i	−0.888555	+	0.458770i	$0.848290\pi$
$642$	−7.39604e6			−0.708210
$643$	9.26925e6	+	9.26925e6i	0.884132	+	0.884132i	0.993952	−	0.109819i	$-0.0350272\pi$
$643$	9.26925e6	+	9.26925e6i	0.884132	+	0.884132i	−0.109819	+	0.993952i	$0.535027\pi$
$644$			880433.i			0.0836530i
$645$	492414.			0.0466048
$646$	3.69916e6	+	2.77782e6i	0.348756	+	0.261892i
$647$	−1.01012e7			−0.948660			−0.474330	−	0.880347i	$-0.657310\pi$
$647$	−1.01012e7			−0.948660			−0.474330	+	0.880347i	$0.657310\pi$
$648$			38221.3i			0.00357576i
$649$	2.69353e6	+	2.69353e6i	0.251021	+	0.251021i
$650$	−8.85998e6			−0.822526
$651$	866741.	+	866741.i	0.0801562	+	0.0801562i
$652$	8.69246e6	−	8.69246e6i	0.800799	−	0.800799i
$653$	8.85501e6	−	8.85501e6i	0.812655	−	0.812655i	−0.172376	−	0.985031i	$-0.555144\pi$
$653$	8.85501e6	−	8.85501e6i	0.812655	−	0.812655i	0.985031	+	0.172376i	$0.0551444\pi$
$654$		−	1.36164e7i		−	1.24485i
$655$			925011.i			0.0842449i
$656$	−1.13000e7	+	1.13000e7i	−1.02523	+	1.02523i
$657$	4.03347e6	−	4.03347e6i	0.364557	−	0.364557i
$658$	−5.98495e6	−	5.98495e6i	−0.538884	−	0.538884i
$659$	−3.40208e6			−0.305162			−0.152581	−	0.988291i	$-0.548759\pi$
$659$	−3.40208e6			−0.305162			−0.152581	+	0.988291i	$0.548759\pi$
$660$	−460200.	−	460200.i	−0.0411232	−	0.0411232i
$661$			6.77375e6i			0.603011i	0.953464	+	0.301506i	$0.0974892\pi$
$661$			6.77375e6i			0.603011i	−0.953464	+	0.301506i	$0.902511\pi$
$662$	−1.83669e7			−1.62889
$663$	−574874.	−	4.04135e6i	−0.0507913	−	0.357061i
$664$	169176.			0.0148909
$665$			78814.9i			0.00691121i
$666$	2.67903e6	+	2.67903e6i	0.234041	+	0.234041i
$667$	−4.99101e6			−0.434384
$668$	−1.41145e7	−	1.41145e7i	−1.22384	−	1.22384i
$669$	−6.21384e6	+	6.21384e6i	−0.536778	+	0.536778i
$670$	1.04861e6	−	1.04861e6i	0.0902455	−	0.0902455i
$671$			2.14389e6i			0.183822i
$672$			3.40076e6i			0.290504i
$673$	−7.16283e6	+	7.16283e6i	−0.609603	+	0.609603i	−0.942842	−	0.333239i	$-0.891858\pi$
$673$	−7.16283e6	+	7.16283e6i	−0.609603	+	0.609603i	0.333239	+	0.942842i	$0.391858\pi$
$674$	−1.16893e6	+	1.16893e6i	−0.0991150	+	0.0991150i
$675$	8.40577e6	+	8.40577e6i	0.710098	+	0.710098i
$676$	8.61659e6			0.725218
$677$	1.33350e7	+	1.33350e7i	1.11821	+	1.11821i	0.992005	+	0.126201i	$0.0402783\pi$
$677$	1.33350e7	+	1.33350e7i	1.11821	+	1.11821i	0.126201	+	0.992005i	$0.459722\pi$
$678$			1.29524e7i			1.08212i
$679$	−1.64303e6			−0.136763
$680$	97796.1	−	13911.3i	0.00811053	−	0.00115371i
$681$	1.05242e6			0.0869603
$682$		−	1.18181e7i		−	0.972942i
$683$	−1.45524e6	−	1.45524e6i	−0.119367	−	0.119367i	0.644900	−	0.764267i	$-0.276899\pi$
$683$	−1.45524e6	−	1.45524e6i	−0.119367	−	0.119367i	−0.764267	+	0.644900i	$0.776899\pi$
$684$	−2.41430e6			−0.197311
$685$	205367.	+	205367.i	0.0167227	+	0.0167227i
$686$	−7.67948e6	+	7.67948e6i	−0.623048	+	0.623048i
$687$	−2.25938e6	+	2.25938e6i	−0.182640	+	0.182640i
$688$			1.18432e7i			0.953893i
$689$			1.58153e6i			0.126920i
$690$	−136838.	+	136838.i	−0.0109416	+	0.0109416i
$691$	4.35018e6	−	4.35018e6i	0.346587	−	0.346587i	−0.512250	−	0.858837i	$-0.671188\pi$
$691$	4.35018e6	−	4.35018e6i	0.346587	−	0.346587i	0.858837	+	0.512250i	$0.171188\pi$
$692$	1.28336e7	+	1.28336e7i	1.01878	+	1.01878i
$693$	2.96865e6			0.234815
$694$	−7.97223e6	−	7.97223e6i	−0.628321	−	0.628321i
$695$		−	332018.i		−	0.0260736i
$696$	1.67812e6			0.131311
$697$	2.01537e7	−	2.86682e6i	1.57135	−	0.223521i
$698$	−2.46057e6			−0.191160
$699$			1.28781e7i			0.996914i
$700$	−3.17401e6	−	3.17401e6i	−0.244829	−	0.244829i
$701$	4.75802e6			0.365705			0.182853	−	0.983140i	$-0.441467\pi$
$701$	4.75802e6			0.365705			0.182853	+	0.983140i	$0.441467\pi$
$702$	7.70357e6	+	7.70357e6i	0.589996	+	0.589996i
$703$	1.06443e6	−	1.06443e6i	0.0812324	−	0.0812324i
$704$	1.29370e7	−	1.29370e7i	0.983790	−	0.983790i
$705$		−	965994.i		−	0.0731984i
$706$		−	2.53902e7i		−	1.91714i
$707$	−4.00290e6	+	4.00290e6i	−0.301180	+	0.301180i
$708$	−1.88598e6	+	1.88598e6i	−0.141402	+	0.141402i
$709$	7.56933e6	+	7.56933e6i	0.565512	+	0.565512i	0.930868	−	0.365356i	$-0.119053\pi$
$709$	7.56933e6	+	7.56933e6i	0.565512	+	0.565512i	−0.365356	+	0.930868i	$0.619053\pi$
$710$	−729131.			−0.0542825
$711$	−4.55361e6	−	4.55361e6i	−0.337817	−	0.337817i
$712$			2.67393e6i			0.197674i
$713$	−1.82466e6			−0.134418
$714$	2.39160e6	−	3.18484e6i	0.175567	−	0.233799i
$715$	−670534.			−0.0490519
$716$			1.43570e7i			1.04660i
$717$	−331312.	−	331312.i	−0.0240680	−	0.0240680i
$718$	1.14828e7			0.831259
$719$	−1.16877e7	−	1.16877e7i	−0.843152	−	0.843152i	0.146115	−	0.989268i	$-0.453323\pi$
$719$	−1.16877e7	−	1.16877e7i	−0.843152	−	0.843152i	−0.989268	+	0.146115i	$0.953323\pi$
$720$	385028.	−	385028.i	0.0276797	−	0.0276797i
$721$	4.15687e6	−	4.15687e6i	0.297803	−	0.297803i
$722$		−	1.83541e7i		−	1.31036i
$723$			4.67833e6i			0.332848i
$724$	3.69330e6	−	3.69330e6i	0.261859	−	0.261859i
$725$	1.79929e7	−	1.79929e7i	1.27132	−	1.27132i
$726$	4.15070e6	+	4.15070e6i	0.292267	+	0.292267i
$727$	−1.04711e7			−0.734776			−0.367388	−	0.930068i	$-0.619748\pi$
$727$	−1.04711e7			−0.734776			−0.367388	+	0.930068i	$0.619748\pi$
$728$	−215663.	−	215663.i	−0.0150816	−	0.0150816i
$729$		−	9.38083e6i		−	0.653766i
$730$	−1.25710e6			−0.0873100
$731$	9.05891e6	−	1.20635e7i	0.627022	−	0.834990i
$732$	−1.50113e6			−0.103548
$733$		−	1.72395e6i		−	0.118513i	−0.998243	−	0.0592563i	$-0.981127\pi$
$733$		−	1.72395e6i		−	0.118513i	0.998243	−	0.0592563i	$-0.0188729\pi$
$734$	1.15916e7	+	1.15916e7i	0.794154	+	0.794154i
$735$	−585821.			−0.0399988
$736$	−3.57963e6	−	3.57963e6i	−0.243581	−	0.243581i
$737$	−1.56929e7	+	1.56929e7i	−1.06423	+	1.06423i
$738$	−1.44676e7	+	1.44676e7i	−0.977814	+	0.977814i
$739$		−	1.20489e7i		−	0.811589i	−0.913964	−	0.405795i	$-0.866995\pi$
$739$		−	1.20489e7i		−	0.811589i	0.913964	−	0.405795i	$-0.133005\pi$
$740$		−	433555.i		−	0.0291048i
$741$	1.15268e6	−	1.15268e6i	0.0771195	−	0.0771195i
$742$	−1.09113e6	+	1.09113e6i	−0.0727559	+	0.0727559i
$743$	8.53488e6	+	8.53488e6i	0.567186	+	0.567186i	0.931339	−	0.364153i	$-0.118642\pi$
$743$	8.53488e6	+	8.53488e6i	0.567186	+	0.567186i	−0.364153	+	0.931339i	$0.618642\pi$
$744$	613502.			0.0406335
$745$	1.26258e6	+	1.26258e6i	0.0833430	+	0.0833430i
$746$			2.96906e7i			1.95331i
$747$	−1.18791e6			−0.0778902
$748$	−1.97406e7	+	2.80806e6i	−1.29005	+	0.183507i
$749$	−3.86055e6			−0.251446
$750$		−	1.97822e6i		−	0.128417i
$751$	−1.35991e7	−	1.35991e7i	−0.879853	−	0.879853i	0.113666	−	0.993519i	$-0.463741\pi$
$751$	−1.35991e7	−	1.35991e7i	−0.879853	−	0.879853i	−0.993519	+	0.113666i	$0.963741\pi$
$752$	2.32335e7			1.49820
$753$	5.11726e6	+	5.11726e6i	0.328890	+	0.328890i
$754$	1.64898e7	−	1.64898e7i	1.05630	−	1.05630i
$755$	−969338.	+	969338.i	−0.0618882	+	0.0618882i
$756$			5.51947e6i			0.351231i
$757$			2.02834e7i			1.28647i	0.765668	+	0.643236i	$0.222409\pi$
$757$			2.02834e7i			1.28647i	−0.765668	+	0.643236i	$0.777591\pi$
$758$	−2.85408e7	+	2.85408e7i	−1.80424	+	1.80424i
$759$	2.04784e6	−	2.04784e6i	0.129030	−	0.129030i
$760$	27893.6	+	27893.6i	0.00175175	+	0.00175175i
$761$	6.11533e6			0.382788			0.191394	−	0.981513i	$-0.438699\pi$
$761$	6.11533e6			0.382788			0.191394	+	0.981513i	$0.438699\pi$
$762$	−1.59410e7	−	1.59410e7i	−0.994554	−	0.994554i
$763$		−	7.10740e6i		−	0.441977i
$764$	−2.38065e7			−1.47558
$765$	−686698.	+	97681.5i	−0.0424241	+	0.00603474i
$766$	−2.65208e7			−1.63311
$767$			2.74797e6i			0.168664i
$768$	−5.97187e6	−	5.97187e6i	−0.365348	−	0.365348i
$769$	−2.69595e7			−1.64398			−0.821990	−	0.569501i	$-0.807136\pi$
$769$	−2.69595e7			−1.64398			−0.821990	+	0.569501i	$0.807136\pi$
$770$	−462616.	−	462616.i	−0.0281186	−	0.0281186i
$771$	−2.43870e6	+	2.43870e6i	−0.147748	+	0.147748i
$772$	1.22140e7	−	1.22140e7i	0.737588	−	0.737588i
$773$		−	1.57812e7i		−	0.949927i	−0.880006	−	0.474963i	$-0.842461\pi$
$773$		−	1.57812e7i		−	0.949927i	0.880006	−	0.474963i	$-0.157539\pi$
$774$			1.51631e7i			0.909777i
$775$	6.57800e6	−	6.57800e6i	0.393405	−	0.393405i
$776$	−581488.	+	581488.i	−0.0346646	+	0.0346646i
$777$	−916436.	−	916436.i	−0.0544565	−	0.0544565i
$778$	2.43941e7			1.44489
$779$	5.74827e6	+	5.74827e6i	0.339386	+	0.339386i
$780$		−	469501.i		−	0.0276312i
$781$	1.09118e7			0.640131
$782$	834960.	+	5.86974e6i	0.0488257	+	0.343244i
$783$	−3.12888e7			−1.82383
$784$		−	1.40898e7i		−	0.818682i
$785$	−718466.	−	718466.i	−0.0416133	−	0.0416133i
$786$	1.86672e7			1.07776
$787$	1.24112e7	+	1.24112e7i	0.714292	+	0.714292i	0.967430	−	0.253138i	$-0.0814628\pi$
$787$	1.24112e7	+	1.24112e7i	0.714292	+	0.714292i	−0.253138	+	0.967430i	$0.581463\pi$
$788$	6.43727e6	−	6.43727e6i	0.369306	−	0.369306i
$789$	6.38473e6	−	6.38473e6i	0.365132	−	0.365132i
$790$			1.41921e6i			0.0809058i
$791$			6.76080e6i			0.384200i
$792$	1.05064e6	−	1.05064e6i	0.0595173	−	0.0595173i
$793$	−1.09361e6	+	1.09361e6i	−0.0617561	+	0.0617561i
$794$	−4.57395e6	−	4.57395e6i	−0.257478	−	0.257478i
$795$	−176113.			−0.00988267
$796$	−2.33219e7	−	2.33219e7i	−1.30461	−	1.30461i
$797$			1.87854e7i			1.04755i	0.851856	+	0.523776i	$0.175477\pi$
$797$			1.87854e7i			1.04755i	−0.851856	+	0.523776i	$0.824523\pi$
$798$	1.59052e6			0.0884164
$799$	−2.36657e7	−	1.77713e7i	−1.31145	−	0.984811i
$800$	2.58095e7			1.42579
$801$		−	1.87756e7i		−	1.03398i
$802$	3.52017e7	+	3.52017e7i	1.93254	+	1.93254i
$803$	1.88132e7			1.02961
$804$	−1.09880e7	−	1.09880e7i	−0.599487	−	0.599487i
$805$	−71425.7	+	71425.7i	−0.00388477	+	0.00388477i
$806$	6.02848e6	−	6.02848e6i	0.326866	−	0.326866i
$807$			8.62063e6i			0.465967i
$808$			2.83336e6i			0.152677i
$809$	1.87823e7	−	1.87823e7i	1.00897	−	1.00897i	0.00900873	−	0.999959i	$-0.497132\pi$
$809$	1.87823e7	−	1.87823e7i	1.00897	−	1.00897i	0.999959	−	0.00900873i	$-0.00286761\pi$
$810$	−41822.7	+	41822.7i	−0.00223975	+	0.00223975i
$811$	−1.35564e7	−	1.35564e7i	−0.723756	−	0.723756i	0.245612	−	0.969368i	$-0.421011\pi$
$811$	−1.35564e7	−	1.35564e7i	−0.723756	−	0.723756i	−0.969368	+	0.245612i	$0.921011\pi$
$812$	1.18146e7			0.628826
$813$	−9.56102e6	−	9.56102e6i	−0.507315	−	0.507315i
$814$			1.24957e7i			0.660997i
$815$	1.41036e6			0.0743767
$816$	1.53967e6	+	1.08238e7i	0.0809473	+	0.569057i
$817$	6.02459e6			0.315771
$818$		−	2.16562e6i		−	0.113162i
$819$	1.51433e6	+	1.51433e6i	0.0788877	+	0.0788877i
$820$	2.34134e6			0.121599
$821$	5.70008e6	+	5.70008e6i	0.295137	+	0.295137i	0.839105	−	0.543969i	$-0.183079\pi$
$821$	5.70008e6	+	5.70008e6i	0.295137	+	0.295137i	−0.543969	+	0.839105i	$0.683079\pi$
$822$	4.14442e6	−	4.14442e6i	0.213936	−	0.213936i
$823$	−1.33650e7	+	1.33650e7i	−0.687811	+	0.687811i	−0.961748	−	0.273937i	$-0.911674\pi$
$823$	−1.33650e7	+	1.33650e7i	−0.687811	+	0.687811i	0.273937	+	0.961748i	$0.411674\pi$
$824$		−	2.94235e6i		−	0.150965i
$825$			1.47652e7i			0.755273i
$826$	−1.89588e6	+	1.89588e6i	−0.0966855	+	0.0966855i
$827$	1.30474e7	−	1.30474e7i	0.663375	−	0.663375i	−0.292799	−	0.956174i	$-0.594587\pi$
$827$	1.30474e7	−	1.30474e7i	0.663375	−	0.663375i	0.956174	+	0.292799i	$0.0945866\pi$
$828$	−2.18795e6	−	2.18795e6i	−0.110908	−	0.110908i
$829$	−2.99464e7			−1.51341			−0.756707	−	0.653754i	$-0.773193\pi$
$829$	−2.99464e7			−1.51341			−0.756707	+	0.653754i	$0.773193\pi$
$830$	185117.	+	185117.i	0.00932719	+	0.00932719i
$831$		−	1.26909e7i		−	0.637512i
$832$	1.31985e7			0.661022
$833$	−1.07773e7	+	1.43519e7i	−0.538143	+	0.716633i
$834$	−6.70030e6			−0.333564
$835$		−	2.29010e6i		−	0.113668i
$836$	−5.63046e6	−	5.63046e6i	−0.278630	−	0.278630i
$837$	−1.14389e7			−0.564377
$838$	4.00172e7	+	4.00172e7i	1.96850	+	1.96850i
$839$	−9.04740e6	+	9.04740e6i	−0.443730	+	0.443730i	−0.893263	−	0.449534i	$-0.851590\pi$
$839$	−9.04740e6	+	9.04740e6i	−0.443730	+	0.443730i	0.449534	+	0.893263i	$0.351590\pi$
$840$	24015.4	−	24015.4i	0.00117433	−	0.00117433i
$841$			4.64638e7i			2.26529i
$842$		−	1.52118e7i		−	0.739438i
$843$	−3.35286e6	+	3.35286e6i	−0.162497	+	0.162497i
$844$	1.84461e7	−	1.84461e7i	0.891351	−	0.891351i
$845$	699026.	+	699026.i	0.0336784	+	0.0336784i
$846$	2.97462e7			1.42891
$847$	2.16656e6	+	2.16656e6i	0.103768	+	0.103768i
$848$		−	4.23577e6i		−	0.202275i
$849$	1.38912e7			0.661411
$850$	−2.41708e7	−	1.81507e7i	−1.14748	−	0.861679i
$851$	1.92928e6			0.0913209
$852$			7.64035e6i			0.360590i
$853$	1.53281e7	+	1.53281e7i	0.721302	+	0.721302i	0.968870	−	0.247569i	$-0.0796316\pi$
$853$	1.53281e7	+	1.53281e7i	0.721302	+	0.721302i	−0.247569	+	0.968870i	$0.579632\pi$
$854$	−1.50901e6			−0.0708025
$855$	−195862.	−	195862.i	−0.00916292	−	0.00916292i
$856$	−1.36630e6	+	1.36630e6i	−0.0637326	+	0.0637326i
$857$	4.03778e6	−	4.03778e6i	0.187798	−	0.187798i	−0.606946	−	0.794743i	$-0.707605\pi$
$857$	4.03778e6	−	4.03778e6i	0.187798	−	0.187798i	0.794743	+	0.606946i	$0.207605\pi$
$858$			1.35317e7i			0.627530i
$859$			3.71265e7i			1.71673i	0.513043	+	0.858363i	$0.328518\pi$
$859$			3.71265e7i			1.71673i	−0.513043	+	0.858363i	$0.671482\pi$
$860$	1.22694e6	−	1.22694e6i	0.0565690	−	0.0565690i
$861$	4.94905e6	−	4.94905e6i	0.227517	−	0.227517i
$862$	−2.90401e7	−	2.90401e7i	−1.33116	−	1.33116i
$863$	835873.			0.0382044			0.0191022	−	0.999818i	$-0.493919\pi$
$863$	835873.			0.0382044			0.0191022	+	0.999818i	$0.493919\pi$
$864$	−2.24408e7	−	2.24408e7i	−1.02272	−	1.02272i
$865$			2.08226e6i			0.0946227i
$866$	−2.93016e7			−1.32769
$867$	6.71086e6	−	1.22029e7i	0.303201	−	0.551333i
$868$	4.31930e6			0.194587
$869$		−	2.12392e7i		−	0.954090i
$870$	1.83624e6	+	1.83624e6i	0.0822491	+	0.0822491i
$871$	−1.60101e7			−0.715070
$872$	−2.51540e6	−	2.51540e6i	−0.112025	−	0.112025i
$873$	4.08306e6	−	4.08306e6i	0.181322	−	0.181322i
$874$	−1.67418e6	+	1.67418e6i	−0.0741351	+	0.0741351i
$875$		−	1.03258e6i		−	0.0455936i
$876$			1.31728e7i			0.579987i
$877$	3.48231e6	−	3.48231e6i	0.152886	−	0.152886i	−0.626520	−	0.779406i	$-0.715521\pi$
$877$	3.48231e6	−	3.48231e6i	0.152886	−	0.152886i	0.779406	+	0.626520i	$0.215521\pi$
$878$	−6.58363e6	+	6.58363e6i	−0.288223	+	0.288223i
$879$	−249715.	−	249715.i	−0.0109012	−	0.0109012i
$880$	1.79587e6			0.0781752
$881$	−9.79309e6	−	9.79309e6i	−0.425089	−	0.425089i	0.461863	−	0.886952i	$-0.347181\pi$
$881$	−9.79309e6	−	9.79309e6i	−0.425089	−	0.425089i	−0.886952	+	0.461863i	$0.847181\pi$
$882$		−	1.80394e7i		−	0.780819i
$883$	417413.			0.0180162			0.00900811	−	0.999959i	$-0.497133\pi$
$883$	417413.			0.0180162			0.00900811	+	0.999959i	$0.497133\pi$
$884$	−1.15022e7	−	8.63739e6i	−0.495052	−	0.371751i
$885$	−306003.			−0.0131331
$886$			603763.i			0.0258394i
$887$	−2.24278e7	−	2.24278e7i	−0.957146	−	0.957146i	0.0419724	−	0.999119i	$-0.486636\pi$
$887$	−2.24278e7	−	2.24278e7i	−0.957146	−	0.957146i	−0.999119	+	0.0419724i	$0.986636\pi$
$888$	−648678.			−0.0276056
$889$	−8.32080e6	−	8.32080e6i	−0.353111	−	0.353111i
$890$	−2.92588e6	+	2.92588e6i	−0.123817	+	0.123817i
$891$	625897.	−	625897.i	0.0264125	−	0.0264125i
$892$			3.09660e7i			1.30308i
$893$		−	1.18187e7i		−	0.495956i
$894$	2.54796e7	−	2.54796e7i	1.06622	−	1.06622i
$895$	−1.16472e6	+	1.16472e6i	−0.0486030	+	0.0486030i
$896$	1.26052e6	+	1.26052e6i	0.0524543	+	0.0524543i
$897$	2.08923e6			0.0866973
$898$	−1.81616e7	−	1.81616e7i	−0.751560	−	0.751560i
$899$			2.44853e7i			1.01043i
$900$	1.57754e7			0.649192
$901$	−3.23995e6	+	4.31456e6i	−0.132961	+	0.177062i
$902$	−6.74808e7			−2.76162
$903$		−	5.18695e6i		−	0.211686i
$904$	2.39274e6	+	2.39274e6i	0.0973810	+	0.0973810i
$905$	599242.			0.0243210
$906$	1.95617e7	+	1.95617e7i	0.791748	+	0.791748i
$907$	2.89987e7	−	2.89987e7i	1.17047	−	1.17047i	0.188374	−	0.982097i	$-0.439678\pi$
$907$	2.89987e7	−	2.89987e7i	1.17047	−	1.17047i	0.982097	−	0.188374i	$-0.0603216\pi$
$908$	2.62230e6	−	2.62230e6i	0.105552	−	0.105552i
$909$		−	1.98951e7i		−	0.798612i
$910$		−	471966.i		−	0.0188933i
$911$	5.38246e6	−	5.38246e6i	0.214874	−	0.214874i	−0.591460	−	0.806334i	$-0.701448\pi$
$911$	5.38246e6	−	5.38246e6i	0.214874	−	0.214874i	0.806334	+	0.591460i	$0.201448\pi$
$912$	−3.08720e6	+	3.08720e6i	−0.122907	+	0.122907i
$913$	−2.77037e6	−	2.77037e6i	−0.109992	−	0.109992i
$914$	−1.54777e7			−0.612831
$915$	−121780.	−	121780.i	−0.00480867	−	0.00480867i
$916$			1.12593e7i			0.443378i
$917$	9.74380e6			0.382653
$918$	5.23440e6	+	3.67977e7i	0.205003	+	1.44116i
$919$	4.13413e7			1.61471			0.807356	−	0.590065i	$-0.200898\pi$
$919$	4.13413e7			1.61471			0.807356	+	0.590065i	$0.200898\pi$
$920$			50557.0i			0.00196930i
$921$	1.94546e7	+	1.94546e7i	0.755740	+	0.755740i
$922$	1.26897e7			0.491613
$923$	5.56618e6	+	5.56618e6i	0.215057	+	0.215057i
$924$	−4.84762e6	+	4.84762e6i	−0.186788	+	0.186788i
$925$	−6.95515e6	+	6.95515e6i	−0.267271	+	0.267271i
$926$		−	4.07352e7i		−	1.56114i
$927$			2.06604e7i			0.789657i
$928$	−4.80355e7	+	4.80355e7i	−1.83102	+	1.83102i
$929$	1.61915e7	−	1.61915e7i	0.615528	−	0.615528i	−0.328853	−	0.944381i	$-0.606662\pi$
$929$	1.61915e7	−	1.61915e7i	0.615528	−	0.615528i	0.944381	+	0.328853i	$0.106662\pi$
$930$	671309.	+	671309.i	0.0254516	+	0.0254516i
$931$	−7.16741e6			−0.271012
$932$	3.20881e7	+	3.20881e7i	1.21005	+	1.21005i
$933$		−	1.34514e7i		−	0.505898i
$934$	4.35173e7			1.63228
$935$	−1.82928e6	−	1.37366e6i	−0.0684306	−	0.0513868i
$936$	1.07188e6			0.0399905
$937$		−	4.00810e6i		−	0.149138i	−0.997216	−	0.0745692i	$-0.976242\pi$
$937$		−	4.00810e6i		−	0.149138i	0.997216	−	0.0745692i	$-0.0237582\pi$
$938$	−1.10457e7	−	1.10457e7i	−0.409909	−	0.409909i
$939$	1.26505e7			0.468212
$940$	−2.40696e6	−	2.40696e6i	−0.0888483	−	0.0888483i
$941$	−1.97794e7	+	1.97794e7i	−0.728179	+	0.728179i	−0.970257	−	0.242078i	$-0.922171\pi$
$941$	−1.97794e7	+	1.97794e7i	−0.728179	+	0.728179i	0.242078	+	0.970257i	$0.422171\pi$
$942$	−1.44990e7	+	1.44990e7i	−0.532367	+	0.532367i
$943$			1.04187e7i			0.381535i
$944$		−	7.35980e6i		−	0.268804i
$945$	−447771.	+	447771.i	−0.0163108	+	0.0163108i
$946$	−3.53623e7	+	3.53623e7i	−1.28473	+	1.28473i
$947$	1.71739e7	+	1.71739e7i	0.622292	+	0.622292i	0.946117	−	0.323825i	$-0.104969\pi$
$947$	1.71739e7	+	1.71739e7i	0.622292	+	0.622292i	−0.323825	+	0.946117i	$0.604969\pi$
$948$	1.48715e7			0.537445
$949$	9.59671e6	+	9.59671e6i	0.345905	+	0.345905i
$950$		−	1.20710e7i		−	0.433946i
$951$	−7.08703e6			−0.254105
$952$	−146538.	−	1.03016e6i	−0.00524031	−	0.0368393i
$953$	1.57038e7			0.560109			0.280055	−	0.959984i	$-0.409647\pi$
$953$	1.57038e7			0.560109			0.280055	+	0.959984i	$0.409647\pi$
$954$		−	5.42312e6i		−	0.192920i
$955$	−1.93132e6	−	1.93132e6i	−0.0685244	−	0.0685244i
$956$	−1.65106e6			−0.0584274
$957$	−2.74802e7	−	2.74802e7i	−0.969930	−	0.969930i
$958$	3.39933e7	−	3.39933e7i	1.19669	−	1.19669i
$959$	2.16328e6	−	2.16328e6i	0.0759568	−	0.0759568i
$960$			1.46973e6i			0.0514707i
$961$		−	1.96776e7i		−	0.687327i
$962$	−6.37413e6	+	6.37413e6i	−0.222066	+	0.222066i
$963$	9.59379e6	−	9.59379e6i	0.333368	−	0.333368i
$964$	1.16570e7	+	1.16570e7i	0.404011	+	0.404011i
$965$	1.98174e6			0.0685058
$966$	1.44141e6	+	1.44141e6i	0.0496986	+	0.0496986i
$967$		−	1.89728e6i		−	0.0652479i	−0.999468	−	0.0326239i	$-0.989614\pi$
$967$		−	1.89728e6i		−	0.0652479i	0.999468	−	0.0326239i	$-0.0103864\pi$
$968$	1.53355e6			0.0526029
$969$	5.50603e6	−	783221.i	0.188377	−	0.0267963i
$970$	−1.27256e6			−0.0434258
$971$			5.63025e7i			1.91637i	0.286145	+	0.958186i	$0.407626\pi$
$971$			5.63025e7i			1.91637i	−0.286145	+	0.958186i	$0.592374\pi$
$972$	−2.22672e7	−	2.22672e7i	−0.755961	−	0.755961i
$973$	−3.49739e6			−0.118430
$974$	−2.98933e7	−	2.98933e7i	−1.00966	−	1.00966i
$975$	−7.53180e6	+	7.53180e6i	−0.253739	+	0.253739i
$976$	2.92899e6	−	2.92899e6i	0.0984222	−	0.0984222i
$977$		−	4.93123e7i		−	1.65279i	−0.563088	−	0.826397i	$-0.690387\pi$
$977$		−	4.93123e7i		−	1.65279i	0.563088	−	0.826397i	$-0.309613\pi$
$978$		−	2.84619e7i		−	0.951516i
$979$	4.37872e7	−	4.37872e7i	1.46013	−	1.46013i
$980$	−1.45968e6	+	1.45968e6i	−0.0485505	+	0.0485505i
$981$	1.76625e7	+	1.76625e7i	0.585975	+	0.585975i
$982$	−8.34012e6			−0.275990
$983$	3.77277e6	+	3.77277e6i	0.124531	+	0.124531i	0.766625	−	0.642095i	$-0.221934\pi$
$983$	3.77277e6	+	3.77277e6i	0.124531	+	0.124531i	−0.642095	+	0.766625i	$0.721934\pi$
$984$		−	3.50307e6i		−	0.115335i
$985$	1.04446e6			0.0343004
$986$	7.87668e7	−	1.12044e7i	2.58018	−	0.367026i
$987$	−1.01755e7			−0.332478
$988$		−	5.74426e6i		−	0.187215i
$989$	5.45977e6	+	5.45977e6i	0.177494	+	0.177494i
$990$	2.29928e6			0.0745597
$991$	1.34466e6	+	1.34466e6i	0.0434940	+	0.0434940i	0.728519	−	0.685025i	$-0.240209\pi$
$991$	1.34466e6	+	1.34466e6i	0.0434940	+	0.0434940i	−0.685025	+	0.728519i	$0.740209\pi$
$992$	−1.75612e7	+	1.75612e7i	−0.566599	+	0.566599i
$993$	−1.56135e7	+	1.56135e7i	−0.502491	+	0.502491i
$994$			7.68046e6i			0.246559i
$995$		−	3.78401e6i		−	0.121170i
$996$	1.93979e6	−	1.93979e6i	0.0619591	−	0.0619591i
$997$	−3.06230e7	+	3.06230e7i	−0.975684	+	0.975684i	−0.999711	−	0.0240273i	$-0.992351\pi$
$997$	−3.06230e7	+	3.06230e7i	−0.975684	+	0.975684i	0.0240273	+	0.999711i	$0.492351\pi$
$998$	−2.65387e6	−	2.65387e6i	−0.0843439	−	0.0843439i
$999$	1.20947e7			0.383426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.6.c.a.13.1	yes	12
3.2	odd	2		153.6.f.a.64.6		12
4.3	odd	2		272.6.o.c.81.4		12
17.2	even	8		289.6.a.g.1.11		12
17.4	even	4	inner	17.6.c.a.4.6	✓	12
17.15	even	8		289.6.a.g.1.12		12
51.38	odd	4		153.6.f.a.55.1		12
68.55	odd	4		272.6.o.c.225.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.6.c.a.4.6	✓	12	17.4	even	4	inner
17.6.c.a.13.1	yes	12	1.1	even	1	trivial
153.6.f.a.55.1		12	51.38	odd	4
153.6.f.a.64.6		12	3.2	odd	2
272.6.o.c.81.4		12	4.3	odd	2
272.6.o.c.225.4		12	68.55	odd	4
289.6.a.g.1.11		12	17.2	even	8
289.6.a.g.1.12		12	17.15	even	8

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-8.15858i q^{2} +(-6.93554 - 6.93554i) q^{3} -34.5625 q^{4} +(-2.80390 - 2.80390i) q^{5} +(-56.5842 + 56.5842i) q^{6} +(-29.5355 + 29.5355i) q^{7} +20.9060i q^{8} -146.796i q^{9} +O(q^{10})\)	\(q-8.15858i q^{2} +(-6.93554 - 6.93554i) q^{3} -34.5625 q^{4} +(-2.80390 - 2.80390i) q^{5} +(-56.5842 + 56.5842i) q^{6} +(-29.5355 + 29.5355i) q^{7} +20.9060i q^{8} -146.796i q^{9} +(-22.8759 + 22.8759i) q^{10} +(342.349 - 342.349i) q^{11} +(239.709 + 239.709i) q^{12} +349.268 q^{13} +(240.968 + 240.968i) q^{14} +38.8932i q^{15} -935.435 q^{16} +(952.835 + 715.515i) q^{17} -1197.65 q^{18} +475.851i q^{19} +(96.9098 + 96.9098i) q^{20} +409.690 q^{21} +(-2793.08 - 2793.08i) q^{22} +(-431.238 + 431.238i) q^{23} +(144.995 - 144.995i) q^{24} -3109.28i q^{25} -2849.53i q^{26} +(-2703.45 + 2703.45i) q^{27} +(1020.82 - 1020.82i) q^{28} +(5786.84 + 5786.84i) q^{29} +317.313 q^{30} +(2115.60 + 2115.60i) q^{31} +8300.82i q^{32} -4748.75 q^{33} +(5837.59 - 7773.78i) q^{34} +165.629 q^{35} +5073.65i q^{36} +(-2236.90 - 2236.90i) q^{37} +3882.27 q^{38} +(-2422.36 - 2422.36i) q^{39} +(58.6185 - 58.6185i) q^{40} +(12080.0 - 12080.0i) q^{41} -3342.49i q^{42} -12660.7i q^{43} +(-11832.4 + 11832.4i) q^{44} +(-411.603 + 411.603i) q^{45} +(3518.29 + 3518.29i) q^{46} -24837.1 q^{47} +(6487.75 + 6487.75i) q^{48} +15062.3i q^{49} -25367.3 q^{50} +(-1645.94 - 11570.9i) q^{51} -12071.6 q^{52} +4528.13i q^{53} +(22056.3 + 22056.3i) q^{54} -1919.83 q^{55} +(-617.470 - 617.470i) q^{56} +(3300.28 - 3300.28i) q^{57} +(47212.4 - 47212.4i) q^{58} +7867.78i q^{59} -1344.24i q^{60} +(-3131.15 + 3131.15i) q^{61} +(17260.3 - 17260.3i) q^{62} +(4335.71 + 4335.71i) q^{63} +37789.0 q^{64} +(-979.314 - 979.314i) q^{65} +38743.1i q^{66} -45839.0 q^{67} +(-32932.3 - 24730.0i) q^{68} +5981.74 q^{69} -1351.30i q^{70} +(15936.7 + 15936.7i) q^{71} +3068.93 q^{72} +(27476.6 + 27476.6i) q^{73} +(-18250.0 + 18250.0i) q^{74} +(-21564.5 + 21564.5i) q^{75} -16446.6i q^{76} +20222.9i q^{77} +(-19763.1 + 19763.1i) q^{78} +(31019.9 - 31019.9i) q^{79} +(2622.87 + 2622.87i) q^{80} +1828.24 q^{81} +(-98555.6 - 98555.6i) q^{82} -8092.24i q^{83} -14159.9 q^{84} +(-665.421 - 4677.89i) q^{85} -103293. q^{86} -80269.7i q^{87} +(7157.15 + 7157.15i) q^{88} +127902. q^{89} +(3358.10 + 3358.10i) q^{90} +(-10315.8 + 10315.8i) q^{91} +(14904.7 - 14904.7i) q^{92} -29345.7i q^{93} +202636. i q^{94} +(1334.24 - 1334.24i) q^{95} +(57570.7 - 57570.7i) q^{96} +(27814.4 + 27814.4i) q^{97} +122887. q^{98} +(-50255.6 - 50255.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7}+O(q^{10}) \) 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7	\( 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7} - 334 q^{10} - 504 q^{11} + 1722 q^{12} + 1600 q^{13} - 2364 q^{14} + 2564 q^{16} + 2432 q^{17} - 6052 q^{18} - 4218 q^{20} + 7144 q^{21} - 2590 q^{22} - 2728 q^{23} - 7246 q^{24} - 3024 q^{27} + 26164 q^{28} - 992 q^{29} + 18072 q^{30} - 14680 q^{31} - 96 q^{33} - 20962 q^{34} - 43744 q^{35} + 33552 q^{37} + 9024 q^{38} + 2720 q^{39} + 30922 q^{40} + 20716 q^{41} - 13682 q^{44} + 44848 q^{45} + 4416 q^{46} + 32032 q^{47} - 144770 q^{48} - 42636 q^{50} - 83368 q^{51} - 132556 q^{52} + 80728 q^{54} + 81040 q^{55} + 122460 q^{56} + 36840 q^{57} + 165766 q^{58} - 143200 q^{61} + 222580 q^{62} + 7592 q^{63} + 18428 q^{64} - 175016 q^{65} - 83648 q^{67} - 231150 q^{68} - 341160 q^{69} + 116088 q^{71} + 347100 q^{72} + 83892 q^{73} - 79282 q^{74} + 245864 q^{75} - 128572 q^{78} + 291672 q^{79} + 195426 q^{80} + 387028 q^{81} - 452240 q^{82} - 798600 q^{84} - 200704 q^{85} - 736076 q^{86} + 431258 q^{88} + 456424 q^{89} - 65406 q^{90} + 36224 q^{91} + 476504 q^{92} - 413488 q^{95} + 884318 q^{96} + 356284 q^{97} + 444704 q^{98} - 640440 q^{99}+O(q^{100}) \) 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7 - 334 * q^10 - 504 * q^11 + 1722 * q^12 + 1600 * q^13 - 2364 * q^14 + 2564 * q^16 + 2432 * q^17 - 6052 * q^18 - 4218 * q^20 + 7144 * q^21 - 2590 * q^22 - 2728 * q^23 - 7246 * q^24 - 3024 * q^27 + 26164 * q^28 - 992 * q^29 + 18072 * q^30 - 14680 * q^31 - 96 * q^33 - 20962 * q^34 - 43744 * q^35 + 33552 * q^37 + 9024 * q^38 + 2720 * q^39 + 30922 * q^40 + 20716 * q^41 - 13682 * q^44 + 44848 * q^45 + 4416 * q^46 + 32032 * q^47 - 144770 * q^48 - 42636 * q^50 - 83368 * q^51 - 132556 * q^52 + 80728 * q^54 + 81040 * q^55 + 122460 * q^56 + 36840 * q^57 + 165766 * q^58 - 143200 * q^61 + 222580 * q^62 + 7592 * q^63 + 18428 * q^64 - 175016 * q^65 - 83648 * q^67 - 231150 * q^68 - 341160 * q^69 + 116088 * q^71 + 347100 * q^72 + 83892 * q^73 - 79282 * q^74 + 245864 * q^75 - 128572 * q^78 + 291672 * q^79 + 195426 * q^80 + 387028 * q^81 - 452240 * q^82 - 798600 * q^84 - 200704 * q^85 - 736076 * q^86 + 431258 * q^88 + 456424 * q^89 - 65406 * q^90 + 36224 * q^91 + 476504 * q^92 - 413488 * q^95 + 884318 * q^96 + 356284 * q^97 + 444704 * q^98 - 640440 * q^99

Introduction

L-functions

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