LMFDB - Embedded newform 13.8.c.a.9.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,8,Mod(3,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.3"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	13.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.06100533129$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 796 x^{14} - 475 x^{13} + 449889 x^{12} - 92038 x^{11} + 116806037 x^{10} + \cdots + 11\!\cdots\!00 $ x^16 - x^15 + 796x^14 - 475x^13 + 449889x^12 - 92038x^11 + 116806037x^10 + 198490961x^9 + 21546318357x^8 + 32373621530x^7 + 2116860322049x^6 + 2147931692741x^5 + 148294262896076x^4 + 71847528967407x^3 + 4924011367741489x^2 - 2411116235274240x + 113340278793830400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{12}\cdot 3\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.3
Root			$4.62264 - 8.00665i$ of defining polynomial
Character	$\chi$	$=$	13.9
Dual form			13.8.c.a.3.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.12264 + 8.87268i) q^{2} +(-4.84859 + 8.39800i) q^{3} +(11.5171 + 19.9481i) q^{4} -294.418 q^{5} +(-49.6752 - 86.0399i) q^{6} +(-715.408 - 1239.12i) q^{7} -1547.39 q^{8} +(1046.48 + 1812.56i) q^{9} +(1508.20 - 2612.27i) q^{10} +(-1358.28 + 2352.62i) q^{11} -223.366 q^{12} +(460.751 + 7907.98i) q^{13} +14659.1 q^{14} +(1427.51 - 2472.52i) q^{15} +(6452.53 - 11176.1i) q^{16} +(2889.72 + 5005.15i) q^{17} -21443.0 q^{18} +(-2298.20 - 3980.60i) q^{19} +(-3390.82 - 5873.08i) q^{20} +13874.9 q^{21} +(-13916.0 - 24103.2i) q^{22} +(-44723.6 + 77463.5i) q^{23} +(7502.65 - 12995.0i) q^{24} +8556.75 q^{25} +(-72525.3 - 36421.7i) q^{26} -41503.6 q^{27} +(16478.8 - 28542.1i) q^{28} +(26102.0 - 45210.1i) q^{29} +(14625.2 + 25331.7i) q^{30} +234286. q^{31} +(-32924.8 - 57027.4i) q^{32} +(-13171.5 - 22813.8i) q^{33} -59212.1 q^{34} +(210629. + 364820. i) q^{35} +(-24104.8 + 41750.7i) q^{36} +(66793.5 - 115690. i) q^{37} +47091.4 q^{38} +(-68645.3 - 34473.2i) q^{39} +455578. q^{40} +(-354622. + 614222. i) q^{41} +(-71076.0 + 123107. i) q^{42} +(-479856. - 831136. i) q^{43} -62573.8 q^{44} +(-308103. - 533650. i) q^{45} +(-458206. - 793636. i) q^{46} +443698. q^{47} +(62571.3 + 108377. i) q^{48} +(-611845. + 1.05975e6i) q^{49} +(-43833.2 + 75921.3i) q^{50} -56044.3 q^{51} +(-152443. + 100268. i) q^{52} +551118. q^{53} +(212608. - 368248. i) q^{54} +(399903. - 692652. i) q^{55} +(1.10701e6 + 1.91740e6i) q^{56} +44572.1 q^{57} +(267423. + 463190. i) q^{58} +(-373820. - 647476. i) q^{59} +65762.8 q^{60} +(248441. + 430313. i) q^{61} +(-1.20016e6 + 2.07874e6i) q^{62} +(1.49732e6 - 2.59344e6i) q^{63} +2.32650e6 q^{64} +(-135653. - 2.32825e6i) q^{65} +269892. q^{66} +(-747946. + 1.29548e6i) q^{67} +(-66562.2 + 115289. i) q^{68} +(-433692. - 751177. i) q^{69} -4.31590e6 q^{70} +(1.31035e6 + 2.26959e6i) q^{71} +(-1.61931e6 - 2.80473e6i) q^{72} -3.41001e6 q^{73} +(684318. + 1.18527e6i) q^{74} +(-41488.2 + 71859.6i) q^{75} +(52937.0 - 91689.6i) q^{76} +3.88691e6 q^{77} +(657515. - 432474. i) q^{78} +1.76854e6 q^{79} +(-1.89974e6 + 3.29044e6i) q^{80} +(-2.08742e6 + 3.61552e6i) q^{81} +(-3.63320e6 - 6.29289e6i) q^{82} -5.50709e6 q^{83} +(159798. + 276778. i) q^{84} +(-850785. - 1.47360e6i) q^{85} +9.83253e6 q^{86} +(253116. + 438410. i) q^{87} +(2.10179e6 - 3.64041e6i) q^{88} +(-2.25150e6 + 3.89971e6i) q^{89} +6.31320e6 q^{90} +(9.46934e6 - 6.22836e6i) q^{91} -2.06033e6 q^{92} +(-1.13596e6 + 1.96753e6i) q^{93} +(-2.27291e6 + 3.93679e6i) q^{94} +(676631. + 1.17196e6i) q^{95} +638555. q^{96} +(7.87248e6 + 1.36355e7i) q^{97} +(-6.26853e6 - 1.08574e7i) q^{98} -5.68568e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 9 q^{2} - 28 q^{3} - 577 q^{4} + 384 q^{5} + 342 q^{6} + 196 q^{7} + 5922 q^{8} - 5988 q^{9} - 6813 q^{10} + 5052 q^{11} - 15816 q^{12} + 17064 q^{13} + 14484 q^{14} - 184 q^{15} - 61377 q^{16} - 22824 q^{17}+ \cdots + 27386736 q^{99}+O(q^{100}) $ 16 * q - 9 * q^2 - 28 * q^3 - 577 * q^4 + 384 * q^5 + 342 * q^6 + 196 * q^7 + 5922 * q^8 - 5988 * q^9 - 6813 * q^10 + 5052 * q^11 - 15816 * q^12 + 17064 * q^13 + 14484 * q^14 - 184 * q^15 - 61377 * q^16 - 22824 * q^17 + 226318 * q^18 + 63692 * q^19 - 121971 * q^20 - 271240 * q^21 - 73726 * q^22 - 72468 * q^23 + 224952 * q^24 + 58488 * q^25 + 154443 * q^26 + 358616 * q^27 - 172816 * q^28 - 221772 * q^29 - 258116 * q^30 + 58432 * q^31 + 77823 * q^32 - 352372 * q^33 + 643334 * q^34 + 31560 * q^35 - 1162993 * q^36 - 368884 * q^37 + 2364492 * q^38 - 672996 * q^39 + 766030 * q^40 - 385824 * q^41 + 1560954 * q^42 + 391492 * q^43 - 6149616 * q^44 + 232096 * q^45 - 2599078 * q^46 + 1089984 * q^47 + 4585712 * q^48 - 1108780 * q^49 + 1626894 * q^50 + 8040712 * q^51 - 1312478 * q^52 + 3329328 * q^53 - 5616702 * q^54 - 418216 * q^55 - 3609156 * q^56 - 12068664 * q^57 + 3685081 * q^58 - 6318924 * q^59 + 1448784 * q^60 + 1763548 * q^61 - 12998388 * q^62 + 6641128 * q^63 + 32227074 * q^64 + 9500508 * q^65 + 16245108 * q^66 - 8607964 * q^67 - 10118091 * q^68 - 4618492 * q^69 - 25381840 * q^70 + 9473220 * q^71 - 35174445 * q^72 + 5020888 * q^73 + 2206221 * q^74 - 21834988 * q^75 + 18702876 * q^76 + 35263992 * q^77 + 28395902 * q^78 + 12644416 * q^79 - 24671247 * q^80 - 9316272 * q^81 - 9347751 * q^82 - 22158432 * q^83 + 37532636 * q^84 - 36911824 * q^85 - 30103956 * q^86 + 5199988 * q^87 - 36676404 * q^88 + 18469860 * q^89 + 132263562 * q^90 - 9614540 * q^91 + 64127424 * q^92 - 26340696 * q^93 - 6026128 * q^94 - 16267080 * q^95 - 164216320 * q^96 + 19660916 * q^97 - 51546651 * q^98 + 27386736 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−5.12264	+	8.87268i	−0.452782	+	0.784241i	−0.998558	−	0.0536900i	$-0.982902\pi$
$2$	−5.12264	+	8.87268i	−0.452782	+	0.784241i	0.545776	+	0.837931i	$0.316235\pi$
$3$	−4.84859	+	8.39800i	−0.103679	+	0.179577i	−0.913198	−	0.407517i	$-0.866395\pi$
$3$	−4.84859	+	8.39800i	−0.103679	+	0.179577i	0.809519	+	0.587094i	$0.199728\pi$
$4$	11.5171	+	19.9481i	0.0899770	+	0.155845i
$5$	−294.418			−1.05334			−0.526670	−	0.850070i	$-0.676560\pi$
$5$	−294.418			−1.05334			−0.526670	+	0.850070i	$0.676560\pi$
$6$	−49.6752	−	86.0399i	−0.0938880	−	0.162619i
$7$	−715.408	−	1239.12i	−0.788334	−	1.36544i	−0.926987	−	0.375094i	$-0.877610\pi$
$7$	−715.408	−	1239.12i	−0.788334	−	1.36544i	0.138652	−	0.990341i	$-0.455723\pi$
$8$	−1547.39			−1.06852
$9$	1046.48	+	1812.56i	0.478501	+	0.828789i
$10$	1508.20	−	2612.27i	0.476934	−	0.826073i
$11$	−1358.28	+	2352.62i	−0.307692	+	0.532939i	−0.977857	−	0.209274i	$-0.932890\pi$
$11$	−1358.28	+	2352.62i	−0.307692	+	0.532939i	0.670165	+	0.742212i	$0.266223\pi$
$12$	−223.366			−0.0373149
$13$	460.751	+	7907.98i	0.0581654	+	0.998307i
$13$	460.751	+	7907.98i	0.0581654	+	0.998307i
$14$	14659.1			1.42777
$15$	1427.51	−	2472.52i	0.109209	−	0.189156i
$16$	6452.53	−	11176.1i	0.393831	−	0.682136i
$17$	2889.72	+	5005.15i	0.142654	+	0.247085i	0.928495	−	0.371344i	$-0.121103\pi$
$17$	2889.72	+	5005.15i	0.142654	+	0.247085i	−0.785841	+	0.618429i	$0.787770\pi$
$18$	−21443.0			−0.866627
$19$	−2298.20	−	3980.60i	−0.0768688	−	0.133141i	0.825029	−	0.565091i	$-0.191159\pi$
$19$	−2298.20	−	3980.60i	−0.0768688	−	0.133141i	−0.901897	+	0.431950i	$0.857826\pi$
$20$	−3390.82	−	5873.08i	−0.0947764	−	0.164158i
$21$	13874.9			0.326935
$22$	−13916.0	−	24103.2i	−0.278635	−	0.482610i
$23$	−44723.6	+	77463.5i	−0.766459	+	1.32755i	0.173013	+	0.984920i	$0.444650\pi$
$23$	−44723.6	+	77463.5i	−0.766459	+	1.32755i	−0.939472	+	0.342626i	$0.888684\pi$
$24$	7502.65	−	12995.0i	0.110784	−	0.191883i
$25$	8556.75			0.109526
$26$	−72525.3	−	36421.7i	−0.809250	−	0.406400i
$27$	−41503.6			−0.405800
$28$	16478.8	−	28542.1i	0.141864	−	0.245716i
$29$	26102.0	−	45210.1i	0.198738	−	0.344225i	−0.749381	−	0.662139i	$-0.769649\pi$
$29$	26102.0	−	45210.1i	0.198738	−	0.344225i	0.948120	+	0.317914i	$0.102982\pi$
$30$	14625.2	+	25331.7i	0.0988960	+	0.171293i
$31$	234286.			1.41247			0.706236	−	0.707976i	$-0.250392\pi$
$31$	234286.			1.41247			0.706236	+	0.707976i	$0.250392\pi$
$32$	−32924.8	−	57027.4i	−0.177622	−	0.307651i
$33$	−13171.5	−	22813.8i	−0.0638025	−	0.110509i
$34$	−59212.1			−0.258365
$35$	210629.	+	364820.i	0.830385	+	1.43827i
$36$	−24104.8	+	41750.7i	−0.0861082	+	0.149144i
$37$	66793.5	−	115690.i	0.216784	−	0.375482i	−0.737039	−	0.675851i	$-0.763776\pi$
$37$	66793.5	−	115690.i	0.216784	−	0.375482i	0.953823	+	0.300369i	$0.0971098\pi$
$38$	47091.4			0.139219
$39$	−68645.3	−	34473.2i	−0.185304	−	0.0930583i
$40$	455578.			1.12552
$41$	−354622.	+	614222.i	−0.803566	+	1.39182i	0.113689	+	0.993516i	$0.463733\pi$
$41$	−354622.	+	614222.i	−0.803566	+	1.39182i	−0.917255	+	0.398301i	$0.869600\pi$
$42$	−71076.0	+	123107.i	−0.148030	+	0.256396i
$43$	−479856.	−	831136.i	−0.920390	−	1.59416i	−0.798813	−	0.601580i	$-0.794538\pi$
$43$	−479856.	−	831136.i	−0.920390	−	1.59416i	−0.121577	−	0.992582i	$-0.538795\pi$
$44$	−62573.8			−0.110741
$45$	−308103.	−	533650.i	−0.504025	−	0.872997i
$46$	−458206.	−	793636.i	−0.694078	−	1.20218i
$47$	443698.			0.623368			0.311684	−	0.950186i	$-0.399107\pi$
$47$	443698.			0.623368			0.311684	+	0.950186i	$0.399107\pi$
$48$	62571.3	+	108377.i	0.0816641	+	0.141446i
$49$	−611845.	+	1.05975e6i	−0.742942	+	1.28681i
$50$	−43833.2	+	75921.3i	−0.0495916	+	0.0858952i
$51$	−56044.3			−0.0591610
$52$	−152443.	+	100268.i	−0.150347	+	0.0988894i
$53$	551118.			0.508486			0.254243	−	0.967140i	$-0.418174\pi$
$53$	551118.			0.508486			0.254243	+	0.967140i	$0.418174\pi$
$54$	212608.	−	368248.i	0.183739	−	0.318245i
$55$	399903.	−	692652.i	0.324105	−	0.561366i
$56$	1.10701e6	+	1.91740e6i	0.842354	+	1.45900i
$57$	44572.1			0.0318787
$58$	267423.	+	463190.i	0.179970	+	0.311717i
$59$	−373820.	−	647476.i	−0.236963	−	0.410432i	0.722878	−	0.690976i	$-0.242819\pi$
$59$	−373820.	−	647476.i	−0.236963	−	0.410432i	−0.959841	+	0.280543i	$0.909485\pi$
$60$	65762.8			0.0393053
$61$	248441.	+	430313.i	0.140142	+	0.242734i	0.927550	−	0.373699i	$-0.121911\pi$
$61$	248441.	+	430313.i	0.140142	+	0.242734i	−0.787408	+	0.616432i	$0.788577\pi$
$62$	−1.20016e6	+	2.07874e6i	−0.639542	+	1.10772i
$63$	1.49732e6	−	2.59344e6i	0.754438	−	1.30673i
$64$	2.32650e6			1.10936
$65$	−135653.	−	2.32825e6i	−0.0612680	−	1.05156i
$66$	269892.			0.115554
$67$	−747946.	+	1.29548e6i	−0.303815	+	0.526222i	−0.976997	−	0.213254i	$-0.931594\pi$
$67$	−747946.	+	1.29548e6i	−0.303815	+	0.526222i	0.673182	+	0.739477i	$0.264927\pi$
$68$	−66562.2	+	115289.i	−0.0256712	+	0.0444638i
$69$	−433692.	−	751177.i	−0.158931	−	0.275277i
$70$	−4.31590e6			−1.50393
$71$	1.31035e6	+	2.26959e6i	0.434494	+	0.752565i	0.997254	−	0.0740548i	$-0.0235940\pi$
$71$	1.31035e6	+	2.26959e6i	0.434494	+	0.752565i	−0.562760	+	0.826620i	$0.690261\pi$
$72$	−1.61931e6	−	2.80473e6i	−0.511290	−	0.885580i
$73$	−3.41001e6			−1.02595			−0.512974	−	0.858404i	$-0.671456\pi$
$73$	−3.41001e6			−1.02595			−0.512974	+	0.858404i	$0.671456\pi$
$74$	684318.	+	1.18527e6i	0.196312	+	0.340023i
$75$	−41488.2	+	71859.6i	−0.0113556	+	0.0196685i
$76$	52937.0	−	91689.6i	0.0138329	−	0.0239592i
$77$	3.88691e6			0.970257
$78$	657515.	−	432474.i	0.156882	−	0.103188i
$79$	1.76854e6			0.403572			0.201786	−	0.979430i	$-0.435326\pi$
$79$	1.76854e6			0.403572			0.201786	+	0.979430i	$0.435326\pi$
$80$	−1.89974e6	+	3.29044e6i	−0.414838	+	0.718521i
$81$	−2.08742e6	+	3.61552e6i	−0.436428	+	0.755916i
$82$	−3.63320e6	−	6.29289e6i	−0.727680	−	1.26038i
$83$	−5.50709e6			−1.05718			−0.528590	−	0.848877i	$-0.677279\pi$
$83$	−5.50709e6			−1.05718			−0.528590	+	0.848877i	$0.677279\pi$
$84$	159798.	+	276778.i	0.0294166	+	0.0509511i
$85$	−850785.	−	1.47360e6i	−0.150264	−	0.260264i
$86$	9.83253e6			1.66694
$87$	253116.	+	438410.i	0.0412100	+	0.0713778i
$88$	2.10179e6	−	3.64041e6i	0.328776	−	0.569457i
$89$	−2.25150e6	+	3.89971e6i	−0.338538	+	0.586365i	−0.984158	−	0.177294i	$-0.943266\pi$
$89$	−2.25150e6	+	3.89971e6i	−0.338538	+	0.586365i	0.645620	+	0.763659i	$0.276599\pi$
$90$	6.31320e6			0.912853
$91$	9.46934e6	−	6.22836e6i	1.31727	−	0.866421i
$92$	−2.06033e6			−0.275855
$93$	−1.13596e6	+	1.96753e6i	−0.146444	+	0.253648i
$94$	−2.27291e6	+	3.93679e6i	−0.282250	+	0.488871i
$95$	676631.	+	1.17196e6i	0.0809691	+	0.140243i
$96$	638555.			0.0736629
$97$	7.87248e6	+	1.36355e7i	0.875812	+	1.51695i	0.855896	+	0.517148i	$0.173006\pi$
$97$	7.87248e6	+	1.36355e7i	0.875812	+	1.51695i	0.0199158	+	0.999802i	$0.493660\pi$
$98$	−6.26853e6	−	1.08574e7i	−0.672782	−	1.16529i
$99$	−5.68568e6			−0.588924
$100$	98548.6	+	170691.i	0.00985486	+	0.0170691i
$101$	−6.36563e6	+	1.10256e7i	−0.614776	+	1.06482i	0.375648	+	0.926762i	$0.377420\pi$
$101$	−6.36563e6	+	1.10256e7i	−0.614776	+	1.06482i	−0.990424	+	0.138060i	$0.955913\pi$
$102$	287095.	−	497263.i	0.0267871	−	0.0463965i
$103$	1.49876e7			1.35146			0.675729	−	0.737150i	$-0.263829\pi$
$103$	1.49876e7			1.35146			0.675729	+	0.737150i	$0.263829\pi$
$104$	−712961.	−	1.22367e7i	−0.0621511	−	1.06671i
$105$	−4.08501e6			−0.344374
$106$	−2.82318e6	+	4.88989e6i	−0.230233	+	0.398776i
$107$	2.54005e6	−	4.39949e6i	0.200447	−	0.347184i	−0.748226	−	0.663444i	$-0.769094\pi$
$107$	2.54005e6	−	4.39949e6i	0.200447	−	0.347184i	0.948672	+	0.316261i	$0.102427\pi$
$108$	−477999.	−	827918.i	−0.0365127	−	0.0632418i
$109$	−1.85661e7			−1.37318			−0.686590	−	0.727045i	$-0.740893\pi$
$109$	−1.85661e7			−1.37318			−0.686590	+	0.727045i	$0.740893\pi$
$110$	4.09712e6	+	7.09642e6i	0.293498	+	0.508353i
$111$	647708.	+	1.12186e6i	0.0449520	+	0.0778591i
$112$	−1.84648e7			−1.24188
$113$	−1.00677e7	−	1.74378e7i	−0.656380	−	1.13688i	−0.981546	−	0.191227i	$-0.938753\pi$
$113$	−1.00677e7	−	1.74378e7i	−0.656380	−	1.13688i	0.325166	−	0.945657i	$-0.394580\pi$
$114$	−228327.	+	395474.i	−0.0144341	+	0.0250006i
$115$	1.31674e7	−	2.28066e7i	0.807342	−	1.39836i
$116$	1.20247e6			0.0715275
$117$	−1.38515e7	+	9.11071e6i	−0.799553	+	0.525898i
$118$	7.65980e6			0.429171
$119$	4.13466e6	−	7.16144e6i	0.224919	−	0.389570i
$120$	−2.20891e6	+	3.82595e6i	−0.116693	+	0.202118i
$121$	6.05371e6	+	1.04853e7i	0.310651	+	0.538063i
$122$	−5.09070e6			−0.253816
$123$	−3.43883e6	−	5.95622e6i	−0.166626	−	0.288605i
$124$	2.69828e6	+	4.67356e6i	0.127090	+	0.220126i
$125$	2.04821e7			0.937972
$126$	1.53405e7	+	2.65705e7i	0.683192	+	1.18332i
$127$	−2.01471e6	+	3.48958e6i	−0.0872769	+	0.151168i	−0.906359	−	0.422508i	$-0.861150\pi$
$127$	−2.01471e6	+	3.48958e6i	−0.0872769	+	0.151168i	0.819082	+	0.573676i	$0.194483\pi$
$128$	−7.70344e6	+	1.33427e7i	−0.324676	+	0.562355i
$129$	9.30651e6			0.381700
$130$	2.13527e7	+	1.07232e7i	0.852416	+	0.428077i
$131$	1.39875e7			0.543614			0.271807	−	0.962352i	$-0.412379\pi$
$131$	1.39875e7			0.543614			0.271807	+	0.962352i	$0.412379\pi$
$132$	303394.	−	525495.i	0.0114815	−	0.0198866i
$133$	−3.28830e6	+	5.69550e6i	−0.121197	+	0.209919i
$134$	−7.66292e6	−	1.32726e7i	−0.275124	−	0.476528i
$135$	1.22194e7			0.427446
$136$	−4.47152e6	−	7.74490e6i	−0.152430	−	0.264016i
$137$	−1.70543e7	−	2.95390e7i	−0.566648	−	0.981463i	−0.996894	−	0.0787512i	$-0.974907\pi$
$137$	−1.70543e7	−	2.95390e7i	−0.566648	−	0.981463i	0.430247	−	0.902711i	$-0.358427\pi$
$138$	8.88660e6			0.287845
$139$	4.17261e6	+	7.22717e6i	0.131782	+	0.228253i	0.924364	−	0.381513i	$-0.124597\pi$
$139$	4.17261e6	+	7.22717e6i	0.131782	+	0.228253i	−0.792582	+	0.609766i	$0.791263\pi$
$140$	−4.85164e6	+	8.40329e6i	−0.149431	+	0.258822i
$141$	−2.15131e6	+	3.72617e6i	−0.0646302	+	0.111943i
$142$	−2.68498e7			−0.786924
$143$	−1.92303e7	−	9.65732e6i	−0.549933	−	0.276173i
$144$	2.70098e7			0.753795
$145$	−7.68490e6	+	1.33106e7i	−0.209339	+	0.362586i
$146$	1.74683e7	−	3.02559e7i	0.464531	−	0.804591i
$147$	−5.93317e6	−	1.02766e7i	−0.154055	−	0.266831i
$148$	3.07706e6			0.0780224
$149$	−2.07034e7	−	3.58594e7i	−0.512732	−	0.888078i	−0.999891	−	0.0147645i	$-0.995300\pi$
$149$	−2.07034e7	−	3.58594e7i	−0.512732	−	0.888078i	0.487159	−	0.873313i	$-0.338033\pi$
$150$	−425058.	−	736222.i	−0.0102832	−	0.0178111i
$151$	5.81255e6			0.137388			0.0686938	−	0.997638i	$-0.478117\pi$
$151$	5.81255e6			0.137388			0.0686938	+	0.997638i	$0.478117\pi$
$152$	3.55621e6	+	6.15953e6i	0.0821362	+	0.142264i
$153$	−6.04809e6	+	1.04756e7i	−0.136521	+	0.236461i
$154$	−1.99113e7	+	3.44873e7i	−0.439315	+	0.760916i
$155$	−6.89779e7			−1.48781
$156$	−102916.	−	1.76637e6i	−0.00217044	−	0.0372517i
$157$	−7.18559e7			−1.48188			−0.740941	−	0.671570i	$-0.765620\pi$
$157$	−7.18559e7			−1.48188			−0.740941	+	0.671570i	$0.765620\pi$
$158$	−9.05961e6	+	1.56917e7i	−0.182730	+	0.316497i
$159$	−2.67214e6	+	4.62829e6i	−0.0527194	+	0.0913126i
$160$	9.69364e6	+	1.67899e7i	0.187097	+	0.324061i
$161$	1.27982e8			2.41690
$162$	−2.13862e7	−	3.70421e7i	−0.395214	−	0.684530i
$163$	5.19566e7	+	8.99915e7i	0.939690	+	1.62759i	0.766050	+	0.642781i	$0.222219\pi$
$163$	5.19566e7	+	8.99915e7i	0.939690	+	1.62759i	0.173640	+	0.984809i	$0.444447\pi$
$164$	−1.63368e7			−0.289210
$165$	3.87793e6	+	6.71677e6i	0.0672057	+	0.116404i
$166$	2.82109e7	−	4.88627e7i	0.478672	−	0.829084i
$167$	3.75090e7	−	6.49675e7i	0.623201	−	1.07941i	−0.365685	−	0.930739i	$-0.619165\pi$
$167$	3.75090e7	−	6.49675e7i	0.623201	−	1.07941i	0.988886	−	0.148676i	$-0.0475013\pi$
$168$	−2.14698e7			−0.349338
$169$	−6.23239e7	+	7.28723e6i	−0.993234	+	0.116134i
$170$	1.74331e7			0.272147
$171$	4.81005e6	−	8.33126e6i	0.0735637	−	0.127416i
$172$	1.10531e7	−	1.91445e7i	0.165628	−	0.286876i
$173$	2.37545e7	+	4.11441e7i	0.348807	+	0.604152i	0.986038	−	0.166522i	$-0.0532535\pi$
$173$	2.37545e7	+	4.11441e7i	0.348807	+	0.604152i	−0.637231	+	0.770673i	$0.719920\pi$
$174$	−5.18649e6			−0.0746365
$175$	−6.12157e6	−	1.06029e7i	−0.0863435	−	0.149551i
$176$	1.75288e7	+	3.03607e7i	0.242358	+	0.419776i
$177$	7.25001e6			0.0982725
$178$	−2.30673e7	−	3.99537e7i	−0.306568	−	0.530991i
$179$	22224.8	−	38494.5i	0.000289636	−	0.000501664i	−0.865881	−	0.500251i	$-0.833241\pi$
$179$	22224.8	−	38494.5i	0.000289636	−	0.000501664i	0.866170	+	0.499749i	$0.166574\pi$
$180$	7.09688e6	−	1.22921e7i	0.0907013	−	0.157099i
$181$	8.82144e7			1.10577			0.552885	−	0.833258i	$-0.313527\pi$
$181$	8.82144e7			1.10577			0.552885	+	0.833258i	$0.313527\pi$
$182$	6.75421e6	+	1.15924e8i	0.0830471	+	1.42536i
$183$	−4.81836e6			−0.0581193
$184$	6.92047e7	−	1.19866e8i	0.818980	−	1.41851i
$185$	−1.96652e7	+	3.40611e7i	−0.228348	+	0.395510i
$186$	−1.16382e7	−	2.01579e7i	−0.132614	−	0.229695i
$187$	−1.57003e7			−0.175574
$188$	5.11009e6	+	8.85094e6i	0.0560888	+	0.0971487i
$189$	2.96920e7	+	5.14280e7i	0.319906	+	0.554094i
$190$	−1.38646e7			−0.146645
$191$	−8.21989e6	−	1.42373e7i	−0.0853589	−	0.147846i	0.820185	−	0.572098i	$-0.193870\pi$
$191$	−8.21989e6	−	1.42373e7i	−0.0853589	−	0.147846i	−0.905544	+	0.424252i	$0.860537\pi$
$192$	−1.12802e7	+	1.95379e7i	−0.115017	+	0.199216i
$193$	−5.87920e7	+	1.01831e8i	−0.588664	+	1.01960i	0.405744	+	0.913987i	$0.367013\pi$
$193$	−5.87920e7	+	1.01831e8i	−0.588664	+	1.01960i	−0.994408	+	0.105609i	$0.966321\pi$
$194$	−1.61312e8			−1.58621
$195$	2.02104e7	+	1.01495e7i	0.195188	+	0.0980221i
$196$	−2.81866e7			−0.267391
$197$	2.91568e7	−	5.05011e7i	0.271712	−	0.470619i	−0.697588	−	0.716499i	$-0.745744\pi$
$197$	2.91568e7	−	5.05011e7i	0.271712	−	0.470619i	0.969300	+	0.245880i	$0.0790769\pi$
$198$	2.91257e7	−	5.04473e7i	0.266654	−	0.461859i
$199$	1.43487e7	+	2.48527e7i	0.129070	+	0.223557i	0.923317	−	0.384039i	$-0.125467\pi$
$199$	1.43487e7	+	2.48527e7i	0.129070	+	0.223557i	−0.794246	+	0.607596i	$0.792134\pi$
$200$	−1.32406e7			−0.117032
$201$	−7.25297e6	−	1.25625e7i	−0.0629984	−	0.109116i
$202$	−6.52177e7	−	1.12960e8i	−0.556719	−	0.964265i
$203$	−7.46944e7			−0.626689
$204$	−645465.	−	1.11798e6i	−0.00532313	−	0.00921994i
$205$	1.04407e8	−	1.80838e8i	0.846429	−	1.46606i
$206$	−7.67762e7	+	1.32980e8i	−0.611915	+	1.05987i
$207$	−1.87210e8			−1.46701
$208$	9.13535e7	+	4.58771e7i	0.703888	+	0.353488i
$209$	1.24864e7			0.0946078
$210$	2.09260e7	−	3.62450e7i	0.155926	−	0.270072i
$211$	1.01655e7	−	1.76072e7i	0.0744973	−	0.129033i	−0.826370	−	0.563127i	$-0.809598\pi$
$211$	1.01655e7	−	1.76072e7i	0.0744973	−	0.129033i	0.900868	+	0.434094i	$0.142931\pi$
$212$	6.34726e6	+	1.09938e7i	0.0457521	+	0.0792449i
$213$	−2.54134e7			−0.180192
$214$	2.60235e7	+	4.50740e7i	0.181517	+	0.314397i
$215$	1.41278e8	+	2.44701e8i	0.969484	+	1.67920i
$216$	6.42221e7			0.433607
$217$	−1.67610e8	−	2.90309e8i	−1.11350	−	1.92864i
$218$	9.51074e7	−	1.64731e8i	0.621751	−	1.07690i
$219$	1.65337e7	−	2.86373e7i	0.106369	−	0.184237i
$220$	1.84228e7			0.116648
$221$	−3.82492e7	+	2.51580e7i	−0.238369	+	0.156785i
$222$	−1.32719e7			−0.0814138
$223$	−5.03791e7	+	8.72592e7i	−0.304217	+	0.526919i	−0.977087	−	0.212842i	$-0.931728\pi$
$223$	−5.03791e7	+	8.72592e7i	−0.304217	+	0.526919i	0.672870	+	0.739761i	$0.265061\pi$
$224$	−4.71093e7	+	8.15957e7i	−0.280052	+	0.485064i
$225$	8.95449e6	+	1.55096e7i	0.0524085	+	0.0907743i
$226$	2.06293e8			1.18879
$227$	8.66071e7	+	1.50008e8i	0.491432	+	0.851185i	0.999951	−	0.00986563i	$-0.00314038\pi$
$227$	8.66071e7	+	1.50008e8i	0.491432	+	0.851185i	−0.508520	+	0.861050i	$0.669807\pi$
$228$	513339.	+	889130.i	0.00286835	+	0.00496813i
$229$	6.87545e7			0.378335			0.189168	−	0.981945i	$-0.439421\pi$
$229$	6.87545e7			0.378335			0.189168	+	0.981945i	$0.439421\pi$
$230$	1.34904e8	+	2.33660e8i	0.731100	+	1.26630i
$231$	−1.88460e7	+	3.26423e7i	−0.100595	+	0.174236i
$232$	−4.03900e7	+	6.99575e7i	−0.212357	+	0.367812i
$233$	3.20272e8			1.65872			0.829359	−	0.558716i	$-0.188706\pi$
$233$	3.20272e8			1.65872			0.829359	+	0.558716i	$0.188706\pi$
$234$	−9.87990e6	−	1.69571e8i	−0.0504077	−	0.865160i
$235$	−1.30632e8			−0.656619
$236$	8.61062e6	−	1.49140e7i	0.0426425	−	0.0738589i
$237$	−8.57493e6	+	1.48522e7i	−0.0418419	+	0.0724723i
$238$	4.23608e7	+	7.33710e7i	0.203678	+	0.352781i
$239$	−2.32563e8			−1.10191			−0.550957	−	0.834534i	$-0.685737\pi$
$239$	−2.32563e8			−1.10191			−0.550957	+	0.834534i	$0.685737\pi$
$240$	−1.84221e7	−	3.19080e7i	−0.0860201	−	0.148991i
$241$	4.04243e7	+	7.00169e7i	0.186030	+	0.322213i	0.943923	−	0.330165i	$-0.107105\pi$
$241$	4.04243e7	+	7.00169e7i	0.186030	+	0.322213i	−0.757893	+	0.652379i	$0.773771\pi$
$242$	−1.24044e8			−0.562629
$243$	−6.56263e7	−	1.13668e8i	−0.293397	−	0.508179i
$244$	−5.72262e6	+	9.91187e6i	−0.0252192	+	0.0436809i
$245$	1.80138e8	−	3.12008e8i	0.782571	−	1.35545i
$246$	7.04635e7			0.301781
$247$	3.04196e7	−	2.00082e7i	0.128444	−	0.0844829i
$248$	−3.62531e8			−1.50926
$249$	2.67016e7	−	4.62486e7i	0.109607	−	0.189846i
$250$	−1.04923e8	+	1.81731e8i	−0.424697	+	0.735596i
$251$	−1.56015e8	−	2.70225e8i	−0.622741	−	1.07862i	−0.988973	−	0.148095i	$-0.952686\pi$
$251$	−1.56015e8	−	2.70225e8i	−0.622741	−	1.07862i	0.366232	−	0.930523i	$-0.380647\pi$
$252$	6.89790e7			0.271528
$253$	−1.21495e8	−	2.10435e8i	−0.471667	−	0.816951i
$254$	−2.06413e7	−	3.57517e7i	−0.0790348	−	0.136892i
$255$	1.65004e7			0.0623167
$256$	6.99718e7	+	1.21195e8i	0.260665	+	0.451486i
$257$	−5.51045e7	+	9.54439e7i	−0.202498	+	0.350737i	−0.949333	−	0.314273i	$-0.898239\pi$
$257$	−5.51045e7	+	9.54439e7i	−0.202498	+	0.350737i	0.746834	+	0.665010i	$0.231573\pi$
$258$	−4.76739e7	+	8.25736e7i	−0.172827	+	0.299345i
$259$	−1.91138e8			−0.683594
$260$	4.48819e7	−	2.95206e7i	0.158367	−	0.104164i
$261$	1.09261e8			0.380386
$262$	−7.16530e7	+	1.24107e8i	−0.246139	+	0.426325i
$263$	9.70287e7	−	1.68059e8i	0.328893	−	0.569660i	−0.653399	−	0.757014i	$-0.726658\pi$
$263$	9.70287e7	−	1.68059e8i	0.328893	−	0.569660i	0.982293	+	0.187354i	$0.0599910\pi$
$264$	2.03815e7	+	3.53017e7i	0.0681744	+	0.118082i
$265$	−1.62259e8			−0.535609
$266$	−3.36896e7	−	5.83521e7i	−0.109751	−	0.190095i
$267$	−2.18332e7	−	3.78162e7i	−0.0701985	−	0.121587i
$268$	−3.44566e7			−0.109345
$269$	9.23944e7	+	1.60032e8i	0.289410	+	0.501272i	0.973669	−	0.227967i	$-0.0732077\pi$
$269$	9.23944e7	+	1.60032e8i	0.289410	+	0.501272i	−0.684259	+	0.729239i	$0.739874\pi$
$270$	−6.25955e7	+	1.08419e8i	−0.193540	+	0.335221i
$271$	−7.43203e6	+	1.28727e7i	−0.0226838	+	0.0392894i	−0.877144	−	0.480227i	$-0.840554\pi$
$271$	−7.43203e6	+	1.28727e7i	−0.0226838	+	0.0392894i	0.854461	+	0.519516i	$0.173888\pi$
$272$	7.45841e7			0.224727
$273$	6.39286e6	+	1.09722e8i	0.0190163	+	0.326381i
$274$	3.49453e8			1.02627
$275$	−1.16225e7	+	2.01308e7i	−0.0337004	+	0.0583709i
$276$	9.98972e6	−	1.73027e7i	0.0286003	−	0.0495373i
$277$	1.56861e8	+	2.71691e8i	0.443441	+	0.768062i	0.997942	−	0.0641206i	$-0.0204242\pi$
$277$	1.56861e8	+	2.71691e8i	0.443441	+	0.768062i	−0.554501	+	0.832183i	$0.687091\pi$
$278$	−8.54991e7			−0.238674
$279$	2.45176e8	+	4.24657e8i	0.675870	+	1.17064i
$280$	−3.25924e8	−	5.64517e8i	−0.887286	−	1.53682i
$281$	1.83059e8			0.492175			0.246088	−	0.969248i	$-0.420855\pi$
$281$	1.83059e8			0.492175			0.246088	+	0.969248i	$0.420855\pi$
$282$	−2.20408e7	−	3.81757e7i	−0.0585268	−	0.101371i
$283$	−2.25146e8	+	3.89964e8i	−0.590488	+	1.02276i	0.403678	+	0.914901i	$0.367732\pi$
$283$	−2.25146e8	+	3.89964e8i	−0.590488	+	1.02276i	−0.994167	+	0.107855i	$0.965602\pi$
$284$	−3.01828e7	+	5.22781e7i	−0.0781889	+	0.135427i
$285$	−1.31228e7			−0.0335792
$286$	1.84196e8	−	1.21153e8i	0.465586	−	0.306234i
$287$	1.01480e9			2.53392
$288$	6.89104e7	−	1.19356e8i	0.169985	−	0.294423i
$289$	1.88468e8	−	3.26437e8i	0.459299	−	0.795530i
$290$	−7.87340e7	−	1.36371e8i	−0.189570	−	0.328345i
$291$	−1.52682e8			−0.363213
$292$	−3.92733e7	−	6.80233e7i	−0.0923118	−	0.159889i
$293$	−3.09952e8	−	5.36853e8i	−0.719876	−	1.24686i	−0.961048	−	0.276380i	$-0.910865\pi$
$293$	−3.09952e8	−	5.36853e8i	−0.719876	−	1.24686i	0.241172	−	0.970482i	$-0.422468\pi$
$294$	1.21574e8			0.279014
$295$	1.10059e8	+	1.90628e8i	0.249603	+	0.432325i
$296$	−1.03355e8	+	1.79017e8i	−0.231639	+	0.401211i
$297$	5.63737e7	−	9.76421e7i	0.124862	−	0.216267i
$298$	4.24225e8			0.928623
$299$	−6.33186e8	−	3.17982e8i	−1.36988	−	0.687944i
$300$	−1.91129e6			−0.00408697
$301$	−6.86586e8	+	1.18920e9i	−1.45115	+	2.51347i
$302$	−2.97756e7	+	5.15729e7i	−0.0622067	+	0.107745i
$303$	−6.17286e7	−	1.06917e8i	−0.127479	−	0.220800i
$304$	−5.93168e7			−0.121093
$305$	−7.31455e7	−	1.26692e8i	−0.147618	−	0.255681i
$306$	−6.19644e7	−	1.07325e8i	−0.123628	−	0.214130i
$307$	1.29658e8			0.255750			0.127875	−	0.991790i	$-0.459184\pi$
$307$	1.29658e8			0.255750			0.127875	+	0.991790i	$0.459184\pi$
$308$	4.47658e7	+	7.75366e7i	0.0873008	+	0.151210i
$309$	−7.26688e7	+	1.25866e8i	−0.140118	+	0.242691i
$310$	3.53349e8	−	6.12018e8i	0.673656	−	1.16681i
$311$	2.74386e8			0.517250			0.258625	−	0.965978i	$-0.416731\pi$
$311$	2.74386e8			0.517250			0.258625	+	0.965978i	$0.416731\pi$
$312$	1.06221e8	+	5.33434e7i	0.198002	+	0.0994350i
$313$	−8.32144e7			−0.153389			−0.0766944	−	0.997055i	$-0.524437\pi$
$313$	−8.32144e7			−0.153389			−0.0766944	+	0.997055i	$0.524437\pi$
$314$	3.68092e8	−	6.37554e8i	0.670969	−	1.16215i
$315$	−4.40838e8	+	7.63555e8i	−0.794680	+	1.37643i
$316$	2.03684e7	+	3.52791e7i	0.0363122	+	0.0628945i
$317$	1.81694e7			0.0320356			0.0160178	−	0.999872i	$-0.494901\pi$
$317$	1.81694e7			0.0320356			0.0160178	+	0.999872i	$0.494901\pi$
$318$	−2.73769e7	−	4.74182e7i	−0.0477407	−	0.0826894i
$319$	7.09080e7	+	1.22816e8i	0.122300	+	0.211831i
$320$	−6.84961e8			−1.16853
$321$	2.46313e7	+	4.26626e7i	0.0415642	+	0.0719913i
$322$	−6.55608e8	+	1.13555e9i	−1.09433	+	1.89544i
$323$	1.32823e7	−	2.30057e7i	0.0219313	−	0.0379862i
$324$	−9.61639e7			−0.157074
$325$	3.94254e6	+	6.76667e7i	0.00637065	+	0.109341i
$326$	−1.06462e9			−1.70190
$327$	9.00192e7	−	1.55918e8i	0.142370	−	0.246592i
$328$	5.48737e8	−	9.50440e8i	0.858629	−	1.48719i
$329$	−3.17425e8	−	5.49796e8i	−0.491423	−	0.851169i
$330$	−7.94610e7			−0.121718
$331$	−3.75738e8	−	6.50798e8i	−0.569492	−	0.986389i	−0.996616	−	0.0821962i	$-0.973807\pi$
$331$	−3.75738e8	−	6.50798e8i	−0.569492	−	0.986389i	0.427124	−	0.904193i	$-0.359527\pi$
$332$	−6.34255e7	−	1.09856e8i	−0.0951219	−	0.164756i
$333$	2.79593e8			0.414926
$334$	3.84290e8	+	6.65611e8i	0.564348	+	0.977479i
$335$	2.20209e8	−	3.81412e8i	0.320020	−	0.554291i
$336$	8.95280e7	−	1.55067e8i	0.128757	−	0.223014i
$337$	1.05380e9			1.49987			0.749936	−	0.661510i	$-0.230084\pi$
$337$	1.05380e9			1.49987			0.749936	+	0.661510i	$0.230084\pi$
$338$	2.54606e8	−	5.90310e8i	0.358641	−	0.831518i
$339$	1.95256e8			0.272211
$340$	1.95971e7	−	3.39431e7i	0.0270405	−	0.0468356i
$341$	−3.18227e8	+	5.51185e8i	−0.434607	+	0.752761i
$342$	4.92804e7	+	8.53561e7i	0.0666166	+	0.115383i
$343$	5.72537e8			0.766080
$344$	7.42524e8	+	1.28609e9i	0.983458	+	1.70340i
$345$	1.27687e8	+	2.21160e8i	0.167409	+	0.289961i
$346$	−4.86744e8			−0.631734
$347$	−3.20975e8	−	5.55945e8i	−0.412399	−	0.714296i	0.582752	−	0.812650i	$-0.301976\pi$
$347$	−3.20975e8	−	5.55945e8i	−0.412399	−	0.714296i	−0.995152	+	0.0983534i	$0.968642\pi$
$348$	−5.83030e6	+	1.00984e7i	−0.00741590	+	0.0128447i
$349$	−2.88140e7	+	4.99074e7i	−0.0362840	+	0.0628457i	−0.883597	−	0.468248i	$-0.844885\pi$
$349$	−2.88140e7	+	4.99074e7i	−0.0362840	+	0.0628457i	0.847313	+	0.531094i	$0.178219\pi$
$350$	1.25434e8			0.156379
$351$	−1.91228e7	−	3.28210e8i	−0.0236035	−	0.405113i
$352$	1.78885e8			0.218612
$353$	−6.19753e8	+	1.07344e9i	−0.749906	+	1.29888i	0.197961	+	0.980210i	$0.436568\pi$
$353$	−6.19753e8	+	1.07344e9i	−0.749906	+	1.29888i	−0.947867	+	0.318666i	$0.896765\pi$
$354$	−3.71392e7	+	6.43270e7i	−0.0444960	+	0.0770693i
$355$	−3.85791e8	−	6.68209e8i	−0.457670	−	0.792707i
$356$	−1.03723e8			−0.121842
$357$	4.00945e7	+	6.94458e7i	0.0466387	+	0.0807806i
$358$	227699.	+	394387.i	0.000262284	+	0.000454289i
$359$	1.50303e9			1.71450			0.857251	−	0.514899i	$-0.172171\pi$
$359$	1.50303e9			1.71450			0.857251	+	0.514899i	$0.172171\pi$
$360$	4.76755e8	+	8.25763e8i	0.538563	+	0.932818i
$361$	4.36372e8	−	7.55819e8i	0.488182	−	0.845557i
$362$	−4.51891e8	+	7.82698e8i	−0.500673	+	0.867190i
$363$	−1.17408e8			−0.128832
$364$	2.33303e8	+	1.17163e8i	0.253551	+	0.127332i
$365$	1.00397e9			1.08067
$366$	2.46827e7	−	4.27517e7i	0.0263154	−	0.0455795i
$367$	−7.32757e7	+	1.26917e8i	−0.0773800	+	0.134026i	−0.902119	−	0.431488i	$-0.857989\pi$
$367$	−7.32757e7	+	1.26917e8i	−0.0773800	+	0.134026i	0.824739	+	0.565514i	$0.191322\pi$
$368$	5.77160e8	+	9.99671e8i	0.603711	+	1.04566i
$369$	−1.48442e9			−1.53803
$370$	−2.01475e8	−	3.48966e8i	−0.206784	−	0.358160i
$371$	−3.94274e8	−	6.82903e8i	−0.400857	−	0.694305i
$372$	−5.23314e7			−0.0527063
$373$	−7.24160e8	−	1.25428e9i	−0.722526	−	1.25145i	−0.959984	−	0.280054i	$-0.909648\pi$
$373$	−7.24160e8	−	1.25428e9i	−0.722526	−	1.25145i	0.237458	−	0.971398i	$-0.423686\pi$
$374$	8.04269e7	−	1.39303e8i	0.0794970	−	0.137693i
$375$	−9.93094e7	+	1.72009e8i	−0.0972480	+	0.168439i
$376$	−6.86572e8			−0.666084
$377$	3.69547e8	+	1.85584e8i	0.355202	+	0.178380i
$378$	−6.08406e8			−0.579391
$379$	−854926.	+	1.48078e6i	−0.000806662	+	0.00139718i	−0.866428	−	0.499301i	$-0.833590\pi$
$379$	−854926.	+	1.48078e6i	−0.000806662	+	0.00139718i	0.865622	+	0.500698i	$0.166923\pi$
$380$	−1.55856e7	+	2.69950e7i	−0.0145707	+	0.0252372i
$381$	−1.95370e7	−	3.38391e7i	−0.0180976	−	0.0313459i
$382$	1.68430e8			0.154596
$383$	3.71796e8	+	6.43970e8i	0.338150	+	0.585693i	0.984085	−	0.177700i	$-0.0568655\pi$
$383$	3.71796e8	+	6.43970e8i	0.338150	+	0.585693i	−0.645935	+	0.763393i	$0.723532\pi$
$384$	−7.47016e7	−	1.29387e8i	−0.0673241	−	0.116609i
$385$	−1.14438e9			−1.02201
$386$	−6.02341e8	−	1.04328e9i	−0.533073	−	0.923309i
$387$	1.00432e9	−	1.73954e9i	0.880815	−	1.52562i
$388$	−1.81336e8	+	3.14083e8i	−0.157606	+	0.272981i
$389$	−1.68890e9			−1.45472			−0.727361	−	0.686255i	$-0.759254\pi$
$389$	−1.68890e9			−1.45472			−0.727361	+	0.686255i	$0.759254\pi$
$390$	−1.93584e8	+	1.27328e8i	−0.165251	+	0.108692i
$391$	−5.16955e8			−0.437355
$392$	9.46762e8	−	1.63984e9i	0.793852	−	1.37499i
$393$	−6.78197e7	+	1.17467e8i	−0.0563614	+	0.0976208i
$394$	2.98720e8	+	5.17398e8i	0.246052	+	0.426175i
$395$	−5.20690e8			−0.425098
$396$	−6.54823e7	−	1.13419e8i	−0.0529897	−	0.0917808i
$397$	6.51199e8	+	1.12791e9i	0.522332	+	0.904706i	0.999662	+	0.0259818i	$0.00827121\pi$
$397$	6.51199e8	+	1.12791e9i	0.522332	+	0.904706i	−0.477330	+	0.878724i	$0.658395\pi$
$398$	−2.94013e8			−0.233763
$399$	−3.18872e7	−	5.52303e7i	−0.0251311	−	0.0435284i
$400$	5.52127e7	−	9.56312e7i	0.0431349	−	0.0747119i
$401$	−4.19950e8	+	7.27374e8i	−0.325231	+	0.563317i	−0.981559	−	0.191159i	$-0.938775\pi$
$401$	−4.19950e8	+	7.27374e8i	−0.325231	+	0.563317i	0.656328	+	0.754476i	$0.272109\pi$
$402$	1.48617e8			0.114098
$403$	1.07947e8	+	1.85273e9i	0.0821571	+	1.41008i
$404$	−2.93253e8			−0.221263
$405$	6.14574e8	−	1.06447e9i	0.459708	−	0.796237i
$406$	3.82633e8	−	6.62739e8i	0.283753	−	0.491475i
$407$	1.81449e8	+	3.14279e8i	0.133406	+	0.231066i
$408$	8.67223e7			0.0632150
$409$	−4.95819e7	−	8.58783e7i	−0.0358337	−	0.0620658i	0.847552	−	0.530712i	$-0.178075\pi$
$409$	−4.95819e7	−	8.58783e7i	−0.0358337	−	0.0620658i	−0.883386	+	0.468646i	$0.844742\pi$
$410$	1.06968e9	+	1.85274e9i	0.766495	+	1.32761i
$411$	3.30758e8			0.234998
$412$	1.72613e8	+	2.98975e8i	0.121600	+	0.210617i
$413$	−5.34868e8	+	9.26419e8i	−0.373613	+	0.647116i
$414$	9.59008e8	−	1.66105e9i	0.664234	−	1.15049i
$415$	1.62139e9			1.11357
$416$	4.35802e8	−	2.86644e8i	0.296799	−	0.195216i
$417$	−8.09250e7			−0.0546521
$418$	−6.39636e7	+	1.10788e8i	−0.0428367	+	0.0741953i
$419$	−3.29784e8	+	5.71202e8i	−0.219018	+	0.379351i	−0.954508	−	0.298185i	$-0.903619\pi$
$419$	−3.29784e8	+	5.71202e8i	−0.219018	+	0.379351i	0.735490	+	0.677536i	$0.236952\pi$
$420$	−4.70473e7	−	8.14882e7i	−0.0309857	−	0.0536689i
$421$	3.03466e6			0.00198208			0.000991042	−	1.00000i	$-0.499685\pi$
$421$	3.03466e6			0.00198208			0.000991042		1.00000i	$0.499685\pi$
$422$	1.04148e8	+	1.80390e8i	0.0674620	+	0.116848i
$423$	4.64322e8	+	8.04229e8i	0.298283	+	0.516641i
$424$	−8.52793e8			−0.543330
$425$	2.47266e7	+	4.28278e7i	0.0156244	+	0.0270623i
$426$	1.30184e8	−	2.25485e8i	0.0815875	−	0.141314i
$427$	3.55474e8	−	6.15698e8i	0.220958	−	0.382711i
$428$	1.17015e8			0.0721423
$429$	1.74342e8	−	1.14672e8i	0.106611	−	0.0701222i
$430$	−2.89487e9			−1.75586
$431$	4.74142e8	−	8.21238e8i	0.285258	−	0.494082i	−0.687414	−	0.726266i	$-0.741254\pi$
$431$	4.74142e8	−	8.21238e8i	0.285258	−	0.494082i	0.972672	+	0.232184i	$0.0745873\pi$
$432$	−2.67803e8	+	4.63849e8i	−0.159817	+	0.276811i
$433$	6.12117e8	+	1.06022e9i	0.362349	+	0.627606i	0.988347	−	0.152218i	$-0.0486417\pi$
$433$	6.12117e8	+	1.06022e9i	0.362349	+	0.627606i	−0.625998	+	0.779824i	$0.715308\pi$
$434$	3.43442e9			2.01669
$435$	−7.45218e7	−	1.29076e8i	−0.0434081	−	0.0751851i
$436$	−2.13826e8	−	3.70358e8i	−0.123555	−	0.214003i
$437$	4.11135e8			0.235667
$438$	1.69393e8	+	2.93397e8i	0.0963242	+	0.166838i
$439$	8.28744e8	−	1.43543e9i	0.467514	−	0.809758i	−0.531797	−	0.846872i	$-0.678483\pi$
$439$	8.28744e8	−	1.43543e9i	0.467514	−	0.809758i	0.999311	+	0.0371140i	$0.0118165\pi$
$440$	−6.18805e8	+	1.07180e9i	−0.346314	+	0.599833i
$441$	−2.56114e9			−1.42200
$442$	−2.72820e7	−	4.68248e8i	−0.0150279	−	0.257928i
$443$	1.03569e9			0.566000			0.283000	−	0.959120i	$-0.408670\pi$
$443$	1.03569e9			0.566000			0.283000	+	0.959120i	$0.408670\pi$
$444$	−1.49194e7	+	2.58411e7i	−0.00808929	+	0.0140111i
$445$	6.62882e8	−	1.14814e9i	0.356596	−	0.617642i
$446$	−5.16148e8	−	8.93995e8i	−0.275488	−	0.477159i
$447$	4.01530e8			0.212638
$448$	−1.66439e9	−	2.88281e9i	−0.874546	−	1.51476i
$449$	8.63675e8	+	1.49593e9i	0.450286	+	0.779918i	0.998404	−	0.0564835i	$-0.0179888\pi$
$449$	8.63675e8	+	1.49593e9i	0.450286	+	0.779918i	−0.548118	+	0.836401i	$0.684655\pi$
$450$	−1.83483e8			−0.0949186
$451$	−9.63354e8	−	1.66858e9i	−0.494502	−	0.856503i
$452$	2.31900e8	−	4.01663e8i	0.118118	−	0.204587i
$453$	−2.81827e7	+	4.88138e7i	−0.0142442	+	0.0246717i
$454$	−1.77463e9			−0.890046
$455$	−2.78794e9	+	1.83374e9i	−1.38753	+	0.912636i
$456$	−6.89703e7			−0.0340632
$457$	−1.45297e9	+	2.51662e9i	−0.712114	+	1.23342i	0.251948	+	0.967741i	$0.418929\pi$
$457$	−1.45297e9	+	2.51662e9i	−0.712114	+	1.23342i	−0.964062	+	0.265677i	$0.914404\pi$
$458$	−3.52205e8	+	6.10037e8i	−0.171303	+	0.296706i
$459$	−1.19934e8	−	2.07731e8i	−0.0578892	−	0.100267i
$460$	6.06599e8			0.290569
$461$	2.99328e8	+	5.18451e8i	0.142296	+	0.246465i	0.928361	−	0.371680i	$-0.121218\pi$
$461$	2.99328e8	+	5.18451e8i	0.142296	+	0.246465i	−0.786065	+	0.618144i	$0.787885\pi$
$462$	−1.93083e8	−	3.34429e8i	−0.0910955	−	0.157782i
$463$	1.62279e9			0.759851			0.379926	−	0.925017i	$-0.375950\pi$
$463$	1.62279e9			0.759851			0.379926	+	0.925017i	$0.375950\pi$
$464$	−3.36848e8	−	5.83439e8i	−0.156539	−	0.271133i
$465$	3.34445e8	−	5.79276e8i	0.154255	−	0.267178i
$466$	−1.64064e9	+	2.84167e9i	−0.751038	+	1.30084i
$467$	−2.87438e9			−1.30598			−0.652988	−	0.757368i	$-0.726485\pi$
$467$	−2.87438e9			−1.30598			−0.652988	+	0.757368i	$0.726485\pi$
$468$	−3.41270e8	−	1.71384e8i	−0.153900	−	0.0772874i
$469$	2.14035e9			0.958030
$470$	6.69183e8	−	1.15906e9i	0.297305	−	0.514948i
$471$	3.48400e8	−	6.03446e8i	0.153640	−	0.266112i
$472$	5.78445e8	+	1.00190e9i	0.253201	+	0.438557i
$473$	2.60713e9			1.13279
$474$	−8.78526e7	−	1.52165e8i	−0.0378905	−	0.0656283i
$475$	−1.96651e7	−	3.40610e7i	−0.00841917	−	0.0145824i
$476$	1.90476e8			0.0809500
$477$	5.76735e8	+	9.98935e8i	0.243311	+	0.421428i
$478$	1.19134e9	−	2.06345e9i	0.498926	−	0.864166i
$479$	−7.73338e8	+	1.33946e9i	−0.321511	+	0.556873i	−0.980800	−	0.195017i	$-0.937524\pi$
$479$	−7.73338e8	+	1.33946e9i	−0.321511	+	0.556873i	0.659289	+	0.751889i	$0.270857\pi$
$480$	−1.88002e8			−0.0775921
$481$	9.45648e8	+	4.74898e8i	0.387455	+	0.194577i
$482$	−8.28317e8			−0.336924
$483$	−6.20534e8	+	1.07480e9i	−0.250582	+	0.434021i
$484$	−1.39442e8	+	2.41520e8i	−0.0559029	+	0.0968266i
$485$	−2.31780e9	−	4.01454e9i	−0.922528	−	1.59787i
$486$	1.34472e9			0.531380
$487$	−1.55778e9	−	2.69816e9i	−0.611161	−	1.05856i	−0.991045	−	0.133528i	$-0.957370\pi$
$487$	−1.55778e9	−	2.69816e9i	−0.611161	−	1.05856i	0.379884	−	0.925034i	$-0.375964\pi$
$488$	−3.84435e8	−	6.65861e8i	−0.149745	−	0.259367i
$489$	−1.00767e9			−0.389704
$490$	1.84557e9	+	3.19661e9i	0.708669	+	1.22745i
$491$	−1.32599e9	+	2.29668e9i	−0.505538	+	0.875618i	0.494441	+	0.869211i	$0.335373\pi$
$491$	−1.32599e9	+	2.29668e9i	−0.505538	+	0.875618i	−0.999979	+	0.00640660i	$0.997961\pi$
$492$	7.92103e7	−	1.37196e8i	0.0299850	−	0.0519355i
$493$	3.01711e8			0.113403
$494$	2.16974e7	+	3.72398e8i	0.00809775	+	0.138984i
$495$	1.67397e9			0.620338
$496$	1.51174e9	−	2.61840e9i	0.556276	−	0.963498i
$497$	1.87487e9	−	3.24737e9i	0.685053	−	1.18655i
$498$	2.73566e8	+	4.73830e8i	0.0992565	+	0.171917i
$499$	−2.53709e8			−0.0914081			−0.0457041	−	0.998955i	$-0.514553\pi$
$499$	−2.53709e8			−0.0914081			−0.0457041	+	0.998955i	$0.514553\pi$
$500$	2.35894e8	+	4.08580e8i	0.0843959	+	0.146178i
$501$	3.63731e8	+	6.30001e8i	0.129226	+	0.223825i
$502$	3.19683e9			1.12786
$503$	8.69013e8	+	1.50517e9i	0.304466	+	0.527350i	0.977142	−	0.212587i	$-0.0681888\pi$
$503$	8.69013e8	+	1.50517e9i	0.304466	+	0.527350i	−0.672677	+	0.739937i	$0.734855\pi$
$504$	−2.31694e9	+	4.01306e9i	−0.806135	+	1.39627i
$505$	1.87415e9	−	3.24613e9i	0.647568	−	1.12162i
$506$	2.48950e9			0.854249
$507$	2.40985e8	−	5.58729e8i	0.0821225	−	0.190403i
$508$	−9.28141e7			−0.0314117
$509$	1.01213e9	−	1.75305e9i	0.340191	−	0.589228i	−0.644277	−	0.764792i	$-0.722842\pi$
$509$	1.01213e9	−	1.75305e9i	0.340191	−	0.589228i	0.984468	+	0.175564i	$0.0561750\pi$
$510$	−8.45258e7	+	1.46403e8i	−0.0282159	+	0.0488714i
$511$	2.43955e9	+	4.22542e9i	0.808791	+	1.40087i
$512$	−3.40584e9			−1.12145
$513$	9.53835e7	+	1.65209e8i	0.0311934	+	0.0540285i
$514$	−5.64562e8	−	9.77850e8i	−0.183375	−	0.317615i
$515$	−4.41262e9			−1.42354
$516$	1.07184e8	+	1.85647e8i	0.0343443	+	0.0594860i
$517$	−6.02668e8	+	1.04385e9i	−0.191806	+	0.332217i
$518$	9.79133e8	−	1.69591e9i	0.309519	−	0.536103i
$519$	−4.60704e8			−0.144656
$520$	2.09908e8	+	3.60271e9i	0.0654663	+	1.12361i
$521$	1.18869e9			0.368245			0.184123	−	0.982903i	$-0.441056\pi$
$521$	1.18869e9			0.368245			0.184123	+	0.982903i	$0.441056\pi$
$522$	−5.59707e8	+	9.69440e8i	−0.172232	+	0.298314i
$523$	−1.39312e9	+	2.41296e9i	−0.425827	+	0.737554i	−0.996497	−	0.0836254i	$-0.973350\pi$
$523$	−1.39312e9	+	2.41296e9i	−0.425827	+	0.737554i	0.570670	+	0.821179i	$0.306683\pi$
$524$	1.61095e8	+	2.79025e8i	0.0489128	+	0.0847194i
$525$	1.18724e8			0.0358080
$526$	9.94087e8	+	1.72181e9i	0.297834	+	0.515864i
$527$	6.77021e8	+	1.17263e9i	0.201495	+	0.349000i
$528$	−3.39959e8			−0.100510
$529$	−2.29798e9	−	3.98022e9i	−0.674919	−	1.16899i
$530$	8.31194e8	−	1.43967e9i	0.242514	−	0.420047i
$531$	7.82393e8	−	1.35514e9i	0.226774	−	0.392785i
$532$	−1.51486e8			−0.0436197
$533$	−5.02065e9	−	2.52134e9i	−1.43620	−	0.721250i
$534$	4.47375e8			0.127139
$535$	−7.47835e8	+	1.29529e9i	−0.211138	+	0.365703i
$536$	1.15736e9	−	2.00461e9i	0.324633	−	0.562281i
$537$	215518.	+	373288.i	6.00583e−5	+	0.000104024i
$538$	−1.89321e9			−0.524158
$539$	−1.66212e9	−	2.87888e9i	−0.457195	−	0.791885i
$540$	1.40731e8	+	2.43754e8i	0.0384603	+	0.0666152i
$541$	6.14365e8			0.166815			0.0834077	−	0.996516i	$-0.473420\pi$
$541$	6.14365e8			0.166815			0.0834077	+	0.996516i	$0.473420\pi$
$542$	−7.61433e7	−	1.31884e8i	−0.0205416	−	0.0355791i
$543$	−4.27716e8	+	7.40825e8i	−0.114645	+	0.198571i
$544$	1.90287e8	−	3.29587e8i	0.0506772	−	0.0877755i
$545$	5.46618e9			1.44643
$546$	−1.00628e9	−	5.05346e8i	−0.264572	−	0.132866i
$547$	−7.42830e9			−1.94059			−0.970295	−	0.241924i	$-0.922222\pi$
$547$	−7.42830e9			−1.94059			−0.970295	+	0.241924i	$0.922222\pi$
$548$	3.92832e8	−	6.80405e8i	0.101971	−	0.176618i
$549$	−5.19979e8	+	9.00630e8i	−0.134117	+	0.232297i
$550$	−1.19076e8	−	2.06246e8i	−0.0305179	−	0.0528585i
$551$	−2.39951e8			−0.0611071
$552$	6.71090e8	+	1.16236e9i	0.169822	+	0.294140i
$553$	−1.26523e9	−	2.19144e9i	−0.318149	−	0.551051i
$554$	−3.21417e9			−0.803128
$555$	−1.90697e8	−	3.30296e8i	−0.0473498	−	0.0820122i
$556$	−9.61123e7	+	1.66471e8i	−0.0237147	+	0.0410750i
$557$	−9.85697e8	+	1.70728e9i	−0.241685	+	0.418611i	−0.961194	−	0.275872i	$-0.911034\pi$
$557$	−9.85697e8	+	1.70728e9i	−0.241685	+	0.418611i	0.719509	+	0.694483i	$0.244367\pi$
$558$	−5.02380e9			−1.22409
$559$	6.35151e9	−	4.17764e9i	1.53793	−	1.01156i
$560$	5.43635e9			1.30813
$561$	7.61241e7	−	1.31851e8i	0.0182034	−	0.0315292i
$562$	−9.37748e8	+	1.62423e9i	−0.222848	+	0.385984i
$563$	−1.69052e9	−	2.92806e9i	−0.399246	−	0.691514i	0.594387	−	0.804179i	$-0.297395\pi$
$563$	−1.69052e9	−	2.92806e9i	−0.399246	−	0.691514i	−0.993633	+	0.112665i	$0.964061\pi$
$564$	−9.91069e7			−0.0232609
$565$	2.96411e9	+	5.13398e9i	0.691392	+	1.19753i
$566$	−2.30668e9	−	3.99529e9i	−0.534725	−	0.926171i
$567$	5.97344e9			1.37621
$568$	−2.02762e9	−	3.51194e9i	−0.464267	−	0.804134i
$569$	3.89642e8	−	6.74879e8i	0.0886691	−	0.153579i	−0.818280	−	0.574820i	$-0.805072\pi$
$569$	3.89642e8	−	6.74879e8i	0.0886691	−	0.153579i	0.906949	+	0.421241i	$0.138405\pi$
$570$	6.72235e7	−	1.16435e8i	0.0152040	−	0.0263342i
$571$	4.43427e9			0.996772			0.498386	−	0.866955i	$-0.333926\pi$
$571$	4.43427e9			0.996772			0.498386	+	0.866955i	$0.333926\pi$
$572$	−2.88309e7	−	4.94832e8i	−0.00644129	−	0.110553i
$573$	1.59419e8			0.0353997
$574$	−5.19844e9	+	9.00396e9i	−1.14731	+	1.98720i
$575$	−3.82688e8	+	6.62836e8i	−0.0839475	+	0.145401i
$576$	2.43464e9	+	4.21691e9i	0.530830	+	0.919425i
$577$	−2.60177e9			−0.563837			−0.281919	−	0.959438i	$-0.590971\pi$
$577$	−2.60177e9			−0.563837			−0.281919	+	0.959438i	$0.590971\pi$
$578$	1.93091e9	+	3.34444e9i	0.415925	+	0.720403i
$579$	−5.70116e8	−	9.87470e8i	−0.122064	−	0.211421i
$580$	−3.54030e8			−0.0753428
$581$	3.93982e9	+	6.82396e9i	0.833412	+	1.44351i
$582$	7.82134e8	−	1.35470e9i	0.164456	−	0.284847i
$583$	−7.48575e8	+	1.29657e9i	−0.156457	+	0.270992i
$584$	5.27661e9			1.09625
$585$	4.07814e9	−	2.68235e9i	0.842202	−	0.553950i
$586$	6.35110e9			1.30379
$587$	−7.56443e8	+	1.31020e9i	−0.154363	+	0.267364i	−0.932827	−	0.360325i	$-0.882666\pi$
$587$	−7.56443e8	+	1.31020e9i	−0.154363	+	0.267364i	0.778464	+	0.627689i	$0.215999\pi$
$588$	1.36665e8	−	2.36711e8i	0.0277228	−	0.0480174i
$589$	−5.38436e8	−	9.32598e8i	−0.108575	−	0.188058i
$590$	−2.25518e9			−0.452063
$591$	2.82739e8	+	4.89718e8i	0.0563416	+	0.0975866i
$592$	−8.61974e8	−	1.49298e9i	−0.170753	−	0.295753i
$593$	2.16134e9			0.425629			0.212815	−	0.977093i	$-0.431737\pi$
$593$	2.16134e9			0.425629			0.212815	+	0.977093i	$0.431737\pi$
$594$	5.77564e8	+	1.00037e9i	0.113070	+	0.195843i
$595$	−1.21732e9	+	2.10845e9i	−0.236916	+	0.410350i
$596$	4.76885e8	−	8.25989e8i	0.0922682	−	0.159813i
$597$	−2.78284e8			−0.0535276
$598$	6.06494e9	−	3.98915e9i	1.15977	−	0.762828i
$599$	−4.90727e9			−0.932924			−0.466462	−	0.884541i	$-0.654472\pi$
$599$	−4.90727e9			−0.932924			−0.466462	+	0.884541i	$0.654472\pi$
$600$	6.41983e7	−	1.11195e8i	0.0121337	−	0.0210162i
$601$	−3.29712e9	+	5.71078e9i	−0.619547	+	1.07309i	0.370021	+	0.929023i	$0.379350\pi$
$601$	−3.29712e9	+	5.71078e9i	−0.619547	+	1.07309i	−0.989568	+	0.144064i	$0.953983\pi$
$602$	−7.03427e9	−	1.21837e10i	−1.31411	−	2.27610i
$603$	−3.13085e9			−0.581503
$604$	6.69435e7	+	1.15950e8i	0.0123617	+	0.0214111i
$605$	−1.78232e9	−	3.08707e9i	−0.327221	−	0.566764i
$606$	1.26486e9			0.230880
$607$	−7.05597e7	−	1.22213e8i	−0.0128055	−	0.0221798i	0.859552	−	0.511049i	$-0.170743\pi$
$607$	−7.05597e7	−	1.22213e8i	−0.0128055	−	0.0221798i	−0.872357	+	0.488869i	$0.837410\pi$
$608$	−1.51335e8	+	2.62121e8i	−0.0273073	+	0.0472976i
$609$	3.62162e8	−	6.27284e8i	0.0649745	−	0.112539i
$610$	1.49879e9			0.267354
$611$	2.04434e8	+	3.50876e9i	0.0362585	+	0.622313i
$612$	−2.78625e8			−0.0491348
$613$	3.75602e9	−	6.50561e9i	0.658591	−	1.14071i	−0.322390	−	0.946607i	$-0.604486\pi$
$613$	3.75602e9	−	6.50561e9i	0.658591	−	1.14071i	0.980981	−	0.194106i	$-0.0621806\pi$
$614$	−6.64193e8	+	1.15042e9i	−0.115799	+	0.200570i
$615$	1.01245e9	+	1.75362e9i	0.175514	+	0.303999i
$616$	−6.01456e9			−1.03674
$617$	2.84916e9	+	4.93489e9i	0.488336	+	0.845823i	0.999910	−	0.0134163i	$-0.00427068\pi$
$617$	2.84916e9	+	4.93489e9i	0.488336	+	0.845823i	−0.511574	+	0.859239i	$0.670937\pi$
$618$	−7.44513e8	−	1.28953e9i	−0.126886	−	0.219772i
$619$	−5.18832e9			−0.879245			−0.439622	−	0.898183i	$-0.644888\pi$
$619$	−5.18832e9			−0.879245			−0.439622	+	0.898183i	$0.644888\pi$
$620$	−7.94422e8	−	1.37598e9i	−0.133869	−	0.231868i
$621$	1.85619e9	−	3.21501e9i	0.311029	−	0.538719i
$622$	−1.40558e9	+	2.43454e9i	−0.234202	+	0.405649i
$623$	6.44297e9			1.06752
$624$	−8.28212e8	+	5.44748e8i	−0.136457	+	0.0897531i
$625$	−6.69879e9			−1.09753
$626$	4.26278e8	−	7.38335e8i	0.0694517	−	0.120294i
$627$	−6.05416e7	+	1.04861e8i	−0.00980884	+	0.0169894i
$628$	−8.27568e8	−	1.43339e9i	−0.133335	−	0.230943i
$629$	7.72058e8			0.123701
$630$	−4.51652e9	−	7.82283e9i	−0.719634	−	1.24644i
$631$	2.08864e9	+	3.61762e9i	0.330948	+	0.573219i	0.982698	−	0.185215i	$-0.0592981\pi$
$631$	2.08864e9	+	3.61762e9i	0.330948	+	0.573219i	−0.651750	+	0.758434i	$0.725965\pi$
$632$	−2.73662e9			−0.431226
$633$	9.85767e7	+	1.70740e8i	0.0154476	+	0.0267560i
$634$	−9.30752e7	+	1.61211e8i	−0.0145051	+	0.0251236i
$635$	5.93166e8	−	1.02739e9i	0.0919323	−	0.159231i
$636$	−1.23101e8			−0.0189741
$637$	−8.66237e9	−	4.35018e9i	−1.32785	−	0.666837i
$638$	−1.45295e9			−0.221502
$639$	−2.74252e9	+	4.75018e9i	−0.415812	+	0.720207i
$640$	2.26803e9	−	3.92834e9i	0.341994	−	0.592351i
$641$	3.48531e9	+	6.03673e9i	0.522683	+	0.905313i	0.999652	+	0.0263927i	$0.00840204\pi$
$641$	3.48531e9	+	6.03673e9i	0.522683	+	0.905313i	−0.476969	+	0.878920i	$0.658265\pi$
$642$	−5.04709e8			−0.0752781
$643$	2.90341e9	+	5.02886e9i	0.430695	+	0.745986i	0.996933	−	0.0782555i	$-0.0249350\pi$
$643$	2.90341e9	+	5.02886e9i	0.430695	+	0.745986i	−0.566238	+	0.824242i	$0.691602\pi$
$644$	1.47398e9	+	2.55301e9i	0.217466	+	0.376662i
$645$	−2.74000e9			−0.402061
$646$	1.36081e8	+	2.35700e8i	0.0198602	+	0.0343989i
$647$	−3.92244e9	+	6.79387e9i	−0.569366	+	0.986171i	0.427263	+	0.904128i	$0.359478\pi$
$647$	−3.92244e9	+	6.79387e9i	−0.569366	+	0.986171i	−0.996629	+	0.0820434i	$0.973855\pi$
$648$	3.23005e9	−	5.59462e9i	0.466334	−	0.807714i
$649$	2.03102e9			0.291647
$650$	−6.20581e8	−	3.11651e8i	−0.0886343	−	0.0445115i
$651$	3.25069e9			0.461787
$652$	−1.19677e9	+	2.07287e9i	−0.169101	+	0.292891i
$653$	−2.30099e9	+	3.98544e9i	−0.323384	+	0.560118i	−0.981184	−	0.193075i	$-0.938154\pi$
$653$	−2.30099e9	+	3.98544e9i	−0.323384	+	0.560118i	0.657800	+	0.753193i	$0.271487\pi$
$654$	9.22273e8	+	1.59742e9i	0.128925	+	0.223305i
$655$	−4.11817e9			−0.572611
$656$	4.57641e9	+	7.92658e9i	0.632939	+	1.09628i
$657$	−3.56851e9	−	6.18085e9i	−0.490918	−	0.850294i
$658$	6.50422e9			0.890029
$659$	−3.94095e9	−	6.82593e9i	−0.536417	−	0.929101i	−0.999093	−	0.0425739i	$-0.986444\pi$
$659$	−3.94095e9	−	6.82593e9i	−0.536417	−	0.929101i	0.462677	−	0.886527i	$-0.346889\pi$
$660$	−8.93247e7	+	1.54715e8i	−0.0120939	+	0.0209473i
$661$	5.80878e9	−	1.00611e10i	0.782311	−	1.35500i	−0.148281	−	0.988945i	$-0.547374\pi$
$661$	5.80878e9	−	1.00611e10i	0.782311	−	1.35500i	0.930592	−	0.366058i	$-0.119293\pi$
$662$	7.69910e9			1.03142
$663$	−2.58225e7	−	4.43197e8i	−0.00344113	−	0.0590609i
$664$	8.52161e9			1.12962
$665$	9.68134e8	−	1.67686e9i	0.127661	−	0.221116i
$666$	−1.43225e9	+	2.48074e9i	−0.187871	+	0.325403i
$667$	2.33475e9	+	4.04391e9i	0.304649	+	0.527668i
$668$	1.72797e9			0.224295
$669$	−4.88535e8	−	8.46168e8i	−0.0630818	−	0.109261i
$670$	2.25610e9	+	3.90768e9i	0.289799	+	0.501946i
$671$	−1.34982e9			−0.172483
$672$	−4.56827e8	−	7.91248e8i	−0.0580710	−	0.100582i
$673$	−1.20378e9	+	2.08501e9i	−0.152228	+	0.263667i	−0.932046	−	0.362339i	$-0.881978\pi$
$673$	−1.20378e9	+	2.08501e9i	−0.152228	+	0.263667i	0.779818	+	0.626006i	$0.215312\pi$
$674$	−5.39825e9	+	9.35004e9i	−0.679115	+	1.17626i
$675$	−3.55136e8			−0.0444459
$676$	−8.63155e8	−	1.15932e9i	−0.107467	−	0.144341i
$677$	5.58773e9			0.692110			0.346055	−	0.938214i	$-0.387521\pi$
$677$	5.58773e9			0.692110			0.346055	+	0.938214i	$0.387521\pi$
$678$	−1.00023e9	+	1.73245e9i	−0.123252	+	0.213479i
$679$	1.12641e10	−	1.95099e10i	1.38086	−	2.39173i
$680$	1.31649e9	+	2.28024e9i	0.160560	+	0.278098i
$681$	−1.67969e9			−0.203805
$682$	−3.26033e9	−	5.64705e9i	−0.393564	−	0.681673i
$683$	−3.55850e9	−	6.16351e9i	−0.427361	−	0.740211i	0.569277	−	0.822146i	$-0.307223\pi$
$683$	−3.55850e9	−	6.16351e9i	−0.427361	−	0.740211i	−0.996638	+	0.0819352i	$0.973890\pi$
$684$	2.21591e8			0.0264762
$685$	5.02110e9	+	8.69680e9i	0.596873	+	1.03381i
$686$	−2.93290e9	+	5.07993e9i	−0.346867	+	0.600791i
$687$	−3.33362e8	+	5.77400e8i	−0.0392255	+	0.0679405i
$688$	−1.23852e10			−1.44991
$689$	2.53928e8	+	4.35823e9i	0.0295763	+	0.507625i
$690$	−2.61637e9			−0.303199
$691$	5.64275e9	−	9.77354e9i	0.650606	−	1.12688i	−0.332370	−	0.943149i	$-0.607848\pi$
$691$	5.64275e9	−	9.77354e9i	0.650606	−	1.12688i	0.982976	−	0.183733i	$-0.0588183\pi$
$692$	−5.47165e8	+	9.47717e8i	−0.0627692	+	0.108719i
$693$	4.06758e9	+	7.04526e9i	0.464269	+	0.804138i
$694$	6.57696e9			0.746908
$695$	−1.22849e9	−	2.12781e9i	−0.138811	−	0.240428i
$696$	−3.91669e8	−	6.78390e8i	−0.0440338	−	0.0762688i
$697$	−4.09903e9			−0.458529
$698$	−2.95208e8	−	5.11316e8i	−0.0328575	−	0.0569108i
$699$	−1.55286e9	+	2.68964e9i	−0.171974	+	0.297868i
$700$	1.41005e8	−	2.44228e8i	0.0155379	−	0.0269124i
$701$	−6.93216e9			−0.760073			−0.380036	−	0.924972i	$-0.624089\pi$
$701$	−6.93216e9			−0.760073			−0.380036	+	0.924972i	$0.624089\pi$
$702$	3.01006e9	+	1.51163e9i	0.328394	+	0.164917i
$703$	−6.14019e8			−0.0666559
$704$	−3.16004e9	+	5.47336e9i	−0.341341	+	0.591220i
$705$	6.33383e8	−	1.09705e9i	0.0680776	−	0.117914i
$706$	−6.34954e9	−	1.09977e10i	−0.679088	−	1.17621i
$707$	1.82161e10			1.93860
$708$	8.34987e7	+	1.44624e8i	0.00884226	+	0.0153152i
$709$	−2.71868e8	−	4.70890e8i	−0.0286482	−	0.0496201i	0.851346	−	0.524605i	$-0.175787\pi$
$709$	−2.71868e8	−	4.70890e8i	−0.0286482	−	0.0496201i	−0.879994	+	0.474985i	$0.842454\pi$
$710$	7.90507e9			0.828899
$711$	1.85075e9	+	3.20559e9i	0.193110	+	0.334475i
$712$	3.48395e9	−	6.03437e9i	0.361736	−	0.626545i
$713$	−1.04781e10	+	1.81486e10i	−1.08260	+	1.87512i
$714$	−8.21560e8			−0.0844686
$715$	5.66174e9	+	2.84329e9i	0.579267	+	0.290904i
$716$	1.02386e6			0.000104242
$717$	1.12760e9	−	1.95306e9i	0.114245	−	0.197879i
$718$	−7.69950e9	+	1.33359e10i	−0.776296	+	1.34458i
$719$	−8.57794e9	−	1.48574e10i	−0.860660	−	1.49071i	−0.871293	−	0.490764i	$-0.836718\pi$
$719$	−8.57794e9	−	1.48574e10i	−0.860660	−	1.49071i	0.0106324	−	0.999943i	$-0.496616\pi$
$720$	−7.95217e9			−0.794003
$721$	−1.07223e10	−	1.85715e10i	−1.06540	−	1.84533i
$722$	4.47076e9	+	7.74358e9i	0.442080	+	0.765706i
$723$	−7.84003e8			−0.0771496
$724$	1.01597e9	+	1.75971e9i	0.0994938	+	0.172328i
$725$	2.23349e8	−	3.86851e8i	0.0217671	−	0.0377017i
$726$	6.01438e8	−	1.04172e9i	0.0583328	−	0.101035i
$727$	−1.49303e10			−1.44112			−0.720558	−	0.693395i	$-0.756114\pi$
$727$	−1.49303e10			−1.44112			−0.720558	+	0.693395i	$0.756114\pi$
$728$	−1.46527e10	+	9.63769e9i	−1.40753	+	0.925791i
$729$	−7.85761e9			−0.751180
$730$	−5.14296e9	+	8.90788e9i	−0.489309	+	0.847509i
$731$	2.77330e9	−	4.80350e9i	0.262595	−	0.454828i
$732$	−5.54933e7	−	9.61172e7i	−0.00522940	−	0.00905758i
$733$	2.63251e9			0.246892			0.123446	−	0.992351i	$-0.460605\pi$
$733$	2.63251e9			0.246892			0.123446	+	0.992351i	$0.460605\pi$
$734$	−7.50730e8	−	1.30030e9i	−0.0700725	−	0.121369i
$735$	1.74683e9	+	3.02560e9i	0.162273	+	0.281064i
$736$	5.89005e9			0.544561
$737$	−2.03185e9	−	3.51926e9i	−0.186963	−	0.323829i
$738$	7.60416e9	−	1.31708e10i	0.696392	−	1.20619i
$739$	5.77871e9	−	1.00090e10i	0.526715	−	0.912297i	−0.472800	−	0.881170i	$-0.656757\pi$
$739$	5.77871e9	−	1.00090e10i	0.526715	−	0.912297i	0.999515	−	0.0311276i	$-0.00990982\pi$
$740$	−9.05940e8			−0.0821842
$741$	2.05367e7	+	3.52476e8i	0.00185424	+	0.0318248i
$742$	8.07890e9			0.726004
$743$	6.54393e9	−	1.13344e10i	0.585299	−	1.01377i	−0.409539	−	0.912293i	$-0.634310\pi$
$743$	6.54393e9	−	1.13344e10i	0.585299	−	1.01377i	0.994838	−	0.101475i	$-0.0323563\pi$
$744$	1.75776e9	−	3.04454e9i	0.156479	−	0.271029i
$745$	6.09546e9	+	1.05576e10i	0.540081	+	0.935448i
$746$	1.48385e10			1.30859
$747$	−5.76308e9	−	9.98194e9i	−0.505862	−	0.876179i
$748$	−1.80821e8	−	3.13191e8i	−0.0157977	−	0.0273624i
$749$	−7.26868e9			−0.632076
$750$	−1.01745e9	−	1.76228e9i	−0.0880643	−	0.152532i
$751$	−1.98344e9	+	3.43542e9i	−0.170876	+	0.295965i	−0.938726	−	0.344664i	$-0.887993\pi$
$751$	−1.98344e9	+	3.43542e9i	−0.170876	+	0.295965i	0.767851	+	0.640629i	$0.221326\pi$
$752$	2.86297e9	−	4.95882e9i	0.245502	−	0.425222i
$753$	3.02580e9			0.258261
$754$	−3.53968e9	+	2.32819e9i	−0.300722	+	0.197797i
$755$	−1.71132e9			−0.144716
$756$	−6.83928e8	+	1.18460e9i	−0.0575684	+	0.0997114i
$757$	−7.94756e9	+	1.37656e10i	−0.665883	+	1.15334i	0.313162	+	0.949700i	$0.398612\pi$
$757$	−7.94756e9	+	1.37656e10i	−0.665883	+	1.15334i	−0.979045	+	0.203644i	$0.934722\pi$
$758$	−8.75896e6	−	1.51710e7i	−0.000730484	−	0.00126523i
$759$	2.35631e9			0.195608
$760$	−1.04701e9	−	1.81347e9i	−0.0865174	−	0.149852i
$761$	−2.30409e8	−	3.99080e8i	−0.0189519	−	0.0328257i	0.856394	−	0.516323i	$-0.172700\pi$
$761$	−2.30409e8	−	3.99080e8i	−0.0189519	−	0.0328257i	−0.875346	+	0.483497i	$0.839366\pi$
$762$	4.00324e8			0.0327770
$763$	1.32823e10	+	2.30056e10i	1.08252	+	1.87499i
$764$	1.89338e8	−	3.27943e8i	0.0153607	−	0.0266055i
$765$	1.78066e9	−	3.08420e9i	0.143803	−	0.249073i
$766$	−7.61832e9			−0.612433
$767$	4.94799e9	−	3.25449e9i	0.395954	−	0.260435i
$768$	−1.35706e9			−0.108102
$769$	−2.97823e9	+	5.15845e9i	−0.236165	+	0.409051i	−0.959611	−	0.281331i	$-0.909224\pi$
$769$	−2.97823e9	+	5.15845e9i	−0.236165	+	0.409051i	0.723445	+	0.690382i	$0.242557\pi$
$770$	5.86222e9	−	1.01537e10i	0.462748	−	0.801504i
$771$	−5.34358e8	−	9.25536e8i	−0.0419897	−	0.0727282i
$772$	−2.70844e9			−0.211865
$773$	8.24164e9	+	1.42749e10i	0.641778	+	1.11159i	0.985036	+	0.172351i	$0.0551365\pi$
$773$	8.24164e9	+	1.42749e10i	0.641778	+	1.11159i	−0.343257	+	0.939242i	$0.611530\pi$
$774$	1.02896e10	+	1.78221e10i	0.797635	+	1.38154i
$775$	2.00473e9			0.154703
$776$	−1.21818e10	−	2.10995e10i	−0.935825	−	1.62090i
$777$	9.26751e8	−	1.60518e9i	0.0708744	−	0.122758i
$778$	8.65163e9	−	1.49851e10i	0.658672	−	1.14085i
$779$	3.25997e9			0.247077
$780$	3.03003e7	+	5.20052e8i	0.00228621	+	0.0392388i
$781$	−7.11932e9			−0.534761
$782$	2.64817e9	−	4.58677e9i	0.198026	−	0.342992i
$783$	−1.08333e9	+	1.87638e9i	−0.0806480	+	0.139686i
$784$	7.89590e9	+	1.36761e10i	0.585188	+	1.01358i
$785$	2.11556e10			1.56093
$786$	−6.94832e8	−	1.20348e9i	−0.0510389	−	0.0884019i
$787$	1.02975e10	+	1.78358e10i	0.753043	+	1.30431i	0.946341	+	0.323169i	$0.104748\pi$
$787$	1.02975e10	+	1.78358e10i	0.753043	+	1.30431i	−0.193298	+	0.981140i	$0.561919\pi$
$788$	1.34320e9			0.0977913
$789$	9.40905e8	+	1.62969e9i	0.0681987	+	0.118124i
$790$	2.66731e9	−	4.61991e9i	0.192477	−	0.333380i
$791$	−1.44050e10	+	2.49502e10i	−1.03489	+	1.79249i
$792$	8.79796e9			0.629280
$793$	−3.28844e9	+	2.16294e9i	−0.234171	+	0.154024i
$794$	−1.33434e10			−0.946010
$795$	7.86727e8	−	1.36265e9i	0.0555314	−	0.0961833i
$796$	−3.30510e8	+	5.72459e8i	−0.0232267	+	0.0402299i
$797$	1.38631e9	+	2.40117e9i	0.0969968	+	0.168003i	0.910440	−	0.413641i	$-0.135743\pi$
$797$	1.38631e9	+	2.40117e9i	0.0969968	+	0.168003i	−0.813443	+	0.581644i	$0.802410\pi$
$798$	6.53388e8			0.0455157
$799$	1.28216e9	+	2.22077e9i	0.0889262	+	0.154025i
$800$	−2.81729e8	−	4.87969e8i	−0.0194544	−	0.0336959i
$801$	−9.42463e9			−0.647963
$802$	−4.30250e9	−	7.45216e9i	−0.294517	−	0.510119i
$803$	4.63176e9	−	8.02245e9i	0.315676	−	0.546767i
$804$	1.67066e8	−	2.89366e8i	0.0113368	−	0.0196359i
$805$	−3.76803e10			−2.54582
$806$	−1.69916e10	−	8.53308e9i	−1.14304	−	0.574028i
$807$	−1.79193e9			−0.120023
$808$	9.85010e9	−	1.70609e10i	0.656902	−	1.13779i
$809$	1.45931e10	−	2.52760e10i	0.969008	−	1.67837i	0.270571	−	0.962700i	$-0.412788\pi$
$809$	1.45931e10	−	2.52760e10i	0.969008	−	1.67837i	0.698437	−	0.715671i	$-0.253879\pi$
$810$	6.29649e9	+	1.09058e10i	0.416295	+	0.721044i
$811$	−3.41436e9			−0.224769			−0.112384	−	0.993665i	$-0.535849\pi$
$811$	−3.41436e9			−0.224769			−0.112384	+	0.993665i	$0.535849\pi$
$812$	−8.60260e8	−	1.49001e9i	−0.0563876	−	0.0976661i
$813$	−7.20697e7	−	1.24828e8i	−0.00470366	−	0.00814698i
$814$	−3.71800e9			−0.241615
$815$	−1.52970e10	−	2.64951e10i	−0.989813	−	1.71441i
$816$	−3.61628e8	+	6.26357e8i	−0.0232995	+	0.0403559i
$817$	−2.20561e9	+	3.82023e9i	−0.141499	+	0.245083i
$818$	1.01596e9			0.0648994
$819$	2.11988e10	+	1.06459e10i	1.34840	+	0.677155i
$820$	4.80984e9			0.304636
$821$	4.91915e9	−	8.52022e9i	0.310234	−	0.537341i	−0.668179	−	0.744000i	$-0.732926\pi$
$821$	4.91915e9	−	8.52022e9i	0.310234	−	0.537341i	0.978413	+	0.206660i	$0.0662594\pi$
$822$	−1.69436e9	+	2.93471e9i	−0.106403	+	0.184295i
$823$	−3.42754e9	−	5.93667e9i	−0.214330	−	0.371230i	0.738735	−	0.673996i	$-0.235423\pi$
$823$	−3.42754e9	−	5.93667e9i	−0.214330	−	0.371230i	−0.953065	+	0.302766i	$0.902090\pi$
$824$	−2.31917e10			−1.44406
$825$	−1.12706e8	−	1.95212e8i	−0.00698806	−	0.0121037i
$826$	−5.47988e9	−	9.49143e9i	−0.338330	−	0.586005i
$827$	−5.48733e9			−0.337359			−0.168679	−	0.985671i	$-0.553950\pi$
$827$	−5.48733e9			−0.337359			−0.168679	+	0.985671i	$0.553950\pi$
$828$	−2.15610e9	−	3.73448e9i	−0.131997	−	0.228625i
$829$	5.70834e9	−	9.88713e9i	0.347992	−	0.602739i	−0.637901	−	0.770118i	$-0.720197\pi$
$829$	5.70834e9	−	9.88713e9i	0.347992	−	0.602739i	0.985893	+	0.167379i	$0.0535305\pi$
$830$	−8.30578e9	+	1.43860e10i	−0.504205	+	0.873308i
$831$	−3.04222e9			−0.183902
$832$	1.07194e9	+	1.83979e10i	0.0645264	+	1.10748i
$833$	−7.07225e9			−0.423936
$834$	4.14550e8	−	7.18022e8i	0.0247455	−	0.0428604i
$835$	−1.10433e10	+	1.91276e10i	−0.656442	+	1.13699i
$836$	1.43807e8	+	2.49081e8i	0.00851252	+	0.0147441i
$837$	−9.72370e9			−0.573182
$838$	−3.37873e9	−	5.85213e9i	−0.198335	−	0.343526i
$839$	1.55672e9	+	2.69631e9i	0.0910002	+	0.157617i	0.907932	−	0.419117i	$-0.137660\pi$
$839$	1.55672e9	+	2.69631e9i	0.0910002	+	0.157617i	−0.816932	+	0.576734i	$0.804327\pi$
$840$	6.32109e9			0.367972
$841$	7.26231e9	+	1.25787e10i	0.421006	+	0.729204i
$842$	−1.55455e7	+	2.69255e7i	−0.000897452	+	0.00155443i
$843$	−8.87580e8	+	1.53733e9i	−0.0510283	+	0.0883836i
$844$	4.68307e8			0.0268122
$845$	1.83493e10	−	2.14549e9i	1.04621	−	0.122329i
$846$	−9.51422e9			−0.540228
$847$	8.66174e9	−	1.50026e10i	0.489794	−	0.848348i
$848$	3.55611e9	−	6.15936e9i	0.200258	−	0.346857i
$849$	−2.18328e9	−	3.78155e9i	−0.122443	−	0.212077i
$850$	−5.06663e8			−0.0282978
$851$	5.97448e9	+	1.03481e10i	0.332313	+	0.575582i
$852$	−2.92688e8	−	5.06950e8i	−0.0162131	−	0.0280819i
$853$	2.09408e10			1.15524			0.577620	−	0.816306i	$-0.303981\pi$
$853$	2.09408e10			1.15524			0.577620	+	0.816306i	$0.303981\pi$
$854$	3.64193e9	+	6.30801e9i	0.200092	+	0.346569i
$855$	−1.41616e9	+	2.45287e9i	−0.0774876	+	0.134212i
$856$	−3.93044e9	+	6.80772e9i	−0.214182	+	0.370974i
$857$	2.57248e10			1.39611			0.698055	−	0.716044i	$-0.254049\pi$
$857$	2.57248e10			1.39611			0.698055	+	0.716044i	$0.254049\pi$
$858$	1.24353e8	+	2.13430e9i	0.00672127	+	0.115359i
$859$	1.58787e10			0.854749			0.427374	−	0.904075i	$-0.359439\pi$
$859$	1.58787e10			0.854749			0.427374	+	0.904075i	$0.359439\pi$
$860$	−3.25422e9	+	5.63647e9i	−0.174462	+	0.302178i
$861$	−4.92033e9	+	8.52226e9i	−0.262714	+	0.455034i
$862$	4.85772e9	+	8.41382e9i	0.258320	+	0.447423i
$863$	−1.61858e10			−0.857229			−0.428614	−	0.903488i	$-0.640998\pi$
$863$	−1.61858e10			−0.857229			−0.428614	+	0.903488i	$0.640998\pi$
$864$	1.36650e9	+	2.36684e9i	0.0720792	+	0.124845i
$865$	−6.99376e9	−	1.21135e10i	−0.367413	−	0.636377i
$866$	−1.25426e10			−0.656260
$867$	1.82761e9	+	3.16551e9i	0.0952395	+	0.164960i
$868$	3.86074e9	−	6.68701e9i	0.200379	−	0.347066i
$869$	−2.40218e9	+	4.16070e9i	−0.124176	+	0.215079i
$870$	1.52700e9			0.0786177
$871$	−1.05893e10	−	5.31785e9i	−0.543003	−	0.272692i
$872$	2.87289e10			1.46727
$873$	−1.64768e10	+	2.85387e10i	−0.838154	+	1.45173i
$874$	−2.10610e9	+	3.64787e9i	−0.106706	+	0.184820i
$875$	−1.46531e10	−	2.53799e10i	−0.739436	−	1.28074i
$876$	7.61680e8			0.0382832
$877$	8.00531e9	+	1.38656e10i	0.400755	+	0.694129i	0.993817	−	0.111028i	$-0.0354144\pi$
$877$	8.00531e9	+	1.38656e10i	0.400755	+	0.694129i	−0.593062	+	0.805157i	$0.702081\pi$
$878$	8.49072e9	+	1.47064e10i	0.423364	+	0.733287i
$879$	6.01132e9			0.298544
$880$	−5.16077e9	−	8.93872e9i	−0.255285	−	0.442167i
$881$	1.80341e10	−	3.12361e10i	0.888546	−	1.53901i	0.0469517	−	0.998897i	$-0.485049\pi$
$881$	1.80341e10	−	3.12361e10i	0.888546	−	1.53901i	0.841594	−	0.540110i	$-0.181617\pi$
$882$	1.31198e10	−	2.27242e10i	0.643854	−	1.11519i
$883$	1.89253e10			0.925081			0.462540	−	0.886598i	$-0.346938\pi$
$883$	1.89253e10			0.925081			0.462540	+	0.886598i	$0.346938\pi$
$884$	−9.42373e8	−	4.73253e8i	−0.0458817	−	0.0230415i
$885$	−2.13453e9			−0.103514
$886$	−5.30547e9	+	9.18934e9i	−0.256275	+	0.443881i
$887$	−4.26782e9	+	7.39208e9i	−0.205340	+	0.355659i	−0.950241	−	0.311516i	$-0.899163\pi$
$887$	−4.26782e9	+	7.39208e9i	−0.205340	+	0.355659i	0.744901	+	0.667175i	$0.232497\pi$
$888$	−1.00226e9	−	1.73596e9i	−0.0480323	−	0.0831943i
$889$	5.76536e9			0.275214
$890$	6.79141e9	+	1.17631e10i	0.322920	+	0.559314i
$891$	−5.67063e9	−	9.82182e9i	−0.268571	−	0.465179i
$892$	−2.32088e9			−0.109490
$893$	−1.01971e9	−	1.76618e9i	−0.0479176	−	0.0829957i
$894$	−2.05689e9	+	3.56264e9i	−0.0962787	+	0.166760i
$895$	−6.54337e6	+	1.13335e7i	−0.000305085	+	0.000528423i
$896$	2.20444e10			1.02381
$897$	5.74047e9	−	3.77574e9i	0.265567	−	0.174674i
$898$	−1.76972e10			−0.815525
$899$	6.11534e9	−	1.05921e10i	0.280712	−	0.486208i
$900$	−2.06259e8	+	3.57251e8i	−0.00943113	+	0.0163352i
$901$	1.59258e9	+	2.75843e9i	0.0725377	+	0.125639i
$902$	1.97397e10			0.895606
$903$	−6.65795e9	−	1.15319e10i	−0.300908	−	0.521187i
$904$	1.55786e10	+	2.69830e10i	0.701358	+	1.21479i
$905$	−2.59719e10			−1.16475
$906$	−2.88740e8	−	5.00112e8i	−0.0128991	−	0.0223418i
$907$	−3.15155e9	+	5.45864e9i	−0.140249	+	0.242918i	−0.927590	−	0.373599i	$-0.878123\pi$
$907$	−3.15155e9	+	5.45864e9i	−0.140249	+	0.242918i	0.787342	+	0.616517i	$0.211457\pi$
$908$	−1.99492e9	+	3.45530e9i	−0.0884351	+	0.153174i
$909$	−2.66461e10			−1.17668
$910$	−1.98856e9	−	3.41301e10i	−0.0874769	−	1.50139i
$911$	−3.57067e10			−1.56471			−0.782357	−	0.622831i	$-0.785983\pi$
$911$	−3.57067e10			−1.56471			−0.782357	+	0.622831i	$0.785983\pi$
$912$	2.87603e8	−	4.98143e8i	0.0125548	−	0.0217456i
$913$	7.48020e9	−	1.29561e10i	0.325286	−	0.563412i
$914$	−1.48861e10	−	2.57835e10i	−0.644865	−	1.11694i
$915$	1.41861e9			0.0612194
$916$	7.91850e8	+	1.37152e9i	0.0340415	+	0.0589616i
$917$	−1.00068e10	−	1.73322e10i	−0.428550	−	0.742270i
$918$	2.45751e9			0.104845
$919$	1.18746e10	+	2.05674e10i	0.504678	+	0.874129i	0.999985	+	0.00541071i	$0.00172229\pi$
$919$	1.18746e10	+	2.05674e10i	0.504678	+	0.874129i	−0.495307	+	0.868718i	$0.664944\pi$
$920$	−2.03751e10	+	3.52907e10i	−0.862665	+	1.49418i
$921$	−6.28659e8	+	1.08887e9i	−0.0265159	+	0.0459269i
$922$	−6.13340e9			−0.257717
$923$	−1.73442e10	+	1.14080e10i	−0.726019	+	0.477531i
$924$	−8.68203e8			−0.0362051
$925$	5.71535e8	−	9.89928e8i	0.0237436	−	0.0411252i
$926$	−8.31297e9	+	1.43985e10i	−0.344047	+	0.595907i
$927$	1.56843e10	+	2.71660e10i	0.646674	+	1.12007i
$928$	−3.43762e9			−0.141202
$929$	2.05409e9	+	3.55779e9i	0.0840553	+	0.145588i	0.904988	−	0.425437i	$-0.139879\pi$
$929$	2.05409e9	+	3.55779e9i	0.0840553	+	0.145588i	−0.820933	+	0.571025i	$0.806546\pi$
$930$	3.42649e9	+	5.93485e9i	0.139688	+	0.241947i
$931$	5.62457e9			0.228436
$932$	3.68859e9	+	6.38882e9i	0.149246	+	0.258502i
$933$	−1.33039e9	+	2.30430e9i	−0.0536280	+	0.0928864i
$934$	1.47244e10	−	2.55035e10i	0.591323	−	1.02420i
$935$	4.62244e9			0.184940
$936$	2.14337e10	−	1.40978e10i	0.854342	−	0.561935i
$937$	1.21125e10			0.481002			0.240501	−	0.970649i	$-0.422688\pi$
$937$	1.21125e10			0.481002			0.240501	+	0.970649i	$0.422688\pi$
$938$	−1.09642e10	+	1.89906e10i	−0.433779	+	0.751327i
$939$	4.03473e8	−	6.98835e8i	0.0159032	−	0.0275451i
$940$	−1.50450e9	−	2.60587e9i	−0.0590806	−	0.102331i
$941$	6.25833e9			0.244847			0.122424	−	0.992478i	$-0.460933\pi$
$941$	6.25833e9			0.244847			0.122424	+	0.992478i	$0.460933\pi$
$942$	3.56945e9	+	6.18247e9i	0.139131	+	0.240982i
$943$	−3.17199e10	−	5.49404e10i	−1.23180	−	2.13354i
$944$	−9.64835e9			−0.373294
$945$	−8.74184e9	−	1.51413e10i	−0.336970	−	0.583650i
$946$	−1.33554e10	+	2.31322e10i	−0.512905	+	0.888378i
$947$	1.19208e9	−	2.06474e9i	0.0456121	−	0.0790025i	−0.842318	−	0.538981i	$-0.818810\pi$
$947$	1.19208e9	−	2.06474e9i	0.0456121	−	0.0790025i	0.887930	+	0.459978i	$0.152143\pi$
$948$	−3.95032e8			−0.0150592
$949$	−1.57117e9	−	2.69663e10i	−0.0596747	−	1.02421i
$950$	4.02950e8			0.0152482
$951$	−8.80958e7	+	1.52586e8i	−0.00332142	+	0.00575286i
$952$	−6.39792e9	+	1.10815e10i	−0.240331	+	0.416265i
$953$	9.51284e9	+	1.64767e10i	0.356029	+	0.616660i	0.987293	−	0.158908i	$-0.0507972\pi$
$953$	9.51284e9	+	1.64767e10i	0.356029	+	0.616660i	−0.631265	+	0.775567i	$0.717464\pi$
$954$	−1.18176e10			−0.440668
$955$	2.42008e9	+	4.19170e9i	0.0899120	+	0.155732i
$956$	−2.67844e9	−	4.63919e9i	−0.0991468	−	0.171727i
$957$	−1.37522e9			−0.0507200
$958$	−7.92307e9	−	1.37232e10i	−0.291148	−	0.504284i
$959$	−2.44016e10	+	4.22649e10i	−0.893416	+	1.54744i
$960$	3.32110e9	−	5.75231e9i	0.121152	−	0.209842i
$961$	2.73772e10			0.995079
$962$	−9.05783e9	+	5.95770e9i	−0.328028	+	0.215757i
$963$	1.06325e10			0.383656
$964$	−9.31137e8	+	1.61278e9i	−0.0334768	+	0.0579836i
$965$	1.73094e10	−	2.99808e10i	0.620064	−	1.07398i
$966$	−6.35754e9	−	1.10116e10i	−0.226918	−	0.393034i
$967$	−3.11987e10			−1.10954			−0.554770	−	0.832003i	$-0.687194\pi$
$967$	−3.11987e10			−1.10954			−0.554770	+	0.832003i	$0.687194\pi$
$968$	−9.36744e9	−	1.62249e10i	−0.331938	−	0.574933i
$969$	1.28801e8	+	2.23090e8i	0.00454764	+	0.00787674i
$970$	4.74930e10			1.67082
$971$	2.10307e10	+	3.64263e10i	0.737202	+	1.27687i	0.953750	+	0.300600i	$0.0971869\pi$
$971$	2.10307e10	+	3.64263e10i	0.737202	+	1.27687i	−0.216548	+	0.976272i	$0.569480\pi$
$972$	1.51164e9	−	2.61824e9i	0.0527980	−	0.0914488i
$973$	5.97023e9	−	1.03407e10i	0.207776	−	0.359879i
$974$	3.19199e10			1.10689
$975$	−5.87381e8	−	2.94978e8i	−0.0202957	−	0.0101923i
$976$	6.41230e9			0.220770
$977$	−1.03521e10	+	1.79304e10i	−0.355140	+	0.615120i	−0.987142	−	0.159846i	$-0.948900\pi$
$977$	−1.03521e10	+	1.79304e10i	−0.355140	+	0.615120i	0.632002	+	0.774967i	$0.282233\pi$
$978$	5.16191e9	−	8.94069e9i	0.176451	−	0.305622i
$979$	−6.11636e9	−	1.05938e10i	−0.208331	−	0.360840i
$980$	8.29864e9			0.281654
$981$	−1.94291e10	−	3.36521e10i	−0.657068	−	1.13808i
$982$	−1.35851e10	−	2.35301e10i	−0.457797	−	0.792928i
$983$	4.03048e10			1.35338			0.676690	−	0.736268i	$-0.263414\pi$
$983$	4.03048e10			1.35338			0.676690	+	0.736268i	$0.263414\pi$
$984$	5.32120e9	+	9.21659e9i	0.178044	+	0.308381i
$985$	−8.58429e9	+	1.48684e10i	−0.286205	+	0.495722i
$986$	−1.54556e9	+	2.67698e9i	−0.0513470	+	0.0889357i
$987$	6.15625e9			0.203801
$988$	7.49471e8	+	3.76379e8i	0.0247232	+	0.0124158i
$989$	8.58436e10			2.82176
$990$	−8.57513e9	+	1.48526e10i	−0.280878	+	0.486495i
$991$	−2.24915e10	+	3.89564e10i	−0.734109	+	1.27151i	0.221004	+	0.975273i	$0.429067\pi$
$991$	−2.24915e10	+	3.89564e10i	−0.734109	+	1.27151i	−0.955113	+	0.296241i	$0.904267\pi$
$992$	−7.71381e9	−	1.33607e10i	−0.250887	−	0.434549i
$993$	7.28721e9			0.236178
$994$	1.92086e10	+	3.32703e10i	0.620359	+	1.07449i
$995$	−4.22451e9	−	7.31707e9i	−0.135955	−	0.235481i
$996$	1.23010e9			0.0394486
$997$	1.80895e9	+	3.13319e9i	0.0578086	+	0.100127i	0.893481	−	0.449100i	$-0.148255\pi$
$997$	1.80895e9	+	3.13319e9i	0.0578086	+	0.100127i	−0.835673	+	0.549228i	$0.814922\pi$
$998$	1.29966e9	−	2.25108e9i	0.0413879	−	0.0716860i
$999$	−2.77217e9	+	4.80154e9i	−0.0879712	+	0.152371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.8.c.a.9.3	yes	16
3.2	odd	2		117.8.g.d.100.6		16
4.3	odd	2		208.8.i.d.113.5		16
13.3	even	3	inner	13.8.c.a.3.3	✓	16
13.4	even	6		169.8.a.e.1.3		8
13.6	odd	12		169.8.b.e.168.4		16
13.7	odd	12		169.8.b.e.168.13		16
13.9	even	3		169.8.a.f.1.6		8
39.29	odd	6		117.8.g.d.55.6		16
52.3	odd	6		208.8.i.d.81.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.c.a.3.3	✓	16	13.3	even	3	inner
13.8.c.a.9.3	yes	16	1.1	even	1	trivial
117.8.g.d.55.6		16	39.29	odd	6
117.8.g.d.100.6		16	3.2	odd	2
169.8.a.e.1.3		8	13.4	even	6
169.8.a.f.1.6		8	13.9	even	3
169.8.b.e.168.4		16	13.6	odd	12
169.8.b.e.168.13		16	13.7	odd	12
208.8.i.d.81.5		16	52.3	odd	6
208.8.i.d.113.5		16	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	13.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.12264 + 8.87268i) q^{2} +(-4.84859 + 8.39800i) q^{3} +(11.5171 + 19.9481i) q^{4} -294.418 q^{5} +(-49.6752 - 86.0399i) q^{6} +(-715.408 - 1239.12i) q^{7} -1547.39 q^{8} +(1046.48 + 1812.56i) q^{9} +(1508.20 - 2612.27i) q^{10} +(-1358.28 + 2352.62i) q^{11} -223.366 q^{12} +(460.751 + 7907.98i) q^{13} +14659.1 q^{14} +(1427.51 - 2472.52i) q^{15} +(6452.53 - 11176.1i) q^{16} +(2889.72 + 5005.15i) q^{17} -21443.0 q^{18} +(-2298.20 - 3980.60i) q^{19} +(-3390.82 - 5873.08i) q^{20} +13874.9 q^{21} +(-13916.0 - 24103.2i) q^{22} +(-44723.6 + 77463.5i) q^{23} +(7502.65 - 12995.0i) q^{24} +8556.75 q^{25} +(-72525.3 - 36421.7i) q^{26} -41503.6 q^{27} +(16478.8 - 28542.1i) q^{28} +(26102.0 - 45210.1i) q^{29} +(14625.2 + 25331.7i) q^{30} +234286. q^{31} +(-32924.8 - 57027.4i) q^{32} +(-13171.5 - 22813.8i) q^{33} -59212.1 q^{34} +(210629. + 364820. i) q^{35} +(-24104.8 + 41750.7i) q^{36} +(66793.5 - 115690. i) q^{37} +47091.4 q^{38} +(-68645.3 - 34473.2i) q^{39} +455578. q^{40} +(-354622. + 614222. i) q^{41} +(-71076.0 + 123107. i) q^{42} +(-479856. - 831136. i) q^{43} -62573.8 q^{44} +(-308103. - 533650. i) q^{45} +(-458206. - 793636. i) q^{46} +443698. q^{47} +(62571.3 + 108377. i) q^{48} +(-611845. + 1.05975e6i) q^{49} +(-43833.2 + 75921.3i) q^{50} -56044.3 q^{51} +(-152443. + 100268. i) q^{52} +551118. q^{53} +(212608. - 368248. i) q^{54} +(399903. - 692652. i) q^{55} +(1.10701e6 + 1.91740e6i) q^{56} +44572.1 q^{57} +(267423. + 463190. i) q^{58} +(-373820. - 647476. i) q^{59} +65762.8 q^{60} +(248441. + 430313. i) q^{61} +(-1.20016e6 + 2.07874e6i) q^{62} +(1.49732e6 - 2.59344e6i) q^{63} +2.32650e6 q^{64} +(-135653. - 2.32825e6i) q^{65} +269892. q^{66} +(-747946. + 1.29548e6i) q^{67} +(-66562.2 + 115289. i) q^{68} +(-433692. - 751177. i) q^{69} -4.31590e6 q^{70} +(1.31035e6 + 2.26959e6i) q^{71} +(-1.61931e6 - 2.80473e6i) q^{72} -3.41001e6 q^{73} +(684318. + 1.18527e6i) q^{74} +(-41488.2 + 71859.6i) q^{75} +(52937.0 - 91689.6i) q^{76} +3.88691e6 q^{77} +(657515. - 432474. i) q^{78} +1.76854e6 q^{79} +(-1.89974e6 + 3.29044e6i) q^{80} +(-2.08742e6 + 3.61552e6i) q^{81} +(-3.63320e6 - 6.29289e6i) q^{82} -5.50709e6 q^{83} +(159798. + 276778. i) q^{84} +(-850785. - 1.47360e6i) q^{85} +9.83253e6 q^{86} +(253116. + 438410. i) q^{87} +(2.10179e6 - 3.64041e6i) q^{88} +(-2.25150e6 + 3.89971e6i) q^{89} +6.31320e6 q^{90} +(9.46934e6 - 6.22836e6i) q^{91} -2.06033e6 q^{92} +(-1.13596e6 + 1.96753e6i) q^{93} +(-2.27291e6 + 3.93679e6i) q^{94} +(676631. + 1.17196e6i) q^{95} +638555. q^{96} +(7.87248e6 + 1.36355e7i) q^{97} +(-6.26853e6 - 1.08574e7i) q^{98} -5.68568e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 9 q^{2} - 28 q^{3} - 577 q^{4} + 384 q^{5} + 342 q^{6} + 196 q^{7} + 5922 q^{8} - 5988 q^{9} - 6813 q^{10} + 5052 q^{11} - 15816 q^{12} + 17064 q^{13} + 14484 q^{14} - 184 q^{15} - 61377 q^{16} - 22824 q^{17}+ \cdots + 27386736 q^{99}+O(q^{100}) \) 16 * q - 9 * q^2 - 28 * q^3 - 577 * q^4 + 384 * q^5 + 342 * q^6 + 196 * q^7 + 5922 * q^8 - 5988 * q^9 - 6813 * q^10 + 5052 * q^11 - 15816 * q^12 + 17064 * q^13 + 14484 * q^14 - 184 * q^15 - 61377 * q^16 - 22824 * q^17 + 226318 * q^18 + 63692 * q^19 - 121971 * q^20 - 271240 * q^21 - 73726 * q^22 - 72468 * q^23 + 224952 * q^24 + 58488 * q^25 + 154443 * q^26 + 358616 * q^27 - 172816 * q^28 - 221772 * q^29 - 258116 * q^30 + 58432 * q^31 + 77823 * q^32 - 352372 * q^33 + 643334 * q^34 + 31560 * q^35 - 1162993 * q^36 - 368884 * q^37 + 2364492 * q^38 - 672996 * q^39 + 766030 * q^40 - 385824 * q^41 + 1560954 * q^42 + 391492 * q^43 - 6149616 * q^44 + 232096 * q^45 - 2599078 * q^46 + 1089984 * q^47 + 4585712 * q^48 - 1108780 * q^49 + 1626894 * q^50 + 8040712 * q^51 - 1312478 * q^52 + 3329328 * q^53 - 5616702 * q^54 - 418216 * q^55 - 3609156 * q^56 - 12068664 * q^57 + 3685081 * q^58 - 6318924 * q^59 + 1448784 * q^60 + 1763548 * q^61 - 12998388 * q^62 + 6641128 * q^63 + 32227074 * q^64 + 9500508 * q^65 + 16245108 * q^66 - 8607964 * q^67 - 10118091 * q^68 - 4618492 * q^69 - 25381840 * q^70 + 9473220 * q^71 - 35174445 * q^72 + 5020888 * q^73 + 2206221 * q^74 - 21834988 * q^75 + 18702876 * q^76 + 35263992 * q^77 + 28395902 * q^78 + 12644416 * q^79 - 24671247 * q^80 - 9316272 * q^81 - 9347751 * q^82 - 22158432 * q^83 + 37532636 * q^84 - 36911824 * q^85 - 30103956 * q^86 + 5199988 * q^87 - 36676404 * q^88 + 18469860 * q^89 + 132263562 * q^90 - 9614540 * q^91 + 64127424 * q^92 - 26340696 * q^93 - 6026128 * q^94 - 16267080 * q^95 - 164216320 * q^96 + 19660916 * q^97 - 51546651 * q^98 + 27386736 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more