LMFDB - Embedded newform 13.8.c.a.9.7

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)

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")

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);

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			9.7
Root			$-5.55707 + 9.62513i$ of defining polynomial
Character	$\chi$	$=$	13.9
Dual form			13.8.c.a.3.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.05707 - 8.75910i) q^{2} +(35.2053 - 60.9774i) q^{3} +(12.8521 + 22.2605i) q^{4} -163.930 q^{5} +(-356.071 - 616.734i) q^{6} +(-123.469 - 213.855i) q^{7} +1554.59 q^{8} +(-1385.33 - 2399.46i) q^{9} +(-829.005 + 1435.88i) q^{10} +(-1015.56 + 1759.01i) q^{11} +1809.85 q^{12} +(7174.32 + 3358.22i) q^{13} -2497.57 q^{14} +(-5771.21 + 9996.02i) q^{15} +(6216.58 - 10767.4i) q^{16} +(17484.9 + 30284.8i) q^{17} -28022.8 q^{18} +(-10739.1 - 18600.7i) q^{19} +(-2106.84 - 3649.16i) q^{20} -17387.1 q^{21} +(10271.6 + 17790.9i) q^{22} +(35146.7 - 60875.8i) q^{23} +(54729.7 - 94794.5i) q^{24} -51252.0 q^{25} +(65696.0 - 45857.9i) q^{26} -41095.4 q^{27} +(3173.67 - 5496.95i) q^{28} +(-103098. + 178571. i) q^{29} +(58370.8 + 101101. i) q^{30} -304382. q^{31} +(36618.1 + 63424.4i) q^{32} +(71506.5 + 123853. i) q^{33} +353690. q^{34} +(20240.3 + 35057.2i) q^{35} +(35608.7 - 61676.0i) q^{36} +(61327.8 - 106223. i) q^{37} -217233. q^{38} +(457349. - 319244. i) q^{39} -254843. q^{40} +(-117759. + 203964. i) q^{41} +(-87927.5 + 152295. i) q^{42} +(-45675.1 - 79111.6i) q^{43} -52208.5 q^{44} +(227097. + 393343. i) q^{45} +(-355478. - 615706. i) q^{46} -967683. q^{47} +(-437713. - 758142. i) q^{48} +(381282. - 660400. i) q^{49} +(-259185. + 448921. i) q^{50} +2.46225e6 q^{51} +(17449.5 + 202864. i) q^{52} +28768.9 q^{53} +(-207823. + 359959. i) q^{54} +(166482. - 288354. i) q^{55} +(-191943. - 332455. i) q^{56} -1.51229e6 q^{57} +(1.04275e6 + 1.80609e6i) q^{58} +(-38248.5 - 66248.4i) q^{59} -296688. q^{60} +(296556. + 513650. i) q^{61} +(-1.53928e6 + 2.66612e6i) q^{62} +(-342090. + 592517. i) q^{63} +2.33217e6 q^{64} +(-1.17609e6 - 550512. i) q^{65} +1.44645e6 q^{66} +(915012. - 1.58485e6i) q^{67} +(-449435. + 778444. i) q^{68} +(-2.47470e6 - 4.28630e6i) q^{69} +409426. q^{70} +(1.41939e6 + 2.45845e6i) q^{71} +(-2.15361e6 - 3.73016e6i) q^{72} +1.74309e6 q^{73} +(-620278. - 1.07435e6i) q^{74} +(-1.80434e6 + 3.12521e6i) q^{75} +(276039. - 478114. i) q^{76} +501563. q^{77} +(-483445. - 5.62041e6i) q^{78} +3.23539e6 q^{79} +(-1.01908e6 + 1.76511e6i) q^{80} +(1.58293e6 - 2.74172e6i) q^{81} +(1.19103e6 + 2.06292e6i) q^{82} -4.95198e6 q^{83} +(-223460. - 387044. i) q^{84} +(-2.86630e6 - 4.96458e6i) q^{85} -923929. q^{86} +(7.25920e6 + 1.25733e7i) q^{87} +(-1.57878e6 + 2.73453e6i) q^{88} +(2.54255e6 - 4.40382e6i) q^{89} +4.59377e6 q^{90} +(-167636. - 1.94890e6i) q^{91} +1.80683e6 q^{92} +(-1.07159e7 + 1.85604e7i) q^{93} +(-4.89364e6 + 8.47603e6i) q^{94} +(1.76046e6 + 3.04920e6i) q^{95} +5.15660e6 q^{96} +(-7.53784e6 - 1.30559e7i) q^{97} +(-3.85634e6 - 6.67938e6i) q^{98} +5.62756e6 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 $

$2$	5.05707	−	8.75910i	0.446986	−	0.774203i	−0.551202	−	0.834372i	$-0.685831\pi$
$2$	5.05707	−	8.75910i	0.446986	−	0.774203i	0.998188	+	0.0601691i	$0.0191640\pi$
$3$	35.2053	−	60.9774i	0.752807	−	1.30390i	−0.193650	−	0.981071i	$-0.562033\pi$
$3$	35.2053	−	60.9774i	0.752807	−	1.30390i	0.946457	−	0.322830i	$-0.104634\pi$
$4$	12.8521	+	22.2605i	0.100407	+	0.173910i
$5$	−163.930			−0.586494			−0.293247	−	0.956037i	$-0.594736\pi$
$5$	−163.930			−0.586494			−0.293247	+	0.956037i	$0.594736\pi$
$6$	−356.071	−	616.734i	−0.672989	−	1.16565i
$7$	−123.469	−	213.855i	−0.136055	−	0.235654i	0.789945	−	0.613178i	$-0.210109\pi$
$7$	−123.469	−	213.855i	−0.136055	−	0.235654i	−0.926000	+	0.377524i	$0.876776\pi$
$8$	1554.59			1.07349
$9$	−1385.33	−	2399.46i	−0.633437	−	1.09715i
$10$	−829.005	+	1435.88i	−0.262155	+	0.454065i
$11$	−1015.56	+	1759.01i	−0.230056	+	0.398468i	−0.957824	−	0.287355i	$-0.907224\pi$
$11$	−1015.56	+	1759.01i	−0.230056	+	0.398468i	0.727768	+	0.685823i	$0.240558\pi$
$12$	1809.85			0.302348
$13$	7174.32	+	3358.22i	0.905689	+	0.423943i
$13$	7174.32	+	3358.22i	0.905689	+	0.423943i
$14$	−2497.57			−0.243259
$15$	−5771.21	+	9996.02i	−0.441517	+	0.764729i
$16$	6216.58	−	10767.4i	0.379430	−	0.657192i
$17$	17484.9	+	30284.8i	0.863162	+	1.49504i	0.868861	+	0.495057i	$0.164853\pi$
$17$	17484.9	+	30284.8i	0.863162	+	1.49504i	−0.00569886	+	0.999984i	$0.501814\pi$
$18$	−28022.8			−1.13255
$19$	−10739.1	−	18600.7i	−0.359195	−	0.622144i	0.628632	−	0.777703i	$-0.283615\pi$
$19$	−10739.1	−	18600.7i	−0.359195	−	0.622144i	−0.987827	+	0.155560i	$0.950282\pi$
$20$	−2106.84	−	3649.16i	−0.0588880	−	0.101997i
$21$	−17387.1			−0.409693
$22$	10271.6	+	17790.9i	0.205663	+	0.356220i
$23$	35146.7	−	60875.8i	0.602333	−	1.04327i	−0.390134	−	0.920758i	$-0.627571\pi$
$23$	35146.7	−	60875.8i	0.602333	−	1.04327i	0.992467	−	0.122513i	$-0.0390953\pi$
$24$	54729.7	−	94794.5i	0.808134	−	1.39973i
$25$	−51252.0			−0.656025
$26$	65696.0	−	45857.9i	0.733048	−	0.511690i
$27$	−41095.4			−0.401810
$28$	3173.67	−	5496.95i	0.0273217	−	0.0473226i
$29$	−103098.	+	178571.i	−0.784979	+	1.35962i	0.144033	+	0.989573i	$0.453993\pi$
$29$	−103098.	+	178571.i	−0.784979	+	1.35962i	−0.929012	+	0.370050i	$0.879341\pi$
$30$	58370.8	+	101101.i	0.394704	+	0.683647i
$31$	−304382.			−1.83507			−0.917537	−	0.397651i	$-0.869825\pi$
$31$	−304382.			−1.83507			−0.917537	+	0.397651i	$0.869825\pi$
$32$	36618.1	+	63424.4i	0.197547	+	0.342162i
$33$	71506.5	+	123853.i	0.346375	+	0.599940i
$34$	353690.			1.54329
$35$	20240.3	+	35057.2i	0.0797954	+	0.138210i
$36$	35608.7	−	61676.0i	0.127203	−	0.220322i
$37$	61327.8	−	106223.i	0.199045	−	0.344756i	−0.749174	−	0.662373i	$-0.769549\pi$
$37$	61327.8	−	106223.i	0.199045	−	0.344756i	0.948219	+	0.317617i	$0.102883\pi$
$38$	−217233.			−0.642220
$39$	457349.	−	319244.i	1.23459	−	0.861781i
$40$	−254843.			−0.629598
$41$	−117759.	+	203964.i	−0.266839	+	0.462179i	−0.968044	−	0.250781i	$-0.919313\pi$
$41$	−117759.	+	203964.i	−0.266839	+	0.462179i	0.701205	+	0.712960i	$0.252646\pi$
$42$	−87927.5	+	152295.i	−0.183127	+	0.317185i
$43$	−45675.1	−	79111.6i	−0.0876072	−	0.151740i	0.818892	−	0.573948i	$-0.194589\pi$
$43$	−45675.1	−	79111.6i	−0.0876072	−	0.151740i	−0.906499	+	0.422207i	$0.861255\pi$
$44$	−52208.5			−0.0923967
$45$	227097.	+	393343.i	0.371507	+	0.643469i
$46$	−355478.	−	615706.i	−0.538469	−	0.932655i
$47$	−967683.			−1.35954			−0.679768	−	0.733427i	$-0.737919\pi$
$47$	−967683.			−1.35954			−0.679768	+	0.733427i	$0.737919\pi$
$48$	−437713.	−	758142.i	−0.571275	−	0.989478i
$49$	381282.	−	660400.i	0.462978	−	0.801901i
$50$	−259185.	+	448921.i	−0.293234	+	0.507896i
$51$	2.46225e6			2.59918
$52$	17449.5	+	202864.i	0.0172096	+	0.200075i
$53$	28768.9			0.0265435			0.0132717	−	0.999912i	$-0.495775\pi$
$53$	28768.9			0.0265435			0.0132717	+	0.999912i	$0.495775\pi$
$54$	−207823.	+	359959.i	−0.179603	+	0.311082i
$55$	166482.	−	288354.i	0.134926	−	0.233699i
$56$	−191943.	−	332455.i	−0.146054	−	0.252973i
$57$	−1.51229e6			−1.08162
$58$	1.04275e6	+	1.80609e6i	0.701749	+	1.21547i
$59$	−38248.5	−	66248.4i	−0.0242456	−	0.0419946i	0.853648	−	0.520850i	$-0.174385\pi$
$59$	−38248.5	−	66248.4i	−0.0242456	−	0.0419946i	−0.877894	+	0.478856i	$0.841052\pi$
$60$	−296688.			−0.177325
$61$	296556.	+	513650.i	0.167283	+	0.289743i	0.937464	−	0.348083i	$-0.113167\pi$
$61$	296556.	+	513650.i	0.167283	+	0.289743i	−0.770180	+	0.637826i	$0.779834\pi$
$62$	−1.53928e6	+	2.66612e6i	−0.820252	+	1.42072i
$63$	−342090.	+	592517.i	−0.172365	+	0.298544i
$64$	2.33217e6			1.11206
$65$	−1.17609e6	−	550512.i	−0.531181	−	0.248640i
$66$	1.44645e6			0.619300
$67$	915012.	−	1.58485e6i	0.371676	−	0.643762i	−0.618147	−	0.786062i	$-0.712116\pi$
$67$	915012.	−	1.58485e6i	0.371676	−	0.643762i	0.989824	+	0.142300i	$0.0454498\pi$
$68$	−449435.	+	778444.i	−0.173335	+	0.300225i
$69$	−2.47470e6	−	4.28630e6i	−0.906881	−	1.57076i
$70$	409426.			0.142670
$71$	1.41939e6	+	2.45845e6i	0.470649	+	0.815188i	0.999436	−	0.0335663i	$-0.0106865\pi$
$71$	1.41939e6	+	2.45845e6i	0.470649	+	0.815188i	−0.528788	+	0.848754i	$0.677353\pi$
$72$	−2.15361e6	−	3.73016e6i	−0.679991	−	1.17778i
$73$	1.74309e6			0.524434			0.262217	−	0.965009i	$-0.415546\pi$
$73$	1.74309e6			0.524434			0.262217	+	0.965009i	$0.415546\pi$
$74$	−620278.	−	1.07435e6i	−0.177941	−	0.308202i
$75$	−1.80434e6	+	3.12521e6i	−0.493860	+	0.855391i
$76$	276039.	−	478114.i	0.0721312	−	0.124935i
$77$	501563.			0.125201
$78$	−483445.	−	5.62041e6i	−0.115350	−	1.34103i
$79$	3.23539e6			0.738298			0.369149	−	0.929370i	$-0.379649\pi$
$79$	3.23539e6			0.738298			0.369149	+	0.929370i	$0.379649\pi$
$80$	−1.01908e6	+	1.76511e6i	−0.222533	+	0.385439i
$81$	1.58293e6	−	2.74172e6i	0.330952	−	0.573226i
$82$	1.19103e6	+	2.06292e6i	0.238547	+	0.413175i
$83$	−4.95198e6			−0.950617			−0.475309	−	0.879819i	$-0.657664\pi$
$83$	−4.95198e6			−0.950617			−0.475309	+	0.879819i	$0.657664\pi$
$84$	−223460.	−	387044.i	−0.0411360	−	0.0712496i
$85$	−2.86630e6	−	4.96458e6i	−0.506239	−	0.876832i
$86$	−923929.			−0.156637
$87$	7.25920e6	+	1.25733e7i	1.18188	+	2.04707i
$88$	−1.57878e6	+	2.73453e6i	−0.246964	+	0.427753i
$89$	2.54255e6	−	4.40382e6i	0.382300	−	0.662163i	−0.609091	−	0.793101i	$-0.708465\pi$
$89$	2.54255e6	−	4.40382e6i	0.382300	−	0.662163i	0.991391	+	0.130938i	$0.0417988\pi$
$90$	4.59377e6			0.664234
$91$	−167636.	−	1.94890e6i	−0.0233197	−	0.271109i
$92$	1.80683e6			0.241913
$93$	−1.07159e7	+	1.85604e7i	−1.38146	+	2.39275i
$94$	−4.89364e6	+	8.47603e6i	−0.607694	+	1.05256i
$95$	1.76046e6	+	3.04920e6i	0.210665	+	0.364883i
$96$	5.15660e6			0.594860
$97$	−7.53784e6	−	1.30559e7i	−0.838583	−	1.45247i	−0.891080	−	0.453847i	$-0.850051\pi$
$97$	−7.53784e6	−	1.30559e7i	−0.838583	−	1.45247i	0.0524965	−	0.998621i	$-0.483282\pi$
$98$	−3.85634e6	−	6.67938e6i	−0.413889	−	0.716878i
$99$	5.62756e6			0.582904
$100$	−658694.	−	1.14089e6i	−0.0658694	−	0.114089i
$101$	−5.83275e6	+	1.01026e7i	−0.563312	+	0.975685i	0.433893	+	0.900965i	$0.357140\pi$
$101$	−5.83275e6	+	1.01026e7i	−0.563312	+	0.975685i	−0.997205	+	0.0747201i	$0.976194\pi$
$102$	1.24518e7	−	2.15671e7i	1.16180	−	2.01229i
$103$	6.15835e6			0.555308			0.277654	−	0.960681i	$-0.410443\pi$
$103$	6.15835e6			0.555308			0.277654	+	0.960681i	$0.410443\pi$
$104$	1.11531e7	+	5.22064e6i	0.972252	+	0.455100i
$105$	2.85026e6			0.240282
$106$	145486.	−	251990.i	0.0118646	−	0.0205500i
$107$	8.05811e6	−	1.39571e7i	0.635902	−	1.10141i	−0.350422	−	0.936592i	$-0.613962\pi$
$107$	8.05811e6	−	1.39571e7i	0.635902	−	1.10141i	0.986323	−	0.164822i	$-0.0527050\pi$
$108$	−528162.	−	914803.i	−0.0403445	−	0.0698787i
$109$	−2.48704e7			−1.83946			−0.919729	−	0.392553i	$-0.871592\pi$
$109$	−2.48704e7			−1.83946			−0.919729	+	0.392553i	$0.871592\pi$
$110$	−1.68382e6	−	2.91646e6i	−0.120620	−	0.208921i
$111$	−4.31813e6	−	7.47921e6i	−0.299685	−	0.519070i
$112$	−3.07022e6			−0.206494
$113$	727777.	+	1.26055e6i	0.0474486	+	0.0821834i	0.888774	−	0.458345i	$-0.151558\pi$
$113$	727777.	+	1.26055e6i	0.0474486	+	0.0821834i	−0.841326	+	0.540529i	$0.818224\pi$
$114$	−7.64777e6	+	1.32463e7i	−0.483468	+	0.837391i
$115$	−5.76159e6	+	9.97937e6i	−0.353264	+	0.611872i
$116$	−5.30010e6			−0.315269
$117$	−1.88089e6	−	2.18667e7i	−0.108571	−	1.26221i
$118$	−773702.			−0.0433497
$119$	4.31769e6	−	7.47846e6i	0.234875	−	0.406816i
$120$	−8.97183e6	+	1.55397e7i	−0.473966	+	0.820932i
$121$	7.68084e6	+	1.33036e7i	0.394149	+	0.682685i
$122$	5.99882e6			0.299093
$123$	8.29146e6	+	1.43612e7i	0.401757	+	0.695863i
$124$	−3.91195e6	−	6.77569e6i	−0.184254	−	0.319137i
$125$	2.12088e7			0.971248
$126$	3.45994e6	+	5.99280e6i	0.154089	+	0.266890i
$127$	6.95145e6	−	1.20403e7i	0.301136	−	0.521582i	−0.675258	−	0.737582i	$-0.735968\pi$
$127$	6.95145e6	−	1.20403e7i	0.301136	−	0.521582i	0.976393	+	0.216000i	$0.0693010\pi$
$128$	7.10681e6	−	1.23094e7i	0.299530	−	0.518801i
$129$	−6.43202e6			−0.263805
$130$	−1.07695e7	+	7.51748e6i	−0.429928	+	0.300103i
$131$	2.68014e7			1.04162			0.520809	−	0.853673i	$-0.325631\pi$
$131$	2.68014e7			1.04162			0.520809	+	0.853673i	$0.325631\pi$
$132$	−1.83802e6	+	3.18354e6i	−0.0695569	+	0.120476i
$133$	−2.65189e6	+	4.59321e6i	−0.0977405	+	0.169292i
$134$	−9.25456e6	−	1.60294e7i	−0.332268	−	0.575506i
$135$	6.73678e6			0.235659
$136$	2.71818e7	+	4.70802e7i	0.926599	+	1.60492i
$137$	3.59209e6	+	6.22169e6i	0.119351	+	0.206722i	0.919511	−	0.393065i	$-0.128585\pi$
$137$	3.59209e6	+	6.22169e6i	0.119351	+	0.206722i	−0.800160	+	0.599787i	$0.795252\pi$
$138$	−5.00589e7			−1.62145
$139$	−9.16798e6	−	1.58794e7i	−0.289549	−	0.501514i	0.684153	−	0.729338i	$-0.260172\pi$
$139$	−9.16798e6	−	1.58794e7i	−0.289549	−	0.501514i	−0.973702	+	0.227825i	$0.926839\pi$
$140$	−520259.	+	901115.i	−0.0160240	+	0.0277544i
$141$	−3.40676e7	+	5.90068e7i	−1.02347	+	1.77270i
$142$	2.87118e7			0.841494
$143$	−1.31931e7	+	9.20921e6i	−0.377287	+	0.263358i
$144$	−3.44480e7			−0.961380
$145$	1.69009e7	−	2.92732e7i	0.460385	−	0.797410i
$146$	8.81495e6	−	1.52679e7i	0.234415	−	0.406018i
$147$	−2.68463e7	−	4.64992e7i	−0.697066	−	1.20735i
$148$	3.15276e6			0.0799419
$149$	−5.10856e6	−	8.84829e6i	−0.126516	−	0.219133i	0.795808	−	0.605549i	$-0.207046\pi$
$149$	−5.10856e6	−	8.84829e6i	−0.126516	−	0.219133i	−0.922325	+	0.386416i	$0.873713\pi$
$150$	1.82494e7	+	3.16088e7i	0.441497	+	0.764696i
$151$	1.08524e7			0.256512			0.128256	−	0.991741i	$-0.459062\pi$
$151$	1.08524e7			0.256512			0.128256	+	0.991741i	$0.459062\pi$
$152$	−1.66948e7	−	2.89163e7i	−0.385593	−	0.667867i
$153$	4.84446e7	−	8.39086e7i	1.09352	−	1.89403i
$154$	2.53644e6	−	4.39324e6i	0.0559631	−	0.0969310i
$155$	4.98974e7			1.07626
$156$	1.29844e7	+	6.07785e6i	0.273833	+	0.128178i
$157$	−3.58959e7			−0.740280			−0.370140	−	0.928976i	$-0.620690\pi$
$157$	−3.58959e7			−0.740280			−0.370140	+	0.928976i	$0.620690\pi$
$158$	1.63616e7	−	2.83391e7i	0.330009	−	0.571592i
$159$	1.01282e6	−	1.75425e6i	0.0199821	−	0.0346100i
$160$	−6.00280e6	−	1.03972e7i	−0.115860	−	0.200676i
$161$	−1.73581e7			−0.327802
$162$	−1.60100e7	−	2.77301e7i	−0.295862	−	0.512448i
$163$	2.59182e7	+	4.48917e7i	0.468758	+	0.811912i	0.999362	−	0.0357073i	$-0.0113684\pi$
$163$	2.59182e7	+	4.48917e7i	0.468758	+	0.811912i	−0.530605	+	0.847619i	$0.678035\pi$
$164$	−6.05378e6			−0.107170
$165$	−1.17221e7	−	2.03032e7i	−0.203147	−	0.351861i
$166$	−2.50425e7	+	4.33749e7i	−0.424913	+	0.735970i
$167$	−3.48738e7	+	6.04031e7i	−0.579417	+	1.00358i	0.416129	+	0.909305i	$0.363386\pi$
$167$	−3.48738e7	+	6.04031e7i	−0.579417	+	1.00358i	−0.995546	+	0.0942740i	$0.969947\pi$
$168$	−2.70297e7			−0.439803
$169$	4.01933e7	+	4.81859e7i	0.640545	+	0.767920i
$170$	−5.79804e7			−0.905127
$171$	−2.97543e7	+	5.15360e7i	−0.455055	+	0.788178i
$172$	1.17404e6	−	2.03350e6i	0.0175927	−	0.0304715i
$173$	2.17440e7	+	3.76617e7i	0.319285	+	0.553018i	0.980339	−	0.197320i	$-0.0632239\pi$
$173$	2.17440e7	+	3.76617e7i	0.319285	+	0.553018i	−0.661054	+	0.750338i	$0.729891\pi$
$174$	1.46841e8			2.11313
$175$	6.32803e6	+	1.09605e7i	0.0892555	+	0.154595i
$176$	1.26267e7	+	2.18701e7i	0.174580	+	0.302382i
$177$	−5.38620e6			−0.0730090
$178$	−2.57157e7	−	4.45409e7i	−0.341766	−	0.591955i
$179$	1.54367e7	−	2.67372e7i	0.201173	−	0.348441i	−0.747734	−	0.663999i	$-0.768858\pi$
$179$	1.54367e7	−	2.67372e7i	0.201173	−	0.348441i	0.948907	+	0.315557i	$0.102191\pi$
$180$	−5.83733e6	+	1.01105e7i	−0.0746037	+	0.129217i
$181$	−1.39507e8			−1.74872			−0.874360	−	0.485278i	$-0.838718\pi$
$181$	−1.39507e8			−1.74872			−0.874360	+	0.485278i	$0.838718\pi$
$182$	−1.79183e7	−	8.38737e6i	−0.220317	−	0.103128i
$183$	4.17614e7			0.503728
$184$	5.46385e7	−	9.46366e7i	0.646601	−	1.11995i
$185$	−1.00535e7	+	1.74131e7i	−0.116739	+	0.202197i
$186$	1.08382e8	+	1.87723e8i	1.23498	+	2.13905i
$187$	−7.10282e7			−0.794302
$188$	−1.24367e7	−	2.15411e7i	−0.136507	−	0.236437i
$189$	5.07401e6	+	8.78845e6i	0.0546682	+	0.0946882i
$190$	3.56111e7			0.376658
$191$	2.06193e7	+	3.57136e7i	0.214120	+	0.370866i	0.953000	−	0.302971i	$-0.0979784\pi$
$191$	2.06193e7	+	3.57136e7i	0.214120	+	0.370866i	−0.738880	+	0.673837i	$0.764645\pi$
$192$	8.21046e7	−	1.42209e8i	0.837169	−	1.45002i
$193$	6.94001e7	−	1.20204e8i	0.694879	−	1.20357i	−0.275342	−	0.961346i	$-0.588791\pi$
$193$	6.94001e7	−	1.20204e8i	0.694879	−	1.20357i	0.970221	−	0.242220i	$-0.0778754\pi$
$194$	−1.52478e8			−1.49934
$195$	−7.49733e7	+	5.23337e7i	−0.724078	+	0.505429i
$196$	1.96011e7			0.185945
$197$	−2.56717e6	+	4.44647e6i	−0.0239234	+	0.0414366i	−0.877739	−	0.479139i	$-0.840949\pi$
$197$	−2.56717e6	+	4.44647e6i	−0.0239234	+	0.0414366i	0.853816	+	0.520575i	$0.174282\pi$
$198$	2.84590e7	−	4.92923e7i	0.260550	−	0.451285i
$199$	−4.81377e7	−	8.33770e7i	−0.433012	−	0.749999i	0.564119	−	0.825693i	$-0.309216\pi$
$199$	−4.81377e7	−	8.33770e7i	−0.433012	−	0.749999i	−0.997131	+	0.0756947i	$0.975883\pi$
$200$	−7.96756e7			−0.704239
$201$	−6.44265e7	−	1.11590e8i	−0.559601	−	0.969258i
$202$	5.89933e7	+	1.02179e8i	0.503585	+	0.872235i
$203$	5.09177e7			0.427201
$204$	3.16450e7	+	5.48107e7i	0.260975	+	0.452022i
$205$	1.93042e7	−	3.34358e7i	0.156499	−	0.271065i
$206$	3.11432e7	−	5.39416e7i	0.248215	−	0.429921i
$207$	−1.94758e8			−1.52616
$208$	8.07591e7	−	5.63724e7i	0.622257	−	0.434355i
$209$	4.36250e7			0.330539
$210$	1.44140e7	−	2.49657e7i	0.107403	−	0.186027i
$211$	−5.38980e7	+	9.33541e7i	−0.394988	+	0.684140i	−0.993100	−	0.117273i	$-0.962585\pi$
$211$	−5.38980e7	+	9.33541e7i	−0.394988	+	0.684140i	0.598112	+	0.801413i	$0.295918\pi$
$212$	369740.	+	640409.i	0.00266515	+	0.00461617i
$213$	1.99880e8			1.41723
$214$	−8.15009e7	−	1.41164e8i	−0.568478	−	0.984634i
$215$	7.48752e6	+	1.29688e7i	0.0513811	+	0.0889946i
$216$	−6.38864e7			−0.431340
$217$	3.75818e7	+	6.50935e7i	0.249671	+	0.432443i
$218$	−1.25771e8	+	2.17842e8i	−0.822212	+	1.42411i
$219$	6.13662e7	−	1.06289e8i	0.394798	−	0.683810i
$220$	8.55853e6			0.0541901
$221$	2.37396e7	+	2.75991e8i	0.147945	+	1.71997i
$222$	−8.73483e7			−0.535820
$223$	−3.77450e6	+	6.53762e6i	−0.0227925	+	0.0394778i	−0.877197	−	0.480131i	$-0.840589\pi$
$223$	−3.77450e6	+	6.53762e6i	−0.0227925	+	0.0394778i	0.854404	+	0.519609i	$0.173922\pi$
$224$	9.04239e6	−	1.56619e7i	0.0537546	−	0.0931056i
$225$	7.10007e7	+	1.22977e8i	0.415551	+	0.719755i
$226$	1.47217e7			0.0848355
$227$	−8.05895e7	−	1.39585e8i	−0.457286	−	0.792043i	0.541530	−	0.840681i	$-0.317845\pi$
$227$	−8.05895e7	−	1.39585e8i	−0.457286	−	0.792043i	−0.998816	+	0.0486385i	$0.984512\pi$
$228$	−1.94361e7	−	3.36643e7i	−0.108602	−	0.188104i
$229$	4.77059e7			0.262511			0.131256	−	0.991349i	$-0.458099\pi$
$229$	4.77059e7			0.262511			0.131256	+	0.991349i	$0.458099\pi$
$230$	5.82735e7	+	1.00933e8i	0.315809	+	0.546997i
$231$	1.76577e7	−	3.05840e7i	0.0942522	−	0.163250i
$232$	−1.60275e8	+	2.77604e8i	−0.842670	+	1.45955i
$233$	1.71967e8			0.890632			0.445316	−	0.895373i	$-0.353091\pi$
$233$	1.71967e8			0.890632			0.445316	+	0.895373i	$0.353091\pi$
$234$	−2.01044e8	−	9.41066e7i	−1.02574	−	0.480136i
$235$	1.58632e8			0.797359
$236$	983146.	−	1.70286e6i	0.00486885	−	0.00843309i
$237$	1.13903e8	−	1.97286e8i	0.555796	−	0.962667i
$238$	−4.36697e7	−	7.56382e7i	−0.209972	−	0.363682i
$239$	2.50000e8			1.18453			0.592266	−	0.805743i	$-0.298234\pi$
$239$	2.50000e8			1.18453			0.592266	+	0.805743i	$0.298234\pi$
$240$	7.17543e7	+	1.24282e8i	0.335049	+	0.580323i
$241$	3.56126e7	+	6.16829e7i	0.163887	+	0.283861i	0.936259	−	0.351309i	$-0.114263\pi$
$241$	3.56126e7	+	6.16829e7i	0.163887	+	0.283861i	−0.772373	+	0.635170i	$0.780930\pi$
$242$	1.55370e8			0.704716
$243$	−1.56393e8	−	2.70881e8i	−0.699191	−	1.21103i
$244$	−7.62273e6	+	1.32030e7i	−0.0335928	+	0.0581844i
$245$	−6.25036e7	+	1.08259e8i	−0.271534	+	0.470310i
$246$	1.67722e8			0.718319
$247$	−1.45807e7	−	1.69511e8i	−0.0615656	−	0.715747i
$248$	−4.73188e8			−1.96994
$249$	−1.74336e8	+	3.01959e8i	−0.715632	+	1.23951i
$250$	1.07254e8	−	1.85770e8i	0.434135	−	0.751943i
$251$	−1.90407e8	−	3.29795e8i	−0.760022	−	1.31640i	−0.942839	−	0.333249i	$-0.891855\pi$
$251$	−1.90407e8	−	3.29795e8i	−0.760022	−	1.31640i	0.182817	−	0.983147i	$-0.441478\pi$
$252$	−1.75863e7			−0.0692264
$253$	7.13874e7	+	1.23647e8i	0.277140	+	0.480021i
$254$	−7.03079e7	−	1.21777e8i	−0.269207	−	0.466280i
$255$	−4.03636e8			−1.52440
$256$	7.73793e7	+	1.34025e8i	0.288260	+	0.499282i
$257$	−2.42914e7	+	4.20740e7i	−0.0892662	+	0.154614i	−0.907201	−	0.420697i	$-0.861786\pi$
$257$	−2.42914e7	+	4.20740e7i	−0.0892662	+	0.154614i	0.817935	+	0.575311i	$0.195119\pi$
$258$	−3.25272e7	+	5.63387e7i	−0.117917	+	0.204239i
$259$	−3.02883e7			−0.108324
$260$	−2.86050e6	−	3.32554e7i	−0.0100933	−	0.117343i
$261$	5.71299e8			1.98894
$262$	1.35537e8	−	2.34756e8i	0.465588	−	0.806423i
$263$	−1.24702e8	+	2.15990e8i	−0.422697	+	0.732132i	−0.996202	−	0.0870697i	$-0.972250\pi$
$263$	−1.24702e8	+	2.15990e8i	−0.422697	+	0.732132i	0.573506	+	0.819202i	$0.305583\pi$
$264$	1.11163e8	+	1.92540e8i	0.371832	+	0.644032i
$265$	−4.71609e6			−0.0155676
$266$	2.68216e7	+	4.64563e7i	0.0873773	+	0.151342i
$267$	−1.79022e8	−	3.10076e8i	−0.575596	−	0.996962i
$268$	4.70392e7			0.149275
$269$	−2.36778e8	−	4.10112e8i	−0.741667	−	1.28460i	−0.951736	−	0.306918i	$-0.900702\pi$
$269$	−2.36778e8	−	4.10112e8i	−0.741667	−	1.28460i	0.210069	−	0.977687i	$-0.432631\pi$
$270$	3.40683e7	−	5.90081e7i	0.105336	−	0.182448i
$271$	7.22227e7	−	1.25093e8i	0.220435	−	0.381805i	−0.734505	−	0.678603i	$-0.762585\pi$
$271$	7.22227e7	−	1.25093e8i	0.220435	−	0.381805i	0.954940	+	0.296798i	$0.0959188\pi$
$272$	4.34786e8			1.31004
$273$	−1.24740e8	−	5.83895e7i	−0.371054	−	0.173686i
$274$	7.26619e7			0.213393
$275$	5.20497e7	−	9.01527e7i	0.150922	−	0.261405i
$276$	6.36100e7	−	1.10176e8i	0.182114	−	0.315431i
$277$	−2.26085e8	−	3.91590e8i	−0.639134	−	1.10701i	−0.985623	−	0.168959i	$-0.945959\pi$
$277$	−2.26085e8	−	3.91590e8i	−0.639134	−	1.10701i	0.346489	−	0.938054i	$-0.387374\pi$
$278$	−1.85453e8			−0.517697
$279$	4.21669e8	+	7.30352e8i	1.16240	+	2.01334i
$280$	3.14652e7	+	5.44994e7i	0.0856599	+	0.148367i
$281$	1.80819e8			0.486151			0.243075	−	0.970007i	$-0.421844\pi$
$281$	1.80819e8			0.486151			0.243075	+	0.970007i	$0.421844\pi$
$282$	3.44564e8	+	5.96803e8i	0.914952	+	1.58474i
$283$	−2.79735e8	+	4.84514e8i	−0.733658	+	1.27073i	0.221652	+	0.975126i	$0.428855\pi$
$283$	−2.79735e8	+	4.84514e8i	−0.733658	+	1.27073i	−0.955310	+	0.295607i	$0.904478\pi$
$284$	−3.64842e7	+	6.31925e7i	−0.0945128	+	0.163701i
$285$	2.47910e8			0.634362
$286$	1.39459e7	+	1.62132e8i	0.0352505	+	0.409814i
$287$	5.81582e7			0.145219
$288$	1.01456e8	−	1.75727e8i	0.250267	−	0.433476i
$289$	−4.06275e8	+	7.03689e8i	−0.990097	+	1.71490i
$290$	−1.70938e8	−	2.96073e8i	−0.411571	−	0.712863i
$291$	−1.06149e9			−2.52517
$292$	2.24024e7	+	3.88021e7i	0.0526568	+	0.0912042i
$293$	1.89521e8	+	3.28260e8i	0.440170	+	0.762397i	0.997702	−	0.0677587i	$-0.0215848\pi$
$293$	1.89521e8	+	3.28260e8i	0.440170	+	0.762397i	−0.557532	+	0.830156i	$0.688251\pi$
$294$	−5.43055e8			−1.24632
$295$	6.27008e6	+	1.08601e7i	0.0142199	+	0.0246296i
$296$	9.53393e7	−	1.65132e8i	0.213674	−	0.370094i
$297$	4.17351e7	−	7.22873e7i	0.0924387	−	0.160108i
$298$	−1.03337e8			−0.226204
$299$	4.56588e8	−	3.18712e8i	0.987813	−	0.689525i
$300$	−9.27581e7			−0.198348
$301$	−1.12789e7	+	1.95357e7i	−0.0238388	+	0.0412900i
$302$	5.48815e7	−	9.50575e7i	0.114657	−	0.198592i
$303$	4.10688e8	+	7.11332e8i	0.848130	+	1.46900i
$304$	−2.67042e8			−0.545157
$305$	−4.86145e7	−	8.42027e7i	−0.0981106	−	0.169933i
$306$	−4.89976e8	−	8.48663e8i	−0.977574	−	1.69321i
$307$	1.00446e9			1.98130			0.990649	−	0.136433i	$-0.0435639\pi$
$307$	1.00446e9			1.98130			0.990649	+	0.136433i	$0.0435639\pi$
$308$	6.44613e6	+	1.11650e7i	0.0125710	+	0.0217737i
$309$	2.16807e8	−	3.75520e8i	0.418040	−	0.724066i
$310$	2.52335e8	−	4.37056e8i	0.481073	−	0.833243i
$311$	4.57084e8			0.861658			0.430829	−	0.902434i	$-0.358221\pi$
$311$	4.57084e8			0.861658			0.430829	+	0.902434i	$0.358221\pi$
$312$	7.10989e8	−	4.96293e8i	1.32532	−	0.925117i
$313$	−6.79628e8			−1.25275			−0.626377	−	0.779520i	$-0.715463\pi$
$313$	−6.79628e8			−1.25275			−0.626377	+	0.779520i	$0.715463\pi$
$314$	−1.81528e8	+	3.14416e8i	−0.330895	+	0.573127i
$315$	5.60788e7	−	9.71313e7i	0.101091	−	0.175094i
$316$	4.15815e7	+	7.20212e7i	0.0741302	+	0.128397i
$317$	1.42499e8			0.251249			0.125625	−	0.992078i	$-0.459907\pi$
$317$	1.42499e8			0.251249			0.125625	+	0.992078i	$0.459907\pi$
$318$	−1.02438e7	−	1.77428e7i	−0.0178635	−	0.0309404i
$319$	−2.09406e8	−	3.62701e8i	−0.361178	−	0.625578i
$320$	−3.82312e8			−0.652218
$321$	−5.67377e8	−	9.82725e8i	−0.957423	−	1.65830i
$322$	−8.77811e7	+	1.52041e8i	−0.146523	+	0.253785i
$323$	3.75544e8	−	6.50462e8i	0.620086	−	1.07402i
$324$	8.13759e7			0.132919
$325$	−3.67698e8	−	1.72115e8i	−0.594155	−	0.278117i
$326$	5.24281e8			0.838113
$327$	−8.75570e8	+	1.51653e9i	−1.38476	+	2.39847i
$328$	−1.83066e8	+	3.17080e8i	−0.286450	+	0.496146i
$329$	1.19479e8	+	2.06943e8i	0.184972	+	0.320380i
$330$	−2.37117e8			−0.363215
$331$	−5.95525e7	−	1.03148e8i	−0.0902614	−	0.156337i	0.817360	−	0.576128i	$-0.195437\pi$
$331$	−5.95525e7	−	1.03148e8i	−0.0902614	−	0.156337i	−0.907621	+	0.419790i	$0.862104\pi$
$332$	−6.36433e7	−	1.10233e8i	−0.0954485	−	0.165322i
$333$	−3.39836e8			−0.504330
$334$	3.52718e8	+	6.10926e8i	0.517982	+	0.897172i
$335$	−1.49998e8	+	2.59804e8i	−0.217986	+	0.377563i
$336$	−1.08088e8	+	1.87214e8i	−0.155450	+	0.269247i
$337$	−3.15254e8			−0.448700			−0.224350	−	0.974509i	$-0.572026\pi$
$337$	−3.15254e8			−0.448700			−0.224350	+	0.974509i	$0.572026\pi$
$338$	6.25325e8	−	1.08378e8i	0.880841	−	0.152662i
$339$	1.02486e8			0.142879
$340$	7.36759e7	−	1.27610e8i	0.101660	−	0.176080i
$341$	3.09120e8	−	5.35411e8i	0.422169	−	0.731219i
$342$	3.00939e8	+	5.21242e8i	0.406806	+	0.704609i
$343$	−3.91670e8			−0.524072
$344$	−7.10058e7	−	1.22986e8i	−0.0940458	−	0.162892i
$345$	4.05677e8	+	7.02653e8i	0.531880	+	0.921243i
$346$	4.39844e8			0.570864
$347$	2.70320e8	+	4.68208e8i	0.347316	+	0.601569i	0.985772	−	0.168089i	$-0.0537598\pi$
$347$	2.70320e8	+	4.68208e8i	0.347316	+	0.601569i	−0.638456	+	0.769659i	$0.720426\pi$
$348$	−1.86592e8	+	3.23186e8i	−0.237337	+	0.411079i
$349$	1.38744e8	−	2.40312e8i	0.174713	−	0.302612i	−0.765349	−	0.643616i	$-0.777434\pi$
$349$	1.38744e8	−	2.40312e8i	0.174713	−	0.302612i	0.940062	+	0.341004i	$0.110767\pi$
$350$	1.28005e8			0.159584
$351$	−2.94832e8	−	1.38007e8i	−0.363915	−	0.170344i
$352$	−1.48752e8			−0.181787
$353$	−3.29885e6	+	5.71377e6i	−0.00399163	+	0.00691371i	−0.868014	−	0.496539i	$-0.834604\pi$
$353$	−3.29885e6	+	5.71377e6i	−0.00399163	+	0.00691371i	0.864023	+	0.503453i	$0.167937\pi$
$354$	−2.72384e7	+	4.71783e7i	−0.0326340	+	0.0565237i
$355$	−2.32680e8	−	4.03014e8i	−0.276033	−	0.478103i
$356$	1.30708e8			0.153542
$357$	−3.04011e8	−	5.26563e8i	−0.353631	−	0.612507i
$358$	−1.56129e8	−	2.70423e8i	−0.179843	−	0.311497i
$359$	6.67727e8			0.761672			0.380836	−	0.924643i	$-0.375636\pi$
$359$	6.67727e8			0.761672			0.380836	+	0.924643i	$0.375636\pi$
$360$	3.53041e8	+	6.11485e8i	0.398810	+	0.690760i
$361$	2.16280e8	−	3.74607e8i	0.241958	−	0.419084i
$362$	−7.05495e8	+	1.22195e9i	−0.781653	+	1.35386i
$363$	1.08163e9			1.18687
$364$	4.12289e7	−	2.87790e7i	0.0448071	−	0.0312767i
$365$	−2.85745e8			−0.307577
$366$	2.11190e8	−	3.65792e8i	0.225160	−	0.389988i
$367$	−4.05024e8	+	7.01522e8i	−0.427710	+	0.740816i	−0.996669	−	0.0815499i	$-0.974013\pi$
$367$	−4.05024e8	+	7.01522e8i	−0.427710	+	0.740816i	0.568959	+	0.822366i	$0.307346\pi$
$368$	−4.36984e8	−	7.56879e8i	−0.457086	−	0.791697i
$369$	6.52537e8			0.676103
$370$	1.01682e8	+	1.76119e8i	0.104361	+	0.180759i
$371$	−3.55207e6	−	6.15236e6i	−0.00361137	−	0.00625508i
$372$	−5.50885e8			−0.554831
$373$	3.26424e8	+	5.65382e8i	0.325687	+	0.564107i	0.981651	−	0.190685i	$-0.0610711\pi$
$373$	3.26424e8	+	5.65382e8i	0.325687	+	0.564107i	−0.655964	+	0.754792i	$0.727738\pi$
$374$	−3.59195e8	+	6.22144e8i	−0.355042	+	0.614950i
$375$	7.46661e8	−	1.29325e9i	0.731163	−	1.26641i
$376$	−1.50435e9			−1.45945
$377$	−1.33934e9	+	9.34902e8i	−1.28735	+	0.898610i
$378$	1.02639e8			0.0977438
$379$	7.44867e8	−	1.29015e9i	0.702816	−	1.21731i	−0.264658	−	0.964342i	$-0.585259\pi$
$379$	7.44867e8	−	1.29015e9i	0.702816	−	1.21731i	0.967474	−	0.252971i	$-0.0814076\pi$
$380$	−4.52511e7	+	7.83772e7i	−0.0423045	+	0.0732736i
$381$	−4.89456e8	−	8.47762e8i	−0.453394	−	0.785302i
$382$	4.17093e8			0.382834
$383$	2.20288e7	+	3.81550e7i	0.0200353	+	0.0347021i	0.875869	−	0.482549i	$-0.160289\pi$
$383$	2.20288e7	+	3.81550e7i	0.0200353	+	0.0347021i	−0.855834	+	0.517251i	$0.826955\pi$
$384$	−5.00395e8	−	8.66710e8i	−0.450976	−	0.781114i
$385$	−8.22212e7			−0.0734296
$386$	−7.01922e8	−	1.21576e9i	−0.621203	−	1.07595i
$387$	−1.26550e8	+	2.19191e8i	−0.110987	+	0.192236i
$388$	1.93754e8	−	3.35592e8i	0.168399	−	0.291676i
$389$	−742221.			−0.000639307			−0.000319654	−	1.00000i	$-0.500102\pi$
$389$	−742221.			−0.000639307			−0.000319654		1.00000i	$0.500102\pi$
$390$	7.92511e7	+	9.21354e8i	0.0676518	+	0.786503i
$391$	2.45814e9			2.07964
$392$	5.92736e8	−	1.02665e9i	0.497004	−	0.860837i
$393$	9.43552e8	−	1.63428e9i	0.784137	−	1.35816i
$394$	2.59647e7	+	4.49723e7i	0.0213869	+	0.0370431i
$395$	−5.30377e8			−0.433007
$396$	7.23258e7	+	1.25272e8i	0.0585275	+	0.101373i
$397$	6.46952e8	+	1.12055e9i	0.518926	+	0.898806i	0.999758	+	0.0219932i	$0.00700121\pi$
$397$	6.46952e8	+	1.12055e9i	0.518926	+	0.898806i	−0.480832	+	0.876813i	$0.659665\pi$
$398$	−9.73744e8			−0.774201
$399$	1.86721e8	+	3.23410e8i	0.147160	+	0.254888i
$400$	−3.18612e8	+	5.51852e8i	−0.248916	+	0.431135i
$401$	−1.13847e9	+	1.97188e9i	−0.881688	+	1.52713i	−0.0322237	+	0.999481i	$0.510259\pi$
$401$	−1.13847e9	+	1.97188e9i	−0.881688	+	1.52713i	−0.849464	+	0.527647i	$0.823074\pi$
$402$	−1.30324e9			−1.00054
$403$	−2.18374e9	−	1.02218e9i	−1.66201	−	0.777966i
$404$	−2.99852e8			−0.226241
$405$	−2.59490e8	+	4.49450e8i	−0.194101	+	0.336193i
$406$	2.57494e8	−	4.45993e8i	0.190953	−	0.330740i
$407$	1.24565e8	+	2.15752e8i	0.0915829	+	0.158626i
$408$	3.82777e9			2.79020
$409$	−1.21746e8	−	2.10871e8i	−0.0879882	−	0.152400i	0.818672	−	0.574261i	$-0.194710\pi$
$409$	−1.21746e8	−	2.10871e8i	−0.0879882	−	0.152400i	−0.906661	+	0.421861i	$0.861377\pi$
$410$	−1.95245e8	−	3.38175e8i	−0.139906	−	0.242325i
$411$	5.05843e8			0.359393
$412$	7.91476e7	+	1.37088e8i	0.0557567	+	0.0965735i
$413$	−9.44501e6	+	1.63592e7i	−0.00659747	+	0.0114271i
$414$	−9.84907e8	+	1.70591e9i	−0.682172	+	1.18156i
$415$	8.11778e8			0.557531
$416$	4.97171e7	+	5.77998e8i	0.0338594	+	0.393641i
$417$	−1.29105e9			−0.871898
$418$	2.20615e8	−	3.82116e8i	0.147746	−	0.255904i
$419$	4.30530e8	−	7.45700e8i	0.285926	−	0.495239i	−0.686907	−	0.726745i	$-0.741032\pi$
$419$	4.30530e8	−	7.45700e8i	0.285926	−	0.495239i	0.972833	+	0.231506i	$0.0743654\pi$
$420$	3.66318e7	+	6.34481e7i	0.0241260	+	0.0417874i
$421$	3.23521e8			0.211308			0.105654	−	0.994403i	$-0.466306\pi$
$421$	3.23521e8			0.211308			0.105654	+	0.994403i	$0.466306\pi$
$422$	5.45132e8	+	9.44196e8i	0.353108	+	0.611602i
$423$	1.34056e9	+	2.32191e9i	0.861180	+	1.49161i
$424$	4.47237e7			0.0284943
$425$	−8.96136e8	−	1.55215e9i	−0.566256	−	0.980784i
$426$	1.01081e9	−	1.75077e9i	0.633483	−	1.09722i
$427$	7.32310e7	−	1.26840e8i	0.0455195	−	0.0788421i
$428$	4.14254e8			0.255396
$429$	9.70858e7	+	1.12870e9i	0.0593684	+	0.690202i
$430$	1.51460e8			0.0918665
$431$	−1.11143e9	+	1.92505e9i	−0.668667	+	1.15817i	0.309610	+	0.950864i	$0.399802\pi$
$431$	−1.11143e9	+	1.92505e9i	−0.668667	+	1.15817i	−0.978277	+	0.207302i	$0.933532\pi$
$432$	−2.55473e8	+	4.42493e8i	−0.152459	+	0.264066i
$433$	1.02721e9	+	1.77918e9i	0.608066	+	1.05320i	0.991559	+	0.129657i	$0.0413876\pi$
$433$	1.02721e9	+	1.77918e9i	0.608066	+	1.05320i	−0.383493	+	0.923544i	$0.625279\pi$
$434$	7.60215e8			0.446398
$435$	−1.19000e9	−	2.06114e9i	−0.693162	−	1.20059i
$436$	−3.19636e8	−	5.53626e8i	−0.184694	−	0.319900i
$437$	−1.50977e9			−0.865419
$438$	−6.20666e8	−	1.07503e9i	−0.352938	−	0.611307i
$439$	1.17568e8	−	2.03634e8i	0.0663229	−	0.114875i	−0.830957	−	0.556336i	$-0.812207\pi$
$439$	1.17568e8	−	2.03634e8i	0.0663229	−	0.114875i	0.897280	+	0.441462i	$0.145540\pi$
$440$	2.58810e8	−	4.48272e8i	0.144843	−	0.250875i
$441$	−2.11280e9			−1.17307
$442$	2.53748e9	+	1.18777e9i	1.39774	+	0.654264i
$443$	−1.35426e9			−0.740100			−0.370050	−	0.929012i	$-0.620659\pi$
$443$	−1.35426e9			−0.740100			−0.370050	+	0.929012i	$0.620659\pi$
$444$	1.10994e8	−	1.92247e8i	0.0601809	−	0.104236i
$445$	−4.16800e8	+	7.21919e8i	−0.224217	+	0.388354i
$446$	3.81758e7	+	6.61224e7i	0.0203759	+	0.0352920i
$447$	−7.19394e8			−0.380970
$448$	−2.87950e8	−	4.98744e8i	−0.151302	−	0.262062i
$449$	9.56886e8	+	1.65738e9i	0.498882	+	0.864089i	0.999999	−	0.00129025i	$-0.000410699\pi$
$449$	9.56886e8	+	1.65738e9i	0.498882	+	0.864089i	−0.501117	+	0.865380i	$0.667077\pi$
$450$	1.43622e9			0.742981
$451$	−2.39183e8	−	4.14277e8i	−0.122776	−	0.212654i
$452$	−1.87069e7	+	3.24013e7i	−0.00952834	+	0.0165036i
$453$	3.82063e8	−	6.61753e8i	0.193104	−	0.334466i
$454$	−1.63019e9			−0.817602
$455$	2.74806e7	+	3.19483e8i	0.0136769	+	0.159004i
$456$	−2.35099e9			−1.16111
$457$	1.64555e9	−	2.85018e9i	0.806500	−	1.39690i	−0.108774	−	0.994067i	$-0.534692\pi$
$457$	1.64555e9	−	2.85018e9i	0.806500	−	1.39690i	0.915274	−	0.402832i	$-0.131974\pi$
$458$	2.41252e8	−	4.17861e8i	0.117339	−	0.203237i
$459$	−7.18550e8	−	1.24457e9i	−0.346827	−	0.600722i
$460$	−2.96194e8			−0.141881
$461$	−8.70376e8	−	1.50754e9i	−0.413765	−	0.716662i	0.581533	−	0.813523i	$-0.302453\pi$
$461$	−8.70376e8	−	1.50754e9i	−0.413765	−	0.716662i	−0.995298	+	0.0968608i	$0.969120\pi$
$462$	−1.78592e8	−	3.09331e8i	−0.0842589	−	0.145941i
$463$	5.88177e7			0.0275407			0.0137703	−	0.999905i	$-0.495617\pi$
$463$	5.88177e7			0.0275407			0.0137703	+	0.999905i	$0.495617\pi$
$464$	1.28184e9	+	2.22021e9i	0.595689	+	1.03176i
$465$	1.75665e9	−	3.04261e9i	0.810215	−	1.40333i
$466$	8.69647e8	−	1.50627e9i	0.398100	−	0.689530i
$467$	1.47573e9			0.670499			0.335249	−	0.942129i	$-0.391179\pi$
$467$	1.47573e9			0.670499			0.335249	+	0.942129i	$0.391179\pi$
$468$	4.62589e8	−	3.22902e8i	0.208610	−	0.145616i
$469$	−4.51902e8			−0.202274
$470$	8.02214e8	−	1.38948e9i	0.356408	−	0.617318i
$471$	−1.26373e9	+	2.18884e9i	−0.557288	+	0.965252i
$472$	−5.94606e7	−	1.02989e8i	−0.0260275	−	0.0450809i
$473$	1.85544e8			0.0806182
$474$	−1.15203e9	−	1.99537e9i	−0.496866	−	0.860598i
$475$	5.50399e8	+	9.53320e8i	0.235641	+	0.408142i
$476$	2.21965e8			0.0943323
$477$	−3.98543e7	−	6.90297e7i	−0.0168136	−	0.0291220i
$478$	1.26427e9	−	2.18977e9i	0.529469	−	0.917067i
$479$	−5.75573e8	+	9.96921e8i	−0.239291	+	0.414464i	−0.960511	−	0.278242i	$-0.910248\pi$
$479$	−5.75573e8	+	9.96921e8i	−0.239291	+	0.414464i	0.721220	+	0.692706i	$0.243582\pi$
$480$	−8.45322e8			−0.348881
$481$	7.96705e8	−	5.56125e8i	0.326430	−	0.227858i
$482$	7.20382e8			0.293021
$483$	−6.11097e8	+	1.05845e9i	−0.246771	+	0.427421i
$484$	−1.97430e8	+	3.41958e8i	−0.0791505	+	0.137093i
$485$	1.23568e9	+	2.14026e9i	0.491824	+	0.851864i
$486$	−3.16356e9			−1.25011
$487$	2.44105e9	+	4.22803e9i	0.957692	+	1.65877i	0.728084	+	0.685487i	$0.240411\pi$
$487$	2.44105e9	+	4.22803e9i	0.957692	+	1.65877i	0.229607	+	0.973283i	$0.426256\pi$
$488$	4.61022e8	+	7.98514e8i	0.179578	+	0.311038i
$489$	3.64983e9			1.41154
$490$	6.32170e8	+	1.09495e9i	0.242744	+	0.420444i
$491$	6.01834e8	−	1.04241e9i	0.229452	−	0.397422i	−0.728194	−	0.685371i	$-0.759640\pi$
$491$	6.01834e8	−	1.04241e9i	0.229452	−	0.397422i	0.957646	+	0.287949i	$0.0929734\pi$
$492$	−2.13125e8	+	3.69143e8i	−0.0806783	+	0.139739i
$493$	−7.21065e9			−2.71025
$494$	−1.55850e9	−	7.29517e8i	−0.581652	−	0.272264i
$495$	−9.22525e8			−0.341869
$496$	−1.89222e9	+	3.27742e9i	−0.696282	+	1.20600i
$497$	3.50501e8	−	6.07085e8i	0.128068	−	0.221821i
$498$	1.76326e9	+	3.05405e9i	0.639755	+	1.10809i
$499$	−3.64043e9			−1.31160			−0.655799	−	0.754935i	$-0.727668\pi$
$499$	−3.64043e9			−1.31160			−0.655799	+	0.754935i	$0.727668\pi$
$500$	2.72577e8	+	4.72117e8i	0.0975200	+	0.168910i
$501$	2.45548e9	+	4.25302e9i	0.872378	+	1.51100i
$502$	−3.85162e9			−1.35888
$503$	−1.65318e9	−	2.86340e9i	−0.579206	−	1.00321i	−0.995571	−	0.0940160i	$-0.970030\pi$
$503$	−1.65318e9	−	2.86340e9i	−0.579206	−	1.00321i	0.416365	−	0.909198i	$-0.363304\pi$
$504$	−5.31808e8	+	9.21118e8i	−0.185032	+	0.320486i
$505$	9.56163e8	−	1.65612e9i	0.330379	−	0.572233i
$506$	1.44404e9			0.495512
$507$	4.35326e9	−	7.54483e8i	1.48350	−	0.257111i
$508$	3.57362e8			0.120944
$509$	5.50673e8	−	9.53794e8i	0.185089	−	0.320584i	−0.758517	−	0.651653i	$-0.774076\pi$
$509$	5.50673e8	−	9.53794e8i	0.185089	−	0.320584i	0.943607	+	0.331069i	$0.107409\pi$
$510$	−2.04122e9	+	3.53549e9i	−0.681386	+	1.18020i
$511$	−2.15218e8	−	3.72769e8i	−0.0713519	−	0.123585i
$512$	3.38459e9			1.11445
$513$	4.41328e8	+	7.64402e8i	0.144328	+	0.249983i
$514$	2.45687e8	+	4.25542e8i	0.0798015	+	0.138220i
$515$	−1.00954e9			−0.325685
$516$	−8.26649e7	−	1.43180e8i	−0.0264879	−	0.0458783i
$517$	9.82745e8	−	1.70216e9i	0.312769	−	0.541732i
$518$	−1.53170e8	+	2.65298e8i	−0.0484195	+	0.0838650i
$519$	3.06202e9			0.961440
$520$	−1.82833e9	−	8.55819e8i	−0.570220	−	0.266913i
$521$	4.27358e9			1.32391			0.661957	−	0.749541i	$-0.269726\pi$
$521$	4.27358e9			1.32391			0.661957	+	0.749541i	$0.269726\pi$
$522$	2.88910e9	−	5.00406e9i	0.889028	−	1.53984i
$523$	1.50948e9	−	2.61450e9i	0.461395	−	0.799159i	−0.537636	−	0.843177i	$-0.680682\pi$
$523$	1.50948e9	−	2.61450e9i	0.461395	−	0.799159i	0.999031	+	0.0440177i	$0.0140158\pi$
$524$	3.44454e8	+	5.96612e8i	0.104586	+	0.181147i
$525$	8.91120e8			0.268769
$526$	1.26125e9	+	2.18456e9i	0.377879	+	0.654506i
$527$	−5.32210e9	−	9.21814e9i	−1.58397	−	2.74351i
$528$	1.77810e9			0.525701
$529$	−7.68162e8	−	1.33050e9i	−0.225610	−	0.390768i
$530$	−2.38496e7	+	4.13087e7i	−0.00695849	+	0.0120525i
$531$	−1.05973e8	+	1.83551e8i	−0.0307161	+	0.0532019i
$532$	−1.36329e8			−0.0392553
$533$	−1.52979e9	+	1.06784e9i	−0.437611	+	0.305466i
$534$	−3.62132e9			−1.02913
$535$	−1.32097e9	+	2.28798e9i	−0.372952	+	0.645973i
$536$	1.42246e9	−	2.46378e9i	0.398992	−	0.691075i
$537$	−1.08691e9	−	1.88258e9i	−0.302888	−	0.524618i
$538$	−4.78962e9			−1.32606
$539$	7.74434e8	+	1.34136e9i	0.213022	+	0.368964i
$540$	8.65816e7	+	1.49964e8i	0.0236618	+	0.0409834i
$541$	2.08205e9			0.565329			0.282664	−	0.959219i	$-0.408782\pi$
$541$	2.08205e9			0.565329			0.282664	+	0.959219i	$0.408782\pi$
$542$	−7.30471e8	−	1.26521e9i	−0.197063	−	0.341323i
$543$	−4.91138e9	+	8.50675e9i	−1.31645	+	2.28016i
$544$	−1.28053e9	+	2.21794e9i	−0.341030	+	0.590682i
$545$	4.07700e9			1.07883
$546$	−1.14226e9	+	7.97333e8i	−0.300324	+	0.209636i
$547$	−1.26947e9			−0.331641			−0.165820	−	0.986156i	$-0.553027\pi$
$547$	−1.26947e9			−0.331641			−0.165820	+	0.986156i	$0.553027\pi$
$548$	−9.23317e7	+	1.59923e8i	−0.0239673	+	0.0415126i
$549$	8.21655e8	−	1.42315e9i	0.211927	−	0.367068i
$550$	−5.26438e8	−	9.11817e8i	−0.134920	−	0.233689i
$551$	4.42872e9			1.12784
$552$	−3.84713e9	−	6.66342e9i	−0.973531	−	1.68621i
$553$	−3.99470e8	−	6.91903e8i	−0.100449	−	0.173983i
$554$	−4.57331e9			−1.14274
$555$	7.07870e8	+	1.22607e9i	0.175763	+	0.304431i
$556$	2.35655e8	−	4.08167e8i	0.0581454	−	0.100711i
$557$	−1.46286e9	+	2.53375e9i	−0.358682	+	0.621256i	−0.987741	−	0.156102i	$-0.950107\pi$
$557$	−1.46286e9	+	2.53375e9i	−0.358682	+	0.621256i	0.629059	+	0.777358i	$0.283441\pi$
$558$	8.52964e9			2.07831
$559$	−6.20140e7	−	7.20959e8i	−0.0150158	−	0.174570i
$560$	5.03301e8			0.121107
$561$	−2.50057e9	+	4.33112e9i	−0.597956	+	1.03569i
$562$	9.14412e8	−	1.58381e9i	0.217303	−	0.376379i
$563$	−4.08319e9	−	7.07229e9i	−0.964318	−	1.67025i	−0.711436	−	0.702751i	$-0.751955\pi$
$563$	−4.08319e9	−	7.07229e9i	−0.964318	−	1.67025i	−0.252882	−	0.967497i	$-0.581379\pi$
$564$	−1.75136e9			−0.411053
$565$	−1.19304e8	−	2.06641e8i	−0.0278283	−	0.0482001i
$566$	2.82927e9	+	4.90045e9i	0.655870	+	1.13600i
$567$	−7.81772e8			−0.180111
$568$	2.20656e9	+	3.82188e9i	0.505239	+	0.875099i
$569$	1.01027e9	−	1.74984e9i	0.229903	−	0.398203i	−0.727876	−	0.685708i	$-0.759493\pi$
$569$	1.01027e9	−	1.74984e9i	0.229903	−	0.398203i	0.957779	+	0.287505i	$0.0928259\pi$
$570$	1.25370e9	−	2.17147e9i	0.283551	−	0.491125i
$571$	4.65062e9			1.04540			0.522702	−	0.852515i	$-0.324924\pi$
$571$	4.65062e9			1.04540			0.522702	+	0.852515i	$0.324924\pi$
$572$	−3.74560e8	−	1.75327e8i	−0.0836827	−	0.0391709i
$573$	2.90363e9			0.644764
$574$	2.94110e8	−	5.09414e8i	0.0649110	−	0.112429i
$575$	−1.80133e9	+	3.12000e9i	−0.395145	+	0.684412i
$576$	−3.23081e9	−	5.59593e9i	−0.704422	−	1.22010i
$577$	5.94249e9			1.28781			0.643907	−	0.765104i	$-0.277312\pi$
$577$	5.94249e9			1.28781			0.643907	+	0.765104i	$0.277312\pi$
$578$	4.10912e9	+	7.11721e9i	0.885119	+	1.53307i
$579$	−4.88650e9	−	8.46367e9i	−1.04622	−	1.81211i
$580$	8.68846e8			0.184903
$581$	6.11416e8	+	1.05900e9i	0.129336	+	0.224017i
$582$	−5.36802e9	+	9.29769e9i	−1.12871	+	1.95499i
$583$	−2.92167e7	+	5.06048e7i	−0.00610648	+	0.0105767i
$584$	2.70979e9			0.562977
$585$	3.08334e8	+	3.58461e9i	0.0636759	+	0.740280i
$586$	3.83368e9			0.787000
$587$	3.98257e8	−	6.89802e8i	0.0812700	−	0.140764i	−0.822526	−	0.568728i	$-0.807436\pi$
$587$	3.98257e8	−	6.89802e8i	0.0812700	−	0.140764i	0.903796	+	0.427964i	$0.140769\pi$
$588$	6.90062e8	−	1.19522e9i	0.139980	−	0.242453i
$589$	3.26879e9	+	5.66171e9i	0.659149	+	1.14168i
$590$	1.26833e8			0.0254244
$591$	1.80756e8	+	3.13079e8i	0.0360194	+	0.0623875i
$592$	−7.62498e8	−	1.32069e9i	−0.151047	−	0.261622i
$593$	−6.11768e9			−1.20475			−0.602373	−	0.798215i	$-0.705778\pi$
$593$	−6.11768e9			−1.20475			−0.602373	+	0.798215i	$0.705778\pi$
$594$	−4.22114e8	−	7.31124e8i	−0.0826376	−	0.143133i
$595$	−7.07799e8	+	1.22594e9i	−0.137753	+	0.238595i
$596$	1.31311e8	−	2.27438e8i	0.0254062	−	0.0440049i
$597$	−6.77881e9			−1.30390
$598$	−4.82640e8	−	5.61105e9i	−0.0922930	−	1.07298i
$599$	4.08018e9			0.775685			0.387843	−	0.921726i	$-0.373220\pi$
$599$	4.08018e9			0.775685			0.387843	+	0.921726i	$0.373220\pi$
$600$	−2.80500e9	+	4.85841e9i	−0.530156	+	0.918257i
$601$	−5.06656e9	+	8.77554e9i	−0.952035	+	1.64897i	−0.211022	+	0.977481i	$0.567679\pi$
$601$	−5.06656e9	+	8.77554e9i	−0.952035	+	1.64897i	−0.741013	+	0.671491i	$0.765654\pi$
$602$	1.14077e8	+	1.97586e8i	0.0213112	+	0.0369121i
$603$	−5.07036e9			−0.941734
$604$	1.39476e8	+	2.41580e8i	0.0257556	+	0.0446099i
$605$	−1.25912e9	−	2.18086e9i	−0.231166	−	0.400391i
$606$	8.30751e9			1.51641
$607$	2.26264e9	+	3.91901e9i	0.410635	+	0.711240i	0.994959	−	0.100280i	$-0.0319738\pi$
$607$	2.26264e9	+	3.91901e9i	0.410635	+	0.711240i	−0.584325	+	0.811520i	$0.698640\pi$
$608$	7.86490e8	−	1.36224e9i	0.141916	−	0.245805i
$609$	1.79257e9	−	3.10483e9i	0.321600	−	0.557028i
$610$	−9.83387e8			−0.175416
$611$	−6.94247e9	−	3.24969e9i	−1.23132	−	0.576365i
$612$	2.49046e9			0.439187
$613$	−4.12211e7	+	7.13970e7i	−0.00722783	+	0.0125190i	−0.869617	−	0.493727i	$-0.835634\pi$
$613$	−4.12211e7	+	7.13970e7i	−0.00722783	+	0.0125190i	0.862389	+	0.506246i	$0.168967\pi$
$614$	5.07964e9	−	8.79820e9i	0.885613	−	1.53393i
$615$	−1.35922e9	−	2.35424e9i	−0.235628	−	0.408119i
$616$	7.79722e8			0.134403
$617$	5.32900e8	+	9.23010e8i	0.0913372	+	0.158201i	0.908074	−	0.418810i	$-0.137553\pi$
$617$	5.32900e8	+	9.23010e8i	0.0913372	+	0.158201i	−0.816737	+	0.577010i	$0.804219\pi$
$618$	−2.19281e9	−	3.79806e9i	−0.373716	−	0.647295i
$619$	−7.35459e8			−0.124635			−0.0623177	−	0.998056i	$-0.519849\pi$
$619$	−7.35459e8			−0.124635			−0.0623177	+	0.998056i	$0.519849\pi$
$620$	6.41285e8	+	1.11074e9i	0.108064	+	0.187172i
$621$	−1.44437e9	+	2.50172e9i	−0.242023	+	0.419197i
$622$	2.31151e9	−	4.00365e9i	0.385149	−	0.667098i
$623$	−1.25570e9			−0.208055
$624$	−5.94292e8	−	6.90909e9i	−0.0979160	−	1.13835i
$625$	5.27307e8			0.0863940
$626$	−3.43693e9	+	5.95293e9i	−0.559964	+	0.969886i
$627$	1.53583e9	−	2.66014e9i	0.248832	−	0.430990i
$628$	−4.61337e8	−	7.99059e8i	−0.0743292	−	0.128742i
$629$	4.28924e9			0.687232
$630$	−5.67189e8	−	9.82400e8i	−0.0903724	−	0.156530i
$631$	−2.07991e8	−	3.60252e8i	−0.0329566	−	0.0570825i	0.849077	−	0.528270i	$-0.177159\pi$
$631$	−2.07991e8	−	3.60252e8i	−0.0329566	−	0.0570825i	−0.882033	+	0.471187i	$0.843826\pi$
$632$	5.02969e9			0.792559
$633$	3.79499e9	+	6.57312e9i	0.594700	+	1.03005i
$634$	7.20628e8	−	1.24816e9i	0.112305	−	0.194518i
$635$	−1.13955e9	+	1.97376e9i	−0.176614	+	0.305905i
$636$	5.20673e7			0.00802537
$637$	4.95321e9	−	3.45750e9i	0.759274	−	0.529997i
$638$	−4.23592e9			−0.645766
$639$	3.93264e9	−	6.81152e9i	0.596253	−	1.03274i
$640$	−1.16502e9	+	2.01787e9i	−0.175672	+	0.304273i
$641$	−2.81157e9	−	4.86978e9i	−0.421644	−	0.730309i	0.574457	−	0.818535i	$-0.305213\pi$
$641$	−2.81157e9	−	4.86978e9i	−0.421644	−	0.730309i	−0.996100	+	0.0882264i	$0.971880\pi$
$642$	−1.14771e10			−1.71182
$643$	−4.47709e9	−	7.75455e9i	−0.664137	−	1.15032i	−0.979519	−	0.201354i	$-0.935466\pi$
$643$	−4.47709e9	−	7.75455e9i	−0.664137	−	1.15032i	0.315382	−	0.948965i	$-0.397867\pi$
$644$	−2.23087e8	−	3.86399e8i	−0.0329135	−	0.0570079i
$645$	1.05440e9			0.154720
$646$	−3.79831e9	−	6.57886e9i	−0.554340	−	0.960145i
$647$	−4.36397e9	+	7.55861e9i	−0.633456	+	1.09718i	0.353384	+	0.935478i	$0.385031\pi$
$647$	−4.36397e9	+	7.55861e9i	−0.633456	+	1.09718i	−0.986840	+	0.161699i	$0.948303\pi$
$648$	2.46080e9	−	4.26224e9i	0.355275	−	0.615354i
$649$	1.55375e8			0.0223113
$650$	−3.36705e9	+	2.35031e9i	−0.480898	+	0.335682i
$651$	5.29231e9			0.751816
$652$	−6.66206e8	+	1.15390e9i	−0.0941330	+	0.163043i
$653$	−2.01742e9	+	3.49427e9i	−0.283531	+	0.491090i	−0.972252	−	0.233937i	$-0.924839\pi$
$653$	−2.01742e9	+	3.49427e9i	−0.283531	+	0.491090i	0.688721	+	0.725026i	$0.258172\pi$
$654$	8.85564e9	+	1.53384e10i	1.23793	+	2.14417i
$655$	−4.39355e9			−0.610902
$656$	1.46411e9	+	2.53592e9i	0.202494	+	0.350729i
$657$	−2.41476e9	−	4.18248e9i	−0.332196	−	0.575380i
$658$	2.41685e9			0.330719
$659$	2.23633e9	+	3.87343e9i	0.304394	+	0.527226i	0.977126	−	0.212660i	$-0.0682126\pi$
$659$	2.23633e9	+	3.87343e9i	0.304394	+	0.527226i	−0.672732	+	0.739886i	$0.734879\pi$
$660$	3.01306e8	−	5.21877e8i	0.0407947	−	0.0706585i
$661$	4.53934e9	−	7.86236e9i	0.611346	−	1.05888i	−0.379668	−	0.925123i	$-0.623962\pi$
$661$	4.53934e9	−	7.86236e9i	0.611346	−	1.05888i	0.991014	−	0.133760i	$-0.0427050\pi$
$662$	−1.20465e9			−0.161382
$663$	1.76650e10	+	8.26876e9i	2.35405	+	1.10190i
$664$	−7.69828e9			−1.02048
$665$	4.34724e8	−	7.52964e8i	0.0573242	−	0.0992884i
$666$	−1.71858e9	+	2.97666e9i	−0.225428	+	0.390454i
$667$	7.24711e9	+	1.25524e10i	0.945637	+	1.63789i
$668$	−1.79280e9			−0.232710
$669$	2.65765e8	+	4.60318e8i	0.0343167	+	0.0594383i
$670$	1.51710e9	+	2.62769e9i	0.194873	+	0.337530i
$671$	−1.20469e9			−0.153938
$672$	−6.36681e8	−	1.10276e9i	−0.0809336	−	0.140181i
$673$	4.13568e9	−	7.16321e9i	0.522991	−	0.905848i	−0.476651	−	0.879093i	$-0.658149\pi$
$673$	4.13568e9	−	7.16321e9i	0.522991	−	0.905848i	0.999642	−	0.0267549i	$-0.00851736\pi$
$674$	−1.59426e9	+	2.76134e9i	−0.200563	+	0.347385i
$675$	2.10622e9			0.263597
$676$	−5.56072e8	+	1.51401e9i	−0.0692337	+	0.188502i
$677$	−7.18333e9			−0.889744			−0.444872	−	0.895594i	$-0.646751\pi$
$677$	−7.18333e9			−0.889744			−0.444872	+	0.895594i	$0.646751\pi$
$678$	5.18281e8	−	8.97689e8i	0.0638648	−	0.110617i
$679$	−1.86138e9	+	3.22400e9i	−0.228187	+	0.395231i
$680$	−4.45591e9	−	7.71786e9i	−0.543445	−	0.941274i
$681$	−1.13487e10			−1.37699
$682$	−3.12648e9	−	5.41523e9i	−0.377408	−	0.653689i
$683$	2.09930e9	+	3.63609e9i	0.252117	+	0.436679i	0.964108	−	0.265509i	$-0.0855400\pi$
$683$	2.09930e9	+	3.63609e9i	0.252117	+	0.436679i	−0.711992	+	0.702188i	$0.752207\pi$
$684$	−1.52962e9			−0.182762
$685$	−5.88852e8	−	1.01992e9i	−0.0699986	−	0.121241i
$686$	−1.98070e9	+	3.43068e9i	−0.234253	+	0.405738i
$687$	1.67950e9	−	2.90898e9i	0.197620	−	0.342289i
$688$	−1.13577e9			−0.132963
$689$	2.06397e8	+	9.66122e7i	0.0240401	+	0.0112529i
$690$	8.20615e9			0.950972
$691$	−6.95215e9	+	1.20415e10i	−0.801579	+	1.38837i	0.116998	+	0.993132i	$0.462673\pi$
$691$	−6.95215e9	+	1.20415e10i	−0.801579	+	1.38837i	−0.918577	+	0.395243i	$0.870661\pi$
$692$	−5.58912e8	+	9.68064e8i	−0.0641168	+	0.111054i
$693$	−6.94829e8	−	1.20348e9i	−0.0793070	−	0.137364i
$694$	5.46811e9			0.620982
$695$	1.50291e9	+	2.60311e9i	0.169819	+	0.294135i
$696$	1.12851e10	+	1.95463e10i	1.26874	+	2.19752i
$697$	−8.23600e9			−0.921302
$698$	−1.40328e9	−	2.43055e9i	−0.156189	−	0.270527i
$699$	6.05414e9	−	1.04861e10i	0.670474	−	1.16130i
$700$	−1.62657e8	+	2.81729e8i	−0.0179237	+	0.0310448i
$701$	9.20624e9			1.00941			0.504707	−	0.863291i	$-0.331601\pi$
$701$	9.20624e9			1.00941			0.504707	+	0.863291i	$0.331601\pi$
$702$	−2.69981e9	+	1.88455e9i	−0.294546	+	0.205602i
$703$	−2.63442e9			−0.285984
$704$	−2.36847e9	+	4.10230e9i	−0.255837	+	0.443122i
$705$	5.58470e9	−	9.67298e9i	0.600258	−	1.03968i
$706$	3.33650e7	+	5.77899e7i	0.00356841	+	0.00618067i
$707$	2.88066e9			0.306566
$708$	−6.92239e7	−	1.19899e8i	−0.00733060	−	0.0126970i
$709$	−7.85494e9	−	1.36052e10i	−0.827716	−	1.43365i	−0.899826	−	0.436249i	$-0.856307\pi$
$709$	−7.85494e9	−	1.36052e10i	−0.827716	−	1.43365i	0.0721104	−	0.997397i	$-0.477027\pi$
$710$	−4.70672e9			−0.493531
$711$	−4.48207e9	−	7.76318e9i	−0.467665	−	0.810020i
$712$	3.95261e9	−	6.84612e9i	0.410397	−	0.710828i
$713$	−1.06980e10	+	1.85295e10i	−1.10532	+	1.91448i
$714$	−6.14962e9			−0.632273
$715$	2.16275e9	−	1.50967e9i	0.221276	−	0.154458i
$716$	7.93575e8			0.0807965
$717$	8.80131e9	−	1.52443e10i	0.891724	−	1.54451i
$718$	3.37674e9	−	5.84869e9i	0.340457	−	0.589689i
$719$	−2.92888e9	−	5.07296e9i	−0.293866	−	0.508992i	0.680854	−	0.732419i	$-0.261609\pi$
$719$	−2.92888e9	−	5.07296e9i	−0.293866	−	0.508992i	−0.974721	+	0.223427i	$0.928275\pi$
$720$	5.64706e9			0.563844
$721$	−7.60365e8	−	1.31699e9i	−0.0755525	−	0.130861i
$722$	−2.18748e9	−	3.78883e9i	−0.216304	−	0.374650i
$723$	5.01501e9			0.493501
$724$	−1.79295e9	−	3.10548e9i	−0.175583	−	0.304119i
$725$	5.28398e9	−	9.15213e9i	0.514966	−	0.891947i
$726$	5.46986e9	−	9.47407e9i	0.530515	−	0.918879i
$727$	7.95539e8			0.0767876			0.0383938	−	0.999263i	$-0.487776\pi$
$727$	7.95539e8			0.0767876			0.0383938	+	0.999263i	$0.487776\pi$
$728$	−2.60605e8	−	3.02973e9i	−0.0250336	−	0.291034i
$729$	−1.50997e10			−1.44352
$730$	−1.44503e9	+	2.50287e9i	−0.137483	+	0.238127i
$731$	1.59725e9	−	2.76652e9i	0.151238	−	0.261953i
$732$	5.36721e8	+	9.29628e8i	0.0505778	+	0.0876033i
$733$	5.89067e9			0.552460			0.276230	−	0.961092i	$-0.410915\pi$
$733$	5.89067e9			0.552460			0.276230	+	0.961092i	$0.410915\pi$
$734$	4.09647e9	+	7.09530e9i	0.382361	+	0.662269i
$735$	4.40092e9	+	7.62261e9i	0.408825	+	0.708106i
$736$	5.14801e9			0.475957
$737$	1.85851e9	+	3.21903e9i	0.171013	+	0.296202i
$738$	3.29993e9	−	5.71564e9i	0.302209	−	0.523441i
$739$	−4.03340e9	+	6.98606e9i	−0.367634	+	0.636761i	−0.989195	−	0.146605i	$-0.953165\pi$
$739$	−4.03340e9	+	6.98606e9i	−0.367634	+	0.636761i	0.621561	+	0.783366i	$0.286499\pi$
$740$	−5.16832e8			−0.0468854
$741$	−1.08497e10	−	5.07860e9i	−0.979609	−	0.458544i
$742$	−7.18522e7			−0.00645693
$743$	9.23486e9	−	1.59953e10i	0.825980	−	1.43064i	−0.0751879	−	0.997169i	$-0.523956\pi$
$743$	9.23486e9	−	1.59953e10i	0.825980	−	1.43064i	0.901168	−	0.433470i	$-0.142711\pi$
$744$	−1.66587e10	+	2.88538e10i	−1.48299	+	2.56861i
$745$	8.37447e8	+	1.45050e9i	0.0742011	+	0.128520i
$746$	6.60299e9			0.582310
$747$	6.86011e9	+	1.18821e10i	0.602156	+	1.04297i
$748$	−9.12861e8	−	1.58112e9i	−0.0797533	−	0.138137i
$749$	−3.97971e9			−0.346071
$750$	−7.55183e9	−	1.30802e10i	−0.653639	−	1.13214i
$751$	−2.05763e9	+	3.56392e9i	−0.177267	+	0.307035i	−0.940943	−	0.338564i	$-0.890059\pi$
$751$	−2.05763e9	+	3.56392e9i	−0.177267	+	0.307035i	0.763677	+	0.645599i	$0.223392\pi$
$752$	−6.01568e9	+	1.04195e10i	−0.515849	+	0.893476i
$753$	−2.68134e10			−2.28860
$754$	1.41576e9	+	1.64593e10i	0.120279	+	1.39833i
$755$	−1.77904e9			−0.150443
$756$	−1.30423e8	+	2.25900e8i	−0.0109781	+	0.0190147i
$757$	5.00576e9	−	8.67023e9i	0.419406	−	0.726432i	−0.576474	−	0.817116i	$-0.695572\pi$
$757$	5.00576e9	−	8.67023e9i	0.419406	−	0.726432i	0.995880	+	0.0906832i	$0.0289051\pi$
$758$	−7.53369e9	−	1.30487e10i	−0.628298	−	1.08824i
$759$	1.00529e10			0.834533
$760$	2.73678e9	+	4.74025e9i	0.226148	+	0.391700i
$761$	9.42141e9	+	1.63184e10i	0.774942	+	1.34224i	0.934827	+	0.355104i	$0.115555\pi$
$761$	9.42141e9	+	1.63184e10i	0.774942	+	1.34224i	−0.159884	+	0.987136i	$0.551112\pi$
$762$	−9.90085e9			−0.810644
$763$	3.07072e9	+	5.31865e9i	0.250268	+	0.433476i
$764$	−5.30001e8	+	9.17989e8i	−0.0429982	+	0.0744751i
$765$	−7.94153e9	+	1.37551e10i	−0.641341	+	1.11084i
$766$	4.45605e8			0.0358219
$767$	−5.19308e7	−	6.03734e8i	−0.00415567	−	0.0483128i
$768$	1.08967e10			0.868018
$769$	3.92588e9	−	6.79983e9i	0.311312	−	0.539207i	−0.667335	−	0.744758i	$-0.732565\pi$
$769$	3.92588e9	−	6.79983e9i	0.311312	−	0.539207i	0.978647	+	0.205550i	$0.0658984\pi$
$770$	−4.15798e8	+	7.20184e8i	−0.0328220	+	0.0568494i
$771$	1.71037e9	+	2.96245e9i	0.134400	+	0.232788i
$772$	3.56774e9			0.279083
$773$	9.70260e9	+	1.68054e10i	0.755544	+	1.30864i	0.945103	+	0.326771i	$0.105961\pi$
$773$	9.70260e9	+	1.68054e10i	0.755544	+	1.30864i	−0.189560	+	0.981869i	$0.560706\pi$
$774$	1.27994e9	+	2.21693e9i	0.0992196	+	0.171853i
$775$	1.56002e10			1.20385
$776$	−1.17182e10	−	2.02966e10i	−0.900214	−	1.55922i
$777$	−1.06631e9	+	1.84690e9i	−0.0815473	+	0.141244i
$778$	−3.75347e6	+	6.50119e6i	−0.000285762	+	0.000494954i
$779$	5.05849e9			0.383389
$780$	−2.12853e9	−	9.96342e8i	−0.160602	−	0.0751757i
$781$	−5.76592e9			−0.433102
$782$	1.24310e10	−	2.15311e10i	0.929572	−	1.61007i
$783$	4.23686e9	−	7.33846e9i	0.315412	−	0.546310i
$784$	−4.74055e9	−	8.21087e9i	−0.351336	−	0.608531i
$785$	5.88442e9			0.434170
$786$	−9.54322e9	−	1.65293e10i	−0.700997	−	1.21416i
$787$	1.26249e10	+	2.18670e10i	0.923246	+	1.59911i	0.794359	+	0.607449i	$0.207807\pi$
$787$	1.26249e10	+	2.18670e10i	0.923246	+	1.59911i	0.128887	+	0.991659i	$0.458859\pi$
$788$	−1.31974e8			−0.00960830
$789$	8.78035e9	+	1.52080e10i	0.636418	+	1.10231i
$790$	−2.68216e9	+	4.64563e9i	−0.193548	+	0.335235i
$791$	1.79716e8	−	3.11277e8i	0.0129112	−	0.0223629i
$792$	8.74852e9			0.625744
$793$	4.02640e8	+	4.68099e9i	0.0286722	+	0.333336i
$794$	1.30867e10			0.927810
$795$	−1.66031e8	+	2.87575e8i	−0.0117194	+	0.0202986i
$796$	1.23734e9	−	2.14314e9i	0.0869548	−	0.150610i
$797$	−1.17485e9	−	2.03490e9i	−0.0822011	−	0.142376i	0.821994	−	0.569496i	$-0.192862\pi$
$797$	−1.17485e9	−	2.03490e9i	−0.0822011	−	0.142376i	−0.904195	+	0.427120i	$0.859528\pi$
$798$	3.77705e9			0.263113
$799$	−1.69199e10	−	2.93060e10i	−1.17350	−	2.03256i
$800$	−1.87675e9	−	3.25062e9i	−0.129596	−	0.224467i
$801$	−1.40890e10			−0.968652
$802$	1.15146e10	+	1.99439e10i	0.788204	+	1.36521i
$803$	−1.77023e9	+	3.06612e9i	−0.120649	+	0.208970i
$804$	1.65603e9	−	2.86833e9i	0.112376	−	0.194640i
$805$	2.84551e9			0.192254
$806$	−1.99967e10	+	1.39583e10i	−1.34520	+	0.938989i
$807$	−3.33434e10			−2.23333
$808$	−9.06751e9	+	1.57054e10i	−0.604712	+	1.04739i
$809$	5.29367e9	−	9.16891e9i	0.351510	−	0.608832i	−0.635005	−	0.772508i	$-0.719002\pi$
$809$	5.29367e9	−	9.16891e9i	0.351510	−	0.608832i	0.986514	+	0.163676i	$0.0523351\pi$
$810$	2.62452e9	+	4.54580e9i	0.173521	+	0.300547i
$811$	−8.44691e9			−0.556064			−0.278032	−	0.960572i	$-0.589682\pi$
$811$	−8.44691e9			−0.556064			−0.278032	+	0.960572i	$0.589682\pi$
$812$	6.54398e8	+	1.13345e9i	0.0428939	+	0.0742945i
$813$	−5.08525e9	−	8.80791e9i	−0.331891	−	0.574852i
$814$	2.51973e9			0.163745
$815$	−4.24877e9	−	7.35909e9i	−0.274923	−	0.476181i
$816$	1.53068e10	−	2.65121e10i	0.986206	−	1.70816i
$817$	−9.81018e8	+	1.69917e9i	−0.0629361	+	0.109009i
$818$	−2.46272e9			−0.157318
$819$	−4.44406e9	+	3.10210e9i	−0.282674	+	0.197316i
$820$	9.92396e8			0.0628545
$821$	4.61864e8	−	7.99972e8i	0.0291281	−	0.0504514i	−0.851094	−	0.525014i	$-0.824060\pi$
$821$	4.61864e8	−	7.99972e8i	0.0291281	−	0.0504514i	0.880222	+	0.474562i	$0.157394\pi$
$822$	2.55808e9	−	4.43073e9i	0.160644	−	0.278243i
$823$	2.97774e9	+	5.15760e9i	0.186203	+	0.322514i	0.943981	−	0.329999i	$-0.107048\pi$
$823$	2.97774e9	+	5.15760e9i	0.186203	+	0.322514i	−0.757778	+	0.652512i	$0.773715\pi$
$824$	9.57368e9			0.596120
$825$	−3.66485e9	−	6.34771e9i	−0.227231	−	0.393575i
$826$	9.55282e7	+	1.65460e8i	0.00589795	+	0.0102156i
$827$	−7.33081e9			−0.450695			−0.225348	−	0.974278i	$-0.572352\pi$
$827$	−7.33081e9			−0.450695			−0.225348	+	0.974278i	$0.572352\pi$
$828$	−2.50305e9	−	4.33541e9i	−0.153237	−	0.265414i
$829$	−1.01384e10	+	1.75603e10i	−0.618059	+	1.07051i	0.371780	+	0.928321i	$0.378748\pi$
$829$	−1.01384e10	+	1.75603e10i	−0.618059	+	1.07051i	−0.989839	+	0.142189i	$0.954586\pi$
$830$	4.10522e9	−	7.11045e9i	0.249209	−	0.431642i
$831$	−3.18375e10			−1.92458
$832$	1.67317e10	+	7.83192e9i	1.00718	+	0.471451i
$833$	2.66668e10			1.59850
$834$	−6.52891e9	+	1.13084e10i	−0.389726	+	0.675026i
$835$	5.71685e9	−	9.90188e9i	0.339824	−	0.588593i
$836$	5.60672e8	+	9.71112e8i	0.0331884	+	0.0574840i
$837$	1.25087e10			0.737350
$838$	−4.35444e9	−	7.54211e9i	−0.255610	−	0.442730i
$839$	−5.98389e9	−	1.03644e10i	−0.349798	−	0.605867i	0.636416	−	0.771346i	$-0.280416\pi$
$839$	−5.98389e9	−	1.03644e10i	−0.349798	−	0.605867i	−0.986213	+	0.165479i	$0.947083\pi$
$840$	4.43097e9			0.257942
$841$	−1.26335e10	−	2.18819e10i	−0.732383	−	1.26852i
$842$	1.63607e9	−	2.83376e9i	0.0944516	−	0.163595i
$843$	6.36577e9	−	1.10258e10i	0.365978	−	0.633892i
$844$	−2.77081e9			−0.158638
$845$	−6.58888e9	−	7.89911e9i	−0.375676	−	0.450380i
$846$	2.71172e10			1.53974
$847$	1.89669e9	−	3.28517e9i	0.107252	−	0.185766i
$848$	1.78844e8	−	3.09767e8i	0.0100714	−	0.0174442i
$849$	1.96963e10	+	3.41150e10i	1.10461	+	1.91323i
$850$	−1.81273e10			−1.01243
$851$	−4.31093e9	−	7.46675e9i	−0.239783	−	0.415316i
$852$	2.56887e9	+	4.44942e9i	0.142300	+	0.246470i
$853$	−1.44625e10			−0.797853			−0.398927	−	0.916983i	$-0.630617\pi$
$853$	−1.44625e10			−0.797853			−0.398927	+	0.916983i	$0.630617\pi$
$854$	−7.40668e8	−	1.28288e9i	−0.0406931	−	0.0704826i
$855$	4.87762e9	−	8.44829e9i	0.266887	−	0.462261i
$856$	1.25270e10	−	2.16974e10i	0.682637	−	1.18236i
$857$	1.74997e10			0.949723			0.474861	−	0.880061i	$-0.342498\pi$
$857$	1.74997e10			0.949723			0.474861	+	0.880061i	$0.342498\pi$
$858$	1.03773e10	+	4.85751e9i	0.560893	+	0.262548i
$859$	−1.21484e10			−0.653945			−0.326973	−	0.945034i	$-0.606028\pi$
$859$	−1.21484e10			−0.653945			−0.326973	+	0.945034i	$0.606028\pi$
$860$	−1.92460e8	+	3.33351e8i	−0.0103180	+	0.0178713i
$861$	2.04748e9	−	3.54633e9i	0.109322	−	0.189351i
$862$	1.12411e10	+	1.94702e10i	0.597770	+	1.03537i
$863$	5.06062e9			0.268019			0.134010	−	0.990980i	$-0.457215\pi$
$863$	5.06062e9			0.268019			0.134010	+	0.990980i	$0.457215\pi$
$864$	−1.50484e9	−	2.60645e9i	−0.0793764	−	0.137484i
$865$	−3.56450e9	−	6.17389e9i	−0.187259	−	0.324341i
$866$	2.07786e10			1.08719
$867$	2.86061e10	+	4.95472e10i	1.49070	+	2.58198i
$868$	−9.66008e8	+	1.67317e9i	−0.0501374	+	0.0868405i
$869$	−3.28575e9	+	5.69108e9i	−0.169850	+	0.294188i
$870$	−2.40717e10			−1.23934
$871$	1.18868e10	−	8.29739e9i	0.609541	−	0.425479i
$872$	−3.86632e10			−1.97465
$873$	−2.08848e10	+	3.61735e10i	−1.06238	+	1.84009i
$874$	−7.63503e9	+	1.32243e10i	−0.386830	+	0.670010i
$875$	−2.61862e9	−	4.53559e9i	−0.132143	−	0.228879i
$876$	3.15473e9			0.158562
$877$	−1.14200e10	−	1.97801e10i	−0.571700	−	0.990213i	−0.996392	−	0.0848754i	$-0.972951\pi$
$877$	−1.14200e10	−	1.97801e10i	−0.571700	−	0.990213i	0.424692	−	0.905338i	$-0.360383\pi$
$878$	−1.18910e9	−	2.05958e9i	−0.0592909	−	0.102695i
$879$	2.66886e10			1.32545
$880$	−2.06989e9	−	3.58516e9i	−0.102390	−	0.177345i
$881$	−1.17368e10	+	2.03287e10i	−0.578273	+	1.00160i	0.417404	+	0.908721i	$0.362940\pi$
$881$	−1.17368e10	+	2.03287e10i	−0.578273	+	1.00160i	−0.995677	+	0.0928780i	$0.970393\pi$
$882$	−1.06846e10	+	1.85063e10i	−0.524346	+	0.908194i
$883$	−1.70477e10			−0.833302			−0.416651	−	0.909067i	$-0.636796\pi$
$883$	−1.70477e10			−0.833302			−0.416651	+	0.909067i	$0.636796\pi$
$884$	−5.83858e9	+	4.07551e9i	−0.284265	+	0.198426i
$885$	8.82960e8			0.0428193
$886$	−6.84861e9	+	1.18621e10i	−0.330814	+	0.572987i
$887$	−7.28432e9	+	1.26168e10i	−0.350474	+	0.607039i	−0.986333	−	0.164766i	$-0.947313\pi$
$887$	−7.28432e9	+	1.26168e10i	−0.350474	+	0.607039i	0.635858	+	0.771806i	$0.280646\pi$
$888$	−6.71290e9	−	1.16271e10i	−0.321710	−	0.557218i
$889$	−3.43315e9			−0.163884
$890$	4.21557e9	+	7.30159e9i	0.200443	+	0.347178i
$891$	3.21514e9	+	5.56879e9i	0.152275	+	0.263748i
$892$	−1.94040e8			−0.00915409
$893$	1.03920e10	+	1.79995e10i	0.488338	+	0.845826i
$894$	−3.63803e9	+	6.30125e9i	−0.170288	+	0.294948i
$895$	−2.53054e9	+	4.38302e9i	−0.117987	+	0.204359i
$896$	−3.50988e9			−0.163010
$897$	−3.35994e9	−	3.90619e10i	−0.155439	−	1.80709i
$898$	1.93562e10			0.891974
$899$	3.13812e10	−	5.43539e10i	1.44049	−	2.49501i
$900$	−1.82501e9	+	3.16102e9i	−0.0834483	+	0.144537i
$901$	5.03022e8	+	8.71259e8i	0.0229113	+	0.0396836i
$902$	−4.83826e9			−0.219516
$903$	7.94155e8	+	1.37552e9i	0.0358920	+	0.0621668i
$904$	1.13139e9	+	1.95963e9i	0.0509358	+	0.0882234i
$905$	2.28693e10			1.02561
$906$	−3.86424e9	−	6.69306e9i	−0.172630	−	0.299003i
$907$	−9.66075e9	+	1.67329e10i	−0.429918	+	0.744640i	−0.996866	−	0.0791142i	$-0.974791\pi$
$907$	−9.66075e9	+	1.67329e10i	−0.429918	+	0.744640i	0.566948	+	0.823754i	$0.308124\pi$
$908$	2.07149e9	−	3.58792e9i	0.0918293	−	0.159053i
$909$	3.23211e10			1.42729
$910$	2.93735e9	+	1.37494e9i	0.129214	+	0.0604838i
$911$	1.95446e10			0.856471			0.428235	−	0.903667i	$-0.359135\pi$
$911$	1.95446e10			0.856471			0.428235	+	0.903667i	$0.359135\pi$
$912$	−9.40129e9	+	1.62835e10i	−0.410398	+	0.710830i
$913$	5.02906e9	−	8.71058e9i	0.218695	−	0.378791i
$914$	−1.66433e10	−	2.88271e10i	−0.720989	−	1.24879i
$915$	−6.84595e9			−0.295433
$916$	6.13120e8	+	1.06196e9i	0.0263579	+	0.0456533i
$917$	−3.30914e9	−	5.73160e9i	−0.141717	−	0.245462i
$918$	−1.45350e10			−0.620107
$919$	−9.81678e9	−	1.70032e10i	−0.417220	−	0.722646i	0.578439	−	0.815726i	$-0.303662\pi$
$919$	−9.81678e9	−	1.70032e10i	−0.417220	−	0.722646i	−0.995659	+	0.0930800i	$0.970329\pi$
$920$	−8.95688e9	+	1.55138e10i	−0.379227	+	0.656841i
$921$	3.53625e10	−	6.12496e10i	1.49154	−	2.58342i
$922$	−1.76062e10			−0.739789
$923$	1.92713e9	+	2.24044e10i	0.0806688	+	0.937835i
$924$	9.07751e8			0.0378543
$925$	−3.14317e9	+	5.44413e9i	−0.130578	+	0.226169i
$926$	2.97445e8	−	5.15190e8i	0.0123103	−	0.0213221i
$927$	−8.53133e9	−	1.47767e10i	−0.351753	−	0.609254i
$928$	−1.51010e10			−0.620281
$929$	1.33151e10	+	2.30625e10i	0.544867	+	0.943737i	0.998615	+	0.0526074i	$0.0167532\pi$
$929$	1.33151e10	+	2.30625e10i	0.544867	+	0.943737i	−0.453748	+	0.891130i	$0.649913\pi$
$930$	−1.77670e10	−	3.07734e10i	−0.724310	−	1.25454i
$931$	−1.63785e10			−0.665197
$932$	2.21013e9	+	3.82805e9i	0.0894256	+	0.154890i
$933$	1.60918e10	−	2.78718e10i	0.648662	−	1.12352i
$934$	7.46287e9	−	1.29261e10i	0.299704	−	0.519102i
$935$	1.16437e10			0.465853
$936$	−2.92400e9	−	3.39937e10i	−0.116550	−	1.35498i
$937$	1.47566e9			0.0585999			0.0292999	−	0.999571i	$-0.490672\pi$
$937$	1.47566e9			0.0585999			0.0292999	+	0.999571i	$0.490672\pi$
$938$	−2.28530e9	+	3.95826e9i	−0.0904136	+	0.156601i
$939$	−2.39265e10	+	4.14419e10i	−0.943083	+	1.63347i
$940$	2.03875e9	+	3.53123e9i	0.0800603	+	0.138669i
$941$	−2.25755e10			−0.883231			−0.441616	−	0.897204i	$-0.645595\pi$
$941$	−2.25755e10			−0.883231			−0.441616	+	0.897204i	$0.645595\pi$
$942$	1.27815e10	+	2.21382e10i	0.498200	+	0.862908i
$943$	8.27765e9	+	1.43373e10i	0.321452	+	0.556771i
$944$	−9.51100e8			−0.0367980
$945$	−8.31783e8	−	1.44069e9i	−0.0320626	−	0.0555340i
$946$	9.38309e8	−	1.62520e9i	0.0360352	−	0.0624148i
$947$	−9.93974e9	+	1.72161e10i	−0.380321	+	0.658735i	−0.991108	−	0.133060i	$-0.957520\pi$
$947$	−9.93974e9	+	1.72161e10i	−0.380321	+	0.658735i	0.610787	+	0.791795i	$0.290853\pi$
$948$	5.85556e9			0.223223
$949$	1.25055e10	+	5.85369e9i	0.474974	+	0.222330i
$950$	1.11336e10			0.421313
$951$	5.01673e9	−	8.68922e9i	0.189142	−	0.327604i
$952$	6.71222e9	−	1.16259e10i	0.252137	−	0.436714i
$953$	−1.23018e10	−	2.13073e10i	−0.460408	−	0.797451i	0.538573	−	0.842579i	$-0.318964\pi$
$953$	−1.23018e10	−	2.13073e10i	−0.460408	−	0.797451i	−0.998981	+	0.0451281i	$0.985630\pi$
$954$	−8.06185e8			−0.0300618
$955$	−3.38012e9	−	5.85454e9i	−0.125580	−	0.217511i
$956$	3.21301e9	+	5.56510e9i	0.118935	+	0.206002i
$957$	−2.94888e10			−1.08759
$958$	5.82142e9	+	1.00830e10i	0.213919	+	0.370519i
$959$	8.87024e8	−	1.53637e9i	0.0324766	−	0.0562511i
$960$	−1.34594e10	+	2.33124e10i	−0.490995	+	0.850427i
$961$	6.51360e10			2.36749
$962$	−8.42163e8	−	9.79078e9i	−0.0304989	−	0.354572i
$963$	−4.46525e10			−1.61122
$964$	−9.15393e8	+	1.58551e9i	−0.0329108	+	0.0570031i
$965$	−1.13767e10	+	1.97051e10i	−0.407542	+	0.705884i
$966$	6.18072e9	+	1.07053e10i	0.220607	+	0.382102i
$967$	1.21598e10			0.432449			0.216224	−	0.976344i	$-0.430626\pi$
$967$	1.21598e10			0.432449			0.216224	+	0.976344i	$0.430626\pi$
$968$	1.19405e10	+	2.06816e10i	0.423116	+	0.732859i
$969$	−2.64423e10	−	4.57994e10i	−0.933611	−	1.61706i
$970$	2.49957e10			0.879353
$971$	−1.72456e10	−	2.98703e10i	−0.604522	−	1.04706i	−0.992127	−	0.125237i	$-0.960031\pi$
$971$	−1.72456e10	−	2.98703e10i	−0.604522	−	1.04706i	0.387605	−	0.921826i	$-0.373303\pi$
$972$	4.01995e9	−	6.96276e9i	0.140407	−	0.243192i
$973$	−2.26392e9	+	3.92123e9i	−0.0787892	+	0.136467i
$974$	4.93783e10			1.71230
$975$	−2.34401e10	+	1.63619e10i	−0.809921	+	0.565350i
$976$	7.37426e9			0.253889
$977$	−1.64824e10	+	2.85484e10i	−0.565445	+	0.979380i	0.431563	+	0.902083i	$0.357962\pi$
$977$	−1.64824e10	+	2.85484e10i	−0.565445	+	0.979380i	−0.997008	+	0.0772970i	$0.975371\pi$
$978$	1.84575e10	−	3.19693e10i	0.630937	−	1.09282i
$979$	5.16425e9	+	8.94474e9i	0.175901	+	0.304669i
$980$	−3.21321e9			−0.109055
$981$	3.44536e10	+	5.96755e10i	1.16518	+	2.01815i
$982$	−6.08703e9	−	1.05430e10i	−0.205123	−	0.355284i
$983$	−4.71393e10			−1.58287			−0.791435	−	0.611253i	$-0.790666\pi$
$983$	−4.71393e10			−1.58287			−0.791435	+	0.611253i	$0.790666\pi$
$984$	1.28898e10	+	2.23258e10i	0.431284	+	0.747005i
$985$	4.20837e8	−	7.28910e8i	0.0140309	−	0.0243023i
$986$	−3.64648e10	+	6.31588e10i	−1.21145	+	2.09829i
$987$	1.68252e10			0.556992
$988$	3.58601e9	−	2.50314e9i	0.118294	−	0.0825727i
$989$	−6.42131e9			−0.211075
$990$	−4.66528e9	+	8.08049e9i	−0.152811	+	0.264676i
$991$	1.18660e10	−	2.05525e10i	0.387300	−	0.670823i	−0.604786	−	0.796388i	$-0.706741\pi$
$991$	1.18660e10	−	2.05525e10i	0.387300	−	0.670823i	0.992085	+	0.125565i	$0.0400745\pi$
$992$	−1.11459e10	−	1.93053e10i	−0.362513	−	0.627892i
$993$	−8.38626e9			−0.271798
$994$	−3.54502e9	−	6.14015e9i	−0.114490	−	0.198302i
$995$	7.89122e9	+	1.36680e10i	0.253959	+	0.439870i
$996$	−8.96232e9			−0.287417
$997$	−6.00395e9	−	1.03991e10i	−0.191869	−	0.332326i	0.754001	−	0.656873i	$-0.228121\pi$
$997$	−6.00395e9	−	1.03991e10i	−0.191869	−	0.332326i	−0.945870	+	0.324547i	$0.894788\pi$
$998$	−1.84099e10	+	3.18869e10i	−0.586266	+	1.01544i
$999$	−2.52029e9	+	4.36527e9i	−0.0799782	+	0.138526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.8.c.a.9.7	yes	16
3.2	odd	2		117.8.g.d.100.2		16
4.3	odd	2		208.8.i.d.113.1		16
13.3	even	3	inner	13.8.c.a.3.7	✓	16
13.4	even	6		169.8.a.e.1.7		8
13.6	odd	12		169.8.b.e.168.12		16
13.7	odd	12		169.8.b.e.168.5		16
13.9	even	3		169.8.a.f.1.2		8
39.29	odd	6		117.8.g.d.55.2		16
52.3	odd	6		208.8.i.d.81.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.c.a.3.7	✓	16	13.3	even	3	inner
13.8.c.a.9.7	yes	16	1.1	even	1	trivial
117.8.g.d.55.2		16	39.29	odd	6
117.8.g.d.100.2		16	3.2	odd	2
169.8.a.e.1.7		8	13.4	even	6
169.8.a.f.1.2		8	13.9	even	3
169.8.b.e.168.5		16	13.7	odd	12
169.8.b.e.168.12		16	13.6	odd	12
208.8.i.d.81.1		16	52.3	odd	6
208.8.i.d.113.1		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+(5.05707 - 8.75910i) q^{2} +(35.2053 - 60.9774i) q^{3} +(12.8521 + 22.2605i) q^{4} -163.930 q^{5} +(-356.071 - 616.734i) q^{6} +(-123.469 - 213.855i) q^{7} +1554.59 q^{8} +(-1385.33 - 2399.46i) q^{9} +(-829.005 + 1435.88i) q^{10} +(-1015.56 + 1759.01i) q^{11} +1809.85 q^{12} +(7174.32 + 3358.22i) q^{13} -2497.57 q^{14} +(-5771.21 + 9996.02i) q^{15} +(6216.58 - 10767.4i) q^{16} +(17484.9 + 30284.8i) q^{17} -28022.8 q^{18} +(-10739.1 - 18600.7i) q^{19} +(-2106.84 - 3649.16i) q^{20} -17387.1 q^{21} +(10271.6 + 17790.9i) q^{22} +(35146.7 - 60875.8i) q^{23} +(54729.7 - 94794.5i) q^{24} -51252.0 q^{25} +(65696.0 - 45857.9i) q^{26} -41095.4 q^{27} +(3173.67 - 5496.95i) q^{28} +(-103098. + 178571. i) q^{29} +(58370.8 + 101101. i) q^{30} -304382. q^{31} +(36618.1 + 63424.4i) q^{32} +(71506.5 + 123853. i) q^{33} +353690. q^{34} +(20240.3 + 35057.2i) q^{35} +(35608.7 - 61676.0i) q^{36} +(61327.8 - 106223. i) q^{37} -217233. q^{38} +(457349. - 319244. i) q^{39} -254843. q^{40} +(-117759. + 203964. i) q^{41} +(-87927.5 + 152295. i) q^{42} +(-45675.1 - 79111.6i) q^{43} -52208.5 q^{44} +(227097. + 393343. i) q^{45} +(-355478. - 615706. i) q^{46} -967683. q^{47} +(-437713. - 758142. i) q^{48} +(381282. - 660400. i) q^{49} +(-259185. + 448921. i) q^{50} +2.46225e6 q^{51} +(17449.5 + 202864. i) q^{52} +28768.9 q^{53} +(-207823. + 359959. i) q^{54} +(166482. - 288354. i) q^{55} +(-191943. - 332455. i) q^{56} -1.51229e6 q^{57} +(1.04275e6 + 1.80609e6i) q^{58} +(-38248.5 - 66248.4i) q^{59} -296688. q^{60} +(296556. + 513650. i) q^{61} +(-1.53928e6 + 2.66612e6i) q^{62} +(-342090. + 592517. i) q^{63} +2.33217e6 q^{64} +(-1.17609e6 - 550512. i) q^{65} +1.44645e6 q^{66} +(915012. - 1.58485e6i) q^{67} +(-449435. + 778444. i) q^{68} +(-2.47470e6 - 4.28630e6i) q^{69} +409426. q^{70} +(1.41939e6 + 2.45845e6i) q^{71} +(-2.15361e6 - 3.73016e6i) q^{72} +1.74309e6 q^{73} +(-620278. - 1.07435e6i) q^{74} +(-1.80434e6 + 3.12521e6i) q^{75} +(276039. - 478114. i) q^{76} +501563. q^{77} +(-483445. - 5.62041e6i) q^{78} +3.23539e6 q^{79} +(-1.01908e6 + 1.76511e6i) q^{80} +(1.58293e6 - 2.74172e6i) q^{81} +(1.19103e6 + 2.06292e6i) q^{82} -4.95198e6 q^{83} +(-223460. - 387044. i) q^{84} +(-2.86630e6 - 4.96458e6i) q^{85} -923929. q^{86} +(7.25920e6 + 1.25733e7i) q^{87} +(-1.57878e6 + 2.73453e6i) q^{88} +(2.54255e6 - 4.40382e6i) q^{89} +4.59377e6 q^{90} +(-167636. - 1.94890e6i) q^{91} +1.80683e6 q^{92} +(-1.07159e7 + 1.85604e7i) q^{93} +(-4.89364e6 + 8.47603e6i) q^{94} +(1.76046e6 + 3.04920e6i) q^{95} +5.15660e6 q^{96} +(-7.53784e6 - 1.30559e7i) q^{97} +(-3.85634e6 - 6.67938e6i) q^{98} +5.62756e6 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

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