LMFDB - Embedded newform 13.8.c.a.3.5

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			3.5
Root			$-3.54173 - 6.13445i$ of defining polynomial
Character	$\chi$	$=$	13.3
Dual form			13.8.c.a.9.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.04173 + 5.26843i) q^{2} +(-12.8141 - 22.1946i) q^{3} +(45.4958 - 78.8010i) q^{4} +442.310 q^{5} +(77.9538 - 135.020i) q^{6} +(-380.773 + 659.518i) q^{7} +1332.23 q^{8} +(765.099 - 1325.19i) q^{9} +(1345.39 + 2330.28i) q^{10} +(-3055.11 - 5291.61i) q^{11} -2331.94 q^{12} +(409.818 + 7910.79i) q^{13} -4632.83 q^{14} +(-5667.79 - 9816.90i) q^{15} +(-1771.19 - 3067.80i) q^{16} +(-18763.5 + 32499.3i) q^{17} +9308.89 q^{18} +(-1697.41 + 2940.00i) q^{19} +(20123.2 - 34854.5i) q^{20} +19517.0 q^{21} +(18585.6 - 32191.3i) q^{22} +(14932.0 + 25863.0i) q^{23} +(-17071.2 - 29568.2i) q^{24} +117513. q^{25} +(-40430.9 + 26221.6i) q^{26} -95264.9 q^{27} +(34647.2 + 60010.6i) q^{28} +(21102.1 + 36549.8i) q^{29} +(34479.7 - 59720.7i) q^{30} -124016. q^{31} +(96037.4 - 166342. i) q^{32} +(-78296.9 + 135614. i) q^{33} -228294. q^{34} +(-168420. + 291712. i) q^{35} +(-69617.6 - 120581. i) q^{36} +(-71061.5 - 123082. i) q^{37} -20652.2 q^{38} +(170325. - 110465. i) q^{39} +589256. q^{40} +(35747.5 + 61916.4i) q^{41} +(59365.4 + 102824. i) q^{42} +(6381.59 - 11053.2i) q^{43} -555979. q^{44} +(338411. - 586145. i) q^{45} +(-90838.0 + 157336. i) q^{46} +437927. q^{47} +(-45392.4 + 78622.0i) q^{48} +(121795. + 210955. i) q^{49} +(357443. + 619109. i) q^{50} +961747. q^{51} +(642023. + 327613. i) q^{52} -1.01220e6 q^{53} +(-289770. - 501896. i) q^{54} +(-1.35131e6 - 2.34053e6i) q^{55} +(-507276. + 878627. i) q^{56} +87002.9 q^{57} +(-128373. + 222349. i) q^{58} +(-879873. + 1.52399e6i) q^{59} -1.03144e6 q^{60} +(845659. - 1.46472e6i) q^{61} +(-377223. - 653370. i) q^{62} +(582659. + 1.00919e6i) q^{63} +715053. q^{64} +(181266. + 3.49902e6i) q^{65} -952631. q^{66} +(-1.70928e6 - 2.96056e6i) q^{67} +(1.70732e6 + 2.95716e6i) q^{68} +(382679. - 662819. i) q^{69} -2.04915e6 q^{70} +(397498. - 688487. i) q^{71} +(1.01928e6 - 1.76545e6i) q^{72} +3.45924e6 q^{73} +(432300. - 748765. i) q^{74} +(-1.50582e6 - 2.60816e6i) q^{75} +(154450. + 267515. i) q^{76} +4.65322e6 q^{77} +(1.10006e6 + 561343. i) q^{78} +6.86376e6 q^{79} +(-783417. - 1.35692e6i) q^{80} +(-452541. - 783825. i) q^{81} +(-217468. + 376666. i) q^{82} -8.04357e6 q^{83} +(887942. - 1.53796e6i) q^{84} +(-8.29928e6 + 1.43748e7i) q^{85} +77644.2 q^{86} +(540807. - 936704. i) q^{87} +(-4.07010e6 - 7.04962e6i) q^{88} +(524871. + 909103. i) q^{89} +4.11742e6 q^{90} +(-5.37336e6 - 2.74193e6i) q^{91} +2.71737e6 q^{92} +(1.58915e6 + 2.75249e6i) q^{93} +(1.33206e6 + 2.30719e6i) q^{94} +(-750781. + 1.30039e6i) q^{95} -4.92252e6 q^{96} +(-562998. + 975142. i) q^{97} +(-740935. + 1.28334e6i) q^{98} -9.34986e6 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 $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.04173	+	5.26843i	0.268853	+	0.465668i	0.968566	−	0.248757i	$-0.0800220\pi$
$2$	3.04173	+	5.26843i	0.268853	+	0.465668i	−0.699713	+	0.714424i	$0.746689\pi$
$3$	−12.8141	−	22.1946i	−0.274008	−	0.474595i	0.695877	−	0.718161i	$-0.255016\pi$
$3$	−12.8141	−	22.1946i	−0.274008	−	0.474595i	−0.969884	+	0.243566i	$0.921683\pi$
$4$	45.4958	−	78.8010i	0.355436	−	0.615633i
$5$	442.310			1.58246			0.791228	−	0.611521i	$-0.209442\pi$
$5$	442.310			1.58246			0.791228	+	0.611521i	$0.209442\pi$
$6$	77.9538	−	135.020i	0.147336	−	0.255193i
$7$	−380.773	+	659.518i	−0.419588	+	0.726748i	−0.995898	−	0.0904833i	$-0.971159\pi$
$7$	−380.773	+	659.518i	−0.419588	+	0.726748i	0.576310	+	0.817231i	$0.304492\pi$
$8$	1332.23			0.919947
$9$	765.099	−	1325.19i	0.349840	−	0.605940i
$10$	1345.39	+	2330.28i	0.425448	+	0.736898i
$11$	−3055.11	−	5291.61i	−0.692075	−	1.19871i	−0.971157	−	0.238441i	$-0.923364\pi$
$11$	−3055.11	−	5291.61i	−0.692075	−	1.19871i	0.279082	−	0.960267i	$-0.409970\pi$
$12$	−2331.94			−0.389569
$13$	409.818	+	7910.79i	0.0517355	+	0.998661i
$13$	409.818	+	7910.79i	0.0517355	+	0.998661i
$14$	−4632.83			−0.451231
$15$	−5667.79	−	9816.90i	−0.433605	−	0.751026i
$16$	−1771.19	−	3067.80i	−0.108105	−	0.187244i
$17$	−18763.5	+	32499.3i	−0.926280	+	1.60436i	−0.136791	+	0.990600i	$0.543679\pi$
$17$	−18763.5	+	32499.3i	−0.926280	+	1.60436i	−0.789489	+	0.613764i	$0.789655\pi$
$18$	9308.89			0.376222
$19$	−1697.41	+	2940.00i	−0.0567739	+	0.0983353i	−0.893016	−	0.450026i	$-0.851415\pi$
$19$	−1697.41	+	2940.00i	−0.0567739	+	0.0983353i	0.836242	+	0.548361i	$0.184748\pi$
$20$	20123.2	−	34854.5i	0.562462	−	0.974212i
$21$	19517.0			0.459881
$22$	18585.6	−	32191.3i	0.372133	−	0.644553i
$23$	14932.0	+	25863.0i	0.255900	+	0.443232i	0.965140	−	0.261736i	$-0.0842949\pi$
$23$	14932.0	+	25863.0i	0.255900	+	0.443232i	−0.709240	+	0.704967i	$0.750962\pi$
$24$	−17071.2	−	29568.2i	−0.252072	−	0.436602i
$25$	117513.			1.50417
$26$	−40430.9	+	26221.6i	−0.451135	+	0.292585i
$27$	−95264.9			−0.931450
$28$	34647.2	+	60010.6i	0.298273	+	0.516625i
$29$	21102.1	+	36549.8i	0.160669	+	0.278287i	0.935109	−	0.354361i	$-0.115302\pi$
$29$	21102.1	+	36549.8i	0.160669	+	0.278287i	−0.774440	+	0.632648i	$0.781968\pi$
$30$	34479.7	−	59720.7i	0.233152	−	0.403832i
$31$	−124016.			−0.747674			−0.373837	−	0.927494i	$-0.621958\pi$
$31$	−124016.			−0.747674			−0.373837	+	0.927494i	$0.621958\pi$
$32$	96037.4	−	166342.i	0.518102	−	0.897379i
$33$	−78296.9	+	135614.i	−0.379267	+	0.656910i
$34$	−228294.			−0.996134
$35$	−168420.	+	291712.i	−0.663980	+	1.15005i
$36$	−69617.6	−	120581.i	−0.248691	−	0.430746i
$37$	−71061.5	−	123082.i	−0.230637	−	0.399474i	0.727359	−	0.686257i	$-0.240748\pi$
$37$	−71061.5	−	123082.i	−0.230637	−	0.399474i	−0.957996	+	0.286783i	$0.907414\pi$
$38$	−20652.2			−0.0610554
$39$	170325.	−	110465.i	0.459784	−	0.298194i
$40$	589256.			1.45578
$41$	35747.5	+	61916.4i	0.0810031	+	0.140301i	0.903681	−	0.428206i	$-0.140854\pi$
$41$	35747.5	+	61916.4i	0.0810031	+	0.140301i	−0.822678	+	0.568508i	$0.807521\pi$
$42$	59365.4	+	102824.i	0.123641	+	0.214152i
$43$	6381.59	−	11053.2i	0.0122402	−	0.0212007i	−0.859840	−	0.510563i	$-0.829437\pi$
$43$	6381.59	−	11053.2i	0.0122402	−	0.0212007i	0.872081	+	0.489362i	$0.162770\pi$
$44$	−555979.			−0.983952
$45$	338411.	−	586145.i	0.553606	−	0.958873i
$46$	−90838.0	+	157336.i	−0.137599	+	0.238328i
$47$	437927.			0.615261			0.307631	−	0.951506i	$-0.400464\pi$
$47$	437927.			0.615261			0.307631	+	0.951506i	$0.400464\pi$
$48$	−45392.4	+	78622.0i	−0.0592433	+	0.102612i
$49$	121795.	+	210955.i	0.147892	+	0.256156i
$50$	357443.	+	619109.i	0.404400	+	0.700442i
$51$	961747.			1.01523
$52$	642023.	+	327613.i	0.633197	+	0.323110i
$53$	−1.01220e6			−0.933900			−0.466950	−	0.884284i	$-0.654647\pi$
$53$	−1.01220e6			−0.933900			−0.466950	+	0.884284i	$0.654647\pi$
$54$	−289770.	−	501896.i	−0.250423	−	0.433746i
$55$	−1.35131e6	−	2.34053e6i	−1.09518	−	1.89690i
$56$	−507276.	+	878627.i	−0.385999	+	0.668570i
$57$	87002.9			0.0622260
$58$	−128373.	+	222349.i	−0.0863927	+	0.149637i
$59$	−879873.	+	1.52399e6i	−0.557748	+	0.966048i	0.439936	+	0.898029i	$0.355001\pi$
$59$	−879873.	+	1.52399e6i	−0.557748	+	0.966048i	−0.997684	+	0.0680190i	$0.978332\pi$
$60$	−1.03144e6			−0.616475
$61$	845659.	−	1.46472e6i	0.477025	−	0.826231i	−0.522629	−	0.852560i	$-0.675049\pi$
$61$	845659.	−	1.46472e6i	0.477025	−	0.826231i	0.999653	+	0.0263296i	$0.00838195\pi$
$62$	−377223.	−	653370.i	−0.201015	−	0.348167i
$63$	582659.	+	1.00919e6i	0.293577	+	0.508490i
$64$	715053.			0.340964
$65$	181266.	+	3.49902e6i	0.0818692	+	1.58034i
$66$	−952631.			−0.407869
$67$	−1.70928e6	−	2.96056e6i	−0.694308	−	1.20258i	−0.970414	−	0.241449i	$-0.922377\pi$
$67$	−1.70928e6	−	2.96056e6i	−0.694308	−	1.20258i	0.276106	−	0.961127i	$-0.410956\pi$
$68$	1.70732e6	+	2.95716e6i	0.658466	+	1.14050i
$69$	382679.	−	662819.i	0.140237	−	0.242898i
$70$	−2.04915e6			−0.714053
$71$	397498.	−	688487.i	0.131805	−	0.228292i	−0.792568	−	0.609784i	$-0.791256\pi$
$71$	397498.	−	688487.i	0.131805	−	0.228292i	0.924372	+	0.381492i	$0.124589\pi$
$72$	1.01928e6	−	1.76545e6i	0.321834	−	0.557433i
$73$	3.45924e6			1.04076			0.520380	−	0.853935i	$-0.325790\pi$
$73$	3.45924e6			1.04076			0.520380	+	0.853935i	$0.325790\pi$
$74$	432300.	−	748765.i	0.124015	−	0.214800i
$75$	−1.50582e6	−	2.60816e6i	−0.412153	−	0.713870i
$76$	154450.	+	267515.i	0.0403590	+	0.0699038i
$77$	4.65322e6			1.16155
$78$	1.10006e6	+	561343.i	0.262474	+	0.133936i
$79$	6.86376e6			1.56627			0.783136	−	0.621851i	$-0.213619\pi$
$79$	6.86376e6			1.56627			0.783136	+	0.621851i	$0.213619\pi$
$80$	−783417.	−	1.35692e6i	−0.171072	−	0.296305i
$81$	−452541.	−	783825.i	−0.0946152	−	0.163878i
$82$	−217468.	+	376666.i	−0.0435559	+	0.0754410i
$83$	−8.04357e6			−1.54410			−0.772050	−	0.635562i	$-0.780768\pi$
$83$	−8.04357e6			−1.54410			−0.772050	+	0.635562i	$0.780768\pi$
$84$	887942.	−	1.53796e6i	0.163458	−	0.283118i
$85$	−8.29928e6	+	1.43748e7i	−1.46580	+	2.53884i
$86$	77644.2			0.0131633
$87$	540807.	−	936704.i	0.0880490	−	0.152505i
$88$	−4.07010e6	−	7.04962e6i	−0.636672	−	1.10275i
$89$	524871.	+	909103.i	0.0789201	+	0.136694i	0.902784	−	0.430094i	$-0.141519\pi$
$89$	524871.	+	909103.i	0.0789201	+	0.136694i	−0.823864	+	0.566787i	$0.808186\pi$
$90$	4.11742e6			0.595355
$91$	−5.37336e6	−	2.74193e6i	−0.747482	−	0.381428i
$92$	2.71737e6			0.363824
$93$	1.58915e6	+	2.75249e6i	0.204868	+	0.354842i
$94$	1.33206e6	+	2.30719e6i	0.165415	+	0.286507i
$95$	−750781.	+	1.30039e6i	−0.0898422	+	0.155611i
$96$	−4.92252e6			−0.567856
$97$	−562998.	+	975142.i	−0.0626334	+	0.108484i	−0.895642	−	0.444776i	$-0.853283\pi$
$97$	−562998.	+	975142.i	−0.0626334	+	0.108484i	0.833008	+	0.553260i	$0.186617\pi$
$98$	−740935.	+	1.28334e6i	−0.0795223	+	0.137737i
$99$	−9.34986e6			−0.968460
$100$	5.34635e6	−	9.26015e6i	0.534635	−	0.926015i
$101$	−6.27747e6	−	1.08729e7i	−0.606261	−	1.05008i	−0.991851	−	0.127405i	$-0.959335\pi$
$101$	−6.27747e6	−	1.08729e7i	−0.606261	−	1.05008i	0.385589	−	0.922670i	$-0.373998\pi$
$102$	2.92537e6	+	5.06689e6i	0.272948	+	0.472760i
$103$	1.06219e7			0.957793			0.478896	−	0.877871i	$-0.341037\pi$
$103$	1.06219e7			0.957793			0.478896	+	0.877871i	$0.341037\pi$
$104$	545969.	+	1.05390e7i	0.0475939	+	0.918715i
$105$	8.63257e6			0.727742
$106$	−3.07883e6	−	5.33270e6i	−0.251082	−	0.434887i
$107$	−1.32550e6	−	2.29584e6i	−0.104602	−	0.181175i	0.808974	−	0.587845i	$-0.200023\pi$
$107$	−1.32550e6	−	2.29584e6i	−0.104602	−	0.181175i	−0.913575	+	0.406670i	$0.866690\pi$
$108$	−4.33415e6	+	7.50697e6i	−0.331071	+	0.573431i
$109$	1.71869e7			1.27117			0.635587	−	0.772029i	$-0.280758\pi$
$109$	1.71869e7			1.27117			0.635587	+	0.772029i	$0.280758\pi$
$110$	8.22061e6	−	1.42385e7i	0.588884	−	1.01998i
$111$	−1.82117e6	+	3.15437e6i	−0.126392	+	0.218918i
$112$	2.69769e6			0.181438
$113$	−4.27067e6	+	7.39703e6i	−0.278434	+	0.482261i	−0.970996	−	0.239097i	$-0.923149\pi$
$113$	−4.27067e6	+	7.39703e6i	−0.278434	+	0.482261i	0.692562	+	0.721358i	$0.256482\pi$
$114$	264639.	+	458368.i	0.0167297	+	0.0289766i
$115$	6.60456e6	+	1.14394e7i	0.404950	+	0.701394i
$116$	3.84022e6			0.228430
$117$	1.07969e7	+	5.50945e6i	0.623228	+	0.318023i
$118$	−1.07053e7			−0.599810
$119$	−1.42893e7	−	2.47497e7i	−0.777312	−	1.34634i
$120$	−7.55077e6	−	1.30783e7i	−0.398894	−	0.690904i
$121$	−8.92385e6	+	1.54566e7i	−0.457934	+	0.793166i
$122$	1.02891e7			0.512998
$123$	916141.	−	1.58680e6i	0.0443909	−	0.0768874i
$124$	−5.64221e6	+	9.77259e6i	−0.265750	+	0.460293i
$125$	1.74217e7			0.797822
$126$	−3.54458e6	+	6.13939e6i	−0.157858	+	0.273419i
$127$	−4.74475e6	−	8.21815e6i	−0.205542	−	0.356009i	0.744763	−	0.667329i	$-0.232562\pi$
$127$	−4.74475e6	−	8.21815e6i	−0.205542	−	0.356009i	−0.950305	+	0.311320i	$0.899229\pi$
$128$	−1.01178e7	−	1.75245e7i	−0.426433	−	0.738604i
$129$	−327096.			−0.0134157
$130$	−1.78830e7	+	1.15981e7i	−0.713901	+	0.463003i
$131$	−9.63395e6			−0.374417			−0.187208	−	0.982320i	$-0.559944\pi$
$131$	−9.63395e6			−0.374417			−0.187208	+	0.982320i	$0.559944\pi$
$132$	7.12435e6	+	1.23397e7i	0.269610	+	0.466979i
$133$	−1.29266e6	−	2.23895e6i	−0.0476433	−	0.0825207i
$134$	1.03983e7	−	1.80105e7i	0.373334	−	0.646633i
$135$	−4.21366e7			−1.47398
$136$	−2.49972e7	+	4.32964e7i	−0.852129	+	1.47593i
$137$	3.18362e6	−	5.51419e6i	0.105779	−	0.183214i	−0.808277	−	0.588802i	$-0.799600\pi$
$137$	3.18362e6	−	5.51419e6i	0.105779	−	0.183214i	0.914056	+	0.405588i	$0.132933\pi$
$138$	4.65602e6			0.150813
$139$	1.27749e7	−	2.21268e7i	0.403465	−	0.698822i	−0.590677	−	0.806908i	$-0.701139\pi$
$139$	1.27749e7	−	2.21268e7i	0.403465	−	0.698822i	0.994141	+	0.108087i	$0.0344724\pi$
$140$	1.53248e7	+	2.65433e7i	0.472004	+	0.817536i
$141$	−5.61163e6	−	9.71963e6i	−0.168586	−	0.292000i
$142$	4.83632e6			0.141744
$143$	4.06088e7	−	2.63369e7i	1.16130	−	0.753164i
$144$	−5.42056e6			−0.151278
$145$	9.33365e6	+	1.61664e7i	0.254251	+	0.440376i
$146$	1.05221e7	+	1.82248e7i	0.279812	+	0.484648i
$147$	3.12138e6	−	5.40639e6i	0.0810468	−	0.140377i
$148$	−1.29320e7			−0.327906
$149$	3.09717e7	−	5.36446e7i	0.767032	−	1.32854i	−0.172134	−	0.985074i	$-0.555066\pi$
$149$	3.09717e7	−	5.36446e7i	0.767032	−	1.32854i	0.939166	−	0.343464i	$-0.111600\pi$
$150$	9.16059e6	−	1.58666e7i	0.221617	−	0.383853i
$151$	−4.34129e7			−1.02612			−0.513061	−	0.858352i	$-0.671489\pi$
$151$	−4.34129e7			−1.02612			−0.513061	+	0.858352i	$0.671489\pi$
$152$	−2.26133e6	+	3.91674e6i	−0.0522290	+	0.0904633i
$153$	2.87119e7	+	4.97304e7i	0.648099	+	1.12254i
$154$	1.41538e7	+	2.45152e7i	0.312285	+	0.540894i
$155$	−5.48535e7			−1.18316
$156$	−955672.	−	1.84475e7i	−0.0201545	−	0.389047i
$157$	5.59503e7			1.15386			0.576931	−	0.816793i	$-0.304250\pi$
$157$	5.59503e7			1.15386			0.576931	+	0.816793i	$0.304250\pi$
$158$	2.08777e7	+	3.61612e7i	0.421097	+	0.729362i
$159$	1.29704e7	+	2.24654e7i	0.255896	+	0.443224i
$160$	4.24783e7	−	7.35746e7i	0.819874	−	1.42006i
$161$	−2.27428e7			−0.429490
$162$	2.75302e6	−	4.76836e6i	0.0508752	−	0.0881184i
$163$	4.25961e7	−	7.37786e7i	0.770395	−	1.33436i	−0.166952	−	0.985965i	$-0.553392\pi$
$163$	4.25961e7	−	7.37786e7i	0.770395	−	1.33436i	0.937347	−	0.348398i	$-0.113274\pi$
$164$	6.50544e6			0.115166
$165$	−3.46315e7	+	5.99835e7i	−0.600174	+	1.03953i
$166$	−2.44663e7	−	4.23769e7i	−0.415136	−	0.719037i
$167$	−3.21320e6	−	5.56543e6i	−0.0533864	−	0.0924679i	0.838097	−	0.545521i	$-0.183668\pi$
$167$	−3.21320e6	−	5.56543e6i	−0.0533864	−	0.0924679i	−0.891484	+	0.453053i	$0.850335\pi$
$168$	2.60011e7			0.423066
$169$	−6.24126e7	+	6.48396e6i	−0.994647	+	0.103332i
$170$	−1.00977e8			−1.57634
$171$	2.59737e6	+	4.49878e6i	0.0397235	+	0.0688032i
$172$	−580671.	−	1.00575e6i	−0.00870122	−	0.0150710i
$173$	−1.60915e7	+	2.78714e7i	−0.236285	+	0.409258i	−0.959645	−	0.281213i	$-0.909263\pi$
$173$	−1.60915e7	+	2.78714e7i	−0.236285	+	0.409258i	0.723360	+	0.690471i	$0.242597\pi$
$174$	6.57994e6			0.0946891
$175$	−4.47458e7	+	7.75020e7i	−0.631131	+	1.09315i
$176$	−1.08224e7	+	1.87449e7i	−0.149634	+	0.259173i
$177$	4.50990e7			0.611309
$178$	−3.19303e6	+	5.53049e6i	−0.0424358	+	0.0735010i
$179$	5.69842e7	+	9.86996e7i	0.742624	+	1.28626i	0.951297	+	0.308277i	$0.0997524\pi$
$179$	5.69842e7	+	9.86996e7i	0.742624	+	1.28626i	−0.208673	+	0.977986i	$0.566914\pi$
$180$	−3.07925e7	−	5.33343e7i	−0.393543	−	0.681636i
$181$	−1.35157e8			−1.69420			−0.847100	−	0.531434i	$-0.821653\pi$
$181$	−1.35157e8			−1.69420			−0.847100	+	0.531434i	$0.821653\pi$
$182$	−1.89862e6	−	3.66494e7i	−0.0233446	−	0.450626i
$183$	−4.33453e7			−0.522833
$184$	1.98928e7	+	3.44553e7i	0.235414	+	0.407749i
$185$	−3.14312e7	−	5.44405e7i	−0.364972	−	0.632151i
$186$	−9.66753e6	+	1.67446e7i	−0.110159	+	0.190801i
$187$	2.29298e8			2.56422
$188$	1.99239e7	−	3.45091e7i	0.218686	−	0.378775i
$189$	3.62743e7	−	6.28289e7i	0.390825	−	0.676930i
$190$	−9.13468e6			−0.0966175
$191$	−3.40819e7	+	5.90316e7i	−0.353922	+	0.613010i	−0.986933	−	0.161132i	$-0.948485\pi$
$191$	−3.40819e7	+	5.90316e7i	−0.353922	+	0.613010i	0.633011	+	0.774143i	$0.281819\pi$
$192$	−9.16274e6	−	1.58703e7i	−0.0934267	−	0.161820i
$193$	−4.11944e7	−	7.13508e7i	−0.412466	−	0.714412i	0.582693	−	0.812692i	$-0.301999\pi$
$193$	−4.11944e7	−	7.13508e7i	−0.412466	−	0.714412i	−0.995159	+	0.0982808i	$0.968666\pi$
$194$	−6.84995e6			−0.0673568
$195$	7.53366e7	−	4.88598e7i	0.727587	−	0.471879i
$196$	2.21647e7			0.210264
$197$	−7.16966e6	−	1.24182e7i	−0.0668139	−	0.115725i	0.830683	−	0.556745i	$-0.187950\pi$
$197$	−7.16966e6	−	1.24182e7i	−0.0668139	−	0.115725i	−0.897497	+	0.441020i	$0.854617\pi$
$198$	−2.84397e7	−	4.92590e7i	−0.260374	−	0.450981i
$199$	−4.68223e7	+	8.10985e7i	−0.421179	+	0.729503i	−0.996055	−	0.0887373i	$-0.971717\pi$
$199$	−4.68223e7	+	8.10985e7i	−0.421179	+	0.729503i	0.574876	+	0.818240i	$0.305050\pi$
$200$	1.56554e8			1.38375
$201$	−4.38057e7	+	7.58737e7i	−0.380491	+	0.659030i
$202$	3.81887e7	−	6.61448e7i	0.325991	−	0.564632i
$203$	−3.21404e7			−0.269659
$204$	4.37554e7	−	7.57866e7i	0.360850	−	0.625010i
$205$	1.58115e7	+	2.73862e7i	0.128184	+	0.222021i
$206$	3.23089e7	+	5.59607e7i	0.257506	+	0.446013i
$207$	4.56978e7			0.358096
$208$	2.35428e7	−	1.52688e7i	0.181400	−	0.117647i
$209$	2.07431e7			0.157167
$210$	2.62579e7	+	4.54801e7i	0.195656	+	0.338886i
$211$	7.18654e7	+	1.24475e8i	0.526661	+	0.912204i	0.999517	+	0.0310642i	$0.00988964\pi$
$211$	7.18654e7	+	1.24475e8i	0.526661	+	0.912204i	−0.472856	+	0.881140i	$0.656777\pi$
$212$	−4.60508e7	+	7.97623e7i	−0.331941	+	0.574939i
$213$	−2.03743e7			−0.144462
$214$	8.06365e6	−	1.39666e7i	0.0562449	−	0.0974191i
$215$	2.82264e6	−	4.88895e6i	0.0193696	−	0.0335491i
$216$	−1.26914e8			−0.856885
$217$	4.72220e7	−	8.17909e7i	0.313715	−	0.543370i
$218$	5.22779e7	+	9.05479e7i	0.341759	+	0.591944i
$219$	−4.43269e7	−	7.67765e7i	−0.285176	−	0.493940i
$220$	−2.45915e8			−1.55706
$221$	−2.64785e8	−	1.35115e8i	−1.65014	−	0.842037i
$222$	−2.21581e7			−0.135924
$223$	−4.88956e7	−	8.46897e7i	−0.295259	−	0.511403i	0.679786	−	0.733410i	$-0.262073\pi$
$223$	−4.88956e7	−	8.46897e7i	−0.295259	−	0.511403i	−0.975045	+	0.222007i	$0.928739\pi$
$224$	7.31369e7	+	1.26677e8i	0.434779	+	0.753060i
$225$	8.99091e7	−	1.55727e8i	0.526217	−	0.911435i
$226$	−5.19609e7			−0.299431
$227$	−7.17206e7	+	1.24224e8i	−0.406962	+	0.704878i	−0.994548	−	0.104284i	$-0.966745\pi$
$227$	−7.17206e7	+	1.24224e8i	−0.406962	+	0.704878i	0.587586	+	0.809162i	$0.300078\pi$
$228$	3.95826e6	−	6.85591e6i	0.0221173	−	0.0383084i
$229$	1.62202e8			0.892551			0.446275	−	0.894896i	$-0.352750\pi$
$229$	1.62202e8			0.892551			0.446275	+	0.894896i	$0.352750\pi$
$230$	−4.01786e7	+	6.95913e7i	−0.217744	+	0.377144i
$231$	−5.96267e7	−	1.03276e8i	−0.318272	−	0.551264i
$232$	2.81127e7	+	4.86926e7i	0.147807	+	0.256009i
$233$	6.89729e7			0.357217			0.178609	−	0.983920i	$-0.442840\pi$
$233$	6.89729e7			0.357217			0.178609	+	0.983920i	$0.442840\pi$
$234$	3.81495e6	+	7.36407e7i	0.0194640	+	0.375718i
$235$	1.93700e8			0.973624
$236$	8.00611e7	+	1.38670e8i	0.396487	+	0.686736i
$237$	−8.79527e7	−	1.52338e8i	−0.429170	−	0.743345i
$238$	8.69281e7	−	1.50564e8i	0.417966	−	0.723938i
$239$	−2.20779e8			−1.04608			−0.523040	−	0.852308i	$-0.675202\pi$
$239$	−2.20779e8			−1.04608			−0.523040	+	0.852308i	$0.675202\pi$
$240$	−2.00775e7	+	3.47753e7i	−0.0937498	+	0.162379i
$241$	−3.90899e7	+	6.77057e7i	−0.179889	+	0.311577i	−0.941842	−	0.336055i	$-0.890907\pi$
$241$	−3.90899e7	+	6.77057e7i	−0.179889	+	0.311577i	0.761953	+	0.647632i	$0.224241\pi$
$242$	−1.08576e8			−0.492469
$243$	−1.15770e8	+	2.00519e8i	−0.517576	+	0.896467i
$244$	−7.69478e7	−	1.33278e8i	−0.339103	−	0.587344i
$245$	5.38712e7	+	9.33076e7i	0.234032	+	0.405355i
$246$	1.11466e7			0.0477386
$247$	−2.39533e7	−	1.22230e7i	−0.101141	−	0.0516105i
$248$	−1.65217e8			−0.687820
$249$	1.03071e8	+	1.78524e8i	0.423095	+	0.732822i
$250$	5.29921e7	+	9.17850e7i	0.214497	+	0.371520i
$251$	1.42200e8	−	2.46297e8i	0.567597	−	0.983107i	−0.429206	−	0.903207i	$-0.641206\pi$
$251$	1.42200e8	−	2.46297e8i	0.567597	−	0.983107i	0.996803	−	0.0799004i	$-0.0254602\pi$
$252$	1.06034e8			0.417391
$253$	9.12378e7	−	1.58028e8i	0.354204	−	0.613499i
$254$	2.88645e7	−	4.99947e7i	0.110521	−	0.191428i
$255$	4.25390e8			1.60656
$256$	1.07315e8	−	1.85874e8i	0.399778	−	0.692435i
$257$	−2.62485e6	−	4.54637e6i	−0.00964580	−	0.0167070i	0.861162	−	0.508330i	$-0.169737\pi$
$257$	−2.62485e6	−	4.54637e6i	−0.00964580	−	0.0167070i	−0.870808	+	0.491623i	$0.836404\pi$
$258$	−994938.	−	1.72328e6i	−0.00360684	−	0.00624723i
$259$	1.08233e8			0.387090
$260$	2.83973e8	+	1.44907e8i	1.00201	+	0.511307i
$261$	6.45807e7			0.224833
$262$	−2.93039e7	−	5.07558e7i	−0.100663	−	0.174354i
$263$	1.24742e8	+	2.16060e8i	0.422833	+	0.732369i	0.996215	−	0.0869194i	$-0.0277023\pi$
$263$	1.24742e8	+	2.16060e8i	0.422833	+	0.732369i	−0.573382	+	0.819288i	$0.694369\pi$
$264$	−1.04309e8	+	1.80669e8i	−0.348906	+	0.604323i
$265$	−4.47706e8			−1.47786
$266$	7.86381e6	−	1.36205e7i	0.0256181	−	0.0443719i
$267$	1.34515e7	−	2.32986e7i	0.0432494	−	0.0749102i
$268$	−3.11061e8			−0.987127
$269$	2.09014e8	−	3.62024e8i	0.654701	−	1.13398i	−0.327267	−	0.944932i	$-0.606128\pi$
$269$	2.09014e8	−	3.62024e8i	0.654701	−	1.13398i	0.981969	−	0.189044i	$-0.0605390\pi$
$270$	−1.28168e8	−	2.21994e8i	−0.396284	−	0.686384i
$271$	2.56322e7	+	4.43963e7i	0.0782336	+	0.135505i	0.902488	−	0.430715i	$-0.141739\pi$
$271$	2.56322e7	+	4.43963e7i	0.0782336	+	0.135505i	−0.824254	+	0.566220i	$0.808405\pi$
$272$	1.32935e8			0.400542
$273$	7.99842e6	+	1.54395e8i	0.0237922	+	0.459266i
$274$	3.87348e7			0.113756
$275$	−3.59016e8	−	6.21833e8i	−1.04100	−	1.80306i
$276$	−3.48206e7	−	6.03110e7i	−0.0996905	−	0.172669i
$277$	−2.55392e8	+	4.42351e8i	−0.721984	+	1.25051i	0.238219	+	0.971211i	$0.423436\pi$
$277$	−2.55392e8	+	4.42351e8i	−0.721984	+	1.25051i	−0.960203	+	0.279302i	$0.909897\pi$
$278$	1.55431e8			0.433891
$279$	−9.48846e7	+	1.64345e8i	−0.261566	+	0.453045i
$280$	−2.24373e8	+	3.88626e8i	−0.610826	+	1.05798i
$281$	−1.08839e8			−0.292626			−0.146313	−	0.989238i	$-0.546741\pi$
$281$	−1.08839e8			−0.292626			−0.146313	+	0.989238i	$0.546741\pi$
$282$	3.41381e7	−	5.91289e7i	0.0906499	−	0.157010i
$283$	2.98734e8	+	5.17423e8i	0.783488	+	1.35704i	0.929898	+	0.367817i	$0.119895\pi$
$283$	2.98734e8	+	5.17423e8i	0.783488	+	1.35704i	−0.146410	+	0.989224i	$0.546772\pi$
$284$	−3.61690e7	−	6.26465e7i	−0.0936962	−	0.162287i
$285$	3.84822e7			0.0984698
$286$	2.62275e8	+	1.33835e8i	0.662943	+	0.338288i
$287$	−5.44467e7			−0.135952
$288$	−1.46956e8	−	2.54536e8i	−0.362505	−	0.627878i
$289$	−4.98968e8	−	8.64237e8i	−1.21599	−	2.10616i
$290$	−5.67808e7	+	9.83473e7i	−0.136713	+	0.236793i
$291$	2.88572e7			0.0686481
$292$	1.57381e8	−	2.72592e8i	0.369923	−	0.640726i
$293$	−1.24556e8	+	2.15738e8i	−0.289287	+	0.501060i	−0.973640	−	0.228091i	$-0.926751\pi$
$293$	−1.24556e8	+	2.15738e8i	−0.289287	+	0.501060i	0.684353	+	0.729151i	$0.260085\pi$
$294$	3.79776e7			0.0871588
$295$	−3.89177e8	+	6.74074e8i	−0.882612	+	1.52873i
$296$	−9.46700e7	−	1.63973e8i	−0.212174	−	0.367495i
$297$	2.91045e8	+	5.04105e8i	0.644633	+	1.11654i
$298$	3.76830e8			0.824876
$299$	−1.98477e8	+	1.28723e8i	−0.429399	+	0.278488i
$300$	−2.74034e8			−0.585976
$301$	4.85987e6	+	8.41755e6i	0.0102717	+	0.0177911i
$302$	−1.32050e8	−	2.28718e8i	−0.275876	−	0.477832i
$303$	−1.60880e8	+	2.78652e8i	−0.332240	+	0.575457i
$304$	1.20258e7			0.0245502
$305$	3.74043e8	−	6.47862e8i	0.754870	−	1.30747i
$306$	−1.74667e8	+	3.02533e8i	−0.348487	+	0.603597i
$307$	−4.09382e7			−0.0807503			−0.0403752	−	0.999185i	$-0.512855\pi$
$307$	−4.09382e7			−0.0807503			−0.0403752	+	0.999185i	$0.512855\pi$
$308$	2.11702e8	−	3.66678e8i	0.412855	−	0.715085i
$309$	−1.36110e8	−	2.35749e8i	−0.262443	−	0.454564i
$310$	−1.66850e8	−	2.88992e8i	−0.318097	−	0.550959i
$311$	9.99852e8			1.88484			0.942420	−	0.334432i	$-0.108545\pi$
$311$	9.99852e8			1.88484			0.942420	+	0.334432i	$0.108545\pi$
$312$	2.26912e8	−	1.47164e8i	0.422977	−	0.274323i
$313$	3.00398e8			0.553722			0.276861	−	0.960910i	$-0.410706\pi$
$313$	3.00398e8			0.553722			0.276861	+	0.960910i	$0.410706\pi$
$314$	1.70186e8	+	2.94770e8i	0.310220	+	0.537316i
$315$	2.57716e8	+	4.46377e8i	0.464573	+	0.804664i
$316$	3.12272e8	−	5.40871e8i	0.556709	−	0.964248i
$317$	−3.26439e8			−0.575566			−0.287783	−	0.957696i	$-0.592918\pi$
$317$	−3.26439e8			−0.575566			−0.287783	+	0.957696i	$0.592918\pi$
$318$	−7.89048e7	+	1.36667e8i	−0.137597	+	0.238325i
$319$	1.28938e8	−	2.23328e8i	0.222390	−	0.385190i
$320$	3.16275e8			0.539560
$321$	−3.39702e7	+	5.88381e7i	−0.0573232	+	0.0992867i
$322$	−6.91774e7	−	1.19819e8i	−0.115470	−	0.200000i
$323$	−6.36986e7	−	1.10329e8i	−0.105177	−	0.182172i
$324$	−8.23549e7			−0.134518
$325$	4.81589e7	+	9.29621e8i	0.0778189	+	1.50215i
$326$	5.18263e8			0.828493
$327$	−2.20234e8	−	3.81457e8i	−0.348311	−	0.603293i
$328$	4.76237e7	+	8.24866e7i	0.0745186	+	0.129070i
$329$	−1.66751e8	+	2.88821e8i	−0.258156	+	0.447140i
$330$	−4.21358e8			−0.645435
$331$	3.90680e8	−	6.76678e8i	0.592139	−	1.02561i	−0.401805	−	0.915725i	$-0.631617\pi$
$331$	3.90680e8	−	6.76678e8i	0.592139	−	1.02561i	0.993944	−	0.109889i	$-0.0350495\pi$
$332$	−3.65948e8	+	6.33841e8i	−0.548828	+	0.950599i
$333$	−2.17476e8			−0.322743
$334$	1.95474e7	−	3.38570e7i	0.0287062	−	0.0497206i
$335$	−7.56032e8	−	1.30949e9i	−1.09871	−	1.90302i
$336$	−3.45684e7	−	5.98743e7i	−0.0497155	−	0.0861098i
$337$	7.52036e7			0.107037			0.0535185	−	0.998567i	$-0.482956\pi$
$337$	7.52036e7			0.107037			0.0535185	+	0.998567i	$0.482956\pi$
$338$	−2.24002e8	−	3.09094e8i	−0.315533	−	0.435393i
$339$	2.18899e8			0.305172
$340$	7.55164e8	+	1.30798e9i	1.04199	+	1.80479i
$341$	3.78883e8	+	6.56245e8i	0.517446	+	0.896243i
$342$	−1.58010e7	+	2.73681e7i	−0.0213596	+	0.0369959i
$343$	−8.12671e8			−1.08739
$344$	8.50171e6	−	1.47254e7i	0.0112603	−	0.0195035i
$345$	1.69263e8	−	2.93172e8i	0.221919	−	0.384375i
$346$	−1.95784e8			−0.254104
$347$	−3.49912e8	+	6.06065e8i	−0.449578	+	0.778692i	−0.998358	−	0.0572742i	$-0.981759\pi$
$347$	−3.49912e8	+	6.06065e8i	−0.449578	+	0.778692i	0.548780	+	0.835967i	$0.315092\pi$
$348$	−4.92088e7	−	8.52322e7i	−0.0625916	−	0.108412i
$349$	4.75572e8	+	8.23715e8i	0.598863	+	1.03726i	0.992989	+	0.118205i	$0.0377140\pi$
$349$	4.75572e8	+	8.23715e8i	0.598863	+	1.03726i	−0.394126	+	0.919056i	$0.628953\pi$
$350$	−5.44418e8			−0.678726
$351$	−3.90412e7	−	7.53620e8i	−0.0481891	−	0.930203i
$352$	−1.17362e9			−1.43426
$353$	−4.71826e8	−	8.17227e8i	−0.570914	−	0.988852i	−0.996472	−	0.0839212i	$-0.973256\pi$
$353$	−4.71826e8	−	8.17227e8i	−0.570914	−	0.988852i	0.425558	−	0.904931i	$-0.360078\pi$
$354$	1.37179e8	+	2.37601e8i	0.164352	+	0.284667i
$355$	1.75817e8	−	3.04525e8i	0.208575	−	0.361263i
$356$	9.55177e7			0.112204
$357$	−3.66207e8	+	6.34290e8i	−0.425979	+	0.737817i
$358$	−3.46661e8	+	6.00434e8i	−0.399314	+	0.691632i
$359$	−6.40002e8			−0.730047			−0.365024	−	0.930998i	$-0.618939\pi$
$359$	−6.40002e8			−0.730047			−0.365024	+	0.930998i	$0.618939\pi$
$360$	4.50840e8	−	7.80877e8i	0.509288	−	0.882113i
$361$	4.41173e8	+	7.64135e8i	0.493553	+	0.854860i
$362$	−4.11112e8	−	7.12067e8i	−0.455491	−	0.788934i
$363$	4.57403e8			0.501910
$364$	−4.60532e8	+	2.98680e8i	−0.500501	+	0.324602i
$365$	1.53006e9			1.64696
$366$	−1.31845e8	−	2.28362e8i	−0.140565	−	0.243467i
$367$	−4.09011e8	−	7.08429e8i	−0.431921	−	0.748109i	0.565118	−	0.825010i	$-0.308831\pi$
$367$	−4.09011e8	−	7.08429e8i	−0.431921	−	0.748109i	−0.997039	+	0.0769013i	$0.975497\pi$
$368$	5.28949e7	−	9.16166e7i	0.0553282	−	0.0958312i
$369$	1.09401e8			0.113352
$370$	1.91210e8	−	3.31186e8i	0.196248	−	0.339912i
$371$	3.85418e8	−	6.67564e8i	0.391853	−	0.678710i
$372$	2.89199e8			0.291270
$373$	3.32688e8	−	5.76232e8i	0.331937	−	0.574932i	−0.650954	−	0.759117i	$-0.725631\pi$
$373$	3.32688e8	−	5.76232e8i	0.331937	−	0.574932i	0.982892	+	0.184185i	$0.0589644\pi$
$374$	6.97463e8	+	1.20804e9i	0.689399	+	1.19407i
$375$	−2.23243e8	−	3.86668e8i	−0.218609	−	0.378642i
$376$	5.83418e8			0.566008
$377$	−2.80490e8	+	1.81913e8i	−0.269602	+	0.174851i
$378$	4.41346e8			0.420299
$379$	−4.06478e8	−	7.04040e8i	−0.383530	−	0.664294i	0.608034	−	0.793911i	$-0.291958\pi$
$379$	−4.06478e8	−	7.04040e8i	−0.383530	−	0.664294i	−0.991564	+	0.129617i	$0.958625\pi$
$380$	6.83147e7	+	1.18325e8i	0.0638663	+	0.110620i
$381$	−1.21599e8	+	2.10616e8i	−0.112640	+	0.195098i
$382$	−4.14672e8			−0.380612
$383$	−1.02861e9	+	1.78160e9i	−0.935522	+	1.62037i	−0.161823	+	0.986820i	$0.551737\pi$
$383$	−1.02861e9	+	1.78160e9i	−0.935522	+	1.62037i	−0.773700	+	0.633552i	$0.781596\pi$
$384$	−2.59300e8	+	4.49121e8i	−0.233692	+	0.404766i
$385$	2.05817e9			1.83809
$386$	2.50604e8	−	4.34060e8i	0.221786	−	0.384144i
$387$	−9.76510e6	−	1.69136e7i	−0.00856423	−	0.0148337i
$388$	5.12281e7	+	8.87297e7i	0.0445243	+	0.0771184i
$389$	−9.78966e8			−0.843226			−0.421613	−	0.906776i	$-0.638536\pi$
$389$	−9.78966e8			−0.843226			−0.421613	+	0.906776i	$0.638536\pi$
$390$	4.86568e8	+	2.48287e8i	0.415353	+	0.211948i
$391$	−1.12070e9			−0.948140
$392$	1.62259e8	+	2.81040e8i	0.136052	+	0.235650i
$393$	1.23450e8	+	2.13822e8i	0.102593	+	0.177696i
$394$	4.36163e7	−	7.55457e7i	0.0359263	−	0.0622261i
$395$	3.03591e9			2.47856
$396$	−4.25379e8	+	7.36778e8i	−0.344226	+	0.596216i
$397$	8.91366e8	−	1.54389e9i	0.714973	−	1.23837i	−0.247997	−	0.968761i	$-0.579772\pi$
$397$	8.91366e8	−	1.54389e9i	0.714973	−	1.23837i	0.962970	−	0.269608i	$-0.0868942\pi$
$398$	−5.69682e8			−0.452941
$399$	−3.31284e7	+	5.73800e7i	−0.0261093	+	0.0452226i
$400$	−2.08138e8	−	3.60506e8i	−0.162608	−	0.281646i
$401$	3.28237e8	+	5.68524e8i	0.254204	+	0.440294i	0.964679	−	0.263428i	$-0.0848532\pi$
$401$	3.28237e8	+	5.68524e8i	0.254204	+	0.440294i	−0.710475	+	0.703723i	$0.751520\pi$
$402$	−5.32980e8			−0.409185
$403$	−5.08240e7	−	9.81065e8i	−0.0386813	−	0.746672i
$404$	−1.14239e9			−0.861948
$405$	−2.00164e8	−	3.46693e8i	−0.149724	−	0.259330i
$406$	−9.77623e7	−	1.69329e8i	−0.0724987	−	0.125571i
$407$	−4.34202e8	+	7.52060e8i	−0.319236	+	0.552932i
$408$	1.28126e9			0.933959
$409$	4.42914e8	−	7.67150e8i	0.320102	−	0.554433i	−0.660407	−	0.750908i	$-0.729616\pi$
$409$	4.42914e8	−	7.67150e8i	0.320102	−	0.554433i	0.980509	+	0.196475i	$0.0629495\pi$
$410$	−9.61883e7	+	1.66603e8i	−0.0689253	+	0.119382i
$411$	−1.63180e8			−0.115937
$412$	4.83251e8	−	8.37016e8i	0.340434	−	0.589649i
$413$	−6.70064e8	−	1.16059e9i	−0.468049	−	0.810685i
$414$	1.39000e8	+	2.40755e8i	0.0962752	+	0.166754i
$415$	−3.55775e9			−2.44347
$416$	1.35525e9	+	6.91562e8i	0.922982	+	0.470982i
$417$	−6.54794e8			−0.442210
$418$	6.30949e7	+	1.09284e8i	0.0422549	+	0.0731876i
$419$	−3.67649e8	−	6.36787e8i	−0.244165	−	0.422907i	0.717731	−	0.696320i	$-0.245181\pi$
$419$	−3.67649e8	−	6.36787e8i	−0.244165	−	0.422907i	−0.961897	+	0.273413i	$0.911847\pi$
$420$	3.92746e8	−	6.80255e8i	0.258666	−	0.448022i
$421$	−1.61920e8			−0.105758			−0.0528791	−	0.998601i	$-0.516840\pi$
$421$	−1.61920e8			−0.105758			−0.0528791	+	0.998601i	$0.516840\pi$
$422$	−4.37190e8	+	7.57235e8i	−0.283189	+	0.490498i
$423$	3.35058e8	−	5.80337e8i	0.215243	−	0.372811i
$424$	−1.34848e9			−0.859138
$425$	−2.20495e9	+	3.81909e9i	−1.39328	+	2.41323i
$426$	−6.19730e7	−	1.07340e8i	−0.0388391	−	0.0672712i
$427$	6.44008e8	+	1.11546e9i	0.400308	+	0.693353i
$428$	−2.41219e8			−0.148717
$429$	−1.10490e9	−	5.63813e8i	−0.675652	−	0.344774i
$430$	3.43428e7			0.0208303
$431$	1.34438e9	+	2.32853e9i	0.808819	+	1.40092i	0.913682	+	0.406430i	$0.133226\pi$
$431$	1.34438e9	+	2.32853e9i	0.808819	+	1.40092i	−0.104863	+	0.994487i	$0.533440\pi$
$432$	1.68733e8	+	2.92253e8i	0.100695	+	0.174408i
$433$	2.44483e8	−	4.23456e8i	0.144724	−	0.250669i	−0.784546	−	0.620071i	$-0.787104\pi$
$433$	2.44483e8	−	4.23456e8i	0.144724	−	0.250669i	0.929270	+	0.369401i	$0.120437\pi$
$434$	5.74546e8			0.337373
$435$	2.39204e8	−	4.14314e8i	0.139334	−	0.241333i
$436$	7.81932e8	−	1.35435e9i	0.451821	−	0.782576i
$437$	−1.01383e8			−0.0581138
$438$	2.69661e8	−	4.67066e8i	0.153341	−	0.265595i
$439$	1.61483e9	+	2.79696e9i	0.910962	+	1.57783i	0.812709	+	0.582670i	$0.197992\pi$
$439$	1.61483e9	+	2.79696e9i	0.910962	+	1.57783i	0.0982529	+	0.995161i	$0.468675\pi$
$440$	−1.80025e9	−	3.11812e9i	−1.00751	−	1.74505i
$441$	3.72741e8			0.206953
$442$	−9.35588e7	−	1.80598e9i	−0.0515355	−	0.994800i
$443$	6.54960e8			0.357933			0.178967	−	0.983855i	$-0.442725\pi$
$443$	6.54960e8			0.357933			0.178967	+	0.983855i	$0.442725\pi$
$444$	1.65712e8	+	2.87021e8i	0.0898488	+	0.155623i
$445$	2.32156e8	+	4.02105e8i	0.124888	+	0.216312i
$446$	2.97454e8	−	5.15206e8i	0.158763	−	0.274985i
$447$	−1.58749e9			−0.840690
$448$	−2.72273e8	+	4.71591e8i	−0.143064	+	0.247795i
$449$	−7.59920e7	+	1.31622e8i	−0.0396192	+	0.0686225i	−0.885155	−	0.465296i	$-0.845948\pi$
$449$	−7.59920e7	+	1.31622e8i	−0.0396192	+	0.0686225i	0.845536	+	0.533919i	$0.179281\pi$
$450$	1.09392e9			0.565901
$451$	2.18425e8	−	3.78323e8i	0.112120	−	0.194198i
$452$	3.88595e8	+	6.73067e8i	0.197931	+	0.342826i
$453$	5.56296e8	+	9.63532e8i	0.281165	+	0.486993i
$454$	−8.72618e8			−0.437652
$455$	−2.37669e9	−	1.21278e9i	−1.18286	−	0.603592i
$456$	1.15907e8			0.0572446
$457$	4.31044e8	+	7.46589e8i	0.211259	+	0.365911i	0.952109	−	0.305760i	$-0.0989104\pi$
$457$	4.31044e8	+	7.46589e8i	0.211259	+	0.365911i	−0.740850	+	0.671670i	$0.765577\pi$
$458$	4.93375e8	+	8.54551e8i	0.239965	+	0.415632i
$459$	1.78750e9	−	3.09604e9i	0.862784	−	1.49439i
$460$	1.20192e9			0.575735
$461$	5.16988e8	−	8.95450e8i	0.245769	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$461$	5.16988e8	−	8.95450e8i	0.245769	−	0.425685i	0.962348	+	0.271822i	$0.0876261\pi$
$462$	3.62736e8	−	6.28278e8i	0.171137	−	0.296418i
$463$	3.43169e8			0.160685			0.0803423	−	0.996767i	$-0.474399\pi$
$463$	3.43169e8			0.160685			0.0803423	+	0.996767i	$0.474399\pi$
$464$	7.47517e7	−	1.29474e8i	0.0347383	−	0.0601684i
$465$	7.02897e8	+	1.21745e9i	0.324195	+	0.561522i
$466$	2.09797e8	+	3.63378e8i	0.0960390	+	0.166344i
$467$	3.03174e9			1.37747			0.688736	−	0.725012i	$-0.258166\pi$
$467$	3.03174e9			1.37747			0.688736	+	0.725012i	$0.258166\pi$
$468$	9.25362e8	−	6.00146e8i	0.417303	−	0.270643i
$469$	2.60339e9			1.16529
$470$	5.89181e8	+	1.02049e9i	0.261762	+	0.453385i
$471$	−7.16951e8	−	1.24180e9i	−0.316167	−	0.547617i
$472$	−1.17219e9	+	2.03029e9i	−0.513099	+	0.888713i
$473$	−7.79859e7			−0.0338846
$474$	5.35056e8	−	9.26744e8i	0.230768	−	0.399701i
$475$	−1.99468e8	+	3.45488e8i	−0.0853975	+	0.147913i
$476$	−2.60041e9			−1.10514
$477$	−7.74433e8	+	1.34136e9i	−0.326715	+	0.565887i
$478$	−6.71549e8	−	1.16316e9i	−0.281242	−	0.487125i
$479$	−1.12488e9	−	1.94836e9i	−0.467664	−	0.810017i	0.531654	−	0.846962i	$-0.321571\pi$
$479$	−1.12488e9	−	1.94836e9i	−0.467664	−	0.810017i	−0.999317	+	0.0369446i	$0.988237\pi$
$480$	−2.17728e9			−0.898607
$481$	9.44555e8	−	6.12594e8i	0.387007	−	0.250995i
$482$	−4.75603e8			−0.193455
$483$	2.91428e8	+	5.04768e8i	0.117684	+	0.203834i
$484$	8.11995e8	+	1.40642e9i	0.325533	+	0.563839i
$485$	−2.49020e8	+	4.31315e8i	−0.0991146	+	0.171672i
$486$	−1.40856e9			−0.556608
$487$	−1.02439e9	+	1.77429e9i	−0.401895	+	0.696103i	−0.993955	−	0.109791i	$-0.964982\pi$
$487$	−1.02439e9	+	1.77429e9i	−0.401895	+	0.696103i	0.592059	+	0.805894i	$0.298315\pi$
$488$	1.12661e9	−	1.95134e9i	0.438837	−	0.760088i
$489$	−2.18332e9			−0.844376
$490$	−3.27723e8	+	5.67633e8i	−0.125840	+	0.217962i
$491$	1.35610e9	+	2.34884e9i	0.517020	+	0.895506i	0.999805	+	0.0197663i	$0.00629221\pi$
$491$	1.35610e9	+	2.34884e9i	0.517020	+	0.895506i	−0.482784	+	0.875739i	$0.660374\pi$
$492$	−8.33611e7	−	1.44386e8i	−0.0315563	−	0.0546570i
$493$	−1.58379e9			−0.595298
$494$	−8.46364e6	−	1.63375e8i	−0.00315873	−	0.0609737i
$495$	−4.13554e9			−1.53255
$496$	2.19657e8	+	3.80456e8i	0.0808273	+	0.139997i
$497$	3.02713e8	+	5.24315e8i	0.110607	+	0.191578i
$498$	−6.27027e8	+	1.08604e9i	−0.227501	+	0.394043i
$499$	2.50551e8			0.0902700			0.0451350	−	0.998981i	$-0.485628\pi$
$499$	2.50551e8			0.0902700			0.0451350	+	0.998981i	$0.485628\pi$
$500$	7.92615e8	−	1.37285e9i	0.283574	−	0.491165i
$501$	−8.23484e7	+	1.42632e8i	−0.0292565	+	0.0506738i
$502$	1.73013e9			0.610401
$503$	3.32443e8	−	5.75808e8i	0.116474	−	0.201739i	−0.801894	−	0.597466i	$-0.796174\pi$
$503$	3.32443e8	−	5.75808e8i	0.116474	−	0.201739i	0.918368	+	0.395727i	$0.129507\pi$
$504$	7.76233e8	+	1.34447e9i	0.270075	+	0.467784i
$505$	−2.77659e9	−	4.80919e9i	−0.959382	−	1.66170i
$506$	1.11008e9			0.380915
$507$	9.43669e8	+	1.30214e9i	0.321582	+	0.443741i
$508$	−8.63464e8			−0.292228
$509$	−1.37347e9	−	2.37892e9i	−0.461643	−	0.799589i	0.537400	−	0.843327i	$-0.319406\pi$
$509$	−1.37347e9	−	2.37892e9i	−0.461643	−	0.799589i	−0.999043	+	0.0437385i	$0.986073\pi$
$510$	1.29392e9	+	2.24114e9i	0.431929	+	0.748122i
$511$	−1.31719e9	+	2.28143e9i	−0.436691	+	0.756370i
$512$	−1.28447e9			−0.422940
$513$	1.61703e8	−	2.80079e8i	0.0528821	−	0.0915945i
$514$	1.59681e7	−	2.76576e7i	0.00518661	−	0.00898347i
$515$	4.69817e9			1.51567
$516$	−1.48815e7	+	2.57755e7i	−0.00476840	+	0.00825912i
$517$	−1.33792e9	−	2.31734e9i	−0.425807	−	0.737519i
$518$	3.29216e8	+	5.70219e8i	0.104070	+	0.180255i
$519$	8.24793e8			0.258976
$520$	2.41488e8	+	4.66148e9i	0.0753153	+	1.45383i
$521$	−4.22280e9			−1.30818			−0.654091	−	0.756416i	$-0.726949\pi$
$521$	−4.22280e9			−1.30818			−0.654091	+	0.756416i	$0.726949\pi$
$522$	1.96437e8	+	3.40239e8i	0.0604472	+	0.104698i
$523$	−1.07951e9	−	1.86976e9i	−0.329966	−	0.571518i	0.652539	−	0.757755i	$-0.273704\pi$
$523$	−1.07951e9	−	1.86976e9i	−0.329966	−	0.571518i	−0.982505	+	0.186238i	$0.940371\pi$
$524$	−4.38304e8	+	7.59165e8i	−0.133081	+	0.230503i
$525$	2.29350e9			0.691738
$526$	−7.58865e8	+	1.31439e9i	−0.227360	+	0.393799i
$527$	2.32697e9	−	4.03044e9i	0.692555	−	1.19954i
$528$	5.54716e8			0.164003
$529$	1.25648e9	−	2.17630e9i	0.369031	−	0.639180i
$530$	−1.36180e9	−	2.35870e9i	−0.397326	−	0.688189i
$531$	1.34638e9	+	2.33200e9i	0.390245	+	0.675924i
$532$	−2.35242e8			−0.0677366
$533$	−4.75158e8	+	3.08165e8i	−0.135923	+	0.0881532i
$534$	1.63663e8			0.0465110
$535$	−5.86284e8	−	1.01547e9i	−0.165527	−	0.286702i
$536$	−2.27715e9	−	3.94414e9i	−0.638726	−	1.10631i
$537$	1.46040e9	−	2.52949e9i	0.406969	−	0.704892i
$538$	2.54306e9			0.704075
$539$	7.44196e8	−	1.28898e9i	0.204704	−	0.354558i
$540$	−1.91704e9	+	3.32041e9i	−0.523905	+	0.907430i
$541$	−4.81795e8			−0.130819			−0.0654097	−	0.997858i	$-0.520835\pi$
$541$	−4.81795e8			−0.130819			−0.0654097	+	0.997858i	$0.520835\pi$
$542$	−1.55932e8	+	2.70083e8i	−0.0420667	+	0.0728617i
$543$	1.73192e9	+	2.99977e9i	0.464224	+	0.804059i
$544$	3.60399e9	+	6.24230e9i	0.959816	+	1.66245i
$545$	7.60194e9			2.01158
$546$	−7.89090e8	+	5.11766e8i	−0.207468	+	0.134554i
$547$	7.26975e9			1.89917			0.949584	−	0.313511i	$-0.101505\pi$
$547$	7.26975e9			1.89917			0.949584	+	0.313511i	$0.101505\pi$
$548$	−2.89682e8	−	5.01745e8i	−0.0751952	−	0.130242i
$549$	−1.29403e9	−	2.24132e9i	−0.333764	−	0.578096i
$550$	2.18406e9	−	3.78289e9i	0.559750	−	0.969516i
$551$	−1.43275e8			−0.0364872
$552$	5.09815e8	−	8.83025e8i	0.129011	−	0.223453i
$553$	−2.61353e9	+	4.52677e9i	−0.657189	+	1.13828i
$554$	−3.10733e9			−0.776431
$555$	−8.05523e8	+	1.39521e9i	−0.200010	+	0.346428i
$556$	−1.16241e9	−	2.01335e9i	−0.286812	−	0.496772i
$557$	1.12713e8	+	1.95225e8i	0.0276364	+	0.0478677i	0.879513	−	0.475875i	$-0.157869\pi$
$557$	1.12713e8	+	1.95225e8i	0.0276364	+	0.0478677i	−0.851876	+	0.523743i	$0.824535\pi$
$558$	−1.15445e9			−0.281291
$559$	9.00551e7	+	4.59536e7i	0.0218055	+	0.0111270i
$560$	1.19322e9			0.287118
$561$	−2.93824e9	−	5.08919e9i	−0.702616	−	1.21697i
$562$	−3.31059e8	−	5.73411e8i	−0.0786735	−	0.136266i
$563$	−2.83522e9	+	4.91075e9i	−0.669588	+	1.15976i	0.308431	+	0.951247i	$0.400196\pi$
$563$	−2.83522e9	+	4.91075e9i	−0.669588	+	1.15976i	−0.978019	+	0.208514i	$0.933137\pi$
$564$	−1.02122e9			−0.239686
$565$	−1.88896e9	+	3.27178e9i	−0.440609	+	0.763158i
$566$	−1.81734e9	+	3.14772e9i	−0.421287	+	0.729690i
$567$	6.89262e8			0.158798
$568$	5.29557e8	−	9.17220e8i	0.121253	−	0.210017i
$569$	−1.06861e9	−	1.85088e9i	−0.243178	−	0.421197i	0.718440	−	0.695589i	$-0.244857\pi$
$569$	−1.06861e9	−	1.85088e9i	−0.243178	−	0.421197i	−0.961618	+	0.274392i	$0.911523\pi$
$570$	1.17052e8	+	2.02741e8i	0.0264739	+	0.0458542i
$571$	−8.39078e9			−1.88615			−0.943075	−	0.332581i	$-0.892081\pi$
$571$	−8.39078e9			−1.88615			−0.943075	+	0.332581i	$0.892081\pi$
$572$	−2.27850e8	−	4.39823e9i	−0.0509053	−	0.982635i
$573$	1.74691e9			0.387909
$574$	−1.65612e8	−	2.86848e8i	−0.0365511	−	0.0633083i
$575$	1.75470e9	+	3.03923e9i	0.384916	+	0.666694i
$576$	5.47086e8	−	9.47581e8i	0.119283	−	0.206604i
$577$	−7.71590e9			−1.67213			−0.836067	−	0.548627i	$-0.815151\pi$
$577$	−7.71590e9			−1.67213			−0.836067	+	0.548627i	$0.815151\pi$
$578$	3.03545e9	−	5.25755e9i	0.653846	−	1.13249i
$579$	−1.05574e9	+	1.82859e9i	−0.226038	+	0.391508i
$580$	1.69857e9			0.361480
$581$	3.06277e9	−	5.30488e9i	0.647886	−	1.12217i
$582$	8.77757e7	+	1.52032e8i	0.0184563	+	0.0319672i
$583$	3.09238e9	+	5.35616e9i	0.646328	+	1.11947i
$584$	4.60849e9			0.957444
$585$	4.77556e9	+	2.43688e9i	0.986230	+	0.503257i
$586$	−1.51546e9			−0.311103
$587$	3.49411e9	+	6.05197e9i	0.713022	+	1.23499i	0.963717	+	0.266924i	$0.0860074\pi$
$587$	3.49411e9	+	6.05197e9i	0.713022	+	1.23499i	−0.250695	+	0.968066i	$0.580659\pi$
$588$	−2.84019e8	−	4.91936e8i	−0.0576139	−	0.0997902i
$589$	2.10506e8	−	3.64607e8i	0.0424484	−	0.0735227i
$590$	−4.73508e9			−0.949172
$591$	−1.83745e8	+	3.18256e8i	−0.0366150	+	0.0634191i
$592$	−2.51727e8	+	4.36005e8i	−0.0498660	+	0.0863705i
$593$	−7.22746e9			−1.42329			−0.711647	−	0.702538i	$-0.752050\pi$
$593$	−7.22746e9			−1.42329			−0.711647	+	0.702538i	$0.752050\pi$
$594$	−1.77056e9	+	3.06670e9i	−0.346623	+	0.600369i
$595$	−6.32028e9	−	1.09471e10i	−1.23006	−	2.13053i
$596$	−2.81816e9	−	4.88120e9i	−0.545261	−	0.944420i
$597$	2.39993e9			0.461625
$598$	−1.28188e9	−	6.54121e8i	−0.245128	−	0.125085i
$599$	4.68289e9			0.890266			0.445133	−	0.895465i	$-0.353156\pi$
$599$	4.68289e9			0.890266			0.445133	+	0.895465i	$0.353156\pi$
$600$	−2.00609e9	−	3.47465e9i	−0.379159	−	0.656723i
$601$	3.17626e9	+	5.50145e9i	0.596837	+	1.03375i	0.993285	+	0.115695i	$0.0369094\pi$
$601$	3.17626e9	+	5.50145e9i	0.596837	+	1.03375i	−0.396448	+	0.918057i	$0.629757\pi$
$602$	−2.95648e7	+	5.12078e7i	−0.00552316	+	0.00956639i
$603$	−5.23108e9			−0.971585
$604$	−1.97510e9	+	3.42098e9i	−0.364721	+	0.631715i
$605$	−3.94711e9	+	6.83659e9i	−0.724661	+	1.25515i
$606$	−1.95741e9			−0.357296
$607$	2.12651e9	−	3.68322e9i	0.385928	−	0.668447i	−0.605969	−	0.795488i	$-0.707215\pi$
$607$	2.12651e9	−	3.68322e9i	0.385928	−	0.668447i	0.991897	+	0.127041i	$0.0405479\pi$
$608$	3.26030e8	+	5.64700e8i	0.0588294	+	0.101896i
$609$	4.11849e8	+	7.13344e8i	0.0738886	+	0.127979i
$610$	4.55095e9			0.811797
$611$	1.79470e8	+	3.46435e9i	0.0318309	+	0.614437i
$612$	5.22508e9			0.921430
$613$	−1.70467e9	−	2.95257e9i	−0.298902	−	0.517713i	0.676983	−	0.735999i	$-0.263287\pi$
$613$	−1.70467e9	−	2.95257e9i	−0.298902	−	0.517713i	−0.975885	+	0.218285i	$0.929954\pi$
$614$	−1.24523e8	−	2.15680e8i	−0.0217100	−	0.0376028i
$615$	4.05218e8	−	7.01858e8i	0.0702467	−	0.121671i
$616$	6.19914e9			1.06856
$617$	1.57876e9	−	2.73449e9i	0.270593	−	0.468682i	−0.698420	−	0.715688i	$-0.746113\pi$
$617$	1.57876e9	−	2.73449e9i	0.270593	−	0.468682i	0.969014	+	0.247006i	$0.0794468\pi$
$618$	8.28017e8	−	1.43417e9i	0.141117	−	0.244422i
$619$	7.34245e9			1.24430			0.622148	−	0.782899i	$-0.286260\pi$
$619$	7.34245e9			1.24430			0.622148	+	0.782899i	$0.286260\pi$
$620$	−2.49561e9	+	4.32251e9i	−0.420538	+	0.728393i
$621$	−1.42249e9	−	2.46383e9i	−0.238358	−	0.412848i
$622$	3.04128e9	+	5.26765e9i	0.506745	+	0.877709i
$623$	−7.99427e8			−0.132456
$624$	−6.40564e8	−	3.26869e8i	−0.105540	−	0.0538552i
$625$	−1.47491e9			−0.241649
$626$	9.13728e8	+	1.58262e9i	0.148870	+	0.257850i
$627$	−2.65804e8	−	4.60385e8i	−0.0430650	−	0.0745908i
$628$	2.54550e9	−	4.40894e9i	0.410124	−	0.710355i
$629$	5.33345e9			0.854537
$630$	−1.56780e9	+	2.71551e9i	−0.249804	+	0.432673i
$631$	−2.28531e9	+	3.95828e9i	−0.362112	+	0.627196i	−0.988308	−	0.152469i	$-0.951277\pi$
$631$	−2.28531e9	+	3.95828e9i	−0.362112	+	0.627196i	0.626196	+	0.779665i	$0.284611\pi$
$632$	9.14407e9			1.44089
$633$	1.84178e9	−	3.19005e9i	0.288618	−	0.499902i
$634$	−9.92939e8	−	1.71982e9i	−0.154743	−	0.268022i
$635$	−2.09865e9	−	3.63497e9i	−0.325261	−	0.563368i
$636$	2.36039e9			0.363818
$637$	−1.61891e9	+	1.04995e9i	−0.248161	+	0.160946i
$638$	1.56878e9			0.239161
$639$	−6.08251e8	−	1.05352e9i	−0.0922210	−	0.159731i
$640$	−4.47520e9	−	7.75127e9i	−0.674812	−	1.16881i
$641$	−4.72358e9	+	8.18148e9i	−0.708383	+	1.22696i	0.257074	+	0.966392i	$0.417242\pi$
$641$	−4.72358e9	+	8.18148e9i	−0.708383	+	1.22696i	−0.965457	+	0.260564i	$0.916092\pi$
$642$	−4.13313e8			−0.0616461
$643$	3.12109e9	−	5.40589e9i	0.462986	−	0.801916i	−0.536122	−	0.844141i	$-0.680111\pi$
$643$	3.12109e9	−	5.40589e9i	0.462986	−	0.801916i	0.999108	+	0.0422246i	$0.0134445\pi$
$644$	−1.03470e9	+	1.79216e9i	−0.152656	+	0.264408i
$645$	−1.44678e8			−0.0212297
$646$	3.87508e8	−	6.71183e8i	0.0565544	−	0.0979551i
$647$	−1.96359e9	−	3.40104e9i	−0.285027	−	0.493681i	0.687589	−	0.726100i	$-0.258669\pi$
$647$	−1.96359e9	−	3.40104e9i	−0.285027	−	0.493681i	−0.972616	+	0.232419i	$0.925336\pi$
$648$	−6.02887e8	−	1.04423e9i	−0.0870409	−	0.150759i
$649$	1.07525e10			1.54401
$650$	−4.75115e9	+	3.08137e9i	−0.678582	+	0.440096i
$651$	−2.42042e9			−0.343841
$652$	−3.87589e9	−	6.71323e9i	−0.547652	−	0.948561i
$653$	3.85082e9	+	6.66982e9i	0.541199	+	0.937384i	0.998836	+	0.0482449i	$0.0153628\pi$
$653$	3.85082e9	+	6.66982e9i	0.541199	+	0.937384i	−0.457636	+	0.889139i	$0.651304\pi$
$654$	1.33978e9	−	2.32057e9i	0.187289	−	0.324394i
$655$	−4.26119e9			−0.592498
$656$	1.26631e8	−	2.19332e8i	0.0175137	−	0.0303346i
$657$	2.64666e9	−	4.58415e9i	0.364099	−	0.630638i
$658$	−2.02884e9			−0.277625
$659$	−3.08277e8	+	5.33952e8i	−0.0419607	+	0.0726781i	−0.886243	−	0.463221i	$-0.846694\pi$
$659$	−3.08277e8	+	5.33952e8i	−0.0419607	+	0.0726781i	0.844282	+	0.535899i	$0.180027\pi$
$660$	3.15117e9	+	5.45799e9i	0.426647	+	0.738974i
$661$	−2.51439e9	−	4.35505e9i	−0.338631	−	0.586527i	0.645544	−	0.763723i	$-0.276631\pi$
$661$	−2.51439e9	−	4.35505e9i	−0.338631	−	0.586527i	−0.984176	+	0.177196i	$0.943297\pi$
$662$	4.75337e9			0.636794
$663$	3.94141e8	+	7.60817e9i	0.0525235	+	1.01387i
$664$	−1.07158e10			−1.42049
$665$	−5.71754e8	−	9.90308e8i	−0.0753935	−	0.130585i
$666$	−6.61504e8	−	1.14576e9i	−0.0867706	−	0.150291i
$667$	−6.30191e8	+	1.09152e9i	−0.0822303	+	0.142427i
$668$	−5.84748e8			−0.0759017
$669$	−1.25310e9	+	2.17044e9i	−0.161806	+	0.280257i
$670$	4.59929e9	−	7.96620e9i	0.590784	−	1.02327i
$671$	−1.03343e10			−1.32055
$672$	1.87436e9	−	3.24649e9i	0.238266	−	0.412688i
$673$	7.60623e9	+	1.31744e10i	0.961871	+	1.66601i	0.717796	+	0.696253i	$0.245151\pi$
$673$	7.60623e9	+	1.31744e10i	0.961871	+	1.66601i	0.244075	+	0.969756i	$0.421516\pi$
$674$	2.28749e8	+	3.96204e8i	0.0287772	+	0.0498436i
$675$	−1.11949e10			−1.40106
$676$	−2.32857e9	+	5.21317e9i	−0.289918	+	0.649065i
$677$	−5.67705e9			−0.703173			−0.351587	−	0.936155i	$-0.614358\pi$
$677$	−5.67705e9			−0.703173			−0.351587	+	0.936155i	$0.614358\pi$
$678$	6.65831e8	+	1.15325e9i	0.0820465	+	0.142109i
$679$	−4.28749e8	−	7.42615e8i	−0.0525605	−	0.0910374i
$680$	−1.10565e10	+	1.91504e10i	−1.34846	+	2.33559i
$681$	3.67613e9			0.446042
$682$	−2.30492e9	+	3.99224e9i	−0.278234	+	0.481916i
$683$	1.76411e9	−	3.05553e9i	0.211862	−	0.366956i	−0.740435	−	0.672128i	$-0.765381\pi$
$683$	1.76411e9	−	3.05553e9i	0.211862	−	0.366956i	0.952297	+	0.305172i	$0.0987140\pi$
$684$	4.72678e8			0.0564767
$685$	1.40815e9	−	2.43898e9i	0.167390	−	0.289929i
$686$	−2.47192e9	−	4.28150e9i	−0.292348	−	0.506362i
$687$	−2.07847e9	−	3.60002e9i	−0.244566	−	0.423600i
$688$	−4.52121e7			−0.00529292
$689$	−4.14817e8	−	8.00729e9i	−0.0483158	−	0.932649i
$690$	2.05940e9			0.238654
$691$	4.01665e9	+	6.95704e9i	0.463117	+	0.802142i	0.999114	−	0.0420777i	$-0.0133977\pi$
$691$	4.01665e9	+	6.95704e9i	0.463117	+	0.802142i	−0.535998	+	0.844220i	$0.680064\pi$
$692$	1.46419e9	+	2.53606e9i	0.167968	+	0.290930i
$693$	3.56018e9	−	6.16641e9i	0.406355	−	0.703827i
$694$	−4.25734e9			−0.483482
$695$	5.65046e9	−	9.78689e9i	0.638465	−	1.10585i
$696$	7.20476e8	−	1.24790e9i	0.0810004	−	0.140297i
$697$	−2.68299e9			−0.300126
$698$	−2.89312e9	+	5.01104e9i	−0.322013	+	0.557742i
$699$	−8.83823e8	−	1.53083e9i	−0.0978803	−	0.169534i
$700$	4.07149e9	+	7.05203e9i	0.448653	+	0.777090i
$701$	−1.78895e9			−0.196149			−0.0980744	−	0.995179i	$-0.531268\pi$
$701$	−1.78895e9			−0.196149			−0.0980744	+	0.995179i	$0.531268\pi$
$702$	3.85164e9	−	2.49799e9i	0.420209	−	0.272528i
$703$	4.82482e8			0.0523766
$704$	−2.18457e9	−	3.78378e9i	−0.235972	−	0.408716i
$705$	−2.48208e9	−	4.29909e9i	−0.266780	−	0.462077i
$706$	2.87033e9	−	4.97157e9i	0.306984	−	0.531712i
$707$	9.56117e9			1.01752
$708$	2.05182e9	−	3.55385e9i	0.217281	−	0.376342i
$709$	−3.96360e9	+	6.86515e9i	−0.417665	+	0.723416i	−0.995704	−	0.0925924i	$-0.970485\pi$
$709$	−3.96360e9	+	6.86515e9i	−0.417665	+	0.723416i	0.578039	+	0.816009i	$0.303818\pi$
$710$	2.13915e9			0.224304
$711$	5.25146e9	−	9.09579e9i	0.547944	−	0.949067i
$712$	6.99247e8	+	1.21113e9i	0.0726023	+	0.125751i
$713$	−1.85181e9	−	3.20742e9i	−0.191330	−	0.331393i
$714$	−4.45561e9			−0.458103
$715$	1.79617e10	−	1.16491e10i	1.83770	−	1.19185i
$716$	1.03702e10			1.05582
$717$	2.82907e9	+	4.90010e9i	0.286634	+	0.496464i
$718$	−1.94671e9	−	3.37181e9i	−0.196276	−	0.339959i
$719$	3.04703e9	−	5.27761e9i	0.305721	−	0.529524i	−0.671701	−	0.740823i	$-0.734436\pi$
$719$	3.04703e9	−	5.27761e9i	0.305721	−	0.529524i	0.977422	+	0.211298i	$0.0677692\pi$
$720$	−2.39757e9			−0.239390
$721$	−4.04453e9	+	7.00533e9i	−0.401879	+	0.696074i
$722$	−2.68386e9	+	4.64858e9i	−0.265387	+	0.459664i
$723$	2.00360e9			0.197164
$724$	−6.14909e9	+	1.06505e10i	−0.602179	+	1.04301i
$725$	2.47977e9	+	4.29508e9i	0.241673	+	0.418590i
$726$	1.39130e9	+	2.40980e9i	0.134940	+	0.233723i
$727$	4.07583e8			0.0393410			0.0196705	−	0.999807i	$-0.493738\pi$
$727$	4.07583e8			0.0393410			0.0196705	+	0.999807i	$0.493738\pi$
$728$	−7.15852e9	−	3.65287e9i	−0.687644	−	0.350893i
$729$	3.95452e9			0.378048
$730$	4.65401e9	+	8.06099e9i	0.442790	+	0.766935i
$731$	2.39482e8	+	4.14794e8i	0.0226757	+	0.0392755i
$732$	−1.97203e9	+	3.41565e9i	−0.185834	+	0.321873i
$733$	−4.77042e9			−0.447396			−0.223698	−	0.974658i	$-0.571813\pi$
$733$	−4.77042e9			−0.447396			−0.223698	+	0.974658i	$0.571813\pi$
$734$	2.48820e9	−	4.30969e9i	0.232247	−	0.402263i
$735$	1.38062e9	−	2.39130e9i	0.128253	−	0.222141i
$736$	5.73611e9			0.530329
$737$	−1.04441e10	+	1.80897e10i	−0.961025	+	1.66454i
$738$	3.32769e8	+	5.76373e8i	0.0304752	+	0.0527845i
$739$	−8.83136e9	−	1.52964e10i	−0.804956	−	1.39422i	−0.916321	−	0.400445i	$-0.868855\pi$
$739$	−8.83136e9	−	1.52964e10i	−0.804956	−	1.39422i	0.111364	−	0.993780i	$-0.464478\pi$
$740$	−5.71995e9			−0.518897
$741$	3.56553e7	+	6.88261e8i	0.00321929	+	0.0621426i
$742$	4.68935e9			0.421404
$743$	7.53659e9	+	1.30538e10i	0.674084	+	1.16755i	0.976736	+	0.214446i	$0.0687947\pi$
$743$	7.53659e9	+	1.30538e10i	0.674084	+	1.16755i	−0.302652	+	0.953101i	$0.597872\pi$
$744$	2.11711e9	+	3.66694e9i	0.188468	+	0.326436i
$745$	1.36991e10	−	2.37275e10i	1.21379	−	2.10235i
$746$	4.04778e9			0.356970
$747$	−6.15413e9	+	1.06593e10i	−0.540187	+	0.935632i
$748$	1.04321e10	−	1.80689e10i	0.911416	−	1.57862i
$749$	2.01887e9			0.175558
$750$	1.35809e9	−	2.35228e9i	0.117548	−	0.203598i
$751$	4.70281e9	+	8.14551e9i	0.405152	+	0.701744i	0.994339	−	0.106253i	$-0.0338853\pi$
$751$	4.70281e9	+	8.14551e9i	0.405152	+	0.701744i	−0.589187	+	0.807997i	$0.700552\pi$
$752$	−7.75654e8	−	1.34347e9i	−0.0665129	−	0.115204i
$753$	−7.28862e9			−0.622104
$754$	−1.81157e9	−	9.24412e8i	−0.153906	−	0.0785355i
$755$	−1.92019e10			−1.62379
$756$	−3.30066e9	−	5.71690e9i	−0.277827	−	0.481210i
$757$	−4.03160e9	−	6.98294e9i	−0.337786	−	0.585063i	0.646230	−	0.763143i	$-0.276345\pi$
$757$	−4.03160e9	−	6.98294e9i	−0.337786	−	0.585063i	−0.984016	+	0.178080i	$0.943011\pi$
$758$	2.47279e9	−	4.28300e9i	0.206227	−	0.357195i
$759$	−4.67651e9			−0.388218
$760$	−1.00021e9	+	1.73241e9i	−0.0826501	+	0.143154i
$761$	−2.79805e8	+	4.84637e8i	−0.0230149	+	0.0398630i	−0.877303	−	0.479936i	$-0.840660\pi$
$761$	−2.79805e8	+	4.84637e8i	−0.0230149	+	0.0398630i	0.854289	+	0.519799i	$0.173993\pi$
$762$	−1.47948e9			−0.121135
$763$	−6.54431e9	+	1.13351e10i	−0.533369	+	0.923823i
$764$	3.10117e9	+	5.37138e9i	0.251593	+	0.435772i
$765$	1.26995e10	+	2.19962e10i	1.02559	+	1.77637i
$766$	−1.25150e10			−1.00607
$767$	−1.24165e10	−	6.33594e9i	−0.993610	−	0.507022i
$768$	−5.50054e9			−0.438169
$769$	−1.57910e9	−	2.73509e9i	−0.125218	−	0.216885i	0.796600	−	0.604507i	$-0.206630\pi$
$769$	−1.57910e9	−	2.73509e9i	−0.125218	−	0.216885i	−0.921818	+	0.387622i	$0.873296\pi$
$770$	6.26038e9	+	1.08433e10i	0.494178	+	0.855941i
$771$	−6.72700e7	+	1.16515e8i	−0.00528605	+	0.00915570i
$772$	−7.49669e9			−0.586420
$773$	4.54224e9	−	7.86739e9i	0.353706	−	0.612636i	−0.633190	−	0.773996i	$-0.718255\pi$
$773$	4.54224e9	−	7.86739e9i	0.353706	−	0.612636i	0.986896	+	0.161360i	$0.0515882\pi$
$774$	5.94055e7	−	1.02893e8i	0.00460504	−	0.00797616i
$775$	−1.45735e10			−1.12463
$776$	−7.50041e8	+	1.29911e9i	−0.0576194	+	0.0997997i
$777$	−1.38691e9	−	2.40220e9i	−0.106066	−	0.183711i
$778$	−2.97775e9	−	5.15761e9i	−0.226704	−	0.392663i
$779$	−2.42712e8			−0.0183955
$780$	−4.22703e8	−	8.15952e9i	−0.0318937	−	0.615649i
$781$	−4.85761e9			−0.364875
$782$	−3.40888e9	−	5.90435e9i	−0.254910	−	0.441518i
$783$	−2.01029e9	−	3.48192e9i	−0.149655	−	0.259210i
$784$	4.31445e8	−	7.47285e8i	0.0319757	−	0.0553835i
$785$	2.47474e10			1.82594
$786$	−7.51003e8	+	1.30078e9i	−0.0551649	+	0.0955484i
$787$	5.13352e8	−	8.89151e8i	0.0375408	−	0.0650226i	−0.846645	−	0.532159i	$-0.821381\pi$
$787$	5.13352e8	−	8.89151e8i	0.0375408	−	0.0650226i	0.884185	+	0.467136i	$0.154714\pi$
$788$	−1.30476e9			−0.0949922
$789$	3.19692e9	−	5.53722e9i	0.231719	−	0.401349i
$790$	9.23440e9	+	1.59945e10i	0.666368	+	1.15418i
$791$	−3.25232e9	−	5.63318e9i	−0.233655	−	0.404702i
$792$	−1.24561e10			−0.890932
$793$	1.19337e10	+	6.08956e9i	0.849803	+	0.433640i
$794$	1.08452e10			0.768891
$795$	5.73693e9	+	9.93665e9i	0.404944	+	0.701383i
$796$	4.26043e9	+	7.37928e9i	0.299404	+	0.518583i
$797$	−4.67944e9	+	8.10504e9i	−0.327409	+	0.567088i	−0.981997	−	0.188897i	$-0.939509\pi$
$797$	−4.67944e9	+	8.10504e9i	−0.327409	+	0.567088i	0.654588	+	0.755986i	$0.272842\pi$
$798$	−4.03070e8			−0.0280783
$799$	−8.21704e9	+	1.42323e10i	−0.569904	+	0.987103i
$800$	1.12856e10	−	1.95473e10i	0.779312	−	1.34981i
$801$	1.60631e9			0.110438
$802$	−1.99682e9	+	3.45859e9i	−0.136687	+	0.236749i
$803$	−1.05684e10	−	1.83050e10i	−0.720284	−	1.24757i
$804$	3.98595e9	+	6.90387e9i	0.270480	+	0.468486i
$805$	−1.00594e10			−0.679649
$806$	5.01408e9	−	3.25189e9i	0.337302	−	0.218758i
$807$	−1.07133e10			−0.717573
$808$	−8.36301e9	−	1.44852e10i	−0.557728	−	0.966014i
$809$	−1.07027e9	−	1.85377e9i	−0.0710682	−	0.123094i	0.828302	−	0.560283i	$-0.189307\pi$
$809$	−1.07027e9	−	1.85377e9i	−0.0710682	−	0.123094i	−0.899370	+	0.437189i	$0.855974\pi$
$810$	1.21769e9	−	2.10909e9i	0.0805078	−	0.139444i
$811$	1.40781e10			0.926769			0.463385	−	0.886157i	$-0.346635\pi$
$811$	1.40781e10			0.926769			0.463385	+	0.886157i	$0.346635\pi$
$812$	−1.46225e9	+	2.53270e9i	−0.0958465	+	0.166011i
$813$	6.56905e8	−	1.13779e9i	0.0428732	−	0.0742586i
$814$	−5.28290e9			−0.343310
$815$	1.88407e10	−	3.26330e10i	1.21912	−	2.11157i
$816$	−1.70344e9	−	2.95044e9i	−0.109752	−	0.190096i
$817$	2.16643e7	+	3.75237e7i	0.00138985	+	0.00240729i
$818$	5.38890e9			0.344242
$819$	−7.74474e9	+	5.02287e9i	−0.492621	+	0.319491i
$820$	2.87742e9			0.182245
$821$	1.41933e10	+	2.45835e10i	0.895120	+	1.55039i	0.833656	+	0.552284i	$0.186244\pi$
$821$	1.41933e10	+	2.45835e10i	0.895120	+	1.55039i	0.0614639	+	0.998109i	$0.480423\pi$
$822$	−4.96350e8	−	8.59704e8i	−0.0311700	−	0.0539880i
$823$	−1.25245e10	+	2.16931e10i	−0.783180	+	1.35651i	0.146900	+	0.989151i	$0.453070\pi$
$823$	−1.25245e10	+	2.16931e10i	−0.783180	+	1.35651i	−0.930080	+	0.367356i	$0.880263\pi$
$824$	1.41508e10			0.881119
$825$	−9.20090e9	+	1.59364e10i	−0.570482	+	0.988103i
$826$	4.07631e9	−	7.06037e9i	0.251673	−	0.435910i
$827$	1.41058e10			0.867220			0.433610	−	0.901101i	$-0.357240\pi$
$827$	1.41058e10			0.867220			0.433610	+	0.901101i	$0.357240\pi$
$828$	2.07906e9	−	3.60103e9i	0.127280	−	0.220455i
$829$	1.51188e10	+	2.61866e10i	0.921675	+	1.59639i	0.796824	+	0.604212i	$0.206512\pi$
$829$	1.51188e10	+	2.61866e10i	0.921675	+	1.59639i	0.124851	+	0.992176i	$0.460155\pi$
$830$	−1.08217e10	−	1.87437e10i	−0.656935	−	1.13784i
$831$	1.30904e10			0.791317
$832$	2.93041e8	+	5.65663e9i	0.0176399	+	0.340507i
$833$	−9.14120e9			−0.547956
$834$	−1.99170e9	−	3.44973e9i	−0.118890	−	0.205923i
$835$	−1.42123e9	−	2.46164e9i	−0.0844816	−	0.146326i
$836$	9.43724e8	−	1.63458e9i	0.0558628	−	0.0967573i
$837$	1.18144e10			0.696421
$838$	2.23658e9	−	3.87386e9i	0.131289	−	0.227400i
$839$	2.50755e9	−	4.34320e9i	0.146583	−	0.253888i	−0.783380	−	0.621543i	$-0.786506\pi$
$839$	2.50755e9	−	4.34320e9i	0.146583	−	0.253888i	0.929962	+	0.367655i	$0.119839\pi$
$840$	1.15005e10			0.669484
$841$	7.73434e9	−	1.33963e10i	0.448371	−	0.776601i
$842$	−4.92518e8	−	8.53066e8i	−0.0284335	−	0.0492482i
$843$	1.39467e9	+	2.41564e9i	0.0801818	+	0.138879i
$844$	1.30783e10			0.748777
$845$	−2.76057e10	+	2.86792e9i	−1.57398	+	0.163519i
$846$	4.07662e9			0.231475
$847$	−6.79592e9	−	1.17709e10i	−0.384288	−	0.665606i
$848$	1.79280e9	+	3.10522e9i	0.100959	+	0.174867i
$849$	7.65600e9	−	1.32606e10i	0.429363	−	0.743679i
$850$	−2.68275e10			−1.49835
$851$	2.12218e9	−	3.67572e9i	0.118040	−	0.204451i
$852$	−9.26944e8	+	1.60551e9i	−0.0513470	+	0.0889355i
$853$	7.42546e9			0.409639			0.204820	−	0.978800i	$-0.434339\pi$
$853$	7.42546e9			0.409639			0.204820	+	0.978800i	$0.434339\pi$
$854$	−3.91780e9	+	6.78582e9i	−0.215248	+	0.372821i
$855$	1.14884e9	+	1.98986e9i	0.0628608	+	0.108878i
$856$	−1.76587e9	−	3.05858e9i	−0.0962278	−	0.166672i
$857$	−2.28360e10			−1.23933			−0.619666	−	0.784865i	$-0.712732\pi$
$857$	−2.28360e10			−1.23933			−0.619666	+	0.784865i	$0.712732\pi$
$858$	−3.90405e8	−	7.53606e9i	−0.0211013	−	0.407323i
$859$	−1.64864e10			−0.887461			−0.443730	−	0.896160i	$-0.646345\pi$
$859$	−1.64864e10			−0.887461			−0.443730	+	0.896160i	$0.646345\pi$
$860$	−2.56836e8	−	4.44854e8i	−0.0137693	−	0.0238491i
$861$	6.97684e8	+	1.20842e9i	0.0372518	+	0.0645221i
$862$	−8.17847e9	+	1.41655e10i	−0.434907	+	0.753282i
$863$	6.67222e9			0.353372			0.176686	−	0.984267i	$-0.443462\pi$
$863$	6.67222e9			0.353372			0.176686	+	0.984267i	$0.443462\pi$
$864$	−9.14899e9	+	1.58465e10i	−0.482586	+	0.835864i
$865$	−7.11745e9	+	1.23278e10i	−0.373911	+	0.647632i
$866$	2.97460e9			0.155638
$867$	−1.27876e10	+	2.21488e10i	−0.666381	+	1.15421i
$868$	−4.29680e9	−	7.44228e9i	−0.223011	−	0.386267i
$869$	−2.09696e10	−	3.63203e10i	−1.08398	−	1.87750i
$870$	2.91037e9			0.149841
$871$	2.27199e10	−	1.47351e10i	1.16505	−	0.755594i
$872$	2.28968e10			1.16941
$873$	8.61499e8	+	1.49216e9i	0.0438233	+	0.0759042i
$874$	−3.08379e8	−	5.34127e8i	−0.0156241	−	0.0270617i
$875$	−6.63372e9	+	1.14899e10i	−0.334757	+	0.579815i
$876$	−8.06676e9			−0.405447
$877$	1.16129e10	−	2.01142e10i	0.581358	−	1.00694i	−0.413961	−	0.910295i	$-0.635855\pi$
$877$	1.16129e10	−	2.01142e10i	0.581358	−	1.00694i	0.995319	−	0.0966463i	$-0.0308116\pi$
$878$	−9.82372e9	+	1.70152e10i	−0.489830	+	0.848410i
$879$	6.38429e9			0.317067
$880$	−4.78685e9	+	8.29107e9i	−0.236789	+	0.410130i
$881$	−1.09710e10	−	1.90023e10i	−0.540542	−	0.936245i	−0.998873	−	0.0474641i	$-0.984886\pi$
$881$	−1.09710e10	−	1.90023e10i	−0.540542	−	0.936245i	0.458331	−	0.888781i	$-0.348447\pi$
$882$	1.13378e9	+	1.96376e9i	0.0556401	+	0.0963715i
$883$	−9.12728e9			−0.446148			−0.223074	−	0.974802i	$-0.571609\pi$
$883$	−9.12728e9			−0.446148			−0.223074	+	0.974802i	$0.571609\pi$
$884$	−2.26938e10	+	1.47181e10i	−1.10490	+	0.716589i
$885$	1.99477e10			0.967370
$886$	1.99221e9	+	3.45061e9i	0.0962315	+	0.166678i
$887$	2.83084e9	+	4.90317e9i	0.136202	+	0.235909i	0.926056	−	0.377386i	$-0.123177\pi$
$887$	2.83084e9	+	4.90317e9i	0.136202	+	0.235909i	−0.789854	+	0.613295i	$0.789844\pi$
$888$	−2.42621e9	+	4.20233e9i	−0.116274	+	0.201393i
$889$	7.22669e9			0.344972
$890$	−1.41231e9	+	2.44619e9i	−0.0671529	+	0.116312i
$891$	−2.76513e9	+	4.78935e9i	−0.130962	+	0.226832i
$892$	−8.89818e9			−0.419782
$893$	−7.43342e8	+	1.28751e9i	−0.0349308	+	0.0605019i
$894$	−4.82873e9	−	8.36360e9i	−0.226022	−	0.391482i
$895$	2.52047e10	+	4.36558e10i	1.17517	+	2.03545i
$896$	1.54103e10			0.715705
$897$	5.40025e9	+	2.75566e9i	0.249828	+	0.127483i
$898$	−9.24588e8			−0.0426070
$899$	−2.61699e9	−	4.53277e9i	−0.120128	−	0.208068i
$900$	−8.18097e9	−	1.41699e10i	−0.374073	−	0.647913i
$901$	1.89924e10	−	3.28958e10i	0.865053	−	1.49832i
$902$	2.65756e9			0.120576
$903$	1.24550e8	−	2.15726e8i	0.00562905	−	0.00974980i
$904$	−5.68950e9	+	9.85451e9i	−0.256144	+	0.443655i
$905$	−5.97814e10			−2.68100
$906$	−3.38420e9	+	5.86161e9i	−0.151185	+	0.261859i
$907$	−1.46377e10	−	2.53532e10i	−0.651399	−	1.12826i	−0.982784	−	0.184760i	$-0.940849\pi$
$907$	−1.46377e10	−	2.53532e10i	−0.651399	−	1.12826i	0.331385	−	0.943496i	$-0.392484\pi$
$908$	6.52597e9	+	1.13033e10i	0.289297	+	0.501078i
$909$	−1.92116e10			−0.848377
$910$	−8.39777e8	−	1.62104e10i	−0.0369419	−	0.713096i
$911$	2.97047e10			1.30170			0.650851	−	0.759206i	$-0.274412\pi$
$911$	2.97047e10			1.30170			0.650851	+	0.759206i	$0.274412\pi$
$912$	−1.54099e8	−	2.66907e8i	−0.00672694	−	0.0116514i
$913$	2.45740e10	+	4.25634e10i	1.06863	+	1.85093i
$914$	−2.62223e9	+	4.54184e9i	−0.113595	+	0.196753i
$915$	−1.91721e10			−0.827361
$916$	7.37952e9	−	1.27817e10i	0.317245	−	0.549484i
$917$	3.66835e9	−	6.35377e9i	0.157101	−	0.272106i
$918$	2.17484e10			0.927849
$919$	5.01208e7	−	8.68117e7i	0.00213017	−	0.00368955i	−0.864958	−	0.501844i	$-0.832655\pi$
$919$	5.01208e7	−	8.68117e7i	0.00213017	−	0.00368955i	0.867089	+	0.498154i	$0.165989\pi$
$920$	8.79877e9	+	1.52399e10i	0.372533	+	0.645246i
$921$	5.24585e8	+	9.08607e8i	0.0221262	+	0.0383237i
$922$	6.29015e9			0.264303
$923$	5.60938e9	+	2.86237e9i	0.234806	+	0.119817i
$924$	−1.08511e10			−0.452501
$925$	−8.35065e9	−	1.44638e10i	−0.346916	−	0.600876i
$926$	1.04383e9	+	1.80796e9i	0.0432006	+	0.0748256i
$927$	8.12680e9	−	1.40760e10i	0.335074	−	0.580365i
$928$	8.10635e9			0.332972
$929$	2.25564e10	−	3.90688e10i	0.923028	−	1.59873i	0.128325	−	0.991732i	$-0.459040\pi$
$929$	2.25564e10	−	3.90688e10i	0.923028	−	1.59873i	0.794703	−	0.606999i	$-0.207627\pi$
$930$	−4.27604e9	+	7.40632e9i	−0.174322	+	0.301934i
$931$	−8.26944e8			−0.0335855
$932$	3.13797e9	−	5.43513e9i	0.126968	−	0.219915i
$933$	−1.28122e10	−	2.21913e10i	−0.516460	−	0.894536i
$934$	9.22172e9	+	1.59725e10i	0.370338	+	0.641444i
$935$	1.01421e11			4.05776
$936$	1.43838e10	+	7.33983e9i	0.573336	+	0.292564i
$937$	−1.13424e10			−0.450420			−0.225210	−	0.974310i	$-0.572307\pi$
$937$	−1.13424e10			−0.450420			−0.225210	+	0.974310i	$0.572307\pi$
$938$	7.91882e9	+	1.37158e10i	0.313293	+	0.542639i
$939$	−3.84932e9	−	6.66721e9i	−0.151724	−	0.262794i
$940$	8.81252e9	−	1.52637e10i	0.346061	−	0.599395i
$941$	−3.29118e10			−1.28762			−0.643811	−	0.765185i	$-0.722648\pi$
$941$	−3.29118e10			−1.28762			−0.643811	+	0.765185i	$0.722648\pi$
$942$	4.36154e9	−	7.55441e9i	0.170005	−	0.294457i
$943$	−1.06756e9	+	1.84907e9i	−0.0414574	+	0.0718063i
$944$	6.23371e9			0.241182
$945$	1.60445e10	−	2.77899e10i	0.618464	−	1.07121i
$946$	−2.37212e8	−	4.10863e8i	−0.00910998	−	0.0157789i
$947$	−1.18606e9	−	2.05431e9i	−0.0453816	−	0.0786033i	0.842442	−	0.538787i	$-0.181117\pi$
$947$	−1.18606e9	−	2.05431e9i	−0.0453816	−	0.0786033i	−0.887824	+	0.460183i	$0.847784\pi$
$948$	−1.60059e10			−0.610170
$949$	1.41766e9	+	2.73653e10i	0.0538443	+	1.03937i
$950$	−2.42691e9			−0.0918375
$951$	4.18302e9	+	7.24519e9i	0.157709	+	0.273161i
$952$	−1.90365e10	−	3.29722e10i	−0.715086	−	1.23857i
$953$	−1.91871e10	+	3.32329e10i	−0.718097	+	1.24378i	0.243656	+	0.969862i	$0.421653\pi$
$953$	−1.91871e10	+	3.32329e10i	−0.718097	+	1.24378i	−0.961753	+	0.273919i	$0.911680\pi$
$954$	−9.42245e9			−0.351354
$955$	−1.50748e10	+	2.61103e10i	−0.560066	+	0.970062i
$956$	−1.00445e10	+	1.73976e10i	−0.371814	+	0.644001i
$957$	−6.60890e9			−0.243746
$958$	6.84318e9	−	1.18527e10i	0.251466	−	0.435552i
$959$	2.42447e9	+	4.19931e9i	0.0887671	+	0.153749i
$960$	−4.05277e9	−	7.01960e9i	−0.147844	−	0.256073i
$961$	−1.21326e10			−0.440984
$962$	6.10048e9	+	3.11297e9i	0.220928	+	0.112736i
$963$	−4.05657e9			−0.146375
$964$	3.55685e9	+	6.16065e9i	0.127878	+	0.221491i
$965$	−1.82207e10	−	3.15592e10i	−0.652709	−	1.13052i
$966$	−1.77289e9	+	3.07073e9i	−0.0632792	+	0.109603i
$967$	−1.57165e10			−0.558937			−0.279468	−	0.960155i	$-0.590158\pi$
$967$	−1.57165e10			−0.558937			−0.279468	+	0.960155i	$0.590158\pi$
$968$	−1.18886e10	+	2.05916e10i	−0.421275	+	0.729670i
$969$	−1.63248e9	+	2.82753e9i	−0.0576387	+	0.0998331i
$970$	−3.02980e9			−0.106589
$971$	−2.41878e10	+	4.18945e10i	−0.847870	+	1.46855i	0.0352345	+	0.999379i	$0.488782\pi$
$971$	−2.41878e10	+	4.18945e10i	−0.847870	+	1.46855i	−0.883105	+	0.469176i	$0.844551\pi$
$972$	1.05341e10	+	1.82456e10i	0.367930	+	0.637273i
$973$	9.72868e9	+	1.68506e10i	0.338578	+	0.586434i
$974$	−1.24636e10			−0.432204
$975$	2.00155e10	−	1.29811e10i	0.691591	−	0.448534i
$976$	−5.99130e9			−0.206275
$977$	−9.90108e9	−	1.71492e10i	−0.339665	−	0.588318i	0.644704	−	0.764432i	$-0.276981\pi$
$977$	−9.90108e9	−	1.71492e10i	−0.339665	−	0.588318i	−0.984370	+	0.176114i	$0.943647\pi$
$978$	−6.64106e9	−	1.15027e10i	−0.227013	−	0.393199i
$979$	3.20708e9	−	5.55483e9i	0.109237	−	0.189204i
$980$	9.80364e9			0.332733
$981$	1.31497e10	−	2.27759e10i	0.444707	−	0.770255i
$982$	−8.24980e9	+	1.42891e10i	−0.278005	+	0.481519i
$983$	1.18661e10			0.398447			0.199223	−	0.979954i	$-0.436158\pi$
$983$	1.18661e10			0.398447			0.199223	+	0.979954i	$0.436158\pi$
$984$	1.22051e9	−	2.11398e9i	0.0408373	−	0.0707323i
$985$	−3.17121e9	−	5.49270e9i	−0.105730	−	0.183130i
$986$	−4.81747e9	−	8.34410e9i	−0.160048	−	0.277211i
$987$	8.54703e9			0.282947
$988$	−2.05296e9	+	1.33145e9i	−0.0677222	+	0.0439214i
$989$	3.81159e8			0.0125291
$990$	−1.25792e10	−	2.17878e10i	−0.412030	−	0.713657i
$991$	1.12447e9	+	1.94764e9i	0.0367021	+	0.0635699i	0.883793	−	0.467878i	$-0.154981\pi$
$991$	1.12447e9	+	1.94764e9i	0.0367021	+	0.0635699i	−0.847091	+	0.531448i	$0.821648\pi$
$992$	−1.19102e10	+	2.06290e10i	−0.387371	+	0.670947i
$993$	−2.00248e10			−0.649002
$994$	−1.84154e9	+	3.18964e9i	−0.0594743	+	0.103013i
$995$	−2.07099e10	+	3.58707e10i	−0.666497	+	1.15441i
$996$	1.87572e10			0.601533
$997$	2.68998e9	−	4.65918e9i	0.0859639	−	0.148894i	−0.819838	−	0.572596i	$-0.805936\pi$
$997$	2.68998e9	−	4.65918e9i	0.0859639	−	0.148894i	0.905802	+	0.423702i	$0.139270\pi$
$998$	7.62107e8	+	1.32001e9i	0.0242694	+	0.0420358i
$999$	6.76967e9	+	1.17254e10i	0.214827	+	0.372091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.8.c.a.3.5	✓	16
3.2	odd	2		117.8.g.d.55.4		16
4.3	odd	2		208.8.i.d.81.6		16
13.2	odd	12		169.8.b.e.168.9		16
13.3	even	3		169.8.a.f.1.4		8
13.9	even	3	inner	13.8.c.a.9.5	yes	16
13.10	even	6		169.8.a.e.1.5		8
13.11	odd	12		169.8.b.e.168.8		16
39.35	odd	6		117.8.g.d.100.4		16
52.35	odd	6		208.8.i.d.113.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.c.a.3.5	✓	16	1.1	even	1	trivial
13.8.c.a.9.5	yes	16	13.9	even	3	inner
117.8.g.d.55.4		16	3.2	odd	2
117.8.g.d.100.4		16	39.35	odd	6
169.8.a.e.1.5		8	13.10	even	6
169.8.a.f.1.4		8	13.3	even	3
169.8.b.e.168.8		16	13.11	odd	12
169.8.b.e.168.9		16	13.2	odd	12
208.8.i.d.81.6		16	4.3	odd	2
208.8.i.d.113.6		16	52.35	odd	6

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+(3.04173 + 5.26843i) q^{2} +(-12.8141 - 22.1946i) q^{3} +(45.4958 - 78.8010i) q^{4} +442.310 q^{5} +(77.9538 - 135.020i) q^{6} +(-380.773 + 659.518i) q^{7} +1332.23 q^{8} +(765.099 - 1325.19i) q^{9} +(1345.39 + 2330.28i) q^{10} +(-3055.11 - 5291.61i) q^{11} -2331.94 q^{12} +(409.818 + 7910.79i) q^{13} -4632.83 q^{14} +(-5667.79 - 9816.90i) q^{15} +(-1771.19 - 3067.80i) q^{16} +(-18763.5 + 32499.3i) q^{17} +9308.89 q^{18} +(-1697.41 + 2940.00i) q^{19} +(20123.2 - 34854.5i) q^{20} +19517.0 q^{21} +(18585.6 - 32191.3i) q^{22} +(14932.0 + 25863.0i) q^{23} +(-17071.2 - 29568.2i) q^{24} +117513. q^{25} +(-40430.9 + 26221.6i) q^{26} -95264.9 q^{27} +(34647.2 + 60010.6i) q^{28} +(21102.1 + 36549.8i) q^{29} +(34479.7 - 59720.7i) q^{30} -124016. q^{31} +(96037.4 - 166342. i) q^{32} +(-78296.9 + 135614. i) q^{33} -228294. q^{34} +(-168420. + 291712. i) q^{35} +(-69617.6 - 120581. i) q^{36} +(-71061.5 - 123082. i) q^{37} -20652.2 q^{38} +(170325. - 110465. i) q^{39} +589256. q^{40} +(35747.5 + 61916.4i) q^{41} +(59365.4 + 102824. i) q^{42} +(6381.59 - 11053.2i) q^{43} -555979. q^{44} +(338411. - 586145. i) q^{45} +(-90838.0 + 157336. i) q^{46} +437927. q^{47} +(-45392.4 + 78622.0i) q^{48} +(121795. + 210955. i) q^{49} +(357443. + 619109. i) q^{50} +961747. q^{51} +(642023. + 327613. i) q^{52} -1.01220e6 q^{53} +(-289770. - 501896. i) q^{54} +(-1.35131e6 - 2.34053e6i) q^{55} +(-507276. + 878627. i) q^{56} +87002.9 q^{57} +(-128373. + 222349. i) q^{58} +(-879873. + 1.52399e6i) q^{59} -1.03144e6 q^{60} +(845659. - 1.46472e6i) q^{61} +(-377223. - 653370. i) q^{62} +(582659. + 1.00919e6i) q^{63} +715053. q^{64} +(181266. + 3.49902e6i) q^{65} -952631. q^{66} +(-1.70928e6 - 2.96056e6i) q^{67} +(1.70732e6 + 2.95716e6i) q^{68} +(382679. - 662819. i) q^{69} -2.04915e6 q^{70} +(397498. - 688487. i) q^{71} +(1.01928e6 - 1.76545e6i) q^{72} +3.45924e6 q^{73} +(432300. - 748765. i) q^{74} +(-1.50582e6 - 2.60816e6i) q^{75} +(154450. + 267515. i) q^{76} +4.65322e6 q^{77} +(1.10006e6 + 561343. i) q^{78} +6.86376e6 q^{79} +(-783417. - 1.35692e6i) q^{80} +(-452541. - 783825. i) q^{81} +(-217468. + 376666. i) q^{82} -8.04357e6 q^{83} +(887942. - 1.53796e6i) q^{84} +(-8.29928e6 + 1.43748e7i) q^{85} +77644.2 q^{86} +(540807. - 936704. i) q^{87} +(-4.07010e6 - 7.04962e6i) q^{88} +(524871. + 909103. i) q^{89} +4.11742e6 q^{90} +(-5.37336e6 - 2.74193e6i) q^{91} +2.71737e6 q^{92} +(1.58915e6 + 2.75249e6i) q^{93} +(1.33206e6 + 2.30719e6i) q^{94} +(-750781. + 1.30039e6i) q^{95} -4.92252e6 q^{96} +(-562998. + 975142. i) q^{97} +(-740935. + 1.28334e6i) q^{98} -9.34986e6 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

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