LMFDB - Embedded newform 59.7.d.a.43.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [59,7,Mod(2,59)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("59.2"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(59, base_ring=CyclotomicField(58)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	59.d (of order $58$, degree $28$, 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:	$13.5731909336$
Analytic rank:	$0$
Dimension:	$812$
Relative dimension:	$29$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			43.3
Character	$\chi$	$=$	59.43
Dual form			59.7.d.a.11.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.82178 + 12.8195i) q^{2} +(-6.70926 - 40.9247i) q^{3} +(-98.2915 - 45.4745i) q^{4} +(-36.2562 - 130.583i) q^{5} +(543.565 + 29.4712i) q^{6} +(400.602 + 379.471i) q^{7} +(351.917 - 462.939i) q^{8} +(-938.976 + 316.378i) q^{9} +(1776.31 - 96.3088i) q^{10} +(-1420.48 - 1206.57i) q^{11} +(-1201.57 + 4327.65i) q^{12} +(15.4791 - 45.9404i) q^{13} +(-5995.02 + 4064.73i) q^{14} +(-5100.82 + 2359.89i) q^{15} +(454.386 + 534.945i) q^{16} +(-404.121 + 382.803i) q^{17} +(-1406.21 - 12929.9i) q^{18} +(-3059.93 + 7679.85i) q^{19} +(-2374.52 + 14483.9i) q^{20} +(12842.0 - 18940.5i) q^{21} +(19475.8 - 14805.1i) q^{22} +(-2125.11 + 19540.1i) q^{23} +(-21306.7 - 11296.1i) q^{24} +(-2349.02 + 1413.36i) q^{25} +(545.253 + 328.068i) q^{26} +(5086.40 + 9593.96i) q^{27} +(-22119.6 - 55515.9i) q^{28} +(-25621.4 + 5639.71i) q^{29} +(-15859.1 - 72048.8i) q^{30} +(-51715.3 + 20605.3i) q^{31} +(24741.7 - 13117.2i) q^{32} +(-39847.9 + 66227.8i) q^{33} +(-3767.00 - 6260.80i) q^{34} +(35028.1 - 66070.0i) q^{35} +(106680. + 11602.2i) q^{36} +(30832.9 + 40560.0i) q^{37} +(-89817.1 - 60897.5i) q^{38} +(-1983.95 - 325.252i) q^{39} +(-73211.2 - 29170.0i) q^{40} +(-59631.3 + 6485.29i) q^{41} +(206570. + 218073. i) q^{42} +(56178.6 - 47718.5i) q^{43} +(84753.1 + 183191. i) q^{44} +(75357.2 + 111144. i) q^{45} +(-244497. - 82380.7i) q^{46} +(51840.1 + 14393.3i) q^{47} +(18843.8 - 22184.7i) q^{48} +(10114.8 + 186557. i) q^{49} +(-11490.1 - 34101.4i) q^{50} +(18377.5 + 13970.2i) q^{51} +(-3610.58 + 3811.64i) q^{52} +(3038.50 - 56041.8i) q^{53} +(-137342. + 38132.9i) q^{54} +(-106056. + 229236. i) q^{55} +(316651. - 51912.2i) q^{56} +(334825. + 73700.6i) q^{57} -344367. i q^{58} +(-128316. - 160360. i) q^{59} +608682. q^{60} +(5190.90 - 23582.5i) q^{61} +(-118219. - 721106. i) q^{62} +(-496212. - 229572. i) q^{63} +(110358. + 397472. i) q^{64} +(-6560.25 - 355.686i) q^{65} +(-736563. - 697710. i) q^{66} +(-101283. + 133236. i) q^{67} +(57129.4 - 19249.2i) q^{68} +(813930. - 44130.0i) q^{69} +(748141. + 635477. i) q^{70} +(18950.2 - 68252.5i) q^{71} +(-183978. + 546027. i) q^{72} +(-413145. + 280119. i) q^{73} +(-606961. + 280810. i) q^{74} +(73601.4 + 86650.3i) q^{75} +(650002. - 615715. i) q^{76} +(-111191. - 1.02238e6i) q^{77} +(9767.82 - 24515.4i) q^{78} +(26727.7 - 163032. i) q^{79} +(53380.4 - 78730.2i) q^{80} +(-216534. + 164605. i) q^{81} +(85128.3 - 782742. i) q^{82} +(138529. + 73443.3i) q^{83} +(-2.12357e6 + 1.27771e6i) q^{84} +(64639.5 + 38892.3i) q^{85} +(453203. + 854831. i) q^{86} +(402704. + 1.01071e6i) q^{87} +(-1.05846e6 + 232984. i) q^{88} +(-169795. - 771388. i) q^{89} +(-1.63744e6 + 652417. i) q^{90} +(23634.0 - 12529.9i) q^{91} +(1.09746e6 - 1.82399e6i) q^{92} +(1.19023e6 + 1.97819e6i) q^{93} +(-330796. + 623948. i) q^{94} +(1.11380e6 + 121133. i) q^{95} +(-702816. - 924538. i) q^{96} +(1.42260e6 + 964545. i) q^{97} +(-2.42011e6 - 396756. i) q^{98} +(1.71553e6 + 683528. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 812 q - 29 q^{2} - 39 q^{3} + 869 q^{4} - 171 q^{5} - 29 q^{6} - 435 q^{7} - 29 q^{8} - 7648 q^{9} - 29 q^{10} - 29 q^{11} + 1095 q^{12} - 29 q^{13} - 29 q^{14} - 569 q^{15} - 25051 q^{16} - 9071 q^{17}+ \cdots + 9513421 q^{99}+O(q^{100}) $ 812 * q - 29 * q^2 - 39 * q^3 + 869 * q^4 - 171 * q^5 - 29 * q^6 - 435 * q^7 - 29 * q^8 - 7648 * q^9 - 29 * q^10 - 29 * q^11 + 1095 * q^12 - 29 * q^13 - 29 * q^14 - 569 * q^15 - 25051 * q^16 - 9071 * q^17 - 29 * q^18 - 3879 * q^19 + 46867 * q^20 - 3729 * q^21 - 11267 * q^22 - 29 * q^23 - 29 * q^24 - 65696 * q^25 + 64561 * q^26 - 36009 * q^27 + 45513 * q^28 + 31701 * q^29 - 29 * q^30 - 29 * q^31 - 29 * q^32 - 29 * q^33 - 29 * q^34 - 46305 * q^35 + 185269 * q^36 - 29 * q^37 - 29 * q^38 - 29 * q^39 - 29 * q^40 - 91943 * q^41 - 29 * q^42 - 29 * q^43 - 29 * q^44 + 1328609 * q^45 + 122071 * q^46 - 472149 * q^47 - 4460721 * q^48 - 992540 * q^49 - 1117341 * q^50 - 161065 * q^51 + 1336291 * q^52 + 1079813 * q^53 + 4504947 * q^54 + 1872907 * q^55 + 3956963 * q^56 + 2677007 * q^57 - 302138 * q^59 - 4965482 * q^60 - 1574381 * q^61 - 2444409 * q^62 - 5085047 * q^63 - 5066455 * q^64 - 1422653 * q^65 + 433939 * q^66 + 876931 * q^67 + 3018437 * q^68 + 5706243 * q^69 + 6798499 * q^70 + 3537645 * q^71 + 6041251 * q^72 - 396749 * q^73 - 3448403 * q^74 - 9552475 * q^75 - 247173 * q^76 - 29 * q^77 + 375035 * q^78 - 4731 * q^79 - 1921013 * q^80 + 841594 * q^81 - 29 * q^82 - 29 * q^83 - 2367333 * q^84 - 864073 * q^85 - 5031139 * q^86 + 4790463 * q^87 - 726023 * q^88 - 29 * q^89 - 29 * q^90 - 29 * q^91 - 29 * q^92 - 29 * q^93 - 2835797 * q^94 - 1047881 * q^95 - 29 * q^96 - 29 * q^97 + 29127484 * q^98 + 9513421 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/59\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{33}{58}\right)$

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 $

$2$	−2.82178	+	12.8195i	−0.352722	+	1.60243i	0.382065	+	0.924136i	$0.375213\pi$
$2$	−2.82178	+	12.8195i	−0.352722	+	1.60243i	−0.734787	+	0.678298i	$0.762718\pi$
$3$	−6.70926	−	40.9247i	−0.248491	−	1.51573i	−0.756281	−	0.654247i	$-0.772985\pi$
$3$	−6.70926	−	40.9247i	−0.248491	−	1.51573i	0.507789	−	0.861481i	$-0.330463\pi$
$4$	−98.2915	−	45.4745i	−1.53581	−	0.710539i
$5$	−36.2562	−	130.583i	−0.290050	−	1.04466i	−0.954715	−	0.297523i	$-0.903840\pi$
$5$	−36.2562	−	130.583i	−0.290050	−	1.04466i	0.664665	−	0.747141i	$-0.268574\pi$
$6$	543.565	+	29.4712i	2.51650	+	0.136441i
$7$	400.602	+	379.471i	1.16794	+	1.10633i	0.992551	+	0.121829i	$0.0388758\pi$
$7$	400.602	+	379.471i	1.16794	+	1.10633i	0.175386	+	0.984500i	$0.443883\pi$
$8$	351.917	−	462.939i	0.687338	−	0.904178i
$9$	−938.976	+	316.378i	−1.28803	+	0.433989i
$10$	1776.31	−	96.3088i	1.77631	−	0.0963088i
$11$	−1420.48	−	1206.57i	−1.06723	−	0.906510i	−0.0713702	−	0.997450i	$-0.522737\pi$
$11$	−1420.48	−	1206.57i	−1.06723	−	0.906510i	−0.995856	+	0.0909394i	$0.971013\pi$
$12$	−1201.57	+	4327.65i	−0.695351	+	2.50443i
$13$	15.4791	−	45.9404i	0.00704557	−	0.0209105i	−0.944073	−	0.329737i	$-0.893040\pi$
$13$	15.4791	−	45.9404i	0.00704557	−	0.0209105i	0.951118	+	0.308827i	$0.0999364\pi$
$14$	−5995.02	+	4064.73i	−2.18478	+	1.48131i
$15$	−5100.82	+	2359.89i	−1.51135	+	0.699226i
$16$	454.386	+	534.945i	0.110934	+	0.130602i
$17$	−404.121	+	382.803i	−0.0822554	+	0.0779164i	−0.727723	−	0.685871i	$-0.759421\pi$
$17$	−404.121	+	382.803i	−0.0822554	+	0.0779164i	0.645467	+	0.763788i	$0.276663\pi$
$18$	−1406.21	−	12929.9i	−0.241120	−	2.21706i
$19$	−3059.93	+	7679.85i	−0.446119	+	1.11967i	0.518277	+	0.855213i	$0.326574\pi$
$19$	−3059.93	+	7679.85i	−0.446119	+	1.11967i	−0.964396	+	0.264462i	$0.914806\pi$
$20$	−2374.52	+	14483.9i	−0.296815	+	1.81049i
$21$	12842.0	−	18940.5i	1.38667	−	2.04519i
$22$	19475.8	−	14805.1i	1.82906	−	1.39041i
$23$	−2125.11	+	19540.1i	−0.174662	+	1.60599i	0.498765	+	0.866737i	$0.333787\pi$
$23$	−2125.11	+	19540.1i	−0.174662	+	1.60599i	−0.673427	+	0.739254i	$0.735178\pi$
$24$	−21306.7	−	11296.1i	−1.54129	−	0.817138i
$25$	−2349.02	+	1413.36i	−0.150337	+	0.0904549i
$26$	545.253	+	328.068i	0.0310226	+	0.0186657i
$27$	5086.40	+	9593.96i	0.258416	+	0.487424i
$28$	−22119.6	−	55515.9i	−1.00763	−	2.52897i
$29$	−25621.4	+	5639.71i	−1.05053	+	0.231240i	−0.706497	−	0.707717i	$-0.749725\pi$
$29$	−25621.4	+	5639.71i	−1.05053	+	0.231240i	−0.344036	+	0.938956i	$0.611794\pi$
$30$	−15859.1	−	72048.8i	−0.587376	−	2.66848i
$31$	−51715.3	+	20605.3i	−1.73594	+	0.691660i	−0.736045	+	0.676932i	$0.763309\pi$
$31$	−51715.3	+	20605.3i	−1.73594	+	0.691660i	−0.999892	+	0.0147282i	$0.995312\pi$
$32$	24741.7	−	13117.2i	0.755056	−	0.400305i
$33$	−39847.9	+	66227.8i	−1.10883	+	1.84289i
$34$	−3767.00	−	6260.80i	−0.0958426	−	0.159292i
$35$	35028.1	−	66070.0i	0.816982	−	1.54099i
$36$	106680.	+	11602.2i	2.28653	+	0.248675i
$37$	30832.9	+	40560.0i	0.608708	+	0.800741i	0.992444	−	0.122702i	$-0.0391558\pi$
$37$	30832.9	+	40560.0i	0.608708	+	0.800741i	−0.383736	+	0.923443i	$0.625363\pi$
$38$	−89817.1	−	60897.5i	−1.63685	−	1.10981i
$39$	−1983.95	−	325.252i	−0.0334454	−	0.00548310i
$40$	−73211.2	−	29170.0i	−1.14392	−	0.455781i
$41$	−59631.3	+	6485.29i	−0.865212	+	0.0940975i	−0.529952	−	0.848028i	$-0.677790\pi$
$41$	−59631.3	+	6485.29i	−0.865212	+	0.0940975i	−0.335261	+	0.942125i	$0.608824\pi$
$42$	206570.	+	218073.i	2.78817	+	2.94343i
$43$	56178.6	−	47718.5i	0.706587	−	0.600180i	−0.220340	−	0.975423i	$-0.570717\pi$
$43$	56178.6	−	47718.5i	0.706587	−	0.600180i	0.926927	+	0.375243i	$0.122441\pi$
$44$	84753.1	+	183191.i	0.994941	+	2.15053i
$45$	75357.2	+	111144.i	0.826966	+	1.21968i
$46$	−244497.	−	82380.7i	−2.51189	−	0.846353i
$47$	51840.1	+	14393.3i	0.499313	+	0.138633i	0.508049	−	0.861328i	$-0.330367\pi$
$47$	51840.1	+	14393.3i	0.499313	+	0.138633i	−0.00873608	+	0.999962i	$0.502781\pi$
$48$	18843.8	−	22184.7i	0.170391	−	0.200599i
$49$	10114.8	+	186557.i	0.0859747	+	1.58571i
$50$	−11490.1	−	34101.4i	−0.0919207	−	0.272811i
$51$	18377.5	+	13970.2i	0.138540	+	0.105315i
$52$	−3610.58	+	3811.64i	−0.0256784	+	0.0271083i
$53$	3038.50	−	56041.8i	0.0204095	−	0.376430i	−0.970430	−	0.241384i	$-0.922399\pi$
$53$	3038.50	−	56041.8i	0.0204095	−	0.376430i	0.990839	−	0.135047i	$-0.0431184\pi$
$54$	−137342.	+	38132.9i	−0.872214	+	0.242169i
$55$	−106056.	+	229236.i	−0.637450	+	1.37783i
$56$	316651.	−	51912.2i	1.80309	−	0.295601i
$57$	334825.	+	73700.6i	1.80798	+	0.397966i
$58$		−	344367.i		−	1.76497i
$59$	−128316.	−	160360.i	−0.624778	−	0.780803i
$59$	−128316.	−	160360.i	−0.624778	−	0.780803i
$60$	608682.			2.81797
$61$	5190.90	−	23582.5i	0.0228693	−	0.103896i	−0.963803	−	0.266614i	$-0.914095\pi$
$61$	5190.90	−	23582.5i	0.0228693	−	0.103896i	0.986673	+	0.162718i	$0.0520261\pi$
$62$	−118219.	−	721106.i	−0.496036	−	3.02569i
$63$	−496212.	−	229572.i	−1.98447	−	0.918116i
$64$	110358.	+	397472.i	0.420981	+	1.51623i
$65$	−6560.25	−	355.686i	−0.0238880	−	0.00129517i
$66$	−736563.	−	697710.i	−2.56199	−	2.42685i
$67$	−101283.	+	133236.i	−0.336754	+	0.442993i	−0.933036	−	0.359782i	$-0.882851\pi$
$67$	−101283.	+	133236.i	−0.336754	+	0.442993i	0.596282	+	0.802775i	$0.296644\pi$
$68$	57129.4	−	19249.2i	0.181691	−	0.0612188i
$69$	813930.	−	44130.0i	2.47765	−	0.134334i
$70$	748141.	+	635477.i	2.18117	+	1.85270i
$71$	18950.2	−	68252.5i	0.0529467	−	0.190697i	−0.932347	−	0.361564i	$-0.882243\pi$
$71$	18950.2	−	68252.5i	0.0529467	−	0.190697i	0.985294	+	0.170867i	$0.0546568\pi$
$72$	−183978.	+	546027.i	−0.492911	+	1.46291i
$73$	−413145.	+	280119.i	−1.06202	+	0.720070i	−0.961483	−	0.274863i	$-0.911368\pi$
$73$	−413145.	+	280119.i	−1.06202	+	0.720070i	−0.100540	+	0.994933i	$0.532057\pi$
$74$	−606961.	+	280810.i	−1.49784	+	0.692974i
$75$	73601.4	+	86650.3i	0.174463	+	0.205393i
$76$	650002.	−	615715.i	1.48072	−	1.40262i
$77$	−111191.	−	1.02238e6i	−0.243555	−	2.23945i
$78$	9767.82	−	24515.4i	0.0205832	−	0.0516600i
$79$	26727.7	−	163032.i	0.0542101	−	0.330667i	−0.945773	−	0.324829i	$-0.894693\pi$
$79$	26727.7	−	163032.i	0.0542101	−	0.330667i	0.999983	−	0.00583817i	$-0.00185836\pi$
$80$	53380.4	−	78730.2i	0.104259	−	0.153770i
$81$	−216534.	+	164605.i	−0.407446	+	0.309733i
$82$	85128.3	−	782742.i	0.154395	−	1.41964i
$83$	138529.	+	73443.3i	0.242273	+	0.128445i	0.585121	−	0.810946i	$-0.301047\pi$
$83$	138529.	+	73443.3i	0.242273	+	0.128445i	−0.342848	+	0.939391i	$0.611392\pi$
$84$	−2.12357e6	+	1.27771e6i	−3.58284	+	2.15573i
$85$	64639.5	+	38892.3i	0.105255	+	0.0633296i
$86$	453203.	+	854831.i	0.712520	+	1.34396i
$87$	402704.	+	1.01071e6i	0.611545	+	1.53486i
$88$	−1.05846e6	+	232984.i	−1.55319	+	0.341883i
$89$	−169795.	−	771388.i	−0.240855	−	1.09422i	−0.929415	−	0.369037i	$-0.879688\pi$
$89$	−169795.	−	771388.i	−0.240855	−	1.09422i	0.688560	−	0.725180i	$-0.258243\pi$
$90$	−1.63744e6	+	652417.i	−2.24615	+	0.894948i
$91$	23634.0	−	12529.9i	0.0313627	−	0.0166274i
$92$	1.09746e6	−	1.82399e6i	1.40937	−	2.34239i
$93$	1.19023e6	+	1.97819e6i	1.47973	+	2.45934i
$94$	−330796.	+	623948.i	−0.398270	+	0.751216i
$95$	1.11380e6	+	121133.i	1.29908	+	0.141283i
$96$	−702816.	−	924538.i	−0.794379	−	1.04499i
$97$	1.42260e6	+	964545.i	1.55872	+	1.05684i	0.968317	+	0.249723i	$0.0803397\pi$
$97$	1.42260e6	+	964545.i	1.55872	+	1.05684i	0.590398	+	0.807112i	$0.298971\pi$
$98$	−2.42011e6	−	396756.i	−2.57132	−	0.421546i
$99$	1.71553e6	+	683528.i	1.76804	+	0.704451i
$100$	295161.	−	32100.6i	0.295161	−	0.0321006i
$101$	−348048.	−	367430.i	−0.337812	−	0.356624i	0.534851	−	0.844946i	$-0.320368\pi$
$101$	−348048.	−	367430.i	−0.337812	−	0.356624i	−0.872663	+	0.488322i	$0.837609\pi$
$102$	−230947.	+	196169.i	−0.217627	+	0.184854i
$103$	−514681.	−	1.11246e6i	−0.471006	−	1.01806i	−0.986889	−	0.161403i	$-0.948398\pi$
$103$	−514681.	−	1.11246e6i	−0.471006	−	1.01806i	0.515883	−	0.856659i	$-0.327464\pi$
$104$	−15820.2	−	23333.1i	−0.0140641	−	0.0207430i
$105$	−2.93891e6	−	990233.i	−2.53874	−	0.855400i
$106$	709852.	+	197089.i	0.596006	+	0.165480i
$107$	−171643.	+	202074.i	−0.140112	+	0.164953i	−0.827742	−	0.561108i	$-0.810375\pi$
$107$	−171643.	+	202074.i	−0.140112	+	0.164953i	0.687630	+	0.726061i	$0.258651\pi$
$108$	−63669.1	−	1.17431e6i	−0.0505426	−	0.932203i
$109$	−734493.	−	2.17990e6i	−0.567163	−	1.68328i	−0.719113	−	0.694893i	$-0.755452\pi$
$109$	−734493.	−	2.17990e6i	−0.567163	−	1.68328i	0.151950	−	0.988388i	$-0.451445\pi$
$110$	−2.63942e6	−	2.00643e6i	−1.98303	−	1.50746i
$111$	1.45304e6	−	1.53395e6i	1.06245	−	1.12161i
$112$	−20967.7	+	386726.i	−0.0149244	+	0.275264i
$113$	478240.	−	132783.i	0.331444	−	0.0920250i	−0.0978196	−	0.995204i	$-0.531187\pi$
$113$	478240.	−	132783.i	0.331444	−	0.0920250i	0.429264	+	0.903179i	$0.358773\pi$
$114$	−1.88960e6	+	4.08431e6i	−1.27543	+	2.75679i
$115$	2.62865e6	−	430946.i	1.72838	−	0.283354i
$116$	2.77483e6	+	610787.i	1.77772	+	0.391306i
$117$			48034.1i			0.0299911i
$118$	2.41782e6	−	1.19244e6i	1.47156	−	0.725759i
$119$	−307154.			−0.182270
$120$	−702580.	+	3.19185e6i	−0.406585	+	1.84714i
$121$	275353.	+	1.67958e6i	0.155429	+	0.948078i
$122$	287667.	+	133089.i	0.158420	+	0.0732931i
$123$	665490.	+	2.39688e6i	0.357624	+	1.28804i
$124$	6.02019e6	+	326405.i	3.15751	+	0.171195i
$125$	−1.26760e6	−	1.20073e6i	−0.649011	−	0.614776i
$126$	4.34319e6	−	5.71337e6i	2.17119	−	2.85615i
$127$	−2.32450e6	+	783216.i	−1.13480	+	0.382358i	−0.823142	−	0.567836i	$-0.807781\pi$
$127$	−2.32450e6	+	783216.i	−1.13480	+	0.382358i	−0.311657	+	0.950195i	$0.600884\pi$
$128$	−3.61717e6	+	196117.i	−1.72480	+	0.0935160i
$129$	−2.32978e6	−	1.97894e6i	−1.08529	−	0.921855i
$130$	23071.3	−	83095.2i	0.0105013	−	0.0378221i
$131$	717497.	−	2.12946e6i	0.319158	−	0.947228i	−0.661235	−	0.750179i	$-0.729967\pi$
$131$	717497.	−	2.12946e6i	0.319158	−	0.947228i	0.980394	−	0.197050i	$-0.0631360\pi$
$132$	6.92839e6	−	4.69757e6i	3.01239	−	2.04245i
$133$	−4.14009e6	+	1.91541e6i	−1.75977	+	0.814155i
$134$	−1.42221e6	−	1.67436e6i	−0.591085	−	0.695880i
$135$	1.06840e6	−	1.01204e6i	0.434241	−	0.411335i
$136$	34997.7	+	321798.i	0.0139131	+	0.127928i
$137$	−180365.	+	452682.i	−0.0701440	+	0.176048i	−0.959869	−	0.280449i	$-0.909517\pi$
$137$	−180365.	+	452682.i	−0.0701440	+	0.176048i	0.889725	+	0.456497i	$0.150896\pi$
$138$	−1.73101e6	+	1.05587e7i	−0.658660	+	4.01765i
$139$	−1.92757e6	+	2.84295e6i	−0.717737	+	1.05858i	0.277464	+	0.960736i	$0.410506\pi$
$139$	−1.92757e6	+	2.84295e6i	−0.717737	+	1.05858i	−0.995201	+	0.0978470i	$0.968804\pi$
$140$	−6.44747e6	+	4.90124e6i	−2.34966	+	1.78617i
$141$	241234.	−	2.21811e6i	0.0860560	−	0.791271i
$142$	821488.	+	435525.i	0.286904	+	0.152107i
$143$	−77417.8	+	46580.8i	−0.0264748	+	0.0159294i
$144$	−595902.	−	358542.i	−0.199566	−	0.120075i
$145$	1.66539e6	+	3.14125e6i	0.546275	+	1.03038i
$146$	−2.42518e6	−	6.08674e6i	−0.779265	−	1.95581i
$147$	7.56693e6	−	1.66561e6i	2.38214	−	0.524349i
$148$	−1.18617e6	−	5.38881e6i	−0.365898	−	1.66229i
$149$	−3.02719e6	+	1.20614e6i	−0.915126	+	0.364620i	−0.779689	−	0.626166i	$-0.784623\pi$
$149$	−3.02719e6	+	1.20614e6i	−0.915126	+	0.364620i	−0.135437	+	0.990786i	$0.543244\pi$
$150$	−1.31850e6	+	699023.i	−0.390666	+	0.207118i
$151$	1.97404e6	−	3.28089e6i	0.573358	−	0.952929i	−0.425491	−	0.904963i	$-0.639899\pi$
$151$	1.97404e6	−	3.28089e6i	0.573358	−	0.952929i	0.998849	−	0.0479660i	$-0.0152739\pi$
$152$	2.47846e6	+	4.11923e6i	0.705750	+	1.17297i
$153$	258349.	−	487298.i	0.0721328	−	0.136057i
$154$	1.34202e7	+	1.45953e6i	3.67448	+	0.399623i
$155$	4.56570e6	+	6.00607e6i	1.22606	+	1.61286i
$156$	180215.	+	122189.i	0.0474697	+	0.0321852i
$157$	−4.76758e6	−	781605.i	−1.23197	−	0.201971i	−0.489590	−	0.871953i	$-0.662854\pi$
$157$	−4.76758e6	−	781605.i	−1.23197	−	0.201971i	−0.742377	+	0.669982i	$0.766302\pi$
$158$	2.01456e6	+	802674.i	0.510751	+	0.203502i
$159$	−2.31388e6	+	251649.i	−0.575638	+	0.0626044i
$160$	−2.60992e6	−	2.75526e6i	−0.637188	−	0.672672i
$161$	−8.26622e6	+	7.02139e6i	−1.98075	+	1.68246i
$162$	−1.49913e6	−	3.24033e6i	−0.352611	−	0.762155i
$163$	2.19012e6	+	3.23019e6i	0.505715	+	0.745874i	0.991767	−	0.128056i	$-0.0408737\pi$
$163$	2.19012e6	+	3.23019e6i	0.505715	+	0.745874i	−0.486052	+	0.873930i	$0.661563\pi$
$164$	6.15617e6	+	2.07425e6i	1.39566	+	0.470252i
$165$	1.00930e7	+	2.80230e6i	2.24681	+	0.623824i
$166$	−1.33240e6	+	1.56862e6i	−0.291280	+	0.342921i
$167$	48666.4	+	897599.i	0.0104491	+	0.192723i	0.999098	+	0.0424752i	$0.0135243\pi$
$167$	48666.4	+	897599.i	0.0104491	+	0.192723i	−0.988648	+	0.150248i	$0.951993\pi$
$168$	−4.24898e6	−	1.26105e7i	−0.896101	−	2.65953i
$169$	3.84072e6	+	2.91964e6i	0.795705	+	0.604880i
$170$	−680977.	+	718899.i	−0.138607	+	0.146326i
$171$	443468.	−	8.17928e6i	0.0886898	−	1.63579i
$172$	−7.69186e6	+	2.13563e6i	−1.51163	+	0.419702i
$173$	2.72260e6	−	5.88479e6i	0.525829	−	1.13656i	−0.444722	−	0.895669i	$-0.646698\pi$
$173$	2.72260e6	−	5.88479e6i	0.525829	−	1.13656i	0.970552	−	0.240893i	$-0.0774403\pi$
$174$	−1.40931e7	+	2.31045e6i	−2.67522	+	0.438580i
$175$	−1.47735e6	−	325189.i	−0.275657	−	0.0606768i
$176$		−	1.30812e6i		−	0.239945i
$177$	−5.70179e6	+	6.32720e6i	−1.02823	+	1.14102i
$178$	1.03679e7			1.83836
$179$	882611.	−	4.00974e6i	0.153890	−	0.699129i	−0.834972	−	0.550293i	$-0.814516\pi$
$179$	882611.	−	4.00974e6i	0.153890	−	0.699129i	0.988862	−	0.148837i	$-0.0475529\pi$
$180$	−2.35278e6	−	1.43513e7i	−0.403426	−	2.46079i
$181$	−3.95693e6	−	1.83067e6i	−0.667302	−	0.308727i	0.0568345	−	0.998384i	$-0.481899\pi$
$181$	−3.95693e6	−	1.83067e6i	−0.667302	−	0.308727i	−0.724136	+	0.689657i	$0.757761\pi$
$182$	93937.4	+	338332.i	0.0155820	+	0.0561215i
$183$	−999932.	−	54214.8i	−0.163161	−	0.00884635i
$184$	8.29801e6	+	7.86029e6i	1.33205	+	1.26178i
$185$	4.17856e6	−	5.49680e6i	0.659950	−	0.868150i
$186$	−2.87179e7	+	9.67618e6i	−4.46286	+	1.50371i
$187$	1.03592e6	−	56166.1i	0.158417	−	0.00858913i
$188$	−4.44092e6	−	3.77215e6i	−0.668342	−	0.567695i
$189$	−1.60301e6	+	5.77350e6i	−0.237438	+	0.855173i
$190$	−4.69575e6	+	1.39365e7i	−0.684612	+	2.03186i
$191$	−78348.0	+	53121.2i	−0.0112442	+	0.00762374i	−0.566796	−	0.823858i	$-0.691817\pi$
$191$	−78348.0	+	53121.2i	−0.0112442	+	0.00762374i	0.555552	+	0.831482i	$0.312507\pi$
$192$	1.55260e7	−	7.18309e6i	2.19359	−	1.01486i
$193$	−8.98034e6	−	1.05725e7i	−1.24917	−	1.47063i	−0.825083	−	0.565011i	$-0.808872\pi$
$193$	−8.98034e6	−	1.05725e7i	−1.24917	−	1.47063i	−0.424084	−	0.905623i	$-0.639404\pi$
$194$	−1.63792e7	+	1.55152e7i	−2.24330	+	2.12497i
$195$	29458.1	+	270862.i	0.00397283	+	0.0365296i
$196$	7.48939e6	−	1.87970e7i	0.994668	−	2.49643i
$197$	644570.	−	3.93170e6i	0.0843085	−	0.514259i	−0.910584	−	0.413323i	$-0.864368\pi$
$197$	644570.	−	3.93170e6i	0.0843085	−	0.514259i	0.994893	−	0.100936i	$-0.0321838\pi$
$198$	−1.36033e7	+	2.00634e7i	−1.75246	+	2.58469i
$199$	−5.39863e6	+	4.10393e6i	−0.685054	+	0.520764i	−0.888821	−	0.458255i	$-0.848475\pi$
$199$	−5.39863e6	+	4.10393e6i	−0.685054	+	0.520764i	0.203767	+	0.979019i	$0.434681\pi$
$200$	−172362.	+	1.58484e6i	−0.0215452	+	0.198105i
$201$	6.13217e6	+	3.25107e6i	0.755137	+	0.400348i
$202$	5.69238e6	−	3.42499e6i	0.690621	−	0.415533i
$203$	−1.24041e7	−	7.46331e6i	−1.48278	−	0.892161i
$204$	−1.17106e6	−	2.20886e6i	−0.137940	−	0.260182i
$205$	3.00887e6	+	7.55170e6i	0.349255	+	0.876563i
$206$	1.57135e7	−	3.45881e6i	1.79751	−	0.395662i
$207$	−4.18662e6	−	1.90200e7i	−0.472012	−	2.14437i
$208$	31609.0	−	12594.2i	0.00351254	−	0.00139952i
$209$	1.36128e7	−	7.21705e6i	1.49111	−	0.790535i
$210$	2.09872e7	−	3.48810e7i	2.26619	−	3.76644i
$211$	8.89768e6	+	1.47881e7i	0.947173	+	1.57421i	0.812212	+	0.583363i	$0.198263\pi$
$211$	8.89768e6	+	1.47881e7i	0.947173	+	1.57421i	0.134961	+	0.990851i	$0.456909\pi$
$212$	−2.84713e6	+	5.37026e6i	−0.298813	+	0.563622i
$213$	−2.92035e6	−	317608.i	−0.302201	−	0.0328664i
$214$	−2.10614e6	−	2.77058e6i	−0.214905	−	0.282703i
$215$	−8.26805e6	−	5.60588e6i	−0.831932	−	0.564064i
$216$	6.23141e6	+	1.02159e6i	0.618337	+	0.101371i
$217$	−2.85364e7	−	1.13699e7i	−2.79267	−	1.11270i
$218$	3.00177e7	−	3.26462e6i	2.89740	−	0.315111i
$219$	1.42357e7	+	1.50284e7i	1.35533	+	1.43081i
$220$	2.08488e7	−	1.77091e7i	1.95800	−	1.66314i
$221$	11330.7	+	24490.9i	0.00104974	+	0.00226897i
$222$	1.55643e7	+	2.29556e7i	1.42256	+	2.09812i
$223$	968699.	+	326393.i	0.0873523	+	0.0294324i	0.362638	−	0.931930i	$-0.381876\pi$
$223$	968699.	+	326393.i	0.0873523	+	0.0294324i	−0.275286	+	0.961362i	$0.588773\pi$
$224$	1.48892e7	+	4.13396e6i	1.32473	+	0.367809i
$225$	1.75852e6	−	2.07029e6i	0.154383	−	0.181754i
$226$	352716.	+	6.50547e6i	0.0305562	+	0.563577i
$227$	3.42737e6	+	1.01721e7i	0.293011	+	0.869625i	0.988518	+	0.151105i	$0.0482833\pi$
$227$	3.42737e6	+	1.01721e7i	0.293011	+	0.869625i	−0.695507	+	0.718519i	$0.744820\pi$
$228$	−2.95590e7	−	2.24701e7i	−2.49393	−	1.89584i
$229$	−4.58962e6	+	4.84520e6i	−0.382182	+	0.403464i	−0.888496	−	0.458885i	$-0.848249\pi$
$229$	−4.58962e6	+	4.84520e6i	−0.382182	+	0.403464i	0.506314	+	0.862349i	$0.331008\pi$
$230$	−1.89298e6	+	3.49140e7i	−0.155583	+	2.86956i
$231$	−4.10947e7	+	1.14099e7i	−3.33388	+	0.925647i
$232$	−6.40579e6	+	1.38459e7i	−0.512989	+	1.10881i
$233$	3.03904e6	−	498226.i	0.240253	−	0.0393875i	−0.0404523	−	0.999181i	$-0.512880\pi$
$233$	3.03904e6	−	498226.i	0.240253	−	0.0393875i	0.280705	+	0.959794i	$0.409432\pi$
$234$	−615772.	−	135542.i	−0.0480588	−	0.0105785i
$235$		−	7.29129e6i		−	0.561824i
$236$	5.32009e6	+	2.15972e7i	0.404746	+	1.64309i
$237$	−6.85134e6			−0.514672
$238$	866722.	−	3.93756e6i	0.0642908	−	0.292076i
$239$	1.03274e6	+	6.29945e6i	0.0756482	+	0.461433i	0.997301	+	0.0734184i	$0.0233908\pi$
$239$	1.03274e6	+	6.29945e6i	0.0756482	+	0.461433i	−0.921653	+	0.388015i	$0.873161\pi$
$240$	−3.58015e6	−	1.65635e6i	−0.258981	−	0.119817i
$241$	−2.52046e6	−	9.07788e6i	−0.180065	−	0.648535i	−0.997380	−	0.0723437i	$-0.976952\pi$
$241$	−2.52046e6	−	9.07788e6i	−0.180065	−	0.648535i	0.817315	−	0.576191i	$-0.195462\pi$
$242$	−2.23083e7	−	1.20952e6i	−1.57406	−	0.0853428i
$243$	1.39363e7	+	1.32011e7i	0.971241	+	0.920009i
$244$	−1.58262e6	+	2.08190e6i	−0.108945	+	0.143315i
$245$	2.39945e7	−	8.08468e6i	1.63160	−	0.549749i
$246$	−3.26046e7	+	1.76777e6i	−2.19015	+	0.118746i
$247$	305450.	+	259452.i	0.0202698	+	0.0172173i
$248$	−8.66052e6	+	3.11924e7i	−0.567792	+	2.04500i
$249$	2.07622e6	−	6.16199e6i	0.134485	−	0.399138i
$250$	1.89697e7	−	1.28618e7i	1.21406	−	0.823152i
$251$	−1.81756e7	+	8.40894e6i	−1.14939	+	0.531766i	−0.899678	−	0.436554i	$-0.856199\pi$
$251$	−1.81756e7	+	8.40894e6i	−1.14939	+	0.531766i	−0.249715	+	0.968319i	$0.580337\pi$
$252$	3.83337e7	+	4.51300e7i	2.39541	+	2.82009i
$253$	2.65951e7	−	2.51922e7i	1.64225	−	1.55562i
$254$	−3.48118e6	−	3.20090e7i	−0.212435	−	1.95331i
$255$	1.15797e6	−	2.90629e6i	0.0698357	−	0.175274i
$256$	3.42161e6	−	2.08709e7i	0.203944	−	1.24400i
$257$	−1.48191e7	+	2.18565e7i	−0.873017	+	1.28760i	0.0836726	+	0.996493i	$0.473335\pi$
$257$	−1.48191e7	+	2.18565e7i	−0.873017	+	1.28760i	−0.956690	+	0.291110i	$0.905975\pi$
$258$	3.19430e7	−	2.42825e7i	1.86002	−	1.41395i
$259$	−3.03959e6	+	2.79486e7i	−0.174951	+	1.60865i
$260$	628642.	+	333285.i	0.0357671	+	0.0189625i
$261$	2.22736e7	−	1.34016e7i	1.25277	−	0.753764i
$262$	2.52739e7	+	1.52068e7i	1.40530	+	0.845539i
$263$	7.65836e6	+	1.44452e7i	0.420987	+	0.794066i	0.999771	−	0.0214155i	$-0.00681728\pi$
$263$	7.65836e6	+	1.44452e7i	0.420987	+	0.794066i	−0.578784	+	0.815481i	$0.696472\pi$
$264$	1.66363e7	+	4.17539e7i	0.904157	+	2.26926i
$265$	−7.42827e6	+	1.63509e6i	−0.399163	+	0.0878624i
$266$	−1.28721e7	−	5.84786e7i	−0.683920	−	3.10708i
$267$	−3.04296e7	+	1.21243e7i	−1.59868	+	0.636974i
$268$	1.60141e7	−	8.49014e6i	0.831952	−	0.441073i
$269$	2.85953e6	−	4.75258e6i	0.146906	−	0.244159i	−0.774663	−	0.632374i	$-0.782081\pi$
$269$	2.85953e6	−	4.75258e6i	0.146906	−	0.244159i	0.921569	+	0.388215i	$0.126908\pi$
$270$	9.95901e6	+	1.65520e7i	0.505970	+	0.840929i
$271$	1.42811e7	−	2.69370e7i	0.717552	−	1.35345i	−0.209238	−	0.977865i	$-0.567098\pi$
$271$	1.42811e7	−	2.69370e7i	0.717552	−	1.35345i	0.926789	−	0.375581i	$-0.122557\pi$
$272$	−388405.	−	42241.6i	−0.0193009	−	0.00209910i
$273$	−671351.	−	883147.i	−0.0329960	−	0.0434055i
$274$	−5.29420e6	−	3.58955e6i	−0.257364	−	0.174497i
$275$	5.04204e6	+	826601.i	0.242442	+	0.0397464i
$276$	−8.20092e7	−	3.26755e7i	−3.90064	−	1.55416i
$277$	−6.06561e6	+	659674.i	−0.285387	+	0.0310378i	−0.249693	−	0.968325i	$-0.580330\pi$
$277$	−6.06561e6	+	659674.i	−0.285387	+	0.0310378i	−0.0356942	+	0.999363i	$0.511364\pi$
$278$	−3.10059e7	−	3.27326e7i	−1.44315	−	1.52351i
$279$	4.20404e7	−	3.57094e7i	1.93577	−	1.64426i
$280$	−1.82594e7	−	3.94670e7i	−0.831788	−	1.79788i
$281$	−7.12428e6	−	1.05075e7i	−0.321087	−	0.473567i	0.632554	−	0.774517i	$-0.282007\pi$
$281$	−7.12428e6	−	1.05075e7i	−0.321087	−	0.473567i	−0.953640	+	0.300949i	$0.902696\pi$
$282$	2.77543e7	+	9.35150e6i	1.23761	+	0.416998i
$283$	1.72434e7	+	4.78760e6i	0.760788	+	0.211232i	0.626192	−	0.779669i	$-0.284613\pi$
$283$	1.72434e7	+	4.78760e6i	0.760788	+	0.211232i	0.134596	+	0.990901i	$0.457026\pi$
$284$	−4.96639e6	+	5.84689e6i	−0.216813	+	0.255252i
$285$	−2.51544e6	−	4.63946e7i	−0.108662	−	2.00416i
$286$	−378685.	−	1.12390e6i	−0.0161875	−	0.0480428i
$287$	−2.63494e7	−	2.00303e7i	−1.11462	−	0.847309i
$288$	−1.90818e7	+	2.01445e7i	−0.798809	+	0.843292i
$289$	−1.29001e6	+	2.37928e7i	−0.0534439	+	0.985715i
$290$	−4.49685e7	+	1.24855e7i	−1.84380	+	0.511930i
$291$	2.99291e7	−	6.46907e7i	1.21455	−	2.62520i
$292$	5.33470e7	−	8.74579e6i	2.14270	−	0.351278i
$293$	−3.49329e7	−	7.68932e6i	−1.38878	−	0.305693i	−0.543225	−	0.839587i	$-0.682797\pi$
$293$	−3.49329e7	−	7.68932e6i	−1.38878	−	0.305693i	−0.845551	+	0.533895i	$0.820728\pi$
$294$			1.01704e8i			4.00217i
$295$	−1.62881e7	+	2.25700e7i	−0.634460	+	0.879155i
$296$	2.96274e7			1.14240
$297$	4.35063e6	−	1.97651e7i	0.166067	−	0.754448i
$298$	−6.92005e6	−	4.22104e7i	−0.261493	−	1.59504i
$299$	864785.	+	400092.i	0.0323515	+	0.0149674i
$300$	−3.29402e6	−	1.18640e7i	−0.122001	−	0.439407i
$301$	4.06131e7	+	2.20198e6i	1.48925	+	0.0807445i
$302$	3.64889e7	+	3.45641e7i	1.32477	+	1.25489i
$303$	−1.27018e7	+	1.67090e7i	−0.456602	+	0.600650i
$304$	−5.49868e6	+	1.85272e6i	−0.195721	+	0.0659461i
$305$	−3.26767e6	+	177168.i	−0.115170	+	0.00624433i
$306$	5.51790e6	+	4.68694e6i	0.192579	+	0.163578i
$307$	−1.27171e6	+	4.58027e6i	−0.0439513	+	0.158298i	−0.982269	−	0.187475i	$-0.939970\pi$
$307$	−1.27171e6	+	4.58027e6i	−0.0439513	+	0.158298i	0.938318	+	0.345773i	$0.112383\pi$
$308$	−3.55632e7	+	1.05548e8i	−1.21716	+	3.61241i
$309$	−4.20741e7	+	2.85270e7i	−1.42607	+	0.966897i
$310$	−8.98780e7	+	4.15820e7i	−3.01695	+	1.39579i
$311$	−3.14529e6	−	3.70292e6i	−0.104563	−	0.123101i	0.707391	−	0.706822i	$-0.249872\pi$
$311$	−3.14529e6	−	3.70292e6i	−0.104563	−	0.123101i	−0.811954	+	0.583721i	$0.801596\pi$
$312$	−848757.	+	803985.i	−0.0279460	+	0.0264719i
$313$	−3.63620e6	−	3.34343e7i	−0.118581	−	1.09033i	−0.890617	−	0.454755i	$-0.849727\pi$
$313$	−3.63620e6	−	3.34343e7i	−0.118581	−	1.09033i	0.772036	−	0.635579i	$-0.219239\pi$
$314$	2.34728e7	−	5.89124e7i	0.758187	−	1.90291i
$315$	−1.19875e7	+	7.31203e7i	−0.383527	+	2.33941i
$316$	−1.00409e7	+	1.48092e7i	−0.318208	+	0.469321i
$317$	2.00107e7	−	1.52118e7i	0.628181	−	0.477531i	−0.241991	−	0.970278i	$-0.577800\pi$
$317$	2.00107e7	−	1.52118e7i	0.628181	−	0.477531i	0.870172	+	0.492747i	$0.164007\pi$
$318$	3.30324e6	−	3.03728e7i	0.102721	−	0.944503i
$319$	4.31994e7	+	2.29029e7i	1.33078	+	0.705534i
$320$	4.79019e7	−	2.88216e7i	1.46185	−	0.879567i
$321$	9.42141e6	+	5.66867e6i	0.284840	+	0.171382i
$322$	−6.66850e7	−	1.25781e8i	−1.99738	−	3.76746i
$323$	−1.70329e6	−	4.27494e6i	−0.0505453	−	0.126859i
$324$	2.87687e7	−	6.33248e6i	0.845836	−	0.186182i
$325$	28569.5	+	129792.i	0.000832247	+	0.00378093i
$326$	−4.75894e7	+	1.89613e7i	−1.37359	+	0.547289i
$327$	−8.42837e7	+	4.46844e7i	−2.41046	+	1.27795i
$328$	−1.79830e7	+	2.98879e7i	−0.509612	+	0.846983i
$329$	1.53054e7	+	2.54378e7i	0.429791	+	0.714319i
$330$	−6.44040e7	+	1.21479e8i	−1.79214	+	3.38033i
$331$	4.37130e7	+	4.75408e6i	1.20539	+	0.131094i	0.688678	−	0.725067i	$-0.258191\pi$
$331$	4.37130e7	+	4.75408e6i	1.20539	+	0.131094i	0.516709	+	0.856161i	$0.327157\pi$
$332$	−1.02764e7	−	1.35184e7i	−0.280819	−	0.369411i
$333$	−4.17836e7	−	2.83300e7i	−1.13155	−	0.767209i
$334$	−1.16441e7	−	1.90895e6i	−0.312511	−	0.0512336i
$335$	2.10705e7	+	8.39524e6i	0.560454	+	0.223305i
$336$	1.59673e7	−	1.73655e6i	0.420934	−	0.0457794i
$337$	3.74831e7	+	3.95705e7i	0.979369	+	1.03391i	0.999418	+	0.0341078i	$0.0108590\pi$
$337$	3.74831e7	+	3.95705e7i	0.979369	+	1.03391i	−0.0200496	+	0.999799i	$0.506382\pi$
$338$	−4.82659e7	+	4.09974e7i	−1.24994	+	1.06171i
$339$	−8.64272e6	−	1.86809e7i	−0.221846	−	0.479512i
$340$	−4.58491e6	−	6.76223e6i	−0.116652	−	0.172050i
$341$	9.83221e7	+	3.31286e7i	2.47964	+	0.835486i
$342$	1.03603e8	+	2.87651e7i	2.58996	+	0.719098i
$343$	−2.47137e7	+	2.90952e7i	−0.612428	+	0.721006i
$344$	−2.32056e6	−	4.28002e7i	−0.0570056	−	1.05141i
$345$	−3.52726e7	−	1.04685e8i	−0.858975	−	2.54935i
$346$	6.77574e7	+	5.15078e7i	1.63579	+	1.24350i
$347$	−1.62756e7	+	1.71820e7i	−0.389538	+	0.411230i	−0.891039	−	0.453927i	$-0.850023\pi$
$347$	−1.62756e7	+	1.71820e7i	−0.389538	+	0.411230i	0.501501	+	0.865157i	$0.332781\pi$
$348$	6.37918e6	−	1.17657e8i	0.151366	−	2.79178i
$349$	1.93040e7	−	5.35972e6i	0.454120	−	0.126086i	−0.0329343	−	0.999458i	$-0.510485\pi$
$349$	1.93040e7	−	5.35972e6i	0.454120	−	0.126086i	0.487054	+	0.873372i	$0.338071\pi$
$350$	8.33751e6	−	1.80212e7i	0.194461	−	0.420320i
$351$	519483.	−	85165.0i	0.0120130	−	0.00196943i
$352$	−5.09718e7	−	1.12197e7i	−1.16870	−	0.257250i
$353$		−	7.49166e7i		−	1.70315i	−0.524229	−	0.851577i	$-0.675646\pi$
$353$		−	7.49166e7i		−	1.70315i	0.524229	−	0.851577i	$-0.324354\pi$
$354$	−6.50222e7	−	9.09479e7i	−1.46572	−	2.05014i
$355$	−9.59968e6			−0.214571
$356$	−1.83891e7	+	8.35423e7i	−0.407577	+	1.85164i
$357$	2.06078e6	+	1.25702e7i	0.0452925	+	0.276272i
$358$	4.89123e7	+	2.26292e7i	1.06603	+	0.493197i
$359$	1.10049e7	+	3.96361e7i	0.237850	+	0.856659i	0.982037	+	0.188688i	$0.0604233\pi$
$359$	1.10049e7	+	3.96361e7i	0.237850	+	0.856659i	−0.744187	+	0.667971i	$0.767163\pi$
$360$	7.79722e7	+	4.22753e6i	1.67122	+	0.0906107i
$361$	−1.54618e7	−	1.46462e7i	−0.328653	−	0.311317i
$362$	3.46338e7	−	4.55600e7i	0.730086	−	0.960412i
$363$	6.68888e7	−	2.25374e7i	1.39841	−	0.471178i
$364$	−2.89281e6	+	156844.i	−0.0599814	+	0.00325210i
$365$	5.15579e7	+	4.37937e7i	1.06027	+	0.900602i
$366$	3.51659e6	−	1.26656e7i	0.0717264	−	0.258335i
$367$	−5.82930e6	+	1.73007e7i	−0.117928	+	0.349999i	−0.990319	−	0.138811i	$-0.955672\pi$
$367$	−5.82930e6	+	1.73007e7i	−0.117928	+	0.349999i	0.872391	+	0.488809i	$0.162569\pi$
$368$	−1.14185e7	+	7.74193e6i	−0.229121	+	0.155348i
$369$	5.39405e7	−	2.49555e7i	1.07358	−	0.496693i
$370$	5.86751e7	+	6.90777e7i	1.15837	+	1.36374i
$371$	2.24834e7	−	2.12975e7i	0.440292	−	0.417067i
$372$	−2.70330e7	−	2.48564e8i	−0.525128	−	4.82847i
$373$	−1.38595e6	+	3.47847e6i	−0.0267067	+	0.0670288i	−0.941725	−	0.336383i	$-0.890796\pi$
$373$	−1.38595e6	+	3.47847e6i	−0.0267067	+	0.0670288i	0.915019	+	0.403412i	$0.132176\pi$
$374$	−2.20312e6	+	1.34385e7i	−0.0421138	+	0.256883i
$375$	−4.06350e7	+	5.99322e7i	−0.770560	+	1.13649i
$376$	2.49067e7	−	1.89336e7i	0.468546	−	0.356179i
$377$	−137507.	+	1.26436e6i	−0.00256626	+	0.0235964i
$378$	−6.94899e7	−	3.68412e7i	−1.28661	−	0.682117i
$379$	6.08736e7	−	3.66264e7i	1.11818	−	0.672786i	0.168403	−	0.985718i	$-0.446139\pi$
$379$	6.08736e7	−	3.66264e7i	1.11818	−	0.672786i	0.949775	+	0.312932i	$0.101311\pi$
$380$	−1.03969e8	−	6.25558e7i	−1.89475	−	1.14003i
$381$	4.76486e7	+	8.98747e7i	0.861539	+	1.62503i
$382$	−459905.	−	1.15428e6i	−0.00825047	−	0.0207071i
$383$	−556403.	+	122474.i	−0.00990360	+	0.00217995i	−0.219919	−	0.975518i	$-0.570579\pi$
$383$	−556403.	+	122474.i	−0.00990360	+	0.00217995i	0.210016	+	0.977698i	$0.432648\pi$
$384$	3.22946e7	+	1.46716e8i	0.570343	+	2.59109i
$385$	−1.29474e8	+	5.15873e7i	−2.26883	+	0.903985i
$386$	1.60874e8	−	8.52900e7i	2.79720	−	1.48298i
$387$	−3.76533e7	+	6.25802e7i	−0.649635	+	1.07970i
$388$	−9.59671e7	−	1.59499e8i	−1.64296	−	2.73062i
$389$	−2.66789e7	+	5.03218e7i	−0.453231	+	0.854884i	0.546616	+	0.837383i	$0.315916\pi$
$389$	−2.66789e7	+	5.03218e7i	−0.453231	+	0.854884i	−0.999847	+	0.0175008i	$0.994429\pi$
$390$	−3.55544e6	−	386677.i	−0.0599376	−	0.00651860i
$391$	−6.62121e6	−	8.71006e6i	−0.110766	−	0.145710i
$392$	8.99242e7	+	6.09701e7i	1.49286	+	1.01218i
$393$	−9.19611e7	−	1.50763e7i	−1.51505	−	0.248380i
$394$	4.85835e7	+	1.93574e7i	0.794329	+	0.316490i
$395$	−2.22582e7	+	2.42073e6i	−0.361159	+	0.0392785i
$396$	−1.37539e8	−	1.45198e8i	−2.21482	−	2.33816i
$397$	−5.43210e7	+	4.61406e7i	−0.868152	+	0.737415i	−0.966207	−	0.257766i	$-0.917014\pi$
$397$	−5.43210e7	+	4.61406e7i	−0.868152	+	0.737415i	0.0980550	+	0.995181i	$0.468738\pi$
$398$	−3.73765e7	−	8.07880e7i	−0.592856	−	1.28144i
$399$	1.06164e8	+	1.56581e8i	1.67132	+	2.46502i
$400$	−1.82343e6	−	614385.i	−0.0284911	−	0.00959977i
$401$	−4.17227e7	−	1.15843e7i	−0.647053	−	0.179653i	−0.0715293	−	0.997439i	$-0.522788\pi$
$401$	−4.17227e7	−	1.15843e7i	−0.647053	−	0.179653i	−0.575524	+	0.817785i	$0.695202\pi$
$402$	−5.89806e7	+	6.94373e7i	−0.907885	+	1.06885i
$403$	146106.	+	2.69477e6i	0.00223231	+	0.0411725i
$404$	1.75015e7	+	5.19426e7i	0.265419	+	0.787734i
$405$	2.93453e7	+	2.23077e7i	0.441746	+	0.335807i
$406$	1.30677e8	−	1.37954e8i	1.95264	−	2.06138i
$407$	5.14080e6	−	9.48164e7i	0.0762513	−	1.40637i
$408$	1.29347e7	−	3.59130e6i	0.190448	−	0.0528775i
$409$	8.67503e6	−	1.87508e7i	0.126795	−	0.274062i	−0.833774	−	0.552107i	$-0.813824\pi$
$409$	8.67503e6	−	1.87508e7i	0.126795	−	0.274062i	0.960568	+	0.278044i	$0.0896862\pi$
$410$	−1.05299e8	+	1.72629e7i	−1.52782	+	0.250474i
$411$	1.97360e7	+	4.34422e6i	0.284272	+	0.0625729i
$412$			1.32751e8i			1.89821i
$413$	9.44829e6	−	1.12933e8i	0.134123	−	1.60314i
$414$	2.55640e8			3.60270
$415$	4.56792e6	−	2.07523e7i	0.0639108	−	0.290350i
$416$	−219630.	−	1.33968e6i	−0.00305079	−	0.0186090i
$417$	1.29279e8	+	5.98110e7i	1.78288	+	0.824846i
$418$	5.41065e7	+	1.94874e8i	0.740833	+	2.66824i
$419$	−5.17074e7	−	2.80350e6i	−0.702928	−	0.0381117i	−0.300790	−	0.953690i	$-0.597250\pi$
$419$	−5.17074e7	−	2.80350e6i	−0.702928	−	0.0381117i	−0.402139	+	0.915579i	$0.631733\pi$
$420$	2.43839e8	+	2.30977e8i	3.29121	+	3.11760i
$421$	−5.19705e7	+	6.83661e7i	−0.696483	+	0.916208i	−0.999321	−	0.0368338i	$-0.988273\pi$
$421$	−5.19705e7	+	6.83661e7i	−0.696483	+	0.916208i	0.302838	+	0.953042i	$0.402066\pi$
$422$	−2.14682e8	+	7.23349e7i	−2.85666	+	0.962522i
$423$	−5.32303e7	+	2.88607e6i	−0.703296	+	0.0381316i
$424$	−2.48746e7	−	2.11287e7i	−0.326332	−	0.277189i
$425$	408249.	−	1.47038e6i	0.00531812	−	0.0191542i
$426$	1.23122e7	−	3.65412e7i	0.159259	−	0.472665i
$427$	1.10283e7	−	7.47740e6i	0.141653	−	0.0960433i
$428$	2.60603e7	−	1.20568e7i	0.332390	−	0.153780i
$429$	2.42572e6	+	2.85578e6i	0.0307233	+	0.0361703i
$430$	9.51950e7	−	9.01735e7i	1.19732	−	1.13416i
$431$	178820.	+	1.64423e6i	0.00223350	+	0.0205367i	0.995202	−	0.0978449i	$-0.0311949\pi$
$431$	178820.	+	1.64423e6i	0.00223350	+	0.0205367i	−0.992968	+	0.118382i	$0.962229\pi$
$432$	−2.82105e6	+	7.08031e6i	−0.0349913	+	0.0878215i
$433$	−1.61811e7	+	9.87005e7i	−0.199317	+	1.21578i	0.677706	+	0.735333i	$0.262974\pi$
$433$	−1.61811e7	+	9.87005e7i	−0.199317	+	1.21578i	−0.877023	+	0.480449i	$0.840474\pi$
$434$	2.26280e8	−	3.33738e8i	2.76807	−	4.08259i
$435$	1.17381e8	−	8.92309e7i	1.42604	−	1.08405i
$436$	−2.69353e7	+	2.47666e8i	−0.324985	+	2.98818i
$437$	−1.43562e8	−	7.61119e7i	−1.72027	−	0.912028i
$438$	−2.32827e8	+	1.40087e8i	−2.77083	+	1.66716i
$439$	−4.28060e7	−	2.57555e7i	−0.505954	−	0.304422i	0.239596	−	0.970873i	$-0.422985\pi$
$439$	−4.28060e7	−	2.57555e7i	−0.505954	−	0.304422i	−0.745549	+	0.666451i	$0.767813\pi$
$440$	6.87994e7	+	1.29769e8i	0.807656	+	1.52340i
$441$	−6.85201e7	−	1.71973e8i	−0.798918	−	2.00513i
$442$	−345933.	+	76145.7i	−0.00400613	+	0.000881817i
$443$	−1.27883e7	−	5.80978e7i	−0.147096	−	0.668265i	−0.991232	−	0.132135i	$-0.957817\pi$
$443$	−1.27883e7	−	5.80978e7i	−0.147096	−	0.668265i	0.844135	−	0.536130i	$-0.180114\pi$
$444$	−2.12577e8	+	8.46984e7i	−2.42866	+	0.967668i
$445$	−9.45741e7	+	5.01400e7i	−1.07323	+	0.568990i
$446$	−6.91764e6	+	1.14972e7i	−0.0779746	+	0.129595i
$447$	6.96712e7	+	1.15794e8i	0.780065	+	1.29648i
$448$	−1.06619e8	+	2.01106e8i	−1.18578	+	2.23661i
$449$	4.40101e7	+	4.78639e6i	0.486199	+	0.0528773i	0.347936	−	0.937518i	$-0.386883\pi$
$449$	4.40101e7	+	4.78639e6i	0.486199	+	0.0528773i	0.138263	+	0.990396i	$0.455848\pi$
$450$	2.15778e7	+	2.83852e7i	0.236794	+	0.311497i
$451$	9.25299e7	+	6.27368e7i	1.00868	+	0.683901i
$452$	−5.30452e7	−	8.69631e6i	−0.574421	−	0.0941716i
$453$	−1.47514e8	−	5.87748e7i	−1.58686	−	0.632261i
$454$	−1.40072e8	+	1.52337e7i	−1.49687	+	0.162794i
$455$	−2.49308e6	−	2.63191e6i	−0.0264668	−	0.0279407i
$456$	1.51950e8	−	1.29067e8i	1.60253	−	1.36120i
$457$	−3.98782e7	−	8.61954e7i	−0.417818	−	0.903099i	−0.996180	−	0.0873191i	$-0.972170\pi$
$457$	−3.98782e7	−	8.61954e7i	−0.417818	−	0.903099i	0.578362	−	0.815780i	$-0.303692\pi$
$458$	−4.91620e7	−	7.25085e7i	−0.511721	−	0.754732i
$459$	−5.72812e6	−	1.93003e6i	−0.0592344	−	0.0199584i
$460$	−2.77971e8	−	7.71784e7i	−2.85579	−	0.792907i
$461$	−3.49896e7	+	4.11929e7i	−0.357138	+	0.420456i	−0.911164	−	0.412044i	$-0.864815\pi$
$461$	−3.49896e7	+	4.11929e7i	−0.357138	+	0.420456i	0.554026	+	0.832499i	$0.313091\pi$
$462$	−3.03085e7	−	5.59008e8i	−0.307354	−	5.66881i
$463$	−1.76569e7	−	5.24038e7i	−0.177898	−	0.527982i	0.821191	−	0.570653i	$-0.193310\pi$
$463$	−1.76569e7	−	5.24038e7i	−0.177898	−	0.527982i	−0.999089	+	0.0426707i	$0.986413\pi$
$464$	−1.46590e7	−	1.11435e7i	−0.146740	−	0.111549i
$465$	2.15164e8	−	2.27146e8i	2.13999	−	2.25916i
$466$	−2.18852e6	+	4.03648e7i	−0.0216268	+	0.398883i
$467$	5.31617e6	−	1.47603e6i	0.0521974	−	0.0144925i	−0.241332	−	0.970443i	$-0.577584\pi$
$467$	5.31617e6	−	1.47603e6i	0.0521974	−	0.0144925i	0.293529	+	0.955950i	$0.405170\pi$
$468$	2.18433e6	−	4.72135e6i	0.0213099	−	0.0460605i
$469$	−9.11333e7	+	1.49406e7i	−0.883403	+	0.144827i
$470$	9.34704e7	+	2.05744e7i	0.900286	+	0.198168i
$471$			2.00356e8i			1.91752i
$472$	−1.19394e8	+	2.96902e6i	−1.13542	+	0.0282350i
$473$	−1.37376e8			−1.29816
$474$	1.93330e7	−	8.78305e7i	0.181536	−	0.824728i
$475$	−3.66654e6	−	2.23649e7i	−0.0342118	−	0.208682i
$476$	3.01907e7	+	1.39677e7i	0.279932	+	0.129510i
$477$	1.48773e7	+	5.35832e7i	0.137078	+	0.493712i
$478$	−8.36698e7	−	4.53644e6i	−0.766099	−	0.0415367i
$479$	3.18358e7	+	3.01565e7i	0.289674	+	0.274394i	0.818712	−	0.574204i	$-0.194688\pi$
$479$	3.18358e7	+	3.01565e7i	0.289674	+	0.274394i	−0.529038	+	0.848598i	$0.677447\pi$
$480$	−9.52476e7	+	1.25296e8i	−0.861252	+	1.13296i
$481$	2.34061e6	−	788642.i	0.0210326	−	0.00708671i
$482$	1.23486e8	−	6.69521e6i	1.10275	−	0.0597892i
$483$	3.42808e8	+	2.91184e8i	3.04236	+	2.58420i
$484$	4.93131e7	−	1.77610e8i	0.434937	−	1.56650i
$485$	7.43752e7	−	2.20738e8i	0.651933	−	1.93487i
$486$	−2.08556e8	+	1.41405e8i	−1.81683	+	1.23184i
$487$	1.70249e7	−	7.87657e6i	0.147400	−	0.0681947i	−0.344802	−	0.938675i	$-0.612054\pi$
$487$	1.70249e7	−	7.87657e6i	0.147400	−	0.0681947i	0.492203	+	0.870481i	$0.336192\pi$
$488$	−9.09049e6	−	1.07021e7i	−0.0782218	−	0.0920898i
$489$	1.17500e8	−	1.11302e8i	1.00488	−	0.951870i
$490$	3.59342e7	+	3.30410e8i	0.305436	+	2.80844i
$491$	4.98327e7	−	1.25071e8i	0.420988	−	1.05660i	−0.553637	−	0.832758i	$-0.686760\pi$
$491$	4.98327e7	−	1.25071e8i	0.420988	−	1.05660i	0.974625	−	0.223843i	$-0.0718603\pi$
$492$	4.35849e7	−	2.65856e8i	0.365966	−	2.23229i
$493$	8.19526e6	−	1.20871e7i	0.0683946	−	0.100875i
$494$	−4.18794e6	+	3.18359e6i	−0.0347392	+	0.0264081i
$495$	2.70587e7	−	2.48801e8i	0.223096	−	2.05133i
$496$	−3.45214e7	−	1.83021e7i	−0.282907	−	0.149988i
$497$	3.34913e7	−	2.01511e7i	0.272812	−	0.164145i
$498$	7.31348e7	+	4.40038e7i	0.592156	+	0.356289i
$499$	−2.78024e7	−	5.24410e7i	−0.223759	−	0.422055i	0.746060	−	0.665878i	$-0.231943\pi$
$499$	−2.78024e7	−	5.24410e7i	−0.223759	−	0.422055i	−0.969820	+	0.243824i	$0.921598\pi$
$500$	6.99916e7	+	1.75666e8i	0.559933	+	1.40532i
$501$	3.64074e7	−	8.01388e6i	0.289519	−	0.0637279i
$502$	−5.65106e7	−	2.56730e8i	−0.446703	−	2.02939i
$503$	2.11619e8	−	8.43168e7i	1.66284	−	0.662537i	0.666305	−	0.745679i	$-0.267875\pi$
$503$	2.11619e8	−	8.43168e7i	1.66284	−	0.662537i	0.996538	+	0.0831416i	$0.0264954\pi$
$504$	−2.80903e8	+	1.48926e8i	−2.19414	+	1.16326i
$505$	−3.53612e7	+	5.87708e7i	−0.274570	+	0.456339i
$506$	2.47905e8	+	4.12022e8i	1.91353	+	3.18030i
$507$	9.37169e7	−	1.76769e8i	0.719108	−	1.35638i
$508$	2.64095e8	+	2.87221e7i	2.01451	+	0.219091i
$509$	5.21632e7	+	6.86195e7i	0.395559	+	0.520349i	0.950158	−	0.311769i	$-0.100921\pi$
$509$	5.21632e7	+	6.86195e7i	0.395559	+	0.520349i	−0.554599	+	0.832118i	$0.687128\pi$
$510$	3.39896e7	+	2.30455e7i	0.256233	+	0.173730i
$511$	−2.71804e8	−	4.45600e7i	−2.03701	−	0.333951i
$512$	4.25257e7	+	1.69438e7i	0.316841	+	0.126241i
$513$	−8.92442e7	+	9.70589e6i	−0.661040	+	0.0718925i
$514$	−2.38373e8	−	2.51647e8i	−1.75537	−	1.85312i
$515$	−1.26609e8	+	1.07542e8i	−0.926919	+	0.787332i
$516$	1.39007e8	+	3.00458e8i	1.01178	+	2.18693i
$517$	−5.62713e7	−	8.29939e7i	−0.407207	−	0.600585i
$518$	−3.49709e8	−	1.17831e8i	−2.51604	−	0.847752i
$519$	−2.59100e8	−	7.19387e7i	−1.85338	−	0.514589i
$520$	−2.47332e6	+	2.91182e6i	−0.0175902	+	0.0207088i
$521$	6.88991e6	+	1.27077e8i	0.0487192	+	0.898574i	0.916105	+	0.400938i	$0.131316\pi$
$521$	6.88991e6	+	1.27077e8i	0.0487192	+	0.898574i	−0.867386	+	0.497636i	$0.834202\pi$
$522$	1.08950e8	+	3.23353e8i	0.765978	+	2.27334i
$523$	1.44074e8	+	1.09522e8i	1.00712	+	0.765592i	0.972284	−	0.233801i	$-0.0751165\pi$
$523$	1.44074e8	+	1.09522e8i	1.00712	+	0.765592i	0.0348346	+	0.999393i	$0.488910\pi$
$524$	−1.67360e8	+	1.76680e8i	−1.16321	+	1.22798i
$525$	−3.39634e6	+	6.26419e7i	−0.0234711	+	0.432899i
$526$	−2.06790e8	+	5.74150e7i	−1.42093	+	0.394519i
$527$	1.30115e7	−	2.81238e7i	0.0888984	−	0.192151i
$528$	−5.35345e7	+	8.77654e6i	−0.363691	+	0.0596241i
$529$	−2.32724e8	−	5.12265e7i	−1.57208	−	0.346041i
$530$		−	9.98403e7i		−	0.670623i
$531$	1.71220e8	+	1.09978e8i	1.14359	+	0.734552i
$532$	4.94038e8			3.28115
$533$	−625103.	+	2.83987e6i	−0.00412829	+	0.0187550i
$534$	−6.95610e7	−	4.24304e8i	−0.456817	−	2.78646i
$535$	3.26106e7	+	1.50872e7i	0.212959	+	0.0985255i
$536$	2.60367e7	+	9.37759e7i	0.169080	+	0.608971i
$537$	−1.70019e8	−	9.21817e6i	−1.09793	−	0.0595281i
$538$	5.28566e7	+	5.00684e7i	0.339432	+	0.321527i
$539$	2.10726e8	−	2.77205e8i	1.34571	−	1.77025i
$540$	−1.51036e8	+	5.08900e7i	−0.959179	+	0.323185i
$541$	1.91157e8	−	1.03642e7i	1.20726	−	0.0654555i	0.560501	−	0.828154i	$-0.310609\pi$
$541$	1.91157e8	−	1.03642e7i	1.20726	−	0.0654555i	0.646754	+	0.762698i	$0.276126\pi$
$542$	3.05020e8	+	2.59086e8i	1.91571	+	1.62722i
$543$	−4.83715e7	+	1.74218e8i	−0.302127	+	1.08816i
$544$	−4.97731e6	+	1.47721e7i	−0.0309171	+	0.0917586i
$545$	−2.58028e8	+	1.74947e8i	−1.59396	+	1.08073i
$546$	1.32159e7	−	6.11432e6i	0.0811929	−	0.0375638i
$547$	7.44275e7	+	8.76228e7i	0.454749	+	0.535372i	0.940982	−	0.338458i	$-0.109905\pi$
$547$	7.44275e7	+	8.76228e7i	0.454749	+	0.535372i	−0.486233	+	0.873829i	$0.661629\pi$
$548$	3.83139e7	−	3.62928e7i	0.232817	−	0.220536i
$549$	2.58685e6	+	2.37857e7i	0.0156334	+	0.143747i
$550$	−2.48241e7	+	6.23038e7i	−0.149206	+	0.374478i
$551$	3.50878e7	−	2.14026e8i	0.209749	−	1.27942i
$552$	2.66006e8	−	3.92330e8i	1.58152	−	2.33257i
$553$	7.25729e7	−	5.51685e7i	0.429140	−	0.326224i
$554$	8.65912e6	−	7.96193e7i	0.0509266	−	0.468262i
$555$	−2.52990e8	−	1.34127e8i	−1.47987	−	0.784578i
$556$	3.18745e8	−	1.91783e8i	1.85447	−	1.11580i
$557$	−1.80395e8	−	1.08540e8i	−1.04390	−	0.628092i	−0.113084	−	0.993585i	$-0.536073\pi$
$557$	−1.80395e8	−	1.08540e8i	−1.04390	−	0.628092i	−0.930814	+	0.365493i	$0.880900\pi$
$558$	3.39147e8	+	6.39699e8i	1.95203	+	3.68191i
$559$	−1.32261e6	−	3.31951e6i	−0.00757177	−	0.0190037i
$560$	5.12601e7	−	1.12832e7i	0.291887	−	0.0642493i
$561$	−9.24885e6	−	4.20180e7i	−0.0523841	−	0.237983i
$562$	1.54804e8	−	6.16796e7i	0.872115	−	0.347482i
$563$	−4.55384e7	+	2.41429e7i	−0.255184	+	0.135290i	−0.591090	−	0.806606i	$-0.701302\pi$
$563$	−4.55384e7	+	2.41429e7i	−0.255184	+	0.135290i	0.335906	+	0.941895i	$0.390957\pi$
$564$	−1.24579e8	+	2.07051e8i	−0.694395	+	1.15409i
$565$	−3.46783e7	−	5.76358e7i	−0.192271	−	0.319556i
$566$	−1.10032e8	+	2.07542e8i	−0.606831	+	1.14461i
$567$	−1.49207e8	−	1.62272e7i	−0.818538	−	0.0890213i
$568$	−2.49278e7	−	3.27920e7i	−0.136032	−	0.178946i
$569$	1.73814e8	+	1.17849e8i	0.943513	+	0.639718i	0.932865	−	0.360226i	$-0.117300\pi$
$569$	1.73814e8	+	1.17849e8i	0.943513	+	0.639718i	0.0106477	+	0.999943i	$0.496611\pi$
$570$	6.01852e8	+	9.86686e7i	3.24986	+	0.532788i
$571$	6.78053e7	+	2.70161e7i	0.364213	+	0.145116i	0.545063	−	0.838395i	$-0.316506\pi$
$571$	6.78053e7	+	2.70161e7i	0.364213	+	0.145116i	−0.180850	+	0.983511i	$0.557885\pi$
$572$	9.72775e6	−	1.05796e6i	0.0519786	−	0.00565301i
$573$	2.69963e6	+	2.84996e6i	0.0143496	+	0.0151487i
$574$	3.31130e8	−	2.81264e8i	1.75091	−	1.48723i
$575$	−2.26252e7	−	4.89036e7i	−0.119012	−	0.257239i
$576$	−2.29374e8	−	3.38302e8i	−1.20027	−	1.77026i
$577$	1.54976e7	+	5.22175e6i	0.0806746	+	0.0271824i	0.359349	−	0.933203i	$-0.382999\pi$
$577$	1.54976e7	+	5.22175e6i	0.0806746	+	0.0271824i	−0.278675	+	0.960386i	$0.589895\pi$
$578$	−3.01371e8	−	8.36751e7i	−1.56069	−	0.433324i
$579$	−3.72424e8	+	4.38451e8i	−1.91867	+	2.25884i
$580$	−2.08465e7	−	3.84491e8i	−0.106844	−	1.97062i
$581$	2.76253e7	+	8.19891e7i	0.140857	+	0.418050i
$582$	7.44847e8	+	5.66218e8i	3.77832	+	2.87220i
$583$	−7.19342e7	+	7.59400e7i	−0.363019	+	0.383235i
$584$	−1.57147e7	+	2.89840e8i	−0.0788981	+	1.45519i
$585$	6.27244e6	−	1.74154e6i	0.0313306	−	0.00869891i
$586$	1.97146e8	−	4.26124e8i	0.979705	−	2.11760i
$587$	1.57466e8	−	2.58152e7i	0.778525	−	0.127633i	0.240599	−	0.970625i	$-0.422656\pi$
$587$	1.57466e8	−	2.58152e7i	0.778525	−	0.127633i	0.537926	+	0.842992i	$0.319208\pi$
$588$	−8.19508e8	−	1.80387e8i	−4.03108	−	0.887307i
$589$		−	4.60216e8i		−	2.25225i
$590$	−2.43374e8	−	2.72492e8i	−1.18500	−	1.32678i
$591$	−1.65228e8			−0.800427
$592$	−7.68730e6	+	3.49238e7i	−0.0370517	+	0.168328i
$593$	4.92611e7	+	3.00480e8i	0.236233	+	1.44096i	0.792459	+	0.609926i	$0.208801\pi$
$593$	4.92611e7	+	3.00480e8i	0.236233	+	1.44096i	−0.556226	+	0.831031i	$0.687751\pi$
$594$	2.41102e8	+	1.11545e8i	1.15038	+	0.532222i
$595$	1.11362e7	+	4.01091e7i	0.0528674	+	0.190411i
$596$	3.52396e8	+	1.91064e7i	1.66453	+	0.0902483i
$597$	2.04173e8	+	1.93403e8i	0.959567	+	0.908950i
$598$	−7.56920e6	+	9.95711e6i	−0.0353954	+	0.0465618i
$599$	−1.65882e8	+	5.58922e7i	−0.771825	+	0.260058i	−0.677539	−	0.735487i	$-0.736953\pi$
$599$	−1.65882e8	+	5.58922e7i	−0.771825	+	0.260058i	−0.0942862	+	0.995545i	$0.530057\pi$
$600$	6.60154e7	−	3.57925e6i	0.305627	−	0.0165706i
$601$	−2.13749e8	−	1.81560e8i	−0.984647	−	0.836367i	0.00187470	−	0.999998i	$-0.499403\pi$
$601$	−2.13749e8	−	1.81560e8i	−0.984647	−	0.836367i	−0.986521	+	0.163632i	$0.947679\pi$
$602$	−1.42829e8	+	5.14424e8i	−0.654678	+	2.35794i
$603$	5.29496e7	−	1.57149e8i	0.241497	−	0.716736i
$604$	−3.43229e8	+	2.32715e8i	−1.55766	+	1.05612i
$605$	2.09341e8	−	9.68515e7i	0.945341	−	0.437361i
$606$	−1.78358e8	−	2.09980e8i	−0.801448	−	0.943537i
$607$	−1.23185e8	+	1.16687e8i	−0.550799	+	0.521745i	−0.911698	−	0.410860i	$-0.865228\pi$
$607$	−1.23185e8	+	1.16687e8i	−0.550799	+	0.521745i	0.360899	+	0.932605i	$0.382470\pi$
$608$	2.50303e7	+	2.30150e8i	0.111367	+	1.02400i
$609$	−2.22211e8	+	5.57708e8i	−0.983816	+	2.46919i
$610$	6.94945e6	−	4.23898e7i	0.0306169	−	0.186755i
$611$	1.46367e6	−	2.15876e6i	0.00641684	−	0.00946412i
$612$	−4.75532e7	+	3.61490e7i	−0.207456	+	0.157704i
$613$	9.16864e6	−	8.43042e7i	0.0398037	−	0.365989i	−0.957249	−	0.289266i	$-0.906589\pi$
$613$	9.16864e6	−	8.43042e7i	0.0398037	−	0.365989i	0.997052	−	0.0767229i	$-0.0244457\pi$
$614$	−5.51281e7	−	2.92271e7i	−0.238160	−	0.126264i
$615$	2.88864e8	−	1.73803e8i	1.24185	−	0.747194i
$616$	−5.12431e8	−	3.08319e8i	−2.19227	−	1.31904i
$617$	−2.15797e7	−	4.07036e7i	−0.0918735	−	0.173292i	0.833316	−	0.552796i	$-0.186439\pi$
$617$	−2.15797e7	−	4.07036e7i	−0.0918735	−	0.173292i	−0.925190	+	0.379505i	$0.876094\pi$
$618$	−2.46977e8	−	6.19865e8i	−1.04638	−	2.62622i
$619$	2.94480e8	−	6.48198e7i	1.24160	−	0.273298i	0.454852	−	0.890567i	$-0.349692\pi$
$619$	2.94480e8	−	6.48198e7i	1.24160	−	0.273298i	0.786752	+	0.617269i	$0.211761\pi$
$620$	−1.75646e8	−	7.97969e8i	−0.736994	−	3.34820i
$621$	−1.98276e8	+	7.90005e7i	−0.827934	+	0.329879i
$622$	5.63447e7	−	2.98721e7i	0.234143	−	0.124135i
$623$	2.24699e8	−	3.73452e8i	0.929259	−	1.54444i
$624$	−727487.	−	1.20909e6i	−0.00299413	−	0.00497629i
$625$	−1.30901e8	+	2.46906e8i	−0.536172	+	1.01133i
$626$	4.38871e8	+	4.77301e7i	1.78901	+	0.194567i
$627$	−3.86687e8	−	5.08678e8i	−1.56876	−	2.06367i
$628$	4.33070e8	+	2.93629e8i	1.74855	+	1.18555i
$629$	−2.79867e7	−	4.58819e6i	−0.112460	−	0.0184369i
$630$	−9.03537e8	−	3.60002e8i	−3.61347	−	1.43974i
$631$	−3.07400e8	+	3.34317e7i	−1.22353	+	0.133067i	−0.696989	−	0.717082i	$-0.745477\pi$
$631$	−3.07400e8	+	3.34317e7i	−1.22353	+	0.133067i	−0.526542	+	0.850149i	$0.676512\pi$
$632$	−6.60678e7	−	6.97469e7i	−0.261721	−	0.276295i
$633$	5.45500e8	−	4.63351e8i	2.15072	−	1.82684i
$634$	1.38541e8	+	2.99451e8i	0.543638	+	1.17505i
$635$	1.86552e8	+	2.75144e8i	0.728584	+	1.07458i
$636$	2.38878e8	+	8.04875e7i	0.928550	+	0.312865i
$637$	8.72707e6	+	2.42306e6i	0.0337637	+	0.00937445i
$638$	−4.15502e8	+	4.89167e8i	−1.59997	+	1.88363i
$639$	3.79978e6	+	7.00829e7i	0.0145632	+	0.268602i
$640$	1.56754e8	+	4.65230e8i	0.597971	+	1.77471i
$641$	−7.28253e7	−	5.53603e7i	−0.276508	−	0.210196i	0.457724	−	0.889094i	$-0.348665\pi$
$641$	−7.28253e7	−	5.53603e7i	−0.276508	−	0.210196i	−0.734232	+	0.678898i	$0.762458\pi$
$642$	−9.92545e7	+	1.04782e8i	−0.375098	+	0.395987i
$643$	−4.00559e6	+	7.38788e7i	−0.0150672	+	0.277899i	0.981285	+	0.192562i	$0.0616796\pi$
$643$	−4.00559e6	+	7.38788e7i	−0.0150672	+	0.277899i	−0.996352	+	0.0853373i	$0.972803\pi$
$644$	1.13179e9	−	3.14241e8i	4.23750	−	1.17654i
$645$	−1.73946e8	+	3.75979e8i	−0.648240	+	1.40115i
$646$	5.96087e7	−	9.77236e6i	0.221112	−	0.0362495i
$647$	1.70814e7	+	3.75990e6i	0.0630683	+	0.0138824i	0.246392	−	0.969170i	$-0.420755\pi$
$647$	1.70814e7	+	3.75990e6i	0.0630683	+	0.0138824i	−0.183324	+	0.983053i	$0.558686\pi$
$648$			1.58169e8i			0.581295i
$649$	−1.12149e7	+	3.82611e8i	−0.0410260	+	1.39966i
$650$	−1.74449e6			−0.00635225
$651$	−2.73853e8	+	1.24412e9i	−0.992599	+	4.50942i
$652$	−6.83793e7	−	4.17095e8i	−0.246707	−	1.50485i
$653$	−6.18277e7	−	2.86045e7i	−0.222046	−	0.102729i	0.305712	−	0.952124i	$-0.401105\pi$
$653$	−6.18277e7	−	2.86045e7i	−0.222046	−	0.102729i	−0.527759	+	0.849394i	$0.676967\pi$
$654$	−3.35000e8	−	1.20656e9i	−1.19760	−	4.31337i
$655$	−3.04084e8	−	1.64870e7i	−1.08211	−	0.0586701i
$656$	−3.05649e7	−	2.89526e7i	−0.108271	−	0.102560i
$657$	2.99310e8	−	3.93735e8i	1.05542	−	1.38838i
$658$	−3.69288e8	+	1.24428e8i	−1.29625	+	0.436756i
$659$	−1.66664e8	+	9.03627e6i	−0.582352	+	0.0315742i	−0.342962	−	0.939349i	$-0.611430\pi$
$659$	−1.66664e8	+	9.03627e6i	−0.582352	+	0.0315742i	−0.239390	+	0.970923i	$0.576948\pi$
$660$	−8.64619e8	−	7.34414e8i	−3.00741	−	2.55452i
$661$	1.03477e8	−	3.72689e8i	0.358293	−	1.29045i	−0.536473	−	0.843917i	$-0.680244\pi$
$661$	1.03477e8	−	3.72689e8i	0.358293	−	1.29045i	0.894766	−	0.446536i	$-0.147342\pi$
$662$	−1.84293e8	+	5.46963e8i	−0.635236	+	1.88531i
$663$	926262.	−	628021.i	0.00317829	−	0.00215493i
$664$	8.27504e7	−	3.82844e7i	0.282661	−	0.130773i
$665$	4.00224e8	+	4.71180e8i	1.36094	+	1.60222i
$666$	4.81079e8	−	4.55702e8i	1.62852	−	1.54262i
$667$	−5.57519e7	−	5.12631e8i	−0.187881	−	1.72754i
$668$	3.60344e7	−	9.04395e7i	0.120889	−	0.303409i
$669$	6.85826e6	−	4.18336e7i	0.0229053	−	0.139716i
$670$	−1.67079e8	+	2.46423e8i	−0.555516	+	0.819325i
$671$	−3.58274e7	+	2.72353e7i	−0.118590	+	0.0901496i
$672$	6.92856e7	−	6.37070e8i	0.228315	−	2.09932i
$673$	5.10596e7	+	2.70701e7i	0.167507	+	0.0888064i	0.550052	−	0.835130i	$-0.314608\pi$
$673$	5.10596e7	+	2.70701e7i	0.167507	+	0.0888064i	−0.382546	+	0.923937i	$0.624953\pi$
$674$	−6.13041e8	+	3.68855e8i	−2.00221	+	1.20469i
$675$	−2.55078e7	−	1.53475e7i	−0.0829394	−	0.0499030i
$676$	−2.44741e8	−	4.61630e8i	−0.792258	−	1.49436i
$677$	−1.53836e8	−	3.86100e8i	−0.495785	−	1.24433i	−0.937756	−	0.347296i	$-0.887100\pi$
$677$	−1.53836e8	−	3.86100e8i	−0.495785	−	1.24433i	0.441971	−	0.897029i	$-0.354279\pi$
$678$	2.63868e8	−	5.80816e7i	0.846636	−	0.186359i
$679$	2.03879e8	+	9.26233e8i	0.651274	+	2.95877i
$680$	4.07525e7	−	1.62373e7i	0.129607	−	0.0516401i
$681$	3.93294e8	−	2.08511e8i	1.24530	−	0.660219i
$682$	−7.02134e8	+	1.16696e9i	−2.21343	+	3.67876i
$683$	2.17605e8	+	3.61663e8i	0.682979	+	1.13512i	0.983424	+	0.181320i	$0.0580371\pi$
$683$	2.17605e8	+	3.61663e8i	0.682979	+	1.13512i	−0.300445	+	0.953799i	$0.597135\pi$
$684$	−4.15538e8	+	7.83788e8i	−1.29850	+	2.44923i
$685$	6.56520e7	+	7.14008e6i	0.204257	+	0.0222142i
$686$	−3.03248e8	−	3.98916e8i	−0.939347	−	1.23569i
$687$	2.29081e8	+	1.55321e8i	0.706511	+	0.479026i
$688$	5.10536e7	+	8.36980e6i	0.156769	+	0.0257010i
$689$	−2.52755e6	−	1.00707e6i	−0.00772755	−	0.00307894i
$690$	1.44154e9	−	1.56777e8i	4.38814	−	0.477239i
$691$	−2.84605e8	−	3.00454e8i	−0.862599	−	0.910635i	0.134170	−	0.990958i	$-0.457163\pi$
$691$	−2.84605e8	−	3.00454e8i	−0.862599	−	0.910635i	−0.996769	+	0.0803236i	$0.974405\pi$
$692$	−5.35216e8	+	4.54617e8i	−1.61514	+	1.37191i
$693$	4.27865e8	+	9.24814e8i	1.28560	+	2.77878i
$694$	−1.74338e8	−	2.57129e8i	−0.521570	−	0.769258i
$695$	4.41127e8	+	1.48633e8i	1.31404	+	0.442753i
$696$	6.09616e8	+	1.69259e8i	1.80813	+	0.502024i
$697$	2.16156e7	−	2.54479e7i	0.0638366	−	0.0751543i
$698$	1.42373e7	+	2.62591e8i	0.0418659	+	0.772170i
$699$	−4.07795e7	−	1.21029e8i	−0.119402	−	0.354371i
$700$	1.30423e8	+	9.91452e7i	0.380243	+	0.289053i
$701$	−1.40115e8	+	1.47917e8i	−0.406752	+	0.429402i	−0.896898	−	0.442238i	$-0.854185\pi$
$701$	−1.40115e8	+	1.47917e8i	−0.406752	+	0.429402i	0.490146	+	0.871640i	$0.336943\pi$
$702$	−374097.	+	6.89982e6i	−0.00108137	+	0.0199446i
$703$	−4.05841e8	+	1.12681e8i	−1.16813	+	0.324328i
$704$	3.22815e8	−	6.97754e8i	0.925201	−	1.99979i
$705$	−2.98394e8	+	4.89191e7i	−0.851573	+	0.139608i
$706$	9.60391e8	+	2.11398e8i	2.72919	+	0.600741i
$707$		−	2.79268e8i		−	0.790246i
$708$	8.48164e8	−	3.62624e8i	2.38990	−	1.02178i
$709$	−3.46633e8			−0.972594			−0.486297	−	0.873794i	$-0.661653\pi$
$709$	−3.46633e8			−0.972594			−0.486297	+	0.873794i	$0.661653\pi$
$710$	2.70882e7	−	1.23063e8i	0.0756841	−	0.343836i
$711$	2.64829e7	+	1.61539e8i	0.0736813	+	0.449436i
$712$	−4.16860e8	−	1.92860e8i	−1.15491	−	0.534321i
$713$	−2.92728e8	−	1.05431e9i	−0.807598	−	2.90871i
$714$	−1.66958e8	−	9.05221e6i	−0.458684	−	0.0248691i
$715$	8.88953e6	+	8.42061e6i	0.0243198	+	0.0230370i
$716$	−2.69094e8	+	3.53988e8i	−0.733104	+	0.964382i
$717$	2.50874e8	−	8.45293e7i	0.680610	−	0.229324i
$718$	−5.39168e8	+	2.92328e7i	−1.45663	+	0.0789764i
$719$	1.24214e7	+	1.05508e7i	0.0334182	+	0.0283857i	0.663940	−	0.747786i	$-0.268883\pi$
$719$	1.24214e7	+	1.05508e7i	0.0334182	+	0.0283857i	−0.630522	+	0.776172i	$0.717159\pi$
$720$	−2.52144e7	+	9.08141e7i	−0.0675540	+	0.243308i
$721$	2.15965e8	−	6.40962e8i	0.576207	−	1.71012i
$722$	2.31386e8	−	1.56883e8i	0.614787	−	0.416836i
$723$	−3.54599e8	+	1.64055e8i	−0.938259	+	0.434085i
$724$	3.05684e8	+	3.59879e8i	0.805483	+	0.948288i
$725$	5.22144e7	−	4.94601e7i	0.137017	−	0.129790i
$726$	1.00173e8	+	9.21074e8i	0.261782	+	2.40705i
$727$	1.89654e7	−	4.75996e7i	0.0493581	−	0.123880i	−0.902230	−	0.431254i	$-0.858071\pi$
$727$	1.89654e7	−	4.75996e7i	0.0493581	−	0.123880i	0.951589	+	0.307375i	$0.0994505\pi$
$728$	2.51660e6	−	1.53506e7i	0.00652260	−	0.0397861i
$729$	3.35475e8	−	4.94788e8i	0.865919	−	1.27713i
$730$	−7.06897e8	+	5.37369e8i	−1.81714	+	1.38135i
$731$	−4.43612e6	+	4.07894e7i	−0.0113567	+	0.104423i
$732$	9.58195e7	+	5.08003e7i	0.244298	+	0.129519i
$733$	−9.00152e7	+	5.41604e7i	−0.228562	+	0.137521i	−0.625229	−	0.780441i	$-0.714994\pi$
$733$	−9.00152e7	+	5.41604e7i	−0.228562	+	0.137521i	0.396667	+	0.917963i	$0.370167\pi$
$734$	−2.05337e8	−	1.23547e8i	−0.519254	−	0.312425i
$735$	−4.91848e8	−	9.27724e8i	−1.23871	−	2.33645i
$736$	2.03733e8	+	5.11330e8i	0.511007	+	1.28253i
$737$	3.04628e8	−	6.70538e7i	0.760970	−	0.167502i
$738$	1.67709e8	+	7.61908e8i	0.417240	+	1.89554i
$739$	2.76809e8	−	1.10291e8i	0.685877	−	0.273279i	−0.00105543	−	0.999999i	$-0.500336\pi$
$739$	2.76809e8	−	1.10291e8i	0.685877	−	0.273279i	0.686933	+	0.726721i	$0.258957\pi$
$740$	−6.60681e8	+	3.50271e8i	−1.63041	+	0.864389i
$741$	8.56863e6	−	1.42412e7i	0.0210599	−	0.0350019i
$742$	2.09579e8	+	3.48323e8i	0.513021	+	0.852648i
$743$	−1.96259e8	+	3.70184e8i	−0.478480	+	0.902509i	0.520341	+	0.853959i	$0.325805\pi$
$743$	−1.96259e8	+	3.70184e8i	−0.478480	+	0.902509i	−0.998821	+	0.0485503i	$0.984540\pi$
$744$	1.33464e9	+	1.45151e8i	3.24076	+	0.352454i
$745$	2.67256e8	+	3.51569e8i	0.646337	+	0.850242i
$746$	−4.06813e7	−	2.75826e7i	−0.0979892	−	0.0664383i
$747$	−1.53311e8	−	2.51340e7i	−0.367800	−	0.0602977i
$748$	−1.04377e8	−	4.15874e7i	−0.249401	−	0.0993704i
$749$	−1.45442e8	+	1.58177e7i	−0.346134	+	0.0376443i
$750$	−6.53636e8	−	6.90035e8i	−1.54936	−	1.63564i
$751$	5.47951e8	−	4.65434e8i	1.29367	−	1.09885i	0.304428	−	0.952535i	$-0.401535\pi$
$751$	5.47951e8	−	4.65434e8i	1.29367	−	1.09885i	0.989238	−	0.146314i	$-0.0467410\pi$
$752$	1.58558e7	+	3.42717e7i	0.0372850	+	0.0805902i
$753$	4.66078e8	+	6.87414e8i	1.09163	+	1.61003i
$754$	−1.58204e7	−	5.33050e6i	−0.0369065	−	0.0124352i
$755$	−4.99999e8	−	1.38824e8i	−1.16179	−	0.322570i
$756$	4.20109e8	−	4.94591e8i	0.972292	−	1.14467i
$757$	2.41363e7	+	4.45167e8i	0.0556394	+	1.02621i	0.884437	+	0.466660i	$0.154543\pi$
$757$	2.41363e7	+	4.45167e8i	0.0556394	+	1.02621i	−0.828798	+	0.559549i	$0.810975\pi$
$758$	2.97759e8	+	8.83719e8i	0.683688	+	2.02911i
$759$	−1.20942e9	−	9.19374e8i	−2.76599	−	2.10265i
$760$	4.48042e8	−	4.72992e8i	1.02065	−	1.07749i
$761$	1.42875e7	−	2.63518e8i	0.0324193	−	0.597939i	−0.936516	−	0.350625i	$-0.885969\pi$
$761$	1.42875e7	−	2.63518e8i	0.0324193	−	0.597939i	0.968935	−	0.247314i	$-0.0795479\pi$
$762$	−1.28660e9	+	3.57223e8i	−2.90789	+	0.807373i
$763$	5.32968e8	−	1.15199e9i	1.19985	−	2.59343i
$764$	1.01166e7	−	1.65853e6i	0.0226858	−	0.00371915i
$765$	−7.29996e7	−	1.60684e7i	−0.163056	−	0.0358913i
$766$		−	7.47839e6i		−	0.0166388i
$767$	−9.35324e6	+	3.41266e6i	−0.0207289	+	0.00756322i
$768$	−8.77090e8			−1.93625
$769$	−3.44143e7	+	1.56346e8i	−0.0756764	+	0.343801i	−0.999211	−	0.0397136i	$-0.987355\pi$
$769$	−3.44143e7	+	1.56346e8i	−0.0756764	+	0.343801i	0.923535	+	0.383515i	$0.125286\pi$
$770$	−2.95974e8	−	1.80536e9i	−0.648308	−	3.95451i
$771$	9.93897e8	+	4.59826e8i	2.16859	+	1.00330i
$772$	4.01913e8	+	1.44756e9i	0.873535	+	3.14619i
$773$	−4.59116e7	−	2.48926e6i	−0.0993995	−	0.00538929i	0.00437204	−	0.999990i	$-0.498608\pi$
$773$	−4.59116e7	−	2.48926e6i	−0.0993995	−	0.00538929i	−0.103772	+	0.994601i	$0.533091\pi$
$774$	−6.95996e8	−	6.59282e8i	−1.50101	−	1.42183i
$775$	9.23576e7	−	1.21494e8i	0.198412	−	0.261006i
$776$	9.47162e8	−	3.19136e8i	2.02693	−	0.682953i
$777$	1.16418e9	−	6.31200e7i	2.48174	−	0.134556i
$778$	−5.69817e8	−	4.84007e8i	−1.21003	−	1.02781i
$779$	1.32662e8	−	4.77804e8i	0.280629	−	1.01073i
$780$	9.42185e6	−	2.79631e7i	0.0198542	−	0.0589252i
$781$	−1.09269e8	+	7.40865e7i	−0.229375	+	0.155520i
$782$	1.30342e8	−	6.03026e7i	0.272561	−	0.126100i
$783$	−1.84428e8	−	2.17125e8i	−0.384186	−	0.452299i
$784$	−9.52017e7	+	9.01798e7i	−0.197559	+	0.187138i
$785$	7.07900e7	+	6.50903e8i	0.146340	+	1.34557i
$786$	4.52764e8	−	1.13635e9i	0.932404	−	2.34016i
$787$	−1.51141e7	+	9.21920e7i	−0.0310069	+	0.189134i	−0.997788	−	0.0664705i	$-0.978826\pi$
$787$	−1.51141e7	+	9.21920e7i	−0.0310069	+	0.189134i	0.966781	+	0.255604i	$0.0822744\pi$
$788$	−2.42148e8	+	3.57142e8i	−0.494883	+	0.729898i
$789$	5.39783e8	−	4.10333e8i	1.09898	−	0.835420i
$790$	3.17753e7	−	2.92169e8i	0.0644479	−	0.592588i
$791$	2.41971e8	+	1.28285e8i	0.488916	+	0.259207i
$792$	9.20154e8	−	5.53639e8i	1.85219	−	1.11442i
$793$	−1.00304e6	−	603508.i	−0.00201140	−	0.00121022i
$794$	−4.38217e8	−	8.26565e8i	−0.875442	−	1.65126i
$795$	1.16754e8	+	2.93029e8i	0.232364	+	0.583190i
$796$	7.17264e8	−	1.57882e8i	1.42213	−	0.313035i
$797$	1.42414e8	+	6.46993e8i	0.281305	+	1.27798i	0.879218	+	0.476420i	$0.158066\pi$
$797$	1.42414e8	+	6.46993e8i	0.281305	+	1.27798i	−0.597913	+	0.801561i	$0.704003\pi$
$798$	−2.30686e9	+	9.19136e8i	−4.53954	+	1.80872i
$799$	−2.64595e7	+	1.40279e7i	−0.0518730	+	0.0275013i
$800$	−3.95794e7	+	6.57814e7i	−0.0773035	+	0.128479i
$801$	4.03484e8	+	6.70596e8i	0.785107	+	1.30486i
$802$	2.66236e8	−	5.02175e8i	0.516113	−	0.973492i
$803$	9.24847e8	+	1.00583e8i	1.78617	+	0.194258i
$804$	−4.54899e8	−	5.98410e8i	−0.875280	−	1.15141i
$805$	1.21658e9	+	8.24859e8i	2.33212	+	1.58122i
$806$	−3.49578e7	−	5.73104e6i	−0.0667635	−	0.0109453i
$807$	−2.13683e8	−	8.51391e7i	−0.406583	−	0.161998i
$808$	−2.92582e8	+	3.18202e7i	−0.554643	+	0.0603211i
$809$	2.00783e8	+	2.11964e8i	0.379211	+	0.400328i	0.887462	−	0.460881i	$-0.152467\pi$
$809$	2.00783e8	+	2.11964e8i	0.379211	+	0.400328i	−0.508251	+	0.861209i	$0.669708\pi$
$810$	−3.68779e8	+	3.13243e8i	−0.693922	+	0.589423i
$811$	−4.14780e8	−	8.96531e8i	−0.777597	−	1.68075i	−0.731529	−	0.681811i	$-0.761193\pi$
$811$	−4.14780e8	−	8.96531e8i	−0.777597	−	1.68075i	−0.0460687	−	0.998938i	$-0.514669\pi$
$812$	8.79829e8	+	1.29765e9i	1.64335	+	2.42376i
$813$	−1.19820e9	−	4.03721e8i	−2.22976	−	0.751294i
$814$	1.20099e9	+	3.33453e8i	2.22672	+	0.618247i
$815$	3.42403e8	−	4.03107e8i	0.632505	−	0.744643i
$816$	877188.	+	1.61788e7i	0.00161444	+	0.0297766i
$817$	1.94568e8	+	5.77458e8i	0.356785	+	1.05890i
$818$	2.15896e8	+	1.64120e8i	0.394443	+	0.299848i
$819$	−1.82275e7	+	1.92426e7i	−0.0331800	+	0.0350277i
$820$	4.76632e7	−	8.79095e8i	0.0864453	−	1.59439i
$821$	−5.45587e8	+	1.51482e8i	−0.985904	+	0.273735i	−0.722819	−	0.691038i	$-0.757154\pi$
$821$	−5.45587e8	+	1.51482e8i	−0.985904	+	0.273735i	−0.263085	+	0.964773i	$0.584740\pi$
$822$	−1.11381e8	+	2.40746e8i	−0.200538	+	0.433455i
$823$	2.92990e8	−	4.80333e7i	0.525597	−	0.0861673i	0.106859	−	0.994274i	$-0.465921\pi$
$823$	2.92990e8	−	4.80333e7i	0.525597	−	0.0861673i	0.418739	+	0.908107i	$0.362472\pi$
$824$	−6.96128e8	−	1.53229e8i	−1.24425	−	0.273880i
$825$		−	2.11890e8i		−	0.377353i
$826$	1.42108e9	+	4.39794e8i	2.52161	+	0.780386i
$827$	−2.81035e8			−0.496871			−0.248436	−	0.968648i	$-0.579916\pi$
$827$	−2.81035e8			−0.496871			−0.248436	+	0.968648i	$0.579916\pi$
$828$	−4.53416e8	+	2.05989e9i	−0.798741	+	3.62872i
$829$	−2.15763e7	−	1.31610e8i	−0.0378716	−	0.231007i	0.961108	−	0.276173i	$-0.0890664\pi$
$829$	−2.15763e7	−	1.31610e8i	−0.0378716	−	0.231007i	−0.998979	+	0.0451667i	$0.985618\pi$
$830$	2.53143e8	+	1.17117e8i	0.442723	+	0.204826i
$831$	6.76927e7	+	2.43807e8i	0.117961	+	0.424857i
$832$	1.99682e7	+	1.08265e6i	0.0346713	+	0.00187982i
$833$	−7.55023e7	−	7.15196e7i	−0.130625	−	0.123734i
$834$	−1.13154e9	+	1.48852e9i	−1.95062	+	2.56600i
$835$	1.15447e8	−	3.88985e7i	0.198300	−	0.0668150i
$836$	−1.66622e9	+	9.03396e7i	−2.85176	+	0.154618i
$837$	−4.60731e8	−	3.91348e8i	−0.785725	−	0.667401i
$838$	1.81846e8	−	6.54951e8i	0.309010	−	1.11295i
$839$	2.02335e7	−	6.00509e7i	0.0342598	−	0.101679i	−0.929159	−	0.369681i	$-0.879467\pi$
$839$	2.02335e7	−	6.00509e7i	0.0342598	−	0.101679i	0.963418	+	0.268002i	$0.0863634\pi$
$840$	−1.49267e9	+	1.01205e9i	−2.51841	+	1.70752i
$841$	8.48053e7	−	3.92351e7i	0.142572	−	0.0659610i
$842$	−7.29767e8	−	8.59148e8i	−1.22250	−	1.43924i
$843$	−3.82219e8	+	3.62057e8i	−0.638012	+	0.604357i
$844$	−2.02087e8	−	1.85816e9i	−0.336133	−	3.09069i
$845$	2.42005e8	−	6.07388e8i	0.401102	−	1.00669i
$846$	1.13206e8	−	6.90529e8i	0.186965	−	1.14044i
$847$	−5.27043e8	+	7.77331e8i	−0.867354	+	1.27925i
$848$	3.13599e7	−	2.38392e7i	0.0514265	−	0.0390934i
$849$	8.02407e7	−	7.37801e8i	0.131121	−	1.20564i
$850$	1.76975e7	+	9.38262e6i	0.0288174	+	0.0152780i
$851$	−8.58069e8	+	5.16283e8i	−1.39230	+	0.837720i
$852$	2.72603e8	+	1.64020e8i	0.440770	+	0.265202i
$853$	3.36744e8	+	6.35167e8i	0.542567	+	1.02339i	0.991535	+	0.129841i	$0.0414468\pi$
$853$	3.36744e8	+	6.35167e8i	0.542567	+	1.02339i	−0.448968	+	0.893548i	$0.648208\pi$
$854$	6.47368e7	+	1.62477e8i	0.103939	+	0.260867i
$855$	−1.08415e9	+	2.38640e8i	−1.73457	+	0.381808i
$856$	3.31438e7	+	1.50574e8i	0.0528421	+	0.240064i
$857$	−4.19329e8	+	1.67076e8i	−0.666212	+	0.265443i	−0.678631	−	0.734480i	$-0.737426\pi$
$857$	−4.19329e8	+	1.67076e8i	−0.666212	+	0.265443i	0.0124186	+	0.999923i	$0.496047\pi$
$858$	−4.34544e7	+	2.30381e7i	−0.0687974	+	0.0364740i
$859$	−1.65956e8	+	2.75821e8i	−0.261827	+	0.435159i	−0.959685	−	0.281076i	$-0.909309\pi$
$859$	−1.65956e8	+	2.75821e8i	−0.261827	+	0.435159i	0.697859	+	0.716235i	$0.254136\pi$
$860$	5.57755e8	+	9.26996e8i	0.876896	+	1.45741i
$861$	−6.42949e8	+	1.21273e9i	−1.00732	+	1.90000i
$862$	−2.15827e7	−	2.34726e6i	−0.0336965	−	0.00366471i
$863$	9.38270e7	+	1.23427e8i	0.145981	+	0.192034i	0.863272	−	0.504739i	$-0.168411\pi$
$863$	9.38270e7	+	1.23427e8i	0.145981	+	0.192034i	−0.717291	+	0.696774i	$0.754618\pi$
$864$	2.51692e8	+	1.70651e8i	0.390237	+	0.264587i
$865$	−8.67165e8	−	1.42165e8i	−1.33984	−	0.219656i
$866$	−1.21963e9	−	4.85944e8i	−1.87791	−	0.748226i
$867$	9.82366e8	−	1.06839e8i	1.50736	−	0.163935i
$868$	2.28784e9	+	2.41524e9i	3.49838	+	3.69319i
$869$	−2.34674e8	+	1.99334e8i	−0.357607	+	0.303754i
$870$	8.12669e8	+	1.75655e9i	1.23412	+	2.66750i
$871$	4.55313e6	+	6.71536e6i	0.00689057	+	0.0101628i
$872$	−1.26764e9	−	4.27118e8i	−1.91182	−	0.644167i
$873$	−1.64095e9	−	4.55606e8i	−2.46633	−	0.684773i
$874$	1.38081e9	−	1.62562e9i	2.06824	−	2.43492i
$875$	−5.21600e7	−	9.62034e8i	−0.0778598	−	1.43604i
$876$	−7.15838e8	−	2.12453e9i	−1.06488	−	3.16046i
$877$	−1.31006e8	−	9.95878e7i	−0.194219	−	0.147641i	0.503546	−	0.863969i	$-0.332029\pi$
$877$	−1.31006e8	−	9.95878e7i	−0.194219	−	0.147641i	−0.697764	+	0.716327i	$0.745822\pi$
$878$	4.50961e8	−	4.76073e8i	0.666278	−	0.703381i
$879$	−8.03088e7	+	1.48121e9i	−0.118249	+	2.18097i
$880$	−1.70819e8	+	4.74276e7i	−0.250661	+	0.0695958i
$881$	−4.51369e8	+	9.75619e8i	−0.660092	+	1.42677i	0.231005	+	0.972952i	$0.425799\pi$
$881$	−4.51369e8	+	9.75619e8i	−0.660092	+	1.42677i	−0.891097	+	0.453813i	$0.850064\pi$
$882$	2.39795e9	−	3.93123e8i	3.49489	−	0.572958i
$883$	3.58865e8	+	7.89923e7i	0.521254	+	0.114737i	0.467801	−	0.883834i	$-0.345046\pi$
$883$	3.58865e8	+	7.89923e7i	0.521254	+	0.114737i	0.0534528	+	0.998570i	$0.482977\pi$
$884$		−	2.92251e6i		−	0.00423057i
$885$	1.03295e9	+	5.15157e8i	1.49022	+	0.743207i
$886$	7.80869e8			1.12273
$887$	−3.12571e7	+	1.42002e8i	−0.0447897	+	0.203482i	−0.993701	−	0.112060i	$-0.964255\pi$
$887$	−3.12571e7	+	1.42002e8i	−0.0447897	+	0.203482i	0.948912	+	0.315542i	$0.102186\pi$
$888$	−1.98778e8	−	1.21249e9i	−0.283876	−	1.73157i
$889$	−1.22841e9	−	5.68322e8i	−1.74839	−	0.808890i
$890$	−3.75901e8	−	1.35387e9i	−0.533217	−	1.92047i
$891$	5.06188e8	+	2.74447e7i	0.715614	+	0.0387994i
$892$	−8.03724e7	−	7.61328e7i	−0.113243	−	0.107270i
$893$	−2.69166e8	+	3.54082e8i	−0.377977	+	0.497220i
$894$	−1.68102e9	+	5.66402e8i	−2.35267	+	0.792706i
$895$	−5.55605e8	+	3.01240e7i	−0.774991	+	0.0420188i
$896$	−1.52347e9	−	1.29404e9i	−2.11792	−	1.79898i
$897$	1.05716e7	−	3.80753e7i	0.0146475	−	0.0527554i
$898$	−1.85546e8	+	5.50680e8i	−0.256225	+	0.760450i
$899$	1.20881e9	−	8.19596e8i	1.66372	−	1.12803i
$900$	−2.66993e8	+	1.23524e8i	−0.366245	+	0.169443i
$901$	2.02251e7	+	2.38108e7i	0.0276513	+	0.0325536i
$902$	−1.06535e9	+	1.00915e9i	−1.45169	+	1.37511i
$903$	−1.82368e8	−	1.67685e9i	−0.247677	−	2.27736i
$904$	1.06831e8	−	2.68124e8i	0.144607	−	0.362937i
$905$	−9.55912e7	+	5.83081e8i	−0.128965	+	0.786652i
$906$	1.16971e9	−	1.72520e9i	1.57288	−	2.31982i
$907$	1.11477e8	−	8.47424e7i	0.149404	−	0.113574i	−0.527802	−	0.849367i	$-0.676984\pi$
$907$	1.11477e8	−	8.47424e7i	0.149404	−	0.113574i	0.677206	+	0.735793i	$0.263191\pi$
$908$	1.25688e8	−	1.15569e9i	0.167895	−	1.54377i
$909$	4.43056e8	+	2.34893e8i	0.589884	+	0.312737i
$910$	4.07746e7	−	2.45333e7i	0.0541085	−	0.0325560i
$911$	1.03824e9	+	6.24691e8i	1.37323	+	0.826247i	0.995040	−	0.0994789i	$-0.0317176\pi$
$911$	1.03824e9	+	6.24691e8i	1.37323	+	0.826247i	0.378194	+	0.925726i	$0.376545\pi$
$912$	1.12714e8	+	2.12601e8i	0.148591	+	0.280273i
$913$	−1.08163e8	−	2.71468e8i	−0.142124	−	0.356703i
$914$	1.21751e9	−	2.67994e8i	1.59453	−	0.350983i
$915$	2.91742e7	+	1.32540e8i	0.0380834	+	0.173015i
$916$	6.71453e8	−	2.67531e8i	0.873634	−	0.348088i
$917$	1.09550e9	−	5.80796e8i	1.42070	−	0.753209i
$918$	4.09054e7	−	6.79854e7i	0.0528753	−	0.0878795i
$919$	−6.01460e8	−	9.99634e8i	−0.774926	−	1.28794i	−0.952714	−	0.303868i	$-0.901722\pi$
$919$	−6.01460e8	−	9.99634e8i	−0.774926	−	1.28794i	0.177789	−	0.984069i	$-0.443106\pi$
$920$	7.25566e8	−	1.36856e9i	0.931781	−	1.75752i
$921$	1.95978e8	+	2.13139e7i	0.250858	+	0.0272825i
$922$	−4.29339e8	−	5.64786e8i	−0.547782	−	0.720594i
$923$	−2.84221e6	−	1.92707e6i	−0.00361453	−	0.00245071i
$924$	4.55812e9	+	7.47265e8i	5.77789	+	0.947238i
$925$	−1.29753e8	−	5.16982e7i	−0.163942	−	0.0653207i
$926$	7.21612e8	−	7.84801e7i	0.908805	−	0.0988385i
$927$	8.35232e8	+	8.81744e8i	1.04850	+	1.10689i
$928$	−5.59940e8	+	4.75618e8i	−0.700645	+	0.595133i
$929$	−5.23389e8	−	1.13129e9i	−0.652796	−	1.41100i	−0.897333	−	0.441355i	$-0.854498\pi$
$929$	−5.23389e8	−	1.13129e9i	−0.652796	−	1.41100i	0.244537	−	0.969640i	$-0.421364\pi$
$930$	2.30475e9	+	3.39924e9i	2.86533	+	4.22604i
$931$	−1.46368e9	−	4.93172e8i	−1.81383	−	0.611152i
$932$	−3.21369e8	−	8.92276e7i	−0.396968	−	0.110218i
$933$	−1.30438e8	+	1.53564e8i	−0.160605	+	0.189079i
$934$	3.92083e6	+	7.23155e7i	0.00481214	+	0.0887546i
$935$	−4.48929e7	−	1.33237e8i	−0.0549216	−	0.163002i
$936$	2.22369e7	+	1.69040e7i	0.0271173	+	0.0206140i
$937$	−2.73359e8	+	2.88581e8i	−0.332288	+	0.350792i	−0.870633	−	0.491932i	$-0.836291\pi$
$937$	−2.73359e8	+	2.88581e8i	−0.332288	+	0.350792i	0.538346	+	0.842724i	$0.319049\pi$
$938$	6.56282e7	−	1.21044e9i	0.0795210	−	1.46668i
$939$	−1.34389e9	+	3.73130e8i	−1.62318	+	0.450675i
$940$	−3.31568e8	+	7.16672e8i	−0.399198	+	0.862853i
$941$	−1.43489e9	+	2.35238e8i	−1.72206	+	0.282318i	−0.940072	−	0.340975i	$-0.889243\pi$
$941$	−1.43489e9	+	2.35238e8i	−1.72206	+	0.282318i	−0.781989	+	0.623293i	$0.785795\pi$
$942$	−2.56845e9	−	5.65360e8i	−3.07269	−	0.676351i
$943$		−	1.17898e9i		−	1.40596i
$944$	2.74788e7	−	1.41508e8i	0.0326650	−	0.168215i
$945$	8.12040e8			0.962237
$946$	3.87645e8	−	1.76109e9i	0.457889	−	2.08021i
$947$	2.62033e8	+	1.59833e9i	0.308536	+	1.88199i	0.451516	+	0.892263i	$0.350884\pi$
$947$	2.62033e8	+	1.59833e9i	0.308536	+	1.88199i	−0.142979	+	0.989726i	$0.545668\pi$
$948$	6.73429e8	+	3.11561e8i	0.790436	+	0.365695i
$949$	6.47367e6	+	2.33161e7i	0.00757446	+	0.0272808i
$950$	2.97052e8	+	1.61057e7i	0.346467	+	0.0187849i
$951$	−7.56793e8	−	7.16873e8i	−0.879905	−	0.833490i
$952$	−1.08093e8	+	1.42194e8i	−0.125281	+	0.164805i
$953$	3.63485e7	−	1.22472e7i	0.0419960	−	0.0141501i	−0.298225	−	0.954496i	$-0.596395\pi$
$953$	3.63485e7	−	1.22472e7i	0.0419960	−	0.0141501i	0.340221	+	0.940345i	$0.389498\pi$
$954$	−7.28889e8	+	3.95192e7i	−0.839491	+	0.0455159i
$955$	9.77733e6	+	8.30494e6i	0.0112256	+	0.00953512i
$956$	1.84955e8	−	6.66146e8i	0.211686	−	0.762423i
$957$	6.47457e8	−	1.92158e9i	0.738711	−	2.19242i
$958$	−4.76424e8	+	3.23023e8i	−0.541872	+	0.367399i
$959$	−2.44034e8	+	1.12902e8i	−0.276691	+	0.128011i
$960$	−1.50090e9	−	1.76700e9i	−1.69644	−	1.99721i
$961$	1.60557e9	−	1.52088e9i	1.80909	−	1.71366i
$962$	3.50530e6	+	3.22307e7i	0.00393731	+	0.0362030i
$963$	9.72370e7	−	2.44047e8i	0.108881	−	0.273271i
$964$	−1.65072e8	+	1.00690e9i	−0.184265	+	1.12397i
$965$	−1.05499e9	+	1.55600e9i	−1.17400	+	1.73152i
$966$	−4.70015e9	+	3.57296e9i	−5.21412	+	3.96367i
$967$	1.16604e8	−	1.07216e9i	0.128954	−	1.18571i	−0.733541	−	0.679645i	$-0.762134\pi$
$967$	1.16604e8	−	1.07216e9i	0.128954	−	1.18571i	0.862495	−	0.506066i	$-0.168901\pi$
$968$	8.74443e8	+	4.63601e8i	0.964063	+	0.511114i
$969$	−1.63523e8	+	9.83883e7i	−0.179724	+	0.108136i
$970$	2.61987e9	+	1.57632e9i	2.87055	+	1.72715i
$971$	−1.82090e8	−	3.43459e8i	−0.198897	−	0.375160i	0.763921	−	0.645310i	$-0.223272\pi$
$971$	−1.82090e8	−	3.43459e8i	−0.198897	−	0.375160i	−0.962818	+	0.270149i	$0.912927\pi$
$972$	−7.69501e8	−	1.93130e9i	−0.837935	−	2.10306i
$973$	−1.85100e9	+	4.07437e8i	−2.00941	+	0.442305i
$974$	5.29329e7	+	2.40477e8i	0.0572860	+	0.260253i
$975$	5.12003e6	−	2.04001e6i	0.00552406	−	0.00220099i
$976$	1.49740e7	−	7.93871e6i	0.0161060	−	0.00853887i
$977$	−6.49524e8	+	1.07952e9i	−0.696485	+	1.15757i	0.283592	+	0.958945i	$0.408474\pi$
$977$	−6.49524e8	+	1.07952e9i	−0.696485	+	1.15757i	−0.980076	+	0.198621i	$0.936354\pi$
$978$	1.09528e9	+	1.82036e9i	1.17087	+	1.94599i
$979$	−6.89540e8	+	1.30061e9i	−0.734871	+	1.38611i
$980$	−2.72610e9	−	2.96481e8i	−2.89643	−	0.315006i
$981$	1.37934e9	+	1.81449e9i	1.46105	+	1.92198i
$982$	1.46272e9	+	9.91751e8i	1.54464	+	1.04729i
$983$	1.52495e9	+	2.50003e8i	1.60544	+	0.263199i	0.896822	−	0.442391i	$-0.145870\pi$
$983$	1.52495e9	+	2.50003e8i	1.60544	+	0.263199i	0.708620	+	0.705590i	$0.249318\pi$
$984$	1.34381e9	+	5.35422e8i	1.41043	+	0.561967i
$985$	−5.36783e8	+	5.83787e7i	−0.561682	+	0.0610866i
$986$	1.31825e8	+	1.39166e8i	0.137520	+	0.145179i
$987$	9.38346e8	−	7.97038e8i	0.975914	−	0.828949i
$988$	−1.82247e7	−	3.93921e7i	−0.0188969	−	0.0408449i
$989$	8.13039e8	+	1.19914e9i	0.840471	+	1.23960i
$990$	3.11314e9	+	1.04894e9i	3.20843	+	1.08105i
$991$	−3.19735e8	−	8.87740e7i	−0.328526	−	0.0912147i	0.0993493	−	0.995053i	$-0.468324\pi$
$991$	−3.19735e8	−	8.87740e7i	−0.328526	−	0.0912147i	−0.427875	+	0.903838i	$0.640738\pi$
$992$	−1.00924e9	+	1.18817e9i	−1.03385	+	1.21715i
$993$	−9.87229e7	−	1.82084e9i	−0.100825	−	1.85962i
$994$	1.63821e8	+	4.86203e8i	0.166805	+	0.495060i
$995$	7.31638e8	+	5.56177e8i	0.742723	+	0.564603i
$996$	−4.84288e8	+	5.11257e8i	−0.490146	+	0.517441i
$997$	−3.15183e7	+	5.81320e8i	−0.0318036	+	0.586583i	0.938587	+	0.345043i	$0.112136\pi$
$997$	−3.15183e7	+	5.81320e8i	−0.0318036	+	0.586583i	−0.970391	+	0.241541i	$0.922347\pi$
$998$	7.50718e8	−	2.08436e8i	0.755240	−	0.209691i
$999$	−2.32302e8	+	5.02114e8i	−0.233001	+	0.503623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.7.d.a.43.3	yes	812
59.11	odd	58	inner	59.7.d.a.11.3	✓	812

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.7.d.a.11.3	✓	812	59.11	odd	58	inner
59.7.d.a.43.3	yes	812	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	59.d (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82178 + 12.8195i) q^{2} +(-6.70926 - 40.9247i) q^{3} +(-98.2915 - 45.4745i) q^{4} +(-36.2562 - 130.583i) q^{5} +(543.565 + 29.4712i) q^{6} +(400.602 + 379.471i) q^{7} +(351.917 - 462.939i) q^{8} +(-938.976 + 316.378i) q^{9} +(1776.31 - 96.3088i) q^{10} +(-1420.48 - 1206.57i) q^{11} +(-1201.57 + 4327.65i) q^{12} +(15.4791 - 45.9404i) q^{13} +(-5995.02 + 4064.73i) q^{14} +(-5100.82 + 2359.89i) q^{15} +(454.386 + 534.945i) q^{16} +(-404.121 + 382.803i) q^{17} +(-1406.21 - 12929.9i) q^{18} +(-3059.93 + 7679.85i) q^{19} +(-2374.52 + 14483.9i) q^{20} +(12842.0 - 18940.5i) q^{21} +(19475.8 - 14805.1i) q^{22} +(-2125.11 + 19540.1i) q^{23} +(-21306.7 - 11296.1i) q^{24} +(-2349.02 + 1413.36i) q^{25} +(545.253 + 328.068i) q^{26} +(5086.40 + 9593.96i) q^{27} +(-22119.6 - 55515.9i) q^{28} +(-25621.4 + 5639.71i) q^{29} +(-15859.1 - 72048.8i) q^{30} +(-51715.3 + 20605.3i) q^{31} +(24741.7 - 13117.2i) q^{32} +(-39847.9 + 66227.8i) q^{33} +(-3767.00 - 6260.80i) q^{34} +(35028.1 - 66070.0i) q^{35} +(106680. + 11602.2i) q^{36} +(30832.9 + 40560.0i) q^{37} +(-89817.1 - 60897.5i) q^{38} +(-1983.95 - 325.252i) q^{39} +(-73211.2 - 29170.0i) q^{40} +(-59631.3 + 6485.29i) q^{41} +(206570. + 218073. i) q^{42} +(56178.6 - 47718.5i) q^{43} +(84753.1 + 183191. i) q^{44} +(75357.2 + 111144. i) q^{45} +(-244497. - 82380.7i) q^{46} +(51840.1 + 14393.3i) q^{47} +(18843.8 - 22184.7i) q^{48} +(10114.8 + 186557. i) q^{49} +(-11490.1 - 34101.4i) q^{50} +(18377.5 + 13970.2i) q^{51} +(-3610.58 + 3811.64i) q^{52} +(3038.50 - 56041.8i) q^{53} +(-137342. + 38132.9i) q^{54} +(-106056. + 229236. i) q^{55} +(316651. - 51912.2i) q^{56} +(334825. + 73700.6i) q^{57} -344367. i q^{58} +(-128316. - 160360. i) q^{59} +608682. q^{60} +(5190.90 - 23582.5i) q^{61} +(-118219. - 721106. i) q^{62} +(-496212. - 229572. i) q^{63} +(110358. + 397472. i) q^{64} +(-6560.25 - 355.686i) q^{65} +(-736563. - 697710. i) q^{66} +(-101283. + 133236. i) q^{67} +(57129.4 - 19249.2i) q^{68} +(813930. - 44130.0i) q^{69} +(748141. + 635477. i) q^{70} +(18950.2 - 68252.5i) q^{71} +(-183978. + 546027. i) q^{72} +(-413145. + 280119. i) q^{73} +(-606961. + 280810. i) q^{74} +(73601.4 + 86650.3i) q^{75} +(650002. - 615715. i) q^{76} +(-111191. - 1.02238e6i) q^{77} +(9767.82 - 24515.4i) q^{78} +(26727.7 - 163032. i) q^{79} +(53380.4 - 78730.2i) q^{80} +(-216534. + 164605. i) q^{81} +(85128.3 - 782742. i) q^{82} +(138529. + 73443.3i) q^{83} +(-2.12357e6 + 1.27771e6i) q^{84} +(64639.5 + 38892.3i) q^{85} +(453203. + 854831. i) q^{86} +(402704. + 1.01071e6i) q^{87} +(-1.05846e6 + 232984. i) q^{88} +(-169795. - 771388. i) q^{89} +(-1.63744e6 + 652417. i) q^{90} +(23634.0 - 12529.9i) q^{91} +(1.09746e6 - 1.82399e6i) q^{92} +(1.19023e6 + 1.97819e6i) q^{93} +(-330796. + 623948. i) q^{94} +(1.11380e6 + 121133. i) q^{95} +(-702816. - 924538. i) q^{96} +(1.42260e6 + 964545. i) q^{97} +(-2.42011e6 - 396756. i) q^{98} +(1.71553e6 + 683528. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 812 q - 29 q^{2} - 39 q^{3} + 869 q^{4} - 171 q^{5} - 29 q^{6} - 435 q^{7} - 29 q^{8} - 7648 q^{9} - 29 q^{10} - 29 q^{11} + 1095 q^{12} - 29 q^{13} - 29 q^{14} - 569 q^{15} - 25051 q^{16} - 9071 q^{17}+ \cdots + 9513421 q^{99}+O(q^{100}) \) 812 * q - 29 * q^2 - 39 * q^3 + 869 * q^4 - 171 * q^5 - 29 * q^6 - 435 * q^7 - 29 * q^8 - 7648 * q^9 - 29 * q^10 - 29 * q^11 + 1095 * q^12 - 29 * q^13 - 29 * q^14 - 569 * q^15 - 25051 * q^16 - 9071 * q^17 - 29 * q^18 - 3879 * q^19 + 46867 * q^20 - 3729 * q^21 - 11267 * q^22 - 29 * q^23 - 29 * q^24 - 65696 * q^25 + 64561 * q^26 - 36009 * q^27 + 45513 * q^28 + 31701 * q^29 - 29 * q^30 - 29 * q^31 - 29 * q^32 - 29 * q^33 - 29 * q^34 - 46305 * q^35 + 185269 * q^36 - 29 * q^37 - 29 * q^38 - 29 * q^39 - 29 * q^40 - 91943 * q^41 - 29 * q^42 - 29 * q^43 - 29 * q^44 + 1328609 * q^45 + 122071 * q^46 - 472149 * q^47 - 4460721 * q^48 - 992540 * q^49 - 1117341 * q^50 - 161065 * q^51 + 1336291 * q^52 + 1079813 * q^53 + 4504947 * q^54 + 1872907 * q^55 + 3956963 * q^56 + 2677007 * q^57 - 302138 * q^59 - 4965482 * q^60 - 1574381 * q^61 - 2444409 * q^62 - 5085047 * q^63 - 5066455 * q^64 - 1422653 * q^65 + 433939 * q^66 + 876931 * q^67 + 3018437 * q^68 + 5706243 * q^69 + 6798499 * q^70 + 3537645 * q^71 + 6041251 * q^72 - 396749 * q^73 - 3448403 * q^74 - 9552475 * q^75 - 247173 * q^76 - 29 * q^77 + 375035 * q^78 - 4731 * q^79 - 1921013 * q^80 + 841594 * q^81 - 29 * q^82 - 29 * q^83 - 2367333 * q^84 - 864073 * q^85 - 5031139 * q^86 + 4790463 * q^87 - 726023 * q^88 - 29 * q^89 - 29 * q^90 - 29 * q^91 - 29 * q^92 - 29 * q^93 - 2835797 * q^94 - 1047881 * q^95 - 29 * q^96 - 29 * q^97 + 29127484 * q^98 + 9513421 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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