LMFDB - Embedded newform 49.7.h.a.3.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(3,49)] 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("49.3"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.h (of order $42$, degree $12$, 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:	$11.2726500974$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			3.4
Character	$\chi$	$=$	49.3
Dual form			49.7.h.a.33.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.73204 + 12.0571i) q^{2} +(-20.1535 - 1.51030i) q^{3} +(-76.0649 - 70.5779i) q^{4} +(43.5678 - 63.9023i) q^{5} +(113.577 - 235.845i) q^{6} +(342.839 + 10.5003i) q^{7} +(464.042 - 223.471i) q^{8} +(-316.975 - 47.7763i) q^{9} +(564.308 + 827.688i) q^{10} +(1954.99 - 294.667i) q^{11} +(1426.38 + 1537.27i) q^{12} +(-744.349 + 593.598i) q^{13} +(-1748.93 + 4083.94i) q^{14} +(-974.556 + 1222.05i) q^{15} +(2.25471 + 30.0870i) q^{16} +(304.791 - 988.107i) q^{17} +(2075.98 - 3595.70i) q^{18} +(-2142.80 + 1237.15i) q^{19} +(-7824.07 + 1785.79i) q^{20} +(-6893.56 - 729.406i) q^{21} +(-5698.28 + 24965.8i) q^{22} +(2384.01 - 735.369i) q^{23} +(-9689.59 + 3802.88i) q^{24} +(3523.11 + 8976.73i) q^{25} +(-3634.75 - 11783.6i) q^{26} +(20679.7 + 4720.01i) q^{27} +(-25336.9 - 24995.6i) q^{28} +(7850.27 + 34394.3i) q^{29} +(-10122.7 - 17533.1i) q^{30} +(21319.6 + 12308.9i) q^{31} +(31125.2 + 9600.85i) q^{32} +(-39844.9 + 2985.96i) q^{33} +(10471.4 + 8350.65i) q^{34} +(15607.8 - 21450.7i) q^{35} +(20738.7 + 26005.5i) q^{36} +(45738.0 - 42438.6i) q^{37} +(-4776.51 - 31690.1i) q^{38} +(15897.7 - 10838.9i) q^{39} +(5937.01 - 39389.5i) q^{40} +(-21442.0 - 44524.8i) q^{41} +(41415.1 - 79664.4i) q^{42} +(107907. + 51965.2i) q^{43} +(-169503. - 115565. i) q^{44} +(-16862.9 + 18173.9i) q^{45} +(-2414.85 + 32223.9i) q^{46} +(-4029.84 - 1581.60i) q^{47} -609.764i q^{48} +(117428. + 7199.82i) q^{49} -124904. q^{50} +(-7634.94 + 19453.5i) q^{51} +(98513.7 + 7382.58i) q^{52} +(-25370.1 - 23540.0i) q^{53} +(-154767. + 227001. i) q^{54} +(66344.7 - 137766. i) q^{55} +(161438. - 71742.1i) q^{56} +(45053.4 - 21696.6i) q^{57} +(-451841. - 68104.1i) q^{58} +(-159216. - 233527. i) q^{59} +(160380. - 24173.3i) q^{60} +(182038. + 196190. i) q^{61} +(-249295. + 198806. i) q^{62} +(-108170. - 19707.9i) q^{63} +(-264248. + 331356. i) q^{64} +(5502.62 + 73427.4i) q^{65} +(152546. - 494542. i) q^{66} +(31587.9 - 54711.9i) q^{67} +(-92922.4 + 53648.8i) q^{68} +(-49156.8 + 11219.7i) q^{69} +(184776. + 289689. i) q^{70} +(-66040.1 + 289341. i) q^{71} +(-157766. + 48664.5i) q^{72} +(609797. - 239328. i) q^{73} +(295251. + 752286. i) q^{74} +(-57445.5 - 186234. i) q^{75} +(250307. + 57130.9i) q^{76} +(673341. - 80495.5i) q^{77} +(55456.3 + 242970. i) q^{78} +(58702.2 + 101675. i) q^{79} +(2020.86 + 1166.74i) q^{80} +(-186337. - 57477.5i) q^{81} +(638302. - 47834.1i) q^{82} +(-564425. - 450114. i) q^{83} +(472878. + 542015. i) q^{84} +(-49863.2 - 62526.5i) q^{85} +(-1.13717e6 + 1.05514e6i) q^{86} +(-106265. - 705022. i) q^{87} +(841348. - 573622. i) q^{88} +(-32620.6 + 216423. i) q^{89} +(-139328. - 289317. i) q^{90} +(-261425. + 195693. i) q^{91} +(-233240. - 112323. i) q^{92} +(-411076. - 280267. i) q^{93} +(38138.8 - 41103.8i) q^{94} +(-14300.7 + 190829. i) q^{95} +(-612782. - 240499. i) q^{96} -1.48393e6i q^{97} +(-642485. + 1.38177e6i) q^{98} -633760. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 13 q^{2} - 11 q^{3} + 819 q^{4} - 179 q^{5} + 770 q^{6} + 392 q^{7} + 828 q^{8} - 1160 q^{9} - 2594 q^{10} - 5305 q^{11} + 7497 q^{12} - 14 q^{13} - 11403 q^{14} - 6196 q^{15} + 27903 q^{16} - 5107 q^{17}+ \cdots - 4449616 q^{99}+O(q^{100}) $ 324 * q - 13 * q^2 - 11 * q^3 + 819 * q^4 - 179 * q^5 + 770 * q^6 + 392 * q^7 + 828 * q^8 - 1160 * q^9 - 2594 * q^10 - 5305 * q^11 + 7497 * q^12 - 14 * q^13 - 11403 * q^14 - 6196 * q^15 + 27903 * q^16 - 5107 * q^17 - 11538 * q^18 - 30006 * q^19 - 50190 * q^20 + 8953 * q^21 + 33042 * q^22 + 54531 * q^23 + 90184 * q^24 - 92804 * q^25 - 93366 * q^26 - 11774 * q^27 - 19180 * q^28 - 80398 * q^29 + 15851 * q^30 + 39378 * q^31 - 197841 * q^32 + 36697 * q^33 - 54698 * q^34 - 819 * q^35 + 706300 * q^36 + 15331 * q^37 - 304462 * q^38 - 179298 * q^39 - 515414 * q^40 - 116046 * q^41 + 1203482 * q^42 - 225018 * q^43 + 1373764 * q^44 + 465772 * q^45 + 1100364 * q^46 + 270021 * q^47 - 767900 * q^49 - 1164040 * q^50 - 1215743 * q^51 - 3954790 * q^52 + 141807 * q^53 - 1093487 * q^54 + 991354 * q^55 - 596680 * q^56 - 388207 * q^57 + 381012 * q^58 + 2015849 * q^59 + 5807298 * q^60 + 258821 * q^61 - 525742 * q^62 - 1265432 * q^63 + 872972 * q^64 - 70154 * q^65 + 497766 * q^66 - 324190 * q^67 - 799617 * q^68 - 2216774 * q^69 + 56140 * q^70 - 1031026 * q^71 + 4633092 * q^72 + 1268305 * q^73 - 1444192 * q^74 - 1699244 * q^75 - 5464011 * q^76 - 2274741 * q^77 - 1285956 * q^78 - 515710 * q^79 + 8314050 * q^80 - 1069027 * q^81 + 357910 * q^82 - 3183054 * q^83 - 10099096 * q^84 - 1596848 * q^85 - 5387681 * q^86 - 4197040 * q^87 - 1024645 * q^88 + 983769 * q^89 + 18547774 * q^90 + 13421086 * q^91 + 5294506 * q^92 + 15477850 * q^93 + 8903632 * q^94 + 5236430 * q^95 + 7804258 * q^96 - 10234553 * q^98 - 4449616 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{42}\right)$

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 $

$2$	−4.73204	+	12.0571i	−0.591505	+	1.50713i	0.250750	+	0.968052i	$0.419323\pi$
$2$	−4.73204	+	12.0571i	−0.591505	+	1.50713i	−0.842255	+	0.539079i	$0.818772\pi$
$3$	−20.1535	−	1.51030i	−0.746426	−	0.0559369i	−0.303914	−	0.952699i	$-0.598294\pi$
$3$	−20.1535	−	1.51030i	−0.746426	−	0.0559369i	−0.442512	+	0.896763i	$0.645913\pi$
$4$	−76.0649	−	70.5779i	−1.18851	−	1.10278i
$5$	43.5678	−	63.9023i	0.348543	−	0.511218i	−0.611435	−	0.791295i	$-0.709407\pi$
$5$	43.5678	−	63.9023i	0.348543	−	0.511218i	0.959978	+	0.280076i	$0.0903598\pi$
$6$	113.577	−	235.845i	0.525819	−	1.09188i
$7$	342.839	+	10.5003i	0.999531	+	0.0306131i
$7$	342.839	+	10.5003i	0.999531	+	0.0306131i
$8$	464.042	−	223.471i	0.906333	−	0.436467i
$9$	−316.975	−	47.7763i	−0.434808	−	0.0655367i
$10$	564.308	+	827.688i	0.564308	+	0.827688i
$11$	1954.99	−	294.667i	1.46881	−	0.221388i	0.634604	−	0.772837i	$-0.281163\pi$
$11$	1954.99	−	294.667i	1.46881	−	0.221388i	0.834208	+	0.551450i	$0.185925\pi$
$12$	1426.38	+	1537.27i	0.825452	+	0.889626i
$13$	−744.349	+	593.598i	−0.338802	+	0.270186i	−0.778080	−	0.628166i	$-0.783806\pi$
$13$	−744.349	+	593.598i	−0.338802	+	0.270186i	0.439277	+	0.898352i	$0.355235\pi$
$14$	−1748.93	+	4083.94i	−0.637366	+	1.48832i
$15$	−974.556	+	1222.05i	−0.288757	+	0.362090i
$16$	2.25471	+	30.0870i	0.000550466	+	0.00734546i
$17$	304.791	−	988.107i	0.0620376	−	0.201121i	−0.919248	−	0.393679i	$-0.871202\pi$
$17$	304.791	−	988.107i	0.0620376	−	0.201121i	0.981286	+	0.192558i	$0.0616784\pi$
$18$	2075.98	−	3595.70i	0.355963	−	0.616547i
$19$	−2142.80	+	1237.15i	−0.312407	+	0.180368i	−0.648003	−	0.761638i	$-0.724396\pi$
$19$	−2142.80	+	1237.15i	−0.312407	+	0.180368i	0.335596	+	0.942006i	$0.391062\pi$
$20$	−7824.07	+	1785.79i	−0.978009	+	0.223224i
$21$	−6893.56	−	729.406i	−0.744364	−	0.0787611i
$22$	−5698.28	+	24965.8i	−0.535150	+	2.34464i
$23$	2384.01	−	735.369i	0.195941	−	0.0604396i	−0.195232	−	0.980757i	$-0.562546\pi$
$23$	2384.01	−	735.369i	0.195941	−	0.0604396i	0.391172	+	0.920318i	$0.372070\pi$
$24$	−9689.59	+	3802.88i	−0.700925	+	0.275093i
$25$	3523.11	+	8976.73i	0.225479	+	0.574511i
$26$	−3634.75	−	11783.6i	−0.206802	−	0.670436i
$27$	20679.7	+	4720.01i	1.05064	+	0.239801i
$28$	−25336.9	−	24995.6i	−1.15420	−	1.13865i
$29$	7850.27	+	34394.3i	0.321878	+	1.41024i	0.834208	+	0.551449i	$0.185925\pi$
$29$	7850.27	+	34394.3i	0.321878	+	1.41024i	−0.512331	+	0.858788i	$0.671218\pi$
$30$	−10122.7	−	17533.1i	−0.374916	−	0.649374i
$31$	21319.6	+	12308.9i	0.715641	+	0.413175i	0.813146	−	0.582060i	$-0.197753\pi$
$31$	21319.6	+	12308.9i	0.715641	+	0.413175i	−0.0975055	+	0.995235i	$0.531086\pi$
$32$	31125.2	+	9600.85i	0.949866	+	0.292995i
$33$	−39844.9	+	2985.96i	−1.10874	+	0.0830889i
$34$	10471.4	+	8350.65i	0.266420	+	0.212463i
$35$	15607.8	−	21450.7i	0.364029	−	0.500309i
$36$	20738.7	+	26005.5i	0.444502	+	0.557388i
$37$	45738.0	−	42438.6i	0.902966	−	0.837830i	−0.0843760	−	0.996434i	$-0.526890\pi$
$37$	45738.0	−	42438.6i	0.902966	−	0.837830i	0.987342	+	0.158604i	$0.0506992\pi$
$38$	−4776.51	−	31690.1i	−0.0870482	−	0.577527i
$39$	15897.7	−	10838.9i	0.268004	−	0.182722i
$40$	5937.01	−	39389.5i	0.0927659	−	0.615461i
$41$	−21442.0	−	44524.8i	−0.311110	−	0.646026i	0.685520	−	0.728054i	$-0.259575\pi$
$41$	−21442.0	−	44524.8i	−0.311110	−	0.646026i	−0.996630	+	0.0820274i	$0.973860\pi$
$42$	41415.1	−	79664.4i	0.558999	−	1.07527i
$43$	107907.	+	51965.2i	1.35720	+	0.653593i	0.964011	−	0.265864i	$-0.0856572\pi$
$43$	107907.	+	51965.2i	1.35720	+	0.653593i	0.393190	+	0.919457i	$0.371371\pi$
$44$	−169503.	−	115565.i	−1.98985	−	1.35665i
$45$	−16862.9	+	18173.9i	−0.185053	+	0.199439i
$46$	−2414.85	+	32223.9i	−0.0248094	+	0.331058i
$47$	−4029.84	−	1581.60i	−0.0388145	−	0.0152336i	0.345854	−	0.938288i	$-0.387589\pi$
$47$	−4029.84	−	1581.60i	−0.0388145	−	0.0152336i	−0.384669	+	0.923055i	$0.625684\pi$
$48$		−	609.764i		−	0.00551364i
$49$	117428.	+	7199.82i	0.998126	+	0.0611974i
$50$	−124904.			−0.999236
$51$	−7634.94	+	19453.5i	−0.0575566	+	0.146652i
$52$	98513.7	+	7382.58i	0.700627	+	0.0525047i
$53$	−25370.1	−	23540.0i	−0.170410	−	0.158117i	0.590358	−	0.807142i	$-0.298987\pi$
$53$	−25370.1	−	23540.0i	−0.170410	−	0.158117i	−0.760767	+	0.649025i	$0.775177\pi$
$54$	−154767.	+	227001.i	−0.982870	+	1.44161i
$55$	66344.7	−	137766.i	0.398766	−	0.828047i
$56$	161438.	−	71742.1i	0.919270	−	0.408517i
$57$	45053.4	−	21696.6i	0.243278	−	0.117156i
$58$	−451841.	−	68104.1i	−2.31581	−	0.349052i
$59$	−159216.	−	233527.i	−0.775232	−	1.13706i	−0.987154	−	0.159770i	$-0.948925\pi$
$59$	−159216.	−	233527.i	−0.775232	−	1.13706i	0.211923	−	0.977286i	$-0.432028\pi$
$60$	160380.	−	24173.3i	0.742498	−	0.111914i
$61$	182038.	+	196190.i	0.801995	+	0.864345i	0.993106	−	0.117224i	$-0.0373995\pi$
$61$	182038.	+	196190.i	0.801995	+	0.864345i	−0.191111	+	0.981568i	$0.561209\pi$
$62$	−249295.	+	198806.i	−1.04601	+	0.834169i
$63$	−108170.	−	19707.9i	−0.432598	−	0.0788168i
$64$	−264248.	+	331356.i	−1.00803	+	1.26402i
$65$	5502.62	+	73427.4i	0.0200368	+	0.267373i
$66$	152546.	−	494542.i	0.530602	−	1.72017i
$67$	31587.9	−	54711.9i	0.105026	−	0.181910i	−0.808723	−	0.588190i	$-0.799841\pi$
$67$	31587.9	−	54711.9i	0.105026	−	0.181910i	0.913749	+	0.406280i	$0.133174\pi$
$68$	−92922.4	+	53648.8i	−0.295525	+	0.170621i
$69$	−49156.8	+	11219.7i	−0.149636	+	0.0341534i
$70$	184776.	+	289689.i	0.538706	+	0.844575i
$71$	−66040.1	+	289341.i	−0.184515	+	0.808415i	0.794929	+	0.606702i	$0.207508\pi$
$71$	−66040.1	+	289341.i	−0.184515	+	0.808415i	−0.979445	+	0.201713i	$0.935349\pi$
$72$	−157766.	+	48664.5i	−0.422685	+	0.130381i
$73$	609797.	−	239328.i	1.56753	−	0.615211i	0.586654	−	0.809837i	$-0.300445\pi$
$73$	609797.	−	239328.i	1.56753	−	0.615211i	0.980877	+	0.194626i	$0.0623495\pi$
$74$	295251.	+	752286.i	0.728611	+	1.85647i
$75$	−57445.5	−	186234.i	−0.136167	−	0.441443i
$76$	250307.	+	57130.9i	0.570206	+	0.130146i
$77$	673341.	−	80495.5i	1.47490	−	0.176319i
$78$	55456.3	+	242970.i	0.116860	+	0.511999i
$79$	58702.2	+	101675.i	0.119062	+	0.206222i	0.919396	−	0.393333i	$-0.128678\pi$
$79$	58702.2	+	101675.i	0.119062	+	0.206222i	−0.800334	+	0.599554i	$0.795345\pi$
$80$	2020.86	+	1166.74i	0.00394699	+	0.00227880i
$81$	−186337.	−	57477.5i	−0.350627	−	0.108154i
$82$	638302.	−	47834.1i	1.15767	−	0.0867553i
$83$	−564425.	−	450114.i	−0.987124	−	0.787205i	−0.0100166	−	0.999950i	$-0.503188\pi$
$83$	−564425.	−	450114.i	−0.987124	−	0.787205i	−0.977108	+	0.212744i	$0.931760\pi$
$84$	472878.	+	542015.i	0.797831	+	0.914478i
$85$	−49863.2	−	62526.5i	−0.0811940	−	0.101814i
$86$	−1.13717e6	+	1.05514e6i	−1.78784	+	1.65888i
$87$	−106265.	−	705022.i	−0.161374	−	1.07064i
$88$	841348.	−	573622.i	1.23460	−	0.841739i
$89$	−32620.6	+	216423.i	−0.0462724	+	0.306997i	0.953708	+	0.300734i	$0.0972317\pi$
$89$	−32620.6	+	216423.i	−0.0462724	+	0.306997i	−0.999980	+	0.00626298i	$0.998006\pi$
$90$	−139328.	−	289317.i	−0.191122	−	0.396868i
$91$	−261425.	+	195693.i	−0.346915	+	0.259687i
$92$	−233240.	−	112323.i	−0.299530	−	0.144246i
$93$	−411076.	−	280267.i	−0.511061	−	0.348436i
$94$	38138.8	−	41103.8i	0.0459180	−	0.0494878i
$95$	−14300.7	+	190829.i	−0.0166796	+	0.222574i
$96$	−612782.	−	240499.i	−0.692616	−	0.271832i
$97$		−	1.48393e6i		−	1.62592i	−0.582321	−	0.812959i	$-0.697855\pi$
$97$		−	1.48393e6i		−	1.62592i	0.582321	−	0.812959i	$-0.302145\pi$
$98$	−642485.	+	1.38177e6i	−0.682629	+	1.46811i
$99$	−633760.			−0.653160
$100$	365574.	−	931468.i	0.365574	−	0.931468i
$101$	453940.	+	34018.1i	0.440590	+	0.0330176i	0.293179	−	0.956058i	$-0.405287\pi$
$101$	453940.	+	34018.1i	0.440590	+	0.0330176i	0.147411	+	0.989075i	$0.452906\pi$
$102$	−198423.	−	184110.i	−0.186978	−	0.173491i
$103$	−196757.	+	288590.i	−0.180061	+	0.264101i	−0.905649	−	0.424029i	$-0.860616\pi$
$103$	−196757.	+	288590.i	−0.180061	+	0.264101i	0.725588	+	0.688130i	$0.241568\pi$
$104$	−212757.	+	441795.i	−0.189140	+	0.392754i
$105$	−346948.	+	408735.i	−0.299707	+	0.353081i
$106$	403875.	−	194496.i	0.339101	−	0.163302i
$107$	−174168.	−	26251.6i	−0.142173	−	0.0214291i	0.0775702	−	0.996987i	$-0.475284\pi$
$107$	−174168.	−	26251.6i	−0.142173	−	0.0214291i	−0.219743	+	0.975558i	$0.570522\pi$
$108$	−1.23987e6	−	1.81856e6i	−0.984250	−	1.44363i
$109$	−11664.0	+	1758.06i	−0.00900673	+	0.00135755i	−0.153544	−	0.988142i	$-0.549069\pi$
$109$	−11664.0	+	1758.06i	−0.00900673	+	0.00135755i	0.144537	+	0.989499i	$0.453831\pi$
$110$	1.34711e6	+	1.45184e6i	1.01210	+	1.09079i
$111$	−985875.	+	786209.i	−0.720863	+	0.574869i
$112$	457.081	+	10338.7i	0.000325341	+	0.00735887i
$113$	−1.09330e6	+	1.37095e6i	−0.757711	+	0.950140i	−0.999798	−	0.0201146i	$-0.993597\pi$
$113$	−1.09330e6	+	1.37095e6i	−0.757711	+	0.950140i	0.242086	+	0.970255i	$0.422168\pi$
$114$	48402.0	+	645880.i	0.0326700	+	0.435950i
$115$	56874.3	−	184382.i	0.0373958	−	0.121234i
$116$	1.83035e6	−	3.17025e6i	1.17263	−	2.03105i
$117$	264300.	−	152593.i	0.165021	−	0.0952749i
$118$	3.56907e6	−	814617.i	2.17225	−	0.495801i
$119$	114870.	−	335562.i	0.0681655	−	0.199128i
$120$	−179142.	+	784870.i	−0.103670	+	0.454207i
$121$	2.04230e6	−	629965.i	1.15282	−	0.355599i
$122$	−3.22688e6	+	1.26646e6i	−1.77707	+	0.697447i
$123$	364886.	+	929714.i	0.196084	+	0.499613i
$124$	−752940.	−	2.44097e6i	−0.394908	−	1.28026i
$125$	1.90529e6	+	434869.i	0.975506	+	0.222653i
$126$	749483.	−	1.21095e6i	0.374671	−	0.605361i
$127$	−413461.	−	1.81149e6i	−0.201847	−	0.884351i	−0.969811	−	0.243858i	$-0.921587\pi$
$127$	−413461.	−	1.81149e6i	−0.201847	−	0.884351i	0.767964	−	0.640494i	$-0.221270\pi$
$128$	−1.70243e6	−	2.94870e6i	−0.811783	−	1.40605i
$129$	−2.09622e6	−	1.21025e6i	−0.976490	−	0.563777i
$130$	−911356.	−	281116.i	−0.414818	−	0.127955i
$131$	2.43597e6	−	182551.i	1.08357	−	0.0812027i	0.479049	−	0.877788i	$-0.340982\pi$
$131$	2.43597e6	−	182551.i	1.08357	−	0.0812027i	0.604526	+	0.796586i	$0.293363\pi$
$132$	3.24154e6	+	2.58504e6i	1.40939	+	1.12395i
$133$	−747626.	+	401642.i	−0.317782	+	0.170720i
$134$	510189.	+	639756.i	0.212039	+	0.265889i
$135$	1.20259e6	−	1.11584e6i	0.488783	−	0.453524i
$136$	−79377.6	−	526636.i	−0.0315559	−	0.209360i
$137$	3.67964e6	−	2.50874e6i	1.43102	−	0.975650i	0.433805	−	0.901007i	$-0.357171\pi$
$137$	3.67964e6	−	2.50874e6i	1.43102	−	0.975650i	0.997210	−	0.0746426i	$-0.0237816\pi$
$138$	97335.3	−	645778.i	0.0370368	−	0.245723i
$139$	1.92019e6	+	3.98732e6i	0.714990	+	1.48469i	0.868050	+	0.496476i	$0.165373\pi$
$139$	1.92019e6	+	3.98732e6i	0.714990	+	1.48469i	−0.153060	+	0.988217i	$0.548913\pi$
$140$	−2.70115e6	+	530085.i	−0.984384	+	0.193180i
$141$	78826.7	+	37961.0i	0.0281201	+	0.0135419i
$142$	−3.17609e6	−	2.16542e6i	−1.10925	−	0.756271i
$143$	−1.28028e6	+	1.37981e6i	−0.437821	+	0.471859i
$144$	722.759	−	9644.54i	0.000242050	−	0.00322994i
$145$	2.53989e6	+	996834.i	0.833127	+	0.326978i
$146$			8.48486e6i			2.72638i
$147$	−2.35572e6	−	322453.i	−0.741604	−	0.101511i
$148$	−6.47428e6			−1.99713
$149$	−474336.	+	1.20859e6i	−0.143393	+	0.365359i	−0.984469	−	0.175558i	$-0.943827\pi$
$149$	−474336.	+	1.20859e6i	−0.143393	+	0.365359i	0.841076	+	0.540916i	$0.181922\pi$
$150$	2.51726e6	+	188643.i	0.745856	+	0.0558942i
$151$	−2.69207e6	−	2.49788e6i	−0.781909	−	0.725505i	0.184411	−	0.982849i	$-0.440962\pi$
$151$	−2.69207e6	−	2.49788e6i	−0.781909	−	0.725505i	−0.966320	+	0.257344i	$0.917153\pi$
$152$	−717883.	+	1.05294e6i	−0.204420	+	0.299829i
$153$	−143819.	+	298643.i	−0.0401552	+	0.0833832i
$154$	−2.21574e6	+	8.49941e6i	−0.606676	+	2.32716i
$155$	1.71542e6	−	826102.i	0.460654	−	0.221839i
$156$	−1.97425e6	−	297570.i	−0.520029	−	0.0783818i
$157$	2.36734e6	+	3.47226e6i	0.611734	+	0.897249i	0.999702	−	0.0244241i	$-0.00777520\pi$
$157$	2.36734e6	+	3.47226e6i	0.611734	+	0.897249i	−0.387968	+	0.921673i	$0.626823\pi$
$158$	−1.50369e6	+	226644.i	−0.381229	+	0.0574610i
$159$	475743.	+	512729.i	0.118354	+	0.127555i
$160$	1.96957e6	−	1.57068e6i	0.480853	−	0.383467i
$161$	825053.	−	227081.i	0.197699	−	0.0544130i
$162$	1.57477e6	−	1.97469e6i	0.370400	−	0.464467i
$163$	397036.	+	5.29808e6i	0.0916784	+	1.22336i	0.833406	+	0.552662i	$0.186388\pi$
$163$	397036.	+	5.29808e6i	0.0916784	+	1.22336i	−0.741727	+	0.670702i	$0.765993\pi$
$164$	−1.51148e6	+	4.90010e6i	−0.342666	+	1.11090i
$165$	−1.54515e6	+	2.67627e6i	−0.343968	+	0.595770i
$166$	8.09793e6	−	4.67534e6i	1.77031	−	1.02209i
$167$	−6.38305e6	+	1.45689e6i	−1.37050	+	0.312808i	−0.843532	−	0.537078i	$-0.819528\pi$
$167$	−6.38305e6	+	1.45689e6i	−1.37050	+	0.312808i	−0.526967	+	0.849886i	$0.676671\pi$
$168$	−3.36190e6	+	1.20203e6i	−0.709018	+	0.253507i
$169$	−872370.	+	3.82210e6i	−0.180734	+	0.791849i
$170$	989840.	−	305325.i	0.201474	−	0.0621464i
$171$	738319.	−	289769.i	0.147658	−	0.0579513i
$172$	−4.54033e6	−	1.15686e7i	−0.892282	−	2.27350i
$173$	−2.69145e6	−	8.72548e6i	−0.519815	−	1.68520i	−0.710624	−	0.703572i	$-0.751587\pi$
$173$	−2.69145e6	−	8.72548e6i	−0.519815	−	1.68520i	0.190809	−	0.981627i	$-0.438889\pi$
$174$	9.00333e6	+	2.05495e6i	1.70905	+	0.390080i
$175$	1.11360e6	+	3.11457e6i	0.207786	+	0.581144i
$176$	13273.6	+	58155.4i	0.00243473	+	0.0106672i
$177$	2.85607e6	+	4.94686e6i	0.515050	+	0.892093i
$178$	−2.45507e6	−	1.41743e6i	−0.435315	−	0.251329i
$179$	−7.81269e6	−	2.40990e6i	−1.36220	−	0.420184i	−0.474360	−	0.880331i	$-0.657321\pi$
$179$	−7.81269e6	−	2.40990e6i	−1.36220	−	0.420184i	−0.887843	+	0.460147i	$0.847797\pi$
$180$	2.56535e6	−	192247.i	0.439875	−	0.0329641i
$181$	−6.75030e6	−	5.38318e6i	−1.13838	−	0.907828i	−0.141754	−	0.989902i	$-0.545274\pi$
$181$	−6.75030e6	−	5.38318e6i	−1.13838	−	0.907828i	−0.996626	+	0.0820739i	$0.973846\pi$
$182$	−1.12241e6	−	4.07804e6i	−0.186181	−	0.676453i
$183$	−3.37239e6	−	4.22884e6i	−0.550281	−	0.690031i
$184$	941947.	−	873999.i	0.151207	−	0.140300i
$185$	−719221.	−	4.77172e6i	−0.113592	−	0.753632i
$186$	5.32442e6	−	3.63013e6i	0.827434	−	0.564135i
$187$	304700.	−	2.02155e6i	0.0465959	−	0.309143i
$188$	194904.	+	404722.i	0.0293323	+	0.0609092i
$189$	7.04026e6	+	1.83535e6i	1.04280	+	0.271852i
$190$	−2.23317e6	−	1.07544e6i	−0.325582	−	0.156792i
$191$	3.87260e6	+	2.64029e6i	0.555779	+	0.378924i	0.808393	−	0.588643i	$-0.200338\pi$
$191$	3.87260e6	+	2.64029e6i	0.555779	+	0.378924i	−0.252614	+	0.967567i	$0.581290\pi$
$192$	5.82596e6	−	6.27890e6i	0.823122	−	0.887114i
$193$	−570874.	+	7.61778e6i	−0.0794087	+	1.05964i	0.805108	+	0.593128i	$0.202107\pi$
$193$	−570874.	+	7.61778e6i	−0.0794087	+	1.05964i	−0.884517	+	0.466508i	$0.845512\pi$
$194$	1.78918e7	+	7.02203e6i	2.45047	+	0.961740i
$195$		−	1.48813e6i		−	0.200695i
$196$	−8.42404e6	−	8.83551e6i	−1.11880	−	1.17345i
$197$	−2.17874e6			−0.284975			−0.142488	−	0.989797i	$-0.545510\pi$
$197$	−2.17874e6			−0.284975			−0.142488	+	0.989797i	$0.545510\pi$
$198$	2.99898e6	−	7.64128e6i	0.386348	−	0.984397i
$199$	1.00699e7	+	754636.i	1.27781	+	0.0957587i	0.696283	−	0.717768i	$-0.254836\pi$
$199$	1.00699e7	+	754636.i	1.27781	+	0.0957587i	0.581528	+	0.813526i	$0.302455\pi$
$200$	3.64091e6	+	3.37827e6i	0.455114	+	0.422284i
$201$	−719239.	+	1.05493e6i	−0.0885697	+	0.129908i
$202$	−2.55822e6	+	5.31220e6i	−0.310373	+	0.644496i
$203$	2.33023e6	+	1.18741e7i	0.278555	+	1.41943i
$204$	1.95374e6	−	940871.i	0.230131	−	0.110825i
$205$	−3.77942e6	−	569655.i	−0.438695	−	0.0661227i
$206$	−2.54848e6	−	3.73793e6i	−0.291528	−	0.427592i
$207$	−790804.	+	119194.i	−0.0891575	+	0.0134383i
$208$	−19537.9	−	21056.8i	−0.00217114	−	0.00233993i
$209$	−3.82460e6	+	3.05002e6i	−0.418936	+	0.334090i
$210$	−3.28637e6	−	6.11732e6i	−0.354861	−	0.660547i
$211$	2.15637e6	−	2.70400e6i	0.229549	−	0.287845i	−0.653696	−	0.756757i	$-0.726783\pi$
$211$	2.15637e6	−	2.70400e6i	0.229549	−	0.287845i	0.883245	+	0.468912i	$0.155354\pi$
$212$	268369.	+	3.58113e6i	0.0281659	+	0.375848i
$213$	1.76793e6	−	5.73149e6i	0.182947	−	0.593101i
$214$	1.14069e6	−	1.97573e6i	0.116392	−	0.201598i
$215$	8.02197e6	−	4.63149e6i	0.807171	−	0.466020i
$216$	1.06510e7	−	2.43103e6i	1.05689	−	0.241229i
$217$	7.17997e6	+	4.44384e6i	0.702657	+	0.434890i
$218$	33997.4	−	148952.i	0.00328153	−	0.0143773i
$219$	−1.26510e7	+	3.90232e6i	−1.20446	+	0.371527i
$220$	−1.47698e7	+	5.79670e6i	−1.38709	+	0.544394i
$221$	359668.	+	916420.i	0.0333216	+	0.0849019i
$222$	−4.81416e6	−	1.56071e7i	−0.440009	−	1.42647i
$223$	−1.18472e7	−	2.70406e6i	−1.06832	−	0.243838i	−0.348013	−	0.937490i	$-0.613143\pi$
$223$	−1.18472e7	−	2.70406e6i	−1.06832	−	0.243838i	−0.720310	+	0.693652i	$0.756001\pi$
$224$	1.05701e7	+	3.61837e6i	0.940451	+	0.321936i
$225$	−687862.	−	3.01372e6i	−0.0603884	−	0.264579i
$226$	−1.13561e7	−	1.96694e7i	−0.983795	−	1.70398i
$227$	−1.47865e7	−	8.53702e6i	−1.26412	−	0.729841i	−0.290253	−	0.956950i	$-0.593739\pi$
$227$	−1.47865e7	−	8.53702e6i	−1.26412	−	0.729841i	−0.973869	+	0.227109i	$0.927073\pi$
$228$	−4.95828e6	−	1.52943e6i	−0.418337	−	0.129040i
$229$	−1.41152e7	+	1.05779e6i	−1.17539	+	0.0880830i	−0.648066	−	0.761584i	$-0.724422\pi$
$229$	−1.41152e7	+	1.05779e6i	−1.17539	+	0.0880830i	−0.527320	+	0.849667i	$0.676803\pi$
$230$	1.95397e6	+	1.55824e6i	0.160596	+	0.128071i
$231$	−1.36918e7	+	605323.i	−1.11077	+	0.0491079i
$232$	1.13290e7	+	1.42061e7i	0.907250	+	1.13766i
$233$	−9.20350e6	+	8.53960e6i	−0.727587	+	0.675102i	−0.954297	−	0.298860i	$-0.903394\pi$
$233$	−9.20350e6	+	8.53960e6i	−0.727587	+	0.675102i	0.226710	+	0.973962i	$0.427203\pi$
$234$	589150.	+	3.90875e6i	0.0459810	+	0.305064i
$235$	−276639.	+	188609.i	−0.0213162	+	0.0145331i
$236$	−4.37111e6	+	2.90004e7i	−0.332549	+	2.20632i
$237$	−1.02950e6	−	2.13777e6i	−0.0773356	−	0.160589i
$238$	3.50232e6	+	2.97288e6i	0.259791	+	0.220519i
$239$	−934637.	−	450097.i	−0.0684619	−	0.0329695i	0.399340	−	0.916803i	$-0.369239\pi$
$239$	−934637.	−	450097.i	−0.0684619	−	0.0329695i	−0.467801	+	0.883834i	$0.654954\pi$
$240$	−38965.3	−	26566.1i	−0.00281867	−	0.00192174i
$241$	1.35712e7	−	1.46263e7i	0.969543	−	1.04492i	−0.0294276	−	0.999567i	$-0.509368\pi$
$241$	1.35712e7	−	1.46263e7i	0.969543	−	1.04492i	0.998971	−	0.0453524i	$-0.0144411\pi$
$242$	−2.06872e6	+	2.76051e7i	−0.145967	+	1.94780i
$243$	−1.07257e7	−	4.20955e6i	−0.747496	−	0.293370i
$244$		−	2.77710e7i		−	1.91171i
$245$	5.57619e6	−	7.19027e6i	0.379175	−	0.488930i
$246$	−1.29363e7			−0.868968
$247$	860622.	−	2.19283e6i	0.0571112	−	0.145517i
$248$	1.26439e7	+	947530.i	0.828946	+	0.0621209i
$249$	1.06953e7	+	9.92382e6i	0.692782	+	0.642808i
$250$	−1.42591e7	+	2.09143e7i	−0.912584	+	1.33852i
$251$	−7.99605e6	+	1.66040e7i	−0.505655	+	1.05000i	0.479373	+	0.877611i	$0.340864\pi$
$251$	−7.99605e6	+	1.66040e7i	−0.505655	+	1.05000i	−0.985028	+	0.172392i	$0.944850\pi$
$252$	6.83698e6	+	9.13347e6i	0.427231	+	0.570735i
$253$	4.44402e6	−	2.14013e6i	0.274419	−	0.132153i
$254$	2.37977e7	+	3.58693e6i	1.45223	+	0.218888i
$255$	910486.	+	1.33544e6i	0.0549101	+	0.0805384i
$256$	1.67871e7	−	2.53024e6i	1.00059	−	0.150814i
$257$	1.58526e7	+	1.70850e7i	0.933900	+	1.00650i	0.999962	+	0.00868908i	$0.00276586\pi$
$257$	1.58526e7	+	1.70850e7i	0.933900	+	1.00650i	−0.0660625	+	0.997815i	$0.521044\pi$
$258$	2.45115e7	−	1.95473e7i	1.42728	−	1.13822i
$259$	1.61264e7	−	1.40694e7i	0.928192	−	0.809795i
$260$	4.76379e6	−	5.97361e6i	0.271040	−	0.339873i
$261$	−845108.	−	1.12772e7i	−0.0475325	−	0.634277i
$262$	−9.32611e6	+	3.02345e7i	−0.518557	+	1.68112i
$263$	1.13397e7	−	1.96409e7i	0.623351	−	1.07968i	−0.365507	−	0.930809i	$-0.619104\pi$
$263$	1.13397e7	−	1.96409e7i	0.623351	−	1.07968i	0.988857	−	0.148866i	$-0.0475624\pi$
$264$	−1.78225e7	+	1.02898e7i	−0.968625	+	0.559236i
$265$	−2.60958e6	+	595619.i	−0.140227	+	0.0320060i
$266$	−1.30482e6	−	1.09147e7i	−0.0693275	−	0.579921i
$267$	984283.	−	4.31243e6i	0.0517114	−	0.226562i
$268$	−6.26419e6	+	1.93225e6i	−0.325432	+	0.100382i
$269$	−5.32309e6	+	2.08916e6i	−0.273468	+	0.107328i	−0.498112	−	0.867112i	$-0.665973\pi$
$269$	−5.32309e6	+	2.08916e6i	−0.273468	+	0.107328i	0.224644	+	0.974441i	$0.427878\pi$
$270$	7.76303e6	+	1.97799e7i	0.394403	+	1.00492i
$271$	−892388.	−	2.89305e6i	−0.0448379	−	0.145361i	0.930386	−	0.366582i	$-0.119472\pi$
$271$	−892388.	−	2.89305e6i	−0.0448379	−	0.145361i	−0.975224	+	0.221221i	$0.928996\pi$
$272$	30416.4	+	6942.35i	0.00151148	+	0.000344984i
$273$	5.56418e6	−	3.54907e6i	0.273472	−	0.174432i
$274$	1.28358e7	+	5.62371e7i	0.623979	+	2.73383i
$275$	9.53279e6	+	1.65113e7i	0.458376	+	0.793930i
$276$	4.53097e6	+	2.61596e6i	0.215508	+	0.124424i
$277$	−4.80666e6	−	1.48266e6i	−0.226154	−	0.0697592i	0.179607	−	0.983738i	$-0.442517\pi$
$277$	−4.80666e6	−	1.48266e6i	−0.226154	−	0.0697592i	−0.405761	+	0.913979i	$0.632993\pi$
$278$	−5.71617e7	+	4.28368e6i	−2.66055	+	0.199380i
$279$	−6.16972e6	−	4.92019e6i	−0.284088	−	0.226552i
$280$	2.44904e6	−	1.34419e7i	0.111564	−	0.612333i
$281$	1.17606e7	+	1.47473e7i	0.530041	+	0.664651i	0.972707	−	0.232036i	$-0.0745386\pi$
$281$	1.17606e7	+	1.47473e7i	0.530041	+	0.664651i	−0.442666	+	0.896687i	$0.645967\pi$
$282$	−830709.	+	770785.i	−0.0370426	+	0.0343705i
$283$	−2.74236e6	−	1.81944e7i	−0.120994	−	0.802745i	−0.964204	−	0.265160i	$-0.914575\pi$
$283$	−2.74236e6	−	1.81944e7i	−0.120994	−	0.802745i	0.843210	−	0.537584i	$-0.180663\pi$
$284$	2.54444e7	−	1.73477e7i	1.11080	−	0.757333i
$285$	576418.	−	3.82428e6i	0.0249002	−	0.165202i
$286$	−1.05781e7	−	2.19657e7i	−0.452180	−	0.938961i
$287$	−6.88364e6	−	1.54900e7i	−0.291187	−	0.655247i
$288$	−9.40721e6	−	4.53027e6i	−0.393807	−	0.189647i
$289$	1.90599e7	+	1.29948e7i	0.789638	+	0.538366i
$290$	−2.40378e7	+	2.59065e7i	−0.985599	+	1.06222i
$291$	−2.24118e6	+	2.99064e7i	−0.0909489	+	1.21363i
$292$	−6.32754e7	−	2.48337e7i	−2.54148	−	0.997456i
$293$		−	3.82889e7i		−	1.52219i	−0.648638	−	0.761097i	$-0.724661\pi$
$293$		−	3.82889e7i		−	1.52219i	0.648638	−	0.761097i	$-0.275339\pi$
$294$	1.50352e7	−	2.68772e7i	0.591654	−	1.05765i
$295$	−2.18596e7			−0.851485
$296$	1.17405e7	−	2.99144e7i	0.452703	−	1.15347i
$297$	4.18194e7	+	3.13393e6i	1.59628	+	0.119625i
$298$	−1.23274e7	−	1.14382e7i	−0.465826	−	0.432223i
$299$	−1.33802e6	+	1.96251e6i	−0.0500552	+	0.0734174i
$300$	−8.77440e6	+	1.82202e7i	−0.324978	+	0.674823i
$301$	3.64491e7	+	1.89488e7i	1.33656	+	0.694835i
$302$	4.28561e7	−	2.06384e7i	1.55594	−	0.749299i
$303$	−9.09710e6	−	1.37117e6i	−0.327021	−	0.0492904i
$304$	−42053.4	−	61681.0i	−0.00149686	−	0.00219549i
$305$	2.04680e7	−	3.08505e6i	0.721398	−	0.108733i
$306$	−2.92020e6	−	3.14723e6i	−0.101917	−	0.109841i
$307$	−6.31555e6	+	5.03649e6i	−0.218271	+	0.174065i	−0.726521	−	0.687144i	$-0.758864\pi$
$307$	−6.31555e6	+	5.03649e6i	−0.218271	+	0.174065i	0.508250	+	0.861210i	$0.330293\pi$
$308$	−5.68988e7	−	4.14001e7i	−1.94738	−	1.41693i
$309$	4.40121e6	−	5.51894e6i	0.149175	−	0.187060i
$310$	1.84292e6	+	2.45920e7i	0.0618616	+	0.825485i
$311$	9.45069e6	−	3.06384e7i	0.314183	−	1.01856i	−0.651460	−	0.758683i	$-0.725843\pi$
$311$	9.45069e6	−	3.06384e7i	0.314183	−	1.01856i	0.965643	−	0.259873i	$-0.0836806\pi$
$312$	4.95505e6	−	8.58240e6i	0.163149	−	0.282582i
$313$	3.30994e7	−	1.91099e7i	1.07941	−	0.623198i	0.148674	−	0.988886i	$-0.452500\pi$
$313$	3.30994e7	−	1.91099e7i	1.07941	−	0.623198i	0.930737	+	0.365688i	$0.119166\pi$
$314$	−5.30676e7	+	1.21123e7i	−1.71412	+	0.391236i
$315$	−5.97210e6	+	6.05366e6i	−0.191071	+	0.193681i
$316$	2.71085e6	−	1.18770e7i	0.0859100	−	0.376396i
$317$	−2.82188e7	+	8.70433e6i	−0.885850	+	0.273249i	−0.704104	−	0.710097i	$-0.748651\pi$
$317$	−2.82188e7	+	8.70433e6i	−0.885850	+	0.273249i	−0.181746	+	0.983346i	$0.558175\pi$
$318$	−8.43324e6	+	3.30980e6i	−0.262249	+	0.102925i
$319$	2.54821e7	+	6.49272e7i	0.784987	+	2.00011i
$320$	9.66171e6	+	3.13225e7i	0.294852	+	0.955887i
$321$	3.47045e6	+	792107.i	0.104923	+	0.0239480i
$322$	−1.16626e6	+	1.10223e7i	−0.0349325	+	0.330144i
$323$	569327.	+	2.49439e6i	0.0168949	+	0.0740212i
$324$	1.01171e7	+	1.75233e7i	0.297455	+	0.515207i
$325$	−7.95099e6	−	4.59051e6i	−0.231618	−	0.133724i
$326$	−6.57580e7	−	2.02836e7i	−1.89800	−	0.585455i
$327$	237725.	−	17815.1i	0.00679880	−	0.000509500i
$328$	−1.99000e7	−	1.58697e7i	−0.563938	−	0.449726i
$329$	−1.36498e6	−	584548.i	−0.0383300	−	0.0164147i
$330$	−2.49563e7	−	3.12942e7i	−0.694445	−	0.870806i
$331$	1.36833e7	−	1.26962e7i	0.377317	−	0.350099i	−0.468603	−	0.883409i	$-0.655243\pi$
$331$	1.36833e7	−	1.26962e7i	0.377317	−	0.350099i	0.845920	+	0.533310i	$0.179052\pi$
$332$	1.11648e7	+	7.40738e7i	0.305097	+	2.02419i
$333$	−1.65253e7	+	1.12668e7i	−0.447525	+	0.305118i
$334$	1.26391e7	−	8.38548e7i	0.339216	−	2.25055i
$335$	−2.12000e6	−	4.40222e6i	−0.0563899	−	0.117095i
$336$	6402.69	−	209051.i	0.000168789	−	0.00551105i
$337$	−1.29790e7	−	6.25037e6i	−0.339119	−	0.163311i	0.256571	−	0.966525i	$-0.417407\pi$
$337$	−1.29790e7	−	6.25037e6i	−0.339119	−	0.163311i	−0.595690	+	0.803214i	$0.703121\pi$
$338$	−4.19552e7	−	2.86046e7i	−1.08651	−	0.740773i
$339$	2.41044e7	−	2.59783e7i	0.618724	−	0.666826i
$340$	−620149.	+	8.27532e6i	−0.0157783	+	0.210546i
$341$	4.53067e7	+	1.77816e7i	1.14261	+	0.448443i
$342$			1.02732e7i			0.256818i
$343$	4.01835e7	+	3.70141e6i	0.995784	+	0.0917244i
$344$	6.16861e7			1.51535
$345$	−1.42469e6	+	3.63005e6i	−0.0346947	+	0.0884006i
$346$	1.17940e8	+	8.83836e6i	2.84729	+	0.213375i
$347$	−4.59486e7	−	4.26340e7i	−1.09972	−	1.02039i	−0.999677	−	0.0254116i	$-0.991910\pi$
$347$	−4.59486e7	−	4.26340e7i	−1.09972	−	1.02039i	−0.100047	−	0.994983i	$-0.531899\pi$
$348$	−4.16759e7	+	6.11274e7i	−0.988889	+	1.45043i
$349$	1.29025e7	−	2.67923e7i	0.303527	−	0.630279i	−0.692294	−	0.721616i	$-0.743400\pi$
$349$	1.29025e7	−	2.67923e7i	0.303527	−	0.630279i	0.995820	+	0.0913367i	$0.0291139\pi$
$350$	−4.28221e7	−	1.31153e6i	−0.998767	−	0.0305897i
$351$	−1.81947e7	+	8.76211e6i	−0.420750	+	0.202622i
$352$	6.36785e7	+	9.59799e6i	1.46004	+	0.220066i
$353$	−4.10625e7	−	6.02276e7i	−0.933514	−	1.36921i	−0.929341	−	0.369222i	$-0.879624\pi$
$353$	−4.10625e7	−	6.02276e7i	−0.933514	−	1.36921i	−0.00417257	−	0.999991i	$-0.501328\pi$
$354$	−7.31596e7	+	1.10270e7i	−1.64916	+	0.248570i
$355$	1.56123e7	+	1.68261e7i	0.348965	+	0.376095i
$356$	1.77560e7	−	1.41599e7i	0.393546	−	0.313842i
$357$	−2.82182e6	+	6.58926e6i	−0.0620191	+	0.144821i
$358$	6.60263e7	−	8.27943e7i	1.43902	−	1.80448i
$359$	1.85851e6	+	2.48001e7i	0.0401681	+	0.536006i	0.980599	+	0.196022i	$0.0628024\pi$
$359$	1.85851e6	+	2.48001e7i	0.0401681	+	0.536006i	−0.940431	+	0.339983i	$0.889579\pi$
$360$	−3.76377e6	+	1.22018e7i	−0.0806706	+	0.261528i
$361$	−2.04619e7	+	3.54410e7i	−0.434935	+	0.753329i
$362$	9.68480e7	−	5.59152e7i	2.04157	−	1.17870i
$363$	−4.21109e7	+	9.61154e6i	−0.880389	+	0.200943i
$364$	3.36969e7	+	3.56546e6i	0.698691	+	0.0739284i
$365$	1.12739e7	−	4.93944e7i	0.231845	−	1.01578i
$366$	6.69457e7	−	2.06500e7i	1.36546	−	0.421189i
$367$	−6.88264e7	+	2.70124e7i	−1.39238	+	0.546468i	−0.938711	−	0.344704i	$-0.887979\pi$
$367$	−6.88264e7	+	2.70124e7i	−1.39238	+	0.546468i	−0.453666	+	0.891172i	$0.649884\pi$
$368$	27500.3	+	70069.6i	0.000551816	+	0.00140600i
$369$	4.66934e6	+	1.51376e7i	0.0929345	+	0.301286i
$370$	6.09362e7	+	1.39083e7i	1.20301	+	0.274580i
$371$	−8.45067e6	−	8.33682e6i	−0.165489	−	0.163260i
$372$	1.14878e7	+	5.03313e7i	0.223156	+	0.977709i
$373$	3.82966e7	+	6.63316e7i	0.737961	+	1.27819i	0.953412	+	0.301672i	$0.0975446\pi$
$373$	3.82966e7	+	6.63316e7i	0.737961	+	1.27819i	−0.215451	+	0.976515i	$0.569122\pi$
$374$	2.29321e7	+	1.32398e7i	0.438358	+	0.253086i
$375$	−3.77414e7	−	1.16417e7i	−0.715689	−	0.220761i
$376$	−2.22346e6	+	166625.i	−0.0418278	+	0.00313456i
$377$	−2.62597e7	−	2.09414e7i	−0.490079	−	0.390825i
$378$	−5.54437e7	+	7.61998e7i	−1.02654	+	1.41084i
$379$	4.77465e6	+	5.98722e6i	0.0877048	+	0.109978i	0.823748	−	0.566957i	$-0.191879\pi$
$379$	4.77465e6	+	5.98722e6i	0.0877048	+	0.109978i	−0.736043	+	0.676935i	$0.763308\pi$
$380$	1.45561e7	−	1.35061e7i	0.265274	−	0.246138i
$381$	5.59680e6	+	3.71323e7i	0.101196	+	0.671394i
$382$	−5.01594e7	+	3.41981e7i	−0.899834	+	0.613497i
$383$	−8.02227e6	+	5.32243e7i	−0.142791	+	0.947356i	0.796600	+	0.604507i	$0.206630\pi$
$383$	−8.02227e6	+	5.32243e7i	−0.142791	+	0.947356i	−0.939391	+	0.342849i	$0.888608\pi$
$384$	2.98566e7	+	6.19978e7i	0.527286	+	1.09492i
$385$	2.41922e7	−	4.65350e7i	0.423928	−	0.815451i
$386$	−8.91465e7	−	4.29307e7i	−1.55004	−	0.746459i
$387$	−3.17211e7	−	2.16271e7i	−0.547287	−	0.373134i
$388$	−1.04733e8	+	1.12875e8i	−1.79303	+	1.93243i
$389$	−3.73965e6	+	4.99021e7i	−0.0635304	+	0.847754i	0.870866	+	0.491520i	$0.163559\pi$
$389$	−3.73965e6	+	4.99021e7i	−0.0635304	+	0.847754i	−0.934397	+	0.356234i	$0.884060\pi$
$390$	1.79425e7	+	7.04189e6i	0.302474	+	0.118712i
$391$		−	2.57979e6i		−	0.0431573i
$392$	5.61008e7	−	2.29008e7i	0.931345	−	0.380184i
$393$	−4.93691e7			−0.813351
$394$	1.03099e7	−	2.62692e7i	0.168564	−	0.429495i
$395$	9.05481e6	+	678564.i	0.146922	+	0.0110103i
$396$	4.82069e7	+	4.47295e7i	0.776290	+	0.720291i
$397$	5.70523e7	−	8.36804e7i	0.911805	−	1.33737i	−0.0294115	−	0.999567i	$-0.509363\pi$
$397$	5.70523e7	−	8.36804e7i	0.911805	−	1.33737i	0.941216	−	0.337805i	$-0.109684\pi$
$398$	−5.67499e7	+	1.17842e8i	−0.900153	+	1.86919i
$399$	1.56739e7	−	6.96536e6i	0.246750	−	0.109654i
$400$	−262139.	+	126240.i	−0.00409593	+	0.00197250i
$401$	4.32098e7	+	6.51282e6i	0.670114	+	0.101003i	0.475282	−	0.879833i	$-0.342346\pi$
$401$	4.32098e7	+	6.51282e6i	0.670114	+	0.101003i	0.194832	+	0.980837i	$0.437584\pi$
$402$	−9.31587e6	−	1.36639e7i	−0.143399	−	0.210327i
$403$	−2.31758e7	+	3.49319e6i	−0.354095	+	0.0533712i
$404$	−3.21280e7	−	3.46257e7i	−0.487236	−	0.525115i
$405$	−1.17913e7	+	9.40322e6i	−0.177499	+	0.141550i
$406$	−1.54194e8	−	2.80932e7i	−2.30403	−	0.419782i
$407$	7.69119e7	−	9.64445e7i	1.14080	−	1.43052i
$408$	804360.	+	1.07334e7i	0.0118432	+	0.158037i
$409$	−5.78844e6	+	1.87657e7i	−0.0846042	+	0.274280i	−0.987983	−	0.154564i	$-0.950603\pi$
$409$	−5.78844e6	+	1.87657e7i	−0.0846042	+	0.274280i	0.903379	+	0.428844i	$0.141079\pi$
$410$	2.47527e7	−	4.28730e7i	0.359146	−	0.622060i
$411$	−7.79467e7	+	4.50025e7i	−1.12272	+	0.648204i
$412$	3.53344e7	−	8.06485e6i	0.505250	−	0.115320i
$413$	−5.21335e7	−	8.17342e7i	−0.740060	−	1.16026i
$414$	2.30498e6	−	1.00988e7i	0.0324838	−	0.142321i
$415$	−5.33541e7	+	1.64576e7i	−0.746489	+	0.230261i
$416$	−2.88671e7	+	1.13295e7i	−0.400980	+	0.157373i
$417$	−3.26766e7	−	8.32585e7i	−0.450638	−	1.14821i
$418$	−1.86760e7	−	6.05462e7i	−0.255715	−	0.829007i
$419$	−6.31949e7	−	1.44238e7i	−0.859092	−	0.196082i	−0.229787	−	0.973241i	$-0.573803\pi$
$419$	−6.31949e7	−	1.44238e7i	−0.859092	−	0.196082i	−0.629305	+	0.777159i	$0.716660\pi$
$420$	5.52382e7	−	6.60354e6i	0.745576	−	0.0891310i
$421$	2.73800e7	+	1.19960e8i	0.366933	+	1.60764i	0.735153	+	0.677902i	$0.237110\pi$
$421$	2.73800e7	+	1.19960e8i	0.366933	+	1.60764i	−0.368219	+	0.929739i	$0.620032\pi$
$422$	2.23982e7	+	3.87948e7i	0.298041	+	0.516222i
$423$	1.20179e6	+	693857.i	0.0158785	+	0.00916745i
$424$	−1.70333e7	−	5.25407e6i	−0.223461	−	0.0689285i
$425$	9.94379e6	−	745184.i	0.129534	−	0.00970726i
$426$	6.07389e7	+	4.84377e7i	0.785667	+	0.626548i
$427$	6.03496e7	+	6.91730e7i	0.775159	+	0.888491i
$428$	1.13953e7	+	1.42892e7i	0.145343	+	0.182254i
$429$	2.78860e7	−	2.58745e7i	0.353195	−	0.327717i
$430$	1.78818e7	+	1.18638e8i	0.224908	+	1.49217i
$431$	2.56113e7	−	1.74615e7i	0.319890	−	0.218097i	−0.392720	−	0.919658i	$-0.628466\pi$
$431$	2.56113e7	−	1.74615e7i	0.319890	−	0.218097i	0.712609	+	0.701561i	$0.247513\pi$
$432$	−95384.2	+	632833.i	−0.00118311	+	0.00784942i
$433$	5.14777e7	+	1.06895e8i	0.634096	+	1.31671i	0.932118	+	0.362155i	$0.117959\pi$
$433$	5.14777e7	+	1.06895e8i	0.634096	+	1.31671i	−0.298021	+	0.954559i	$0.596327\pi$
$434$	−8.75555e7	+	6.55408e7i	−1.07106	+	0.801756i
$435$	−4.96822e7	−	2.39257e7i	−0.603578	−	0.290668i
$436$	1.01130e6	+	689493.i	0.0122017	+	0.00831898i
$437$	−4.19869e6	+	4.52511e6i	−0.0503118	+	0.0542232i
$438$	1.28146e7	−	1.71000e8i	0.152505	−	2.03504i
$439$	−1.43592e8	−	5.63558e7i	−1.69722	−	0.666109i	−0.698447	−	0.715662i	$-0.746125\pi$
$439$	−1.43592e8	−	5.63558e7i	−1.69722	−	0.666109i	−0.998772	+	0.0495527i	$0.984220\pi$
$440$		−	7.87555e7i		−	0.924534i
$441$	−3.68779e7	−	7.89245e6i	−0.429982	−	0.0920230i
$442$	−1.27513e7			−0.147668
$443$	−2.28088e6	+	5.81159e6i	−0.0262356	+	0.0668472i	−0.943391	−	0.331682i	$-0.892384\pi$
$443$	−2.28088e6	+	5.81159e6i	−0.0262356	+	0.0668472i	0.917156	+	0.398529i	$0.130479\pi$
$444$	1.30479e8	+	9.77809e6i	1.49071	+	0.111713i
$445$	1.24087e7	+	1.15136e7i	0.140815	+	0.130657i
$446$	8.86646e7	−	1.30047e8i	0.999415	−	1.46587i
$447$	1.13849e7	−	2.36409e7i	0.127469	−	0.264692i
$448$	−9.40738e7	+	1.10827e8i	−1.04625	+	1.23257i
$449$	6.58487e7	−	3.17110e7i	0.727458	−	0.350325i	−0.0332258	−	0.999448i	$-0.510578\pi$
$449$	6.58487e7	−	3.17110e7i	0.727458	−	0.350325i	0.760684	+	0.649123i	$0.224864\pi$
$450$	3.95916e7	+	5.96747e6i	0.434475	+	0.0654866i
$451$	−5.50389e7	−	8.07272e7i	−0.599984	−	0.880015i
$452$	1.79921e8	−	2.71187e7i	1.94835	−	0.293666i
$453$	5.04822e7	+	5.44069e7i	0.543055	+	0.585274i
$454$	1.72902e8	−	1.37885e8i	1.84770	−	1.47349i
$455$	1.11551e6	+	2.52316e7i	0.0118423	+	0.267861i
$456$	1.60581e7	−	2.01362e7i	0.169356	−	0.212366i
$457$	−1.19000e6	−	1.58794e7i	−0.0124680	−	0.166374i	−0.999962	−	0.00871754i	$-0.997225\pi$
$457$	−1.19000e6	−	1.58794e7i	−0.0124680	−	0.166374i	0.987494	−	0.157657i	$-0.0503940\pi$
$458$	5.40399e7	−	1.75193e8i	0.562494	−	1.82356i
$459$	1.09669e7	−	1.89952e7i	0.113408	−	0.196429i
$460$	−1.73394e7	+	1.00109e7i	−0.178140	+	0.102849i
$461$	1.12995e7	−	2.57904e6i	0.115334	−	0.0263242i	−0.164464	−	0.986383i	$-0.552590\pi$
$461$	1.12995e7	−	2.57904e6i	0.115334	−	0.0263242i	0.279798	+	0.960059i	$0.409732\pi$
$462$	5.74916e7	−	1.67947e8i	0.583013	−	1.70312i
$463$	−3.88116e7	+	1.70045e8i	−0.391038	+	1.71325i	0.269970	+	0.962869i	$0.412986\pi$
$463$	−3.88116e7	+	1.70045e8i	−0.391038	+	1.71325i	−0.661008	+	0.750379i	$0.729871\pi$
$464$	−1.01712e6	+	313740.i	−0.0101817	+	0.00314063i
$465$	−3.58194e7	+	1.40581e7i	−0.356253	+	0.139819i
$466$	−5.94110e7	−	1.51377e8i	−0.587096	−	1.49590i
$467$	2.79947e7	+	9.07566e7i	0.274869	+	0.891102i	0.982777	+	0.184798i	$0.0591629\pi$
$467$	2.79947e7	+	9.07566e7i	0.274869	+	0.891102i	−0.707908	+	0.706305i	$0.750361\pi$
$468$	−3.08737e7	−	7.04671e6i	−0.301197	−	0.0687462i
$469$	1.14041e7	−	1.84257e7i	0.110546	−	0.178610i
$470$	−965004.	−	4.22796e6i	−0.00929470	−	0.0407227i
$471$	−4.24662e7	−	7.35536e7i	−0.406425	−	0.703949i
$472$	−1.26070e8	−	7.27864e7i	−1.19891	−	0.692188i
$473$	2.26269e8	+	6.97948e7i	2.13817	+	0.659538i
$474$	3.06468e7	−	2.29666e6i	0.287773	−	0.0215656i
$475$	−1.86548e7	−	1.48767e7i	−0.174065	−	0.138812i
$476$	−3.24208e7	+	1.74172e7i	−0.300610	+	0.161494i
$477$	6.91702e6	+	8.67366e6i	0.0637329	+	0.0799185i
$478$	9.84959e6	−	9.13908e6i	0.0901850	−	0.0836795i
$479$	1.45951e7	+	9.68322e7i	0.132801	+	0.881076i	0.951676	+	0.307104i	$0.0993599\pi$
$479$	1.45951e7	+	9.68322e7i	0.132801	+	0.881076i	−0.818875	+	0.573972i	$0.805402\pi$
$480$	−4.20660e7	+	2.86801e7i	−0.380371	+	0.259333i
$481$	−8.85349e6	+	5.87391e7i	−0.0795572	+	0.527827i
$482$	1.12130e8	+	2.32841e8i	1.00134	+	2.07930i
$483$	−1.69707e7	+	3.33040e6i	−0.150611	+	0.0295566i
$484$	−1.99809e8	−	9.62228e7i	−1.76229	−	0.848676i
$485$	−9.48266e7	−	6.46517e7i	−0.831199	−	0.566702i
$486$	1.01509e8	−	1.09401e8i	0.884296	−	0.953044i
$487$	6.58830e6	−	8.79148e7i	0.0570409	−	0.761158i	−0.893203	−	0.449653i	$-0.851548\pi$
$487$	6.58830e6	−	8.79148e7i	0.0570409	−	0.761158i	0.950244	−	0.311505i	$-0.100833\pi$
$488$	1.28316e8	+	5.03603e7i	1.10413	+	0.433340i
$489$		−	1.07374e8i		−	0.918279i
$490$	6.03066e7	+	1.01257e8i	0.512598	+	0.860671i
$491$	−1.37824e8			−1.16434			−0.582169	−	0.813068i	$-0.697796\pi$
$491$	−1.37824e8			−1.16434			−0.582169	+	0.813068i	$0.697796\pi$
$492$	3.78623e7	−	9.64715e7i	0.317915	−	0.810035i
$493$	3.63779e7	+	2.72615e6i	0.303597	+	0.0227514i
$494$	2.23665e7	+	2.07531e7i	0.185532	+	0.172148i
$495$	−2.76116e7	+	4.04987e7i	−0.227654	+	0.333907i
$496$	−322268.	+	669197.i	−0.00264103	+	0.00548415i
$497$	−2.56793e7	+	9.85039e7i	−0.209177	+	0.802388i
$498$	−1.70263e8	+	8.19943e7i	−1.37858	+	0.663889i
$499$	−2.07032e8	−	3.12050e7i	−1.66623	−	0.251144i	−0.752834	−	0.658210i	$-0.771314\pi$
$499$	−2.07032e8	−	3.12050e7i	−1.66623	−	0.251144i	−0.913399	+	0.407066i	$0.866552\pi$
$500$	−1.14233e8	−	1.67549e8i	−0.913866	−	1.34039i
$501$	1.30841e8	−	1.97211e7i	1.04047	−	0.156826i
$502$	−1.62357e8	−	1.74979e8i	−1.28340	−	1.38317i
$503$	−1.37163e6	+	1.09384e6i	−0.0107779	+	0.00859507i	−0.628864	−	0.777515i	$-0.716480\pi$
$503$	−1.37163e6	+	1.09384e6i	−0.0107779	+	0.00859507i	0.618086	+	0.786110i	$0.287908\pi$
$504$	−5.45995e7	+	1.50275e7i	−0.426478	+	0.117380i
$505$	2.19510e7	−	2.75257e7i	0.170443	−	0.213729i
$506$	4.77433e6	+	6.37090e7i	0.0368520	+	0.491755i
$507$	2.33538e7	−	7.57112e7i	0.179198	−	0.580947i
$508$	−9.64014e7	+	1.66972e8i	−0.735346	+	1.27366i
$509$	−1.76371e8	+	1.01828e8i	−1.33744	+	0.772172i	−0.986427	−	0.164199i	$-0.947496\pi$
$509$	−1.76371e8	+	1.01828e8i	−1.33744	+	0.772172i	−0.351013	+	0.936370i	$0.614163\pi$
$510$	−2.04099e7	+	4.65842e6i	−0.153862	+	0.0351179i
$511$	2.11575e8	−	7.56478e7i	1.58563	−	0.566936i
$512$	−439989.	+	1.92772e6i	−0.00327817	+	0.0143626i
$513$	−5.01518e7	+	1.54698e7i	−0.371479	+	0.114586i
$514$	−2.81010e8	+	1.10288e8i	−2.06934	+	0.812157i
$515$	9.86927e6	+	2.51465e7i	0.0722542	+	0.184101i
$516$	7.40316e7	+	2.40005e8i	0.538850	+	1.74691i
$517$	−8.34434e6	−	1.90454e6i	−0.0603838	−	0.0137822i
$518$	9.33243e7	+	2.61013e8i	0.671437	+	1.87790i
$519$	4.10642e7	+	1.79914e8i	0.293739	+	1.28695i
$520$	1.89623e7	+	3.28437e7i	0.134860	+	0.233584i
$521$	−5.20145e7	−	3.00306e7i	−0.367800	−	0.212349i	0.304697	−	0.952449i	$-0.401445\pi$
$521$	−5.20145e7	−	3.00306e7i	−0.367800	−	0.212349i	−0.672497	+	0.740100i	$0.734778\pi$
$522$	1.39969e8	+	4.31746e7i	0.984054	+	0.303541i
$523$	4.72698e7	−	3.54238e6i	0.330429	−	0.0247622i	0.0915173	−	0.995803i	$-0.470828\pi$
$523$	4.72698e7	−	3.54238e6i	0.330429	−	0.0247622i	0.238912	+	0.971041i	$0.423209\pi$
$524$	−1.98176e8	−	1.58040e8i	−1.37739	−	1.09843i
$525$	−1.77391e7	−	6.44514e7i	−0.122589	−	0.445404i
$526$	1.83151e8	+	2.29664e8i	1.25850	+	1.57811i
$527$	1.86606e7	−	1.73145e7i	0.127495	−	0.118298i
$528$	−179677.	−	1.19208e6i	−0.00122065	−	0.00809849i
$529$	−1.17170e8	+	7.98853e7i	−0.791499	+	0.539635i
$530$	5.16722e6	−	3.42823e7i	0.0347080	−	0.230273i
$531$	3.93105e7	+	8.16291e7i	0.262558	+	0.545207i
$532$	8.52151e7	+	2.22150e7i	0.565955	+	0.147541i
$533$	4.23901e7	+	2.04140e7i	0.279952	+	0.134818i
$534$	4.73375e7	+	3.22741e7i	0.310872	+	0.211949i
$535$	−9.26565e6	+	9.98600e6i	−0.0605083	+	0.0652124i
$536$	2.43161e6	−	3.24476e7i	0.0157907	−	0.210712i
$537$	1.53814e8	+	6.03674e7i	0.993280	+	0.389834i
$538$		−	7.40668e7i		−	0.475638i
$539$	2.31693e8	−	2.05268e7i	1.47961	−	0.131085i
$540$	−1.70229e8			−1.08106
$541$	−6.33756e7	+	1.61478e8i	−0.400249	+	1.01982i	0.578669	+	0.815563i	$0.303572\pi$
$541$	−6.33756e7	+	1.61478e8i	−0.400249	+	1.01982i	−0.978918	+	0.204255i	$0.934523\pi$
$542$	3.91045e7	+	2.93047e6i	0.245600	+	0.0184052i
$543$	1.27912e8	+	1.18685e8i	0.798936	+	0.741304i
$544$	1.89733e7	−	2.78288e7i	0.117855	−	0.172861i
$545$	−395830.	+	821950.i	−0.00244523	+	0.00507757i
$546$	1.64614e7	+	8.38820e7i	0.101132	+	0.515336i
$547$	2.65709e8	−	1.27959e8i	1.62347	−	0.781823i	0.623472	−	0.781846i	$-0.285721\pi$
$547$	2.65709e8	−	1.27959e8i	1.62347	−	0.781823i	1.00000		2.26096e-5i	$7.19686e-6\pi$
$548$	−4.56953e8	−	6.88746e7i	−2.77671	−	0.418521i
$549$	−4.83281e7	−	7.08843e7i	−0.292067	−	0.428384i
$550$	−2.44187e8	+	3.68052e7i	−1.46769	+	0.221219i
$551$	−5.93723e7	−	6.39881e7i	−0.354919	−	0.382511i
$552$	−2.03035e7	+	1.61915e7i	−0.120713	+	0.0962655i
$553$	1.90578e7	+	3.54747e7i	0.112693	+	0.209770i
$554$	4.06218e7	−	5.09381e7i	0.238907	−	0.299580i
$555$	7.28811e6	+	9.72531e7i	0.0426320	+	0.568885i
$556$	1.35357e8	−	4.38818e8i	0.787513	−	2.55306i
$557$	6.06077e7	−	1.04976e8i	0.350721	−	0.607467i	−0.635655	−	0.771974i	$-0.719270\pi$
$557$	6.06077e7	−	1.04976e8i	0.350721	−	0.607467i	0.986376	+	0.164506i	$0.0526031\pi$
$558$	8.85183e7	−	5.11061e7i	0.509484	−	0.294151i
$559$	−1.11167e8	+	2.53731e7i	−0.636414	+	0.145257i
$560$	680579.	+	421225.i	0.00387538	+	0.00239856i
$561$	−9.19391e6	+	4.02812e7i	−0.0520729	+	0.228146i
$562$	−2.33461e8	+	7.20130e7i	−1.31524	+	0.405697i
$563$	2.86441e8	−	1.12420e8i	1.60513	−	0.629968i	0.617473	−	0.786592i	$-0.288156\pi$
$563$	2.86441e8	−	1.12420e8i	1.60513	−	0.629968i	0.987658	+	0.156624i	$0.0500612\pi$
$564$	−3.31674e6	−	8.45092e6i	−0.0184873	−	0.0471050i
$565$	3.99744e7	+	1.29594e8i	0.221634	+	0.718520i
$566$	2.32347e8	+	5.30318e7i	1.28141	+	0.292474i
$567$	−6.32803e7	−	2.16621e7i	−0.347152	−	0.118837i
$568$	3.40138e7	+	1.49024e8i	0.185614	+	0.813228i
$569$	−7.94508e7	−	1.37613e8i	−0.431282	−	0.747003i	0.565702	−	0.824610i	$-0.308605\pi$
$569$	−7.94508e7	−	1.37613e8i	−0.431282	−	0.747003i	−0.996984	+	0.0776070i	$0.975272\pi$
$570$	4.33820e7	+	2.50466e7i	0.234253	+	0.135246i
$571$	1.56712e8	+	4.83394e7i	0.841773	+	0.259653i	0.685510	−	0.728063i	$-0.259579\pi$
$571$	1.56712e8	+	4.83394e7i	0.841773	+	0.259653i	0.156263	+	0.987716i	$0.450055\pi$
$572$	1.94769e8	−	1.45959e7i	1.04071	−	0.0779907i
$573$	−7.40588e7	−	5.90599e7i	−0.393652	−	0.313927i
$574$	2.19337e8	−	9.69706e6i	1.15978	−	0.0512749i
$575$	1.50003e7	+	1.88098e7i	0.0789037	+	0.0989421i
$576$	9.95908e7	−	9.24068e7i	0.521137	−	0.483544i
$577$	1.11572e7	+	7.40234e7i	0.0580804	+	0.385338i	0.998919	+	0.0464833i	$0.0148014\pi$
$577$	1.11572e7	+	7.40234e7i	0.0580804	+	0.385338i	−0.940839	+	0.338855i	$0.889960\pi$
$578$	−2.46872e8	+	1.68314e8i	−1.27846	+	0.871641i
$579$	2.30102e7	−	1.52663e8i	0.118545	−	0.786498i
$580$	−1.22842e8	−	2.55084e8i	−0.629598	−	1.30737i
$581$	−1.88781e8	−	1.60243e8i	−0.962563	−	0.817055i
$582$	−3.49978e8	−	1.68541e8i	−1.77530	−	0.854939i
$583$	−5.65346e7	−	3.85447e7i	−0.285305	−	0.194517i
$584$	2.29489e8	−	2.47330e8i	1.15219	−	1.24176i
$585$	1.76389e6	−	2.35375e7i	0.00881058	−	0.117569i
$586$	4.61651e8	+	1.81185e8i	2.29415	+	0.900386i
$587$		−	1.82818e8i		−	0.903869i	−0.892051	−	0.451934i	$-0.850734\pi$
$587$		−	1.82818e8i		−	0.903869i	0.892051	−	0.451934i	$-0.149266\pi$
$588$	1.56430e8	+	1.90789e8i	0.769462	+	0.938474i
$589$	−6.09116e7			−0.298095
$590$	1.03441e8	−	2.63563e8i	0.503658	−	1.28330i
$591$	4.39093e7	+	3.29054e6i	0.212713	+	0.0159406i
$592$	1.37998e6	+	1.28043e6i	0.00665130	+	0.00617151i
$593$	−1.29362e8	+	1.89739e8i	−0.620358	+	0.909897i	−0.999883	−	0.0152838i	$-0.995135\pi$
$593$	−1.29362e8	+	1.89739e8i	−0.620358	+	0.909897i	0.379526	+	0.925181i	$0.376087\pi$
$594$	−2.35677e8	+	4.89389e8i	−1.12450	+	2.33504i
$595$	−1.64385e7	−	2.19601e7i	−0.0780391	−	0.104252i
$596$	1.21380e8	−	5.84535e7i	0.573335	−	0.276103i
$597$	−2.01804e8	−	3.04171e7i	−0.948435	−	0.142954i
$598$	−1.73306e7	−	2.54193e7i	−0.0810418	−	0.118867i
$599$	2.05545e8	−	3.09809e7i	0.956369	−	0.144149i	0.347728	−	0.937595i	$-0.386953\pi$
$599$	2.05545e8	−	3.09809e7i	0.956369	−	0.144149i	0.608641	+	0.793446i	$0.291715\pi$
$600$	−6.82750e7	−	7.35829e7i	−0.316088	−	0.340662i
$601$	1.62121e8	−	1.29287e8i	0.746821	−	0.595570i	−0.174370	−	0.984680i	$-0.555789\pi$
$601$	1.62121e8	−	1.29287e8i	0.746821	−	0.595570i	0.921191	+	0.389110i	$0.127218\pi$
$602$	−4.00945e8	+	3.49802e8i	−1.83779	+	1.60337i
$603$	−1.26265e7	+	1.58331e7i	−0.0575879	+	0.0722130i
$604$	2.84772e7	+	3.80002e8i	0.129237	+	1.72455i
$605$	4.87223e7	−	1.57954e8i	0.220020	−	0.713286i
$606$	5.95801e7	−	1.03196e8i	0.267722	−	0.463708i
$607$	−1.44301e8	+	8.33124e7i	−0.645215	+	0.372515i	−0.786620	−	0.617437i	$-0.788171\pi$
$607$	−1.44301e8	+	8.33124e7i	−0.645215	+	0.372515i	0.141406	+	0.989952i	$0.454838\pi$
$608$	−7.85727e7	+	1.79337e7i	−0.349592	+	0.0797920i
$609$	−2.90289e7	−	2.42825e8i	−0.128522	−	1.07508i
$610$	−5.96587e7	+	2.61382e8i	−0.262836	+	1.15156i
$611$	3.93844e6	−	1.21485e6i	0.0172663	−	0.00532596i
$612$	3.20172e7	−	1.25658e7i	0.139678	−	0.0548197i
$613$	−6.96837e7	−	1.77551e8i	−0.302517	−	0.770800i	−0.998603	−	0.0528419i	$-0.983172\pi$
$613$	−6.96837e7	−	1.77551e8i	−0.302517	−	0.770800i	0.696086	−	0.717958i	$-0.254923\pi$
$614$	−3.08397e7	−	9.99798e7i	−0.133231	−	0.431924i
$615$	7.53081e7	+	1.71886e7i	0.323755	+	0.0738950i
$616$	2.94470e8	−	1.87826e8i	1.25979	−	0.803549i
$617$	5.45747e7	+	2.39107e8i	0.232346	+	1.01798i	0.947687	+	0.319200i	$0.103414\pi$
$617$	5.45747e7	+	2.39107e8i	0.232346	+	1.01798i	−0.715341	+	0.698776i	$0.753729\pi$
$618$	4.57154e7	+	7.91815e7i	0.193686	+	0.335473i
$619$	−2.02844e8	−	1.17112e8i	−0.855245	−	0.493776i	0.00717228	−	0.999974i	$-0.497717\pi$
$619$	−2.02844e8	−	1.17112e8i	−0.855245	−	0.493776i	−0.862417	+	0.506199i	$0.831050\pi$
$620$	−1.88788e8	−	5.82333e7i	−0.792134	−	0.244341i
$621$	5.27716e7	−	3.95468e6i	0.220356	−	0.0165134i
$622$	3.24688e8	+	2.58930e8i	1.34926	+	1.07600i
$623$	−1.34561e7	+	7.38559e7i	−0.0556488	+	0.305437i
$624$	361955.	+	453877.i	0.00148971	+	0.00186803i
$625$	344043.	−	319226.i	0.00140920	−	0.00130755i
$626$	7.37818e7	+	4.89510e8i	0.300764	+	1.99544i
$627$	8.16856e7	−	5.56923e7i	0.331393	−	0.225940i
$628$	6.49928e7	−	4.31199e8i	0.262414	−	1.74100i
$629$	−2.79934e7	−	5.81289e7i	−0.112487	−	0.233582i
$630$	−4.47291e7	−	1.00652e8i	−0.178883	−	0.402533i
$631$	2.72855e8	+	1.31400e8i	1.08604	+	0.523007i	0.889242	−	0.457437i	$-0.151233\pi$
$631$	2.72855e8	+	1.31400e8i	1.08604	+	0.523007i	0.196794	+	0.980445i	$0.436947\pi$
$632$	4.99618e7	+	3.40634e7i	0.197919	+	0.134939i
$633$	−4.75422e7	+	5.12383e7i	−0.187442	+	0.202015i
$634$	2.85838e7	−	3.81424e8i	0.112164	−	1.49672i
$635$	−1.33772e8	−	5.25016e7i	−0.522449	−	0.205046i
$636$		−	7.25777e7i		−	0.282119i
$637$	−9.16815e7	+	6.43462e7i	−0.354702	+	0.248946i
$638$	−9.03413e8			−3.47876
$639$	3.47567e7	−	8.85585e7i	0.133210	−	0.339413i
$640$	−2.62600e8	−	1.96791e7i	−1.00174	−	0.0750700i
$641$	−4.11228e7	−	3.81564e7i	−0.156138	−	0.144875i	0.598235	−	0.801320i	$-0.295869\pi$
$641$	−4.11228e7	−	3.81564e7i	−0.156138	−	0.144875i	−0.754374	+	0.656445i	$0.772059\pi$
$642$	−2.59728e7	+	3.80951e7i	−0.0981552	+	0.143967i
$643$	−3.03314e7	+	6.29838e7i	−0.114093	+	0.236917i	−0.950194	−	0.311659i	$-0.899115\pi$
$643$	−3.03314e7	+	6.29838e7i	−0.114093	+	0.236917i	0.836101	+	0.548576i	$0.184830\pi$
$644$	−7.87845e7	−	4.09577e7i	−0.294974	−	0.153348i
$645$	−1.68666e8	+	8.12251e7i	−0.628561	+	0.302699i
$646$	−3.27690e7	−	4.93913e6i	−0.121553	−	0.0183212i
$647$	5.11695e7	+	7.50518e7i	0.188929	+	0.277108i	0.909003	−	0.416789i	$-0.136845\pi$
$647$	5.11695e7	+	7.50518e7i	0.188929	+	0.277108i	−0.720074	+	0.693897i	$0.755892\pi$
$648$	−9.93130e7	+	1.49690e7i	−0.364990	+	0.0550134i
$649$	−3.80079e8	−	4.09628e8i	−1.39040	−	1.49849i
$650$	9.29725e7	−	7.41431e7i	0.338543	−	0.269979i
$651$	−1.37990e8	−	1.00403e8i	−0.500155	−	0.363917i
$652$	3.43727e8	−	4.31020e8i	1.24014	−	1.55509i
$653$	−3.97360e7	−	5.30240e8i	−0.142707	−	1.90429i	−0.367727	−	0.929934i	$-0.619864\pi$
$653$	−3.97360e7	−	5.30240e8i	−0.142707	−	1.90429i	0.225020	−	0.974354i	$-0.427755\pi$
$654$	−910130.	+	2.95057e6i	−0.00325364	+	0.0105481i
$655$	9.44647e7	−	1.63618e8i	0.336160	−	0.582246i
$656$	1.29127e6	−	745516.i	0.00457410	−	0.00264086i
$657$	−2.04724e8	+	4.67270e7i	−0.721894	+	0.164768i
$658$	1.35071e7	−	1.36915e7i	0.0474115	−	0.0480590i
$659$	1.00074e7	−	4.38452e7i	0.0349675	−	0.153202i	−0.954430	−	0.298434i	$-0.903536\pi$
$659$	1.00074e7	−	4.38452e7i	0.0349675	−	0.153202i	0.989398	+	0.145232i	$0.0463928\pi$
$660$	3.06417e8	−	9.45172e7i	1.06581	−	0.328760i
$661$	−3.18612e8	+	1.25046e8i	−1.10321	+	0.432977i	−0.845894	−	0.533350i	$-0.820933\pi$
$661$	−3.18612e8	+	1.25046e8i	−1.10321	+	0.432977i	−0.257314	+	0.966328i	$0.582837\pi$
$662$	8.83292e7	+	2.25059e8i	0.304460	+	0.775751i
$663$	−5.86451e6	−	1.90123e7i	−0.0201229	−	0.0652369i
$664$	−3.62505e8	−	8.27393e7i	−1.23825	−	0.282623i
$665$	−6.90660e6	+	6.52737e7i	−0.0234855	+	0.221959i
$666$	−5.76456e7	−	2.52562e8i	−0.195139	−	0.854958i
$667$	4.40076e7	+	7.62234e7i	0.148303	+	0.256869i
$668$	5.88350e8	+	3.39684e8i	1.97382	+	1.13958i
$669$	2.34680e8	+	7.23891e7i	0.783785	+	0.241766i
$670$	6.31097e7	−	4.72942e6i	0.209832	−	0.0157247i
$671$	4.13692e8	+	3.29908e8i	1.36933	+	1.09201i
$672$	−2.07560e8	−	8.88869e7i	−0.683969	−	0.292907i
$673$	1.87049e8	+	2.34552e8i	0.613636	+	0.769475i	0.987433	−	0.158035i	$-0.0505160\pi$
$673$	1.87049e8	+	2.34552e8i	0.613636	+	0.769475i	−0.373798	+	0.927510i	$0.621945\pi$
$674$	1.36778e8	−	1.26912e8i	0.446722	−	0.414498i
$675$	3.04866e7	+	2.02265e8i	0.0991283	+	0.657673i
$676$	3.36113e8	−	2.29158e8i	1.08804	−	0.741813i
$677$	−8.78389e6	+	5.82773e7i	−0.0283087	+	0.187816i	−0.998516	−	0.0544605i	$-0.982656\pi$
$677$	−8.78389e6	+	5.82773e7i	−0.0283087	+	0.187816i	0.970207	+	0.242277i	$0.0778942\pi$
$678$	1.99159e8	+	4.13558e8i	0.639015	+	1.32693i
$679$	1.55817e7	−	5.08750e8i	0.0497743	−	1.62516i
$680$	−3.71115e7	−	1.78720e7i	−0.118027	−	0.0568389i
$681$	2.85107e8	+	1.94383e8i	0.902749	+	0.615484i
$682$	−4.28787e8	+	4.62122e8i	−1.35172	+	1.45681i
$683$	1.00371e7	−	1.33936e8i	0.0315027	−	0.420374i	−0.959050	−	0.283238i	$-0.908591\pi$
$683$	1.00371e7	−	1.33936e8i	0.0315027	−	0.420374i	0.990552	−	0.137136i	$-0.0437896\pi$
$684$	−7.66115e7	−	3.00678e7i	−0.239401	−	0.0939579i
$685$		−	3.44438e8i		−	1.07162i
$686$	−2.34778e8	+	4.66979e8i	−0.727253	+	1.44652i
$687$	2.86068e8			0.882266
$688$	−1.32018e6	+	3.36376e6i	−0.00405385	+	0.0103290i
$689$	3.28575e7	+	2.46233e6i	0.100456	+	0.00752814i
$690$	−3.70260e7	−	3.43551e7i	−0.112709	−	0.104579i
$691$	−1.14307e8	+	1.67657e8i	−0.346448	+	0.508145i	−0.959428	−	0.281952i	$-0.909018\pi$
$691$	−1.14307e8	+	1.67657e8i	−0.346448	+	0.508145i	0.612981	+	0.790098i	$0.289970\pi$
$692$	−4.11101e8	+	8.53660e8i	−1.24060	+	2.57612i
$693$	−2.17278e8	−	6.65466e6i	−0.652854	−	0.0199952i
$694$	7.31471e8	−	3.52258e8i	2.18836	−	1.05386i
$695$	3.38457e8	+	5.10142e7i	1.00821	+	0.151963i
$696$	−2.06863e8	−	3.03413e8i	−0.613559	−	0.899925i
$697$	−5.05306e7	+	7.61626e6i	−0.149230	+	0.0224928i
$698$	2.61981e8	+	2.82348e8i	0.770376	+	0.830268i
$699$	1.98380e8	−	1.58203e8i	0.580853	−	0.463215i
$700$	1.35114e8	−	3.15505e8i	0.393918	−	0.919840i
$701$	−2.59819e8	+	3.25803e8i	−0.754253	+	0.945804i	−0.999721	−	0.0236010i	$-0.992487\pi$
$701$	−2.59819e8	+	3.25803e8i	−0.754253	+	0.945804i	0.245468	+	0.969405i	$0.421058\pi$
$702$	−1.95470e7	−	2.60837e8i	−0.0565028	−	0.753977i
$703$	−4.55045e7	+	1.47522e8i	−0.130975	+	0.424610i
$704$	−4.18962e8	+	7.25663e8i	−1.20076	+	2.07978i
$705$	5.86010e6	−	3.38333e6i	0.0167239	−	0.00965555i
$706$	9.20476e8	−	2.10093e8i	2.61576	−	0.597031i
$707$	1.55271e8	+	1.64292e7i	0.439372	+	0.0464899i
$708$	1.31892e8	−	5.77858e8i	0.371638	−	1.62825i
$709$	1.48814e8	−	4.59030e7i	0.417546	−	0.128796i	−0.0788613	−	0.996886i	$-0.525128\pi$
$709$	1.48814e8	−	4.59030e7i	0.417546	−	0.128796i	0.496407	+	0.868090i	$0.334652\pi$
$710$	−2.76751e8	+	1.08617e8i	−0.773239	+	0.303474i
$711$	−1.37495e7	−	3.50331e7i	−0.0382540	−	0.0974696i
$712$	3.32270e7	+	1.07719e8i	0.0920559	+	0.298438i
$713$	5.98778e7	+	1.36667e7i	0.165195	+	0.0377047i
$714$	−6.60940e7	−	6.52035e7i	−0.181580	−	0.179133i
$715$	3.23942e7	+	1.41928e8i	0.0886235	+	0.388285i
$716$	4.24186e8	+	7.34712e8i	1.15563	+	2.00160i
$717$	1.81564e7	+	1.04826e7i	0.0492576	+	0.0284389i
$718$	−3.07810e8	−	9.49468e7i	−0.831590	−	0.256512i
$719$	−2.44863e8	+	1.83500e7i	−0.658775	+	0.0493684i	−0.399923	−	0.916549i	$-0.630963\pi$
$719$	−2.44863e8	+	1.83500e7i	−0.658775	+	0.0493684i	−0.258852	+	0.965917i	$0.583344\pi$
$720$	−584819.	−	466378.i	−0.00156684	−	0.00124951i
$721$	−7.04864e7	+	9.68740e7i	−0.188061	+	0.258465i
$722$	−3.30488e8	−	4.14418e8i	−0.878099	−	1.10110i
$723$	−2.95597e8	+	2.74274e8i	−0.782142	+	0.725722i
$724$	1.33527e8	+	8.85894e8i	0.351847	+	2.33435i
$725$	−2.81091e8	+	1.91645e8i	−0.737620	+	0.502901i
$726$	8.33838e7	−	5.53215e8i	0.217907	−	1.44572i
$727$	6.21311e7	+	1.29016e8i	0.161698	+	0.335770i	0.966038	−	0.258400i	$-0.0831951\pi$
$727$	6.21311e7	+	1.29016e8i	0.161698	+	0.335770i	−0.804340	+	0.594170i	$0.797481\pi$
$728$	−7.75805e7	+	1.49231e8i	−0.201075	+	0.386780i
$729$	3.37882e8	+	1.62715e8i	0.872131	+	0.419996i
$730$	5.42202e8	+	3.69667e8i	1.39377	+	0.950259i
$731$	8.42363e7	−	9.07851e7i	0.215649	−	0.232414i
$732$	−4.19424e7	+	5.59683e8i	−0.106935	+	1.42695i
$733$	−8.80539e6	−	3.45586e6i	−0.0223582	−	0.00877495i	0.354136	−	0.935194i	$-0.384775\pi$
$733$	−8.80539e6	−	3.45586e6i	−0.0223582	−	0.00877495i	−0.376494	+	0.926419i	$0.622870\pi$
$734$		−	9.57667e8i		−	2.42173i
$735$	−1.23239e8	+	1.36487e8i	−0.310375	+	0.343740i
$736$	8.12629e7			0.203826
$737$	4.56323e7	−	1.16269e8i	0.113991	−	0.290444i
$738$	−2.04611e8	−	1.53335e7i	−0.509049	−	0.0381480i
$739$	−5.10166e8	−	4.73365e8i	−1.26409	−	1.17290i	−0.976586	−	0.215125i	$-0.930984\pi$
$739$	−5.10166e8	−	4.73365e8i	−1.26409	−	1.17290i	−0.287504	−	0.957779i	$-0.592825\pi$
$740$	−2.82070e8	+	4.13721e8i	−0.696085	+	1.02097i
$741$	−2.06564e7	+	4.28934e7i	−0.0507691	+	0.105423i
$742$	1.40506e8	−	6.24400e7i	0.343941	−	0.152845i
$743$	2.15611e8	−	1.03833e8i	0.525661	−	0.253145i	−0.152181	−	0.988353i	$-0.548630\pi$
$743$	2.15611e8	−	1.03833e8i	0.525661	−	0.253145i	0.677842	+	0.735208i	$0.262915\pi$
$744$	−2.53388e8	−	3.81921e7i	−0.615272	−	0.0927374i
$745$	5.65657e7	+	8.29667e7i	0.136800	+	0.200648i
$746$	−9.80985e8	+	1.47860e8i	−2.36290	+	0.356150i
$747$	1.57404e8	+	1.69641e8i	0.377618	+	0.406976i
$748$	−1.65854e8	+	1.32264e8i	−0.396297	+	0.316036i
$749$	−5.94359e7	−	1.08289e7i	−0.141450	−	0.0257714i
$750$	3.18958e8	−	3.99961e8i	0.756049	−	0.948056i
$751$	7.04299e6	+	9.39821e7i	0.0166279	+	0.221884i	0.999327	+	0.0366757i	$0.0116768\pi$
$751$	7.04299e6	+	9.39821e7i	0.0166279	+	0.221884i	−0.982699	+	0.185208i	$0.940704\pi$
$752$	38499.4	−	124812.i	9.05316e−5	−	0.000293496i
$753$	1.86225e8	−	3.22552e8i	0.436168	−	0.755465i
$754$	3.76754e8	−	2.17519e8i	0.878909	−	0.507438i
$755$	−2.76908e8	+	6.32024e7i	−0.643420	+	0.146856i
$756$	−4.05981e8	−	6.36492e8i	−0.939595	−	1.47308i
$757$	−1.09664e7	+	4.80471e7i	−0.0252801	+	0.110759i	−0.985994	−	0.166782i	$-0.946662\pi$
$757$	−1.09664e7	+	4.80471e7i	−0.0252801	+	0.110759i	0.960714	+	0.277541i	$0.0895195\pi$
$758$	−9.47820e7	+	2.92364e7i	−0.217630	+	0.0671299i
$759$	−9.27948e7	+	3.64193e7i	−0.212226	+	0.0832926i
$760$	3.60087e7	+	9.17488e7i	0.0820289	+	0.209006i
$761$	1.13091e8	+	3.66631e8i	0.256609	+	0.831907i	0.988597	+	0.150589i	$0.0481169\pi$
$761$	1.13091e8	+	3.66631e8i	0.256609	+	0.831907i	−0.731987	+	0.681318i	$0.761407\pi$
$762$	−4.74191e8	−	1.08231e8i	−1.07174	−	0.244617i
$763$	−4.01733e6	+	480258.i	−0.00904407	+	0.00108119i
$764$	−1.08222e8	−	4.74153e8i	−0.242682	−	1.06326i
$765$	1.28181e7	+	2.22016e7i	0.0286312	+	0.0495907i
$766$	−6.03766e8	−	3.48584e8i	−1.34333	−	0.775571i
$767$	2.57134e8	+	7.93153e7i	0.569867	+	0.175781i
$768$	−3.42140e8	+	2.56398e7i	−0.755300	+	0.0566019i
$769$	−1.76406e8	−	1.40679e8i	−0.387914	−	0.309351i	0.410042	−	0.912067i	$-0.365514\pi$
$769$	−1.76406e8	−	1.40679e8i	−0.387914	−	0.309351i	−0.797956	+	0.602715i	$0.794085\pi$
$770$	4.46597e8	+	5.11892e8i	0.978236	+	1.12126i
$771$	−2.93681e8	−	3.68265e8i	−0.640787	−	0.803521i
$772$	5.81070e8	−	5.39155e8i	1.26292	−	1.17182i
$773$	−8.41124e7	−	5.58050e8i	−0.182105	−	1.20819i	−0.873904	−	0.486098i	$-0.838420\pi$
$773$	−8.41124e7	−	5.58050e8i	−0.182105	−	1.20819i	0.691800	−	0.722090i	$-0.256818\pi$
$774$	4.10864e8	−	2.80122e8i	0.886085	−	0.604122i
$775$	−3.53823e7	+	2.34746e8i	−0.0760119	+	0.504306i
$776$	−3.31616e8	−	6.88607e8i	−0.709660	−	1.47362i
$777$	−3.46252e8	+	2.59191e8i	−0.738124	+	0.552532i
$778$	−5.83976e8	−	2.81228e8i	−1.24010	−	0.597200i
$779$	1.01029e8	+	6.88807e7i	0.213715	+	0.145709i
$780$	−1.05029e8	+	1.13194e8i	−0.221323	+	0.238529i
$781$	−4.38485e7	+	5.85118e8i	−0.0920453	+	1.22826i
$782$	3.11047e7	+	1.22077e7i	0.0650437	+	0.0255278i
$783$			7.48317e8i			1.55884i
$784$	48146.2	+	3.54930e6i	9.99111e−5	+	0.00736538i
$785$	3.25025e8			0.671905
$786$	2.33617e8	−	5.95246e8i	0.481101	−	1.22583i
$787$	3.01001e8	+	2.25569e7i	0.617509	+	0.0462759i	0.379812	−	0.925064i	$-0.375989\pi$
$787$	3.01001e8	+	2.25569e7i	0.617509	+	0.0462759i	0.237696	+	0.971339i	$0.423608\pi$
$788$	1.65726e8	+	1.53771e8i	0.338697	+	0.314265i
$789$	−2.58197e8	+	3.78706e8i	−0.525679	+	0.771030i
$790$	−5.10292e7	+	1.05963e8i	−0.103499	+	0.214919i
$791$	−3.89221e8	+	4.58537e8i	−0.786443	+	0.926499i
$792$	−2.94092e8	+	1.41627e8i	−0.591980	+	0.285083i
$793$	−2.51957e8	−	3.79765e7i	−0.505251	−	0.0761544i
$794$	7.38965e8	+	1.08386e9i	1.47626	+	2.16527i
$795$	5.34917e7	−	8.06257e6i	0.106460	−	0.0160462i
$796$	−7.12706e8	−	7.68115e8i	−1.41310	−	1.52295i
$797$	3.04725e8	−	2.43010e8i	0.601911	−	0.480008i	−0.274490	−	0.961590i	$-0.588509\pi$
$797$	3.04725e8	−	2.43010e8i	0.601911	−	0.480008i	0.876401	+	0.481582i	$0.159938\pi$
$798$	9.81219e6	+	2.21941e8i	0.0193089	+	0.436746i
$799$	−2.79104e6	+	3.49986e6i	−0.00547175	+	0.00686136i
$800$	2.34732e7	+	3.13228e8i	0.0458460	+	0.611773i
$801$	2.06798e7	−	6.70423e7i	0.0402392	−	0.130452i
$802$	−2.82996e8	+	4.90163e8i	−0.548602	+	0.950206i
$803$	1.12162e9	−	6.47570e8i	2.16621	−	1.25066i
$804$	1.29164e8	−	2.94807e7i	0.248526	−	0.0567245i
$805$	2.14348e7	−	6.26162e7i	0.0410896	−	0.120033i
$806$	6.75513e7	−	2.95962e8i	0.129012	−	0.565237i
$807$	1.10434e8	−	3.40644e7i	0.210128	−	0.0648158i
$808$	2.18249e8	−	8.56566e7i	0.413732	−	0.162378i
$809$	2.48679e7	+	6.33625e7i	0.0469672	+	0.119670i	0.952432	−	0.304750i	$-0.0985730\pi$
$809$	2.48679e7	+	6.33625e7i	0.0469672	+	0.119670i	−0.905465	+	0.424421i	$0.860478\pi$
$810$	−5.75783e7	−	1.86664e8i	−0.108344	−	0.351242i
$811$	−6.71756e8	−	1.53324e8i	−1.25936	−	0.287440i	−0.459796	−	0.888025i	$-0.652077\pi$
$811$	−6.71756e8	−	1.53324e8i	−1.25936	−	0.287440i	−0.799561	+	0.600585i	$0.794935\pi$
$812$	6.60803e8	−	1.06767e9i	1.23425	−	1.99420i
$813$	1.36154e7	+	5.96529e7i	0.0253372	+	0.111009i
$814$	7.98886e8	+	1.38371e9i	1.48119	+	2.56550i
$815$	3.55857e8	+	2.05454e8i	0.657359	+	0.379527i
$816$	−602512.	−	185850.i	−0.00110891	−	0.000342053i
$817$	−2.95511e8	+	2.21455e7i	−0.541886	+	0.0406088i
$818$	−1.98868e8	−	1.58592e8i	−0.363332	−	0.289748i
$819$	9.22146e7	−	4.95398e7i	0.167860	−	0.0901784i
$820$	2.47276e8	+	3.10074e8i	0.448477	+	0.562372i
$821$	3.54204e8	−	3.28654e8i	0.640066	−	0.593894i	−0.291896	−	0.956450i	$-0.594286\pi$
$821$	3.54204e8	−	3.28654e8i	0.640066	−	0.593894i	0.931962	+	0.362556i	$0.118096\pi$
$822$	−1.73751e8	−	1.15276e9i	−0.312832	−	2.07551i
$823$	4.98828e8	−	3.40095e8i	0.894853	−	0.610100i	−0.0261495	−	0.999658i	$-0.508325\pi$
$823$	4.98828e8	−	3.40095e8i	0.894853	−	0.610100i	0.921002	+	0.389558i	$0.127372\pi$
$824$	−2.68122e7	+	1.77888e8i	−0.0479238	+	0.317954i
$825$	−1.67182e8	−	3.47157e8i	−0.297734	−	0.618251i
$826$	1.23217e9	−	2.41806e8i	2.18641	−	0.429070i
$827$	−4.64386e8	−	2.23636e8i	−0.821036	−	0.395390i	−0.0242906	−	0.999705i	$-0.507733\pi$
$827$	−4.64386e8	−	2.23636e8i	−0.821036	−	0.395390i	−0.796746	+	0.604315i	$0.793447\pi$
$828$	6.85649e7	+	4.67468e7i	0.120784	+	0.0823494i
$829$	−5.95686e6	+	6.41996e6i	−0.0104557	+	0.0112686i	−0.738258	−	0.674518i	$-0.764351\pi$
$829$	−5.95686e6	+	6.41996e6i	−0.0104557	+	0.0112686i	0.727802	+	0.685787i	$0.240542\pi$
$830$	5.40443e7	−	7.21171e8i	0.0945182	−	1.26126i
$831$	9.46317e7	+	3.71402e7i	0.164905	+	0.0647204i
$832$		−	4.03501e8i		−	0.700608i
$833$	4.29053e7	−	1.13838e8i	0.0742294	−	0.196947i
$834$	1.15848e9			1.99706
$835$	−1.84997e8	+	4.71365e8i	−0.317765	+	0.809651i
$836$	5.06182e8	+	3.79331e7i	0.866339	+	0.0649231i
$837$	3.82786e8	+	3.55174e8i	0.652799	+	0.605709i
$838$	4.72949e8	−	6.93689e8i	0.803679	−	1.17878i
$839$	2.14863e8	−	4.46168e8i	0.363811	−	0.755462i	−0.636058	−	0.771641i	$-0.719436\pi$
$839$	2.14863e8	−	4.46168e8i	0.363811	−	0.755462i	0.999869	+	0.0161797i	$0.00515039\pi$
$840$	−6.96581e7	+	2.67203e8i	−0.117526	+	0.450821i
$841$	−5.85423e8	+	2.81925e8i	−0.984196	+	0.473964i
$842$	−1.57592e9	−	2.37532e8i	−2.63997	−	0.397911i
$843$	−2.14744e8	−	3.14972e8i	−0.358458	−	0.525762i
$844$	−3.54866e8	+	5.34875e7i	−0.590252	+	0.0889661i
$845$	2.06234e8	+	2.22267e8i	0.341814	+	0.368388i
$846$	−1.40528e7	+	1.12067e7i	−0.0232088	+	0.0185084i
$847$	7.06795e8	−	1.94532e8i	1.16317	−	0.320141i
$848$	651045.	−	816385.i	0.00106764	−	0.00133877i
$849$	2.77893e7	+	3.70822e8i	0.0454103	+	0.605958i
$850$	−3.80697e7	+	1.23419e8i	−0.0619902	+	0.200967i
$851$	7.78316e7	−	1.34808e8i	0.126290	−	0.218740i
$852$	−5.38994e8	+	3.11188e8i	−0.871496	+	0.503158i
$853$	−2.11067e8	+	4.81747e7i	−0.340074	+	0.0776197i	−0.389148	−	0.921175i	$-0.627230\pi$
$853$	−2.11067e8	+	4.81747e7i	−0.340074	+	0.0776197i	0.0490733	+	0.998795i	$0.484373\pi$
$854$	−1.11960e9	+	4.00308e8i	−1.79758	+	0.642718i
$855$	1.36501e7	−	5.98049e7i	0.0218392	−	0.0956838i
$856$	−8.66878e7	+	2.67396e7i	−0.138209	+	0.0426318i
$857$	2.15366e8	−	8.45250e7i	0.342165	−	0.134290i	−0.188035	−	0.982162i	$-0.560212\pi$
$857$	2.15366e8	−	8.45250e7i	0.342165	−	0.134290i	0.530200	+	0.847872i	$0.322117\pi$
$858$	1.80012e8	+	4.58663e8i	0.284996	+	0.726159i
$859$	−1.46930e8	−	4.76336e8i	−0.231810	−	0.751509i	−0.994499	−	0.104744i	$-0.966598\pi$
$859$	−1.46930e8	−	4.76336e8i	−0.231810	−	0.751509i	0.762690	−	0.646765i	$-0.223878\pi$
$860$	−9.37071e8	−	2.13880e8i	−1.47325	−	0.336260i
$861$	1.15335e8	+	3.22574e8i	0.180697	+	0.505382i
$862$	8.93404e7	+	3.91426e8i	0.139484	+	0.611121i
$863$	−9.74353e7	−	1.68763e8i	−0.151595	−	0.262570i	0.780219	−	0.625506i	$-0.215107\pi$
$863$	−9.74353e7	−	1.68763e8i	−0.151595	−	0.262570i	−0.931814	+	0.362937i	$0.881774\pi$
$864$	5.98344e8	+	3.45454e8i	0.927705	+	0.535611i
$865$	−6.74839e8	−	2.08160e8i	−1.04268	−	0.321625i
$866$	−1.53243e9	+	1.14840e8i	−2.35953	+	0.176823i
$867$	−3.64499e8	−	2.90678e8i	−0.559292	−	0.446020i
$868$	−2.32507e8	−	8.44767e8i	−0.355530	−	1.29175i
$869$	1.44723e8	+	1.81476e8i	0.220535	+	0.276542i
$870$	5.23572e8	−	4.85804e8i	0.795094	−	0.737740i
$871$	8.96446e6	+	5.94753e7i	0.0135666	+	0.0900082i
$872$	−5.01971e6	+	3.42238e6i	−0.00757058	+	0.00516153i
$873$	−7.08967e7	+	4.70369e8i	−0.106557	+	0.706962i
$874$	−3.46911e7	−	7.20369e7i	−0.0519618	−	0.107900i
$875$	6.48640e8	+	1.69096e8i	0.968233	+	0.252412i
$876$	1.23771e9	+	5.96052e8i	1.84123	+	0.886690i
$877$	−6.75719e8	−	4.60698e8i	−1.00177	−	0.682995i	−0.0528789	−	0.998601i	$-0.516840\pi$
$877$	−6.75719e8	−	4.60698e8i	−1.00177	−	0.682995i	−0.948890	+	0.315606i	$0.897792\pi$
$878$	1.35897e9	−	1.46462e9i	2.00783	−	2.16392i
$879$	−5.78276e7	+	7.71656e8i	−0.0851468	+	1.13621i
$880$	4.29456e6	+	1.68549e6i	0.00630189	+	0.00247331i
$881$			4.47322e7i			0.0654172i	0.999465	+	0.0327086i	$0.0104133\pi$
$881$			4.47322e7i			0.0654172i	−0.999465	+	0.0327086i	$0.989587\pi$
$882$	2.69667e8	−	4.07291e8i	0.393027	−	0.593607i
$883$	−3.14242e8			−0.456439			−0.228219	−	0.973610i	$-0.573290\pi$
$883$	−3.14242e8			−0.456439			−0.228219	+	0.973610i	$0.573290\pi$
$884$	3.73209e7	−	9.50920e7i	0.0540250	−	0.137653i
$885$	4.40549e8	+	3.30146e7i	0.635571	+	0.0476295i
$886$	−5.92774e7	−	5.50014e7i	−0.0852291	−	0.0790810i
$887$	−5.26070e8	+	7.71603e8i	−0.753829	+	1.10566i	0.237127	+	0.971479i	$0.423794\pi$
$887$	−5.26070e8	+	7.71603e8i	−0.753829	+	1.10566i	−0.990956	+	0.134186i	$0.957158\pi$
$888$	−2.81793e8	+	5.85149e8i	−0.402431	+	0.835656i
$889$	−1.22729e8	−	6.25391e8i	−0.174680	−	0.890116i
$890$	−1.97539e8	+	9.51298e7i	−0.280210	+	0.134942i
$891$	−3.81224e8	−	5.74603e7i	−0.538949	−	0.0812335i
$892$	7.10313e8	+	1.04184e9i	1.00082	+	1.46793i
$893$	1.05918e7	−	1.59646e6i	0.0148736	−	0.00224183i
$894$	2.31166e8	+	2.49138e8i	0.323528	+	0.348680i
$895$	−4.94380e8	+	3.94255e8i	−0.689591	+	0.549931i
$896$	−5.52699e8	−	1.02881e9i	−0.768359	−	1.43024i
$897$	2.99298e7	−	3.75307e7i	0.0414692	−	0.0520008i
$898$	7.07429e7	+	9.43999e8i	0.0976909	+	1.30359i
$899$	−2.55991e8	+	8.29902e8i	−0.352327	+	1.14222i
$900$	−1.60380e8	+	2.77786e8i	−0.220000	+	0.381051i
$901$	−3.09926e7	+	1.78936e7i	−0.0423724	+	0.0244637i
$902$	1.23378e9	−	2.81602e8i	1.68119	−	0.383721i
$903$	−7.05959e8	−	4.36933e8i	−0.958773	−	0.593406i
$904$	−2.00969e8	+	8.80502e8i	−0.272034	+	1.19186i
$905$	−6.38094e8	+	1.96826e8i	−0.860872	+	0.265544i
$906$	−8.94870e8	+	3.51211e8i	−1.20330	+	0.472262i
$907$	9.41363e7	+	2.39855e8i	0.126164	+	0.321461i	0.979974	−	0.199123i	$-0.0638095\pi$
$907$	9.41363e7	+	2.39855e8i	0.126164	+	0.321461i	−0.853810	+	0.520584i	$0.825714\pi$
$908$	5.22212e8	+	1.69297e9i	0.697573	+	2.26148i
$909$	−1.42262e8	−	3.24704e7i	−0.189408	−	0.0432311i
$910$	−3.09497e8	−	1.05947e8i	−0.410707	−	0.140593i
$911$	8.67591e7	+	3.80116e8i	0.114752	+	0.502761i	0.999338	+	0.0363838i	$0.0115839\pi$
$911$	8.67591e7	+	3.80116e8i	0.114752	+	0.502761i	−0.884586	+	0.466377i	$0.845559\pi$
$912$	754367.	+	1.30660e6i	0.000994484	+	0.00172250i
$913$	−1.23608e9	−	7.13650e8i	−1.62418	−	0.937720i
$914$	1.97090e8	+	6.07943e7i	0.258123	+	0.0796204i
$915$	−4.17160e8	+	3.12619e7i	−0.544553	+	0.0408086i
$916$	1.14833e9	+	9.15761e8i	1.49410	+	1.19150i
$917$	8.37064e8	−	3.70073e7i	1.08555	−	0.0479931i
$918$	1.77130e8	+	2.22114e8i	0.228962	+	0.287110i
$919$	4.33776e8	−	4.02486e8i	0.558881	−	0.518566i	−0.349374	−	0.936983i	$-0.613606\pi$
$919$	4.33776e8	−	4.02486e8i	0.558881	−	0.518566i	0.908255	+	0.418418i	$0.137415\pi$
$920$	−1.48119e7	−	9.82708e7i	−0.0190217	−	0.126201i
$921$	1.34887e8	−	9.19645e7i	0.172660	−	0.117718i
$922$	−2.23741e7	+	1.48443e8i	−0.0285465	+	0.189394i
$923$	−1.22595e8	−	2.54572e8i	−0.155908	−	0.323746i
$924$	1.08418e9	+	9.20292e8i	1.37432	+	1.16657i
$925$	5.42100e8	+	2.61062e8i	0.684943	+	0.329851i
$926$	−1.86658e9	−	1.27261e9i	−2.35079	−	1.60274i
$927$	7.61549e7	−	8.20754e7i	0.0956001	−	0.103032i
$928$	−8.58732e7	+	1.14590e9i	−0.107452	+	1.43385i
$929$	−6.10291e8	−	2.39521e8i	−0.761184	−	0.298743i	−0.0471819	−	0.998886i	$-0.515024\pi$
$929$	−6.10291e8	−	2.39521e8i	−0.761184	−	0.298743i	−0.714002	+	0.700144i	$0.753119\pi$
$930$		−	4.98399e8i		−	0.619624i
$931$	−2.60533e8	+	1.29848e8i	−0.322859	+	0.160912i
$932$	1.30277e9			1.60924
$933$	−2.36738e8	+	6.03198e8i	−0.291489	+	0.742702i
$934$	−1.22673e9	−	9.19306e7i	−1.50559	−	0.112829i
$935$	−1.15907e8	−	1.07546e8i	−0.141799	−	0.131570i
$936$	8.85460e7	−	1.29873e8i	0.107980	−	0.158377i
$937$	2.06362e8	−	4.28514e8i	0.250848	−	0.520891i	−0.737080	−	0.675805i	$-0.763796\pi$
$937$	2.06362e8	−	4.28514e8i	0.250848	−	0.520891i	0.987928	+	0.154915i	$0.0495103\pi$
$938$	1.68195e8	+	2.24691e8i	0.203800	+	0.272256i
$939$	−6.95930e8	+	3.35142e8i	−0.840561	+	0.404793i
$940$	3.43542e7	+	5.17806e6i	0.0413615	+	0.00623424i
$941$	2.43468e8	+	3.57103e8i	0.292196	+	0.428572i	0.944065	−	0.329759i	$-0.106967\pi$
$941$	2.43468e8	+	3.57103e8i	0.292196	+	0.428572i	−0.651870	+	0.758331i	$0.726015\pi$
$942$	1.08779e9	−	1.63958e8i	1.30135	−	0.196146i
$943$	−8.38600e7	−	9.03796e7i	−0.100005	−	0.107779i
$944$	6.66715e6	−	5.31688e6i	0.00792546	−	0.00632034i
$945$	4.24012e8	−	3.69926e8i	0.502438	−	0.438349i
$946$	−1.91224e9	+	2.39787e9i	−2.25875	+	2.83238i
$947$	−2.76877e7	−	3.69467e8i	−0.0326015	−	0.435036i	−0.989492	−	0.144588i	$-0.953814\pi$
$947$	−2.76877e7	−	3.69467e8i	−0.0326015	−	0.435036i	0.956891	−	0.290449i	$-0.0938046\pi$
$948$	−7.25709e7	+	2.35269e8i	−0.0851800	+	0.276147i
$949$	−3.11837e8	+	5.40117e8i	−0.364862	+	0.631960i
$950$	2.67645e8	−	1.54525e8i	0.312168	−	0.180230i
$951$	5.81853e8	−	1.32804e8i	0.676506	−	0.154408i
$952$	−2.16839e7	−	1.81385e8i	−0.0251320	−	0.210228i
$953$	1.84758e8	−	8.09477e8i	0.213464	−	0.935246i	−0.748729	−	0.662876i	$-0.769335\pi$
$953$	1.84758e8	−	8.09477e8i	0.213464	−	0.935246i	0.962193	−	0.272370i	$-0.0878074\pi$
$954$	−1.37310e8	+	4.23547e7i	−0.158146	+	0.0487816i
$955$	3.37441e8	−	1.32436e8i	0.387425	−	0.152053i
$956$	3.93261e7	+	1.00201e8i	0.0450098	+	0.114683i
$957$	−4.15494e8	−	1.34700e9i	−0.474055	−	1.53685i
$958$	−1.23658e9	−	2.82240e8i	−1.40645	−	0.321013i
$959$	1.28787e9	−	8.21457e8i	1.46021	−	0.931385i
$960$	−1.47411e8	−	6.45850e8i	−0.166616	−	0.729992i
$961$	−1.40734e8	−	2.43758e8i	−0.158572	−	0.274655i
$962$	−6.66325e8	−	3.84703e8i	−0.748447	−	0.432116i
$963$	5.39526e7	+	1.66422e7i	0.0604134	+	0.0186351i
$964$	−2.06458e9	+	1.54719e8i	−2.30463	+	0.172708i
$965$	4.61922e8	+	3.68370e8i	0.514028	+	0.409923i
$966$	4.01512e7	−	2.20376e8i	0.0445418	−	0.244474i
$967$	−6.32279e8	−	7.92853e8i	−0.699245	−	0.876825i	0.297722	−	0.954653i	$-0.403773\pi$
$967$	−6.32279e8	−	7.92853e8i	−0.699245	−	0.876825i	−0.996967	+	0.0778272i	$0.975202\pi$
$968$	8.06934e8	−	7.48725e8i	0.889635	−	0.825461i
$969$	−7.70668e6	−	5.11305e7i	−0.00847024	−	0.0561964i
$970$	1.22823e9	−	8.37395e8i	1.34575	−	0.917519i
$971$	3.78615e7	−	2.51194e8i	0.0413561	−	0.274380i	−0.958590	−	0.284791i	$-0.908076\pi$
$971$	3.78615e7	−	2.51194e8i	0.0413561	−	0.274380i	0.999946	+	0.0104109i	$0.00331395\pi$
$972$	5.18752e8	+	1.07720e9i	0.564886	+	1.17300i
$973$	6.16449e8	+	1.38717e9i	0.669204	+	1.50589i
$974$	1.02882e9	+	4.95452e8i	1.11343	+	0.536197i
$975$	1.53307e8	+	1.04523e8i	0.165405	+	0.112771i
$976$	−5.49232e6	+	5.91932e6i	−0.00590754	+	0.00636681i
$977$	3.72167e7	−	4.96623e8i	0.0399075	−	0.532528i	−0.941045	−	0.338281i	$-0.890155\pi$
$977$	3.72167e7	−	4.96623e8i	0.0399075	−	0.532528i	0.980953	−	0.194247i	$-0.0622264\pi$
$978$	1.29462e9	+	5.08101e8i	1.38397	+	0.543167i
$979$			4.32718e8i			0.461165i
$980$	−9.31626e8	+	1.53371e8i	−0.989837	+	0.162954i
$981$	3.78118e6			0.00400517
$982$	6.52187e8	−	1.66175e9i	0.688712	−	1.75481i
$983$	−8.28545e8	−	6.20909e7i	−0.872279	−	0.0653683i	−0.368936	−	0.929455i	$-0.620278\pi$
$983$	−8.28545e8	−	6.20909e7i	−0.872279	−	0.0653683i	−0.503343	+	0.864087i	$0.667897\pi$
$984$	3.77087e8	+	3.49885e8i	0.395782	+	0.367232i
$985$	−9.49230e7	+	1.39226e8i	−0.0993260	+	0.145684i
$986$	−2.05011e8	+	4.25710e8i	−0.213869	+	0.444103i
$987$	2.66263e7	+	1.38422e7i	0.0276923	+	0.0143964i
$988$	−2.20228e8	+	1.06056e8i	−0.228351	+	0.109968i
$989$	2.95465e8	+	4.45341e7i	0.305434	+	0.0460367i
$990$	−3.57636e8	−	5.24556e8i	−0.368583	−	0.540612i
$991$	1.40186e9	−	2.11296e8i	1.44040	−	0.217105i	0.618072	−	0.786122i	$-0.287914\pi$
$991$	1.40186e9	−	2.11296e8i	1.44040	−	0.217105i	0.822326	+	0.569017i	$0.192676\pi$
$992$	5.45402e8	+	5.87804e8i	0.558704	+	0.602140i
$993$	−2.94941e8	+	2.35208e8i	−0.301223	+	0.240217i
$994$	−1.06615e9	−	7.75741e8i	−1.08557	−	0.789874i
$995$	4.86947e8	−	6.10612e8i	0.494325	−	0.619864i
$996$	−1.13137e8	−	1.50971e9i	−0.114506	−	1.52797i
$997$	−1.58011e8	+	5.12259e8i	−0.159442	+	0.516897i	−0.999679	−	0.0253210i	$-0.991939\pi$
$997$	−1.58011e8	+	5.12259e8i	−0.159442	+	0.516897i	0.840238	+	0.542218i	$0.182415\pi$
$998$	1.35592e9	−	2.34853e9i	1.36409	−	2.36268i
$999$	1.14616e9	−	6.61735e8i	1.14960	−	0.663724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.h.a.3.4	✓	324
49.33	odd	42	inner	49.7.h.a.33.4	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.h.a.3.4	✓	324	1.1	even	1	trivial
49.7.h.a.33.4	yes	324	49.33	odd	42	inner

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.h (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.73204 + 12.0571i) q^{2} +(-20.1535 - 1.51030i) q^{3} +(-76.0649 - 70.5779i) q^{4} +(43.5678 - 63.9023i) q^{5} +(113.577 - 235.845i) q^{6} +(342.839 + 10.5003i) q^{7} +(464.042 - 223.471i) q^{8} +(-316.975 - 47.7763i) q^{9} +(564.308 + 827.688i) q^{10} +(1954.99 - 294.667i) q^{11} +(1426.38 + 1537.27i) q^{12} +(-744.349 + 593.598i) q^{13} +(-1748.93 + 4083.94i) q^{14} +(-974.556 + 1222.05i) q^{15} +(2.25471 + 30.0870i) q^{16} +(304.791 - 988.107i) q^{17} +(2075.98 - 3595.70i) q^{18} +(-2142.80 + 1237.15i) q^{19} +(-7824.07 + 1785.79i) q^{20} +(-6893.56 - 729.406i) q^{21} +(-5698.28 + 24965.8i) q^{22} +(2384.01 - 735.369i) q^{23} +(-9689.59 + 3802.88i) q^{24} +(3523.11 + 8976.73i) q^{25} +(-3634.75 - 11783.6i) q^{26} +(20679.7 + 4720.01i) q^{27} +(-25336.9 - 24995.6i) q^{28} +(7850.27 + 34394.3i) q^{29} +(-10122.7 - 17533.1i) q^{30} +(21319.6 + 12308.9i) q^{31} +(31125.2 + 9600.85i) q^{32} +(-39844.9 + 2985.96i) q^{33} +(10471.4 + 8350.65i) q^{34} +(15607.8 - 21450.7i) q^{35} +(20738.7 + 26005.5i) q^{36} +(45738.0 - 42438.6i) q^{37} +(-4776.51 - 31690.1i) q^{38} +(15897.7 - 10838.9i) q^{39} +(5937.01 - 39389.5i) q^{40} +(-21442.0 - 44524.8i) q^{41} +(41415.1 - 79664.4i) q^{42} +(107907. + 51965.2i) q^{43} +(-169503. - 115565. i) q^{44} +(-16862.9 + 18173.9i) q^{45} +(-2414.85 + 32223.9i) q^{46} +(-4029.84 - 1581.60i) q^{47} -609.764i q^{48} +(117428. + 7199.82i) q^{49} -124904. q^{50} +(-7634.94 + 19453.5i) q^{51} +(98513.7 + 7382.58i) q^{52} +(-25370.1 - 23540.0i) q^{53} +(-154767. + 227001. i) q^{54} +(66344.7 - 137766. i) q^{55} +(161438. - 71742.1i) q^{56} +(45053.4 - 21696.6i) q^{57} +(-451841. - 68104.1i) q^{58} +(-159216. - 233527. i) q^{59} +(160380. - 24173.3i) q^{60} +(182038. + 196190. i) q^{61} +(-249295. + 198806. i) q^{62} +(-108170. - 19707.9i) q^{63} +(-264248. + 331356. i) q^{64} +(5502.62 + 73427.4i) q^{65} +(152546. - 494542. i) q^{66} +(31587.9 - 54711.9i) q^{67} +(-92922.4 + 53648.8i) q^{68} +(-49156.8 + 11219.7i) q^{69} +(184776. + 289689. i) q^{70} +(-66040.1 + 289341. i) q^{71} +(-157766. + 48664.5i) q^{72} +(609797. - 239328. i) q^{73} +(295251. + 752286. i) q^{74} +(-57445.5 - 186234. i) q^{75} +(250307. + 57130.9i) q^{76} +(673341. - 80495.5i) q^{77} +(55456.3 + 242970. i) q^{78} +(58702.2 + 101675. i) q^{79} +(2020.86 + 1166.74i) q^{80} +(-186337. - 57477.5i) q^{81} +(638302. - 47834.1i) q^{82} +(-564425. - 450114. i) q^{83} +(472878. + 542015. i) q^{84} +(-49863.2 - 62526.5i) q^{85} +(-1.13717e6 + 1.05514e6i) q^{86} +(-106265. - 705022. i) q^{87} +(841348. - 573622. i) q^{88} +(-32620.6 + 216423. i) q^{89} +(-139328. - 289317. i) q^{90} +(-261425. + 195693. i) q^{91} +(-233240. - 112323. i) q^{92} +(-411076. - 280267. i) q^{93} +(38138.8 - 41103.8i) q^{94} +(-14300.7 + 190829. i) q^{95} +(-612782. - 240499. i) q^{96} -1.48393e6i q^{97} +(-642485. + 1.38177e6i) q^{98} -633760. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 13 q^{2} - 11 q^{3} + 819 q^{4} - 179 q^{5} + 770 q^{6} + 392 q^{7} + 828 q^{8} - 1160 q^{9} - 2594 q^{10} - 5305 q^{11} + 7497 q^{12} - 14 q^{13} - 11403 q^{14} - 6196 q^{15} + 27903 q^{16} - 5107 q^{17}+ \cdots - 4449616 q^{99}+O(q^{100}) \) 324 * q - 13 * q^2 - 11 * q^3 + 819 * q^4 - 179 * q^5 + 770 * q^6 + 392 * q^7 + 828 * q^8 - 1160 * q^9 - 2594 * q^10 - 5305 * q^11 + 7497 * q^12 - 14 * q^13 - 11403 * q^14 - 6196 * q^15 + 27903 * q^16 - 5107 * q^17 - 11538 * q^18 - 30006 * q^19 - 50190 * q^20 + 8953 * q^21 + 33042 * q^22 + 54531 * q^23 + 90184 * q^24 - 92804 * q^25 - 93366 * q^26 - 11774 * q^27 - 19180 * q^28 - 80398 * q^29 + 15851 * q^30 + 39378 * q^31 - 197841 * q^32 + 36697 * q^33 - 54698 * q^34 - 819 * q^35 + 706300 * q^36 + 15331 * q^37 - 304462 * q^38 - 179298 * q^39 - 515414 * q^40 - 116046 * q^41 + 1203482 * q^42 - 225018 * q^43 + 1373764 * q^44 + 465772 * q^45 + 1100364 * q^46 + 270021 * q^47 - 767900 * q^49 - 1164040 * q^50 - 1215743 * q^51 - 3954790 * q^52 + 141807 * q^53 - 1093487 * q^54 + 991354 * q^55 - 596680 * q^56 - 388207 * q^57 + 381012 * q^58 + 2015849 * q^59 + 5807298 * q^60 + 258821 * q^61 - 525742 * q^62 - 1265432 * q^63 + 872972 * q^64 - 70154 * q^65 + 497766 * q^66 - 324190 * q^67 - 799617 * q^68 - 2216774 * q^69 + 56140 * q^70 - 1031026 * q^71 + 4633092 * q^72 + 1268305 * q^73 - 1444192 * q^74 - 1699244 * q^75 - 5464011 * q^76 - 2274741 * q^77 - 1285956 * q^78 - 515710 * q^79 + 8314050 * q^80 - 1069027 * q^81 + 357910 * q^82 - 3183054 * q^83 - 10099096 * q^84 - 1596848 * q^85 - 5387681 * q^86 - 4197040 * q^87 - 1024645 * q^88 + 983769 * q^89 + 18547774 * q^90 + 13421086 * q^91 + 5294506 * q^92 + 15477850 * q^93 + 8903632 * q^94 + 5236430 * q^95 + 7804258 * q^96 - 10234553 * q^98 - 4449616 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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