LMFDB - Embedded newform 60.7.l.a.23.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(23,60)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.17
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.11516 - 5.15798i) q^{2} +(20.2023 - 17.9128i) q^{3} +(10.7904 + 63.0838i) q^{4} +(49.4715 - 114.794i) q^{5} +(-215.934 + 5.33675i) q^{6} +(261.181 + 261.181i) q^{7} +(259.400 - 441.424i) q^{8} +(87.2628 - 723.758i) q^{9} +O(q^{10})$	\(q+(-6.11516 - 5.15798i) q^{2} +(20.2023 - 17.9128i) q^{3} +(10.7904 + 63.0838i) q^{4} +(49.4715 - 114.794i) q^{5} +(-215.934 + 5.33675i) q^{6} +(261.181 + 261.181i) q^{7} +(259.400 - 441.424i) q^{8} +(87.2628 - 723.758i) q^{9} +(-894.630 + 446.808i) q^{10} +1357.89 q^{11} +(1348.00 + 1081.15i) q^{12} +(2086.27 + 2086.27i) q^{13} +(-249.996 - 2944.33i) q^{14} +(-1056.84 - 3205.26i) q^{15} +(-3863.13 + 1361.40i) q^{16} +(204.191 + 204.191i) q^{17} +(-4266.76 + 3975.80i) q^{18} +5303.53 q^{19} +(7775.43 + 1882.18i) q^{20} +(9954.93 + 597.963i) q^{21} +(-8303.71 - 7003.97i) q^{22} +(-15716.7 - 15716.7i) q^{23} +(-2666.68 - 13564.4i) q^{24} +(-10730.1 - 11358.0i) q^{25} +(-1996.93 - 23518.8i) q^{26} +(-11201.6 - 16184.7i) q^{27} +(-13658.0 + 19294.5i) q^{28} -2104.69 q^{29} +(-10070.0 + 25051.9i) q^{30} -36742.8i q^{31} +(30645.8 + 11600.8i) q^{32} +(27432.4 - 24323.6i) q^{33} +(-195.447 - 2301.87i) q^{34} +(42902.9 - 17060.9i) q^{35} +(46599.0 - 2304.77i) q^{36} +(-41818.9 + 41818.9i) q^{37} +(-32431.9 - 27355.5i) q^{38} +(79518.3 + 4776.42i) q^{39} +(-37839.8 - 51615.4i) q^{40} +87984.8i q^{41} +(-57791.7 - 55004.0i) q^{42} +(71857.2 - 71857.2i) q^{43} +(14652.2 + 85660.8i) q^{44} +(-78765.8 - 45822.7i) q^{45} +(15043.7 + 177177. i) q^{46} +(-87772.4 + 87772.4i) q^{47} +(-53657.6 + 96702.9i) q^{48} +18781.9i q^{49} +(7031.94 + 124802. i) q^{50} +(7782.75 + 467.487i) q^{51} +(-109098. + 154121. i) q^{52} +(34618.2 - 34618.2i) q^{53} +(-14980.5 + 156750. i) q^{54} +(67176.9 - 155877. i) q^{55} +(183042. - 47541.2i) q^{56} +(107143. - 95001.1i) q^{57} +(12870.5 + 10856.0i) q^{58} +166041. i q^{59} +(190797. - 101255. i) q^{60} +132973. q^{61} +(-189519. + 224688. i) q^{62} +(211823. - 166240. i) q^{63} +(-127567. - 229011. i) q^{64} +(342701. - 136279. i) q^{65} +(-293215. + 7246.71i) q^{66} +(-50730.4 - 50730.4i) q^{67} +(-10677.8 + 15084.4i) q^{68} +(-599043. - 35982.7i) q^{69} +(-350358. - 116963. i) q^{70} +254279. q^{71} +(-296849. - 226263. i) q^{72} +(237265. + 237265. i) q^{73} +(471430. - 40028.1i) q^{74} +(-420227. - 37251.2i) q^{75} +(57227.2 + 334567. i) q^{76} +(354655. + 354655. i) q^{77} +(-461630. - 439362. i) q^{78} +137456. q^{79} +(-34835.3 + 510814. i) q^{80} +(-516211. - 126314. i) q^{81} +(453824. - 538041. i) q^{82} +(-405414. - 405414. i) q^{83} +(69695.9 + 634447. i) q^{84} +(33541.5 - 13338.2i) q^{85} +(-810056. + 68780.1i) q^{86} +(-42519.5 + 37700.9i) q^{87} +(352237. - 599406. i) q^{88} -163824. q^{89} +(245313. + 686486. i) q^{90} +1.08979e6i q^{91} +(821880. - 1.16106e6i) q^{92} +(-658167. - 742288. i) q^{93} +(989471. - 84013.8i) q^{94} +(262374. - 608811. i) q^{95} +(826917. - 314589. i) q^{96} +(-240019. + 240019. i) q^{97} +(96876.7 - 114854. i) q^{98} +(118493. - 982784. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 4 q^{6}+O(q^{10}) $ 136 * q - 4 * q^6	$ 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) $ 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−6.11516	−	5.15798i	−0.764395	−	0.644748i
$2$	−6.11516	−	5.15798i	−0.764395	−	0.644748i
$3$	20.2023	−	17.9128i	0.748232	−	0.663437i
$3$	20.2023	−	17.9128i	0.748232	−	0.663437i
$4$	10.7904	+	63.0838i	0.168600	+	0.985685i
$5$	49.4715	−	114.794i	0.395772	−	0.918349i
$5$	49.4715	−	114.794i	0.395772	−	0.918349i
$6$	−215.934	+	5.33675i	−0.999695	+	0.0247072i
$7$	261.181	+	261.181i	0.761460	+	0.761460i	0.976586	−	0.215126i	$-0.0690162\pi$
$7$	261.181	+	261.181i	0.761460	+	0.761460i	−0.215126	+	0.976586i	$0.569016\pi$
$8$	259.400	−	441.424i	0.506641	−	0.862157i
$9$	87.2628	−	723.758i	0.119702	−	0.992810i
$10$	−894.630	+	446.808i	−0.894630	+	0.446808i
$11$	1357.89			1.02020			0.510101	−	0.860114i	$-0.329608\pi$
$11$	1357.89			1.02020			0.510101	+	0.860114i	$0.329608\pi$
$12$	1348.00	+	1081.15i	0.780092	+	0.625665i
$13$	2086.27	+	2086.27i	0.949599	+	0.949599i	0.998789	−	0.0491908i	$-0.0156642\pi$
$13$	2086.27	+	2086.27i	0.949599	+	0.949599i	−0.0491908	+	0.998789i	$0.515664\pi$
$14$	−249.996	−	2944.33i	−0.0911066	−	1.07301i
$15$	−1056.84	−	3205.26i	−0.313137	−	0.949708i
$16$	−3863.13	+	1361.40i	−0.943148	+	0.332373i
$17$	204.191	+	204.191i	0.0415614	+	0.0415614i	0.727582	−	0.686021i	$-0.240644\pi$
$17$	204.191	+	204.191i	0.0415614	+	0.0415614i	−0.686021	+	0.727582i	$0.740644\pi$
$18$	−4266.76	+	3975.80i	−0.731612	+	0.681721i
$19$	5303.53			0.773222			0.386611	−	0.922243i	$-0.373646\pi$
$19$	5303.53			0.773222			0.386611	+	0.922243i	$0.373646\pi$
$20$	7775.43	+	1882.18i	0.971929	+	0.235273i
$21$	9954.93	+	597.963i	1.07493	+	0.0645678i
$22$	−8303.71	−	7003.97i	−0.779838	−	0.657773i
$23$	−15716.7	−	15716.7i	−1.29175	−	1.29175i	−0.933705	−	0.358044i	$-0.883444\pi$
$23$	−15716.7	−	15716.7i	−1.29175	−	1.29175i	−0.358044	−	0.933705i	$-0.616556\pi$
$24$	−2666.68	−	13564.4i	−0.192902	−	0.981218i
$25$	−10730.1	−	11358.0i	−0.686728	−	0.726914i
$26$	−1996.93	−	23518.8i	−0.113617	−	1.33812i
$27$	−11201.6	−	16184.7i	−0.569102	−	0.822267i
$28$	−13658.0	+	19294.5i	−0.622177	+	0.878942i
$29$	−2104.69			−0.0862968			−0.0431484	−	0.999069i	$-0.513739\pi$
$29$	−2104.69			−0.0862968			−0.0431484	+	0.999069i	$0.513739\pi$
$30$	−10070.0	+	25051.9i	−0.372962	+	0.927847i
$31$		−	36742.8i		−	1.23335i	−0.787216	−	0.616677i	$-0.788479\pi$
$31$		−	36742.8i		−	1.23335i	0.787216	−	0.616677i	$-0.211521\pi$
$32$	30645.8	+	11600.8i	0.935235	+	0.354029i
$33$	27432.4	−	24323.6i	0.763348	−	0.676840i
$34$	−195.447	−	2301.87i	−0.00497270	−	0.0585659i
$35$	42902.9	−	17060.9i	1.00065	−	0.397921i
$36$	46599.0	−	2304.77i	0.998779	−	0.0493993i
$37$	−41818.9	+	41818.9i	−0.825595	+	0.825595i	−0.986904	−	0.161309i	$-0.948428\pi$
$37$	−41818.9	+	41818.9i	−0.825595	+	0.825595i	0.161309	+	0.986904i	$0.448428\pi$
$38$	−32431.9	−	27355.5i	−0.591047	−	0.498533i
$39$	79518.3	+	4776.42i	1.34052	+	0.0805210i
$40$	−37839.8	−	51615.4i	−0.591246	−	0.806491i
$41$			87984.8i			1.27660i	0.769786	+	0.638302i	$0.220363\pi$
$41$			87984.8i			1.27660i	−0.769786	+	0.638302i	$0.779637\pi$
$42$	−57791.7	−	55004.0i	−0.780041	−	0.742414i
$43$	71857.2	−	71857.2i	0.903784	−	0.903784i	−0.0919770	−	0.995761i	$-0.529319\pi$
$43$	71857.2	−	71857.2i	0.903784	−	0.903784i	0.995761	+	0.0919770i	$0.0293186\pi$
$44$	14652.2	+	85660.8i	0.172006	+	1.00560i
$45$	−78765.8	−	45822.7i	−0.864371	−	0.502855i
$46$	15043.7	+	177177.i	0.154554	+	1.82026i
$47$	−87772.4	+	87772.4i	−0.845404	+	0.845404i	−0.989556	−	0.144151i	$-0.953955\pi$
$47$	−87772.4	+	87772.4i	−0.845404	+	0.845404i	0.144151	+	0.989556i	$0.453955\pi$
$48$	−53657.6	+	96702.9i	−0.485185	+	0.874412i
$49$			18781.9i			0.159643i
$50$	7031.94	+	124802.i	0.0562555	+	0.998416i
$51$	7782.75	+	467.487i	0.0586709	+	0.00352418i
$52$	−109098.	+	154121.i	−0.775902	+	1.09611i
$53$	34618.2	−	34618.2i	0.232529	−	0.232529i	−0.581219	−	0.813747i	$-0.697424\pi$
$53$	34618.2	−	34618.2i	0.232529	−	0.232529i	0.813747	+	0.581219i	$0.197424\pi$
$54$	−14980.5	+	156750.i	−0.0951360	+	0.995464i
$55$	67176.9	−	155877.i	0.403768	−	0.936902i
$56$	183042.	−	47541.2i	1.04229	−	0.270711i
$57$	107143.	−	95001.1i	0.578549	−	0.512984i
$58$	12870.5	+	10856.0i	0.0659648	+	0.0556397i
$59$			166041.i			0.808461i	0.914657	+	0.404231i	$0.132461\pi$
$59$			166041.i			0.808461i	−0.914657	+	0.404231i	$0.867539\pi$
$60$	190797.	−	101255.i	0.883317	−	0.468775i
$61$	132973.			0.585833			0.292916	−	0.956138i	$-0.405374\pi$
$61$	132973.			0.585833			0.292916	+	0.956138i	$0.405374\pi$
$62$	−189519.	+	224688.i	−0.795202	+	0.942769i
$63$	211823.	−	166240.i	0.847134	−	0.664837i
$64$	−127567.	−	229011.i	−0.486630	−	0.873608i
$65$	342701.	−	136279.i	1.24789	−	0.496238i
$66$	−293215.	+	7246.71i	−1.01989	+	0.0252063i
$67$	−50730.4	−	50730.4i	−0.168672	−	0.168672i	0.617723	−	0.786396i	$-0.288055\pi$
$67$	−50730.4	−	50730.4i	−0.168672	−	0.168672i	−0.786396	+	0.617723i	$0.788055\pi$
$68$	−10677.8	+	15084.4i	−0.0339591	+	0.0479736i
$69$	−599043.	−	35982.7i	−1.82352	−	0.109533i
$70$	−350358.	−	116963.i	−1.02145	−	0.340999i
$71$	254279.			0.710454			0.355227	−	0.934780i	$-0.384404\pi$
$71$	254279.			0.710454			0.355227	+	0.934780i	$0.384404\pi$
$72$	−296849.	−	226263.i	−0.795312	−	0.606200i
$73$	237265.	+	237265.i	0.609909	+	0.609909i	0.942922	−	0.333014i	$-0.108065\pi$
$73$	237265.	+	237265.i	0.609909	+	0.609909i	−0.333014	+	0.942922i	$0.608065\pi$
$74$	471430.	−	40028.1i	1.16338	−	0.0987801i
$75$	−420227.	−	37251.2i	−0.996094	−	0.0882991i
$76$	57227.2	+	334567.i	0.130365	+	0.762153i
$77$	354655.	+	354655.i	0.776844	+	0.776844i
$78$	−461630.	−	439362.i	−0.972771	−	0.925847i
$79$	137456.			0.278794			0.139397	−	0.990237i	$-0.455484\pi$
$79$	137456.			0.278794			0.139397	+	0.990237i	$0.455484\pi$
$80$	−34835.3	+	510814.i	−0.0680378	+	0.997683i
$81$	−516211.	−	126314.i	−0.971343	−	0.237683i
$82$	453824.	−	538041.i	0.823087	−	0.975829i
$83$	−405414.	−	405414.i	−0.709030	−	0.709030i	0.257301	−	0.966331i	$-0.417167\pi$
$83$	−405414.	−	405414.i	−0.709030	−	0.709030i	−0.966331	+	0.257301i	$0.917167\pi$
$84$	69695.9	+	634447.i	0.117590	+	1.07043i
$85$	33541.5	−	13338.2i	0.0546167	−	0.0217190i
$86$	−810056.	+	68780.1i	−1.27356	+	0.108135i
$87$	−42519.5	+	37700.9i	−0.0645700	+	0.0572525i
$88$	352237.	−	599406.i	0.516876	−	0.879575i
$89$	−163824.			−0.232385			−0.116193	−	0.993227i	$-0.537069\pi$
$89$	−163824.			−0.232385			−0.116193	+	0.993227i	$0.537069\pi$
$90$	245313.	+	686486.i	0.336506	+	0.941681i
$91$			1.08979e6i			1.44616i
$92$	821880.	−	1.16106e6i	1.05547	−	1.49105i
$93$	−658167.	−	742288.i	−0.818253	−	0.922834i
$94$	989471.	−	84013.8i	1.19130	−	0.101150i
$95$	262374.	−	608811.i	0.306020	−	0.710087i
$96$	826917.	−	314589.i	0.934648	−	0.355574i
$97$	−240019.	+	240019.i	−0.262985	+	0.262985i	−0.826266	−	0.563281i	$-0.809539\pi$
$97$	−240019.	+	240019.i	−0.262985	+	0.262985i	0.563281	+	0.826266i	$0.309539\pi$
$98$	96876.7	−	114854.i	0.102930	−	0.122031i
$99$	118493.	−	982784.i	0.122120	−	1.01287i
$100$	600726.	−	799455.i	0.600726	−	0.799455i
$101$			743832.i			0.721956i	0.932574	+	0.360978i	$0.117557\pi$
$101$			743832.i			0.721956i	−0.932574	+	0.360978i	$0.882443\pi$
$102$	−45181.5	−	43002.1i	−0.0425755	−	0.0405218i
$103$	−210242.	+	210242.i	−0.192401	+	0.192401i	−0.796733	−	0.604332i	$-0.793440\pi$
$103$	−210242.	+	210242.i	−0.192401	+	0.192401i	0.604332	+	0.796733i	$0.293440\pi$
$104$	1.46211e6	−	379751.i	1.29981	−	0.337597i
$105$	561128.	−	1.11318e6i	0.484723	−	0.961606i
$106$	−390256.	+	33135.7i	−0.327666	+	0.0278214i
$107$	−771000.	+	771000.i	−0.629365	+	0.629365i	−0.947908	−	0.318543i	$-0.896806\pi$
$107$	−771000.	+	771000.i	−0.629365	+	0.629365i	0.318543	+	0.947908i	$0.396806\pi$
$108$	900121.	−	881281.i	0.714545	−	0.699589i
$109$			1.80615e6i			1.39468i	0.716742	+	0.697339i	$0.245633\pi$
$109$			1.80615e6i			1.39468i	−0.716742	+	0.697339i	$0.754367\pi$
$110$	−1.21481e6	+	606716.i	−0.912704	+	0.455834i
$111$	−95742.5	+	1.59393e6i	−0.0700061	+	1.16547i
$112$	−1.36455e6	−	653405.i	−0.971258	−	0.465081i
$113$	340132.	−	340132.i	0.235728	−	0.235728i	−0.579350	−	0.815079i	$-0.696694\pi$
$113$	340132.	−	340132.i	0.235728	−	0.235728i	0.815079	+	0.579350i	$0.196694\pi$
$114$	−1.14521e6	+	28303.6i	−0.772986	+	0.0191041i
$115$	−2.58171e6	+	1.02665e6i	−1.69751	+	0.675037i
$116$	−22710.5	−	132772.i	−0.0145496	−	0.0850614i
$117$	1.69201e6	−	1.32790e6i	1.05644	−	0.829102i
$118$	856436.	−	1.01537e6i	0.521254	−	0.617984i
$119$			106662.i			0.0632947i
$120$	−1.68903e6	−	364932.i	−0.977446	−	0.211188i
$121$	72302.8			0.0408130
$122$	−813151.	−	685872.i	−0.447808	−	0.377715i
$123$	1.57605e6	+	1.77749e6i	0.846946	+	0.955195i
$124$	2.31788e6	−	396470.i	1.21570	−	0.207943i
$125$	−1.83467e6	+	669851.i	−0.939349	+	0.342964i
$126$	−2.15280e6	−	75993.5i	−1.07620	−	0.0379896i
$127$	−1.33395e6	−	1.33395e6i	−0.651223	−	0.651223i	0.302064	−	0.953288i	$-0.402324\pi$
$127$	−1.33395e6	−	1.33395e6i	−0.651223	−	0.651223i	−0.953288	+	0.302064i	$0.902324\pi$
$128$	−401143.	+	2.05843e6i	−0.191280	+	0.981536i
$129$	164514.	−	2.73884e6i	0.0766361	−	1.27584i
$130$	−2.79860e6	−	934277.i	−1.27383	−	0.425251i
$131$	1.57927e6			0.702492			0.351246	−	0.936283i	$-0.385758\pi$
$131$	1.57927e6			0.702492			0.351246	+	0.936283i	$0.385758\pi$
$132$	1.83043e6	+	1.46808e6i	0.795852	+	0.638305i
$133$	1.38518e6	+	1.38518e6i	0.588778	+	0.588778i
$134$	48558.0	+	571891.i	0.0201812	+	0.237683i
$135$	−2.41206e6	+	485195.i	−0.980363	+	0.197204i
$136$	143102.	−	37167.7i	0.0568891	−	0.0147757i
$137$	−1.33644e6	−	1.33644e6i	−0.519743	−	0.519743i	0.397750	−	0.917494i	$-0.369791\pi$
$137$	−1.33644e6	−	1.33644e6i	−0.519743	−	0.519743i	−0.917494	+	0.397750i	$0.869791\pi$
$138$	3.47765e6	+	3.30990e6i	1.32327	+	1.25944i
$139$	2.24891e6			0.837391			0.418695	−	0.908127i	$-0.362487\pi$
$139$	2.24891e6			0.837391			0.418695	+	0.908127i	$0.362487\pi$
$140$	1.53920e6	+	2.52239e6i	0.560934	+	0.919237i
$141$	−200951.	+	3.34545e6i	−0.0716858	+	1.19343i
$142$	−1.55496e6	−	1.31157e6i	−0.543067	−	0.458064i
$143$	2.83292e6	+	2.83292e6i	0.968783	+	0.968783i
$144$	648216.	+	2.91478e6i	0.217086	+	0.976152i
$145$	−104122.	+	241605.i	−0.0341539	+	0.0792505i
$146$	−227105.	−	2.67472e6i	−0.0729738	−	0.859448i
$147$	336436.	+	379437.i	0.105913	+	0.119450i
$148$	−3.08934e6	−	2.18685e6i	−0.952971	−	0.674581i
$149$	2.75801e6			0.833752			0.416876	−	0.908963i	$-0.363125\pi$
$149$	2.75801e6			0.833752			0.416876	+	0.908963i	$0.363125\pi$
$150$	2.37762e6	+	2.39532e6i	0.704479	+	0.709725i
$151$			4.52508e6i			1.31430i	0.753759	+	0.657151i	$0.228238\pi$
$151$			4.52508e6i			1.31430i	−0.753759	+	0.657151i	$0.771762\pi$
$152$	1.37574e6	−	2.34111e6i	0.391746	−	0.666639i
$153$	165603.	−	129967.i	0.0462375	−	0.0362875i
$154$	−339468.	−	3.99807e6i	−0.0929472	−	1.09468i
$155$	−4.21784e6	−	1.81772e6i	−1.13265	−	0.488127i
$156$	556719.	+	5.06785e6i	0.146643	+	1.33490i
$157$	−4.29058e6	+	4.29058e6i	−1.10871	+	1.10871i	−0.115388	+	0.993321i	$0.536811\pi$
$157$	−4.29058e6	+	4.29058e6i	−1.10871	+	1.10871i	−0.993321	+	0.115388i	$0.963189\pi$
$158$	−840566.	−	708996.i	−0.213108	−	0.179752i
$159$	79256.8	−	1.31947e6i	0.0197172	−	0.328254i
$160$	2.84779e6	−	2.94403e6i	0.695262	−	0.718757i
$161$		−	8.20980e6i		−	1.96723i
$162$	2.50519e6	+	3.43504e6i	0.589244	+	0.807955i
$163$	4.93975e6	−	4.93975e6i	1.14062	−	1.14062i	0.152288	−	0.988336i	$-0.451336\pi$
$163$	4.93975e6	−	4.93975e6i	1.14062	−	1.14062i	0.988336	−	0.152288i	$-0.0486641\pi$
$164$	−5.55042e6	+	949391.i	−1.25833	+	0.215235i
$165$	−1.43507e6	−	4.35239e6i	−0.319463	−	0.968894i
$166$	388053.	+	4.57029e6i	0.0848334	+	0.999125i
$167$	−2.31273e6	+	2.31273e6i	−0.496565	+	0.496565i	−0.910367	−	0.413802i	$-0.864201\pi$
$167$	−2.31273e6	+	2.31273e6i	−0.496565	+	0.496565i	0.413802	+	0.910367i	$0.364201\pi$
$168$	2.84627e6	−	4.23924e6i	0.600271	−	0.894046i
$169$			3.87822e6i			0.803475i
$170$	−273909.	−	91441.2i	−0.0557520	−	0.0186121i
$171$	462801.	−	3.83847e6i	0.0925563	−	0.767662i
$172$	5.30839e6	+	3.75766e6i	1.04322	+	0.738468i
$173$	−4.57544e6	+	4.57544e6i	−0.883679	+	0.883679i	−0.993906	−	0.110228i	$-0.964842\pi$
$173$	−4.57544e6	+	4.57544e6i	−0.883679	+	0.883679i	0.110228	+	0.993906i	$0.464842\pi$
$174$	454475.	−	11232.2i	0.0862704	−	0.00213215i
$175$	163996.	−	5.76901e6i	0.0305998	−	1.07643i
$176$	−5.24571e6	+	1.84863e6i	−0.962202	+	0.339088i
$177$	2.97426e6	+	3.35440e6i	0.536363	+	0.604916i
$178$	1.00181e6	+	845004.i	0.177634	+	0.149830i
$179$		−	7.83869e6i		−	1.36674i	−0.730074	−	0.683368i	$-0.760515\pi$
$179$		−	7.83869e6i		−	1.36674i	0.730074	−	0.683368i	$-0.239485\pi$
$180$	2.04075e6	−	5.46329e6i	0.349923	−	0.936778i
$181$	2.09945e6			0.354054			0.177027	−	0.984206i	$-0.443352\pi$
$181$	2.09945e6			0.354054			0.177027	+	0.984206i	$0.443352\pi$
$182$	5.62110e6	−	6.66422e6i	0.932411	−	1.10544i
$183$	2.68635e6	−	2.38192e6i	0.438339	−	0.388663i
$184$	−1.10147e7	+	2.86082e6i	−1.76814	+	0.459237i
$185$	2.73169e6	+	6.86938e6i	0.431436	+	1.08493i
$186$	196087.	+	7.93403e6i	0.0304727	+	1.23298i
$187$	277269.	+	277269.i	0.0424010	+	0.0424010i
$188$	−6.48412e6	−	4.58992e6i	−0.975837	−	0.690767i
$189$	1.30148e6	−	7.15278e6i	0.192775	−	1.05947i
$190$	−4.74470e6	+	2.36966e6i	−0.691747	+	0.345482i
$191$	7.85594e6			1.12745			0.563726	−	0.825962i	$-0.309367\pi$
$191$	7.85594e6			1.12745			0.563726	+	0.825962i	$0.309367\pi$
$192$	−6.67938e6	−	2.34146e6i	−0.943696	−	0.330814i
$193$	942578.	+	942578.i	0.131113	+	0.131113i	0.769618	−	0.638505i	$-0.220447\pi$
$193$	942578.	+	942578.i	0.131113	+	0.131113i	−0.638505	+	0.769618i	$0.720447\pi$
$194$	2.70577e6	−	229741.i	0.370583	−	0.0314654i
$195$	4.48219e6	−	8.89189e6i	0.604487	−	1.19920i
$196$	−1.18483e6	+	202664.i	−0.157358	+	0.0269159i
$197$	−9.30389e6	−	9.30389e6i	−1.21693	−	1.21693i	−0.968701	−	0.248230i	$-0.920151\pi$
$197$	−9.30389e6	−	9.30389e6i	−1.21693	−	1.21693i	−0.248230	−	0.968701i	$-0.579849\pi$
$198$	−5.79379e6	+	5.39870e6i	−0.746392	+	0.695494i
$199$	−1.61487e6			−0.204917			−0.102458	−	0.994737i	$-0.532671\pi$
$199$	−1.61487e6			−0.204917			−0.102458	+	0.994737i	$0.532671\pi$
$200$	−7.79711e6	+	1.79027e6i	−0.974639	+	0.223783i
$201$	−1.93359e6	−	116145.i	−0.238110	−	0.0143025i
$202$	3.83667e6	−	4.54865e6i	0.465480	−	0.551860i
$203$	−549705.	−	549705.i	−0.0657116	−	0.0657116i
$204$	54488.2	+	496010.i	0.00641818	+	0.0584252i
$205$	1.01001e7	+	4.35274e6i	1.17237	+	0.505244i
$206$	2.37009e6	−	201239.i	0.271120	−	0.0230202i
$207$	−1.27466e7	+	1.00036e7i	−1.43709	+	1.12784i
$208$	−1.08998e7	−	5.21929e6i	−1.21123	−	0.579991i
$209$	7.20160e6			0.788843
$210$	−9.17315e6	+	3.91298e6i	−0.990514	+	0.422523i
$211$		−	1.30393e7i		−	1.38806i	−0.719946	−	0.694030i	$-0.755834\pi$
$211$		−	1.30393e7i		−	1.38806i	0.719946	−	0.694030i	$-0.244166\pi$
$212$	2.55739e6	+	1.81030e6i	0.268404	+	0.189996i
$213$	5.13702e6	−	4.55485e6i	0.531584	−	0.471342i
$214$	8.69159e6	−	737984.i	0.886866	−	0.0753018i
$215$	−4.69386e6	−	1.18036e7i	−0.472296	−	1.18768i
$216$	−1.00500e7	+	746366.i	−0.997254	+	0.0740612i
$217$	9.59653e6	−	9.59653e6i	0.939150	−	0.939150i
$218$	9.31608e6	−	1.10449e7i	0.899216	−	1.06608i
$219$	9.04336e6	+	543208.i	0.860989	+	0.0517170i
$220$	1.05582e7	+	2.55580e6i	0.991565	+	0.240026i
$221$			851994.i			0.0789332i
$222$	8.80694e6	−	9.25329e6i	0.804945	−	0.845741i
$223$	−3.41634e6	+	3.41634e6i	−0.308068	+	0.308068i	−0.844160	−	0.536092i	$-0.819900\pi$
$223$	−3.41634e6	+	3.41634e6i	−0.308068	+	0.308068i	0.536092	+	0.844160i	$0.319900\pi$
$224$	4.97418e6	+	1.10340e7i	0.442565	+	0.981723i
$225$	−9.15681e6	+	6.77489e6i	−0.803890	+	0.594778i
$226$	−3.83436e6	+	325567.i	−0.332175	+	0.0282043i
$227$	−1.05014e7	+	1.05014e7i	−0.897775	+	0.897775i	−0.995239	−	0.0974638i	$-0.968927\pi$
$227$	−1.05014e7	+	1.05014e7i	−0.897775	+	0.897775i	0.0974638	+	0.995239i	$0.468927\pi$
$228$	7.14915e6	+	5.73391e6i	0.603184	+	0.483778i
$229$			1.14312e7i			0.951884i	0.879477	+	0.475942i	$0.157893\pi$
$229$			1.14312e7i			0.951884i	−0.879477	+	0.475942i	$0.842107\pi$
$230$	2.10830e7	+	7.03829e6i	1.73280	+	0.578474i
$231$	1.35177e7	+	811967.i	1.09665	+	0.0658722i
$232$	−545958.	+	929063.i	−0.0437215	+	0.0744014i
$233$	−4.98284e6	+	4.98284e6i	−0.393921	+	0.393921i	−0.876082	−	0.482162i	$-0.839852\pi$
$233$	−4.98284e6	+	4.98284e6i	−0.393921	+	0.393921i	0.482162	+	0.876082i	$0.339852\pi$
$234$	−1.71962e7	−	607023.i	−1.34210	−	0.0473759i
$235$	5.73347e6	+	1.44179e7i	0.441788	+	1.11096i
$236$	−1.04745e7	+	1.79165e6i	−0.796888	+	0.136307i
$237$	2.77692e6	−	2.46222e6i	0.208602	−	0.184962i
$238$	550159.	−	652253.i	0.0408091	−	0.0483821i
$239$			1.44812e7i			1.06075i	0.847765	+	0.530373i	$0.177948\pi$
$239$			1.44812e7i			1.06075i	−0.847765	+	0.530373i	$0.822052\pi$
$240$	8.44635e6	+	1.09436e7i	0.610992	+	0.791637i
$241$	−6.61637e6			−0.472682			−0.236341	−	0.971670i	$-0.575948\pi$
$241$	−6.61637e6			−0.472682			−0.236341	+	0.971670i	$0.575948\pi$
$242$	−442143.	−	372937.i	−0.0311973	−	0.0263141i
$243$	−1.26913e7	+	6.69496e6i	−0.884477	+	0.466583i
$244$	1.43483e6	+	8.38844e6i	0.0987714	+	0.577446i
$245$	2.15604e6	+	929169.i	0.146608	+	0.0631825i
$246$	−469553.	−	1.89989e7i	−0.0315413	−	1.27621i
$247$	1.10646e7	+	1.10646e7i	0.734250	+	0.734250i
$248$	−1.62192e7	−	9.53110e6i	−1.06334	−	0.624868i
$249$	−1.54524e7	−	928178.i	−1.00092	−	0.0601220i
$250$	1.46744e7	+	5.36693e6i	0.939159	+	0.343483i
$251$	1.42028e7			0.898157			0.449079	−	0.893492i	$-0.351752\pi$
$251$	1.42028e7			0.898157			0.449079	+	0.893492i	$0.351752\pi$
$252$	1.27727e7	+	1.15688e7i	0.798146	+	0.722915i
$253$	−2.13415e7	−	2.13415e7i	−1.31785	−	1.31785i
$254$	1.27683e6	+	1.50379e7i	0.0779170	+	0.917667i
$255$	438689.	−	870283.i	0.0264568	−	0.0524856i
$256$	1.30704e7	−	1.05185e7i	0.779057	−	0.626954i
$257$	5.64731e6	+	5.64731e6i	0.332692	+	0.332692i	0.853608	−	0.520916i	$-0.174410\pi$
$257$	5.64731e6	+	5.64731e6i	0.332692	+	0.332692i	−0.520916	+	0.853608i	$0.674410\pi$
$258$	−1.51329e7	+	1.58999e7i	−0.881178	+	0.925838i
$259$	−2.18446e7			−1.25732
$260$	1.22949e7	+	2.01484e7i	0.699528	+	1.14636i
$261$	−183661.	+	1.52329e6i	−0.0103299	+	0.0856763i
$262$	−9.65747e6	−	8.14583e6i	−0.536982	−	0.452930i
$263$	2.30697e7	+	2.30697e7i	1.26816	+	1.26816i	0.947036	+	0.321126i	$0.104061\pi$
$263$	2.30697e7	+	2.30697e7i	1.26816	+	1.26816i	0.321126	+	0.947036i	$0.395939\pi$
$264$	−3.62105e6	−	1.84189e7i	−0.196799	−	1.00104i
$265$	−2.26133e6	−	5.68656e6i	−0.121514	−	0.305571i
$266$	−1.32586e6	−	1.56153e7i	−0.0704456	−	0.829672i
$267$	−3.30962e6	+	2.93456e6i	−0.173878	+	0.154173i
$268$	2.65287e6	−	3.74767e6i	0.137820	−	0.194696i
$269$	6.26139e6			0.321673			0.160836	−	0.986981i	$-0.448581\pi$
$269$	6.26139e6			0.321673			0.160836	+	0.986981i	$0.448581\pi$
$270$	1.72528e7	+	9.47432e6i	0.876531	+	0.481345i
$271$		−	9.47777e6i		−	0.476210i	−0.971239	−	0.238105i	$-0.923474\pi$
$271$		−	9.47777e6i		−	0.476210i	0.971239	−	0.238105i	$-0.0765262\pi$
$272$	−1.06680e6	−	510832.i	−0.0530124	−	0.0253846i
$273$	1.95211e7	+	2.20162e7i	0.959438	+	1.08207i
$274$	1.27921e6	+	1.50659e7i	0.0621858	+	0.732393i
$275$	−1.45703e7	−	1.54230e7i	−0.700602	−	0.741600i
$276$	−4.19399e6	−	3.81782e7i	−0.199480	−	1.81588i
$277$	−2.37799e7	+	2.37799e7i	−1.11885	+	1.11885i	−0.126934	+	0.991911i	$0.540514\pi$
$277$	−2.37799e7	+	2.37799e7i	−1.11885	+	1.11885i	−0.991911	+	0.126934i	$0.959486\pi$
$278$	−1.37525e7	−	1.15999e7i	−0.640098	−	0.539906i
$279$	−2.65929e7	−	3.20628e6i	−1.22449	−	0.147635i
$280$	3.59794e6	−	2.33640e7i	0.163900	−	1.06432i
$281$			2.20213e7i			0.992484i	0.868184	+	0.496242i	$0.165287\pi$
$281$			2.20213e7i			0.992484i	−0.868184	+	0.496242i	$0.834713\pi$
$282$	1.84846e7	−	1.94215e7i	0.824259	−	0.866034i
$283$	−2.67713e7	+	2.67713e7i	−1.18116	+	1.18116i	−0.201718	+	0.979444i	$0.564653\pi$
$283$	−2.67713e7	+	2.67713e7i	−1.18116	+	1.18116i	−0.979444	+	0.201718i	$0.935347\pi$
$284$	2.74378e6	+	1.60409e7i	0.119783	+	0.700283i
$285$	−5.60497e6	−	1.69992e7i	−0.242124	−	0.734335i
$286$	−2.71161e6	−	3.19359e7i	−0.115912	−	1.36515i
$287$	−2.29799e7	+	2.29799e7i	−0.972083	+	0.972083i
$288$	1.10704e7	−	2.11678e7i	0.463433	−	0.886132i
$289$		−	2.40542e7i		−	0.996545i
$290$	1.88292e6	−	940393.i	0.0772037	−	0.0385581i
$291$	−549514.	+	9.14835e6i	−0.0222997	+	0.371248i
$292$	−1.24074e7	+	1.75277e7i	−0.498347	+	0.704008i
$293$	2.09288e7	−	2.09288e7i	0.832036	−	0.832036i	−0.155759	−	0.987795i	$-0.549782\pi$
$293$	2.09288e7	−	2.09288e7i	0.832036	−	0.832036i	0.987795	+	0.155759i	$0.0497825\pi$
$294$	−100234.	−	4.05565e6i	−0.00394434	−	0.159595i
$295$	1.90604e7	+	8.21430e6i	0.742449	+	0.319967i
$296$	7.61204e6	+	2.93077e7i	0.293512	+	1.13007i
$297$	−1.52106e7	−	2.19770e7i	−0.580599	−	0.838879i
$298$	−1.68657e7	−	1.42258e7i	−0.637316	−	0.537560i
$299$		−	6.55785e7i		−	2.45329i
$300$	−2.18447e6	−	2.69115e7i	−0.0809064	−	0.996722i
$301$	3.75354e7			1.37639
$302$	2.33403e7	−	2.76716e7i	0.847393	−	1.00465i
$303$	1.33241e7	+	1.50271e7i	0.478973	+	0.540191i
$304$	−2.04882e7	+	7.22022e6i	−0.729263	+	0.256998i
$305$	6.57838e6	−	1.52644e7i	0.231856	−	0.537999i
$306$	−1.68306e6	−	59411.7i	−0.0587401	−	0.00207352i
$307$	−5.30818e6	−	5.30818e6i	−0.183455	−	0.183455i	0.609404	−	0.792860i	$-0.291409\pi$
$307$	−5.30818e6	−	5.30818e6i	−0.183455	−	0.183455i	−0.792860	+	0.609404i	$0.791409\pi$
$308$	−1.85461e7	+	2.61998e7i	−0.634747	+	0.896699i
$309$	−481340.	+	8.01338e6i	−0.0163146	+	0.271606i
$310$	1.64170e7	+	3.28712e7i	0.551072	+	1.10339i
$311$	713162.			0.0237087			0.0118543	−	0.999930i	$-0.496227\pi$
$311$	713162.			0.0237087			0.0118543	+	0.999930i	$0.496227\pi$
$312$	2.27355e7	−	3.38623e7i	0.748584	−	1.11494i
$313$	−1.25351e7	−	1.25351e7i	−0.408786	−	0.408786i	0.472529	−	0.881315i	$-0.343341\pi$
$313$	−1.25351e7	−	1.25351e7i	−0.408786	−	0.408786i	−0.881315	+	0.472529i	$0.843341\pi$
$314$	4.83684e7	−	4.10685e6i	1.56233	−	0.132654i
$315$	−8.60411e6	−	3.25401e7i	−0.275280	−	1.04109i
$316$	1.48321e6	+	8.67125e6i	0.0470046	+	0.274802i
$317$	4.04787e7	+	4.04787e7i	1.27072	+	1.27072i	0.945713	+	0.325004i	$0.105366\pi$
$317$	4.04787e7	+	4.04787e7i	1.27072	+	1.27072i	0.325004	+	0.945713i	$0.394634\pi$
$318$	−7.29049e6	+	7.65999e6i	−0.226713	+	0.238203i
$319$	−2.85794e6			−0.0880402
$320$	−3.26000e7	+	3.31434e6i	−0.994872	+	0.101146i
$321$	−1.76517e6	+	2.93867e7i	−0.0533669	+	0.888456i
$322$	−4.23460e7	+	5.02043e7i	−1.26837	+	1.50374i
$323$	1.08293e6	+	1.08293e6i	0.0321362	+	0.0321362i
$324$	2.39827e6	−	3.39276e7i	0.0705119	−	0.997511i
$325$	1.30997e6	−	4.60818e7i	0.0381602	−	1.34239i
$326$	−5.56866e7	+	4.72822e6i	−1.60730	+	0.136472i
$327$	3.23532e7	+	3.64883e7i	0.925281	+	1.04354i
$328$	3.88386e7	+	2.28233e7i	1.10063	+	0.646780i
$329$	−4.58489e7			−1.28748
$330$	−1.36739e7	+	3.40177e7i	−0.380497	+	0.946591i
$331$			1.40494e6i			0.0387412i	0.999812	+	0.0193706i	$0.00616625\pi$
$331$			1.40494e6i			0.0387412i	−0.999812	+	0.0193706i	$0.993834\pi$
$332$	2.12005e7	−	2.99496e7i	0.579337	−	0.818422i
$333$	2.66175e7	+	3.39160e7i	0.720833	+	0.918484i
$334$	2.60718e7	−	2.21370e6i	0.699731	−	0.0594126i
$335$	−8.33324e6	+	3.31381e6i	−0.221656	+	0.0881442i
$336$	−3.92713e7	+	1.12426e7i	−1.03528	+	0.296381i
$337$	1.08562e7	−	1.08562e7i	0.283653	−	0.283653i	−0.550911	−	0.834564i	$-0.685720\pi$
$337$	1.08562e7	−	1.08562e7i	0.283653	−	0.283653i	0.834564	+	0.550911i	$0.185720\pi$
$338$	2.00038e7	−	2.37159e7i	0.518039	−	0.614172i
$339$	778718.	−	1.29642e7i	0.0199885	−	0.332771i
$340$	1.20335e6	+	1.97200e6i	0.0306164	+	0.0501730i
$341$		−	4.98927e7i		−	1.25827i
$342$	−2.26289e7	+	2.10858e7i	−0.565698	+	0.527122i
$343$	2.58222e7	−	2.58222e7i	0.639898	−	0.639898i
$344$	−1.30797e7	−	5.03593e7i	−0.321310	−	1.23710i
$345$	−3.37662e7	+	6.69862e7i	−0.822289	+	1.63128i
$346$	5.15796e7	−	4.37951e6i	1.24523	−	0.105730i
$347$	1.64334e7	−	1.64334e7i	0.393315	−	0.393315i	−0.482552	−	0.875867i	$-0.660290\pi$
$347$	1.64334e7	−	1.64334e7i	0.393315	−	0.393315i	0.875867	+	0.482552i	$0.160290\pi$
$348$	−2.83712e6	−	2.27549e6i	−0.0673194	−	0.0539929i
$349$		−	1.55948e6i		−	0.0366863i	−0.999832	−	0.0183432i	$-0.994161\pi$
$349$		−	1.55948e6i		−	0.0366863i	0.999832	−	0.0183432i	$-0.00583913\pi$
$350$	−3.07593e7	+	3.44325e7i	−0.717418	+	0.803091i
$351$	1.03960e7	−	5.71352e7i	0.240405	−	1.32124i
$352$	4.16136e7	+	1.57526e7i	0.954129	+	0.361181i
$353$	−2.94741e7	+	2.94741e7i	−0.670065	+	0.670065i	−0.957731	−	0.287666i	$-0.907121\pi$
$353$	−2.94741e7	+	2.94741e7i	−0.670065	+	0.670065i	0.287666	+	0.957731i	$0.407121\pi$
$354$	−886119.	−	3.58539e7i	−0.0199748	−	0.808214i
$355$	1.25796e7	−	2.91896e7i	0.281178	−	0.652444i
$356$	−1.76773e6	−	1.03347e7i	−0.0391802	−	0.229059i
$357$	1.91061e6	+	2.15480e6i	0.0419920	+	0.0473591i
$358$	−4.04318e7	+	4.79349e7i	−0.881200	+	1.04473i
$359$			5.84946e7i			1.26425i	0.774867	+	0.632124i	$0.217817\pi$
$359$			5.84946e7i			1.26425i	−0.774867	+	0.632124i	$0.782183\pi$
$360$	−4.06591e7	+	2.28827e7i	−0.871466	+	0.490456i
$361$	−1.89185e7			−0.402128
$362$	−1.28385e7	−	1.08289e7i	−0.270637	−	0.228276i
$363$	1.46068e6	−	1.29515e6i	0.0305376	−	0.0270769i
$364$	−6.87479e7	+	1.17592e7i	−1.42546	+	0.243823i
$365$	3.89743e7	−	1.54986e7i	0.801494	−	0.318724i
$366$	−2.87134e7	+	709643.i	−0.585654	+	0.0144743i
$367$	−2.14583e7	−	2.14583e7i	−0.434108	−	0.434108i	0.455915	−	0.890023i	$-0.349312\pi$
$367$	−2.14583e7	−	2.14583e7i	−0.434108	−	0.434108i	−0.890023	+	0.455915i	$0.849312\pi$
$368$	8.21125e7	+	3.93190e7i	1.64765	+	0.788968i
$369$	6.36797e7	+	7.67780e6i	1.26742	+	0.152812i
$370$	1.87274e7	−	5.60974e7i	0.369720	−	1.10748i
$371$	1.80832e7			0.354123
$372$	3.97245e7	−	4.95293e7i	0.771666	−	0.962129i
$373$	−3.74921e7	−	3.74921e7i	−0.722459	−	0.722459i	0.246646	−	0.969106i	$-0.420671\pi$
$373$	−3.74921e7	−	3.74921e7i	−0.722459	−	0.722459i	−0.969106	+	0.246646i	$0.920671\pi$
$374$	−265395.	−	3.12569e6i	−0.00507316	−	0.0597491i
$375$	−2.50655e7	+	4.63965e7i	−0.475316	+	0.879815i
$376$	1.59767e7	+	6.15131e7i	0.300555	+	1.15719i
$377$	−4.39095e6	−	4.39095e6i	−0.0819473	−	0.0819473i
$378$	−4.48527e7	+	3.70274e7i	−0.830449	+	0.685564i
$379$	4.92407e7			0.904495			0.452248	−	0.891892i	$-0.350622\pi$
$379$	4.92407e7			0.904495			0.452248	+	0.891892i	$0.350622\pi$
$380$	4.12372e7	+	9.98222e6i	0.751517	+	0.181918i
$381$	−5.08438e7	−	3.05403e6i	−0.919312	−	0.0552203i
$382$	−4.80404e7	−	4.05208e7i	−0.861819	−	0.726923i
$383$	1.15608e7	+	1.15608e7i	0.205775	+	0.205775i	0.802469	−	0.596694i	$-0.203519\pi$
$383$	1.15608e7	+	1.15608e7i	0.205775	+	0.205775i	−0.596694	+	0.802469i	$0.703519\pi$
$384$	2.87682e7	+	4.87705e7i	0.508065	+	0.861318i
$385$	5.82574e7	−	2.31668e7i	1.02087	−	0.405960i
$386$	−902215.	−	1.06258e7i	−0.0156873	−	0.184757i
$387$	−4.57368e7	−	5.82777e7i	−0.789101	−	1.00547i
$388$	−1.77312e7	−	1.25514e7i	−0.303559	−	0.214881i
$389$	−9.27101e7			−1.57499			−0.787496	−	0.616320i	$-0.788623\pi$
$389$	−9.27101e7			−1.57499			−0.787496	+	0.616320i	$0.788623\pi$
$390$	−7.32736e7	+	3.12562e7i	−1.23525	+	0.526918i
$391$		−	6.41842e6i		−	0.107374i
$392$	8.29078e6	+	4.87203e6i	0.137638	+	0.0808819i
$393$	3.19048e7	−	2.82891e7i	0.525627	−	0.466059i
$394$	8.90548e6	+	1.04884e8i	0.145602	+	1.71483i
$395$	6.80016e6	−	1.57791e7i	0.110339	−	0.256030i
$396$	6.32763e7	−	3.12963e6i	1.01896	−	0.0503972i
$397$	−1.34098e7	+	1.34098e7i	−0.214314	+	0.214314i	−0.806097	−	0.591783i	$-0.798424\pi$
$397$	−1.34098e7	+	1.34098e7i	−0.214314	+	0.214314i	0.591783	+	0.806097i	$0.298424\pi$
$398$	9.87517e6	+	8.32946e6i	0.156637	+	0.132120i
$399$	5.27962e7	+	3.17131e6i	0.831159	+	0.0499252i
$400$	5.69148e7	+	2.92696e7i	0.889293	+	0.457338i
$401$		−	6.24439e6i		−	0.0968405i	−0.998827	−	0.0484203i	$-0.984581\pi$
$401$		−	6.24439e6i		−	0.0968405i	0.998827	−	0.0484203i	$-0.0154187\pi$
$402$	1.12252e7	+	1.06837e7i	0.172788	+	0.164453i
$403$	7.66554e7	−	7.66554e7i	1.17119	−	1.17119i
$404$	−4.69238e7	+	8.02625e6i	−0.711621	+	0.121722i
$405$	−4.00379e7	+	5.30088e7i	−0.602706	+	0.797963i
$406$	526166.	+	6.19691e6i	0.00786220	+	0.0925970i
$407$	−5.67854e7	+	5.67854e7i	−0.842274	+	0.842274i
$408$	2.22521e6	−	3.31423e6i	0.0327635	−	0.0487980i
$409$			4.69396e7i			0.686071i	0.939322	+	0.343036i	$0.111455\pi$
$409$			4.69396e7i			0.686071i	−0.939322	+	0.343036i	$0.888545\pi$
$410$	−3.93123e7	−	7.87138e7i	−0.570396	−	1.14209i
$411$	−5.09386e7	−	3.05973e6i	−0.733706	−	0.0440715i
$412$	−1.55314e7	−	1.09943e7i	−0.222085	−	0.157208i
$413$	−4.33667e7	+	4.33667e7i	−0.615611	+	0.615611i
$414$	1.29546e8	+	4.57295e6i	1.82567	+	0.0644460i
$415$	−6.65954e7	+	2.64825e7i	−0.931751	+	0.370522i
$416$	3.97329e7	+	8.81377e7i	0.551912	+	1.22428i
$417$	4.54331e7	−	4.02843e7i	0.626563	−	0.555556i
$418$	−4.40390e7	−	3.71458e7i	−0.602988	−	0.508605i
$419$		−	4.27331e7i		−	0.580928i	−0.956886	−	0.290464i	$-0.906190\pi$
$419$		−	4.27331e7i		−	0.580928i	0.956886	−	0.290464i	$-0.0938097\pi$
$420$	7.62784e7	+	2.33864e7i	1.02956	+	0.315657i
$421$	7.23166e7			0.969152			0.484576	−	0.874749i	$-0.338974\pi$
$421$	7.23166e7			0.969152			0.484576	+	0.874749i	$0.338974\pi$
$422$	−6.72567e7	+	7.97377e7i	−0.894949	+	1.06103i
$423$	5.58667e7	+	7.11853e7i	0.738129	+	0.940522i
$424$	−6.30134e6	−	2.42613e7i	−0.0826677	−	0.318285i
$425$	128212.	−	4.51020e6i	0.00167017	−	0.0587529i
$426$	−5.49075e7	+	1.35702e6i	−0.710237	+	0.0175533i
$427$	3.47300e7	+	3.47300e7i	0.446088	+	0.446088i
$428$	−5.69570e7	−	4.03182e7i	−0.726467	−	0.514245i
$429$	1.07977e8	+	6.48585e6i	1.36760	+	0.0821477i
$430$	−3.21792e7	+	9.63919e7i	−0.404735	+	1.21237i
$431$	5.82751e6			0.0727865			0.0363933	−	0.999338i	$-0.488413\pi$
$431$	5.82751e6			0.0727865			0.0363933	+	0.999338i	$0.488413\pi$
$432$	6.53072e7	+	4.72737e7i	0.810047	+	0.586365i
$433$	−2.49460e7	−	2.49460e7i	−0.307283	−	0.307283i	0.536572	−	0.843855i	$-0.319719\pi$
$433$	−2.49460e7	−	2.49460e7i	−0.307283	−	0.307283i	−0.843855	+	0.536572i	$0.819719\pi$
$434$	−1.08183e8	+	9.18558e6i	−1.32340	+	0.112367i
$435$	2.22432e6	+	6.74609e6i	0.0270227	+	0.0819567i
$436$	−1.13939e8	+	1.94891e7i	−1.37471	+	0.235143i
$437$	−8.33540e7	−	8.33540e7i	−0.998808	−	0.998808i
$438$	−5.24998e7	−	4.99673e7i	−0.624791	−	0.594653i
$439$	1.92253e7			0.227237			0.113618	−	0.993524i	$-0.463756\pi$
$439$	1.92253e7			0.227237			0.113618	+	0.993524i	$0.463756\pi$
$440$	−5.13822e7	−	7.00881e7i	−0.603191	−	0.822784i
$441$	1.35935e7	+	1.63896e6i	0.158496	+	0.0191097i
$442$	4.39457e6	−	5.21008e6i	0.0508920	−	0.0603362i
$443$	−9.90369e7	−	9.90369e7i	−1.13916	−	1.13916i	−0.988600	−	0.150563i	$-0.951892\pi$
$443$	−9.90369e7	−	9.90369e7i	−1.13916	−	1.13916i	−0.150563	−	0.988600i	$-0.548108\pi$
$444$	−1.01584e8	+	1.11593e7i	−1.16059	+	0.127494i
$445$	−8.10465e6	+	1.88060e7i	−0.0919717	+	0.213411i
$446$	3.85129e7	−	3.27005e6i	0.434112	−	0.0368595i
$447$	5.57180e7	−	4.94037e7i	0.623840	−	0.553142i
$448$	2.64953e7	−	9.31314e7i	0.294669	−	1.03577i
$449$	1.07108e8			1.18327			0.591634	−	0.806207i	$-0.298483\pi$
$449$	1.07108e8			1.18327			0.591634	+	0.806207i	$0.298483\pi$
$450$	9.09402e7	+	5.80115e6i	0.997972	+	0.0636615i
$451$			1.19474e8i			1.30239i
$452$	2.51270e7	+	1.77867e7i	0.272098	+	0.192610i
$453$	8.10568e7	+	9.14168e7i	0.871956	+	0.983402i
$454$	1.18383e8	−	1.00517e7i	1.26509	−	0.107416i
$455$	1.25101e8	+	5.39134e7i	1.32808	+	0.572351i
$456$	−1.41428e7	−	7.19390e7i	−0.149156	−	0.758699i
$457$	−157114.	+	157114.i	−0.00164614	+	0.00164614i	−0.707929	−	0.706283i	$-0.750371\pi$
$457$	−157114.	+	157114.i	−0.00164614	+	0.00164614i	0.706283	+	0.707929i	$0.250371\pi$
$458$	5.89618e7	−	6.99034e7i	0.613725	−	0.727616i
$459$	1.01749e6	−	5.59204e6i	0.0105219	−	0.0578272i
$460$	−9.26225e7	−	1.51786e8i	−0.951575	−	1.55940i
$461$			4.16732e6i			0.0425357i	0.999774	+	0.0212679i	$0.00677028\pi$
$461$			4.16732e6i			0.0425357i	−0.999774	+	0.0212679i	$0.993230\pi$
$462$	−7.84747e7	−	7.46893e7i	−0.795800	−	0.757413i
$463$	−3.68969e7	+	3.68969e7i	−0.371746	+	0.371746i	−0.868113	−	0.496367i	$-0.834667\pi$
$463$	−3.68969e7	+	3.68969e7i	−0.371746	+	0.371746i	0.496367	+	0.868113i	$0.334667\pi$
$464$	8.13071e6	−	2.86533e6i	0.0813906	−	0.0286827i
$465$	−1.17770e8	+	3.88312e7i	−1.17133	+	0.386209i
$466$	5.61722e7	−	4.76946e6i	0.555091	−	0.0471315i
$467$	1.27299e8	−	1.27299e8i	1.24989	−	1.24989i	0.294127	−	0.955766i	$-0.404971\pi$
$467$	1.27299e8	−	1.27299e8i	1.24989	−	1.24989i	0.955766	−	0.294127i	$-0.0950289\pi$
$468$	1.02026e8	+	9.24097e7i	0.995349	+	0.901530i
$469$		−	2.64996e7i		−	0.256875i
$470$	3.93064e7	−	1.17741e8i	0.378591	−	1.13406i
$471$	−9.82311e6	+	1.63536e8i	−0.0940126	+	1.56513i
$472$	7.32945e7	+	4.30711e7i	0.697020	+	0.409600i
$473$	9.75741e7	−	9.75741e7i	0.922043	−	0.922043i
$474$	−2.96814e7	+	733568.i	−0.278708	+	0.00688820i
$475$	−5.69076e7	−	6.02376e7i	−0.530993	−	0.562066i
$476$	−6.72862e6	+	1.15092e6i	−0.0623886	+	0.0106715i
$477$	−2.20343e7	−	2.80761e7i	−0.203023	−	0.258691i
$478$	7.46938e7	−	8.85549e7i	0.683913	−	0.810828i
$479$			1.27478e8i			1.15993i	0.814643	+	0.579963i	$0.196933\pi$
$479$			1.27478e8i			1.15993i	−0.814643	+	0.579963i	$0.803067\pi$
$480$	4.79605e6	−	1.10488e8i	0.0433671	−	0.999059i
$481$	−1.74491e8			−1.56797
$482$	4.04602e7	+	3.41271e7i	0.361316	+	0.304761i
$483$	−1.47061e8	−	1.65857e8i	−1.30513	−	1.47194i
$484$	780176.	+	4.56114e6i	0.00688108	+	0.0402288i
$485$	1.56785e7	+	3.94268e7i	0.137430	+	0.345594i
$486$	1.12142e8	+	2.45207e7i	0.976919	+	0.213611i
$487$	−9.86694e7	−	9.86694e7i	−0.854270	−	0.854270i	0.136385	−	0.990656i	$-0.456451\pi$
$487$	−9.86694e7	−	9.86694e7i	−0.854270	−	0.854270i	−0.990656	+	0.136385i	$0.956451\pi$
$488$	3.44932e7	−	5.86975e7i	0.296807	−	0.505080i
$489$	1.13094e7	−	1.88279e8i	0.0967189	−	1.61018i
$490$	−8.39190e6	−	1.68028e7i	−0.0713299	−	0.142822i
$491$	−1.23576e8			−1.04398			−0.521988	−	0.852953i	$-0.674809\pi$
$491$	−1.23576e8			−1.04398			−0.521988	+	0.852953i	$0.674809\pi$
$492$	−9.51247e7	+	1.18603e8i	−0.798726	+	0.995868i
$493$	−429759.	−	429759.i	−0.00358661	−	0.00358661i
$494$	−1.05908e7	−	1.24733e8i	−0.0878510	−	1.03466i
$495$	−1.06955e8	−	6.22221e7i	−0.881833	−	0.513014i
$496$	5.00217e7	+	1.41943e8i	0.409933	+	1.16323i
$497$	6.64129e7	+	6.64129e7i	0.540982	+	0.540982i
$498$	8.97063e7	+	8.53791e7i	0.726331	+	0.691295i
$499$	−1.55195e8			−1.24904			−0.624521	−	0.781008i	$-0.714706\pi$
$499$	−1.55195e8			−1.24904			−0.624521	+	0.781008i	$0.714706\pi$
$500$	−6.20535e7	−	1.08510e8i	−0.496428	−	0.868078i
$501$	−5.29491e6	+	8.81500e7i	−0.0421061	+	0.700986i
$502$	−8.68523e7	−	7.32577e7i	−0.686547	−	0.579085i
$503$	−8.27616e7	−	8.27616e7i	−0.650317	−	0.650317i	0.302753	−	0.953069i	$-0.402094\pi$
$503$	−8.27616e7	−	8.27616e7i	−0.650317	−	0.650317i	−0.953069	+	0.302753i	$0.902094\pi$
$504$	−1.84356e7	−	1.36627e8i	−0.144001	−	1.06720i
$505$	8.53872e7	+	3.67985e7i	0.663007	+	0.285730i
$506$	2.04277e7	+	2.40586e8i	0.157676	+	1.85703i
$507$	6.94698e7	+	7.83488e7i	0.533055	+	0.601186i
$508$	6.97570e7	−	9.85449e7i	0.532104	−	0.751697i
$509$	−8.10897e7			−0.614911			−0.307455	−	0.951562i	$-0.599478\pi$
$509$	−8.10897e7			−0.614911			−0.307455	+	0.951562i	$0.599478\pi$
$510$	−7.17156e6	+	3.05917e6i	−0.0540634	+	0.0230618i
$511$			1.23938e8i			0.928842i
$512$	−1.34182e8	−	3.09436e6i	−0.999734	−	0.0230547i
$513$	−5.94082e7	−	8.58359e7i	−0.440042	−	0.635795i
$514$	−5.40548e6	−	6.36629e7i	−0.0398056	−	0.468810i
$515$	1.37334e7	+	3.45354e7i	0.100544	+	0.252838i
$516$	1.74552e8	−	1.91750e7i	1.27050	−	0.139568i
$517$	−1.19185e8	+	1.19185e8i	−0.862483	+	0.862483i
$518$	1.33583e8	+	1.12674e8i	0.961086	+	0.810652i
$519$	−1.04753e7	+	1.74393e8i	−0.0749313	+	1.24746i
$520$	2.87397e7	−	1.86628e8i	0.204396	−	1.32729i
$521$		−	1.79621e8i		−	1.27012i	−0.772463	−	0.635060i	$-0.780976\pi$
$521$		−	1.79621e8i		−	1.27012i	0.772463	−	0.635060i	$-0.219024\pi$
$522$	8.98022e6	−	8.36783e6i	0.0631357	−	0.0588304i
$523$	−8.73949e7	+	8.73949e7i	−0.610916	+	0.610916i	−0.943185	−	0.332269i	$-0.892186\pi$
$523$	−8.73949e7	+	8.73949e7i	−0.610916	+	0.610916i	0.332269	+	0.943185i	$0.392186\pi$
$524$	1.70409e7	+	9.96261e7i	0.118440	+	0.692436i
$525$	−1.00026e8	−	1.19485e8i	−0.691250	−	0.825722i
$526$	−2.20818e7	−	2.60068e8i	−0.151732	−	1.78702i
$527$	7.50256e6	−	7.50256e6i	0.0512599	−	0.0512599i
$528$	−7.28611e7	+	1.31312e8i	−0.494987	+	0.892077i
$529$			3.45994e8i			2.33723i
$530$	−1.55028e7	+	4.64381e7i	−0.104131	+	0.311923i
$531$	1.20174e8	+	1.44892e7i	0.802648	+	0.0967745i
$532$	−7.24358e7	+	1.02329e8i	−0.481081	+	0.679617i
$533$	−1.83560e8	+	1.83560e8i	−1.21226	+	1.21226i
$534$	3.53753e7	−	874290.i	0.232314	−	0.00574158i
$535$	5.03633e7	+	1.26648e8i	0.328891	+	0.827062i
$536$	−3.55531e7	+	9.23416e6i	−0.230878	+	0.0599657i
$537$	−1.40413e8	−	1.58359e8i	−0.906743	−	1.02263i
$538$	−3.82894e7	−	3.22962e7i	−0.245885	−	0.207398i
$539$			2.55037e7i			0.162869i
$540$	−5.66350e7	−	1.46926e8i	−0.359670	−	0.933080i
$541$	1.77523e8			1.12115			0.560573	−	0.828105i	$-0.310581\pi$
$541$	1.77523e8			1.12115			0.560573	+	0.828105i	$0.310581\pi$
$542$	−4.88862e7	+	5.79581e7i	−0.307035	+	0.364012i
$543$	4.24137e7	−	3.76070e7i	0.264915	−	0.234893i
$544$	3.88881e6	+	8.62637e6i	0.0241557	+	0.0535835i
$545$	2.07334e8	+	8.93529e7i	1.28080	+	0.551975i
$546$	−5.81592e6	−	2.35322e8i	−0.0357306	−	1.44572i
$547$	5.70174e7	+	5.70174e7i	0.348374	+	0.348374i	0.859504	−	0.511130i	$-0.170773\pi$
$547$	5.70174e7	+	5.70174e7i	0.348374	+	0.348374i	−0.511130	+	0.859504i	$0.670773\pi$
$548$	6.98872e7	−	9.87287e7i	0.424674	−	0.599932i
$549$	1.16036e7	−	9.62403e7i	0.0701254	−	0.581621i
$550$	9.54860e6	+	1.69467e8i	0.0573920	+	1.01859i
$551$	−1.11623e7			−0.0667265
$552$	−1.71276e8	+	2.55098e8i	−1.01831	+	1.51667i
$553$	3.59009e7	+	3.59009e7i	0.212290	+	0.212290i
$554$	2.68074e8	−	2.27615e7i	1.57661	−	0.133867i
$555$	1.78236e8	+	8.98447e7i	1.04260	+	0.525550i
$556$	2.42667e7	+	1.41870e8i	0.141184	+	0.825403i
$557$	2.29505e8	+	2.29505e8i	1.32809	+	1.32809i	0.907036	+	0.421054i	$0.138340\pi$
$557$	2.29505e8	+	2.29505e8i	1.32809	+	1.32809i	0.421054	+	0.907036i	$0.361660\pi$
$558$	1.46082e8	+	1.56773e8i	0.840803	+	0.902336i
$559$	2.99827e8			1.71646
$560$	−1.42513e8	+	1.24316e8i	−0.811504	+	0.707888i
$561$	1.05681e7	+	634795.i	0.0598562	+	0.00359538i
$562$	1.13585e8	−	1.34664e8i	0.639902	−	0.758650i
$563$	1.21751e8	+	1.21751e8i	0.682256	+	0.682256i	0.960508	−	0.278252i	$-0.0897552\pi$
$563$	1.21751e8	+	1.21751e8i	0.682256	+	0.682256i	−0.278252	+	0.960508i	$0.589755\pi$
$564$	−2.13212e8	+	2.34220e7i	−1.18843	+	0.130553i
$565$	−2.22181e7	−	5.58718e7i	−0.123186	−	0.309776i
$566$	3.01796e8	−	2.56248e7i	1.66443	−	0.141323i
$567$	−1.01834e8	−	1.67815e8i	−0.558653	−	0.920625i
$568$	6.59601e7	−	1.12245e8i	0.359945	−	0.612523i
$569$	−2.18270e8			−1.18483			−0.592417	−	0.805631i	$-0.701826\pi$
$569$	−2.18270e8			−1.18483			−0.592417	+	0.805631i	$0.701826\pi$
$570$	−5.34064e7	+	1.32863e8i	−0.288382	+	0.717431i
$571$		−	1.74583e8i		−	0.937763i	−0.883261	−	0.468882i	$-0.844657\pi$
$571$		−	1.74583e8i		−	0.937763i	0.883261	−	0.468882i	$-0.155343\pi$
$572$	−1.48143e8	+	2.09280e8i	−0.791577	+	1.11825i
$573$	1.58708e8	−	1.40722e8i	0.843596	−	0.747994i
$574$	2.59056e8	−	2.19959e7i	1.36980	−	0.116307i
$575$	−9.86852e6	+	3.47153e8i	−0.0519097	+	1.82607i
$576$	−1.76881e8	+	7.23435e7i	−0.925578	+	0.378558i
$577$	1.14387e8	−	1.14387e8i	0.595454	−	0.595454i	−0.343645	−	0.939099i	$-0.611662\pi$
$577$	1.14387e8	−	1.14387e8i	0.595454	−	0.595454i	0.939099	+	0.343645i	$0.111662\pi$
$578$	−1.24071e8	+	1.47095e8i	−0.642521	+	0.761754i
$579$	3.59264e7	+	2.15799e6i	0.185088	+	0.0111177i
$580$	−1.63649e7	−	3.96142e6i	−0.0838744	−	0.0203033i
$581$		−	2.11773e8i		−	1.07980i
$582$	5.05474e7	−	5.31092e7i	0.256407	−	0.269402i
$583$	4.70077e7	−	4.70077e7i	0.237226	−	0.237226i
$584$	1.66281e8	−	4.31879e7i	0.834842	−	0.216832i
$585$	−6.87282e7	−	2.59925e8i	−0.343295	−	1.29832i
$586$	−2.35934e8	+	2.00326e7i	−1.17246	+	0.0995507i
$587$	1.69603e8	−	1.69603e8i	0.838533	−	0.838533i	−0.150133	−	0.988666i	$-0.547970\pi$
$587$	1.69603e8	−	1.69603e8i	0.838533	−	0.838533i	0.988666	+	0.150133i	$0.0479701\pi$
$588$	−2.03060e7	+	2.53180e7i	−0.0998833	+	0.124537i
$589$		−	1.94867e8i		−	0.953656i
$590$	−7.41884e7	−	1.48545e8i	−0.361227	−	0.723274i
$591$	−3.54618e8	−	2.13009e7i	−1.71790	−	0.103189i
$592$	1.04620e8	−	2.18484e8i	0.504253	−	1.05306i
$593$	−1.04281e8	+	1.04281e8i	−0.500082	+	0.500082i	−0.911463	−	0.411381i	$-0.865047\pi$
$593$	−1.04281e8	+	1.04281e8i	−0.500082	+	0.500082i	0.411381	+	0.911463i	$0.365047\pi$
$594$	−2.03419e7	+	2.12849e8i	−0.0970580	+	1.01558i
$595$	1.22441e7	+	5.27671e6i	0.0581266	+	0.0250503i
$596$	2.97600e7	+	1.73986e8i	0.140571	+	0.821816i
$597$	−3.26240e7	+	2.89268e7i	−0.153325	+	0.135949i
$598$	−3.38253e8	+	4.01023e8i	−1.58175	+	1.87528i
$599$		−	1.14196e8i		−	0.531335i	−0.964065	−	0.265668i	$-0.914408\pi$
$599$		−	1.14196e8i		−	0.531335i	0.964065	−	0.265668i	$-0.0855924\pi$
$600$	−1.25451e8	+	1.75836e8i	−0.580790	+	0.814054i
$601$	9.52213e7			0.438643			0.219321	−	0.975653i	$-0.429616\pi$
$601$	9.52213e7			0.438643			0.219321	+	0.975653i	$0.429616\pi$
$602$	−2.29535e8	−	1.93607e8i	−1.05211	−	0.887426i
$603$	−4.11434e7	+	3.22897e7i	−0.187650	+	0.147269i
$604$	−2.85459e8	+	4.88274e7i	−1.29549	+	0.221591i
$605$	3.57693e6	−	8.29990e6i	0.0161527	−	0.0374806i
$606$	−3.96964e6	−	1.60619e8i	−0.0178375	−	0.721736i
$607$	−5.11312e6	−	5.11312e6i	−0.0228623	−	0.0228623i	0.695583	−	0.718446i	$-0.255146\pi$
$607$	−5.11312e6	−	5.11312e6i	−0.0228623	−	0.0228623i	−0.718446	+	0.695583i	$0.755146\pi$
$608$	1.62531e8	+	6.15252e7i	0.723144	+	0.273743i
$609$	−2.09521e7	−	1.25853e6i	−0.0927630	−	0.00557199i
$610$	−1.18962e8	+	5.94134e7i	−0.524104	+	0.261755i
$611$	−3.66234e8			−1.60559
$612$	9.98572e6	+	9.04449e6i	0.0435637	+	0.0394575i
$613$	2.53063e8	+	2.53063e8i	1.09862	+	1.09862i	0.994573	+	0.104046i	$0.0331789\pi$
$613$	2.53063e8	+	2.53063e8i	1.09862	+	1.09862i	0.104046	+	0.994573i	$0.466821\pi$
$614$	5.08087e6	+	5.98398e7i	0.0219499	+	0.258515i
$615$	2.82014e8	−	9.29856e7i	1.21240	−	0.399752i
$616$	2.48551e8	−	6.45557e7i	1.06334	−	0.276180i
$617$	1.38214e8	+	1.38214e8i	0.588431	+	0.588431i	0.937206	−	0.348775i	$-0.113402\pi$
$617$	1.38214e8	+	1.38214e8i	0.588431	+	0.588431i	−0.348775	+	0.937206i	$0.613402\pi$
$618$	4.42763e7	−	4.65204e7i	0.187589	−	0.197096i
$619$	−2.23588e8			−0.942706			−0.471353	−	0.881945i	$-0.656234\pi$
$619$	−2.23588e8			−0.942706			−0.471353	+	0.881945i	$0.656234\pi$
$620$	6.91568e7	−	2.85691e8i	0.290175	−	1.19873i
$621$	−7.83170e7	+	4.30423e8i	−0.327025	+	1.79730i
$622$	−4.36110e6	−	3.67848e6i	−0.0181228	−	0.0152861i
$623$	−4.27878e7	−	4.27878e7i	−0.176952	−	0.176952i
$624$	−3.13692e8	+	8.98041e7i	−1.29107	+	0.369609i
$625$	−1.38692e7	+	2.43746e8i	−0.0568081	+	0.998385i
$626$	1.19983e7	+	1.41310e8i	0.0489100	+	0.576037i
$627$	1.45489e8	−	1.29001e8i	0.590237	−	0.523348i
$628$	−3.16963e8	−	2.24369e8i	−1.27976	−	0.905908i
$629$	−1.70781e7			−0.0686257
$630$	−1.15226e8	+	2.43368e8i	−0.460817	+	0.973289i
$631$		−	3.67203e8i		−	1.46156i	−0.682611	−	0.730782i	$-0.739156\pi$
$631$		−	3.67203e8i		−	1.46156i	0.682611	−	0.730782i	$-0.260844\pi$
$632$	3.56561e7	−	6.06765e7i	0.141248	−	0.240364i
$633$	−2.33571e8	−	2.63424e8i	−0.920891	−	1.03859i
$634$	−3.87453e7	−	4.56322e8i	−0.152038	−	1.79062i
$635$	−2.19122e8	+	8.71366e7i	−0.855786	+	0.340314i
$636$	8.40927e7	−	9.23783e6i	0.326879	−	0.0359086i
$637$	−3.91841e7	+	3.91841e7i	−0.151597	+	0.151597i
$638$	1.74768e7	+	1.47412e7i	0.0672975	+	0.0567637i
$639$	2.21891e7	−	1.84037e8i	0.0850428	−	0.705346i
$640$	2.16449e8	+	1.47882e8i	0.825689	+	0.564126i
$641$			7.77280e7i			0.295123i	0.989053	+	0.147562i	$0.0471425\pi$
$641$			7.77280e7i			0.295123i	−0.989053	+	0.147562i	$0.952858\pi$
$642$	1.62370e8	−	1.70600e8i	0.613623	−	0.644723i
$643$	1.86163e8	−	1.86163e8i	0.700261	−	0.700261i	−0.264206	−	0.964466i	$-0.585110\pi$
$643$	1.86163e8	−	1.86163e8i	0.700261	−	0.700261i	0.964466	+	0.264206i	$0.0851098\pi$
$644$	5.17906e8	−	8.85871e7i	1.93907	−	0.331675i
$645$	−3.06263e8	−	1.54380e8i	−1.14134	−	0.575323i
$646$	−1.03656e6	−	1.22081e7i	−0.00384500	−	0.0452844i
$647$	3.29523e8	−	3.29523e8i	1.21667	−	1.21667i	0.247881	−	0.968790i	$-0.420266\pi$
$647$	3.29523e8	−	3.29523e8i	1.21667	−	1.21667i	0.968790	−	0.247881i	$-0.0797343\pi$
$648$	−1.89664e8	+	1.95102e8i	−0.697042	+	0.717030i
$649$			2.25465e8i			0.824794i
$650$	−2.45700e8	+	2.75041e8i	−0.894675	+	1.00151i
$651$	2.19708e7	−	3.65772e8i	0.0796349	−	1.32577i
$652$	3.64920e8	+	2.58317e8i	1.31660	+	0.931986i
$653$	2.73103e8	−	2.73103e8i	0.980815	−	0.980815i	−0.0190042	−	0.999819i	$-0.506050\pi$
$653$	2.73103e8	−	2.73103e8i	0.980815	−	0.980815i	0.999819	+	0.0190042i	$0.00604959\pi$
$654$	−9.63896e6	−	3.90009e8i	−0.0344585	−	1.39425i
$655$	7.81288e7	−	1.81290e8i	0.278027	−	0.645133i
$656$	−1.19782e8	−	3.39897e8i	−0.424308	−	1.20403i
$657$	1.92427e8	−	1.51018e8i	0.678531	−	0.532516i
$658$	2.80374e8	+	2.36488e8i	0.984146	+	0.830102i
$659$		−	2.84879e7i		−	0.0995417i	−0.998761	−	0.0497708i	$-0.984151\pi$
$659$		−	2.84879e7i		−	0.0995417i	0.998761	−	0.0497708i	$-0.0158491\pi$
$660$	2.59081e8	−	1.37494e8i	0.901163	−	0.478246i
$661$	−1.91780e8			−0.664047			−0.332024	−	0.943271i	$-0.607731\pi$
$661$	−1.91780e8			−0.664047			−0.332024	+	0.943271i	$0.607731\pi$
$662$	7.24665e6	−	8.59143e6i	0.0249783	−	0.0296136i
$663$	1.52616e7	+	1.72122e7i	0.0523672	+	0.0590604i
$664$	−2.84124e8	+	7.37952e7i	−0.970519	+	0.252071i
$665$	2.27537e8	−	9.04828e7i	0.773725	−	0.307681i
$666$	1.21677e7	−	3.44694e8i	0.0411893	−	1.16684i
$667$	3.30788e7	+	3.30788e7i	0.111474	+	0.111474i
$668$	−1.70851e8	−	1.20941e8i	−0.573178	−	0.405736i
$669$	−7.82157e6	+	1.30214e8i	−0.0261225	+	0.434890i
$670$	6.80517e7	+	2.27182e7i	0.226263	+	0.0755352i
$671$	1.80563e8			0.597668
$672$	2.98140e8	+	1.33810e8i	0.982453	+	0.440942i
$673$	−3.12667e8	−	3.12667e8i	−1.02574	−	1.02574i	−0.999660	−	0.0260794i	$-0.991698\pi$
$673$	−3.12667e8	−	3.12667e8i	−1.02574	−	1.02574i	−0.0260794	−	0.999660i	$-0.508302\pi$
$674$	−1.22383e8	+	1.03913e7i	−0.399708	+	0.0339383i
$675$	−6.36311e7	+	3.00892e8i	−0.206899	+	0.978362i
$676$	−2.44653e8	+	4.18476e7i	−0.791973	+	0.135466i
$677$	−2.08606e8	−	2.08606e8i	−0.672297	−	0.672297i	0.285948	−	0.958245i	$-0.407692\pi$
$677$	−2.08606e8	−	2.08606e8i	−0.672297	−	0.672297i	−0.958245	+	0.285948i	$0.907692\pi$
$678$	−7.16309e7	+	7.52613e7i	−0.229832	+	0.241481i
$679$	−1.25377e8			−0.400505
$680$	2.81287e6	−	1.82659e7i	0.00894587	−	0.0580919i
$681$	−2.40424e7	+	4.00260e8i	−0.0761266	+	1.26736i
$682$	−2.57346e8	+	3.05102e8i	−0.811267	+	0.961816i
$683$	−7.53661e7	−	7.53661e7i	−0.236545	−	0.236545i	0.578873	−	0.815418i	$-0.303493\pi$
$683$	−7.53661e7	−	7.53661e7i	−0.236545	−	0.236545i	−0.815418	+	0.578873i	$0.803493\pi$
$684$	2.47139e8	−	1.22234e7i	0.772278	−	0.0381966i
$685$	−2.19531e8	+	8.72992e7i	−0.683006	+	0.271606i
$686$	−2.91097e8	+	2.47164e7i	−0.901708	+	0.0765620i
$687$	2.04764e8	+	2.30935e8i	0.631515	+	0.712230i
$688$	−1.79768e8	+	3.75420e8i	−0.552009	+	1.15280i
$689$	1.44446e8			0.441618
$690$	5.51999e8	−	2.35466e8i	1.68032	−	0.716772i
$691$			1.73004e8i			0.524351i	0.965020	+	0.262176i	$0.0844400\pi$
$691$			1.73004e8i			0.524351i	−0.965020	+	0.262176i	$0.915560\pi$
$692$	−3.38007e8	−	2.39265e8i	−1.02002	−	0.722040i
$693$	2.87633e8	−	2.25736e8i	0.864248	−	0.678268i
$694$	−1.85257e8	+	1.57297e7i	−0.554237	+	0.0470590i
$695$	1.11257e8	−	2.58161e8i	0.331416	−	0.769017i
$696$	5.61254e6	+	2.85488e7i	0.0166468	+	0.0846760i
$697$	−1.79657e7	+	1.79657e7i	−0.0530574	+	0.0530574i
$698$	−8.04378e6	+	9.53648e6i	−0.0236534	+	0.0280428i
$699$	−1.14080e7	+	1.89921e8i	−0.0334024	+	0.556086i
$700$	3.65700e8	−	5.19044e7i	1.06618	−	0.151325i
$701$		−	4.15307e8i		−	1.20563i	−0.797880	−	0.602816i	$-0.794045\pi$
$701$		−	4.15307e8i		−	1.20563i	0.797880	−	0.602816i	$-0.205955\pi$
$702$	−3.58275e8	+	2.95769e8i	−1.03563	+	0.854950i
$703$	−2.21787e8	+	2.21787e8i	−0.638368	+	0.638368i
$704$	−1.73222e8	−	3.10972e8i	−0.496461	−	0.891257i
$705$	3.74095e8	+	1.88573e8i	1.06761	+	0.538160i
$706$	3.32266e8	−	2.82120e7i	0.944218	−	0.0801714i
$707$	−1.94275e8	+	1.94275e8i	−0.549741	+	0.549741i
$708$	−1.79515e8	+	2.23823e8i	−0.505826	+	0.630674i
$709$		−	3.93832e8i		−	1.10503i	−0.833504	−	0.552513i	$-0.813669\pi$
$709$		−	3.93832e8i		−	1.10503i	0.833504	−	0.552513i	$-0.186331\pi$
$710$	−2.27486e8	+	1.13614e8i	−0.635593	+	0.317436i
$711$	1.19948e7	−	9.94850e7i	0.0333722	−	0.276789i
$712$	−4.24961e7	+	7.23161e7i	−0.117736	+	0.200353i
$713$	−5.77476e8	+	5.77476e8i	−1.59318	+	1.59318i
$714$	−569226.	−	2.30319e7i	−0.00156383	−	0.0632753i
$715$	4.65350e8	−	1.85052e8i	1.27310	−	0.506263i
$716$	4.94494e8	−	8.45826e7i	1.34717	−	0.230432i
$717$	2.59399e8	+	2.92553e8i	0.703738	+	0.793683i
$718$	3.01714e8	−	3.57704e8i	0.815121	−	0.966385i
$719$			1.92397e8i			0.517620i	0.965928	+	0.258810i	$0.0833304\pi$
$719$			1.92397e8i			0.517620i	−0.965928	+	0.258810i	$0.916670\pi$
$720$	3.66666e8	+	6.97874e7i	0.982365	+	0.186973i
$721$	−1.09822e8			−0.293011
$722$	1.15690e8	+	9.75812e7i	0.307385	+	0.259271i
$723$	−1.33666e8	+	1.18518e8i	−0.353675	+	0.313595i
$724$	2.26539e7	+	1.32441e8i	0.0596936	+	0.348986i
$725$	2.25836e7	+	2.39052e7i	0.0592625	+	0.0627303i
$726$	−1.56126e7	+	385862.i	−0.0408006	+	0.00100837i
$727$	1.19250e8	+	1.19250e8i	0.310352	+	0.310352i	0.845046	−	0.534694i	$-0.179573\pi$
$727$	1.19250e8	+	1.19250e8i	0.310352	+	0.310352i	−0.534694	+	0.845046i	$0.679573\pi$
$728$	4.81058e8	+	2.82691e8i	1.24682	+	0.732686i
$729$	−1.36467e8	+	3.62590e8i	−0.352246	+	0.935908i
$730$	−3.18276e8	−	1.06252e8i	−0.818154	−	0.273131i
$731$	2.93452e7			0.0751250
$732$	1.79247e8	+	1.43764e8i	0.457003	+	0.366535i
$733$	2.50488e8	+	2.50488e8i	0.636027	+	0.636027i	0.949573	−	0.313546i	$-0.101517\pi$
$733$	2.50488e8	+	2.50488e8i	0.636027	+	0.636027i	−0.313546	+	0.949573i	$0.601517\pi$
$734$	2.05394e7	+	2.41903e8i	0.0519398	+	0.611721i
$735$	6.02009e7	−	1.98494e7i	0.151615	−	0.0499903i
$736$	−2.99324e8	−	6.63977e8i	−0.750772	−	1.66540i
$737$	−6.88863e7	−	6.88863e7i	−0.172080	−	0.172080i
$738$	−3.49810e8	−	3.75410e8i	−0.870288	−	0.933978i
$739$	−4.02436e7			−0.0997157			−0.0498578	−	0.998756i	$-0.515877\pi$
$739$	−4.02436e7			−0.0997157			−0.0498578	+	0.998756i	$0.515877\pi$
$740$	−4.03871e8	+	2.46449e8i	−0.996660	+	0.608180i
$741$	4.21727e8	+	2.53319e7i	1.03652	+	0.0622606i
$742$	−1.10582e8	−	9.32729e7i	−0.270690	−	0.228320i
$743$	−1.93136e8	−	1.93136e8i	−0.470865	−	0.470865i	0.431329	−	0.902194i	$-0.358045\pi$
$743$	−1.93136e8	−	1.93136e8i	−0.470865	−	0.470865i	−0.902194	+	0.431329i	$0.858045\pi$
$744$	−4.98393e8	+	9.79813e7i	−1.21019	+	0.237916i
$745$	1.36443e8	−	3.16602e8i	0.329976	−	0.765675i
$746$	3.58866e7	+	4.22654e8i	0.0864402	+	1.01805i
$747$	−3.28799e8	+	2.58044e8i	−0.788804	+	0.619059i
$748$	−1.44993e7	+	2.04830e7i	−0.0346452	+	0.0489428i
$749$	−4.02741e8			−0.958474
$750$	3.92592e8	−	1.54435e8i	0.930588	−	0.366068i
$751$			2.28465e8i			0.539386i	0.962946	+	0.269693i	$0.0869223\pi$
$751$			2.28465e8i			0.539386i	−0.962946	+	0.269693i	$0.913078\pi$
$752$	2.19583e8	−	4.58570e8i	0.516352	−	1.07833i
$753$	2.86928e8	−	2.54412e8i	0.672030	−	0.595871i
$754$	4.20292e6	+	4.94998e7i	0.00980476	+	0.115475i
$755$	5.19450e8	+	2.23862e8i	1.20699	+	0.520164i
$756$	4.65268e8	+	4.92065e6i	1.07681	+	0.0113883i
$757$	−1.63256e7	+	1.63256e7i	−0.0376342	+	0.0376342i	−0.725673	−	0.688039i	$-0.758472\pi$
$757$	−1.63256e7	+	1.63256e7i	−0.0376342	+	0.0376342i	0.688039	+	0.725673i	$0.258472\pi$
$758$	−3.01115e8	−	2.53983e8i	−0.691392	−	0.583171i
$759$	−8.13435e8	−	4.88606e7i	−1.86036	−	0.111746i
$760$	−2.00684e8	−	2.73744e8i	−0.457164	−	0.623596i
$761$		−	3.86040e8i		−	0.875948i	−0.898988	−	0.437974i	$-0.855696\pi$
$761$		−	3.86040e8i		−	0.875948i	0.898988	−	0.437974i	$-0.144304\pi$
$762$	2.95165e8	+	2.80927e8i	0.667114	+	0.634935i
$763$	−4.71731e8	+	4.71731e8i	−1.06199	+	1.06199i
$764$	8.47688e7	+	4.95583e8i	0.190089	+	1.11131i
$765$	−6.72669e6	−	2.54398e7i	−0.0150251	−	0.0568238i
$766$	−1.10658e7	−	1.30327e8i	−0.0246204	−	0.289966i
$767$	−3.46406e8	+	3.46406e8i	−0.767714	+	0.767714i
$768$	7.56351e7	−	4.46626e8i	0.166971	−	0.985962i
$769$		−	6.66598e8i		−	1.46584i	−0.680317	−	0.732918i	$-0.738158\pi$
$769$		−	6.66598e8i		−	1.46584i	0.680317	−	0.732918i	$-0.261842\pi$
$770$	−4.75747e8	−	1.58822e8i	−1.04209	−	0.347888i
$771$	2.15248e8	+	1.29293e7i	0.469651	+	0.0282105i
$772$	−4.92906e7	+	6.96322e7i	−0.107130	+	0.151342i
$773$	−2.30960e8	+	2.30960e8i	−0.500032	+	0.500032i	−0.911448	−	0.411416i	$-0.865034\pi$
$773$	−2.30960e8	+	2.30960e8i	−0.500032	+	0.500032i	0.411416	+	0.911448i	$0.365034\pi$
$774$	−2.09077e7	+	5.92287e8i	−0.0450902	+	1.27735i
$775$	−4.17326e8	+	3.94255e8i	−0.896542	+	0.846979i
$776$	4.36893e7	+	1.68211e8i	0.0934953	+	0.359973i
$777$	−4.41310e8	+	3.91298e8i	−0.940764	+	0.834150i
$778$	5.66937e8	+	4.78197e8i	1.20392	+	1.01547i
$779$			4.66630e8i			0.987097i
$780$	6.09299e8	+	1.86807e8i	1.28395	+	0.393649i
$781$	3.45283e8			0.724807
$782$	−3.31061e7	+	3.92497e7i	−0.0692290	+	0.0820759i
$783$	2.35760e7	+	3.40638e7i	0.0491117	+	0.0709590i
$784$	−2.55697e7	−	7.25570e7i	−0.0530611	−	0.150567i
$785$	2.80270e8	+	7.04793e8i	0.579385	+	1.45698i
$786$	−3.41017e8	+	8.42815e6i	−0.702278	+	0.0173566i
$787$	−6.81594e7	−	6.81594e7i	−0.139830	−	0.139830i	0.633727	−	0.773557i	$-0.281524\pi$
$787$	−6.81594e7	−	6.81594e7i	−0.139830	−	0.139830i	−0.773557	+	0.633727i	$0.781524\pi$
$788$	4.86532e8	−	6.87318e8i	0.994335	−	1.40468i
$789$	8.79304e8	+	5.28171e7i	1.79023	+	0.107534i
$790$	−1.22972e8	+	6.14165e7i	−0.249417	+	0.124567i
$791$	1.77672e8			0.358996
$792$	−4.03088e8	−	3.07240e8i	−0.811379	−	0.618447i
$793$	2.77417e8	+	2.77417e8i	0.556306	+	0.556306i
$794$	1.51171e8	−	1.28356e7i	0.301999	−	0.0256421i
$795$	−1.47546e8	−	7.43746e7i	−0.293648	−	0.148021i
$796$	−1.74251e7	−	1.01872e8i	−0.0345490	−	0.201983i
$797$	−5.25947e8	−	5.25947e8i	−1.03888	−	1.03888i	−0.999213	−	0.0396706i	$-0.987369\pi$
$797$	−5.25947e8	−	5.25947e8i	−1.03888	−	1.03888i	−0.0396706	−	0.999213i	$-0.512631\pi$
$798$	−3.06500e8	−	2.91715e8i	−0.603145	−	0.574051i
$799$	−3.58447e7			−0.0702723
$800$	−1.97071e8	−	4.72554e8i	−0.384904	−	0.922957i
$801$	−1.42958e7	+	1.18569e8i	−0.0278170	+	0.230714i
$802$	−3.22085e7	+	3.81855e7i	−0.0624377	+	0.0740244i
$803$	3.22179e8	+	3.22179e8i	0.622230	+	0.622230i
$804$	−1.35374e7	−	1.23232e8i	−0.0260475	−	0.237112i
$805$	−9.42433e8	−	4.06152e8i	−1.80660	−	0.778575i
$806$	−8.64148e8	+	7.33728e7i	−1.65038	+	0.140130i
$807$	1.26494e8	−	1.12159e8i	0.240686	−	0.213410i
$808$	3.28346e8	+	1.92950e8i	0.622440	+	0.365773i
$809$	−8.10218e7			−0.153023			−0.0765114	−	0.997069i	$-0.524378\pi$
$809$	−8.10218e7			−0.153023			−0.0765114	+	0.997069i	$0.524378\pi$
$810$	5.18256e8	−	1.17643e8i	0.975191	−	0.221365i
$811$		−	2.88768e8i		−	0.541360i	−0.962669	−	0.270680i	$-0.912751\pi$
$811$		−	2.88768e8i		−	0.541360i	0.962669	−	0.270680i	$-0.0872485\pi$
$812$	2.87460e7	−	4.06090e7i	0.0536919	−	0.0758498i
$813$	−1.69773e8	−	1.91472e8i	−0.315935	−	0.356315i
$814$	6.40150e8	−	5.43537e7i	1.18688	−	0.100776i
$815$	−3.22675e8	−	8.11429e8i	−0.596063	−	1.49892i
$816$	−3.07023e7	+	8.78947e6i	−0.0565067	+	0.0161768i
$817$	3.81096e8	−	3.81096e8i	0.698826	−	0.698826i
$818$	2.42114e8	−	2.87043e8i	0.442343	−	0.524429i
$819$	7.88742e8	+	9.50979e7i	1.43577	+	0.173109i
$820$	−1.65604e8	+	6.84120e8i	−0.300350	+	1.24077i
$821$		−	6.88823e8i		−	1.24474i	−0.782724	−	0.622370i	$-0.786170\pi$
$821$		−	6.88823e8i		−	1.24474i	0.782724	−	0.622370i	$-0.213830\pi$
$822$	2.95716e8	+	2.81451e8i	0.532426	+	0.506743i
$823$	−4.20517e7	+	4.20517e7i	−0.0754369	+	0.0754369i	−0.743819	−	0.668382i	$-0.766987\pi$
$823$	−4.20517e7	+	4.20517e7i	−0.0754369	+	0.0754369i	0.668382	+	0.743819i	$0.266987\pi$
$824$	3.82691e7	+	1.47343e8i	0.0684016	+	0.263358i
$825$	−5.70622e8	−	5.05830e7i	−1.01622	−	0.0900830i
$826$	4.88879e8	−	4.15096e7i	0.867484	−	0.0736561i
$827$	−3.50042e8	+	3.50042e8i	−0.618875	+	0.618875i	−0.945243	−	0.326368i	$-0.894175\pi$
$827$	−3.50042e8	+	3.50042e8i	−0.618875	+	0.618875i	0.326368	+	0.945243i	$0.394175\pi$
$828$	−7.68607e8	−	6.96160e8i	−1.35398	−	1.22636i
$829$		−	2.32683e8i		−	0.408415i	−0.978928	−	0.204207i	$-0.934538\pi$
$829$		−	2.32683e8i		−	0.408415i	0.978928	−	0.204207i	$-0.0654617\pi$
$830$	5.43838e8	+	1.81553e8i	0.951119	+	0.317519i
$831$	−5.44430e7	+	9.06371e8i	−0.0948722	+	1.57944i
$832$	2.11640e8	−	7.43918e8i	0.367475	−	1.29168i
$833$	−3.83509e6	+	3.83509e6i	−0.00663500	+	0.00663500i
$834$	−4.85617e8	+	1.20019e7i	−0.837135	+	0.0206896i
$835$	1.51072e8	+	3.79902e8i	0.259493	+	0.652547i
$836$	7.77082e7	+	4.54305e8i	0.132999	+	0.777550i
$837$	−5.94671e8	+	4.11580e8i	−1.01415	+	0.701904i
$838$	−2.20417e8	+	2.61320e8i	−0.374552	+	0.444059i
$839$		−	7.66640e8i		−	1.29809i	−0.760749	−	0.649046i	$-0.775168\pi$
$839$		−	7.66640e8i		−	1.29809i	0.760749	−	0.649046i	$-0.224832\pi$
$840$	−3.45828e8	−	5.36455e8i	−0.583475	−	0.905097i
$841$	−5.90394e8			−0.992553
$842$	−4.42228e8	−	3.73008e8i	−0.740815	−	0.624859i
$843$	3.94463e8	+	4.44880e8i	0.658451	+	0.742608i
$844$	8.22571e8	−	1.40700e8i	1.36819	−	0.234027i
$845$	4.45195e8	+	1.91862e8i	0.737870	+	0.317993i
$846$	2.55384e7	−	7.23469e8i	0.0421776	−	1.19484i
$847$	1.88841e7	+	1.88841e7i	0.0310775	+	0.0310775i
$848$	−8.66055e7	+	1.80864e8i	−0.142023	+	0.296595i
$849$	−6.12917e7	+	1.02039e9i	−0.100156	+	1.66741i
$850$	−2.40476e7	+	2.69193e7i	−0.0391575	+	0.0438336i
$851$	1.31451e9			2.13292
$852$	3.42768e8	+	2.74914e8i	0.554219	+	0.444506i
$853$	−1.21093e8	−	1.21093e8i	−0.195107	−	0.195107i	0.602792	−	0.797898i	$-0.294055\pi$
$853$	−1.21093e8	−	1.21093e8i	−0.195107	−	0.195107i	−0.797898	+	0.602792i	$0.794055\pi$
$854$	−3.32428e7	−	3.91516e8i	−0.0533732	−	0.628603i
$855$	−4.17737e8	−	2.43022e8i	−0.668350	−	0.388818i
$856$	1.40341e8	+	5.40336e8i	0.223749	+	0.861474i
$857$	6.56327e8	+	6.56327e8i	1.04274	+	1.04274i	0.999045	+	0.0436995i	$0.0139144\pi$
$857$	6.56327e8	+	6.56327e8i	1.04274	+	1.04274i	0.0436995	+	0.999045i	$0.486086\pi$
$858$	−6.26843e8	−	5.96606e8i	−0.992423	−	0.944551i
$859$	3.63159e8			0.572952			0.286476	−	0.958087i	$-0.407516\pi$
$859$	3.63159e8			0.572952			0.286476	+	0.958087i	$0.407516\pi$
$860$	6.93969e8	−	4.23472e8i	1.09105	−	0.665778i
$861$	−5.26116e7	+	8.75882e8i	−0.0824275	+	1.37226i
$862$	−3.56361e7	−	3.00582e7i	−0.0556377	−	0.0469290i
$863$	−5.75037e8	−	5.75037e8i	−0.894671	−	0.894671i	0.100288	−	0.994958i	$-0.468024\pi$
$863$	−5.75037e8	−	5.75037e8i	−0.894671	−	0.894671i	−0.994958	+	0.100288i	$0.968024\pi$
$864$	−1.55527e8	−	6.25940e8i	−0.241138	−	0.970491i
$865$	2.98877e8	+	7.51585e8i	0.461790	+	1.16126i
$866$	2.38778e7	+	2.81220e8i	0.0367655	+	0.433005i
$867$	−4.30878e8	−	4.85949e8i	−0.661145	−	0.745647i
$868$	7.08936e8	+	5.01835e8i	1.08405	+	0.767365i
$869$	1.86650e8			0.284426
$870$	2.11942e7	−	5.27265e7i	0.0321854	−	0.0800702i
$871$		−	2.11674e8i		−	0.320342i
$872$	7.97278e8	+	4.68515e8i	1.20243	+	0.706601i
$873$	1.52771e8	+	1.94661e8i	0.229614	+	0.292574i
$874$	7.97846e7	+	9.39662e8i	0.119505	+	1.40746i
$875$	−6.54132e8	−	3.04227e8i	−0.976430	−	0.454124i
$876$	6.33139e7	+	5.76351e8i	0.0941861	+	0.857383i
$877$	1.90408e8	−	1.90408e8i	0.282283	−	0.282283i	−0.551736	−	0.834019i	$-0.686034\pi$
$877$	1.90408e8	−	1.90408e8i	0.282283	−	0.282283i	0.834019	+	0.551736i	$0.186034\pi$
$878$	−1.17566e8	−	9.91636e7i	−0.173699	−	0.146511i
$879$	4.79156e7	−	7.97703e8i	0.0705522	−	1.17456i
$880$	−4.73025e7	+	6.93628e8i	−0.0694123	+	1.01784i
$881$		−	5.16585e8i		−	0.755465i	−0.925915	−	0.377732i	$-0.876704\pi$
$881$		−	5.16585e8i		−	0.755465i	0.925915	−	0.377732i	$-0.123296\pi$
$882$	−7.46730e7	−	8.01378e7i	−0.108832	−	0.116797i
$883$	2.64049e8	−	2.64049e8i	0.383532	−	0.383532i	−0.488841	−	0.872373i	$-0.662580\pi$
$883$	2.64049e8	−	2.64049e8i	0.383532	−	0.383532i	0.872373	+	0.488841i	$0.162580\pi$
$884$	−5.37470e7	+	9.19336e6i	−0.0778033	+	0.0133081i
$885$	5.32205e8	−	1.75478e8i	0.767802	−	0.253159i
$886$	9.47959e7	+	1.11646e9i	0.136298	+	1.60524i
$887$	−1.43878e8	+	1.43878e8i	−0.206169	+	0.206169i	−0.802637	−	0.596468i	$-0.796570\pi$
$887$	−1.43878e8	+	1.43878e8i	−0.206169	+	0.206169i	0.596468	+	0.802637i	$0.296570\pi$
$888$	6.78763e8	+	4.55729e8i	0.969348	+	0.650830i
$889$		−	6.96807e8i		−	0.991761i
$890$	1.46562e8	−	7.31981e7i	0.207899	−	0.103832i
$891$	−7.00958e8	−	1.71521e8i	−0.990966	−	0.242485i
$892$	−2.52380e8	−	1.78652e8i	−0.355598	−	0.251718i
$893$	−4.65503e8	+	4.65503e8i	−0.653685	+	0.653685i
$894$	−5.95548e8	+	1.47188e7i	−0.833497	+	0.0205997i
$895$	−8.99831e8	−	3.87792e8i	−1.25514	−	0.540916i
$896$	−6.42393e8	+	4.32851e8i	−0.893052	+	0.601748i
$897$	−1.17470e9	−	1.32483e9i	−1.62760	−	1.83563i
$898$	−6.54983e8	−	5.52462e8i	−0.904484	−	0.762910i
$899$			7.73324e7i			0.106434i
$900$	−5.26191e8	−	5.04543e8i	−0.721799	−	0.692103i
$901$	1.41374e7			0.0193284
$902$	6.16243e8	−	7.30600e8i	0.839716	−	0.995544i
$903$	7.58301e8	−	6.72365e8i	1.02986	−	0.913149i
$904$	−6.19122e7	−	2.38373e8i	−0.0838052	−	0.322665i
$905$	1.03863e8	−	2.41003e8i	0.140125	−	0.325145i
$906$	−2.41492e7	−	9.77118e8i	−0.0324727	−	1.31390i
$907$	1.25387e8	+	1.25387e8i	0.168047	+	0.168047i	0.786120	−	0.618074i	$-0.212087\pi$
$907$	1.25387e8	+	1.25387e8i	0.168047	+	0.168047i	−0.618074	+	0.786120i	$0.712087\pi$
$908$	−7.75779e8	−	5.49152e8i	−1.03629	−	0.733558i
$909$	5.38355e8	+	6.49089e7i	0.716765	+	0.0864197i
$910$	−4.86925e8	−	9.74956e8i	−0.646157	−	1.29378i
$911$	−2.00672e8			−0.265419			−0.132710	−	0.991155i	$-0.542368\pi$
$911$	−2.00672e8			−0.265419			−0.132710	+	0.991155i	$0.542368\pi$
$912$	−2.84574e8	+	5.12867e8i	−0.375156	+	0.676114i
$913$	−5.50507e8	−	5.50507e8i	−0.723354	−	0.723354i
$914$	1.77117e6	−	150386.i	0.00231964	−	0.000196956i
$915$	−1.40531e8	−	4.26213e8i	−0.183446	−	0.556370i
$916$	−7.21121e8	+	1.23347e8i	−0.938257	+	0.160488i
$917$	4.12474e8	+	4.12474e8i	0.534920	+	0.534920i
$918$	−3.50658e7	+	2.89480e7i	−0.0453268	+	0.0374189i
$919$	4.61364e8			0.594425			0.297212	−	0.954811i	$-0.403943\pi$
$919$	4.61364e8			0.594425			0.297212	+	0.954811i	$0.403943\pi$
$920$	−2.16508e8	+	1.40594e9i	−0.278042	+	1.80553i
$921$	−2.02321e8	−	1.21528e7i	−0.258978	−	0.0155560i
$922$	2.14950e7	−	2.54838e7i	0.0274248	−	0.0325141i
$923$	5.30495e8	+	5.30495e8i	0.674646	+	0.674646i
$924$	9.46393e7	+	8.61509e8i	0.119965	+	1.09205i
$925$	9.23702e8	+	2.62581e7i	1.16710	+	0.0331770i
$926$	4.15944e8	−	3.53169e7i	0.523844	−	0.0444784i
$927$	1.33818e8	+	1.70510e8i	0.167987	+	0.214048i
$928$	−6.44999e7	−	2.44161e7i	−0.0807077	−	0.0305515i
$929$	5.98439e8			0.746402			0.373201	−	0.927751i	$-0.378260\pi$
$929$	5.98439e8			0.746402			0.373201	+	0.927751i	$0.378260\pi$
$930$	9.20476e8	+	3.69999e8i	1.14436	+	0.459994i
$931$			9.96103e7i			0.123440i
$932$	−3.68103e8	−	2.60570e8i	−0.454697	−	0.321867i
$933$	1.44075e7	−	1.27747e7i	0.0177396	−	0.0157292i
$934$	−1.43506e9	+	1.21847e8i	−1.76128	+	0.149546i
$935$	4.55456e7	−	1.81118e7i	0.0557201	−	0.0221578i
$936$	−1.47260e8	−	1.09135e9i	−0.179580	−	1.33087i
$937$	1.14784e9	−	1.14784e9i	1.39528	−	1.39528i	0.582334	−	0.812949i	$-0.302139\pi$
$937$	1.14784e9	−	1.14784e9i	1.39528	−	1.39528i	0.812949	−	0.582334i	$-0.197861\pi$
$938$	−1.36685e8	+	1.62049e8i	−0.165619	+	0.196354i
$939$	−4.77777e8	−	2.86986e7i	−0.577070	−	0.0346629i
$940$	−8.47672e8	+	5.17265e8i	−1.02057	+	0.622772i
$941$			1.53112e8i			0.183755i	0.995770	+	0.0918775i	$0.0292868\pi$
$941$			1.53112e8i			0.183755i	−0.995770	+	0.0918775i	$0.970713\pi$
$942$	9.03585e8	−	9.49381e8i	1.08098	−	1.13576i
$943$	1.38283e9	−	1.38283e9i	1.64905	−	1.64905i
$944$	−2.26048e8	−	6.41438e8i	−0.268711	−	0.762499i
$945$	−7.56707e8	−	5.03260e8i	−0.896670	−	0.596344i
$946$	−1.09997e9	+	9.33957e7i	−1.29929	+	0.110320i
$947$	−8.55786e8	+	8.55786e8i	−1.00766	+	1.00766i	−0.00769273	+	0.999970i	$0.502449\pi$
$947$	−8.55786e8	+	8.55786e8i	−1.00766	+	1.00766i	−0.999970	+	0.00769273i	$0.997551\pi$
$948$	1.85291e8	+	1.48611e8i	0.217485	+	0.174431i
$949$			9.89996e8i			1.15834i
$950$	3.72941e7	+	6.61891e8i	0.0434980	+	0.771997i
$951$	1.54285e9	+	9.26743e7i	1.79383	+	0.107750i
$952$	4.70830e7	+	2.76680e7i	0.0545699	+	0.0320677i
$953$	8.11319e8	−	8.11319e8i	0.937375	−	0.937375i	−0.0607767	−	0.998151i	$-0.519358\pi$
$953$	8.11319e8	−	8.11319e8i	0.937375	−	0.937375i	0.998151	+	0.0607767i	$0.0193578\pi$
$954$	−1.00726e7	+	2.85342e8i	−0.0116010	+	0.328641i
$955$	3.88646e8	−	9.01812e8i	0.446215	−	1.03539i
$956$	−9.13530e8	+	1.56258e8i	−1.04556	+	0.178842i
$957$	−5.77368e7	+	5.11937e7i	−0.0658745	+	0.0584091i
$958$	6.57531e8	−	7.79551e8i	0.747859	−	0.886641i
$959$		−	6.98107e8i		−	0.791528i
$960$	−5.99224e8	+	6.50914e8i	−0.677291	+	0.735715i
$961$	−4.62532e8			−0.521161
$962$	1.06704e9	+	9.00020e8i	1.19855	+	1.01094i
$963$	4.90738e8	+	6.25297e8i	0.549504	+	0.700177i
$964$	−7.13933e7	−	4.17386e8i	−0.0796941	−	0.465915i
$965$	1.54833e8	−	6.15711e7i	0.172298	−	0.0685165i
$966$	4.38137e7	+	1.77278e9i	0.0486047	+	1.96663i
$967$	−2.43796e8	−	2.43796e8i	−0.269617	−	0.269617i	0.559329	−	0.828946i	$-0.311059\pi$
$967$	−2.43796e8	−	2.43796e8i	−0.269617	−	0.269617i	−0.828946	+	0.559329i	$0.811059\pi$
$968$	1.87554e7	−	3.19162e7i	0.0206776	−	0.0351873i
$969$	4.12760e7	+	2.47933e6i	0.0453656	+	0.00272498i
$970$	1.07486e8	−	3.21971e8i	0.117770	−	0.352778i
$971$	1.86629e7			0.0203855			0.0101928	−	0.999948i	$-0.496755\pi$
$971$	1.86629e7			0.0203855			0.0101928	+	0.999948i	$0.496755\pi$
$972$	−5.59287e8	−	7.28373e8i	−0.609027	−	0.793150i
$973$	5.87373e8	+	5.87373e8i	0.637640	+	0.637640i
$974$	9.44441e7	+	1.11231e9i	0.102211	+	1.20379i
$975$	−7.98991e8	−	9.54423e8i	−0.862041	−	1.02974i
$976$	−5.13692e8	+	1.81029e8i	−0.552527	+	0.194715i
$977$	6.44397e8	+	6.44397e8i	0.690987	+	0.690987i	0.962449	−	0.271462i	$-0.0875072\pi$
$977$	6.44397e8	+	6.44397e8i	0.690987	+	0.690987i	−0.271462	+	0.962449i	$0.587507\pi$
$978$	−1.04030e9	+	1.09302e9i	−1.11209	+	1.16846i
$979$	−2.22456e8			−0.237080
$980$	−3.53510e7	+	1.46037e8i	−0.0375598	+	0.155162i
$981$	1.30721e9	+	1.57610e8i	1.38465	+	0.166946i
$982$	7.55689e8	+	6.37404e8i	0.798010	+	0.673101i
$983$	1.21423e9	+	1.21423e9i	1.27832	+	1.27832i	0.941605	+	0.336718i	$0.109317\pi$
$983$	1.21423e9	+	1.21423e9i	1.27832	+	1.27832i	0.336718	+	0.941605i	$0.390683\pi$
$984$	1.19346e9	−	2.34627e8i	1.25263	−	0.246259i
$985$	−1.52830e9	+	6.07749e8i	−1.59919	+	0.635939i
$986$	411356.	+	4.84474e6i	0.000429128	+	0.00505405i
$987$	−9.26252e8	+	8.21283e8i	−0.963336	+	0.854164i
$988$	−5.78605e8	+	8.17387e8i	−0.599945	+	0.847534i
$989$	−2.25872e9			−2.33492
$990$	3.33108e8	+	9.32172e8i	0.343304	+	0.960706i
$991$			1.07909e9i			1.10875i	0.832265	+	0.554377i	$0.187044\pi$
$991$			1.07909e9i			1.10875i	−0.832265	+	0.554377i	$0.812956\pi$
$992$	4.26247e8	−	1.12601e9i	0.436642	−	1.15347i
$993$	2.51664e7	+	2.83830e7i	0.0257024	+	0.0289874i
$994$	−6.35689e7	−	7.48682e8i	−0.0647270	−	0.762322i
$995$	−7.98899e7	+	1.85376e8i	−0.0811004	+	0.188185i
$996$	−1.08184e8	−	9.84811e8i	−0.109493	−	0.996724i
$997$	−6.82326e8	+	6.82326e8i	−0.688504	+	0.688504i	−0.961901	−	0.273397i	$-0.911853\pi$
$997$	−6.82326e8	+	6.82326e8i	−0.688504	+	0.688504i	0.273397	+	0.961901i	$0.411853\pi$
$998$	9.49044e8	+	8.00495e8i	0.954761	+	0.805317i
$999$	1.14526e9	+	2.08385e8i	1.14871	+	0.209012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.17	✓	136
3.2	odd	2	inner	60.7.l.a.23.52	yes	136
4.3	odd	2	inner	60.7.l.a.23.18	yes	136
5.2	odd	4	inner	60.7.l.a.47.51	yes	136
12.11	even	2	inner	60.7.l.a.23.51	yes	136
15.2	even	4	inner	60.7.l.a.47.18	yes	136
20.7	even	4	inner	60.7.l.a.47.52	yes	136
60.47	odd	4	inner	60.7.l.a.47.17	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.17	✓	136	1.1	even	1	trivial
60.7.l.a.23.18	yes	136	4.3	odd	2	inner
60.7.l.a.23.51	yes	136	12.11	even	2	inner
60.7.l.a.23.52	yes	136	3.2	odd	2	inner
60.7.l.a.47.17	yes	136	60.47	odd	4	inner
60.7.l.a.47.18	yes	136	15.2	even	4	inner
60.7.l.a.47.51	yes	136	5.2	odd	4	inner
60.7.l.a.47.52	yes	136	20.7	even	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.11516 - 5.15798i) q^{2} +(20.2023 - 17.9128i) q^{3} +(10.7904 + 63.0838i) q^{4} +(49.4715 - 114.794i) q^{5} +(-215.934 + 5.33675i) q^{6} +(261.181 + 261.181i) q^{7} +(259.400 - 441.424i) q^{8} +(87.2628 - 723.758i) q^{9} +O(q^{10})\)	\(q+(-6.11516 - 5.15798i) q^{2} +(20.2023 - 17.9128i) q^{3} +(10.7904 + 63.0838i) q^{4} +(49.4715 - 114.794i) q^{5} +(-215.934 + 5.33675i) q^{6} +(261.181 + 261.181i) q^{7} +(259.400 - 441.424i) q^{8} +(87.2628 - 723.758i) q^{9} +(-894.630 + 446.808i) q^{10} +1357.89 q^{11} +(1348.00 + 1081.15i) q^{12} +(2086.27 + 2086.27i) q^{13} +(-249.996 - 2944.33i) q^{14} +(-1056.84 - 3205.26i) q^{15} +(-3863.13 + 1361.40i) q^{16} +(204.191 + 204.191i) q^{17} +(-4266.76 + 3975.80i) q^{18} +5303.53 q^{19} +(7775.43 + 1882.18i) q^{20} +(9954.93 + 597.963i) q^{21} +(-8303.71 - 7003.97i) q^{22} +(-15716.7 - 15716.7i) q^{23} +(-2666.68 - 13564.4i) q^{24} +(-10730.1 - 11358.0i) q^{25} +(-1996.93 - 23518.8i) q^{26} +(-11201.6 - 16184.7i) q^{27} +(-13658.0 + 19294.5i) q^{28} -2104.69 q^{29} +(-10070.0 + 25051.9i) q^{30} -36742.8i q^{31} +(30645.8 + 11600.8i) q^{32} +(27432.4 - 24323.6i) q^{33} +(-195.447 - 2301.87i) q^{34} +(42902.9 - 17060.9i) q^{35} +(46599.0 - 2304.77i) q^{36} +(-41818.9 + 41818.9i) q^{37} +(-32431.9 - 27355.5i) q^{38} +(79518.3 + 4776.42i) q^{39} +(-37839.8 - 51615.4i) q^{40} +87984.8i q^{41} +(-57791.7 - 55004.0i) q^{42} +(71857.2 - 71857.2i) q^{43} +(14652.2 + 85660.8i) q^{44} +(-78765.8 - 45822.7i) q^{45} +(15043.7 + 177177. i) q^{46} +(-87772.4 + 87772.4i) q^{47} +(-53657.6 + 96702.9i) q^{48} +18781.9i q^{49} +(7031.94 + 124802. i) q^{50} +(7782.75 + 467.487i) q^{51} +(-109098. + 154121. i) q^{52} +(34618.2 - 34618.2i) q^{53} +(-14980.5 + 156750. i) q^{54} +(67176.9 - 155877. i) q^{55} +(183042. - 47541.2i) q^{56} +(107143. - 95001.1i) q^{57} +(12870.5 + 10856.0i) q^{58} +166041. i q^{59} +(190797. - 101255. i) q^{60} +132973. q^{61} +(-189519. + 224688. i) q^{62} +(211823. - 166240. i) q^{63} +(-127567. - 229011. i) q^{64} +(342701. - 136279. i) q^{65} +(-293215. + 7246.71i) q^{66} +(-50730.4 - 50730.4i) q^{67} +(-10677.8 + 15084.4i) q^{68} +(-599043. - 35982.7i) q^{69} +(-350358. - 116963. i) q^{70} +254279. q^{71} +(-296849. - 226263. i) q^{72} +(237265. + 237265. i) q^{73} +(471430. - 40028.1i) q^{74} +(-420227. - 37251.2i) q^{75} +(57227.2 + 334567. i) q^{76} +(354655. + 354655. i) q^{77} +(-461630. - 439362. i) q^{78} +137456. q^{79} +(-34835.3 + 510814. i) q^{80} +(-516211. - 126314. i) q^{81} +(453824. - 538041. i) q^{82} +(-405414. - 405414. i) q^{83} +(69695.9 + 634447. i) q^{84} +(33541.5 - 13338.2i) q^{85} +(-810056. + 68780.1i) q^{86} +(-42519.5 + 37700.9i) q^{87} +(352237. - 599406. i) q^{88} -163824. q^{89} +(245313. + 686486. i) q^{90} +1.08979e6i q^{91} +(821880. - 1.16106e6i) q^{92} +(-658167. - 742288. i) q^{93} +(989471. - 84013.8i) q^{94} +(262374. - 608811. i) q^{95} +(826917. - 314589. i) q^{96} +(-240019. + 240019. i) q^{97} +(96876.7 - 114854. i) q^{98} +(118493. - 982784. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 4 q^{6}+O(q^{10}) \) 136 * q - 4 * q^6	\( 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) \) 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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