LMFDB - Embedded newform 62.7.f.a.23.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,7,Mod(15,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.15"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	62.f (of order $10$, degree $4$, 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:	$14.2633531844$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	62.23
Dual form			62.7.f.a.27.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.74806 + 5.37999i) q^{2} +(-35.2660 + 11.4586i) q^{3} +(-25.8885 - 18.8091i) q^{4} -54.3091 q^{5} -209.761i q^{6} +(-333.682 - 242.434i) q^{7} +(146.448 - 106.400i) q^{8} +(522.615 - 379.702i) q^{9} +(94.9357 - 292.182i) q^{10} +(300.800 - 414.015i) q^{11} +(1128.51 + 366.675i) q^{12} +(-2719.08 + 883.482i) q^{13} +(1887.59 - 1371.41i) q^{14} +(1915.26 - 622.306i) q^{15} +(316.433 + 973.882i) q^{16} +(2454.72 + 3378.63i) q^{17} +(1129.23 + 3475.41i) q^{18} +(219.934 - 676.886i) q^{19} +(1405.98 + 1021.51i) q^{20} +(14545.6 + 4726.14i) q^{21} +(1701.58 + 2342.02i) q^{22} +(10513.2 + 14470.1i) q^{23} +(-3945.42 + 5430.40i) q^{24} -12675.5 q^{25} -16173.0i q^{26} +(1809.30 - 2490.28i) q^{27} +(4078.56 + 12552.5i) q^{28} +(-9187.17 - 2985.09i) q^{29} +11391.9i q^{30} +(28873.1 + 7338.24i) q^{31} -5792.62 q^{32} +(-5863.95 + 18047.4i) q^{33} +(-22468.0 + 7300.29i) q^{34} +(18121.9 + 13166.4i) q^{35} -20671.6 q^{36} -19536.6i q^{37} +(3257.18 + 2366.48i) q^{38} +(85767.4 - 62313.7i) q^{39} +(-7953.44 + 5778.51i) q^{40} +(28906.2 - 88964.1i) q^{41} +(-50853.1 + 69993.3i) q^{42} +(78463.6 + 25494.4i) q^{43} +(-15574.5 + 5060.47i) q^{44} +(-28382.7 + 20621.3i) q^{45} +(-96226.8 + 31266.0i) q^{46} +(-17891.9 - 55065.5i) q^{47} +(-22318.7 - 30719.0i) q^{48} +(16213.7 + 49900.6i) q^{49} +(22157.6 - 68194.2i) q^{50} +(-125282. - 91022.9i) q^{51} +(87010.5 + 28271.4i) q^{52} +(-2984.73 - 4108.13i) q^{53} +(10234.9 + 14087.2i) q^{54} +(-16336.2 + 22484.8i) q^{55} -74662.0 q^{56} +26391.2i q^{57} +(32119.5 - 44208.7i) q^{58} +(11416.1 + 35135.3i) q^{59} +(-61288.4 - 19913.8i) q^{60} -414903. i q^{61} +(-89951.6 + 142509. i) q^{62} -266440. q^{63} +(10125.9 - 31164.2i) q^{64} +(147671. - 47981.1i) q^{65} +(-86844.2 - 63096.0i) q^{66} +47941.8 q^{67} -133639. i q^{68} +(-536564. - 389837. i) q^{69} +(-102513. + 74480.1i) q^{70} +(-89243.3 + 64839.1i) q^{71} +(36135.3 - 111213. i) q^{72} +(-218642. + 300935. i) q^{73} +(105107. + 34151.3i) q^{74} +(447015. - 145244. i) q^{75} +(-18425.4 + 13386.8i) q^{76} +(-200743. + 65225.3i) q^{77} +(185320. + 570356. i) q^{78} +(415527. + 571924. i) q^{79} +(-17185.2 - 52890.6i) q^{80} +(-180795. + 556431. i) q^{81} +(428096. + 311030. i) q^{82} +(697420. + 226606. i) q^{83} +(-287669. - 395942. i) q^{84} +(-133313. - 183490. i) q^{85} +(-274319. + 377568. i) q^{86} +358199. q^{87} -92636.9i q^{88} +(238829. - 328720. i) q^{89} +(-61327.3 - 188746. i) q^{90} +(1.12149e6 + 364395. i) q^{91} -572354. i q^{92} +(-1.10232e6 + 72054.9i) q^{93} +327528. q^{94} +(-11944.4 + 36761.0i) q^{95} +(204282. - 66375.3i) q^{96} +(979561. + 711693. i) q^{97} -296807. q^{98} -330585. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) $ 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.74806	+	5.37999i	−0.218508	+	0.672499i
$2$	−1.74806	+	5.37999i	−0.218508	+	0.672499i
$3$	−35.2660	+	11.4586i	−1.30615	+	0.424393i	−0.877716	−	0.479182i	$-0.840934\pi$
$3$	−35.2660	+	11.4586i	−1.30615	+	0.424393i	−0.428431	+	0.903574i	$0.640934\pi$
$4$	−25.8885	−	18.8091i	−0.404508	−	0.293893i
$5$	−54.3091			−0.434472			−0.217236	−	0.976119i	$-0.569704\pi$
$5$	−54.3091			−0.434472			−0.217236	+	0.976119i	$0.569704\pi$
$6$		−	209.761i		−	0.971115i
$7$	−333.682	−	242.434i	−0.972833	−	0.706804i	−0.0167372	−	0.999860i	$-0.505328\pi$
$7$	−333.682	−	242.434i	−0.972833	−	0.706804i	−0.956095	+	0.293056i	$0.905328\pi$
$8$	146.448	−	106.400i	0.286031	−	0.207813i
$9$	522.615	−	379.702i	0.716893	−	0.520853i
$10$	94.9357	−	292.182i	0.0949357	−	0.292182i
$11$	300.800	−	414.015i	0.225995	−	0.311056i	−0.680929	−	0.732349i	$-0.738424\pi$
$11$	300.800	−	414.015i	0.225995	−	0.311056i	0.906924	+	0.421294i	$0.138424\pi$
$12$	1128.51	+	366.675i	0.653073	+	0.212196i
$13$	−2719.08	+	883.482i	−1.23763	+	0.402131i	−0.853474	−	0.521136i	$-0.825508\pi$
$13$	−2719.08	+	883.482i	−1.23763	+	0.402131i	−0.384159	+	0.923267i	$0.625508\pi$
$14$	1887.59	−	1371.41i	0.687897	−	0.499786i
$15$	1915.26	−	622.306i	0.567485	−	0.184387i
$16$	316.433	+	973.882i	0.0772542	+	0.237764i
$17$	2454.72	+	3378.63i	0.499637	+	0.687691i	0.982129	−	0.188209i	$-0.0602683\pi$
$17$	2454.72	+	3378.63i	0.499637	+	0.687691i	−0.482492	+	0.875900i	$0.660268\pi$
$18$	1129.23	+	3475.41i	0.193626	+	0.595920i
$19$	219.934	−	676.886i	0.0320650	−	0.0986858i	−0.933743	−	0.357944i	$-0.883478\pi$
$19$	219.934	−	676.886i	0.0320650	−	0.0986858i	0.965808	+	0.259258i	$0.0834780\pi$
$20$	1405.98	+	1021.51i	0.175748	+	0.127688i
$21$	14545.6	+	4726.14i	1.57062	+	0.510327i
$22$	1701.58	+	2342.02i	0.159803	+	0.219950i
$23$	10513.2	+	14470.1i	0.864072	+	1.18929i	0.980583	+	0.196104i	$0.0628289\pi$
$23$	10513.2	+	14470.1i	0.864072	+	1.18929i	−0.116511	+	0.993189i	$0.537171\pi$
$24$	−3945.42	+	5430.40i	−0.285404	+	0.392824i
$25$	−12675.5			−0.811234
$26$		−	16173.0i		−	0.920175i
$27$	1809.30	−	2490.28i	0.0919218	−	0.126519i
$28$	4078.56	+	12552.5i	0.185794	+	0.571817i
$29$	−9187.17	−	2985.09i	−0.376693	−	0.122395i	0.114550	−	0.993417i	$-0.463457\pi$
$29$	−9187.17	−	2985.09i	−0.376693	−	0.122395i	−0.491243	+	0.871022i	$0.663457\pi$
$30$			11391.9i			0.421923i
$31$	28873.1	+	7338.24i	0.969188	+	0.246324i
$31$	28873.1	+	7338.24i	0.969188	+	0.246324i
$32$	−5792.62			−0.176777
$33$	−5863.95	+	18047.4i	−0.163173	+	0.502195i
$34$	−22468.0	+	7300.29i	−0.571646	+	0.185739i
$35$	18121.9	+	13166.4i	0.422669	+	0.307087i
$36$	−20671.6			−0.443064
$37$		−	19536.6i		−	0.385695i	−0.981229	−	0.192848i	$-0.938228\pi$
$37$		−	19536.6i		−	0.385695i	0.981229	−	0.192848i	$-0.0617723\pi$
$38$	3257.18	+	2366.48i	0.0593596	+	0.0431273i
$39$	85767.4	−	62313.7i	1.44587	−	1.05048i
$40$	−7953.44	+	5778.51i	−0.124272	+	0.0902892i
$41$	28906.2	−	88964.1i	0.419411	−	1.29081i	−0.488835	−	0.872376i	$-0.662578\pi$
$41$	28906.2	−	88964.1i	0.419411	−	1.29081i	0.908246	−	0.418437i	$-0.137422\pi$
$42$	−50853.1	+	69993.3i	−0.686388	+	0.944732i
$43$	78463.6	+	25494.4i	0.986877	+	0.320656i	0.757610	−	0.652708i	$-0.226367\pi$
$43$	78463.6	+	25494.4i	0.986877	+	0.320656i	0.229267	+	0.973364i	$0.426367\pi$
$44$	−15574.5	+	5060.47i	−0.182834	+	0.0594064i
$45$	−28382.7	+	20621.3i	−0.311470	+	0.226296i
$46$	−96226.8	+	31266.0i	−0.988604	+	0.321217i
$47$	−17891.9	−	55065.5i	−0.172330	−	0.530379i	0.827171	−	0.561950i	$-0.189949\pi$
$47$	−17891.9	−	55065.5i	−0.172330	−	0.530379i	−0.999501	+	0.0315716i	$0.989949\pi$
$48$	−22318.7	−	30719.0i	−0.201811	−	0.277769i
$49$	16213.7	+	49900.6i	0.137814	+	0.424148i
$50$	22157.6	−	68194.2i	0.177261	−	0.545553i
$51$	−125282.	−	91022.9i	−0.944450	−	0.686183i
$52$	87010.5	+	28271.4i	0.618816	+	0.201066i
$53$	−2984.73	−	4108.13i	−0.0200483	−	0.0275942i	0.798875	−	0.601497i	$-0.205429\pi$
$53$	−2984.73	−	4108.13i	−0.0200483	−	0.0275942i	−0.818923	+	0.573903i	$0.805429\pi$
$54$	10234.9	+	14087.2i	0.0649985	+	0.0894628i
$55$	−16336.2	+	22484.8i	−0.0981887	+	0.135145i
$56$	−74662.0			−0.425143
$57$			26391.2i			0.142506i
$58$	32119.5	−	44208.7i	0.164621	−	0.226581i
$59$	11416.1	+	35135.3i	0.0555857	+	0.171075i	0.974995	−	0.222227i	$-0.0713326\pi$
$59$	11416.1	+	35135.3i	0.0555857	+	0.171075i	−0.919409	+	0.393302i	$0.871333\pi$
$60$	−61288.4	−	19913.8i	−0.283742	−	0.0921935i
$61$		−	414903.i		−	1.82792i	−0.405807	−	0.913959i	$-0.633009\pi$
$61$		−	414903.i		−	1.82792i	0.405807	−	0.913959i	$-0.366991\pi$
$62$	−89951.6	+	142509.i	−0.377428	+	0.597953i
$63$	−266440.			−1.06556
$64$	10125.9	−	31164.2i	0.0386271	−	0.118882i
$65$	147671.	−	47981.1i	0.537717	−	0.174715i
$66$	−86844.2	−	63096.0i	−0.302071	−	0.219467i
$67$	47941.8			0.159401			0.0797003	−	0.996819i	$-0.474604\pi$
$67$	47941.8			0.159401			0.0797003	+	0.996819i	$0.474604\pi$
$68$		−	133639.i		−	0.425016i
$69$	−536564.	−	389837.i	−1.63333	−	1.18669i
$70$	−102513.	+	74480.1i	−0.298872	+	0.217143i
$71$	−89243.3	+	64839.1i	−0.249345	+	0.181160i	−0.705436	−	0.708773i	$-0.749249\pi$
$71$	−89243.3	+	64839.1i	−0.249345	+	0.181160i	0.456091	+	0.889933i	$0.349249\pi$
$72$	36135.3	−	111213.i	0.0968131	−	0.297960i
$73$	−218642.	+	300935.i	−0.562038	+	0.773579i	−0.991584	−	0.129466i	$-0.958674\pi$
$73$	−218642.	+	300935.i	−0.562038	+	0.773579i	0.429546	+	0.903045i	$0.358674\pi$
$74$	105107.	+	34151.3i	0.259380	+	0.0842775i
$75$	447015.	−	145244.i	1.05959	−	0.344282i
$76$	−18425.4	+	13386.8i	−0.0419736	+	0.0304956i
$77$	−200743.	+	65225.3i	−0.439711	+	0.142871i
$78$	185320.	+	570356.i	0.390516	+	1.20188i
$79$	415527.	+	571924.i	0.842787	+	1.16000i	0.985406	+	0.170219i	$0.0544476\pi$
$79$	415527.	+	571924.i	0.842787	+	1.16000i	−0.142619	+	0.989778i	$0.545552\pi$
$80$	−17185.2	−	52890.6i	−0.0335648	−	0.103302i
$81$	−180795.	+	556431.i	−0.340198	+	1.04702i
$82$	428096.	+	311030.i	0.776425	+	0.564106i
$83$	697420.	+	226606.i	1.21972	+	0.396311i	0.846980	−	0.531625i	$-0.178418\pi$
$83$	697420.	+	226606.i	1.21972	+	0.396311i	0.372740	+	0.927936i	$0.378418\pi$
$84$	−287669.	−	395942.i	−0.485350	−	0.668027i
$85$	−133313.	−	183490.i	−0.217078	−	0.298783i
$86$	−274319.	+	377568.i	−0.431281	+	0.593608i
$87$	358199.			0.543960
$88$		−	92636.9i		−	0.135936i
$89$	238829.	−	328720.i	0.338780	−	0.466290i	−0.605305	−	0.795994i	$-0.706949\pi$
$89$	238829.	−	328720.i	0.338780	−	0.466290i	0.944085	+	0.329704i	$0.106949\pi$
$90$	−61327.3	−	188746.i	−0.0841253	−	0.258911i
$91$	1.12149e6	+	364395.i	1.48824	+	0.483558i
$92$		−	572354.i		−	0.735024i
$93$	−1.10232e6	+	72054.9i	−1.37044	+	0.0895808i
$94$	327528.			0.394335
$95$	−11944.4	+	36761.0i	−0.0139313	+	0.0428763i
$96$	204282.	−	66375.3i	0.230896	−	0.0750228i
$97$	979561.	+	711693.i	1.07329	+	0.779789i	0.976500	−	0.215516i	$-0.0691433\pi$
$97$	979561.	+	711693.i	1.07329	+	0.779789i	0.0967876	+	0.995305i	$0.469143\pi$
$98$	−296807.			−0.315352
$99$		−	330585.i		−	0.340704i
$100$	328151.	+	238416.i	0.328151	+	0.238416i
$101$	429640.	−	312152.i	0.417004	−	0.302971i	−0.359427	−	0.933173i	$-0.617028\pi$
$101$	429640.	−	312152.i	0.417004	−	0.302971i	0.776431	+	0.630202i	$0.217028\pi$
$102$	708703.	−	514903.i	0.667827	−	0.485205i
$103$	121364.	−	373520.i	0.111065	−	0.341824i	−0.880041	−	0.474898i	$-0.842485\pi$
$103$	121364.	−	373520.i	0.111065	−	0.341824i	0.991106	+	0.133074i	$0.0424849\pi$
$104$	−304200.	+	418695.i	−0.270433	+	0.372219i
$105$	−789955.	−	256672.i	−0.682393	−	0.221723i
$106$	27319.2	−	8876.55i	0.0229377	−	0.00745293i
$107$	247505.	−	179823.i	0.202038	−	0.146789i	−0.482166	−	0.876080i	$-0.660150\pi$
$107$	247505.	−	179823.i	0.202038	−	0.146789i	0.684204	+	0.729291i	$0.260150\pi$
$108$	−93680.1	+	30438.5i	−0.0743663	+	0.0241631i
$109$	−55628.6	−	171207.i	−0.0429555	−	0.132203i	0.927279	−	0.374371i	$-0.122141\pi$
$109$	−55628.6	−	171207.i	−0.0429555	−	0.132203i	−0.970234	+	0.242168i	$0.922141\pi$
$110$	−92411.2	−	127193.i	−0.0694299	−	0.0955621i
$111$	223863.	+	688978.i	0.163686	+	0.503775i
$112$	130514.	−	401681.i	0.0928972	−	0.285908i
$113$	−789200.	−	573387.i	−0.546955	−	0.397386i	0.279707	−	0.960086i	$-0.409763\pi$
$113$	−789200.	−	573387.i	−0.546955	−	0.397386i	−0.826661	+	0.562700i	$0.809763\pi$
$114$	−141984.	−	46133.5i	−0.0958353	−	0.0311388i
$115$	−570960.	−	785859.i	−0.375416	−	0.516715i
$116$	181695.	+	250082.i	0.116405	+	0.160217i
$117$	−1.08557e6	+	1.49416e6i	−0.677799	+	0.932910i
$118$	−208983.			−0.127194
$119$		−	1.72249e6i		−	1.02215i
$120$	214272.	−	294920.i	0.124000	−	0.170671i
$121$	466514.	+	1.43578e6i	0.263335	+	0.810462i
$122$	2.23217e6	+	725276.i	1.22927	+	0.399415i
$123$			3.46863e6i			1.86399i
$124$	−609456.	−	733054.i	−0.319652	−	0.384477i
$125$	1.53697e6			0.786931
$126$	465754.	−	1.43344e6i	0.232833	−	0.716586i
$127$	−2.69819e6	+	876695.i	−1.31723	+	0.427994i	−0.881543	−	0.472104i	$-0.843495\pi$
$127$	−2.69819e6	+	876695.i	−1.31723	+	0.427994i	−0.435687	+	0.900098i	$0.643495\pi$
$128$	149962.	+	108954.i	0.0715077	+	0.0519534i
$129$	−3.05923e6			−1.42509
$130$			878340.i			0.399791i
$131$	−3.05343e6	−	2.21845e6i	−1.35823	−	0.986814i	−0.998555	−	0.0537378i	$-0.982886\pi$
$131$	−3.05343e6	−	2.21845e6i	−1.35823	−	0.986814i	−0.359678	−	0.933076i	$-0.617114\pi$
$132$	491265.	−	356925.i	0.213596	−	0.155187i
$133$	−237488.	+	172545.i	−0.100945	+	0.0733411i
$134$	−83805.3	+	257926.i	−0.0348303	+	0.107197i
$135$	−98261.2	+	135245.i	−0.0399375	+	0.0549692i
$136$	718975.	+	233609.i	0.285823	+	0.0928695i
$137$	−2.88687e6	+	938001.i	−1.12270	+	0.364789i	−0.810799	−	0.585324i	$-0.800967\pi$
$137$	−2.88687e6	+	938001.i	−1.12270	+	0.364789i	−0.311906	+	0.950113i	$0.600967\pi$
$138$	3.03527e6	−	2.20525e6i	1.15494	−	0.839113i
$139$	2.28882e6	−	743683.i	0.852250	−	0.276913i	0.149862	−	0.988707i	$-0.452117\pi$
$139$	2.28882e6	−	743683.i	0.852250	−	0.276913i	0.702388	+	0.711794i	$0.252117\pi$
$140$	−221503.	−	681715.i	−0.0807226	−	0.248439i
$141$	1.26195e6	+	1.73692e6i	0.450178	+	0.619617i
$142$	−192830.	−	593471.i	−0.0673458	−	0.207269i
$143$	−452123.	+	1.39149e6i	−0.154614	+	0.475853i
$144$	535158.	+	388815.i	0.179223	+	0.130213i
$145$	498947.	+	162118.i	0.163663	+	0.0531773i
$146$	−1.23683e6	−	1.70235e6i	−0.397421	−	0.547003i
$147$	−1.14358e6	−	1.57401e6i	−0.360011	−	0.495512i
$148$	−367467.	+	505775.i	−0.113353	+	0.156017i
$149$	−1.45583e6			−0.440100			−0.220050	−	0.975489i	$-0.570622\pi$
$149$	−1.45583e6			−0.440100			−0.220050	+	0.975489i	$0.570622\pi$
$150$			2.65883e6i			0.787801i
$151$	1.11022e6	−	1.52809e6i	0.322463	−	0.443832i	−0.616754	−	0.787156i	$-0.711553\pi$
$151$	1.11022e6	−	1.52809e6i	0.322463	−	0.443832i	0.939217	+	0.343324i	$0.111553\pi$
$152$	−39812.2	−	122529.i	−0.0113367	−	0.0348907i
$153$	2.56574e6	+	833660.i	0.716372	+	0.232764i
$154$		−	1.19401e6i		−	0.326924i
$155$	−1.56807e6	−	398533.i	−0.421085	−	0.107021i
$156$	−3.39246e6			−0.893596
$157$	1.24337e6	−	3.82671e6i	0.321294	−	0.988841i	−0.651792	−	0.758398i	$-0.725982\pi$
$157$	1.24337e6	−	3.82671e6i	0.321294	−	0.988841i	0.973086	−	0.230443i	$-0.0740176\pi$
$158$	−3.80331e6	+	1.23577e6i	−0.964252	+	0.313304i
$159$	152333.	+	110676.i	0.0378968	+	0.0275336i
$160$	314592.			0.0768046
$161$		−	7.37716e6i		−	1.76771i
$162$	−2.67755e6	−	1.94535e6i	−0.629785	−	0.457566i
$163$	3.39140e6	−	2.46399e6i	0.783097	−	0.568954i	−0.122810	−	0.992430i	$-0.539190\pi$
$163$	3.39140e6	−	2.46399e6i	0.783097	−	0.568954i	0.905907	+	0.423477i	$0.139190\pi$
$164$	−2.42168e6	+	1.75945e6i	−0.549016	+	0.398883i
$165$	318466.	−	980137.i	0.0708943	−	0.218190i
$166$	−2.43827e6	+	3.35599e6i	−0.533037	+	0.733663i
$167$	−5.90882e6	−	1.91989e6i	−1.26868	−	0.412218i	−0.404099	−	0.914715i	$-0.632415\pi$
$167$	−5.90882e6	−	1.91989e6i	−1.26868	−	0.412218i	−0.864579	+	0.502497i	$0.832415\pi$
$168$	2.63303e6	−	855522.i	0.555300	−	0.180428i
$169$	2.70787e6	−	1.96739e6i	0.561007	−	0.407596i
$170$	1.22021e6	−	396472.i	0.248364	−	0.0806985i
$171$	−142074.	−	437260.i	−0.0284137	−	0.0874483i
$172$	−1.55178e6	−	2.13585e6i	−0.304962	−	0.419744i
$173$	−107419.	−	330603.i	−0.0207465	−	0.0638511i	0.940147	−	0.340768i	$-0.110687\pi$
$173$	−107419.	−	330603.i	−0.0207465	−	0.0638511i	−0.960894	+	0.276917i	$0.910687\pi$
$174$	−626155.	+	1.92711e6i	−0.118860	+	0.365812i
$175$	4.22959e6	+	3.07298e6i	0.789195	+	0.573383i
$176$	498385.	+	161935.i	0.0914170	+	0.0297032i
$177$	−805202.	−	1.10827e6i	−0.145206	−	0.199859i
$178$	1.35102e6	+	1.85952e6i	0.239553	+	0.329717i
$179$	5.58411e6	−	7.68586e6i	0.973631	−	1.34009i	0.0334404	−	0.999441i	$-0.489354\pi$
$179$	5.58411e6	−	7.68586e6i	0.973631	−	1.34009i	0.940191	−	0.340648i	$-0.110646\pi$
$180$	1.12266e6			0.192499
$181$			1.57924e6i			0.266325i	0.991094	+	0.133162i	$0.0425132\pi$
$181$			1.57924e6i			0.266325i	−0.991094	+	0.133162i	$0.957487\pi$
$182$	−3.92088e6	+	5.39663e6i	−0.650383	+	0.895176i
$183$	4.75421e6	+	1.46319e7i	0.775755	+	2.38753i
$184$	3.07926e6	+	1.00051e6i	0.494302	+	0.160609i
$185$			1.06102e6i			0.167574i
$186$	1.53928e6	−	6.05644e6i	0.239209	−	0.941193i
$187$	2.13718e6			0.326826
$188$	−572540.	+	1.76210e6i	−0.0861652	+	0.265189i
$189$	−1.20746e6	+	392327.i	−0.178849	+	0.0581116i
$190$	−176894.	−	128521.i	−0.0257901	−	0.0187376i
$191$	6.62418e6			0.950675			0.475338	−	0.879803i	$-0.342326\pi$
$191$	6.62418e6			0.950675			0.475338	+	0.879803i	$0.342326\pi$
$192$			1.21506e6i			0.171671i
$193$	1.05172e7	+	7.64117e6i	1.46294	+	1.06289i	0.982585	+	0.185816i	$0.0594928\pi$
$193$	1.05172e7	+	7.64117e6i	1.46294	+	1.06289i	0.480357	+	0.877073i	$0.340507\pi$
$194$	−5.54123e6	+	4.02594e6i	−0.758929	+	0.551394i
$195$	−4.65795e6	+	3.38420e6i	−0.628190	+	0.456407i
$196$	518838.	−	1.59682e6i	0.0689070	−	0.212074i
$197$	−7.28548e6	+	1.00276e7i	−0.952927	+	1.31159i	−0.00271213	+	0.999996i	$0.500863\pi$
$197$	−7.28548e6	+	1.00276e7i	−0.952927	+	1.31159i	−0.950215	+	0.311595i	$0.899137\pi$
$198$	1.77854e6	+	577884.i	0.229123	+	0.0744466i
$199$	1.20522e7	−	3.91601e6i	1.52935	−	0.496917i	0.580939	−	0.813947i	$-0.302686\pi$
$199$	1.20522e7	−	3.91601e6i	1.52935	−	0.496917i	0.948416	+	0.317030i	$0.102686\pi$
$200$	−1.85630e6	+	1.34868e6i	−0.232038	+	0.168585i
$201$	−1.69071e6	+	549346.i	−0.208201	+	0.0676485i
$202$	928334.	+	2.85712e6i	0.112629	+	0.346636i
$203$	2.34190e6	+	3.22335e6i	0.279950	+	0.385318i
$204$	1.53131e6	+	4.71290e6i	0.180374	+	0.555134i
$205$	−1.56987e6	+	4.83156e6i	−0.182222	+	0.560823i
$206$	1.79738e6	+	1.30587e6i	0.205607	+	0.149383i
$207$	1.09887e7	+	3.57044e6i	1.23889	+	0.402541i
$208$	−1.72081e6	−	2.36850e6i	−0.191225	−	0.263198i
$209$	−214085.	−	294663.i	−0.0234503	−	0.0322765i
$210$	2.76179e6	−	3.80127e6i	0.298217	−	0.410460i
$211$	−7.41958e6			−0.789827			−0.394913	−	0.918718i	$-0.629225\pi$
$211$	−7.41958e6			−0.789827			−0.394913	+	0.918718i	$0.629225\pi$
$212$			162494.i			0.0170541i
$213$	2.40429e6	−	3.30922e6i	0.248798	−	0.342441i
$214$	534791.	+	1.64592e6i	0.0545686	+	0.167945i
$215$	−4.26129e6	−	1.38458e6i	−0.428771	−	0.139316i
$216$		−	557206.i		−	0.0552910i
$217$	−7.85537e6	−	9.44844e6i	−0.768754	−	0.924658i
$218$	1.01834e6			0.0982928
$219$	4.26233e6	−	1.31181e7i	0.405803	−	1.24893i
$220$	845838.	−	274830.i	0.0794364	−	0.0258104i
$221$	−9.65952e6	−	7.01805e6i	−0.894909	−	0.650189i
$222$	−4.09802e6			−0.374555
$223$			525473.i			0.0473844i	0.999719	+	0.0236922i	$0.00754217\pi$
$223$			525473.i			0.0473844i	−0.999719	+	0.0236922i	$0.992458\pi$
$224$	1.93289e6	+	1.40433e6i	0.171974	+	0.124947i
$225$	−6.62442e6	+	4.81292e6i	−0.581568	+	0.422534i
$226$	4.46439e6	−	3.24357e6i	0.386755	−	0.280994i
$227$	2.11365e6	−	6.50514e6i	0.180699	−	0.556134i	−0.819149	−	0.573581i	$-0.805554\pi$
$227$	2.11365e6	−	6.50514e6i	0.180699	−	0.556134i	0.999848	+	0.0174470i	$0.00555384\pi$
$228$	496395.	−	683229.i	0.0418816	−	0.0576450i
$229$	−1.64378e7	−	5.34095e6i	−1.36879	−	0.444746i	−0.469821	−	0.882762i	$-0.655681\pi$
$229$	−1.64378e7	−	5.34095e6i	−1.36879	−	0.444746i	−0.898967	+	0.438016i	$0.855681\pi$
$230$	5.22599e6	−	1.69803e6i	0.429521	−	0.139560i
$231$	6.33199e6	−	4.60046e6i	0.513694	−	0.373221i
$232$	−1.66306e6	+	540359.i	−0.133181	+	0.0432732i
$233$	6.98138e6	+	2.14865e7i	0.551916	+	1.69862i	0.703951	+	0.710249i	$0.251418\pi$
$233$	6.98138e6	+	2.14865e7i	0.551916	+	1.69862i	−0.152034	+	0.988375i	$0.548582\pi$
$234$	−6.14092e6	−	8.45225e6i	−0.479276	−	0.659667i
$235$	971691.	+	2.99056e6i	0.0748729	+	0.230435i
$236$	365316.	−	1.12433e6i	0.0277928	−	0.0855376i
$237$	−2.12074e7	−	1.54081e7i	−1.59310	−	1.15745i
$238$	9.26698e6	+	3.01103e6i	0.687397	+	0.223349i
$239$	8.41795e6	+	1.15863e7i	0.616613	+	0.848695i	0.997101	−	0.0760912i	$-0.0242440\pi$
$239$	8.41795e6	+	1.15863e7i	0.616613	+	0.848695i	−0.380488	+	0.924786i	$0.624244\pi$
$240$	1.21211e6	+	1.66832e6i	0.0876812	+	0.120683i
$241$	1.07988e7	−	1.48633e7i	0.771480	−	1.06185i	−0.224691	−	0.974430i	$-0.572137\pi$
$241$	1.07988e7	−	1.48633e7i	0.771480	−	1.06185i	0.996171	−	0.0874214i	$-0.0278627\pi$
$242$	−8.53999e6			−0.602575
$243$		−	1.94507e7i		−	1.35556i
$244$	−7.80396e6	+	1.07412e7i	−0.537212	+	0.739408i
$245$	−880550.	−	2.71005e6i	−0.0598764	−	0.184281i
$246$	−1.86612e7	−	6.06339e6i	−1.25353	−	0.407296i
$247$			2.03481e6i			0.135031i
$248$	5.00919e6	−	1.99744e6i	0.328407	−	0.130954i
$249$	−2.71918e7			−1.76133
$250$	−2.68673e6	+	8.26891e6i	−0.171951	+	0.529210i
$251$	6.15740e6	−	2.00066e6i	0.389382	−	0.126518i	−0.107782	−	0.994175i	$-0.534375\pi$
$251$	6.15740e6	−	2.00066e6i	0.389382	−	0.126518i	0.497164	+	0.867657i	$0.334375\pi$
$252$	6.89774e6	+	5.01150e6i	0.431027	+	0.313160i
$253$	9.15321e6			0.565213
$254$		−	1.60488e7i		−	0.979355i
$255$	6.80396e6	+	4.94337e6i	0.410338	+	0.298128i
$256$	−848316.	+	616338.i	−0.0505636	+	0.0367366i
$257$	−1.39594e7	+	1.01421e7i	−0.822368	+	0.597485i	−0.917390	−	0.397990i	$-0.869708\pi$
$257$	−1.39594e7	+	1.01421e7i	−0.822368	+	0.597485i	0.0950217	+	0.995475i	$0.469708\pi$
$258$	5.34772e6	−	1.64586e7i	0.311394	−	0.958371i
$259$	−4.73634e6	+	6.51901e6i	−0.272611	+	0.375217i
$260$	−4.72546e6	−	1.53539e6i	−0.268859	−	0.0873575i
$261$	−5.93480e6	+	1.92833e6i	−0.333799	+	0.108458i
$262$	1.72728e7	−	1.25494e7i	0.960416	−	0.697783i
$263$	3.33394e7	−	1.08326e7i	1.83270	−	0.595479i	0.833628	−	0.552326i	$-0.186260\pi$
$263$	3.33394e7	−	1.08326e7i	1.83270	−	0.595479i	0.999068	−	0.0431535i	$-0.0137405\pi$
$264$	1.06149e6	+	3.26693e6i	0.0576904	+	0.177553i
$265$	162098.	+	223109.i	0.00871045	+	0.0119889i
$266$	−513146.	−	1.57930e6i	−0.0272644	−	0.0839112i
$267$	−4.65587e6	+	1.43293e7i	−0.244606	+	0.752819i
$268$	−1.24114e6	−	901743.i	−0.0644789	−	0.0468467i
$269$	−7.63099e6	−	2.47946e6i	−0.392034	−	0.127380i	0.106365	−	0.994327i	$-0.466079\pi$
$269$	−7.63099e6	−	2.47946e6i	−0.392034	−	0.127380i	−0.498399	+	0.866947i	$0.666079\pi$
$270$	−555849.	−	765061.i	−0.0282401	−	0.0388691i
$271$	1.73295e7	+	2.38521e7i	0.870722	+	1.19845i	0.978905	+	0.204314i	$0.0654965\pi$
$271$	1.73295e7	+	2.38521e7i	0.870722	+	1.19845i	−0.108184	+	0.994131i	$0.534503\pi$
$272$	−2.51363e6	+	3.45971e6i	−0.124909	+	0.171923i
$273$	−4.37260e7			−2.14907
$274$		−	1.71710e7i		−	0.834727i
$275$	−3.81280e6	+	5.24786e6i	−0.183335	+	0.252339i
$276$	6.55838e6	+	2.01846e7i	0.311939	+	0.960049i
$277$	3.12467e7	+	1.01527e7i	1.47016	+	0.477685i	0.931157	−	0.364618i	$-0.118800\pi$
$277$	3.12467e7	+	1.01527e7i	1.47016	+	0.477685i	0.539005	+	0.842302i	$0.318800\pi$
$278$			1.36138e7i			0.633645i
$279$	1.78758e7	−	7.12809e6i	0.823103	−	0.328217i
$280$	4.05482e6			0.184713
$281$	7.18228e6	−	2.21048e7i	0.323700	−	0.996248i	−0.648323	−	0.761365i	$-0.724529\pi$
$281$	7.18228e6	−	2.21048e7i	0.323700	−	0.996248i	0.972024	−	0.234882i	$-0.0754705\pi$
$282$	−1.15506e7	+	3.75301e6i	−0.515059	+	0.167353i
$283$	−6.32559e6	−	4.59581e6i	−0.279088	−	0.202770i	0.439431	−	0.898276i	$-0.355180\pi$
$283$	−6.32559e6	−	4.59581e6i	−0.279088	−	0.202770i	−0.718520	+	0.695507i	$0.755180\pi$
$284$	3.52995e6			0.154104
$285$		−	1.43328e6i		−	0.0619151i
$286$	−6.69587e6	−	4.86483e6i	−0.286226	−	0.207955i
$287$	−3.12134e7	+	2.26779e7i	−1.32037	+	0.959304i
$288$	−3.02731e6	+	2.19947e6i	−0.126730	+	0.0920747i
$289$	2.06943e6	−	6.36906e6i	0.0857349	−	0.263865i
$290$	−1.74438e6	+	2.40093e6i	−0.0715233	+	0.0984433i
$291$	−4.27002e7	−	1.38741e7i	−1.73281	−	0.563024i
$292$	1.13207e7	−	3.67831e6i	0.454698	−	0.147740i
$293$	−1.24669e7	+	9.05771e6i	−0.495626	+	0.360094i	−0.807344	−	0.590081i	$-0.799096\pi$
$293$	−1.24669e7	+	9.05771e6i	−0.495626	+	0.360094i	0.311718	+	0.950175i	$0.399096\pi$
$294$	1.04672e7	−	3.40099e6i	0.411896	−	0.133833i
$295$	−620000.	−	1.90816e6i	−0.0241505	−	0.0743275i
$296$	−2.07871e6	−	2.86109e6i	−0.0801527	−	0.110321i
$297$	−486779.	−	1.49815e6i	−0.0185807	−	0.0571856i
$298$	2.54488e6	−	7.83234e6i	0.0961654	−	0.295967i
$299$	−4.13702e7	−	3.00572e7i	−1.54766	−	1.12444i
$300$	−1.43045e7	−	4.64780e6i	−0.529795	−	0.172141i
$301$	−2.00012e7	−	2.75292e7i	−0.733425	−	1.00947i
$302$	6.28037e6	+	8.64419e6i	0.228016	+	0.313837i
$303$	−1.15748e7	+	1.59314e7i	−0.416090	+	0.572698i
$304$	728801.			0.0259411
$305$			2.25330e7i			0.794180i
$306$	−8.97017e6	+	1.23464e7i	−0.313066	+	0.430899i
$307$	1.59300e7	+	4.90274e7i	0.550554	+	1.69443i	0.707405	+	0.706808i	$0.249866\pi$
$307$	1.59300e7	+	4.90274e7i	0.550554	+	1.69443i	−0.156851	+	0.987622i	$0.550134\pi$
$308$	6.42377e6	+	2.08721e6i	0.219856	+	0.0714354i
$309$			1.45632e7i			0.493607i
$310$	4.88519e6	−	7.73953e6i	0.163982	−	0.259794i
$311$	4.06030e7			1.34982			0.674912	−	0.737898i	$-0.264182\pi$
$311$	4.06030e7			1.34982			0.674912	+	0.737898i	$0.264182\pi$
$312$	5.93024e6	−	1.82514e7i	0.195258	−	0.600942i
$313$	5.01596e7	−	1.62979e7i	1.63577	−	0.531493i	0.660180	−	0.751108i	$-0.270480\pi$
$313$	5.01596e7	−	1.62979e7i	1.63577	−	0.531493i	0.975587	+	0.219615i	$0.0704800\pi$
$314$	1.84142e7	+	1.33787e7i	0.594789	+	0.432139i
$315$	1.44701e7			0.462956
$316$		−	2.26220e7i		−	0.716917i
$317$	1.88475e7	+	1.36935e7i	0.591664	+	0.429869i	0.842910	−	0.538054i	$-0.180840\pi$
$317$	1.88475e7	+	1.36935e7i	0.591664	+	0.429869i	−0.251247	+	0.967923i	$0.580840\pi$
$318$	−861726.	+	626080.i	−0.0267971	+	0.0194692i
$319$	−3.99937e6	+	2.90571e6i	−0.123203	+	0.0895119i
$320$	−549926.	+	1.69250e6i	−0.0167824	+	0.0516510i
$321$	−6.66799e6	+	9.17770e6i	−0.201595	+	0.277472i
$322$	3.96890e7	+	1.28958e7i	1.18878	+	0.386259i
$323$	2.82682e6	−	918489.i	0.0838862	−	0.0272563i
$324$	1.51465e7	−	1.10046e7i	0.445325	−	0.323548i
$325$	3.44657e7	−	1.11986e7i	1.00401	−	0.326222i
$326$	7.32788e6	+	2.25529e7i	0.211507	+	0.650953i
$327$	3.92360e6	+	5.40037e6i	0.112212	+	0.154447i
$328$	−5.23258e6	−	1.61042e7i	−0.148284	−	0.456371i
$329$	−7.37956e6	+	2.27119e7i	−0.207225	+	0.637774i
$330$	4.71643e6	+	3.42669e6i	0.131242	+	0.0953526i
$331$	−7.47477e6	−	2.42870e6i	−0.206117	−	0.0669715i	0.204139	−	0.978942i	$-0.434561\pi$
$331$	−7.47477e6	−	2.42870e6i	−0.206117	−	0.0669715i	−0.410256	+	0.911970i	$0.634561\pi$
$332$	−1.37929e7	−	1.89844e7i	−0.376914	−	0.518778i
$333$	−7.41810e6	−	1.02101e7i	−0.200891	−	0.276502i
$334$	2.06580e7	−	2.84333e7i	0.554433	−	0.763111i
$335$	−2.60367e6			−0.0692552
$336$			1.56612e7i			0.412863i
$337$	−154961.	+	213286.i	−0.00404887	+	0.00557279i	−0.811037	−	0.584995i	$-0.801096\pi$
$337$	−154961.	+	213286.i	−0.00404887	+	0.00557279i	0.806988	+	0.590568i	$0.201096\pi$
$338$	5.85098e6	+	1.80075e7i	0.151523	+	0.466339i
$339$	3.44021e7	+	1.11779e7i	0.883051	+	0.286921i
$340$			7.25780e6i			0.184658i
$341$	1.17232e7	−	9.74655e6i	0.295652	−	0.245803i
$342$	2.60081e6			0.0650175
$343$	−8.30757e6	+	2.55681e7i	−0.205869	+	0.633601i
$344$	1.42034e7	−	4.61498e6i	0.348914	−	0.113369i
$345$	2.91403e7	+	2.11717e7i	0.709638	+	0.515582i
$346$	1.96641e6			0.0474730
$347$		−	4.71784e7i		−	1.12916i	−0.825379	−	0.564579i	$-0.809038\pi$
$347$		−	4.71784e7i		−	1.12916i	0.825379	−	0.564579i	$-0.190962\pi$
$348$	−9.27326e6	−	6.73742e6i	−0.220036	−	0.159866i
$349$	−6.06221e7	+	4.40445e7i	−1.42611	+	1.03613i	−0.435391	+	0.900241i	$0.643390\pi$
$349$	−6.06221e7	+	4.40445e7i	−1.42611	+	1.03613i	−0.990724	+	0.135892i	$0.956610\pi$
$350$	−2.39262e7	+	1.73834e7i	−0.558045	+	0.405443i
$351$	−2.71950e6	+	8.36975e6i	−0.0628879	+	0.193549i
$352$	−1.74242e6	+	2.39823e6i	−0.0399507	+	0.0549874i
$353$	−2.41021e6	−	783126.i	−0.0547938	−	0.0178036i	0.281492	−	0.959564i	$-0.409171\pi$
$353$	−2.41021e6	−	783126.i	−0.0547938	−	0.0178036i	−0.336286	+	0.941760i	$0.609171\pi$
$354$	7.37000e6	−	2.39466e6i	0.166134	−	0.0539801i
$355$	4.84672e6	−	3.52135e6i	0.108334	−	0.0787089i
$356$	−1.23659e7	+	4.01792e6i	−0.274079	+	0.0890535i
$357$	1.97374e7	+	6.07453e7i	0.433795	+	1.33508i
$358$	3.15885e7	+	4.34778e7i	0.688461	+	0.947586i
$359$	−1.54722e7	−	4.76185e7i	−0.334402	−	1.02918i	−0.967016	−	0.254716i	$-0.918018\pi$
$359$	−1.54722e7	−	4.76185e7i	−0.334402	−	1.02918i	0.632614	−	0.774467i	$-0.281982\pi$
$360$	−1.96247e6	+	6.03987e6i	−0.0420626	+	0.129455i
$361$	3.76511e7	+	2.73551e7i	0.800306	+	0.581457i
$362$	−8.49628e6	−	2.76061e6i	−0.179103	−	0.0581941i
$363$	−3.29041e7	−	4.52887e7i	−0.687909	−	0.946825i
$364$	−2.21798e7	−	3.05279e7i	−0.459891	−	0.632985i
$365$	1.18743e7	−	1.63435e7i	0.244190	−	0.336099i
$366$	−8.70303e7			−1.77512
$367$		−	4.92284e7i		−	0.995905i	−0.867204	−	0.497952i	$-0.834085\pi$
$367$		−	4.92284e7i		−	0.995905i	0.867204	−	0.497952i	$-0.165915\pi$
$368$	−1.07655e7	+	1.48174e7i	−0.216018	+	0.297323i
$369$	−1.86731e7	−	5.74698e7i	−0.371652	−	1.14383i
$370$	−5.70825e6	−	1.85472e6i	−0.112693	−	0.0366163i
$371$			2.09441e6i			0.0410147i
$372$	2.98928e7	+	1.88683e7i	0.580681	+	0.366526i
$373$	3.61543e7			0.696680			0.348340	−	0.937368i	$-0.386746\pi$
$373$	3.61543e7			0.696680			0.348340	+	0.937368i	$0.386746\pi$
$374$	−3.73593e6	+	1.14980e7i	−0.0714141	+	0.219790i
$375$	−5.42029e7	+	1.76116e7i	−1.02785	+	0.333968i
$376$	−8.47922e6	−	6.16051e6i	−0.159512	−	0.115892i
$377$	2.76179e7			0.515426
$378$		−	7.18192e6i		−	0.132974i
$379$	−3.77543e7	−	2.74301e7i	−0.693503	−	0.503859i	0.184307	−	0.982869i	$-0.440996\pi$
$379$	−3.77543e7	−	2.74301e7i	−0.693503	−	0.503859i	−0.877810	+	0.479009i	$0.840996\pi$
$380$	1.00067e6	−	727026.i	0.0182364	−	0.0132495i
$381$	8.51086e7	−	6.18350e7i	1.53886	−	1.11805i
$382$	−1.15795e7	+	3.56380e7i	−0.207730	+	0.639328i
$383$	−7.24056e6	+	9.96578e6i	−0.128877	+	0.177384i	−0.868579	−	0.495550i	$-0.834966\pi$
$383$	−7.24056e6	+	9.96578e6i	−0.128877	+	0.177384i	0.739702	+	0.672935i	$0.234966\pi$
$384$	−6.53703e6	−	2.12401e6i	−0.115448	−	0.0375114i
$385$	1.09021e7	−	3.54232e6i	0.191042	−	0.0620734i
$386$	−5.94941e7	+	4.32250e7i	−1.03446	+	0.751576i
$387$	5.06866e7	−	1.64691e7i	0.874500	−	0.284142i
$388$	−1.19731e7	−	3.68494e7i	−0.204980	−	0.630863i
$389$	−5.95923e7	−	8.20218e7i	−1.01237	−	1.39341i	−0.917414	−	0.397934i	$-0.869727\pi$
$389$	−5.95923e7	−	8.20218e7i	−1.01237	−	1.39341i	−0.0949608	−	0.995481i	$-0.530273\pi$
$390$	−1.00646e7	−	3.09755e7i	−0.169668	−	0.522185i
$391$	−2.30823e7	+	7.10401e7i	−0.386144	+	1.18843i
$392$	7.68390e6	+	5.58268e6i	0.127563	+	0.0926797i
$393$	1.33103e8	+	4.32476e7i	2.19285	+	0.712500i
$394$	−4.12129e7	−	5.67247e7i	−0.673821	−	0.927435i
$395$	−2.25669e7	−	3.10606e7i	−0.366168	−	0.503987i
$396$	−6.21802e6	+	8.55836e6i	−0.100130	+	0.137818i
$397$	−6.63170e7			−1.05987			−0.529936	−	0.848038i	$-0.677784\pi$
$397$	−6.63170e7			−1.05987			−0.529936	+	0.848038i	$0.677784\pi$
$398$			7.16863e7i			1.13707i
$399$	6.39811e6	−	8.80625e6i	0.100724	−	0.138635i
$400$	−4.01096e6	−	1.23445e7i	−0.0626712	−	0.192882i
$401$	1.33804e7	+	4.34756e6i	0.207509	+	0.0674237i	0.410927	−	0.911668i	$-0.365205\pi$
$401$	1.33804e7	+	4.34756e6i	0.207509	+	0.0674237i	−0.203418	+	0.979092i	$0.565205\pi$
$402$		−	1.00563e7i		−	0.154796i
$403$	−8.49913e7	+	5.55558e6i	−1.29855	+	0.0848818i
$404$	−1.69940e7			−0.257723
$405$	9.81882e6	−	3.02192e7i	0.147807	−	0.454902i
$406$	−2.14354e7	+	6.96478e6i	−0.320297	+	0.104071i
$407$	−8.08846e6	−	5.87661e6i	−0.119973	−	0.0871654i
$408$	−2.80322e7			−0.412740
$409$		−	1.00842e7i		−	0.147391i	−0.997281	−	0.0736955i	$-0.976521\pi$
$409$		−	1.00842e7i		−	0.147391i	0.997281	−	0.0736955i	$-0.0234793\pi$
$410$	−2.32495e7	−	1.68917e7i	−0.337335	−	0.245089i
$411$	9.10601e7	−	6.61590e7i	1.31160	−	0.952936i
$412$	−1.01675e7	+	7.38714e6i	−0.145386	+	0.105629i
$413$	4.70862e6	−	1.44916e7i	0.0668411	−	0.205716i
$414$	−3.84178e7	+	5.28776e7i	−0.541417	+	0.745196i
$415$	−3.78762e7	−	1.23067e7i	−0.529935	−	0.172186i
$416$	1.57506e7	−	5.11767e6i	0.218785	−	0.0710874i
$417$	−7.21959e7	+	5.24534e7i	−0.995644	+	0.723378i
$418$	1.95952e6	−	636686.i	0.0268300	−	0.00871759i
$419$	−5.99529e6	−	1.84516e7i	−0.0815020	−	0.250837i	0.902000	−	0.431737i	$-0.142099\pi$
$419$	−5.99529e6	−	1.84516e7i	−0.0815020	−	0.250837i	−0.983502	+	0.180900i	$0.942099\pi$
$420$	1.56230e7	+	2.15032e7i	0.210871	+	0.290239i
$421$	3.97655e7	+	1.22386e8i	0.532918	+	1.64015i	0.748105	+	0.663580i	$0.230964\pi$
$421$	3.97655e7	+	1.22386e8i	0.532918	+	1.64015i	−0.215187	+	0.976573i	$0.569036\pi$
$422$	1.29699e7	−	3.99172e7i	0.172583	−	0.531157i
$423$	−3.02591e7	−	2.19845e7i	−0.399792	−	0.290466i
$424$	−874215.	−	284050.i	−0.0114689	−	0.00372646i
$425$	−3.11148e7	−	4.28259e7i	−0.405322	−	0.557878i
$426$	1.36007e7	+	1.87198e7i	0.175927	+	0.242143i
$427$	−1.00586e8	+	1.38445e8i	−1.29198	+	1.77826i
$428$	−9.78987e6			−0.124866
$429$		−	5.42530e7i		−	0.687150i
$430$	1.48980e7	−	2.05053e7i	0.187380	−	0.257906i
$431$	1.22902e7	+	3.78253e7i	0.153506	+	0.472444i	0.998006	−	0.0631113i	$-0.0201023\pi$
$431$	1.22902e7	+	3.78253e7i	0.153506	+	0.472444i	−0.844500	+	0.535555i	$0.820102\pi$
$432$	2.99776e6	+	974032.i	0.0371831	+	0.0120815i
$433$		−	2.52608e6i		−	0.0311160i	−0.999879	−	0.0155580i	$-0.995048\pi$
$433$		−	2.52608e6i		−	0.0311160i	0.999879	−	0.0155580i	$-0.00495246\pi$
$434$	6.45642e7	−	2.57453e7i	0.789810	−	0.314941i
$435$	−1.94535e7			−0.236336
$436$	−1.78012e6	+	5.47864e6i	−0.0214778	+	0.0661017i
$437$	1.21068e7	−	3.93375e6i	0.145073	−	0.0471370i
$438$	6.31244e7	+	4.58626e7i	0.751234	+	0.545803i
$439$	4.56356e7			0.539400			0.269700	−	0.962944i	$-0.413076\pi$
$439$	4.56356e7			0.539400			0.269700	+	0.962944i	$0.413076\pi$
$440$			5.03102e6i			0.0590606i
$441$	2.74209e7	+	1.99224e7i	0.319717	+	0.232288i
$442$	5.46425e7	−	3.97001e7i	0.632796	−	0.459753i
$443$	7.97189e7	−	5.79192e7i	0.916959	−	0.666210i	−0.0258059	−	0.999667i	$-0.508215\pi$
$443$	7.97189e7	−	5.79192e7i	0.916959	−	0.666210i	0.942765	+	0.333457i	$0.108215\pi$
$444$	7.16360e6	−	2.20473e7i	0.0818432	−	0.251887i
$445$	−1.29706e7	+	1.78525e7i	−0.147190	+	0.202590i
$446$	−2.82704e6	−	918560.i	−0.0318659	−	0.0103539i
$447$	5.13412e7	−	1.66818e7i	0.574835	−	0.186775i
$448$	−1.09341e7	+	7.94407e6i	−0.121604	+	0.0883505i
$449$	1.33187e8	−	4.32751e7i	1.47138	−	0.478079i	0.539852	−	0.841760i	$-0.318480\pi$
$449$	1.33187e8	−	4.32751e7i	1.47138	−	0.478079i	0.931523	+	0.363681i	$0.118480\pi$
$450$	−1.43136e7	−	4.40526e7i	−0.157076	−	0.483431i
$451$	−2.81375e7	−	3.87280e7i	−0.306730	−	0.422178i
$452$	9.64632e6	+	2.96883e7i	0.104459	+	0.321492i
$453$	−2.16433e7	+	6.66112e7i	−0.232825	+	0.716560i
$454$	3.13028e7	+	2.27428e7i	0.334515	+	0.243039i
$455$	−6.09072e7	−	1.97899e7i	−0.646598	−	0.210092i
$456$	2.80803e6	+	3.86493e6i	0.0296147	+	0.0407612i
$457$	−4.85407e7	−	6.68105e7i	−0.508577	−	0.699997i	0.475101	−	0.879931i	$-0.342411\pi$
$457$	−4.85407e7	−	6.68105e7i	−0.508577	−	0.699997i	−0.983679	+	0.179934i	$0.942411\pi$
$458$	5.74685e7	−	7.90986e7i	0.598182	−	0.823327i
$459$	1.28550e7			0.132934
$460$			3.10840e7i			0.319348i
$461$	5.01526e7	−	6.90292e7i	0.511907	−	0.704579i	−0.472333	−	0.881420i	$-0.656588\pi$
$461$	5.01526e7	−	6.90292e7i	0.511907	−	0.704579i	0.984239	+	0.176841i	$0.0565879\pi$
$462$	1.36817e7	+	4.21080e7i	0.138744	+	0.427010i
$463$	−1.65249e8	−	5.36927e7i	−1.66493	−	0.540969i	−0.683035	−	0.730386i	$-0.739340\pi$
$463$	−1.65249e8	−	5.36927e7i	−1.66493	−	0.540969i	−0.981897	+	0.189417i	$0.939340\pi$
$464$		−	9.89180e6i		−	0.0990196i
$465$	5.98661e7	−	3.91323e6i	0.595418	−	0.0389204i
$466$	−1.27801e8			−1.26292
$467$	−179383.	+	552085.i	−0.00176129	+	0.00542070i	−0.951933	−	0.306305i	$-0.900907\pi$
$467$	−179383.	+	552085.i	−0.00176129	+	0.00542070i	0.950172	+	0.311726i	$0.100907\pi$
$468$	5.62077e7	−	1.82630e7i	0.548351	−	0.178170i
$469$	−1.59973e7	−	1.16227e7i	−0.155070	−	0.112665i
$470$	−1.77877e7			−0.171327
$471$			1.49200e8i			1.42793i
$472$	5.41028e6	+	3.93080e6i	0.0514509	+	0.0373813i
$473$	3.41569e7	−	2.48164e7i	0.322771	−	0.234507i
$474$	1.19967e8	−	8.71613e7i	1.12649	−	0.818443i
$475$	−2.78777e6	+	8.57989e6i	−0.0260122	+	0.0800573i
$476$	−3.23986e7	+	4.45928e7i	−0.300403	+	0.413470i
$477$	−3.11973e6	−	1.01366e6i	−0.0287450	−	0.00933982i
$478$	−7.70493e7	+	2.50348e7i	−0.705481	+	0.229225i
$479$	−2.02999e7	+	1.47487e7i	−0.184709	+	0.134199i	−0.676297	−	0.736629i	$-0.736416\pi$
$479$	−2.02999e7	+	1.47487e7i	−0.184709	+	0.134199i	0.491588	+	0.870828i	$0.336416\pi$
$480$	−1.10944e7	+	3.60478e6i	−0.100318	+	0.0325953i
$481$	1.72603e7	+	5.31216e7i	0.155100	+	0.477349i
$482$	6.10873e7	+	8.40795e7i	0.545519	+	0.750842i
$483$	8.45320e7	+	2.60163e8i	0.750205	+	2.30889i
$484$	1.49285e7	−	4.59451e7i	0.131668	−	0.405231i
$485$	−5.31990e7	−	3.86514e7i	−0.466314	−	0.338797i
$486$	1.04645e8	+	3.40012e7i	0.911609	+	0.296200i
$487$	−5.14910e7	−	7.08713e7i	−0.445805	−	0.613597i	0.525685	−	0.850679i	$-0.323809\pi$
$487$	−5.14910e7	−	7.08713e7i	−0.445805	−	0.613597i	−0.971490	+	0.237082i	$0.923809\pi$
$488$	−4.41458e7	−	6.07615e7i	−0.379866	−	0.522841i
$489$	−9.13669e7	+	1.25756e8i	−0.781380	+	1.07548i
$490$	1.61193e7			0.137012
$491$			7.92578e7i			0.669572i	0.942294	+	0.334786i	$0.108664\pi$
$491$			7.92578e7i			0.669572i	−0.942294	+	0.334786i	$0.891336\pi$
$492$	6.52419e7	−	8.97978e7i	0.547812	−	0.753998i
$493$	−1.24664e7	−	3.83676e7i	−0.104040	−	0.320202i
$494$	−1.09473e7	−	3.55698e6i	−0.0908082	−	0.0295054i
$495$			1.79538e7i			0.148027i
$496$	1.98982e6	+	3.04410e7i	0.0163068	+	0.249468i
$497$	4.54980e7			0.370615
$498$	4.75330e7	−	1.46291e8i	0.384864	−	1.18449i
$499$	−3.94752e7	+	1.28263e7i	−0.317704	+	0.103228i	−0.463528	−	0.886082i	$-0.653417\pi$
$499$	−3.94752e7	+	1.28263e7i	−0.317704	+	0.103228i	0.145824	+	0.989311i	$0.453417\pi$
$500$	−3.97900e7	−	2.89092e7i	−0.318320	−	0.231273i
$501$	2.30380e8			1.83202
$502$			3.66240e7i			0.289504i
$503$	−1.68929e8	−	1.22734e8i	−1.32739	−	0.964407i	−0.999808	−	0.0195846i	$-0.993766\pi$
$503$	−1.68929e8	−	1.22734e8i	−1.32739	−	0.964407i	−0.327584	−	0.944822i	$-0.606234\pi$
$504$	−3.90195e7	+	2.83493e7i	−0.304782	+	0.221437i
$505$	−2.33333e7	+	1.69527e7i	−0.181177	+	0.131633i
$506$	−1.60004e7	+	4.92442e7i	−0.123504	+	0.380105i
$507$	−7.29523e7	+	1.00410e8i	−0.559777	+	0.770467i
$508$	8.63421e7	+	2.80542e7i	0.658615	+	0.213997i
$509$	4.83604e7	−	1.57133e7i	0.366722	−	0.119155i	−0.119858	−	0.992791i	$-0.538244\pi$
$509$	4.83604e7	−	1.57133e7i	0.366722	−	0.119155i	0.486580	+	0.873636i	$0.338244\pi$
$510$	−3.84890e7	+	2.79639e7i	−0.290152	+	0.210808i
$511$	1.45914e8	−	4.74103e7i	1.09354	−	0.355312i
$512$	−1.83298e6	−	5.64133e6i	−0.0136568	−	0.0420312i
$513$	−1.28771e6	−	1.77238e6i	−0.00953821	−	0.0131282i
$514$	−3.01624e7	−	9.28302e7i	−0.222114	−	0.683597i
$515$	−6.59117e6	+	2.02855e7i	−0.0482548	+	0.148513i
$516$	7.91989e7	+	5.75414e7i	0.576461	+	0.418824i
$517$	−2.81798e7	−	9.15618e6i	−0.203923	−	0.0662587i
$518$	−2.67928e7	−	3.68771e7i	−0.192765	−	0.265319i
$519$	7.57649e6	+	1.04281e7i	0.0541959	+	0.0745942i
$520$	1.65208e7	−	2.27389e7i	0.117496	−	0.161719i
$521$	2.43972e8			1.72515			0.862573	−	0.505932i	$-0.168851\pi$
$521$	2.43972e8			1.72515			0.862573	+	0.505932i	$0.168851\pi$
$522$		−	3.53000e7i		−	0.248178i
$523$	1.24430e8	−	1.71264e8i	0.869803	−	1.19718i	−0.109339	−	0.994005i	$-0.534873\pi$
$523$	1.24430e8	−	1.71264e8i	0.869803	−	1.19718i	0.979142	−	0.203177i	$-0.0651266\pi$
$524$	3.73218e7	+	1.14865e8i	0.259399	+	0.798349i
$525$	−1.84373e8	−	5.99063e7i	−1.27414	−	0.413994i
$526$			1.98302e8i			1.36260i
$527$	4.60820e7	+	1.15565e8i	0.314847	+	0.789574i
$528$	−1.94316e7			−0.132010
$529$	−5.31124e7	+	1.63463e8i	−0.358781	+	1.10421i
$530$	−1.48368e6	+	482077.i	−0.00996582	+	0.00323809i
$531$	1.93072e7	+	1.40275e7i	0.128954	+	0.0936906i
$532$	9.39364e6			0.0623877
$533$			2.67439e8i			1.76621i
$534$	−6.89526e7	−	5.00970e7i	−0.452821	−	0.328994i
$535$	−1.34418e7	+	9.76602e6i	−0.0877800	+	0.0637759i
$536$	7.02097e6	−	5.10103e6i	0.0455935	−	0.0331256i
$537$	−1.08860e8	+	3.35035e8i	−0.702982	+	2.16355i
$538$	2.66789e7	−	3.67204e7i	0.171325	−	0.235809i
$539$	2.55367e7	+	8.29737e6i	0.163079	+	0.0529876i
$540$	5.08768e6	−	1.65309e6i	0.0323101	−	0.0104982i
$541$	−4.30626e7	+	3.12868e7i	−0.271962	+	0.197592i	−0.715404	−	0.698711i	$-0.753757\pi$
$541$	−4.30626e7	+	3.12868e7i	−0.271962	+	0.197592i	0.443442	+	0.896303i	$0.353757\pi$
$542$	−1.58617e8	+	5.15378e7i	−0.996212	+	0.323689i
$543$	−1.80959e7	−	5.56933e7i	−0.113026	−	0.347859i
$544$	−1.42192e7	−	1.95711e7i	−0.0883241	−	0.121568i
$545$	3.02114e6	+	9.29811e6i	0.0186630	+	0.0574388i
$546$	7.64358e7	−	2.35245e8i	0.469590	−	1.44525i
$547$	1.35801e8	+	9.86655e7i	0.829741	+	0.602842i	0.919486	−	0.393123i	$-0.128605\pi$
$547$	1.35801e8	+	9.86655e7i	0.829741	+	0.602842i	−0.0897453	+	0.995965i	$0.528605\pi$
$548$	9.23799e7	+	3.00160e7i	0.561352	+	0.182394i
$549$	−1.57539e8	−	2.16834e8i	−0.952077	−	1.31042i
$550$	−2.15684e7	−	2.96864e7i	−0.129637	−	0.178431i
$551$	−4.04113e6	+	5.56214e6i	−0.0241573	+	0.0332497i
$552$	−1.20057e8			−0.713792
$553$		−	2.91578e8i		−	1.72417i
$554$	−1.09243e8	+	1.50360e8i	−0.642485	+	0.884304i
$555$	−1.21578e7	−	3.74178e7i	−0.0711172	−	0.218876i
$556$	−7.32422e7	−	2.37978e7i	−0.426125	−	0.138456i
$557$		−	2.33159e8i		−	1.34923i	−0.738168	−	0.674616i	$-0.764309\pi$
$557$		−	2.33159e8i		−	1.34923i	0.738168	−	0.674616i	$-0.235691\pi$
$558$	7.10090e6	+	1.08632e8i	0.0408706	+	0.625253i
$559$	−2.35873e8			−1.35034
$560$	−7.08809e6	+	2.18149e7i	−0.0403613	+	0.124219i
$561$	−7.53697e7	+	2.44891e7i	−0.426883	+	0.138703i
$562$	1.06368e8	+	7.72812e7i	0.599244	+	0.435376i
$563$	2.88585e8			1.61714			0.808572	−	0.588397i	$-0.200241\pi$
$563$	2.88585e8			1.61714			0.808572	+	0.588397i	$0.200241\pi$
$564$		−	6.87025e7i		−	0.382944i
$565$	4.28607e7	+	3.11401e7i	0.237637	+	0.172653i
$566$	3.57829e7	−	2.59978e7i	0.197345	−	0.143380i
$567$	1.95226e8	−	1.41840e8i	1.07100	−	0.778124i
$568$	−6.17057e6	+	1.89911e7i	−0.0336729	+	0.103634i
$569$	1.05672e8	−	1.45445e8i	0.573619	−	0.789519i	−0.419359	−	0.907821i	$-0.637745\pi$
$569$	1.05672e8	−	1.45445e8i	0.573619	−	0.789519i	0.992978	+	0.118302i	$0.0377450\pi$
$570$	7.71103e6	+	2.50546e6i	0.0416378	+	0.0135289i
$571$	−1.09434e8	+	3.55572e7i	−0.587818	+	0.190994i	−0.587800	−	0.809006i	$-0.700006\pi$
$571$	−1.09434e8	+	3.55572e7i	−0.587818	+	0.190994i	−1.83258e−5		1.00000i	$0.500006\pi$
$572$	3.78775e7	−	2.75196e7i	0.202392	−	0.147047i
$573$	−2.33608e8	+	7.59039e7i	−1.24172	+	0.403460i
$574$	−6.74436e7	−	2.07570e8i	−0.356619	−	1.09756i
$575$	−1.33260e8	−	1.83416e8i	−0.700964	−	0.964795i
$576$	−6.54119e6	−	2.01317e7i	−0.0342286	−	0.105345i
$577$	1.21581e6	−	3.74187e6i	0.00632903	−	0.0194788i	−0.947842	−	0.318740i	$-0.896740\pi$
$577$	1.21581e6	−	3.74187e6i	0.00632903	−	0.0194788i	0.954171	+	0.299261i	$0.0967403\pi$
$578$	3.06480e7	+	2.22671e7i	0.158715	+	0.115313i
$579$	−4.58455e8	−	1.48961e8i	−2.36190	−	0.767427i
$580$	−9.86771e6	−	1.35817e7i	−0.0505746	−	0.0696099i
$581$	−1.77779e8	−	2.44692e8i	−0.906469	−	1.24765i
$582$	1.49285e8	−	2.05474e8i	0.757265	−	1.04229i
$583$	−2.59864e6			−0.0131141
$584$			6.73349e7i			0.338066i
$585$	5.89564e7	−	8.11465e7i	0.294485	−	0.405324i
$586$	−2.69375e7	−	8.29050e7i	−0.133864	−	0.411991i
$587$	2.54472e7	+	8.26829e6i	0.125813	+	0.0408791i	0.371247	−	0.928534i	$-0.378930\pi$
$587$	2.54472e7	+	8.26829e6i	0.125813	+	0.0408791i	−0.245434	+	0.969413i	$0.578930\pi$
$588$			6.22585e7i			0.306243i
$589$	1.13173e7	−	1.79298e7i	0.0553857	−	0.0877467i
$590$	1.13497e7			0.0552622
$591$	1.42027e8	−	4.37115e8i	0.688033	−	2.11755i
$592$	1.90264e7	−	6.18204e6i	0.0917045	−	0.0297966i
$593$	2.55677e8	+	1.85760e8i	1.22611	+	0.890817i	0.996592	−	0.0824881i	$-0.0262867\pi$
$593$	2.55677e8	+	1.85760e8i	1.22611	+	0.890817i	0.229513	+	0.973306i	$0.426287\pi$
$594$	8.91097e6			0.0425173
$595$			9.35469e7i			0.444098i
$596$	3.76893e7	+	2.73829e7i	0.178024	+	0.129342i
$597$	−3.80161e8	+	2.76203e8i	−1.78667	+	1.29809i
$598$	2.34025e8	−	1.70029e8i	1.09436	−	0.795097i
$599$	−1.30572e8	+	4.01859e8i	−0.607531	+	1.86979i	−0.129180	+	0.991621i	$0.541234\pi$
$599$	−1.30572e8	+	4.01859e8i	−0.607531	+	1.86979i	−0.478352	+	0.878168i	$0.658766\pi$
$600$	5.00103e7	−	6.88332e7i	0.231529	−	0.318672i
$601$	−7.58903e7	−	2.46583e7i	−0.349593	−	0.113590i	0.128956	−	0.991650i	$-0.458837\pi$
$601$	−7.58903e7	−	2.46583e7i	−0.349593	−	0.113590i	−0.478549	+	0.878061i	$0.658837\pi$
$602$	1.83070e8	−	5.94832e7i	0.839129	−	0.272649i
$603$	2.50551e7	−	1.82036e7i	0.114273	−	0.0830243i
$604$	−5.74841e7	+	1.86777e7i	−0.260878	+	0.0847643i
$605$	−2.53359e7	−	7.79760e7i	−0.114412	−	0.352124i
$606$	−6.54772e7	−	9.01216e7i	−0.294220	−	0.404959i
$607$	−4.93168e7	−	1.51781e8i	−0.220510	−	0.678660i	−0.998716	−	0.0506516i	$-0.983870\pi$
$607$	−4.93168e7	−	1.51781e8i	−0.220510	−	0.678660i	0.778206	−	0.628009i	$-0.216130\pi$
$608$	−1.27399e6	+	3.92094e6i	−0.00566834	+	0.0174454i
$609$	−1.19525e8	−	8.68396e7i	−0.529182	−	0.384473i
$610$	−1.21227e8	−	3.93891e7i	−0.534085	−	0.173535i
$611$	9.72988e7	+	1.33920e8i	0.426564	+	0.587114i
$612$	−5.07429e7	−	6.98416e7i	−0.221371	−	0.304691i
$613$	4.70417e7	−	6.47474e7i	0.204222	−	0.281087i	−0.694605	−	0.719391i	$-0.744421\pi$
$613$	4.70417e7	−	6.47474e7i	0.204222	−	0.281087i	0.898827	+	0.438304i	$0.144421\pi$
$614$	−2.91613e8			−1.25980
$615$		−	1.88378e8i		−	0.809851i
$616$	−2.24583e7	+	3.09112e7i	−0.0960804	+	0.132243i
$617$	−3.84861e7	−	1.18448e8i	−0.163851	−	0.504280i	0.835099	−	0.550100i	$-0.185410\pi$
$617$	−3.84861e7	−	1.18448e8i	−0.163851	−	0.504280i	−0.998950	+	0.0458191i	$0.985410\pi$
$618$	−7.83499e7	−	2.54574e7i	−0.331950	−	0.107857i
$619$			4.12173e8i			1.73783i	0.494962	+	0.868915i	$0.335182\pi$
$619$			4.12173e8i			1.73783i	−0.494962	+	0.868915i	$0.664818\pi$
$620$	3.30990e7	+	3.98115e7i	0.138880	+	0.167045i
$621$	5.50561e7			0.229896
$622$	−7.09766e7	+	2.18444e8i	−0.294947	+	0.907754i
$623$	−1.59386e8	+	5.17876e7i	−0.659152	+	0.214171i
$624$	8.78259e7	+	6.38092e7i	0.361467	+	0.262621i
$625$	1.14583e8			0.469334
$626$			2.98348e8i			1.21619i
$627$	1.09263e7	+	7.93846e6i	0.0443274	+	0.0322058i
$628$	−1.04166e8	+	7.56812e7i	−0.420579	+	0.305569i
$629$	6.60070e7	−	4.79569e7i	0.265239	−	0.192708i
$630$	−2.52946e7	+	7.78489e7i	−0.101160	+	0.311337i
$631$	−1.64232e8	+	2.26046e8i	−0.653686	+	0.899721i	−0.999252	−	0.0386732i	$-0.987687\pi$
$631$	−1.64232e8	+	2.26046e8i	−0.653686	+	0.899721i	0.345566	+	0.938394i	$0.387687\pi$
$632$	1.21706e8	+	3.95447e7i	0.482126	+	0.156652i
$633$	2.61659e8	−	8.50180e7i	1.03163	−	0.335197i
$634$	−1.06617e8	+	7.74620e7i	−0.418369	+	0.303963i
$635$	1.46536e8	−	4.76125e7i	0.572300	−	0.185952i
$636$	−1.86195e6	−	5.73050e6i	−0.00723765	−	0.0222752i
$637$	−8.81725e7	−	1.21359e8i	−0.341126	−	0.469520i
$638$	−8.64155e6	−	2.65959e7i	−0.0332759	−	0.102413i
$639$	−2.20204e7	+	6.77718e7i	−0.0843961	+	0.259744i
$640$	−8.14432e6	−	5.91720e6i	−0.0310681	−	0.0225723i
$641$	3.04105e8	+	9.88097e7i	1.15465	+	0.375168i	0.822892	−	0.568198i	$-0.192359\pi$
$641$	3.04105e8	+	9.88097e7i	1.15465	+	0.375168i	0.331755	+	0.943366i	$0.392359\pi$
$642$	−3.77199e7	−	5.19169e7i	−0.142549	−	0.196202i
$643$	3.30125e7	+	4.54378e7i	0.124178	+	0.170917i	0.866580	−	0.499038i	$-0.166313\pi$
$643$	3.30125e7	+	4.54378e7i	0.124178	+	0.170917i	−0.742402	+	0.669955i	$0.766313\pi$
$644$	−1.38758e8	+	1.90984e8i	−0.519518	+	0.715055i
$645$	1.66144e8			0.619163
$646$			1.68138e7i			0.0623690i
$647$	2.47186e8	−	3.40222e8i	0.912663	−	1.25617i	−0.0535861	−	0.998563i	$-0.517065\pi$
$647$	2.47186e8	−	3.40222e8i	0.912663	−	1.25617i	0.966249	−	0.257610i	$-0.0829348\pi$
$648$	3.27274e7	+	1.00725e8i	0.120278	+	0.370178i
$649$	1.79805e7	+	5.84222e6i	0.0657761	+	0.0213719i
$650$			2.05001e8i			0.746477i
$651$	3.85293e8	+	2.43197e8i	1.39652	+	0.881485i
$652$	−1.34144e8			−0.483981
$653$	−9.65021e7	+	2.97003e8i	−0.346575	+	1.06665i	0.614160	+	0.789181i	$0.289495\pi$
$653$	−9.65021e7	+	2.97003e8i	−0.346575	+	1.06665i	−0.960735	+	0.277466i	$0.910505\pi$
$654$	−3.59126e7	+	1.16687e7i	−0.128385	+	0.0417147i
$655$	1.65829e8	+	1.20482e8i	0.590115	+	0.428744i
$656$	9.57875e7			0.339310
$657$			2.40292e8i			0.847313i
$658$	−1.09290e8	−	7.94039e7i	−0.383621	−	0.278717i
$659$	8.64235e7	−	6.27904e7i	0.301978	−	0.219400i	−0.426469	−	0.904502i	$-0.640243\pi$
$659$	8.64235e7	−	6.27904e7i	0.301978	−	0.219400i	0.728447	+	0.685102i	$0.240243\pi$
$660$	−2.66801e7	+	1.93843e7i	−0.0928018	+	0.0674244i
$661$	5.32133e6	−	1.63774e7i	0.0184253	−	0.0567074i	−0.941421	−	0.337233i	$-0.890509\pi$
$661$	5.32133e6	−	1.63774e7i	0.0184253	−	0.0567074i	0.959846	+	0.280526i	$0.0905089\pi$
$662$	2.61328e7	−	3.59687e7i	0.0900765	−	0.123980i
$663$	4.21069e8	+	1.36814e8i	1.44482	+	0.469450i
$664$	1.26247e8	−	4.10200e7i	0.431236	−	0.140117i
$665$	1.28977e7	−	9.37076e6i	0.0438580	−	0.0318647i
$666$	6.78977e7	−	2.20613e7i	0.229844	−	0.0746807i
$667$	−5.33915e7	−	1.64322e8i	−0.179926	−	0.553757i
$668$	1.16859e8	+	1.60843e8i	0.392043	+	0.539601i
$669$	−6.02118e6	−	1.85313e7i	−0.0201096	−	0.0618910i
$670$	4.55139e6	−	1.40077e7i	0.0151328	−	0.0465740i
$671$	−1.71776e8	−	1.24803e8i	−0.568585	−	0.413101i
$672$	−8.42569e7	−	2.73767e7i	−0.277650	−	0.0902139i
$673$	2.70419e8	+	3.72200e8i	0.887139	+	1.22104i	0.974392	+	0.224856i	$0.0721911\pi$
$673$	2.70419e8	+	3.72200e8i	0.887139	+	1.22104i	−0.0872530	+	0.996186i	$0.527809\pi$
$674$	−876593.	−	1.20653e6i	−0.00286298	−	0.00394055i
$675$	−2.29338e7	+	3.15656e7i	−0.0745700	+	0.102637i
$676$	−1.07108e8			−0.346722
$677$		−	2.53192e8i		−	0.815989i	−0.912984	−	0.407995i	$-0.866228\pi$
$677$		−	2.53192e8i		−	0.815989i	0.912984	−	0.407995i	$-0.133772\pi$
$678$	−1.20274e8	+	1.65543e8i	−0.385907	+	0.531156i
$679$	−1.54323e8	−	4.74957e8i	−0.492971	−	1.51721i
$680$	−3.90469e7	−	1.26871e7i	−0.124182	−	0.0403492i
$681$			2.53630e8i			0.803080i
$682$	3.19435e7	+	8.01080e7i	0.100700	+	0.252536i
$683$	−1.24914e8			−0.392057			−0.196029	−	0.980598i	$-0.562805\pi$
$683$	−1.24914e8			−0.392057			−0.196029	+	0.980598i	$0.562805\pi$
$684$	−4.54638e6	+	1.39923e7i	−0.0142068	+	0.0437242i
$685$	1.56783e8	−	5.09420e7i	0.487784	−	0.158491i
$686$	−1.23034e8	−	8.93893e7i	−0.381112	−	0.276894i
$687$	6.40893e8			1.97659
$688$			8.44816e7i			0.259416i
$689$	1.17452e7	+	8.53338e6i	0.0359089	+	0.0260894i
$690$	−1.64842e8	+	1.19765e8i	−0.501790	+	0.364572i
$691$	−1.71197e8	+	1.24382e8i	−0.518874	+	0.376984i	−0.816180	−	0.577798i	$-0.803912\pi$
$691$	−1.71197e8	+	1.24382e8i	−0.518874	+	0.376984i	0.297306	+	0.954782i	$0.403912\pi$
$692$	−3.43742e6	+	1.05793e7i	−0.0103732	+	0.0319255i
$693$	−8.01450e7	+	1.10310e8i	−0.240811	+	0.331448i
$694$	2.53819e8	+	8.24709e7i	0.759357	+	0.246730i
$695$	−1.24304e8	+	4.03887e7i	−0.370279	+	0.120311i
$696$	5.24575e7	−	3.81126e7i	0.155589	−	0.113042i
$697$	3.71533e8	−	1.20718e8i	1.09723	−	0.356513i
$698$	−1.30988e8	−	4.03139e8i	−0.385180	−	1.18546i
$699$	−4.92410e8	−	6.77744e8i	−1.44177	−	1.98442i
$700$	−5.16979e7	−	1.59110e8i	−0.150723	−	0.463877i
$701$	7.83861e7	−	2.41248e8i	0.227554	−	0.700340i	−0.770468	−	0.637479i	$-0.779977\pi$
$701$	7.83861e7	−	2.41248e8i	0.227554	−	0.700340i	0.998022	−	0.0628614i	$-0.0200226\pi$
$702$	−4.02753e7	−	2.92617e7i	−0.116420	−	0.0845841i
$703$	−1.32241e7	−	4.29676e6i	−0.0380627	−	0.0123673i
$704$	−9.85661e6	−	1.35665e7i	−0.0282494	−	0.0388820i
$705$	−6.85352e7	−	9.43306e7i	−0.195590	−	0.269206i
$706$	8.42642e6	−	1.15980e7i	0.0239458	−	0.0329585i
$707$	−2.19039e8			−0.619817
$708$			4.38365e7i			0.123520i
$709$	2.10337e8	−	2.89504e8i	0.590169	−	0.812298i	−0.404595	−	0.914496i	$-0.632588\pi$
$709$	2.10337e8	−	2.89504e8i	0.590169	−	0.812298i	0.994764	+	0.102198i	$0.0325875\pi$
$710$	1.04724e7	+	3.22308e7i	0.0292599	+	0.0900527i
$711$	4.34321e8	+	1.41120e8i	1.20838	+	0.392625i
$712$		−	7.35519e7i		−	0.203776i
$713$	1.97362e8	+	4.94945e8i	0.544496	+	1.36549i
$714$	−3.61311e8			−0.992629
$715$	2.45544e7	−	7.55706e7i	0.0671755	−	0.206745i
$716$	−2.89129e8	+	9.39436e7i	−0.787684	+	0.255934i
$717$	−4.29630e8	−	3.12144e8i	−1.16557	−	0.846834i
$718$	2.83233e8			0.765194
$719$		−	3.01096e8i		−	0.810062i	−0.914303	−	0.405031i	$-0.867261\pi$
$719$		−	3.01096e8i		−	0.810062i	0.914303	−	0.405031i	$-0.132739\pi$
$720$	−2.90639e7	−	2.11162e7i	−0.0778676	−	0.0565741i
$721$	−1.31051e8	+	9.52140e7i	−0.349651	+	0.254036i
$722$	−2.12987e8	+	1.54744e8i	−0.565902	+	0.411152i
$723$	−2.10518e8	+	6.47907e8i	−0.557024	+	1.71434i
$724$	2.97041e7	−	4.08842e7i	0.0782709	−	0.107731i
$725$	1.16452e8	+	3.78376e7i	0.305586	+	0.0992910i
$726$	3.01171e8	−	9.78564e7i	0.787052	−	0.255729i
$727$	−2.54223e8	+	1.84704e8i	−0.661624	+	0.480698i	−0.867211	−	0.497941i	$-0.834090\pi$
$727$	−2.54223e8	+	1.84704e8i	−0.661624	+	0.480698i	0.205587	+	0.978639i	$0.434090\pi$
$728$	2.03012e8	−	6.59625e7i	0.526171	−	0.170963i
$729$	9.10787e7	+	2.80311e8i	0.235090	+	0.723533i
$730$	6.71709e7	+	9.24529e7i	0.172668	+	0.237658i
$731$	1.06470e8	+	3.27681e8i	0.272568	+	0.838878i
$732$	1.52135e8	−	4.68222e8i	0.387878	−	1.19376i
$733$	−2.34682e8	−	1.70507e8i	−0.595893	−	0.432942i	0.248526	−	0.968625i	$-0.420054\pi$
$733$	−2.34682e8	−	1.70507e8i	−0.595893	−	0.432942i	−0.844419	+	0.535684i	$0.820054\pi$
$734$	2.64848e8	+	8.60545e7i	0.669745	+	0.217613i
$735$	6.21069e7	+	8.54828e7i	0.156415	+	0.215286i
$736$	−6.08988e7	−	8.38199e7i	−0.152748	−	0.210239i
$737$	1.44209e7	−	1.98486e7i	0.0360238	−	0.0495825i
$738$	3.41828e8			0.850431
$739$		−	4.63476e8i		−	1.14840i	−0.818714	−	0.574201i	$-0.805313\pi$
$739$		−	4.63476e8i		−	1.14840i	0.818714	−	0.574201i	$-0.194687\pi$
$740$	1.99568e7	−	2.74682e7i	0.0492488	−	0.0677851i
$741$	−2.33161e7	−	7.17597e7i	−0.0573062	−	0.176370i
$742$	−1.12679e7	−	3.66116e6i	−0.0275823	−	0.00896205i
$743$			2.48135e8i			0.604953i	0.953157	+	0.302476i	$0.0978133\pi$
$743$			2.48135e8i			0.604953i	−0.953157	+	0.302476i	$0.902187\pi$
$744$	−1.53766e8	+	1.27840e8i	−0.373372	+	0.310419i
$745$	7.90647e7			0.191211
$746$	−6.32000e7	+	1.94510e8i	−0.152230	+	0.468516i
$747$	4.50525e8	−	1.46384e8i	1.08083	−	0.351183i
$748$	−5.53285e7	−	4.01985e7i	−0.132204	−	0.0960517i
$749$	−1.26183e8			−0.300300
$750$		−	3.22397e8i		−	0.764201i
$751$	908915.	+	660366.i	0.00214587	+	0.00155907i	0.588858	−	0.808237i	$-0.299578\pi$
$751$	908915.	+	660366.i	0.00214587	+	0.00155907i	−0.586712	+	0.809796i	$0.699578\pi$
$752$	4.79657e7	−	3.48491e7i	0.112792	−	0.0819480i
$753$	−1.94222e8	+	1.41110e8i	−0.454897	+	0.330502i
$754$	−4.82779e7	+	1.48584e8i	−0.112625	+	0.346624i
$755$	−6.02952e7	+	8.29892e7i	−0.140101	+	0.192833i
$756$	3.86386e7	+	1.25545e7i	0.0894245	+	0.0290558i
$757$	2.13314e8	−	6.93099e7i	0.491736	−	0.159775i	−0.0526444	−	0.998613i	$-0.516765\pi$
$757$	2.13314e8	−	6.93099e7i	0.491736	−	0.159775i	0.544380	+	0.838839i	$0.316765\pi$
$758$	2.13570e8	−	1.55168e8i	0.490381	−	0.356282i
$759$	−3.22797e8	+	1.04883e8i	−0.738251	+	0.239872i
$760$	2.16216e6	+	6.65446e6i	0.00492547	+	0.0151591i
$761$	−2.61027e8	−	3.59272e8i	−0.592285	−	0.815211i	0.402689	−	0.915337i	$-0.368075\pi$
$761$	−2.61027e8	−	3.59272e8i	−0.592285	−	0.815211i	−0.994975	+	0.100126i	$0.968075\pi$
$762$	1.83896e8	+	5.65975e8i	0.415631	+	1.27918i
$763$	−2.29442e7	+	7.06150e7i	−0.0516535	+	0.158973i
$764$	−1.71490e8	−	1.24595e8i	−0.384556	−	0.279396i
$765$	−1.39343e8	−	4.52753e7i	−0.311244	−	0.101129i
$766$	−4.09588e7	−	5.63750e7i	−0.0911299	−	0.125430i
$767$	−6.20827e7	−	8.54495e7i	−0.137589	−	0.189375i
$768$	2.28543e7	−	3.14563e7i	0.0504527	−	0.0694422i
$769$	−6.55855e8			−1.44221			−0.721106	−	0.692825i	$-0.756366\pi$
$769$	−6.55855e8			−1.44221			−0.721106	+	0.692825i	$0.756366\pi$
$770$			6.48456e7i			0.142039i
$771$	3.76076e8	−	5.17625e8i	0.820565	−	1.12941i
$772$	−1.28550e8	−	3.95638e8i	−0.279397	−	0.859895i
$773$	−3.84273e8	−	1.24858e8i	−0.831959	−	0.270320i	−0.138089	−	0.990420i	$-0.544096\pi$
$773$	−3.84273e8	−	1.24858e8i	−0.831959	−	0.270320i	−0.693870	+	0.720100i	$0.744096\pi$
$774$			3.01482e8i			0.650187i
$775$	−3.65981e8	−	9.30161e7i	−0.786238	−	0.199826i
$776$	2.19179e8			0.469044
$777$	9.23328e7	−	2.84171e8i	0.196831	−	0.605783i
$778$	5.45447e8	−	1.77227e8i	1.15828	−	0.376348i
$779$	−5.38611e7	−	3.91324e7i	−0.113937	−	0.0827798i
$780$	1.84241e8			0.388243
$781$			5.64517e7i			0.118501i
$782$	−3.41846e8	−	2.48365e8i	−0.714841	−	0.519363i
$783$	−2.40560e7	+	1.74777e7i	−0.0501117	+	0.0364082i
$784$	−4.34667e7	+	3.15804e7i	−0.0902004	+	0.0655344i
$785$	−6.75264e7	+	2.07825e8i	−0.139593	+	0.429624i
$786$	−4.65344e8	+	6.40490e8i	−0.958310	+	1.31900i
$787$	2.43997e8	+	7.92795e7i	0.500565	+	0.162643i	0.548407	−	0.836211i	$-0.315234\pi$
$787$	2.43997e8	+	7.92795e7i	0.500565	+	0.162643i	−0.0478421	+	0.998855i	$0.515234\pi$
$788$	3.77221e8	−	1.22567e8i	0.770934	−	0.250492i
$789$	−1.05162e9	+	7.64046e8i	−2.14105	+	1.55557i
$790$	2.06554e8	−	6.71135e7i	0.418941	−	0.136122i
$791$	1.24333e8	+	3.82657e8i	0.251221	+	0.773180i
$792$	−3.51744e7	−	4.84134e7i	−0.0708029	−	0.0974519i
$793$	3.66559e8	+	1.12815e9i	0.735063	+	2.26229i
$794$	1.15926e8	−	3.56785e8i	0.231591	−	0.712763i
$795$	−8.27306e6	−	6.01073e6i	−0.0164651	−	0.0119626i
$796$	−3.85671e8	−	1.25312e8i	−0.764677	−	0.248459i
$797$	−3.98864e8	−	5.48989e8i	−0.787861	−	1.08440i	−0.994371	−	0.105953i	$-0.966211\pi$
$797$	−3.98864e8	−	5.48989e8i	−0.787861	−	1.08440i	0.206510	−	0.978444i	$-0.433789\pi$
$798$	3.61932e7	+	4.98157e7i	0.0712227	+	0.0980296i
$799$	1.42126e8	−	1.95620e8i	0.278634	−	0.383507i
$800$	7.34245e7			0.143407
$801$		−	2.62478e8i		−	0.510735i
$802$	−4.67796e7	+	6.43866e7i	−0.0906846	+	0.124817i
$803$	5.88243e7	+	1.81043e8i	0.113608	+	0.349650i
$804$	5.41028e7	+	1.75791e7i	0.104100	+	0.0338242i
$805$			4.00647e8i			0.768023i
$806$	1.18681e8	−	4.66964e8i	0.226661	−	0.891822i
$807$	2.97525e8			0.566113
$808$	2.97067e7	−	9.14278e7i	0.0563145	−	0.173318i
$809$	−6.53157e8	+	2.12224e8i	−1.23359	+	0.400819i	−0.852015	−	0.523518i	$-0.824619\pi$
$809$	−6.53157e8	+	2.12224e8i	−1.23359	+	0.400819i	−0.381578	+	0.924336i	$0.624619\pi$
$810$	1.45415e8	+	1.05650e8i	0.273624	+	0.198800i
$811$	1.49777e8			0.280790			0.140395	−	0.990096i	$-0.455163\pi$
$811$	1.49777e8			0.280790			0.140395	+	0.990096i	$0.455163\pi$
$812$		−	1.27497e8i		−	0.238140i
$813$	−8.84455e8	−	6.42594e8i	−1.64590	−	1.19582i
$814$	4.57553e7	−	3.32431e7i	0.0848336	−	0.0616352i
$815$	−1.84184e8	+	1.33817e8i	−0.340234	+	0.247195i
$816$	4.90020e7	−	1.50813e8i	0.0901870	−	0.277567i
$817$	3.45136e7	−	4.75039e7i	0.0632884	−	0.0871090i
$818$	5.42528e7	+	1.76278e7i	0.0991203	+	0.0322061i
$819$	7.24470e8	−	2.35395e8i	1.31877	−	0.428494i
$820$	1.31519e8	−	9.55542e7i	0.238532	−	0.173304i
$821$	−8.69216e8	+	2.82425e8i	−1.57072	+	0.510357i	−0.959644	−	0.281216i	$-0.909262\pi$
$821$	−8.69216e8	+	2.82425e8i	−1.57072	+	0.510357i	−0.611074	+	0.791574i	$0.709262\pi$
$822$	1.96756e8	+	6.05552e8i	0.354252	+	1.09028i
$823$	3.00245e8	+	4.13252e8i	0.538612	+	0.741336i	0.988412	−	0.151793i	$-0.0485048\pi$
$823$	3.00245e8	+	4.13252e8i	0.538612	+	0.741336i	−0.449800	+	0.893129i	$0.648505\pi$
$824$	−2.19692e7	−	6.76144e7i	−0.0392675	−	0.120853i
$825$	7.43287e7	−	2.28760e8i	0.132372	−	0.407398i
$826$	6.97339e7	+	5.06646e7i	0.123738	+	0.0899011i
$827$	2.33332e8	+	7.58141e7i	0.412532	+	0.134040i	0.507928	−	0.861400i	$-0.330412\pi$
$827$	2.33332e8	+	7.58141e7i	0.412532	+	0.134040i	−0.0953960	+	0.995439i	$0.530412\pi$
$828$	−2.17324e8	−	2.99121e8i	−0.382840	−	0.526933i
$829$	−4.51563e8	−	6.21523e8i	−0.792601	−	1.09092i	−0.993779	−	0.111367i	$-0.964477\pi$
$829$	−4.51563e8	−	6.21523e8i	−0.792601	−	1.09092i	0.201179	−	0.979555i	$-0.435523\pi$
$830$	1.32420e8	−	1.82261e8i	0.231590	−	0.318756i
$831$	−1.21828e9			−2.12297
$832$			9.36840e7i			0.162665i
$833$	−1.28795e8	+	1.77272e8i	−0.222826	+	0.306693i
$834$	−1.55995e8	−	4.80105e8i	−0.268914	−	0.827633i
$835$	3.20903e8	+	1.04268e8i	0.551206	+	0.179098i
$836$			1.16552e7i			0.0199480i
$837$	7.05142e7	−	5.86250e7i	0.120254	−	0.0999785i
$838$	1.09750e8			0.186497
$839$	3.02649e8	−	9.31458e8i	0.512452	−	1.57717i	−0.275418	−	0.961325i	$-0.588816\pi$
$839$	3.02649e8	−	9.31458e8i	0.512452	−	1.57717i	0.787870	−	0.615841i	$-0.211184\pi$
$840$	−1.42997e8	+	4.64626e7i	−0.241262	+	0.0783909i
$841$	−4.05729e8	−	2.94779e8i	−0.682100	−	0.495575i
$842$	−7.27946e8			−1.21945
$843$			8.61845e8i			1.43862i
$844$	1.92082e8	+	1.39556e8i	0.319492	+	0.232124i
$845$	−1.47062e8	+	1.06847e8i	−0.243742	+	0.177089i
$846$	1.71171e8	−	1.24363e8i	0.282696	−	0.205390i
$847$	1.92415e8	−	5.92193e8i	0.316657	−	0.974570i
$848$	3.05637e6	−	4.20673e6i	0.00501208	−	0.00689854i
$849$	2.75740e8	+	8.95932e7i	0.450584	+	0.146404i
$850$	2.84793e8	−	9.25350e7i	0.463738	−	0.150678i
$851$	2.82698e8	−	2.05392e8i	0.458705	−	0.333269i
$852$	−1.24487e8	+	4.04483e7i	−0.201282	+	0.0654005i
$853$	1.01189e8	+	3.11428e8i	0.163037	+	0.501777i	0.998886	−	0.0471826i	$-0.0150243\pi$
$853$	1.01189e8	+	3.11428e8i	0.163037	+	0.501777i	−0.835849	+	0.548959i	$0.815024\pi$
$854$	−5.69003e8	−	7.83165e8i	−0.913568	−	1.25742i
$855$	7.71593e6	+	2.37472e7i	0.0123450	+	0.0379939i
$856$	1.71133e7	−	5.26694e7i	0.0272843	−	0.0839725i
$857$	−1.83599e8	−	1.33393e8i	−0.291694	−	0.211928i	0.432308	−	0.901726i	$-0.357699\pi$
$857$	−1.83599e8	−	1.33393e8i	−0.291694	−	0.211928i	−0.724002	+	0.689798i	$0.757699\pi$
$858$	2.91880e8	+	9.48377e7i	0.462108	+	0.150148i
$859$	3.78144e8	+	5.20471e8i	0.596593	+	0.821140i	0.995391	−	0.0958989i	$-0.0305726\pi$
$859$	3.78144e8	+	5.20471e8i	0.596593	+	0.821140i	−0.398798	+	0.917039i	$0.630573\pi$
$860$	8.42758e7	+	1.15996e8i	0.132498	+	0.182367i
$861$	8.40914e8	−	1.15742e9i	1.31747	−	1.81335i
$862$	−2.24984e8			−0.351260
$863$			4.43081e8i			0.689368i	0.938719	+	0.344684i	$0.112014\pi$
$863$			4.43081e8i			0.689368i	−0.938719	+	0.344684i	$0.887986\pi$
$864$	−1.04806e7	+	1.44253e7i	−0.0162496	+	0.0223657i
$865$	5.83384e6	+	1.79547e7i	0.00901377	+	0.0277415i
$866$	1.35903e7	+	4.41575e6i	0.0209254	+	0.00679909i
$867$			2.48324e8i			0.381032i
$868$	2.56471e7	+	3.92359e8i	0.0392175	+	0.599963i
$869$	3.61776e8			0.551290
$870$	3.40059e7	−	1.04659e8i	0.0516412	−	0.158935i
$871$	−1.30357e8	+	4.23557e7i	−0.197279	+	0.0640999i
$872$	−2.63632e7	−	1.91540e7i	−0.0397603	−	0.0288875i
$873$	7.82165e8			1.17559
$874$			7.20110e7i			0.107861i
$875$	−5.12860e8	−	3.72615e8i	−0.765552	−	0.556206i
$876$	−3.57086e8	+	2.59438e8i	−0.531203	+	0.385941i
$877$	1.15480e8	−	8.39012e7i	0.171202	−	0.124385i	−0.498885	−	0.866668i	$-0.666257\pi$
$877$	1.15480e8	−	8.39012e7i	0.171202	−	0.124385i	0.670087	+	0.742283i	$0.266257\pi$
$878$	−7.97740e7	+	2.45519e8i	−0.117863	+	0.362745i
$879$	3.35867e8	−	4.62282e8i	0.494540	−	0.680675i
$880$	−2.70668e7	−	8.79455e6i	−0.0397182	−	0.0129052i
$881$	−3.96963e8	+	1.28981e8i	−0.580527	+	0.188625i	−0.584537	−	0.811367i	$-0.698724\pi$
$881$	−3.96963e8	+	1.28981e8i	−0.580527	+	0.188625i	0.00400967	+	0.999992i	$0.498724\pi$
$882$	−1.55116e8	+	1.12698e8i	−0.226074	+	0.164252i
$883$	7.85708e8	−	2.55292e8i	1.14125	−	0.370813i	0.323407	−	0.946260i	$-0.395172\pi$
$883$	7.85708e8	−	2.55292e8i	1.14125	−	0.370813i	0.817839	+	0.575447i	$0.195172\pi$
$884$	1.18067e8	+	3.63374e8i	0.170912	+	0.526014i
$885$	4.37298e7	+	6.01889e7i	0.0630881	+	0.0868333i
$886$	1.72251e8	+	5.30133e8i	0.247662	+	0.762226i
$887$	−2.35325e8	+	7.24256e8i	−0.337208	+	1.03782i	0.628417	+	0.777877i	$0.283703\pi$
$887$	−2.35325e8	+	7.24256e8i	−0.337208	+	1.03782i	−0.965624	+	0.259942i	$0.916297\pi$
$888$	1.06092e8	+	7.70802e7i	0.151511	+	0.110079i
$889$	1.11288e9	+	3.61596e8i	1.58395	+	0.514657i
$890$	−7.33727e7	−	1.00989e8i	−0.104079	−	0.143253i
$891$	1.75988e8	+	2.42226e8i	0.248799	+	0.342443i
$892$	9.88368e6	−	1.36037e7i	0.0139259	−	0.0191674i
$893$	−4.12081e7			−0.0578666
$894$			3.05376e8i			0.427388i
$895$	−3.03268e8	+	4.17412e8i	−0.423016	+	0.582232i
$896$	−2.36255e7	−	7.27120e7i	−0.0328441	−	0.101084i
$897$	1.80337e9	+	5.85952e8i	2.49867	+	0.811866i
$898$			7.92193e8i			1.09396i
$899$	−2.43356e8	−	1.53606e8i	−0.334937	−	0.211412i
$900$	2.62024e8			0.359429
$901$	6.55318e6	−	2.01686e7i	0.00895937	−	0.0275741i
$902$	2.57542e8	−	8.36806e7i	0.350937	−	0.114026i
$903$	1.02081e9	+	7.41660e8i	1.38637	+	1.00726i
$904$	−1.76585e8			−0.239028
$905$		−	8.57669e7i		−	0.115711i
$906$	−3.20534e8	−	2.32881e8i	−0.431012	−	0.313148i
$907$	1.64146e8	−	1.19259e8i	0.219993	−	0.159834i	−0.472331	−	0.881421i	$-0.656587\pi$
$907$	1.64146e8	−	1.19259e8i	0.219993	−	0.159834i	0.692323	+	0.721587i	$0.256587\pi$
$908$	−1.77075e8	+	1.28653e8i	−0.236538	+	0.171855i
$909$	1.06012e8	−	3.26270e8i	0.141144	−	0.434396i
$910$	2.12939e8	−	2.93086e8i	0.282574	−	0.388929i
$911$	1.64202e8	+	5.33525e7i	0.217182	+	0.0705667i	0.415587	−	0.909553i	$-0.363576\pi$
$911$	1.64202e8	+	5.33525e7i	0.217182	+	0.0705667i	−0.198405	+	0.980120i	$0.563576\pi$
$912$	−2.57019e7	+	8.35105e6i	−0.0338829	+	0.0110092i
$913$	3.03602e8	−	2.20580e8i	0.398926	−	0.289837i
$914$	4.44292e8	−	1.44359e8i	0.581875	−	0.189063i
$915$	−2.58196e8	−	7.94647e8i	−0.337044	−	1.03732i
$916$	3.25091e8	+	4.47449e8i	0.422979	+	0.582180i
$917$	4.81047e8	+	1.48051e9i	0.623849	+	1.92001i
$918$	−2.24714e7	+	6.91600e7i	−0.0290471	+	0.0893978i
$919$	7.62434e8	+	5.53941e8i	0.982326	+	0.713702i	0.958227	−	0.286008i	$-0.0923283\pi$
$919$	7.62434e8	+	5.53941e8i	0.982326	+	0.713702i	0.0240989	+	0.999710i	$0.492328\pi$
$920$	−1.67232e8	−	5.43368e7i	−0.214761	−	0.0697800i
$921$	−1.12357e9	−	1.54646e9i	−1.43821	−	1.97952i
$922$	2.83706e8	+	3.90488e8i	0.361973	+	0.498213i
$923$	1.85375e8	−	2.55147e8i	0.235747	−	0.324479i
$924$	−2.50457e8			−0.317480
$925$			2.47637e8i			0.312889i
$926$	5.77732e8	−	7.95181e8i	0.727602	−	1.00146i
$927$	−7.83997e7	−	2.41289e8i	−0.0984182	−	0.302900i
$928$	5.32178e7	+	1.72915e7i	0.0665906	+	0.0216366i
$929$			1.04870e9i			1.30799i	0.756497	+	0.653997i	$0.226909\pi$
$929$			1.04870e9i			1.30799i	−0.756497	+	0.653997i	$0.773091\pi$
$930$	−8.35966e7	+	3.28919e8i	−0.103930	+	0.408922i
$931$	3.73429e7			0.0462764
$932$	2.23404e8	−	6.87567e8i	0.275958	−	0.849312i
$933$	−1.43190e9	+	4.65254e8i	−1.76307	+	0.572855i
$934$	−2.65664e6	−	1.93016e6i	−0.00326056	−	0.00236893i
$935$	−1.16068e8			−0.141997
$936$			3.34322e8i			0.407697i
$937$	−7.71808e8	−	5.60751e8i	−0.938189	−	0.681634i	0.00979504	−	0.999952i	$-0.496882\pi$
$937$	−7.71808e8	−	5.60751e8i	−0.938189	−	0.681634i	−0.947984	+	0.318318i	$0.896882\pi$
$938$	9.04944e7	−	6.57480e7i	0.109651	−	0.0796662i
$939$	−1.58218e9	+	1.14952e9i	−1.91099	+	1.38842i
$940$	3.10941e7	−	9.56978e7i	0.0374364	−	0.115217i
$941$	−3.31981e8	+	4.56933e8i	−0.398423	+	0.548382i	−0.960347	−	0.278806i	$-0.910061\pi$
$941$	−3.31981e8	+	4.56933e8i	−0.398423	+	0.548382i	0.561924	+	0.827189i	$0.310061\pi$
$942$	−8.02694e8	−	2.60811e8i	−0.960278	−	0.312013i
$943$	1.59122e9	−	5.17018e8i	1.89756	−	0.616553i
$944$	−3.06051e7	+	2.22359e7i	−0.0363813	+	0.0264326i
$945$	6.55759e7	−	2.13069e7i	0.0777050	−	0.0252479i
$946$	7.38037e7	+	2.27145e8i	0.0871776	+	0.268305i
$947$	−1.95289e8	−	2.68793e8i	−0.229947	−	0.316495i	0.678415	−	0.734679i	$-0.262667\pi$
$947$	−1.95289e8	−	2.68793e8i	−0.229947	−	0.316495i	−0.908363	+	0.418183i	$0.862667\pi$
$948$	2.59216e8	+	7.97786e8i	0.304255	+	0.936399i
$949$	3.28634e8	−	1.01143e9i	0.384516	−	1.18342i
$950$	−4.12865e7	−	2.99964e7i	−0.0481545	−	0.0349863i
$951$	−8.21582e8	−	2.66948e8i	−0.955233	−	0.310374i
$952$	−1.83274e8	−	2.52255e8i	−0.212417	−	0.292367i
$953$	−4.18027e8	−	5.75365e8i	−0.482976	−	0.664760i	0.496097	−	0.868267i	$-0.334766\pi$
$953$	−4.18027e8	−	5.75365e8i	−0.482976	−	0.664760i	−0.979073	+	0.203507i	$0.934766\pi$
$954$	1.09070e7	−	1.50122e7i	0.0125620	−	0.0172902i
$955$	−3.59753e8			−0.413042
$956$		−	4.58287e8i		−	0.524522i
$957$	1.07746e8	−	1.48300e8i	0.122932	−	0.169202i
$958$	−4.38625e7	−	1.34995e8i	−0.0498881	−	0.153540i
$959$	1.19070e9	+	3.86881e8i	1.35004	+	0.438654i
$960$		−	6.59890e7i		−	0.0745861i
$961$	7.79804e8	+	4.23755e8i	0.878649	+	0.477469i
$962$	−3.15966e8			−0.354907
$963$	6.10708e7	−	1.87957e8i	0.0683840	−	0.210464i
$964$	−5.59131e8	+	1.81673e8i	−0.624141	+	0.202796i
$965$	−5.71178e8	−	4.14985e8i	−0.635608	−	0.461796i
$966$	−1.54744e9			−1.71665
$967$			2.73106e8i			0.302032i	0.988531	+	0.151016i	$0.0482544\pi$
$967$			2.73106e8i			0.302032i	−0.988531	+	0.151016i	$0.951746\pi$
$968$	2.21088e8	+	1.60630e8i	0.243747	+	0.177092i
$969$	−8.91659e7	+	6.47828e7i	−0.0980003	+	0.0712014i
$970$	3.00939e8	−	2.18645e8i	0.329734	−	0.239566i
$971$	4.02283e8	−	1.23810e9i	0.439414	−	1.35238i	−0.449080	−	0.893492i	$-0.648248\pi$
$971$	4.02283e8	−	1.23810e9i	0.439414	−	1.35238i	0.888495	−	0.458887i	$-0.151752\pi$
$972$	−3.65852e8	+	5.03552e8i	−0.398388	+	0.548334i
$973$	−9.44031e8	−	3.06734e8i	−1.02482	−	0.332984i
$974$	4.71296e8	−	1.53133e8i	0.510055	−	0.165727i
$975$	−1.08715e9	+	7.89859e8i	−1.17294	+	0.852188i
$976$	4.04066e8	−	1.31289e8i	0.434613	−	0.141214i
$977$	3.42372e7	+	1.05371e8i	0.0367126	+	0.112990i	0.967733	−	0.251976i	$-0.0810806\pi$
$977$	3.42372e7	+	1.05371e8i	0.0367126	+	0.112990i	−0.931021	+	0.364966i	$0.881081\pi$
$978$	−5.16849e8	−	7.11382e8i	−0.552519	−	0.760478i
$979$	−6.42554e7	−	1.97758e8i	−0.0684797	−	0.210759i
$980$	−2.81776e7	+	8.67217e7i	−0.0299382	+	0.0921403i
$981$	−9.40802e7	−	6.83532e7i	−0.0996532	−	0.0724023i
$982$	−4.26406e8	−	1.38548e8i	−0.450286	−	0.146307i
$983$	−1.35078e7	−	1.85919e7i	−0.0142208	−	0.0195732i	0.801847	−	0.597529i	$-0.203851\pi$
$983$	−1.35078e7	−	1.85919e7i	−0.0142208	−	0.0195732i	−0.816068	+	0.577956i	$0.803851\pi$
$984$	3.69064e8	+	5.07973e8i	0.387362	+	0.533157i
$985$	3.95668e8	−	5.44590e8i	0.414021	−	0.569850i
$986$	2.28209e8			0.238069
$987$		−	8.85518e8i		−	0.920971i
$988$	3.82731e7	−	5.26784e7i	0.0396846	−	0.0546212i
$989$	4.55994e8	+	1.40341e9i	0.471379	+	1.45076i
$990$	−9.65910e7	−	3.13843e7i	−0.0995477	−	0.0323450i
$991$			2.69345e8i			0.276750i	0.990380	+	0.138375i	$0.0441879\pi$
$991$			2.69345e8i			0.276750i	−0.990380	+	0.138375i	$0.955812\pi$
$992$	−1.67251e8	−	4.25076e7i	−0.171330	−	0.0435444i
$993$	2.91435e8			0.297641
$994$	−7.95335e7	+	2.44779e8i	−0.0809824	+	0.249238i
$995$	−6.54545e8	+	2.12675e8i	−0.664462	+	0.215897i
$996$	7.03956e8	+	5.11454e8i	0.712471	+	0.517641i
$997$	1.29180e8			0.130350			0.0651748	−	0.997874i	$-0.479240\pi$
$997$	1.29180e8			0.130350			0.0651748	+	0.997874i	$0.479240\pi$
$998$		−	2.34797e8i		−	0.236212i
$999$	−4.86517e7	−	3.53476e7i	−0.0487980	−	0.0354538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.7.f.a.23.2	✓	64
31.27	odd	10	inner	62.7.f.a.27.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.7.f.a.23.2	✓	64	1.1	even	1	trivial
62.7.f.a.27.2	yes	64	31.27	odd	10	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	62.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.74806 + 5.37999i) q^{2} +(-35.2660 + 11.4586i) q^{3} +(-25.8885 - 18.8091i) q^{4} -54.3091 q^{5} -209.761i q^{6} +(-333.682 - 242.434i) q^{7} +(146.448 - 106.400i) q^{8} +(522.615 - 379.702i) q^{9} +(94.9357 - 292.182i) q^{10} +(300.800 - 414.015i) q^{11} +(1128.51 + 366.675i) q^{12} +(-2719.08 + 883.482i) q^{13} +(1887.59 - 1371.41i) q^{14} +(1915.26 - 622.306i) q^{15} +(316.433 + 973.882i) q^{16} +(2454.72 + 3378.63i) q^{17} +(1129.23 + 3475.41i) q^{18} +(219.934 - 676.886i) q^{19} +(1405.98 + 1021.51i) q^{20} +(14545.6 + 4726.14i) q^{21} +(1701.58 + 2342.02i) q^{22} +(10513.2 + 14470.1i) q^{23} +(-3945.42 + 5430.40i) q^{24} -12675.5 q^{25} -16173.0i q^{26} +(1809.30 - 2490.28i) q^{27} +(4078.56 + 12552.5i) q^{28} +(-9187.17 - 2985.09i) q^{29} +11391.9i q^{30} +(28873.1 + 7338.24i) q^{31} -5792.62 q^{32} +(-5863.95 + 18047.4i) q^{33} +(-22468.0 + 7300.29i) q^{34} +(18121.9 + 13166.4i) q^{35} -20671.6 q^{36} -19536.6i q^{37} +(3257.18 + 2366.48i) q^{38} +(85767.4 - 62313.7i) q^{39} +(-7953.44 + 5778.51i) q^{40} +(28906.2 - 88964.1i) q^{41} +(-50853.1 + 69993.3i) q^{42} +(78463.6 + 25494.4i) q^{43} +(-15574.5 + 5060.47i) q^{44} +(-28382.7 + 20621.3i) q^{45} +(-96226.8 + 31266.0i) q^{46} +(-17891.9 - 55065.5i) q^{47} +(-22318.7 - 30719.0i) q^{48} +(16213.7 + 49900.6i) q^{49} +(22157.6 - 68194.2i) q^{50} +(-125282. - 91022.9i) q^{51} +(87010.5 + 28271.4i) q^{52} +(-2984.73 - 4108.13i) q^{53} +(10234.9 + 14087.2i) q^{54} +(-16336.2 + 22484.8i) q^{55} -74662.0 q^{56} +26391.2i q^{57} +(32119.5 - 44208.7i) q^{58} +(11416.1 + 35135.3i) q^{59} +(-61288.4 - 19913.8i) q^{60} -414903. i q^{61} +(-89951.6 + 142509. i) q^{62} -266440. q^{63} +(10125.9 - 31164.2i) q^{64} +(147671. - 47981.1i) q^{65} +(-86844.2 - 63096.0i) q^{66} +47941.8 q^{67} -133639. i q^{68} +(-536564. - 389837. i) q^{69} +(-102513. + 74480.1i) q^{70} +(-89243.3 + 64839.1i) q^{71} +(36135.3 - 111213. i) q^{72} +(-218642. + 300935. i) q^{73} +(105107. + 34151.3i) q^{74} +(447015. - 145244. i) q^{75} +(-18425.4 + 13386.8i) q^{76} +(-200743. + 65225.3i) q^{77} +(185320. + 570356. i) q^{78} +(415527. + 571924. i) q^{79} +(-17185.2 - 52890.6i) q^{80} +(-180795. + 556431. i) q^{81} +(428096. + 311030. i) q^{82} +(697420. + 226606. i) q^{83} +(-287669. - 395942. i) q^{84} +(-133313. - 183490. i) q^{85} +(-274319. + 377568. i) q^{86} +358199. q^{87} -92636.9i q^{88} +(238829. - 328720. i) q^{89} +(-61327.3 - 188746. i) q^{90} +(1.12149e6 + 364395. i) q^{91} -572354. i q^{92} +(-1.10232e6 + 72054.9i) q^{93} +327528. q^{94} +(-11944.4 + 36761.0i) q^{95} +(204282. - 66375.3i) q^{96} +(979561. + 711693. i) q^{97} -296807. q^{98} -330585. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) \) 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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