LMFDB - Embedded newform 60.7.f.a.19.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(19,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.f (of order $2$, degree $1$, 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:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.26
Character	$\chi$	$=$	60.19
Dual form			60.7.f.a.19.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.30858 + 6.74063i) q^{2} -15.5885 q^{3} +(-26.8722 + 58.0851i) q^{4} +(-108.897 + 61.3721i) q^{5} +(-67.1642 - 105.076i) q^{6} +118.127 q^{7} +(-507.312 + 69.1287i) q^{8} +243.000 q^{9} +O(q^{10})$	\(q+(4.30858 + 6.74063i) q^{2} -15.5885 q^{3} +(-26.8722 + 58.0851i) q^{4} +(-108.897 + 61.3721i) q^{5} +(-67.1642 - 105.076i) q^{6} +118.127 q^{7} +(-507.312 + 69.1287i) q^{8} +243.000 q^{9} +(-882.876 - 469.605i) q^{10} -184.093i q^{11} +(418.897 - 905.458i) q^{12} -2860.25i q^{13} +(508.962 + 796.254i) q^{14} +(1697.53 - 956.696i) q^{15} +(-2651.77 - 3121.75i) q^{16} -4931.62i q^{17} +(1046.99 + 1637.97i) q^{18} +4722.79i q^{19} +(-638.508 - 7974.48i) q^{20} -1841.43 q^{21} +(1240.90 - 793.180i) q^{22} -19598.7 q^{23} +(7908.21 - 1077.61i) q^{24} +(8091.94 - 13366.4i) q^{25} +(19279.9 - 12323.6i) q^{26} -3788.00 q^{27} +(-3174.35 + 6861.45i) q^{28} +12484.2 q^{29} +(13762.7 + 7320.42i) q^{30} +15858.3i q^{31} +(9617.25 - 31324.9i) q^{32} +2869.73i q^{33} +(33242.2 - 21248.3i) q^{34} +(-12863.7 + 7249.73i) q^{35} +(-6529.95 + 14114.7i) q^{36} -7833.21i q^{37} +(-31834.6 + 20348.5i) q^{38} +44586.9i q^{39} +(51002.0 - 38662.6i) q^{40} -110210. q^{41} +(-7933.93 - 12412.4i) q^{42} +39192.8 q^{43} +(10693.1 + 4946.99i) q^{44} +(-26461.9 + 14913.4i) q^{45} +(-84442.7 - 132108. i) q^{46} -135300. q^{47} +(41336.9 + 48663.3i) q^{48} -103695. q^{49} +(124963. - 3045.50i) q^{50} +76876.4i q^{51} +(166138. + 76861.4i) q^{52} -25404.6i q^{53} +(-16320.9 - 25533.5i) q^{54} +(11298.2 + 20047.1i) q^{55} +(-59927.5 + 8166.00i) q^{56} -73621.0i q^{57} +(53789.3 + 84151.6i) q^{58} +406325. i q^{59} +(9953.36 + 124310. i) q^{60} -291031. q^{61} +(-106895. + 68326.9i) q^{62} +28705.0 q^{63} +(252586. - 70139.6i) q^{64} +(175540. + 311472. i) q^{65} +(-19343.8 + 12364.5i) q^{66} +53725.2 q^{67} +(286454. + 132524. i) q^{68} +305514. q^{69} +(-104292. - 55473.3i) q^{70} -67140.7i q^{71} +(-123277. + 16798.3i) q^{72} -342236. i q^{73} +(52800.8 - 33750.0i) q^{74} +(-126141. + 208362. i) q^{75} +(-274324. - 126912. i) q^{76} -21746.5i q^{77} +(-300544. + 192106. i) q^{78} -670535. i q^{79} +(480357. + 177204. i) q^{80} +59049.0 q^{81} +(-474849. - 742885. i) q^{82} +273204. q^{83} +(49483.2 - 106959. i) q^{84} +(302664. + 537037. i) q^{85} +(168865. + 264184. i) q^{86} -194610. q^{87} +(12726.1 + 93392.6i) q^{88} -721920. q^{89} +(-214539. - 114114. i) q^{90} -337875. i q^{91} +(526661. - 1.13839e6i) q^{92} -247207. i q^{93} +(-582950. - 912006. i) q^{94} +(-289847. - 514295. i) q^{95} +(-149918. + 488307. i) q^{96} -1.49639e6i q^{97} +(-446778. - 698969. i) q^{98} -44734.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	4.30858	+	6.74063i	0.538573	+	0.842579i
$2$	4.30858	+	6.74063i	0.538573	+	0.842579i
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	−26.8722	+	58.0851i	−0.419879	+	0.907580i
$5$	−108.897	+	61.3721i	−0.871173	+	0.490976i
$5$	−108.897	+	61.3721i	−0.871173	+	0.490976i
$6$	−67.1642	−	105.076i	−0.310945	−	0.486463i
$7$	118.127			0.344395			0.172198	−	0.985062i	$-0.444913\pi$
$7$	118.127			0.344395			0.172198	+	0.985062i	$0.444913\pi$
$8$	−507.312	+	69.1287i	−0.990843	+	0.135017i
$9$	243.000			0.333333
$10$	−882.876	−	469.605i	−0.882876	−	0.469605i
$11$		−	184.093i		−	0.138312i	−0.997606	−	0.0691559i	$-0.977969\pi$
$11$		−	184.093i		−	0.138312i	0.997606	−	0.0691559i	$-0.0220306\pi$
$12$	418.897	−	905.458i	0.242417	−	0.523992i
$13$		−	2860.25i		−	1.30189i	−0.759125	−	0.650945i	$-0.774373\pi$
$13$		−	2860.25i		−	1.30189i	0.759125	−	0.650945i	$-0.225627\pi$
$14$	508.962	+	796.254i	0.185482	+	0.290180i
$15$	1697.53	−	956.696i	0.502972	−	0.283465i
$16$	−2651.77	−	3121.75i	−0.647404	−	0.762147i
$17$		−	4931.62i		−	1.00379i	−0.864929	−	0.501895i	$-0.832636\pi$
$17$		−	4931.62i		−	1.00379i	0.864929	−	0.501895i	$-0.167364\pi$
$18$	1046.99	+	1637.97i	0.179524	+	0.280860i
$19$			4722.79i			0.688553i	0.938868	+	0.344277i	$0.111876\pi$
$19$			4722.79i			0.688553i	−0.938868	+	0.344277i	$0.888124\pi$
$20$	−638.508	−	7974.48i	−0.0798136	−	0.996810i
$21$	−1841.43			−0.198837
$22$	1240.90	−	793.180i	0.116539	−	0.0744910i
$23$	−19598.7			−1.61081			−0.805404	−	0.592726i	$-0.798052\pi$
$23$	−19598.7			−1.61081			−0.805404	+	0.592726i	$0.798052\pi$
$24$	7908.21	−	1077.61i	0.572064	−	0.0779521i
$25$	8091.94	−	13366.4i	0.517884	−	0.855451i
$26$	19279.9	−	12323.6i	1.09695	−	0.701163i
$27$	−3788.00			−0.192450
$28$	−3174.35	+	6861.45i	−0.144604	+	0.312566i
$29$	12484.2			0.511879			0.255940	−	0.966693i	$-0.417615\pi$
$29$	12484.2			0.511879			0.255940	+	0.966693i	$0.417615\pi$
$30$	13762.7	+	7320.42i	0.509729	+	0.271127i
$31$			15858.3i			0.532319i	0.963929	+	0.266160i	$0.0857548\pi$
$31$			15858.3i			0.532319i	−0.963929	+	0.266160i	$0.914245\pi$
$32$	9617.25	−	31324.9i	0.293495	−	0.955961i
$33$			2869.73i			0.0798544i
$34$	33242.2	−	21248.3i	0.845772	−	0.540614i
$35$	−12863.7	+	7249.73i	−0.300028	+	0.169090i
$36$	−6529.95	+	14114.7i	−0.139960	+	0.302527i
$37$		−	7833.21i		−	0.154645i	−0.997006	−	0.0773223i	$-0.975363\pi$
$37$		−	7833.21i		−	0.154645i	0.997006	−	0.0773223i	$-0.0246370\pi$
$38$	−31834.6	+	20348.5i	−0.580160	+	0.370836i
$39$			44586.9i			0.751647i
$40$	51002.0	−	38662.6i	0.796906	−	0.604104i
$41$	−110210.			−1.59908			−0.799539	−	0.600615i	$-0.794923\pi$
$41$	−110210.			−1.59908			−0.799539	+	0.600615i	$0.794923\pi$
$42$	−7933.93	−	12412.4i	−0.107088	−	0.167536i
$43$	39192.8			0.492948			0.246474	−	0.969149i	$-0.420728\pi$
$43$	39192.8			0.492948			0.246474	+	0.969149i	$0.420728\pi$
$44$	10693.1	+	4946.99i	0.125529	+	0.0580742i
$45$	−26461.9	+	14913.4i	−0.290391	+	0.163659i
$46$	−84442.7	−	132108.i	−0.867538	−	1.35723i
$47$	−135300.			−1.30318			−0.651588	−	0.758573i	$-0.725897\pi$
$47$	−135300.			−1.30318			−0.651588	+	0.758573i	$0.725897\pi$
$48$	41336.9	+	48663.3i	0.373779	+	0.440026i
$49$	−103695.			−0.881392
$50$	124963.	−	3045.50i	0.999703	−	0.0243640i
$51$			76876.4i			0.579538i
$52$	166138.	+	76861.4i	1.18157	+	0.546636i
$53$		−	25404.6i		−	0.170641i	−0.996354	−	0.0853207i	$-0.972809\pi$
$53$		−	25404.6i		−	0.170641i	0.996354	−	0.0853207i	$-0.0271915\pi$
$54$	−16320.9	−	25533.5i	−0.103648	−	0.162154i
$55$	11298.2	+	20047.1i	0.0679079	+	0.120494i
$56$	−59927.5	+	8166.00i	−0.341241	+	0.0464992i
$57$		−	73621.0i		−	0.397536i
$58$	53789.3	+	84151.6i	0.275684	+	0.431299i
$59$			406325.i			1.97841i	0.146522	+	0.989207i	$0.453192\pi$
$59$			406325.i			1.97841i	−0.146522	+	0.989207i	$0.546808\pi$
$60$	9953.36	+	124310.i	0.0460804	+	0.575508i
$61$	−291031.			−1.28218			−0.641092	−	0.767464i	$-0.721518\pi$
$61$	−291031.			−1.28218			−0.641092	+	0.767464i	$0.721518\pi$
$62$	−106895.	+	68326.9i	−0.448521	+	0.286693i
$63$	28705.0			0.114798
$64$	252586.	−	70139.6i	0.963541	−	0.267561i
$65$	175540.	+	311472.i	0.639197	+	1.13417i
$66$	−19343.8	+	12364.5i	−0.0672836	+	0.0430074i
$67$	53725.2			0.178630			0.0893149	−	0.996003i	$-0.471532\pi$
$67$	53725.2			0.178630			0.0893149	+	0.996003i	$0.471532\pi$
$68$	286454.	+	132524.i	0.911020	+	0.421470i
$69$	305514.			0.930001
$70$	−104292.	−	55473.3i	−0.304058	−	0.161730i
$71$		−	67140.7i		−	0.187591i	−0.995592	−	0.0937953i	$-0.970100\pi$
$71$		−	67140.7i		−	0.187591i	0.995592	−	0.0937953i	$-0.0298999\pi$
$72$	−123277.	+	16798.3i	−0.330281	+	0.0450057i
$73$		−	342236.i		−	0.879747i	−0.898060	−	0.439873i	$-0.855023\pi$
$73$		−	342236.i		−	0.879747i	0.898060	−	0.439873i	$-0.144977\pi$
$74$	52800.8	−	33750.0i	0.130300	−	0.0832874i
$75$	−126141.	+	208362.i	−0.299001	+	0.493895i
$76$	−274324.	−	126912.i	−0.624917	−	0.289109i
$77$		−	21746.5i		−	0.0476339i
$78$	−300544.	+	192106.i	−0.633322	+	0.404816i
$79$		−	670535.i		−	1.36000i	−0.733210	−	0.680002i	$-0.761979\pi$
$79$		−	670535.i		−	1.36000i	0.733210	−	0.680002i	$-0.238021\pi$
$80$	480357.	+	177204.i	0.938197	+	0.346102i
$81$	59049.0			0.111111
$82$	−474849.	−	742885.i	−0.861220	−	1.34735i
$83$	273204.			0.477806			0.238903	−	0.971043i	$-0.423212\pi$
$83$	273204.			0.477806			0.238903	+	0.971043i	$0.423212\pi$
$84$	49483.2	−	106959.i	0.0834872	−	0.180460i
$85$	302664.	+	537037.i	0.492837	+	0.874475i
$86$	168865.	+	264184.i	0.265488	+	0.415348i
$87$	−194610.			−0.295534
$88$	12726.1	+	93392.6i	0.0186745	+	0.137045i
$89$	−721920.			−1.02404			−0.512022	−	0.858972i	$-0.671104\pi$
$89$	−721920.			−1.02404			−0.512022	+	0.858972i	$0.671104\pi$
$90$	−214539.	−	114114.i	−0.294292	−	0.156535i
$91$		−	337875.i		−	0.448365i
$92$	526661.	−	1.13839e6i	0.676344	−	1.46194i
$93$		−	247207.i		−	0.307335i
$94$	−582950.	−	912006.i	−0.701856	−	1.09803i
$95$	−289847.	−	514295.i	−0.338063	−	0.599849i
$96$	−149918.	+	488307.i	−0.169450	+	0.551924i
$97$		−	1.49639e6i		−	1.63957i	−0.572672	−	0.819784i	$-0.694093\pi$
$97$		−	1.49639e6i		−	1.63957i	0.572672	−	0.819784i	$-0.305907\pi$
$98$	−446778.	−	698969.i	−0.474694	−	0.742642i
$99$		−	44734.6i		−	0.0461040i
$100$	558942.	+	829207.i	0.558942	+	0.829207i
$101$	607043.			0.589190			0.294595	−	0.955622i	$-0.404815\pi$
$101$	607043.			0.589190			0.294595	+	0.955622i	$0.404815\pi$
$102$	−518195.	+	331228.i	−0.488307	+	0.312124i
$103$	278509.			0.254875			0.127438	−	0.991847i	$-0.459325\pi$
$103$	278509.			0.254875			0.127438	+	0.991847i	$0.459325\pi$
$104$	197726.	+	1.45104e6i	0.175777	+	1.28997i
$105$	200525.	−	113012.i	0.173221	−	0.0976241i
$106$	171243.	−	109458.i	0.143779	−	0.0919028i
$107$	−1.08481e6			−0.885531			−0.442766	−	0.896637i	$-0.646003\pi$
$107$	−1.08481e6			−0.885531			−0.442766	+	0.896637i	$0.646003\pi$
$108$	101792.	−	220026.i	0.0808057	−	0.174664i
$109$	1.03474e6			0.799011			0.399505	−	0.916731i	$-0.369182\pi$
$109$	1.03474e6			0.799011			0.399505	+	0.916731i	$0.369182\pi$
$110$	−86451.1	+	162531.i	−0.0649520	+	0.122112i
$111$			122108.i			0.0892841i
$112$	−313246.	−	368765.i	−0.222963	−	0.262480i
$113$			2.38091e6i			1.65009i	0.565067	+	0.825045i	$0.308850\pi$
$113$			2.38091e6i			1.65009i	−0.565067	+	0.825045i	$0.691150\pi$
$114$	496252.	−	317202.i	0.334956	−	0.214102i
$115$	2.13423e6	−	1.20281e6i	1.40329	−	0.790869i
$116$	−335479.	+	725148.i	−0.214927	+	0.464572i
$117$		−	695041.i		−	0.433963i
$118$	−2.73889e6	+	1.75068e6i	−1.66697	+	1.06552i
$119$		−	582560.i		−	0.345700i
$120$	−795042.	+	602691.i	−0.460094	+	0.348780i
$121$	1.73767e6			0.980870
$122$	−1.25393e6	−	1.96173e6i	−0.690549	−	1.08034i
$123$	1.71800e6			0.923228
$124$	−921133.	−	426149.i	−0.483122	−	0.223510i
$125$	−60860.7	+	1.95218e6i	−0.0311607	+	0.999514i
$126$	123678.	+	193490.i	0.0618273	+	0.0967267i
$127$	531512.			0.259479			0.129739	−	0.991548i	$-0.458586\pi$
$127$	531512.			0.259479			0.129739	+	0.991548i	$0.458586\pi$
$128$	1.56107e6	+	1.40039e6i	0.744379	+	0.667758i
$129$	−610955.			−0.284604
$130$	−1.34319e6	+	2.52525e6i	−0.611375	+	1.14941i
$131$		−	3.53427e6i		−	1.57212i	−0.618150	−	0.786060i	$-0.712118\pi$
$131$		−	3.53427e6i		−	1.57212i	0.618150	−	0.786060i	$-0.287882\pi$
$132$	−166688.	−	77116.0i	−0.0724743	−	0.0335292i
$133$			557891.i			0.237134i
$134$	231480.	+	362142.i	0.0962052	+	0.150510i
$135$	412500.	−	232477.i	0.167657	−	0.0944885i
$136$	340917.	+	2.50187e6i	0.135529	+	0.994599i
$137$			471202.i			0.183251i	0.995794	+	0.0916253i	$0.0292062\pi$
$137$			471202.i			0.183251i	−0.995794	+	0.0916253i	$0.970794\pi$
$138$	1.31633e6	+	2.05936e6i	0.500873	+	0.783599i
$139$			4.72496e6i			1.75936i	0.475570	+	0.879678i	$0.342242\pi$
$139$			4.72496e6i			1.75936i	−0.475570	+	0.879678i	$0.657758\pi$
$140$	−75425.4	−	942005.i	−0.0274874	−	0.343296i
$141$	2.10911e6			0.752390
$142$	452571.	−	289281.i	0.158060	−	0.101031i
$143$	−526553.			−0.180067
$144$	−644379.	−	758586.i	−0.215801	−	0.254049i
$145$	−1.35949e6	+	766183.i	−0.445935	+	0.251321i
$146$	2.30689e6	−	1.47455e6i	0.741256	−	0.473808i
$147$	1.61644e6			0.508872
$148$	454993.	+	210496.i	0.140352	+	0.0649320i
$149$	−4.63111e6			−1.40000			−0.699998	−	0.714145i	$-0.746816\pi$
$149$	−4.63111e6			−1.40000			−0.699998	+	0.714145i	$0.746816\pi$
$150$	−1.94798e6	+	47474.6i	−0.577179	+	0.0140666i
$151$			2.81545e6i			0.817743i	0.912592	+	0.408872i	$0.134078\pi$
$151$			2.81545e6i			0.817743i	−0.912592	+	0.408872i	$0.865922\pi$
$152$	−326480.	−	2.39593e6i	−0.0929664	−	0.682248i
$153$		−	1.19838e6i		−	0.334597i
$154$	146585.	−	93696.4i	0.0401353	−	0.0256543i
$155$	−973258.	−	1.72692e6i	−0.261356	−	0.463742i
$156$	−2.58984e6	−	1.19815e6i	−0.682180	−	0.315600i
$157$		−	1.89173e6i		−	0.488832i	−0.969670	−	0.244416i	$-0.921404\pi$
$157$		−	1.89173e6i		−	0.488832i	0.969670	−	0.244416i	$-0.0785963\pi$
$158$	4.51983e6	−	2.88906e6i	1.14591	−	0.732461i
$159$			396018.i			0.0985198i
$160$	875188.	+	4.00141e6i	0.213669	+	0.976906i
$161$	−2.31515e6			−0.554755
$162$	254417.	+	398028.i	0.0598414	+	0.0936199i
$163$	−5.26032e6			−1.21464			−0.607322	−	0.794456i	$-0.707756\pi$
$163$	−5.26032e6			−1.21464			−0.607322	+	0.794456i	$0.707756\pi$
$164$	2.96159e6	−	6.40156e6i	0.671419	−	1.45129i
$165$	−176121.	−	312504.i	−0.0392066	−	0.0695670i
$166$	1.17712e6	+	1.84156e6i	0.257334	+	0.402590i
$167$	−5.59513e6			−1.20133			−0.600663	−	0.799502i	$-0.705097\pi$
$167$	−5.59513e6			−1.20133			−0.600663	+	0.799502i	$0.705097\pi$
$168$	934177.	−	127295.i	0.197016	−	0.0268463i
$169$	−3.35424e6			−0.694918
$170$	−2.31592e6	+	4.35401e6i	−0.471385	+	0.886223i
$171$			1.14764e6i			0.229518i
$172$	−1.05320e6	+	2.27652e6i	−0.206978	+	0.447390i
$173$			3.49625e6i			0.675248i	0.941281	+	0.337624i	$0.109623\pi$
$173$			3.49625e6i			0.675248i	−0.941281	+	0.337624i	$0.890377\pi$
$174$	−838493.	−	1.31179e6i	−0.159166	−	0.249011i
$175$	955881.	−	1.57894e6i	0.178357	−	0.294613i
$176$	−574693.	+	488172.i	−0.105414	+	0.0895436i
$177$		−	6.33398e6i		−	1.14224i
$178$	−3.11045e6	−	4.86620e6i	−0.551523	−	0.862839i
$179$			8.67841e6i			1.51315i	0.653909	+	0.756573i	$0.273128\pi$
$179$			8.67841e6i			1.51315i	−0.653909	+	0.756573i	$0.726872\pi$
$180$	−155158.	−	1.93780e6i	−0.0266045	−	0.332270i
$181$	4.27709e6			0.721295			0.360648	−	0.932702i	$-0.382556\pi$
$181$	4.27709e6			0.721295			0.360648	+	0.932702i	$0.382556\pi$
$182$	2.27749e6	−	1.45576e6i	0.377783	−	0.241477i
$183$	4.53673e6			0.740269
$184$	9.94266e6	−	1.35483e6i	1.59606	−	0.217487i
$185$	480740.	+	853010.i	0.0759268	+	0.134722i
$186$	1.66633e6	−	1.06511e6i	0.258954	−	0.165522i
$187$	−907877.			−0.138836
$188$	3.63581e6	−	7.85890e6i	0.547176	−	1.18274i
$189$	−447466.			−0.0662789
$190$	2.21785e6	−	4.16964e6i	0.323348	−	0.607907i
$191$		−	4.72408e6i		−	0.677981i	−0.940790	−	0.338990i	$-0.889915\pi$
$191$		−	4.72408e6i		−	0.677981i	0.940790	−	0.338990i	$-0.110085\pi$
$192$	−3.93743e6	+	1.09337e6i	−0.556301	+	0.154477i
$193$		−	4.25604e6i		−	0.592017i	−0.955185	−	0.296009i	$-0.904344\pi$
$193$		−	4.25604e6i		−	0.592017i	0.955185	−	0.296009i	$-0.0956557\pi$
$194$	1.00866e7	−	6.44732e6i	1.38147	−	0.883027i
$195$	−2.73639e6	−	4.85537e6i	−0.369041	−	0.654814i
$196$	2.78651e6	−	6.02313e6i	0.370078	−	0.799934i
$197$		−	3.08365e6i		−	0.403336i	−0.979454	−	0.201668i	$-0.935364\pi$
$197$		−	3.08365e6i		−	0.403336i	0.979454	−	0.201668i	$-0.0646361\pi$
$198$	301540.	−	192743.i	0.0388462	−	0.0248303i
$199$			1.09082e7i			1.38418i	0.721810	+	0.692091i	$0.243310\pi$
$199$			1.09082e7i			1.38418i	−0.721810	+	0.692091i	$0.756690\pi$
$200$	−3.18113e6	+	7.34033e6i	−0.397642	+	0.917541i
$201$	−837494.			−0.103132
$202$	2.61550e6	+	4.09186e6i	0.317322	+	0.496439i
$203$	1.47473e6			0.176289
$204$	−4.46537e6	−	2.06584e6i	−0.525978	−	0.243336i
$205$	1.20015e7	−	6.76381e6i	1.39307	−	0.785109i
$206$	1.19998e6	+	1.87733e6i	0.137269	+	0.214752i
$207$	−4.76249e6			−0.536936
$208$	−8.92901e6	+	7.58472e6i	−0.992232	+	0.842849i
$209$	869432.			0.0952351
$210$	1.62575e6	+	864743.i	0.175548	+	0.0933747i
$211$			2.67497e6i			0.284755i	0.989812	+	0.142378i	$0.0454747\pi$
$211$			2.67497e6i			0.284755i	−0.989812	+	0.142378i	$0.954525\pi$
$212$	1.47563e6	+	682678.i	0.154871	+	0.0716487i
$213$			1.04662e6i			0.108305i
$214$	−4.67401e6	−	7.31233e6i	−0.476923	−	0.746130i
$215$	−4.26796e6	+	2.40534e6i	−0.429443	+	0.242026i
$216$	1.92169e6	−	261859.i	0.190688	−	0.0259840i
$217$			1.87330e6i			0.183328i
$218$	4.45827e6	+	6.97481e6i	0.430325	+	0.673229i
$219$			5.33494e6i			0.507922i
$220$	−1.46805e6	+	117545.i	−0.137871	+	0.0110392i
$221$	−1.41057e7			−1.30682
$222$	−823083.	+	526111.i	−0.0752289	+	0.0480860i
$223$	−1.57717e7			−1.42221			−0.711104	−	0.703086i	$-0.751805\pi$
$223$	−1.57717e7			−1.42221			−0.711104	+	0.703086i	$0.751805\pi$
$224$	1.13606e6	−	3.70033e6i	0.101078	−	0.329228i
$225$	1.96634e6	−	3.24804e6i	0.172628	−	0.285150i
$226$	−1.60488e7	+	1.02583e7i	−1.39033	+	0.888694i
$227$	1.28948e7			1.10240			0.551198	−	0.834374i	$-0.314171\pi$
$227$	1.28948e7			1.10240			0.551198	+	0.834374i	$0.314171\pi$
$228$	4.27628e6	+	1.97836e6i	0.360796	+	0.166917i
$229$	−1.70125e7			−1.41664			−0.708322	−	0.705890i	$-0.750547\pi$
$229$	−1.70125e7			−1.41664			−0.708322	+	0.705890i	$0.750547\pi$
$230$	1.73032e7	+	9.20366e6i	1.42215	+	0.756445i
$231$			338994.i			0.0275015i
$232$	−6.33340e6	+	863019.i	−0.507192	+	0.0691125i
$233$			4.70775e6i			0.372174i	0.982533	+	0.186087i	$0.0595806\pi$
$233$			4.70775e6i			0.372174i	−0.982533	+	0.186087i	$0.940419\pi$
$234$	4.68502e6	−	2.99464e6i	0.365648	−	0.233721i
$235$	1.47337e7	−	8.30362e6i	1.13529	−	0.639829i
$236$	−2.36014e7	−	1.09189e7i	−1.79557	−	0.830694i
$237$			1.04526e7i			0.785199i
$238$	3.92682e6	−	2.51001e6i	0.291280	−	0.186185i
$239$			1.90786e6i			0.139750i	0.997556	+	0.0698752i	$0.0222601\pi$
$239$			1.90786e6i			0.139750i	−0.997556	+	0.0698752i	$0.977740\pi$
$240$	−7.48802e6	−	2.76234e6i	−0.541668	−	0.199822i
$241$	354061.			0.0252945			0.0126473	−	0.999920i	$-0.495974\pi$
$241$	354061.			0.0252945			0.0126473	+	0.999920i	$0.495974\pi$
$242$	7.48690e6	+	1.17130e7i	0.528270	+	0.826460i
$243$	−920483.			−0.0641500
$244$	7.82066e6	−	1.69046e7i	0.538361	−	1.16368i
$245$	1.12920e7	−	6.36397e6i	0.767845	−	0.432743i
$246$	7.40216e6	+	1.15804e7i	0.497225	+	0.777892i
$247$	1.35084e7			0.896421
$248$	−1.09627e6	−	8.04511e6i	−0.0718722	−	0.527445i
$249$	−4.25882e6			−0.275862
$250$	−1.34211e7	+	8.00087e6i	−0.858952	+	0.512056i
$251$		−	1.18789e7i		−	0.751198i	−0.926782	−	0.375599i	$-0.877437\pi$
$251$		−	1.18789e7i		−	0.751198i	0.926782	−	0.375599i	$-0.122563\pi$
$252$	−771367.	+	1.66733e6i	−0.0482014	+	0.104189i
$253$			3.60799e6i			0.222794i
$254$	2.29006e6	+	3.58272e6i	0.139748	+	0.218631i
$255$	−4.71806e6	−	8.37157e6i	−0.284540	−	0.504878i
$256$	−2.71349e6	+	1.65563e7i	−0.161737	+	0.986834i
$257$			2.43638e7i			1.43531i	0.696397	+	0.717656i	$0.254785\pi$
$257$			2.43638e7i			1.43531i	−0.696397	+	0.717656i	$0.745215\pi$
$258$	−2.63235e6	−	4.11823e6i	−0.153280	−	0.239801i
$259$		−	925318.i		−	0.0532588i
$260$	−2.28090e7	+	1.82630e6i	−1.29774	+	0.103908i
$261$	3.03367e6			0.170626
$262$	2.38232e7	−	1.52277e7i	1.32463	−	0.846701i
$263$	1.08755e6			0.0597834			0.0298917	−	0.999553i	$-0.490484\pi$
$263$	1.08755e6			0.0597834			0.0298917	+	0.999553i	$0.490484\pi$
$264$	−198381.	−	1.45585e6i	−0.0107817	−	0.0791232i
$265$	1.55913e6	+	2.76647e6i	0.0837809	+	0.148658i
$266$	−3.76054e6	+	2.40372e6i	−0.199804	+	0.127714i
$267$	1.12536e7			0.591233
$268$	−1.44372e6	+	3.12064e6i	−0.0750029	+	0.162121i
$269$	4.15736e6			0.213580			0.106790	−	0.994282i	$-0.465943\pi$
$269$	4.15736e6			0.213580			0.106790	+	0.994282i	$0.465943\pi$
$270$	3.34433e6	+	1.77886e6i	0.169910	+	0.0903756i
$271$		−	3.55164e7i		−	1.78452i	−0.451526	−	0.892258i	$-0.649120\pi$
$271$		−	3.55164e7i		−	1.78452i	0.451526	−	0.892258i	$-0.350880\pi$
$272$	−1.53953e7	+	1.30775e7i	−0.765036	+	0.649857i
$273$			5.26694e6i			0.258863i
$274$	−3.17620e6	+	2.03021e6i	−0.154403	+	0.0986938i
$275$	−2.46066e6	−	1.48967e6i	−0.118319	−	0.0716295i
$276$	−8.20984e6	+	1.77458e7i	−0.390488	+	0.844051i
$277$			3.27703e7i			1.54185i	0.636927	+	0.770924i	$0.280205\pi$
$277$			3.27703e7i			1.54185i	−0.636927	+	0.770924i	$0.719795\pi$
$278$	−3.18492e7	+	2.03579e7i	−1.48240	+	0.947541i
$279$			3.85357e6i			0.177440i
$280$	6.02473e6	−	4.56712e6i	0.274450	−	0.208050i
$281$	2.76292e7			1.24523			0.622615	−	0.782528i	$-0.286070\pi$
$281$	2.76292e7			1.24523			0.622615	+	0.782528i	$0.286070\pi$
$282$	9.08729e6	+	1.42168e7i	0.405217	+	0.633948i
$283$	3.70016e7			1.63253			0.816264	−	0.577679i	$-0.196041\pi$
$283$	3.70016e7			1.63253			0.816264	+	0.577679i	$0.196041\pi$
$284$	3.89988e6	+	1.80422e6i	0.170254	+	0.0787653i
$285$	4.51827e6	+	8.01707e6i	0.195181	+	0.346323i
$286$	−2.26870e6	−	3.54930e6i	−0.0969791	−	0.151721i
$287$	−1.30188e7			−0.550714
$288$	2.33699e6	−	7.61195e6i	0.0978317	−	0.318654i
$289$	−183315.			−0.00759459
$290$	−1.10220e7	−	5.86266e6i	−0.451926	−	0.240381i
$291$			2.33264e7i			0.946606i
$292$	1.98788e7	+	9.19666e6i	0.798441	+	0.369387i
$293$		−	4.02045e7i		−	1.59835i	−0.601097	−	0.799176i	$-0.705270\pi$
$293$		−	4.02045e7i		−	1.59835i	0.601097	−	0.799176i	$-0.294730\pi$
$294$	6.96458e6	+	1.08959e7i	0.274065	+	0.428765i
$295$	−2.49370e7	−	4.42474e7i	−0.971355	−	1.72354i
$296$	541500.	+	3.97388e6i	0.0208797	+	0.153229i
$297$			697344.i			0.0266181i
$298$	−1.99535e7	−	3.12166e7i	−0.753999	−	1.17961i
$299$			5.60573e7i			2.09710i
$300$	−8.71304e6	−	1.29261e7i	−0.322705	−	0.478743i
$301$	4.62975e6			0.169769
$302$	−1.89779e7	+	1.21306e7i	−0.689013	+	0.440414i
$303$	−9.46287e6			−0.340169
$304$	1.47434e7	−	1.25237e7i	0.524779	−	0.445772i
$305$	3.16923e7	−	1.78612e7i	1.11700	−	0.629522i
$306$	8.07786e6	−	5.16334e6i	0.281924	−	0.180205i
$307$	−4.09171e6			−0.141413			−0.0707065	−	0.997497i	$-0.522525\pi$
$307$	−4.09171e6			−0.141413			−0.0707065	+	0.997497i	$0.522525\pi$
$308$	1.26315e6	+	584376.i	0.0432316	+	0.0200005i
$309$	−4.34152e6			−0.147152
$310$	7.44715e6	−	1.40009e7i	0.249980	−	0.469972i
$311$		−	5.32473e7i		−	1.77018i	−0.465424	−	0.885088i	$-0.654098\pi$
$311$		−	5.32473e7i		−	1.77018i	0.465424	−	0.885088i	$-0.345902\pi$
$312$	−3.08224e6	−	2.26195e7i	−0.101485	−	0.744764i
$313$		−	2.94026e7i		−	0.958854i	−0.877582	−	0.479427i	$-0.840844\pi$
$313$		−	2.94026e7i		−	0.958854i	0.877582	−	0.479427i	$-0.159156\pi$
$314$	1.27514e7	−	8.15067e6i	0.411880	−	0.263272i
$315$	−3.12587e6	+	1.76168e6i	−0.100009	+	0.0563633i
$316$	3.89481e7	+	1.80188e7i	1.23431	+	0.571037i
$317$		−	3.90304e7i		−	1.22525i	−0.790373	−	0.612626i	$-0.790113\pi$
$317$		−	3.90304e7i		−	1.22525i	0.790373	−	0.612626i	$-0.209887\pi$
$318$	−2.66941e6	+	1.70628e6i	−0.0830107	+	0.0530601i
$319$		−	2.29826e6i		−	0.0707990i
$320$	−2.32012e7	+	2.31397e7i	−0.708044	+	0.706168i
$321$	1.69106e7			0.511262
$322$	−9.97500e6	−	1.56056e7i	−0.298776	−	0.467425i
$323$	2.32910e7			0.691163
$324$	−1.58678e6	+	3.42987e6i	−0.0466532	+	0.100842i
$325$	−3.82313e7	−	2.31450e7i	−1.11370	−	0.674229i
$326$	−2.26645e7	−	3.54579e7i	−0.654174	−	1.02343i
$327$	−1.61300e7			−0.461309
$328$	5.59108e7	−	7.61868e6i	1.58444	−	0.215903i
$329$	−1.59826e7			−0.448808
$330$	1.34764e6	−	2.53361e6i	0.0375001	−	0.0705016i
$331$			3.90363e7i			1.07643i	0.842809	+	0.538213i	$0.180900\pi$
$331$			3.90363e7i			1.07643i	−0.842809	+	0.538213i	$0.819100\pi$
$332$	−7.34159e6	+	1.58691e7i	−0.200621	+	0.433648i
$333$		−	1.90347e6i		−	0.0515482i
$334$	−2.41071e7	−	3.77147e7i	−0.647002	−	1.01221i
$335$	−5.85050e6	+	3.29723e6i	−0.155617	+	0.0877030i
$336$	4.88303e6	+	5.74848e6i	0.128728	+	0.151543i
$337$			4.17462e7i			1.09076i	0.838190	+	0.545378i	$0.183614\pi$
$337$			4.17462e7i			1.09076i	−0.838190	+	0.545378i	$0.816386\pi$
$338$	−1.44520e7	−	2.26097e7i	−0.374264	−	0.585524i
$339$		−	3.71147e7i		−	0.952680i
$340$	−3.93271e7	+	3.14888e6i	−1.00059	+	0.0801161i
$341$	2.91941e6			0.0736261
$342$	−7.73580e6	+	4.94469e6i	−0.193387	+	0.123612i
$343$	−2.61468e7			−0.647942
$344$	−1.98830e7	+	2.70935e6i	−0.488434	+	0.0665564i
$345$	−3.32694e7	+	1.87500e7i	−0.810192	+	0.456609i
$346$	−2.35669e7	+	1.50639e7i	−0.568950	+	0.363670i
$347$	7.41088e7			1.77371			0.886853	−	0.462052i	$-0.152887\pi$
$347$	7.41088e7			1.77371			0.886853	+	0.462052i	$0.152887\pi$
$348$	5.22960e6	−	1.13039e7i	0.124088	−	0.268221i
$349$	−1.88604e7			−0.443685			−0.221842	−	0.975083i	$-0.571207\pi$
$349$	−1.88604e7			−0.443685			−0.221842	+	0.975083i	$0.571207\pi$
$350$	1.47616e7	−	359757.i	0.344293	−	0.00839084i
$351$			1.08346e7i			0.250549i
$352$	−5.76670e6	−	1.77047e6i	−0.132221	−	0.0405939i
$353$		−	1.77120e7i		−	0.402666i	−0.979523	−	0.201333i	$-0.935473\pi$
$353$		−	1.77120e7i		−	0.402666i	0.979523	−	0.201333i	$-0.0645273\pi$
$354$	4.26950e7	−	2.72905e7i	0.962426	−	0.615178i
$355$	4.12057e6	+	7.31140e6i	0.0921026	+	0.163424i
$356$	1.93996e7	−	4.19328e7i	0.429975	−	0.929403i
$357$			9.08121e6i			0.199590i
$358$	−5.84979e7	+	3.73916e7i	−1.27495	+	0.814939i
$359$			6.73275e7i			1.45515i	0.686026	+	0.727577i	$0.259354\pi$
$359$			6.73275e7i			1.45515i	−0.686026	+	0.727577i	$0.740646\pi$
$360$	1.23935e7	−	9.39502e6i	0.265635	−	0.201368i
$361$	2.47412e7			0.525894
$362$	1.84282e7	+	2.88303e7i	0.388470	+	0.607748i
$363$	−2.70876e7			−0.566305
$364$	1.96255e7	+	9.07944e6i	0.406927	+	0.188259i
$365$	2.10038e7	+	3.72684e7i	0.431935	+	0.766411i
$366$	1.95469e7	+	3.05804e7i	0.398689	+	0.623735i
$367$	−8.21243e7			−1.66140			−0.830699	−	0.556722i	$-0.812059\pi$
$367$	−8.21243e7			−1.66140			−0.830699	+	0.556722i	$0.812059\pi$
$368$	5.19712e7	+	6.11824e7i	1.04284	+	1.22767i
$369$	−2.67810e7			−0.533026
$370$	−3.67852e6	+	6.91576e6i	−0.0726219	+	0.136532i
$371$		−	3.00098e6i		−	0.0587680i
$372$	1.43590e7	+	6.64300e6i	0.278931	+	0.129043i
$373$			2.31099e7i			0.445320i	0.974896	+	0.222660i	$0.0714740\pi$
$373$			2.31099e7i			0.445320i	−0.974896	+	0.222660i	$0.928526\pi$
$374$	−3.91166e6	−	6.11967e6i	−0.0747733	−	0.116980i
$375$	948725.	−	3.04314e7i	0.0179906	−	0.577070i
$376$	6.86392e7	−	9.35310e6i	1.29124	−	0.175951i
$377$		−	3.57081e7i		−	0.666411i
$378$	−1.92795e6	−	3.01621e6i	−0.0356960	−	0.0558452i
$379$			3.42188e7i			0.628561i	0.949330	+	0.314281i	$0.101763\pi$
$379$			3.42188e7i			0.628561i	−0.949330	+	0.314281i	$0.898237\pi$
$380$	3.76618e7	−	3.01554e6i	0.686357	−	0.0549559i
$381$	−8.28545e6			−0.149810
$382$	3.18433e7	−	2.03541e7i	0.571252	−	0.365142i
$383$	−4.80434e7			−0.855141			−0.427570	−	0.903982i	$-0.640630\pi$
$383$	−4.80434e7			−0.855141			−0.427570	+	0.903982i	$0.640630\pi$
$384$	−2.43347e7	−	2.18299e7i	−0.429767	−	0.385530i
$385$	1.33462e6	+	2.36811e6i	0.0233871	+	0.0414974i
$386$	2.86884e7	−	1.83375e7i	0.498821	−	0.318844i
$387$	9.52385e6			0.164316
$388$	8.69180e7	+	4.02114e7i	1.48804	+	0.688420i
$389$	−3.28035e7			−0.557277			−0.278639	−	0.960396i	$-0.589883\pi$
$389$	−3.28035e7			−0.557277			−0.278639	+	0.960396i	$0.589883\pi$
$390$	2.09383e7	−	3.93647e7i	0.352977	−	0.663611i
$391$			9.66534e7i			1.61691i
$392$	5.26056e7	−	7.16830e6i	0.873321	−	0.119003i
$393$			5.50938e7i			0.907664i
$394$	2.07858e7	−	1.32862e7i	0.339842	−	0.217226i
$395$	4.11521e7	+	7.30190e7i	0.667730	+	1.18480i
$396$	2.59842e6	+	1.20212e6i	0.0418430	+	0.0193581i
$397$			1.24359e7i			0.198749i	0.995050	+	0.0993745i	$0.0316842\pi$
$397$			1.24359e7i			0.198749i	−0.995050	+	0.0993745i	$0.968316\pi$
$398$	−7.35280e7	+	4.69988e7i	−1.16628	+	0.745483i
$399$		−	8.69666e6i		−	0.136910i
$400$	−6.31846e7	+	1.01835e7i	−0.987260	+	0.159118i
$401$	−6.30036e7			−0.977085			−0.488543	−	0.872540i	$-0.662471\pi$
$401$	−6.30036e7			−0.977085			−0.488543	+	0.872540i	$0.662471\pi$
$402$	−3.60841e6	−	5.64524e6i	−0.0555441	−	0.0868968i
$403$	4.53588e7			0.693021
$404$	−1.63126e7	+	3.52602e7i	−0.247388	+	0.534737i
$405$	−6.43024e6	+	3.62396e6i	−0.0967970	+	0.0545529i
$406$	6.35400e6	+	9.94062e6i	0.0949443	+	0.148537i
$407$	−1.44204e6			−0.0213892
$408$	−5.31437e6	−	3.90003e7i	−0.0782476	−	0.574232i
$409$	−1.05508e6			−0.0154211			−0.00771055	−	0.999970i	$-0.502454\pi$
$409$	−1.05508e6			−0.0154211			−0.00771055	+	0.999970i	$0.502454\pi$
$410$	9.73018e7	+	5.17552e7i	1.41179	+	0.750935i
$411$		−	7.34531e6i		−	0.105800i
$412$	−7.48416e6	+	1.61772e7i	−0.107017	+	0.231320i
$413$			4.79981e7i			0.681356i
$414$	−2.05196e7	−	3.21022e7i	−0.289179	−	0.452411i
$415$	−2.97509e7	+	1.67671e7i	−0.416252	+	0.234592i
$416$	−8.95972e7	−	2.75078e7i	−1.24456	−	0.382099i
$417$		−	7.36548e7i		−	1.01576i
$418$	3.74602e6	+	5.86052e6i	0.0512910	+	0.0802431i
$419$		−	3.99861e7i		−	0.543585i	−0.962356	−	0.271792i	$-0.912384\pi$
$419$		−	3.99861e7i		−	0.543585i	0.962356	−	0.271792i	$-0.0876164\pi$
$420$	1.17577e6	+	1.46844e7i	0.0158699	+	0.198202i
$421$	−1.07962e7			−0.144685			−0.0723426	−	0.997380i	$-0.523047\pi$
$421$	−1.07962e7			−0.144685			−0.0723426	+	0.997380i	$0.523047\pi$
$422$	−1.80310e7	+	1.15253e7i	−0.239929	+	0.153361i
$423$	−3.28778e7			−0.434392
$424$	1.75619e6	+	1.28880e7i	0.0230395	+	0.169079i
$425$	−6.59181e7	−	3.99064e7i	−0.858693	−	0.519847i
$426$	−7.05488e6	+	4.50945e6i	−0.0912559	+	0.0583304i
$427$	−3.43788e7			−0.441578
$428$	2.91514e7	−	6.30116e7i	0.371816	−	0.803691i
$429$	8.20815e6			0.103962
$430$	−3.46024e7	−	1.84052e7i	−0.435212	−	0.231491i
$431$		−	7.20408e7i		−	0.899802i	−0.893079	−	0.449901i	$-0.851459\pi$
$431$		−	7.20408e7i		−	0.899802i	0.893079	−	0.449901i	$-0.148541\pi$
$432$	1.00449e7	+	1.18252e7i	0.124593	+	0.146675i
$433$			6.02974e7i			0.742736i	0.928486	+	0.371368i	$0.121111\pi$
$433$			6.02974e7i			0.742736i	−0.928486	+	0.371368i	$0.878889\pi$
$434$	−1.26273e7	+	8.07128e6i	−0.154468	+	0.0987355i
$435$	2.11924e7	−	1.19436e7i	0.257461	−	0.145100i
$436$	−2.78058e7	+	6.01031e7i	−0.335488	+	0.725166i
$437$		−	9.25605e7i		−	1.10913i
$438$	−3.59609e7	+	2.29860e7i	−0.427964	+	0.273553i
$439$		−	8.38718e7i		−	0.991340i	−0.868511	−	0.495670i	$-0.834923\pi$
$439$		−	8.38718e7i		−	0.991340i	0.868511	−	0.495670i	$-0.165077\pi$
$440$	−7.11753e6	−	9.38911e6i	−0.0835547	−	0.110221i
$441$	−2.51979e7			−0.293797
$442$	−6.07755e7	−	9.50812e7i	−0.703820	−	1.10110i
$443$	2.85229e7			0.328082			0.164041	−	0.986453i	$-0.447547\pi$
$443$	2.85229e7			0.328082			0.164041	+	0.986453i	$0.447547\pi$
$444$	−7.09264e6	−	3.28131e6i	−0.0810325	−	0.0374885i
$445$	7.86146e7	−	4.43057e7i	0.892120	−	0.502782i
$446$	−6.79536e7	−	1.06311e8i	−0.765963	−	1.19832i
$447$	7.21919e7			0.808288
$448$	2.98374e7	−	8.28542e6i	0.331839	−	0.0921468i
$449$	1.42207e8			1.57102			0.785509	−	0.618850i	$-0.212401\pi$
$449$	1.42207e8			1.57102			0.785509	+	0.618850i	$0.212401\pi$
$450$	3.03660e7	−	740056.i	0.333234	−	0.00812133i
$451$			2.02889e7i			0.221171i
$452$	−1.38295e8	−	6.39804e7i	−1.49759	−	0.692838i
$453$		−	4.38885e7i		−	0.472124i
$454$	5.55584e7	+	8.69193e7i	0.593721	+	0.928856i
$455$	2.07361e7	+	3.67934e7i	0.220136	+	0.390603i
$456$	5.08932e6	+	3.73488e7i	0.0536742	+	0.393896i
$457$		−	3.85466e7i		−	0.403866i	−0.979399	−	0.201933i	$-0.935278\pi$
$457$		−	3.85466e7i		−	0.403866i	0.979399	−	0.201933i	$-0.0647224\pi$
$458$	−7.32996e7	−	1.14675e8i	−0.762966	−	1.19363i
$459$			1.86810e7i			0.193179i
$460$	1.25139e7	+	1.56290e8i	0.128564	+	1.60567i
$461$	1.42621e7			0.145573			0.0727867	−	0.997348i	$-0.476811\pi$
$461$	1.42621e7			0.145573			0.0727867	+	0.997348i	$0.476811\pi$
$462$	−2.28503e6	+	1.46058e6i	−0.0231721	+	0.0148115i
$463$	8.63503e7			0.870003			0.435002	−	0.900430i	$-0.356748\pi$
$463$	8.63503e7			0.870003			0.435002	+	0.900430i	$0.356748\pi$
$464$	−3.31052e7	−	3.89727e7i	−0.331393	−	0.390128i
$465$	1.51716e7	+	2.69200e7i	0.150894	+	0.267742i
$466$	−3.17332e7	+	2.02837e7i	−0.313586	+	0.200443i
$467$	−7.07112e7			−0.694284			−0.347142	−	0.937812i	$-0.612848\pi$
$467$	−7.07112e7			−0.694284			−0.347142	+	0.937812i	$0.612848\pi$
$468$	4.03716e7	+	1.86773e7i	0.393857	+	0.182212i
$469$	6.34643e6			0.0615192
$470$	1.19453e8	+	6.35375e7i	1.15054	+	0.611979i
$471$			2.94891e7i			0.282227i
$472$	−2.80887e7	−	2.06133e8i	−0.267120	−	1.96030i
$473$		−	7.21513e6i		−	0.0681805i
$474$	−7.04572e7	+	4.50359e7i	−0.661592	+	0.422887i
$475$	6.31267e7	+	3.82165e7i	0.589023	+	0.356591i
$476$	3.38381e7	+	1.56547e7i	0.313751	+	0.145152i
$477$		−	6.17331e6i		−	0.0568804i
$478$	−1.28602e7	+	8.22018e6i	−0.117751	+	0.0752658i
$479$		−	1.88435e8i		−	1.71457i	−0.514845	−	0.857283i	$-0.672151\pi$
$479$		−	1.88435e8i		−	1.71457i	0.514845	−	0.857283i	$-0.327849\pi$
$480$	−1.36428e7	−	6.23758e7i	−0.123362	−	0.564017i
$481$	−2.24050e7			−0.201330
$482$	1.52550e6	+	2.38659e6i	0.0136230	+	0.0213126i
$483$	3.60896e7			0.320288
$484$	−4.66951e7	+	1.00933e8i	−0.411846	+	0.890218i
$485$	9.18365e7	+	1.62952e8i	0.804990	+	1.42835i
$486$	−3.96598e6	−	6.20464e6i	−0.0345495	−	0.0540515i
$487$	−1.58690e8			−1.37392			−0.686960	−	0.726695i	$-0.741055\pi$
$487$	−1.58690e8			−1.37392			−0.686960	+	0.726695i	$0.741055\pi$
$488$	1.47644e8	−	2.01186e7i	1.27044	−	0.173117i
$489$	8.20002e7			0.701275
$490$	9.15498e7	+	4.86957e7i	0.778160	+	0.413906i
$491$		−	1.10536e8i		−	0.933810i	−0.884307	−	0.466905i	$-0.845369\pi$
$491$		−	1.10536e8i		−	0.933810i	0.884307	−	0.466905i	$-0.154631\pi$
$492$	−4.61666e7	+	9.97905e7i	−0.387644	+	0.837903i
$493$		−	6.15675e7i		−	0.513820i
$494$	5.82019e7	+	9.10549e7i	0.482788	+	0.755305i
$495$	2.74546e6	+	4.87145e6i	0.0226360	+	0.0401645i
$496$	4.95058e7	−	4.20526e7i	0.405706	−	0.344625i
$497$		−	7.93117e6i		−	0.0646053i
$498$	−1.83495e7	−	2.87071e7i	−0.148572	−	0.232435i
$499$		−	1.03133e8i		−	0.830037i	−0.909813	−	0.415018i	$-0.863775\pi$
$499$		−	1.03133e8i		−	0.830037i	0.909813	−	0.415018i	$-0.136225\pi$
$500$	−1.11757e8	−	5.59945e7i	−0.894056	−	0.447956i
$501$	8.72195e7			0.693586
$502$	8.00712e7	−	5.11811e7i	0.632944	−	0.404575i
$503$	−1.94397e8			−1.52752			−0.763758	−	0.645503i	$-0.776648\pi$
$503$	−1.94397e8			−1.52752			−0.763758	+	0.645503i	$0.776648\pi$
$504$	−1.45624e7	+	1.98434e6i	−0.113747	+	0.0154997i
$505$	−6.61050e7	+	3.72555e7i	−0.513287	+	0.289279i
$506$	−2.43201e7	+	1.55453e7i	−0.187722	+	0.119991i
$507$	5.22874e7			0.401211
$508$	−1.42829e7	+	3.08729e7i	−0.108950	+	0.235498i
$509$	1.01418e8			0.769063			0.384532	−	0.923112i	$-0.374363\pi$
$509$	1.01418e8			0.769063			0.384532	+	0.923112i	$0.374363\pi$
$510$	3.61016e7	−	6.78723e7i	0.272154	−	0.511661i
$511$		−	4.04275e7i		−	0.302980i
$512$	−1.23291e8	+	5.30436e7i	−0.918593	+	0.395206i
$513$		−	1.78899e7i		−	0.132512i
$514$	−1.64228e8	+	1.04974e8i	−1.20936	+	0.773020i
$515$	−3.03287e7	+	1.70927e7i	−0.222040	+	0.125138i
$516$	1.64177e7	−	3.54874e7i	0.119499	−	0.258301i
$517$			2.49077e7i			0.180245i
$518$	6.23723e6	−	3.98681e6i	0.0448748	−	0.0286838i
$519$		−	5.45011e7i		−	0.389855i
$520$	−1.10585e8	−	1.45878e8i	−0.786477	−	1.03748i
$521$	−2.56993e8			−1.81722			−0.908612	−	0.417642i	$-0.862857\pi$
$521$	−2.56993e8			−1.81722			−0.908612	+	0.417642i	$0.862857\pi$
$522$	1.30708e7	+	2.04488e7i	0.0918948	+	0.143766i
$523$	1.58446e8			1.10758			0.553791	−	0.832656i	$-0.313181\pi$
$523$	1.58446e8			1.10758			0.553791	+	0.832656i	$0.313181\pi$
$524$	2.05288e8	+	9.49737e7i	1.42682	+	0.660100i
$525$	−1.49007e7	+	2.46133e7i	−0.102974	+	0.170095i
$526$	4.68578e6	+	7.33075e6i	0.0321977	+	0.0503722i
$527$	7.82072e7			0.534337
$528$	8.95858e6	−	7.60984e6i	0.0608608	−	0.0516980i
$529$	2.36074e8			1.59471
$530$	−1.19301e7	+	2.24291e7i	−0.0801341	+	0.150655i
$531$			9.87369e7i			0.659472i
$532$	−3.24052e7	−	1.49918e7i	−0.215218	−	0.0995676i
$533$			3.15229e8i			2.08182i
$534$	4.84871e7	+	7.58565e7i	0.318422	+	0.498160i
$535$	1.18133e8	−	6.65772e7i	0.771451	−	0.434775i
$536$	−2.72554e7	+	3.71396e6i	−0.176994	+	0.0241181i
$537$		−	1.35283e8i		−	0.873615i
$538$	1.79123e7	+	2.80233e7i	0.115029	+	0.179958i
$539$			1.90895e7i			0.121907i
$540$	2.41867e6	+	3.02073e7i	0.0153601	+	0.191836i
$541$	−9.44508e6			−0.0596504			−0.0298252	−	0.999555i	$-0.509495\pi$
$541$	−9.44508e6			−0.0596504			−0.0298252	+	0.999555i	$0.509495\pi$
$542$	2.39403e8	−	1.53025e8i	1.50360	−	0.961092i
$543$	−6.66733e7			−0.416440
$544$	−1.54483e8	−	4.74286e7i	−0.959584	−	0.294608i
$545$	−1.12680e8	+	6.35042e7i	−0.696076	+	0.392295i
$546$	−3.55025e7	+	2.26931e7i	−0.218113	+	0.139417i
$547$	1.60703e8			0.981886			0.490943	−	0.871192i	$-0.336652\pi$
$547$	1.60703e8			0.981886			0.490943	+	0.871192i	$0.336652\pi$
$548$	−2.73698e7	−	1.26622e7i	−0.166315	−	0.0769430i
$549$	−7.07206e7			−0.427394
$550$	−560655.	−	2.30048e7i	−0.00336983	−	0.138271i
$551$			5.89603e7i			0.352456i
$552$	−1.54991e8	+	2.11198e7i	−0.921485	+	0.125566i
$553$		−	7.92086e7i		−	0.468379i
$554$	−2.20893e8	+	1.41194e8i	−1.29913	+	0.830397i
$555$	−7.49400e6	−	1.32971e7i	−0.0438364	−	0.0777819i
$556$	−2.74450e8	−	1.26970e8i	−1.59676	−	0.738716i
$557$			2.73464e7i			0.158247i	0.996865	+	0.0791235i	$0.0252121\pi$
$557$			2.73464e7i			0.158247i	−0.996865	+	0.0791235i	$0.974788\pi$
$558$	−2.59755e7	+	1.66034e7i	−0.149507	+	0.0955642i
$559$		−	1.12101e8i		−	0.641764i
$560$	5.67433e7	+	2.09327e7i	0.323110	+	0.119196i
$561$	1.41524e7			0.0801570
$562$	1.19043e8	+	1.86238e8i	0.670647	+	1.04920i
$563$	1.22588e8			0.686946			0.343473	−	0.939162i	$-0.388397\pi$
$563$	1.22588e8			0.686946			0.343473	+	0.939162i	$0.388397\pi$
$564$	−5.66766e7	+	1.22508e8i	−0.315912	+	0.682854i
$565$	−1.46121e8	−	2.59273e8i	−0.810155	−	1.43751i
$566$	1.59424e8	+	2.49414e8i	0.879235	+	1.37553i
$567$	6.97531e6			0.0382661
$568$	4.64135e6	+	3.40613e7i	0.0253279	+	0.185873i
$569$	−7.45159e7			−0.404494			−0.202247	−	0.979335i	$-0.564824\pi$
$569$	−7.45159e7			−0.404494			−0.202247	+	0.979335i	$0.564824\pi$
$570$	−3.45728e7	+	6.49982e7i	−0.186685	+	0.350975i
$571$			2.25067e7i			0.120893i	0.998171	+	0.0604467i	$0.0192525\pi$
$571$			2.25067e7i			0.120893i	−0.998171	+	0.0604467i	$0.980747\pi$
$572$	1.41497e7	−	3.05849e7i	0.0756062	−	0.163425i
$573$			7.36412e7i			0.391432i
$574$	−5.60927e7	−	8.77552e7i	−0.296600	−	0.464020i
$575$	−1.58592e8	+	2.61965e8i	−0.834213	+	1.37797i
$576$	6.13785e7	−	1.70439e7i	0.321180	−	0.0891872i
$577$			2.54573e8i			1.32521i	0.748969	+	0.662605i	$0.230549\pi$
$577$			2.54573e8i			1.32521i	−0.748969	+	0.662605i	$0.769451\pi$
$578$	−789828.	−	1.23566e6i	−0.00409024	−	0.00639904i
$579$			6.63452e7i			0.341801i
$580$	−7.97129e6	−	9.95552e7i	−0.0408549	−	0.510246i
$581$	3.22728e7			0.164554
$582$	−1.57235e8	+	1.00504e8i	−0.797590	+	0.509816i
$583$	−4.67681e6			−0.0236017
$584$	2.36584e7	+	1.73621e8i	0.118781	+	0.871691i
$585$	4.26561e7	+	7.56877e7i	0.213066	+	0.378057i
$586$	2.71004e8	−	1.73225e8i	1.34674	−	0.860829i
$587$	−1.88848e7			−0.0933682			−0.0466841	−	0.998910i	$-0.514865\pi$
$587$	−1.88848e7			−0.0933682			−0.0466841	+	0.998910i	$0.514865\pi$
$588$	−4.34375e7	+	9.38913e7i	−0.213664	+	0.461842i
$589$	−7.48955e7			−0.366530
$590$	1.90812e8	−	3.58735e8i	0.929074	−	1.74670i
$591$			4.80694e7i			0.232866i
$592$	−2.44534e7	+	2.07718e7i	−0.117862	+	0.100117i
$593$			2.23347e7i			0.107106i	0.998565	+	0.0535532i	$0.0170547\pi$
$593$			2.23347e7i			0.107106i	−0.998565	+	0.0535532i	$0.982945\pi$
$594$	−4.70054e6	+	3.00456e6i	−0.0224279	+	0.0143358i
$595$	3.57529e7	+	6.34388e7i	0.169731	+	0.301165i
$596$	1.24448e8	−	2.68999e8i	0.587828	−	1.27061i
$597$		−	1.70042e8i		−	0.799158i
$598$	−3.77861e8	+	2.41527e8i	−1.76697	+	1.12944i
$599$		−	2.70295e8i		−	1.25764i	−0.777550	−	0.628822i	$-0.783538\pi$
$599$		−	2.70295e8i		−	1.25764i	0.777550	−	0.628822i	$-0.216462\pi$
$600$	4.95890e7	−	1.14424e8i	0.229579	−	0.529742i
$601$	1.56526e8			0.721047			0.360523	−	0.932750i	$-0.382598\pi$
$601$	1.56526e8			0.721047			0.360523	+	0.932750i	$0.382598\pi$
$602$	1.99477e7	+	3.12074e7i	0.0914329	+	0.143044i
$603$	1.30552e7			0.0595433
$604$	−1.63536e8	−	7.56574e7i	−0.742168	−	0.343353i
$605$	−1.89226e8	+	1.06644e8i	−0.854507	+	0.481584i
$606$	−4.07715e7	−	6.37857e7i	−0.183206	−	0.286619i
$607$	−1.25355e8			−0.560500			−0.280250	−	0.959927i	$-0.590417\pi$
$607$	−1.25355e8			−0.560500			−0.280250	+	0.959927i	$0.590417\pi$
$608$	1.47941e8	+	4.54202e7i	0.658230	+	0.202087i
$609$	−2.29888e7			−0.101780
$610$	2.56945e8	+	1.36670e8i	1.13201	+	0.602120i
$611$			3.86991e8i			1.69659i
$612$	6.96083e7	+	3.22033e7i	0.303673	+	0.140490i
$613$		−	3.91174e8i		−	1.69820i	−0.528234	−	0.849099i	$-0.677146\pi$
$613$		−	3.91174e8i		−	1.69820i	0.528234	−	0.849099i	$-0.322854\pi$
$614$	−1.76295e7	−	2.75807e7i	−0.0761612	−	0.119152i
$615$	−1.87085e8	+	1.05437e8i	−0.804291	+	0.453283i
$616$	1.50330e6	+	1.10322e7i	0.00643139	+	0.0471977i
$617$		−	5.20913e6i		−	0.0221774i	−0.999939	−	0.0110887i	$-0.996470\pi$
$617$		−	5.20913e6i		−	0.0221774i	0.999939	−	0.0110887i	$-0.00352971\pi$
$618$	−1.87058e7	−	2.92646e7i	−0.0792522	−	0.123987i
$619$			6.60299e7i			0.278400i	0.990264	+	0.139200i	$0.0444531\pi$
$619$			6.60299e7i			0.278400i	−0.990264	+	0.139200i	$0.955547\pi$
$620$	1.26462e8	−	1.01257e7i	0.530621	−	0.0424863i
$621$	7.42398e7			0.310000
$622$	3.58920e8	−	2.29420e8i	1.49151	−	0.953368i
$623$	−8.52786e7			−0.352676
$624$	1.39189e8	−	1.18234e8i	0.572865	−	0.486619i
$625$	−1.13182e8	−	2.16321e8i	−0.463592	−	0.886049i
$626$	1.98192e8	−	1.26683e8i	0.807910	−	0.516413i
$627$	−1.35531e7			−0.0549840
$628$	1.09881e8	+	5.08350e7i	0.443654	+	0.205250i
$629$	−3.86304e7			−0.155231
$630$	−2.53429e7	−	1.34800e7i	−0.101353	−	0.0539099i
$631$		−	2.82333e7i		−	0.112376i	−0.998420	−	0.0561880i	$-0.982105\pi$
$631$		−	2.82333e7i		−	0.112376i	0.998420	−	0.0561880i	$-0.0178946\pi$
$632$	4.63533e7	+	3.40170e8i	0.183624	+	1.34755i
$633$		−	4.16987e7i		−	0.164403i
$634$	2.63090e8	−	1.68166e8i	1.03237	−	0.659887i
$635$	−5.78798e7	+	3.26200e7i	−0.226051	+	0.127398i
$636$	−2.30028e7	−	1.06419e7i	−0.0894146	−	0.0413664i
$637$			2.96594e8i			1.14748i
$638$	1.54917e7	−	9.90224e6i	0.0596537	−	0.0381304i
$639$		−	1.63152e7i		−	0.0625302i
$640$	−2.55941e8	−	5.66913e7i	−0.976336	−	0.216260i
$641$	1.35106e8			0.512978			0.256489	−	0.966547i	$-0.417434\pi$
$641$	1.35106e8			0.512978			0.256489	+	0.966547i	$0.417434\pi$
$642$	7.28606e7	+	1.13988e8i	0.275352	+	0.430778i
$643$	−3.61840e8			−1.36108			−0.680539	−	0.732712i	$-0.738254\pi$
$643$	−3.61840e8			−1.36108			−0.680539	+	0.732712i	$0.738254\pi$
$644$	6.22132e7	−	1.34476e8i	0.232930	−	0.503484i
$645$	6.65310e7	−	3.74956e7i	0.247939	−	0.139734i
$646$	1.00351e8	+	1.56996e8i	0.372242	+	0.582359i
$647$	−8.60221e7			−0.317612			−0.158806	−	0.987310i	$-0.550764\pi$
$647$	−8.60221e7			−0.317612			−0.158806	+	0.987310i	$0.550764\pi$
$648$	−2.99563e7	+	4.08198e6i	−0.110094	+	0.0150019i
$649$	7.48016e7			0.273638
$650$	−8.71090e6	−	3.57425e8i	−0.0317193	−	1.30150i
$651$		−	2.92019e7i		−	0.105845i
$652$	1.41356e8	−	3.05546e8i	0.510003	−	1.10239i
$653$		−	2.03609e8i		−	0.731237i	−0.930765	−	0.365619i	$-0.880857\pi$
$653$		−	2.03609e8i		−	0.731237i	0.930765	−	0.365619i	$-0.119143\pi$
$654$	−6.94976e7	−	1.08727e8i	−0.248448	−	0.388689i
$655$	2.16905e8	+	3.84870e8i	0.771874	+	1.36959i
$656$	2.92251e8	+	3.44049e8i	1.03525	+	1.21873i
$657$		−	8.31634e7i		−	0.293249i
$658$	−6.88624e7	−	1.07733e8i	−0.241716	−	0.378156i
$659$		−	1.57376e8i		−	0.549898i	−0.961459	−	0.274949i	$-0.911339\pi$
$659$		−	1.57376e8i		−	0.549898i	0.961459	−	0.274949i	$-0.0886609\pi$
$660$	2.28846e7	−	1.83235e6i	0.0795996	−	0.00637346i
$661$	−2.40911e8			−0.834167			−0.417084	−	0.908868i	$-0.636948\pi$
$661$	−2.40911e8			−0.834167			−0.417084	+	0.908868i	$0.636948\pi$
$662$	−2.63129e8	+	1.68191e8i	−0.906974	+	0.579734i
$663$	2.19886e8			0.754496
$664$	−1.38599e8	+	1.88862e7i	−0.473431	+	0.0645120i
$665$	−3.42389e7	−	6.07524e7i	−0.116427	−	0.206585i
$666$	1.28306e7	−	8.20126e6i	0.0434334	−	0.0277625i
$667$	−2.44675e8			−0.824540
$668$	1.50354e8	−	3.24994e8i	0.504411	−	1.09030i
$669$	2.45856e8			0.821113
$670$	−4.74327e7	−	2.52297e7i	−0.157708	−	0.0838855i
$671$			5.35768e7i			0.177341i
$672$	−1.77094e7	+	5.76825e7i	−0.0583576	+	0.190080i
$673$		−	1.97914e8i		−	0.649280i	−0.945838	−	0.324640i	$-0.894757\pi$
$673$		−	1.97914e8i		−	0.649280i	0.945838	−	0.324640i	$-0.105243\pi$
$674$	−2.81396e8	+	1.79867e8i	−0.919048	+	0.587451i
$675$	−3.06522e7	+	5.06319e7i	−0.0996669	+	0.164632i
$676$	9.01359e7	−	1.94831e8i	0.291781	−	0.630694i
$677$			8.16343e7i			0.263091i	0.991310	+	0.131546i	$0.0419940\pi$
$677$			8.16343e7i			0.263091i	−0.991310	+	0.131546i	$0.958006\pi$
$678$	2.50177e8	−	1.59912e8i	0.802708	−	0.513087i
$679$		−	1.76765e8i		−	0.564659i
$680$	−1.90670e8	−	2.51522e8i	−0.606393	−	0.799926i
$681$	−2.01010e8			−0.636469
$682$	1.25785e7	+	1.96787e7i	0.0396530	+	0.0620358i
$683$	−7.31775e7			−0.229676			−0.114838	−	0.993384i	$-0.536635\pi$
$683$	−7.31775e7			−0.229676			−0.114838	+	0.993384i	$0.536635\pi$
$684$	−6.66607e7	−	3.08396e7i	−0.208306	−	0.0963696i
$685$	−2.89186e7	−	5.13123e7i	−0.0899717	−	0.159643i
$686$	−1.12656e8	−	1.76246e8i	−0.348964	−	0.545942i
$687$	2.65198e8			0.817900
$688$	−1.03930e8	−	1.22350e8i	−0.319136	−	0.375699i
$689$	−7.26635e7			−0.222156
$690$	−2.69731e8	−	1.43471e8i	−0.821076	−	0.436733i
$691$			1.32288e8i			0.400947i	0.979699	+	0.200473i	$0.0642480\pi$
$691$			1.32288e8i			0.400947i	−0.979699	+	0.200473i	$0.935752\pi$
$692$	−2.03080e8	−	9.39519e7i	−0.612842	−	0.283522i
$693$		−	5.28439e6i		−	0.0158780i
$694$	3.19304e8	+	4.99540e8i	0.955269	+	1.49449i
$695$	−2.89980e8	−	5.14532e8i	−0.863802	−	1.53270i
$696$	9.87279e7	−	1.34531e7i	0.292828	−	0.0399021i
$697$			5.43514e8i			1.60514i
$698$	−8.12616e7	−	1.27131e8i	−0.238957	−	0.373840i
$699$		−	7.33866e7i		−	0.214875i
$700$	6.60264e7	+	9.79522e7i	0.192497	+	0.285575i
$701$	3.09373e8			0.898106			0.449053	−	0.893505i	$-0.351761\pi$
$701$	3.09373e8			0.898106			0.449053	+	0.893505i	$0.351761\pi$
$702$	−7.30322e7	+	4.66819e7i	−0.211107	+	0.134939i
$703$	3.69946e7			0.106481
$704$	−1.29122e7	−	4.64994e7i	−0.0370069	−	0.133269i
$705$	−2.29675e8	+	1.29441e8i	−0.655461	+	0.369406i
$706$	1.19390e8	−	7.63138e7i	0.339278	−	0.216865i
$707$	7.17085e7			0.202914
$708$	3.67910e8	+	1.70208e8i	1.03667	+	0.479602i
$709$	−2.86816e8			−0.804756			−0.402378	−	0.915474i	$-0.631816\pi$
$709$	−2.86816e8			−0.804756			−0.402378	+	0.915474i	$0.631816\pi$
$710$	−3.15297e7	+	5.92770e7i	−0.0880936	+	0.165619i
$711$		−	1.62940e8i		−	0.453335i
$712$	3.66238e8	−	4.99054e7i	1.01467	−	0.138264i
$713$		−	3.10803e8i		−	0.857465i
$714$	−6.12131e7	+	3.91271e7i	−0.168170	+	0.107494i
$715$	5.73398e7	−	3.23156e7i	0.156869	−	0.0884086i
$716$	−5.04086e8	−	2.33208e8i	−1.37330	−	0.635338i
$717$		−	2.97406e7i		−	0.0806850i
$718$	−4.53830e8	+	2.90086e8i	−1.22608	+	0.783706i
$719$			5.71608e8i			1.53784i	0.639345	+	0.768920i	$0.279206\pi$
$719$			5.71608e8i			1.53784i	−0.639345	+	0.768920i	$0.720794\pi$
$720$	1.16727e8	+	4.30606e7i	0.312732	+	0.115367i
$721$	3.28996e7			0.0877777
$722$	1.06599e8	+	1.66771e8i	0.283232	+	0.443108i
$723$	−5.51926e6			−0.0146038
$724$	−1.14935e8	+	2.48436e8i	−0.302856	+	0.654633i
$725$	1.01022e8	−	1.66869e8i	0.265094	−	0.437888i
$726$	−1.16709e8	−	1.82588e8i	−0.304997	−	0.477157i
$727$	1.93570e8			0.503774			0.251887	−	0.967757i	$-0.418949\pi$
$727$	1.93570e8			0.503774			0.251887	+	0.967757i	$0.418949\pi$
$728$	2.33568e7	+	1.71408e8i	0.0605369	+	0.444259i
$729$	1.43489e7			0.0370370
$730$	−1.60716e8	+	3.02152e8i	−0.413134	+	0.776708i
$731$		−	1.93284e8i		−	0.494816i
$732$	−1.21912e8	+	2.63516e8i	−0.310823	+	0.671853i
$733$		−	2.59266e7i		−	0.0658316i	−0.999458	−	0.0329158i	$-0.989521\pi$
$733$		−	2.59266e7i		−	0.0658316i	0.999458	−	0.0329158i	$-0.0104793\pi$
$734$	−3.53839e8	−	5.53570e8i	−0.894784	−	1.39986i
$735$	−1.76025e8	+	9.92045e7i	−0.443315	+	0.249844i
$736$	−1.88486e8	+	6.13928e8i	−0.472765	+	1.53987i
$737$		−	9.89044e6i		−	0.0247066i
$738$	−1.15388e8	−	1.80521e8i	−0.287073	−	0.449116i
$739$		−	1.13086e8i		−	0.280205i	−0.990137	−	0.140102i	$-0.955257\pi$
$739$		−	1.13086e8i		−	0.280205i	0.990137	−	0.140102i	$-0.0447432\pi$
$740$	−6.24658e7	+	5.00157e6i	−0.154151	+	0.0123427i
$741$	−2.10575e8			−0.517549
$742$	2.02285e7	−	1.29300e7i	0.0495167	−	0.0316509i
$743$	4.12020e8			1.00451			0.502253	−	0.864721i	$-0.332505\pi$
$743$	4.12020e8			1.00451			0.502253	+	0.864721i	$0.332505\pi$
$744$	1.70891e7	+	1.25411e8i	0.0414954	+	0.304520i
$745$	5.04313e8	−	2.84221e8i	1.21964	−	0.687365i
$746$	−1.55776e8	+	9.95711e7i	−0.375217	+	0.239837i
$747$	6.63885e7			0.159269
$748$	2.43967e7	−	5.27342e7i	0.0582943	−	0.126005i
$749$	−1.28146e8			−0.304973
$750$	2.09215e8	−	1.24721e8i	0.495916	−	0.295636i
$751$			1.55124e8i			0.366235i	0.983091	+	0.183117i	$0.0586188\pi$
$751$			1.55124e8i			0.366235i	−0.983091	+	0.183117i	$0.941381\pi$
$752$	3.58783e8	+	4.22373e8i	0.843682	+	0.993213i
$753$			1.85173e8i			0.433704i
$754$	2.40695e8	−	1.53851e8i	0.561504	−	0.358911i
$755$	−1.72790e8	−	3.06593e8i	−0.401493	−	0.712396i
$756$	1.20244e7	−	2.59911e7i	0.0278291	−	0.0601534i
$757$			6.66452e8i			1.53632i	0.640259	+	0.768159i	$0.278827\pi$
$757$			6.66452e8i			1.53632i	−0.640259	+	0.768159i	$0.721173\pi$
$758$	−2.30657e8	+	1.47435e8i	−0.529612	+	0.338526i
$759$		−	5.62430e7i		−	0.128630i
$760$	1.82595e8	+	2.40871e8i	0.415958	+	0.548712i
$761$	−1.86003e8			−0.422052			−0.211026	−	0.977480i	$-0.567681\pi$
$761$	−1.86003e8			−0.422052			−0.211026	+	0.977480i	$0.567681\pi$
$762$	−3.56985e7	−	5.58491e7i	−0.0806836	−	0.126227i
$763$	1.22231e8			0.275175
$764$	2.74399e8	+	1.26947e8i	0.615322	+	0.284670i
$765$	7.35473e7	+	1.30500e8i	0.164279	+	0.291492i
$766$	−2.06999e8	−	3.23843e8i	−0.460555	−	0.720523i
$767$	1.16219e9			2.57568
$768$	4.22992e7	−	2.58088e8i	0.0933787	−	0.569749i
$769$	8.69413e8			1.91182			0.955910	−	0.293659i	$-0.0948729\pi$
$769$	8.69413e8			1.91182			0.955910	+	0.293659i	$0.0948729\pi$
$770$	−1.02123e7	+	1.91994e7i	−0.0223691	+	0.0420549i
$771$		−	3.79795e8i		−	0.828678i
$772$	2.47213e8	+	1.14369e8i	0.537303	+	0.248575i
$773$			2.76327e8i			0.598253i	0.954213	+	0.299127i	$0.0966953\pi$
$773$			2.76327e8i			0.598253i	−0.954213	+	0.299127i	$0.903305\pi$
$774$	4.10343e7	+	6.41968e7i	0.0884961	+	0.138449i
$775$	2.11969e8	+	1.28325e8i	0.455373	+	0.275680i
$776$	1.03444e8	+	7.59136e8i	0.221370	+	1.62456i
$777$			1.44243e7i			0.0307490i
$778$	−1.41337e8	−	2.21116e8i	−0.300134	−	0.469550i
$779$		−	5.20498e8i		−	1.10105i
$780$	3.55558e8	−	2.84691e7i	0.749249	−	0.0599916i
$781$	−1.23601e7			−0.0259460
$782$	−6.51505e8	+	4.16439e8i	−1.36238	+	0.870826i
$783$	−4.72902e7			−0.0985112
$784$	2.74975e8	+	3.23710e8i	0.570617	+	0.671751i
$785$	1.16099e8	+	2.06003e8i	0.240005	+	0.425857i
$786$	−3.71367e8	+	2.37376e8i	−0.764778	+	0.488843i
$787$	−7.88652e8			−1.61793			−0.808967	−	0.587854i	$-0.799973\pi$
$787$	−7.88652e8			−1.61793			−0.808967	+	0.587854i	$0.799973\pi$
$788$	1.79114e8	+	8.28646e7i	0.366059	+	0.169352i
$789$	−1.69532e7			−0.0345160
$790$	−3.14887e8	+	5.92000e8i	−0.638665	+	1.20072i
$791$			2.81251e8i			0.568283i
$792$	3.09245e6	+	2.26944e7i	0.00622482	+	0.0456818i
$793$			8.32423e8i			1.66926i
$794$	−8.38257e7	+	5.35810e7i	−0.167462	+	0.107041i
$795$	−2.43044e7	−	4.31250e7i	−0.0483709	−	0.0858278i
$796$	−6.33603e8	−	2.93127e8i	−1.25626	−	0.581188i
$797$		−	7.07132e8i		−	1.39677i	−0.715722	−	0.698386i	$-0.753902\pi$
$797$		−	7.07132e8i		−	1.39677i	0.715722	−	0.698386i	$-0.246098\pi$
$798$	5.86210e7	−	3.74703e7i	0.115357	−	0.0737358i
$799$			6.67247e8i			1.30812i
$800$	−3.40880e8	−	3.82028e8i	−0.665781	−	0.746148i
$801$	−1.75427e8			−0.341348
$802$	−2.71456e8	−	4.24684e8i	−0.526232	−	0.823272i
$803$	−6.30034e7			−0.121679
$804$	2.25053e7	−	4.86459e7i	0.0433029	−	0.0936005i
$805$	2.52112e8	−	1.42085e8i	0.483287	−	0.272371i
$806$	1.95432e8	+	3.05747e8i	0.373242	+	0.583925i
$807$	−6.48069e7			−0.123311
$808$	−3.07960e8	+	4.19641e7i	−0.583795	+	0.0795507i
$809$	3.69743e8			0.698320			0.349160	−	0.937063i	$-0.386467\pi$
$809$	3.69743e8			0.698320			0.349160	+	0.937063i	$0.386467\pi$
$810$	−5.21330e7	−	2.77297e7i	−0.0980974	−	0.0521784i
$811$		−	9.29714e8i		−	1.74296i	−0.490433	−	0.871479i	$-0.663161\pi$
$811$		−	9.29714e8i		−	1.74296i	0.490433	−	0.871479i	$-0.336839\pi$
$812$	−3.96293e7	+	8.56599e7i	−0.0740199	+	0.159996i
$813$			5.53645e8i			1.03029i
$814$	−6.21315e6	−	9.72026e6i	−0.0115196	−	0.0180221i
$815$	5.72831e8	−	3.22836e8i	1.05816	−	0.596362i
$816$	2.39989e8	−	2.03858e8i	0.441694	−	0.375195i
$817$			1.85099e8i			0.339421i
$818$	−4.54590e6	−	7.11190e6i	−0.00830538	−	0.0129935i
$819$		−	8.21035e7i		−	0.149455i
$820$	7.03700e7	+	8.78867e8i	0.127628	+	1.59398i
$821$	2.33839e8			0.422558			0.211279	−	0.977426i	$-0.432237\pi$
$821$	2.33839e8			0.422558			0.211279	+	0.977426i	$0.432237\pi$
$822$	4.95120e7	−	3.16479e7i	0.0891447	−	0.0569809i
$823$	−3.48857e8			−0.625817			−0.312909	−	0.949783i	$-0.601303\pi$
$823$	−3.48857e8			−0.625817			−0.312909	+	0.949783i	$0.601303\pi$
$824$	−1.41291e8	+	1.92530e7i	−0.252541	+	0.0344125i
$825$	3.83580e7	+	2.32217e7i	0.0683115	+	0.0413553i
$826$	−3.23538e8	+	2.06804e8i	−0.574096	+	0.366960i
$827$	−2.50224e8			−0.442397			−0.221199	−	0.975229i	$-0.570997\pi$
$827$	−2.50224e8			−0.442397			−0.221199	+	0.975229i	$0.570997\pi$
$828$	1.27979e8	−	2.76630e8i	0.225448	−	0.487313i
$829$	−8.94859e8			−1.57069			−0.785346	−	0.619057i	$-0.787515\pi$
$829$	−8.94859e8			−1.57069			−0.785346	+	0.619057i	$0.787515\pi$
$830$	−2.41205e8	−	1.28298e8i	−0.421844	−	0.224380i
$831$		−	5.10839e8i		−	0.890186i
$832$	−2.00617e8	−	7.22461e8i	−0.348336	−	1.25442i
$833$			5.11384e8i			0.884733i
$834$	4.96480e8	−	3.17348e8i	0.855862	−	0.547063i
$835$	6.09291e8	−	3.43385e8i	1.04656	−	0.589823i
$836$	−2.33636e7	+	5.05011e7i	−0.0399872	+	0.0864335i
$837$		−	6.00712e7i		−	0.102445i
$838$	2.69532e8	−	1.72283e8i	0.458013	−	0.292760i
$839$			5.12354e8i			0.867529i	0.901026	+	0.433765i	$0.142815\pi$
$839$			5.12354e8i			0.867529i	−0.901026	+	0.433765i	$0.857185\pi$
$840$	−9.39163e7	+	7.11944e7i	−0.158454	+	0.120118i
$841$	−4.38967e8			−0.737979
$842$	−4.65162e7	−	7.27731e7i	−0.0779235	−	0.121909i
$843$	−4.30697e8			−0.718934
$844$	−1.55376e8	−	7.18824e7i	−0.258438	−	0.119563i
$845$	3.65265e8	−	2.05856e8i	0.605394	−	0.341188i
$846$	−1.41657e8	−	2.21617e8i	−0.233952	−	0.366010i
$847$	2.05267e8			0.337807
$848$	−7.93068e7	+	6.73670e7i	−0.130054	+	0.110474i
$849$	−5.76797e8			−0.942541
$850$	−1.50192e7	−	6.16270e8i	−0.0244563	−	1.00349i
$851$			1.53521e8i			0.249103i
$852$	−6.07931e7	−	2.81250e7i	−0.0982959	−	0.0454752i
$853$		−	8.76211e8i		−	1.41176i	−0.708330	−	0.705881i	$-0.750551\pi$
$853$		−	8.76211e8i		−	1.41176i	0.708330	−	0.705881i	$-0.249449\pi$
$854$	−1.48124e8	−	2.31735e8i	−0.237822	−	0.372064i
$855$	−7.04328e7	−	1.24974e8i	−0.112688	−	0.199950i
$856$	5.50339e8	−	7.49918e7i	0.877423	−	0.119562i
$857$		−	1.11391e9i		−	1.76974i	−0.465841	−	0.884869i	$-0.654248\pi$
$857$		−	1.11391e9i		−	1.76974i	0.465841	−	0.884869i	$-0.345752\pi$
$858$	3.53655e7	+	5.53281e7i	0.0559909	+	0.0875959i
$859$			2.89184e8i			0.456242i	0.973633	+	0.228121i	$0.0732582\pi$
$859$			2.89184e8i			0.456242i	−0.973633	+	0.228121i	$0.926742\pi$
$860$	−2.50249e7	−	3.12542e8i	−0.0393439	−	0.491375i
$861$	2.02944e8			0.317955
$862$	4.85601e8	−	3.10394e8i	0.758154	−	0.484609i
$863$	3.46416e8			0.538970			0.269485	−	0.963005i	$-0.413146\pi$
$863$	3.46416e8			0.538970			0.269485	+	0.963005i	$0.413146\pi$
$864$	−3.64301e7	+	1.18659e8i	−0.0564832	+	0.183975i
$865$	−2.14572e8	−	3.80729e8i	−0.331531	−	0.588258i
$866$	−4.06442e8	+	2.59796e8i	−0.625814	+	0.400017i
$867$	2.85760e6			0.00438474
$868$	−1.08811e8	−	5.03399e7i	−0.166385	−	0.0769756i
$869$	−1.23441e8			−0.188105
$870$	1.71816e8	+	9.13898e7i	0.260920	+	0.138784i
$871$		−	1.53668e8i		−	0.232556i
$872$	−5.24937e8	+	7.15304e7i	−0.791694	+	0.107880i
$873$		−	3.63623e8i		−	0.546523i
$874$	6.23916e8	−	3.98805e8i	0.934528	−	0.597346i
$875$	−7.18932e6	+	2.30606e8i	−0.0107316	+	0.344228i
$876$	−3.09881e8	−	1.43362e8i	−0.460980	−	0.213266i
$877$			9.53475e7i			0.141355i	0.997499	+	0.0706774i	$0.0225161\pi$
$877$			9.53475e7i			0.141355i	−0.997499	+	0.0706774i	$0.977484\pi$
$878$	5.65349e8	−	3.61369e8i	0.835282	−	0.533909i
$879$			6.26727e8i			0.922809i
$880$	3.26221e7	−	8.84304e7i	0.0478700	−	0.129764i
$881$	7.73083e8			1.13057			0.565286	−	0.824895i	$-0.308766\pi$
$881$	7.73083e8			1.13057			0.565286	+	0.824895i	$0.308766\pi$
$882$	−1.08567e8	−	1.69849e8i	−0.158231	−	0.247547i
$883$	−9.11958e8			−1.32462			−0.662312	−	0.749228i	$-0.730425\pi$
$883$	−9.11958e8			−1.32462			−0.662312	+	0.749228i	$0.730425\pi$
$884$	3.79051e8	−	8.19330e8i	0.548708	−	1.18605i
$885$	3.88729e8	+	6.89749e8i	0.560812	+	0.995087i
$886$	1.22893e8	+	1.92263e8i	0.176696	+	0.276435i
$887$	−3.79394e7			−0.0543651			−0.0271825	−	0.999630i	$-0.508654\pi$
$887$	−3.79394e7			−0.0543651			−0.0271825	+	0.999630i	$0.508654\pi$
$888$	−8.44115e6	−	6.19467e7i	−0.0120549	−	0.0884665i
$889$	6.27861e7			0.0893631
$890$	6.37366e8	+	3.39018e8i	0.904105	+	0.480897i
$891$		−	1.08705e7i		−	0.0153680i
$892$	4.23820e8	−	9.16100e8i	0.597155	−	1.29077i
$893$		−	6.38992e8i		−	0.897307i
$894$	3.11045e8	+	4.86619e8i	0.435322	+	0.681046i
$895$	−5.32612e8	−	9.45049e8i	−0.742919	−	1.31821i
$896$	1.84406e8	+	1.65425e8i	0.256360	+	0.229972i
$897$		−	8.73846e8i		−	1.21076i
$898$	6.12710e8	+	9.58564e8i	0.846108	+	1.32371i
$899$			1.97979e8i			0.272483i
$900$	1.35823e8	+	2.01497e8i	0.186314	+	0.276402i
$901$	−1.25286e8			−0.171288
$902$	−1.36760e8	+	8.74164e7i	−0.186354	+	0.119117i
$903$	−7.21706e7			−0.0980161
$904$	−1.64589e8	−	1.20786e9i	−0.222790	−	1.63498i
$905$	−4.65761e8	+	2.62494e8i	−0.628373	+	0.354139i
$906$	2.95836e8	−	1.89097e8i	0.397802	−	0.254273i
$907$	−8.59188e8			−1.15151			−0.575753	−	0.817624i	$-0.695291\pi$
$907$	−8.59188e8			−1.15151			−0.575753	+	0.817624i	$0.695291\pi$
$908$	−3.46513e8	+	7.48998e8i	−0.462873	+	1.00051i
$909$	1.47512e8			0.196397
$910$	−1.58668e8	+	2.98301e8i	−0.210554	+	0.395850i
$911$			1.22268e9i			1.61717i	0.588379	+	0.808586i	$0.299767\pi$
$911$			1.22268e9i			1.61717i	−0.588379	+	0.808586i	$0.700233\pi$
$912$	−2.29827e8	+	1.95226e8i	−0.302981	+	0.257367i
$913$		−	5.02949e7i		−	0.0660863i
$914$	2.59828e8	−	1.66081e8i	0.340289	−	0.217511i
$915$	−4.94034e8	+	2.78428e8i	−0.644902	+	0.363455i
$916$	4.57163e8	−	9.88171e8i	0.594818	−	1.28572i
$917$		−	4.17494e8i		−	0.541430i
$918$	−1.25921e8	+	8.04884e7i	−0.162769	+	0.104041i
$919$			6.57654e8i			0.847327i	0.905820	+	0.423663i	$0.139256\pi$
$919$			6.57654e8i			0.847327i	−0.905820	+	0.423663i	$0.860744\pi$
$920$	−9.99573e8	+	7.57738e8i	−1.28366	+	0.973096i
$921$	6.37834e7			0.0816449
$922$	6.14496e7	+	9.61358e7i	0.0784019	+	0.122657i
$923$	−1.92040e8			−0.244222
$924$	−1.96905e7	−	9.10952e6i	−0.0249598	−	0.0115473i
$925$	−1.04702e8	−	6.33859e7i	−0.132291	−	0.0800880i
$926$	3.72047e8	+	5.82056e8i	0.468560	+	0.733046i
$927$	6.76777e7			0.0849584
$928$	1.20064e8	−	3.91067e8i	0.150234	−	0.489337i
$929$	−5.34007e8			−0.666039			−0.333020	−	0.942920i	$-0.608068\pi$
$929$	−5.34007e8			−0.666039			−0.333020	+	0.942920i	$0.608068\pi$
$930$	−1.16090e8	+	2.18253e8i	−0.144326	+	0.271339i
$931$		−	4.89729e8i		−	0.606885i
$932$	−2.73451e8	−	1.26508e8i	−0.337778	−	0.156268i
$933$			8.30043e8i			1.02201i
$934$	−3.04665e8	−	4.76638e8i	−0.373923	−	0.584990i
$935$	9.88648e7	−	5.57183e7i	0.120950	−	0.0681652i
$936$	4.80473e7	+	3.52603e8i	0.0585925	+	0.429990i
$937$			1.04806e9i			1.27400i	0.770866	+	0.636998i	$0.219824\pi$
$937$			1.04806e9i			1.27400i	−0.770866	+	0.636998i	$0.780176\pi$
$938$	2.73441e7	+	4.27789e7i	0.0331326	+	0.0518348i
$939$			4.58341e8i			0.553595i
$940$	8.63900e7	+	1.07894e9i	0.104011	+	1.29902i
$941$	3.78858e8			0.454682			0.227341	−	0.973815i	$-0.426997\pi$
$941$	3.78858e8			0.454682			0.227341	+	0.973815i	$0.426997\pi$
$942$	−1.98775e8	+	1.27056e8i	−0.237799	+	0.152000i
$943$	2.15997e9			2.57581
$944$	1.26845e9	−	1.07748e9i	1.50784	−	1.28083i
$945$	4.87276e7	−	2.74619e7i	0.0577403	−	0.0325414i
$946$	4.86345e7	−	3.10870e7i	0.0574475	−	0.0367202i
$947$	−4.98377e8			−0.586825			−0.293412	−	0.955986i	$-0.594791\pi$
$947$	−4.98377e8			−0.586825			−0.293412	+	0.955986i	$0.594791\pi$
$948$	−6.07141e8	−	2.80885e8i	−0.712631	−	0.329688i
$949$	−9.78883e8			−1.14533
$950$	1.43832e7	+	5.90173e8i	0.0167759	+	0.688349i
$951$			6.08424e8i			0.707400i
$952$	4.02716e7	+	2.95540e8i	0.0466754	+	0.342535i
$953$		−	1.47950e8i		−	0.170937i	−0.996341	−	0.0854686i	$-0.972761\pi$
$953$		−	1.47950e8i		−	0.170937i	0.996341	−	0.0854686i	$-0.0272387\pi$
$954$	4.16120e7	−	2.65982e7i	0.0479263	−	0.0306343i
$955$	2.89927e8	+	5.14437e8i	0.332873	+	0.590639i
$956$	−1.10818e8	−	5.12685e7i	−0.126835	−	0.0586782i
$957$			3.58263e7i			0.0408758i
$958$	1.27017e9	−	8.11886e8i	1.44466	−	0.923419i
$959$			5.56619e7i			0.0631106i
$960$	3.61671e8	−	3.60712e8i	0.408790	−	0.407706i
$961$	6.36017e8			0.716636
$962$	−9.65337e7	−	1.51024e8i	−0.108431	−	0.169637i
$963$	−2.63610e8			−0.295177
$964$	−9.51441e6	+	2.05657e7i	−0.0106206	+	0.0229568i
$965$	2.61202e8	+	4.63469e8i	0.290666	+	0.515749i
$966$	1.55495e8	+	2.43266e8i	0.172498	+	0.269868i
$967$	−1.35920e8			−0.150315			−0.0751577	−	0.997172i	$-0.523946\pi$
$967$	−1.35920e8			−0.150315			−0.0751577	+	0.997172i	$0.523946\pi$
$968$	−8.81541e8	+	1.20123e8i	−0.971888	+	0.132434i
$969$	−3.63071e8			−0.399043
$970$	−7.02713e8	+	1.32113e9i	−0.769950	+	1.44754i
$971$			9.03014e8i			0.986363i	0.869927	+	0.493181i	$0.164166\pi$
$971$			9.03014e8i			0.986363i	−0.869927	+	0.493181i	$0.835834\pi$
$972$	2.47354e7	−	5.34664e7i	0.0269352	−	0.0582213i
$973$			5.58148e8i			0.605913i
$974$	−6.83727e8	−	1.06967e9i	−0.739956	−	1.15764i
$975$	5.95967e8	+	3.60795e8i	0.642997	+	0.389266i
$976$	7.71747e8	+	9.08528e8i	0.830090	+	0.977212i
$977$		−	6.36642e8i		−	0.682671i	−0.939942	−	0.341336i	$-0.889121\pi$
$977$		−	6.36642e8i		−	0.682671i	0.939942	−	0.341336i	$-0.110879\pi$
$978$	3.53305e8	+	5.52733e8i	0.377688	+	0.590880i
$979$			1.32900e8i			0.141638i
$980$	6.62101e7	+	8.26913e8i	0.0703470	+	0.878580i
$981$	2.51442e8			0.266337
$982$	7.45081e8	−	4.76253e8i	0.786809	−	0.502925i
$983$	−1.06304e9			−1.11915			−0.559576	−	0.828779i	$-0.689036\pi$
$983$	−1.06304e9			−1.11915			−0.559576	+	0.828779i	$0.689036\pi$
$984$	−8.71564e8	+	1.18763e8i	−0.914774	+	0.124651i
$985$	1.89250e8	+	3.35799e8i	0.198028	+	0.351375i
$986$	4.15004e8	−	2.65269e8i	0.432934	−	0.276729i
$987$	2.49144e8			0.259119
$988$	−3.63000e8	+	7.84635e8i	−0.376388	+	0.813574i
$989$	−7.68129e8			−0.794045
$990$	−2.10076e7	+	3.94951e7i	−0.0216507	+	0.0407041i
$991$		−	8.66816e8i		−	0.890648i	−0.895370	−	0.445324i	$-0.853089\pi$
$991$		−	8.66816e8i		−	0.890648i	0.895370	−	0.445324i	$-0.146911\pi$
$992$	4.96761e8	+	1.52513e8i	0.508876	+	0.156233i
$993$		−	6.08515e8i		−	0.621475i
$994$	5.34611e7	−	3.41721e7i	0.0544350	−	0.0347946i
$995$	−6.69457e8	−	1.18786e9i	−0.679601	−	1.20586i
$996$	1.14444e8	−	2.47374e8i	0.115828	−	0.250367i
$997$		−	1.70377e9i		−	1.71919i	−0.510973	−	0.859597i	$-0.670715\pi$
$997$		−	1.70377e9i		−	1.71919i	0.510973	−	0.859597i	$-0.329285\pi$
$998$	6.95184e8	−	4.44358e8i	0.699372	−	0.447035i
$999$			2.96722e7i			0.0297614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.f.a.19.26	yes	36
3.2	odd	2		180.7.f.g.19.11		36
4.3	odd	2	inner	60.7.f.a.19.12	yes	36
5.4	even	2	inner	60.7.f.a.19.11	✓	36
12.11	even	2		180.7.f.g.19.25		36
15.14	odd	2		180.7.f.g.19.26		36
20.19	odd	2	inner	60.7.f.a.19.25	yes	36
60.59	even	2		180.7.f.g.19.12		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.11	✓	36	5.4	even	2	inner
60.7.f.a.19.12	yes	36	4.3	odd	2	inner
60.7.f.a.19.25	yes	36	20.19	odd	2	inner
60.7.f.a.19.26	yes	36	1.1	even	1	trivial
180.7.f.g.19.11		36	3.2	odd	2
180.7.f.g.19.12		36	60.59	even	2
180.7.f.g.19.25		36	12.11	even	2
180.7.f.g.19.26		36	15.14	odd	2

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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.30858 + 6.74063i) q^{2} -15.5885 q^{3} +(-26.8722 + 58.0851i) q^{4} +(-108.897 + 61.3721i) q^{5} +(-67.1642 - 105.076i) q^{6} +118.127 q^{7} +(-507.312 + 69.1287i) q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+(4.30858 + 6.74063i) q^{2} -15.5885 q^{3} +(-26.8722 + 58.0851i) q^{4} +(-108.897 + 61.3721i) q^{5} +(-67.1642 - 105.076i) q^{6} +118.127 q^{7} +(-507.312 + 69.1287i) q^{8} +243.000 q^{9} +(-882.876 - 469.605i) q^{10} -184.093i q^{11} +(418.897 - 905.458i) q^{12} -2860.25i q^{13} +(508.962 + 796.254i) q^{14} +(1697.53 - 956.696i) q^{15} +(-2651.77 - 3121.75i) q^{16} -4931.62i q^{17} +(1046.99 + 1637.97i) q^{18} +4722.79i q^{19} +(-638.508 - 7974.48i) q^{20} -1841.43 q^{21} +(1240.90 - 793.180i) q^{22} -19598.7 q^{23} +(7908.21 - 1077.61i) q^{24} +(8091.94 - 13366.4i) q^{25} +(19279.9 - 12323.6i) q^{26} -3788.00 q^{27} +(-3174.35 + 6861.45i) q^{28} +12484.2 q^{29} +(13762.7 + 7320.42i) q^{30} +15858.3i q^{31} +(9617.25 - 31324.9i) q^{32} +2869.73i q^{33} +(33242.2 - 21248.3i) q^{34} +(-12863.7 + 7249.73i) q^{35} +(-6529.95 + 14114.7i) q^{36} -7833.21i q^{37} +(-31834.6 + 20348.5i) q^{38} +44586.9i q^{39} +(51002.0 - 38662.6i) q^{40} -110210. q^{41} +(-7933.93 - 12412.4i) q^{42} +39192.8 q^{43} +(10693.1 + 4946.99i) q^{44} +(-26461.9 + 14913.4i) q^{45} +(-84442.7 - 132108. i) q^{46} -135300. q^{47} +(41336.9 + 48663.3i) q^{48} -103695. q^{49} +(124963. - 3045.50i) q^{50} +76876.4i q^{51} +(166138. + 76861.4i) q^{52} -25404.6i q^{53} +(-16320.9 - 25533.5i) q^{54} +(11298.2 + 20047.1i) q^{55} +(-59927.5 + 8166.00i) q^{56} -73621.0i q^{57} +(53789.3 + 84151.6i) q^{58} +406325. i q^{59} +(9953.36 + 124310. i) q^{60} -291031. q^{61} +(-106895. + 68326.9i) q^{62} +28705.0 q^{63} +(252586. - 70139.6i) q^{64} +(175540. + 311472. i) q^{65} +(-19343.8 + 12364.5i) q^{66} +53725.2 q^{67} +(286454. + 132524. i) q^{68} +305514. q^{69} +(-104292. - 55473.3i) q^{70} -67140.7i q^{71} +(-123277. + 16798.3i) q^{72} -342236. i q^{73} +(52800.8 - 33750.0i) q^{74} +(-126141. + 208362. i) q^{75} +(-274324. - 126912. i) q^{76} -21746.5i q^{77} +(-300544. + 192106. i) q^{78} -670535. i q^{79} +(480357. + 177204. i) q^{80} +59049.0 q^{81} +(-474849. - 742885. i) q^{82} +273204. q^{83} +(49483.2 - 106959. i) q^{84} +(302664. + 537037. i) q^{85} +(168865. + 264184. i) q^{86} -194610. q^{87} +(12726.1 + 93392.6i) q^{88} -721920. q^{89} +(-214539. - 114114. i) q^{90} -337875. i q^{91} +(526661. - 1.13839e6i) q^{92} -247207. i q^{93} +(-582950. - 912006. i) q^{94} +(-289847. - 514295. i) q^{95} +(-149918. + 488307. i) q^{96} -1.49639e6i q^{97} +(-446778. - 698969. i) q^{98} -44734.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more