LMFDB - Embedded newform 60.7.f.a.19.11

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			19.11
Character	$\chi$	$=$	60.19
Dual form			60.7.f.a.19.12

$q$-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} +(55.5036 + 998.458i) 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} +(6491.10 - 4676.07i) 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} +(865.215 + 15564.4i) 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} +(-59487.1 - 23606.9i) 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} +(55233.3 - 112135. i) 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} +(101186. - 72892.7i) 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} +(-6556.50 - 117945. i) 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} +(97179.8 + 502693. 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} +(13487.4 + 242625. 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	$-0.555087\pi$
$7$	−118.127			−0.344395			−0.172198	+	0.985062i	$0.555087\pi$
$8$	507.312	−	69.1287i	0.990843	−	0.135017i
$9$	243.000			0.333333
$10$	55.5036	+	998.458i	0.0555036	+	0.998458i
$11$		−	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	$0.225627\pi$
$13$			2860.25i			1.30189i	−0.759125	+	0.650945i	$0.774373\pi$
$14$	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	$0.167364\pi$
$17$			4931.62i			1.00379i	−0.864929	+	0.501895i	$0.832636\pi$
$18$	−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	$0.888124\pi$
$20$	6491.10	−	4676.07i	0.811387	−	0.584509i
$21$	−1841.43			−0.198837
$22$	−1240.90	+	793.180i	−0.116539	+	0.0744910i
$23$	19598.7			1.61081			0.805404	−	0.592726i	$-0.201948\pi$
$23$	19598.7			1.61081			0.805404	+	0.592726i	$0.201948\pi$
$24$	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	$0.417615\pi$
$30$	865.215	+	15564.4i	0.0320450	+	0.576460i
$31$			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	$0.0246370\pi$
$37$			7833.21i			0.154645i	−0.997006	+	0.0773223i	$0.975363\pi$
$38$	31834.6	−	20348.5i	0.580160	−	0.370836i
$39$			44586.9i			0.751647i
$40$	−59487.1	−	23606.9i	−0.929486	−	0.368857i
$41$	−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	$-0.579272\pi$
$43$	−39192.8			−0.492948			−0.246474	+	0.969149i	$0.579272\pi$
$44$	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	$-0.274103\pi$
$47$	135300.			1.30318			0.651588	+	0.758573i	$0.274103\pi$
$48$	−41336.9	−	48663.3i	−0.373779	−	0.440026i
$49$	−103695.			−0.881392
$50$	55233.3	−	112135.i	0.441866	−	0.897081i
$51$			76876.4i			0.579538i
$52$	−166138.	−	76861.4i	−1.18157	−	0.546636i
$53$			25404.6i			0.170641i	0.996354	+	0.0853207i	$0.0271915\pi$
$53$			25404.6i			0.170641i	−0.996354	+	0.0853207i	$0.972809\pi$
$54$	−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	$0.546808\pi$
$60$	101186.	−	72892.7i	0.468455	−	0.337466i
$61$	−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	$-0.528468\pi$
$67$	−53725.2			−0.178630			−0.0893149	+	0.996003i	$0.528468\pi$
$68$	−286454.	−	132524.i	−0.911020	−	0.421470i
$69$	305514.			0.930001
$70$	−6556.50	−	117945.i	−0.0191152	−	0.343864i
$71$		−	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	$0.144977\pi$
$73$			342236.i			0.879747i	−0.898060	+	0.439873i	$0.855023\pi$
$74$	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	$-0.238021\pi$
$80$	97179.8	+	502693.i	0.189804	+	0.981822i
$81$	59049.0			0.111111
$82$	474849.	+	742885.i	0.861220	+	1.34735i
$83$	−273204.			−0.477806			−0.238903	−	0.971043i	$-0.576788\pi$
$83$	−273204.			−0.477806			−0.238903	+	0.971043i	$0.576788\pi$
$84$	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	$0.671104\pi$
$90$	13487.4	+	242625.i	0.0185012	+	0.332819i
$91$		−	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	$0.305907\pi$
$97$			1.49639e6i			1.63957i	−0.572672	+	0.819784i	$0.694093\pi$
$98$	446778.	+	698969.i	0.474694	+	0.742642i
$99$		−	44734.6i		−	0.0461040i
$100$	−993839.	+	110836.i	−0.993839	+	0.110836i
$101$	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	$-0.540675\pi$
$103$	−278509.			−0.254875			−0.127438	+	0.991847i	$0.540675\pi$
$104$	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	$-0.353997\pi$
$107$	1.08481e6			0.885531			0.442766	+	0.896637i	$0.353997\pi$
$108$	−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	$0.369182\pi$
$110$	183809.	−	10217.8i	0.138099	−	0.00767681i
$111$			122108.i			0.0892841i
$112$	313246.	+	368765.i	0.222963	+	0.262480i
$113$		−	2.38091e6i		−	1.65009i	−0.565067	−	0.825045i	$-0.691150\pi$
$113$		−	2.38091e6i		−	1.65009i	0.565067	−	0.825045i	$-0.308850\pi$
$114$	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
$120$	−927312.	−	367995.i	−0.536639	−	0.212960i
$121$	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	$-0.541414\pi$
$127$	−531512.			−0.259479			−0.129739	+	0.991548i	$0.541414\pi$
$128$	−1.56107e6	−	1.40039e6i	−0.744379	−	0.667758i
$129$	−610955.			−0.284604
$130$	−2.85584e6	+	158754.i	−1.29988	+	0.0722596i
$131$		−	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	$-0.970794\pi$
$137$		−	471202.i		−	0.183251i	0.995794	−	0.0916253i	$-0.0292062\pi$
$138$	−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	$0.657758\pi$
$140$	−766777.	+	552372.i	−0.279438	+	0.201302i
$141$	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	$0.746816\pi$
$150$	861002.	−	1.74801e6i	0.255112	−	0.517930i
$151$			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	$0.0785963\pi$
$157$			1.89173e6i			0.488832i	−0.969670	+	0.244416i	$0.921404\pi$
$158$	−4.51983e6	+	2.88906e6i	−1.14591	+	0.732461i
$159$			396018.i			0.0985198i
$160$	2.96976e6	−	2.82095e6i	0.725039	−	0.688708i
$161$	−2.31515e6			−0.554755
$162$	−254417.	−	398028.i	−0.0598414	−	0.0936199i
$163$	5.26032e6			1.21464			0.607322	−	0.794456i	$-0.292244\pi$
$163$	5.26032e6			1.21464			0.607322	+	0.794456i	$0.292244\pi$
$164$	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	$-0.294903\pi$
$167$	5.59513e6			1.20133			0.600663	+	0.799502i	$0.294903\pi$
$168$	−934177.	+	127295.i	−0.197016	+	0.0268463i
$169$	−3.35424e6			−0.694918
$170$	−4.92402e6	+	273723.i	−1.00224	+	0.0557140i
$171$			1.14764e6i			0.229518i
$172$	1.05320e6	−	2.27652e6i	0.206978	−	0.447390i
$173$		−	3.49625e6i		−	0.675248i	−0.941281	−	0.337624i	$-0.890377\pi$
$173$		−	3.49625e6i		−	0.675248i	0.941281	−	0.337624i	$-0.109623\pi$
$174$	−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	$0.726872\pi$
$180$	1.57734e6	−	1.13628e6i	0.270462	−	0.194836i
$181$	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
$190$	−4.71551e6	+	262132.i	−0.687492	+	0.0382172i
$191$		−	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	$0.0956557\pi$
$193$			4.25604e6i			0.592017i	−0.955185	+	0.296009i	$0.904344\pi$
$194$	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	$0.0646361\pi$
$197$			3.08365e6i			0.403336i	−0.979454	+	0.201668i	$0.935364\pi$
$198$	−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	$0.756690\pi$
$200$	5.02914e6	+	6.22155e6i	0.628643	+	0.777694i
$201$	−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
$210$	−102206.	−	1.83859e6i	−0.0110361	−	0.198530i
$211$			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
$220$	−860832.	−	1.19497e6i	−0.0808445	−	0.112224i
$221$	−1.41057e7			−1.30682
$222$	823083.	−	526111.i	0.0752289	−	0.0480860i
$223$	1.57717e7			1.42221			0.711104	−	0.703086i	$-0.248195\pi$
$223$	1.57717e7			1.42221			0.711104	+	0.703086i	$0.248195\pi$
$224$	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	$-0.685829\pi$
$227$	−1.28948e7			−1.10240			−0.551198	+	0.834374i	$0.685829\pi$
$228$	−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	$0.750547\pi$
$230$	1.08780e6	+	1.95685e7i	0.0894057	+	1.60833i
$231$			338994.i			0.0275015i
$232$	6.33340e6	−	863019.i	0.507192	−	0.0691125i
$233$		−	4.70775e6i		−	0.372174i	−0.982533	−	0.186087i	$-0.940419\pi$
$233$		−	4.70775e6i		−	0.372174i	0.982533	−	0.186087i	$-0.0595806\pi$
$234$	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	$0.977740\pi$
$240$	1.51488e6	+	7.83621e6i	0.109584	+	0.566855i
$241$	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
$250$	−1.28967e7	+	8.82135e6i	−0.825388	+	0.564567i
$251$		−	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	$-0.745215\pi$
$257$		−	2.43638e7i		−	1.43531i	0.696397	−	0.717656i	$-0.254785\pi$
$258$	2.63235e6	+	4.11823e6i	0.153280	+	0.239801i
$259$		−	925318.i		−	0.0532588i
$260$	1.33747e7	+	1.85662e7i	0.760966	+	1.05634i
$261$	3.03367e6			0.170626
$262$	−2.38232e7	+	1.52277e7i	−1.32463	+	0.846701i
$263$	−1.08755e6			−0.0597834			−0.0298917	−	0.999553i	$-0.509516\pi$
$263$	−1.08755e6			−0.0597834			−0.0298917	+	0.999553i	$0.509516\pi$
$264$	−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	$0.465943\pi$
$270$	210247.	+	3.78216e6i	0.0106817	+	0.192153i
$271$		−	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	$-0.719795\pi$
$277$		−	3.27703e7i		−	1.54185i	0.636927	−	0.770924i	$-0.280205\pi$
$278$	3.18492e7	−	2.03579e7i	1.48240	−	0.947541i
$279$			3.85357e6i			0.177440i
$280$	7.02706e6	+	2.78862e6i	0.320110	+	0.127033i
$281$	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	$-0.803959\pi$
$283$	−3.70016e7			−1.63253			−0.816264	+	0.577679i	$0.803959\pi$
$284$	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
$290$	692920.	+	1.24650e7i	0.0284112	+	0.511090i
$291$			2.33264e7i			0.946606i
$292$	−1.98788e7	−	9.19666e6i	−0.798441	−	0.369387i
$293$			4.02045e7i			1.59835i	0.601097	+	0.799176i	$0.294730\pi$
$293$			4.02045e7i			1.59835i	−0.601097	+	0.799176i	$0.705270\pi$
$294$	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
$300$	−1.54924e7	+	1.72776e6i	−0.573793	+	0.0639912i
$301$	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	$-0.477475\pi$
$307$	4.09171e6			0.141413			0.0707065	+	0.997497i	$0.477475\pi$
$308$	−1.26315e6	−	584376.i	−0.0432316	−	0.0200005i
$309$	−4.34152e6			−0.147152
$310$	−1.58339e7	+	880194.i	−0.531499	+	0.0295456i
$311$		−	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	$0.159156\pi$
$313$			2.94026e7i			0.958854i	−0.877582	+	0.479427i	$0.840844\pi$
$314$	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	$0.209887\pi$
$317$			3.90304e7i			1.22525i	−0.790373	+	0.612626i	$0.790113\pi$
$318$	2.66941e6	−	1.70628e6i	0.0830107	−	0.0530601i
$319$		−	2.29826e6i		−	0.0707990i
$320$	−3.18104e7	−	7.86378e6i	−0.970777	−	0.239983i
$321$	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
$330$	2.86530e6	−	159280.i	0.0797313	−	0.00443221i
$331$			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	$-0.816386\pi$
$337$		−	4.17462e7i		−	1.09076i	0.838190	−	0.545378i	$-0.183614\pi$
$338$	1.44520e7	+	2.26097e7i	0.374264	+	0.585524i
$339$		−	3.71147e7i		−	0.952680i
$340$	2.30606e7	+	3.20116e7i	0.586724	+	0.814463i
$341$	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	$-0.847113\pi$
$347$	−7.41088e7			−1.77371			−0.886853	+	0.462052i	$0.847113\pi$
$348$	−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	$0.571207\pi$
$350$	−6.52457e6	+	1.32462e7i	−0.152177	+	0.308950i
$351$			1.08346e7i			0.250549i
$352$	5.76670e6	+	1.77047e6i	0.132221	+	0.0405939i
$353$			1.77120e7i			0.402666i	0.979523	+	0.201333i	$0.0645273\pi$
$353$			1.77120e7i			0.402666i	−0.979523	+	0.201333i	$0.935473\pi$
$354$	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	$0.740646\pi$
$360$	−1.44554e7	−	5.73647e6i	−0.309829	−	0.122952i
$361$	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	$-0.187941\pi$
$367$	8.21243e7			1.66140			0.830699	+	0.556722i	$0.187941\pi$
$368$	−5.19712e7	−	6.11824e7i	−1.04284	−	1.22767i
$369$	−2.67810e7			−0.533026
$370$	−7.82114e6	+	434771.i	−0.154406	+	0.00858333i
$371$		−	3.00098e6i		−	0.0587680i
$372$	−1.43590e7	−	6.64300e6i	−0.278931	−	0.129043i
$373$		−	2.31099e7i		−	0.445320i	−0.974896	−	0.222660i	$-0.928526\pi$
$373$		−	2.31099e7i		−	0.445320i	0.974896	−	0.222660i	$-0.0714740\pi$
$374$	−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	$0.898237\pi$
$380$	2.20841e7	+	3.06561e7i	0.402465	+	0.558683i
$381$	−8.28545e6			−0.149810
$382$	−3.18433e7	+	2.03541e7i	−0.571252	+	0.365142i
$383$	4.80434e7			0.855141			0.427570	−	0.903982i	$-0.359370\pi$
$383$	4.80434e7			0.855141			0.427570	+	0.903982i	$0.359370\pi$
$384$	−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	$0.589883\pi$
$390$	−4.45182e7	+	2.47474e6i	−0.750488	+	0.0417191i
$391$			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	$-0.968316\pi$
$397$		−	1.24359e7i		−	0.198749i	0.995050	−	0.0993745i	$-0.0316842\pi$
$398$	7.35280e7	−	4.69988e7i	1.16628	−	0.745483i
$399$		−	8.69666e6i		−	0.136910i
$400$	2.02687e7	−	6.07057e7i	0.316699	−	0.948526i
$401$	−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	$0.502454\pi$
$410$	−6.11705e6	−	1.10040e8i	−0.0887545	−	1.59661i
$411$		−	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	$-0.0876164\pi$
$420$	−1.19529e7	+	8.61063e6i	−0.161333	+	0.116222i
$421$	−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
$430$	−2.17534e6	−	3.91324e7i	−0.0273604	−	0.492188i
$431$		−	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	$-0.878889\pi$
$433$		−	6.02974e7i		−	0.742736i	0.928486	−	0.371368i	$-0.121111\pi$
$434$	−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	$-0.165077\pi$
$440$	−4.34586e6	+	1.09512e7i	−0.0510174	+	0.128559i
$441$	−2.51979e7			−0.293797
$442$	6.07755e7	+	9.50812e7i	0.703820	+	1.10110i
$443$	−2.85229e7			−0.328082			−0.164041	−	0.986453i	$-0.552453\pi$
$443$	−2.85229e7			−0.328082			−0.164041	+	0.986453i	$0.552453\pi$
$444$	−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	$0.212401\pi$
$450$	1.34217e7	−	2.72488e7i	0.147289	−	0.299027i
$451$			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	$0.0647224\pi$
$457$			3.85466e7i			0.403866i	−0.979399	+	0.201933i	$0.935278\pi$
$458$	7.32996e7	+	1.14675e8i	0.762966	+	1.19363i
$459$			1.86810e7i			0.193179i
$460$	1.27217e8	−	9.16450e7i	1.30699	−	0.941532i
$461$	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	$-0.643252\pi$
$463$	−8.63503e7			−0.870003			−0.435002	+	0.900430i	$0.643252\pi$
$464$	−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	$-0.387152\pi$
$467$	7.07112e7			0.694284			0.347142	+	0.937812i	$0.387152\pi$
$468$	−4.03716e7	−	1.86773e7i	−0.393857	−	0.182212i
$469$	6.34643e6			0.0615192
$470$	7.50962e6	+	1.35091e8i	0.0723310	+	1.30117i
$471$			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	$-0.327849\pi$
$480$	4.62940e7	−	4.39742e7i	0.418602	−	0.397626i
$481$	−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	$-0.258945\pi$
$487$	1.58690e8			1.37392			0.686960	+	0.726695i	$0.258945\pi$
$488$	−1.47644e8	+	2.01186e7i	−1.27044	+	0.173117i
$489$	8.20002e7			0.701275
$490$	−5.75544e6	−	1.03535e8i	−0.0489204	−	0.880033i
$491$		−	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	$-0.136225\pi$
$500$	1.15028e8	+	4.89242e7i	0.920223	+	0.391394i
$501$	8.72195e7			0.693586
$502$	−8.00712e7	+	5.11811e7i	−0.632944	+	0.404575i
$503$	1.94397e8			1.52752			0.763758	−	0.645503i	$-0.223352\pi$
$503$	1.94397e8			1.52752			0.763758	+	0.645503i	$0.223352\pi$
$504$	−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	$0.374363\pi$
$510$	−7.67579e7	+	4.26691e6i	−0.578645	+	0.0321665i
$511$		−	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
$520$	6.75216e7	−	1.70148e8i	0.480212	−	1.21009i
$521$	−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	$-0.686819\pi$
$523$	−1.58446e8			−1.10758			−0.553791	+	0.832656i	$0.686819\pi$
$524$	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
$530$	−2.53654e7	+	1.41005e6i	−0.170378	+	0.00947121i
$531$			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
$540$	2.45883e7	−	1.77129e7i	0.156152	−	0.112489i
$541$	−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	$-0.663348\pi$
$547$	−1.60703e8			−0.981886			−0.490943	+	0.871192i	$0.663348\pi$
$548$	2.73698e7	+	1.26622e7i	0.166315	+	0.0769430i
$549$	−7.07206e7			−0.427394
$550$	−2.06433e7	−	1.01681e7i	−0.124077	−	0.0611154i
$551$			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	$-0.974788\pi$
$557$		−	2.73464e7i		−	0.158247i	0.996865	−	0.0791235i	$-0.0252121\pi$
$558$	2.59755e7	−	1.66034e7i	0.149507	−	0.0955642i
$559$		−	1.12101e8i		−	0.641764i
$560$	−1.14796e7	−	5.93818e7i	−0.0653677	−	0.338135i
$561$	1.41524e7			0.0801570
$562$	−1.19043e8	−	1.86238e8i	−0.670647	−	1.04920i
$563$	−1.22588e8			−0.686946			−0.343473	−	0.939162i	$-0.611603\pi$
$563$	−1.22588e8			−0.686946			−0.343473	+	0.939162i	$0.611603\pi$
$564$	−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	$0.564824\pi$
$570$	−7.35075e7	+	4.08623e6i	−0.396924	+	0.0220647i
$571$			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	$-0.769451\pi$
$577$		−	2.54573e8i		−	1.32521i	0.748969	−	0.662605i	$-0.230549\pi$
$578$	789828.	+	1.23566e6i	0.00409024	+	0.00639904i
$579$			6.63452e7i			0.341801i
$580$	8.10364e7	−	5.83771e7i	0.415333	−	0.299198i
$581$	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	$-0.485135\pi$
$587$	1.88848e7			0.0933682			0.0466841	+	0.998910i	$0.485135\pi$
$588$	4.34375e7	−	9.38913e7i	0.213664	−	0.461842i
$589$	−7.48955e7			−0.366530
$590$	−4.05699e8	+	2.25525e7i	−1.97537	+	0.109809i
$591$			4.80694e7i			0.232866i
$592$	2.44534e7	−	2.07718e7i	0.117862	−	0.100117i
$593$		−	2.23347e7i		−	0.107106i	−0.998565	−	0.0535532i	$-0.982945\pi$
$593$		−	2.23347e7i		−	0.107106i	0.998565	−	0.0535532i	$-0.0170547\pi$
$594$	−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	$-0.216462\pi$
$600$	7.83966e7	+	9.69844e7i	0.362947	+	0.449002i
$601$	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	$-0.409583\pi$
$607$	1.25355e8			0.560500			0.280250	+	0.959927i	$0.409583\pi$
$608$	−1.47941e8	−	4.54202e7i	−0.658230	−	0.202087i
$609$	−2.29888e7			−0.101780
$610$	−1.61533e7	−	2.90583e8i	−0.0711658	−	1.28021i
$611$			3.86991e8i			1.69659i
$612$	−6.96083e7	−	3.22033e7i	−0.303673	−	0.140490i
$613$			3.91174e8i			1.69820i	0.528234	+	0.849099i	$0.322854\pi$
$613$			3.91174e8i			1.69820i	−0.528234	+	0.849099i	$0.677146\pi$
$614$	−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	$0.00352971\pi$
$617$			5.20913e6i			0.0221774i	−0.999939	+	0.0110887i	$0.996470\pi$
$618$	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	$0.955547\pi$
$620$	7.41546e7	+	1.02938e8i	0.311145	+	0.431917i
$621$	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
$630$	−1.59323e6	−	2.86607e7i	−0.00637172	−	0.114621i
$631$		−	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
$640$	8.40510e7	+	2.48304e8i	0.320629	+	0.947205i
$641$	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	$-0.261746\pi$
$643$	3.61840e8			1.36108			0.680539	+	0.732712i	$0.261746\pi$
$644$	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	$-0.449236\pi$
$647$	8.60221e7			0.317612			0.158806	+	0.987310i	$0.449236\pi$
$648$	2.99563e7	−	4.08198e6i	0.110094	−	0.0150019i
$649$	7.48016e7			0.273638
$650$	3.20735e8	+	1.57981e8i	1.16790	+	0.575261i
$651$		−	2.92019e7i		−	0.105845i
$652$	−1.41356e8	+	3.05546e8i	−0.510003	+	1.10239i
$653$			2.03609e8i			0.731237i	0.930765	+	0.365619i	$0.119143\pi$
$653$			2.03609e8i			0.731237i	−0.930765	+	0.365619i	$0.880857\pi$
$654$	−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	$-0.0886609\pi$
$660$	−1.34190e7	−	1.86277e7i	−0.0466756	−	0.0647928i
$661$	−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
$670$	−2.98194e6	−	5.36424e7i	−0.00991460	−	0.178354i
$671$			5.35768e7i			0.177341i
$672$	1.77094e7	−	5.76825e7i	0.0583576	−	0.190080i
$673$			1.97914e8i			0.649280i	0.945838	+	0.324640i	$0.105243\pi$
$673$			1.97914e8i			0.649280i	−0.945838	+	0.324640i	$0.894757\pi$
$674$	−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	$-0.958006\pi$
$677$		−	8.16343e7i		−	0.263091i	0.991310	−	0.131546i	$-0.0419940\pi$
$678$	−2.50177e8	+	1.59912e8i	−0.802708	+	0.513087i
$679$		−	1.76765e8i		−	0.564659i
$680$	1.16420e8	−	2.93368e8i	0.370255	−	0.933009i
$681$	−2.01010e8			−0.636469
$682$	−1.25785e7	−	1.96787e7i	−0.0396530	−	0.0620358i
$683$	7.31775e7			0.229676			0.114838	−	0.993384i	$-0.463365\pi$
$683$	7.31775e7			0.229676			0.114838	+	0.993384i	$0.463365\pi$
$684$	−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
$690$	1.69571e7	+	3.05043e8i	0.0516184	+	0.928567i
$691$			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
$700$	1.17400e8	−	1.30928e7i	0.342273	−	0.0381714i
$701$	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	$0.631816\pi$
$710$	6.70373e7	−	3.72655e6i	0.187301	−	0.0104120i
$711$		−	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	$0.720794\pi$
$720$	2.36147e7	+	1.22154e8i	0.0632681	+	0.327274i
$721$	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	$-0.581051\pi$
$727$	−1.93570e8			−0.503774			−0.251887	+	0.967757i	$0.581051\pi$
$728$	−2.33568e7	−	1.71408e8i	−0.0605369	−	0.444259i
$729$	1.43489e7			0.0370370
$730$	−3.41709e8	+	1.89954e7i	−0.878391	+	0.0488291i
$731$		−	1.93284e8i		−	0.494816i
$732$	1.21912e8	−	2.63516e8i	0.310823	−	0.671853i
$733$			2.59266e7i			0.0658316i	0.999458	+	0.0329158i	$0.0104793\pi$
$733$			2.59266e7i			0.0658316i	−0.999458	+	0.0329158i	$0.989521\pi$
$734$	−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	$-0.0447432\pi$
$740$	3.66287e7	+	5.08462e7i	0.0903911	+	0.125477i
$741$	−2.10575e8			−0.517549
$742$	−2.02285e7	+	1.29300e7i	−0.0495167	+	0.0316509i
$743$	−4.12020e8			−1.00451			−0.502253	−	0.864721i	$-0.667495\pi$
$743$	−4.12020e8			−1.00451			−0.502253	+	0.864721i	$0.667495\pi$
$744$	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
$750$	−2.01039e8	+	1.37511e8i	−0.476538	+	0.325953i
$751$			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	$-0.721173\pi$
$757$		−	6.66452e8i		−	1.53632i	0.640259	−	0.768159i	$-0.278827\pi$
$758$	2.30657e8	−	1.47435e8i	0.529612	−	0.338526i
$759$		−	5.62430e7i		−	0.128630i
$760$	1.11490e8	−	2.80945e8i	0.253978	−	0.640001i
$761$	−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	$0.0948729\pi$
$770$	−2.17129e7	+	1.20701e6i	−0.0475605	+	0.00264385i
$771$		−	3.79795e8i		−	0.828678i
$772$	−2.47213e8	−	1.14369e8i	−0.537303	−	0.248575i
$773$		−	2.76327e8i		−	0.598253i	−0.954213	−	0.299127i	$-0.903305\pi$
$773$		−	2.76327e8i		−	0.598253i	0.954213	−	0.299127i	$-0.0966953\pi$
$774$	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
$780$	2.08492e8	+	2.89418e8i	0.439344	+	0.609877i
$781$	−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	$-0.200027\pi$
$787$	7.88652e8			1.61793			0.808967	+	0.587854i	$0.200027\pi$
$788$	−1.79114e8	−	8.28646e7i	−0.366059	−	0.169352i
$789$	−1.69532e7			−0.0345160
$790$	6.69502e8	−	3.72171e7i	1.35791	−	0.0754851i
$791$			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	$0.246098\pi$
$797$			7.07132e8i			1.39677i	−0.715722	+	0.698386i	$0.753902\pi$
$798$	−5.86210e7	+	3.74703e7i	−0.115357	+	0.0737358i
$799$			6.67247e8i			1.30812i
$800$	−4.96524e8	+	1.24931e8i	−0.969774	+	0.244006i
$801$	−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	$0.386467\pi$
$810$	3.27743e6	+	5.89580e7i	0.00616707	+	0.110940i
$811$		−	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
$820$	−7.15384e8	+	5.15350e8i	−1.29747	+	0.934675i
$821$	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	$-0.398697\pi$
$823$	3.48857e8			0.625817			0.312909	+	0.949783i	$0.398697\pi$
$824$	−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	$-0.429003\pi$
$827$	2.50224e8			0.442397			0.221199	+	0.975229i	$0.429003\pi$
$828$	−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	$0.787515\pi$
$830$	−1.51638e7	−	2.72782e8i	−0.0265200	−	0.477070i
$831$		−	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	$0.857185\pi$
$840$	1.09541e8	+	4.34703e7i	0.184816	+	0.0733424i
$841$	−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
$850$	5.53008e8	+	2.72390e8i	0.900481	+	0.443541i
$851$			1.53521e8i			0.249103i
$852$	6.07931e7	+	2.81250e7i	0.0982959	+	0.0454752i
$853$			8.76211e8i			1.41176i	0.708330	+	0.705881i	$0.249449\pi$
$853$			8.76211e8i			1.41176i	−0.708330	+	0.705881i	$0.750551\pi$
$854$	−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	$0.345752\pi$
$857$			1.11391e9i			1.76974i	−0.465841	+	0.884869i	$0.654248\pi$
$858$	−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	$0.926742\pi$
$860$	−2.54404e8	+	1.83268e8i	−0.399972	+	0.288132i
$861$	2.02944e8			0.317955
$862$	−4.85601e8	+	3.10394e8i	−0.758154	+	0.484609i
$863$	−3.46416e8			−0.538970			−0.269485	−	0.963005i	$-0.586854\pi$
$863$	−3.46416e8			−0.538970			−0.269485	+	0.963005i	$0.586854\pi$
$864$	−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
$870$	1.08015e7	+	1.94310e8i	0.0164032	+	0.295078i
$871$		−	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	$-0.977484\pi$
$877$		−	9.53475e7i		−	0.141355i	0.997499	−	0.0706774i	$-0.0225161\pi$
$878$	−5.65349e8	+	3.61369e8i	−0.835282	+	0.533909i
$879$			6.26727e8i			0.922809i
$880$	9.25423e7	−	1.78901e7i	0.135798	−	0.0262522i
$881$	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	$-0.269575\pi$
$883$	9.11958e8			1.32462			0.662312	+	0.749228i	$0.269575\pi$
$884$	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	$-0.491346\pi$
$887$	3.79394e7			0.0543651			0.0271825	+	0.999630i	$0.491346\pi$
$888$	8.44115e6	+	6.19467e7i	0.0120549	+	0.0884665i
$889$	6.27861e7			0.0893631
$890$	−4.00692e7	−	7.20807e8i	−0.0568382	−	1.02247i
$891$		−	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
$900$	−2.41503e8	+	2.69332e7i	−0.331280	+	0.0369454i
$901$	−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	$-0.304709\pi$
$907$	8.59188e8			1.15151			0.575753	+	0.817624i	$0.304709\pi$
$908$	3.46513e8	−	7.48998e8i	0.462873	−	1.00051i
$909$	1.47512e8			0.196397
$910$	3.37354e8	−	1.87532e7i	0.447673	−	0.0248858i
$911$			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	$0.860744\pi$
$920$	−1.16587e9	−	4.62664e8i	−1.49722	−	0.594159i
$921$	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	$0.608068\pi$
$930$	−2.46826e8	+	1.37209e7i	−0.306861	+	0.0170582i
$931$		−	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	$-0.780176\pi$
$937$		−	1.04806e9i		−	1.27400i	0.770866	−	0.636998i	$-0.219824\pi$
$938$	−2.73441e7	−	4.27789e7i	−0.0331326	−	0.0518348i
$939$			4.58341e8i			0.553595i
$940$	8.78244e8	−	6.32671e8i	1.05738	−	0.761718i
$941$	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	$-0.405209\pi$
$947$	4.98377e8			0.586825			0.293412	+	0.955986i	$0.405209\pi$
$948$	6.07141e8	+	2.80885e8i	0.712631	+	0.329688i
$949$	−9.78883e8			−1.14533
$950$	5.29590e8	+	2.60855e8i	0.617688	+	0.304248i
$951$			6.08424e8i			0.707400i
$952$	−4.02716e7	−	2.95540e8i	−0.0466754	−	0.342535i
$953$			1.47950e8i			0.170937i	0.996341	+	0.0854686i	$0.0272387\pi$
$953$			1.47950e8i			0.170937i	−0.996341	+	0.0854686i	$0.972761\pi$
$954$	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
$960$	−4.95875e8	−	1.22584e8i	−0.560478	−	0.138555i
$961$	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	$-0.476054\pi$
$967$	1.35920e8			0.150315			0.0751577	+	0.997172i	$0.476054\pi$
$968$	8.81541e8	−	1.20123e8i	0.971888	−	0.132434i
$969$	−3.63071e8			−0.399043
$970$	−1.49408e9	+	8.30550e7i	−1.63704	+	0.0910020i
$971$			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	$0.110879\pi$
$977$			6.36642e8i			0.682671i	−0.939942	+	0.341336i	$0.889121\pi$
$978$	−3.53305e8	−	5.52733e8i	−0.377688	−	0.590880i
$979$			1.32900e8i			0.141638i
$980$	−6.73094e8	+	4.84885e8i	−0.715150	+	0.515181i
$981$	2.51442e8			0.266337
$982$	−7.45081e8	+	4.76253e8i	−0.786809	+	0.502925i
$983$	1.06304e9			1.11915			0.559576	−	0.828779i	$-0.310964\pi$
$983$	1.06304e9			1.11915			0.559576	+	0.828779i	$0.310964\pi$
$984$	−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
$990$	4.46657e7	−	2.48293e6i	0.0460329	−	0.00255894i
$991$		−	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	$0.329285\pi$
$997$			1.70377e9i			1.71919i	−0.510973	+	0.859597i	$0.670715\pi$
$998$	−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.19.11	✓	36
3.2	odd	2		180.7.f.g.19.26		36
4.3	odd	2	inner	60.7.f.a.19.25	yes	36
5.4	even	2	inner	60.7.f.a.19.26	yes	36
12.11	even	2		180.7.f.g.19.12		36
15.14	odd	2		180.7.f.g.19.11		36
20.19	odd	2	inner	60.7.f.a.19.12	yes	36
60.59	even	2		180.7.f.g.19.25		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.11	✓	36	1.1	even	1	trivial
60.7.f.a.19.12	yes	36	20.19	odd	2	inner
60.7.f.a.19.25	yes	36	4.3	odd	2	inner
60.7.f.a.19.26	yes	36	5.4	even	2	inner
180.7.f.g.19.11		36	15.14	odd	2
180.7.f.g.19.12		36	12.11	even	2
180.7.f.g.19.25		36	60.59	even	2
180.7.f.g.19.26		36	3.2	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} +(55.5036 + 998.458i) 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} +(6491.10 - 4676.07i) 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} +(865.215 + 15564.4i) 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} +(-59487.1 - 23606.9i) 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} +(55233.3 - 112135. i) 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} +(101186. - 72892.7i) 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} +(-6556.50 - 117945. i) 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} +(97179.8 + 502693. 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} +(13487.4 + 242625. 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

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