LMFDB - Embedded newform 20.7.d.d.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,7,Mod(19,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("20.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	20.d (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:	$4.60108167240$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} - 10x^{8} - 1775x^{6} - 1000x^{4} + 160000x^{2} + 1000000 $ x^12 + 16x^10 - 10x^8 - 1775x^6 - 1000x^4 + 160000*x^2 + 1000000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.12
Root			$0.826519 - 3.05235i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.7.d.d.19.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.42116 + 2.98770i) q^{2} -6.08848 q^{3} +(46.1473 + 44.3444i) q^{4} +(26.7958 + 122.094i) q^{5} +(-45.1836 - 18.1905i) q^{6} +422.345 q^{7} +(209.979 + 466.961i) q^{8} -691.930 q^{9} +O(q^{10})$	\(q+(7.42116 + 2.98770i) q^{2} -6.08848 q^{3} +(46.1473 + 44.3444i) q^{4} +(26.7958 + 122.094i) q^{5} +(-45.1836 - 18.1905i) q^{6} +422.345 q^{7} +(209.979 + 466.961i) q^{8} -691.930 q^{9} +(-165.925 + 986.138i) q^{10} -1743.93i q^{11} +(-280.967 - 269.990i) q^{12} +898.704i q^{13} +(3134.29 + 1261.84i) q^{14} +(-163.146 - 743.368i) q^{15} +(163.152 + 4092.75i) q^{16} -5542.94i q^{17} +(-5134.93 - 2067.28i) q^{18} -8906.74i q^{19} +(-4177.64 + 6822.56i) q^{20} -2571.44 q^{21} +(5210.33 - 12942.0i) q^{22} -3740.11 q^{23} +(-1278.46 - 2843.09i) q^{24} +(-14189.0 + 6543.22i) q^{25} +(-2685.06 + 6669.43i) q^{26} +8651.31 q^{27} +(19490.1 + 18728.6i) q^{28} +31180.3 q^{29} +(1010.23 - 6004.09i) q^{30} +22647.9i q^{31} +(-11017.1 + 30860.4i) q^{32} +10617.9i q^{33} +(16560.6 - 41135.1i) q^{34} +(11317.1 + 51565.8i) q^{35} +(-31930.7 - 30683.2i) q^{36} +14997.5i q^{37} +(26610.7 - 66098.4i) q^{38} -5471.75i q^{39} +(-51386.7 + 38149.8i) q^{40} +6598.75 q^{41} +(-19083.1 - 7682.68i) q^{42} -81078.0 q^{43} +(77333.4 - 80477.6i) q^{44} +(-18540.8 - 84480.7i) q^{45} +(-27756.0 - 11174.3i) q^{46} -30231.0 q^{47} +(-993.349 - 24918.6i) q^{48} +60726.1 q^{49} +(-124848. + 6165.93i) q^{50} +33748.1i q^{51} +(-39852.5 + 41472.8i) q^{52} +17256.7i q^{53} +(64202.8 + 25847.5i) q^{54} +(212923. - 46729.9i) q^{55} +(88683.7 + 197219. i) q^{56} +54228.6i q^{57} +(231394. + 93157.4i) q^{58} -294323. i q^{59} +(25435.5 - 41539.1i) q^{60} -211992. q^{61} +(-67665.1 + 168074. i) q^{62} -292233. q^{63} +(-173961. + 196104. i) q^{64} +(-109727. + 24081.5i) q^{65} +(-31723.0 + 78797.0i) q^{66} +452884. q^{67} +(245798. - 255792. i) q^{68} +22771.6 q^{69} +(-70077.4 + 416490. i) q^{70} -246386. i q^{71} +(-145291. - 323105. i) q^{72} +476862. i q^{73} +(-44807.9 + 111299. i) q^{74} +(86389.3 - 39838.3i) q^{75} +(394964. - 411022. i) q^{76} -736539. i q^{77} +(16347.9 - 40606.7i) q^{78} +680467. i q^{79} +(-495329. + 129588. i) q^{80} +451744. q^{81} +(48970.4 + 19715.1i) q^{82} -1.03860e6 q^{83} +(-118665. - 114029. i) q^{84} +(676761. - 148528. i) q^{85} +(-601693. - 242237. i) q^{86} -189841. q^{87} +(814346. - 366189. i) q^{88} -937027. q^{89} +(114808. - 682339. i) q^{90} +379563. i q^{91} +(-172596. - 165853. i) q^{92} -137891. i q^{93} +(-224349. - 90321.0i) q^{94} +(1.08746e6 - 238663. i) q^{95} +(67077.6 - 187893. i) q^{96} +957172. i q^{97} +(450659. + 181431. i) q^{98} +1.20668e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 64 q^{4} + 460 q^{5} - 672 q^{6} + 1956 q^{9}+O(q^{10}) $ 12 * q + 64 * q^4 + 460 * q^5 - 672 * q^6 + 1956 * q^9	$ 12 q + 64 q^{4} + 460 q^{5} - 672 q^{6} + 1956 q^{9} + 2000 q^{10} + 512 q^{14} - 20928 q^{16} - 13760 q^{20} + 51216 q^{21} - 20928 q^{24} - 55700 q^{25} + 14496 q^{26} - 16072 q^{29} + 83520 q^{30} + 257216 q^{34} - 144960 q^{36} - 36800 q^{40} - 192136 q^{41} - 165120 q^{44} - 57180 q^{45} - 49472 q^{46} + 145796 q^{49} - 36000 q^{50} - 118656 q^{54} + 1078208 q^{56} - 902400 q^{60} + 215384 q^{61} - 6656 q^{64} + 710400 q^{65} - 1403520 q^{66} + 1015824 q^{69} + 530080 q^{70} - 1020384 q^{74} + 2515200 q^{76} - 127040 q^{80} - 2327652 q^{81} + 424704 q^{84} - 44800 q^{85} - 5268832 q^{86} - 4346152 q^{89} + 3582000 q^{90} + 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) $ 12 * q + 64 * q^4 + 460 * q^5 - 672 * q^6 + 1956 * q^9 + 2000 * q^10 + 512 * q^14 - 20928 * q^16 - 13760 * q^20 + 51216 * q^21 - 20928 * q^24 - 55700 * q^25 + 14496 * q^26 - 16072 * q^29 + 83520 * q^30 + 257216 * q^34 - 144960 * q^36 - 36800 * q^40 - 192136 * q^41 - 165120 * q^44 - 57180 * q^45 - 49472 * q^46 + 145796 * q^49 - 36000 * q^50 - 118656 * q^54 + 1078208 * q^56 - 902400 * q^60 + 215384 * q^61 - 6656 * q^64 + 710400 * q^65 - 1403520 * q^66 + 1015824 * q^69 + 530080 * q^70 - 1020384 * q^74 + 2515200 * q^76 - 127040 * q^80 - 2327652 * q^81 + 424704 * q^84 - 44800 * q^85 - 5268832 * q^86 - 4346152 * q^89 + 3582000 * q^90 + 4292992 * q^94 + 7673088 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	7.42116	+	2.98770i	0.927645	+	0.373462i
$2$	7.42116	+	2.98770i	0.927645	+	0.373462i
$3$	−6.08848			−0.225499			−0.112750	−	0.993623i	$-0.535966\pi$
$3$	−6.08848			−0.225499			−0.112750	+	0.993623i	$0.535966\pi$
$4$	46.1473	+	44.3444i	0.721052	+	0.692881i
$5$	26.7958	+	122.094i	0.214366	+	0.976753i
$5$	26.7958	+	122.094i	0.214366	+	0.976753i
$6$	−45.1836	−	18.1905i	−0.209184	−	0.0842155i
$7$	422.345			1.23133			0.615663	−	0.788010i	$-0.288888\pi$
$7$	422.345			1.23133			0.615663	+	0.788010i	$0.288888\pi$
$8$	209.979	+	466.961i	0.410116	+	0.912033i
$9$	−691.930			−0.949150
$10$	−165.925	+	986.138i	−0.165925	+	0.986138i
$11$		−	1743.93i		−	1.31024i	−0.755526	−	0.655119i	$-0.772618\pi$
$11$		−	1743.93i		−	1.31024i	0.755526	−	0.655119i	$-0.227382\pi$
$12$	−280.967	−	269.990i	−0.162597	−	0.156244i
$13$			898.704i			0.409060i	0.978860	+	0.204530i	$0.0655666\pi$
$13$			898.704i			0.409060i	−0.978860	+	0.204530i	$0.934433\pi$
$14$	3134.29	+	1261.84i	1.14223	+	0.459854i
$15$	−163.146	−	743.368i	−0.0483395	−	0.220257i
$16$	163.152	+	4092.75i	0.0398321	+	0.999206i
$17$		−	5542.94i		−	1.12822i	−0.825700	−	0.564110i	$-0.809219\pi$
$17$		−	5542.94i		−	1.12822i	0.825700	−	0.564110i	$-0.190781\pi$
$18$	−5134.93	−	2067.28i	−0.880475	−	0.354472i
$19$		−	8906.74i		−	1.29855i	−0.760554	−	0.649274i	$-0.775073\pi$
$19$		−	8906.74i		−	1.29855i	0.760554	−	0.649274i	$-0.224927\pi$
$20$	−4177.64	+	6822.56i	−0.522205	+	0.852820i
$21$	−2571.44			−0.277663
$22$	5210.33	−	12942.0i	0.489324	−	1.21544i
$23$	−3740.11			−0.307398			−0.153699	−	0.988118i	$-0.549119\pi$
$23$	−3740.11			−0.307398			−0.153699	+	0.988118i	$0.549119\pi$
$24$	−1278.46	−	2843.09i	−0.0924809	−	0.205663i
$25$	−14189.0	+	6543.22i	−0.908094	+	0.418766i
$26$	−2685.06	+	6669.43i	−0.152768	+	0.379462i
$27$	8651.31			0.439532
$28$	19490.1	+	18728.6i	0.887850	+	0.853162i
$29$	31180.3			1.27846			0.639229	−	0.769016i	$-0.279253\pi$
$29$	31180.3			1.27846			0.639229	+	0.769016i	$0.279253\pi$
$30$	1010.23	−	6004.09i	0.0374159	−	0.222374i
$31$			22647.9i			0.760227i	0.924940	+	0.380113i	$0.124115\pi$
$31$			22647.9i			0.760227i	−0.924940	+	0.380113i	$0.875885\pi$
$32$	−11017.1	+	30860.4i	−0.336216	+	0.941785i
$33$			10617.9i			0.295458i
$34$	16560.6	−	41135.1i	0.421347	−	1.04659i
$35$	11317.1	+	51565.8i	0.263955	+	1.20270i
$36$	−31930.7	−	30683.2i	−0.684387	−	0.657648i
$37$			14997.5i			0.296082i	0.988981	+	0.148041i	$0.0472968\pi$
$37$			14997.5i			0.296082i	−0.988981	+	0.148041i	$0.952703\pi$
$38$	26610.7	−	66098.4i	0.484959	−	1.20459i
$39$		−	5471.75i		−	0.0922427i
$40$	−51386.7	+	38149.8i	−0.802917	+	0.596091i
$41$	6598.75			0.0957436			0.0478718	−	0.998853i	$-0.484756\pi$
$41$	6598.75			0.0957436			0.0478718	+	0.998853i	$0.484756\pi$
$42$	−19083.1	−	7682.68i	−0.257573	−	0.103697i
$43$	−81078.0			−1.01976			−0.509880	−	0.860246i	$-0.670310\pi$
$43$	−81078.0			−1.01976			−0.509880	+	0.860246i	$0.670310\pi$
$44$	77333.4	−	80477.6i	0.907839	−	0.944750i
$45$	−18540.8	−	84480.7i	−0.203466	−	0.927085i
$46$	−27756.0	−	11174.3i	−0.285156	−	0.114802i
$47$	−30231.0			−0.291178			−0.145589	−	0.989345i	$-0.546508\pi$
$47$	−30231.0			−0.291178			−0.145589	+	0.989345i	$0.546508\pi$
$48$	−993.349	−	24918.6i	−0.00898211	−	0.225320i
$49$	60726.1			0.516164
$50$	−124848.	+	6165.93i	−0.998783	+	0.0493274i
$51$			33748.1i			0.254413i
$52$	−39852.5	+	41472.8i	−0.283430	+	0.294953i
$53$			17256.7i			0.115913i	0.998319	+	0.0579563i	$0.0184584\pi$
$53$			17256.7i			0.115913i	−0.998319	+	0.0579563i	$0.981542\pi$
$54$	64202.8	+	25847.5i	0.407730	+	0.164149i
$55$	212923.	−	46729.9i	1.27978	−	0.280871i
$56$	88683.7	+	197219.i	0.504986	+	1.12301i
$57$			54228.6i			0.292822i
$58$	231394.	+	93157.4i	1.18596	+	0.477456i
$59$		−	294323.i		−	1.43307i	−0.697550	−	0.716536i	$-0.745727\pi$
$59$		−	294323.i		−	1.43307i	0.697550	−	0.716536i	$-0.254273\pi$
$60$	25435.5	−	41539.1i	0.117757	−	0.192310i
$61$	−211992.			−0.933963			−0.466982	−	0.884267i	$-0.654659\pi$
$61$	−211992.			−0.933963			−0.466982	+	0.884267i	$0.654659\pi$
$62$	−67665.1	+	168074.i	−0.283916	+	0.705221i
$63$	−292233.			−1.16871
$64$	−173961.	+	196104.i	−0.663610	+	0.748079i
$65$	−109727.	+	24081.5i	−0.399550	+	0.0876886i
$66$	−31723.0	+	78797.0i	−0.110342	+	0.274080i
$67$	452884.			1.50578			0.752891	−	0.658145i	$-0.228659\pi$
$67$	452884.			1.50578			0.752891	+	0.658145i	$0.228659\pi$
$68$	245798.	−	255792.i	0.781722	−	0.813505i
$69$	22771.6			0.0693181
$70$	−70077.4	+	416490.i	−0.204307	+	1.21426i
$71$		−	246386.i		−	0.688401i	−0.938896	−	0.344201i	$-0.888150\pi$
$71$		−	246386.i		−	0.688401i	0.938896	−	0.344201i	$-0.111850\pi$
$72$	−145291.	−	323105.i	−0.389261	−	0.865657i
$73$			476862.i			1.22581i	0.790155	+	0.612907i	$0.210000\pi$
$73$			476862.i			1.22581i	−0.790155	+	0.612907i	$0.790000\pi$
$74$	−44807.9	+	111299.i	−0.110576	+	0.274659i
$75$	86389.3	−	39838.3i	0.204775	−	0.0944315i
$76$	394964.	−	411022.i	0.899740	−	0.936321i
$77$		−	736539.i		−	1.61333i
$78$	16347.9	−	40606.7i	0.0344492	−	0.0855686i
$79$			680467.i			1.38015i	0.723738	+	0.690075i	$0.242422\pi$
$79$			680467.i			1.38015i	−0.723738	+	0.690075i	$0.757578\pi$
$80$	−495329.	+	129588.i	−0.967440	+	0.253102i
$81$	451744.			0.850036
$82$	48970.4	+	19715.1i	0.0888161	+	0.0357566i
$83$	−1.03860e6			−1.81641			−0.908207	−	0.418521i	$-0.862549\pi$
$83$	−1.03860e6			−1.81641			−0.908207	+	0.418521i	$0.862549\pi$
$84$	−118665.	−	114029.i	−0.200210	−	0.192388i
$85$	676761.	−	148528.i	1.10199	−	0.241852i
$86$	−601693.	−	242237.i	−0.945975	−	0.380842i
$87$	−189841.			−0.288292
$88$	814346.	−	366189.i	1.19498	−	0.537349i
$89$	−937027.			−1.32918			−0.664588	−	0.747210i	$-0.731393\pi$
$89$	−937027.			−1.32918			−0.664588	+	0.747210i	$0.731393\pi$
$90$	114808.	−	682339.i	0.157487	−	0.935993i
$91$			379563.i			0.503686i
$92$	−172596.	−	165853.i	−0.221650	−	0.212990i
$93$		−	137891.i		−	0.171431i
$94$	−224349.	−	90321.0i	−0.270110	−	0.108744i
$95$	1.08746e6	−	238663.i	1.26836	−	0.278365i
$96$	67077.6	−	187893.i	0.0758165	−	0.212372i
$97$			957172.i			1.04876i	0.851485	+	0.524379i	$0.175702\pi$
$97$			957172.i			1.04876i	−0.851485	+	0.524379i	$0.824298\pi$
$98$	450659.	+	181431.i	0.478817	+	0.192768i
$99$			1.20668e6i			1.24361i
$100$	−944938.	−	327249.i	−0.944938	−	0.327249i
$101$	561162.			0.544658			0.272329	−	0.962204i	$-0.412206\pi$
$101$	561162.			0.544658			0.272329	+	0.962204i	$0.412206\pi$
$102$	−100829.	+	250450.i	−0.0950136	+	0.236005i
$103$	−649255.			−0.594161			−0.297080	−	0.954852i	$-0.596013\pi$
$103$	−649255.			−0.594161			−0.297080	+	0.954852i	$0.596013\pi$
$104$	−419660.	+	188709.i	−0.373076	+	0.167762i
$105$	−68903.7	−	313958.i	−0.0595216	−	0.271209i
$106$	−51557.9	+	128065.i	−0.0432890	+	0.107526i
$107$	1.01005e6			0.824501			0.412251	−	0.911070i	$-0.364743\pi$
$107$	1.01005e6			0.824501			0.412251	+	0.911070i	$0.364743\pi$
$108$	399235.	+	383637.i	0.316926	+	0.304543i
$109$	202984.			0.156741			0.0783703	−	0.996924i	$-0.475028\pi$
$109$	202984.			0.156741			0.0783703	+	0.996924i	$0.475028\pi$
$110$	1.71975e6	+	289360.i	1.29208	+	0.217401i
$111$		−	91311.8i		−	0.0667664i
$112$	68906.4	+	1.72855e6i	0.0490462	+	1.23035i
$113$			1.50469e6i			1.04283i	0.853305	+	0.521413i	$0.174595\pi$
$113$			1.50469e6i			1.04283i	−0.853305	+	0.521413i	$0.825405\pi$
$114$	−162019.	+	402439.i	−0.109358	+	0.271635i
$115$	−100219.	−	456646.i	−0.0658958	−	0.300252i
$116$	1.43889e6	+	1.38267e6i	0.921835	+	0.885820i
$117$		−	621841.i		−	0.388259i
$118$	879347.	−	2.18422e6i	0.535198	−	1.32938i
$119$		−	2.34103e6i		−	1.38921i
$120$	312867.	−	232275.i	0.181057	−	0.134418i
$121$	−1.26972e6			−0.716725
$122$	−1.57323e6	−	633368.i	−0.866387	−	0.348800i
$123$	−40176.4			−0.0215901
$124$	−1.00431e6	+	1.04514e6i	−0.526747	+	0.548163i
$125$	−1.17909e6	−	1.55706e6i	−0.603696	−	0.797215i
$126$	−2.16871e6	−	873104.i	−1.08415	−	0.436470i
$127$	−1.14744e6			−0.560168			−0.280084	−	0.959975i	$-0.590362\pi$
$127$	−1.14744e6			−0.560168			−0.280084	+	0.959975i	$0.590362\pi$
$128$	−1.87690e6	+	935578.i	−0.894974	+	0.446118i
$129$	493642.			0.229955
$130$	−886247.	−	149117.i	−0.403390	−	0.0678731i
$131$		−	2.85296e6i		−	1.26906i	−0.772899	−	0.634529i	$-0.781194\pi$
$131$		−	2.85296e6i		−	1.26906i	0.772899	−	0.634529i	$-0.218806\pi$
$132$	−470843.	+	489987.i	−0.204717	+	0.213041i
$133$		−	3.76172e6i		−	1.59894i
$134$	3.36092e6	+	1.35308e6i	1.39683	+	0.562353i
$135$	231819.	+	1.05627e6i	0.0942209	+	0.429315i
$136$	2.58834e6	−	1.16390e6i	1.02897	−	0.462701i
$137$			1.39333e6i			0.541866i	0.962598	+	0.270933i	$0.0873321\pi$
$137$			1.39333e6i			0.541866i	−0.962598	+	0.270933i	$0.912668\pi$
$138$	168992.	+	68034.7i	0.0643026	+	0.0258877i
$139$		−	489730.i		−	0.182353i	−0.995835	−	0.0911764i	$-0.970937\pi$
$139$		−	489730.i		−	0.182353i	0.995835	−	0.0911764i	$-0.0290627\pi$
$140$	−1.76440e6	+	2.88147e6i	−0.643004	+	1.05010i
$141$	184061.			0.0656605
$142$	736128.	−	1.82847e6i	0.257092	−	0.638592i
$143$	1.56727e6			0.535966
$144$	−112890.	−	2.83190e6i	−0.0378066	−	0.948397i
$145$	835501.	+	3.80694e6i	0.274058	+	1.24874i
$146$	−1.42472e6	+	3.53887e6i	−0.457795	+	1.13712i
$147$	−369730.			−0.116395
$148$	−665053.	+	692093.i	−0.205150	+	0.213491i
$149$	1.02592e6			0.310138			0.155069	−	0.987904i	$-0.450440\pi$
$149$	1.02592e6			0.310138			0.155069	+	0.987904i	$0.450440\pi$
$150$	760134.	−	37541.2i	0.225225	−	0.0111233i
$151$			4.68243e6i			1.36000i	0.733210	+	0.680002i	$0.238021\pi$
$151$			4.68243e6i			1.36000i	−0.733210	+	0.680002i	$0.761979\pi$
$152$	4.15910e6	−	1.87023e6i	1.18432	−	0.532555i
$153$			3.83533e6i			1.07085i
$154$	2.20055e6	−	5.46597e6i	0.602518	−	1.49660i
$155$	−2.76518e6	+	606869.i	−0.742554	+	0.162967i
$156$	242641.	−	252507.i	0.0639132	−	0.0665118i
$157$		−	3.46076e6i		−	0.894278i	−0.894464	−	0.447139i	$-0.852443\pi$
$157$		−	3.46076e6i		−	0.894278i	0.894464	−	0.447139i	$-0.147557\pi$
$158$	−2.03303e6	+	5.04986e6i	−0.515433	+	1.28029i
$159$		−	105067.i		−	0.0261382i
$160$	−4.06309e6	−	518197.i	−0.991965	−	0.126513i
$161$	−1.57962e6			−0.378507
$162$	3.35246e6	+	1.34967e6i	0.788532	+	0.317456i
$163$	5.02544e6			1.16041			0.580205	−	0.814471i	$-0.302972\pi$
$163$	5.02544e6			1.16041			0.580205	+	0.814471i	$0.302972\pi$
$164$	304514.	+	292617.i	0.0690361	+	0.0663389i
$165$	−1.29638e6	+	284514.i	−0.288590	+	0.0633362i
$166$	−7.70764e6	−	3.10303e6i	−1.68499	−	0.678362i
$167$	1.81735e6			0.390201			0.195101	−	0.980783i	$-0.437497\pi$
$167$	1.81735e6			0.390201			0.195101	+	0.980783i	$0.437497\pi$
$168$	−539949.	−	1.20076e6i	−0.113874	−	0.253238i
$169$	4.01914e6			0.832670
$170$	5.46611e6	+	919711.i	1.11258	+	0.187199i
$171$			6.16285e6i			1.23252i
$172$	−3.74153e6	−	3.59535e6i	−0.735300	−	0.706572i
$173$		−	2.12346e6i		−	0.410115i	−0.978750	−	0.205058i	$-0.934262\pi$
$173$		−	2.12346e6i		−	0.410115i	0.978750	−	0.205058i	$-0.0657382\pi$
$174$	−1.40884e6	−	567187.i	−0.267432	−	0.107666i
$175$	−5.99264e6	+	2.76349e6i	−1.11816	+	0.515637i
$176$	7.13746e6	−	284525.i	1.30920	−	0.0521895i
$177$			1.79198e6i			0.323157i
$178$	−6.95383e6	−	2.79955e6i	−1.23300	−	0.496397i
$179$		−	1.28491e6i		−	0.224034i	−0.993706	−	0.112017i	$-0.964269\pi$
$179$		−	1.28491e6i		−	0.224034i	0.993706	−	0.112017i	$-0.0357312\pi$
$180$	2.89063e6	−	4.72074e6i	0.495650	−	0.809454i
$181$	1.89832e6			0.320136			0.160068	−	0.987106i	$-0.448829\pi$
$181$	1.89832e6			0.320136			0.160068	+	0.987106i	$0.448829\pi$
$182$	−1.13402e6	+	2.81680e6i	−0.188108	+	0.467242i
$183$	1.29071e6			0.210608
$184$	−785346.	−	1.74649e6i	−0.126069	−	0.280357i
$185$	−1.83110e6	+	401869.i	−0.289199	+	0.0634700i
$186$	411978.	−	1.02332e6i	0.0640229	−	0.159027i
$187$	−9.66649e6			−1.47824
$188$	−1.39508e6	−	1.34057e6i	−0.209955	−	0.201752i
$189$	3.65384e6			0.541207
$190$	8.78328e6	+	1.47785e6i	1.28055	+	0.215461i
$191$		−	1.10365e7i		−	1.58391i	−0.610581	−	0.791954i	$-0.709064\pi$
$191$		−	1.10365e7i		−	1.58391i	0.610581	−	0.791954i	$-0.290936\pi$
$192$	1.05916e6	−	1.19398e6i	0.149644	−	0.168691i
$193$		−	9.60496e6i		−	1.33605i	−0.744137	−	0.668027i	$-0.767139\pi$
$193$		−	9.60496e6i		−	1.33605i	0.744137	−	0.668027i	$-0.232861\pi$
$194$	−2.85974e6	+	7.10333e6i	−0.391671	+	0.972875i
$195$	668068.	−	146620.i	0.0900984	−	0.0197737i
$196$	2.80235e6	+	2.69286e6i	0.372181	+	0.357640i
$197$			3.52707e6i			0.461334i	0.973033	+	0.230667i	$0.0740908\pi$
$197$			3.52707e6i			0.461334i	−0.973033	+	0.230667i	$0.925909\pi$
$198$	−3.60518e6	+	8.95494e6i	−0.464442	+	1.15363i
$199$			1.68919e6i			0.214347i	0.994240	+	0.107174i	$0.0341801\pi$
$199$			1.68919e6i			0.214347i	−0.994240	+	0.107174i	$0.965820\pi$
$200$	−6.03482e6	−	5.25176e6i	−0.754352	−	0.656470i
$201$	−2.75738e6			−0.339553
$202$	4.16448e6	+	1.67658e6i	0.505250	+	0.203409i
$203$	1.31688e7			1.57420
$204$	−1.49654e6	+	1.55739e6i	−0.176278	+	0.183445i
$205$	176819.	+	805668.i	0.0205242	+	0.0935179i
$206$	−4.81823e6	−	1.93978e6i	−0.551170	−	0.221897i
$207$	2.58790e6			0.291767
$208$	−3.67817e6	+	146625.i	−0.408735	+	0.0162937i
$209$	−1.55327e7			−1.70141
$210$	426665.	−	2.53580e6i	0.0460712	−	0.273814i
$211$		−	5.46799e6i		−	0.582077i	−0.956711	−	0.291038i	$-0.905999\pi$
$211$		−	5.46799e6i		−	0.582077i	0.956711	−	0.291038i	$-0.0940007\pi$
$212$	−765239.	+	796352.i	−0.0803136	+	0.0835790i
$213$			1.50012e6i			0.155234i
$214$	7.49574e6	+	3.01772e6i	0.764845	+	0.307920i
$215$	−2.17255e6	−	9.89915e6i	−0.218602	−	0.996053i
$216$	1.81660e6	+	4.03983e6i	0.180259	+	0.400868i
$217$			9.56523e6i			0.936087i
$218$	1.50637e6	+	606453.i	0.145400	+	0.0585367i
$219$		−	2.90337e6i		−	0.276420i
$220$	1.18981e7	+	7.28549e6i	1.11740	+	0.684212i
$221$	4.98147e6			0.461509
$222$	272812.	−	677640.i	0.0249347	−	0.0619355i
$223$	6.77154e6			0.610622			0.305311	−	0.952253i	$-0.401240\pi$
$223$	6.77154e6			0.610622			0.305311	+	0.952253i	$0.401240\pi$
$224$	−4.65302e6	+	1.30337e7i	−0.413991	+	1.15964i
$225$	9.81778e6	−	4.52745e6i	0.861918	−	0.397472i
$226$	−4.49556e6	+	1.11665e7i	−0.389456	+	0.967372i
$227$	−5.17157e6			−0.442125			−0.221062	−	0.975260i	$-0.570952\pi$
$227$	−5.17157e6			−0.442125			−0.221062	+	0.975260i	$0.570952\pi$
$228$	−2.40473e6	+	2.50250e6i	−0.202891	+	0.211140i
$229$	−1.14858e7			−0.956432			−0.478216	−	0.878242i	$-0.658716\pi$
$229$	−1.14858e7			−0.956432			−0.478216	+	0.878242i	$0.658716\pi$
$230$	620577.	−	3.68827e6i	0.0510049	−	0.303137i
$231$			4.48440e6i			0.363805i
$232$	6.54722e6	+	1.45600e7i	0.524316	+	1.16600i
$233$			611879.i			0.0483724i	0.999707	+	0.0241862i	$0.00769946\pi$
$233$			611879.i			0.0483724i	−0.999707	+	0.0241862i	$0.992301\pi$
$234$	1.85787e6	−	4.61478e6i	0.145000	−	0.360167i
$235$	−810063.	−	3.69103e6i	−0.0624188	−	0.284409i
$236$	1.30516e7	−	1.35822e7i	0.992948	−	1.03332i
$237$		−	4.14301e6i		−	0.311223i
$238$	6.99430e6	−	1.73732e7i	0.518816	−	1.28869i
$239$			1.88564e7i			1.38123i	0.723225	+	0.690613i	$0.242659\pi$
$239$			1.88564e7i			1.38123i	−0.723225	+	0.690613i	$0.757341\pi$
$240$	3.01580e6	−	788997.i	0.218157	−	0.0570744i
$241$	1.19579e7			0.854285			0.427143	−	0.904184i	$-0.359520\pi$
$241$	1.19579e7			0.854285			0.427143	+	0.904184i	$0.359520\pi$
$242$	−9.42281e6	−	3.79354e6i	−0.664866	−	0.267670i
$243$	−9.05724e6			−0.631215
$244$	−9.78286e6	−	9.40065e6i	−0.673436	−	0.647125i
$245$	1.62720e6	+	7.41431e6i	0.110648	+	0.504165i
$246$	−298155.	−	120035.i	−0.0200280	−	0.00806310i
$247$	8.00453e6			0.531184
$248$	−1.05757e7	+	4.75559e6i	−0.693352	+	0.311781i
$249$	6.32351e6			0.409600
$250$	−4.09822e6	−	1.50780e7i	−0.262286	−	0.964990i
$251$			4.43941e6i			0.280740i	0.990099	+	0.140370i	$0.0448292\pi$
$251$			4.43941e6i			0.280740i	−0.990099	+	0.140370i	$0.955171\pi$
$252$	−1.34858e7	−	1.29589e7i	−0.842703	−	0.809779i
$253$			6.52249e6i			0.402765i
$254$	−8.51533e6	−	3.42820e6i	−0.519637	−	0.209202i
$255$	−4.12045e6	+	904308.i	−0.248499	+	0.0545376i
$256$	−1.67240e7	+	1.33548e6i	−0.996827	+	0.0796009i
$257$		−	3.02099e7i		−	1.77971i	−0.456240	−	0.889857i	$-0.650804\pi$
$257$		−	3.02099e7i		−	1.77971i	0.456240	−	0.889857i	$-0.349196\pi$
$258$	3.66340e6	+	1.47485e6i	0.213317	+	0.0858796i
$259$			6.33410e6i			0.364574i
$260$	−6.13147e6	−	3.75446e6i	−0.348854	−	0.213613i
$261$	−2.15746e7			−1.21345
$262$	8.52378e6	−	2.11723e7i	0.473946	−	1.17724i
$263$	−2.91425e7			−1.60199			−0.800994	−	0.598673i	$-0.795695\pi$
$263$	−2.91425e7			−1.60199			−0.800994	+	0.598673i	$0.795695\pi$
$264$	−4.95813e6	+	2.22953e6i	−0.269468	+	0.121172i
$265$	−2.10695e6	+	462407.i	−0.113218	+	0.0248478i
$266$	1.12389e7	−	2.79163e7i	0.597142	−	1.48325i
$267$	5.70508e6			0.299728
$268$	2.08994e7	+	2.00828e7i	1.08575	+	1.04333i
$269$	2.25831e7			1.16018			0.580091	−	0.814552i	$-0.303017\pi$
$269$	2.25831e7			1.16018			0.580091	+	0.814552i	$0.303017\pi$
$270$	−1.43547e6	+	8.53139e6i	−0.0729292	+	0.433440i
$271$			7.50243e6i			0.376959i	0.982077	+	0.188479i	$0.0603559\pi$
$271$			7.50243e6i			0.376959i	−0.982077	+	0.188479i	$0.939644\pi$
$272$	2.26859e7	−	904343.i	1.12732	−	0.0449393i
$273$		−	2.31096e6i		−	0.113581i
$274$	−4.16284e6	+	1.03401e7i	−0.202366	+	0.502659i
$275$	1.14109e7	+	2.47445e7i	0.548683	+	1.18982i
$276$	1.05085e6	+	1.00979e6i	0.0499820	+	0.0480292i
$277$			2.36803e7i			1.11416i	0.830459	+	0.557080i	$0.188078\pi$
$277$			2.36803e7i			1.11416i	−0.830459	+	0.557080i	$0.811922\pi$
$278$	1.46317e6	−	3.63437e6i	0.0681019	−	0.169159i
$279$		−	1.56708e7i		−	0.721569i
$280$	−2.17029e7	+	1.61124e7i	−0.988652	+	0.733983i
$281$	2.22984e7			1.00498			0.502488	−	0.864584i	$-0.332418\pi$
$281$	2.22984e7			1.00498			0.502488	+	0.864584i	$0.332418\pi$
$282$	1.36595e6	+	549918.i	0.0609097	+	0.0245217i
$283$	−2.01491e6			−0.0888988			−0.0444494	−	0.999012i	$-0.514153\pi$
$283$	−2.01491e6			−0.0888988			−0.0444494	+	0.999012i	$0.514153\pi$
$284$	1.09258e7	−	1.13701e7i	0.476980	−	0.496373i
$285$	−6.62099e6	+	1.45310e6i	−0.286015	+	0.0627711i
$286$	1.16310e7	+	4.68254e6i	0.497186	+	0.200163i
$287$	2.78695e6			0.117892
$288$	7.62308e6	−	2.13533e7i	0.319119	−	0.893895i
$289$	−6.58667e6			−0.272880
$290$	−5.17358e6	+	3.07481e7i	−0.212128	+	1.26074i
$291$		−	5.82773e6i		−	0.236494i
$292$	−2.11462e7	+	2.20059e7i	−0.849343	+	0.883875i
$293$			3.19886e7i			1.27172i	0.771804	+	0.635861i	$0.219355\pi$
$293$			3.19886e7i			1.27172i	−0.771804	+	0.635861i	$0.780645\pi$
$294$	−2.74383e6	−	1.10464e6i	−0.107973	−	0.0434690i
$295$	3.59351e7	−	7.88661e6i	1.39976	−	0.307202i
$296$	−7.00323e6	+	3.14916e6i	−0.270037	+	0.121428i
$297$		−	1.50873e7i		−	0.575892i
$298$	7.61353e6	+	3.06514e6i	0.287698	+	0.115825i
$299$		−	3.36126e6i		−	0.125744i
$300$	5.75324e6	+	1.99245e6i	0.213083	+	0.0737945i
$301$	−3.42429e7			−1.25566
$302$	−1.39897e7	+	3.47491e7i	−0.507910	+	1.26160i
$303$	−3.41663e6			−0.122820
$304$	3.64531e7	−	1.45315e6i	1.29752	−	0.0517239i
$305$	−5.68049e6	−	2.58830e7i	−0.200210	−	0.912252i
$306$	−1.14588e7	+	2.84626e7i	−0.399922	+	0.993369i
$307$	1.45346e7			0.502328			0.251164	−	0.967945i	$-0.419187\pi$
$307$	1.45346e7			0.502328			0.251164	+	0.967945i	$0.419187\pi$
$308$	3.26613e7	−	3.39893e7i	1.11785	−	1.16330i
$309$	3.95298e6			0.133983
$310$	−2.23340e7	−	3.75785e6i	−0.749689	−	0.126140i
$311$		−	5.75145e6i		−	0.191204i	−0.995420	−	0.0956018i	$-0.969522\pi$
$311$		−	5.75145e6i		−	0.191204i	0.995420	−	0.0956018i	$-0.0304776\pi$
$312$	2.55509e6	−	1.14895e6i	0.0841285	−	0.0378302i
$313$		−	8.24901e6i		−	0.269010i	−0.990913	−	0.134505i	$-0.957056\pi$
$313$		−	8.24901e6i		−	0.269010i	0.990913	−	0.134505i	$-0.0429444\pi$
$314$	1.03397e7	−	2.56829e7i	0.333979	−	0.829573i
$315$	−7.83062e6	−	3.56800e7i	−0.250533	−	1.14154i
$316$	−3.01749e7	+	3.14018e7i	−0.956279	+	0.995159i
$317$			2.38162e7i			0.747643i	0.927501	+	0.373821i	$0.121953\pi$
$317$			2.38162e7i			0.747643i	−0.927501	+	0.373821i	$0.878047\pi$
$318$	313909.	−	779721.i	0.00976164	−	0.0242470i
$319$		−	5.43762e7i		−	1.67509i
$320$	−2.86046e7	−	1.59849e7i	−0.872944	−	0.487821i
$321$	−6.14967e6			−0.185925
$322$	−1.17226e7	−	4.71942e6i	−0.351121	−	0.141358i
$323$	−4.93696e7			−1.46505
$324$	2.08468e7	+	2.00323e7i	0.612920	+	0.588974i
$325$	−5.88042e6	−	1.27517e7i	−0.171300	−	0.371465i
$326$	3.72946e7	+	1.50145e7i	1.07645	+	0.433369i
$327$	−1.23586e6			−0.0353449
$328$	1.38560e6	+	3.08136e6i	0.0392660	+	0.0873214i
$329$	−1.27679e7			−0.358535
$330$	−1.04707e7	−	1.76177e6i	−0.291363	−	0.0490237i
$331$			467508.i			0.0128915i	0.999979	+	0.00644577i	$0.00205177\pi$
$331$			467508.i			0.0128915i	−0.999979	+	0.00644577i	$0.997948\pi$
$332$	−4.79287e7	−	4.60562e7i	−1.30973	−	1.25856i
$333$		−	1.03772e7i		−	0.281026i
$334$	1.34868e7	+	5.42968e6i	0.361968	+	0.145725i
$335$	1.21354e7	+	5.52945e7i	0.322789	+	1.47078i
$336$	−419536.	−	1.05243e7i	−0.0110599	−	0.277443i
$337$		−	2.14399e7i		−	0.560186i	−0.959973	−	0.280093i	$-0.909635\pi$
$337$		−	2.14399e7i		−	0.560186i	0.959973	−	0.280093i	$-0.0903653\pi$
$338$	2.98267e7	+	1.20080e7i	0.772423	+	0.310971i
$339$		−	9.16128e6i		−	0.235156i
$340$	3.78171e7	+	2.31564e7i	0.962169	+	0.589162i
$341$	3.94963e7			0.996078
$342$	−1.84127e7	+	4.57355e7i	−0.460299	+	1.14334i
$343$	−2.40411e7			−0.595760
$344$	−1.70247e7	−	3.78603e7i	−0.418219	−	0.930055i
$345$	610183.	+	2.78028e6i	0.0148595	+	0.0677067i
$346$	6.34425e6	−	1.57585e7i	0.153162	−	0.380441i
$347$	2.74539e7			0.657077			0.328538	−	0.944491i	$-0.393444\pi$
$347$	2.74539e7			0.657077			0.328538	+	0.944491i	$0.393444\pi$
$348$	−8.76065e6	−	8.41838e6i	−0.207873	−	0.199752i
$349$	5.59712e7			1.31670			0.658352	−	0.752710i	$-0.271254\pi$
$349$	5.59712e7			1.31670			0.658352	+	0.752710i	$0.271254\pi$
$350$	−5.27288e7	+	2.60415e6i	−1.22983	+	0.0607382i
$351$			7.77497e6i			0.179795i
$352$	5.38183e7	+	1.92131e7i	1.23396	+	0.440523i
$353$		−	2.18485e7i		−	0.496704i	−0.968670	−	0.248352i	$-0.920111\pi$
$353$		−	2.18485e7i		−	0.496704i	0.968670	−	0.248352i	$-0.0798889\pi$
$354$	−5.35389e6	+	1.32986e7i	−0.120687	+	0.299775i
$355$	3.00823e7	−	6.60211e6i	0.672398	−	0.147570i
$356$	−4.32413e7	−	4.15519e7i	−0.958404	−	0.920960i
$357$			1.42533e7i			0.313265i
$358$	3.83893e6	−	9.53554e6i	0.0836683	−	0.207824i
$359$			5.17942e7i			1.11943i	0.828685	+	0.559716i	$0.189090\pi$
$359$			5.17942e7i			1.11943i	−0.828685	+	0.559716i	$0.810910\pi$
$360$	3.55560e7	−	2.63970e7i	0.762088	−	0.565780i
$361$	−3.22842e7			−0.686228
$362$	1.40878e7	+	5.67162e6i	0.296973	+	0.119559i
$363$	7.73068e6			0.161621
$364$	−1.68315e7	+	1.75158e7i	−0.348994	+	0.363184i
$365$	−5.82221e7	+	1.27779e7i	−1.19732	+	0.262773i
$366$	9.57857e6	+	3.85625e6i	0.195370	+	0.0786542i
$367$	−6.56443e7			−1.32800			−0.664001	−	0.747732i	$-0.731143\pi$
$367$	−6.56443e7			−1.32800			−0.664001	+	0.747732i	$0.731143\pi$
$368$	−610207.	−	1.53073e7i	−0.0122443	−	0.307154i
$369$	−4.56587e6			−0.0908750
$370$	−1.47896e7	−	2.48845e6i	−0.291978	−	0.0491273i
$371$			7.28829e6i			0.142726i
$372$	6.11471e6	−	6.36332e6i	0.118781	−	0.123610i
$373$			8.58466e7i			1.65423i	0.562031	+	0.827116i	$0.310020\pi$
$373$			8.58466e7i			1.65423i	−0.562031	+	0.827116i	$0.689980\pi$
$374$	−7.17366e7	−	2.88806e7i	−1.37128	−	0.552066i
$375$	7.17889e6	+	9.48014e6i	0.136133	+	0.179771i
$376$	−6.34788e6	−	1.41167e7i	−0.119417	−	0.265564i
$377$			2.80219e7i			0.522966i
$378$	2.71157e7	+	1.09166e7i	0.502049	+	0.202120i
$379$			4.15395e7i			0.763034i	0.924362	+	0.381517i	$0.124598\pi$
$379$			4.15395e7i			0.763034i	−0.924362	+	0.381517i	$0.875402\pi$
$380$	6.07668e7	+	3.72091e7i	1.10743	+	0.678108i
$381$	6.98616e6			0.126318
$382$	3.29736e7	−	8.19034e7i	0.591530	−	1.46930i
$383$	4.94031e7			0.879343			0.439671	−	0.898159i	$-0.355095\pi$
$383$	4.94031e7			0.879343			0.439671	+	0.898159i	$0.355095\pi$
$384$	1.14275e7	−	5.69625e6i	0.201816	−	0.100599i
$385$	8.99271e7	−	1.97361e7i	1.57583	−	0.345844i
$386$	2.86967e7	−	7.12800e7i	0.498965	−	1.23938i
$387$	5.61003e7			0.967905
$388$	−4.24452e7	+	4.41709e7i	−0.726664	+	0.756208i
$389$	−2.48999e7			−0.423008			−0.211504	−	0.977377i	$-0.567836\pi$
$389$	−2.48999e7			−0.423008			−0.211504	+	0.977377i	$0.567836\pi$
$390$	5.39590e6	+	907897.i	0.0909641	+	0.0153053i
$391$			2.07312e7i			0.346813i
$392$	1.27512e7	+	2.83567e7i	0.211687	+	0.470759i
$393$			1.73702e7i			0.286172i
$394$	−1.05378e7	+	2.61750e7i	−0.172291	+	0.427955i
$395$	−8.30811e7	+	1.82337e7i	−1.34807	+	0.295857i
$396$	−5.35093e7	+	5.56849e7i	−0.861676	+	0.896710i
$397$		−	1.03578e8i		−	1.65537i	−0.561190	−	0.827687i	$-0.689656\pi$
$397$		−	1.03578e8i		−	1.65537i	0.561190	−	0.827687i	$-0.310344\pi$
$398$	−5.04678e6	+	1.25357e7i	−0.0800507	+	0.198838i
$399$			2.29032e7i			0.360559i
$400$	−2.90947e7	−	5.70044e7i	−0.454605	−	0.890693i
$401$	8.14381e7			1.26297			0.631487	−	0.775386i	$-0.282445\pi$
$401$	8.14381e7			1.26297			0.631487	+	0.775386i	$0.282445\pi$
$402$	−2.04629e7	−	8.23820e6i	−0.314985	−	0.126810i
$403$	−2.03538e7			−0.310978
$404$	2.58961e7	+	2.48844e7i	0.392727	+	0.377383i
$405$	1.21048e7	+	5.51553e7i	0.182219	+	0.830275i
$406$	9.77282e7	+	3.93445e7i	1.46030	+	0.587904i
$407$	2.61545e7			0.387938
$408$	−1.57591e7	+	7.08641e6i	−0.232033	+	0.104339i
$409$	−9.56658e7			−1.39826			−0.699128	−	0.714996i	$-0.746428\pi$
$409$	−9.56658e7			−1.39826			−0.699128	+	0.714996i	$0.746428\pi$
$410$	−1.09489e6	+	6.50728e6i	−0.0158862	+	0.0944165i
$411$		−	8.48325e6i		−	0.122190i
$412$	−2.99614e7	−	2.87908e7i	−0.428421	−	0.411683i
$413$		−	1.24306e8i		−	1.76458i
$414$	1.92052e7	+	7.73186e6i	0.270656	+	0.108964i
$415$	−2.78302e7	−	1.26807e8i	−0.389378	−	1.77419i
$416$	−2.77344e7	−	9.90113e6i	−0.385246	−	0.137532i
$417$			2.98171e6i			0.0411205i
$418$	−1.15271e8	−	4.64071e7i	−1.57830	−	0.635412i
$419$		−	2.42825e6i		−	0.0330105i	−0.999864	−	0.0165053i	$-0.994746\pi$
$419$		−	2.42825e6i		−	0.0330105i	0.999864	−	0.0165053i	$-0.00525402\pi$
$420$	1.07425e7	−	1.75438e7i	0.144997	−	0.236797i
$421$	−5.13368e7			−0.687991			−0.343995	−	0.938971i	$-0.611780\pi$
$421$	−5.13368e7			−0.687991			−0.343995	+	0.938971i	$0.611780\pi$
$422$	1.63367e7	−	4.05788e7i	0.217384	−	0.539961i
$423$	2.09177e7			0.276372
$424$	−8.05822e6	+	3.62355e6i	−0.105716	+	0.0475376i
$425$	3.62687e7	+	7.86487e7i	0.472460	+	1.02453i
$426$	−4.48190e6	+	1.11326e7i	−0.0579740	+	0.144002i
$427$	−8.95337e7			−1.15001
$428$	4.66111e7	+	4.47900e7i	0.594508	+	0.571281i
$429$	−9.54233e6			−0.120860
$430$	1.34528e7	−	7.99541e7i	0.169203	−	1.00562i
$431$		−	8.99001e7i		−	1.12287i	−0.827522	−	0.561434i	$-0.810250\pi$
$431$		−	8.99001e7i		−	1.12287i	0.827522	−	0.561434i	$-0.189750\pi$
$432$	1.41148e6	+	3.54077e7i	0.0175075	+	0.439183i
$433$		−	3.62806e7i		−	0.446900i	−0.974715	−	0.223450i	$-0.928268\pi$
$433$		−	3.62806e7i		−	0.446900i	0.974715	−	0.223450i	$-0.0717320\pi$
$434$	−2.85780e7	+	7.09851e7i	−0.349593	+	0.868357i
$435$	−5.08694e6	−	2.31785e7i	−0.0618000	−	0.281590i
$436$	9.36715e6	+	9.00118e6i	0.113018	+	0.108603i
$437$			3.33122e7i			0.399171i
$438$	8.67439e6	−	2.15464e7i	0.103232	−	0.256420i
$439$		−	2.02544e7i		−	0.239401i	−0.992810	−	0.119701i	$-0.961806\pi$
$439$		−	2.02544e7i		−	0.239401i	0.992810	−	0.119701i	$-0.0381935\pi$
$440$	6.65305e7	+	8.96146e7i	0.781022	+	1.05201i
$441$	−4.20183e7			−0.489917
$442$	3.69683e7	+	1.48831e7i	0.428117	+	0.172356i
$443$	1.42522e8			1.63935			0.819676	−	0.572828i	$-0.194154\pi$
$443$	1.42522e8			1.63935			0.819676	+	0.572828i	$0.194154\pi$
$444$	4.04916e6	−	4.21379e6i	0.0462612	−	0.0481420i
$445$	−2.51084e7	−	1.14406e8i	−0.284930	−	1.29828i
$446$	5.02527e7	+	2.02313e7i	0.566441	+	0.228044i
$447$	−6.24631e6			−0.0699360
$448$	−7.34717e7	+	8.28236e7i	−0.817120	+	0.921129i
$449$	−8.30869e7			−0.917896			−0.458948	−	0.888463i	$-0.651774\pi$
$449$	−8.30869e7			−0.917896			−0.458948	+	0.888463i	$0.651774\pi$
$450$	8.63860e7	−	4.26639e6i	0.947995	−	0.0468191i
$451$		−	1.15077e7i		−	0.125447i
$452$	−6.67245e7	+	6.94374e7i	−0.722554	+	0.751931i
$453$		−	2.85089e7i		−	0.306680i
$454$	−3.83790e7	−	1.54511e7i	−0.410135	−	0.165117i
$455$	−4.63424e7	+	1.01707e7i	−0.491977	+	0.107973i
$456$	−2.53226e7	+	1.13869e7i	−0.267063	+	0.120091i
$457$			1.72794e8i			1.81043i	0.424956	+	0.905214i	$0.360289\pi$
$457$			1.72794e8i			1.81043i	−0.424956	+	0.905214i	$0.639711\pi$
$458$	−8.52378e7	−	3.43160e7i	−0.887229	−	0.357191i
$459$		−	4.79537e7i		−	0.495889i
$460$	1.56248e7	−	2.55172e7i	0.160525	−	0.262155i
$461$	1.94634e7			0.198663			0.0993315	−	0.995054i	$-0.468330\pi$
$461$	1.94634e7			0.198663			0.0993315	+	0.995054i	$0.468330\pi$
$462$	−1.33980e7	+	3.32795e7i	−0.135867	+	0.337482i
$463$	1.61739e8			1.62957			0.814785	−	0.579763i	$-0.196855\pi$
$463$	1.61739e8			1.62957			0.814785	+	0.579763i	$0.196855\pi$
$464$	5.08714e6	+	1.27613e8i	0.0509236	+	1.27744i
$465$	1.68357e7	−	3.69491e6i	0.167446	−	0.0367490i
$466$	−1.82811e6	+	4.54085e6i	−0.0180653	+	0.0448725i
$467$	−5.34609e7			−0.524911			−0.262455	−	0.964944i	$-0.584532\pi$
$467$	−5.34609e7			−0.524911			−0.262455	+	0.964944i	$0.584532\pi$
$468$	2.75751e7	−	2.86963e7i	0.269017	−	0.279955i
$469$	1.91273e8			1.85411
$470$	5.01606e6	−	2.98119e7i	0.0483136	−	0.287142i
$471$			2.10708e7i			0.201659i
$472$	1.37437e8	−	6.18017e7i	1.30701	−	0.587725i
$473$			1.41394e8i			1.33613i
$474$	1.23781e7	−	3.07460e7i	0.116230	−	0.288704i
$475$	5.82788e7	+	1.26378e8i	0.543788	+	1.17920i
$476$	1.03812e8	−	1.08032e8i	0.962555	−	1.00169i
$477$		−	1.19404e7i		−	0.110018i
$478$	−5.63371e7	+	1.39936e8i	−0.515835	+	1.28129i
$479$			5.20964e7i			0.474024i	0.971507	+	0.237012i	$0.0761682\pi$
$479$			5.20964e7i			0.474024i	−0.971507	+	0.237012i	$0.923832\pi$
$480$	2.47381e7	+	3.15503e6i	0.223688	+	0.0285286i
$481$	−1.34783e7			−0.121115
$482$	8.87413e7	+	3.57265e7i	0.792474	+	0.319043i
$483$	9.61748e6			0.0853532
$484$	−5.85943e7	−	5.63050e7i	−0.516796	−	0.496605i
$485$	−1.16865e8	+	2.56482e7i	−1.02438	+	0.224818i
$486$	−6.72153e7	−	2.70603e7i	−0.585544	−	0.235735i
$487$	−4.49422e7			−0.389105			−0.194553	−	0.980892i	$-0.562326\pi$
$487$	−4.49422e7			−0.389105			−0.194553	+	0.980892i	$0.562326\pi$
$488$	−4.45139e7	−	9.89920e7i	−0.383033	−	0.851806i
$489$	−3.05973e7			−0.261672
$490$	−1.00760e7	+	5.98844e7i	−0.0856442	+	0.509009i
$491$		−	2.58692e7i		−	0.218543i	−0.994012	−	0.109272i	$-0.965148\pi$
$491$		−	2.58692e7i		−	0.218543i	0.994012	−	0.109272i	$-0.0348519\pi$
$492$	−1.85403e6	−	1.78160e6i	−0.0155676	−	0.0149594i
$493$		−	1.72831e8i		−	1.44238i
$494$	5.94029e7	+	2.39151e7i	0.492750	+	0.198377i
$495$	−1.47328e8	+	3.23338e7i	−1.21470	+	0.266589i
$496$	−9.26922e7	+	3.69506e6i	−0.759623	+	0.0302814i
$497$		−	1.04060e8i		−	0.847646i
$498$	4.69278e7	+	1.88927e7i	0.379964	+	0.152970i
$499$		−	2.14540e7i		−	0.172666i	−0.996266	−	0.0863329i	$-0.972485\pi$
$499$		−	2.14540e7i		−	0.172666i	0.996266	−	0.0863329i	$-0.0275149\pi$
$500$	1.46349e7	−	1.24140e8i	0.117079	−	0.993123i
$501$	−1.10649e7			−0.0879901
$502$	−1.32636e7	+	3.29456e7i	−0.104846	+	0.260427i
$503$	−1.02143e8			−0.802607			−0.401303	−	0.915945i	$-0.631443\pi$
$503$	−1.02143e8			−0.802607			−0.401303	+	0.915945i	$0.631443\pi$
$504$	−6.13629e7	−	1.36462e8i	−0.479308	−	1.06591i
$505$	1.50368e7	+	6.85146e7i	0.116756	+	0.531997i
$506$	−1.94872e7	+	4.84044e7i	−0.150417	+	0.373623i
$507$	−2.44705e7			−0.187767
$508$	−5.29512e7	−	5.08825e7i	−0.403910	−	0.388130i
$509$	1.68263e8			1.27595			0.637976	−	0.770056i	$-0.279772\pi$
$509$	1.68263e8			1.27595			0.637976	+	0.770056i	$0.279772\pi$
$510$	−3.32803e7	−	5.59964e6i	−0.250886	−	0.0422134i
$511$			2.01400e8i			1.50938i
$512$	−1.28101e8	−	4.00554e7i	−0.954430	−	0.298436i
$513$		−	7.70550e7i		−	0.570754i
$514$	9.02581e7	−	2.24193e8i	0.664656	−	1.65094i
$515$	−1.73973e7	−	7.92703e7i	−0.127368	−	0.580348i
$516$	2.27803e7	+	2.18903e7i	0.165810	+	0.159332i
$517$			5.27206e7i			0.381513i
$518$	−1.89244e7	+	4.70064e7i	−0.136155	+	0.338195i
$519$			1.29287e7i			0.0924807i
$520$	−3.42854e7	−	4.61814e7i	−0.243837	−	0.328441i
$521$	7.03931e7			0.497756			0.248878	−	0.968535i	$-0.419938\pi$
$521$	7.03931e7			0.497756			0.248878	+	0.968535i	$0.419938\pi$
$522$	−1.60109e8	−	6.44584e7i	−1.12565	−	0.453177i
$523$	1.32429e7			0.0925719			0.0462859	−	0.998928i	$-0.485261\pi$
$523$	1.32429e7			0.0925719			0.0462859	+	0.998928i	$0.485261\pi$
$524$	1.26513e8	−	1.31656e8i	0.879307	−	0.915058i
$525$	3.64861e7	−	1.68255e7i	0.252144	−	0.116276i
$526$	−2.16271e8	−	8.70689e7i	−1.48608	−	0.598282i
$527$	1.25536e8			0.857703
$528$	−4.34563e7	+	1.73233e6i	−0.295224	+	0.0117687i
$529$	−1.34047e8			−0.905506
$530$	−1.70175e7	−	2.86331e6i	−0.114306	−	0.0192327i
$531$			2.03651e8i			1.36020i
$532$	1.66811e8	−	1.73593e8i	1.10787	−	1.15292i
$533$			5.93032e6i			0.0391649i
$534$	4.23383e7	+	1.70450e7i	0.278042	+	0.111937i
$535$	2.70651e7	+	1.23321e8i	0.176745	+	0.805334i
$536$	9.50962e7	+	2.11479e8i	0.617545	+	1.37332i
$537$			7.82317e6i			0.0505196i
$538$	1.67593e8	+	6.74713e7i	1.07624	+	0.433284i
$539$		−	1.05902e8i		−	0.676297i
$540$	−3.61420e7	+	5.90241e7i	−0.229526	+	0.374842i
$541$	8.75392e6			0.0552855			0.0276427	−	0.999618i	$-0.491200\pi$
$541$	8.75392e6			0.0552855			0.0276427	+	0.999618i	$0.491200\pi$
$542$	−2.24150e7	+	5.56767e7i	−0.140780	+	0.349684i
$543$	−1.15579e7			−0.0721905
$544$	1.71058e8	+	6.10673e7i	1.06254	+	0.379325i
$545$	5.43910e6	+	2.47831e7i	0.0335999	+	0.153097i
$546$	6.90446e6	−	1.71500e7i	0.0424182	−	0.105363i
$547$	−1.27352e8			−0.778114			−0.389057	−	0.921214i	$-0.627199\pi$
$547$	−1.27352e8			−0.778114			−0.389057	+	0.921214i	$0.627199\pi$
$548$	−6.17862e7	+	6.42983e7i	−0.375448	+	0.390713i
$549$	1.46684e8			0.886471
$550$	1.07529e7	+	2.17726e8i	0.0646307	+	1.30864i
$551$		−	2.77715e8i		−	1.66014i
$552$	4.78157e6	+	1.06335e7i	0.0284284	+	0.0632204i
$553$			2.87392e8i			1.69941i
$554$	−7.07495e7	+	1.75735e8i	−0.416096	+	1.03354i
$555$	1.11486e7	−	2.44677e6i	0.0652143	−	0.0143125i
$556$	2.17168e7	−	2.25997e7i	0.126349	−	0.131486i
$557$		−	2.82592e8i		−	1.63529i	−0.575723	−	0.817645i	$-0.695279\pi$
$557$		−	2.82592e8i		−	1.63529i	0.575723	−	0.817645i	$-0.304721\pi$
$558$	4.68196e7	−	1.16295e8i	0.269479	−	0.669360i
$559$		−	7.28652e7i		−	0.417143i
$560$	−2.09200e8	+	5.47310e7i	−1.19123	+	0.311651i
$561$	5.88543e7			0.333342
$562$	1.65480e8	+	6.66210e7i	0.932261	+	0.375320i
$563$	−2.23747e7			−0.125381			−0.0626905	−	0.998033i	$-0.519968\pi$
$563$	−2.23747e7			−0.125381			−0.0626905	+	0.998033i	$0.519968\pi$
$564$	8.49392e6	+	8.16207e6i	0.0473446	+	0.0454949i
$565$	−1.83714e8	+	4.03193e7i	−1.01858	+	0.223547i
$566$	−1.49530e7	−	6.01993e6i	−0.0824665	−	0.0332003i
$567$	1.90792e8			1.04667
$568$	1.15053e8	−	5.17360e7i	0.627845	−	0.282324i
$569$	−2.06789e8			−1.12251			−0.561256	−	0.827642i	$-0.689682\pi$
$569$	−2.06789e8			−1.12251			−0.561256	+	0.827642i	$0.689682\pi$
$570$	−5.34769e7	−	8.99785e6i	−0.288763	−	0.0485864i
$571$		−	1.67454e8i		−	0.899473i	−0.893161	−	0.449737i	$-0.851518\pi$
$571$		−	1.67454e8i		−	0.899473i	0.893161	−	0.449737i	$-0.148482\pi$
$572$	7.23256e7	+	6.94998e7i	0.386459	+	0.371360i
$573$			6.71954e7i			0.357170i
$574$	2.06824e7	+	8.32655e6i	0.109362	+	0.0440280i
$575$	5.30684e7	−	2.44724e7i	0.279146	−	0.128728i
$576$	1.20369e8	−	1.35691e8i	0.629865	−	0.710039i
$577$			1.29395e8i			0.673583i	0.941579	+	0.336792i	$0.109342\pi$
$577$			1.29395e8i			0.673583i	−0.941579	+	0.336792i	$0.890658\pi$
$578$	−4.88807e7	−	1.96790e7i	−0.253136	−	0.101910i
$579$			5.84797e7i			0.301279i
$580$	−1.30260e8	+	2.12730e8i	−0.667617	+	1.09030i
$581$	−4.38648e8			−2.23660
$582$	1.74115e7	−	4.32485e7i	0.0883216	−	0.219383i
$583$	3.00945e7			0.151873
$584$	−2.22676e8	+	1.00131e8i	−1.11798	+	0.502725i
$585$	7.59231e7	−	1.66627e7i	0.379233	−	0.0832296i
$586$	−9.55722e7	+	2.37393e8i	−0.474940	+	1.17971i
$587$	1.84946e8			0.914386			0.457193	−	0.889367i	$-0.348855\pi$
$587$	1.84946e8			0.914386			0.457193	+	0.889367i	$0.348855\pi$
$588$	−1.70621e7	−	1.63955e7i	−0.0839266	−	0.0806476i
$589$	2.01719e8			0.987191
$590$	2.90243e8	+	4.88354e7i	1.41321	+	0.237782i
$591$		−	2.14745e7i		−	0.104031i
$592$	−6.13808e7	+	2.44687e6i	−0.295847	+	0.0117936i
$593$		−	1.51763e8i		−	0.727784i	−0.931441	−	0.363892i	$-0.881448\pi$
$593$		−	1.51763e8i		−	0.727784i	0.931441	−	0.363892i	$-0.118552\pi$
$594$	4.50762e7	−	1.11965e8i	0.215074	−	0.534224i
$595$	2.85827e8	−	6.27298e7i	1.35691	−	0.297799i
$596$	4.73436e7	+	4.54939e7i	0.223626	+	0.214889i
$597$		−	1.02846e7i		−	0.0483352i
$598$	1.00424e7	−	2.49444e7i	0.0469607	−	0.116646i
$599$		−	2.67870e8i		−	1.24636i	−0.782079	−	0.623180i	$-0.785841\pi$
$599$		−	2.67870e8i		−	1.24636i	0.782079	−	0.623180i	$-0.214159\pi$
$600$	3.67429e7	+	3.19752e7i	0.170106	+	0.148034i
$601$	2.92898e8			1.34925			0.674626	−	0.738160i	$-0.264305\pi$
$601$	2.92898e8			1.34925			0.674626	+	0.738160i	$0.264305\pi$
$602$	−2.54122e8	−	1.02307e8i	−1.16480	−	0.468940i
$603$	−3.13364e8			−1.42921
$604$	−2.07639e8	+	2.16082e8i	−0.942322	+	0.980634i
$605$	−3.40232e7	−	1.55026e8i	−0.153642	−	0.700063i
$606$	−2.53553e7	−	1.02078e7i	−0.113934	−	0.0458687i
$607$	−2.54116e8			−1.13623			−0.568115	−	0.822949i	$-0.692327\pi$
$607$	−2.54116e8			−1.13623			−0.568115	+	0.822949i	$0.692327\pi$
$608$	2.74866e8	+	9.81267e7i	1.22295	+	0.436592i
$609$	−8.01783e7			−0.354981
$610$	3.51747e7	−	2.09053e8i	0.154967	−	0.921017i
$611$		−	2.71687e7i		−	0.119109i
$612$	−1.70075e8	+	1.76990e8i	−0.741972	+	0.772139i
$613$		−	3.65576e7i		−	0.158707i	−0.996847	−	0.0793534i	$-0.974714\pi$
$613$		−	3.65576e7i		−	0.158707i	0.996847	−	0.0793534i	$-0.0252856\pi$
$614$	1.07864e8	+	4.34249e7i	0.465982	+	0.187601i
$615$	−1.07656e6	−	4.90530e6i	−0.00462819	−	0.0210882i
$616$	3.43935e8	−	1.54658e8i	1.47141	−	0.661652i
$617$			1.37267e8i			0.584400i	0.956357	+	0.292200i	$0.0943872\pi$
$617$			1.37267e8i			0.584400i	−0.956357	+	0.292200i	$0.905613\pi$
$618$	2.93357e7	+	1.18103e7i	0.124289	+	0.0500375i
$619$			2.41038e8i			1.01628i	0.861275	+	0.508140i	$0.169667\pi$
$619$			2.41038e8i			1.01628i	−0.861275	+	0.508140i	$0.830333\pi$
$620$	−1.54517e8	−	9.46148e7i	−0.648337	−	0.396994i
$621$	−3.23569e7			−0.135111
$622$	1.71836e7	−	4.26825e7i	0.0714073	−	0.177369i
$623$	−3.95749e8			−1.63665
$624$	2.23945e7	−	892727.i	0.0921695	−	0.00367422i
$625$	1.58513e8	−	1.85683e8i	0.649270	−	0.760558i
$626$	2.46455e7	−	6.12172e7i	0.100465	−	0.249546i
$627$	9.45707e7			0.383667
$628$	1.53465e8	−	1.59705e8i	0.619628	−	0.644821i
$629$	8.31301e7			0.334046
$630$	4.84887e7	−	2.88182e8i	0.193918	−	1.15251i
$631$			2.23847e8i			0.890968i	0.895290	+	0.445484i	$0.146968\pi$
$631$			2.23847e8i			0.890968i	−0.895290	+	0.445484i	$0.853032\pi$
$632$	−3.17752e8	+	1.42884e8i	−1.25874	+	0.566021i
$633$			3.32918e7i			0.131258i
$634$	−7.11555e7	+	1.76744e8i	−0.279216	+	0.693547i
$635$	−3.07465e7	−	1.40096e8i	−0.120081	−	0.547146i
$636$	4.65914e6	−	4.84857e6i	0.0181107	−	0.0188470i
$637$			5.45748e7i			0.211142i
$638$	1.62460e8	−	4.03535e8i	0.625581	−	1.55389i
$639$			1.70482e8i			0.653396i
$640$	−1.64522e8	−	2.04089e8i	−0.627600	−	0.778536i
$641$	5.85061e7			0.222140			0.111070	−	0.993813i	$-0.464572\pi$
$641$	5.85061e7			0.222140			0.111070	+	0.993813i	$0.464572\pi$
$642$	−4.56377e7	−	1.83734e7i	−0.172472	−	0.0694358i
$643$	−2.24198e7			−0.0843331			−0.0421666	−	0.999111i	$-0.513426\pi$
$643$	−2.24198e7			−0.0843331			−0.0421666	+	0.999111i	$0.513426\pi$
$644$	−7.28951e7	−	7.00472e7i	−0.272923	−	0.262260i
$645$	1.32275e7	+	6.02708e7i	0.0492946	+	0.224609i
$646$	−3.66380e8	−	1.47501e8i	−1.35905	−	0.547140i
$647$	1.77477e8			0.655283			0.327641	−	0.944802i	$-0.393746\pi$
$647$	1.77477e8			0.655283			0.327641	+	0.944802i	$0.393746\pi$
$648$	9.48569e7	+	2.10947e8i	0.348613	+	0.775261i
$649$	−5.13278e8			−1.87767
$650$	−5.54135e6	−	1.12201e8i	−0.0201779	−	0.408562i
$651$		−	5.82378e7i		−	0.211087i
$652$	2.31911e8	+	2.22850e8i	0.836716	+	0.804026i
$653$			3.43085e8i			1.23215i	0.787689	+	0.616073i	$0.211277\pi$
$653$			3.43085e8i			1.23215i	−0.787689	+	0.616073i	$0.788723\pi$
$654$	−9.17153e6	−	3.69238e6i	−0.0327875	−	0.0132000i
$655$	3.48330e8	−	7.64473e7i	1.23956	−	0.272043i
$656$	1.07660e6	+	2.70070e7i	0.00381366	+	0.0956676i
$657$		−	3.29955e8i		−	1.16348i
$658$	−9.47527e7	−	3.81466e7i	−0.332594	−	0.133899i
$659$			2.57705e8i			0.900465i	0.892911	+	0.450233i	$0.148659\pi$
$659$			2.57705e8i			0.900465i	−0.892911	+	0.450233i	$0.851341\pi$
$660$	−7.24411e7	−	4.43576e7i	−0.251973	−	0.154290i
$661$	1.58848e8			0.550018			0.275009	−	0.961442i	$-0.411319\pi$
$661$	1.58848e8			0.550018			0.275009	+	0.961442i	$0.411319\pi$
$662$	−1.39677e6	+	3.46945e6i	−0.00481450	+	0.0119588i
$663$	−3.03296e7			−0.104070
$664$	−2.18085e8	−	4.84987e8i	−0.744940	−	1.65663i
$665$	4.59284e8	−	1.00798e8i	1.56177	−	0.342758i
$666$	3.10039e7	−	7.70109e7i	0.104953	−	0.260693i
$667$	−1.16618e8			−0.392996
$668$	8.38657e7	+	8.05891e7i	0.281355	+	0.270363i
$669$	−4.12284e7			−0.137695
$670$	−7.51445e7	+	4.46606e8i	−0.249846	+	1.48491i
$671$			3.69699e8i			1.22371i
$672$	2.83299e7	−	7.93557e7i	0.0933548	−	0.261499i
$673$		−	2.76715e8i		−	0.907793i	−0.891054	−	0.453897i	$-0.850034\pi$
$673$		−	2.76715e8i		−	0.907793i	0.891054	−	0.453897i	$-0.149966\pi$
$674$	6.40558e7	−	1.59109e8i	0.209208	−	0.519654i
$675$	−1.22753e8	+	5.66074e7i	−0.399137	+	0.184061i
$676$	1.85473e8	+	1.78226e8i	0.600398	+	0.576941i
$677$			4.19801e8i			1.35294i	0.736472	+	0.676468i	$0.236490\pi$
$677$			4.19801e8i			1.35294i	−0.736472	+	0.676468i	$0.763510\pi$
$678$	2.73711e7	−	6.79873e7i	0.0878220	−	0.218142i
$679$			4.04257e8i			1.29136i
$680$	2.11462e8	+	2.84833e8i	0.672522	+	0.905867i
$681$	3.14870e7			0.0996988
$682$	2.93109e8	+	1.18003e8i	0.924008	+	0.371998i
$683$	−9.99621e7			−0.313742			−0.156871	−	0.987619i	$-0.550141\pi$
$683$	−9.99621e7			−0.313742			−0.156871	+	0.987619i	$0.550141\pi$
$684$	−2.73288e8	+	2.84399e8i	−0.853988	+	0.888709i
$685$	−1.70117e8	+	3.73353e7i	−0.529269	+	0.116158i
$686$	−1.78413e8	−	7.18275e7i	−0.552654	−	0.222494i
$687$	6.99310e7			0.215675
$688$	−1.32280e7	−	3.31832e8i	−0.0406191	−	1.01895i
$689$	−1.55087e7			−0.0474152
$690$	−3.77837e6	+	2.24560e7i	−0.0115016	+	0.0683572i
$691$		−	2.78223e8i		−	0.843254i	−0.906769	−	0.421627i	$-0.861459\pi$
$691$		−	2.78223e8i		−	0.843254i	0.906769	−	0.421627i	$-0.138541\pi$
$692$	9.41635e7	−	9.79920e7i	0.284161	−	0.295714i
$693$			5.09633e8i			1.53129i
$694$	2.03740e8	+	8.20241e7i	0.609534	+	0.245393i
$695$	5.97932e7	−	1.31227e7i	0.178114	−	0.0390903i
$696$	−3.98627e7	−	8.86483e7i	−0.118233	−	0.262932i
$697$		−	3.65765e7i		−	0.108020i
$698$	4.15372e8	+	1.67225e8i	1.22144	+	0.491739i
$699$		−	3.72542e6i		−	0.0109080i
$700$	−3.99090e8	−	1.38212e8i	−1.16353	−	0.402950i
$701$	1.43797e8			0.417443			0.208721	−	0.977975i	$-0.433070\pi$
$701$	1.43797e8			0.417443			0.208721	+	0.977975i	$0.433070\pi$
$702$	−2.32293e7	+	5.76993e7i	−0.0671466	+	0.166786i
$703$	1.33579e8			0.384477
$704$	3.41992e8	+	3.03376e8i	0.980161	+	0.869487i
$705$	4.93206e6	+	2.24728e7i	0.0140754	+	0.0641341i
$706$	6.52767e7	−	1.62141e8i	0.185500	−	0.460765i
$707$	2.37004e8			0.670652
$708$	−7.94642e7	+	8.26951e7i	−0.223909	+	0.233013i
$709$	3.30939e8			0.928558			0.464279	−	0.885689i	$-0.346314\pi$
$709$	3.30939e8			0.928558			0.464279	+	0.885689i	$0.346314\pi$
$710$	2.42971e8	+	4.08815e7i	0.678859	+	0.114223i
$711$		−	4.70836e8i		−	1.30997i
$712$	−1.96756e8	−	4.37555e8i	−0.545116	−	1.21225i
$713$		−	8.47058e7i		−	0.233692i
$714$	−4.25847e7	+	1.05776e8i	−0.116993	+	0.290599i
$715$	4.19964e7	+	1.91355e8i	0.114893	+	0.523506i
$716$	5.69786e7	−	5.92953e7i	0.155229	−	0.161540i
$717$		−	1.14807e8i		−	0.311466i
$718$	−1.54745e8	+	3.84373e8i	−0.418065	+	1.03844i
$719$		−	3.88053e8i		−	1.04401i	−0.852943	−	0.522004i	$-0.825185\pi$
$719$		−	3.88053e8i		−	1.04401i	0.852943	−	0.522004i	$-0.174815\pi$
$720$	3.42733e8	−	8.96661e7i	0.918245	−	0.240232i
$721$	−2.74210e8			−0.731605
$722$	−2.39586e8	−	9.64555e7i	−0.636577	−	0.256280i
$723$	−7.28053e7			−0.192641
$724$	8.76026e7	+	8.41800e7i	0.230835	+	0.221816i
$725$	−4.42417e8	+	2.04020e8i	−1.16096	+	0.535375i
$726$	5.73706e7	+	2.30969e7i	0.149927	+	0.0603593i
$727$	−6.94954e8			−1.80864			−0.904322	−	0.426852i	$-0.859623\pi$
$727$	−6.94954e8			−1.80864			−0.904322	+	0.426852i	$0.859623\pi$
$728$	−1.77241e8	+	7.97004e7i	−0.459378	+	0.206570i
$729$	−2.74176e8			−0.707697
$730$	−4.70252e8	−	7.91232e7i	−1.20882	−	0.203393i
$731$			4.49411e8i			1.15051i
$732$	5.95628e7	+	5.72357e7i	0.151859	+	0.145926i
$733$		−	6.03758e8i		−	1.53303i	−0.642226	−	0.766515i	$-0.721989\pi$
$733$		−	6.03758e8i		−	1.53303i	0.642226	−	0.766515i	$-0.278011\pi$
$734$	−4.87157e8	−	1.96125e8i	−1.23191	−	0.495958i
$735$	−9.90721e6	−	4.51419e7i	−0.0249511	−	0.113689i
$736$	4.12053e7	−	1.15421e8i	0.103352	−	0.289503i
$737$		−	7.89796e8i		−	1.97293i
$738$	−3.38841e7	−	1.36414e7i	−0.0842998	−	0.0339384i
$739$		−	7.73026e8i		−	1.91540i	−0.287760	−	0.957702i	$-0.592911\pi$
$739$		−	7.73026e8i		−	1.91540i	0.287760	−	0.957702i	$-0.407089\pi$
$740$	−1.02321e8	−	6.26539e7i	−0.252505	−	0.154616i
$741$	−4.87355e7			−0.119782
$742$	−2.17752e7	+	5.40876e7i	−0.0533028	+	0.132399i
$743$	6.42826e7			0.156721			0.0783605	−	0.996925i	$-0.475031\pi$
$743$	6.42826e7			0.156721			0.0783605	+	0.996925i	$0.475031\pi$
$744$	6.43900e7	−	2.89544e7i	0.156351	−	0.0703064i
$745$	2.74904e7	+	1.25259e8i	0.0664832	+	0.302929i
$746$	−2.56484e8	+	6.37082e8i	−0.617793	+	1.53454i
$747$	7.18640e8			1.72405
$748$	−4.46083e8	−	4.28655e8i	−1.06589	−	1.02424i
$749$	4.26589e8			1.01523
$750$	2.49519e7	+	9.18020e7i	0.0591454	+	0.217605i
$751$		−	6.17586e8i		−	1.45807i	−0.684477	−	0.729034i	$-0.739970\pi$
$751$		−	6.17586e8i		−	1.45807i	0.684477	−	0.729034i	$-0.260030\pi$
$752$	−4.93225e6	−	1.23728e8i	−0.0115982	−	0.290947i
$753$		−	2.70293e7i		−	0.0633067i
$754$	−8.37209e7	+	2.07955e8i	−0.195308	+	0.485127i
$755$	−5.71697e8	+	1.25469e8i	−1.32839	+	0.291539i
$756$	1.68615e8	+	1.62027e8i	0.390239	+	0.374992i
$757$			3.20889e8i			0.739719i	0.929088	+	0.369859i	$0.120594\pi$
$757$			3.20889e8i			0.739719i	−0.929088	+	0.369859i	$0.879406\pi$
$758$	−1.24107e8	+	3.08271e8i	−0.284964	+	0.707825i
$759$		−	3.97121e7i		−	0.0908232i
$760$	3.39791e8	+	4.57688e8i	0.774053	+	1.04263i
$761$	−7.08784e7			−0.160827			−0.0804136	−	0.996762i	$-0.525624\pi$
$761$	−7.08784e7			−0.160827			−0.0804136	+	0.996762i	$0.525624\pi$
$762$	5.18455e7	+	2.08725e7i	0.117178	+	0.0471748i
$763$	8.57290e7			0.192999
$764$	4.89405e8	−	5.09303e8i	1.09746	−	1.14208i
$765$	−4.68272e8	+	1.02771e8i	−1.04596	+	0.229554i
$766$	3.66629e8	+	1.47602e8i	0.815718	+	0.328401i
$767$	2.64509e8			0.586212
$768$	1.01824e8	−	8.13106e6i	0.224784	−	0.0179500i
$769$	2.07387e8			0.456040			0.228020	−	0.973656i	$-0.426775\pi$
$769$	2.07387e8			0.456040			0.228020	+	0.973656i	$0.426775\pi$
$770$	7.26329e8	+	1.22210e8i	1.59097	+	0.267691i
$771$			1.83933e8i			0.401324i
$772$	4.25926e8	−	4.43243e8i	0.925726	−	0.963364i
$773$			4.62098e8i			1.00045i	0.865895	+	0.500226i	$0.166750\pi$
$773$			4.62098e8i			1.00045i	−0.865895	+	0.500226i	$0.833250\pi$
$774$	4.16330e8	+	1.67611e8i	0.897872	+	0.361476i
$775$	−1.48190e8	−	3.21351e8i	−0.318357	−	0.690358i
$776$	−4.46962e8	+	2.00986e8i	−0.956502	+	0.430112i
$777$		−	3.85651e7i		−	0.0822112i
$778$	−1.84786e8	−	7.43934e7i	−0.392402	−	0.157978i
$779$		−	5.87733e7i		−	0.124328i
$780$	3.73313e7	+	2.28590e7i	0.0786665	+	0.0481696i
$781$	−4.29680e8			−0.901970
$782$	−6.19387e7	+	1.53850e8i	−0.129521	+	0.321719i
$783$	2.69751e8			0.561924
$784$	9.90760e6	+	2.48537e8i	0.0205599	+	0.515754i
$785$	4.22539e8	−	9.27338e7i	0.873489	−	0.191703i
$786$	−5.18969e7	+	1.28907e8i	−0.106874	+	0.265466i
$787$	−6.57367e8			−1.34860			−0.674301	−	0.738457i	$-0.735555\pi$
$787$	−6.57367e8			−1.34860			−0.674301	+	0.738457i	$0.735555\pi$
$788$	−1.56406e8	+	1.62765e8i	−0.319650	+	0.332646i
$789$	1.77433e8			0.361247
$790$	−6.71035e8	−	1.12906e8i	−1.36102	−	0.229001i
$791$			6.35498e8i			1.28406i
$792$	−5.63471e8	+	2.53377e8i	−1.13422	+	0.510025i
$793$		−	1.90518e8i		−	0.382047i
$794$	3.09460e8	−	7.68669e8i	0.618219	−	1.53560i
$795$	1.28281e7	−	2.81536e6i	0.0255306	−	0.00560315i
$796$	−7.49059e7	+	7.79515e7i	−0.148517	+	0.154556i
$797$			3.81335e8i			0.753238i	0.926368	+	0.376619i	$0.122913\pi$
$797$			3.81335e8i			0.753238i	−0.926368	+	0.376619i	$0.877087\pi$
$798$	−6.84277e7	+	1.69968e8i	−0.134655	+	0.334471i
$799$			1.67569e8i			0.328513i
$800$	−4.56048e7	−	5.09965e8i	−0.0890719	−	0.996025i
$801$	6.48358e8			1.26159
$802$	6.04366e8	+	2.43313e8i	1.17159	+	0.471673i
$803$	8.31613e8			1.60611
$804$	−1.27245e8	−	1.22274e8i	−0.244835	−	0.235270i
$805$	−4.23271e7	−	1.92862e8i	−0.0811392	−	0.369708i
$806$	−1.51049e8	−	6.08109e7i	−0.288477	−	0.116139i
$807$	−1.37497e8			−0.261620
$808$	1.17832e8	+	2.62041e8i	0.223373	+	0.496747i
$809$	−2.89351e8			−0.546487			−0.273243	−	0.961945i	$-0.588096\pi$
$809$	−2.89351e8			−0.546487			−0.273243	+	0.961945i	$0.588096\pi$
$810$	−7.49554e7	+	4.45482e8i	−0.141042	+	0.838253i
$811$			2.32956e8i			0.436729i	0.975867	+	0.218364i	$0.0700721\pi$
$811$			2.32956e8i			0.436729i	−0.975867	+	0.218364i	$0.929928\pi$
$812$	6.07707e8	+	5.83964e8i	1.13508	+	1.09073i
$813$		−	4.56784e7i		−	0.0850040i
$814$	1.94097e8	+	7.81416e7i	0.359869	+	0.144880i
$815$	1.34661e8	+	6.13577e8i	0.248753	+	1.13343i
$816$	−1.38123e8	+	5.50608e6i	−0.254211	+	0.0101338i
$817$			7.22141e8i			1.32421i
$818$	−7.09952e8	−	2.85821e8i	−1.29709	−	0.522196i
$819$		−	2.62631e8i		−	0.478073i
$820$	−2.75672e7	+	4.50203e7i	−0.0499977	+	0.0816521i
$821$	−4.41895e8			−0.798528			−0.399264	−	0.916836i	$-0.630734\pi$
$821$	−4.41895e8			−0.798528			−0.399264	+	0.916836i	$0.630734\pi$
$822$	2.53454e7	−	6.29556e7i	0.0456335	−	0.113349i
$823$	8.93586e8			1.60301			0.801506	−	0.597987i	$-0.204032\pi$
$823$	8.93586e8			1.60301			0.801506	+	0.597987i	$0.204032\pi$
$824$	−1.36330e8	−	3.03177e8i	−0.243675	−	0.541894i
$825$	−6.94751e7	−	1.50657e8i	−0.123728	−	0.268304i
$826$	3.71388e8	−	9.22493e8i	0.659003	−	1.63690i
$827$	−5.74698e8			−1.01607			−0.508034	−	0.861337i	$-0.669628\pi$
$827$	−5.74698e8			−1.01607			−0.508034	+	0.861337i	$0.669628\pi$
$828$	1.19425e8	+	1.14759e8i	0.210379	+	0.202160i
$829$	−5.62396e7			−0.0987139			−0.0493570	−	0.998781i	$-0.515717\pi$
$829$	−5.62396e7			−0.0987139			−0.0493570	+	0.998781i	$0.515717\pi$
$830$	1.72330e8	−	1.02421e9i	0.301388	−	1.79124i
$831$		−	1.44177e8i		−	0.251242i
$832$	−1.76240e8	−	1.56340e8i	−0.306009	−	0.271456i
$833$		−	3.36602e8i		−	0.582346i
$834$	−8.90846e6	+	2.21278e7i	−0.0153569	+	0.0381452i
$835$	4.86972e7	+	2.21887e8i	0.0836459	+	0.381130i
$836$	−7.16793e8	−	6.88789e8i	−1.22680	−	1.17887i
$837$			1.95934e8i			0.334144i
$838$	7.25489e6	−	1.80205e7i	0.0123282	−	0.0306220i
$839$			6.14216e8i			1.04001i	0.854165	+	0.520003i	$0.174069\pi$
$839$			6.14216e8i			1.04001i	−0.854165	+	0.520003i	$0.825931\pi$
$840$	1.32138e8	−	9.81000e7i	0.222941	−	0.165513i
$841$	3.77390e8			0.634457
$842$	−3.80979e8	−	1.53379e8i	−0.638211	−	0.256938i
$843$	−1.35764e8			−0.226621
$844$	2.42475e8	−	2.52333e8i	0.403310	−	0.419708i
$845$	1.07696e8	+	4.90714e8i	0.178496	+	0.813313i
$846$	1.55234e8	+	6.24959e7i	0.256375	+	0.103214i
$847$	−5.36260e8			−0.882522
$848$	−7.06274e7	+	2.81547e6i	−0.115821	+	0.00461704i
$849$	1.22677e7			0.0200466
$850$	3.41774e7	+	6.92025e8i	0.0556522	+	1.12685i
$851$		−	5.60922e7i		−	0.0910151i
$852$	−6.65219e7	+	6.92265e7i	−0.107559	+	0.111932i
$853$		−	7.29239e8i		−	1.17496i	−0.809239	−	0.587480i	$-0.800120\pi$
$853$		−	7.29239e8i		−	1.17496i	0.809239	−	0.587480i	$-0.199880\pi$
$854$	−6.64444e8	−	2.67500e8i	−1.06680	−	0.429486i
$855$	−7.52448e8	+	1.65138e8i	−1.20387	+	0.264210i
$856$	2.12089e8	+	4.71654e8i	0.338141	+	0.751973i
$857$		−	5.93996e6i		−	0.00943716i	−0.999989	−	0.00471858i	$-0.998498\pi$
$857$		−	5.93996e6i		−	0.00943716i	0.999989	−	0.00471858i	$-0.00150198\pi$
$858$	−7.08152e7	−	2.85096e7i	−0.112115	−	0.0451366i
$859$			2.37950e8i			0.375410i	0.982225	+	0.187705i	$0.0601049\pi$
$859$			2.37950e8i			0.375410i	−0.982225	+	0.187705i	$0.939895\pi$
$860$	3.38714e8	−	5.53160e8i	0.532523	−	0.869672i
$861$	−1.69683e7			−0.0265845
$862$	2.68594e8	−	6.67163e8i	0.419348	−	1.04162i
$863$	−9.36443e8			−1.45696			−0.728482	−	0.685065i	$-0.759774\pi$
$863$	−9.36443e8			−1.45696			−0.728482	+	0.685065i	$0.759774\pi$
$864$	−9.53125e7	+	2.66983e8i	−0.147778	+	0.413945i
$865$	2.59262e8	−	5.68998e7i	0.400581	−	0.0879148i
$866$	1.08395e8	−	2.69244e8i	0.166900	−	0.414565i
$867$	4.01028e7			0.0615344
$868$	−4.24164e8	+	4.41410e8i	−0.648597	+	0.674967i
$869$	1.18669e9			1.80832
$870$	3.14993e7	−	1.87209e8i	0.0478347	−	0.284296i
$871$			4.07008e8i			0.615955i
$872$	4.26223e7	+	9.47854e7i	0.0642818	+	0.142953i
$873$		−	6.62297e8i		−	0.995428i
$874$	−9.95269e7	+	2.47216e8i	−0.149075	+	0.370290i
$875$	−4.97984e8	−	6.57616e8i	−0.743346	−	0.981631i
$876$	1.28748e8	−	1.33983e8i	0.191526	−	0.199313i
$877$		−	4.37126e8i		−	0.648050i	−0.946049	−	0.324025i	$-0.894964\pi$
$877$		−	4.37126e8i		−	0.648050i	0.946049	−	0.324025i	$-0.105036\pi$
$878$	6.05141e7	−	1.50312e8i	0.0894074	−	0.222080i
$879$		−	1.94762e8i		−	0.286773i
$880$	2.25993e8	+	8.63818e8i	0.331624	+	1.26758i
$881$	−3.67911e8			−0.538041			−0.269020	−	0.963134i	$-0.586700\pi$
$881$	−3.67911e8			−0.538041			−0.269020	+	0.963134i	$0.586700\pi$
$882$	−3.11824e8	−	1.25538e8i	−0.454469	−	0.182965i
$883$	9.70524e8			1.40969			0.704846	−	0.709360i	$-0.251016\pi$
$883$	9.70524e8			1.40969			0.704846	+	0.709360i	$0.251016\pi$
$884$	2.29881e8	+	2.20900e8i	0.332772	+	0.319771i
$885$	−2.18790e8	+	4.80175e7i	−0.315645	+	0.0692739i
$886$	1.05768e9	+	4.25814e8i	1.52074	+	0.612236i
$887$	8.13859e8			1.16621			0.583107	−	0.812395i	$-0.301837\pi$
$887$	8.13859e8			1.16621			0.583107	+	0.812395i	$0.301837\pi$
$888$	4.26390e7	−	1.91736e7i	0.0608932	−	0.0273819i
$889$	−4.84615e8			−0.689750
$890$	1.55476e8	−	9.24039e8i	0.220543	−	1.31075i
$891$		−	7.87808e8i		−	1.11375i
$892$	3.12488e8	+	3.00280e8i	0.440290	+	0.423089i
$893$			2.69260e8i			0.378109i
$894$	−4.63549e7	−	1.86621e7i	−0.0648758	−	0.0261185i
$895$	1.56880e8	−	3.44302e7i	0.218826	−	0.0480254i
$896$	−7.92697e8	+	3.95137e8i	−1.10200	+	0.549317i
$897$			2.04650e7i			0.0283552i
$898$	−6.16602e8	−	2.48239e8i	−0.851482	−	0.342800i
$899$			7.06169e8i			0.971919i
$900$	6.53831e8	+	2.26434e8i	0.896888	+	0.310609i
$901$	9.56531e7			0.130775
$902$	3.43816e7	−	8.54008e7i	0.0468497	−	0.116370i
$903$	2.08487e8			0.283150
$904$	−7.02631e8	+	3.15954e8i	−0.951091	+	0.427679i
$905$	5.08671e7	+	2.31774e8i	0.0686264	+	0.312694i
$906$	8.51760e7	−	2.11569e8i	0.114534	−	0.284491i
$907$	−1.02901e8			−0.137910			−0.0689551	−	0.997620i	$-0.521967\pi$
$907$	−1.02901e8			−0.137910			−0.0689551	+	0.997620i	$0.521967\pi$
$908$	−2.38654e8	−	2.29330e8i	−0.318795	−	0.306340i
$909$	−3.88285e8			−0.516962
$910$	−3.74302e8	−	6.29788e7i	−0.496704	−	0.0835739i
$911$			1.62697e8i			0.215191i	0.994195	+	0.107596i	$0.0343152\pi$
$911$			1.62697e8i			0.215191i	−0.994195	+	0.107596i	$0.965685\pi$
$912$	−2.21944e8	+	8.84751e6i	−0.292590	+	0.0116637i
$913$			1.81125e9i			2.37994i
$914$	−5.16258e8	+	1.28234e9i	−0.676126	+	1.67944i
$915$	3.45856e7	+	1.57588e8i	0.0451473	+	0.205712i
$916$	−5.30038e8	−	5.09330e8i	−0.689637	−	0.662693i
$917$		−	1.20493e9i		−	1.56263i
$918$	1.43271e8	−	3.55873e8i	0.185196	−	0.460009i
$919$		−	1.40533e9i		−	1.81064i	−0.424730	−	0.905320i	$-0.639631\pi$
$919$		−	1.40533e9i		−	1.81064i	0.424730	−	0.905320i	$-0.360369\pi$
$920$	1.92192e8	−	1.42685e8i	0.246815	−	0.183237i
$921$	−8.84936e7			−0.113275
$922$	1.44441e8	+	5.81509e7i	0.184289	+	0.0741931i
$923$	2.21428e8			0.281597
$924$	−1.98858e8	+	2.06943e8i	−0.252074	+	0.262322i
$925$	−9.81316e7	−	2.12798e8i	−0.123989	−	0.268871i
$926$	1.20030e9	+	4.83229e8i	1.51166	+	0.608583i
$927$	4.49239e8			0.563948
$928$	−3.43517e8	+	9.62238e8i	−0.429838	+	1.20403i
$929$	−1.57221e9			−1.96093			−0.980467	−	0.196685i	$-0.936982\pi$
$929$	−1.57221e9			−1.96093			−0.980467	+	0.196685i	$0.936982\pi$
$930$	1.35980e8	+	2.28796e7i	0.169054	+	0.0284446i
$931$		−	5.40872e8i		−	0.670264i
$932$	−2.71334e7	+	2.82366e7i	−0.0335163	+	0.0348790i
$933$			3.50176e7i			0.0431163i
$934$	−3.96742e8	−	1.59725e8i	−0.486931	−	0.196034i
$935$	−2.59021e8	−	1.18022e9i	−0.316884	−	1.44387i
$936$	2.90375e8	−	1.30574e8i	0.354105	−	0.159231i
$937$			5.23220e8i			0.636013i	0.948089	+	0.318006i	$0.103013\pi$
$937$			5.23220e8i			0.636013i	−0.948089	+	0.318006i	$0.896987\pi$
$938$	1.41947e9	+	5.71466e8i	1.71996	+	0.692440i
$939$			5.02239e7i			0.0606616i
$940$	1.26294e8	−	2.06253e8i	0.152055	−	0.248323i
$941$	3.00726e8			0.360912			0.180456	−	0.983583i	$-0.442243\pi$
$941$	3.00726e8			0.360912			0.180456	+	0.983583i	$0.442243\pi$
$942$	−6.29531e7	+	1.56370e8i	−0.0753121	+	0.187068i
$943$	−2.46801e7			−0.0294314
$944$	1.20459e9	−	4.80194e7i	1.43193	−	0.0570822i
$945$	9.79074e7	+	4.46112e8i	0.116017	+	0.528626i
$946$	−4.22443e8	+	1.04931e9i	−0.498993	+	1.23945i
$947$	−4.73433e8			−0.557453			−0.278727	−	0.960370i	$-0.589912\pi$
$947$	−4.73433e8			−0.557453			−0.278727	+	0.960370i	$0.589912\pi$
$948$	1.83719e8	−	1.91189e8i	0.215640	−	0.224408i
$949$	−4.28558e8			−0.501431
$950$	5.49184e7	+	1.11199e9i	0.0640541	+	1.29697i
$951$		−	1.45004e8i		−	0.168593i
$952$	1.09317e9	−	4.91569e8i	1.26700	−	0.569736i
$953$		−	6.45528e8i		−	0.745824i	−0.927867	−	0.372912i	$-0.878359\pi$
$953$		−	6.45528e8i		−	0.745824i	0.927867	−	0.372912i	$-0.121641\pi$
$954$	3.56744e7	−	8.86120e7i	0.0410877	−	0.102058i
$955$	1.34749e9	−	2.95731e8i	1.54709	−	0.339536i
$956$	−8.36174e8	+	8.70171e8i	−0.957025	+	0.995935i
$957$			3.31069e8i			0.377731i
$958$	−1.55648e8	+	3.86616e8i	−0.177030	+	0.439727i
$959$			5.88465e8i			0.667213i
$960$	1.74159e8	+	9.73238e7i	0.196848	+	0.110003i
$961$	3.74576e8			0.422055
$962$	−1.00024e8	−	4.02690e7i	−0.112352	−	0.0452320i
$963$	−6.98884e8			−0.782575
$964$	5.51824e8	+	5.30264e8i	0.615984	+	0.591918i
$965$	1.17271e9	−	2.57372e8i	1.30499	−	0.286405i
$966$	7.13729e7	+	2.87341e7i	0.0791775	+	0.0318762i
$967$	6.01748e8			0.665481			0.332740	−	0.943018i	$-0.392027\pi$
$967$	6.01748e8			0.665481			0.332740	+	0.943018i	$0.392027\pi$
$968$	−2.66615e8	−	5.92911e8i	−0.293940	−	0.653677i
$969$	3.00586e8			0.330368
$970$	−9.43904e8	−	1.58818e8i	−1.03422	−	0.174015i
$971$			3.59534e8i			0.392719i	0.980532	+	0.196360i	$0.0629120\pi$
$971$			3.59534e8i			0.392719i	−0.980532	+	0.196360i	$0.937088\pi$
$972$	−4.17968e8	−	4.01638e8i	−0.455139	−	0.437357i
$973$		−	2.06835e8i		−	0.224536i
$974$	−3.33523e8	−	1.34274e8i	−0.360952	−	0.145316i
$975$	3.58028e7	+	7.76385e7i	0.0386281	+	0.0837651i
$976$	−3.45869e7	−	8.67630e8i	−0.0372017	−	0.933222i
$977$			3.41034e8i			0.365691i	0.983142	+	0.182845i	$0.0585308\pi$
$977$			3.41034e8i			0.365691i	−0.983142	+	0.182845i	$0.941469\pi$
$978$	−2.27068e8	−	9.14155e7i	−0.242739	−	0.0977245i
$979$			1.63411e9i			1.74154i
$980$	−2.53692e8	+	4.14308e8i	−0.269543	+	0.440195i
$981$	−1.40450e8			−0.148770
$982$	7.72892e7	−	1.91979e8i	0.0816177	−	0.202731i
$983$	−7.22351e8			−0.760480			−0.380240	−	0.924888i	$-0.624159\pi$
$983$	−7.22351e8			−0.760480			−0.380240	+	0.924888i	$0.624159\pi$
$984$	−8.43620e6	−	1.87608e7i	−0.00885445	−	0.0196909i
$985$	−4.30635e8	+	9.45106e7i	−0.450610	+	0.0988945i
$986$	5.16366e8	−	1.28261e9i	0.538675	−	1.33802i
$987$	7.77372e7			0.0808495
$988$	3.69388e8	+	3.54956e8i	0.383011	+	0.368047i
$989$	3.03241e8			0.313472
$990$	−1.18995e9	−	2.00217e8i	−1.22637	−	0.206346i
$991$		−	1.09281e9i		−	1.12286i	−0.827526	−	0.561428i	$-0.810252\pi$
$991$		−	1.09281e9i		−	1.12286i	0.827526	−	0.561428i	$-0.189748\pi$
$992$	−6.98924e8	−	2.49515e8i	−0.715970	−	0.255600i
$993$		−	2.84641e6i		−	0.00290703i
$994$	3.10900e8	−	7.72246e8i	0.316564	−	0.786315i
$995$	−2.06240e8	+	4.52631e7i	−0.209365	+	0.0459489i
$996$	2.91813e8	+	2.80412e8i	0.295343	+	0.283804i
$997$		−	9.59556e8i		−	0.968245i	−0.875000	−	0.484122i	$-0.839139\pi$
$997$		−	9.59556e8i		−	0.968245i	0.875000	−	0.484122i	$-0.160861\pi$
$998$	6.40980e7	−	1.59213e8i	0.0644841	−	0.160173i
$999$			1.29748e8i			0.130138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.7.d.d.19.12	yes	12
3.2	odd	2		180.7.f.e.19.1		12
4.3	odd	2	inner	20.7.d.d.19.2	yes	12
5.2	odd	4		100.7.b.f.51.6		12
5.3	odd	4		100.7.b.f.51.7		12
5.4	even	2	inner	20.7.d.d.19.1	✓	12
8.3	odd	2		320.7.h.f.319.5		12
8.5	even	2		320.7.h.f.319.7		12
12.11	even	2		180.7.f.e.19.11		12
15.14	odd	2		180.7.f.e.19.12		12
20.3	even	4		100.7.b.f.51.8		12
20.7	even	4		100.7.b.f.51.5		12
20.19	odd	2	inner	20.7.d.d.19.11	yes	12
40.19	odd	2		320.7.h.f.319.8		12
40.29	even	2		320.7.h.f.319.6		12
60.59	even	2		180.7.f.e.19.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.d.d.19.1	✓	12	5.4	even	2	inner
20.7.d.d.19.2	yes	12	4.3	odd	2	inner
20.7.d.d.19.11	yes	12	20.19	odd	2	inner
20.7.d.d.19.12	yes	12	1.1	even	1	trivial
100.7.b.f.51.5		12	20.7	even	4
100.7.b.f.51.6		12	5.2	odd	4
100.7.b.f.51.7		12	5.3	odd	4
100.7.b.f.51.8		12	20.3	even	4
180.7.f.e.19.1		12	3.2	odd	2
180.7.f.e.19.2		12	60.59	even	2
180.7.f.e.19.11		12	12.11	even	2
180.7.f.e.19.12		12	15.14	odd	2
320.7.h.f.319.5		12	8.3	odd	2
320.7.h.f.319.6		12	40.29	even	2
320.7.h.f.319.7		12	8.5	even	2
320.7.h.f.319.8		12	40.19	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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(7.42116 + 2.98770i) q^{2} -6.08848 q^{3} +(46.1473 + 44.3444i) q^{4} +(26.7958 + 122.094i) q^{5} +(-45.1836 - 18.1905i) q^{6} +422.345 q^{7} +(209.979 + 466.961i) q^{8} -691.930 q^{9} +O(q^{10})\)	\(q+(7.42116 + 2.98770i) q^{2} -6.08848 q^{3} +(46.1473 + 44.3444i) q^{4} +(26.7958 + 122.094i) q^{5} +(-45.1836 - 18.1905i) q^{6} +422.345 q^{7} +(209.979 + 466.961i) q^{8} -691.930 q^{9} +(-165.925 + 986.138i) q^{10} -1743.93i q^{11} +(-280.967 - 269.990i) q^{12} +898.704i q^{13} +(3134.29 + 1261.84i) q^{14} +(-163.146 - 743.368i) q^{15} +(163.152 + 4092.75i) q^{16} -5542.94i q^{17} +(-5134.93 - 2067.28i) q^{18} -8906.74i q^{19} +(-4177.64 + 6822.56i) q^{20} -2571.44 q^{21} +(5210.33 - 12942.0i) q^{22} -3740.11 q^{23} +(-1278.46 - 2843.09i) q^{24} +(-14189.0 + 6543.22i) q^{25} +(-2685.06 + 6669.43i) q^{26} +8651.31 q^{27} +(19490.1 + 18728.6i) q^{28} +31180.3 q^{29} +(1010.23 - 6004.09i) q^{30} +22647.9i q^{31} +(-11017.1 + 30860.4i) q^{32} +10617.9i q^{33} +(16560.6 - 41135.1i) q^{34} +(11317.1 + 51565.8i) q^{35} +(-31930.7 - 30683.2i) q^{36} +14997.5i q^{37} +(26610.7 - 66098.4i) q^{38} -5471.75i q^{39} +(-51386.7 + 38149.8i) q^{40} +6598.75 q^{41} +(-19083.1 - 7682.68i) q^{42} -81078.0 q^{43} +(77333.4 - 80477.6i) q^{44} +(-18540.8 - 84480.7i) q^{45} +(-27756.0 - 11174.3i) q^{46} -30231.0 q^{47} +(-993.349 - 24918.6i) q^{48} +60726.1 q^{49} +(-124848. + 6165.93i) q^{50} +33748.1i q^{51} +(-39852.5 + 41472.8i) q^{52} +17256.7i q^{53} +(64202.8 + 25847.5i) q^{54} +(212923. - 46729.9i) q^{55} +(88683.7 + 197219. i) q^{56} +54228.6i q^{57} +(231394. + 93157.4i) q^{58} -294323. i q^{59} +(25435.5 - 41539.1i) q^{60} -211992. q^{61} +(-67665.1 + 168074. i) q^{62} -292233. q^{63} +(-173961. + 196104. i) q^{64} +(-109727. + 24081.5i) q^{65} +(-31723.0 + 78797.0i) q^{66} +452884. q^{67} +(245798. - 255792. i) q^{68} +22771.6 q^{69} +(-70077.4 + 416490. i) q^{70} -246386. i q^{71} +(-145291. - 323105. i) q^{72} +476862. i q^{73} +(-44807.9 + 111299. i) q^{74} +(86389.3 - 39838.3i) q^{75} +(394964. - 411022. i) q^{76} -736539. i q^{77} +(16347.9 - 40606.7i) q^{78} +680467. i q^{79} +(-495329. + 129588. i) q^{80} +451744. q^{81} +(48970.4 + 19715.1i) q^{82} -1.03860e6 q^{83} +(-118665. - 114029. i) q^{84} +(676761. - 148528. i) q^{85} +(-601693. - 242237. i) q^{86} -189841. q^{87} +(814346. - 366189. i) q^{88} -937027. q^{89} +(114808. - 682339. i) q^{90} +379563. i q^{91} +(-172596. - 165853. i) q^{92} -137891. i q^{93} +(-224349. - 90321.0i) q^{94} +(1.08746e6 - 238663. i) q^{95} +(67077.6 - 187893. i) q^{96} +957172. i q^{97} +(450659. + 181431. i) q^{98} +1.20668e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 64 q^{4} + 460 q^{5} - 672 q^{6} + 1956 q^{9}+O(q^{10}) \) 12 * q + 64 * q^4 + 460 * q^5 - 672 * q^6 + 1956 * q^9	\( 12 q + 64 q^{4} + 460 q^{5} - 672 q^{6} + 1956 q^{9} + 2000 q^{10} + 512 q^{14} - 20928 q^{16} - 13760 q^{20} + 51216 q^{21} - 20928 q^{24} - 55700 q^{25} + 14496 q^{26} - 16072 q^{29} + 83520 q^{30} + 257216 q^{34} - 144960 q^{36} - 36800 q^{40} - 192136 q^{41} - 165120 q^{44} - 57180 q^{45} - 49472 q^{46} + 145796 q^{49} - 36000 q^{50} - 118656 q^{54} + 1078208 q^{56} - 902400 q^{60} + 215384 q^{61} - 6656 q^{64} + 710400 q^{65} - 1403520 q^{66} + 1015824 q^{69} + 530080 q^{70} - 1020384 q^{74} + 2515200 q^{76} - 127040 q^{80} - 2327652 q^{81} + 424704 q^{84} - 44800 q^{85} - 5268832 q^{86} - 4346152 q^{89} + 3582000 q^{90} + 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) \) 12 * q + 64 * q^4 + 460 * q^5 - 672 * q^6 + 1956 * q^9 + 2000 * q^10 + 512 * q^14 - 20928 * q^16 - 13760 * q^20 + 51216 * q^21 - 20928 * q^24 - 55700 * q^25 + 14496 * q^26 - 16072 * q^29 + 83520 * q^30 + 257216 * q^34 - 144960 * q^36 - 36800 * q^40 - 192136 * q^41 - 165120 * q^44 - 57180 * q^45 - 49472 * q^46 + 145796 * q^49 - 36000 * q^50 - 118656 * q^54 + 1078208 * q^56 - 902400 * q^60 + 215384 * q^61 - 6656 * q^64 + 710400 * q^65 - 1403520 * q^66 + 1015824 * q^69 + 530080 * q^70 - 1020384 * q^74 + 2515200 * q^76 - 127040 * q^80 - 2327652 * q^81 + 424704 * q^84 - 44800 * q^85 - 5268832 * q^86 - 4346152 * q^89 + 3582000 * q^90 + 4292992 * q^94 + 7673088 * q^96

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