LMFDB - Embedded newform 20.7.d.d.19.3

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			19.3
Root			$-0.954985 - 3.01463i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.7.d.d.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.94356 - 5.35482i) q^{2} +40.3729 q^{3} +(6.65182 + 63.6534i) q^{4} +(-32.9271 + 120.585i) q^{5} +(-239.959 - 216.189i) q^{6} +450.705 q^{7} +(301.317 - 413.947i) q^{8} +900.969 q^{9} +O(q^{10})$	\(q+(-5.94356 - 5.35482i) q^{2} +40.3729 q^{3} +(6.65182 + 63.6534i) q^{4} +(-32.9271 + 120.585i) q^{5} +(-239.959 - 216.189i) q^{6} +450.705 q^{7} +(301.317 - 413.947i) q^{8} +900.969 q^{9} +(841.416 - 540.387i) q^{10} +390.888i q^{11} +(268.553 + 2569.87i) q^{12} -3234.51i q^{13} +(-2678.79 - 2413.44i) q^{14} +(-1329.36 + 4868.37i) q^{15} +(-4007.51 + 846.821i) q^{16} +4937.20i q^{17} +(-5354.96 - 4824.53i) q^{18} +1980.00i q^{19} +(-7894.69 - 1293.81i) q^{20} +18196.2 q^{21} +(2093.14 - 2323.27i) q^{22} +1077.32 q^{23} +(12165.0 - 16712.2i) q^{24} +(-13456.6 - 7941.04i) q^{25} +(-17320.2 + 19224.5i) q^{26} +6942.88 q^{27} +(2998.00 + 28688.9i) q^{28} -21158.1 q^{29} +(33970.4 - 21817.0i) q^{30} -33221.4i q^{31} +(28353.4 + 16426.3i) q^{32} +15781.3i q^{33} +(26437.8 - 29344.6i) q^{34} +(-14840.4 + 54348.3i) q^{35} +(5993.08 + 57349.7i) q^{36} -14159.5i q^{37} +(10602.6 - 11768.3i) q^{38} -130586. i q^{39} +(39994.4 + 49964.4i) q^{40} -42870.4 q^{41} +(-108150. - 97437.6i) q^{42} +57775.6 q^{43} +(-24881.4 + 2600.12i) q^{44} +(-29666.3 + 108644. i) q^{45} +(-6403.13 - 5768.87i) q^{46} -138151. q^{47} +(-161795. + 34188.6i) q^{48} +85485.6 q^{49} +(37457.3 + 119256. i) q^{50} +199329. i q^{51} +(205887. - 21515.4i) q^{52} -277123. i q^{53} +(-41265.4 - 37177.9i) q^{54} +(-47135.4 - 12870.8i) q^{55} +(135805. - 186568. i) q^{56} +79938.4i q^{57} +(125755. + 113298. i) q^{58} +28176.1i q^{59} +(-318731. - 52234.8i) q^{60} -34082.0 q^{61} +(-177894. + 197453. i) q^{62} +406071. q^{63} +(-80560.3 - 249458. i) q^{64} +(390034. + 106503. i) q^{65} +(84506.0 - 93797.1i) q^{66} +230002. q^{67} +(-314270. + 32841.4i) q^{68} +43494.6 q^{69} +(379230. - 243555. i) q^{70} +214659. i q^{71} +(271477. - 372953. i) q^{72} -21193.6i q^{73} +(-75821.5 + 84157.8i) q^{74} +(-543282. - 320603. i) q^{75} +(-126034. + 13170.6i) q^{76} +176175. i q^{77} +(-699267. + 776148. i) q^{78} +365752. i q^{79} +(29841.3 - 511130. i) q^{80} -376502. q^{81} +(254803. + 229563. i) q^{82} +50231.1 q^{83} +(121038. + 1.15825e6i) q^{84} +(-595354. - 162568. i) q^{85} +(-343393. - 309378. i) q^{86} -854215. q^{87} +(161807. + 117781. i) q^{88} -177274. q^{89} +(758090. - 486872. i) q^{90} -1.45781e6i q^{91} +(7166.15 + 68575.2i) q^{92} -1.34124e6i q^{93} +(821109. + 739774. i) q^{94} +(-238759. - 65195.7i) q^{95} +(1.14471e6 + 663179. i) q^{96} +1.15267e6i q^{97} +(-508089. - 457760. i) q^{98} +352178. i 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 $

$2$	−5.94356	−	5.35482i	−0.742945	−	0.669352i
$2$	−5.94356	−	5.35482i	−0.742945	−	0.669352i
$3$	40.3729			1.49529			0.747646	−	0.664098i	$-0.231184\pi$
$3$	40.3729			1.49529			0.747646	+	0.664098i	$0.231184\pi$
$4$	6.65182	+	63.6534i	0.103935	+	0.994584i
$5$	−32.9271	+	120.585i	−0.263417	+	0.964682i
$5$	−32.9271	+	120.585i	−0.263417	+	0.964682i
$6$	−239.959	−	216.189i	−1.11092	−	1.00088i
$7$	450.705			1.31401			0.657004	−	0.753887i	$-0.271824\pi$
$7$	450.705			1.31401			0.657004	+	0.753887i	$0.271824\pi$
$8$	301.317	−	413.947i	0.588510	−	0.808490i
$9$	900.969			1.23590
$10$	841.416	−	540.387i	0.841416	−	0.540387i
$11$			390.888i			0.293680i	0.989160	+	0.146840i	$0.0469103\pi$
$11$			390.888i			0.293680i	−0.989160	+	0.146840i	$0.953090\pi$
$12$	268.553	+	2569.87i	0.155413	+	1.48719i
$13$		−	3234.51i		−	1.47224i	−0.676852	−	0.736119i	$-0.736656\pi$
$13$		−	3234.51i		−	1.47224i	0.676852	−	0.736119i	$-0.263344\pi$
$14$	−2678.79	−	2413.44i	−0.976235	−	0.879534i
$15$	−1329.36	+	4868.37i	−0.393885	+	1.44248i
$16$	−4007.51	+	846.821i	−0.978395	+	0.206744i
$17$			4937.20i			1.00493i	0.864599	+	0.502463i	$0.167573\pi$
$17$			4937.20i			1.00493i	−0.864599	+	0.502463i	$0.832427\pi$
$18$	−5354.96	−	4824.53i	−0.918204	−	0.827251i
$19$			1980.00i			0.288672i	0.989529	+	0.144336i	$0.0461047\pi$
$19$			1980.00i			0.288672i	−0.989529	+	0.144336i	$0.953895\pi$
$20$	−7894.69	−	1293.81i	−0.986836	−	0.161726i
$21$	18196.2			1.96482
$22$	2093.14	−	2323.27i	0.196576	−	0.218188i
$23$	1077.32			0.0885446			0.0442723	−	0.999020i	$-0.485903\pi$
$23$	1077.32			0.0885446			0.0442723	+	0.999020i	$0.485903\pi$
$24$	12165.0	−	16712.2i	0.879993	−	1.20893i
$25$	−13456.6	−	7941.04i	−0.861223	−	0.508227i
$26$	−17320.2	+	19224.5i	−0.985447	+	1.09379i
$27$	6942.88			0.352735
$28$	2998.00	+	28688.9i	0.136571	+	1.30689i
$29$	−21158.1			−0.867528			−0.433764	−	0.901027i	$-0.642815\pi$
$29$	−21158.1			−0.867528			−0.433764	+	0.901027i	$0.642815\pi$
$30$	33970.4	−	21817.0i	1.25816	−	0.808036i
$31$		−	33221.4i		−	1.11515i	−0.830127	−	0.557574i	$-0.811732\pi$
$31$		−	33221.4i		−	1.11515i	0.830127	−	0.557574i	$-0.188268\pi$
$32$	28353.4	+	16426.3i	0.865278	+	0.501292i
$33$			15781.3i			0.439138i
$34$	26437.8	−	29344.6i	0.672650	−	0.746605i
$35$	−14840.4	+	54348.3i	−0.346132	+	1.26760i
$36$	5993.08	+	57349.7i	0.128453	+	1.22920i
$37$		−	14159.5i		−	0.279539i	−0.990184	−	0.139769i	$-0.955364\pi$
$37$		−	14159.5i		−	0.279539i	0.990184	−	0.139769i	$-0.0446362\pi$
$38$	10602.6	−	11768.3i	0.193223	−	0.214468i
$39$		−	130586.i		−	2.20143i
$40$	39994.4	+	49964.4i	0.624913	+	0.780695i
$41$	−42870.4			−0.622023			−0.311011	−	0.950406i	$-0.600668\pi$
$41$	−42870.4			−0.622023			−0.311011	+	0.950406i	$0.600668\pi$
$42$	−108150.	−	97437.6i	−1.45976	−	1.31516i
$43$	57775.6			0.726673			0.363337	−	0.931658i	$-0.381637\pi$
$43$	57775.6			0.726673			0.363337	+	0.931658i	$0.381637\pi$
$44$	−24881.4	+	2600.12i	−0.292090	+	0.0305236i
$45$	−29666.3	+	108644.i	−0.325556	+	1.19225i
$46$	−6403.13	−	5768.87i	−0.0657838	−	0.0592676i
$47$	−138151.			−1.33064			−0.665320	−	0.746558i	$-0.731705\pi$
$47$	−138151.			−1.33064			−0.665320	+	0.746558i	$0.731705\pi$
$48$	−161795.	+	34188.6i	−1.46299	+	0.309142i
$49$	85485.6			0.726616
$50$	37457.3	+	119256.i	0.299659	+	0.954046i
$51$			199329.i			1.50266i
$52$	205887.	−	21515.4i	1.46427	−	0.153017i
$53$		−	277123.i		−	1.86142i	−0.365756	−	0.930711i	$-0.619189\pi$
$53$		−	277123.i		−	1.86142i	0.365756	−	0.930711i	$-0.380811\pi$
$54$	−41265.4	−	37177.9i	−0.262063	−	0.236104i
$55$	−47135.4	−	12870.8i	−0.283308	−	0.0773603i
$56$	135805.	−	186568.i	0.773306	−	1.06236i
$57$			79938.4i			0.431649i
$58$	125755.	+	113298.i	0.644525	+	0.580682i
$59$			28176.1i			0.137191i	0.997645	+	0.0685954i	$0.0218518\pi$
$59$			28176.1i			0.137191i	−0.997645	+	0.0685954i	$0.978148\pi$
$60$	−318731.	−	52234.8i	−1.47561	−	0.241828i
$61$	−34082.0			−0.150154			−0.0750769	−	0.997178i	$-0.523920\pi$
$61$	−34082.0			−0.150154			−0.0750769	+	0.997178i	$0.523920\pi$
$62$	−177894.	+	197453.i	−0.746427	+	0.828494i
$63$	406071.			1.62398
$64$	−80560.3	−	249458.i	−0.307313	−	0.951608i
$65$	390034.	+	106503.i	1.42024	+	0.387812i
$66$	84506.0	−	93797.1i	0.293938	−	0.326255i
$67$	230002.			0.764730			0.382365	−	0.924011i	$-0.375110\pi$
$67$	230002.			0.764730			0.382365	+	0.924011i	$0.375110\pi$
$68$	−314270.	+	32841.4i	−0.999484	+	0.104447i
$69$	43494.6			0.132400
$70$	379230.	−	243555.i	1.10563	−	0.710073i
$71$			214659.i			0.599757i	0.953977	+	0.299878i	$0.0969461\pi$
$71$			214659.i			0.599757i	−0.953977	+	0.299878i	$0.903054\pi$
$72$	271477.	−	372953.i	0.727337	−	0.999211i
$73$		−	21193.6i		−	0.0544800i	−0.999629	−	0.0272400i	$-0.991328\pi$
$73$		−	21193.6i		−	0.0544800i	0.999629	−	0.0272400i	$-0.00867183\pi$
$74$	−75821.5	+	84157.8i	−0.187110	+	0.207682i
$75$	−543282.	−	320603.i	−1.28778	−	0.759947i
$76$	−126034.	+	13170.6i	−0.287109	+	0.0300030i
$77$			176175.i			0.385898i
$78$	−699267.	+	776148.i	−1.47353	+	1.63554i
$79$			365752.i			0.741832i	0.928666	+	0.370916i	$0.120956\pi$
$79$			365752.i			0.741832i	−0.928666	+	0.370916i	$0.879044\pi$
$80$	29841.3	−	511130.i	0.0582838	−	0.998300i
$81$	−376502.			−0.708456
$82$	254803.	+	229563.i	0.462129	+	0.416352i
$83$	50231.1			0.0878493			0.0439247	−	0.999035i	$-0.486014\pi$
$83$	50231.1			0.0878493			0.0439247	+	0.999035i	$0.486014\pi$
$84$	121038.	+	1.15825e6i	0.204213	+	1.95418i
$85$	−595354.	−	162568.i	−0.969435	−	0.264714i
$86$	−343393.	−	309378.i	−0.539878	−	0.486401i
$87$	−854215.			−1.29721
$88$	161807.	+	117781.i	0.237438	+	0.172834i
$89$	−177274.			−0.251463			−0.125731	−	0.992064i	$-0.540128\pi$
$89$	−177274.			−0.251463			−0.125731	+	0.992064i	$0.540128\pi$
$90$	758090.	−	486872.i	1.03990	−	0.667863i
$91$		−	1.45781e6i		−	1.93453i
$92$	7166.15	+	68575.2i	0.00920286	+	0.0880651i
$93$		−	1.34124e6i		−	1.66747i
$94$	821109.	+	739774.i	0.988592	+	0.890667i
$95$	−238759.	−	65195.7i	−0.278477	−	0.0760411i
$96$	1.14471e6	+	663179.i	1.29384	+	0.749578i
$97$			1.15267e6i			1.26296i	0.775393	+	0.631479i	$0.217552\pi$
$97$			1.15267e6i			1.26296i	−0.775393	+	0.631479i	$0.782448\pi$
$98$	−508089.	−	457760.i	−0.539836	−	0.486362i
$99$			352178.i			0.362959i
$100$	415963.	−	909381.i	0.415963	−	0.909381i
$101$	1.27960e6			1.24197			0.620985	−	0.783822i	$-0.286733\pi$
$101$	1.27960e6			1.24197			0.620985	+	0.783822i	$0.286733\pi$
$102$	1.06737e6	−	1.18472e6i	1.00581	−	1.11639i
$103$	2.08267e6			1.90593			0.952967	−	0.303074i	$-0.0980128\pi$
$103$	2.08267e6			1.90593			0.952967	+	0.303074i	$0.0980128\pi$
$104$	−1.33892e6	−	974612.i	−1.19029	−	0.866427i
$105$	−599149.	+	2.19420e6i	−0.517568	+	1.89543i
$106$	−1.48394e6	+	1.64710e6i	−1.24595	+	1.38293i
$107$	512122.			0.418044			0.209022	−	0.977911i	$-0.432972\pi$
$107$	512122.			0.418044			0.209022	+	0.977911i	$0.432972\pi$
$108$	46182.8	+	441938.i	0.0366614	+	0.350824i
$109$	−1.32906e6			−1.02628			−0.513141	−	0.858305i	$-0.671518\pi$
$109$	−1.32906e6			−1.02628			−0.513141	+	0.858305i	$0.671518\pi$
$110$	211231.	+	328900.i	0.158701	+	0.247107i
$111$		−	571659.i		−	0.417992i
$112$	−1.80620e6	+	381666.i	−1.28562	+	0.271663i
$113$		−	160172.i		−	0.111007i	−0.998458	−	0.0555035i	$-0.982324\pi$
$113$		−	160172.i		−	0.111007i	0.998458	−	0.0555035i	$-0.0176764\pi$
$114$	428056.	−	475119.i	0.288925	−	0.320692i
$115$	−35473.1	+	129909.i	−0.0233241	+	0.0854174i
$116$	−140740.	−	1.34679e6i	−0.0901662	−	0.862829i
$117$		−	2.91419e6i		−	1.81954i
$118$	150878.	−	167466.i	0.0918290	−	0.101925i
$119$			2.22522e6i			1.32048i
$120$	1.61469e6	+	2.01721e6i	0.934427	+	1.16737i
$121$	1.61877e6			0.913752
$122$	202569.	+	182503.i	0.111556	+	0.100506i
$123$	−1.73080e6			−0.930105
$124$	2.11465e6	−	220982.i	1.10911	−	0.115903i
$125$	1.40066e6	−	1.36119e6i	0.717138	−	0.696931i
$126$	−2.41351e6	−	2.17444e6i	−1.20653	−	1.08701i
$127$	−1.90105e6			−0.928071			−0.464036	−	0.885816i	$-0.653599\pi$
$127$	−1.90105e6			−0.928071			−0.464036	+	0.885816i	$0.653599\pi$
$128$	−856990.	+	1.91406e6i	−0.408645	+	0.912693i
$129$	2.33257e6			1.08659
$130$	−1.74789e6	−	2.72157e6i	−0.795579	−	1.23877i
$131$			2.76248e6i			1.22881i	0.788990	+	0.614407i	$0.210605\pi$
$131$			2.76248e6i			1.22881i	−0.788990	+	0.614407i	$0.789395\pi$
$132$	−1.00453e6	+	104974.i	−0.436759	+	0.0456416i
$133$			892396.i			0.379317i
$134$	−1.36703e6	−	1.23162e6i	−0.568152	−	0.511874i
$135$	−228609.	+	837209.i	−0.0929162	+	0.340277i
$136$	2.04374e6	+	1.48766e6i	0.812473	+	0.591409i
$137$			2.60078e6i			1.01144i	0.862696	+	0.505722i	$0.168774\pi$
$137$			2.60078e6i			1.01144i	−0.862696	+	0.505722i	$0.831226\pi$
$138$	−258513.	−	232906.i	−0.0983660	−	0.0886223i
$139$		−	3.07350e6i		−	1.14443i	−0.820104	−	0.572214i	$-0.806085\pi$
$139$		−	3.07350e6i		−	1.14443i	0.820104	−	0.572214i	$-0.193915\pi$
$140$	−3.55817e6	−	583126.i	−1.29671	−	0.212509i
$141$	−5.57755e6			−1.98969
$142$	1.14946e6	−	1.27584e6i	0.401448	−	0.445586i
$143$	1.26433e6			0.432368
$144$	−3.61064e6	+	762960.i	−1.20920	+	0.255514i
$145$	696676.	−	2.55136e6i	0.228521	−	0.836889i
$146$	−113488.	+	125966.i	−0.0364663	+	0.0404756i
$147$	3.45130e6			1.08650
$148$	901299.	−	94186.3i	0.278025	−	0.0290538i
$149$	2.10750e6			0.637102			0.318551	−	0.947906i	$-0.396804\pi$
$149$	2.10750e6			0.637102			0.318551	+	0.947906i	$0.396804\pi$
$150$	1.51226e6	+	4.81470e6i	0.448077	+	1.42658i
$151$			2.20804e6i			0.641323i	0.947194	+	0.320662i	$0.103905\pi$
$151$			2.20804e6i			0.641323i	−0.947194	+	0.320662i	$0.896095\pi$
$152$	819616.	+	596608.i	0.233389	+	0.169886i
$153$			4.44827e6i			1.24199i
$154$	943387.	−	1.04711e6i	0.258302	−	0.286701i
$155$	4.00601e6	+	1.09388e6i	1.07576	+	0.293749i
$156$	8.31227e6	−	868637.i	2.18950	−	0.228805i
$157$		−	821139.i		−	0.212187i	−0.994356	−	0.106093i	$-0.966166\pi$
$157$		−	821139.i		−	0.212187i	0.994356	−	0.106093i	$-0.0338342\pi$
$158$	1.95854e6	−	2.17387e6i	0.496547	−	0.551140i
$159$		−	1.11882e7i		−	2.78337i
$160$	−2.91437e6	+	2.87813e6i	−0.711516	+	0.702670i
$161$	485554.			0.116348
$162$	2.23776e6	+	2.01610e6i	0.526344	+	0.474206i
$163$	−7.70810e6			−1.77985			−0.889927	−	0.456103i	$-0.849245\pi$
$163$	−7.70810e6			−1.77985			−0.889927	+	0.456103i	$0.849245\pi$
$164$	−285166.	−	2.72885e6i	−0.0646497	−	0.618654i
$165$	−1.90299e6	−	519632.i	−0.423628	−	0.115676i
$166$	−298552.	−	268979.i	−0.0652672	−	0.0588022i
$167$	2.37157e6			0.509197			0.254599	−	0.967047i	$-0.418057\pi$
$167$	2.37157e6			0.509197			0.254599	+	0.967047i	$0.418057\pi$
$168$	5.48283e6	−	7.53228e6i	1.15632	−	1.58854i
$169$	−5.63524e6			−1.16749
$170$	2.66800e6	+	4.15424e6i	0.543049	+	0.845562i
$171$			1.78392e6i			0.356769i
$172$	384313.	+	3.67761e6i	0.0755266	+	0.722738i
$173$		−	5.22589e6i		−	1.00930i	−0.863323	−	0.504652i	$-0.831621\pi$
$173$		−	5.22589e6i		−	1.00930i	0.863323	−	0.504652i	$-0.168379\pi$
$174$	5.07708e6	+	4.57417e6i	0.963753	+	0.868289i
$175$	−6.06496e6	−	3.57906e6i	−1.13165	−	0.667814i
$176$	−331013.	−	1.56649e6i	−0.0607165	−	0.287335i
$177$			1.13755e6i			0.205140i
$178$	1.05364e6	+	949268.i	0.186823	+	0.168317i
$179$			6.41696e6i			1.11885i	0.828882	+	0.559423i	$0.188977\pi$
$179$			6.41696e6i			1.11885i	−0.828882	+	0.559423i	$0.811023\pi$
$180$	−7.11287e6	−	1.16568e6i	−1.21963	−	0.199877i
$181$	−2.74959e6			−0.463694			−0.231847	−	0.972752i	$-0.574477\pi$
$181$	−2.74959e6			−0.463694			−0.231847	+	0.972752i	$0.574477\pi$
$182$	−7.80630e6	+	8.66457e6i	−1.29488	+	1.43725i
$183$	−1.37599e6			−0.224524
$184$	324615.	−	445954.i	0.0521094	−	0.0715875i
$185$	1.70743e6	+	466231.i	0.269666	+	0.0736352i
$186$	−7.18211e6	+	7.97175e6i	−1.11613	+	1.23884i
$187$	−1.92990e6			−0.295127
$188$	−918955.	−	8.79378e6i	−0.138300	−	1.32343i
$189$	3.12919e6			0.463496
$190$	1.06997e6	+	1.66601e6i	0.155995	+	0.242894i
$191$		−	7.97496e6i		−	1.14453i	−0.820068	−	0.572267i	$-0.806064\pi$
$191$		−	7.97496e6i		−	1.14453i	0.820068	−	0.572267i	$-0.193936\pi$
$192$	−3.25245e6	−	1.00714e7i	−0.459523	−	1.42293i
$193$			1.21860e7i			1.69508i	0.530734	+	0.847539i	$0.321916\pi$
$193$			1.21860e7i			1.69508i	−0.530734	+	0.847539i	$0.678084\pi$
$194$	6.17233e6	−	6.85095e6i	0.845364	−	0.938308i
$195$	1.57468e7	+	4.29983e6i	2.12368	+	0.579893i
$196$	568635.	+	5.44145e6i	0.0755206	+	0.722681i
$197$		−	5.27192e6i		−	0.689557i	−0.938684	−	0.344778i	$-0.887954\pi$
$197$		−	5.27192e6i		−	0.689557i	0.938684	−	0.344778i	$-0.112046\pi$
$198$	1.88585e6	−	2.09319e6i	0.242947	−	0.269658i
$199$			1.14435e7i			1.45210i	0.687639	+	0.726052i	$0.258647\pi$
$199$			1.14435e7i			1.45210i	−0.687639	+	0.726052i	$0.741353\pi$
$200$	−7.34188e6	+	3.17755e6i	−0.917735	+	0.397194i
$201$	9.28586e6			1.14349
$202$	−7.60540e6	−	6.85205e6i	−0.922716	−	0.831316i
$203$	−9.53607e6			−1.13994
$204$	−1.26880e7	+	1.32590e6i	−1.49452	+	0.156178i
$205$	1.41160e6	−	5.16954e6i	0.163851	−	0.600054i
$206$	−1.23785e7	−	1.11523e7i	−1.41600	−	1.27574i
$207$	970634.			0.109432
$208$	2.73905e6	+	1.29623e7i	0.304376	+	1.44043i
$209$	−773960.			−0.0847773
$210$	1.53106e7	−	9.83301e6i	1.65324	−	1.06177i
$211$		−	3.30342e6i		−	0.351655i	−0.984421	−	0.175828i	$-0.943740\pi$
$211$		−	3.30342e6i		−	0.351655i	0.984421	−	0.175828i	$-0.0562601\pi$
$212$	1.76398e7	−	1.84337e6i	1.85134	−	0.193466i
$213$			8.66642e6i			0.896811i
$214$	−3.04383e6	−	2.74232e6i	−0.310584	−	0.279819i
$215$	−1.90238e6	+	6.96689e6i	−0.191418	+	0.701009i
$216$	2.09201e6	−	2.87398e6i	0.207588	−	0.285183i
$217$		−	1.49730e7i		−	1.46531i
$218$	7.89937e6	+	7.11690e6i	0.762471	+	0.686944i
$219$		−	855648.i		−	0.0814634i
$220$	505735.	−	3.08594e6i	0.0474958	−	0.289814i
$221$	1.59694e7			1.47949
$222$	−3.06113e6	+	3.39769e6i	−0.279784	+	0.310545i
$223$	1.43034e7			1.28981			0.644903	−	0.764265i	$-0.276898\pi$
$223$	1.43034e7			1.28981			0.644903	+	0.764265i	$0.276898\pi$
$224$	1.27790e7	+	7.40343e6i	1.13698	+	0.658702i
$225$	−1.21240e7	−	7.15463e6i	−1.06438	−	0.628116i
$226$	−857690.	+	951990.i	−0.0743028	+	0.0824721i
$227$	879277.			0.0751706			0.0375853	−	0.999293i	$-0.488033\pi$
$227$	879277.			0.0751706			0.0375853	+	0.999293i	$0.488033\pi$
$228$	−5.08835e6	+	531736.i	−0.429311	+	0.0448633i
$229$	−363899.			−0.0303022			−0.0151511	−	0.999885i	$-0.504823\pi$
$229$	−363899.			−0.0303022			−0.0151511	+	0.999885i	$0.504823\pi$
$230$	906477.	−	582171.i	0.0745029	−	0.0478484i
$231$			7.11270e6i			0.577030i
$232$	−6.37530e6	+	8.75835e6i	−0.510548	+	0.701388i
$233$		−	3.19027e6i		−	0.252208i	−0.992017	−	0.126104i	$-0.959753\pi$
$233$		−	3.19027e6i		−	0.252208i	0.992017	−	0.126104i	$-0.0402474\pi$
$234$	−1.56050e7	+	1.73207e7i	−1.21791	+	1.35182i
$235$	4.54891e6	−	1.66590e7i	0.350513	−	1.28364i
$236$	−1.79350e6	+	187422.i	−0.136448	+	0.0142589i
$237$			1.47665e7i			1.10926i
$238$	1.19157e7	−	1.32257e7i	0.883867	−	0.981045i
$239$			1.72090e7i			1.26056i	0.776368	+	0.630279i	$0.217060\pi$
$239$			1.72090e7i			1.26056i	−0.776368	+	0.630279i	$0.782940\pi$
$240$	1.20478e6	−	2.06358e7i	0.0871513	−	1.49275i
$241$	−1.26609e7			−0.904508			−0.452254	−	0.891889i	$-0.649380\pi$
$241$	−1.26609e7			−0.904508			−0.452254	+	0.891889i	$0.649380\pi$
$242$	−9.62124e6	−	8.66821e6i	−0.678867	−	0.611622i
$243$	−2.02618e7			−1.41208
$244$	−226708.	−	2.16944e6i	−0.0156062	−	0.149341i
$245$	−2.81479e6	+	1.03083e7i	−0.191403	+	0.700953i
$246$	1.02871e7	+	9.26813e6i	0.691017	+	0.622568i
$247$	6.40434e6			0.424995
$248$	−1.37519e7	−	1.00102e7i	−0.901586	−	0.656275i
$249$	2.02797e6			0.131360
$250$	−1.56139e7	+	590058.i	−0.999287	+	0.0377637i
$251$		−	2.69052e7i		−	1.70143i	−0.525625	−	0.850716i	$-0.676168\pi$
$251$		−	2.69052e7i		−	1.70143i	0.525625	−	0.850716i	$-0.323832\pi$
$252$	2.70111e6	+	2.58478e7i	0.168788	+	1.61518i
$253$			421113.i			0.0260038i
$254$	1.12990e7	+	1.01798e7i	0.689506	+	0.621207i
$255$	−2.40362e7	−	6.56333e6i	−1.44959	−	0.395825i
$256$	1.53430e7	−	6.78729e6i	0.914514	−	0.404554i
$257$			7.81210e6i			0.460223i	0.973164	+	0.230112i	$0.0739091\pi$
$257$			7.81210e6i			0.460223i	−0.973164	+	0.230112i	$0.926091\pi$
$258$	−1.38638e7	−	1.24905e7i	−0.807276	−	0.727311i
$259$		−	6.38175e6i		−	0.367316i
$260$	−4.18484e6	+	2.55354e7i	−0.238100	+	1.45286i
$261$	−1.90628e7			−1.07217
$262$	1.47926e7	−	1.64190e7i	0.822509	−	0.912941i
$263$	1.33139e7			0.731877			0.365938	−	0.930639i	$-0.380748\pi$
$263$	1.33139e7			0.731877			0.365938	+	0.930639i	$0.380748\pi$
$264$	6.53262e6	+	4.75517e6i	0.355039	+	0.258437i
$265$	3.34169e7	+	9.12485e6i	1.79568	+	0.490330i
$266$	4.77862e6	−	5.30401e6i	0.253897	−	0.281812i
$267$	−7.15704e6			−0.376010
$268$	1.52993e6	+	1.46404e7i	0.0794819	+	0.760588i
$269$	−1.73876e7			−0.893271			−0.446635	−	0.894716i	$-0.647378\pi$
$269$	−1.73876e7			−0.893271			−0.446635	+	0.894716i	$0.647378\pi$
$270$	5.84185e6	−	3.75184e6i	0.296797	−	0.190613i
$271$			2.13357e7i			1.07201i	0.844215	+	0.536005i	$0.180067\pi$
$271$			2.13357e7i			1.07201i	−0.844215	+	0.536005i	$0.819933\pi$
$272$	−4.18093e6	−	1.97859e7i	−0.207762	−	0.983215i
$273$		−	5.88559e7i		−	2.89269i
$274$	1.39267e7	−	1.54579e7i	0.677013	−	0.751447i
$275$	3.10406e6	−	5.26004e6i	0.149256	−	0.252924i
$276$	289318.	+	2.76858e6i	0.0137610	+	0.131683i
$277$			1.72036e7i			0.809431i	0.914443	+	0.404716i	$0.132629\pi$
$277$			1.72036e7i			0.809431i	−0.914443	+	0.404716i	$0.867371\pi$
$278$	−1.64580e7	+	1.82675e7i	−0.766025	+	0.850247i
$279$		−	2.99314e7i		−	1.37821i
$280$	1.80257e7	+	2.25192e7i	0.821140	+	1.02584i
$281$	−2.56886e7			−1.15777			−0.578883	−	0.815411i	$-0.696511\pi$
$281$	−2.56886e7			−1.15777			−0.578883	+	0.815411i	$0.696511\pi$
$282$	3.31505e7	+	2.98668e7i	1.47823	+	1.33181i
$283$	1.39377e7			0.614937			0.307469	−	0.951558i	$-0.400518\pi$
$283$	1.39377e7			0.614937			0.307469	+	0.951558i	$0.400518\pi$
$284$	−1.36638e7	+	1.42788e6i	−0.596508	+	0.0623355i
$285$	−9.63939e6	−	2.63214e6i	−0.416404	−	0.113704i
$286$	−7.51464e6	−	6.77027e6i	−0.321225	−	0.289406i
$287$	−1.93219e7			−0.817342
$288$	2.55456e7	+	1.47996e7i	1.06939	+	0.619545i
$289$	−238417.			−0.00987743
$290$	−1.78028e7	+	1.14336e7i	−0.729952	+	0.468801i
$291$			4.65365e7i			1.88849i
$292$	1.34905e6	−	140976.i	0.0541849	−	0.00566235i
$293$			3.28329e7i			1.30529i	0.757665	+	0.652644i	$0.226340\pi$
$293$			3.28329e7i			1.30529i	−0.757665	+	0.652644i	$0.773660\pi$
$294$	−2.05130e7	−	1.84811e7i	−0.807212	−	0.727253i
$295$	−3.39762e6	−	927757.i	−0.132345	−	0.0361383i
$296$	−5.86128e6	−	4.26649e6i	−0.226005	−	0.164511i
$297$			2.71389e6i			0.103591i
$298$	−1.25261e7	−	1.12853e7i	−0.473332	−	0.426446i
$299$		−	3.48461e6i		−	0.130359i
$300$	1.67936e7	−	3.67143e7i	0.621986	−	1.35979i
$301$	2.60397e7			0.954854
$302$	1.18237e7	−	1.31236e7i	0.429271	−	0.476468i
$303$	5.16613e7			1.85711
$304$	−1.67671e6	−	7.93487e6i	−0.0596811	−	0.282436i
$305$	1.12222e6	−	4.10979e6i	0.0395530	−	0.144851i
$306$	2.38197e7	−	2.64385e7i	0.831326	−	0.922727i
$307$	3.20799e7			1.10871			0.554356	−	0.832280i	$-0.312965\pi$
$307$	3.20799e7			1.10871			0.554356	+	0.832280i	$0.312965\pi$
$308$	−1.12141e7	+	1.17189e6i	−0.383808	+	0.0401082i
$309$	8.40832e7			2.84993
$310$	−1.79524e7	−	2.79530e7i	−0.602612	−	0.938304i
$311$		−	3.21955e7i		−	1.07032i	−0.844751	−	0.535160i	$-0.820251\pi$
$311$		−	3.21955e7i		−	1.07032i	0.844751	−	0.535160i	$-0.179749\pi$
$312$	−5.40559e7	−	3.93479e7i	−1.77983	−	1.29556i
$313$		−	3.62694e6i		−	0.118279i	−0.998250	−	0.0591394i	$-0.981164\pi$
$313$		−	3.62694e6i		−	0.118279i	0.998250	−	0.0591394i	$-0.0188357\pi$
$314$	−4.39705e6	+	4.88049e6i	−0.142028	+	0.157643i
$315$	−1.33707e7	+	4.89662e7i	−0.427783	+	1.56662i
$316$	−2.32814e7	+	2.43292e6i	−0.737814	+	0.0771020i
$317$		−	2.70689e7i		−	0.849754i	−0.905251	−	0.424877i	$-0.860317\pi$
$317$		−	2.70689e7i		−	0.849754i	0.905251	−	0.424877i	$-0.139683\pi$
$318$	−5.99110e7	+	6.64980e7i	−1.86305	+	2.06789i
$319$		−	8.27047e6i		−	0.254776i
$320$	3.27336e7	−	1.50044e6i	0.998951	−	0.0457898i
$321$	2.06758e7			0.625098
$322$	−2.88592e6	−	2.60006e6i	−0.0864404	−	0.0778780i
$323$	−9.77568e6			−0.290094
$324$	−2.50443e6	−	2.39656e7i	−0.0736331	−	0.704619i
$325$	−2.56854e7	+	4.35255e7i	−0.748231	+	1.26793i
$326$	4.58135e7	+	4.12755e7i	1.32233	+	1.19135i
$327$	−5.36581e7			−1.53459
$328$	−1.29176e7	+	1.77461e7i	−0.366066	+	0.502899i
$329$	−6.22653e7			−1.74847
$330$	8.52801e6	+	1.32786e7i	0.237304	+	0.369498i
$331$			3.35438e7i			0.924972i	0.886627	+	0.462486i	$0.153042\pi$
$331$			3.35438e7i			0.924972i	−0.886627	+	0.462486i	$0.846958\pi$
$332$	334128.	+	3.19738e6i	0.00913059	+	0.0873736i
$333$		−	1.27573e7i		−	0.345481i
$334$	−1.40955e7	−	1.26993e7i	−0.378305	−	0.340832i
$335$	−7.57331e6	+	2.77349e7i	−0.201443	+	0.737721i
$336$	−7.29215e7	+	1.54090e7i	−1.92237	+	0.406215i
$337$		−	5.29894e7i		−	1.38452i	−0.721648	−	0.692260i	$-0.756615\pi$
$337$		−	5.29894e7i		−	1.38452i	0.721648	−	0.692260i	$-0.243385\pi$
$338$	3.34934e7	+	3.01757e7i	0.867379	+	0.781461i
$339$		−	6.46659e6i		−	0.165988i
$340$	6.38780e6	−	3.89777e7i	0.162523	−	0.991697i
$341$	1.29859e7			0.327497
$342$	9.55257e6	−	1.06028e7i	0.238804	−	0.265060i
$343$	−1.44962e7			−0.359229
$344$	1.74088e7	−	2.39160e7i	0.427654	−	0.587508i
$345$	−1.43215e6	+	5.24481e6i	−0.0348764	+	0.127724i
$346$	−2.79837e7	+	3.10604e7i	−0.675580	+	0.749858i
$347$	−1.30197e7			−0.311611			−0.155805	−	0.987788i	$-0.549797\pi$
$347$	−1.30197e7			−0.311611			−0.155805	+	0.987788i	$0.549797\pi$
$348$	−5.68208e6	−	5.43737e7i	−0.134825	−	1.29018i
$349$	−1.95421e7			−0.459721			−0.229860	−	0.973224i	$-0.573827\pi$
$349$	−1.95421e7			−0.459721			−0.229860	+	0.973224i	$0.573827\pi$
$350$	1.68822e7	+	5.37491e7i	0.393754	+	1.25362i
$351$		−	2.24568e7i		−	0.519310i
$352$	−6.42087e6	+	1.10830e7i	−0.147220	+	0.254115i
$353$		−	4.20948e7i		−	0.956984i	−0.878092	−	0.478492i	$-0.841184\pi$
$353$		−	4.20948e7i		−	0.956984i	0.878092	−	0.478492i	$-0.158816\pi$
$354$	6.09138e6	−	6.76110e6i	0.137311	−	0.152408i
$355$	−2.58848e7	−	7.06811e6i	−0.578574	−	0.157986i
$356$	−1.17919e6	−	1.12841e7i	−0.0261357	−	0.250101i
$357$			8.98386e7i			1.97450i
$358$	3.43617e7	−	3.81396e7i	0.748902	−	0.831241i
$359$		−	6.88488e6i		−	0.148803i	−0.997228	−	0.0744017i	$-0.976295\pi$
$359$		−	6.88488e6i		−	0.148803i	0.997228	−	0.0744017i	$-0.0237047\pi$
$360$	3.60337e7	+	4.50164e7i	0.772328	+	0.964858i
$361$	4.31255e7			0.916668
$362$	1.63423e7	+	1.47235e7i	0.344499	+	0.310375i
$363$	6.53543e7			1.36633
$364$	9.27944e7	−	9.69707e6i	1.92406	−	0.201065i
$365$	2.55564e6	+	697844.i	0.0525558	+	0.0143509i
$366$	8.17828e6	+	7.36818e6i	0.166809	+	0.150285i
$367$	1.25791e7			0.254480			0.127240	−	0.991872i	$-0.459388\pi$
$367$	1.25791e7			0.254480			0.127240	+	0.991872i	$0.459388\pi$
$368$	−4.31738e6	+	912300.i	−0.0866316	+	0.0183060i
$369$	−3.86249e7			−0.768756
$370$	−7.65161e6	−	1.19140e7i	−0.151059	−	0.235209i
$371$		−	1.24901e8i		−	2.44592i
$372$	8.53746e7	−	8.92170e6i	1.65844	−	0.173308i
$373$		−	5.80469e7i		−	1.11854i	−0.828984	−	0.559272i	$-0.811081\pi$
$373$		−	5.80469e7i		−	1.11854i	0.828984	−	0.559272i	$-0.188919\pi$
$374$	1.14705e7	+	1.03342e7i	0.219263	+	0.197544i
$375$	5.65487e7	−	5.49553e7i	1.07233	−	1.04212i
$376$	−4.16272e7	+	5.71872e7i	−0.783094	+	1.07581i
$377$			6.84362e7i			1.27721i
$378$	−1.85985e7	−	1.67562e7i	−0.344352	−	0.310242i
$379$			4.35438e7i			0.799850i	0.916548	+	0.399925i	$0.130964\pi$
$379$			4.35438e7i			0.799850i	−0.916548	+	0.399925i	$0.869036\pi$
$380$	2.56175e6	−	1.56315e7i	0.0466859	−	0.284872i
$381$	−7.67507e7			−1.38774
$382$	−4.27045e7	+	4.73997e7i	−0.766096	+	0.850325i
$383$	−2.94725e6			−0.0524591			−0.0262296	−	0.999656i	$-0.508350\pi$
$383$	−2.94725e6			−0.0524591			−0.0262296	+	0.999656i	$0.508350\pi$
$384$	−3.45992e7	+	7.72760e7i	−0.611043	+	1.36474i
$385$	−2.12441e7	−	5.80094e6i	−0.372269	−	0.101652i
$386$	6.52539e7	−	7.24283e7i	1.13460	−	1.25935i
$387$	5.20540e7			0.898094
$388$	−7.33712e7	+	7.66733e6i	−1.25612	+	0.131265i
$389$	1.87700e7			0.318871			0.159436	−	0.987208i	$-0.449033\pi$
$389$	1.87700e7			0.318871			0.159436	+	0.987208i	$0.449033\pi$
$390$	−7.05672e7	−	1.09878e8i	−1.18962	−	1.85232i
$391$			5.31896e6i			0.0889809i
$392$	2.57583e7	−	3.53865e7i	0.427620	−	0.587462i
$393$			1.11529e8i			1.83743i
$394$	−2.82302e7	+	3.13340e7i	−0.461556	+	0.512303i
$395$	−4.41043e7	−	1.20432e7i	−0.715632	−	0.195411i
$396$	−2.24173e7	+	2.34263e6i	−0.360993	+	0.0377240i
$397$		−	3.99848e7i		−	0.639033i	−0.947581	−	0.319517i	$-0.896479\pi$
$397$		−	3.99848e7i		−	0.639033i	0.947581	−	0.319517i	$-0.103521\pi$
$398$	6.12776e7	−	6.80149e7i	0.971970	−	1.07883i
$399$			3.60286e7i			0.567190i
$400$	6.06521e7	+	2.04284e7i	0.947689	+	0.319194i
$401$	6.49364e6			0.100706			0.0503530	−	0.998731i	$-0.483965\pi$
$401$	6.49364e6			0.100706			0.0503530	+	0.998731i	$0.483965\pi$
$402$	−5.51911e7	−	4.97241e7i	−0.849553	−	0.765401i
$403$	−1.07455e8			−1.64176
$404$	8.51169e6	+	8.14511e7i	0.129084	+	1.23524i
$405$	1.23971e7	−	4.54006e7i	0.186619	−	0.683434i
$406$	5.66782e7	+	5.10639e7i	0.846911	+	0.763020i
$407$	5.53478e6			0.0820951
$408$	8.25117e7	+	6.00612e7i	1.21488	+	0.884329i
$409$	2.76062e7			0.403494			0.201747	−	0.979438i	$-0.435338\pi$
$409$	2.76062e7			0.403494			0.201747	+	0.979438i	$0.435338\pi$
$410$	−3.60719e7	+	2.31666e7i	−0.523380	+	0.336133i
$411$			1.05001e8i			1.51240i
$412$	1.38535e7	+	1.32569e8i	0.198093	+	1.89561i
$413$			1.26991e7i			0.180270i
$414$	−5.76902e6	−	5.19757e6i	−0.0813020	−	0.0732486i
$415$	−1.65396e6	+	6.05713e6i	−0.0231410	+	0.0847467i
$416$	5.31311e7	−	9.17094e7i	0.738022	−	1.27390i
$417$		−	1.24086e8i		−	1.71125i
$418$	4.60008e6	+	4.14442e6i	0.0629849	+	0.0567459i
$419$		−	1.47995e7i		−	0.201190i	−0.994927	−	0.100595i	$-0.967925\pi$
$419$		−	1.47995e7i		−	0.201190i	0.994927	−	0.100595i	$-0.0320746\pi$
$420$	−1.43654e8	−	2.35425e7i	−1.93896	−	0.317764i
$421$	−3.29248e7			−0.441242			−0.220621	−	0.975360i	$-0.570808\pi$
$421$	−3.29248e7			−0.441242			−0.220621	+	0.975360i	$0.570808\pi$
$422$	−1.76892e7	+	1.96341e7i	−0.235381	+	0.261260i
$423$	−1.24470e8			−1.64453
$424$	−1.14714e8	−	8.35018e7i	−1.50494	−	1.09546i
$425$	3.92066e7	−	6.64381e7i	0.510731	−	0.865466i
$426$	4.64071e7	−	5.15094e7i	0.600283	−	0.666281i
$427$	−1.53609e7			−0.197303
$428$	3.40654e6	+	3.25983e7i	0.0434493	+	0.415780i
$429$	5.10447e7			0.646516
$430$	4.86134e7	−	3.12212e7i	0.611435	−	0.392685i
$431$			9.46095e7i			1.18169i	0.806786	+	0.590844i	$0.201205\pi$
$431$			9.46095e7i			1.18169i	−0.806786	+	0.590844i	$0.798795\pi$
$432$	−2.78236e7	+	5.87938e6i	−0.345114	+	0.0729256i
$433$			6.50578e7i			0.801375i	0.916215	+	0.400687i	$0.131229\pi$
$433$			6.50578e7i			0.801375i	−0.916215	+	0.400687i	$0.868771\pi$
$434$	−8.01778e7	+	8.89931e7i	−0.980811	+	1.08865i
$435$	2.81268e7	−	1.03006e8i	0.341706	−	1.25139i
$436$	−8.84069e6	−	8.45994e7i	−0.106666	−	1.02072i
$437$			2.13310e6i			0.0255604i
$438$	−4.58184e6	+	5.08559e6i	−0.0545277	+	0.0605228i
$439$			5.30694e7i			0.627264i	0.949545	+	0.313632i	$0.101546\pi$
$439$			5.30694e7i			0.627264i	−0.949545	+	0.313632i	$0.898454\pi$
$440$	−1.95305e7	+	1.56334e7i	−0.229275	+	0.183525i
$441$	7.70199e7			0.898022
$442$	−9.49153e7	−	8.55134e7i	−1.09918	−	0.990302i
$443$	1.37420e8			1.58066			0.790328	−	0.612684i	$-0.209910\pi$
$443$	1.37420e8			1.58066			0.790328	+	0.612684i	$0.209910\pi$
$444$	3.63880e7	−	3.80257e6i	0.415729	−	0.0434439i
$445$	5.83710e6	−	2.13766e7i	0.0662395	−	0.242582i
$446$	−8.50130e7	−	7.65921e7i	−0.958255	−	0.863335i
$447$	8.50859e7			0.952654
$448$	−3.63089e7	−	1.12432e8i	−0.403812	−	1.25042i
$449$	1.37603e6			0.0152016			0.00760078	−	0.999971i	$-0.497581\pi$
$449$	1.37603e6			0.0152016			0.00760078	+	0.999971i	$0.497581\pi$
$450$	3.37479e7	+	1.07446e8i	0.370347	+	1.17910i
$451$		−	1.67576e7i		−	0.182676i
$452$	1.01955e7	−	1.06543e6i	0.110406	−	0.0115375i
$453$			8.91451e7i			0.958965i
$454$	−5.22603e6	−	4.70837e6i	−0.0558476	−	0.0503156i
$455$	1.75790e8	+	4.80014e7i	1.86621	+	0.509588i
$456$	3.30903e7	+	2.40868e7i	0.348984	+	0.254030i
$457$			1.19484e8i			1.25187i	0.779873	+	0.625937i	$0.215283\pi$
$457$			1.19484e8i			1.25187i	−0.779873	+	0.625937i	$0.784717\pi$
$458$	2.16285e6	+	1.94861e6i	0.0225129	+	0.0202828i
$459$			3.42784e7i			0.354473i
$460$	−8.50512e6	−	1.39385e6i	−0.0873790	−	0.0143200i
$461$	−1.26030e8			−1.28639			−0.643194	−	0.765703i	$-0.722391\pi$
$461$	−1.26030e8			−1.28639			−0.643194	+	0.765703i	$0.722391\pi$
$462$	3.80872e7	−	4.22748e7i	0.386237	−	0.428702i
$463$	−1.01206e8			−1.01968			−0.509839	−	0.860270i	$-0.670295\pi$
$463$	−1.01206e8			−1.01968			−0.509839	+	0.860270i	$0.670295\pi$
$464$	8.47914e7	−	1.79172e7i	0.848785	−	0.179356i
$465$	1.61734e8	+	4.41632e7i	1.60858	+	0.439240i
$466$	−1.70833e7	+	1.89616e7i	−0.168816	+	0.187377i
$467$	−9.72528e7			−0.954886			−0.477443	−	0.878663i	$-0.658436\pi$
$467$	−9.72528e7			−0.954886			−0.477443	+	0.878663i	$0.658436\pi$
$468$	1.85498e8	−	1.93847e7i	1.80968	−	0.189113i
$469$	1.03663e8			1.00486
$470$	−1.16243e8	+	7.46550e7i	−1.11962	+	0.719061i
$471$		−	3.31517e7i		−	0.317281i
$472$	1.16634e7	+	8.48994e6i	0.110917	+	0.0807381i
$473$			2.25838e7i			0.213410i
$474$	7.90717e7	−	8.77654e7i	0.742483	−	0.824116i
$475$	1.57233e7	−	2.66441e7i	0.146711	−	0.248611i
$476$	−1.41643e8	+	1.48018e7i	−1.31333	+	0.137244i
$477$		−	2.49679e8i		−	2.30053i
$478$	9.21513e7	−	1.02283e8i	0.843758	−	0.936526i
$479$			6.06291e7i			0.551664i	0.961206	+	0.275832i	$0.0889533\pi$
$479$			6.06291e7i			0.551664i	−0.961206	+	0.275832i	$0.911047\pi$
$480$	−1.17662e8	+	1.16199e8i	−1.06392	+	1.05070i
$481$	−4.57990e7			−0.411548
$482$	7.52506e7	+	6.77967e7i	0.672000	+	0.605435i
$483$	1.96032e7			0.173975
$484$	1.07677e7	+	1.03040e8i	0.0949705	+	0.908803i
$485$	−1.38995e8	−	3.79540e7i	−1.21835	−	0.332684i
$486$	1.20427e8	+	1.08498e8i	1.04910	+	0.945181i
$487$	1.20117e8			1.03996			0.519979	−	0.854179i	$-0.325940\pi$
$487$	1.20117e8			1.03996			0.519979	+	0.854179i	$0.325940\pi$
$488$	−1.02695e7	+	1.41082e7i	−0.0883669	+	0.121398i
$489$	−3.11198e8			−2.66140
$490$	7.19290e7	−	4.61953e7i	0.611387	−	0.392654i
$491$		−	1.17425e8i		−	0.992011i	−0.868319	−	0.496005i	$-0.834800\pi$
$491$		−	1.17425e8i		−	0.992011i	0.868319	−	0.496005i	$-0.165200\pi$
$492$	−1.15130e7	−	1.10171e8i	−0.0966701	−	0.925068i
$493$		−	1.04462e8i		−	0.871802i
$494$	−3.80646e7	−	3.42941e7i	−0.315748	−	0.284471i
$495$	−4.24675e7	−	1.15962e7i	−0.350140	−	0.0956094i
$496$	2.81326e7	+	1.33135e8i	0.230550	+	1.09106i
$497$			9.67480e7i			0.788085i
$498$	−1.20534e7	−	1.08594e7i	−0.0975935	−	0.0879264i
$499$		−	2.08663e8i		−	1.67936i	−0.543083	−	0.839679i	$-0.682743\pi$
$499$		−	2.08663e8i		−	1.67936i	0.543083	−	0.839679i	$-0.317257\pi$
$500$	9.59615e7	+	8.01023e7i	0.767692	+	0.640819i
$501$	9.57470e7			0.761398
$502$	−1.44072e8	+	1.59913e8i	−1.13886	+	1.26407i
$503$	−2.10295e8			−1.65244			−0.826220	−	0.563348i	$-0.809513\pi$
$503$	−2.10295e8			−1.65244			−0.826220	+	0.563348i	$0.809513\pi$
$504$	1.22356e8	−	1.68092e8i	0.955727	−	1.31297i
$505$	−4.21336e7	+	1.54301e8i	−0.327156	+	1.19811i
$506$	2.25498e6	−	2.50291e6i	0.0174057	−	0.0193194i
$507$	−2.27511e8			−1.74573
$508$	−1.26454e7	−	1.21008e8i	−0.0964588	−	0.923045i
$509$	1.78286e8			1.35196			0.675980	−	0.736920i	$-0.263721\pi$
$509$	1.78286e8			1.35196			0.675980	+	0.736920i	$0.263721\pi$
$510$	1.07715e8	+	1.67719e8i	0.812017	+	1.26436i
$511$		−	9.55206e6i		−	0.0715871i
$512$	−1.27537e8	−	4.18184e7i	−0.950223	−	0.311571i
$513$			1.37469e7i			0.101825i
$514$	4.18324e7	−	4.64317e7i	0.308052	−	0.341921i
$515$	−6.85761e7	+	2.51139e8i	−0.502055	+	1.83862i
$516$	1.55158e7	+	1.48476e8i	0.112934	+	1.08070i
$517$		−	5.40016e7i		−	0.390783i
$518$	−3.41731e7	+	3.79303e7i	−0.245864	+	0.272896i
$519$		−	2.10984e8i		−	1.50920i
$520$	1.61610e8	−	1.29362e8i	1.14937	−	0.920021i
$521$	2.05210e8			1.45106			0.725531	−	0.688189i	$-0.241594\pi$
$521$	2.05210e8			1.45106			0.725531	+	0.688189i	$0.241594\pi$
$522$	1.13301e8	+	1.02078e8i	0.796567	+	0.717663i
$523$	7.21180e7			0.504125			0.252063	−	0.967711i	$-0.418891\pi$
$523$	7.21180e7			0.504125			0.252063	+	0.967711i	$0.418891\pi$
$524$	−1.75841e8	+	1.83755e7i	−1.22216	+	0.127716i
$525$	−2.44860e8	−	1.44497e8i	−1.69215	−	0.998576i
$526$	−7.91320e7	−	7.12935e7i	−0.543744	−	0.489884i
$527$	1.64021e8			1.12064
$528$	−1.33639e7	−	6.32436e7i	−0.0907889	−	0.429650i
$529$	−1.46875e8			−0.992160
$530$	−1.49754e8	−	2.33176e8i	−1.00589	−	1.56623i
$531$			2.53858e7i			0.169554i
$532$	−5.68040e7	+	5.93606e6i	−0.377263	+	0.0394242i
$533$			1.38665e8i			0.915766i
$534$	4.25383e7	+	3.83247e7i	0.279355	+	0.251683i
$535$	−1.68627e7	+	6.17544e7i	−0.110120	+	0.403280i
$536$	6.93036e7	−	9.52088e7i	0.450051	−	0.618277i
$537$			2.59071e8i			1.67300i
$538$	1.03344e8	+	9.31075e7i	0.663651	+	0.597913i
$539$			3.34153e7i			0.213393i
$540$	−5.48118e7	−	8.98276e6i	−0.348091	−	0.0570464i
$541$	−1.48242e7			−0.0936225			−0.0468112	−	0.998904i	$-0.514906\pi$
$541$	−1.48242e7			−0.0936225			−0.0468112	+	0.998904i	$0.514906\pi$
$542$	1.14249e8	−	1.26810e8i	0.717552	−	0.796444i
$543$	−1.11009e8			−0.693358
$544$	−8.11002e7	+	1.39987e8i	−0.503762	+	0.869541i
$545$	4.37622e7	−	1.60266e8i	0.270340	−	0.990035i
$546$	−3.15163e8	+	3.49814e8i	−1.93623	+	2.14911i
$547$	2.59533e8			1.58574			0.792869	−	0.609392i	$-0.208587\pi$
$547$	2.59533e8			1.58574			0.792869	+	0.609392i	$0.208587\pi$
$548$	−1.65548e8	+	1.72999e7i	−1.00597	+	0.105124i
$549$	−3.07069e7			−0.185575
$550$	−4.66157e7	+	1.46416e7i	−0.280185	+	0.0880039i
$551$		−	4.18932e7i		−	0.250431i
$552$	1.31057e7	−	1.80045e7i	0.0779187	−	0.107044i
$553$			1.64846e8i			0.974773i
$554$	9.21221e7	−	1.02251e8i	0.541795	−	0.601363i
$555$	6.89337e7	+	1.88231e7i	0.403230	+	0.110106i
$556$	1.95638e8	−	2.04443e7i	1.13823	−	0.118946i
$557$		−	3.21717e7i		−	0.186169i	−0.995658	−	0.0930847i	$-0.970327\pi$
$557$		−	3.21717e7i		−	0.186169i	0.995658	−	0.0930847i	$-0.0296727\pi$
$558$	−1.60277e8	+	1.77899e8i	−0.922507	+	1.02393i
$559$		−	1.86876e8i		−	1.06984i
$560$	1.34496e7	−	2.30368e8i	0.0765854	−	1.31177i
$561$	−7.79155e7			−0.441301
$562$	1.52681e8	+	1.37558e8i	0.860156	+	0.774953i
$563$	2.80885e8			1.57400			0.786999	−	0.616955i	$-0.211634\pi$
$563$	2.80885e8			1.57400			0.786999	+	0.616955i	$0.211634\pi$
$564$	−3.71009e7	−	3.55030e8i	−0.206798	−	1.97892i
$565$	1.93143e7	+	5.27398e6i	0.107086	+	0.0292411i
$566$	−8.28394e7	−	7.46337e7i	−0.456865	−	0.411610i
$567$	−1.69691e8			−0.930916
$568$	8.88576e7	+	6.46805e7i	0.484897	+	0.352962i
$569$	3.50834e8			1.90443			0.952216	−	0.305426i	$-0.0987987\pi$
$569$	3.50834e8			1.90443			0.952216	+	0.305426i	$0.0987987\pi$
$570$	4.31977e7	+	6.72615e7i	0.233258	+	0.363197i
$571$			1.49375e8i			0.802360i	0.915999	+	0.401180i	$0.131400\pi$
$571$			1.49375e8i			0.802360i	−0.915999	+	0.401180i	$0.868600\pi$
$572$	8.41011e6	+	8.04790e7i	0.0449380	+	0.430026i
$573$		−	3.21972e8i		−	1.71141i
$574$	1.14841e8	+	1.03465e8i	0.607240	+	0.547090i
$575$	−1.44971e7	−	8.55506e6i	−0.0762567	−	0.0450008i
$576$	−7.25823e7	−	2.24754e8i	−0.379807	−	1.17609i
$577$		−	3.18308e8i		−	1.65699i	−0.559996	−	0.828496i	$-0.689197\pi$
$577$		−	3.18308e8i		−	1.65699i	0.559996	−	0.828496i	$-0.310803\pi$
$578$	1.41705e6	+	1.27668e6i	0.00733839	+	0.00661148i
$579$			4.91984e8i			2.53463i
$580$	1.67037e8	+	2.73746e7i	0.856107	+	0.140302i
$581$	2.26394e7			0.115435
$582$	2.49195e8	−	2.76592e8i	1.26407	−	1.40304i
$583$	1.08324e8			0.546663
$584$	−8.77304e6	−	6.38600e6i	−0.0440465	−	0.0320620i
$585$	3.51409e8	+	9.59559e7i	1.75527	+	0.479296i
$586$	1.75814e8	−	1.95144e8i	0.873697	−	0.969757i
$587$	−3.05295e8			−1.50940			−0.754702	−	0.656068i	$-0.772218\pi$
$587$	−3.05295e8			−1.50940			−0.754702	+	0.656068i	$0.772218\pi$
$588$	2.29574e7	+	2.19687e8i	0.112925	+	1.08062i
$589$	6.57784e7			0.321912
$590$	1.52260e7	+	2.37078e7i	0.0741361	+	0.115435i
$591$		−	2.12842e8i		−	1.03109i
$592$	1.19906e7	+	5.67442e7i	0.0577929	+	0.273500i
$593$		−	3.16115e8i		−	1.51594i	−0.652292	−	0.757968i	$-0.726192\pi$
$593$		−	3.16115e8i		−	1.51594i	0.652292	−	0.757968i	$-0.273808\pi$
$594$	1.45324e7	−	1.61302e7i	0.0693391	−	0.0769626i
$595$	−2.68329e8	−	7.32700e7i	−1.27384	−	0.347837i
$596$	1.40187e7	+	1.34150e8i	0.0662170	+	0.633652i
$597$			4.62005e8i			2.17132i
$598$	−1.86595e7	+	2.07110e7i	−0.0872560	+	0.0968495i
$599$			1.45523e8i			0.677097i	0.940949	+	0.338549i	$0.109936\pi$
$599$			1.45523e8i			0.677097i	−0.940949	+	0.338549i	$0.890064\pi$
$600$	−2.96413e8	+	1.28287e8i	−1.37228	+	0.593921i
$601$	−1.38073e8			−0.636040			−0.318020	−	0.948084i	$-0.603018\pi$
$601$	−1.38073e8			−0.636040			−0.318020	+	0.948084i	$0.603018\pi$
$602$	−1.54769e8	−	1.39438e8i	−0.709404	−	0.639134i
$603$	2.07225e8			0.945128
$604$	−1.40550e8	+	1.46875e7i	−0.637850	+	0.0666557i
$605$	−5.33013e7	+	1.95199e8i	−0.240697	+	0.881480i
$606$	−3.07052e8	−	2.76637e8i	−1.37973	−	1.24306i
$607$	2.20855e8			0.987510			0.493755	−	0.869601i	$-0.335624\pi$
$607$	2.20855e8			0.987510			0.493755	+	0.869601i	$0.335624\pi$
$608$	−3.25242e7	+	5.61399e7i	−0.144709	+	0.249782i
$609$	−3.84998e8			−1.70454
$610$	−2.86772e7	+	1.84175e7i	−0.126342	+	0.0811411i
$611$			4.46851e8i			1.95902i
$612$	−2.83147e8	+	2.95891e7i	−1.23526	+	0.129085i
$613$			6.60483e7i			0.286735i	0.989670	+	0.143367i	$0.0457931\pi$
$613$			6.60483e7i			0.286735i	−0.989670	+	0.143367i	$0.954207\pi$
$614$	−1.90669e8	−	1.71782e8i	−0.823712	−	0.742119i
$615$	5.69903e7	−	2.08709e8i	0.245005	−	0.897256i
$616$	7.29272e7	+	5.30846e7i	0.311995	+	0.227105i
$617$		−	9.38189e6i		−	0.0399425i	−0.999801	−	0.0199712i	$-0.993643\pi$
$617$		−	9.38189e6i		−	0.0399425i	0.999801	−	0.0199712i	$-0.00635746\pi$
$618$	−4.99754e8	−	4.50250e8i	−2.11734	−	1.90761i
$619$		−	3.27827e8i		−	1.38221i	−0.722756	−	0.691103i	$-0.757125\pi$
$619$		−	3.27827e8i		−	1.38221i	0.722756	−	0.691103i	$-0.242875\pi$
$620$	−4.29821e7	+	2.62272e8i	−0.180349	+	1.10047i
$621$	7.47972e6			0.0312328
$622$	−1.72401e8	+	1.91356e8i	−0.716421	+	0.795188i
$623$	−7.98980e7			−0.330424
$624$	1.10583e8	+	5.23326e8i	0.455131	+	2.15387i
$625$	1.18020e8	+	2.13719e8i	0.483411	+	0.875393i
$626$	−1.94216e7	+	2.15569e7i	−0.0791702	+	0.0878747i
$627$	−3.12470e7			−0.126767
$628$	5.22683e7	−	5.46207e6i	0.211037	−	0.0220535i
$629$	6.99083e7			0.280916
$630$	3.41675e8	−	2.19435e8i	1.36644	−	0.877577i
$631$			2.66189e8i			1.05950i	0.848153	+	0.529751i	$0.177715\pi$
$631$			2.66189e8i			1.05950i	−0.848153	+	0.529751i	$0.822285\pi$
$632$	1.51402e8	+	1.10207e8i	0.599764	+	0.436575i
$633$		−	1.33369e8i		−	0.525827i
$634$	−1.44949e8	+	1.60886e8i	−0.568785	+	0.631320i
$635$	6.25959e7	−	2.29238e8i	0.244470	−	0.895294i
$636$	7.12170e8	−	7.44222e7i	2.76829	−	0.289288i
$637$		−	2.76504e8i		−	1.06975i
$638$	−4.42869e7	+	4.91560e7i	−0.170535	+	0.189284i
$639$			1.93401e8i			0.741237i
$640$	−2.02589e8	−	1.66365e8i	−0.772815	−	0.634631i
$641$	4.00719e7			0.152148			0.0760739	−	0.997102i	$-0.475762\pi$
$641$	4.00719e7			0.152148			0.0760739	+	0.997102i	$0.475762\pi$
$642$	−1.22888e8	−	1.10715e8i	−0.464413	−	0.418411i
$643$	−7.15926e7			−0.269299			−0.134650	−	0.990893i	$-0.542991\pi$
$643$	−7.15926e7			−0.269299			−0.134650	+	0.990893i	$0.542991\pi$
$644$	3.22982e6	+	3.09072e7i	0.0120926	+	0.115718i
$645$	−7.68047e7	+	2.81273e8i	−0.286226	+	1.04821i
$646$	5.81023e7	+	5.23470e7i	0.215524	+	0.194175i
$647$	−4.24659e8			−1.56793			−0.783966	−	0.620803i	$-0.786807\pi$
$647$	−4.24659e8			−1.56793			−0.783966	+	0.620803i	$0.786807\pi$
$648$	−1.13447e8	+	1.55852e8i	−0.416933	+	0.572779i
$649$	−1.10137e7			−0.0402902
$650$	3.85734e8	−	1.21156e8i	1.40458	−	0.441169i
$651$		−	6.04504e8i		−	2.19107i
$652$	−5.12728e7	−	4.90646e8i	−0.184988	−	1.77021i
$653$		−	3.37874e8i		−	1.21343i	−0.794918	−	0.606716i	$-0.792486\pi$
$653$		−	3.37874e8i		−	1.21343i	0.794918	−	0.606716i	$-0.207514\pi$
$654$	3.18920e8	+	2.87330e8i	1.14012	+	1.02718i
$655$	−3.33115e8	−	9.09606e7i	−1.18541	−	0.323690i
$656$	1.71803e8	−	3.63036e7i	0.608584	−	0.128599i
$657$		−	1.90948e7i		−	0.0673316i
$658$	3.70077e8	+	3.33419e8i	1.29902	+	1.17034i
$659$		−	2.03482e8i		−	0.711001i	−0.934676	−	0.355501i	$-0.884310\pi$
$659$		−	2.03482e8i		−	0.711001i	0.934676	−	0.355501i	$-0.115690\pi$
$660$	2.04180e7	−	1.24588e8i	0.0710201	−	0.433357i
$661$	−5.04157e8			−1.74567			−0.872833	−	0.488019i	$-0.837720\pi$
$661$	−5.04157e8			−1.74567			−0.872833	+	0.488019i	$0.837720\pi$
$662$	1.79621e8	−	1.99370e8i	0.619132	−	0.687203i
$663$	6.44732e8			2.21227
$664$	1.51355e7	−	2.07930e7i	0.0517002	−	0.0710253i
$665$	−1.07610e8	−	2.93840e7i	−0.365921	−	0.0999186i
$666$	−6.83128e7	+	7.58235e7i	−0.231249	+	0.256674i
$667$	−2.27941e7			−0.0768149
$668$	1.57752e7	+	1.50958e8i	0.0529232	+	0.506439i
$669$	5.77469e8			1.92864
$670$	1.93528e8	−	1.24290e8i	0.643456	−	0.413250i
$671$		−	1.33223e7i		−	0.0440972i
$672$	5.15926e8	+	2.98898e8i	1.70012	+	0.984951i
$673$			2.63250e8i			0.863621i	0.901964	+	0.431810i	$0.142125\pi$
$673$			2.63250e8i			0.863621i	−0.901964	+	0.431810i	$0.857875\pi$
$674$	−2.83749e8	+	3.14946e8i	−0.926732	+	1.02862i
$675$	−9.34276e7	−	5.51337e7i	−0.303783	−	0.179269i
$676$	−3.74846e7	−	3.58702e8i	−0.121342	−	1.16116i
$677$			2.04498e8i			0.659056i	0.944146	+	0.329528i	$0.106890\pi$
$677$			2.04498e8i			0.659056i	−0.944146	+	0.329528i	$0.893110\pi$
$678$	−3.46274e7	+	3.84346e7i	−0.111104	+	0.123320i
$679$			5.19513e8i			1.65954i
$680$	−2.46685e8	+	1.97461e8i	−0.784541	+	0.627992i
$681$	3.54989e7			0.112402
$682$	−7.71822e7	−	6.95369e7i	−0.243312	−	0.219211i
$683$	−9.73212e7			−0.305454			−0.152727	−	0.988268i	$-0.548805\pi$
$683$	−9.73212e7			−0.305454			−0.152727	+	0.988268i	$0.548805\pi$
$684$	−1.13553e8	+	1.18663e7i	−0.354837	+	0.0370807i
$685$	−3.13616e8	−	8.56361e7i	−0.975722	−	0.266431i
$686$	8.61589e7	+	7.76244e7i	0.266887	+	0.240451i
$687$	−1.46916e7			−0.0453106
$688$	−2.31536e8	+	4.89256e7i	−0.710974	+	0.150235i
$689$	−8.96356e8			−2.74046
$690$	3.65971e7	−	2.35039e7i	0.111404	−	0.0715473i
$691$		−	4.93368e8i		−	1.49533i	−0.664076	−	0.747665i	$-0.731175\pi$
$691$		−	4.93368e8i		−	1.49533i	0.664076	−	0.747665i	$-0.268825\pi$
$692$	3.32646e8	−	3.47617e7i	1.00384	−	0.104902i
$693$			1.58728e8i			0.476930i
$694$	7.73833e7	+	6.97181e7i	0.231510	+	0.208577i
$695$	3.70618e8	+	1.01201e8i	1.10401	+	0.301461i
$696$	−2.57389e8	+	3.53600e8i	−0.763419	+	1.04878i
$697$		−	2.11660e8i		−	0.625087i
$698$	1.16149e8	+	1.04644e8i	0.341547	+	0.307715i
$699$		−	1.28800e8i		−	0.377125i
$700$	1.87477e8	−	4.09862e8i	0.546579	−	1.19493i
$701$	−1.60818e6			−0.00466855			−0.00233427	−	0.999997i	$-0.500743\pi$
$701$	−1.60818e6			−0.00466855			−0.00233427	+	0.999997i	$0.500743\pi$
$702$	−1.20252e8	+	1.33473e8i	−0.347601	+	0.385819i
$703$	2.80358e7			0.0806951
$704$	9.75104e7	−	3.14901e7i	0.279469	−	0.0902518i
$705$	1.83653e8	−	6.72571e8i	0.524119	−	1.91942i
$706$	−2.25410e8	+	2.50193e8i	−0.640559	+	0.710986i
$707$	5.76723e8			1.63196
$708$	−7.24089e7	+	7.56678e6i	−0.204029	+	0.0213212i
$709$	5.27495e8			1.48006			0.740031	−	0.672573i	$-0.234811\pi$
$709$	5.27495e8			1.48006			0.740031	+	0.672573i	$0.234811\pi$
$710$	1.15999e8	+	1.80618e8i	0.324101	+	0.504645i
$711$			3.29531e8i			0.916828i
$712$	−5.34155e7	+	7.33819e7i	−0.147988	+	0.203305i
$713$		−	3.57901e7i		−	0.0987404i
$714$	4.81069e8	−	5.33961e8i	1.32164	−	1.46695i
$715$	−4.16308e7	+	1.52460e8i	−0.113893	+	0.417097i
$716$	−4.08461e8	+	4.26845e7i	−1.11279	+	0.116287i
$717$			6.94779e8i			1.88490i
$718$	−3.68673e7	+	4.09207e7i	−0.0996020	+	0.110553i
$719$		−	3.85369e8i		−	1.03679i	−0.855142	−	0.518394i	$-0.826530\pi$
$719$		−	3.85369e8i		−	1.03679i	0.855142	−	0.518394i	$-0.173470\pi$
$720$	2.68861e7	−	4.60512e8i	0.0720328	−	1.23380i
$721$	9.38667e8			2.50441
$722$	−2.56319e8	−	2.30929e8i	−0.681034	−	0.613574i
$723$	−5.11156e8			−1.35250
$724$	−1.82898e7	−	1.75021e8i	−0.0481939	−	0.461183i
$725$	2.84717e8	+	1.68018e8i	0.747135	+	0.440901i
$726$	−3.88437e8	−	3.49960e8i	−1.01510	−	0.914553i
$727$	−2.91515e8			−0.758679			−0.379339	−	0.925258i	$-0.623849\pi$
$727$	−2.91515e8			−0.758679			−0.379339	+	0.925258i	$0.623849\pi$
$728$	−6.03455e8	−	4.39262e8i	−1.56405	−	1.13849i
$729$	−5.43559e8			−1.40302
$730$	−1.14528e7	−	1.78327e7i	−0.0294403	−	0.0458403i
$731$			2.85250e8i			0.730254i
$732$	−9.15283e6	−	8.75864e7i	−0.0233358	−	0.223308i
$733$			4.31296e8i			1.09512i	0.836765	+	0.547562i	$0.184444\pi$
$733$			4.31296e8i			1.09512i	−0.836765	+	0.547562i	$0.815556\pi$
$734$	−7.47649e7	−	6.73591e7i	−0.189064	−	0.170337i
$735$	−1.13641e8	+	4.16176e8i	−0.286203	+	1.04813i
$736$	3.05458e7	+	1.76965e7i	0.0766157	+	0.0443867i
$737$			8.99053e7i			0.224586i
$738$	2.29569e8	+	2.06829e8i	0.571143	+	0.514569i
$739$			6.53807e8i			1.62000i	0.586427	+	0.810002i	$0.300534\pi$
$739$			6.53807e8i			1.62000i	−0.586427	+	0.810002i	$0.699466\pi$
$740$	−1.83197e7	+	1.11785e8i	−0.0452088	+	0.275859i
$741$	2.58561e8			0.635491
$742$	−6.68820e8	+	7.42354e8i	−1.63718	+	1.81719i
$743$	3.07461e8			0.749589			0.374794	−	0.927108i	$-0.377713\pi$
$743$	3.07461e8			0.749589			0.374794	+	0.927108i	$0.377713\pi$
$744$	−5.55203e8	−	4.04139e8i	−1.34813	−	0.981323i
$745$	−6.93939e7	+	2.54134e8i	−0.167823	+	0.614601i
$746$	−3.10831e8	+	3.45005e8i	−0.748700	+	0.831016i
$747$	4.52567e7			0.108573
$748$	−1.28373e7	−	1.22844e8i	−0.0306739	−	0.293529i
$749$	2.30816e8			0.549313
$750$	−6.30376e8	+	2.38223e7i	−1.49423	+	0.0564677i
$751$		−	4.94845e8i		−	1.16829i	−0.811650	−	0.584143i	$-0.801431\pi$
$751$		−	4.94845e8i		−	1.16829i	0.811650	−	0.584143i	$-0.198569\pi$
$752$	5.53641e8	−	1.16989e8i	1.30189	−	0.275101i
$753$		−	1.08624e9i		−	2.54414i
$754$	3.66463e8	−	4.06755e8i	0.854902	−	0.948895i
$755$	−2.66258e8	−	7.27045e7i	−0.618673	−	0.168935i
$756$	2.08148e7	+	1.99183e8i	0.0481733	+	0.460986i
$757$		−	8.18948e8i		−	1.88786i	−0.330152	−	0.943928i	$-0.607100\pi$
$757$		−	8.18948e8i		−	1.88786i	0.330152	−	0.943928i	$-0.392900\pi$
$758$	2.33169e8	−	2.58805e8i	0.535382	−	0.594245i
$759$			1.70015e7i			0.0388833i
$760$	−9.89298e7	+	7.91891e7i	−0.225365	+	0.180395i
$761$	−4.68400e7			−0.106283			−0.0531414	−	0.998587i	$-0.516923\pi$
$761$	−4.68400e7			−0.106283			−0.0531414	+	0.998587i	$0.516923\pi$
$762$	4.56172e8	+	4.10986e8i	1.03101	+	0.928885i
$763$	−5.99015e8			−1.34854
$764$	5.07633e8	−	5.30480e7i	1.13833	−	0.118957i
$765$	−5.36396e8	−	1.46468e8i	−1.19812	−	0.327160i
$766$	1.75172e7	+	1.57820e7i	0.0389742	+	0.0351136i
$767$	9.11359e7			0.201978
$768$	6.19441e8	−	2.74022e8i	1.36747	−	0.604926i
$769$	−5.79761e6			−0.0127488			−0.00637441	−	0.999980i	$-0.502029\pi$
$769$	−5.79761e6			−0.0127488			−0.00637441	+	0.999980i	$0.502029\pi$
$770$	9.52028e7	+	1.48237e8i	0.208534	+	0.324701i
$771$			3.15397e8i			0.688168i
$772$	−7.75681e8	+	8.10591e7i	−1.68590	+	0.176177i
$773$			4.58350e8i			0.992335i	0.868227	+	0.496168i	$0.165260\pi$
$773$			4.58350e8i			0.992335i	−0.868227	+	0.496168i	$0.834740\pi$
$774$	−3.09386e8	−	2.78740e8i	−0.667234	−	0.601141i
$775$	−2.63812e8	+	4.47047e8i	−0.566748	+	0.960391i
$776$	4.77143e8	+	3.47318e8i	1.02109	+	0.743263i
$777$		−	2.57649e8i		−	0.549245i
$778$	−1.11561e8	−	1.00510e8i	−0.236904	−	0.213437i
$779$		−	8.48835e7i		−	0.179561i
$780$	−1.68954e8	+	1.03094e9i	−0.356028	+	2.17245i
$781$	−8.39079e7			−0.176137
$782$	2.84821e7	−	3.16136e7i	0.0595595	−	0.0661079i
$783$	−1.46898e8			−0.306007
$784$	−3.42584e8	+	7.23911e7i	−0.710917	+	0.150223i
$785$	9.90173e7	+	2.70377e7i	0.204693	+	0.0558935i
$786$	5.97220e8	−	6.62882e8i	1.22989	−	1.36511i
$787$	8.86461e8			1.81859			0.909297	−	0.416149i	$-0.136620\pi$
$787$	8.86461e8			1.81859			0.909297	+	0.416149i	$0.136620\pi$
$788$	3.35575e8	−	3.50678e7i	0.685822	−	0.0716688i
$789$	5.37520e8			1.09437
$790$	1.97648e8	+	3.07750e8i	0.400876	+	0.624190i
$791$		−	7.21901e7i		−	0.145864i
$792$	1.45783e8	+	1.06117e8i	0.293448	+	0.213605i
$793$			1.10239e8i			0.221062i
$794$	−2.14111e8	+	2.37652e8i	−0.427739	+	0.474767i
$795$	1.34914e9	+	3.68396e8i	2.68507	+	0.733186i
$796$	−7.28415e8	+	7.61198e7i	−1.44424	+	0.150924i
$797$			5.08284e8i			1.00400i	0.864869	+	0.501998i	$0.167401\pi$
$797$			5.08284e8i			1.00400i	−0.864869	+	0.501998i	$0.832599\pi$
$798$	1.92927e8	−	2.14138e8i	0.379650	−	0.421391i
$799$		−	6.82080e8i		−	1.33720i
$800$	−2.51099e8	−	4.46199e8i	−0.490428	−	0.871482i
$801$	−1.59718e8			−0.310782
$802$	−3.85954e7	−	3.47723e7i	−0.0748190	−	0.0674078i
$803$	8.28434e6			0.0159997
$804$	6.17679e7	+	5.91077e8i	0.118849	+	1.13730i
$805$	−1.59879e7	+	5.85507e7i	−0.0306481	+	0.112239i
$806$	6.38664e8	+	5.75401e8i	1.21974	+	1.09892i
$807$	−7.01988e8			−1.33570
$808$	3.85566e8	−	5.29688e8i	0.730912	−	1.00412i
$809$	−3.14322e6			−0.00593648			−0.00296824	−	0.999996i	$-0.500945\pi$
$809$	−3.14322e6			−0.00593648			−0.00296824	+	0.999996i	$0.500945\pi$
$810$	−3.16795e8	+	2.03457e8i	−0.596106	+	0.382840i
$811$			3.62482e8i			0.679553i	0.940506	+	0.339777i	$0.110352\pi$
$811$			3.62482e8i			0.679553i	−0.940506	+	0.339777i	$0.889648\pi$
$812$	−6.34322e7	−	6.07003e8i	−0.118479	−	1.13376i
$813$			8.61382e8i			1.60297i
$814$	−3.28963e7	−	2.96378e7i	−0.0609921	−	0.0549506i
$815$	2.53805e8	−	9.29483e8i	0.468843	−	1.71699i
$816$	−1.68796e8	−	7.98813e8i	−0.310665	−	1.47019i
$817$			1.14396e8i			0.209770i
$818$	−1.64079e8	−	1.47826e8i	−0.299774	−	0.270080i
$819$		−	1.31344e9i		−	2.39088i
$820$	3.38448e8	+	5.54661e7i	0.613834	+	0.100597i
$821$	−7.24735e8			−1.30963			−0.654816	−	0.755788i	$-0.727254\pi$
$821$	−7.24735e8			−1.30963			−0.654816	+	0.755788i	$0.727254\pi$
$822$	5.62261e8	−	6.24080e8i	1.01233	−	1.12363i
$823$	5.63218e8			1.01036			0.505181	−	0.863013i	$-0.331426\pi$
$823$	5.63218e8			1.01036			0.505181	+	0.863013i	$0.331426\pi$
$824$	6.27542e8	−	8.62113e8i	1.12166	−	1.54093i
$825$	1.25320e8	−	2.12363e8i	0.223182	−	0.378196i
$826$	6.80014e7	−	7.54779e7i	0.120664	−	0.133930i
$827$	−6.66821e8			−1.17894			−0.589471	−	0.807789i	$-0.700664\pi$
$827$	−6.66821e8			−1.17894			−0.589471	+	0.807789i	$0.700664\pi$
$828$	6.45648e6	+	6.17841e7i	0.0113738	+	0.108839i
$829$	−5.69391e8			−0.999418			−0.499709	−	0.866193i	$-0.666560\pi$
$829$	−5.69391e8			−0.999418			−0.499709	+	0.866193i	$0.666560\pi$
$830$	4.22653e7	−	2.71442e7i	0.0739179	−	0.0474727i
$831$			6.94558e8i			1.21034i
$832$	−8.06876e8	+	2.60573e8i	−1.40100	+	0.452438i
$833$			4.22060e8i			0.730196i
$834$	−6.64458e8	+	7.37512e8i	−1.14543	+	1.27137i
$835$	−7.80888e7	+	2.85976e8i	−0.134131	+	0.491213i
$836$	−5.14824e6	−	4.92652e7i	−0.00881130	−	0.0843182i
$837$		−	2.30652e8i		−	0.393351i
$838$	−7.92488e7	+	8.79619e7i	−0.134667	+	0.149473i
$839$		−	9.23641e8i		−	1.56393i	−0.623322	−	0.781965i	$-0.714217\pi$
$839$		−	9.23641e8i		−	1.56393i	0.623322	−	0.781965i	$-0.285783\pi$
$840$	7.27748e8	+	9.09165e8i	1.22784	+	1.53393i
$841$	−1.47157e8			−0.247396
$842$	1.95691e8	+	1.76306e8i	0.327819	+	0.295346i
$843$	−1.03712e9			−1.73120
$844$	2.10274e8	−	2.19738e7i	0.349751	−	0.0365492i
$845$	1.85552e8	−	6.79527e8i	0.307536	−	1.12625i
$846$	7.39793e8	+	6.66513e8i	1.22180	+	1.10077i
$847$	7.29586e8			1.20068
$848$	2.34674e8	+	1.11057e9i	0.384837	+	1.82121i
$849$	5.62704e8			0.919511
$850$	−5.88790e8	+	1.84935e8i	−0.958747	+	0.301135i
$851$		−	1.52543e7i		−	0.0247517i
$852$	−5.51647e8	+	5.76474e7i	−0.891954	+	0.0932097i
$853$			7.92638e7i			0.127711i	0.997959	+	0.0638555i	$0.0203397\pi$
$853$			7.92638e7i			0.127711i	−0.997959	+	0.0638555i	$0.979660\pi$
$854$	9.12986e7	+	8.22550e7i	0.146585	+	0.132065i
$855$	−2.15115e8	−	5.87393e7i	−0.344169	−	0.0939789i
$856$	1.54311e8	−	2.11991e8i	0.246023	−	0.337985i
$857$		−	8.08687e8i		−	1.28481i	−0.766366	−	0.642404i	$-0.777937\pi$
$857$		−	8.08687e8i		−	1.28481i	0.766366	−	0.642404i	$-0.222063\pi$
$858$	−3.03387e8	−	2.73335e8i	−0.480326	−	0.432747i
$859$			1.08418e9i			1.71049i	0.518225	+	0.855244i	$0.326593\pi$
$859$			1.08418e9i			1.71049i	−0.518225	+	0.855244i	$0.673407\pi$
$860$	−4.56120e8	−	7.47506e7i	−0.717107	−	0.117522i
$861$	−7.80080e8			−1.22217
$862$	5.06617e8	−	5.62317e8i	0.790966	−	0.877929i
$863$	−8.65764e8			−1.34700			−0.673499	−	0.739188i	$-0.735210\pi$
$863$	−8.65764e8			−1.34700			−0.673499	+	0.739188i	$0.735210\pi$
$864$	1.96854e8	+	1.14046e8i	0.305214	+	0.176823i
$865$	6.30166e8	+	1.72073e8i	0.973658	+	0.265868i
$866$	3.48373e8	−	3.86675e8i	0.536402	−	0.595377i
$867$	−9.62558e6			−0.0147696
$868$	9.53084e8	−	9.95978e7i	1.45738	−	0.152297i
$869$	−1.42968e8			−0.217861
$870$	−7.18750e8	+	4.61607e8i	−1.09149	+	0.700994i
$871$		−	7.43945e8i		−	1.12587i
$872$	−4.00469e8	+	5.50162e8i	−0.603976	+	0.829738i
$873$			1.03852e9i			1.56089i
$874$	1.14224e7	−	1.26782e7i	0.0171089	−	0.0189900i
$875$	6.31284e8	−	6.13496e8i	0.942325	−	0.915773i
$876$	5.44649e7	−	5.69161e6i	0.0810222	−	0.00846687i
$877$		−	6.80856e8i		−	1.00938i	−0.863299	−	0.504692i	$-0.831606\pi$
$877$		−	6.80856e8i		−	1.00938i	0.863299	−	0.504692i	$-0.168394\pi$
$878$	2.84177e8	−	3.15421e8i	0.419861	−	0.466023i
$879$			1.32556e9i			1.95179i
$880$	1.99795e8	+	1.16646e7i	0.293181	+	0.0171168i
$881$	−1.01305e9			−1.48150			−0.740750	−	0.671780i	$-0.765530\pi$
$881$	−1.01305e9			−1.48150			−0.740750	+	0.671780i	$0.765530\pi$
$882$	−4.57772e8	−	4.12428e8i	−0.667181	−	0.601093i
$883$	−7.97017e8			−1.15767			−0.578836	−	0.815444i	$-0.696493\pi$
$883$	−7.97017e8			−1.15767			−0.578836	+	0.815444i	$0.696493\pi$
$884$	1.06226e8	+	1.01651e9i	0.153770	+	1.47148i
$885$	−1.37172e8	−	3.74562e7i	−0.197895	−	0.0540374i
$886$	−8.16761e8	−	7.35857e8i	−1.17434	−	1.05802i
$887$	−8.37782e8			−1.20049			−0.600247	−	0.799815i	$-0.704931\pi$
$887$	−8.37782e8			−1.20049			−0.600247	+	0.799815i	$0.704931\pi$
$888$	−2.36637e8	−	1.72251e8i	−0.337943	−	0.245992i
$889$	−8.56810e8			−1.21949
$890$	−1.49161e8	+	9.57964e7i	−0.211585	+	0.135887i
$891$		−	1.47170e8i		−	0.208059i
$892$	9.51435e7	+	9.10459e8i	0.134056	+	1.28282i
$893$		−	2.73539e8i		−	0.384119i
$894$	−5.05713e8	−	4.55620e8i	−0.707769	−	0.637661i
$895$	−7.73791e8	−	2.11292e8i	−1.07933	−	0.294723i
$896$	−3.86249e8	+	8.62674e8i	−0.536962	+	1.19929i
$897$		−	1.40684e8i		−	0.194924i
$898$	−8.17851e6	−	7.36838e6i	−0.0112939	−	0.0101752i
$899$			7.02902e8i			0.967422i
$900$	3.74770e8	−	8.19324e8i	0.514088	−	1.12390i
$901$	1.36821e9			1.87059
$902$	−8.97337e7	+	9.95995e7i	−0.122274	+	0.135718i
$903$	1.05130e9			1.42779
$904$	−6.63026e7	−	4.82624e7i	−0.0897481	−	0.0653287i
$905$	9.05359e7	−	3.31560e8i	0.122145	−	0.447318i
$906$	4.77356e8	−	5.29839e8i	0.641886	−	0.712458i
$907$	8.35297e8			1.11949			0.559743	−	0.828666i	$-0.310900\pi$
$907$	8.35297e8			1.11949			0.559743	+	0.828666i	$0.310900\pi$
$908$	5.84879e6	+	5.59689e7i	0.00781283	+	0.0747635i
$909$	1.15288e9			1.53495
$910$	−7.87781e8	−	1.22662e9i	−1.04540	−	1.62775i
$911$			5.22073e8i			0.690519i	0.938507	+	0.345260i	$0.112209\pi$
$911$			5.22073e8i			0.690519i	−0.938507	+	0.345260i	$0.887791\pi$
$912$	−6.76936e7	−	3.20354e8i	−0.0892407	−	0.422323i
$913$			1.96348e7i			0.0257996i
$914$	6.39815e8	−	7.10160e8i	0.837945	−	0.930074i
$915$	4.53073e7	−	1.65924e8i	0.0591433	−	0.216594i
$916$	−2.42059e6	−	2.31634e7i	−0.00314945	−	0.0301381i
$917$			1.24506e9i			1.61467i
$918$	1.83555e8	−	2.03736e8i	0.237267	−	0.263354i
$919$			7.05912e7i			0.0909502i	0.998965	+	0.0454751i	$0.0144802\pi$
$919$			7.05912e7i			0.0909502i	−0.998965	+	0.0454751i	$0.985520\pi$
$920$	4.30869e7	+	5.38278e7i	0.0553327	+	0.0691263i
$921$	1.29516e9			1.65785
$922$	7.49069e8	+	6.74870e8i	0.955716	+	0.861047i
$923$	6.94318e8			0.882985
$924$	−4.52747e8	+	4.73124e7i	−0.573905	+	0.0599734i
$925$	−1.12441e8	+	1.90539e8i	−0.142069	+	0.240745i
$926$	6.01523e8	+	5.41939e8i	0.757564	+	0.682524i
$927$	1.87642e9			2.35554
$928$	−5.99906e8	−	3.47551e8i	−0.750653	−	0.434885i
$929$	−3.30334e8			−0.412008			−0.206004	−	0.978551i	$-0.566046\pi$
$929$	−3.30334e8			−0.412008			−0.206004	+	0.978551i	$0.566046\pi$
$930$	−7.24790e8	−	1.12854e9i	−0.901080	−	1.40304i
$931$			1.69262e8i			0.209754i
$932$	2.03071e8	−	2.12211e7i	0.250843	−	0.0262132i
$933$		−	1.29982e9i		−	1.60044i
$934$	5.78028e8	+	5.20771e8i	0.709428	+	0.639155i
$935$	6.35459e7	−	2.32717e8i	0.0777414	−	0.284704i
$936$	−1.20632e9	−	8.78095e8i	−1.47108	−	1.07081i
$937$			1.37475e9i			1.67111i	0.549406	+	0.835556i	$0.314854\pi$
$937$			1.37475e9i			1.67111i	−0.549406	+	0.835556i	$0.685146\pi$
$938$	−6.16128e8	−	5.55098e8i	−0.746557	−	0.672606i
$939$		−	1.46430e8i		−	0.176861i
$940$	1.09066e9	+	1.78741e8i	1.31312	+	0.215199i
$941$	1.35847e9			1.63035			0.815177	−	0.579211i	$-0.196639\pi$
$941$	1.35847e9			1.63035			0.815177	+	0.579211i	$0.196639\pi$
$942$	−1.77522e8	+	1.97039e8i	−0.212373	+	0.235722i
$943$	−4.61853e7			−0.0550768
$944$	−2.38601e7	−	1.12916e8i	−0.0283633	−	0.134227i
$945$	−1.03035e8	+	3.77334e8i	−0.122093	+	0.447126i
$946$	1.20932e8	−	1.34228e8i	0.142846	−	0.158552i
$947$	−3.76294e8			−0.443075			−0.221537	−	0.975152i	$-0.571108\pi$
$947$	−3.76294e8			−0.443075			−0.221537	+	0.975152i	$0.571108\pi$
$948$	−9.39935e8	+	9.82238e7i	−1.10325	+	0.115290i
$949$	−6.85510e7			−0.0802075
$950$	−2.36127e8	+	7.41656e7i	−0.275407	+	0.0865032i
$951$		−	1.09285e9i		−	1.27063i
$952$	9.21123e8	+	6.70497e8i	1.06760	+	0.777116i
$953$		−	6.28773e8i		−	0.726465i	−0.931698	−	0.363233i	$-0.881673\pi$
$953$		−	6.28773e8i		−	0.726465i	0.931698	−	0.363233i	$-0.118327\pi$
$954$	−1.33699e9	+	1.48398e9i	−1.53986	+	1.70916i
$955$	9.61663e8	+	2.62592e8i	1.10411	+	0.301489i
$956$	−1.09541e9	+	1.14471e8i	−1.25373	+	0.131016i
$957$		−	3.33903e8i		−	0.380964i
$958$	3.24658e8	−	3.60353e8i	0.369258	−	0.409856i
$959$			1.17218e9i			1.32905i
$960$	1.32155e9	−	6.05771e7i	1.49372	−	0.0684691i
$961$	−2.16156e8			−0.243555
$962$	2.72209e8	+	2.45245e8i	0.305758	+	0.275471i
$963$	4.61406e8			0.516660
$964$	−8.42178e7	−	8.05907e8i	−0.0940097	−	0.899609i
$965$	−1.46945e9	−	4.01250e8i	−1.63521	−	0.446512i
$966$	−1.16513e8	−	1.04972e8i	−0.129254	−	0.116450i
$967$	−6.61713e8			−0.731796			−0.365898	−	0.930655i	$-0.619238\pi$
$967$	−6.61713e8			−0.731796			−0.365898	+	0.930655i	$0.619238\pi$
$968$	4.87762e8	−	6.70084e8i	0.537752	−	0.738759i
$969$	−3.94672e8			−0.433776
$970$	6.22887e8	+	9.69873e8i	0.682486	+	1.06267i
$971$			8.80062e7i			0.0961292i	0.998844	+	0.0480646i	$0.0153053\pi$
$971$			8.80062e7i			0.0961292i	−0.998844	+	0.0480646i	$0.984695\pi$
$972$	−1.34778e8	−	1.28973e9i	−0.146764	−	1.40443i
$973$		−	1.38524e9i		−	1.50379i
$974$	−7.13920e8	−	6.43202e8i	−0.772632	−	0.696099i
$975$	−1.03699e9	+	1.75725e9i	−1.11882	+	1.89592i
$976$	1.36584e8	−	2.88614e7i	0.146910	−	0.0310433i
$977$			7.15460e8i			0.767188i	0.923502	+	0.383594i	$0.125314\pi$
$977$			7.15460e8i			0.767188i	−0.923502	+	0.383594i	$0.874686\pi$
$978$	1.84962e9	+	1.66641e9i	1.97727	+	1.78141i
$979$		−	6.92942e7i		−	0.0738497i
$980$	−6.74882e8	−	1.10602e8i	−0.717050	−	0.117513i
$981$	−1.19745e9			−1.26838
$982$	−6.28790e8	+	6.97923e8i	−0.664005	+	0.737010i
$983$	−1.11848e8			−0.117752			−0.0588760	−	0.998265i	$-0.518752\pi$
$983$	−1.11848e8			−0.117752			−0.0588760	+	0.998265i	$0.518752\pi$
$984$	−5.21520e8	+	7.16460e8i	−0.547376	+	0.751981i
$985$	6.35716e8	+	1.73589e8i	0.665203	+	0.181641i
$986$	−5.59375e8	+	6.20876e8i	−0.583543	+	0.647701i
$987$	−2.51383e9			−2.61447
$988$	4.26005e7	+	4.07658e8i	0.0441717	+	0.422693i
$989$	6.22430e7			0.0643430
$990$	1.90313e8	+	2.96329e8i	0.196138	+	0.305399i
$991$		−	1.31906e8i		−	0.135532i	−0.997701	−	0.0677661i	$-0.978413\pi$
$991$		−	1.31906e8i		−	0.135532i	0.997701	−	0.0677661i	$-0.0215872\pi$
$992$	5.45706e8	−	9.41940e8i	0.559015	−	0.964913i
$993$			1.35426e9i			1.38310i
$994$	5.18068e8	−	5.75028e8i	0.527506	−	0.585504i
$995$	−1.37991e9	−	3.76800e8i	−1.40082	−	0.382509i
$996$	1.34897e7	+	1.29087e8i	0.0136529	+	0.130649i
$997$		−	1.67136e9i		−	1.68649i	−0.537527	−	0.843246i	$-0.680641\pi$
$997$		−	1.67136e9i		−	1.68649i	0.537527	−	0.843246i	$-0.319359\pi$
$998$	−1.11735e9	+	1.24020e9i	−1.12408	+	1.24767i
$999$		−	9.83076e7i		−	0.0986031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.7.d.d.19.3	✓	12
3.2	odd	2		180.7.f.e.19.10		12
4.3	odd	2	inner	20.7.d.d.19.9	yes	12
5.2	odd	4		100.7.b.f.51.9		12
5.3	odd	4		100.7.b.f.51.4		12
5.4	even	2	inner	20.7.d.d.19.10	yes	12
8.3	odd	2		320.7.h.f.319.11		12
8.5	even	2		320.7.h.f.319.1		12
12.11	even	2		180.7.f.e.19.4		12
15.14	odd	2		180.7.f.e.19.3		12
20.3	even	4		100.7.b.f.51.3		12
20.7	even	4		100.7.b.f.51.10		12
20.19	odd	2	inner	20.7.d.d.19.4	yes	12
40.19	odd	2		320.7.h.f.319.2		12
40.29	even	2		320.7.h.f.319.12		12
60.59	even	2		180.7.f.e.19.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.d.d.19.3	✓	12	1.1	even	1	trivial
20.7.d.d.19.4	yes	12	20.19	odd	2	inner
20.7.d.d.19.9	yes	12	4.3	odd	2	inner
20.7.d.d.19.10	yes	12	5.4	even	2	inner
100.7.b.f.51.3		12	20.3	even	4
100.7.b.f.51.4		12	5.3	odd	4
100.7.b.f.51.9		12	5.2	odd	4
100.7.b.f.51.10		12	20.7	even	4
180.7.f.e.19.3		12	15.14	odd	2
180.7.f.e.19.4		12	12.11	even	2
180.7.f.e.19.9		12	60.59	even	2
180.7.f.e.19.10		12	3.2	odd	2
320.7.h.f.319.1		12	8.5	even	2
320.7.h.f.319.2		12	40.19	odd	2
320.7.h.f.319.11		12	8.3	odd	2
320.7.h.f.319.12		12	40.29	even	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)

\(f(q)\)	\(=\)	\(q+(-5.94356 - 5.35482i) q^{2} +40.3729 q^{3} +(6.65182 + 63.6534i) q^{4} +(-32.9271 + 120.585i) q^{5} +(-239.959 - 216.189i) q^{6} +450.705 q^{7} +(301.317 - 413.947i) q^{8} +900.969 q^{9} +O(q^{10})\)	\(q+(-5.94356 - 5.35482i) q^{2} +40.3729 q^{3} +(6.65182 + 63.6534i) q^{4} +(-32.9271 + 120.585i) q^{5} +(-239.959 - 216.189i) q^{6} +450.705 q^{7} +(301.317 - 413.947i) q^{8} +900.969 q^{9} +(841.416 - 540.387i) q^{10} +390.888i q^{11} +(268.553 + 2569.87i) q^{12} -3234.51i q^{13} +(-2678.79 - 2413.44i) q^{14} +(-1329.36 + 4868.37i) q^{15} +(-4007.51 + 846.821i) q^{16} +4937.20i q^{17} +(-5354.96 - 4824.53i) q^{18} +1980.00i q^{19} +(-7894.69 - 1293.81i) q^{20} +18196.2 q^{21} +(2093.14 - 2323.27i) q^{22} +1077.32 q^{23} +(12165.0 - 16712.2i) q^{24} +(-13456.6 - 7941.04i) q^{25} +(-17320.2 + 19224.5i) q^{26} +6942.88 q^{27} +(2998.00 + 28688.9i) q^{28} -21158.1 q^{29} +(33970.4 - 21817.0i) q^{30} -33221.4i q^{31} +(28353.4 + 16426.3i) q^{32} +15781.3i q^{33} +(26437.8 - 29344.6i) q^{34} +(-14840.4 + 54348.3i) q^{35} +(5993.08 + 57349.7i) q^{36} -14159.5i q^{37} +(10602.6 - 11768.3i) q^{38} -130586. i q^{39} +(39994.4 + 49964.4i) q^{40} -42870.4 q^{41} +(-108150. - 97437.6i) q^{42} +57775.6 q^{43} +(-24881.4 + 2600.12i) q^{44} +(-29666.3 + 108644. i) q^{45} +(-6403.13 - 5768.87i) q^{46} -138151. q^{47} +(-161795. + 34188.6i) q^{48} +85485.6 q^{49} +(37457.3 + 119256. i) q^{50} +199329. i q^{51} +(205887. - 21515.4i) q^{52} -277123. i q^{53} +(-41265.4 - 37177.9i) q^{54} +(-47135.4 - 12870.8i) q^{55} +(135805. - 186568. i) q^{56} +79938.4i q^{57} +(125755. + 113298. i) q^{58} +28176.1i q^{59} +(-318731. - 52234.8i) q^{60} -34082.0 q^{61} +(-177894. + 197453. i) q^{62} +406071. q^{63} +(-80560.3 - 249458. i) q^{64} +(390034. + 106503. i) q^{65} +(84506.0 - 93797.1i) q^{66} +230002. q^{67} +(-314270. + 32841.4i) q^{68} +43494.6 q^{69} +(379230. - 243555. i) q^{70} +214659. i q^{71} +(271477. - 372953. i) q^{72} -21193.6i q^{73} +(-75821.5 + 84157.8i) q^{74} +(-543282. - 320603. i) q^{75} +(-126034. + 13170.6i) q^{76} +176175. i q^{77} +(-699267. + 776148. i) q^{78} +365752. i q^{79} +(29841.3 - 511130. i) q^{80} -376502. q^{81} +(254803. + 229563. i) q^{82} +50231.1 q^{83} +(121038. + 1.15825e6i) q^{84} +(-595354. - 162568. i) q^{85} +(-343393. - 309378. i) q^{86} -854215. q^{87} +(161807. + 117781. i) q^{88} -177274. q^{89} +(758090. - 486872. i) q^{90} -1.45781e6i q^{91} +(7166.15 + 68575.2i) q^{92} -1.34124e6i q^{93} +(821109. + 739774. i) q^{94} +(-238759. - 65195.7i) q^{95} +(1.14471e6 + 663179. i) q^{96} +1.15267e6i q^{97} +(-508089. - 457760. i) q^{98} +352178. i 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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