LMFDB - Embedded newform 51.7.f.a.38.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,7,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.7327582646$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.1
Character	$\chi$	$=$	51.38
Dual form			51.7.f.a.47.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-15.2598 q^{2} +(-17.0979 - 20.8965i) q^{3} +168.862 q^{4} +(23.5746 + 23.5746i) q^{5} +(260.911 + 318.876i) q^{6} +(-238.814 - 238.814i) q^{7} -1600.18 q^{8} +(-144.325 + 714.571i) q^{9} +(-359.744 - 359.744i) q^{10} +(-420.942 + 420.942i) q^{11} +(-2887.19 - 3528.62i) q^{12} -2961.38 q^{13} +(3644.26 + 3644.26i) q^{14} +(89.5501 - 895.702i) q^{15} +13611.3 q^{16} +(4604.13 - 1714.52i) q^{17} +(2202.37 - 10904.2i) q^{18} +7725.35i q^{19} +(3980.86 + 3980.86i) q^{20} +(-907.156 + 9073.59i) q^{21} +(6423.51 - 6423.51i) q^{22} +(-6931.52 + 6931.52i) q^{23} +(27359.7 + 33438.1i) q^{24} -14513.5i q^{25} +45190.2 q^{26} +(17399.7 - 9201.77i) q^{27} +(-40326.7 - 40326.7i) q^{28} +(7400.22 + 7400.22i) q^{29} +(-1366.52 + 13668.3i) q^{30} +(10833.7 - 10833.7i) q^{31} -105294. q^{32} +(15993.4 + 1598.99i) q^{33} +(-70258.2 + 26163.2i) q^{34} -11259.9i q^{35} +(-24371.0 + 120664. i) q^{36} +(58346.5 - 58346.5i) q^{37} -117887. i q^{38} +(50633.4 + 61882.5i) q^{39} +(-37723.6 - 37723.6i) q^{40} +(20535.6 - 20535.6i) q^{41} +(13843.0 - 138461. i) q^{42} +155233. i q^{43} +(-71081.2 + 71081.2i) q^{44} +(-20248.1 + 13443.3i) q^{45} +(105774. - 105774. i) q^{46} +53202.6i q^{47} +(-232724. - 284427. i) q^{48} -3584.66i q^{49} +221473. i q^{50} +(-114548. - 66895.4i) q^{51} -500066. q^{52} +209181. q^{53} +(-265516. + 140417. i) q^{54} -19847.1 q^{55} +(382145. + 382145. i) q^{56} +(161432. - 132087. i) q^{57} +(-112926. - 112926. i) q^{58} +134671. q^{59} +(15121.6 - 151250. i) q^{60} +(200441. + 200441. i) q^{61} +(-165320. + 165320. i) q^{62} +(205116. - 136183. i) q^{63} +735646. q^{64} +(-69813.5 - 69813.5i) q^{65} +(-244057. - 24400.2i) q^{66} +76427.8 q^{67} +(777463. - 289517. i) q^{68} +(263359. + 26330.0i) q^{69} +171824. i q^{70} +(-215857. - 215857. i) q^{71} +(230945. - 1.14344e6i) q^{72} +(272831. - 272831. i) q^{73} +(-890357. + 890357. i) q^{74} +(-303280. + 248150. i) q^{75} +1.30452e6i q^{76} +201054. q^{77} +(-772657. - 944316. i) q^{78} +(117505. + 117505. i) q^{79} +(320880. + 320880. i) q^{80} +(-489782. - 206261. i) q^{81} +(-313369. + 313369. i) q^{82} -910431. q^{83} +(-153184. + 1.53219e6i) q^{84} +(148960. + 68121.5i) q^{85} -2.36883e6i q^{86} +(28110.4 - 281166. i) q^{87} +(673583. - 673583. i) q^{88} -352605. i q^{89} +(308983. - 205143. i) q^{90} +(707220. + 707220. i) q^{91} +(-1.17047e6 + 1.17047e6i) q^{92} +(-411619. - 41152.7i) q^{93} -811862. i q^{94} +(-182122. + 182122. i) q^{95} +(1.80030e6 + 2.20027e6i) q^{96} +(-806854. + 806854. i) q^{97} +54701.2i q^{98} +(-240041. - 361545. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) $ 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−15.2598			−1.90748			−0.953739	−	0.300636i	$-0.902801\pi$
$2$	−15.2598			−1.90748			−0.953739	+	0.300636i	$0.902801\pi$
$3$	−17.0979	−	20.8965i	−0.633255	−	0.773943i
$3$	−17.0979	−	20.8965i	−0.633255	−	0.773943i
$4$	168.862			2.63847
$5$	23.5746	+	23.5746i	0.188597	+	0.188597i	0.795089	−	0.606492i	$-0.207424\pi$
$5$	23.5746	+	23.5746i	0.188597	+	0.188597i	−0.606492	+	0.795089i	$0.707424\pi$
$6$	260.911	+	318.876i	1.20792	+	1.47628i
$7$	−238.814	−	238.814i	−0.696251	−	0.696251i	0.267349	−	0.963600i	$-0.413852\pi$
$7$	−238.814	−	238.814i	−0.696251	−	0.696251i	−0.963600	+	0.267349i	$0.913852\pi$
$8$	−1600.18			−3.12535
$9$	−144.325	+	714.571i	−0.197976	+	0.980207i
$10$	−359.744	−	359.744i	−0.359744	−	0.359744i
$11$	−420.942	+	420.942i	−0.316260	+	0.316260i	−0.847329	−	0.531069i	$-0.821791\pi$
$11$	−420.942	+	420.942i	−0.316260	+	0.316260i	0.531069	+	0.847329i	$0.321791\pi$
$12$	−2887.19	−	3528.62i	−1.67083	−	2.04203i
$13$	−2961.38			−1.34792			−0.673961	−	0.738767i	$-0.735408\pi$
$13$	−2961.38			−1.34792			−0.673961	+	0.738767i	$0.735408\pi$
$14$	3644.26	+	3644.26i	1.32808	+	1.32808i
$15$	89.5501	−	895.702i	0.0265334	−	0.265393i
$16$	13611.3			3.32306
$17$	4604.13	−	1714.52i	0.937132	−	0.348975i
$17$	4604.13	−	1714.52i	0.937132	−	0.348975i
$18$	2202.37	−	10904.2i	0.377636	−	1.86972i
$19$			7725.35i			1.12631i	0.826352	+	0.563154i	$0.190412\pi$
$19$			7725.35i			1.12631i	−0.826352	+	0.563154i	$0.809588\pi$
$20$	3980.86	+	3980.86i	0.497607	+	0.497607i
$21$	−907.156	+	9073.59i	−0.0979544	+	0.979763i
$22$	6423.51	−	6423.51i	0.603259	−	0.603259i
$23$	−6931.52	+	6931.52i	−0.569699	+	0.569699i	−0.932044	−	0.362345i	$-0.881976\pi$
$23$	−6931.52	+	6931.52i	−0.569699	+	0.569699i	0.362345	+	0.932044i	$0.381976\pi$
$24$	27359.7	+	33438.1i	1.97914	+	2.41884i
$25$		−	14513.5i		−	0.928862i
$26$	45190.2			2.57113
$27$	17399.7	−	9201.77i	0.883994	−	0.467498i
$28$	−40326.7	−	40326.7i	−1.83704	−	1.83704i
$29$	7400.22	+	7400.22i	0.303424	+	0.303424i	0.842352	−	0.538928i	$-0.181170\pi$
$29$	7400.22	+	7400.22i	0.303424	+	0.303424i	−0.538928	+	0.842352i	$0.681170\pi$
$30$	−1366.52	+	13668.3i	−0.0506118	+	0.506232i
$31$	10833.7	−	10833.7i	0.363657	−	0.363657i	−0.501500	−	0.865157i	$-0.667218\pi$
$31$	10833.7	−	10833.7i	0.363657	−	0.363657i	0.865157	+	0.501500i	$0.167218\pi$
$32$	−105294.			−3.21332
$33$	15993.4	+	1598.99i	0.445041	+	0.0444941i
$34$	−70258.2	+	26163.2i	−1.78756	+	0.665663i
$35$		−	11259.9i		−	0.262621i
$36$	−24371.0	+	120664.i	−0.522355	+	2.58625i
$37$	58346.5	−	58346.5i	1.15189	−	1.15189i	0.165712	−	0.986174i	$-0.447008\pi$
$37$	58346.5	−	58346.5i	1.15189	−	1.15189i	0.986174	−	0.165712i	$-0.0529923\pi$
$38$		−	117887.i		−	2.14841i
$39$	50633.4	+	61882.5i	0.853578	+	1.04322i
$40$	−37723.6	−	37723.6i	−0.589431	−	0.589431i
$41$	20535.6	−	20535.6i	0.297958	−	0.297958i	−0.542256	−	0.840214i	$-0.682430\pi$
$41$	20535.6	−	20535.6i	0.297958	−	0.297958i	0.840214	+	0.542256i	$0.182430\pi$
$42$	13843.0	−	138461.i	0.186846	−	1.86888i
$43$			155233.i			1.95245i	0.216767	+	0.976223i	$0.430449\pi$
$43$			155233.i			1.95245i	−0.216767	+	0.976223i	$0.569551\pi$
$44$	−71081.2	+	71081.2i	−0.834444	+	0.834444i
$45$	−20248.1	+	13443.3i	−0.222202	+	0.147526i
$46$	105774.	−	105774.i	1.08669	−	1.08669i
$47$			53202.6i			0.512435i	0.966619	+	0.256218i	$0.0824764\pi$
$47$			53202.6i			0.512435i	−0.966619	+	0.256218i	$0.917524\pi$
$48$	−232724.	−	284427.i	−2.10434	−	2.57186i
$49$		−	3584.66i		−	0.0304691i
$50$			221473.i			1.77178i
$51$	−114548.	−	66895.4i	−0.863531	−	0.504297i
$52$	−500066.			−3.55645
$53$	209181.			1.40506			0.702530	−	0.711654i	$-0.252054\pi$
$53$	209181.			1.40506			0.702530	+	0.711654i	$0.252054\pi$
$54$	−265516.	+	140417.i	−1.68620	+	0.891743i
$55$	−19847.1			−0.119291
$56$	382145.	+	382145.i	2.17603	+	2.17603i
$57$	161432.	−	132087.i	0.871699	−	0.713240i
$58$	−112926.	−	112926.i	−0.578775	−	0.578775i
$59$	134671.			0.655721			0.327861	−	0.944726i	$-0.393672\pi$
$59$	134671.			0.655721			0.327861	+	0.944726i	$0.393672\pi$
$60$	15121.6	−	151250.i	0.0700075	−	0.700232i
$61$	200441.	+	200441.i	0.883073	+	0.883073i	0.993846	−	0.110773i	$-0.0353326\pi$
$61$	200441.	+	200441.i	0.883073	+	0.883073i	−0.110773	+	0.993846i	$0.535333\pi$
$62$	−165320.	+	165320.i	−0.693667	+	0.693667i
$63$	205116.	−	136183.i	0.820311	−	0.544629i
$64$	735646.			2.80627
$65$	−69813.5	−	69813.5i	−0.254214	−	0.254214i
$66$	−244057.	−	24400.2i	−0.848905	−	0.0848715i
$67$	76427.8			0.254113			0.127056	−	0.991895i	$-0.459447\pi$
$67$	76427.8			0.254113			0.127056	+	0.991895i	$0.459447\pi$
$68$	777463.	−	289517.i	2.47260	−	0.920761i
$69$	263359.	+	26330.0i	0.801679	+	0.0801499i
$70$			171824.i			0.500945i
$71$	−215857.	−	215857.i	−0.603102	−	0.603102i	0.338032	−	0.941134i	$-0.390239\pi$
$71$	−215857.	−	215857.i	−0.603102	−	0.603102i	−0.941134	+	0.338032i	$0.890239\pi$
$72$	230945.	−	1.14344e6i	0.618745	−	3.06349i
$73$	272831.	−	272831.i	0.701336	−	0.701336i	−0.263362	−	0.964697i	$-0.584831\pi$
$73$	272831.	−	272831.i	0.701336	−	0.701336i	0.964697	+	0.263362i	$0.0848312\pi$
$74$	−890357.	+	890357.i	−2.19720	+	2.19720i
$75$	−303280.	+	248150.i	−0.718887	+	0.588207i
$76$			1.30452e6i			2.97173i
$77$	201054.			0.440393
$78$	−772657.	−	944316.i	−1.62818	−	1.98991i
$79$	117505.	+	117505.i	0.238328	+	0.238328i	0.816158	−	0.577829i	$-0.196100\pi$
$79$	117505.	+	117505.i	0.238328	+	0.238328i	−0.577829	+	0.816158i	$0.696100\pi$
$80$	320880.	+	320880.i	0.626719	+	0.626719i
$81$	−489782.	−	206261.i	−0.921611	−	0.388116i
$82$	−313369.	+	313369.i	−0.568348	+	0.568348i
$83$	−910431.			−1.59226			−0.796128	−	0.605128i	$-0.793122\pi$
$83$	−910431.			−1.59226			−0.796128	+	0.605128i	$0.793122\pi$
$84$	−153184.	+	1.53219e6i	−0.258450	+	2.58508i
$85$	148960.	+	68121.5i	0.242556	+	0.110924i
$86$		−	2.36883e6i		−	3.72425i
$87$	28110.4	−	281166.i	0.0426883	−	0.426978i
$88$	673583.	−	673583.i	0.988423	−	0.988423i
$89$		−	352605.i		−	0.500171i	−0.968224	−	0.250086i	$-0.919541\pi$
$89$		−	352605.i		−	0.500171i	0.968224	−	0.250086i	$-0.0804588\pi$
$90$	308983.	−	205143.i	0.423845	−	0.281403i
$91$	707220.	+	707220.i	0.938492	+	0.938492i
$92$	−1.17047e6	+	1.17047e6i	−1.50313	+	1.50313i
$93$	−411619.	−	41152.7i	−0.511737	−	0.0511623i
$94$		−	811862.i		−	0.977459i
$95$	−182122.	+	182122.i	−0.212418	+	0.212418i
$96$	1.80030e6	+	2.20027e6i	2.03485	+	2.48692i
$97$	−806854.	+	806854.i	−0.884056	+	0.884056i	−0.993944	−	0.109888i	$-0.964951\pi$
$97$	−806854.	+	806854.i	−0.884056	+	0.884056i	0.109888	+	0.993944i	$0.464951\pi$
$98$			54701.2i			0.0581191i
$99$	−240041.	−	361545.i	−0.247388	−	0.372612i
$100$		−	2.45078e6i		−	2.45078i
$101$		−	191480.i		−	0.185849i	−0.995673	−	0.0929245i	$-0.970378\pi$
$101$		−	191480.i		−	0.185849i	0.995673	−	0.0929245i	$-0.0296215\pi$
$102$	1.74798e6	+	1.02081e6i	1.64717	+	0.961935i
$103$	1.34378e6			1.22975			0.614874	−	0.788625i	$-0.289207\pi$
$103$	1.34378e6			1.22975			0.614874	+	0.788625i	$0.289207\pi$
$104$	4.73874e6			4.21273
$105$	−235292.	+	192520.i	−0.203254	+	0.166306i
$106$	−3.19207e6			−2.68012
$107$	810648.	+	810648.i	0.661730	+	0.661730i	0.955788	−	0.294057i	$-0.0950057\pi$
$107$	810648.	+	810648.i	0.661730	+	0.661730i	−0.294057	+	0.955788i	$0.595006\pi$
$108$	2.93814e6	−	1.55383e6i	2.33239	−	1.23348i
$109$	913354.	+	913354.i	0.705277	+	0.705277i	0.965538	−	0.260262i	$-0.0838088\pi$
$109$	913354.	+	913354.i	0.705277	+	0.705277i	−0.260262	+	0.965538i	$0.583809\pi$
$110$	302863.			0.227546
$111$	−2.21684e6	−	221634.i	−1.62093	−	0.162057i
$112$	−3.25056e6	−	3.25056e6i	−2.31368	−	2.31368i
$113$	−1.21732e6	+	1.21732e6i	−0.843664	+	0.843664i	−0.989333	−	0.145669i	$-0.953467\pi$
$113$	−1.21732e6	+	1.21732e6i	−0.843664	+	0.843664i	0.145669	+	0.989333i	$0.453467\pi$
$114$	−2.46343e6	+	2.01563e6i	−1.66275	+	1.36049i
$115$	−326816.			−0.214887
$116$	1.24962e6	+	1.24962e6i	0.800577	+	0.800577i
$117$	427401.	−	2.11612e6i	0.266857	−	1.32124i
$118$	−2.05506e6			−1.25077
$119$	−1.50898e6	−	690080.i	−0.895453	−	0.409505i
$120$	−143296.	+	1.43328e6i	−0.0829260	+	0.829446i
$121$			1.41718e6i			0.799959i
$122$	−3.05869e6	−	3.05869e6i	−1.68444	−	1.68444i
$123$	−780235.	−	78006.1i	−0.419286	−	0.0419192i
$124$	1.82940e6	−	1.82940e6i	0.959498	−	0.959498i
$125$	710503.	−	710503.i	0.363777	−	0.363777i
$126$	−3.13004e6	+	2.07812e6i	−1.56473	+	1.03887i
$127$		−	597965.i		−	0.291920i	−0.989290	−	0.145960i	$-0.953373\pi$
$127$		−	597965.i		−	0.291920i	0.989290	−	0.145960i	$-0.0466271\pi$
$128$	−4.48702e6			−2.13958
$129$	3.24383e6	−	2.65416e6i	1.51108	−	1.23640i
$130$	1.06534e6	+	1.06534e6i	0.484907	+	0.484907i
$131$	2.05313e6	+	2.05313e6i	0.913278	+	0.913278i	0.996529	−	0.0832508i	$-0.0265303\pi$
$131$	2.05313e6	+	2.05313e6i	0.913278	+	0.913278i	−0.0832508	+	0.996529i	$0.526530\pi$
$132$	2.70069e6	+	270008.i	1.17423	+	0.117396i
$133$	1.84492e6	−	1.84492e6i	0.784193	−	0.784193i
$134$	−1.16627e6			−0.484715
$135$	627118.	+	193262.i	0.254887	+	0.0785498i
$136$	−7.36743e6	+	2.74353e6i	−2.92886	+	1.09067i
$137$			1.59032e6i			0.618475i	0.950985	+	0.309238i	$0.100074\pi$
$137$			1.59032e6i			0.618475i	−0.950985	+	0.309238i	$0.899926\pi$
$138$	−4.01881e6	−	401791.i	−1.52918	−	0.152884i
$139$	−793627.	+	793627.i	−0.295510	+	0.295510i	−0.839252	−	0.543742i	$-0.817007\pi$
$139$	−793627.	+	793627.i	−0.295510	+	0.295510i	0.543742	+	0.839252i	$0.317007\pi$
$140$		−	1.90137e6i		−	0.692919i
$141$	1.11175e6	−	909651.i	0.396596	−	0.324502i
$142$	3.29394e6	+	3.29394e6i	1.15040	+	1.15040i
$143$	1.24657e6	−	1.24657e6i	0.426294	−	0.426294i
$144$	−1.96444e6	+	9.72620e6i	−0.657887	+	3.25729i
$145$			348914.i			0.114450i
$146$	−4.16336e6	+	4.16336e6i	−1.33778	+	1.33778i
$147$	−74906.7	+	61290.1i	−0.0235813	+	0.0192947i
$148$	9.85252e6	−	9.85252e6i	3.03922	−	3.03922i
$149$		−	2.96977e6i		−	0.897767i	−0.893590	−	0.448883i	$-0.851822\pi$
$149$		−	2.96977e6i		−	0.897767i	0.893590	−	0.448883i	$-0.148178\pi$
$150$	4.62800e6	−	3.78672e6i	1.37126	−	1.12199i
$151$			3.77053e6i			1.09514i	0.836759	+	0.547572i	$0.184448\pi$
$151$			3.77053e6i			1.09514i	−0.836759	+	0.547572i	$0.815552\pi$
$152$		−	1.23619e7i		−	3.52010i
$153$	560653.	+	3.53742e6i	0.156538	+	0.987672i
$154$	−3.06805e6			−0.840040
$155$	510801.			0.137169
$156$	8.55007e6	+	1.04496e7i	2.25214	+	2.75249i
$157$	−1.42891e6			−0.369237			−0.184618	−	0.982810i	$-0.559105\pi$
$157$	−1.42891e6			−0.369237			−0.184618	+	0.982810i	$0.559105\pi$
$158$	−1.79311e6	−	1.79311e6i	−0.454606	−	0.454606i
$159$	−3.57656e6	−	4.37115e6i	−0.889762	−	1.08744i
$160$	−2.48226e6	−	2.48226e6i	−0.606021	−	0.606021i
$161$	3.31069e6			0.793306
$162$	7.47398e6	+	3.14750e6i	1.75795	+	0.740322i
$163$	−3.65655e6	−	3.65655e6i	−0.844323	−	0.844323i	0.145095	−	0.989418i	$-0.453651\pi$
$163$	−3.65655e6	−	3.65655e6i	−0.844323	−	0.844323i	−0.989418	+	0.145095i	$0.953651\pi$
$164$	3.46768e6	−	3.46768e6i	0.786154	−	0.786154i
$165$	339343.	+	414734.i	0.0755418	+	0.0923247i
$166$	1.38930e7			3.03719
$167$	4.91236e6	+	4.91236e6i	1.05473	+	1.05473i	0.998413	+	0.0563153i	$0.0179352\pi$
$167$	4.91236e6	+	4.91236e6i	1.05473	+	1.05473i	0.0563153	+	0.998413i	$0.482065\pi$
$168$	1.45161e6	−	1.45194e7i	0.306142	−	3.06210i
$169$	3.94299e6			0.816894
$170$	−2.27310e6	−	1.03952e6i	−0.462670	−	0.211586i
$171$	−5.52031e6	−	1.11496e6i	−1.10401	−	0.222982i
$172$			2.62130e7i			5.15148i
$173$	589178.	+	589178.i	0.113791	+	0.113791i	0.761710	−	0.647919i	$-0.224360\pi$
$173$	589178.	+	589178.i	0.113791	+	0.113791i	−0.647919	+	0.761710i	$0.724360\pi$
$174$	−428959.	+	4.29055e6i	−0.0814269	+	0.814452i
$175$	−3.46602e6	+	3.46602e6i	−0.646721	+	0.646721i
$176$	−5.72955e6	+	5.72955e6i	−1.05095	+	1.05095i
$177$	−2.30260e6	−	2.81416e6i	−0.415239	−	0.507491i
$178$			5.38069e6i			0.954066i
$179$	1.53027e6			0.266815			0.133407	−	0.991061i	$-0.457408\pi$
$179$	1.53027e6			0.266815			0.133407	+	0.991061i	$0.457408\pi$
$180$	−3.41914e6	+	2.27007e6i	−0.586273	+	0.389244i
$181$	−705408.	−	705408.i	−0.118961	−	0.118961i	0.645120	−	0.764081i	$-0.276807\pi$
$181$	−705408.	−	705408.i	−0.118961	−	0.118961i	−0.764081	+	0.645120i	$0.776807\pi$
$182$	−1.07921e7	−	1.07921e7i	−1.79015	−	1.79015i
$183$	761391.	−	7.61562e6i	0.124238	−	1.24266i
$184$	1.10917e7	−	1.10917e7i	1.78051	−	1.78051i
$185$	2.75099e6			0.434484
$186$	6.28124e6	+	627983.i	0.976128	+	0.0975909i
$187$	−1.21636e6	+	2.65979e6i	−0.186011	+	0.406745i
$188$			8.98390e6i			1.35205i
$189$	−6.35279e6	−	1.95777e6i	−0.940978	−	0.289986i
$190$	2.77915e6	−	2.77915e6i	0.405183	−	0.405183i
$191$			1.13100e7i			1.62316i	0.584240	+	0.811581i	$0.301393\pi$
$191$			1.13100e7i			1.62316i	−0.584240	+	0.811581i	$0.698607\pi$
$192$	−1.25780e7	−	1.53724e7i	−1.77708	−	2.17189i
$193$	2.07148e6	+	2.07148e6i	0.288143	+	0.288143i	0.836346	−	0.548203i	$-0.184688\pi$
$193$	2.07148e6	+	2.07148e6i	0.288143	+	0.288143i	−0.548203	+	0.836346i	$0.684688\pi$
$194$	1.23124e7	−	1.23124e7i	1.68632	−	1.68632i
$195$	−265192.	+	2.65252e6i	−0.0357649	+	0.357729i
$196$		−	605313.i		−	0.0803918i
$197$	−1.45086e6	+	1.45086e6i	−0.189770	+	0.189770i	−0.795597	−	0.605827i	$-0.792842\pi$
$197$	−1.45086e6	+	1.45086e6i	−0.189770	+	0.189770i	0.605827	+	0.795597i	$0.292842\pi$
$198$	3.66298e6	+	5.51712e6i	0.471888	+	0.710750i
$199$	3.41193e6	−	3.41193e6i	0.432954	−	0.432954i	−0.456678	−	0.889632i	$-0.650961\pi$
$199$	3.41193e6	−	3.41193e6i	0.432954	−	0.432954i	0.889632	+	0.456678i	$0.150961\pi$
$200$			2.32241e7i			2.90302i
$201$	−1.30675e6	−	1.59707e6i	−0.160918	−	0.196669i
$202$			2.92196e6i			0.354503i
$203$		−	3.53455e6i		−	0.422519i
$204$	−1.93429e7	−	1.12961e7i	−2.27840	−	1.33057i
$205$	968236.			0.112388
$206$	−2.05058e7			−2.34572
$207$	−3.95267e6	−	5.95345e6i	−0.445636	−	0.671209i
$208$	−4.03082e7			−4.47923
$209$	−3.25193e6	−	3.25193e6i	−0.356206	−	0.356206i
$210$	3.59051e6	−	2.93783e6i	0.387703	−	0.317226i
$211$	−7.89307e6	−	7.89307e6i	−0.840230	−	0.840230i	0.148658	−	0.988889i	$-0.452505\pi$
$211$	−7.89307e6	−	7.89307e6i	−0.840230	−	0.840230i	−0.988889	+	0.148658i	$0.952505\pi$
$212$	3.53228e7			3.70721
$213$	−819951.	+	8.20134e6i	−0.0848494	+	0.848684i
$214$	−1.23703e7	−	1.23703e7i	−1.26224	−	1.26224i
$215$	−3.65956e6	+	3.65956e6i	−0.368225	+	0.368225i
$216$	−2.78425e7	+	1.47245e7i	−2.76279	+	1.46109i
$217$	−5.17448e6			−0.506393
$218$	−1.39376e7	−	1.39376e7i	−1.34530	−	1.34530i
$219$	−1.03661e7	−	1.03637e6i	−0.986918	−	0.0986697i
$220$	−3.35142e6			−0.314747
$221$	−1.36346e7	+	5.07734e6i	−1.26318	+	0.470392i
$222$	3.38285e7	+	3.38210e6i	3.09189	+	0.309120i
$223$			84242.1i			0.00759651i	0.999993	+	0.00379826i	$0.00120903\pi$
$223$			84242.1i			0.00759651i	−0.999993	+	0.00379826i	$0.998791\pi$
$224$	2.51457e7	+	2.51457e7i	2.23727	+	2.23727i
$225$	1.03709e7	+	2.09465e6i	0.910477	+	0.183893i
$226$	1.85761e7	−	1.85761e7i	1.60927	−	1.60927i
$227$	3.26373e6	−	3.26373e6i	0.279021	−	0.279021i	−0.553697	−	0.832718i	$-0.686784\pi$
$227$	3.26373e6	−	3.26373e6i	0.279021	−	0.279021i	0.832718	+	0.553697i	$0.186784\pi$
$228$	2.72598e7	−	2.23045e7i	2.29995	−	1.88186i
$229$			7.26476e6i			0.604943i	0.953158	+	0.302472i	$0.0978117\pi$
$229$			7.26476e6i			0.604943i	−0.953158	+	0.302472i	$0.902188\pi$
$230$	4.98715e6			0.409892
$231$	−3.43760e6	−	4.20132e6i	−0.278881	−	0.340839i
$232$	−1.18417e7	−	1.18417e7i	−0.948307	−	0.948307i
$233$	1.55710e6	+	1.55710e6i	0.123097	+	0.123097i	0.765972	−	0.642874i	$-0.222258\pi$
$233$	1.55710e6	+	1.55710e6i	0.123097	+	0.123097i	−0.642874	+	0.765972i	$0.722258\pi$
$234$	−6.52207e6	+	3.22916e7i	−0.509023	+	2.52024i
$235$	−1.25423e6	+	1.25423e6i	−0.0966437	+	0.0966437i
$236$	2.27409e7			1.73010
$237$	446353.	−	4.46453e6i	0.0335300	−	0.335375i
$238$	2.30268e7	+	1.05305e7i	1.70806	+	0.781121i
$239$			2.20456e6i			0.161484i	0.996735	+	0.0807418i	$0.0257289\pi$
$239$			2.20456e6i			0.161484i	−0.996735	+	0.0807418i	$0.974271\pi$
$240$	1.21889e6	−	1.21916e7i	0.0881720	−	0.881917i
$241$	2.83724e6	−	2.83724e6i	0.202696	−	0.202696i	−0.598458	−	0.801154i	$-0.704220\pi$
$241$	2.83724e6	−	2.83724e6i	0.202696	−	0.202696i	0.801154	+	0.598458i	$0.204220\pi$
$242$		−	2.16259e7i		−	1.52590i
$243$	4.06411e6	+	1.37613e7i	0.283235	+	0.959051i
$244$	3.38469e7	+	3.38469e7i	2.32996	+	2.32996i
$245$	84506.9	−	84506.9i	0.00574637	−	0.00574637i
$246$	1.19063e7	+	1.19036e6i	0.799779	+	0.0799600i
$247$		−	2.28777e7i		−	1.51818i
$248$	−1.73359e7	+	1.73359e7i	−1.13655	+	1.13655i
$249$	1.55664e7	+	1.90248e7i	1.00830	+	1.23232i
$250$	−1.08421e7	+	1.08421e7i	−0.693897	+	0.693897i
$251$		−	2.58950e7i		−	1.63755i	−0.574112	−	0.818777i	$-0.694653\pi$
$251$		−	2.58950e7i		−	1.63755i	0.574112	−	0.818777i	$-0.305347\pi$
$252$	3.46364e7	−	2.29961e7i	2.16437	−	1.43699i
$253$		−	5.83554e6i		−	0.360346i
$254$			9.12483e6i			0.556831i
$255$	−1.12339e6	−	4.27746e6i	−0.0677504	−	0.257968i
$256$	2.13898e7			1.27493
$257$	−2.53118e7			−1.49116			−0.745578	−	0.666419i	$-0.767826\pi$
$257$	−2.53118e7			−1.49116			−0.745578	+	0.666419i	$0.767826\pi$
$258$	−4.95002e7	+	4.05020e7i	−2.88236	+	2.35840i
$259$	−2.78679e7			−1.60400
$260$	−1.17889e7	−	1.17889e7i	−0.670736	−	0.670736i
$261$	−6.35601e6	+	4.21994e6i	−0.357490	+	0.237348i
$262$	−3.13304e7	−	3.13304e7i	−1.74206	−	1.74206i
$263$	−1.09360e7			−0.601159			−0.300579	−	0.953757i	$-0.597180\pi$
$263$	−1.09360e7			−0.601159			−0.300579	+	0.953757i	$0.597180\pi$
$264$	−2.55923e7	−	2.55866e6i	−1.39091	−	0.139060i
$265$	4.93136e6	+	4.93136e6i	0.264990	+	0.264990i
$266$	−2.81532e7	+	2.81532e7i	−1.49583	+	1.49583i
$267$	−7.36821e6	+	6.02881e6i	−0.387104	+	0.316736i
$268$	1.29058e7			0.670470
$269$	2.37468e7	+	2.37468e7i	1.21997	+	1.21997i	0.967642	+	0.252327i	$0.0811959\pi$
$269$	2.37468e7	+	2.37468e7i	1.21997	+	1.21997i	0.252327	+	0.967642i	$0.418804\pi$
$270$	−9.56971e6	−	2.94914e6i	−0.486192	−	0.149832i
$271$	−1.08797e7			−0.546649			−0.273324	−	0.961922i	$-0.588123\pi$
$271$	−1.08797e7			−0.546649			−0.273324	+	0.961922i	$0.588123\pi$
$272$	6.26680e7	−	2.33367e7i	3.11415	−	1.15967i
$273$	2.68644e6	−	2.68704e7i	0.132035	−	1.32064i
$274$		−	2.42680e7i		−	1.17973i
$275$	6.10934e6	+	6.10934e6i	0.293762	+	0.293762i
$276$	4.44713e7	+	4.44614e6i	2.11521	+	0.211473i
$277$	−5.94028e6	+	5.94028e6i	−0.279491	+	0.279491i	−0.832906	−	0.553415i	$-0.813324\pi$
$277$	−5.94028e6	+	5.94028e6i	−0.279491	+	0.279491i	0.553415	+	0.832906i	$0.313324\pi$
$278$	1.21106e7	−	1.21106e7i	0.563678	−	0.563678i
$279$	6.17788e6	+	9.30502e6i	0.284463	+	0.428454i
$280$			1.80178e7i			0.820783i
$281$	1.33799e7			0.603021			0.301510	−	0.953463i	$-0.402509\pi$
$281$	1.33799e7			0.603021			0.301510	+	0.953463i	$0.402509\pi$
$282$	−1.69650e7	+	1.38811e7i	−0.756498	+	0.618981i
$283$	6.70465e6	+	6.70465e6i	0.295813	+	0.295813i	0.839371	−	0.543558i	$-0.182923\pi$
$283$	6.70465e6	+	6.70465e6i	0.295813	+	0.295813i	−0.543558	+	0.839371i	$0.682923\pi$
$284$	−3.64501e7	−	3.64501e7i	−1.59127	−	1.59127i
$285$	6.91961e6	+	691806.i	0.298914	+	0.0298848i
$286$	−1.90225e7	+	1.90225e7i	−0.813147	+	0.813147i
$287$	−9.80836e6			−0.414907
$288$	1.51965e7	−	7.52399e7i	0.636160	−	3.14971i
$289$	1.82584e7	−	1.57877e7i	0.756432	−	0.654072i
$290$		−	5.32437e6i		−	0.218310i
$291$	3.06559e7	+	3.06490e6i	1.24404	+	0.124376i
$292$	4.60709e7	−	4.60709e7i	1.85045	−	1.85045i
$293$			1.45063e7i			0.576706i	0.957524	+	0.288353i	$0.0931076\pi$
$293$			1.45063e7i			0.576706i	−0.957524	+	0.288353i	$0.906892\pi$
$294$	1.14306e6	−	935276.i	0.0449809	−	0.0368042i
$295$	3.17482e6	+	3.17482e6i	0.123667	+	0.123667i
$296$	−9.33648e7	+	9.33648e7i	−3.60005	+	3.60005i
$297$	−3.45084e6	+	1.11977e7i	−0.131721	+	0.427423i
$298$			4.53181e7i			1.71247i
$299$	2.05269e7	−	2.05269e7i	0.767909	−	0.767909i
$300$	−5.12126e7	+	4.19031e7i	−1.89676	+	1.55197i
$301$	3.70719e7	−	3.70719e7i	1.35939	−	1.35939i
$302$		−	5.75376e7i		−	2.08896i
$303$	−4.00127e6	+	3.27391e6i	−0.143837	+	0.117690i
$304$			1.05152e8i			3.74279i
$305$			9.45063e6i			0.333090i
$306$	−8.55546e6	−	5.39804e7i	−0.298593	−	1.88396i
$307$	−759535.			−0.0262502			−0.0131251	−	0.999914i	$-0.504178\pi$
$307$	−759535.			−0.0262502			−0.0131251	+	0.999914i	$0.504178\pi$
$308$	3.39504e7			1.16196
$309$	−2.29758e7	−	2.80802e7i	−0.778744	−	0.951756i
$310$	−7.79472e6			−0.261647
$311$	3.77550e7	+	3.77550e7i	1.25514	+	1.25514i	0.953385	+	0.301757i	$0.0975732\pi$
$311$	3.77550e7	+	3.77550e7i	1.25514	+	1.25514i	0.301757	+	0.953385i	$0.402427\pi$
$312$	−8.10225e7	−	9.90230e7i	−2.66773	−	3.26041i
$313$	1.50789e7	+	1.50789e7i	0.491741	+	0.491741i	0.908854	−	0.417113i	$-0.136958\pi$
$313$	1.50789e7	+	1.50789e7i	0.491741	+	0.491741i	−0.417113	+	0.908854i	$0.636958\pi$
$314$	2.18049e7			0.704311
$315$	8.04599e6	+	1.62508e6i	0.257423	+	0.0519928i
$316$	1.98422e7	+	1.98422e7i	0.628822	+	0.628822i
$317$	3.46421e7	−	3.46421e7i	1.08749	−	1.08749i	0.0917067	−	0.995786i	$-0.470768\pi$
$317$	3.46421e7	−	3.46421e7i	1.08749	−	1.08749i	0.995786	−	0.0917067i	$-0.0292322\pi$
$318$	5.45776e7	+	6.67029e7i	1.69720	+	2.07426i
$319$	−6.23013e6			−0.191922
$320$	1.73426e7	+	1.73426e7i	0.529253	+	0.529253i
$321$	3.07932e6	−	3.08001e7i	0.0930978	−	0.931186i
$322$	−5.05205e7			−1.51321
$323$	1.32452e7	+	3.55685e7i	0.393054	+	1.05550i
$324$	−8.27056e7	−	3.48296e7i	−2.43164	−	1.02403i
$325$			4.29800e7i			1.25203i
$326$	5.57983e7	+	5.57983e7i	1.61053	+	1.61053i
$327$	3.46945e6	−	3.47023e7i	0.0992242	−	0.992464i
$328$	−3.28606e7	+	3.28606e7i	−0.931222	+	0.931222i
$329$	1.27055e7	−	1.27055e7i	0.356784	−	0.356784i
$330$	−5.17832e6	−	6.32877e6i	−0.144094	−	0.176107i
$331$		−	6.32084e7i		−	1.74297i	−0.490420	−	0.871486i	$-0.663157\pi$
$331$		−	6.32084e7i		−	1.74297i	0.490420	−	0.871486i	$-0.336843\pi$
$332$	−1.53737e8			−4.20112
$333$	3.32719e7	+	5.01135e7i	0.901041	+	1.35713i
$334$	−7.49617e7	−	7.49617e7i	−2.01187	−	2.01187i
$335$	1.80175e6	+	1.80175e6i	0.0479249	+	0.0479249i
$336$	−1.23475e7	+	1.23503e8i	−0.325508	+	3.25581i
$337$	9.40366e6	−	9.40366e6i	0.245701	−	0.245701i	−0.573503	−	0.819204i	$-0.694416\pi$
$337$	9.40366e6	−	9.40366e6i	0.245701	−	0.245701i	0.819204	+	0.573503i	$0.194416\pi$
$338$	−6.01694e7			−1.55821
$339$	4.62513e7	+	4.62410e6i	1.18720	+	0.118694i
$340$	2.51536e7	+	1.15031e7i	0.639976	+	0.292671i
$341$			9.12073e6i			0.230020i
$342$	8.42389e7	+	1.70141e7i	2.10588	+	0.425334i
$343$	−2.89523e7	+	2.89523e7i	−0.717465	+	0.717465i
$344$		−	2.48401e8i		−	6.10208i
$345$	5.58786e6	+	6.82930e6i	0.136078	+	0.166310i
$346$	−8.99076e6	−	8.99076e6i	−0.217054	−	0.217054i
$347$	−1.55531e7	+	1.55531e7i	−0.372246	+	0.372246i	−0.868295	−	0.496049i	$-0.834784\pi$
$347$	−1.55531e7	+	1.55531e7i	−0.372246	+	0.372246i	0.496049	+	0.868295i	$0.334784\pi$
$348$	4.74678e6	−	4.74784e7i	0.112632	−	1.12657i
$349$		−	6.63380e6i		−	0.156058i	−0.996951	−	0.0780290i	$-0.975137\pi$
$349$		−	6.63380e6i		−	0.156058i	0.996951	−	0.0780290i	$-0.0248627\pi$
$350$	5.28909e7	−	5.28909e7i	1.23361	−	1.23361i
$351$	−5.15271e7	+	2.72500e7i	−1.19156	+	0.630151i
$352$	4.43227e7	−	4.43227e7i	1.01624	−	1.01624i
$353$			3.37303e7i			0.766824i	0.923577	+	0.383412i	$0.125251\pi$
$353$			3.37303e7i			0.766824i	−0.923577	+	0.383412i	$0.874749\pi$
$354$	3.51372e7	+	4.29435e7i	0.792059	+	0.968028i
$355$		−	1.01775e7i		−	0.227486i
$356$		−	5.95417e7i		−	1.31969i
$357$	1.13801e7	+	4.33313e7i	0.250117	+	0.952351i
$358$	−2.33517e7			−0.508943
$359$	−1.57841e7			−0.341143			−0.170572	−	0.985345i	$-0.554561\pi$
$359$	−1.57841e7			−0.341143			−0.170572	+	0.985345i	$0.554561\pi$
$360$	3.24006e7	−	2.15117e7i	0.694457	−	0.461071i
$361$	−1.26351e7			−0.268570
$362$	1.07644e7	+	1.07644e7i	0.226916	+	0.226916i
$363$	2.96140e7	−	2.42307e7i	0.619123	−	0.506578i
$364$	1.19423e8	+	1.19423e8i	2.47618	+	2.47618i
$365$	1.28638e7			0.264539
$366$	−1.16187e7	+	1.16213e8i	−0.236981	+	2.37034i
$367$	−1.69503e7	−	1.69503e7i	−0.342910	−	0.342910i	0.514551	−	0.857460i	$-0.327959\pi$
$367$	−1.69503e7	−	1.69503e7i	−0.342910	−	0.342910i	−0.857460	+	0.514551i	$0.827959\pi$
$368$	−9.43467e7	+	9.43467e7i	−1.89314	+	1.89314i
$369$	1.17103e7	+	1.76379e7i	0.233072	+	0.351049i
$370$	−4.19796e7			−0.828769
$371$	−4.99554e7	−	4.99554e7i	−0.978275	−	0.978275i
$372$	−6.95070e7	−	6.94914e6i	−1.35020	−	0.134990i
$373$	7.84989e7			1.51265			0.756323	−	0.654199i	$-0.226994\pi$
$373$	7.84989e7			1.51265			0.756323	+	0.654199i	$0.226994\pi$
$374$	1.85614e7	−	4.05878e7i	0.354811	−	0.775856i
$375$	−2.69951e7	−	2.69890e6i	−0.511907	−	0.0511792i
$376$		−	8.51336e7i		−	1.60154i
$377$	−2.19149e7	−	2.19149e7i	−0.408992	−	0.408992i
$378$	9.69425e7	+	2.98752e7i	1.79489	+	0.553141i
$379$	−3.28448e7	+	3.28448e7i	−0.603322	+	0.603322i	−0.941192	−	0.337871i	$-0.890293\pi$
$379$	−3.28448e7	+	3.28448e7i	−0.603322	+	0.603322i	0.337871	+	0.941192i	$0.390293\pi$
$380$	−3.07535e7	+	3.07535e7i	−0.560459	+	0.560459i
$381$	−1.24953e7	+	1.02239e7i	−0.225930	+	0.184860i
$382$		−	1.72588e8i		−	3.09615i
$383$	−1.56749e7			−0.279002			−0.139501	−	0.990222i	$-0.544550\pi$
$383$	−1.56749e7			−0.279002			−0.139501	+	0.990222i	$0.544550\pi$
$384$	7.67185e7	+	9.37628e7i	1.35490	+	1.65591i
$385$	4.73977e6	+	4.73977e6i	0.0830567	+	0.0830567i
$386$	−3.16103e7	−	3.16103e7i	−0.549626	−	0.549626i
$387$	−1.10925e8	−	2.24040e7i	−1.91380	−	0.386538i
$388$	−1.36247e8	+	1.36247e8i	−2.33256	+	2.33256i
$389$	6.63876e7			1.12782			0.563908	−	0.825838i	$-0.309297\pi$
$389$	6.63876e7			1.12782			0.563908	+	0.825838i	$0.309297\pi$
$390$	4.04679e6	−	4.04770e7i	0.0682208	−	0.682361i
$391$	−2.00294e7	+	4.37978e7i	−0.335072	+	0.732693i
$392$			5.73609e6i			0.0952265i
$393$	7.79899e6	−	7.80074e7i	0.128488	−	1.28516i
$394$	2.21399e7	−	2.21399e7i	0.361982	−	0.361982i
$395$			5.54027e6i			0.0898959i
$396$	−4.05338e7	−	6.10514e7i	−0.652727	−	0.983127i
$397$	3.48544e7	+	3.48544e7i	0.557039	+	0.557039i	0.928463	−	0.371424i	$-0.121130\pi$
$397$	3.48544e7	+	3.48544e7i	0.557039	+	0.557039i	−0.371424	+	0.928463i	$0.621130\pi$
$398$	−5.20655e7	+	5.20655e7i	−0.825849	+	0.825849i
$399$	−7.00966e7	−	7.00809e6i	−1.10352	−	0.110327i
$400$		−	1.97547e8i		−	3.08667i
$401$	−3.16606e7	+	3.16606e7i	−0.491005	+	0.491005i	−0.908623	−	0.417618i	$-0.862865\pi$
$401$	−3.16606e7	+	3.16606e7i	−0.491005	+	0.491005i	0.417618	+	0.908623i	$0.362865\pi$
$402$	1.99408e7	+	2.43710e7i	0.306948	+	0.375142i
$403$	−3.20828e7	+	3.20828e7i	−0.490181	+	0.490181i
$404$		−	3.23338e7i		−	0.490357i
$405$	−6.68390e6	−	1.64089e7i	−0.100616	−	0.247010i
$406$			5.39366e7i			0.805946i
$407$			4.91210e7i			0.728592i
$408$	1.83297e8	+	1.07045e8i	2.69883	+	1.57610i
$409$	3.63910e7			0.531893			0.265947	−	0.963988i	$-0.414315\pi$
$409$	3.63910e7			0.531893			0.265947	+	0.963988i	$0.414315\pi$
$410$	−1.47751e7			−0.214377
$411$	3.32320e7	−	2.71911e7i	0.478665	−	0.391653i
$412$	2.26914e8			3.24466
$413$	−3.21614e7	−	3.21614e7i	−0.456547	−	0.456547i
$414$	6.03171e7	+	9.08486e7i	0.850040	+	1.28032i
$415$	−2.14631e7	−	2.14631e7i	−0.300294	−	0.300294i
$416$	3.11816e8			4.33130
$417$	3.01533e7	+	3.01466e6i	0.415841	+	0.0415748i
$418$	4.96238e7	+	4.96238e7i	0.679456	+	0.679456i
$419$	414134.	−	414134.i	0.00562988	−	0.00562988i	−0.704286	−	0.709916i	$-0.748733\pi$
$419$	414134.	−	414134.i	0.00562988	−	0.00562988i	0.709916	+	0.704286i	$0.248733\pi$
$420$	−3.97319e7	+	3.25094e7i	−0.536280	+	0.438795i
$421$	3.79603e6			0.0508725			0.0254362	−	0.999676i	$-0.491903\pi$
$421$	3.79603e6			0.0508725			0.0254362	+	0.999676i	$0.491903\pi$
$422$	1.20447e8	+	1.20447e8i	1.60272	+	1.60272i
$423$	−3.80170e7	−	7.67845e6i	−0.502292	−	0.101450i
$424$	−3.34727e8			−4.39130
$425$	−2.48836e7	−	6.68219e7i	−0.324150	−	0.870467i
$426$	1.25123e7	−	1.25151e8i	0.161848	−	1.61885i
$427$		−	9.57362e7i		−	1.22968i
$428$	1.36888e8	+	1.36888e8i	1.74596	+	1.74596i
$429$	−4.73627e7	−	4.73521e6i	−0.599880	−	0.0599746i
$430$	5.58443e7	−	5.58443e7i	0.702382	−	0.702382i
$431$	−7.35810e7	+	7.35810e7i	−0.919039	+	0.919039i	−0.996960	−	0.0779203i	$-0.975172\pi$
$431$	−7.35810e7	+	7.35810e7i	−0.919039	+	0.919039i	0.0779203	+	0.996960i	$0.475172\pi$
$432$	2.36831e8	−	1.25248e8i	2.93756	−	1.55352i
$433$		−	751266.i		−	0.00925401i	−0.999989	−	0.00462701i	$-0.998527\pi$
$433$		−	751266.i		−	0.00925401i	0.999989	−	0.00462701i	$-0.00147283\pi$
$434$	7.89617e7			0.965933
$435$	7.29108e6	−	5.96570e6i	0.0885776	−	0.0724759i
$436$	1.54231e8	+	1.54231e8i	1.86085	+	1.86085i
$437$	−5.35484e7	−	5.35484e7i	−0.641656	−	0.641656i
$438$	1.58184e8	+	1.58149e7i	1.88252	+	0.188210i
$439$	−3.20575e7	+	3.20575e7i	−0.378910	+	0.378910i	−0.870709	−	0.491799i	$-0.836340\pi$
$439$	−3.20575e7	+	3.20575e7i	−0.378910	+	0.378910i	0.491799	+	0.870709i	$0.336340\pi$
$440$	3.17589e7			0.372827
$441$	2.56149e6	+	517355.i	0.0298660	+	0.00603216i
$442$	2.08062e8	−	7.74793e7i	2.40949	−	0.897261i
$443$		−	6.99943e6i		−	0.0805103i	−0.999189	−	0.0402551i	$-0.987183\pi$
$443$		−	6.99943e6i		−	0.0805103i	0.999189	−	0.0402551i	$-0.0128171\pi$
$444$	−3.74340e8	−	3.74256e7i	−4.27678	−	0.427583i
$445$	8.31253e6	−	8.31253e6i	0.0943308	−	0.0943308i
$446$		−	1.28552e6i		−	0.0144902i
$447$	−6.20576e7	+	5.07767e7i	−0.694821	+	0.568515i
$448$	−1.75683e8	−	1.75683e8i	−1.95387	−	1.95387i
$449$	9.20114e7	−	9.20114e7i	1.01649	−	1.01649i	0.0166270	−	0.999862i	$-0.494707\pi$
$449$	9.20114e7	−	9.20114e7i	1.01649	−	1.01649i	0.999862	−	0.0166270i	$-0.00529277\pi$
$450$	−1.58258e8	−	3.19640e7i	−1.73672	−	0.350771i
$451$			1.72886e7i			0.188465i
$452$	−2.05559e8	+	2.05559e8i	−2.22598	+	2.22598i
$453$	7.87907e7	−	6.44680e7i	0.847579	−	0.693505i
$454$	−4.98039e7	+	4.98039e7i	−0.532226	+	0.532226i
$455$			3.33449e7i			0.353993i
$456$	−2.58321e8	+	2.11363e8i	−2.72436	+	2.22912i
$457$		−	3.64671e7i		−	0.382078i	−0.981582	−	0.191039i	$-0.938814\pi$
$457$		−	3.64671e7i		−	0.382078i	0.981582	−	0.191039i	$-0.0611857\pi$
$458$		−	1.10859e8i		−	1.15392i
$459$	6.43337e7	−	7.21981e7i	0.665274	−	0.746600i
$460$	−5.51868e7			−0.566972
$461$	−4.79025e7			−0.488940			−0.244470	−	0.969657i	$-0.578614\pi$
$461$	−4.79025e7			−0.488940			−0.244470	+	0.969657i	$0.578614\pi$
$462$	5.24571e7	+	6.41113e7i	0.531959	+	0.650143i
$463$	−8.44380e7			−0.850736			−0.425368	−	0.905020i	$-0.639855\pi$
$463$	−8.44380e7			−0.850736			−0.425368	+	0.905020i	$0.639855\pi$
$464$	1.00726e8	+	1.00726e8i	1.00830	+	1.00830i
$465$	−8.73361e6	−	1.06739e7i	−0.0868630	−	0.106161i
$466$	−2.37611e7	−	2.37611e7i	−0.234806	−	0.234806i
$467$	1.02861e8			1.00995			0.504977	−	0.863133i	$-0.331501\pi$
$467$	1.02861e8			1.00995			0.504977	+	0.863133i	$0.331501\pi$
$468$	7.21719e7	−	3.57332e8i	0.704094	−	3.48606i
$469$	−1.82520e7	−	1.82520e7i	−0.176926	−	0.176926i
$470$	1.91393e7	−	1.91393e7i	0.184346	−	0.184346i
$471$	2.44313e7	+	2.98591e7i	0.233821	+	0.285768i
$472$	−2.15498e8			−2.04936
$473$	−6.53442e7	−	6.53442e7i	−0.617481	−	0.617481i
$474$	−6.81127e6	+	6.81279e7i	−0.0639577	+	0.639720i
$475$	1.12122e8			1.04619
$476$	−2.54810e8	−	1.16528e8i	−2.36263	−	1.08047i
$477$	−3.01900e7	+	1.49475e8i	−0.278169	+	1.37725i
$478$		−	3.36412e7i		−	0.308026i
$479$	−7.13954e7	−	7.13954e7i	−0.649627	−	0.649627i	0.303276	−	0.952903i	$-0.401920\pi$
$479$	−7.13954e7	−	7.13954e7i	−0.649627	−	0.649627i	−0.952903	+	0.303276i	$0.901920\pi$
$480$	−9.42908e6	+	9.43119e7i	−0.0852601	+	0.852792i
$481$	−1.72786e8	+	1.72786e8i	−1.55265	+	1.55265i
$482$	−4.32957e7	+	4.32957e7i	−0.386638	+	0.386638i
$483$	−5.66058e7	−	6.91817e7i	−0.502365	−	0.613974i
$484$			2.39307e8i			2.11067i
$485$	−3.80425e7			−0.333460
$486$	−6.20177e7	−	2.09995e8i	−0.540265	−	1.82937i
$487$	1.36293e8	+	1.36293e8i	1.18001	+	1.18001i	0.979741	+	0.200271i	$0.0641822\pi$
$487$	1.36293e8	+	1.36293e8i	1.18001	+	1.18001i	0.200271	+	0.979741i	$0.435818\pi$
$488$	−3.20741e8	−	3.20741e8i	−2.75991	−	2.75991i
$489$	−1.38897e7	+	1.38928e8i	−0.118786	+	1.18813i
$490$	−1.28956e6	+	1.28956e6i	−0.0109611	+	0.0109611i
$491$	4.49123e7			0.379420			0.189710	−	0.981840i	$-0.439245\pi$
$491$	4.49123e7			0.379420			0.189710	+	0.981840i	$0.439245\pi$
$492$	−1.31752e8	−	1.31723e7i	−1.10627	−	0.110603i
$493$	4.67593e7	+	2.13838e7i	0.390236	+	0.178461i
$494$			3.49110e8i			2.89589i
$495$	2.86443e6	−	1.41822e7i	0.0236169	−	0.116930i
$496$	1.47460e8	−	1.47460e8i	1.20845	−	1.20845i
$497$			1.03099e8i			0.839821i
$498$	−2.37541e8	−	2.90315e8i	−1.92332	−	2.35061i
$499$	−1.73419e7	−	1.73419e7i	−0.139571	−	0.139571i	0.633869	−	0.773440i	$-0.281466\pi$
$499$	−1.73419e7	−	1.73419e7i	−0.139571	−	0.139571i	−0.773440	+	0.633869i	$0.781466\pi$
$500$	1.19977e8	−	1.19977e8i	0.959816	−	0.959816i
$501$	1.86600e7	−	1.86642e8i	0.148388	−	1.48421i
$502$			3.95154e8i			3.12360i
$503$	−4.63602e7	+	4.63602e7i	−0.364285	+	0.364285i	−0.865388	−	0.501103i	$-0.832928\pi$
$503$	−4.63602e7	+	4.63602e7i	−0.364285	+	0.364285i	0.501103	+	0.865388i	$0.332928\pi$
$504$	−3.28223e8	+	2.17917e8i	−2.56376	+	1.70215i
$505$	4.51408e6	−	4.51408e6i	0.0350505	−	0.0350505i
$506$			8.90493e7i			0.687352i
$507$	−6.74168e7	−	8.23946e7i	−0.517302	−	0.632230i
$508$		−	1.00974e8i		−	0.770223i
$509$		−	7.08079e7i		−	0.536943i	−0.963288	−	0.268471i	$-0.913481\pi$
$509$		−	7.08079e7i		−	0.536943i	0.963288	−	0.268471i	$-0.0865185\pi$
$510$	1.71428e7	+	6.52733e7i	0.129232	+	0.492068i
$511$	−1.30312e8			−0.976611
$512$	−3.92346e7			−0.292321
$513$	7.10869e7	+	1.34418e8i	0.526547	+	0.995649i
$514$	3.86253e8			2.84435
$515$	3.16791e7	+	3.16791e7i	0.231927	+	0.231927i
$516$	5.47759e8	−	4.48187e8i	3.98695	−	3.26220i
$517$	−2.23952e7	−	2.23952e7i	−0.162063	−	0.162063i
$518$	4.25260e8			3.05960
$519$	2.23804e6	−	2.23855e7i	0.0160091	−	0.160127i
$520$	1.11714e8	+	1.11714e8i	0.794507	+	0.794507i
$521$	1.44506e8	−	1.44506e8i	1.02182	−	1.02182i	0.0220629	−	0.999757i	$-0.492977\pi$
$521$	1.44506e8	−	1.44506e8i	1.02182	−	1.02182i	0.999757	−	0.0220629i	$-0.00702341\pi$
$522$	9.69916e7	−	6.43956e7i	0.681903	−	0.452736i
$523$	8.30169e7			0.580312			0.290156	−	0.956979i	$-0.406293\pi$
$523$	8.30169e7			0.580312			0.290156	+	0.956979i	$0.406293\pi$
$524$	3.46696e8	+	3.46696e8i	2.40966	+	2.40966i
$525$	1.31689e8	+	1.31660e7i	0.910065	+	0.0909862i
$526$	1.66881e8			1.14670
$527$	3.13052e7	−	6.84543e7i	0.213887	−	0.467702i
$528$	2.17691e8	+	2.17642e7i	1.47890	+	0.147857i
$529$			5.19439e7i			0.350887i
$530$	−7.52517e7	−	7.52517e7i	−0.505463	−	0.505463i
$531$	−1.94364e7	+	9.62322e7i	−0.129817	+	0.642742i
$532$	3.11537e8	−	3.11537e8i	2.06907	−	2.06907i
$533$	−6.08137e7	+	6.08137e7i	−0.401624	+	0.401624i
$534$	1.12438e8	−	9.19985e7i	0.738393	−	0.604167i
$535$			3.82214e7i			0.249601i
$536$	−1.22298e8			−0.794191
$537$	−2.61644e7	−	3.19773e7i	−0.168962	−	0.206499i
$538$	−3.62372e8	−	3.62372e8i	−2.32706	−	2.32706i
$539$	1.50893e6	+	1.50893e6i	0.00963616	+	0.00963616i
$540$	1.05897e8	+	3.26346e7i	0.672513	+	0.207251i
$541$	7.37004e7	−	7.37004e7i	0.465456	−	0.465456i	−0.434983	−	0.900439i	$-0.643246\pi$
$541$	7.37004e7	−	7.37004e7i	0.465456	−	0.465456i	0.900439	+	0.434983i	$0.143246\pi$
$542$	1.66022e8			1.04272
$543$	−2.67955e6	+	2.68015e7i	−0.0167364	+	0.167402i
$544$	−4.84787e8	+	1.80528e8i	−3.01130	+	1.12137i
$545$			4.30639e7i			0.266026i
$546$	−4.09946e7	+	4.10037e8i	−0.251854	+	2.51910i
$547$	−1.56061e8	+	1.56061e8i	−0.953528	+	0.953528i	−0.998967	−	0.0454389i	$-0.985531\pi$
$547$	−1.56061e8	+	1.56061e8i	−0.953528	+	0.953528i	0.0454389	+	0.998967i	$0.485531\pi$
$548$			2.68545e8i			1.63183i
$549$	−1.72158e8	+	1.14301e8i	−1.04042	+	0.690767i
$550$	−9.32274e7	−	9.32274e7i	−0.560345	−	0.560345i
$551$	−5.71692e7	+	5.71692e7i	−0.341749	+	0.341749i
$552$	−4.21421e8	−	4.21326e7i	−2.50552	−	0.250496i
$553$		−	5.61238e7i		−	0.331873i
$554$	9.06476e7	−	9.06476e7i	0.533123	−	0.533123i
$555$	−4.70361e7	−	5.74860e7i	−0.275139	−	0.336266i
$556$	−1.34014e8	+	1.34014e8i	−0.779694	+	0.779694i
$557$		−	3.76507e7i		−	0.217875i	−0.994049	−	0.108937i	$-0.965255\pi$
$557$		−	3.76507e7i		−	0.217875i	0.994049	−	0.108937i	$-0.0347448\pi$
$558$	−9.42733e7	−	1.41993e8i	−0.542608	−	0.817267i
$559$		−	4.59705e8i		−	2.63175i
$560$		−	1.53261e8i		−	0.872707i
$561$	7.63773e7	−	2.00591e7i	0.432589	−	0.113611i
$562$	−2.04174e8			−1.15025
$563$	2.50557e8			1.40405			0.702023	−	0.712155i	$-0.252281\pi$
$563$	2.50557e8			1.40405			0.702023	+	0.712155i	$0.252281\pi$
$564$	1.87732e8	−	1.53606e8i	1.04641	−	0.856190i
$565$	−5.73957e7			−0.318225
$566$	−1.02312e8	−	1.02312e8i	−0.564256	−	0.564256i
$567$	6.77089e7	+	1.66225e8i	0.371447	+	0.911898i
$568$	3.45409e8	+	3.45409e8i	1.88490	+	1.88490i
$569$	−2.80625e8			−1.52331			−0.761657	−	0.647980i	$-0.775614\pi$
$569$	−2.80625e8			−1.52331			−0.761657	+	0.647980i	$0.775614\pi$
$570$	−1.05592e8	−	1.05568e7i	−0.570173	−	0.0570045i
$571$	2.23650e8	+	2.23650e8i	1.20132	+	1.20132i	0.973764	+	0.227561i	$0.0730751\pi$
$571$	2.23650e8	+	2.23650e8i	1.20132	+	1.20132i	0.227561	+	0.973764i	$0.426925\pi$
$572$	2.10499e8	−	2.10499e8i	1.12476	−	1.12476i
$573$	2.36339e8	−	1.93377e8i	1.25624	−	1.02788i
$574$	1.49674e8			0.791426
$575$	1.00600e8	+	1.00600e8i	0.529172	+	0.529172i
$576$	−1.06172e8	+	5.25671e8i	−0.555575	+	2.75072i
$577$	2.00369e8			1.04305			0.521523	−	0.853237i	$-0.325364\pi$
$577$	2.00369e8			1.04305			0.521523	+	0.853237i	$0.325364\pi$
$578$	−2.78621e8	+	2.40918e8i	−1.44288	+	1.24763i
$579$	7.86868e6	−	7.87044e7i	0.0405383	−	0.405474i
$580$			5.89184e7i			0.301972i
$581$	2.17424e8	+	2.17424e8i	1.10861	+	1.10861i
$582$	−4.67803e8	−	4.67699e7i	−2.37298	−	0.237245i
$583$	−8.80532e7	+	8.80532e7i	−0.444365	+	0.444365i
$584$	−4.36579e8	+	4.36579e8i	−2.19192	+	2.19192i
$585$	5.99625e7	−	3.98109e7i	0.299510	−	0.198854i
$586$		−	2.21364e8i		−	1.10005i
$587$	1.45031e8			0.717046			0.358523	−	0.933521i	$-0.383280\pi$
$587$	1.45031e8			0.717046			0.358523	+	0.933521i	$0.383280\pi$
$588$	−1.26489e7	+	1.03496e7i	−0.0622187	+	0.0509085i
$589$	8.36941e7	+	8.36941e7i	0.409590	+	0.409590i
$590$	−4.84473e7	−	4.84473e7i	−0.235892	−	0.235892i
$591$	5.51245e7	+	5.51122e6i	0.267044	+	0.0266984i
$592$	7.94169e8	−	7.94169e8i	3.82779	−	3.82779i
$593$	−2.32028e8			−1.11270			−0.556348	−	0.830949i	$-0.687798\pi$
$593$	−2.32028e8			−1.11270			−0.556348	+	0.830949i	$0.687798\pi$
$594$	5.26591e7	−	1.70874e8i	0.251255	−	0.815300i
$595$	−1.93053e7	−	5.18420e7i	−0.0916484	−	0.246111i
$596$		−	5.01481e8i		−	2.36873i
$597$	−1.29634e8	−	1.29605e7i	−0.609251	−	0.0609115i
$598$	−3.13237e8	+	3.13237e8i	−1.46477	+	1.46477i
$599$		−	3.10125e8i		−	1.44297i	−0.692431	−	0.721484i	$-0.743460\pi$
$599$		−	3.10125e8i		−	1.44297i	0.692431	−	0.721484i	$-0.256540\pi$
$600$	4.85303e8	−	3.97084e8i	2.24677	−	1.83835i
$601$	1.38324e8	+	1.38324e8i	0.637197	+	0.637197i	0.949863	−	0.312666i	$-0.101222\pi$
$601$	1.38324e8	+	1.38324e8i	0.637197	+	0.637197i	−0.312666	+	0.949863i	$0.601222\pi$
$602$	−5.65710e8	+	5.65710e8i	−2.59301	+	2.59301i
$603$	−1.10304e7	+	5.46131e7i	−0.0503084	+	0.249083i
$604$			6.36699e8i			2.88951i
$605$	−3.34094e7	+	3.34094e7i	−0.150870	+	0.150870i
$606$	6.10586e7	−	4.99593e7i	0.274365	−	0.224491i
$607$	1.85251e8	−	1.85251e8i	0.828311	−	0.828311i	−0.158972	−	0.987283i	$-0.550818\pi$
$607$	1.85251e8	−	1.85251e8i	0.828311	−	0.828311i	0.987283	+	0.158972i	$0.0508180\pi$
$608$		−	8.13432e8i		−	3.61918i
$609$	−7.38597e7	+	6.04334e7i	−0.327006	+	0.267562i
$610$		−	1.44215e8i		−	0.635361i
$611$		−	1.57553e8i		−	0.690723i
$612$	9.46731e7	+	5.97337e8i	0.413021	+	2.60594i
$613$	−1.03703e8			−0.450205			−0.225102	−	0.974335i	$-0.572272\pi$
$613$	−1.03703e8			−0.450205			−0.225102	+	0.974335i	$0.572272\pi$
$614$	1.15904e7			0.0500717
$615$	−1.65548e7	−	2.02327e7i	−0.0711702	−	0.0869818i
$616$	−3.21722e8			−1.37638
$617$	−2.12905e8	−	2.12905e8i	−0.906423	−	0.906423i	0.0895583	−	0.995982i	$-0.471454\pi$
$617$	−2.12905e8	−	2.12905e8i	−0.906423	−	0.906423i	−0.995982	+	0.0895583i	$0.971454\pi$
$618$	3.50606e8	+	4.28500e8i	1.48544	+	1.81545i
$619$	−1.76698e8	−	1.76698e8i	−0.745006	−	0.745006i	0.228530	−	0.973537i	$-0.426608\pi$
$619$	−1.76698e8	−	1.76698e8i	−0.745006	−	0.745006i	−0.973537	+	0.228530i	$0.926608\pi$
$620$	8.62549e7			0.361917
$621$	−5.68238e7	+	1.84388e8i	−0.237277	+	0.769943i
$622$	−5.76134e8	−	5.76134e8i	−2.39416	−	2.39416i
$623$	−8.42071e7	+	8.42071e7i	−0.348245	+	0.348245i
$624$	6.89184e8	+	8.42298e8i	2.83649	+	3.46667i
$625$	−1.93273e8			−0.791648
$626$	−2.30101e8	−	2.30101e8i	−0.937985	−	0.937985i
$627$	−1.23527e7	+	1.23555e8i	−0.0501141	+	0.501253i
$628$	−2.41288e8			−0.974221
$629$	1.68599e8	−	3.68671e8i	0.677490	−	1.48145i
$630$	−1.22780e8	−	2.47985e7i	−0.491029	−	0.0991752i
$631$			3.83665e6i			0.0152709i	0.999971	+	0.00763544i	$0.00243046\pi$
$631$			3.83665e6i			0.0152709i	−0.999971	+	0.00763544i	$0.997570\pi$
$632$	−1.88029e8	−	1.88029e8i	−0.744859	−	0.744859i
$633$	−2.99825e7	+	2.99892e8i	−0.118211	+	1.18237i
$634$	−5.28632e8	+	5.28632e8i	−2.07437	+	2.07437i
$635$	1.40968e7	−	1.40968e7i	0.0550552	−	0.0550552i
$636$	−6.03945e8	−	7.38122e8i	−2.34761	−	2.86917i
$637$			1.06156e7i			0.0410700i
$638$	9.50707e7			0.366087
$639$	1.85399e8	−	1.23092e8i	0.710565	−	0.471765i
$640$	−1.05780e8	−	1.05780e8i	−0.403517	−	0.403517i
$641$	1.40814e8	+	1.40814e8i	0.534651	+	0.534651i	0.921953	−	0.387302i	$-0.126593\pi$
$641$	1.40814e8	+	1.40814e8i	0.534651	+	0.534651i	−0.387302	+	0.921953i	$0.626593\pi$
$642$	−4.69898e7	+	4.70003e8i	−0.177582	+	1.77622i
$643$	6.04659e7	−	6.04659e7i	0.227446	−	0.227446i	−0.584179	−	0.811625i	$-0.698583\pi$
$643$	6.04659e7	−	6.04659e7i	0.227446	−	0.227446i	0.811625	+	0.584179i	$0.198583\pi$
$644$	5.59050e8			2.09312
$645$	1.39043e8	+	1.39012e7i	0.518166	+	0.0518050i
$646$	−2.02120e8	−	5.42769e8i	−0.749741	−	2.01334i
$647$			1.76341e8i			0.651087i	0.945527	+	0.325544i	$0.105547\pi$
$647$			1.76341e8i			0.651087i	−0.945527	+	0.325544i	$0.894453\pi$
$648$	7.83738e8	+	3.30054e8i	2.88035	+	1.21300i
$649$	−5.66889e7	+	5.66889e7i	−0.207379	+	0.207379i
$650$		−	6.55867e8i		−	2.38823i
$651$	8.84727e7	+	1.08128e8i	0.320676	+	0.391919i
$652$	−6.17453e8	−	6.17453e8i	−2.22772	−	2.22772i
$653$	−3.11790e8	+	3.11790e8i	−1.11975	+	1.11975i	−0.127975	+	0.991777i	$0.540848\pi$
$653$	−3.11790e8	+	3.11790e8i	−1.11975	+	1.11975i	−0.991777	+	0.127975i	$0.959152\pi$
$654$	−5.29432e7	+	5.29551e8i	−0.189268	+	1.89310i
$655$			9.68035e7i			0.344483i
$656$	2.79515e8	−	2.79515e8i	0.990132	−	0.990132i
$657$	1.55581e8	+	2.34334e8i	0.548606	+	0.826302i
$658$	−1.93884e8	+	1.93884e8i	−0.680557	+	0.680557i
$659$		−	3.31126e8i		−	1.15701i	−0.815679	−	0.578505i	$-0.803636\pi$
$659$		−	3.31126e8i		−	1.15701i	0.815679	−	0.578505i	$-0.196364\pi$
$660$	5.73023e7	+	7.00329e7i	0.199315	+	0.243596i
$661$		−	2.94269e8i		−	1.01892i	−0.860494	−	0.509460i	$-0.829845\pi$
$661$		−	2.94269e8i		−	1.01892i	0.860494	−	0.509460i	$-0.170155\pi$
$662$			9.64548e8i			3.32468i
$663$	3.39221e8	+	1.98103e8i	1.16397	+	0.679753i
$664$	1.45685e9			4.97635
$665$	8.69866e7			0.295793
$666$	−5.07723e8	−	7.64724e8i	−1.71871	−	2.58870i
$667$	−1.02590e8			−0.345721
$668$	8.29511e8	+	8.29511e8i	2.78287	+	2.78287i
$669$	1.76036e6	−	1.44036e6i	0.00587927	−	0.00481053i
$670$	−2.74945e7	−	2.74945e7i	−0.0914157	−	0.0914157i
$671$	−1.68748e8			−0.558562
$672$	9.55180e7	−	9.55393e8i	0.314758	−	3.14829i
$673$	−3.30792e8	−	3.30792e8i	−1.08520	−	1.08520i	−0.996015	−	0.0891852i	$-0.971574\pi$
$673$	−3.30792e8	−	3.30792e8i	−1.08520	−	1.08520i	−0.0891852	−	0.996015i	$-0.528426\pi$
$674$	−1.43498e8	+	1.43498e8i	−0.468670	+	0.468670i
$675$	−1.33550e8	−	2.52529e8i	−0.434242	−	0.821109i
$676$	6.65822e8			2.15535
$677$	−1.28471e8	−	1.28471e8i	−0.414036	−	0.414036i	0.469106	−	0.883142i	$-0.344576\pi$
$677$	−1.28471e8	−	1.28471e8i	−0.414036	−	0.414036i	−0.883142	+	0.469106i	$0.844576\pi$
$678$	−7.05787e8	−	7.05629e7i	−2.26456	−	0.226406i
$679$	3.85376e8			1.23105
$680$	−2.38362e8	−	1.09007e8i	−0.758071	−	0.346678i
$681$	−1.24003e8	−	1.23976e7i	−0.392638	−	0.0392550i
$682$		−	1.39181e8i		−	0.438759i
$683$	−1.23001e8	−	1.23001e8i	−0.386051	−	0.386051i	0.487225	−	0.873276i	$-0.338009\pi$
$683$	−1.23001e8	−	1.23001e8i	−0.386051	−	0.386051i	−0.873276	+	0.487225i	$0.838009\pi$
$684$	−9.32171e8	−	1.88274e8i	−2.91291	−	0.588333i
$685$	−3.74911e7	+	3.74911e7i	−0.116642	+	0.116642i
$686$	4.41807e8	−	4.41807e8i	1.36855	−	1.36855i
$687$	1.51808e8	−	1.24212e8i	0.468192	−	0.383083i
$688$			2.11292e9i			6.48810i
$689$	−6.19466e8			−1.89391
$690$	−8.52697e7	−	1.04214e8i	−0.259566	−	0.317233i
$691$	4.33525e8	+	4.33525e8i	1.31395	+	1.31395i	0.918475	+	0.395478i	$0.129421\pi$
$691$	4.33525e8	+	4.33525e8i	1.31395	+	1.31395i	0.395478	+	0.918475i	$0.370579\pi$
$692$	9.94900e7	+	9.94900e7i	0.300235	+	0.300235i
$693$	−2.90171e7	+	1.43667e8i	−0.0871874	+	0.431676i
$694$	2.37338e8	−	2.37338e8i	0.710050	−	0.710050i
$695$	−3.74189e7			−0.111464
$696$	−4.49816e7	+	4.49916e8i	−0.133416	+	1.33446i
$697$	5.93398e7	−	1.29757e8i	0.175246	−	0.383206i
$698$			1.01231e8i			0.297677i
$699$	5.91478e6	−	5.91610e7i	0.0173184	−	0.173222i
$700$	−5.85280e8	+	5.85280e8i	−1.70636	+	1.70636i
$701$		−	3.76172e8i		−	1.09202i	−0.837777	−	0.546012i	$-0.816145\pi$
$701$		−	3.76172e8i		−	1.09202i	0.837777	−	0.546012i	$-0.183855\pi$
$702$	7.86294e8	−	4.15830e8i	2.27286	−	1.20200i
$703$	4.50747e8	+	4.50747e8i	1.29738	+	1.29738i
$704$	−3.09665e8	+	3.09665e8i	−0.887511	+	0.887511i
$705$	4.76536e7	+	4.76430e6i	0.135997	+	0.0135966i
$706$		−	5.14718e8i		−	1.46270i
$707$	−4.57282e7	+	4.57282e7i	−0.129398	+	0.129398i
$708$	−3.88821e8	−	4.75205e8i	−1.09560	−	1.33900i
$709$	−1.67316e8	+	1.67316e8i	−0.469459	+	0.469459i	−0.901739	−	0.432280i	$-0.857709\pi$
$709$	−1.67316e8	+	1.67316e8i	−0.469459	+	0.469459i	0.432280	+	0.901739i	$0.357709\pi$
$710$			1.55307e8i			0.433925i
$711$	−1.00925e8	+	6.70068e7i	−0.280794	+	0.186428i
$712$			5.64231e8i			1.56321i
$713$			1.50188e8i			0.414350i
$714$	−1.73659e8	−	6.61228e8i	−0.477093	−	1.81659i
$715$	5.87749e7			0.160795
$716$	2.58405e8			0.703983
$717$	4.60675e7	−	3.76933e7i	0.124979	−	0.102260i
$718$	2.40863e8			0.650723
$719$	2.89739e8	+	2.89739e8i	0.779509	+	0.779509i	0.979747	−	0.200238i	$-0.0641717\pi$
$719$	2.89739e8	+	2.89739e8i	0.779509	+	0.779509i	−0.200238	+	0.979747i	$0.564172\pi$
$720$	−2.75602e8	+	1.82980e8i	−0.738389	+	0.490238i
$721$	−3.20913e8	−	3.20913e8i	−0.856214	−	0.856214i
$722$	1.92809e8			0.512291
$723$	−1.07799e8	−	1.07775e7i	−0.285233	−	0.0285169i
$724$	−1.19117e8	−	1.19117e8i	−0.313875	−	0.313875i
$725$	1.07403e8	−	1.07403e8i	0.281840	−	0.281840i
$726$	−4.51904e8	+	3.69756e8i	−1.18096	+	0.966286i
$727$	−3.42620e8			−0.891680			−0.445840	−	0.895113i	$-0.647095\pi$
$727$	−3.42620e8			−0.891680			−0.445840	+	0.895113i	$0.647095\pi$
$728$	−1.13168e9	−	1.13168e9i	−2.93311	−	2.93311i
$729$	2.18075e8	−	3.20215e8i	0.562891	−	0.826531i
$730$	−1.96299e8			−0.504603
$731$	2.66150e8	+	7.14714e8i	0.681356	+	1.82970i
$732$	1.28570e8	−	1.28599e9i	0.327799	−	3.27872i
$733$		−	2.50002e8i		−	0.634793i	−0.948293	−	0.317397i	$-0.897191\pi$
$733$		−	2.50002e8i		−	0.634793i	0.948293	−	0.317397i	$-0.102809\pi$
$734$	2.58659e8	+	2.58659e8i	0.654092	+	0.654092i
$735$	−3.21078e6	−	321007.i	−0.00808629	−	0.000808448i
$736$	7.29847e8	−	7.29847e8i	1.83062	−	1.83062i
$737$	−3.21717e7	+	3.21717e7i	−0.0803658	+	0.0803658i
$738$	−1.78697e8	−	2.69151e8i	−0.444579	−	0.669618i
$739$		−	4.69365e8i		−	1.16299i	−0.813549	−	0.581497i	$-0.802467\pi$
$739$		−	4.69365e8i		−	1.16299i	0.813549	−	0.581497i	$-0.197533\pi$
$740$	4.64538e8			1.14637
$741$	−4.78064e8	+	3.91161e8i	−1.17498	+	0.961392i
$742$	7.62311e8	+	7.62311e8i	1.86604	+	1.86604i
$743$	−2.74325e7	−	2.74325e7i	−0.0668805	−	0.0668805i	0.672875	−	0.739756i	$-0.265059\pi$
$743$	−2.74325e7	−	2.74325e7i	−0.0668805	−	0.0668805i	−0.739756	+	0.672875i	$0.765059\pi$
$744$	6.58664e8	+	6.58517e7i	1.59936	+	0.159900i
$745$	7.00111e7	−	7.00111e7i	0.169316	−	0.169316i
$746$	−1.19788e9			−2.88534
$747$	1.31398e8	−	6.50567e8i	0.315229	−	1.56074i
$748$	−2.05397e8	+	4.49137e8i	−0.490783	+	1.07318i
$749$		−	3.87188e8i		−	0.921461i
$750$	4.11940e8	+	4.11848e7i	0.976451	+	0.0976232i
$751$	2.61229e8	−	2.61229e8i	0.616739	−	0.616739i	−0.327954	−	0.944694i	$-0.606359\pi$
$751$	2.61229e8	−	2.61229e8i	0.616739	−	0.616739i	0.944694	+	0.327954i	$0.106359\pi$
$752$			7.24154e8i			1.70285i
$753$	−5.41115e8	+	4.42750e8i	−1.26737	+	1.03699i
$754$	3.34417e8	+	3.34417e8i	0.780144	+	0.780144i
$755$	−8.88887e7	+	8.88887e7i	−0.206541	+	0.206541i
$756$	−1.07275e9	−	3.30593e8i	−2.48274	−	0.765118i
$757$			5.35646e8i			1.23478i	0.786656	+	0.617391i	$0.211810\pi$
$757$			5.35646e8i			1.23478i	−0.786656	+	0.617391i	$0.788190\pi$
$758$	5.01206e8	−	5.01206e8i	1.15082	−	1.15082i
$759$	−1.21942e8	+	9.97754e7i	−0.278887	+	0.228191i
$760$	2.91428e8	−	2.91428e8i	0.663881	−	0.663881i
$761$		−	2.20129e8i		−	0.499485i	−0.968312	−	0.249743i	$-0.919654\pi$
$761$		−	2.20129e8i		−	0.499485i	0.968312	−	0.249743i	$-0.0803460\pi$
$762$	1.90677e8	−	1.56015e8i	0.430956	−	0.352616i
$763$		−	4.36243e8i		−	0.982099i
$764$			1.90983e9i			4.28267i
$765$	−7.01762e7	+	9.66105e7i	−0.156749	+	0.215794i
$766$	2.39196e8			0.532190
$767$	−3.98814e8			−0.883861
$768$	−3.65719e8	−	4.46970e8i	−0.807355	−	0.986722i
$769$	−5.25360e8			−1.15526			−0.577628	−	0.816300i	$-0.696021\pi$
$769$	−5.25360e8			−1.15526			−0.577628	+	0.816300i	$0.696021\pi$
$770$	−7.23280e7	−	7.23280e7i	−0.158429	−	0.158429i
$771$	4.32778e8	+	5.28926e8i	0.944282	+	1.15407i
$772$	3.49794e8	+	3.49794e8i	0.760257	+	0.760257i
$773$	5.37859e8			1.16447			0.582237	−	0.813019i	$-0.302177\pi$
$773$	5.37859e8			1.16447			0.582237	+	0.813019i	$0.302177\pi$
$774$	1.69270e9	+	3.41881e8i	3.65053	+	0.737313i
$775$	−1.57235e8	−	1.57235e8i	−0.337787	−	0.337787i
$776$	1.29111e9	−	1.29111e9i	2.76298	−	2.76298i
$777$	4.76483e8	+	5.82341e8i	1.01574	+	1.24141i
$778$	−1.01306e9			−2.15128
$779$	1.58644e8	+	1.58644e8i	0.335593	+	0.335593i
$780$	−4.47810e7	+	4.47910e8i	−0.0943647	+	0.943859i
$781$	1.81727e8			0.381474
$782$	3.05645e8	−	6.68347e8i	0.639142	−	1.39760i
$783$	1.96856e8	+	6.06661e7i	0.410076	+	0.126375i
$784$		−	4.87917e7i		−	0.101251i
$785$	−3.36859e7	−	3.36859e7i	−0.0696369	−	0.0696369i
$786$	−1.19011e8	+	1.19038e9i	−0.245087	+	2.45142i
$787$	−1.23201e8	+	1.23201e8i	−0.252748	+	0.252748i	−0.822097	−	0.569348i	$-0.807196\pi$
$787$	−1.23201e8	+	1.23201e8i	−0.252748	+	0.252748i	0.569348	+	0.822097i	$0.307196\pi$
$788$	−2.44996e8	+	2.44996e8i	−0.500702	+	0.500702i
$789$	1.86982e8	+	2.28523e8i	0.380687	+	0.465263i
$790$		−	8.45436e7i		−	0.171474i
$791$	5.81427e8			1.17480
$792$	3.84108e8	+	5.78537e8i	0.773175	+	1.16454i
$793$	−5.93582e8	−	5.93582e8i	−1.19031	−	1.19031i
$794$	−5.31871e8	−	5.31871e8i	−1.06254	−	1.06254i
$795$	1.87322e7	−	1.87364e8i	0.0372810	−	0.372893i
$796$	5.76146e8	−	5.76146e8i	1.14234	−	1.14234i
$797$	3.09298e8			0.610946			0.305473	−	0.952201i	$-0.401185\pi$
$797$	3.09298e8			0.610946			0.305473	+	0.952201i	$0.401185\pi$
$798$	1.06966e9	+	1.06942e8i	2.10493	+	0.210446i
$799$	9.12166e7	+	2.44951e8i	0.178827	+	0.480219i
$800$			1.52818e9i			2.98473i
$801$	2.51961e8	+	5.08897e7i	0.490271	+	0.0990221i
$802$	4.83135e8	−	4.83135e8i	0.936582	−	0.936582i
$803$			2.29693e8i			0.443609i
$804$	−2.20661e8	−	2.69685e8i	−0.424578	−	0.518906i
$805$	7.80482e7	+	7.80482e7i	0.149615	+	0.149615i
$806$	4.89577e8	−	4.89577e8i	0.935010	−	0.935010i
$807$	9.02044e7	−	9.02245e8i	0.171635	−	1.71674i
$808$			3.06403e8i			0.580843i
$809$	2.52769e7	−	2.52769e7i	0.0477396	−	0.0477396i	−0.682834	−	0.730574i	$-0.739253\pi$
$809$	2.52769e7	−	2.52769e7i	0.0477396	−	0.0477396i	0.730574	+	0.682834i	$0.239253\pi$
$810$	1.01995e8	+	2.50397e8i	0.191922	+	0.471167i
$811$	−3.58265e8	+	3.58265e8i	−0.671648	+	0.671648i	−0.958096	−	0.286448i	$-0.907525\pi$
$811$	−3.58265e8	+	3.58265e8i	−0.671648	+	0.671648i	0.286448	+	0.958096i	$0.407525\pi$
$812$		−	5.96852e8i		−	1.11480i
$813$	1.86019e8	+	2.27347e8i	0.346168	+	0.423075i
$814$		−	7.49578e8i		−	1.38977i
$815$		−	1.72403e8i		−	0.318473i
$816$	−1.55914e9	−	9.10531e8i	−2.86956	−	1.67581i
$817$	−1.19923e9			−2.19906
$818$	−5.55321e8			−1.01457
$819$	−6.07428e8	+	4.03290e8i	−1.10572	+	0.734117i
$820$	1.63498e8			0.296532
$821$	3.79844e8	+	3.79844e8i	0.686398	+	0.686398i	0.961434	−	0.275036i	$-0.0886898\pi$
$821$	3.79844e8	+	3.79844e8i	0.686398	+	0.686398i	−0.275036	+	0.961434i	$0.588690\pi$
$822$	−5.07115e8	+	4.14931e8i	−0.913042	+	0.747068i
$823$	1.51913e8	+	1.51913e8i	0.272519	+	0.272519i	0.830113	−	0.557595i	$-0.188276\pi$
$823$	1.51913e8	+	1.51913e8i	0.272519	+	0.272519i	−0.557595	+	0.830113i	$0.688276\pi$
$824$	−2.15029e9			−3.84339
$825$	2.32068e7	−	2.32120e8i	0.0413289	−	0.413382i
$826$	4.90778e8	+	4.90778e8i	0.870853	+	0.870853i
$827$	−5.43885e8	+	5.43885e8i	−0.961592	+	0.961592i	−0.999289	−	0.0376971i	$-0.987998\pi$
$827$	−5.43885e8	+	5.43885e8i	−0.961592	+	0.961592i	0.0376971	+	0.999289i	$0.487998\pi$
$828$	−6.67457e8	−	1.00531e9i	−1.17580	−	1.77097i
$829$	5.87071e8			1.03045			0.515225	−	0.857055i	$-0.327708\pi$
$829$	5.87071e8			1.03045			0.515225	+	0.857055i	$0.327708\pi$
$830$	3.27522e8	+	3.27522e8i	0.572805	+	0.572805i
$831$	2.25697e8	+	2.25647e7i	0.393299	+	0.0393211i
$832$	−2.17853e9			−3.78263
$833$	−6.14595e6	−	1.65042e7i	−0.0106330	−	0.0285536i
$834$	−4.60134e8	−	4.60032e7i	−0.793207	−	0.0793030i
$835$			2.31614e8i			0.397837i
$836$	−5.49127e8	−	5.49127e8i	−0.939840	−	0.939840i
$837$	8.88134e7	−	2.88192e8i	0.151462	−	0.491479i
$838$	−6.31961e6	+	6.31961e6i	−0.0107389	+	0.0107389i
$839$	6.70944e8	−	6.70944e8i	1.13606	−	1.13606i	0.146908	−	0.989150i	$-0.453068\pi$
$839$	6.70944e8	−	6.70944e8i	1.13606	−	1.13606i	0.989150	−	0.146908i	$-0.0469321\pi$
$840$	3.76509e8	−	3.08067e8i	0.635240	−	0.519765i
$841$		−	4.85297e8i		−	0.815867i
$842$	−5.79267e7			−0.0970381
$843$	−2.28767e8	−	2.79592e8i	−0.381866	−	0.466704i
$844$	−1.33284e9	−	1.33284e9i	−2.21692	−	2.21692i
$845$	9.29545e7	+	9.29545e7i	0.154064	+	0.154064i
$846$	5.80133e8	+	1.17172e8i	0.958112	+	0.193514i
$847$	3.38442e8	−	3.38442e8i	0.556972	−	0.556972i
$848$	2.84722e9			4.66910
$849$	2.54682e7	−	2.54739e8i	0.0416174	−	0.416267i
$850$	3.79719e8	+	1.01969e9i	0.618309	+	1.66040i
$851$			8.08860e8i			1.31246i
$852$	−1.38459e8	+	1.38490e9i	−0.223873	+	2.23923i
$853$	−5.50732e8	+	5.50732e8i	−0.887347	+	0.887347i	−0.994268	−	0.106921i	$-0.965901\pi$
$853$	−5.50732e8	+	5.50732e8i	−0.887347	+	0.887347i	0.106921	+	0.994268i	$0.465901\pi$
$854$			1.46092e9i			2.34559i
$855$	−1.03854e8	−	1.56424e8i	−0.166160	−	0.250267i
$856$	−1.29718e9	−	1.29718e9i	−2.06814	−	2.06814i
$857$	4.85205e8	−	4.85205e8i	0.770873	−	0.770873i	−0.207386	−	0.978259i	$-0.566496\pi$
$857$	4.85205e8	−	4.85205e8i	0.770873	−	0.770873i	0.978259	+	0.207386i	$0.0664957\pi$
$858$	7.22746e8	+	7.22585e7i	1.14426	+	0.114400i
$859$		−	2.37862e7i		−	0.0375271i	−0.999824	−	0.0187636i	$-0.994027\pi$
$859$		−	2.37862e7i		−	0.0375271i	0.999824	−	0.0187636i	$-0.00597298\pi$
$860$	−6.17961e8	+	6.17961e8i	−0.971552	+	0.971552i
$861$	1.67702e8	+	2.04960e8i	0.262742	+	0.321115i
$862$	1.12283e9	−	1.12283e9i	1.75305	−	1.75305i
$863$		−	2.63011e8i		−	0.409206i	−0.978845	−	0.204603i	$-0.934410\pi$
$863$		−	2.63011e8i		−	0.409206i	0.978845	−	0.204603i	$-0.0655903\pi$
$864$	−1.83208e9	+	9.68890e8i	−2.84055	+	1.50222i
$865$			2.77793e7i			0.0429213i
$866$			1.14642e7i			0.0176518i
$867$	−6.42088e8	−	1.11601e8i	−0.985229	−	0.171242i
$868$	−8.73774e8			−1.33610
$869$	−9.89258e7			−0.150747
$870$	−1.11261e8	+	9.10355e7i	−0.168960	+	0.138246i
$871$	−2.26332e8			−0.342525
$872$	−1.46153e9	−	1.46153e9i	−2.20423	−	2.20423i
$873$	−4.60105e8	−	6.93003e8i	−0.691535	−	1.04158i
$874$	8.17139e8	+	8.17139e8i	1.22394	+	1.22394i
$875$	−3.39356e8			−0.506561
$876$	−1.75043e9	−	1.75004e8i	−2.60396	−	0.260337i
$877$	1.82339e8	+	1.82339e8i	0.270321	+	0.270321i	0.829230	−	0.558908i	$-0.188780\pi$
$877$	1.82339e8	+	1.82339e8i	0.270321	+	0.270321i	−0.558908	+	0.829230i	$0.688780\pi$
$878$	4.89192e8	−	4.89192e8i	0.722763	−	0.722763i
$879$	3.03131e8	−	2.48027e8i	0.446337	−	0.365202i
$880$	−2.70144e8			−0.396412
$881$	7.42980e7	+	7.42980e7i	0.108655	+	0.108655i	0.759344	−	0.650689i	$-0.225520\pi$
$881$	7.42980e7	+	7.42980e7i	0.108655	+	0.108655i	−0.650689	+	0.759344i	$0.725520\pi$
$882$	−3.90879e7	−	7.89474e6i	−0.0569688	−	0.0115062i
$883$	1.01452e9			1.47360			0.736798	−	0.676113i	$-0.236337\pi$
$883$	1.01452e9			1.47360			0.736798	+	0.676113i	$0.236337\pi$
$884$	−2.30237e9	+	8.57371e8i	−3.33287	+	1.24111i
$885$	1.20598e7	−	1.20625e8i	0.0173985	−	0.174024i
$886$			1.06810e8i			0.153572i
$887$	4.92232e7	+	4.92232e7i	0.0705341	+	0.0705341i	0.741494	−	0.670960i	$-0.234118\pi$
$887$	4.92232e7	+	4.92232e7i	0.0705341	+	0.0705341i	−0.670960	+	0.741494i	$0.734118\pi$
$888$	3.54733e9	+	3.54654e8i	5.06598	+	0.506484i
$889$	−1.42802e8	+	1.42802e8i	−0.203250	+	0.203250i
$890$	−1.26848e8	+	1.26848e8i	−0.179934	+	0.179934i
$891$	2.92994e8	−	1.19346e8i	0.414214	−	0.168723i
$892$			1.42253e7i			0.0200432i
$893$	−4.11008e8			−0.577160
$894$	9.46988e8	−	7.74844e8i	1.32535	−	1.08443i
$895$	3.60756e7	+	3.60756e7i	0.0503204	+	0.0503204i
$896$	1.07156e9	+	1.07156e9i	1.48968	+	1.48968i
$897$	−7.79906e8	−	7.79732e7i	−1.08060	−	0.108036i
$898$	−1.40408e9	+	1.40408e9i	−1.93893	+	1.93893i
$899$	1.60344e8			0.220685
$900$	1.75125e9	+	3.53708e8i	2.40227	+	0.485196i
$901$	9.63097e8	−	3.58644e8i	1.31673	−	0.490331i
$902$		−	2.63821e8i		−	0.359492i
$903$	−1.40852e9	−	1.40821e8i	−1.91294	−	0.191251i
$904$	1.94793e9	−	1.94793e9i	2.63674	−	2.63674i
$905$		−	3.32594e7i		−	0.0448714i
$906$	−1.20233e9	+	9.83771e8i	−1.61674	+	1.32285i
$907$	1.73514e8	+	1.73514e8i	0.232547	+	0.232547i	0.813755	−	0.581208i	$-0.197420\pi$
$907$	1.73514e8	+	1.73514e8i	0.232547	+	0.232547i	−0.581208	+	0.813755i	$0.697420\pi$
$908$	5.51120e8	−	5.51120e8i	0.736188	−	0.736188i
$909$	1.36826e8	+	2.76354e7i	0.182171	+	0.0367937i
$910$		−	5.08837e8i		−	0.675234i
$911$	−6.53134e8	+	6.53134e8i	−0.863867	+	0.863867i	−0.991785	−	0.127918i	$-0.959171\pi$
$911$	−6.53134e8	+	6.53134e8i	−0.863867	+	0.863867i	0.127918	+	0.991785i	$0.459171\pi$
$912$	2.19730e9	−	1.79787e9i	2.89671	−	2.37014i
$913$	3.83239e8	−	3.83239e8i	0.503567	−	0.503567i
$914$			5.56481e8i			0.728805i
$915$	1.97485e8	−	1.61586e8i	0.257792	−	0.210931i
$916$			1.22674e9i			1.59613i
$917$		−	9.80634e8i		−	1.27174i
$918$	−9.81720e8	+	1.10173e9i	−1.26899	+	1.42412i
$919$	−2.43683e8			−0.313963			−0.156982	−	0.987602i	$-0.550176\pi$
$919$	−2.43683e8			−0.313963			−0.156982	+	0.987602i	$0.550176\pi$
$920$	5.22963e8			0.671596
$921$	1.29864e7	+	1.58716e7i	0.0166231	+	0.0203162i
$922$	7.30984e8			0.932642
$923$	6.39235e8	+	6.39235e8i	0.812935	+	0.812935i
$924$	−5.80480e8	−	7.09443e8i	−0.735820	−	0.899294i
$925$	−8.46811e8	−	8.46811e8i	−1.06994	−	1.06994i
$926$	1.28851e9			1.62276
$927$	−1.93941e8	+	9.60226e8i	−0.243461	+	1.20541i
$928$	−7.79198e8	−	7.79198e8i	−0.974998	−	0.974998i
$929$	1.94683e8	−	1.94683e8i	0.242818	−	0.242818i	−0.575197	−	0.818015i	$-0.695075\pi$
$929$	1.94683e8	−	1.94683e8i	0.242818	−	0.242818i	0.818015	+	0.575197i	$0.195075\pi$
$930$	1.33273e8	+	1.62882e8i	0.165689	+	0.202500i
$931$	2.76927e7			0.0343176
$932$	2.62935e8	+	2.62935e8i	0.324789	+	0.324789i
$933$	1.43415e8	−	1.43448e9i	0.176584	−	1.76623i
$934$	−1.56965e9			−1.92647
$935$	−9.13786e7	+	3.40282e7i	−0.111792	+	0.0416297i
$936$	−6.83918e8	+	3.38617e9i	−0.834020	+	4.12934i
$937$			9.07969e8i			1.10370i	0.833943	+	0.551851i	$0.186078\pi$
$937$			9.07969e8i			1.10370i	−0.833943	+	0.551851i	$0.813922\pi$
$938$	2.78523e8	+	2.78523e8i	0.337483	+	0.337483i
$939$	5.72785e7	−	5.72913e8i	0.0691822	−	0.691977i
$940$	−2.11792e8	+	2.11792e8i	−0.254992	+	0.254992i
$941$	−6.16802e8	+	6.16802e8i	−0.740248	+	0.740248i	−0.972626	−	0.232378i	$-0.925349\pi$
$941$	−6.16802e8	+	6.16802e8i	−0.740248	+	0.740248i	0.232378	+	0.972626i	$0.425349\pi$
$942$	−3.72817e8	−	4.55645e8i	−0.446008	−	0.545097i
$943$			2.84685e8i			0.339493i
$944$	1.83305e9			2.17900
$945$	−1.03611e8	−	1.95918e8i	−0.122775	−	0.232156i
$946$	9.97141e8	+	9.97141e8i	1.17783	+	1.17783i
$947$	−8.11432e7	−	8.11432e7i	−0.0955437	−	0.0955437i	0.657719	−	0.753263i	$-0.271521\pi$
$947$	−8.11432e7	−	8.11432e7i	−0.0955437	−	0.0955437i	−0.753263	+	0.657719i	$0.771521\pi$
$948$	7.53722e7	−	7.53890e8i	0.0884679	−	0.884878i
$949$	−8.07959e8	+	8.07959e8i	−0.945346	+	0.945346i
$950$	−1.71096e9			−1.99558
$951$	−1.31620e9	−	1.31591e8i	−1.53032	−	0.152998i
$952$	2.41464e9	+	1.10425e9i	2.79860	+	1.27984i
$953$			3.45868e8i			0.399605i	0.979836	+	0.199803i	$0.0640301\pi$
$953$			3.45868e8i			0.399605i	−0.979836	+	0.199803i	$0.935970\pi$
$954$	4.60694e8	−	2.28096e9i	0.530601	−	2.62707i
$955$	−2.66628e8	+	2.66628e8i	−0.306123	+	0.306123i
$956$			3.72267e8i			0.426070i
$957$	1.06522e8	+	1.30188e8i	0.121536	+	0.148537i
$958$	1.08948e9	+	1.08948e9i	1.23915	+	1.23915i
$959$	3.79790e8	−	3.79790e8i	0.430614	−	0.430614i
$960$	6.58772e7	−	6.58920e8i	0.0744597	−	0.744764i
$961$			6.52765e8i			0.735507i
$962$	2.63669e9	−	2.63669e9i	2.96165	−	2.96165i
$963$	−6.96262e8	+	4.62269e8i	−0.779640	+	0.517626i
$964$	4.79102e8	−	4.79102e8i	0.534807	−	0.534807i
$965$			9.76684e7i			0.108686i
$966$	8.63794e8	+	1.05570e9i	0.958250	+	1.17114i
$967$			4.48886e8i			0.496428i	0.968705	+	0.248214i	$0.0798437\pi$
$967$			4.48886e8i			0.496428i	−0.968705	+	0.248214i	$0.920156\pi$
$968$		−	2.26773e9i		−	2.50015i
$969$	5.16791e8	−	8.84924e8i	0.567993	−	0.972601i
$970$	5.80522e8			0.636068
$971$	−1.51320e9			−1.65287			−0.826437	−	0.563030i	$-0.809636\pi$
$971$	−1.51320e9			−1.65287			−0.826437	+	0.563030i	$0.809636\pi$
$972$	6.86275e8	+	2.32377e9i	0.747308	+	2.53043i
$973$	3.79058e8			0.411498
$974$	−2.07980e9	−	2.07980e9i	−2.25085	−	2.25085i
$975$	8.98130e8	−	7.34867e8i	0.969004	−	0.792857i
$976$	2.72825e9	+	2.72825e9i	2.93450	+	2.93450i
$977$	−5.18852e8			−0.556365			−0.278183	−	0.960528i	$-0.589732\pi$
$977$	−5.18852e8			−0.556365			−0.278183	+	0.960528i	$0.589732\pi$
$978$	2.11955e8	−	2.12002e9i	0.226582	−	2.26633i
$979$	1.48427e8	+	1.48427e8i	0.158184	+	0.158184i
$980$	1.42700e7	−	1.42700e7i	0.0151616	−	0.0151616i
$981$	−7.84475e8	+	5.20836e8i	−0.830945	+	0.551689i
$982$	−6.85354e8			−0.723736
$983$	9.17740e8	+	9.17740e8i	0.966183	+	0.966183i	0.999447	−	0.0332638i	$-0.0105901\pi$
$983$	9.17740e8	+	9.17740e8i	0.966183	+	0.966183i	−0.0332638	+	0.999447i	$0.510590\pi$
$984$	1.24852e9	+	1.24824e8i	1.31041	+	0.131012i
$985$	−6.84070e7			−0.0715800
$986$	−7.13539e8	−	3.26313e8i	−0.744367	−	0.340411i
$987$	−4.82738e8	−	4.82630e7i	−0.502065	−	0.0501953i
$988$		−	3.86318e9i		−	4.00566i
$989$	−1.07600e9	−	1.07600e9i	−1.11231	−	1.11231i
$990$	−4.37107e7	+	2.16417e8i	−0.0450487	+	0.223042i
$991$	−5.30369e8	+	5.30369e8i	−0.544951	+	0.544951i	−0.924976	−	0.380025i	$-0.875915\pi$
$991$	−5.30369e8	+	5.30369e8i	−0.544951	+	0.544951i	0.380025	+	0.924976i	$0.375915\pi$
$992$	−1.14072e9	+	1.14072e9i	−1.16854	+	1.16854i
$993$	−1.32083e9	+	1.08073e9i	−1.34896	+	1.10375i
$994$		−	1.57328e9i		−	1.60194i
$995$	1.60870e8			0.163307
$996$	2.62858e9	+	3.21257e9i	2.66038	+	3.25143i
$997$	8.14672e8	+	8.14672e8i	0.822048	+	0.822048i	0.986402	−	0.164353i	$-0.0525537\pi$
$997$	8.14672e8	+	8.14672e8i	0.822048	+	0.822048i	−0.164353	+	0.986402i	$0.552554\pi$
$998$	2.64634e8	+	2.64634e8i	0.266228	+	0.266228i
$999$	4.78318e8	−	1.55210e9i	0.479756	−	1.55677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.7.f.a.38.1	✓	68
3.2	odd	2	inner	51.7.f.a.38.34	yes	68
17.13	even	4	inner	51.7.f.a.47.34	yes	68
51.47	odd	4	inner	51.7.f.a.47.1	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.7.f.a.38.1	✓	68	1.1	even	1	trivial
51.7.f.a.38.34	yes	68	3.2	odd	2	inner
51.7.f.a.47.1	yes	68	51.47	odd	4	inner
51.7.f.a.47.34	yes	68	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-15.2598 q^{2} +(-17.0979 - 20.8965i) q^{3} +168.862 q^{4} +(23.5746 + 23.5746i) q^{5} +(260.911 + 318.876i) q^{6} +(-238.814 - 238.814i) q^{7} -1600.18 q^{8} +(-144.325 + 714.571i) q^{9} +(-359.744 - 359.744i) q^{10} +(-420.942 + 420.942i) q^{11} +(-2887.19 - 3528.62i) q^{12} -2961.38 q^{13} +(3644.26 + 3644.26i) q^{14} +(89.5501 - 895.702i) q^{15} +13611.3 q^{16} +(4604.13 - 1714.52i) q^{17} +(2202.37 - 10904.2i) q^{18} +7725.35i q^{19} +(3980.86 + 3980.86i) q^{20} +(-907.156 + 9073.59i) q^{21} +(6423.51 - 6423.51i) q^{22} +(-6931.52 + 6931.52i) q^{23} +(27359.7 + 33438.1i) q^{24} -14513.5i q^{25} +45190.2 q^{26} +(17399.7 - 9201.77i) q^{27} +(-40326.7 - 40326.7i) q^{28} +(7400.22 + 7400.22i) q^{29} +(-1366.52 + 13668.3i) q^{30} +(10833.7 - 10833.7i) q^{31} -105294. q^{32} +(15993.4 + 1598.99i) q^{33} +(-70258.2 + 26163.2i) q^{34} -11259.9i q^{35} +(-24371.0 + 120664. i) q^{36} +(58346.5 - 58346.5i) q^{37} -117887. i q^{38} +(50633.4 + 61882.5i) q^{39} +(-37723.6 - 37723.6i) q^{40} +(20535.6 - 20535.6i) q^{41} +(13843.0 - 138461. i) q^{42} +155233. i q^{43} +(-71081.2 + 71081.2i) q^{44} +(-20248.1 + 13443.3i) q^{45} +(105774. - 105774. i) q^{46} +53202.6i q^{47} +(-232724. - 284427. i) q^{48} -3584.66i q^{49} +221473. i q^{50} +(-114548. - 66895.4i) q^{51} -500066. q^{52} +209181. q^{53} +(-265516. + 140417. i) q^{54} -19847.1 q^{55} +(382145. + 382145. i) q^{56} +(161432. - 132087. i) q^{57} +(-112926. - 112926. i) q^{58} +134671. q^{59} +(15121.6 - 151250. i) q^{60} +(200441. + 200441. i) q^{61} +(-165320. + 165320. i) q^{62} +(205116. - 136183. i) q^{63} +735646. q^{64} +(-69813.5 - 69813.5i) q^{65} +(-244057. - 24400.2i) q^{66} +76427.8 q^{67} +(777463. - 289517. i) q^{68} +(263359. + 26330.0i) q^{69} +171824. i q^{70} +(-215857. - 215857. i) q^{71} +(230945. - 1.14344e6i) q^{72} +(272831. - 272831. i) q^{73} +(-890357. + 890357. i) q^{74} +(-303280. + 248150. i) q^{75} +1.30452e6i q^{76} +201054. q^{77} +(-772657. - 944316. i) q^{78} +(117505. + 117505. i) q^{79} +(320880. + 320880. i) q^{80} +(-489782. - 206261. i) q^{81} +(-313369. + 313369. i) q^{82} -910431. q^{83} +(-153184. + 1.53219e6i) q^{84} +(148960. + 68121.5i) q^{85} -2.36883e6i q^{86} +(28110.4 - 281166. i) q^{87} +(673583. - 673583. i) q^{88} -352605. i q^{89} +(308983. - 205143. i) q^{90} +(707220. + 707220. i) q^{91} +(-1.17047e6 + 1.17047e6i) q^{92} +(-411619. - 41152.7i) q^{93} -811862. i q^{94} +(-182122. + 182122. i) q^{95} +(1.80030e6 + 2.20027e6i) q^{96} +(-806854. + 806854. i) q^{97} +54701.2i q^{98} +(-240041. - 361545. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) \) 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

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