LMFDB - Embedded newform 45.10.e.a.31.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,10,Mod(16,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.16"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$N$	$=$	$45 = 3^{2} \cdot 5$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	45.e (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$23.1766126274$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	45.31
Dual form			45.10.e.a.16.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.6441 - 32.2925i) q^{2} +(-106.488 + 91.3412i) q^{3} +(-439.206 + 760.727i) q^{4} +(312.500 - 541.266i) q^{5} +(4935.02 + 1735.80i) q^{6} +(-5448.66 - 9437.36i) q^{7} +13662.8 q^{8} +(2996.55 - 19453.6i) q^{9} -23305.1 q^{10} +(-21032.2 - 36428.8i) q^{11} +(-22715.4 - 121126. i) q^{12} +(79458.4 - 137626. i) q^{13} +(-203171. + 351902. i) q^{14} +(16162.3 + 86182.7i) q^{15} +(-29857.9 - 51715.4i) q^{16} -604411. q^{17} +(-684073. + 265928. i) q^{18} -192909. q^{19} +(274504. + 475454. i) q^{20} +(1.44224e6 + 507282. i) q^{21} +(-784252. + 1.35836e6i) q^{22} +(945856. - 1.63827e6i) q^{23} +(-1.45493e6 + 1.24798e6i) q^{24} +(-195312. - 338291. i) q^{25} -5.92572e6 q^{26} +(1.45781e6 + 2.34529e6i) q^{27} +9.57233e6 q^{28} +(-301473. - 522167. i) q^{29} +(2.48173e6 - 2.12872e6i) q^{30} +(1.83104e6 - 3.17145e6i) q^{31} +(2.38433e6 - 4.12979e6i) q^{32} +(5.56713e6 + 1.95814e6i) q^{33} +(1.12687e7 + 1.95180e7i) q^{34} -6.81083e6 q^{35} +(1.34827e7 + 1.08237e7i) q^{36} -3.78885e6 q^{37} +(3.59661e6 + 6.22951e6i) q^{38} +(4.10953e6 + 2.19134e7i) q^{39} +(4.26963e6 - 7.39522e6i) q^{40} +(-7.36472e6 + 1.27561e7i) q^{41} +(-1.05079e7 - 5.60314e7i) q^{42} +(1.00762e7 + 1.74525e7i) q^{43} +3.69498e7 q^{44} +(-9.59313e6 - 7.70117e6i) q^{45} -7.05385e7 q^{46} +(-750391. - 1.29972e6i) q^{47} +(7.90327e6 + 2.77983e6i) q^{48} +(-3.91990e7 + 6.78947e7i) q^{49} +(-7.28286e6 + 1.26143e7i) q^{50} +(6.43628e7 - 5.52077e7i) q^{51} +(6.97971e7 + 1.20892e8i) q^{52} -6.96257e7 q^{53} +(4.85556e7 - 9.08023e7i) q^{54} -2.62902e7 q^{55} +(-7.44441e7 - 1.28941e8i) q^{56} +(2.05425e7 - 1.76205e7i) q^{57} +(-1.12414e7 + 1.94707e7i) q^{58} +(-3.17208e7 + 5.49420e7i) q^{59} +(-7.26600e7 - 2.55568e7i) q^{60} +(5.66733e7 + 9.81611e7i) q^{61} -1.36552e8 q^{62} +(-1.99917e8 + 7.77163e7i) q^{63} -2.08390e8 q^{64} +(-4.96615e7 - 8.60162e7i) q^{65} +(-4.05609e7 - 2.16284e8i) q^{66} +(9.27242e7 - 1.60603e8i) q^{67} +(2.65461e8 - 4.59792e8i) q^{68} +(4.89190e7 + 2.60852e8i) q^{69} +(1.26982e8 + 2.19939e8i) q^{70} +2.00388e8 q^{71} +(4.09414e7 - 2.65791e8i) q^{72} +3.82089e8 q^{73} +(7.06397e7 + 1.22352e8i) q^{74} +(5.16985e7 + 1.81840e7i) q^{75} +(8.47265e7 - 1.46751e8i) q^{76} +(-2.29194e8 + 3.96976e8i) q^{77} +(6.31021e8 - 5.41263e8i) q^{78} +(5.61469e6 + 9.72492e6i) q^{79} -3.73224e7 q^{80} +(-3.69462e8 - 1.16587e8i) q^{81} +5.49234e8 q^{82} +(-3.41292e8 - 5.91136e8i) q^{83} +(-1.01934e9 + 8.74349e8i) q^{84} +(-1.88878e8 + 3.27147e8i) q^{85} +(3.75723e8 - 6.50771e8i) q^{86} +(7.97988e7 + 2.80678e7i) q^{87} +(-2.87359e8 - 4.97720e8i) q^{88} -6.19813e8 q^{89} +(-6.98351e7 + 4.53368e8i) q^{90} -1.73177e9 q^{91} +(8.30850e8 + 1.43907e9i) q^{92} +(9.47000e7 + 5.04972e8i) q^{93} +(-2.79808e7 + 4.84641e7i) q^{94} +(-6.02839e7 + 1.04415e8i) q^{95} +(1.23316e8 + 6.57563e8i) q^{96} +(1.88745e8 + 3.26916e8i) q^{97} +2.92332e9 q^{98} +(-7.71693e8 + 2.99990e8i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$34 q - 16 q^{2} - 285 q^{3} - 3840 q^{4} + 10625 q^{5} + 1635 q^{6} + 9946 q^{7} + 38772 q^{8} + 7959 q^{9} - 20000 q^{10} - 32881 q^{11} + 595719 q^{12} + 100272 q^{13} - 333129 q^{14} - 157500 q^{15}+ \cdots - 3426367056 q^{99}+O(q^{100})$ 34 * q - 16 * q^2 - 285 * q^3 - 3840 * q^4 + 10625 * q^5 + 1635 * q^6 + 9946 * q^7 + 38772 * q^8 + 7959 * q^9 - 20000 * q^10 - 32881 * q^11 + 595719 * q^12 + 100272 * q^13 - 333129 * q^14 - 157500 * q^15 - 292740 * q^16 - 103174 * q^17 - 401577 * q^18 - 1954002 * q^19 + 2400000 * q^20 + 846540 * q^21 - 603517 * q^22 - 2528832 * q^23 + 2610864 * q^24 - 6640625 * q^25 - 11356132 * q^26 + 13389570 * q^27 + 1233322 * q^28 + 4997116 * q^29 - 2246250 * q^30 + 7154764 * q^31 - 3848138 * q^32 + 37701447 * q^33 - 1842211 * q^34 + 12432500 * q^35 + 31228485 * q^36 - 29485864 * q^37 - 27825985 * q^38 - 48378006 * q^39 + 12116250 * q^40 - 1432577 * q^41 + 645597 * q^42 + 30233475 * q^43 + 172245706 * q^44 - 4490625 * q^45 - 38739414 * q^46 - 51256132 * q^47 - 273587937 * q^48 - 97033283 * q^49 - 6250000 * q^50 + 191039205 * q^51 + 170396546 * q^52 + 198356324 * q^53 + 65145240 * q^54 - 41101250 * q^55 - 446494149 * q^56 - 442487301 * q^57 + 199102621 * q^58 - 163581061 * q^59 + 110338125 * q^60 + 263506344 * q^61 + 682090404 * q^62 - 131178564 * q^63 - 504872168 * q^64 - 62670000 * q^65 - 888863958 * q^66 + 624947419 * q^67 - 77685671 * q^68 + 1347472386 * q^69 + 208205625 * q^70 + 520490800 * q^71 - 150538482 * q^72 - 1740248610 * q^73 - 479177876 * q^74 + 12890625 * q^75 + 1071379103 * q^76 - 777961272 * q^77 + 2208863298 * q^78 + 847184266 * q^79 - 365925000 * q^80 - 455780961 * q^81 - 2343238688 * q^82 - 663595350 * q^83 - 1445250609 * q^84 - 32241875 * q^85 - 1041586195 * q^86 + 945629148 * q^87 + 1122086037 * q^88 + 729648408 * q^89 - 437745000 * q^90 - 2090033068 * q^91 + 157159431 * q^92 - 150985728 * q^93 + 3068174993 * q^94 - 610625625 * q^95 + 1273538655 * q^96 + 186406391 * q^97 - 1334731394 * q^98 - 3426367056 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$ .

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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

)

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

$2$	−18.6441	−	32.2925i	−0.823961	−	1.42714i	−0.902711	−	0.430248i	$-0.858426\pi$
$2$	−18.6441	−	32.2925i	−0.823961	−	1.42714i	0.0787497	−	0.996894i	$-0.474907\pi$
$3$	−106.488	+	91.3412i	−0.759026	+	0.651060i
$3$	−106.488	+	91.3412i	−0.759026	+	0.651060i
$4$	−439.206	+	760.727i	−0.857824	+	1.48579i
$5$	312.500	−	541.266i	0.223607	−	0.387298i
$5$	312.500	−	541.266i	0.223607	−	0.387298i
$6$	4935.02	+	1735.80i	1.55456	+	0.546790i
$7$	−5448.66	−	9437.36i	−0.857726	−	1.48563i	−0.874093	−	0.485759i	$-0.838543\pi$
$7$	−5448.66	−	9437.36i	−0.857726	−	1.48563i	0.0163665	−	0.999866i	$-0.494790\pi$
$8$	13662.8			1.17933
$9$	2996.55	−	19453.6i	0.152241	−	0.988343i
$10$	−23305.1			−0.736973
$11$	−21032.2	−	36428.8i	−0.433128	−	0.750200i	0.564012	−	0.825766i	$-0.309257\pi$
$11$	−21032.2	−	36428.8i	−0.433128	−	0.750200i	−0.997141	+	0.0755659i	$0.975924\pi$
$12$	−22715.4	−	121126.i	−0.316231	−	1.68625i
$13$	79458.4	−	137626.i	0.771604	−	1.33646i	−0.165079	−	0.986280i	$-0.552788\pi$
$13$	79458.4	−	137626.i	0.771604	−	1.33646i	0.936683	−	0.350177i	$-0.113879\pi$
$14$	−203171.	+	351902.i	−1.41347	+	2.44819i
$15$	16162.3	+	86182.7i	0.0824313	+	0.439551i
$16$	−29857.9	−	51715.4i	−0.113899	−	0.197279i
$17$	−604411.			−1.75514			−0.877571	−	0.479446i	$-0.840837\pi$
$17$	−604411.			−1.75514			−0.877571	+	0.479446i	$0.840837\pi$
$18$	−684073.	+	265928.i	−1.53595	+	0.597087i
$19$	−192909.			−0.339594			−0.169797	−	0.985479i	$-0.554311\pi$
$19$	−192909.			−0.339594			−0.169797	+	0.985479i	$0.554311\pi$
$20$	274504.	+	475454.i	0.383630	+	0.664467i
$21$	1.44224e6	+	507282.i	1.61827	+	0.569197i
$22$	−784252.	+	1.35836e6i	−0.713762	+	1.23627i
$23$	945856.	−	1.63827e6i	0.704774	−	1.22070i	−0.262000	−	0.965068i	$-0.584382\pi$
$23$	945856.	−	1.63827e6i	0.704774	−	1.22070i	0.966773	−	0.255636i	$-0.0822847\pi$
$24$	−1.45493e6	+	1.24798e6i	−0.895142	+	0.767815i
$25$	−195312.	−	338291.i	−0.100000	−	0.173205i
$26$	−5.92572e6			−2.54309
$27$	1.45781e6	+	2.34529e6i	0.527917	+	0.849296i
$28$	9.57233e6			2.94311
$29$	−301473.	−	522167.i	−0.0791513	−	0.137094i	0.823733	−	0.566978i	$-0.191888\pi$
$29$	−301473.	−	522167.i	−0.0791513	−	0.137094i	−0.902884	+	0.429884i	$0.858554\pi$
$30$	2.48173e6	−	2.12872e6i	0.559382	−	0.479814i
$31$	1.83104e6	−	3.17145e6i	0.356098	−	0.616780i	−0.631207	−	0.775614i	$-0.717440\pi$
$31$	1.83104e6	−	3.17145e6i	0.356098	−	0.616780i	0.987305	+	0.158834i	$0.0507735\pi$
$32$	2.38433e6	−	4.12979e6i	0.401969	−	0.696230i
$33$	5.56713e6	+	1.95814e6i	0.817181	+	0.287429i
$34$	1.12687e7	+	1.95180e7i	1.44617	+	2.50484i
$35$	−6.81083e6			−0.767174
$36$	1.34827e7	+	1.08237e7i	1.33788	+	1.07402i
$37$	−3.78885e6			−0.332353			−0.166176	−	0.986096i	$-0.553142\pi$
$37$	−3.78885e6			−0.332353			−0.166176	+	0.986096i	$0.553142\pi$
$38$	3.59661e6	+	6.22951e6i	0.279812	+	0.484649i
$39$	4.10953e6	+	2.19134e7i	0.284447	+	1.51677i
$40$	4.26963e6	−	7.39522e6i	0.263706	−	0.456753i
$41$	−7.36472e6	+	1.27561e7i	−0.407032	+	0.705000i	−0.994556	−	0.104207i	$-0.966770\pi$
$41$	−7.36472e6	+	1.27561e7i	−0.407032	+	0.705000i	0.587524	+	0.809207i	$0.300103\pi$
$42$	−1.05079e7	−	5.60314e7i	−0.521065	−	2.77849i
$43$	1.00762e7	+	1.74525e7i	0.449457	+	0.778482i	0.998351	−	0.0574103i	$-0.0182843\pi$
$43$	1.00762e7	+	1.74525e7i	0.449457	+	0.778482i	−0.548894	+	0.835892i	$0.684951\pi$
$44$	3.69498e7			1.48619
$45$	−9.59313e6	−	7.70117e6i	−0.348742	−	0.279963i
$46$	−7.05385e7			−2.32282
$47$	−750391.	−	1.29972e6i	−0.0224309	−	0.0388515i	0.854592	−	0.519300i	$-0.173807\pi$
$47$	−750391.	−	1.29972e6i	−0.0224309	−	0.0388515i	−0.877023	+	0.480448i	$0.840474\pi$
$48$	7.90327e6	+	2.77983e6i	0.214893	+	0.0755846i
$49$	−3.91990e7	+	6.78947e7i	−0.971388	+	1.68249i
$50$	−7.28286e6	+	1.26143e7i	−0.164792	+	0.285428i
$51$	6.43628e7	−	5.52077e7i	1.33220	−	1.14270i
$52$	6.97971e7	+	1.20892e8i	1.32380	+	2.29289i
$53$	−6.96257e7			−1.21207			−0.606036	−	0.795437i	$-0.707241\pi$
$53$	−6.96257e7			−1.21207			−0.606036	+	0.795437i	$0.707241\pi$
$54$	4.85556e7	−	9.08023e7i	0.777084	−	1.45320i
$55$	−2.62902e7			−0.387402
$56$	−7.44441e7	−	1.28941e8i	−1.01154	−	1.75204i
$57$	2.05425e7	−	1.76205e7i	0.257761	−	0.221096i
$58$	−1.12414e7	+	1.94707e7i	−0.130435	+	0.225920i
$59$	−3.17208e7	+	5.49420e7i	−0.340808	+	0.590297i	−0.984583	−	0.174918i	$-0.944034\pi$
$59$	−3.17208e7	+	5.49420e7i	−0.340808	+	0.590297i	0.643775	+	0.765215i	$0.277367\pi$
$60$	−7.26600e7	−	2.55568e7i	−0.723794	−	0.254581i
$61$	5.66733e7	+	9.81611e7i	0.524076	+	0.907727i	0.999607	+	0.0280278i	$0.00892269\pi$
$61$	5.66733e7	+	9.81611e7i	0.524076	+	0.907727i	−0.475531	+	0.879699i	$0.657744\pi$
$62$	−1.36552e8			−1.17364
$63$	−1.99917e8	+	7.77163e7i	−1.59889	+	0.621555i
$64$	−2.08390e8			−1.55262
$65$	−4.96615e7	−	8.60162e7i	−0.345072	−	0.597682i
$66$	−4.05609e7	−	2.16284e8i	−0.263124	−	1.40306i
$67$	9.27242e7	−	1.60603e8i	0.562155	−	0.973682i	−0.435153	−	0.900357i	$-0.643306\pi$
$67$	9.27242e7	−	1.60603e8i	0.562155	−	0.973682i	0.997308	−	0.0733251i	$-0.0233611\pi$
$68$	2.65461e8	−	4.59792e8i	1.50560	−	2.60778i
$69$	4.89190e7	+	2.60852e8i	0.259810	+	1.38540i
$70$	1.26982e8	+	2.19939e8i	0.632121	+	1.09487i
$71$	2.00388e8			0.935857			0.467928	−	0.883766i	$-0.345000\pi$
$71$	2.00388e8			0.935857			0.467928	+	0.883766i	$0.345000\pi$
$72$	4.09414e7	−	2.65791e8i	0.179542	−	1.16558i
$73$	3.82089e8			1.57475			0.787376	−	0.616473i	$-0.211439\pi$
$73$	3.82089e8			1.57475			0.787376	+	0.616473i	$0.211439\pi$
$74$	7.06397e7	+	1.22352e8i	0.273846	+	0.474315i
$75$	5.16985e7	+	1.81840e7i	0.188670	+	0.0663611i
$76$	8.47265e7	−	1.46751e8i	0.291312	−	0.504567i
$77$	−2.29194e8	+	3.96976e8i	−0.743011	+	1.28693i
$78$	6.31021e8	−	5.41263e8i	1.93027	−	1.65570i
$79$	5.61469e6	+	9.72492e6i	0.0162182	+	0.0280908i	0.874021	−	0.485889i	$-0.161504\pi$
$79$	5.61469e6	+	9.72492e6i	0.0162182	+	0.0280908i	−0.857802	+	0.513980i	$0.828171\pi$
$80$	−3.73224e7			−0.101874
$81$	−3.69462e8	−	1.16587e8i	−0.953646	−	0.300932i
$82$	5.49234e8			1.34151
$83$	−3.41292e8	−	5.91136e8i	−0.789360	−	1.36721i	−0.926359	−	0.376641i	$-0.877079\pi$
$83$	−3.41292e8	−	5.91136e8i	−0.789360	−	1.36721i	0.136999	−	0.990571i	$-0.456254\pi$
$84$	−1.01934e9	+	8.74349e8i	−2.23390	+	1.91614i
$85$	−1.88878e8	+	3.27147e8i	−0.392462	+	0.679764i
$86$	3.75723e8	−	6.50771e8i	0.740669	−	1.28288i
$87$	7.97988e7	+	2.80678e7i	0.149334	+	0.0525257i
$88$	−2.87359e8	−	4.97720e8i	−0.510802	−	0.884734i
$89$	−6.19813e8			−1.04714			−0.523571	−	0.851982i	$-0.675401\pi$
$89$	−6.19813e8			−1.04714			−0.523571	+	0.851982i	$0.675401\pi$
$90$	−6.98351e7	+	4.53368e8i	−0.112197	+	0.728383i
$91$	−1.73177e9			−2.64730
$92$	8.30850e8	+	1.43907e9i	1.20914	+	2.09430i
$93$	9.47000e7	+	5.04972e8i	0.131273	+	0.699994i
$94$	−2.79808e7	+	4.84641e7i	−0.0369644	+	0.0640243i
$95$	−6.02839e7	+	1.04415e8i	−0.0759356	+	0.131524i
$96$	1.23316e8	+	6.57563e8i	0.148183	+	0.790163i
$97$	1.88745e8	+	3.26916e8i	0.216473	+	0.374942i	0.953727	−	0.300674i	$-0.0972114\pi$
$97$	1.88745e8	+	3.26916e8i	0.216473	+	0.374942i	−0.737254	+	0.675615i	$0.763878\pi$
$98$	2.92332e9			3.20154
$99$	−7.71693e8	+	2.99990e8i	−0.807395	+	0.313869i
$100$	3.43129e8			0.343129
$101$	−3.78336e8	−	6.55298e8i	−0.361770	−	0.626603i	0.626483	−	0.779435i	$-0.284494\pi$
$101$	−3.78336e8	−	6.55298e8i	−0.361770	−	0.626603i	−0.988252	+	0.152832i	$0.951161\pi$
$102$	−2.98278e9	−	1.04914e9i	−2.72848	−	0.959694i
$103$	9.24257e7	−	1.60086e8i	0.0809143	−	0.140148i	−0.822729	−	0.568434i	$-0.807549\pi$
$103$	9.24257e7	−	1.60086e8i	0.0809143	−	0.140148i	0.903643	+	0.428287i	$0.140883\pi$
$104$	1.08563e9	−	1.88036e9i	0.909977	−	1.57613i
$105$	7.25274e8	−	6.22109e8i	0.582305	−	0.499476i
$106$	1.29811e9	+	2.24839e9i	0.998700	+	1.72980i
$107$	1.05514e9			0.778184			0.389092	−	0.921199i	$-0.372789\pi$
$107$	1.05514e9			0.778184			0.389092	+	0.921199i	$0.372789\pi$
$108$	−2.42440e9	+	7.89348e7i	−1.71474	+	0.0558292i
$109$	−5.25218e8			−0.356386			−0.178193	−	0.983996i	$-0.557025\pi$
$109$	−5.25218e8			−0.356386			−0.178193	+	0.983996i	$0.557025\pi$
$110$	4.90157e8	+	8.48977e8i	0.319204	+	0.552878i
$111$	4.03468e8	−	3.46078e8i	0.252264	−	0.216382i
$112$	−3.25371e8	+	5.63560e8i	−0.195388	+	0.338422i
$113$	8.13702e7	−	1.40937e8i	0.0469475	−	0.0813154i	−0.841597	−	0.540106i	$-0.818384\pi$
$113$	8.13702e7	−	1.40937e8i	0.0469475	−	0.0813154i	0.888544	+	0.458791i	$0.151717\pi$
$114$	−9.52008e8	−	3.34852e8i	−0.527921	−	0.185687i
$115$	−5.91160e8	−	1.02392e9i	−0.315184	−	0.545915i
$116$	5.29635e8			0.271591
$117$	−2.43921e9	−	1.95815e9i	−1.20341	−	0.966073i
$118$	2.36562e9			1.12325
$119$	3.29323e9	+	5.70404e9i	1.50543	+	2.60748i
$120$	2.20822e8	+	1.17750e9i	0.0972137	+	0.518376i
$121$	2.94271e8	−	5.09692e8i	0.124800	−	0.216159i
$122$	2.11325e9	−	3.66025e9i	0.863637	−	1.49586i
$123$	−3.80898e8	−	2.03107e9i	−0.150050	−	0.800116i
$124$	1.60841e9	+	2.78584e9i	0.610939	+	1.05818i
$125$	−2.44141e8			−0.0894427
$126$	6.23694e9	+	5.00689e9i	2.20447	+	1.76970i
$127$	8.49515e8			0.289770			0.144885	−	0.989448i	$-0.453719\pi$
$127$	8.49515e8			0.289770			0.144885	+	0.989448i	$0.453719\pi$
$128$	2.66446e9	+	4.61498e9i	0.877333	+	1.51959i
$129$	−2.66712e9	−	9.38113e8i	−0.847988	−	0.298264i
$130$	−1.85179e9	+	3.20739e9i	−0.568652	+	0.984934i
$131$	2.31378e9	−	4.00758e9i	0.686438	−	1.18895i	−0.286545	−	0.958067i	$-0.592507\pi$
$131$	2.31378e9	−	4.00758e9i	0.686438	−	1.18895i	0.972983	−	0.230878i	$-0.0741599\pi$
$132$	−3.93472e9	+	3.37504e9i	−1.12806	+	0.967600i
$133$	1.05109e9	+	1.82055e9i	0.291279	+	0.504510i
$134$	−6.91504e9			−1.85278
$135$	1.72499e9	−	5.61630e7i	0.446977	−	0.0145529i
$136$	−8.25796e9			−2.06989
$137$	−1.81180e8	−	3.13814e8i	−0.0439409	−	0.0761078i	0.843218	−	0.537571i	$-0.180658\pi$
$137$	−1.81180e8	−	3.13814e8i	−0.0439409	−	0.0761078i	−0.887159	+	0.461463i	$0.847325\pi$
$138$	7.51154e9	−	6.44308e9i	1.76308	−	1.51230i
$139$	1.15432e9	−	1.99935e9i	0.262277	−	0.454278i	−0.704569	−	0.709635i	$-0.748860\pi$
$139$	1.15432e9	−	1.99935e9i	0.262277	−	0.454278i	0.966847	+	0.255357i	$0.0821931\pi$
$140$	2.99135e9	−	5.18118e9i	0.658100	−	1.13986i
$141$	1.98626e8	+	6.98630e7i	0.0423203	+	0.0148854i
$142$	−3.73606e9	−	6.47104e9i	−0.771110	−	1.33560i
$143$	−6.68472e9			−1.33681
$144$	−1.09552e9	+	4.25875e8i	−0.212319	+	0.0825374i
$145$	−3.76842e8			−0.0707951
$146$	−7.12372e9	−	1.23386e10i	−1.29753	−	2.24740i
$147$	−2.02735e9	−	1.08105e10i	−0.358096	−	1.90949i
$148$	1.66408e9	−	2.88228e9i	0.285100	−	0.493808i
$149$	−4.80072e8	+	8.31510e8i	−0.0797937	+	0.138207i	−0.903161	−	0.429302i	$-0.858759\pi$
$149$	−4.80072e8	+	8.31510e8i	−0.0797937	+	0.138207i	0.823367	+	0.567509i	$0.192093\pi$
$150$	−3.76664e8	−	2.00850e9i	−0.0607496	−	0.323937i
$151$	4.60124e9	+	7.96957e9i	0.720242	+	1.24750i	0.960903	+	0.276886i	$0.0893024\pi$
$151$	4.60124e9	+	7.96957e9i	0.720242	+	1.24750i	−0.240661	+	0.970609i	$0.577364\pi$
$152$	−2.63568e9			−0.400494
$153$	−1.81115e9	+	1.17580e10i	−0.267204	+	1.73468i
$154$	1.70925e10			2.44885
$155$	−1.14440e9	−	1.98216e9i	−0.159252	−	0.275833i
$156$	−1.84750e10	−	6.49826e9i	−2.49761	−	0.878489i
$157$	−1.04842e8	+	1.81592e8i	−0.0137717	+	0.0238533i	−0.872829	−	0.488026i	$-0.837717\pi$
$157$	−1.04842e8	+	1.81592e8i	−0.0137717	+	0.0238533i	0.859057	+	0.511879i	$0.171050\pi$
$158$	2.09362e8	−	3.62625e8i	0.0267264	−	0.0462915i
$159$	7.41433e9	−	6.35970e9i	0.919994	−	0.789132i
$160$	−1.49021e9	−	2.58112e9i	−0.179766	−	0.311364i
$161$	−2.06146e10			−2.41801
$162$	3.12339e9	+	1.41045e10i	0.356294	+	1.60894i
$163$	7.50515e9			0.832751			0.416376	−	0.909193i	$-0.363300\pi$
$163$	7.50515e9			0.832751			0.416376	+	0.909193i	$0.363300\pi$
$164$	−6.46925e9	−	1.12051e10i	−0.698323	−	1.20953i
$165$	2.79960e9	−	2.40138e9i	0.294048	−	0.252222i
$166$	−1.27262e10	+	2.20424e10i	−1.30080	+	2.25306i
$167$	−3.38574e9	+	5.86428e9i	−0.336845	+	0.583433i	−0.983837	−	0.179064i	$-0.942693\pi$
$167$	−3.38574e9	+	5.86428e9i	−0.336845	+	0.583433i	0.646993	+	0.762496i	$0.276026\pi$
$168$	1.97051e10	+	6.93090e9i	1.90847	+	0.671271i
$169$	−7.32502e9	−	1.26873e10i	−0.690746	−	1.19641i
$170$	1.40859e10			1.29349
$171$	−5.78061e8	+	3.75276e9i	−0.0517001	+	0.335636i
$172$	−1.77021e10			−1.54222
$173$	−2.72905e9	−	4.72685e9i	−0.231635	−	0.401204i	0.726654	−	0.687003i	$-0.241074\pi$
$173$	−2.72905e9	−	4.72685e9i	−0.231635	−	0.401204i	−0.958289	+	0.285800i	$0.907741\pi$
$174$	−5.81397e8	−	3.10021e9i	−0.0480841	−	0.256400i
$175$	−2.12838e9	+	3.68647e9i	−0.171545	+	0.297125i
$176$	−1.25595e9	+	2.17537e9i	−0.0986657	+	0.170894i
$177$	−1.64058e9	−	8.74811e9i	−0.125637	−	0.669938i
$178$	1.15559e10	+	2.00153e10i	0.862804	+	1.49442i
$179$	−1.12748e10			−0.820863			−0.410432	−	0.911891i	$-0.634622\pi$
$179$	−1.12748e10			−0.820863			−0.410432	+	0.911891i	$0.634622\pi$
$180$	1.00718e10	−	3.91535e9i	0.715126	−	0.278000i
$181$	−4.52124e9			−0.313115			−0.156558	−	0.987669i	$-0.550040\pi$
$181$	−4.52124e9			−0.313115			−0.156558	+	0.987669i	$0.550040\pi$
$182$	3.22873e10	+	5.59232e10i	2.18127	+	3.77808i
$183$	−1.50012e10	−	5.27640e9i	−0.988773	−	0.347783i
$184$	1.29231e10	−	2.23834e10i	0.831161	−	1.43961i
$185$	−1.18402e9	+	2.05077e9i	−0.0743164	+	0.128720i
$186$	1.45412e10	−	1.24729e10i	0.890827	−	0.764114i
$187$	1.27121e10	+	2.20179e10i	0.760202	+	1.31671i
$188$	1.31830e9			0.0769671
$189$	1.41902e10	−	2.65366e10i	0.808928	−	1.51275i
$190$	4.49576e9			0.250272
$191$	1.06073e10	+	1.83724e10i	0.576705	+	0.998883i	0.995854	+	0.0909655i	$0.0289953\pi$
$191$	1.06073e10	+	1.83724e10i	0.576705	+	0.998883i	−0.419149	+	0.907918i	$0.637671\pi$
$192$	2.21911e10	−	1.90346e10i	1.17848	−	1.01085i
$193$	1.97105e9	−	3.41396e9i	0.102256	−	0.177113i	−0.810358	−	0.585936i	$-0.800727\pi$
$193$	1.97105e9	−	3.41396e9i	0.102256	−	0.177113i	0.912614	+	0.408822i	$0.134060\pi$
$194$	7.03797e9	−	1.21901e10i	0.356730	−	0.617875i
$195$	1.31452e10	+	4.62359e9i	0.651046	+	0.228994i
$196$	−3.44329e10	−	5.96395e10i	−1.66656	−	2.88657i
$197$	−1.08034e10			−0.511049			−0.255525	−	0.966803i	$-0.582248\pi$
$197$	−1.08034e10			−0.511049			−0.255525	+	0.966803i	$0.582248\pi$
$198$	2.40750e10	+	1.93269e10i	1.11320	+	0.893653i
$199$	1.67929e10			0.759078			0.379539	−	0.925176i	$-0.376083\pi$
$199$	1.67929e10			0.759078			0.379539	+	0.925176i	$0.376083\pi$
$200$	−2.66852e9	−	4.62201e9i	−0.117933	−	0.204266i
$201$	4.79563e9	+	2.55719e10i	0.207235	+	1.10505i
$202$	−1.41075e10	+	2.44349e10i	−0.596168	+	1.03259i
$203$	−3.28525e9	+	5.69022e9i	−0.135780	+	0.235178i
$204$	1.37294e10	+	7.32100e10i	0.555031	+	2.95961i
$205$	4.60295e9	+	7.97254e9i	0.182030	+	0.315286i
$206$	−6.89278e9			−0.266681
$207$	−2.90359e10	−	2.33094e10i	−1.09918	−	0.882399i
$208$	−9.48985e9			−0.351540
$209$	4.05728e9	+	7.02742e9i	0.147088	+	0.254764i
$210$	−3.36116e10	−	1.18223e10i	−1.19262	−	0.419483i
$211$	1.82806e10	−	3.16630e10i	0.634921	−	1.09972i	−0.351611	−	0.936146i	$-0.614366\pi$
$211$	1.82806e10	−	3.16630e10i	0.634921	−	1.09972i	0.986532	−	0.163569i	$-0.0523008\pi$
$212$	3.05800e10	−	5.29661e10i	1.03974	−	1.80089i
$213$	−2.13390e10	+	1.83037e10i	−0.710340	+	0.609299i
$214$	−1.96721e10	−	3.40731e10i	−0.641193	−	1.11058i
$215$	1.25952e10			0.402006
$216$	1.99179e10	+	3.20433e10i	0.622588	+	1.00160i
$217$	−3.99068e10			−1.22174
$218$	9.79222e9	+	1.69606e10i	0.293648	+	0.508613i
$219$	−4.06881e10	+	3.49005e10i	−1.19528	+	1.02526i
$220$	1.15468e10	−	1.99996e10i	0.332322	−	0.575599i
$221$	−4.80255e10	+	8.31827e10i	−1.35428	+	2.34567i
$222$	−1.86981e10	−	6.57670e9i	−0.516664	−	0.181727i
$223$	5.39130e9	+	9.33800e9i	0.145989	+	0.252861i	0.929742	−	0.368213i	$-0.120030\pi$
$223$	5.39130e9	+	9.33800e9i	0.145989	+	0.252861i	−0.783752	+	0.621074i	$0.786697\pi$
$224$	−5.19657e10			−1.37912
$225$	−7.16623e9	+	2.78582e9i	−0.186410	+	0.0724655i
$226$	−6.06830e9			−0.154732
$227$	−5.18751e8	−	8.98502e8i	−0.0129671	−	0.0224596i	0.859469	−	0.511188i	$-0.170794\pi$
$227$	−5.18751e8	−	8.98502e8i	−0.0129671	−	0.0224596i	−0.872436	+	0.488728i	$0.837461\pi$
$228$	4.38200e9	+	2.33663e10i	0.107390	+	0.572641i
$229$	2.94610e10	−	5.10280e10i	0.707927	−	1.22617i	−0.257698	−	0.966225i	$-0.582964\pi$
$229$	2.94610e10	−	5.10280e10i	0.707927	−	1.22617i	0.965625	−	0.259940i	$-0.0837027\pi$
$230$	−2.20433e10	+	3.81801e10i	−0.519399	+	0.899626i
$231$	−1.18538e10	−	6.32082e10i	−0.273906	−	1.46056i
$232$	−4.11898e9	−	7.13428e9i	−0.0933455	−	0.161679i
$233$	4.53778e9			0.100865			0.0504326	−	0.998727i	$-0.483940\pi$
$233$	4.53778e9			0.100865			0.0504326	+	0.998727i	$0.483940\pi$
$234$	−1.77567e10	+	1.15276e11i	−0.387161	+	2.51344i
$235$	−9.37989e8			−0.0200628
$236$	−2.78639e10	−	4.82617e10i	−0.584707	−	1.01274i
$237$	−1.48619e9	−	5.22739e8i	−0.0305989	−	0.0107626i
$238$	1.22799e11	−	2.12694e11i	2.48083	−	4.29693i
$239$	1.04891e10	−	1.81676e10i	0.207944	−	0.360170i	−0.743122	−	0.669155i	$-0.766656\pi$
$239$	1.04891e10	−	1.81676e10i	0.207944	−	0.360170i	0.951067	+	0.308985i	$0.0999894\pi$
$240$	3.97440e9	−	3.40907e9i	0.0773252	−	0.0663263i
$241$	2.37237e10	+	4.10906e10i	0.453007	+	0.784631i	0.998571	−	0.0534378i	$-0.0170179\pi$
$241$	2.37237e10	+	4.10906e10i	0.453007	+	0.784631i	−0.545564	+	0.838069i	$0.683685\pi$
$242$	−2.19457e10			−0.411320
$243$	4.99926e10	−	2.13319e10i	0.919767	−	0.392466i
$244$	−9.95650e10			−1.79826
$245$	2.44994e10	+	4.24342e10i	0.434418	+	0.752434i
$246$	−5.84871e10	+	5.01677e10i	−1.01824	+	0.873407i
$247$	−1.53282e10	+	2.65492e10i	−0.262032	+	0.453853i
$248$	2.50172e10	−	4.33310e10i	0.419958	−	0.727388i
$249$	9.03387e10	+	3.17750e10i	1.48928	+	0.523828i
$250$	4.55178e9	+	7.88392e9i	0.0736973	+	0.127647i
$251$	7.25652e10			1.15398			0.576988	−	0.816753i	$-0.304228\pi$
$251$	7.25652e10			1.15398			0.576988	+	0.816753i	$0.304228\pi$
$252$	2.86840e10	−	1.86216e11i	0.448061	−	2.90880i
$253$	−7.95735e10			−1.22103
$254$	−1.58384e10	−	2.74330e10i	−0.238760	−	0.413544i
$255$	−9.76866e9	−	5.20898e10i	−0.144679	−	0.771475i
$256$	4.60052e10	−	7.96834e10i	0.669464	−	1.15955i
$257$	−1.34124e10	+	2.32309e10i	−0.191781	+	0.332175i	−0.945841	−	0.324631i	$-0.894760\pi$
$257$	−1.34124e10	+	2.32309e10i	−0.191781	+	0.332175i	0.754059	+	0.656806i	$0.228093\pi$
$258$	1.94321e10	+	1.03619e11i	0.273043	+	1.45596i
$259$	2.06442e10	+	3.57567e10i	0.285068	+	0.493752i
$260$	8.72464e10			1.18404
$261$	−1.10614e10	+	4.30003e9i	−0.147546	+	0.0573574i
$262$	−1.72553e11			−2.26239
$263$	−5.90570e10	−	1.02290e11i	−0.761151	−	1.31835i	−0.942258	−	0.334888i	$-0.891301\pi$
$263$	−5.90570e10	−	1.02290e11i	−0.761151	−	1.31835i	0.181107	−	0.983463i	$-0.442032\pi$
$264$	7.60627e10	+	2.67537e10i	0.963727	+	0.338974i
$265$	−2.17580e10	+	3.76860e10i	−0.271027	+	0.469433i
$266$	3.91934e10	−	6.78850e10i	0.480005	−	0.831393i
$267$	6.60029e10	−	5.66145e10i	0.794808	−	0.681753i
$268$	8.14500e10	+	1.41075e11i	0.964460	+	1.67049i
$269$	−5.47230e10			−0.637213			−0.318606	−	0.947887i	$-0.603215\pi$
$269$	−5.47230e10			−0.637213			−0.318606	+	0.947887i	$0.603215\pi$
$270$	−3.39746e10	−	5.46572e10i	−0.389060	−	0.625908i
$271$	1.15363e11			1.29929			0.649643	−	0.760239i	$-0.274918\pi$
$271$	1.15363e11			1.29929			0.649643	+	0.760239i	$0.274918\pi$
$272$	1.80465e10	+	3.12574e10i	0.199909	+	0.346252i
$273$	1.84413e11	−	1.58182e11i	2.00937	−	1.72355i
$274$	−6.75590e9	+	1.17016e10i	−0.0724112	+	0.125420i
$275$	−8.21568e9	+	1.42300e10i	−0.0866257	+	0.150040i
$276$	−2.19923e11	−	7.73539e10i	−2.28128	−	0.802400i
$277$	−7.80926e9	−	1.35260e10i	−0.0796986	−	0.138042i	0.823421	−	0.567431i	$-0.192062\pi$
$277$	−7.80926e9	−	1.35260e10i	−0.0796986	−	0.138042i	−0.903120	+	0.429388i	$0.858729\pi$
$278$	−8.60853e10			−0.864425
$279$	−5.62092e10	−	4.51237e10i	−0.555378	−	0.445847i
$280$	−9.30551e10			−0.904751
$281$	7.08916e10	+	1.22788e11i	0.678291	+	1.17484i	0.975495	+	0.220021i	$0.0706126\pi$
$281$	7.08916e10	+	1.22788e11i	0.678291	+	1.17484i	−0.297204	+	0.954814i	$0.596054\pi$
$282$	−1.44714e9	−	7.71666e9i	−0.0136267	−	0.0726622i
$283$	−9.96093e10	+	1.72528e11i	−0.923126	+	1.59890i	−0.128578	+	0.991699i	$0.541041\pi$
$283$	−9.96093e10	+	1.72528e11i	−0.923126	+	1.59890i	−0.794548	+	0.607202i	$0.792292\pi$
$284$	−8.80116e10	+	1.52441e11i	−0.802800	+	1.39049i
$285$	−3.11784e9	−	1.66254e10i	−0.0279932	−	0.149269i
$286$	1.24631e11	+	2.15867e11i	1.10148	+	1.90783i
$287$	1.60511e11			1.39649
$288$	−7.31943e10	−	5.87589e10i	−0.626919	−	0.503278i
$289$	2.46725e11			2.08052
$290$	7.02588e9	+	1.21692e10i	0.0583324	+	0.101035i
$291$	−4.99601e10	−	1.75726e10i	−0.408418	−	0.143654i
$292$	−1.67816e11	+	2.90666e11i	−1.35086	+	2.33976i
$293$	−6.68253e10	+	1.15745e11i	−0.529708	+	0.917482i	0.469691	+	0.882831i	$0.344365\pi$
$293$	−6.68253e10	+	1.15745e11i	−0.529708	+	0.917482i	−0.999399	+	0.0346510i	$0.988968\pi$
$294$	−3.11300e11	+	2.67020e11i	−2.43006	+	2.08440i
$295$	1.98255e10	+	3.43388e10i	0.152414	+	0.263989i
$296$	−5.17664e10			−0.391954
$297$	5.47749e10	−	1.02433e11i	0.408487	−	0.763898i
$298$	3.58021e10			0.262988
$299$	−1.50312e11	−	2.60349e11i	−1.08761	−	1.88380i
$300$	−3.65393e10	+	3.13419e10i	−0.260444	+	0.223398i
$301$	1.09803e11	−	1.90185e11i	0.771021	−	1.33545i
$302$	1.71572e11	−	2.97171e11i	1.18690	−	2.05577i
$303$	1.00144e11	+	3.52239e10i	0.682549	+	0.240074i
$304$	5.75985e9	+	9.97635e9i	0.0386794	+	0.0669947i
$305$	7.08417e10			0.468748
$306$	4.13461e11	−	1.60730e11i	2.69581	−	1.04797i
$307$	−1.45850e11			−0.937097			−0.468549	−	0.883438i	$-0.655223\pi$
$307$	−1.45850e11			−0.937097			−0.468549	+	0.883438i	$0.655223\pi$
$308$	−2.01327e11	−	3.48708e11i	−1.27474	−	2.20792i
$309$	4.78019e9	+	2.54896e10i	0.0298285	+	0.159056i
$310$	−4.26726e10	+	7.39111e10i	−0.262435	+	0.454551i
$311$	−4.79138e10	+	8.29892e10i	−0.290429	+	0.503037i	−0.973911	−	0.226930i	$-0.927131\pi$
$311$	−4.79138e10	+	8.29892e10i	−0.290429	+	0.503037i	0.683483	+	0.729967i	$0.260465\pi$
$312$	5.61478e10	+	2.99399e11i	0.335457	+	1.78877i
$313$	−1.41298e11	−	2.44736e11i	−0.832122	−	1.44128i	−0.896352	−	0.443343i	$-0.853792\pi$
$313$	−1.41298e11	−	2.44736e11i	−0.832122	−	1.44128i	0.0642299	−	0.997935i	$-0.479541\pi$
$314$	7.81875e9			0.0453894
$315$	−2.04090e10	+	1.32495e11i	−0.116795	+	0.758231i
$316$	−9.86401e9			−0.0556495
$317$	9.55717e10	+	1.65535e11i	0.531573	+	0.920711i	0.999321	+	0.0368489i	$0.0117320\pi$
$317$	9.55717e10	+	1.65535e11i	0.531573	+	0.920711i	−0.467748	+	0.883862i	$0.654935\pi$
$318$	−3.43604e11	−	1.20857e11i	−1.88424	−	0.662748i
$319$	−1.26813e10	+	2.19646e10i	−0.0685653	+	0.118759i
$320$	−6.51218e10	+	1.12794e11i	−0.347177	+	0.601329i
$321$	−1.12360e11	+	9.63776e10i	−0.590662	+	0.506645i
$322$	3.84341e11	+	6.65698e11i	1.99235	+	3.45085i
$323$	1.16596e11			0.596036
$324$	2.50961e11	−	2.29854e11i	1.26518	−	1.15877i
$325$	−6.20769e10			−0.308642
$326$	−1.39927e11	−	2.42360e11i	−0.686154	−	1.18845i
$327$	5.59296e10	−	4.79741e10i	0.270506	−	0.232029i
$328$	−1.00623e11	+	1.74284e11i	−0.480025	+	0.831428i
$329$	−8.17726e9	+	1.41634e10i	−0.0384792	+	0.0666479i
$330$	−1.29743e11	−	4.56346e10i	−0.602241	−	0.211827i
$331$	−1.47429e10	−	2.55355e10i	−0.0675083	−	0.116928i	0.830296	−	0.557323i	$-0.188172\pi$
$331$	−1.47429e10	−	2.55355e10i	−0.0675083	−	0.116928i	−0.897804	+	0.440395i	$0.854838\pi$
$332$	5.99590e11			2.70853
$333$	−1.13535e10	+	7.37066e10i	−0.0505976	+	0.328479i
$334$	2.52497e11			1.11019
$335$	−5.79526e10	−	1.00377e11i	−0.251404	−	0.435444i
$336$	−1.68280e10	−	8.97324e10i	−0.0720286	−	0.384081i
$337$	5.97432e10	−	1.03478e11i	0.252321	−	0.437034i	−0.711843	−	0.702339i	$-0.752139\pi$
$337$	5.97432e10	−	1.03478e11i	0.252321	−	0.437034i	0.964165	+	0.265305i	$0.0854726\pi$
$338$	−2.73137e11	+	4.73087e11i	−1.13830	+	1.97159i
$339$	4.20841e9	+	2.24406e10i	0.0173069	+	0.0922861i
$340$	−1.65913e11	−	2.87370e11i	−0.673326	−	1.16623i
$341$	−1.54043e11			−0.616945
$342$	1.31964e11	−	5.12998e10i	0.521599	−	0.202767i
$343$	4.14583e11			1.61729
$344$	1.37669e11	+	2.38450e11i	0.530058	+	0.918087i
$345$	1.56478e11	+	5.50382e10i	0.594657	+	0.209160i
$346$	−1.01761e11	+	1.76256e11i	−0.381716	+	0.661152i
$347$	2.44998e10	−	4.24349e10i	0.0907153	−	0.157123i	−0.817097	−	0.576500i	$-0.804418\pi$
$347$	2.44998e10	−	4.24349e10i	0.0907153	−	0.157123i	0.907812	+	0.419377i	$0.137751\pi$
$348$	−5.64000e10	+	4.83775e10i	−0.206145	+	0.176822i
$349$	−8.18964e10	−	1.41849e11i	−0.295495	−	0.511813i	0.679605	−	0.733578i	$-0.262151\pi$
$349$	−8.18964e10	−	1.41849e11i	−0.295495	−	0.511813i	−0.975100	+	0.221766i	$0.928818\pi$
$350$	1.58727e11			0.565386
$351$	4.38608e11	−	1.42804e10i	1.54239	−	0.0502178i
$352$	−2.00591e11			−0.696416
$353$	−1.76396e11	−	3.05526e11i	−0.604646	−	1.04728i	−0.992107	−	0.125392i	$-0.959981\pi$
$353$	−1.76396e11	−	3.05526e11i	−0.604646	−	1.04728i	0.387461	−	0.921886i	$-0.373352\pi$
$354$	−2.51911e11	+	2.16079e11i	−0.852576	+	0.731304i
$355$	6.26213e10	−	1.08463e11i	0.209264	−	0.362456i
$356$	2.72225e11	−	4.71508e11i	0.898263	−	1.55584i
$357$	−8.71706e11	−	3.06607e11i	−2.84029	−	0.999021i
$358$	2.10209e11	+	3.64092e11i	0.676359	+	1.17149i
$359$	1.55228e11			0.493224			0.246612	−	0.969114i	$-0.420683\pi$
$359$	1.55228e11			0.493224			0.246612	+	0.969114i	$0.420683\pi$
$360$	−1.31069e11	−	1.05220e11i	−0.411282	−	0.330169i
$361$	−2.85474e11			−0.884676
$362$	8.42945e10	+	1.46002e11i	0.257995	+	0.446860i
$363$	1.52195e10	+	8.11554e10i	0.0460066	+	0.245323i
$364$	7.60602e11	−	1.31740e12i	2.27092	−	3.93334i
$365$	1.19403e11	−	2.06812e11i	0.352125	−	0.609899i
$366$	1.09296e11	+	5.82801e11i	0.318374	+	1.69768i
$367$	−3.25487e11	−	5.63760e11i	−0.936561	−	1.62217i	−0.771827	−	0.635833i	$-0.780657\pi$
$367$	−3.25487e11	−	5.63760e11i	−0.936561	−	1.62217i	−0.164734	−	0.986338i	$-0.552677\pi$
$368$	−1.12965e11			−0.321092
$369$	2.26082e11	+	1.81494e11i	0.634816	+	0.509617i
$370$	8.82996e10			0.244935
$371$	3.79367e11	+	6.57083e11i	1.03963	+	1.80068i
$372$	−4.25739e11	−	1.49746e11i	−1.15266	−	0.405426i
$373$	−2.99346e11	+	5.18483e11i	−0.800726	+	1.38690i	0.118412	+	0.992965i	$0.462220\pi$
$373$	−2.99346e11	+	5.18483e11i	−0.800726	+	1.38690i	−0.919139	+	0.393934i	$0.871114\pi$
$374$	4.74010e11	−	8.21010e11i	1.25275	−	2.16983i
$375$	2.59981e10	−	2.23001e10i	0.0678893	−	0.0582326i
$376$	−1.02525e10	−	1.77578e10i	−0.0264535	−	0.0458188i
$377$	−9.58183e10			−0.244294
$378$	−1.12150e12	+	3.65142e10i	−2.82543	+	0.0919917i
$379$	−7.27144e11			−1.81027			−0.905136	−	0.425123i	$-0.860231\pi$
$379$	−7.27144e11			−1.81027			−0.905136	+	0.425123i	$0.860231\pi$
$380$	−5.29541e10	−	9.17192e10i	−0.130279	−	0.225649i
$381$	−9.04634e10	+	7.75957e10i	−0.219943	+	0.188658i
$382$	3.95527e11	−	6.85072e11i	0.950366	−	1.64608i
$383$	−2.31796e11	+	4.01483e11i	−0.550442	+	0.953394i	0.447800	+	0.894134i	$0.352208\pi$
$383$	−2.31796e11	+	4.01483e11i	−0.550442	+	0.953394i	−0.998243	+	0.0592605i	$0.981126\pi$
$384$	−7.05272e11	−	2.48067e11i	−1.65526	−	0.582208i
$385$	1.43246e11	+	2.48110e11i	0.332285	+	0.575534i
$386$	−1.46994e11			−0.337021
$387$	3.69706e11	−	1.43720e11i	0.837833	−	0.325701i
$388$	−3.31592e11			−0.742781
$389$	2.82989e11	+	4.90151e11i	0.626608	+	1.08532i	0.988228	+	0.152991i	$0.0488905\pi$
$389$	2.82989e11	+	4.90151e11i	0.626608	+	1.08532i	−0.361620	+	0.932326i	$0.617776\pi$
$390$	−9.57732e10	−	5.10695e11i	−0.209630	−	1.11782i
$391$	−5.71686e11	+	9.90189e11i	−1.23698	+	2.14251i
$392$	−5.35569e11	+	9.27633e11i	−1.14559	+	1.98422i
$393$	1.19667e11	+	6.38105e11i	0.253051	+	1.34935i
$394$	2.01420e11	+	3.48870e11i	0.421085	+	0.729340i
$395$	7.01836e9			0.0145060
$396$	1.10722e11	−	7.18805e11i	0.226259	−	1.46887i
$397$	−7.04940e11			−1.42428			−0.712139	−	0.702038i	$-0.752273\pi$
$397$	−7.04940e11			−1.42428			−0.712139	+	0.702038i	$0.752273\pi$
$398$	−3.13088e11	−	5.42285e11i	−0.625450	−	1.08331i
$399$	−2.78220e11	−	9.78590e10i	−0.549555	−	0.193296i
$400$	−1.16632e10	+	2.02013e10i	−0.0227798	+	0.0394557i
$401$	2.43385e11	−	4.21555e11i	0.470050	−	0.814150i	−0.529364	−	0.848395i	$-0.677569\pi$
$401$	2.43385e11	−	4.21555e11i	0.470050	−	0.814150i	0.999413	+	0.0342450i	$0.0109026\pi$
$402$	7.36371e11	−	6.31628e11i	1.40631	−	1.20627i
$403$	−2.90983e11	−	5.03997e11i	−0.549534	−	0.951821i
$404$	6.64670e11			1.24134
$405$	−1.78562e11	+	1.63544e11i	−0.329792	+	0.302055i
$406$	2.45002e11			0.447511
$407$	7.96876e10	+	1.38023e11i	0.143951	+	0.249331i
$408$	8.79377e11	−	7.54293e11i	1.57110	−	1.34763i
$409$	3.72083e11	−	6.44467e11i	0.657484	−	1.13880i	−0.323780	−	0.946132i	$-0.604954\pi$
$409$	3.72083e11	−	6.44467e11i	0.657484	−	1.13880i	0.981265	−	0.192664i	$-0.0617127\pi$
$410$	1.71636e11	−	2.97282e11i	0.299972	−	0.519566i
$411$	4.79578e10	+	1.68683e10i	0.0829031	+	0.0291597i
$412$	8.11878e10	+	1.40621e11i	0.138820	+	0.240444i
$413$	6.91344e11			1.16928
$414$	−2.11372e11	+	1.37223e12i	−0.353628	+	2.29575i
$415$	−4.26615e11			−0.706025
$416$	−3.78911e11	−	6.56293e11i	−0.620322	−	1.07443i
$417$	5.97008e10	+	3.18344e11i	0.0966869	+	0.515567i
$418$	1.51289e11	−	2.62040e11i	0.242389	−	0.419831i
$419$	−2.90614e11	+	5.03358e11i	−0.460631	+	0.797837i	−0.998993	−	0.0448774i	$-0.985710\pi$
$419$	−2.90614e11	+	5.03358e11i	−0.460631	+	0.797837i	0.538361	+	0.842714i	$0.319044\pi$
$420$	1.54711e11	+	8.24969e11i	0.242604	+	1.29365i
$421$	2.34465e11	+	4.06106e11i	0.363755	+	0.630042i	0.988576	−	0.150726i	$-0.0481612\pi$
$421$	2.34465e11	+	4.06106e11i	0.363755	+	0.630042i	−0.624821	+	0.780768i	$0.714828\pi$
$422$	−1.36330e12			−2.09260
$423$	−2.75327e10	+	1.07031e10i	−0.0418135	+	0.0162547i
$424$	−9.51284e11			−1.42943
$425$	1.18049e11	+	2.04467e11i	0.175514	+	0.304000i
$426$	9.88920e11	+	3.47835e11i	1.45485	+	0.511717i
$427$	6.17588e11	−	1.06969e12i	0.899028	−	1.55716i
$428$	−4.63422e11	+	8.02671e11i	−0.667544	+	1.15622i
$429$	7.11845e11	−	6.10591e11i	1.01468	−	0.870347i
$430$	−2.34827e11	−	4.06732e11i	−0.331237	−	0.573720i
$431$	7.03212e10			0.0981609			0.0490805	−	0.998795i	$-0.484371\pi$
$431$	7.03212e10			0.0981609			0.0490805	+	0.998795i	$0.484371\pi$
$432$	7.77602e10	−	1.45417e11i	0.107419	−	0.200881i
$433$	−1.03802e12			−1.41909			−0.709546	−	0.704659i	$-0.751100\pi$
$433$	−1.03802e12			−1.41909			−0.709546	+	0.704659i	$0.751100\pi$
$434$	7.44028e11	+	1.28869e12i	1.00667	+	1.74360i
$435$	4.01293e10	−	3.44212e10i	0.0537353	−	0.0460919i
$436$	2.30679e11	−	3.99547e11i	0.305716	−	0.529516i
$437$	−1.82464e11	+	3.16036e11i	−0.239337	+	0.414544i
$438$	1.88562e12	+	6.63233e11i	2.44805	+	0.861058i
$439$	−5.29355e11	−	9.16870e11i	−0.680231	−	1.17820i	−0.974910	−	0.222599i	$-0.928546\pi$
$439$	−5.29355e11	−	9.16870e11i	−0.680231	−	1.17820i	0.294679	−	0.955596i	$-0.404787\pi$
$440$	−3.59198e11			−0.456875
$441$	1.20333e12	+	9.66011e11i	1.51500	+	1.21621i
$442$	3.58157e12			4.46348
$443$	−6.36001e11	−	1.10159e12i	−0.784587	−	1.35894i	−0.929245	−	0.369463i	$-0.879542\pi$
$443$	−6.36001e11	−	1.10159e12i	−0.784587	−	1.35894i	0.144658	−	0.989482i	$-0.453792\pi$
$444$	8.60652e10	+	4.58929e11i	0.105100	+	0.560430i
$445$	−1.93692e11	+	3.35484e11i	−0.234148	+	0.405556i
$446$	2.01032e11	−	3.48197e11i	0.240579	−	0.416695i
$447$	−2.48290e10	−	1.32397e11i	−0.0294154	−	0.156853i
$448$	1.13544e12	+	1.96665e12i	1.33173	+	2.30662i
$449$	5.63101e11			0.653850			0.326925	−	0.945050i	$-0.393988\pi$
$449$	5.63101e11			0.653850			0.326925	+	0.945050i	$0.393988\pi$
$450$	2.23569e11	+	1.79477e11i	0.257013	+	0.206325i
$451$	6.19583e11			0.705189
$452$	7.14765e10	+	1.23801e11i	0.0805453	+	0.139509i
$453$	−1.21793e12	−	4.28385e11i	−1.35888	−	0.477960i
$454$	−1.93433e10	+	3.35036e10i	−0.0213687	+	0.0370117i
$455$	−5.41177e11	+	9.37347e11i	−0.591954	+	1.02530i
$456$	2.80669e11	−	2.40746e11i	0.303985	−	0.260746i
$457$	8.48723e11	+	1.47003e12i	0.910213	+	1.57654i	0.813762	+	0.581198i	$0.197416\pi$
$457$	8.48723e11	+	1.47003e12i	0.910213	+	1.57654i	0.0964515	+	0.995338i	$0.469251\pi$
$458$	−2.19710e12			−2.33322
$459$	−8.81119e11	−	1.41752e12i	−0.926569	−	1.49064i
$460$	1.03856e12			1.08149
$461$	4.59500e11	+	7.95877e11i	0.473839	+	0.820714i	0.999551	−	0.0299488i	$-0.00953443\pi$
$461$	4.59500e11	+	7.95877e11i	0.473839	+	0.820714i	−0.525712	+	0.850663i	$0.676201\pi$
$462$	−1.82015e12	+	1.56125e12i	−1.85874	+	1.59435i
$463$	3.26301e11	−	5.65170e11i	0.329992	−	0.571563i	−0.652518	−	0.757773i	$-0.726287\pi$
$463$	3.26301e11	−	5.65170e11i	0.329992	−	0.571563i	0.982510	+	0.186210i	$0.0596205\pi$
$464$	−1.80027e10	+	3.11816e10i	−0.0180305	+	0.0312297i
$465$	3.02918e11	+	1.06546e11i	0.300460	+	0.105681i
$466$	−8.46029e10	−	1.46536e11i	−0.0831091	−	0.143949i
$467$	−1.48402e12			−1.44382			−0.721912	−	0.691985i	$-0.756736\pi$
$467$	−1.48402e12			−1.44382			−0.721912	+	0.691985i	$0.756736\pi$
$468$	2.56093e12	−	9.95543e11i	2.46770	−	0.959299i
$469$	−2.02089e12			−1.92870
$470$	1.74880e10	+	3.02901e10i	0.0165310	+	0.0286325i
$471$	−5.42236e9	−	2.89138e10i	−0.00507685	−	0.0270715i
$472$	−4.33396e11	+	7.50663e11i	−0.401926	+	0.696155i
$473$	4.23847e11	−	7.34125e11i	0.389345	−	0.674365i
$474$	1.08280e10	+	5.77387e10i	0.00985252	+	0.0525369i
$475$	3.76775e10	+	6.52593e10i	0.0339594	+	0.0588195i
$476$	−5.78562e12			−5.16558
$477$	−2.08637e11	+	1.35447e12i	−0.184527	+	1.19794i
$478$	−7.82239e11			−0.685352
$479$	−3.73220e11	−	6.46435e11i	−0.323933	−	0.561068i	0.657363	−	0.753574i	$-0.271672\pi$
$479$	−3.73220e11	−	6.46435e11i	−0.323933	−	0.561068i	−0.981296	+	0.192506i	$0.938338\pi$
$480$	3.94453e11	+	1.38742e11i	0.339164	+	0.119295i
$481$	−3.01056e11	+	5.21444e11i	−0.256445	+	0.444176i
$482$	8.84613e11	−	1.53219e12i	0.746520	−	1.29301i
$483$	2.19521e12	−	1.88296e12i	1.83533	−	1.57427i
$484$	2.58491e11	+	4.47719e11i	0.214112	+	0.370853i
$485$	2.35931e11			0.193619
$486$	−1.62093e12	−	1.21667e12i	−1.31796	−	0.989262i
$487$	−1.38873e12			−1.11876			−0.559380	−	0.828911i	$-0.688961\pi$
$487$	−1.38873e12			−1.11876			−0.559380	+	0.828911i	$0.688961\pi$
$488$	7.74318e11	+	1.34116e12i	0.618059	+	1.07051i
$489$	−7.99211e11	+	6.85530e11i	−0.632080	+	0.542171i
$490$	9.13539e11	−	1.58230e12i	0.715887	−	1.23995i
$491$	1.12038e12	−	1.94056e12i	0.869959	−	1.50681i	0.00792238	−	0.999969i	$-0.497478\pi$
$491$	1.12038e12	−	1.94056e12i	0.869959	−	1.50681i	0.862037	−	0.506845i	$-0.169188\pi$
$492$	1.71238e12	+	6.02300e11i	1.31752	+	0.463415i
$493$	1.82214e11	+	3.15604e11i	0.138922	+	0.240620i
$494$	1.14312e12			0.863618
$495$	−7.87800e10	+	5.11438e11i	−0.0589783	+	0.382886i
$496$	−2.18684e11			−0.162237
$497$	−1.09185e12	−	1.89113e12i	−0.802709	−	1.39033i
$498$	−6.58189e11	−	3.50968e12i	−0.479533	−	2.55703i
$499$	−7.28291e11	+	1.26144e12i	−0.525839	+	0.910779i	0.473708	+	0.880682i	$0.342915\pi$
$499$	−7.28291e11	+	1.26144e12i	−0.525839	+	0.910779i	−0.999547	+	0.0300975i	$0.990418\pi$
$500$	1.07228e11	−	1.85724e11i	0.0767261	−	0.132893i
$501$	−1.75108e11	−	9.33736e11i	−0.124176	−	0.662147i
$502$	−1.35291e12	−	2.34331e12i	−0.950830	−	1.64689i
$503$	2.67237e12			1.86140			0.930702	−	0.365778i	$-0.119197\pi$
$503$	2.67237e12			1.86140			0.930702	+	0.365778i	$0.119197\pi$
$504$	−2.73144e12	+	1.06182e12i	−1.88562	+	0.733019i
$505$	−4.72921e11			−0.323577
$506$	1.48358e12	+	2.56963e12i	1.00608	+	1.74258i
$507$	1.93890e12	+	6.81974e11i	1.30323	+	0.458387i
$508$	−3.73112e11	+	6.46248e11i	−0.248572	+	0.430539i
$509$	−4.01831e11	+	6.95992e11i	−0.265347	+	0.459594i	−0.967654	−	0.252280i	$-0.918820\pi$
$509$	−4.01831e11	+	6.95992e11i	−0.265347	+	0.459594i	0.702308	+	0.711873i	$0.252153\pi$
$510$	−1.49998e12	+	1.28662e12i	−0.981794	+	0.842142i
$511$	−2.08188e12	−	3.60592e12i	−1.35071	−	2.33949i
$512$	−7.02499e11			−0.451784
$513$	−2.81225e11	−	4.52426e11i	−0.179277	−	0.288416i
$514$	1.00025e12			0.632081
$515$	−5.77660e10	−	1.00054e11i	−0.0361860	−	0.0626759i
$516$	1.88506e12	−	1.61693e12i	1.17058	−	1.00408i
$517$	−3.15647e10	+	5.46716e10i	−0.0194309	+	0.0336554i
$518$	7.69784e11	−	1.33330e12i	0.469769	−	0.813665i
$519$	7.22369e11	+	2.54080e11i	0.437025	+	0.153716i
$520$	−6.78516e11	−	1.17522e12i	−0.406954	−	0.704865i
$521$	−2.27529e12			−1.35290			−0.676452	−	0.736487i	$-0.736483\pi$
$521$	−2.27529e12			−1.35290			−0.676452	+	0.736487i	$0.736483\pi$
$522$	3.45089e11	+	2.77030e11i	0.203429	+	0.163309i
$523$	2.45020e12			1.43200			0.716000	−	0.698100i	$-0.245971\pi$
$523$	2.45020e12			1.43200			0.716000	+	0.698100i	$0.245971\pi$
$524$	2.03245e12	+	3.52031e12i	1.17768	+	2.03981i
$525$	−1.10078e11	−	5.86975e11i	−0.0632391	−	0.337212i
$526$	−2.20213e12	+	3.81420e12i	−1.25432	+	2.17254i
$527$	−1.10670e12	+	1.91686e12i	−0.625003	+	1.08254i
$528$	−6.49570e10	−	3.46372e11i	−0.0363725	−	0.193950i
$529$	−8.88710e11	−	1.53929e12i	−0.493412	−	0.854614i
$530$	1.62264e12			0.893264
$531$	9.73765e11	+	7.81719e11i	0.531531	+	0.426703i
$532$	−1.84659e12			−0.999464
$533$	1.17038e12	+	2.02715e12i	0.628135	+	1.08796i
$534$	−3.05879e12	−	1.07587e12i	−1.62785	−	0.572567i
$535$	3.29731e11	−	5.71110e11i	0.174007	−	0.301389i
$536$	1.26687e12	−	2.19429e12i	0.662967	−	1.14829i
$537$	1.20064e12	−	1.02986e12i	0.623056	−	0.534431i
$538$	1.02026e12	+	1.76714e12i	0.525038	+	0.909393i
$539$	3.29776e12			1.68294
$540$	−7.14901e11	+	1.33691e12i	−0.361805	+	0.676599i
$541$	1.85361e12			0.930317			0.465158	−	0.885228i	$-0.345997\pi$
$541$	1.85361e12			0.930317			0.465158	+	0.885228i	$0.345997\pi$
$542$	−2.15084e12	−	3.72537e12i	−1.07056	−	1.85427i
$543$	4.81460e11	−	4.12976e11i	0.237663	−	0.203857i
$544$	−1.44112e12	+	2.49609e12i	−0.705512	+	1.22198i
$545$	−1.64131e11	+	2.84283e11i	−0.0796903	+	0.138028i
$546$	−8.54631e12	−	3.00601e12i	−4.11540	−	1.44752i
$547$	1.56444e10	+	2.70970e10i	0.00747166	+	0.0129413i	0.869737	−	0.493515i	$-0.164288\pi$
$547$	1.56444e10	+	2.70970e10i	0.00747166	+	0.0129413i	−0.862265	+	0.506457i	$0.830955\pi$
$548$	3.18302e11			0.150774
$549$	2.07941e12	−	8.08354e11i	0.976932	−	0.379774i
$550$	6.12697e11			0.285505
$551$	5.81568e10	+	1.00731e11i	0.0268793	+	0.0465564i
$552$	6.68372e11	+	3.56398e12i	0.306402	+	1.63384i
$553$	6.11851e10	−	1.05976e11i	0.0278216	−	0.0481884i
$554$	−2.91193e11	+	5.04362e11i	−0.131337	+	0.227483i
$555$	−6.12364e10	−	3.26533e11i	−0.0273963	−	0.146086i
$556$	1.01397e12	+	1.75625e12i	0.449975	+	0.779380i
$557$	1.41814e12			0.624266			0.312133	−	0.950038i	$-0.398956\pi$
$557$	1.41814e12			0.624266			0.312133	+	0.950038i	$0.398956\pi$
$558$	−4.09186e11	+	2.65643e12i	−0.178676	+	1.15996i
$559$	3.20255e12			1.38721
$560$	2.03357e11	+	3.52225e11i	0.0873802	+	0.151347i
$561$	−3.36483e12	−	1.18352e12i	−1.43427	−	0.504478i
$562$	2.64342e12	−	4.57854e12i	1.11777	−	1.93604i
$563$	−1.02504e11	+	1.77542e11i	−0.0429984	+	0.0744754i	−0.886724	−	0.462300i	$-0.847024\pi$
$563$	−1.02504e11	+	1.77542e11i	−0.0429984	+	0.0744754i	0.843725	+	0.536775i	$0.180358\pi$
$564$	−1.40384e11	+	1.20416e11i	−0.0584201	+	0.0501103i
$565$	−5.08564e10	−	8.80858e10i	−0.0209955	−	0.0363654i
$566$	7.42851e12			3.04248
$567$	9.12797e11	+	4.12199e12i	0.370894	+	1.67488i
$568$	2.73787e12			1.10368
$569$	5.34919e11	+	9.26507e11i	0.213935	+	0.370547i	0.952943	−	0.303150i	$-0.0980384\pi$
$569$	5.34919e11	+	9.26507e11i	0.213935	+	0.370547i	−0.739007	+	0.673697i	$0.764705\pi$
$570$	−4.78746e11	+	4.10648e11i	−0.189963	+	0.162942i
$571$	1.99130e12	−	3.44903e12i	0.783924	−	1.35780i	−0.145715	−	0.989327i	$-0.546548\pi$
$571$	1.99130e12	−	3.44903e12i	0.783924	−	1.35780i	0.929640	−	0.368470i	$-0.120118\pi$
$572$	2.93597e12	−	5.08525e12i	1.14675	−	1.98623i
$573$	−2.80771e12	−	9.87560e11i	−1.08807	−	0.382708i
$574$	−2.99259e12	−	5.18332e12i	−1.15065	−	1.99299i
$575$	−7.38950e11			−0.281909
$576$	−6.24451e11	+	4.05392e12i	−0.236373	+	1.53453i
$577$	−2.58044e12			−0.969175			−0.484588	−	0.874743i	$-0.661030\pi$
$577$	−2.58044e12			−0.969175			−0.484588	+	0.874743i	$0.661030\pi$
$578$	−4.59997e12	−	7.96738e12i	−1.71427	−	2.96920i
$579$	1.01941e11	+	5.43586e11i	0.0376962	+	0.201008i
$580$	1.65511e11	−	2.86673e11i	0.0607297	−	0.105187i
$581$	−3.71917e12	+	6.44180e12i	−1.35411	+	2.34539i
$582$	3.63999e11	+	1.94096e12i	0.131506	+	0.701236i
$583$	1.46438e12	+	2.53638e12i	0.524983	+	0.909297i
$584$	5.22042e12			1.85715
$585$	−1.82214e12	+	7.08341e11i	−0.643249	+	0.250058i
$586$	4.98360e12			1.74584
$587$	−2.02041e11	−	3.49945e11i	−0.0702374	−	0.121655i	0.828768	−	0.559592i	$-0.189042\pi$
$587$	−2.02041e11	−	3.49945e11i	−0.0702374	−	0.121655i	−0.899005	+	0.437938i	$0.855709\pi$
$588$	9.11424e12	+	3.20577e12i	3.14429	+	1.10595i
$589$	−3.53223e11	+	6.11800e11i	−0.120929	+	0.209455i
$590$	7.39258e11	−	1.28043e12i	0.251166	−	0.435033i
$591$	1.15044e12	−	9.86797e11i	0.387900	−	0.332724i
$592$	1.13127e11	+	1.95942e11i	0.0378546	+	0.0655661i
$593$	−2.76913e12			−0.919597			−0.459799	−	0.888023i	$-0.652078\pi$
$593$	−2.76913e12			−0.919597			−0.459799	+	0.888023i	$0.652078\pi$
$594$	−4.32905e12	+	1.40947e11i	−1.42677	+	0.0464533i
$595$	4.11654e12			1.34650
$596$	−4.21701e11	−	7.30407e11i	−0.136898	−	0.237114i
$597$	−1.78825e12	+	1.53388e12i	−0.576160	+	0.494205i
$598$	−5.60488e12	+	9.70793e12i	−1.79230	+	3.10436i
$599$	1.61215e12	−	2.79233e12i	0.511665	−	0.886229i	−0.488244	−	0.872707i	$-0.662362\pi$
$599$	1.61215e12	−	2.79233e12i	0.511665	−	0.886229i	0.999909	−	0.0135219i	$-0.00430430\pi$
$600$	7.06347e11	+	2.48445e11i	0.222504	+	0.0782617i
$601$	2.60286e11	+	4.50829e11i	0.0813797	+	0.140954i	0.903843	−	0.427865i	$-0.140734\pi$
$601$	2.60286e11	+	4.50829e11i	0.0813797	+	0.140954i	−0.822463	+	0.568818i	$0.807401\pi$
$602$	−8.18874e12			−2.54117
$603$	−2.84645e12	−	2.28507e12i	−0.876749	−	0.703837i
$604$	−8.08356e12			−2.47136
$605$	−1.83919e11	−	3.18558e11i	−0.0558121	−	0.0966693i
$606$	−7.29630e11	−	3.89063e12i	−0.219774	−	1.17191i
$607$	−2.03663e11	+	3.52755e11i	−0.0608924	+	0.105469i	−0.894865	−	0.446338i	$-0.852728\pi$
$607$	−2.03663e11	+	3.52755e11i	−0.0608924	+	0.105469i	0.833972	+	0.551807i	$0.186061\pi$
$608$	−4.59959e11	+	7.96672e11i	−0.136506	+	0.236436i
$609$	−1.69911e11	−	9.06022e11i	−0.0500545	−	0.266908i
$610$	−1.32078e12	−	2.28766e12i	−0.386230	−	0.668970i
$611$	−2.38499e11			−0.0692312
$612$	−8.14912e12	−	6.54195e12i	−2.34817	−	1.88506i
$613$	−1.26382e12			−0.361505			−0.180753	−	0.983529i	$-0.557853\pi$
$613$	−1.26382e12			−0.361505			−0.180753	+	0.983529i	$0.557853\pi$
$614$	2.71925e12	+	4.70988e12i	0.772131	+	1.33737i
$615$	−1.21838e12	−	4.28544e11i	−0.343436	−	0.120797i
$616$	−3.13144e12	+	5.42381e12i	−0.876256	+	1.51772i
$617$	−1.96595e12	+	3.40512e12i	−0.546121	+	0.945909i	0.452415	+	0.891808i	$0.350563\pi$
$617$	−1.96595e12	+	3.40512e12i	−0.546121	+	0.945909i	−0.998535	+	0.0541012i	$0.982771\pi$
$618$	7.34001e11	−	6.29595e11i	0.202418	−	0.173625i
$619$	2.14274e12	+	3.71133e12i	0.586626	+	1.01607i	0.994671	+	0.103105i	$0.0328776\pi$
$619$	2.14274e12	+	3.71133e12i	0.586626	+	1.01607i	−0.408044	+	0.912962i	$0.633789\pi$
$620$	2.01051e12			0.546441
$621$	5.22110e12	−	1.69991e11i	1.40880	−	0.0458683i
$622$	3.57324e12			0.957207
$623$	3.37715e12	+	5.84940e12i	0.898161	+	1.55566i
$624$	1.01056e12	−	8.66814e11i	0.266828	−	0.228873i
$625$	−7.62939e10	+	1.32145e11i	−0.0200000	+	0.0346410i
$626$	−5.26876e12	+	9.12576e12i	−1.37127	+	2.37511i
$627$	−1.07395e12	−	3.77741e11i	−0.277510	−	0.0976092i
$628$	−9.20945e10	−	1.59512e11i	−0.0236274	−	0.0409238i
$629$	2.29002e12			0.583327
$630$	4.65910e12	−	1.81119e12i	1.17834	−	0.458070i
$631$	−4.73856e12			−1.18991			−0.594955	−	0.803759i	$-0.702830\pi$
$631$	−4.73856e12			−1.18991			−0.594955	+	0.803759i	$0.702830\pi$
$632$	7.67125e10	+	1.32870e11i	0.0191267	+	0.0331284i
$633$	9.45461e11	+	5.04151e12i	0.234060	+	1.24808i
$634$	3.56370e12	−	6.17251e12i	0.875990	−	1.51726i
$635$	2.65473e11	−	4.59813e11i	0.0647946	−	0.112228i
$636$	1.58158e12	+	8.43349e12i	0.383295	+	2.04386i
$637$	6.22938e12	+	1.07896e13i	1.49905	+	2.59644i
$638$	9.45724e11			0.225981
$639$	6.00474e11	−	3.89826e12i	0.142475	−	0.924948i
$640$	3.33058e12			0.784711
$641$	−2.06154e12	−	3.57069e12i	−0.482314	−	0.835393i	0.517480	−	0.855695i	$-0.326870\pi$
$641$	−2.06154e12	−	3.57069e12i	−0.482314	−	0.835393i	−0.999794	+	0.0203029i	$0.993537\pi$
$642$	5.20713e12	+	1.83151e12i	1.20974	+	0.425503i
$643$	−1.44048e12	+	2.49499e12i	−0.332322	+	0.575598i	−0.982967	−	0.183784i	$-0.941165\pi$
$643$	−1.44048e12	+	2.49499e12i	−0.332322	+	0.575598i	0.650645	+	0.759382i	$0.274499\pi$
$644$	9.05404e12	−	1.56821e13i	2.07423	−	3.59267i
$645$	−1.34124e12	+	1.15046e12i	−0.305133	+	0.261730i
$646$	−2.17383e12	−	3.76519e12i	−0.491111	−	0.850629i
$647$	4.34155e12			0.974037			0.487018	−	0.873392i	$-0.338084\pi$
$647$	4.34155e12			0.974037			0.487018	+	0.873392i	$0.338084\pi$
$648$	−5.04789e12	−	1.59291e12i	−1.12466	−	0.354898i
$649$	2.66863e12			0.590455
$650$	1.15737e12	+	2.00462e12i	0.254309	+	0.440476i
$651$	4.24962e12	−	3.64514e12i	0.927332	−	0.795426i
$652$	−3.29630e12	+	5.70937e12i	−0.714353	+	1.23730i
$653$	9.86190e10	−	1.70813e11i	0.0212252	−	0.0367631i	−0.855218	−	0.518269i	$-0.826577\pi$
$653$	9.86190e10	−	1.70813e11i	0.0212252	−	0.0367631i	0.876443	+	0.481506i	$0.159910\pi$
$654$	−2.59196e12	−	9.11676e11i	−0.554024	−	0.194868i
$655$	−1.44611e12	−	2.50474e12i	−0.306984	−	0.531712i
$656$	8.79580e11			0.185442
$657$	1.14495e12	−	7.43300e12i	0.239741	−	1.55640i
$658$	6.09831e11			0.126821
$659$	−4.02565e12	−	6.97263e12i	−0.831480	−	1.44017i	−0.896864	−	0.442306i	$-0.854161\pi$
$659$	−4.02565e12	−	6.97263e12i	−0.831480	−	1.44017i	0.0653844	−	0.997860i	$-0.479173\pi$
$660$	5.97192e11	+	3.18443e12i	0.122509	+	0.653257i
$661$	−3.03963e12	+	5.26479e12i	−0.619319	+	1.07269i	0.370292	+	0.928916i	$0.379258\pi$
$661$	−3.03963e12	+	5.26479e12i	−0.619319	+	1.07269i	−0.989610	+	0.143776i	$0.954076\pi$
$662$	−5.49737e11	+	9.52172e11i	−0.111248	+	0.192688i
$663$	−2.48385e12	−	1.32447e13i	−0.499245	−	2.66214i
$664$	−4.66302e12	−	8.07658e12i	−0.930916	−	1.61239i
$665$	1.31387e12			0.260528
$666$	2.59185e12	−	1.00756e12i	0.510476	−	0.198444i
$667$	−1.14060e12			−0.223135
$668$	−2.97408e12	−	5.15125e12i	−0.577907	−	1.00096i
$669$	−1.42706e12	−	5.01941e11i	−0.275438	−	0.0968802i
$670$	−2.16095e12	+	3.74287e12i	−0.414293	+	0.717577i
$671$	2.38392e12	−	4.12908e12i	0.453985	−	0.786325i
$672$	5.53375e12	−	4.74661e12i	1.04679	−	0.897888i
$673$	−3.25319e11	−	5.63469e11i	−0.0611282	−	0.105877i	0.833842	−	0.552004i	$-0.186137\pi$
$673$	−3.25319e11	−	5.63469e11i	−0.0611282	−	0.105877i	−0.894970	+	0.446126i	$0.852803\pi$
$674$	−4.45544e12			−0.831612
$675$	5.08661e11	−	9.51230e11i	0.0943107	−	0.176367i
$676$	1.28688e13			2.37015
$677$	−1.28416e11	−	2.22423e11i	−0.0234947	−	0.0406940i	0.854039	−	0.520209i	$-0.174146\pi$
$677$	−1.28416e11	−	2.22423e11i	−0.0234947	−	0.0406940i	−0.877534	+	0.479515i	$0.840813\pi$
$678$	6.46203e11	−	5.54286e11i	0.117445	−	0.100740i
$679$	2.05682e12	−	3.56251e12i	0.371349	−	0.643195i
$680$	−2.58061e12	+	4.46975e12i	−0.462842	+	0.801666i
$681$	1.37311e11	+	4.82967e10i	0.0244649	+	0.00860510i
$682$	2.87199e12	+	4.97443e12i	0.508339	+	0.880469i
$683$	−3.25277e12			−0.571952			−0.285976	−	0.958237i	$-0.592318\pi$
$683$	−3.25277e12			−0.571952			−0.285976	+	0.958237i	$0.592318\pi$
$684$	−2.60094e12	−	2.08798e12i	−0.454336	−	0.364732i
$685$	−2.26476e11			−0.0393019
$686$	−7.72952e12	−	1.33879e13i	−1.33258	−	2.30810i
$687$	1.52370e12	+	8.12490e12i	0.260973	+	1.39159i
$688$	6.01707e11	−	1.04219e12i	0.102385	−	0.177336i
$689$	−5.53235e12	+	9.58231e12i	−0.935240	+	1.61988i
$690$	−1.14006e12	−	6.07920e12i	−0.191473	−	1.02100i
$691$	5.84876e11	+	1.01303e12i	0.0975916	+	0.169034i	0.910687	−	0.413096i	$-0.135553\pi$
$691$	5.84876e11	+	1.01303e12i	0.0975916	+	0.169034i	−0.813096	+	0.582130i	$0.802219\pi$
$692$	4.79446e12			0.794808
$693$	7.03580e12	+	5.64820e12i	1.15882	+	0.930274i
$694$	−1.82711e12			−0.298983
$695$	−7.21452e11	−	1.24959e12i	−0.117294	−	0.203159i
$696$	1.09028e12	+	3.83485e11i	0.176115	+	0.0619451i
$697$	4.45132e12	−	7.70991e12i	0.714399	−	1.23738i
$698$	−3.05377e12	+	5.28929e12i	−0.486953	+	0.843427i
$699$	−4.83221e11	+	4.14486e11i	−0.0765594	+	0.0656694i
$700$	−1.86960e12	−	3.23824e12i	−0.294311	−	0.509762i
$701$	−2.95656e11			−0.0462441			−0.0231220	−	0.999733i	$-0.507361\pi$
$701$	−2.95656e11			−0.0462441			−0.0231220	+	0.999733i	$0.507361\pi$
$702$	−8.63861e12	−	1.38975e13i	−1.34254	−	2.15983i
$703$	7.30901e11			0.112865
$704$	4.38288e12	+	7.59138e12i	0.672486	+	1.16478i
$705$	9.98849e10	−	8.56771e10i	0.0152282	−	0.0130621i
$706$	−6.57748e12	+	1.13925e13i	−0.996410	+	1.72583i
$707$	−4.12285e12	+	7.14099e12i	−0.620598	+	1.07491i
$708$	7.37547e12	+	2.59419e12i	1.10316	+	0.388018i
$709$	6.06682e11	+	1.05080e12i	0.0901681	+	0.156176i	0.907582	−	0.419875i	$-0.137926\pi$
$709$	6.06682e11	+	1.05080e12i	0.0901681	+	0.156176i	−0.817414	+	0.576051i	$0.804593\pi$
$710$	−4.67007e12			−0.689701
$711$	2.06009e11	−	8.00844e10i	0.0302324	−	0.0117526i
$712$	−8.46840e12			−1.23493
$713$	−3.46380e12	−	5.99947e12i	−0.501937	−	0.869381i
$714$	6.35106e12	+	3.38660e13i	0.914544	+	4.87665i
$715$	−2.08898e12	+	3.61821e12i	−0.298921	+	0.517746i
$716$	4.95196e12	−	8.57705e12i	0.704156	−	1.21963i
$717$	5.42488e11	+	2.89273e12i	0.0766574	+	0.408763i
$718$	−2.89408e12	−	5.01269e12i	−0.406397	−	0.703900i
$719$	3.91784e12			0.546722			0.273361	−	0.961912i	$-0.411865\pi$
$719$	3.91784e12			0.546722			0.273361	+	0.961912i	$0.411865\pi$
$720$	−1.11839e11	+	7.26054e11i	−0.0155094	+	0.100687i
$721$	−2.01439e12			−0.277609
$722$	5.32241e12	+	9.21868e12i	0.728938	+	1.26256i
$723$	−6.27956e12	−	2.20872e12i	−0.854687	−	0.300621i
$724$	1.98575e12	−	3.43943e12i	0.268598	−	0.465225i
$725$	−1.17763e11	+	2.03972e11i	−0.0158303	+	0.0274188i
$726$	2.33696e12	−	2.00455e12i	0.312203	−	0.267794i
$727$	−3.50658e12	−	6.07358e12i	−0.465564	−	0.806380i	0.533663	−	0.845697i	$-0.320815\pi$
$727$	−3.50658e12	−	6.07358e12i	−0.465564	−	0.806380i	−0.999227	+	0.0393173i	$0.987482\pi$
$728$	−2.36608e13			−3.12204
$729$	−3.37515e12	+	6.83799e12i	−0.442608	+	0.896715i
$730$	−8.90465e12			−1.16055
$731$	−6.09015e12	−	1.05485e13i	−0.788860	−	1.36635i
$732$	1.06025e13	−	9.09439e12i	1.36493	−	1.17078i
$733$	4.56777e12	−	7.91162e12i	0.584436	−	1.01227i	−0.410510	−	0.911856i	$-0.634649\pi$
$733$	4.56777e12	−	7.91162e12i	0.584436	−	1.01227i	0.994946	−	0.100416i	$-0.0320174\pi$
$734$	−1.21368e13	+	2.10216e13i	−1.54338	+	2.67321i
$735$	−6.48489e12	−	2.28094e12i	−0.819615	−	0.288285i
$736$	−4.51047e12	−	7.81237e12i	−0.566594	−	0.981370i
$737$	−7.80076e12			−0.973942
$738$	1.64581e12	−	1.06846e13i	0.204233	−	1.32588i
$739$	1.21341e13			1.49661			0.748306	−	0.663354i	$-0.230867\pi$
$739$	1.21341e13			1.49661			0.748306	+	0.663354i	$0.230867\pi$
$740$	−1.04005e12	−	1.80142e12i	−0.127501	−	0.220838i
$741$	−7.92764e11	−	4.22728e12i	−0.0965966	−	0.515085i
$742$	1.41459e13	−	2.45014e13i	1.71322	−	2.96739i
$743$	−5.38552e10	+	9.32800e10i	−0.00648303	+	0.0112289i	−0.869249	−	0.494375i	$-0.835397\pi$
$743$	−5.38552e10	+	9.32800e10i	−0.00648303	+	0.0112289i	0.862766	+	0.505604i	$0.168730\pi$
$744$	1.29387e12	+	6.89935e12i	0.154815	+	0.825524i
$745$	3.00045e11	+	5.19694e11i	0.0356848	+	0.0618079i
$746$	2.23242e13			2.63907
$747$	−1.25224e13	+	4.86798e12i	−1.47145	+	0.572014i
$748$	−2.23328e13			−2.60848
$749$	−5.74909e12	−	9.95771e12i	−0.667469	−	1.15609i
$750$	−1.20484e12	−	4.23780e11i	−0.139044	−	0.0489064i
$751$	2.81465e12	−	4.87511e12i	0.322882	−	0.559248i	−0.658199	−	0.752844i	$-0.728682\pi$
$751$	2.81465e12	−	4.87511e12i	0.322882	−	0.559248i	0.981081	+	0.193595i	$0.0620149\pi$
$752$	−4.48102e10	+	7.76136e10i	−0.00510972	+	0.00885029i
$753$	−7.72735e12	+	6.62819e12i	−0.875897	+	0.751307i
$754$	1.78645e12	+	3.09422e12i	0.201289	+	0.348642i
$755$	5.75155e12			0.644204
$756$	1.39547e13	+	2.24499e13i	1.55372	+	2.49957i
$757$	−2.12797e12			−0.235524			−0.117762	−	0.993042i	$-0.537572\pi$
$757$	−2.12797e12			−0.235524			−0.117762	+	0.993042i	$0.537572\pi$
$758$	1.35569e13	+	2.34813e13i	1.49159	+	2.58352i
$759$	8.47366e12	−	7.26835e12i	0.926793	−	0.794964i
$760$	−8.23649e11	+	1.42660e12i	−0.0895532	+	0.155111i
$761$	−3.54059e12	+	6.13248e12i	−0.382688	+	0.662835i	−0.991446	−	0.130521i	$-0.958335\pi$
$761$	−3.54059e12	+	6.13248e12i	−0.382688	+	0.662835i	0.608758	+	0.793356i	$0.291668\pi$
$762$	4.19237e12	+	1.47459e12i	0.450467	+	0.158443i
$763$	2.86174e12	+	4.95667e12i	0.305681	+	0.529456i
$764$	−1.86351e13			−1.97885
$765$	5.79819e12	+	4.65467e12i	0.612091	+	0.491375i
$766$	1.72865e13			1.81417
$767$	5.04097e12	+	8.73121e12i	0.525938	+	0.910952i
$768$	2.37936e12	+	1.26875e13i	0.246794	+	1.31599i
$769$	8.37816e12	−	1.45114e13i	0.863933	−	1.49638i	−0.00416976	−	0.999991i	$-0.501327\pi$
$769$	8.37816e12	−	1.45114e13i	0.863933	−	1.49638i	0.868103	−	0.496385i	$-0.165339\pi$
$770$	5.34140e12	−	9.25158e12i	0.547579	−	0.948435i
$771$	−6.93678e11	−	3.69892e12i	−0.0706990	−	0.376991i
$772$	1.73139e12	+	2.99886e12i	0.175436	+	0.303864i
$773$	8.00430e12			0.806335			0.403168	−	0.915126i	$-0.367909\pi$
$773$	8.00430e12			0.806335			0.403168	+	0.915126i	$0.367909\pi$
$774$	−1.15339e13	−	9.25921e12i	−1.15516	−	0.927342i
$775$	−1.43050e12			−0.142439
$776$	2.57879e12	+	4.46660e12i	0.255293	+	0.442180i
$777$	−5.46443e12	−	1.92201e12i	−0.537836	−	0.189174i
$778$	1.05521e13	−	1.82768e13i	1.03260	−	1.78852i
$779$	1.42072e12	−	2.46075e12i	0.138226	−	0.239414i
$780$	−9.29073e12	+	7.96920e12i	−0.898720	+	0.770884i
$781$	−4.21459e12	−	7.29989e12i	−0.405346	−	0.702080i
$782$	4.26343e13			4.07689
$783$	7.85140e11	−	1.46826e12i	0.0746482	−	0.139597i
$784$	4.68160e12			0.442560
$785$	6.55263e10	+	1.13495e11i	0.00615889	+	0.0106675i
$786$	1.83749e13	−	1.57612e13i	1.71721	−	1.47295i
$787$	−7.89254e12	+	1.36703e13i	−0.733383	+	1.27026i	0.222047	+	0.975036i	$0.428726\pi$
$787$	−7.89254e12	+	1.36703e13i	−0.733383	+	1.27026i	−0.955429	+	0.295220i	$0.904607\pi$
$788$	4.74492e12	−	8.21844e12i	0.438390	−	0.759314i
$789$	1.56322e13	+	5.49833e12i	1.43606	+	0.505108i
$790$	−1.30851e11	−	2.26641e11i	−0.0119524	−	0.0207022i
$791$	−1.77343e12			−0.161072
$792$	−1.05435e13	+	4.09871e12i	−0.952186	+	0.370155i
$793$	1.80127e13			1.61752
$794$	1.31430e13	+	2.27643e13i	1.17355	+	2.03265i
$795$	−1.12531e12	−	6.00053e12i	−0.0999126	−	0.532767i
$796$	−7.37553e12	+	1.27748e13i	−0.651155	+	1.12783i
$797$	−2.42031e12	+	4.19210e12i	−0.212475	+	0.368018i	−0.952489	−	0.304574i	$-0.901486\pi$
$797$	−2.42031e12	+	4.19210e12i	−0.212475	+	0.368018i	0.740013	+	0.672592i	$0.234819\pi$
$798$	2.02706e12	+	1.08089e13i	0.176951	+	0.943561i
$799$	4.53545e11	+	7.85563e11i	0.0393695	+	0.0681899i
$800$	−1.86276e12			−0.160788
$801$	−1.85730e12	+	1.20576e13i	−0.159418	+	1.03494i
$802$	−1.81508e13			−1.54921
$803$	−8.03616e12	−	1.39190e13i	−0.682070	−	1.18138i
$804$	−2.15595e13	−	7.58316e12i	−1.81964	−	0.640027i
$805$	−6.44206e12	+	1.11580e13i	−0.540684	+	0.936492i
$806$	−1.08502e13	+	1.87931e13i	−0.905589	+	1.56853i
$807$	5.82736e12	−	4.99846e12i	0.483661	−	0.414864i
$808$	−5.16914e12	−	8.95322e12i	−0.426646	−	0.738972i
$809$	5.13155e12			0.421192			0.210596	−	0.977573i	$-0.432460\pi$
$809$	5.13155e12			0.421192			0.210596	+	0.977573i	$0.432460\pi$
$810$	8.61036e12	+	2.71708e12i	0.702811	+	0.221779i
$811$	2.59972e12			0.211025			0.105512	−	0.994418i	$-0.466352\pi$
$811$	2.59972e12			0.211025			0.105512	+	0.994418i	$0.466352\pi$
$812$	−2.88580e12	−	4.99836e12i	−0.232951	−	0.403483i
$813$	−1.22848e13	+	1.05374e13i	−0.986192	+	0.845914i
$814$	2.97141e12	−	5.14663e12i	0.237221	−	0.410878i
$815$	2.34536e12	−	4.06228e12i	0.186209	−	0.322523i
$816$	−4.77683e12	−	1.68016e12i	−0.377167	−	0.132662i
$817$	−1.94378e12	−	3.36673e12i	−0.152633	−	0.264368i
$818$	−2.77487e13			−2.16697
$819$	−5.18933e12	+	3.36890e13i	−0.403027	+	2.61644i
$820$	−8.08656e12			−0.624599
$821$	−4.58732e12	−	7.94547e12i	−0.352383	−	0.610345i	0.634284	−	0.773100i	$-0.281295\pi$
$821$	−4.58732e12	−	7.94547e12i	−0.352383	−	0.610345i	−0.986666	+	0.162755i	$0.947962\pi$
$822$	−3.49410e11	−	1.86317e12i	−0.0266939	−	0.142341i
$823$	−8.06655e12	+	1.39717e13i	−0.612898	+	1.06157i	0.377851	+	0.925866i	$0.376663\pi$
$823$	−8.06655e12	+	1.39717e13i	−0.612898	+	1.06157i	−0.990749	+	0.135705i	$0.956670\pi$
$824$	1.26280e12	−	2.18723e12i	0.0954247	−	0.165280i
$825$	−4.24909e11	−	2.26576e12i	−0.0319340	−	0.170283i
$826$	−1.28895e13	−	2.23252e13i	−0.963442	−	1.66873i
$827$	2.56251e13			1.90498			0.952491	−	0.304568i	$-0.0985121\pi$
$827$	2.56251e13			1.90498			0.952491	+	0.304568i	$0.0985121\pi$
$828$	3.04848e13	−	1.18507e13i	2.25397	−	0.876211i
$829$	−2.32426e13			−1.70918			−0.854592	−	0.519300i	$-0.826193\pi$
$829$	−2.32426e13			−1.70918			−0.854592	+	0.519300i	$0.826193\pi$
$830$	7.95386e12	+	1.37765e13i	0.581737	+	1.00760i
$831$	2.06708e12	+	7.27058e11i	0.150367	+	0.0528889i
$832$	−1.65583e13	+	2.86798e13i	−1.19801	+	2.07502i
$833$	2.36923e13	−	4.10363e13i	1.70492	−	2.95302i
$834$	9.16708e12	−	7.86314e12i	0.656121	−	0.562793i
$835$	2.11609e12	+	3.66518e12i	0.150642	+	0.260919i
$836$	−7.12793e12			−0.504702
$837$	1.01073e13	−	3.29077e11i	0.711819	−	0.0231757i
$838$	2.16730e13			1.51817
$839$	4.33711e11	+	7.51210e11i	0.0302184	+	0.0523398i	0.880739	−	0.473602i	$-0.157046\pi$
$839$	4.33711e11	+	7.51210e11i	0.0302184	+	0.0523398i	−0.850521	+	0.525942i	$0.823713\pi$
$840$	9.90929e12	−	8.49977e12i	0.686730	−	0.589048i
$841$	7.07180e12	−	1.22487e13i	0.487470	−	0.844323i
$842$	8.74279e12	−	1.51430e13i	0.599440	−	1.03826i
$843$	−1.87647e13	−	6.60015e12i	−1.27973	−	0.450122i
$844$	1.60579e13	+	2.78131e13i	1.08930	+	1.88672i
$845$	−9.15627e12			−0.617822
$846$	8.58953e11	+	6.89551e11i	0.0576505	+	0.0462807i
$847$	−6.41353e12			−0.428175
$848$	2.07888e12	+	3.60072e12i	0.138054	+	0.239116i
$849$	−5.15172e12	−	2.74707e13i	−0.340305	−	1.81462i
$850$	4.40184e12	−	7.62421e12i	0.289234	−	0.500968i
$851$	−3.58370e12	+	6.20716e12i	−0.234234	+	0.405704i
$852$	−4.55190e12	−	2.42722e13i	−0.295947	−	1.57809i
$853$	8.44918e12	+	1.46344e13i	0.546442	+	0.946466i	0.998515	+	0.0544843i	$0.0173515\pi$
$853$	8.44918e12	+	1.46344e13i	0.546442	+	0.946466i	−0.452073	+	0.891981i	$0.649315\pi$
$854$	−4.60575e13			−2.96306
$855$	1.85060e12	+	1.48562e12i	0.118431	+	0.0950738i
$856$	1.44162e13			0.917736
$857$	6.90715e12	+	1.19635e13i	0.437407	+	0.757611i	0.997489	−	0.0708265i	$-0.0225637\pi$
$857$	6.90715e12	+	1.19635e13i	0.437407	+	0.757611i	−0.560082	+	0.828437i	$0.689230\pi$
$858$	−3.29893e13	−	1.16034e13i	−2.07816	−	0.730957i
$859$	1.13677e12	−	1.96894e12i	0.0712365	−	0.123385i	−0.828207	−	0.560422i	$-0.810639\pi$
$859$	1.13677e12	−	1.96894e12i	0.0712365	−	0.123385i	0.899443	+	0.437037i	$0.143972\pi$
$860$	−5.53189e12	+	9.58152e12i	−0.344850	+	0.597298i
$861$	−1.70926e13	+	1.46613e13i	−1.05997	+	0.909198i
$862$	−1.31108e12	−	2.27085e12i	−0.0808808	−	0.140090i
$863$	−1.15324e13			−0.707735			−0.353867	−	0.935296i	$-0.615134\pi$
$863$	−1.15324e13			−0.707735			−0.353867	+	0.935296i	$0.615134\pi$
$864$	1.31615e13	−	4.28516e11i	0.803512	−	0.0261611i
$865$	−3.41131e12			−0.207181
$866$	1.93530e13	+	3.35203e13i	1.16928	+	2.02525i
$867$	−2.62733e13	+	2.25362e13i	−1.57917	+	1.35455i
$868$	1.75273e13	−	3.03582e13i	1.04804	−	1.81525i
$869$	2.36178e11	−	4.09072e11i	0.0140492	−	0.0243339i
$870$	−1.85972e12	−	6.54124e11i	−0.110055	−	0.0387100i
$871$	−1.47354e13	−	2.55225e13i	−0.867523	−	1.50259i
$872$	−7.17596e12			−0.420297
$873$	6.92527e12	−	2.69214e12i	0.403527	−	0.156868i
$874$	1.36075e13			0.788818
$875$	1.33024e12	+	2.30404e12i	0.0767174	+	0.132878i
$876$	−8.67932e12	−	4.62810e13i	−0.497986	−	2.65543i
$877$	−1.28644e13	+	2.22819e13i	−0.734333	+	1.27190i	0.220683	+	0.975346i	$0.429171\pi$
$877$	−1.28644e13	+	2.22819e13i	−0.734333	+	1.27190i	−0.955015	+	0.296556i	$0.904162\pi$
$878$	−1.97387e13	+	3.41884e13i	−1.12097	+	1.94157i
$879$	−3.45616e12	−	1.84294e13i	−0.195274	−	1.04126i
$880$	7.84970e11	+	1.35961e12i	0.0441246	+	0.0764261i
$881$	−2.74537e12			−0.153536			−0.0767678	−	0.997049i	$-0.524460\pi$
$881$	−2.74537e12			−0.153536			−0.0767678	+	0.997049i	$0.524460\pi$
$882$	8.75989e12	−	5.68691e13i	0.487405	−	3.16423i
$883$	−2.05360e13			−1.13682			−0.568412	−	0.822744i	$-0.692442\pi$
$883$	−2.05360e13			−1.13682			−0.568412	+	0.822744i	$0.692442\pi$
$884$	−4.21862e13	−	7.30686e13i	−2.32346	−	4.02435i
$885$	−5.24773e12	−	1.84579e12i	−0.287559	−	0.101144i
$886$	−2.37154e13	+	4.10762e13i	−1.29294	+	2.23944i
$887$	−5.88393e12	+	1.01913e13i	−0.319162	+	0.552805i	−0.980313	−	0.197448i	$-0.936735\pi$
$887$	−5.88393e12	+	1.01913e13i	−0.319162	+	0.552805i	0.661151	+	0.750253i	$0.270068\pi$
$888$	5.51252e12	−	4.72840e12i	0.297503	−	0.255186i
$889$	−4.62872e12	−	8.01717e12i	−0.248544	−	0.430490i
$890$	1.44448e13			0.771716
$891$	3.52345e12	+	1.59111e13i	0.187292	+	0.845768i
$892$	−9.47155e12			−0.500933
$893$	1.44757e11	+	2.50726e11i	0.00761742	+	0.0131938i
$894$	−3.81251e12	+	3.27021e12i	−0.199614	+	0.171221i
$895$	−3.52338e12	+	6.10267e12i	−0.183551	+	0.317919i
$896$	2.90355e13	−	5.02909e13i	1.50502	−	2.60678i
$897$	3.97871e13	+	1.39944e13i	2.05199	+	0.721752i
$898$	−1.04985e13	−	1.81840e13i	−0.538747	−	0.933137i
$899$	−2.20804e12			−0.112743
$900$	1.02821e12	−	6.67509e12i	0.0522383	−	0.339130i
$901$	4.20826e13			2.12736
$902$	−1.15516e13	−	2.00079e13i	−0.581048	−	1.00640i
$903$	5.67895e12	+	3.02821e13i	0.284232	+	1.51562i
$904$	1.11175e12	−	1.92560e12i	0.0553666	−	0.0958977i
$905$	−1.41289e12	+	2.44719e12i	−0.0700147	+	0.121269i
$906$	8.87358e12	+	4.73169e13i	0.437544	+	2.33313i
$907$	8.74959e12	+	1.51547e13i	0.429294	+	0.743559i	0.996811	−	0.0798029i	$-0.0254291\pi$
$907$	8.74959e12	+	1.51547e13i	0.429294	+	0.743559i	−0.567517	+	0.823362i	$0.692096\pi$
$908$	9.11353e11			0.0444939
$909$	−1.38816e13	+	5.39636e12i	−0.674375	+	0.262158i
$910$	4.03591e13			1.95099
$911$	−1.10016e12	−	1.90554e12i	−0.0529206	−	0.0916612i	0.838352	−	0.545130i	$-0.183520\pi$
$911$	−1.10016e12	−	1.90554e12i	−0.0529206	−	0.0916612i	−0.891272	+	0.453469i	$0.850186\pi$
$912$	−1.52461e12	−	5.36254e11i	−0.0729763	−	0.0256681i
$913$	−1.43562e13	+	2.48657e13i	−0.683788	+	1.18436i
$914$	3.16474e13	−	5.48149e13i	1.49996	−	2.59801i
$915$	−7.54382e12	+	6.47077e12i	−0.355792	+	0.305183i
$916$	2.58789e13	+	4.48236e13i	1.21455	+	2.10367i
$917$	−5.04280e13			−2.35510
$918$	−2.93476e13	+	5.48820e13i	−1.36389	+	2.55057i
$919$	−1.16444e13			−0.538513			−0.269257	−	0.963068i	$-0.586778\pi$
$919$	−1.16444e13			−0.538513			−0.269257	+	0.963068i	$0.586778\pi$
$920$	−8.07691e12	−	1.39896e13i	−0.371707	−	0.643815i
$921$	1.55314e13	−	1.33221e13i	0.711281	−	0.610107i
$922$	1.71339e13	−	2.96768e13i	0.780850	−	1.35247i
$923$	1.59225e13	−	2.75786e13i	0.722111	−	1.25073i
$924$	5.32904e13	+	1.87439e13i	2.40506	+	0.845935i
$925$	7.40009e11	+	1.28173e12i	0.0332353	+	0.0575652i
$926$	−2.43344e13			−1.08760
$927$	−2.83728e12	−	2.27771e12i	−0.126196	−	0.101307i
$928$	−2.87525e12			−0.127265
$929$	−3.48739e12	−	6.04034e12i	−0.153614	−	0.266067i	0.778940	−	0.627099i	$-0.215758\pi$
$929$	−3.48739e12	−	6.04034e12i	−0.153614	−	0.266067i	−0.932553	+	0.361032i	$0.882424\pi$
$930$	−2.20700e12	−	1.17684e13i	−0.0967450	−	0.515877i
$931$	7.56183e12	−	1.30975e13i	0.329878	−	0.571365i
$932$	−1.99302e12	+	3.45201e12i	−0.0865246	+	0.149865i
$933$	−2.47807e12	−	1.32139e13i	−0.107065	−	0.570905i
$934$	2.76683e13	+	4.79228e13i	1.18965	+	2.06054i
$935$	1.58901e13			0.679945
$936$	−3.33266e13	−	2.67539e13i	−1.41922	−	1.13932i
$937$	−1.38125e13			−0.585389			−0.292695	−	0.956206i	$-0.594552\pi$
$937$	−1.38125e13			−0.585389			−0.292695	+	0.956206i	$0.594552\pi$
$938$	3.76777e13	+	6.52597e13i	1.58918	+	2.75253i
$939$	3.74011e13	+	1.31552e13i	1.56996	+	0.552205i
$940$	4.11970e11	−	7.13553e11i	0.0172104	−	0.0298092i
$941$	−1.16009e13	+	2.00934e13i	−0.482325	+	0.835411i	−0.999794	−	0.0202908i	$-0.993541\pi$
$941$	−1.16009e13	+	2.00934e13i	−0.482325	+	0.835411i	0.517469	+	0.855702i	$0.326874\pi$
$942$	−8.32606e11	+	7.14175e11i	−0.0344517	+	0.0295512i
$943$	1.39319e13	+	2.41308e13i	0.573731	+	0.993731i
$944$	3.78847e12			0.155271
$945$	−9.92892e12	−	1.59733e13i	−0.405004	−	0.651558i
$946$	−3.16090e13			−1.28322
$947$	−1.20278e13	−	2.08327e13i	−0.485970	−	0.841725i	0.513900	−	0.857850i	$-0.328200\pi$
$947$	−1.20278e13	−	2.08327e13i	−0.485970	−	0.841725i	−0.999870	+	0.0161249i	$0.994867\pi$
$948$	1.05040e12	−	9.00991e11i	0.0422394	−	0.0362312i
$949$	3.03602e13	−	5.25854e13i	1.21509	−	2.10459i
$950$	1.40493e12	−	2.43340e12i	0.0559625	−	0.0969299i
$951$	−2.52974e13	−	8.89792e12i	−1.00292	−	0.352757i
$952$	4.49949e13	+	7.79334e13i	1.77540	+	3.07509i
$953$	3.58676e13			1.40859			0.704295	−	0.709907i	$-0.251263\pi$
$953$	3.58676e13			1.40859			0.704295	+	0.709907i	$0.251263\pi$
$954$	4.76291e13	−	1.85154e13i	1.86168	−	0.723713i
$955$	1.32591e13			0.515821
$956$	9.21373e12	+	1.59587e13i	0.356759	+	0.617925i
$957$	−6.55866e11	−	3.49730e12i	−0.0252762	−	0.134781i
$958$	−1.39167e13	+	2.41044e13i	−0.533816	+	0.924596i
$959$	−1.97438e12	+	3.41973e12i	−0.0753785	+	0.130559i
$960$	−3.36805e12	−	1.79596e13i	−0.127985	−	0.682458i
$961$	6.51440e12	+	1.12833e13i	0.246388	+	0.426756i
$962$	2.24517e13			0.845202
$963$	3.16178e12	−	2.05262e13i	0.118471	−	0.769113i
$964$	−4.16783e13			−1.55440
$965$	−1.23191e12	−	2.13373e12i	−0.0457304	−	0.0792074i
$966$	−1.01733e14	−	3.57829e13i	−3.75895	−	1.32214i
$967$	1.69645e13	−	2.93834e13i	0.623910	−	1.08064i	−0.364841	−	0.931070i	$-0.618877\pi$
$967$	1.69645e13	−	2.93834e13i	0.623910	−	1.08064i	0.988751	−	0.149574i	$-0.0477902\pi$
$968$	4.02057e12	−	6.96383e12i	0.147180	−	0.254923i
$969$	−1.24161e13	+	1.06500e13i	−0.452407	+	0.388056i
$970$	−4.39873e12	−	7.61883e12i	−0.159535	−	0.276322i
$971$	4.36066e12			0.157422			0.0787110	−	0.996897i	$-0.474920\pi$
$971$	4.36066e12			0.157422			0.0787110	+	0.996897i	$0.474920\pi$
$972$	−5.72929e12	+	4.73998e13i	−0.205875	+	1.70325i
$973$	−2.51581e13			−0.899849
$974$	2.58916e13	+	4.48456e13i	0.921815	+	1.59663i
$975$	6.61046e12	−	5.67018e12i	0.234267	−	0.200944i
$976$	3.38430e12	−	5.86177e12i	0.119383	−	0.206778i
$977$	2.55081e13	−	4.41814e13i	0.895680	−	1.55136i	0.0627203	−	0.998031i	$-0.480022\pi$
$977$	2.55081e13	−	4.41814e13i	0.895680	−	1.55136i	0.832960	−	0.553333i	$-0.186644\pi$
$978$	3.70381e13	+	1.30275e13i	1.29456	+	0.455340i
$979$	1.30360e13	+	2.25790e13i	0.453547	+	0.785567i
$980$	−4.30411e13			−1.49062
$981$	−1.57384e12	+	1.02174e13i	−0.0542564	+	0.352232i
$982$	−8.35540e13			−2.86725
$983$	1.90377e13	+	3.29742e13i	0.650314	+	1.12638i	0.983047	+	0.183355i	$0.0586959\pi$
$983$	1.90377e13	+	3.29742e13i	0.650314	+	1.12638i	−0.332733	+	0.943021i	$0.607971\pi$
$984$	−5.20414e12	−	2.77502e13i	−0.176958	−	0.943601i
$985$	−3.37607e12	+	5.84752e12i	−0.114274	+	0.197929i
$986$	6.79443e12	−	1.17683e13i	0.228932	−	0.396522i
$987$	−4.22922e11	−	2.25516e12i	−0.0141851	−	0.0756398i
$988$	−1.34645e13	−	2.33211e13i	−0.449555	−	0.778652i
$989$	3.81224e13			1.26706
$990$	1.79844e13	−	6.99130e12i	0.595029	−	0.231313i
$991$	−3.62637e12			−0.119437			−0.0597187	−	0.998215i	$-0.519020\pi$
$991$	−3.62637e12			−0.119437			−0.0597187	+	0.998215i	$0.519020\pi$
$992$	−8.73162e12	−	1.51236e13i	−0.286281	−	0.495853i
$993$	3.90239e12	+	1.37260e12i	0.127368	+	0.0447993i
$994$	−4.07130e13	+	7.05171e13i	−1.32280	+	2.29116i
$995$	5.24777e12	−	9.08941e12i	0.169735	−	0.293990i
$996$	−6.38494e13	+	5.47673e13i	−2.05584	+	1.76341i
$997$	−3.67454e12	−	6.36449e12i	−0.117781	−	0.204002i	0.801107	−	0.598521i	$-0.204245\pi$
$997$	−3.67454e12	−	6.36449e12i	−0.117781	−	0.204002i	−0.918888	+	0.394519i	$0.870911\pi$
$998$	5.43134e13			1.73308
$999$	−5.52344e12	−	8.88594e12i	−0.175455	−	0.282266i

Display

a_p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.10.e.a.31.2	yes	34
3.2	odd	2		135.10.e.a.91.16		34
9.2	odd	6		135.10.e.a.46.16		34
9.7	even	3	inner	45.10.e.a.16.2	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.10.e.a.16.2	✓	34	9.7	even	3	inner
45.10.e.a.31.2	yes	34	1.1	even	1	trivial
135.10.e.a.46.16		34	9.2	odd	6
135.10.e.a.91.16		34	3.2	odd	2

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	45.10.e.a.31.2

Level	$45$
Weight	$10$
Character	45.31
Analytic conductor	$23.177$
Analytic rank	$0$
Dimension	$34$
Inner twists	$2$