LMFDB - Embedded newform 48.9.i.a.29.49

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$124$
Relative dimension:	$62$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.49
Character	$\chi$	$=$	48.29
Dual form			48.9.i.a.5.49

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.8620 + 9.51679i) q^{2} +(-79.8454 - 13.6278i) q^{3} +(74.8613 + 244.810i) q^{4} +(792.195 + 792.195i) q^{5} +(-897.276 - 935.153i) q^{6} -2103.96i q^{7} +(-1366.94 + 3861.18i) q^{8} +(6189.56 + 2176.24i) q^{9} +O(q^{10})$	\(q+(12.8620 + 9.51679i) q^{2} +(-79.8454 - 13.6278i) q^{3} +(74.8613 + 244.810i) q^{4} +(792.195 + 792.195i) q^{5} +(-897.276 - 935.153i) q^{6} -2103.96i q^{7} +(-1366.94 + 3861.18i) q^{8} +(6189.56 + 2176.24i) q^{9} +(2650.04 + 17728.3i) q^{10} +(10440.0 + 10440.0i) q^{11} +(-2641.10 - 20567.1i) q^{12} +(-20888.5 - 20888.5i) q^{13} +(20023.0 - 27061.1i) q^{14} +(-52457.2 - 74049.0i) q^{15} +(-54327.6 + 36653.6i) q^{16} +149626. i q^{17} +(58899.2 + 86895.6i) q^{18} +(-14625.2 - 14625.2i) q^{19} +(-134632. + 253242. i) q^{20} +(-28672.5 + 167992. i) q^{21} +(34923.7 + 233634. i) q^{22} -363633. q^{23} +(161763. - 289669. i) q^{24} +864520. i q^{25} +(-69876.2 - 467460. i) q^{26} +(-464550. - 258113. i) q^{27} +(515071. - 157505. i) q^{28} +(-285083. + 285083. i) q^{29} +(30005.6 - 1.45164e6i) q^{30} +509822. q^{31} +(-1.04758e6 - 45586.7i) q^{32} +(-691309. - 975858. i) q^{33} +(-1.42396e6 + 1.92448e6i) q^{34} +(1.66675e6 - 1.66675e6i) q^{35} +(-69406.0 + 1.67818e6i) q^{36} +(1.08753e6 - 1.08753e6i) q^{37} +(-48924.0 - 327294. i) q^{38} +(1.38319e6 + 1.95252e6i) q^{39} +(-4.14169e6 + 1.97592e6i) q^{40} -805987. q^{41} +(-1.96753e6 + 1.88784e6i) q^{42} +(2.25502e6 - 2.25502e6i) q^{43} +(-1.77426e6 + 3.33736e6i) q^{44} +(3.17933e6 + 6.62735e6i) q^{45} +(-4.67705e6 - 3.46062e6i) q^{46} -171169. i q^{47} +(4.83731e6 - 2.18625e6i) q^{48} +1.33814e6 q^{49} +(-8.22745e6 + 1.11194e7i) q^{50} +(2.03908e6 - 1.19469e7i) q^{51} +(3.54997e6 - 6.67746e6i) q^{52} +(274252. + 274252. i) q^{53} +(-3.51863e6 - 7.74088e6i) q^{54} +1.65410e7i q^{55} +(8.12378e6 + 2.87599e6i) q^{56} +(968443. + 1.36706e6i) q^{57} +(-6.37980e6 + 953656. i) q^{58} +(1.53059e7 + 1.53059e7i) q^{59} +(1.42009e7 - 1.83854e7i) q^{60} +(-1.03351e6 - 1.03351e6i) q^{61} +(6.55732e6 + 4.85187e6i) q^{62} +(4.57873e6 - 1.30226e7i) q^{63} +(-1.30402e7 - 1.05560e7i) q^{64} -3.30956e7i q^{65} +(395430. - 1.91305e7i) q^{66} +(-1.80334e7 - 1.80334e7i) q^{67} +(-3.66298e7 + 1.12012e7i) q^{68} +(2.90344e7 + 4.95554e6i) q^{69} +(3.72998e7 - 5.57560e6i) q^{70} +2.46586e7 q^{71} +(-1.68636e7 + 2.09242e7i) q^{72} +1.45791e7i q^{73} +(2.43375e7 - 3.63799e6i) q^{74} +(1.17815e7 - 6.90279e7i) q^{75} +(2.48553e6 - 4.67525e6i) q^{76} +(2.19653e7 - 2.19653e7i) q^{77} +(-791185. + 3.82768e7i) q^{78} +3.44767e7 q^{79} +(-7.20748e7 - 1.40013e7i) q^{80} +(3.35747e7 + 2.69400e7i) q^{81} +(-1.03666e7 - 7.67041e6i) q^{82} +(-2.71225e7 + 2.71225e7i) q^{83} +(-4.32725e7 + 5.55678e6i) q^{84} +(-1.18533e8 + 1.18533e8i) q^{85} +(5.04646e7 - 7.54348e6i) q^{86} +(2.66476e7 - 1.88775e7i) q^{87} +(-5.45814e7 + 2.60398e7i) q^{88} +3.89270e7 q^{89} +(-2.21785e7 + 1.15498e8i) q^{90} +(-4.39487e7 + 4.39487e7i) q^{91} +(-2.72221e7 - 8.90209e7i) q^{92} +(-4.07069e7 - 6.94778e6i) q^{93} +(1.62898e6 - 2.20157e6i) q^{94} -2.31720e7i q^{95} +(8.30235e7 + 1.79162e7i) q^{96} +1.38769e8 q^{97} +(1.72111e7 + 1.27348e7i) q^{98} +(4.18990e7 + 8.73388e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 124 q - 2 q^{3} - 4 q^{4} - 3236 q^{6}+O(q^{10}) $ 124 * q - 2 * q^3 - 4 * q^4 - 3236 * q^6	$ 124 q - 2 q^{3} - 4 q^{4} - 3236 q^{6} + 17496 q^{10} + 8608 q^{12} - 4 q^{13} - 4 q^{15} - 116560 q^{16} - 290364 q^{18} - 167556 q^{19} + 13120 q^{21} + 190552 q^{22} - 714296 q^{24} - 25538 q^{27} + 1391160 q^{28} + 3794052 q^{30} - 8 q^{31} - 4 q^{33} + 2752744 q^{34} + 1313476 q^{36} - 4 q^{37} + 12578584 q^{40} - 5150600 q^{42} + 5384956 q^{43} - 781252 q^{45} - 25980296 q^{46} + 26695408 q^{48} - 82354308 q^{49} - 15081600 q^{51} + 24748672 q^{52} - 38189720 q^{54} + 74539832 q^{58} + 68522688 q^{60} + 24476028 q^{61} + 23059200 q^{63} - 63032488 q^{64} + 79650868 q^{66} - 74704388 q^{67} - 13124 q^{69} + 109805784 q^{70} - 100711608 q^{72} - 99849278 q^{75} - 151417912 q^{76} + 158736908 q^{78} - 72203272 q^{79} - 4 q^{81} + 98422144 q^{82} + 7625392 q^{84} - 105397504 q^{85} + 53374432 q^{88} + 175196592 q^{90} - 152141184 q^{91} + 138242812 q^{93} + 114812016 q^{94} - 193537240 q^{96} - 8 q^{97} + 228915068 q^{99}+O(q^{100}) $ 124 * q - 2 * q^3 - 4 * q^4 - 3236 * q^6 + 17496 * q^10 + 8608 * q^12 - 4 * q^13 - 4 * q^15 - 116560 * q^16 - 290364 * q^18 - 167556 * q^19 + 13120 * q^21 + 190552 * q^22 - 714296 * q^24 - 25538 * q^27 + 1391160 * q^28 + 3794052 * q^30 - 8 * q^31 - 4 * q^33 + 2752744 * q^34 + 1313476 * q^36 - 4 * q^37 + 12578584 * q^40 - 5150600 * q^42 + 5384956 * q^43 - 781252 * q^45 - 25980296 * q^46 + 26695408 * q^48 - 82354308 * q^49 - 15081600 * q^51 + 24748672 * q^52 - 38189720 * q^54 + 74539832 * q^58 + 68522688 * q^60 + 24476028 * q^61 + 23059200 * q^63 - 63032488 * q^64 + 79650868 * q^66 - 74704388 * q^67 - 13124 * q^69 + 109805784 * q^70 - 100711608 * q^72 - 99849278 * q^75 - 151417912 * q^76 + 158736908 * q^78 - 72203272 * q^79 - 4 * q^81 + 98422144 * q^82 + 7625392 * q^84 - 105397504 * q^85 + 53374432 * q^88 + 175196592 * q^90 - 152141184 * q^91 + 138242812 * q^93 + 114812016 * q^94 - 193537240 * q^96 - 8 * q^97 + 228915068 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	12.8620	+	9.51679i	0.803874	+	0.594800i
$2$	12.8620	+	9.51679i	0.803874	+	0.594800i
$3$	−79.8454	−	13.6278i	−0.985745	−	0.168245i
$3$	−79.8454	−	13.6278i	−0.985745	−	0.168245i
$4$	74.8613	+	244.810i	0.292427	+	0.956288i
$5$	792.195	+	792.195i	1.26751	+	1.26751i	0.947370	+	0.320142i	$0.103731\pi$
$5$	792.195	+	792.195i	1.26751	+	1.26751i	0.320142	+	0.947370i	$0.396269\pi$
$6$	−897.276	−	935.153i	−0.692343	−	0.721569i
$7$		−	2103.96i		−	0.876286i	−0.898905	−	0.438143i	$-0.855636\pi$
$7$		−	2103.96i		−	0.876286i	0.898905	−	0.438143i	$-0.144364\pi$
$8$	−1366.94	+	3861.18i	−0.333725	+	0.942670i
$9$	6189.56	+	2176.24i	0.943387	+	0.331693i
$10$	2650.04	+	17728.3i	0.265004	+	1.77283i
$11$	10440.0	+	10440.0i	0.713065	+	0.713065i	0.967175	−	0.254111i	$-0.0817827\pi$
$11$	10440.0	+	10440.0i	0.713065	+	0.713065i	−0.254111	+	0.967175i	$0.581783\pi$
$12$	−2641.10	−	20567.1i	−0.127368	−	0.991856i
$13$	−20888.5	−	20888.5i	−0.731366	−	0.731366i	0.239524	−	0.970890i	$-0.423008\pi$
$13$	−20888.5	−	20888.5i	−0.731366	−	0.731366i	−0.970890	+	0.239524i	$0.923008\pi$
$14$	20023.0	−	27061.1i	0.521215	−	0.704424i
$15$	−52457.2	−	74049.0i	−1.03619	−	1.46270i
$16$	−54327.6	+	36653.6i	−0.828973	+	0.559289i
$17$			149626.i			1.79147i	0.444585	+	0.895737i	$0.353351\pi$
$17$			149626.i			1.79147i	−0.444585	+	0.895737i	$0.646649\pi$
$18$	58899.2	+	86895.6i	0.561073	+	0.827766i
$19$	−14625.2	−	14625.2i	−0.112224	−	0.112224i	0.648765	−	0.760989i	$-0.275286\pi$
$19$	−14625.2	−	14625.2i	−0.112224	−	0.112224i	−0.760989	+	0.648765i	$0.775286\pi$
$20$	−134632.	+	253242.i	−0.841451	+	1.58276i
$21$	−28672.5	+	167992.i	−0.147431	+	0.863795i
$22$	34923.7	+	233634.i	0.149084	+	0.997345i
$23$	−363633.			−1.29943			−0.649714	−	0.760179i	$-0.725111\pi$
$23$	−363633.			−1.29943			−0.649714	+	0.760179i	$0.725111\pi$
$24$	161763.	−	289669.i	0.487568	−	0.873085i
$25$			864520.i			2.21317i
$26$	−69876.2	−	467460.i	−0.152910	−	1.02294i
$27$	−464550.	−	258113.i	−0.874134	−	0.485686i
$28$	515071.	−	157505.i	0.837982	−	0.256250i
$29$	−285083.	+	285083.i	−0.403068	+	0.403068i	−0.879313	−	0.476244i	$-0.841998\pi$
$29$	−285083.	+	285083.i	−0.403068	+	0.403068i	0.476244	+	0.879313i	$0.341998\pi$
$30$	30005.6	−	1.45164e6i	0.0370439	−	1.79215i
$31$	509822.			0.552042			0.276021	−	0.961152i	$-0.410984\pi$
$31$	509822.			0.552042			0.276021	+	0.961152i	$0.410984\pi$
$32$	−1.04758e6	−	45586.7i	−0.999055	−	0.0434749i
$33$	−691309.	−	975858.i	−0.582930	−	0.822870i
$34$	−1.42396e6	+	1.92448e6i	−1.06557	+	1.44012i
$35$	1.66675e6	−	1.66675e6i	1.11070	−	1.11070i
$36$	−69406.0	+	1.67818e6i	−0.0413225	+	0.999146i
$37$	1.08753e6	−	1.08753e6i	0.580274	−	0.580274i	−0.354705	−	0.934978i	$-0.615419\pi$
$37$	1.08753e6	−	1.08753e6i	0.580274	−	0.580274i	0.934978	+	0.354705i	$0.115419\pi$
$38$	−48924.0	−	327294.i	−0.0234632	−	0.156965i
$39$	1.38319e6	+	1.95252e6i	0.597892	+	0.843989i
$40$	−4.14169e6	+	1.97592e6i	−1.61785	+	0.771845i
$41$	−805987.			−0.285228			−0.142614	−	0.989778i	$-0.545551\pi$
$41$	−805987.			−0.285228			−0.142614	+	0.989778i	$0.545551\pi$
$42$	−1.96753e6	+	1.88784e6i	−0.632301	+	0.606691i
$43$	2.25502e6	−	2.25502e6i	0.659595	−	0.659595i	−0.295690	−	0.955284i	$-0.595549\pi$
$43$	2.25502e6	−	2.25502e6i	0.659595	−	0.659595i	0.955284	+	0.295690i	$0.0955494\pi$
$44$	−1.77426e6	+	3.33736e6i	−0.473376	+	0.890414i
$45$	3.17933e6	+	6.62735e6i	0.775329	+	1.61618i
$46$	−4.67705e6	−	3.46062e6i	−1.04458	−	0.772899i
$47$		−	171169.i		−	0.0350779i	−0.999846	−	0.0175389i	$-0.994417\pi$
$47$		−	171169.i		−	0.0350779i	0.999846	−	0.0175389i	$-0.00558310\pi$
$48$	4.83731e6	−	2.18625e6i	0.911254	−	0.411846i
$49$	1.33814e6			0.232122
$50$	−8.22745e6	+	1.11194e7i	−1.31639	+	1.77911i
$51$	2.03908e6	−	1.19469e7i	0.301406	−	1.76594i
$52$	3.54997e6	−	6.67746e6i	0.485525	−	0.913267i
$53$	274252.	+	274252.i	0.0347573	+	0.0347573i	0.724272	−	0.689515i	$-0.242176\pi$
$53$	274252.	+	274252.i	0.0347573	+	0.0347573i	−0.689515	+	0.724272i	$0.742176\pi$
$54$	−3.51863e6	−	7.74088e6i	−0.413808	−	0.910364i
$55$			1.65410e7i			1.80764i
$56$	8.12378e6	+	2.87599e6i	0.826049	+	0.292439i
$57$	968443.	+	1.36706e6i	0.0917434	+	0.129506i
$58$	−6.37980e6	+	953656.i	−0.563761	+	0.0842714i
$59$	1.53059e7	+	1.53059e7i	1.26314	+	1.26314i	0.949564	+	0.313574i	$0.101526\pi$
$59$	1.53059e7	+	1.53059e7i	1.26314	+	1.26314i	0.313574	+	0.949564i	$0.398474\pi$
$60$	1.42009e7	−	1.83854e7i	1.09575	−	1.41863i
$61$	−1.03351e6	−	1.03351e6i	−0.0746441	−	0.0746441i	0.668799	−	0.743443i	$-0.266809\pi$
$61$	−1.03351e6	−	1.03351e6i	−0.0746441	−	0.0746441i	−0.743443	+	0.668799i	$0.766809\pi$
$62$	6.55732e6	+	4.85187e6i	0.443772	+	0.328354i
$63$	4.57873e6	−	1.30226e7i	0.290659	−	0.826677i
$64$	−1.30402e7	−	1.05560e7i	−0.777255	−	0.629186i
$65$		−	3.30956e7i		−	1.85403i
$66$	395430.	−	1.91305e7i	0.0208398	−	1.00821i
$67$	−1.80334e7	−	1.80334e7i	−0.894908	−	0.894908i	0.100072	−	0.994980i	$-0.468093\pi$
$67$	−1.80334e7	−	1.80334e7i	−0.894908	−	0.894908i	−0.994980	+	0.100072i	$0.968093\pi$
$68$	−3.66298e7	+	1.12012e7i	−1.71316	+	0.523875i
$69$	2.90344e7	+	4.95554e6i	1.28090	+	0.218622i
$70$	3.72998e7	−	5.57560e6i	1.55351	−	0.232220i
$71$	2.46586e7			0.970365			0.485182	−	0.874413i	$-0.338753\pi$
$71$	2.46586e7			0.970365			0.485182	+	0.874413i	$0.338753\pi$
$72$	−1.68636e7	+	2.09242e7i	−0.627510	+	0.778609i
$73$			1.45791e7i			0.513382i	0.966494	+	0.256691i	$0.0826322\pi$
$73$			1.45791e7i			0.513382i	−0.966494	+	0.256691i	$0.917368\pi$
$74$	2.43375e7	−	3.63799e6i	0.811614	−	0.121321i
$75$	1.17815e7	−	6.90279e7i	0.372355	−	2.18162i
$76$	2.48553e6	−	4.67525e6i	0.0745013	−	0.140136i
$77$	2.19653e7	−	2.19653e7i	0.624849	−	0.624849i
$78$	−791185.	+	3.82768e7i	−0.0213747	+	1.03409i
$79$	3.44767e7			0.885151			0.442575	−	0.896731i	$-0.354065\pi$
$79$	3.44767e7			0.885151			0.442575	+	0.896731i	$0.354065\pi$
$80$	−7.20748e7	−	1.40013e7i	−1.75964	−	0.341828i
$81$	3.35747e7	+	2.69400e7i	0.779959	+	0.625831i
$82$	−1.03666e7	−	7.67041e6i	−0.229288	−	0.169654i
$83$	−2.71225e7	+	2.71225e7i	−0.571501	+	0.571501i	−0.932548	−	0.361047i	$-0.882419\pi$
$83$	−2.71225e7	+	2.71225e7i	−0.571501	+	0.571501i	0.361047	+	0.932548i	$0.382419\pi$
$84$	−4.32725e7	+	5.55678e6i	−0.869150	+	0.111611i
$85$	−1.18533e8	+	1.18533e8i	−2.27071	+	2.27071i
$86$	5.04646e7	−	7.54348e6i	0.922558	−	0.137904i
$87$	2.66476e7	−	1.88775e7i	0.465137	−	0.329509i
$88$	−5.45814e7	+	2.60398e7i	−0.910153	+	0.434217i
$89$	3.89270e7			0.620428			0.310214	−	0.950667i	$-0.399599\pi$
$89$	3.89270e7			0.620428			0.310214	+	0.950667i	$0.399599\pi$
$90$	−2.21785e7	+	1.15498e8i	−0.338036	+	1.76037i
$91$	−4.39487e7	+	4.39487e7i	−0.640886	+	0.640886i
$92$	−2.72221e7	−	8.90209e7i	−0.379988	−	1.24263i
$93$	−4.07069e7	−	6.94778e6i	−0.544172	−	0.0928783i
$94$	1.62898e6	−	2.20157e6i	0.0208643	−	0.0281982i
$95$		−	2.31720e7i		−	0.284491i
$96$	8.30235e7	+	1.79162e7i	0.977499	+	0.210941i
$97$	1.38769e8			1.56750			0.783748	−	0.621078i	$-0.213305\pi$
$97$	1.38769e8			1.56750			0.783748	+	0.621078i	$0.213305\pi$
$98$	1.72111e7	+	1.27348e7i	0.186597	+	0.138066i
$99$	4.18990e7	+	8.73388e7i	0.436177	+	0.909215i
$100$	−2.11643e8	+	6.47191e7i	−2.11643	+	0.647191i
$101$	−1.14533e8	−	1.14533e8i	−1.10064	−	1.10064i	−0.994333	−	0.106311i	$-0.966096\pi$
$101$	−1.14533e8	−	1.14533e8i	−1.10064	−	1.10064i	−0.106311	−	0.994333i	$-0.533904\pi$
$102$	1.39923e8	−	1.34256e8i	1.29267	−	1.24031i
$103$		−	6.22988e7i		−	0.553517i	−0.960940	−	0.276758i	$-0.910740\pi$
$103$		−	6.22988e7i		−	0.553517i	0.960940	−	0.276758i	$-0.0892602\pi$
$104$	1.09208e8	−	5.21010e7i	0.933512	−	0.445362i
$105$	−1.55796e8	+	1.10368e8i	−1.28174	+	0.908000i
$106$	917425.	+	6.13742e6i	0.00726686	+	0.0486141i
$107$	4.22271e7	+	4.22271e7i	0.322148	+	0.322148i	0.849591	−	0.527442i	$-0.176849\pi$
$107$	4.22271e7	+	4.22271e7i	0.322148	+	0.322148i	−0.527442	+	0.849591i	$0.676849\pi$
$108$	2.84117e7	−	1.33049e8i	0.208835	−	0.977951i
$109$	3.21388e7	+	3.21388e7i	0.227680	+	0.227680i	0.811723	−	0.584043i	$-0.198530\pi$
$109$	3.21388e7	+	3.21388e7i	0.227680	+	0.227680i	−0.584043	+	0.811723i	$0.698530\pi$
$110$	−1.57417e8	+	2.12750e8i	−1.07518	+	1.45311i
$111$	−1.01655e8	+	7.20133e7i	−0.669630	+	0.474374i
$112$	7.71177e7	+	1.14303e8i	0.490097	+	0.726418i
$113$			9.52710e7i			0.584315i	0.956370	+	0.292157i	$0.0943731\pi$
$113$			9.52710e7i			0.584315i	−0.956370	+	0.292157i	$0.905627\pi$
$114$	−553951.	+	2.67996e7i	−0.00327983	+	0.158675i
$115$	−2.88068e8	−	2.88068e8i	−1.64704	−	1.64704i
$116$	−9.11327e7	−	4.84493e7i	−0.503318	−	0.267581i
$117$	−8.38324e7	−	1.74749e8i	−0.447372	−	0.932550i
$118$	5.12012e7	+	3.42527e8i	0.264090	+	1.76672i
$119$	3.14807e8			1.56984
$120$	3.57622e8	−	1.01326e8i	1.72464	−	0.488648i
$121$			3.62746e6i			0.0169224i
$122$	−3.45729e6	−	2.31287e7i	−0.0156062	−	0.104403i
$123$	6.43543e7	+	1.09839e7i	0.281162	+	0.0479882i
$124$	3.81660e7	+	1.24809e8i	0.161432	+	0.527911i
$125$	−3.75417e8	+	3.75417e8i	−1.53771	+	1.53771i
$126$	1.82825e8	−	1.23922e8i	0.725360	−	0.491661i
$127$	−3.74074e7			−0.143795			−0.0718973	−	0.997412i	$-0.522905\pi$
$127$	−3.74074e7			−0.143795			−0.0718973	+	0.997412i	$0.522905\pi$
$128$	−6.72635e7	−	2.59872e8i	−0.250576	−	0.968097i
$129$	−2.10784e8	+	1.49322e8i	−0.761166	+	0.539219i
$130$	3.14964e8	−	4.25675e8i	1.10278	−	1.49041i
$131$	6.00349e7	−	6.00349e7i	0.203854	−	0.203854i	−0.597795	−	0.801649i	$-0.703956\pi$
$131$	6.00349e7	−	6.00349e7i	0.203854	−	0.203854i	0.801649	+	0.597795i	$0.203956\pi$
$132$	1.87147e8	−	2.42293e8i	0.616436	−	0.798079i
$133$	−3.07708e7	+	3.07708e7i	−0.0983406	+	0.0983406i
$134$	−6.03252e7	−	4.03566e8i	−0.187103	−	1.25168i
$135$	−1.63538e8	−	5.72490e8i	−0.492362	−	1.72359i
$136$	−5.77731e8	−	2.04529e8i	−1.68877	−	0.597859i
$137$	2.65123e7			0.0752601			0.0376301	−	0.999292i	$-0.488019\pi$
$137$	2.65123e7			0.0752601			0.0376301	+	0.999292i	$0.488019\pi$
$138$	3.26280e8	+	3.40053e8i	0.899650	+	0.937627i
$139$	3.39377e8	−	3.39377e8i	0.909123	−	0.909123i	−0.0870781	−	0.996201i	$-0.527753\pi$
$139$	3.39377e8	−	3.39377e8i	0.909123	−	0.909123i	0.996201	+	0.0870781i	$0.0277530\pi$
$140$	5.32811e8	+	2.83261e8i	1.38695	+	0.737352i
$141$	−2.33266e6	+	1.36670e7i	−0.00590167	+	0.0345778i
$142$	3.17159e8	+	2.34671e8i	0.780051	+	0.577172i
$143$		−	4.36152e8i		−	1.04302i
$144$	−4.16031e8	+	1.08640e8i	−0.967555	+	0.252661i
$145$	−4.51682e8			−1.02179
$146$	−1.38747e8	+	1.87517e8i	−0.305359	+	0.412694i
$147$	−1.06844e8	−	1.82359e7i	−0.228813	−	0.0390534i
$148$	3.47651e8	+	1.84823e8i	0.724597	+	0.385221i
$149$	3.32703e8	+	3.32703e8i	0.675012	+	0.675012i	0.958867	−	0.283855i	$-0.0916134\pi$
$149$	3.32703e8	+	3.32703e8i	0.675012	+	0.675012i	−0.283855	+	0.958867i	$0.591613\pi$
$150$	8.08458e8	−	7.75713e8i	1.59695	−	1.53227i
$151$			2.05500e8i			0.395279i	0.980275	+	0.197640i	$0.0633276\pi$
$151$			2.05500e8i			0.395279i	−0.980275	+	0.197640i	$0.936672\pi$
$152$	7.64621e7	−	3.64787e7i	0.143243	−	0.0683384i
$153$	−3.25621e8	+	9.26117e8i	−0.594220	+	1.69005i
$154$	4.91557e8	−	7.34783e7i	0.873960	−	0.130640i
$155$	4.03878e8	+	4.03878e8i	0.699719	+	0.699719i
$156$	−3.74448e8	+	4.84786e8i	−0.632257	+	0.818562i
$157$	5.57474e8	+	5.57474e8i	0.917542	+	0.917542i	0.996850	−	0.0793078i	$-0.0252710\pi$
$157$	5.57474e8	+	5.57474e8i	0.917542	+	0.917542i	−0.0793078	+	0.996850i	$0.525271\pi$
$158$	4.43439e8	+	3.28108e8i	0.711550	+	0.526487i
$159$	−1.81603e7	−	2.56352e7i	−0.0284141	−	0.0401096i
$160$	−7.93777e8	−	8.66004e8i	−1.21121	−	1.32142i
$161$			7.65071e8i			1.13867i
$162$	1.75455e8	+	6.66025e8i	0.254745	+	0.967008i
$163$	−7.09437e8	−	7.09437e8i	−1.00499	−	1.00499i	−0.999987	−	0.00500615i	$-0.998406\pi$
$163$	−7.09437e8	−	7.09437e8i	−1.00499	−	1.00499i	−0.00500615	−	0.999987i	$-0.501594\pi$
$164$	−6.03372e7	−	1.97313e8i	−0.0834085	−	0.272760i
$165$	2.25418e8	−	1.32072e9i	0.304126	−	1.78187i
$166$	−6.06968e8	+	9.07299e7i	−0.799343	+	0.119486i
$167$	−1.55632e7			−0.0200094			−0.0100047	−	0.999950i	$-0.503185\pi$
$167$	−1.55632e7			−0.0200094			−0.0100047	+	0.999950i	$0.503185\pi$
$168$	−6.09453e8	−	3.40344e8i	−0.765073	−	0.427249i
$169$			5.69315e7i			0.0697920i
$170$	−2.65261e9	+	3.96514e8i	−3.17599	+	0.474748i
$171$	−5.86956e7	−	1.22351e8i	−0.0686469	−	0.143095i
$172$	7.20865e8	+	3.83237e8i	0.823646	+	0.437879i
$173$	5.41161e8	−	5.41161e8i	0.604147	−	0.604147i	−0.337264	−	0.941410i	$-0.609501\pi$
$173$	5.41161e8	−	5.41161e8i	0.604147	−	0.604147i	0.941410	+	0.337264i	$0.109501\pi$
$174$	5.22394e8	+	1.07979e7i	0.569903	+	0.0117800i
$175$	1.81892e9			1.93937
$176$	−9.49841e8	−	1.84516e8i	−0.989920	−	0.192302i
$177$	−1.01352e9	−	1.43069e9i	−1.03262	−	1.45765i
$178$	5.00679e8	+	3.70461e8i	0.498746	+	0.369030i
$179$	3.48127e8	−	3.48127e8i	0.339099	−	0.339099i	−0.516929	−	0.856028i	$-0.672925\pi$
$179$	3.48127e8	−	3.48127e8i	0.339099	−	0.339099i	0.856028	+	0.516929i	$0.172925\pi$
$180$	−1.38443e9	+	1.27446e9i	−1.31881	+	1.21405i
$181$	5.26525e8	−	5.26525e8i	0.490575	−	0.490575i	−0.417913	−	0.908487i	$-0.637238\pi$
$181$	5.26525e8	−	5.26525e8i	0.490575	−	0.490575i	0.908487	+	0.417913i	$0.137238\pi$
$182$	−9.83519e8	+	1.47017e8i	−0.896390	+	0.133993i
$183$	6.84365e7	+	9.66055e7i	0.0610216	+	0.0861386i
$184$	4.97064e8	−	1.40405e9i	0.433652	−	1.22493i
$185$	1.72307e9			1.47101
$186$	−4.57451e8	−	4.76762e8i	−0.382202	−	0.398336i
$187$	−1.56209e9	+	1.56209e9i	−1.27744	+	1.27744i
$188$	4.19038e7	−	1.28139e7i	0.0335445	−	0.0102577i
$189$	−5.43061e8	+	9.77397e8i	−0.425600	+	0.765991i
$190$	2.20523e8	−	2.98038e8i	0.169215	−	0.228695i
$191$		−	7.62338e8i		−	0.572815i	−0.958108	−	0.286407i	$-0.907539\pi$
$191$		−	7.62338e8i		−	0.572815i	0.958108	−	0.286407i	$-0.0924611\pi$
$192$	8.97342e8	+	1.02056e9i	0.660318	+	0.750986i
$193$	2.26910e8			0.163540			0.0817702	−	0.996651i	$-0.473943\pi$
$193$	2.26910e8			0.163540			0.0817702	+	0.996651i	$0.473943\pi$
$194$	1.78485e9	+	1.32064e9i	1.26007	+	0.932346i
$195$	−4.51022e8	+	2.64253e9i	−0.311931	+	1.82760i
$196$	1.00175e8	+	3.27589e8i	0.0678788	+	0.221976i
$197$	−1.68124e9	−	1.68124e9i	−1.11626	−	1.11626i	−0.992286	−	0.123972i	$-0.960437\pi$
$197$	−1.68124e9	−	1.68124e9i	−1.11626	−	1.11626i	−0.123972	−	0.992286i	$-0.539563\pi$
$198$	−2.92281e8	+	1.52209e9i	−0.190169	+	0.990332i
$199$			1.06776e9i			0.680864i	0.940269	+	0.340432i	$0.110573\pi$
$199$			1.06776e9i			0.680864i	−0.940269	+	0.340432i	$0.889427\pi$
$200$	−3.33806e9	−	1.18174e9i	−2.08629	−	0.738590i
$201$	1.19413e9	+	1.68564e9i	0.731588	+	1.03272i
$202$	−3.83136e8	−	2.56312e9i	−0.230117	−	1.53944i
$203$	5.99804e8	+	5.99804e8i	0.353203	+	0.353203i
$204$	3.07737e9	−	3.95176e8i	1.77688	−	0.228176i
$205$	−6.38499e8	−	6.38499e8i	−0.361530	−	0.361530i
$206$	5.92885e8	−	8.01287e8i	0.329232	−	0.444958i
$207$	−2.25073e9	−	7.91354e8i	−1.22586	−	0.431012i
$208$	1.90046e9	+	3.69184e8i	1.01533	+	0.197238i
$209$		−	3.05373e8i		−	0.160046i
$210$	−3.05420e9	−	6.31306e7i	−1.57044	−	0.0324611i
$211$	1.02570e9	+	1.02570e9i	0.517476	+	0.517476i	0.916807	−	0.399331i	$-0.130758\pi$
$211$	1.02570e9	+	1.02570e9i	0.517476	+	0.517476i	−0.399331	+	0.916807i	$0.630758\pi$
$212$	−4.66086e7	+	8.76703e7i	−0.0230740	+	0.0434019i
$213$	−1.96887e9	−	3.36044e8i	−0.956532	−	0.163259i
$214$	1.41258e8	+	9.44990e8i	0.0673530	+	0.450580i
$215$	3.57283e9			1.67209
$216$	1.63163e9	−	1.44089e9i	0.749562	−	0.661935i
$217$		−	1.07265e9i		−	0.483747i
$218$	1.07511e8	+	7.19228e8i	0.0476020	+	0.318449i
$219$	1.98682e8	−	1.16408e9i	0.0863739	−	0.506063i
$220$	−4.04939e9	+	1.23828e9i	−1.72862	+	0.528601i
$221$	3.12546e9	−	3.12546e9i	1.31022	−	1.31022i
$222$	−1.99282e9	−	4.11917e7i	−0.820456	−	0.0169589i
$223$	1.35451e9			0.547725			0.273863	−	0.961769i	$-0.411699\pi$
$223$	1.35451e9			0.547725			0.273863	+	0.961769i	$0.411699\pi$
$224$	−9.59128e7	+	2.20408e9i	−0.0380965	+	0.875458i
$225$	−1.88140e9	+	5.35100e9i	−0.734094	+	2.08788i
$226$	−9.06674e8	+	1.22537e9i	−0.347550	+	0.469716i
$227$	−2.30011e9	+	2.30011e9i	−0.866255	+	0.866255i	−0.992056	−	0.125800i	$-0.959850\pi$
$227$	−2.30011e9	+	2.30011e9i	−0.866255	+	0.866255i	0.125800	+	0.992056i	$0.459850\pi$
$228$	−2.62171e8	+	3.39424e8i	−0.0970165	+	0.125604i
$229$	2.67719e9	−	2.67719e9i	0.973504	−	0.973504i	−0.0261536	−	0.999658i	$-0.508326\pi$
$229$	2.67719e9	−	2.67719e9i	0.973504	−	0.973504i	0.999658	+	0.0261536i	$0.00832590\pi$
$230$	−9.63644e8	−	6.44662e9i	−0.344354	−	2.30367i
$231$	−2.05317e9	+	1.45449e9i	−0.721069	+	0.510814i
$232$	−7.11065e8	−	1.49045e9i	−0.245447	−	0.514475i
$233$	4.38348e9			1.48729			0.743644	−	0.668576i	$-0.233096\pi$
$233$	4.38348e9			1.48729			0.743644	+	0.668576i	$0.233096\pi$
$234$	5.84803e8	−	3.04544e9i	0.195050	−	1.01575i
$235$	1.35599e8	−	1.35599e8i	0.0444616	−	0.0444616i
$236$	−2.60121e9	+	4.89285e9i	−0.838548	+	1.57730i
$237$	−2.75280e9	−	4.69843e8i	−0.872533	−	0.148922i
$238$	4.04904e9	+	2.99595e9i	1.26196	+	0.933742i
$239$		−	1.74824e9i		−	0.535810i	−0.963445	−	0.267905i	$-0.913669\pi$
$239$		−	1.74824e9i		−	0.535810i	0.963445	−	0.267905i	$-0.0863313\pi$
$240$	5.56403e9	+	2.10016e9i	1.67704	+	0.633005i
$241$	5.72636e9			1.69750			0.848751	−	0.528793i	$-0.177355\pi$
$241$	5.72636e9			1.69750			0.848751	+	0.528793i	$0.177355\pi$
$242$	−3.45218e7	+	4.66563e7i	−0.0100654	+	0.0136035i
$243$	−2.31365e9	−	2.60858e9i	−0.663548	−	0.748134i
$244$	1.75643e8	−	3.30383e8i	0.0495533	−	0.0932092i
$245$	1.06007e9	+	1.06007e9i	0.294217	+	0.294217i
$246$	7.23193e8	+	7.53721e8i	0.197476	+	0.205812i
$247$			6.10997e8i			0.164154i
$248$	−6.96895e8	+	1.96851e9i	−0.184230	+	0.520393i
$249$	2.53522e9	−	1.79598e9i	0.659506	−	0.467202i
$250$	−8.40137e9	+	1.25584e9i	−2.15075	+	0.321495i
$251$	−1.73999e9	−	1.73999e9i	−0.438382	−	0.438382i	0.453085	−	0.891467i	$-0.350323\pi$
$251$	−1.73999e9	−	1.73999e9i	−0.438382	−	0.438382i	−0.891467	+	0.453085i	$0.850323\pi$
$252$	3.53083e9	+	1.46028e8i	0.875538	+	0.0362104i
$253$	−3.79632e9	−	3.79632e9i	−0.926576	−	0.926576i
$254$	−4.81133e8	−	3.55998e8i	−0.115593	−	0.0855289i
$255$	1.10796e10	−	7.84893e9i	2.62038	−	1.85631i
$256$	1.60800e9	−	3.98260e9i	0.374392	−	0.927271i
$257$			2.47055e9i			0.566319i	0.959073	+	0.283160i	$0.0913826\pi$
$257$			2.47055e9i			0.566319i	−0.959073	+	0.283160i	$0.908617\pi$
$258$	−4.13217e9	−	8.54124e7i	−0.932608	−	0.0192771i
$259$	−2.28812e9	−	2.28812e9i	−0.508486	−	0.508486i
$260$	8.10212e9	−	2.47758e9i	1.77299	−	0.542168i
$261$	−2.38495e9	+	1.14413e9i	−0.513945	+	0.246554i
$262$	1.34351e9	−	2.00828e8i	0.285125	−	0.0426206i
$263$	2.13971e9			0.447231			0.223616	−	0.974677i	$-0.428214\pi$
$263$	2.13971e9			0.447231			0.223616	+	0.974677i	$0.428214\pi$
$264$	4.71294e9	−	1.33533e9i	0.970233	−	0.274899i
$265$			4.34521e8i			0.0881105i
$266$	−6.88614e8	+	1.02934e8i	−0.137546	+	0.0205605i
$267$	−3.10814e9	−	5.30492e8i	−0.611584	−	0.104384i
$268$	3.06475e9	−	5.76476e9i	0.594094	−	1.11749i
$269$	−5.88755e9	+	5.88755e9i	−1.12441	+	1.12441i	−0.133343	+	0.991070i	$0.542571\pi$
$269$	−5.88755e9	+	5.88755e9i	−1.12441	+	1.12441i	−0.991070	+	0.133343i	$0.957429\pi$
$270$	3.34484e9	−	8.91972e9i	0.629391	−	1.67840i
$271$	−6.60420e9			−1.22446			−0.612228	−	0.790681i	$-0.709727\pi$
$271$	−6.60420e9			−1.22446			−0.612228	+	0.790681i	$0.709727\pi$
$272$	−5.48431e9	−	8.12880e9i	−1.00195	−	1.48508i
$273$	4.10803e9	−	2.91018e9i	0.739576	−	0.523924i
$274$	3.41001e8	+	2.52312e8i	0.0604997	+	0.0447647i
$275$	−9.02557e9	+	9.02557e9i	−1.57813	+	1.57813i
$276$	9.60392e8	+	7.47889e9i	0.165505	+	1.28884i
$277$	4.32091e9	−	4.32091e9i	0.733932	−	0.733932i	−0.237464	−	0.971396i	$-0.576316\pi$
$277$	4.32091e9	−	4.32091e9i	0.733932	−	0.733932i	0.971396	+	0.237464i	$0.0763162\pi$
$278$	7.59484e9	−	1.13528e9i	1.27157	−	0.190075i
$279$	3.15558e9	+	1.10950e9i	0.520789	+	0.183109i
$280$	4.15727e9	+	8.71396e9i	0.676357	+	1.41770i
$281$	5.15737e8			0.0827186			0.0413593	−	0.999144i	$-0.486831\pi$
$281$	5.15737e8			0.0827186			0.0413593	+	0.999144i	$0.486831\pi$
$282$	−1.60069e8	+	1.53586e8i	−0.0253111	+	0.0242859i
$283$	−5.96137e9	+	5.96137e9i	−0.929395	+	0.929395i	−0.997667	−	0.0682718i	$-0.978252\pi$
$283$	−5.96137e9	+	5.96137e9i	−0.929395	+	0.929395i	0.0682718	+	0.997667i	$0.478252\pi$
$284$	1.84598e9	+	6.03666e9i	0.283761	+	0.927948i
$285$	−3.15784e8	+	1.85017e9i	−0.0478642	+	0.280436i
$286$	4.15077e9	−	5.60978e9i	0.620389	−	0.838459i
$287$			1.69577e9i			0.249942i
$288$	−6.38488e9	−	2.56196e9i	−0.928075	−	0.372394i
$289$	−1.54121e10			−2.20938
$290$	−5.80953e9	−	4.29856e9i	−0.821389	−	0.607759i
$291$	−1.10801e10	−	1.89113e9i	−1.54515	−	0.263724i
$292$	−3.56911e9	+	1.09141e9i	−0.490941	+	0.150127i
$293$	−5.95443e9	−	5.95443e9i	−0.807922	−	0.807922i	0.176397	−	0.984319i	$-0.443556\pi$
$293$	−5.95443e9	−	5.95443e9i	−0.807922	−	0.807922i	−0.984319	+	0.176397i	$0.943556\pi$
$294$	−1.20068e9	−	1.25136e9i	−0.160708	−	0.167492i
$295$			2.42505e10i			3.20208i
$296$	2.71255e9	+	5.68572e9i	0.353355	+	0.740659i
$297$	−2.15520e9	−	7.54459e9i	−0.276989	−	0.969639i
$298$	1.11296e9	+	7.44549e9i	0.141128	+	0.944122i
$299$	7.59577e9	+	7.59577e9i	0.950357	+	0.950357i
$300$	1.77807e10	−	2.28328e9i	2.19515	−	0.281887i
$301$	−4.74449e9	−	4.74449e9i	−0.577994	−	0.577994i
$302$	−1.95570e9	+	2.64314e9i	−0.235112	+	0.317755i
$303$	7.58412e9	+	1.07058e10i	0.899776	+	1.27013i
$304$	1.33062e9	+	2.58486e8i	0.155797	+	0.0302651i
$305$		−	1.63748e9i		−	0.189224i
$306$	−1.30018e10	+	8.81283e9i	−1.48292	+	1.00515i
$307$	−3.02415e9	−	3.02415e9i	−0.340447	−	0.340447i	0.516088	−	0.856535i	$-0.327388\pi$
$307$	−3.02415e9	−	3.02415e9i	−0.340447	−	0.340447i	−0.856535	+	0.516088i	$0.827388\pi$
$308$	7.02168e9	+	3.73297e9i	0.780258	+	0.414813i
$309$	−8.48999e8	+	4.97427e9i	−0.0931265	+	0.545627i
$310$	1.35105e9	+	9.03830e9i	0.146293	+	0.978679i
$311$	−1.44344e10			−1.54297			−0.771483	−	0.636250i	$-0.780485\pi$
$311$	−1.44344e10			−1.54297			−0.771483	+	0.636250i	$0.780485\pi$
$312$	−9.42975e9	+	2.67176e9i	−0.995135	+	0.281955i
$313$			9.54023e9i			0.993988i	0.867754	+	0.496994i	$0.165563\pi$
$313$			9.54023e9i			0.993988i	−0.867754	+	0.496994i	$0.834437\pi$
$314$	1.86486e9	+	1.24756e10i	0.191835	+	1.28334i
$315$	1.39437e10	−	6.68920e9i	1.41624	−	0.679410i
$316$	2.58097e9	+	8.44023e9i	0.258842	+	0.846459i
$317$	2.70211e9	−	2.70211e9i	0.267588	−	0.267588i	−0.560540	−	0.828128i	$-0.689406\pi$
$317$	2.70211e9	−	2.70211e9i	0.267588	−	0.267588i	0.828128	+	0.560540i	$0.189406\pi$
$318$	1.03877e7	−	5.02547e8i	0.00101581	−	0.0491437i
$319$	−5.95251e9			−0.574828
$320$	−1.96797e9	−	1.86928e10i	−0.187680	−	1.78268i
$321$	−2.79617e9	−	3.94710e9i	−0.263356	−	0.371756i
$322$	−7.28102e9	+	9.84033e9i	−0.677281	+	0.915348i
$323$	2.18830e9	−	2.18830e9i	0.201047	−	0.201047i
$324$	−4.08172e9	+	1.02362e10i	−0.370393	+	0.928875i
$325$	1.80586e10	−	1.80586e10i	1.61864	−	1.61864i
$326$	−2.37320e9	−	1.58763e10i	−0.210119	−	1.40566i
$327$	−2.12815e9	−	3.00412e9i	−0.186128	−	0.262740i
$328$	1.10173e9	−	3.11206e9i	0.0951878	−	0.268876i
$329$	−3.60133e8			−0.0307382
$330$	1.54684e10	−	1.48418e10i	1.30433	−	1.25150i
$331$	1.90009e9	−	1.90009e9i	0.158294	−	0.158294i	−0.623517	−	0.781810i	$-0.714297\pi$
$331$	1.90009e9	−	1.90009e9i	0.158294	−	0.158294i	0.781810	+	0.623517i	$0.214297\pi$
$332$	−8.67027e9	−	4.60942e9i	−0.713642	−	0.379397i
$333$	9.09804e9	−	4.36460e9i	0.739896	−	0.354950i
$334$	−2.00174e8	−	1.48112e8i	−0.0160850	−	0.0119016i
$335$		−	2.85719e10i		−	2.26861i
$336$	−4.59979e9	−	1.01775e10i	−0.360895	−	0.798519i
$337$	−4.96670e9			−0.385078			−0.192539	−	0.981289i	$-0.561672\pi$
$337$	−4.96670e9			−0.385078			−0.192539	+	0.981289i	$0.561672\pi$
$338$	−5.41805e8	+	7.32252e8i	−0.0415123	+	0.0561040i
$339$	1.29834e9	−	7.60695e9i	0.0983081	−	0.575986i
$340$	−3.78914e10	−	2.01444e10i	−2.83547	−	1.50744i
$341$	5.32253e9	+	5.32253e9i	0.393641	+	0.393641i
$342$	4.09451e8	−	2.13228e9i	0.0299294	−	0.155861i
$343$		−	1.49443e10i		−	1.07969i
$344$	5.62457e9	+	1.17895e10i	0.401657	+	0.841904i
$345$	1.90752e10	+	2.69267e10i	1.34646	+	1.90067i
$346$	1.21105e10	−	1.81029e9i	0.845004	−	0.126312i
$347$	−1.36042e10	−	1.36042e10i	−0.938331	−	0.938331i	0.0598748	−	0.998206i	$-0.480930\pi$
$347$	−1.36042e10	−	1.36042e10i	−0.938331	−	0.938331i	−0.998206	+	0.0598748i	$0.980930\pi$
$348$	6.61626e9	+	5.11040e9i	0.451124	+	0.348448i
$349$	1.45839e10	+	1.45839e10i	0.983040	+	0.983040i	0.999859	−	0.0168187i	$-0.00535382\pi$
$349$	1.45839e10	+	1.45839e10i	0.983040	+	0.983040i	−0.0168187	+	0.999859i	$0.505354\pi$
$350$	2.33949e10	+	1.73103e10i	1.55901	+	1.15354i
$351$	4.31217e9	+	1.50954e10i	0.284098	+	0.994525i
$352$	−1.04608e10	−	1.14127e10i	−0.681390	−	0.743391i
$353$			1.81919e10i			1.17160i	0.810457	+	0.585799i	$0.199219\pi$
$353$			1.81919e10i			1.17160i	−0.810457	+	0.585799i	$0.800781\pi$
$354$	5.79734e8	−	2.80470e10i	0.0369161	−	1.78596i
$355$	1.95344e10	+	1.95344e10i	1.22995	+	1.22995i
$356$	2.91413e9	+	9.52972e9i	0.181430	+	0.593308i
$357$	−2.51359e10	−	4.29014e9i	−1.54747	−	0.264118i
$358$	7.79066e9	−	1.16455e9i	0.474288	−	0.0708969i
$359$	7.53732e9			0.453773			0.226887	−	0.973921i	$-0.427145\pi$
$359$	7.53732e9			0.453773			0.226887	+	0.973921i	$0.427145\pi$
$360$	−2.99353e10	+	3.21680e9i	−1.78227	+	0.191520i
$361$		−	1.65558e10i		−	0.974811i
$362$	1.17830e10	−	1.76133e9i	0.686154	−	0.102567i
$363$	4.94345e7	−	2.89636e8i	0.00284711	−	0.0166811i
$364$	−1.40491e10	−	7.46901e9i	−0.800284	−	0.425459i
$365$	−1.15495e10	+	1.15495e10i	−0.650717	+	0.650717i
$366$	−3.91457e7	+	1.89383e9i	−0.00218153	+	0.105540i
$367$	6.37717e9			0.351531			0.175766	−	0.984432i	$-0.443760\pi$
$367$	6.37717e9			0.351531			0.175766	+	0.984432i	$0.443760\pi$
$368$	1.97553e10	−	1.33285e10i	1.07719	−	0.726756i
$369$	−4.98871e9	−	1.75402e9i	−0.269081	−	0.0946084i
$370$	2.21620e10	+	1.63981e10i	1.18250	+	0.874955i
$371$	5.77016e8	−	5.77016e8i	0.0304573	−	0.0304573i
$372$	−1.34649e9	−	1.04856e10i	−0.0703124	−	0.547546i
$373$	−2.55641e9	+	2.55641e9i	−0.132067	+	0.132067i	−0.770050	−	0.637983i	$-0.779769\pi$
$373$	−2.55641e9	+	2.55641e9i	−0.132067	+	0.132067i	0.637983	+	0.770050i	$0.279769\pi$
$374$	−3.49576e10	+	5.22549e9i	−1.78672	+	0.267079i
$375$	3.50914e10	−	2.48592e10i	1.77450	−	1.25708i
$376$	6.60913e8	+	2.33977e8i	0.0330669	+	0.0117064i
$377$	1.19099e10			0.589581
$378$	−1.62865e10	+	7.40307e9i	−0.797740	+	0.362614i
$379$	−1.60788e10	+	1.60788e10i	−0.779284	+	0.779284i	−0.979709	−	0.200425i	$-0.935768\pi$
$379$	−1.60788e10	+	1.60788e10i	−0.779284	+	0.779284i	0.200425	+	0.979709i	$0.435768\pi$
$380$	5.67272e9	−	1.73468e9i	0.272055	−	0.0831929i
$381$	2.98681e9	+	5.09782e8i	0.141745	+	0.0241927i
$382$	7.25502e9	−	9.80518e9i	0.340710	−	0.460471i
$383$		−	6.81680e9i		−	0.316800i	−0.987375	−	0.158400i	$-0.949366\pi$
$383$		−	6.81680e9i		−	0.316800i	0.987375	−	0.158400i	$-0.0506336\pi$
$384$	1.82919e9	+	2.16662e10i	0.0841266	+	0.996455i
$385$	3.48016e10			1.58401
$386$	2.91852e9	+	2.15946e9i	0.131466	+	0.0972738i
$387$	1.88651e10	−	9.05013e9i	0.841036	−	0.403470i
$388$	1.03885e10	+	3.39721e10i	0.458378	+	1.49898i
$389$	−2.47967e10	−	2.47967e10i	−1.08292	−	1.08292i	−0.996236	−	0.0866832i	$-0.972373\pi$
$389$	−2.47967e10	−	2.47967e10i	−1.08292	−	1.08292i	−0.0866832	−	0.996236i	$-0.527627\pi$
$390$	−3.09494e10	+	2.96959e10i	−1.33781	+	1.28362i
$391$		−	5.44089e10i		−	2.32789i
$392$	−1.82915e9	+	5.16679e9i	−0.0774650	+	0.218815i
$393$	−5.61165e9	+	3.97536e9i	−0.235245	+	0.166650i
$394$	−5.62407e9	−	3.76241e10i	−0.233381	−	1.56128i
$395$	2.73122e10	+	2.73122e10i	1.12194	+	1.12194i
$396$	−1.82448e10	+	1.67956e10i	−0.741921	+	0.682990i
$397$	−6.97559e9	−	6.97559e9i	−0.280814	−	0.280814i	0.552620	−	0.833434i	$-0.313628\pi$
$397$	−6.97559e9	−	6.97559e9i	−0.280814	−	0.280814i	−0.833434	+	0.552620i	$0.813628\pi$
$398$	−1.01616e10	+	1.37335e10i	−0.404977	+	0.547329i
$399$	2.87625e9	−	2.03757e9i	0.113484	−	0.0803935i
$400$	−3.16877e10	−	4.69672e10i	−1.23780	−	1.83466i
$401$		−	5.25685e9i		−	0.203305i	−0.994820	−	0.101652i	$-0.967587\pi$
$401$		−	5.25685e9i		−	0.203305i	0.994820	−	0.101652i	$-0.0324130\pi$
$402$	−6.83042e8	+	3.30449e10i	−0.0261543	+	1.26532i
$403$	−1.06494e10	−	1.06494e10i	−0.403744	−	0.403744i
$404$	1.94648e10	−	3.66130e10i	0.730674	−	1.37439i
$405$	5.25598e9	+	4.79394e10i	0.195359	+	1.78185i
$406$	2.00646e9	+	1.34229e10i	0.0738458	+	0.494016i
$407$	2.27075e10			0.827546
$408$	4.33419e10	+	2.42039e10i	1.56411	+	0.873464i
$409$			2.68070e10i			0.957976i	0.877821	+	0.478988i	$0.158996\pi$
$409$			2.68070e10i			0.957976i	−0.877821	+	0.478988i	$0.841004\pi$
$410$	−2.13590e9	−	1.42888e10i	−0.0755867	−	0.505663i
$411$	−2.11688e9	−	3.61305e8i	−0.0741873	−	0.0126621i
$412$	1.52514e10	−	4.66377e9i	0.529322	−	0.161863i
$413$	3.22030e10	−	3.22030e10i	1.10687	−	1.10687i
$414$	−2.14177e10	−	3.15981e10i	−0.729074	−	1.07562i
$415$	−4.29726e10			−1.44877
$416$	2.09303e10	+	2.28348e10i	0.698878	+	0.762470i
$417$	−3.17226e10	+	2.24727e10i	−1.04912	+	0.743208i
$418$	2.90617e9	−	3.92770e9i	0.0951955	−	0.128657i
$419$	1.73016e10	−	1.73016e10i	0.561345	−	0.561345i	−0.368345	−	0.929689i	$-0.620075\pi$
$419$	1.73016e10	−	1.73016e10i	0.561345	−	0.561345i	0.929689	+	0.368345i	$0.120075\pi$
$420$	−3.86823e10	−	2.98782e10i	−1.24312	−	0.960189i
$421$	−1.15857e9	+	1.15857e9i	−0.0368804	+	0.0368804i	−0.725306	−	0.688426i	$-0.758302\pi$
$421$	−1.15857e9	+	1.15857e9i	−0.0368804	+	0.0368804i	0.688426	+	0.725306i	$0.258302\pi$
$422$	3.43116e9	+	2.29539e10i	0.108191	+	0.723780i
$423$	3.72504e8	−	1.05946e9i	0.0116351	−	0.0330920i
$424$	−1.43382e9	+	6.84050e8i	−0.0443640	+	0.0211653i
$425$	−1.29354e11			−3.96483
$426$	−2.21256e10	−	2.30596e10i	−0.671825	−	0.700185i
$427$	−2.17447e9	+	2.17447e9i	−0.0654096	+	0.0654096i
$428$	−7.17642e9	+	1.34988e10i	−0.213862	+	0.402271i
$429$	−5.94381e9	+	3.48247e10i	−0.175483	+	1.02815i
$430$	4.59537e10	+	3.40019e10i	1.34415	+	0.994557i
$431$			2.85848e10i			0.828372i	0.910192	+	0.414186i	$0.135934\pi$
$431$			2.85848e10i			0.828372i	−0.910192	+	0.414186i	$0.864066\pi$
$432$	3.46987e10	−	3.00476e9i	0.996272	−	0.0862731i
$433$	5.43760e10			1.54688			0.773438	−	0.633872i	$-0.218535\pi$
$433$	5.43760e10			1.54688			0.773438	+	0.633872i	$0.218535\pi$
$434$	1.02082e10	−	1.37964e10i	0.287732	−	0.388871i
$435$	3.60647e10	+	6.15545e9i	1.00722	+	0.171911i
$436$	−5.46194e9	+	1.02738e10i	−0.151148	+	0.284307i
$437$	5.31820e9	+	5.31820e9i	0.145827	+	0.145827i
$438$	1.36337e10	−	1.30815e10i	0.370440	−	0.355436i
$439$			7.03658e10i			1.89454i	0.320437	+	0.947270i	$0.396170\pi$
$439$			7.03658e10i			1.89454i	−0.320437	+	0.947270i	$0.603830\pi$
$440$	−6.38677e10	−	2.26105e10i	−1.70400	−	0.603253i
$441$	8.28249e9	+	2.91211e9i	0.218981	+	0.0769934i
$442$	6.99440e10	−	1.04553e10i	1.83257	−	0.273934i
$443$	−1.52930e10	−	1.52930e10i	−0.397079	−	0.397079i	0.480123	−	0.877201i	$-0.340592\pi$
$443$	−1.52930e10	−	1.52930e10i	−0.397079	−	0.397079i	−0.877201	+	0.480123i	$0.840592\pi$
$444$	−2.52396e10	−	1.94950e10i	−0.649456	−	0.501640i
$445$	3.08378e10	+	3.08378e10i	0.786400	+	0.786400i
$446$	1.74217e10	+	1.28906e10i	0.440302	+	0.325787i
$447$	−2.20308e10	−	3.10988e10i	−0.551823	−	0.778958i
$448$	−2.22094e10	+	2.74361e10i	−0.551347	+	0.681098i
$449$		−	3.37163e10i		−	0.829572i	−0.909919	−	0.414786i	$-0.863856\pi$
$449$		−	3.37163e10i		−	0.829572i	0.909919	−	0.414786i	$-0.136144\pi$
$450$	−7.51229e10	+	5.09195e10i	−1.83199	+	1.24175i
$451$	−8.41449e9	−	8.41449e9i	−0.203386	−	0.203386i
$452$	−2.33233e10	+	7.13211e9i	−0.558773	+	0.170869i
$453$	2.80052e9	−	1.64082e10i	0.0665038	−	0.389645i
$454$	−5.14737e10	+	7.69432e9i	−1.21161	+	0.181112i
$455$	−6.96319e10			−1.62466
$456$	−6.60227e9	+	1.87064e9i	−0.152698	+	0.0432644i
$457$		−	4.93520e10i		−	1.13146i	−0.824590	−	0.565731i	$-0.808594\pi$
$457$		−	4.93520e10i		−	1.13146i	0.824590	−	0.565731i	$-0.191406\pi$
$458$	5.99123e10	−	8.95573e9i	1.36161	−	0.203535i
$459$	3.86203e10	−	6.95086e10i	0.870092	−	1.56599i
$460$	4.89567e10	−	9.20871e10i	1.09341	−	2.05668i
$461$	−4.63349e10	+	4.63349e10i	−1.02590	+	1.02590i	−0.0262428	+	0.999656i	$0.508354\pi$
$461$	−4.63349e10	+	4.63349e10i	−1.02590	+	1.02590i	−0.999656	+	0.0262428i	$0.991646\pi$
$462$	−4.02499e10	−	8.31970e8i	−0.883481	−	0.0182616i
$463$	3.26333e10			0.710129			0.355065	−	0.934842i	$-0.384459\pi$
$463$	3.26333e10			0.710129			0.355065	+	0.934842i	$0.384459\pi$
$464$	5.03856e9	−	2.59371e10i	0.108701	−	0.559565i
$465$	−2.67438e10	−	3.77518e10i	−0.572020	−	0.807469i
$466$	5.63802e10	+	4.17166e10i	1.19559	+	0.884638i
$467$	−3.84880e10	+	3.84880e10i	−0.809204	+	0.809204i	−0.984513	−	0.175309i	$-0.943907\pi$
$467$	−3.84880e10	+	3.84880e10i	−0.809204	+	0.809204i	0.175309	+	0.984513i	$0.443907\pi$
$468$	3.65045e10	−	3.36050e10i	0.760963	−	0.700519i
$469$	−3.79416e10	+	3.79416e10i	−0.784196	+	0.784196i
$470$	3.03454e9	−	4.53605e8i	0.0621872	−	0.00929578i
$471$	−3.69146e10	−	5.21089e10i	−0.750091	−	1.05884i
$472$	−8.00210e10	+	3.81766e10i	−1.61226	+	0.769182i
$473$	4.70848e10			0.940667
$474$	−3.09351e10	−	3.22410e10i	−0.612828	−	0.638697i
$475$	1.26438e10	−	1.26438e10i	0.248371	−	0.248371i
$476$	2.35669e10	+	7.70678e10i	0.459065	+	1.50122i
$477$	1.10066e9	+	2.29434e9i	0.0212608	+	0.0443183i
$478$	1.66377e10	−	2.24859e10i	0.318699	−	0.430723i
$479$			5.32491e10i			1.01151i	0.862677	+	0.505755i	$0.168786\pi$
$479$			5.32491e10i			1.01151i	−0.862677	+	0.505755i	$0.831214\pi$
$480$	5.15777e10	+	7.99639e10i	0.971621	+	1.50636i
$481$	−4.54337e10			−0.848785
$482$	7.36523e10	+	5.44966e10i	1.36458	+	1.00967i
$483$	1.04263e10	−	6.10874e10i	0.191576	−	1.12244i
$484$	−8.88037e8	+	2.71556e8i	−0.0161827	+	0.00494856i
$485$	1.09932e11	+	1.09932e11i	1.98682	+	1.98682i
$486$	−4.93277e9	−	5.55700e10i	−0.0884191	−	0.996083i
$487$			2.72311e10i			0.484116i	0.970262	+	0.242058i	$0.0778224\pi$
$487$			2.72311e10i			0.484116i	−0.970262	+	0.242058i	$0.922178\pi$
$488$	5.40331e9	−	2.57782e9i	0.0952754	−	0.0454542i
$489$	4.69771e10	+	6.63133e10i	0.821582	+	1.15975i
$490$	3.54612e9	+	2.37230e10i	0.0615134	+	0.411514i
$491$	6.32587e9	+	6.32587e9i	0.108841	+	0.108841i	0.759430	−	0.650589i	$-0.225478\pi$
$491$	6.32587e9	+	6.32587e9i	0.108841	+	0.108841i	−0.650589	+	0.759430i	$0.725478\pi$
$492$	2.12869e9	+	1.65768e10i	0.0363289	+	0.282905i
$493$	−4.26557e10	−	4.26557e10i	−0.722086	−	0.722086i
$494$	−5.81473e9	+	7.85864e9i	−0.0976387	+	0.131959i
$495$	−3.59972e10	+	1.02382e11i	−0.599581	+	1.70530i
$496$	−2.76974e10	+	1.86868e10i	−0.457628	+	0.308751i
$497$		−	5.18808e10i		−	0.850317i
$498$	4.97000e10	+	1.02730e9i	0.808052	+	0.0167025i
$499$	−5.13911e10	−	5.13911e10i	−0.828869	−	0.828869i	0.158491	−	0.987360i	$-0.449337\pi$
$499$	−5.13911e10	−	5.13911e10i	−0.828869	−	0.828869i	−0.987360	+	0.158491i	$0.949337\pi$
$500$	−1.20010e11	−	6.38015e10i	−1.92016	−	1.02082i
$501$	1.24265e9	+	2.12093e8i	0.0197241	+	0.00336648i
$502$	−5.82061e9	−	3.89389e10i	−0.0916545	−	0.613153i
$503$	−3.57746e10			−0.558859			−0.279430	−	0.960166i	$-0.590145\pi$
$503$	−3.57746e10			−0.558859			−0.279430	+	0.960166i	$0.590145\pi$
$504$	4.40238e10	+	3.54804e10i	0.682284	+	0.549878i
$505$		−	1.81465e11i		−	2.79016i
$506$	−1.26994e10	−	8.49571e10i	−0.193723	−	1.29598i
$507$	7.75854e8	−	4.54572e9i	0.0117422	−	0.0687972i
$508$	−2.80037e9	−	9.15769e9i	−0.0420494	−	0.137509i
$509$	8.20486e10	−	8.20486e10i	1.22236	−	1.22236i	0.255574	−	0.966790i	$-0.417736\pi$
$509$	8.20486e10	−	8.20486e10i	1.22236	−	1.22236i	0.966790	−	0.255574i	$-0.0822643\pi$
$510$	2.17203e11	+	4.48960e9i	3.21059	+	0.0663631i
$511$	3.06740e10			0.449869
$512$	5.85836e10	−	3.59211e10i	0.852504	−	0.522721i
$513$	3.01918e9	+	1.05691e10i	0.0435933	+	0.152605i
$514$	−2.35117e10	+	3.17762e10i	−0.336846	+	0.455249i
$515$	4.93528e10	−	4.93528e10i	0.701589	−	0.701589i
$516$	−5.23351e10	−	4.04236e10i	−0.738234	−	0.570211i
$517$	1.78700e9	−	1.78700e9i	0.0250128	−	0.0250128i
$518$	−7.65419e9	−	5.12053e10i	−0.106312	−	0.711206i
$519$	−5.05841e10	+	3.58344e10i	−0.697179	+	0.493890i
$520$	1.27788e11	+	4.52396e10i	1.74774	+	0.618736i
$521$	−1.28301e11			−1.74132			−0.870660	−	0.491886i	$-0.836308\pi$
$521$	−1.28301e11			−1.74132			−0.870660	+	0.491886i	$0.836308\pi$
$522$	−4.15636e10	−	7.98127e9i	−0.559797	−	0.107495i
$523$	−3.41674e9	+	3.41674e9i	−0.0456673	+	0.0456673i	−0.729572	−	0.683904i	$-0.760281\pi$
$523$	−3.41674e9	+	3.41674e9i	−0.0456673	+	0.0456673i	0.683904	+	0.729572i	$0.260281\pi$
$524$	1.91914e10	+	1.02028e10i	0.254555	+	0.135330i
$525$	−1.45232e11	−	2.47879e10i	−1.91173	−	0.326290i
$526$	2.75209e10	+	2.03632e10i	0.359518	+	0.266013i
$527$			7.62824e10i			0.988968i
$528$	7.33258e10	+	2.76771e10i	0.943455	+	0.356110i
$529$	5.39182e10			0.688513
$530$	−4.13525e9	+	5.58881e9i	−0.0524081	+	0.0708298i
$531$	6.14275e10	+	1.28046e11i	0.772653	+	1.61060i
$532$	−9.83655e9	−	5.22945e9i	−0.122799	−	0.0652845i
$533$	1.68359e10	+	1.68359e10i	0.208606	+	0.208606i
$534$	−3.49283e10	−	3.64027e10i	−0.429549	−	0.447681i
$535$			6.69041e10i			0.816654i
$536$	9.42807e10	−	4.49796e10i	1.14226	−	0.544950i
$537$	−3.25406e10	+	2.30521e10i	−0.391316	+	0.277213i
$538$	−1.31756e11	+	1.96950e10i	−1.57269	+	0.235086i
$539$	1.39701e10	+	1.39701e10i	0.165518	+	0.165518i
$540$	1.27908e11	−	8.28932e10i	1.50426	−	0.974863i
$541$	1.14532e10	+	1.14532e10i	0.133702	+	0.133702i	0.770790	−	0.637089i	$-0.219862\pi$
$541$	1.14532e10	+	1.14532e10i	0.133702	+	0.133702i	−0.637089	+	0.770790i	$0.719862\pi$
$542$	−8.49432e10	−	6.28508e10i	−0.984309	−	0.728306i
$543$	−4.92160e10	+	3.48652e10i	−0.566118	+	0.401045i
$544$	6.82094e9	−	1.56745e11i	0.0778841	−	1.78978i
$545$			5.09204e10i			0.577173i
$546$	8.05329e10	+	1.66462e9i	0.906156	+	0.0187303i
$547$	3.09412e10	+	3.09412e10i	0.345611	+	0.345611i	0.858472	−	0.512861i	$-0.171414\pi$
$547$	3.09412e10	+	3.09412e10i	0.345611	+	0.345611i	−0.512861	+	0.858472i	$0.671414\pi$
$548$	1.98474e9	+	6.49046e9i	0.0220081	+	0.0719703i
$549$	−4.14781e9	−	8.64614e9i	−0.0456593	−	0.0951772i
$550$	−2.01981e11	+	3.01923e10i	−2.20729	+	0.329948i
$551$	8.33877e9			0.0904681
$552$	−5.88225e10	+	1.05333e11i	−0.633559	+	1.13451i
$553$		−	7.25377e10i		−	0.775646i
$554$	9.66966e10	−	1.44543e10i	1.02653	−	0.153447i
$555$	−1.37579e11	−	2.34817e10i	−1.45004	−	0.247490i
$556$	1.08489e11	+	5.76765e10i	1.13524	+	0.603531i
$557$	1.22011e11	−	1.22011e11i	1.26759	−	1.26759i	0.320255	−	0.947331i	$-0.396231\pi$
$557$	1.22011e11	−	1.22011e11i	1.26759	−	1.26759i	0.947331	−	0.320255i	$-0.103769\pi$
$558$	3.00281e10	+	4.43013e10i	0.309736	+	0.456961i
$559$	−9.42083e10			−0.964810
$560$	−2.94581e10	+	1.51643e11i	−0.299539	+	1.54195i
$561$	1.46013e11	−	1.03438e11i	1.47415	−	1.04430i
$562$	6.63341e9	+	4.90817e9i	0.0664954	+	0.0492010i
$563$	4.65139e10	−	4.65139e10i	0.462966	−	0.462966i	−0.436660	−	0.899626i	$-0.643839\pi$
$563$	4.65139e10	−	4.65139e10i	0.462966	−	0.462966i	0.899626	+	0.436660i	$0.143839\pi$
$564$	−3.52045e9	+	4.52074e8i	−0.0347922	+	0.00446779i
$565$	−7.54732e10	+	7.54732e10i	−0.740626	+	0.740626i
$566$	−1.33408e11	+	1.99419e10i	−1.29992	+	0.194313i
$567$	5.66807e10	−	7.06399e10i	0.548407	−	0.683467i
$568$	−3.37068e10	+	9.52112e10i	−0.323835	+	0.914734i
$569$	−3.23887e10			−0.308990			−0.154495	−	0.987994i	$-0.549375\pi$
$569$	−3.23887e10			−0.308990			−0.154495	+	0.987994i	$0.549375\pi$
$570$	−2.16693e10	+	2.07917e10i	−0.205280	+	0.196965i
$571$	−4.44920e10	+	4.44920e10i	−0.418541	+	0.418541i	−0.884701	−	0.466160i	$-0.845637\pi$
$571$	−4.44920e10	+	4.44920e10i	−0.418541	+	0.418541i	0.466160	+	0.884701i	$0.345637\pi$
$572$	1.06774e11	−	3.26509e10i	0.997430	−	0.305008i
$573$	−1.03890e10	+	6.08692e10i	−0.0963733	+	0.564650i
$574$	−1.61383e10	+	2.18109e10i	−0.148665	+	0.200922i
$575$		−	3.14368e11i		−	2.87586i
$576$	−5.77406e10	−	9.37155e10i	−0.524556	−	0.851376i
$577$	1.33258e11			1.20224			0.601118	−	0.799160i	$-0.294722\pi$
$577$	1.33258e11			1.20224			0.601118	+	0.799160i	$0.294722\pi$
$578$	−1.98230e11	−	1.46673e11i	−1.77606	−	1.31414i
$579$	−1.81177e10	−	3.09230e9i	−0.161209	−	0.0275149i
$580$	−3.38135e10	−	1.10576e11i	−0.298798	−	0.977123i
$581$	5.70647e10	+	5.70647e10i	0.500798	+	0.500798i
$582$	−1.24514e11	−	1.29771e11i	−1.08525	−	1.13106i
$583$			5.72636e9i			0.0495684i
$584$	−5.62926e10	−	1.99288e10i	−0.483950	−	0.171328i
$585$	7.20240e10	−	2.04847e11i	0.614969	−	1.74907i
$586$	−1.99187e10	−	1.33253e11i	−0.168916	−	1.13002i
$587$	5.96566e10	+	5.96566e10i	0.502465	+	0.502465i	0.912203	−	0.409738i	$-0.134380\pi$
$587$	5.96566e10	+	5.96566e10i	0.502465	+	0.502465i	−0.409738	+	0.912203i	$0.634380\pi$
$588$	−3.53416e9	−	2.75216e10i	−0.0295649	−	0.230232i
$589$	−7.45624e9	−	7.45624e9i	−0.0619525	−	0.0619525i
$590$	−2.30787e11	+	3.11910e11i	−1.90460	+	2.57407i
$591$	1.11327e11	+	1.57151e11i	0.912541	+	1.28815i
$592$	−1.92210e10	+	9.89444e10i	−0.156491	+	0.805572i
$593$			9.54214e10i			0.771662i	0.922570	+	0.385831i	$0.126085\pi$
$593$			9.54214e10i			0.771662i	−0.922570	+	0.385831i	$0.873915\pi$
$594$	4.40802e10	−	1.17549e11i	0.354077	−	0.944220i
$595$	2.49388e11	+	2.49388e11i	1.98979	+	1.98979i
$596$	−5.65423e10	+	1.06356e11i	−0.448114	+	0.842898i
$597$	1.45512e10	−	8.52555e10i	0.114552	−	0.671158i
$598$	2.54093e10	+	1.69984e11i	0.198696	+	1.32924i
$599$	8.98598e10			0.698005			0.349002	−	0.937122i	$-0.386521\pi$
$599$	8.98598e10			0.698005			0.349002	+	0.937122i	$0.386521\pi$
$600$	2.50424e11	+	1.39847e11i	1.93229	+	1.07907i
$601$			1.74841e11i			1.34013i	0.742305	+	0.670063i	$0.233733\pi$
$601$			1.74841e11i			1.34013i	−0.742305	+	0.670063i	$0.766267\pi$
$602$	−1.58712e10	−	1.06176e11i	−0.120844	−	0.808425i
$603$	−7.23739e10	−	1.50864e11i	−0.547410	−	1.14108i
$604$	−5.03084e10	+	1.53840e10i	−0.378001	+	0.115590i
$605$	−2.87365e9	+	2.87365e9i	−0.0214493	+	0.0214493i
$606$	−4.33812e9	+	2.09874e11i	−0.0321671	+	1.55621i
$607$	−1.21232e11			−0.893026			−0.446513	−	0.894777i	$-0.647334\pi$
$607$	−1.21232e11			−0.893026			−0.446513	+	0.894777i	$0.647334\pi$
$608$	1.46544e10	+	1.59878e10i	0.107239	+	0.116997i
$609$	−3.97175e10	−	5.60656e10i	−0.288744	−	0.407593i
$610$	1.55836e10	−	2.10613e10i	0.112551	−	0.152113i
$611$	−3.57546e9	+	3.57546e9i	−0.0256547	+	0.0256547i
$612$	−2.51099e11	−	1.03849e10i	−1.78994	−	0.0740282i
$613$	−4.16915e10	+	4.16915e10i	−0.295261	+	0.295261i	−0.839154	−	0.543893i	$-0.816950\pi$
$613$	−4.16915e10	+	4.16915e10i	−0.295261	+	0.295261i	0.543893	+	0.839154i	$0.316950\pi$
$614$	−1.01164e10	−	6.76767e10i	−0.0711788	−	0.476174i
$615$	4.22798e10	+	5.96825e10i	0.295551	+	0.417202i
$616$	5.47868e10	+	1.14837e11i	0.380499	+	0.797554i
$617$	1.65276e11			1.14043			0.570216	−	0.821495i	$-0.306860\pi$
$617$	1.65276e11			1.14043			0.570216	+	0.821495i	$0.306860\pi$
$618$	−5.82589e10	+	5.58993e10i	−0.399400	+	0.383224i
$619$	−7.92478e10	+	7.92478e10i	−0.539789	+	0.539789i	−0.923467	−	0.383678i	$-0.874657\pi$
$619$	−7.92478e10	+	7.92478e10i	−0.539789	+	0.539789i	0.383678	+	0.923467i	$0.374657\pi$
$620$	−6.86385e10	+	1.29108e11i	−0.464516	+	0.873750i
$621$	1.68926e11	+	9.38585e10i	1.13587	+	0.631113i
$622$	−1.85655e11	−	1.37369e11i	−1.24035	−	0.917755i
$623$		−	8.19011e10i		−	0.543673i
$624$	−1.46712e11	−	5.53769e10i	−0.967670	−	0.365250i
$625$	−2.57103e11			−1.68495
$626$	−9.07924e10	+	1.22706e11i	−0.591224	+	0.799042i
$627$	−4.16158e9	+	2.43826e10i	−0.0269270	+	0.157765i
$628$	−9.47418e10	+	1.78208e11i	−0.609120	+	1.14575i
$629$	1.62722e11	+	1.62722e11i	1.03955	+	1.03955i
$630$	2.43003e11	+	4.66629e10i	1.54259	+	0.296216i
$631$		−	1.46500e11i		−	0.924100i	−0.886854	−	0.462050i	$-0.847114\pi$
$631$		−	1.46500e11i		−	0.924100i	0.886854	−	0.462050i	$-0.152886\pi$
$632$	−4.71275e10	+	1.33121e11i	−0.295397	+	0.834405i
$633$	−6.79192e10	−	9.58754e10i	−0.423037	−	0.597162i
$634$	6.04700e10	−	9.03909e9i	0.374268	−	0.0559458i
$635$	−2.96339e10	−	2.96339e10i	−0.182261	−	0.182261i
$636$	4.91624e9	−	6.36489e9i	0.0300472	−	0.0389012i
$637$	−2.79517e10	−	2.79517e10i	−0.169766	−	0.169766i
$638$	−7.65612e10	−	5.66488e10i	−0.462089	−	0.341907i
$639$	1.52626e11	+	5.36631e10i	0.915430	+	0.321864i
$640$	1.52583e11	−	2.59155e11i	0.909466	−	1.54468i
$641$			5.22910e9i			0.0309739i	0.999880	+	0.0154869i	$0.00492984\pi$
$641$			5.22910e9i			0.0309739i	−0.999880	+	0.0154869i	$0.995070\pi$
$642$	1.59941e9	−	7.73781e10i	0.00941501	−	0.455489i
$643$	−5.91565e10	−	5.91565e10i	−0.346066	−	0.346066i	0.512576	−	0.858642i	$-0.328691\pi$
$643$	−5.91565e10	−	5.91565e10i	−0.346066	−	0.346066i	−0.858642	+	0.512576i	$0.828691\pi$
$644$	−1.87297e11	+	5.72742e10i	−1.08890	+	0.332978i
$645$	−2.85274e11	−	4.86900e10i	−1.64825	−	0.281320i
$646$	4.89715e10	−	7.32029e9i	0.281199	−	0.0420338i
$647$	−2.99812e11			−1.71093			−0.855464	−	0.517862i	$-0.826728\pi$
$647$	−2.99812e11			−1.71093			−0.855464	+	0.517862i	$0.826728\pi$
$648$	−1.49914e11	+	9.28125e10i	−0.850244	+	0.526389i
$649$			3.19586e11i			1.80140i
$650$	4.04128e11	−	6.04093e10i	2.26395	−	0.338416i
$651$	−1.46179e10	+	8.56459e10i	−0.0813880	+	0.476851i
$652$	1.20568e11	−	2.26786e11i	0.667176	−	1.25495i
$653$	1.10212e11	−	1.10212e11i	0.606143	−	0.606143i	−0.335793	−	0.941936i	$-0.609004\pi$
$653$	1.10212e11	−	1.10212e11i	0.606143	−	0.606143i	0.941936	+	0.335793i	$0.109004\pi$
$654$	1.21731e9	−	5.88921e10i	0.00665409	−	0.321919i
$655$	9.51186e10			0.516774
$656$	4.37873e10	−	2.95423e10i	0.236447	−	0.159525i
$657$	−3.17277e10	+	9.02385e10i	−0.170285	+	0.484318i
$658$	−4.63202e9	−	3.42731e9i	−0.0247097	−	0.0182831i
$659$	−5.02901e10	+	5.02901e10i	−0.266650	+	0.266650i	−0.827749	−	0.561099i	$-0.810379\pi$
$659$	−5.02901e10	+	5.02901e10i	−0.266650	+	0.266650i	0.561099	+	0.827749i	$0.310379\pi$
$660$	3.40200e11	−	4.36864e10i	1.79291	−	0.230235i
$661$	2.36083e11	−	2.36083e11i	1.23668	−	1.23668i	0.275334	−	0.961349i	$-0.411212\pi$
$661$	2.36083e11	−	2.36083e11i	1.23668	−	1.23668i	0.961349	−	0.275334i	$-0.0887883\pi$
$662$	4.25218e10	−	6.35618e9i	0.221401	−	0.0330951i
$663$	−2.92147e11	+	2.06960e11i	−1.51198	+	1.07111i
$664$	−6.76500e10	−	1.41799e11i	−0.348013	−	0.729461i
$665$	−4.87530e10			−0.249296
$666$	1.58556e11	+	3.04468e10i	0.805907	+	0.154755i
$667$	1.03666e11	−	1.03666e11i	0.523759	−	0.523759i
$668$	−1.16508e9	−	3.81003e9i	−0.00585128	−	0.0191347i
$669$	−1.08151e11	−	1.84591e10i	−0.539917	−	0.0921520i
$670$	2.71913e11	−	3.67492e11i	1.34937	−	1.82368i
$671$		−	2.15797e10i		−	0.106452i
$672$	3.76951e10	−	1.74678e11i	0.184845	−	0.856569i
$673$	−1.63888e11			−0.798892			−0.399446	−	0.916757i	$-0.630797\pi$
$673$	−1.63888e11			−0.798892			−0.399446	+	0.916757i	$0.630797\pi$
$674$	−6.38817e10	−	4.72671e10i	−0.309554	−	0.229044i
$675$	2.23144e11	−	4.01613e11i	1.07490	−	1.93461i
$676$	−1.39374e10	+	4.26197e9i	−0.0667413	+	0.0204091i
$677$	−9.48865e10	−	9.48865e10i	−0.451700	−	0.451700i	0.444219	−	0.895918i	$-0.353481\pi$
$677$	−9.48865e10	−	9.48865e10i	−0.451700	−	0.451700i	−0.895918	+	0.444219i	$0.853481\pi$
$678$	8.90929e10	−	8.54844e10i	0.421623	−	0.404546i
$679$		−	2.91966e11i		−	1.37358i
$680$	−2.95649e11	−	6.19702e11i	−1.38274	−	2.89833i
$681$	2.14999e11	−	1.52308e11i	0.999650	−	0.708164i
$682$	1.78049e10	+	1.19112e11i	0.0823004	+	0.550576i
$683$	2.87616e11	+	2.87616e11i	1.32169	+	1.32169i	0.912407	+	0.409285i	$0.134222\pi$
$683$	2.87616e11	+	2.87616e11i	1.32169	+	1.32169i	0.409285	+	0.912407i	$0.365778\pi$
$684$	2.55588e10	−	2.35286e10i	0.116766	−	0.107491i
$685$	2.10029e10	+	2.10029e10i	0.0953931	+	0.0953931i
$686$	1.42222e11	−	1.92214e11i	0.642200	−	0.867936i
$687$	−2.50246e11	+	1.77277e11i	−1.12341	+	0.795840i
$688$	−3.98553e10	+	2.05164e11i	−0.177882	+	0.915690i
$689$		−	1.14574e10i		−	0.0508406i
$690$	−1.09110e10	+	5.27865e11i	−0.0481359	+	2.32877i
$691$	3.50780e10	+	3.50780e10i	0.153859	+	0.153859i	0.779839	−	0.625980i	$-0.215301\pi$
$691$	3.50780e10	+	3.50780e10i	0.153859	+	0.153859i	−0.625980	+	0.779839i	$0.715301\pi$
$692$	1.72994e11	+	9.19695e10i	0.754407	+	0.401069i
$693$	1.83758e11	−	8.81540e10i	0.796733	−	0.382216i
$694$	−4.55088e10	−	3.04446e11i	−0.196181	−	1.31242i
$695$	5.37705e11			2.30465
$696$	3.64637e10	+	1.28695e11i	0.155390	+	0.548436i
$697$		−	1.20596e11i		−	0.510979i
$698$	4.87859e10	+	3.26369e11i	0.205529	+	1.37495i
$699$	−3.50000e11	−	5.97374e10i	−1.46609	−	0.250229i
$700$	1.36167e11	+	4.45289e11i	0.567124	+	1.85460i
$701$	−9.97947e10	+	9.97947e10i	−0.413271	+	0.413271i	−0.882877	−	0.469605i	$-0.844396\pi$
$701$	−9.97947e10	+	9.97947e10i	−0.413271	+	0.413271i	0.469605	+	0.882877i	$0.344396\pi$
$702$	−8.81966e10	+	2.35195e11i	−0.363164	+	0.968454i
$703$	−3.18105e10			−0.130242
$704$	−2.59350e10	−	2.46343e11i	−0.105583	−	1.00288i
$705$	−1.26749e10	+	8.97902e9i	−0.0513082	+	0.0363473i
$706$	−1.73128e11	+	2.33984e11i	−0.696866	+	0.941817i
$707$	−2.40974e11	+	2.40974e11i	−0.964479	+	0.964479i
$708$	2.74374e11	−	3.55223e11i	1.09197	−	1.41373i
$709$	2.57987e11	−	2.57987e11i	1.02097	−	1.02097i	0.0211944	−	0.999775i	$-0.493253\pi$
$709$	2.57987e11	−	2.57987e11i	1.02097	−	1.02097i	0.999775	−	0.0211944i	$-0.00674689\pi$
$710$	6.53464e10	+	4.37156e11i	0.257151	+	1.72030i
$711$	2.13396e11	+	7.50296e10i	0.835040	+	0.293599i
$712$	−5.32108e10	+	1.50304e11i	−0.207052	+	0.584859i
$713$	−1.85388e11			−0.717338
$714$	−2.82469e11	−	2.94393e11i	−1.08687	−	1.13275i
$715$	3.45517e11	−	3.45517e11i	1.32204	−	1.32204i
$716$	1.11286e11	+	5.91637e10i	0.423437	+	0.225114i
$717$	−2.38248e10	+	1.39589e11i	−0.0901473	+	0.528172i
$718$	9.69448e10	+	7.17311e10i	0.364777	+	0.269904i
$719$			1.90115e11i			0.711380i	0.934604	+	0.355690i	$0.115754\pi$
$719$			1.90115e11i			0.711380i	−0.934604	+	0.355690i	$0.884246\pi$
$720$	−4.15641e11	−	2.43514e11i	−1.54664	−	0.906136i
$721$	−1.31074e11			−0.485039
$722$	1.57558e11	−	2.12940e11i	0.579817	−	0.783626i
$723$	−4.57223e11	−	7.80379e10i	−1.67330	−	0.285596i
$724$	1.68315e11	+	8.94821e10i	0.612588	+	0.325673i
$725$	−2.46460e11	−	2.46460e11i	−0.892059	−	0.892059i
$726$	3.39223e9	−	3.25483e9i	0.0122107	−	0.0117161i
$727$		−	2.66440e11i		−	0.953810i	−0.878955	−	0.476905i	$-0.841759\pi$
$727$		−	2.66440e11i		−	0.953810i	0.878955	−	0.476905i	$-0.158241\pi$
$728$	−1.09619e11	−	2.29769e11i	−0.390265	−	0.818024i
$729$	1.49185e11	+	2.39813e11i	0.528219	+	0.849108i
$730$	−2.58464e11	+	3.86353e10i	−0.910141	+	0.136048i
$731$	3.37409e11	+	3.37409e11i	1.18165	+	1.18165i
$732$	−1.85267e10	+	2.39859e10i	−0.0645289	+	0.0835434i
$733$	1.95518e10	+	1.95518e10i	0.0677283	+	0.0677283i	0.740160	−	0.672431i	$-0.234750\pi$
$733$	1.95518e10	+	1.95518e10i	0.0677283	+	0.0677283i	−0.672431	+	0.740160i	$0.734750\pi$
$734$	8.20231e10	+	6.06902e10i	0.282587	+	0.209091i
$735$	−7.01949e10	−	9.90877e10i	−0.240523	−	0.339524i
$736$	3.80937e11	+	1.65769e10i	1.29820	+	0.0564925i
$737$		−	3.76537e11i		−	1.27625i
$738$	−4.74720e10	−	7.00367e10i	−0.160034	−	0.236102i
$739$	−2.17845e11	−	2.17845e11i	−0.730417	−	0.730417i	0.240285	−	0.970702i	$-0.422759\pi$
$739$	−2.17845e11	−	2.17845e11i	−0.730417	−	0.730417i	−0.970702	+	0.240285i	$0.922759\pi$
$740$	1.28991e11	+	4.21823e11i	0.430162	+	1.40671i
$741$	8.32658e9	−	4.87853e10i	0.0276181	−	0.161814i
$742$	1.29129e10	−	1.93023e9i	0.0425999	−	0.00636785i
$743$	−5.53060e11			−1.81475			−0.907376	−	0.420321i	$-0.861918\pi$
$743$	−5.53060e11			−1.81475			−0.907376	+	0.420321i	$0.861918\pi$
$744$	8.24704e10	−	1.47680e11i	0.269158	−	0.481979i
$745$			5.27131e11i			1.71117i
$746$	−5.72094e10	+	8.55170e9i	−0.184719	+	0.0276119i
$747$	−2.26901e11	+	1.08851e11i	−0.728710	+	0.349583i
$748$	−4.99354e11	−	2.65474e11i	−1.59515	−	0.848040i
$749$	8.88442e10	−	8.88442e10i	0.282294	−	0.282294i
$750$	6.87925e11	+	1.42195e10i	2.17418	+	0.0449406i
$751$	5.39896e11			1.69727			0.848633	−	0.528982i	$-0.177426\pi$
$751$	5.39896e11			1.69727			0.848633	+	0.528982i	$0.177426\pi$
$752$	6.27394e9	+	9.29918e9i	0.0196187	+	0.0290786i
$753$	1.15218e11	+	1.62643e11i	0.358377	+	0.505889i
$754$	1.53185e11	+	1.13344e11i	0.473949	+	0.350683i
$755$	−1.62796e11	+	1.62796e11i	−0.501021	+	0.501021i
$756$	−2.79931e11	−	5.97773e10i	−0.856965	−	0.182999i
$757$	−2.93533e11	+	2.93533e11i	−0.893867	+	0.893867i	−0.994885	−	0.101018i	$-0.967790\pi$
$757$	−2.93533e11	+	2.93533e11i	−0.893867	+	0.893867i	0.101018	+	0.994885i	$0.467790\pi$
$758$	−3.59823e11	+	5.37865e10i	−1.08996	+	0.162928i
$759$	2.51383e11	+	3.54855e11i	0.757476	+	1.06926i
$760$	8.94711e10	+	3.16746e10i	0.268181	+	0.0949418i
$761$	−5.35726e11			−1.59737			−0.798683	−	0.601752i	$-0.794469\pi$
$761$	−5.35726e11			−1.59737			−0.798683	+	0.601752i	$0.794469\pi$
$762$	3.35648e10	+	3.49816e10i	0.0995552	+	0.103758i
$763$	6.76189e10	−	6.76189e10i	0.199512	−	0.199512i
$764$	1.86628e11	−	5.70697e10i	0.547776	−	0.167507i
$765$	−9.91621e11	+	4.75710e11i	−2.89534	+	1.38898i
$766$	6.48741e10	−	8.76776e10i	0.188433	−	0.254667i
$767$		−	6.39436e11i		−	1.84763i
$768$	−1.82666e11	+	2.96078e11i	−0.525064	+	0.851063i
$769$	−8.03616e10			−0.229797			−0.114898	−	0.993377i	$-0.536654\pi$
$769$	−8.03616e10			−0.229797			−0.114898	+	0.993377i	$0.536654\pi$
$770$	4.47618e11	+	3.31200e11i	1.27334	+	0.942166i
$771$	3.36683e10	−	1.97262e11i	0.0952804	−	0.558246i
$772$	1.69868e10	+	5.55499e10i	0.0478236	+	0.156392i
$773$	−1.27562e10	−	1.27562e10i	−0.0357277	−	0.0357277i	0.689017	−	0.724745i	$-0.258042\pi$
$773$	−1.27562e10	−	1.27562e10i	−0.0357277	−	0.0357277i	−0.724745	+	0.689017i	$0.758042\pi$
$774$	3.28771e11	+	6.31324e10i	0.916071	+	0.175909i
$775$			4.40751e11i			1.22176i
$776$	−1.89689e11	+	5.35813e11i	−0.523113	+	1.47763i
$777$	1.51513e11	+	2.13878e11i	0.415688	+	0.586788i
$778$	−8.29498e10	−	5.54921e11i	−0.226411	−	1.51465i
$779$	1.17877e10	+	1.17877e10i	0.0320095	+	0.0320095i
$780$	−6.80681e11	+	8.74087e10i	−1.83893	+	0.236144i
$781$	2.57435e11	+	2.57435e11i	0.691933	+	0.691933i
$782$	5.17798e11	−	6.99806e11i	1.38463	−	1.87133i
$783$	2.06019e11	−	5.88517e10i	0.548100	−	0.156571i
$784$	−7.26978e10	+	4.90475e10i	−0.192423	+	0.129823i
$785$			8.83256e11i			2.32599i
$786$	−1.10010e11	−	2.27391e9i	−0.288231	−	0.00595776i
$787$	−4.29079e11	−	4.29079e11i	−1.11851	−	1.11851i	−0.991961	−	0.126544i	$-0.959611\pi$
$787$	−4.29079e11	−	4.29079e11i	−1.11851	−	1.11851i	−0.126544	−	0.991961i	$-0.540389\pi$
$788$	2.85724e11	−	5.37443e11i	0.741040	−	1.39389i
$789$	−1.70846e11	−	2.91597e10i	−0.440856	−	0.0752445i
$790$	9.13647e10	+	6.11215e11i	0.234569	+	1.56923i
$791$	2.00447e11			0.512027
$792$	−3.94504e11	+	4.23928e10i	−1.00265	+	0.107743i
$793$			4.31770e10i			0.109184i
$794$	−2.33347e10	−	1.56105e11i	−0.0587110	−	0.392767i
$795$	5.92159e9	−	3.46945e10i	0.0148242	−	0.0868545i
$796$	−2.61397e11	+	7.99337e10i	−0.651102	+	0.199103i
$797$	1.46528e11	−	1.46528e11i	0.363150	−	0.363150i	−0.501821	−	0.864971i	$-0.667336\pi$
$797$	1.46528e11	−	1.46528e11i	0.363150	−	0.363150i	0.864971	+	0.501821i	$0.167336\pi$
$798$	5.63854e10	+	1.16549e9i	0.139045	+	0.00287407i
$799$	2.56112e10			0.0628410
$800$	3.94106e10	−	9.05657e11i	0.0962173	−	2.21108i
$801$	2.40941e11	+	8.47146e10i	0.585304	+	0.205792i
$802$	5.00283e10	−	6.76135e10i	0.120926	−	0.163432i
$803$	−1.52206e11	+	1.52206e11i	−0.366074	+	0.366074i
$804$	−3.23267e11	+	4.18523e11i	−0.773637	+	1.00160i
$805$	−6.06085e11	+	6.06085e11i	−1.44328	+	1.44328i
$806$	−3.56244e10	−	2.38321e11i	−0.0844127	−	0.564707i
$807$	5.50328e11	−	3.89859e11i	1.29756	−	0.919207i
$808$	5.98794e11	−	2.85674e11i	1.40486	−	0.670232i
$809$	8.63005e10			0.201474			0.100737	−	0.994913i	$-0.467880\pi$
$809$	8.63005e10			0.201474			0.100737	+	0.994913i	$0.467880\pi$
$810$	−3.88627e11	+	6.66615e11i	−0.902802	+	1.54859i
$811$	3.53389e11	−	3.53389e11i	0.816902	−	0.816902i	−0.168756	−	0.985658i	$-0.553975\pi$
$811$	3.53389e11	−	3.53389e11i	0.816902	−	0.816902i	0.985658	+	0.168756i	$0.0539750\pi$
$812$	−1.01936e11	+	1.91740e11i	−0.234478	+	0.441050i
$813$	5.27315e11	+	9.00011e10i	1.20700	+	0.206009i
$814$	2.92064e11	+	2.16103e11i	0.665242	+	0.492224i
$815$		−	1.12402e12i		−	2.54768i
$816$	3.27119e11	+	7.23786e11i	0.737810	+	1.63249i
$817$	−6.59602e10			−0.148045
$818$	−2.55116e11	+	3.44791e11i	−0.569804	+	0.770092i
$819$	−3.67666e11	+	1.76380e11i	−0.817181	+	0.392026i
$820$	1.08512e11	−	2.04109e11i	0.240006	−	0.451448i
$821$	−2.56538e11	−	2.56538e11i	−0.564650	−	0.564650i	0.365975	−	0.930625i	$-0.380736\pi$
$821$	−2.56538e11	−	2.56538e11i	−0.564650	−	0.564650i	−0.930625	+	0.365975i	$0.880736\pi$
$822$	−2.37888e10	−	2.47930e10i	−0.0521058	−	0.0543053i
$823$		−	4.68423e11i		−	1.02103i	−0.859868	−	0.510516i	$-0.829454\pi$
$823$		−	4.68423e11i		−	1.02103i	0.859868	−	0.510516i	$-0.170546\pi$
$824$	2.40547e11	+	8.51586e10i	0.521784	+	0.184722i
$825$	8.43649e11	−	5.97651e11i	1.82115	−	1.29012i
$826$	7.20665e11	−	1.07725e11i	1.54815	−	0.231418i
$827$	−5.78886e11	−	5.78886e11i	−1.23757	−	1.23757i	−0.960990	−	0.276583i	$-0.910798\pi$
$827$	−5.78886e11	−	5.78886e11i	−1.23757	−	1.23757i	−0.276583	−	0.960990i	$-0.589202\pi$
$828$	2.52383e10	−	6.10243e11i	0.0536957	−	1.29832i
$829$	−3.32922e11	−	3.32922e11i	−0.704895	−	0.704895i	0.260562	−	0.965457i	$-0.416092\pi$
$829$	−3.32922e11	−	3.32922e11i	−0.704895	−	0.704895i	−0.965457	+	0.260562i	$0.916092\pi$
$830$	−5.52712e11	−	4.08961e11i	−1.16463	−	0.861726i
$831$	−4.03889e11	+	2.86120e11i	−0.846950	+	0.599990i
$832$	5.18912e10	+	4.92889e11i	0.108293	+	1.02862i
$833$			2.00220e11i			0.415841i
$834$	−6.21884e11	−	1.28544e10i	−1.28542	−	0.0265698i
$835$	−1.23291e10	−	1.23291e10i	−0.0253621	−	0.0253621i
$836$	7.47583e10	−	2.28606e10i	0.153050	−	0.0468019i
$837$	−2.36838e11	−	1.31592e11i	−0.482558	−	0.268119i
$838$	3.87188e11	−	5.78771e10i	0.785138	−	0.117363i
$839$	7.10185e11			1.43326			0.716628	−	0.697456i	$-0.245685\pi$
$839$	7.10185e11			1.43326			0.716628	+	0.697456i	$0.245685\pi$
$840$	−2.13186e11	−	7.52424e11i	−0.428196	−	1.51128i
$841$			3.37702e11i			0.675072i
$842$	−2.59275e10	+	3.87565e9i	−0.0515836	+	0.00771074i
$843$	−4.11792e10	−	7.02839e9i	−0.0815395	−	0.0139170i
$844$	−1.74316e11	+	3.27886e11i	−0.343532	+	0.646180i
$845$	−4.51008e10	+	4.51008e10i	−0.0884622	+	0.0884622i
$846$	1.48738e10	−	1.00817e10i	0.0290363	−	0.0196812i
$847$	7.63205e9			0.0148288
$848$	−2.49517e10	−	4.84713e9i	−0.0482522	−	0.00937349i
$849$	5.57228e11	−	3.94747e11i	1.07251	−	0.759781i
$850$	−1.66375e12	−	1.23104e12i	−3.18723	−	2.35828i
$851$	−3.95461e11	+	3.95461e11i	−0.754024	+	0.754024i
$852$	−6.51258e10	−	5.07156e11i	−0.123593	−	0.962462i
$853$	7.87135e10	−	7.87135e10i	0.148680	−	0.148680i	−0.628848	−	0.777528i	$-0.716473\pi$
$853$	7.87135e10	−	7.87135e10i	0.148680	−	0.148680i	0.777528	+	0.628848i	$0.216473\pi$
$854$	−4.86619e10	+	7.27401e9i	−0.0914867	+	0.0136755i
$855$	5.04278e10	−	1.43424e11i	0.0943638	−	0.268385i
$856$	−2.20768e11	+	1.05324e11i	−0.411189	+	0.196171i
$857$	−8.34302e11			−1.54668			−0.773339	−	0.633992i	$-0.781415\pi$
$857$	−8.34302e11			−1.54668			−0.773339	+	0.633992i	$0.781415\pi$
$858$	−4.07869e11	+	3.91349e11i	−0.752612	+	0.722129i
$859$	−6.28851e11	+	6.28851e11i	−1.15498	+	1.15498i	−0.169441	+	0.985540i	$0.554196\pi$
$859$	−6.28851e11	+	6.28851e11i	−1.15498	+	1.15498i	−0.985540	+	0.169441i	$0.945804\pi$
$860$	2.67467e11	+	8.74664e11i	0.488964	+	1.59900i
$861$	2.31097e10	−	1.35399e11i	0.0420514	−	0.246379i
$862$	−2.72035e11	+	3.67657e11i	−0.492715	+	0.665907i
$863$			2.21272e11i			0.398918i	0.979906	+	0.199459i	$0.0639185\pi$
$863$			2.21272e11i			0.398918i	−0.979906	+	0.199459i	$0.936081\pi$
$864$	4.74889e11	+	2.91573e11i	0.852192	+	0.523229i
$865$	8.57410e11			1.53153
$866$	6.99383e11	+	5.17485e11i	1.24349	+	0.920081i
$867$	1.23058e12	+	2.10033e11i	2.17788	+	0.371716i
$868$	2.62594e11	−	8.02998e10i	0.462601	−	0.141461i
$869$	3.59936e11	+	3.59936e11i	0.631170	+	0.631170i
$870$	4.05284e11	+	4.22392e11i	0.707428	+	0.737290i
$871$			7.53383e11i			1.30901i
$872$	−1.68025e11	+	8.01619e10i	−0.290609	+	0.138644i
$873$	8.58922e11	+	3.01996e11i	1.47876	+	0.519928i
$874$	1.77904e10	+	1.19015e11i	0.0304888	+	0.203965i
$875$	7.89863e11	+	7.89863e11i	1.34747	+	1.34747i
$876$	2.99851e11	−	3.85049e10i	0.509200	−	0.0653883i
$877$	−3.28140e11	−	3.28140e11i	−0.554703	−	0.554703i	0.373092	−	0.927795i	$-0.378298\pi$
$877$	−3.28140e11	−	3.28140e11i	−0.554703	−	0.554703i	−0.927795	+	0.373092i	$0.878298\pi$
$878$	−6.69657e11	+	9.05044e11i	−1.12687	+	1.52297i
$879$	3.94287e11	+	5.56579e11i	0.660476	+	0.932334i
$880$	−6.06286e11	−	8.98632e11i	−1.01099	−	1.49848i
$881$			1.57450e11i			0.261360i	0.991425	+	0.130680i	$0.0417161\pi$
$881$			1.57450e11i			0.261360i	−0.991425	+	0.130680i	$0.958284\pi$
$882$	7.88153e10	+	1.16278e11i	0.130238	+	0.192143i
$883$	−1.72172e11	−	1.72172e11i	−0.283217	−	0.283217i	0.551174	−	0.834391i	$-0.314180\pi$
$883$	−1.72172e11	−	1.72172e11i	−0.283217	−	0.283217i	−0.834391	+	0.551174i	$0.814180\pi$
$884$	9.99119e11	+	5.31167e11i	1.63609	+	0.869805i
$885$	3.30482e11	−	1.93629e12i	0.538735	−	3.15644i
$886$	−5.11579e10	−	3.42238e11i	−0.0830190	−	0.555383i
$887$	2.83305e11			0.457678			0.228839	−	0.973464i	$-0.426507\pi$
$887$	2.83305e11			0.457678			0.228839	+	0.973464i	$0.426507\pi$
$888$	−1.39101e11	−	4.90944e11i	−0.223706	−	0.789551i
$889$			7.87038e10i			0.126005i
$890$	1.03158e11	+	6.90112e11i	0.164416	+	1.09992i
$891$	6.92662e10	+	6.31772e11i	0.109903	+	1.00242i
$892$	1.01400e11	+	3.31597e11i	0.160170	+	0.523783i
$893$	−2.50337e9	+	2.50337e9i	−0.00393659	+	0.00393659i
$894$	1.26016e10	−	6.09655e11i	0.0197277	−	0.954408i
$895$	5.51569e11			0.859622
$896$	−5.46760e11	+	1.41520e11i	−0.848330	+	0.219576i
$897$	−5.02973e11	−	7.10001e11i	−0.776917	−	1.09670i
$898$	3.20871e11	−	4.33658e11i	0.493429	−	0.666872i
$899$	−1.45341e11	+	1.45341e11i	−0.222511	+	0.222511i
$900$	−1.45082e12	−	6.00029e10i	−2.21128	−	0.0914538i
$901$	−4.10351e10	+	4.10351e10i	−0.0622667	+	0.0622667i
$902$	−2.81481e10	−	1.88306e11i	−0.0425229	−	0.284471i
$903$	3.14168e11	+	4.43482e11i	0.472510	+	0.666999i
$904$	−3.67858e11	−	1.30230e11i	−0.550816	−	0.195001i
$905$	8.34221e11			1.24362
$906$	1.92174e11	−	1.84390e11i	0.285221	−	0.273669i
$907$	5.48970e10	−	5.48970e10i	0.0811183	−	0.0811183i	−0.665383	−	0.746502i	$-0.731732\pi$
$907$	5.48970e10	−	5.48970e10i	0.0811183	−	0.0811183i	0.746502	+	0.665383i	$0.231732\pi$
$908$	−7.35280e11	−	3.90901e11i	−1.08171	−	0.575073i
$909$	−4.59659e11	−	9.58164e11i	−0.673257	−	1.40341i
$910$	−8.95604e11	−	6.62672e11i	−1.30602	−	0.966347i
$911$		−	3.84284e11i		−	0.557929i	−0.960301	−	0.278964i	$-0.910009\pi$
$911$		−	3.84284e11i		−	0.557929i	0.960301	−	0.278964i	$-0.0899911\pi$
$912$	−1.02721e11	−	3.87723e10i	−0.148484	−	0.0560457i
$913$	−5.66316e11			−0.815034
$914$	4.69673e11	−	6.34765e11i	0.672993	−	0.909553i
$915$	−2.23154e10	+	1.30745e11i	−0.0318361	+	0.186527i
$916$	8.55821e11	+	4.54985e11i	1.21563	+	0.646271i
$917$	−1.26311e11	−	1.26311e11i	−0.178634	−	0.178634i
$918$	1.15823e12	−	5.26477e11i	1.63089	−	0.741326i
$919$			2.04008e11i			0.286013i	0.989722	+	0.143006i	$0.0456769\pi$
$919$			2.04008e11i			0.286013i	−0.989722	+	0.143006i	$0.954323\pi$
$920$	1.50605e12	−	7.18512e11i	2.10227	−	1.00296i
$921$	2.00252e11	+	2.82677e11i	0.278315	+	0.392873i
$922$	−1.03692e12	+	1.54999e11i	−1.43490	+	0.214489i
$923$	−5.15082e11	−	5.15082e11i	−0.709692	−	0.709692i
$924$	−5.09776e11	−	3.93751e11i	−0.699345	−	0.540174i
$925$	9.40188e11	+	9.40188e11i	1.28425	+	1.28425i
$926$	4.19729e11	+	3.10565e11i	0.570855	+	0.422385i
$927$	1.35577e11	−	3.85603e11i	0.183598	−	0.522181i
$928$	3.11644e11	−	2.85652e11i	0.420211	−	0.385164i
$929$		−	4.72369e10i		−	0.0634189i	−0.999497	−	0.0317095i	$-0.989905\pi$
$929$		−	4.72369e10i		−	0.0634189i	0.999497	−	0.0317095i	$-0.0100951\pi$
$930$	1.52975e10	−	7.40078e11i	0.0204498	−	0.989341i
$931$	−1.95705e10	−	1.95705e10i	−0.0260497	−	0.0260497i
$932$	3.28153e11	+	1.07312e12i	0.434923	+	1.42228i
$933$	1.15252e12	+	1.96709e11i	1.52097	+	0.259596i
$934$	−8.61315e11	+	1.28750e11i	−1.13181	+	0.169184i
$935$	−2.47496e12			−3.23833
$936$	7.89332e11	−	8.48204e10i	1.02839	−	0.110509i
$937$		−	1.65452e11i		−	0.214642i	−0.994224	−	0.107321i	$-0.965773\pi$
$937$		−	1.65452e11i		−	0.214642i	0.994224	−	0.107321i	$-0.0342273\pi$
$938$	−8.49087e11	+	1.26922e11i	−1.09683	+	0.163955i
$939$	1.30013e11	−	7.61743e11i	0.167234	−	0.979819i
$940$	4.33471e10	+	2.30448e10i	0.0555198	+	0.0295163i
$941$	9.95576e11	−	9.95576e11i	1.26974	−	1.26974i	0.323523	−	0.946220i	$-0.395133\pi$
$941$	9.95576e11	−	9.95576e11i	1.26974	−	1.26974i	0.946220	−	0.323523i	$-0.104867\pi$
$942$	2.11152e10	−	1.02153e12i	0.0268158	−	1.29732i
$943$	2.93084e11			0.370634
$944$	−1.39255e12	−	2.70517e11i	−1.75357	−	0.340648i
$945$	−1.20450e12	+	3.44079e11i	−1.51036	+	0.431450i
$946$	6.05604e11	+	4.48096e11i	0.756178	+	0.559508i
$947$	4.51277e11	−	4.51277e11i	0.561104	−	0.561104i	−0.368517	−	0.929621i	$-0.620134\pi$
$947$	4.51277e11	−	4.51277e11i	0.561104	−	0.561104i	0.929621	+	0.368517i	$0.120134\pi$
$948$	−9.10564e10	−	7.09086e11i	−0.112740	−	0.877942i
$949$	3.04537e11	−	3.04537e11i	0.375470	−	0.375470i
$950$	2.82952e11	−	4.22958e10i	0.347391	−	0.0519281i
$951$	−2.52575e11	+	1.78927e11i	−0.308794	+	0.218753i
$952$	−4.30321e11	+	1.21553e12i	−0.523896	+	1.47985i
$953$	2.79897e11			0.339333			0.169667	−	0.985502i	$-0.445731\pi$
$953$	2.79897e11			0.339333			0.169667	+	0.985502i	$0.445731\pi$
$954$	−7.67804e9	+	3.99845e10i	−0.00926951	+	0.0482723i
$955$	6.03920e11	−	6.03920e11i	0.726049	−	0.726049i
$956$	4.27987e11	−	1.30876e11i	0.512388	−	0.156685i
$957$	4.75281e11	+	8.11200e10i	0.566634	+	0.0967119i
$958$	−5.06760e11	+	6.84889e11i	−0.601645	+	0.813126i
$959$		−	5.57809e10i		−	0.0659494i
$960$	−9.76089e10	+	1.51935e12i	−0.114922	+	1.78884i
$961$	−5.92973e11			−0.695250
$962$	−5.84368e11	−	4.32383e11i	−0.682316	−	0.504857i
$963$	1.69471e11	+	3.53264e11i	0.197056	+	0.410765i
$964$	4.28683e11	+	1.40187e12i	0.496395	+	1.62330i
$965$	1.79757e11	+	1.79757e11i	0.207289	+	0.207289i
$966$	7.15459e11	−	6.86480e11i	0.821629	−	0.788351i
$967$		−	1.12920e11i		−	0.129141i	−0.997913	−	0.0645706i	$-0.979432\pi$
$967$		−	1.12920e11i		−	0.129141i	0.997913	−	0.0645706i	$-0.0205678\pi$
$968$	−1.40063e10	−	4.95851e9i	−0.0159522	−	0.00564742i
$969$	−2.04548e11	+	1.44904e11i	−0.232006	+	0.164356i
$970$	3.67745e11	+	2.46015e12i	0.415393	+	2.77891i
$971$	4.62149e11	+	4.62149e11i	0.519883	+	0.519883i	0.917536	−	0.397653i	$-0.130175\pi$
$971$	4.62149e11	+	4.62149e11i	0.519883	+	0.519883i	−0.397653	+	0.917536i	$0.630175\pi$
$972$	4.65403e11	−	7.61685e11i	0.521392	−	0.853317i
$973$	−7.14036e11	−	7.14036e11i	−0.796652	−	0.796652i
$974$	−2.59153e11	+	3.50246e11i	−0.287952	+	0.389168i
$975$	−1.68799e12	+	1.19579e12i	−1.86789	+	1.32324i
$976$	9.40299e10	+	1.82663e10i	0.103626	+	0.0201303i
$977$		−	4.99943e11i		−	0.548709i	−0.961629	−	0.274355i	$-0.911536\pi$
$977$		−	4.99943e11i		−	0.548709i	0.961629	−	0.274355i	$-0.0884642\pi$
$978$	−2.68710e10	+	1.29999e12i	−0.0293716	+	1.42097i
$979$	4.06398e11	+	4.06398e11i	0.442405	+	0.442405i
$980$	−1.80156e11	+	3.38872e11i	−0.195319	+	0.367394i
$981$	1.28983e11	+	2.68867e11i	0.139270	+	0.290310i
$982$	2.11613e10	+	1.41565e11i	0.0227560	+	0.152234i
$983$	−4.34252e11			−0.465080			−0.232540	−	0.972587i	$-0.574704\pi$
$983$	−4.34252e11			−0.465080			−0.232540	+	0.972587i	$0.574704\pi$
$984$	−1.30379e11	+	2.33469e11i	−0.139068	+	0.249029i
$985$		−	2.66374e12i		−	2.82974i
$986$	−1.42691e11	−	9.54582e11i	−0.150970	−	1.00996i
$987$	2.87549e10	+	4.90784e9i	0.0303001	+	0.00517156i
$988$	−1.49578e11	+	4.57401e10i	−0.156978	+	0.0480031i
$989$	−8.20001e11	+	8.20001e11i	−0.857096	+	0.857096i
$990$	−1.43734e12	+	9.74252e11i	−1.49630	+	1.01422i
$991$	9.26881e11			0.961013			0.480507	−	0.876991i	$-0.340453\pi$
$991$	9.26881e11			0.961013			0.480507	+	0.876991i	$0.340453\pi$
$992$	−5.34082e11	−	2.32411e10i	−0.551520	−	0.0240000i
$993$	−1.77608e11	+	1.25820e11i	−0.182669	+	0.129405i
$994$	4.93739e11	−	6.67290e11i	0.505768	−	0.683548i
$995$	−8.45872e11	+	8.45872e11i	−0.863003	+	0.863003i
$996$	6.29464e11	+	4.86198e11i	0.639637	+	0.494055i
$997$	−1.16834e11	+	1.16834e11i	−0.118247	+	0.118247i	−0.763754	−	0.645507i	$-0.776646\pi$
$997$	−1.16834e11	+	1.16834e11i	−0.118247	+	0.118247i	0.645507	+	0.763754i	$0.276646\pi$
$998$	−1.71913e11	−	1.15007e12i	−0.173295	−	1.15932i
$999$	−7.85916e11	+	2.24506e11i	−0.789068	+	0.225406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.i.a.29.49	yes	124
3.2	odd	2	inner	48.9.i.a.29.14	yes	124
16.5	even	4	inner	48.9.i.a.5.14	✓	124
48.5	odd	4	inner	48.9.i.a.5.49	yes	124

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.i.a.5.14	✓	124	16.5	even	4	inner
48.9.i.a.5.49	yes	124	48.5	odd	4	inner
48.9.i.a.29.14	yes	124	3.2	odd	2	inner
48.9.i.a.29.49	yes	124	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(12.8620 + 9.51679i) q^{2} +(-79.8454 - 13.6278i) q^{3} +(74.8613 + 244.810i) q^{4} +(792.195 + 792.195i) q^{5} +(-897.276 - 935.153i) q^{6} -2103.96i q^{7} +(-1366.94 + 3861.18i) q^{8} +(6189.56 + 2176.24i) q^{9} +O(q^{10})\)	\(q+(12.8620 + 9.51679i) q^{2} +(-79.8454 - 13.6278i) q^{3} +(74.8613 + 244.810i) q^{4} +(792.195 + 792.195i) q^{5} +(-897.276 - 935.153i) q^{6} -2103.96i q^{7} +(-1366.94 + 3861.18i) q^{8} +(6189.56 + 2176.24i) q^{9} +(2650.04 + 17728.3i) q^{10} +(10440.0 + 10440.0i) q^{11} +(-2641.10 - 20567.1i) q^{12} +(-20888.5 - 20888.5i) q^{13} +(20023.0 - 27061.1i) q^{14} +(-52457.2 - 74049.0i) q^{15} +(-54327.6 + 36653.6i) q^{16} +149626. i q^{17} +(58899.2 + 86895.6i) q^{18} +(-14625.2 - 14625.2i) q^{19} +(-134632. + 253242. i) q^{20} +(-28672.5 + 167992. i) q^{21} +(34923.7 + 233634. i) q^{22} -363633. q^{23} +(161763. - 289669. i) q^{24} +864520. i q^{25} +(-69876.2 - 467460. i) q^{26} +(-464550. - 258113. i) q^{27} +(515071. - 157505. i) q^{28} +(-285083. + 285083. i) q^{29} +(30005.6 - 1.45164e6i) q^{30} +509822. q^{31} +(-1.04758e6 - 45586.7i) q^{32} +(-691309. - 975858. i) q^{33} +(-1.42396e6 + 1.92448e6i) q^{34} +(1.66675e6 - 1.66675e6i) q^{35} +(-69406.0 + 1.67818e6i) q^{36} +(1.08753e6 - 1.08753e6i) q^{37} +(-48924.0 - 327294. i) q^{38} +(1.38319e6 + 1.95252e6i) q^{39} +(-4.14169e6 + 1.97592e6i) q^{40} -805987. q^{41} +(-1.96753e6 + 1.88784e6i) q^{42} +(2.25502e6 - 2.25502e6i) q^{43} +(-1.77426e6 + 3.33736e6i) q^{44} +(3.17933e6 + 6.62735e6i) q^{45} +(-4.67705e6 - 3.46062e6i) q^{46} -171169. i q^{47} +(4.83731e6 - 2.18625e6i) q^{48} +1.33814e6 q^{49} +(-8.22745e6 + 1.11194e7i) q^{50} +(2.03908e6 - 1.19469e7i) q^{51} +(3.54997e6 - 6.67746e6i) q^{52} +(274252. + 274252. i) q^{53} +(-3.51863e6 - 7.74088e6i) q^{54} +1.65410e7i q^{55} +(8.12378e6 + 2.87599e6i) q^{56} +(968443. + 1.36706e6i) q^{57} +(-6.37980e6 + 953656. i) q^{58} +(1.53059e7 + 1.53059e7i) q^{59} +(1.42009e7 - 1.83854e7i) q^{60} +(-1.03351e6 - 1.03351e6i) q^{61} +(6.55732e6 + 4.85187e6i) q^{62} +(4.57873e6 - 1.30226e7i) q^{63} +(-1.30402e7 - 1.05560e7i) q^{64} -3.30956e7i q^{65} +(395430. - 1.91305e7i) q^{66} +(-1.80334e7 - 1.80334e7i) q^{67} +(-3.66298e7 + 1.12012e7i) q^{68} +(2.90344e7 + 4.95554e6i) q^{69} +(3.72998e7 - 5.57560e6i) q^{70} +2.46586e7 q^{71} +(-1.68636e7 + 2.09242e7i) q^{72} +1.45791e7i q^{73} +(2.43375e7 - 3.63799e6i) q^{74} +(1.17815e7 - 6.90279e7i) q^{75} +(2.48553e6 - 4.67525e6i) q^{76} +(2.19653e7 - 2.19653e7i) q^{77} +(-791185. + 3.82768e7i) q^{78} +3.44767e7 q^{79} +(-7.20748e7 - 1.40013e7i) q^{80} +(3.35747e7 + 2.69400e7i) q^{81} +(-1.03666e7 - 7.67041e6i) q^{82} +(-2.71225e7 + 2.71225e7i) q^{83} +(-4.32725e7 + 5.55678e6i) q^{84} +(-1.18533e8 + 1.18533e8i) q^{85} +(5.04646e7 - 7.54348e6i) q^{86} +(2.66476e7 - 1.88775e7i) q^{87} +(-5.45814e7 + 2.60398e7i) q^{88} +3.89270e7 q^{89} +(-2.21785e7 + 1.15498e8i) q^{90} +(-4.39487e7 + 4.39487e7i) q^{91} +(-2.72221e7 - 8.90209e7i) q^{92} +(-4.07069e7 - 6.94778e6i) q^{93} +(1.62898e6 - 2.20157e6i) q^{94} -2.31720e7i q^{95} +(8.30235e7 + 1.79162e7i) q^{96} +1.38769e8 q^{97} +(1.72111e7 + 1.27348e7i) q^{98} +(4.18990e7 + 8.73388e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 124 q - 2 q^{3} - 4 q^{4} - 3236 q^{6}+O(q^{10}) \) 124 * q - 2 * q^3 - 4 * q^4 - 3236 * q^6	\( 124 q - 2 q^{3} - 4 q^{4} - 3236 q^{6} + 17496 q^{10} + 8608 q^{12} - 4 q^{13} - 4 q^{15} - 116560 q^{16} - 290364 q^{18} - 167556 q^{19} + 13120 q^{21} + 190552 q^{22} - 714296 q^{24} - 25538 q^{27} + 1391160 q^{28} + 3794052 q^{30} - 8 q^{31} - 4 q^{33} + 2752744 q^{34} + 1313476 q^{36} - 4 q^{37} + 12578584 q^{40} - 5150600 q^{42} + 5384956 q^{43} - 781252 q^{45} - 25980296 q^{46} + 26695408 q^{48} - 82354308 q^{49} - 15081600 q^{51} + 24748672 q^{52} - 38189720 q^{54} + 74539832 q^{58} + 68522688 q^{60} + 24476028 q^{61} + 23059200 q^{63} - 63032488 q^{64} + 79650868 q^{66} - 74704388 q^{67} - 13124 q^{69} + 109805784 q^{70} - 100711608 q^{72} - 99849278 q^{75} - 151417912 q^{76} + 158736908 q^{78} - 72203272 q^{79} - 4 q^{81} + 98422144 q^{82} + 7625392 q^{84} - 105397504 q^{85} + 53374432 q^{88} + 175196592 q^{90} - 152141184 q^{91} + 138242812 q^{93} + 114812016 q^{94} - 193537240 q^{96} - 8 q^{97} + 228915068 q^{99}+O(q^{100}) \) 124 * q - 2 * q^3 - 4 * q^4 - 3236 * q^6 + 17496 * q^10 + 8608 * q^12 - 4 * q^13 - 4 * q^15 - 116560 * q^16 - 290364 * q^18 - 167556 * q^19 + 13120 * q^21 + 190552 * q^22 - 714296 * q^24 - 25538 * q^27 + 1391160 * q^28 + 3794052 * q^30 - 8 * q^31 - 4 * q^33 + 2752744 * q^34 + 1313476 * q^36 - 4 * q^37 + 12578584 * q^40 - 5150600 * q^42 + 5384956 * q^43 - 781252 * q^45 - 25980296 * q^46 + 26695408 * q^48 - 82354308 * q^49 - 15081600 * q^51 + 24748672 * q^52 - 38189720 * q^54 + 74539832 * q^58 + 68522688 * q^60 + 24476028 * q^61 + 23059200 * q^63 - 63032488 * q^64 + 79650868 * q^66 - 74704388 * q^67 - 13124 * q^69 + 109805784 * q^70 - 100711608 * q^72 - 99849278 * q^75 - 151417912 * q^76 + 158736908 * q^78 - 72203272 * q^79 - 4 * q^81 + 98422144 * q^82 + 7625392 * q^84 - 105397504 * q^85 + 53374432 * q^88 + 175196592 * q^90 - 152141184 * q^91 + 138242812 * q^93 + 114812016 * q^94 - 193537240 * q^96 - 8 * q^97 + 228915068 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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