LMFDB - Embedded newform 29.13.c.a.12.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,13,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	29.c (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:	$26.5058207010$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.2
Character	$\chi$	$=$	29.12
Dual form			29.13.c.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-79.7284 - 79.7284i) q^{2} +(-520.777 - 520.777i) q^{3} +8617.22i q^{4} -29504.0i q^{5} +83041.4i q^{6} -164320. q^{7} +(360470. - 360470. i) q^{8} +10976.2i q^{9} +O(q^{10})$	\(q+(-79.7284 - 79.7284i) q^{2} +(-520.777 - 520.777i) q^{3} +8617.22i q^{4} -29504.0i q^{5} +83041.4i q^{6} -164320. q^{7} +(360470. - 360470. i) q^{8} +10976.2i q^{9} +(-2.35231e6 + 2.35231e6i) q^{10} +(481016. + 481016. i) q^{11} +(4.48765e6 - 4.48765e6i) q^{12} +1.83971e6i q^{13} +(1.31010e7 + 1.31010e7i) q^{14} +(-1.53650e7 + 1.53650e7i) q^{15} -2.21832e7 q^{16} +(3.38984e7 + 3.38984e7i) q^{17} +(875113. - 875113. i) q^{18} +(-2.31945e6 - 2.31945e6i) q^{19} +2.54243e8 q^{20} +(8.55742e7 + 8.55742e7i) q^{21} -7.67013e7i q^{22} -1.29217e8 q^{23} -3.75449e8 q^{24} -6.26347e8 q^{25} +(1.46677e8 - 1.46677e8i) q^{26} +(-2.71046e8 + 2.71046e8i) q^{27} -1.41598e9i q^{28} +(-1.19919e8 - 5.82610e8i) q^{29} +2.45006e9 q^{30} +(6.98008e8 + 6.98008e8i) q^{31} +(2.92143e8 + 2.92143e8i) q^{32} -5.01004e8i q^{33} -5.40533e9i q^{34} +4.84811e9i q^{35} -9.45842e7 q^{36} +(8.85509e8 - 8.85509e8i) q^{37} +3.69852e8i q^{38} +(9.58079e8 - 9.58079e8i) q^{39} +(-1.06353e10 - 1.06353e10i) q^{40} +(2.80850e9 - 2.80850e9i) q^{41} -1.36454e10i q^{42} +(-3.34488e9 - 3.34488e9i) q^{43} +(-4.14502e9 + 4.14502e9i) q^{44} +3.23842e8 q^{45} +(1.03023e10 + 1.03023e10i) q^{46} +(-1.19640e10 + 1.19640e10i) q^{47} +(1.15525e10 + 1.15525e10i) q^{48} +1.31599e10 q^{49} +(4.99376e10 + 4.99376e10i) q^{50} -3.53070e10i q^{51} -1.58532e10 q^{52} +1.12745e9 q^{53} +4.32201e10 q^{54} +(1.41919e10 - 1.41919e10i) q^{55} +(-5.92325e10 + 5.92325e10i) q^{56} +2.41584e9i q^{57} +(-3.68895e10 + 5.60115e10i) q^{58} -1.49669e9 q^{59} +(-1.32404e11 - 1.32404e11i) q^{60} +(-1.12099e10 - 1.12099e10i) q^{61} -1.11302e11i q^{62} -1.80361e9i q^{63} +4.42780e10i q^{64} +5.42789e10 q^{65} +(-3.99443e10 + 3.99443e10i) q^{66} +5.36718e10i q^{67} +(-2.92110e11 + 2.92110e11i) q^{68} +(6.72933e10 + 6.72933e10i) q^{69} +(3.86532e11 - 3.86532e11i) q^{70} -1.25698e11i q^{71} +(3.95658e9 + 3.95658e9i) q^{72} +(-4.61522e10 + 4.61522e10i) q^{73} -1.41200e11 q^{74} +(3.26187e11 + 3.26187e11i) q^{75} +(1.99872e10 - 1.99872e10i) q^{76} +(-7.90408e10 - 7.90408e10i) q^{77} -1.52772e11 q^{78} +(-1.24351e11 - 1.24351e11i) q^{79} +6.54493e11i q^{80} +2.88142e11 q^{81} -4.47835e11 q^{82} +4.68034e10 q^{83} +(-7.37412e11 + 7.37412e11i) q^{84} +(1.00014e12 - 1.00014e12i) q^{85} +5.33364e11i q^{86} +(-2.40958e11 + 3.65861e11i) q^{87} +3.46784e11 q^{88} +(2.10905e11 + 2.10905e11i) q^{89} +(-2.58194e10 - 2.58194e10i) q^{90} -3.02302e11i q^{91} -1.11349e12i q^{92} -7.27013e11i q^{93} +1.90774e12 q^{94} +(-6.84332e10 + 6.84332e10i) q^{95} -3.04283e11i q^{96} +(-8.22947e11 + 8.22947e11i) q^{97} +(-1.04922e12 - 1.04922e12i) q^{98} +(-5.27972e9 + 5.27972e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8}+O(q^{10}) $ 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8	\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8} - 1957890 q^{10} + 4120990 q^{11} + 2920062 q^{12} - 1824520 q^{14} - 8383600 q^{15} - 133743512 q^{16} + 33971578 q^{17} - 122384158 q^{18} + 65838718 q^{19} - 59408388 q^{20} + 200896236 q^{21} + 104539676 q^{23} + 163907064 q^{24} - 3086882294 q^{25} + 607848030 q^{26} - 1190867840 q^{27} + 817714294 q^{29} + 5793833612 q^{30} - 1059975938 q^{31} + 2323254598 q^{32} + 517001400 q^{36} - 864725342 q^{37} + 18048639408 q^{39} - 22547920086 q^{40} - 17292603926 q^{41} - 3344004962 q^{43} - 53750811886 q^{44} - 16067938640 q^{45} + 43310099300 q^{46} - 15159905282 q^{47} - 4602803862 q^{48} + 32036753022 q^{49} - 16057299278 q^{50} + 81167587800 q^{52} - 69552844564 q^{53} + 38996274808 q^{54} + 3944882736 q^{55} - 156397031424 q^{56} + 107434998568 q^{58} + 82613255468 q^{59} - 147410252946 q^{60} + 128229759922 q^{61} + 125938412928 q^{65} + 364716671994 q^{66} - 141670411468 q^{68} + 529640675916 q^{69} + 518962441956 q^{70} - 180699442320 q^{72} - 428225274062 q^{73} + 307721180948 q^{74} - 617987210610 q^{75} - 455232145048 q^{76} - 963484794004 q^{77} + 688403957040 q^{78} - 183006289538 q^{79} + 1001949265154 q^{81} - 1176460419184 q^{82} + 361042835756 q^{83} - 402324805420 q^{84} + 832273178976 q^{85} - 1065344596322 q^{87} - 1836857960940 q^{88} + 1922736257242 q^{89} - 1170237151648 q^{90} - 2759662014220 q^{94} + 5518358548560 q^{95} + 1356111950818 q^{97} - 2518255928616 q^{98} + 3259343912178 q^{99}+O(q^{100}) \) 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8 - 1957890 * q^10 + 4120990 * q^11 + 2920062 * q^12 - 1824520 * q^14 - 8383600 * q^15 - 133743512 * q^16 + 33971578 * q^17 - 122384158 * q^18 + 65838718 * q^19 - 59408388 * q^20 + 200896236 * q^21 + 104539676 * q^23 + 163907064 * q^24 - 3086882294 * q^25 + 607848030 * q^26 - 1190867840 * q^27 + 817714294 * q^29 + 5793833612 * q^30 - 1059975938 * q^31 + 2323254598 * q^32 + 517001400 * q^36 - 864725342 * q^37 + 18048639408 * q^39 - 22547920086 * q^40 - 17292603926 * q^41 - 3344004962 * q^43 - 53750811886 * q^44 - 16067938640 * q^45 + 43310099300 * q^46 - 15159905282 * q^47 - 4602803862 * q^48 + 32036753022 * q^49 - 16057299278 * q^50 + 81167587800 * q^52 - 69552844564 * q^53 + 38996274808 * q^54 + 3944882736 * q^55 - 156397031424 * q^56 + 107434998568 * q^58 + 82613255468 * q^59 - 147410252946 * q^60 + 128229759922 * q^61 + 125938412928 * q^65 + 364716671994 * q^66 - 141670411468 * q^68 + 529640675916 * q^69 + 518962441956 * q^70 - 180699442320 * q^72 - 428225274062 * q^73 + 307721180948 * q^74 - 617987210610 * q^75 - 455232145048 * q^76 - 963484794004 * q^77 + 688403957040 * q^78 - 183006289538 * q^79 + 1001949265154 * q^81 - 1176460419184 * q^82 + 361042835756 * q^83 - 402324805420 * q^84 + 832273178976 * q^85 - 1065344596322 * q^87 - 1836857960940 * q^88 + 1922736257242 * q^89 - 1170237151648 * q^90 - 2759662014220 * q^94 + 5518358548560 * q^95 + 1356111950818 * q^97 - 2518255928616 * q^98 + 3259343912178 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−79.7284	−	79.7284i	−1.24576	−	1.24576i	−0.957577	−	0.288179i	$-0.906950\pi$
$2$	−79.7284	−	79.7284i	−1.24576	−	1.24576i	−0.288179	−	0.957577i	$-0.593050\pi$
$3$	−520.777	−	520.777i	−0.714372	−	0.714372i	0.253075	−	0.967447i	$-0.418558\pi$
$3$	−520.777	−	520.777i	−0.714372	−	0.714372i	−0.967447	+	0.253075i	$0.918558\pi$
$4$			8617.22i			2.10381i
$5$		−	29504.0i		−	1.88826i	−0.329576	−	0.944129i	$-0.606906\pi$
$5$		−	29504.0i		−	1.88826i	0.329576	−	0.944129i	$-0.393094\pi$
$6$			83041.4i			1.77986i
$7$	−164320.			−1.39670			−0.698350	−	0.715757i	$-0.746082\pi$
$7$	−164320.			−1.39670			−0.698350	+	0.715757i	$0.746082\pi$
$8$	360470.	−	360470.i	1.37508	−	1.37508i
$9$			10976.2i			0.0206536i
$10$	−2.35231e6	+	2.35231e6i	−2.35231	+	2.35231i
$11$	481016.	+	481016.i	0.271521	+	0.271521i	0.829712	−	0.558191i	$-0.188504\pi$
$11$	481016.	+	481016.i	0.271521	+	0.271521i	−0.558191	+	0.829712i	$0.688504\pi$
$12$	4.48765e6	−	4.48765e6i	1.50291	−	1.50291i
$13$			1.83971e6i			0.381144i	0.981673	+	0.190572i	$0.0610343\pi$
$13$			1.83971e6i			0.381144i	−0.981673	+	0.190572i	$0.938966\pi$
$14$	1.31010e7	+	1.31010e7i	1.73995	+	1.73995i
$15$	−1.53650e7	+	1.53650e7i	−1.34892	+	1.34892i
$16$	−2.21832e7			−1.32222
$17$	3.38984e7	+	3.38984e7i	1.40438	+	1.40438i	0.785418	+	0.618966i	$0.212448\pi$
$17$	3.38984e7	+	3.38984e7i	1.40438	+	1.40438i	0.618966	+	0.785418i	$0.287552\pi$
$18$	875113.	−	875113.i	0.0257294	−	0.0257294i
$19$	−2.31945e6	−	2.31945e6i	−0.0493019	−	0.0493019i	0.682026	−	0.731328i	$-0.261099\pi$
$19$	−2.31945e6	−	2.31945e6i	−0.0493019	−	0.0493019i	−0.731328	+	0.682026i	$0.761099\pi$
$20$	2.54243e8			3.97254
$21$	8.55742e7	+	8.55742e7i	0.997763	+	0.997763i
$22$		−	7.67013e7i		−	0.676498i
$23$	−1.29217e8			−0.872877			−0.436438	−	0.899734i	$-0.643760\pi$
$23$	−1.29217e8			−0.872877			−0.436438	+	0.899734i	$0.643760\pi$
$24$	−3.75449e8			−1.96464
$25$	−6.26347e8			−2.56552
$26$	1.46677e8	−	1.46677e8i	0.474812	−	0.474812i
$27$	−2.71046e8	+	2.71046e8i	−0.699617	+	0.699617i
$28$		−	1.41598e9i		−	2.93840i
$29$	−1.19919e8	−	5.82610e8i	−0.201605	−	0.979467i
$29$	−1.19919e8	−	5.82610e8i	−0.201605	−	0.979467i
$30$	2.45006e9			3.36084
$31$	6.98008e8	+	6.98008e8i	0.786485	+	0.786485i	0.980916	−	0.194431i	$-0.0622861\pi$
$31$	6.98008e8	+	6.98008e8i	0.786485	+	0.786485i	−0.194431	+	0.980916i	$0.562286\pi$
$32$	2.92143e8	+	2.92143e8i	0.272080	+	0.272080i
$33$		−	5.01004e8i		−	0.387934i
$34$		−	5.40533e9i		−	3.49904i
$35$			4.84811e9i			2.63733i
$36$	−9.45842e7			−0.0434514
$37$	8.85509e8	−	8.85509e8i	0.345130	−	0.345130i	−0.513162	−	0.858292i	$-0.671526\pi$
$37$	8.85509e8	−	8.85509e8i	0.345130	−	0.345130i	0.858292	+	0.513162i	$0.171526\pi$
$38$			3.69852e8i			0.122836i
$39$	9.58079e8	−	9.58079e8i	0.272279	−	0.272279i
$40$	−1.06353e10	−	1.06353e10i	−2.59651	−	2.59651i
$41$	2.80850e9	−	2.80850e9i	0.591251	−	0.591251i	−0.346719	−	0.937969i	$-0.612704\pi$
$41$	2.80850e9	−	2.80850e9i	0.591251	−	0.591251i	0.937969	+	0.346719i	$0.112704\pi$
$42$		−	1.36454e10i		−	2.48594i
$43$	−3.34488e9	−	3.34488e9i	−0.529139	−	0.529139i	0.391176	−	0.920316i	$-0.372068\pi$
$43$	−3.34488e9	−	3.34488e9i	−0.529139	−	0.529139i	−0.920316	+	0.391176i	$0.872068\pi$
$44$	−4.14502e9	+	4.14502e9i	−0.571230	+	0.571230i
$45$	3.23842e8			0.0389994
$46$	1.03023e10	+	1.03023e10i	1.08739	+	1.08739i
$47$	−1.19640e10	+	1.19640e10i	−1.10991	+	1.10991i	−0.116750	+	0.993161i	$0.537248\pi$
$47$	−1.19640e10	+	1.19640e10i	−1.10991	+	1.10991i	−0.993161	+	0.116750i	$0.962752\pi$
$48$	1.15525e10	+	1.15525e10i	0.944556	+	0.944556i
$49$	1.31599e10			0.950770
$50$	4.99376e10	+	4.99376e10i	3.19601	+	3.19601i
$51$		−	3.53070e10i		−	2.00650i
$52$	−1.58532e10			−0.801856
$53$	1.12745e9			0.0508675			0.0254337	−	0.999677i	$-0.491903\pi$
$53$	1.12745e9			0.0508675			0.0254337	+	0.999677i	$0.491903\pi$
$54$	4.32201e10			1.74310
$55$	1.41919e10	−	1.41919e10i	0.512702	−	0.512702i
$56$	−5.92325e10	+	5.92325e10i	−1.92058	+	1.92058i
$57$			2.41584e9i			0.0704398i
$58$	−3.68895e10	+	5.60115e10i	−0.969026	+	1.47133i
$59$	−1.49669e9			−0.0354830			−0.0177415	−	0.999843i	$-0.505648\pi$
$59$	−1.49669e9			−0.0354830			−0.0177415	+	0.999843i	$0.505648\pi$
$60$	−1.32404e11	−	1.32404e11i	−2.83787	−	2.83787i
$61$	−1.12099e10	−	1.12099e10i	−0.217583	−	0.217583i	0.589896	−	0.807479i	$-0.299169\pi$
$61$	−1.12099e10	−	1.12099e10i	−0.217583	−	0.217583i	−0.807479	+	0.589896i	$0.799169\pi$
$62$		−	1.11302e11i		−	1.95954i
$63$		−	1.80361e9i		−	0.0288469i
$64$			4.42780e10i			0.644330i
$65$	5.42789e10			0.719699
$66$	−3.99443e10	+	3.99443e10i	−0.483271	+	0.483271i
$67$			5.36718e10i			0.593331i	0.954981	+	0.296665i	$0.0958746\pi$
$67$			5.36718e10i			0.593331i	−0.954981	+	0.296665i	$0.904125\pi$
$68$	−2.92110e11	+	2.92110e11i	−2.95456	+	2.95456i
$69$	6.72933e10	+	6.72933e10i	0.623558	+	0.623558i
$70$	3.86532e11	−	3.86532e11i	3.28547	−	3.28547i
$71$		−	1.25698e11i		−	0.981246i	−0.871372	−	0.490623i	$-0.836769\pi$
$71$		−	1.25698e11i		−	0.981246i	0.871372	−	0.490623i	$-0.163231\pi$
$72$	3.95658e9	+	3.95658e9i	0.0284004	+	0.0284004i
$73$	−4.61522e10	+	4.61522e10i	−0.304969	+	0.304969i	−0.842954	−	0.537985i	$-0.819186\pi$
$73$	−4.61522e10	+	4.61522e10i	−0.304969	+	0.304969i	0.537985	+	0.842954i	$0.319186\pi$
$74$	−1.41200e11			−0.859896
$75$	3.26187e11	+	3.26187e11i	1.83273	+	1.83273i
$76$	1.99872e10	−	1.99872e10i	0.103722	−	0.103722i
$77$	−7.90408e10	−	7.90408e10i	−0.379234	−	0.379234i
$78$	−1.52772e11			−0.678385
$79$	−1.24351e11	−	1.24351e11i	−0.511550	−	0.511550i	0.403451	−	0.915001i	$-0.367811\pi$
$79$	−1.24351e11	−	1.24351e11i	−0.511550	−	0.511550i	−0.915001	+	0.403451i	$0.867811\pi$
$80$			6.54493e11i			2.49669i
$81$	2.88142e11			1.02023
$82$	−4.47835e11			−1.47311
$83$	4.68034e10			0.143156			0.0715779	−	0.997435i	$-0.477197\pi$
$83$	4.68034e10			0.143156			0.0715779	+	0.997435i	$0.477197\pi$
$84$	−7.37412e11	+	7.37412e11i	−2.09911	+	2.09911i
$85$	1.00014e12	−	1.00014e12i	2.65184	−	2.65184i
$86$			5.33364e11i			1.31836i
$87$	−2.40958e11	+	3.65861e11i	−0.555682	+	0.843724i
$88$	3.46784e11			0.746728
$89$	2.10905e11	+	2.10905e11i	0.424373	+	0.424373i	0.886706	−	0.462333i	$-0.152988\pi$
$89$	2.10905e11	+	2.10905e11i	0.424373	+	0.424373i	−0.462333	+	0.886706i	$0.652988\pi$
$90$	−2.58194e10	−	2.58194e10i	−0.0485837	−	0.0485837i
$91$		−	3.02302e11i		−	0.532344i
$92$		−	1.11349e12i		−	1.83637i
$93$		−	7.27013e11i		−	1.12369i
$94$	1.90774e12			2.76536
$95$	−6.84332e10	+	6.84332e10i	−0.0930948	+	0.0930948i
$96$		−	3.04283e11i		−	0.388732i
$97$	−8.22947e11	+	8.22947e11i	−0.987965	+	0.987965i	−0.999928	−	0.0119633i	$-0.996192\pi$
$97$	−8.22947e11	+	8.22947e11i	−0.987965	+	0.987965i	0.0119633	+	0.999928i	$0.496192\pi$
$98$	−1.04922e12	−	1.04922e12i	−1.18443	−	1.18443i
$99$	−5.27972e9	+	5.27972e9i	−0.00560790	+	0.00560790i
$100$		−	5.39737e12i		−	5.39737i
$101$	1.04643e12	+	1.04643e12i	0.985782	+	0.985782i	0.999900	−	0.0141188i	$-0.00449429\pi$
$101$	1.04643e12	+	1.04643e12i	0.985782	+	0.985782i	−0.0141188	+	0.999900i	$0.504494\pi$
$102$	−2.81497e12	+	2.81497e12i	−2.49961	+	2.49961i
$103$	−5.19962e11			−0.435460			−0.217730	−	0.976009i	$-0.569865\pi$
$103$	−5.19962e11			−0.435460			−0.217730	+	0.976009i	$0.569865\pi$
$104$	6.63160e11	+	6.63160e11i	0.524105	+	0.524105i
$105$	2.52479e12	−	2.52479e12i	1.88403	−	1.88403i
$106$	−8.98893e10	−	8.98893e10i	−0.0633684	−	0.0633684i
$107$	4.38462e11			0.292166			0.146083	−	0.989272i	$-0.453333\pi$
$107$	4.38462e11			0.292166			0.146083	+	0.989272i	$0.453333\pi$
$108$	−2.33566e12	−	2.33566e12i	−1.47186	−	1.47186i
$109$			2.17222e12i			1.29522i	0.761971	+	0.647612i	$0.224232\pi$
$109$			2.17222e12i			1.29522i	−0.761971	+	0.647612i	$0.775768\pi$
$110$	−2.26300e12			−1.27740
$111$	−9.22306e11			−0.493102
$112$	3.64514e12			1.84674
$113$	1.18540e12	−	1.18540e12i	0.569369	−	0.569369i	−0.362582	−	0.931952i	$-0.618105\pi$
$113$	1.18540e12	−	1.18540e12i	0.569369	−	0.569369i	0.931952	+	0.362582i	$0.118105\pi$
$114$	1.92611e11	−	1.92611e11i	0.0877508	−	0.0877508i
$115$			3.81243e12i			1.64822i
$116$	5.02048e12	−	1.03337e12i	2.06062	−	0.424140i
$117$	−2.01930e10			−0.00787201
$118$	1.19329e11	+	1.19329e11i	0.0442031	+	0.0442031i
$119$	−5.57020e12	−	5.57020e12i	−1.96150	−	1.96150i
$120$			1.10772e13i			3.70975i
$121$		−	2.67567e12i		−	0.852552i
$122$			1.78750e12i			0.542110i
$123$	−2.92521e12			−0.844745
$124$	−6.01489e12	+	6.01489e12i	−1.65462	+	1.65462i
$125$			1.12766e13i			2.95610i
$126$	−1.43799e11	+	1.43799e11i	−0.0359362	+	0.0359362i
$127$	2.94471e12	+	2.94471e12i	0.701811	+	0.701811i	0.964799	−	0.262988i	$-0.0847080\pi$
$127$	2.94471e12	+	2.94471e12i	0.701811	+	0.701811i	−0.262988	+	0.964799i	$0.584708\pi$
$128$	4.72683e12	−	4.72683e12i	1.07476	−	1.07476i
$129$			3.48387e12i			0.756004i
$130$	−4.32757e12	−	4.32757e12i	−0.896569	−	0.896569i
$131$	8.93594e11	−	8.93594e11i	0.176812	−	0.176812i	−0.613152	−	0.789965i	$-0.710099\pi$
$131$	8.93594e11	−	8.93594e11i	0.176812	−	0.176812i	0.789965	+	0.613152i	$0.210099\pi$
$132$	4.31727e12			0.816141
$133$	3.81133e11	+	3.81133e11i	0.0688600	+	0.0688600i
$134$	4.27916e12	−	4.27916e12i	0.739145	−	0.739145i
$135$	7.99695e12	+	7.99695e12i	1.32106	+	1.32106i
$136$	2.44387e13			3.86229
$137$	−6.70637e12	−	6.70637e12i	−1.01430	−	1.01430i	−0.999896	−	0.0143989i	$-0.995417\pi$
$137$	−6.70637e12	−	6.70637e12i	−1.01430	−	1.01430i	−0.0143989	−	0.999896i	$-0.504583\pi$
$138$		−	1.07304e13i		−	1.55360i
$139$	−8.44787e12			−1.17127			−0.585637	−	0.810573i	$-0.699156\pi$
$139$	−8.44787e12			−1.17127			−0.585637	+	0.810573i	$0.699156\pi$
$140$	−4.17773e13			−5.54845
$141$	1.24611e13			1.58578
$142$	−1.00217e13	+	1.00217e13i	−1.22239	+	1.22239i
$143$	−8.84931e11	+	8.84931e11i	−0.103489	+	0.103489i
$144$		−	2.43486e11i		−	0.0273086i
$145$	−1.71893e13	+	3.53811e12i	−1.84949	+	0.380682i
$146$	7.35928e12			0.759833
$147$	−6.85336e12	−	6.85336e12i	−0.679203	−	0.679203i
$148$	7.63063e12	+	7.63063e12i	0.726090	+	0.726090i
$149$			1.48428e13i			1.35643i	0.734864	+	0.678215i	$0.237246\pi$
$149$			1.48428e13i			1.35643i	−0.734864	+	0.678215i	$0.762754\pi$
$150$		−	5.20128e13i		−	4.56628i
$151$		−	3.23177e12i		−	0.272633i	−0.990665	−	0.136317i	$-0.956474\pi$
$151$		−	3.23177e12i		−	0.272633i	0.990665	−	0.136317i	$-0.0435265\pi$
$152$	−1.67218e12			−0.135588
$153$	−3.72075e11	+	3.72075e11i	−0.0290056	+	0.0290056i
$154$			1.26036e13i			0.944865i
$155$	2.05941e13	−	2.05941e13i	1.48509	−	1.48509i
$156$	8.25598e12	+	8.25598e12i	0.572823	+	0.572823i
$157$	1.42724e13	−	1.42724e13i	0.953012	−	0.953012i	−0.0459329	−	0.998945i	$-0.514626\pi$
$157$	1.42724e13	−	1.42724e13i	0.953012	−	0.953012i	0.998945	+	0.0459329i	$0.0146260\pi$
$158$			1.98287e13i			1.27453i
$159$	−5.87147e11	−	5.87147e11i	−0.0363383	−	0.0363383i
$160$	8.61941e12	−	8.61941e12i	0.513757	−	0.513757i
$161$	2.12330e13			1.21915
$162$	−2.29731e13	−	2.29731e13i	−1.27095	−	1.27095i
$163$	−1.70979e13	+	1.70979e13i	−0.911628	+	0.911628i	−0.996400	−	0.0847719i	$-0.972984\pi$
$163$	−1.70979e13	+	1.70979e13i	−0.911628	+	0.911628i	0.0847719	+	0.996400i	$0.472984\pi$
$164$	2.42015e13	+	2.42015e13i	1.24388	+	1.24388i
$165$	−1.47817e13			−0.732520
$166$	−3.73156e12	−	3.73156e12i	−0.178337	−	0.178337i
$167$			1.02299e13i			0.471599i	0.971802	+	0.235799i	$0.0757709\pi$
$167$			1.02299e13i			0.471599i	−0.971802	+	0.235799i	$0.924229\pi$
$168$	6.16938e13			2.74401
$169$	1.99136e13			0.854729
$170$	−1.59479e14			−6.60709
$171$	2.54587e10	−	2.54587e10i	0.00101826	−	0.00101826i
$172$	2.88236e13	−	2.88236e13i	1.11321	−	1.11321i
$173$			3.13678e12i			0.117006i	0.998287	+	0.0585029i	$0.0186327\pi$
$173$			3.13678e12i			0.117006i	−0.998287	+	0.0585029i	$0.981367\pi$
$174$	4.83807e13	−	9.95827e12i	1.74332	−	0.358830i
$175$	1.02922e14			3.58326
$176$	−1.06705e13	−	1.06705e13i	−0.359011	−	0.359011i
$177$	7.79442e11	+	7.79442e11i	0.0253480	+	0.0253480i
$178$		−	3.36303e13i		−	1.05733i
$179$			3.71058e13i			1.12804i	0.825762	+	0.564018i	$0.190745\pi$
$179$			3.71058e13i			1.12804i	−0.825762	+	0.564018i	$0.809255\pi$
$180$			2.79062e12i			0.0820474i
$181$	1.66113e13			0.472424			0.236212	−	0.971702i	$-0.424094\pi$
$181$	1.66113e13			0.472424			0.236212	+	0.971702i	$0.424094\pi$
$182$	−2.41020e13	+	2.41020e13i	−0.663170	+	0.663170i
$183$			1.16758e13i			0.310870i
$184$	−4.65788e13	+	4.65788e13i	−1.20028	+	1.20028i
$185$	−2.61261e13	−	2.61261e13i	−0.651695	−	0.651695i
$186$	−5.79636e13	+	5.79636e13i	−1.39984	+	1.39984i
$187$			3.26114e13i			0.762640i
$188$	−1.03096e14	−	1.03096e14i	−2.33505	−	2.33505i
$189$	4.45384e13	−	4.45384e13i	0.977155	−	0.977155i
$190$	1.09121e13			0.231947
$191$	−1.25993e12	−	1.25993e12i	−0.0259506	−	0.0259506i	0.694012	−	0.719963i	$-0.255841\pi$
$191$	−1.25993e12	−	1.25993e12i	−0.0259506	−	0.0259506i	−0.719963	+	0.694012i	$0.755841\pi$
$192$	2.30590e13	−	2.30590e13i	0.460291	−	0.460291i
$193$	−4.35337e13	−	4.35337e13i	−0.842329	−	0.842329i	0.146832	−	0.989161i	$-0.453092\pi$
$193$	−4.35337e13	−	4.35337e13i	−0.842329	−	0.842329i	−0.989161	+	0.146832i	$0.953092\pi$
$194$	1.31224e14			2.46153
$195$	−2.82672e13	−	2.82672e13i	−0.514132	−	0.514132i
$196$			1.13402e14i			2.00024i
$197$	4.51153e13			0.771838			0.385919	−	0.922533i	$-0.373884\pi$
$197$	4.51153e13			0.771838			0.385919	+	0.922533i	$0.373884\pi$
$198$	8.41887e11			0.0139721
$199$	5.71171e13			0.919703			0.459852	−	0.887996i	$-0.347903\pi$
$199$	5.71171e13			0.919703			0.459852	+	0.887996i	$0.347903\pi$
$200$	−2.25779e14	+	2.25779e14i	−3.52780	+	3.52780i
$201$	2.79510e13	−	2.79510e13i	0.423859	−	0.423859i
$202$		−	1.66860e14i		−	2.45609i
$203$	1.97052e13	+	9.57346e13i	0.281582	+	1.36802i
$204$	3.04248e14			4.22131
$205$	−8.28622e13	−	8.28622e13i	−1.11643	−	1.11643i
$206$	4.14557e13	+	4.14557e13i	0.542477	+	0.542477i
$207$		−	1.41831e12i		−	0.0180281i
$208$		−	4.08106e13i		−	0.503956i
$209$		−	2.23139e12i		−	0.0267730i
$210$	−4.02594e14			−4.69409
$211$	8.82435e13	−	8.82435e13i	0.999973	−	0.999973i	−2.74375e−5	−	1.00000i	$-0.500009\pi$
$211$	8.82435e13	−	8.82435e13i	0.999973	−	0.999973i	1.00000		2.74375e-5i	$8.73363e-6\pi$
$212$			9.71544e12i			0.107016i
$213$	−6.54606e13	+	6.54606e13i	−0.700974	+	0.700974i
$214$	−3.49578e13	−	3.49578e13i	−0.363967	−	0.363967i
$215$	−9.86875e13	+	9.86875e13i	−0.999152	+	0.999152i
$216$			1.95408e14i			1.92406i
$217$	−1.14697e14	−	1.14697e14i	−1.09848	−	1.09848i
$218$	1.73187e14	−	1.73187e14i	1.61353	−	1.61353i
$219$	4.80700e13			0.435722
$220$	1.22295e14	+	1.22295e14i	1.07863	+	1.07863i
$221$	−6.23632e13	+	6.23632e13i	−0.535273	+	0.535273i
$222$	7.35339e13	+	7.35339e13i	0.614285	+	0.614285i
$223$	2.36154e14			1.92028			0.960142	−	0.279514i	$-0.0901733\pi$
$223$	2.36154e14			1.92028			0.960142	+	0.279514i	$0.0901733\pi$
$224$	−4.80051e13	−	4.80051e13i	−0.380014	−	0.380014i
$225$		−	6.87490e12i		−	0.0529873i
$226$	−1.89020e14			−1.41859
$227$	−1.50426e14			−1.09943			−0.549715	−	0.835353i	$-0.685263\pi$
$227$	−1.50426e14			−1.09943			−0.549715	+	0.835353i	$0.685263\pi$
$228$	−2.08178e13			−0.148192
$229$	4.99148e11	−	4.99148e11i	0.00346112	−	0.00346112i	−0.705374	−	0.708835i	$-0.749221\pi$
$229$	4.99148e11	−	4.99148e11i	0.00346112	−	0.00346112i	0.708835	+	0.705374i	$0.249221\pi$
$230$	3.03958e14	−	3.03958e14i	2.05328	−	2.05328i
$231$			8.23252e13i			0.541827i
$232$	−2.53240e14	−	1.66786e14i	−1.62407	−	1.06962i
$233$	−1.99288e14			−1.24551			−0.622753	−	0.782419i	$-0.713986\pi$
$233$	−1.99288e14			−1.24551			−0.622753	+	0.782419i	$0.713986\pi$
$234$	1.60995e12	+	1.60995e12i	0.00980660	+	0.00980660i
$235$	3.52985e14	+	3.52985e14i	2.09580	+	2.09580i
$236$		−	1.28973e13i		−	0.0746496i
$237$			1.29519e14i			0.730874i
$238$			8.88206e14i			4.88711i
$239$	−1.23800e14			−0.664251			−0.332126	−	0.943235i	$-0.607766\pi$
$239$	−1.23800e14			−0.664251			−0.332126	+	0.943235i	$0.607766\pi$
$240$	3.40845e14	−	3.40845e14i	1.78357	−	1.78357i
$241$		−	1.96080e14i		−	1.00076i	−0.865805	−	0.500382i	$-0.833193\pi$
$241$		−	1.96080e14i		−	1.00076i	0.865805	−	0.500382i	$-0.166807\pi$
$242$	−2.13327e14	+	2.13327e14i	−1.06207	+	1.06207i
$243$	−6.01284e12	−	6.01284e12i	−0.0292040	−	0.0292040i
$244$	9.65986e13	−	9.65986e13i	0.457754	−	0.457754i
$245$		−	3.88270e14i		−	1.79530i
$246$	2.33222e14	+	2.33222e14i	1.05235	+	1.05235i
$247$	4.26712e12	−	4.26712e12i	0.0187911	−	0.0187911i
$248$	5.03222e14			2.16296
$249$	−2.43741e13	−	2.43741e13i	−0.102266	−	0.102266i
$250$	8.99068e14	−	8.99068e14i	3.68258	−	3.68258i
$251$	3.18970e13	+	3.18970e13i	0.127558	+	0.127558i	0.768003	−	0.640446i	$-0.221250\pi$
$251$	3.18970e13	+	3.18970e13i	0.127558	+	0.127558i	−0.640446	+	0.768003i	$0.721250\pi$
$252$	1.55421e13			0.0606885
$253$	−6.21555e13	−	6.21555e13i	−0.237005	−	0.237005i
$254$		−	4.69554e14i		−	1.74857i
$255$	−1.04170e15			−3.78880
$256$	−5.72362e14			−2.03344
$257$	−1.38365e14			−0.480206			−0.240103	−	0.970747i	$-0.577181\pi$
$257$	−1.38365e14			−0.480206			−0.240103	+	0.970747i	$0.577181\pi$
$258$	2.77764e14	−	2.77764e14i	0.941796	−	0.941796i
$259$	−1.45507e14	+	1.45507e14i	−0.482043	+	0.482043i
$260$			4.67733e14i			1.51411i
$261$	6.39483e12	−	1.31626e12i	0.0202295	−	0.00416387i
$262$	−1.42490e14			−0.440530
$263$	−1.18773e14	−	1.18773e14i	−0.358907	−	0.358907i	0.504503	−	0.863410i	$-0.331676\pi$
$263$	−1.18773e14	−	1.18773e14i	−0.358907	−	0.358907i	−0.863410	+	0.504503i	$0.831676\pi$
$264$	−1.80597e14	−	1.80597e14i	−0.533441	−	0.533441i
$265$		−	3.32642e13i		−	0.0960509i
$266$		−	6.07743e13i		−	0.171565i
$267$		−	2.19669e14i		−	0.606320i
$268$	−4.62501e14			−1.24826
$269$	3.38757e14	−	3.38757e14i	0.894075	−	0.894075i	−0.100829	−	0.994904i	$-0.532149\pi$
$269$	3.38757e14	−	3.38757e14i	0.894075	−	0.894075i	0.994904	+	0.100829i	$0.0321494\pi$
$270$		−	1.27517e15i		−	3.29143i
$271$	2.15962e14	−	2.15962e14i	0.545206	−	0.545206i	−0.379844	−	0.925050i	$-0.624022\pi$
$271$	2.15962e14	−	2.15962e14i	0.545206	−	0.545206i	0.925050	+	0.379844i	$0.124022\pi$
$272$	−7.51974e14	−	7.51974e14i	−1.85690	−	1.85690i
$273$	−1.57432e14	+	1.57432e14i	−0.380291	+	0.380291i
$274$			1.06938e15i			2.52713i
$275$	−3.01283e14	−	3.01283e14i	−0.696593	−	0.696593i
$276$	−5.79881e14	+	5.79881e14i	−1.31185	+	1.31185i
$277$	−1.54301e13			−0.0341578			−0.0170789	−	0.999854i	$-0.505437\pi$
$277$	−1.54301e13			−0.0341578			−0.0170789	+	0.999854i	$0.505437\pi$
$278$	6.73535e14	+	6.73535e14i	1.45912	+	1.45912i
$279$	−7.66147e12	+	7.66147e12i	−0.0162438	+	0.0162438i
$280$	1.74760e15	+	1.74760e15i	3.62655	+	3.62655i
$281$	−3.72055e13			−0.0755735			−0.0377867	−	0.999286i	$-0.512031\pi$
$281$	−3.72055e13			−0.0755735			−0.0377867	+	0.999286i	$0.512031\pi$
$282$	−9.93505e14	−	9.93505e14i	−1.97549	−	1.97549i
$283$			1.06373e14i			0.207067i	0.994626	+	0.103534i	$0.0330149\pi$
$283$			1.06373e14i			0.207067i	−0.994626	+	0.103534i	$0.966985\pi$
$284$	1.08317e15			2.06436
$285$	7.12769e13			0.133009
$286$	1.41108e14			0.257843
$287$	−4.61494e14	+	4.61494e14i	−0.825800	+	0.825800i
$288$	−3.20662e12	+	3.20662e12i	−0.00561943	+	0.00561943i
$289$			1.71558e15i			2.94459i
$290$	1.65257e15	+	1.08839e15i	2.77825	+	1.82977i
$291$	8.57144e14			1.41155
$292$	−3.97704e14	−	3.97704e14i	−0.641598	−	0.641598i
$293$	3.07202e14	+	3.07202e14i	0.485532	+	0.485532i	0.906893	−	0.421361i	$-0.138447\pi$
$293$	3.07202e14	+	3.07202e14i	0.485532	+	0.485532i	−0.421361	+	0.906893i	$0.638447\pi$
$294$			1.09282e15i			1.69224i
$295$			4.41584e13i			0.0670010i
$296$		−	6.38399e14i		−	0.949165i
$297$	−2.60755e14			−0.379922
$298$	1.18339e15	−	1.18339e15i	1.68978	−	1.68978i
$299$		−	2.37722e14i		−	0.332692i
$300$	−2.81083e15	+	2.81083e15i	−3.85573	+	3.85573i
$301$	5.49632e14	+	5.49632e14i	0.739049	+	0.739049i
$302$	−2.57664e14	+	2.57664e14i	−0.339634	+	0.339634i
$303$		−	1.08991e15i		−	1.40843i
$304$	5.14528e13	+	5.14528e13i	0.0651880	+	0.0651880i
$305$	−3.30739e14	+	3.30739e14i	−0.410852	+	0.410852i
$306$	5.93299e13			0.0722678
$307$	−6.44174e14	−	6.44174e14i	−0.769437	−	0.769437i	0.208570	−	0.978007i	$-0.433119\pi$
$307$	−6.44174e14	−	6.44174e14i	−0.769437	−	0.769437i	−0.978007	+	0.208570i	$0.933119\pi$
$308$	6.81112e14	−	6.81112e14i	0.797837	−	0.797837i
$309$	2.70784e14	+	2.70784e14i	0.311080	+	0.311080i
$310$	−3.28386e15			−3.70011
$311$	−3.47288e14	−	3.47288e14i	−0.383819	−	0.383819i	0.488657	−	0.872476i	$-0.337487\pi$
$311$	−3.47288e14	−	3.47288e14i	−0.383819	−	0.383819i	−0.872476	+	0.488657i	$0.837487\pi$
$312$		−	6.90716e14i		−	0.748811i
$313$	−1.06621e15			−1.13390			−0.566951	−	0.823752i	$-0.691877\pi$
$313$	−1.06621e15			−1.13390			−0.566951	+	0.823752i	$0.691877\pi$
$314$	−2.27583e15			−2.37444
$315$	−5.32138e13			−0.0544704
$316$	1.07156e15	−	1.07156e15i	1.07621	−	1.07621i
$317$	6.05325e14	−	6.05325e14i	0.596531	−	0.596531i	−0.342857	−	0.939388i	$-0.611394\pi$
$317$	6.05325e14	−	6.05325e14i	0.596531	−	0.596531i	0.939388	+	0.342857i	$0.111394\pi$
$318$			9.36246e13i			0.0905372i
$319$	2.22562e14	−	3.37928e14i	0.211206	−	0.320686i
$320$	1.30638e15			1.21666
$321$	−2.28341e14	−	2.28341e14i	−0.208715	−	0.208715i
$322$	−1.69287e15	−	1.69287e15i	−1.51876	−	1.51876i
$323$		−	1.57252e14i		−	0.138478i
$324$			2.48299e15i			2.14637i
$325$		−	1.15230e15i		−	0.977833i
$326$	2.72638e15			2.27133
$327$	1.13124e15	−	1.13124e15i	0.925271	−	0.925271i
$328$		−	2.02476e15i		−	1.62604i
$329$	1.96592e15	−	1.96592e15i	1.55021	−	1.55021i
$330$	1.17852e15	+	1.17852e15i	0.912541	+	0.912541i
$331$	−1.43585e15	+	1.43585e15i	−1.09179	+	1.09179i	−0.0964571	+	0.995337i	$0.530751\pi$
$331$	−1.43585e15	+	1.43585e15i	−1.09179	+	1.09179i	−0.995337	+	0.0964571i	$0.969249\pi$
$332$			4.03315e14i			0.301173i
$333$	9.71951e12	+	9.71951e12i	0.00712819	+	0.00712819i
$334$	8.15614e14	−	8.15614e14i	0.587497	−	0.587497i
$335$	1.58353e15			1.12036
$336$	−1.89831e15	−	1.89831e15i	−1.31926	−	1.31926i
$337$	4.48665e14	−	4.48665e14i	0.306297	−	0.306297i	−0.537174	−	0.843471i	$-0.680508\pi$
$337$	4.48665e14	−	4.48665e14i	0.306297	−	0.306297i	0.843471	+	0.537174i	$0.180508\pi$
$338$	−1.58767e15	−	1.58767e15i	−1.06478	−	1.06478i
$339$	−1.23466e15			−0.813482
$340$	8.61843e15	+	8.61843e15i	5.57898	+	5.57898i
$341$			6.71507e14i			0.427095i
$342$	−4.05957e12			−0.00253702
$343$	1.11968e14			0.0687590
$344$	−2.41146e15			−1.45522
$345$	1.98542e15	−	1.98542e15i	1.17744	−	1.17744i
$346$	2.50090e14	−	2.50090e14i	0.145761	−	0.145761i
$347$			1.35157e15i			0.774216i	0.922034	+	0.387108i	$0.126526\pi$
$347$			1.35157e15i			0.774216i	−0.922034	+	0.387108i	$0.873474\pi$
$348$	−3.15271e15	−	2.07639e15i	−1.77504	−	1.16905i
$349$	1.14514e15			0.633732			0.316866	−	0.948470i	$-0.397370\pi$
$349$	1.14514e15			0.633732			0.316866	+	0.948470i	$0.397370\pi$
$350$	−8.20577e15	−	8.20577e15i	−4.46387	−	4.46387i
$351$	−4.98646e14	−	4.98646e14i	−0.266655	−	0.266655i
$352$			2.81051e14i			0.147751i
$353$			2.10759e15i			1.08927i	0.838672	+	0.544637i	$0.183333\pi$
$353$			2.10759e15i			1.08927i	−0.838672	+	0.544637i	$0.816667\pi$
$354$		−	1.24287e14i		−	0.0631549i
$355$	−3.70860e15			−1.85285
$356$	−1.81742e15	+	1.81742e15i	−0.892802	+	0.892802i
$357$			5.80166e15i			2.80248i
$358$	2.95838e15	−	2.95838e15i	1.40526	−	1.40526i
$359$	8.25678e14	+	8.25678e14i	0.385695	+	0.385695i	0.873149	−	0.487454i	$-0.162074\pi$
$359$	8.25678e14	+	8.25678e14i	0.385695	+	0.385695i	−0.487454	+	0.873149i	$0.662074\pi$
$360$	1.16735e14	−	1.16735e14i	0.0536274	−	0.0536274i
$361$		−	2.20256e15i		−	0.995139i
$362$	−1.32439e15	−	1.32439e15i	−0.588525	−	0.588525i
$363$	−1.39343e15	+	1.39343e15i	−0.609039	+	0.609039i
$364$	2.60500e15			1.11995
$365$	1.36168e15	+	1.36168e15i	0.575860	+	0.575860i
$366$	9.30889e14	−	9.30889e14i	0.387268	−	0.387268i
$367$	1.84859e15	+	1.84859e15i	0.756562	+	0.756562i	0.975695	−	0.219133i	$-0.0703229\pi$
$367$	1.84859e15	+	1.84859e15i	0.756562	+	0.756562i	−0.219133	+	0.975695i	$0.570323\pi$
$368$	2.86644e15			1.15413
$369$	3.08266e13	+	3.08266e13i	0.0122115	+	0.0122115i
$370$			4.16598e15i			1.62370i
$371$	−1.85262e14			−0.0710466
$372$	6.26483e15			2.36402
$373$	9.33283e14			0.346545			0.173273	−	0.984874i	$-0.444566\pi$
$373$	9.33283e14			0.346545			0.173273	+	0.984874i	$0.444566\pi$
$374$	2.60005e15	−	2.60005e15i	0.950063	−	0.950063i
$375$	5.87261e15	−	5.87261e15i	2.11176	−	2.11176i
$376$			8.62530e15i			3.05244i
$377$	1.07183e15	−	2.20617e14i	0.373318	−	0.0768406i
$378$	−7.10194e15			−2.43459
$379$	2.02986e15	+	2.02986e15i	0.684905	+	0.684905i	0.961101	−	0.276197i	$-0.0890741\pi$
$379$	2.02986e15	+	2.02986e15i	0.684905	+	0.684905i	−0.276197	+	0.961101i	$0.589074\pi$
$380$	−5.89704e14	−	5.89704e14i	−0.195854	−	0.195854i
$381$		−	3.06707e15i		−	1.00271i
$382$			2.00905e14i			0.0646563i
$383$			1.17058e15i			0.370860i	0.982658	+	0.185430i	$0.0593677\pi$
$383$			1.17058e15i			0.370860i	−0.982658	+	0.185430i	$0.940632\pi$
$384$	−4.92325e15			−1.53555
$385$	−2.33202e15	+	2.33202e15i	−0.716091	+	0.716091i
$386$			6.94174e15i			2.09867i
$387$	3.67140e13	−	3.67140e13i	0.0109286	−	0.0109286i
$388$	−7.09152e15	−	7.09152e15i	−2.07849	−	2.07849i
$389$	−2.09799e15	+	2.09799e15i	−0.605489	+	0.605489i	−0.941764	−	0.336275i	$-0.890833\pi$
$389$	−2.09799e15	+	2.09799e15i	−0.605489	+	0.605489i	0.336275	+	0.941764i	$0.390833\pi$
$390$			4.50739e15i			1.28097i
$391$	−4.38025e15	−	4.38025e15i	−1.22585	−	1.22585i
$392$	4.74374e15	−	4.74374e15i	1.30739	−	1.30739i
$393$	−9.30726e14			−0.252619
$394$	−3.59697e15	−	3.59697e15i	−0.961522	−	0.961522i
$395$	−3.66887e15	+	3.66887e15i	−0.965938	+	0.965938i
$396$	−4.54966e13	−	4.54966e13i	−0.0117980	−	0.0117980i
$397$	5.58663e15			1.42694			0.713472	−	0.700683i	$-0.247121\pi$
$397$	5.58663e15			1.42694			0.713472	+	0.700683i	$0.247121\pi$
$398$	−4.55385e15	−	4.55385e15i	−1.14573	−	1.14573i
$399$		−	3.96971e14i		−	0.0983833i
$400$	1.38944e16			3.39218
$401$	3.00684e15			0.723177			0.361589	−	0.932338i	$-0.382235\pi$
$401$	3.00684e15			0.723177			0.361589	+	0.932338i	$0.382235\pi$
$402$	−4.45698e15			−1.05605
$403$	−1.28413e15	+	1.28413e15i	−0.299764	+	0.299764i
$404$	−9.01729e15	+	9.01729e15i	−2.07390	+	2.07390i
$405$		−	8.50136e15i		−	1.92645i
$406$	6.06170e15	−	9.20383e15i	1.35344	−	2.05500i
$407$	8.51889e14			0.187420
$408$	−1.27271e16	−	1.27271e16i	−2.75911	−	2.75911i
$409$	−1.69863e15	−	1.69863e15i	−0.362877	−	0.362877i	0.501994	−	0.864871i	$-0.332600\pi$
$409$	−1.69863e15	−	1.69863e15i	−0.362877	−	0.362877i	−0.864871	+	0.501994i	$0.832600\pi$
$410$			1.32129e16i			2.78161i
$411$			6.98505e15i			1.44917i
$412$		−	4.48063e15i		−	0.916127i
$413$	2.45937e14			0.0495591
$414$	−1.13080e14	+	1.13080e14i	−0.0224586	+	0.0224586i
$415$		−	1.38089e15i		−	0.270315i
$416$	−5.37459e14	+	5.37459e14i	−0.103702	+	0.103702i
$417$	4.39946e15	+	4.39946e15i	0.836725	+	0.836725i
$418$	−1.77905e14	+	1.77905e14i	−0.0333527	+	0.0333527i
$419$			8.12754e15i			1.50202i	0.660292	+	0.751009i	$0.270433\pi$
$419$			8.12754e15i			1.50202i	−0.660292	+	0.751009i	$0.729567\pi$
$420$	2.17566e16	+	2.17566e16i	3.96366	+	3.96366i
$421$	−7.40191e15	+	7.40191e15i	−1.32939	+	1.32939i	−0.423480	+	0.905905i	$0.639192\pi$
$421$	−7.40191e15	+	7.40191e15i	−1.32939	+	1.32939i	−0.905905	+	0.423480i	$0.860808\pi$
$422$	−1.40710e16			−2.49144
$423$	−1.31319e14	−	1.31319e14i	−0.0229237	−	0.0229237i
$424$	4.06410e14	−	4.06410e14i	0.0699470	−	0.0699470i
$425$	−2.12322e16	−	2.12322e16i	−3.60297	−	3.60297i
$426$	1.04381e16			1.74649
$427$	1.84202e15	+	1.84202e15i	0.303898	+	0.303898i
$428$			3.77832e15i			0.614662i
$429$	9.21703e14			0.147859
$430$	1.57364e16			2.48940
$431$	5.09736e15			0.795210			0.397605	−	0.917557i	$-0.369842\pi$
$431$	5.09736e15			0.795210			0.397605	+	0.917557i	$0.369842\pi$
$432$	6.01266e15	−	6.01266e15i	0.925047	−	0.925047i
$433$	3.90998e15	−	3.90998e15i	0.593263	−	0.593263i	−0.345248	−	0.938511i	$-0.612205\pi$
$433$	3.90998e15	−	3.90998e15i	0.593263	−	0.593263i	0.938511	+	0.345248i	$0.112205\pi$
$434$			1.82892e16i			2.73688i
$435$	1.07944e16	+	7.10925e15i	1.59317	+	1.04927i
$436$	−1.87185e16			−2.72491
$437$	2.99713e14	+	2.99713e14i	0.0430345	+	0.0430345i
$438$	−3.83254e15	−	3.83254e15i	−0.542803	−	0.542803i
$439$			8.42516e15i			1.17704i	0.808483	+	0.588520i	$0.200289\pi$
$439$			8.42516e15i			1.17704i	−0.808483	+	0.588520i	$0.799711\pi$
$440$		−	1.02315e16i		−	1.41002i
$441$			1.44445e14i			0.0196369i
$442$	9.94424e15			1.33364
$443$	9.29950e15	−	9.29950e15i	1.23037	−	1.23037i	0.266555	−	0.963820i	$-0.414115\pi$
$443$	9.29950e15	−	9.29950e15i	1.23037	−	1.23037i	0.963820	−	0.266555i	$-0.0858853\pi$
$444$		−	7.94771e15i		−	1.03740i
$445$	6.22256e15	−	6.22256e15i	0.801325	−	0.801325i
$446$	−1.88281e16	−	1.88281e16i	−2.39220	−	2.39220i
$447$	7.72977e15	−	7.72977e15i	0.968995	−	0.968995i
$448$		−	7.27578e15i		−	0.899935i
$449$	3.42388e15	+	3.42388e15i	0.417870	+	0.417870i	0.884469	−	0.466599i	$-0.154521\pi$
$449$	3.42388e15	+	3.42388e15i	0.417870	+	0.417870i	−0.466599	+	0.884469i	$0.654521\pi$
$450$	−5.48125e14	+	5.48125e14i	−0.0660092	+	0.0660092i
$451$	2.70187e15			0.321074
$452$	1.02148e16	+	1.02148e16i	1.19785	+	1.19785i
$453$	−1.68303e15	+	1.68303e15i	−0.194761	+	0.194761i
$454$	1.19932e16	+	1.19932e16i	1.36962	+	1.36962i
$455$	−8.91912e15			−1.00520
$456$	8.70835e14	+	8.70835e14i	0.0968606	+	0.0968606i
$457$			3.09612e15i			0.339876i	0.985455	+	0.169938i	$0.0543567\pi$
$457$			3.09612e15i			0.339876i	−0.985455	+	0.169938i	$0.945643\pi$
$458$	−7.95925e13			−0.00862342
$459$	−1.83761e16			−1.96506
$460$	−3.28525e16			−3.46754
$461$	−1.13270e16	+	1.13270e16i	−1.18007	+	1.18007i	−0.200345	+	0.979725i	$0.564206\pi$
$461$	−1.13270e16	+	1.13270e16i	−1.18007	+	1.18007i	−0.979725	+	0.200345i	$0.935794\pi$
$462$	6.56365e15	−	6.56365e15i	0.674985	−	0.674985i
$463$			2.85875e15i			0.290195i	0.989417	+	0.145098i	$0.0463496\pi$
$463$			2.85875e15i			0.290195i	−0.989417	+	0.145098i	$0.953650\pi$
$464$	2.66019e15	+	1.29241e16i	0.266566	+	1.29507i
$465$	−2.14498e16			−2.12181
$466$	1.58889e16	+	1.58889e16i	1.55160	+	1.55160i
$467$	1.30950e16	+	1.30950e16i	1.26242	+	1.26242i	0.949915	+	0.312507i	$0.101169\pi$
$467$	1.30950e16	+	1.30950e16i	1.26242	+	1.26242i	0.312507	+	0.949915i	$0.398831\pi$
$468$		−	1.74008e14i		−	0.0165612i
$469$		−	8.81936e15i		−	0.828705i
$470$		−	5.62859e16i		−	5.22171i
$471$	−1.48654e16			−1.36161
$472$	−5.39512e14	+	5.39512e14i	−0.0487920	+	0.0487920i
$473$		−	3.21789e15i		−	0.287345i
$474$	1.03263e16	−	1.03263e16i	0.910490	−	0.910490i
$475$	1.45278e15	+	1.45278e15i	0.126485	+	0.126485i
$476$	4.79996e16	−	4.79996e16i	4.12664	−	4.12664i
$477$			1.23750e13i			0.00105060i
$478$	9.87035e15	+	9.87035e15i	0.827495	+	0.827495i
$479$	7.24502e15	−	7.24502e15i	0.599828	−	0.599828i	−0.340439	−	0.940267i	$-0.610576\pi$
$479$	7.24502e15	−	7.24502e15i	0.599828	−	0.599828i	0.940267	+	0.340439i	$0.110576\pi$
$480$	−8.97758e15			−0.734026
$481$	1.62908e15	+	1.62908e15i	0.131544	+	0.131544i
$482$	−1.56332e16	+	1.56332e16i	−1.24671	+	1.24671i
$483$	−1.10577e16	−	1.10577e16i	−0.870924	−	0.870924i
$484$	2.30569e16			1.79361
$485$	2.42803e16	+	2.42803e16i	1.86553	+	1.86553i
$486$			9.58788e14i			0.0727621i
$487$	−2.30481e16			−1.72767			−0.863837	−	0.503772i	$-0.831945\pi$
$487$	−2.30481e16			−1.72767			−0.863837	+	0.503772i	$0.831945\pi$
$488$	−8.08169e15			−0.598388
$489$	1.78084e16			1.30248
$490$	−3.09561e16	+	3.09561e16i	−2.23650	+	2.23650i
$491$	−1.31927e16	+	1.31927e16i	−0.941552	+	0.941552i	−0.998384	−	0.0568321i	$-0.981900\pi$
$491$	−1.31927e16	+	1.31927e16i	−0.941552	+	0.941552i	0.0568321	+	0.998384i	$0.481900\pi$
$492$		−	2.52072e16i		−	1.77719i
$493$	1.56845e16	−	2.38146e16i	1.09242	−	1.65868i
$494$	−6.80421e14			−0.0468184
$495$	1.55773e14	+	1.55773e14i	0.0105892	+	0.0105892i
$496$	−1.54840e16	−	1.54840e16i	−1.03991	−	1.03991i
$497$			2.06547e16i			1.37051i
$498$			3.88662e15i			0.254798i
$499$			4.65535e15i			0.301543i	0.988569	+	0.150772i	$0.0481758\pi$
$499$			4.65535e15i			0.301543i	−0.988569	+	0.150772i	$0.951824\pi$
$500$	−9.71733e16			−6.21909
$501$	5.32750e15	−	5.32750e15i	0.336897	−	0.336897i
$502$		−	5.08618e15i		−	0.317812i
$503$	7.82743e15	−	7.82743e15i	0.483294	−	0.483294i	−0.422888	−	0.906182i	$-0.638984\pi$
$503$	7.82743e15	−	7.82743e15i	0.483294	−	0.483294i	0.906182	+	0.422888i	$0.138984\pi$
$504$	−6.50147e14	−	6.50147e14i	−0.0396669	−	0.0396669i
$505$	3.08738e16	−	3.08738e16i	1.86141	−	1.86141i
$506$			9.91112e15i			0.590500i
$507$	−1.03705e16	−	1.03705e16i	−0.610594	−	0.610594i
$508$	−2.53752e16	+	2.53752e16i	−1.47648	+	1.47648i
$509$	4.07797e15			0.234497			0.117248	−	0.993103i	$-0.462593\pi$
$509$	4.07797e15			0.234497			0.117248	+	0.993103i	$0.462593\pi$
$510$	8.30530e16	+	8.30530e16i	4.71992	+	4.71992i
$511$	7.58375e15	−	7.58375e15i	0.425950	−	0.425950i
$512$	2.62724e16	+	2.62724e16i	1.45841	+	1.45841i
$513$	1.25736e15			0.0689850
$514$	1.10316e16	+	1.10316e16i	0.598219	+	0.598219i
$515$			1.53410e16i			0.822261i
$516$	−3.00213e16			−1.59049
$517$	−1.15097e16			−0.602729
$518$	2.32021e16			1.20102
$519$	1.63356e15	−	1.63356e15i	0.0835857	−	0.0835857i
$520$	1.95659e16	−	1.95659e16i	0.989645	−	0.989645i
$521$		−	3.15648e16i		−	1.57825i	−0.614231	−	0.789126i	$-0.710534\pi$
$521$		−	3.15648e16i		−	1.57825i	0.614231	−	0.789126i	$-0.289466\pi$
$522$	−6.14792e14	−	4.04906e14i	−0.0303882	−	0.0200139i
$523$	4.73293e15			0.231270			0.115635	−	0.993292i	$-0.463110\pi$
$523$	4.73293e15			0.231270			0.115635	+	0.993292i	$0.463110\pi$
$524$	7.70030e15	+	7.70030e15i	0.371980	+	0.371980i
$525$	−5.35992e16	−	5.35992e16i	−2.55978	−	2.55978i
$526$			1.89391e16i			0.894220i
$527$			4.73227e16i			2.20905i
$528$			1.11139e16i			0.512934i
$529$	−5.21756e15			−0.238086
$530$	−2.65210e15	+	2.65210e15i	−0.119656	+	0.119656i
$531$		−	1.64280e13i		−	0.000732852i
$532$	−3.28431e15	+	3.28431e15i	−0.144869	+	0.144869i
$533$	5.16683e15	+	5.16683e15i	0.225352	+	0.225352i
$534$	−1.75139e16	+	1.75139e16i	−0.755326	+	0.755326i
$535$		−	1.29364e16i		−	0.551684i
$536$	1.93470e16	+	1.93470e16i	0.815879	+	0.815879i
$537$	1.93238e16	−	1.93238e16i	0.805837	−	0.805837i
$538$	−5.40170e16			−2.22760
$539$	6.33012e15	+	6.33012e15i	0.258154	+	0.258154i
$540$	−6.89115e16	+	6.89115e16i	−2.77926	+	2.77926i
$541$	−2.01036e16	−	2.01036e16i	−0.801843	−	0.801843i	0.181540	−	0.983383i	$-0.441892\pi$
$541$	−2.01036e16	−	2.01036e16i	−0.801843	−	0.801843i	−0.983383	+	0.181540i	$0.941892\pi$
$542$	−3.44365e16			−1.35839
$543$	−8.65078e15	−	8.65078e15i	−0.337486	−	0.337486i
$544$			1.98064e16i			0.764209i
$545$	6.40892e16			2.44572
$546$	2.51036e16			0.947500
$547$	−1.59061e16			−0.593800			−0.296900	−	0.954909i	$-0.595953\pi$
$547$	−1.59061e16			−0.593800			−0.296900	+	0.954909i	$0.595953\pi$
$548$	5.77903e16	−	5.77903e16i	2.13389	−	2.13389i
$549$	1.23042e14	−	1.23042e14i	0.00449387	−	0.00449387i
$550$			4.80417e16i			1.73557i
$551$	−1.07319e15	+	1.62948e15i	−0.0383501	+	0.0582291i
$552$	4.85144e16			1.71489
$553$	2.04335e16	+	2.04335e16i	0.714482	+	0.714482i
$554$	1.23022e15	+	1.23022e15i	0.0425523	+	0.0425523i
$555$			2.72117e16i			0.931104i
$556$		−	7.27972e16i		−	2.46414i
$557$			6.19995e15i			0.207614i	0.994597	+	0.103807i	$0.0331025\pi$
$557$			6.19995e15i			0.207614i	−0.994597	+	0.103807i	$0.966898\pi$
$558$	1.22167e15			0.0404715
$559$	6.15361e15	−	6.15361e15i	0.201678	−	0.201678i
$560$		−	1.07546e17i		−	3.48713i
$561$	1.69833e16	−	1.69833e16i	0.544808	−	0.544808i
$562$	2.96634e15	+	2.96634e15i	0.0941461	+	0.0941461i
$563$	−2.69541e16	+	2.69541e16i	−0.846398	+	0.846398i	−0.989682	−	0.143284i	$-0.954234\pi$
$563$	−2.69541e16	+	2.69541e16i	−0.846398	+	0.846398i	0.143284	+	0.989682i	$0.454234\pi$
$564$			1.07380e17i			3.33618i
$565$	−3.49741e16	−	3.49741e16i	−1.07512	−	1.07512i
$566$	8.48092e15	−	8.48092e15i	0.257955	−	0.257955i
$567$	−4.73476e16			−1.42495
$568$	−4.53103e16	−	4.53103e16i	−1.34929	−	1.34929i
$569$	−1.41105e16	+	1.41105e16i	−0.415786	+	0.415786i	−0.883748	−	0.467962i	$-0.844988\pi$
$569$	−1.41105e16	+	1.41105e16i	−0.415786	+	0.415786i	0.467962	+	0.883748i	$0.344988\pi$
$570$	−5.68279e15	−	5.68279e15i	−0.165696	−	0.165696i
$571$	4.82905e14			0.0139330			0.00696651	−	0.999976i	$-0.497782\pi$
$571$	4.82905e14			0.0139330			0.00696651	+	0.999976i	$0.497782\pi$
$572$	−7.62564e15	−	7.62564e15i	−0.217721	−	0.217721i
$573$			1.31229e15i			0.0370768i
$574$	7.35883e16			2.05749
$575$	8.09348e16			2.23938
$576$	−4.86003e14			−0.0133077
$577$	−3.86406e16	+	3.86406e16i	−1.04710	+	1.04710i	−0.0482670	+	0.998834i	$0.515370\pi$
$577$	−3.86406e16	+	3.86406e16i	−1.04710	+	1.04710i	−0.998834	+	0.0482670i	$0.984630\pi$
$578$	1.36781e17	−	1.36781e17i	3.66824	−	3.66824i
$579$			4.53427e16i			1.20347i
$580$	−3.04886e16	−	1.48124e17i	−0.800885	−	3.89098i
$581$	−7.69075e15			−0.199946
$582$	−6.83387e16	−	6.83387e16i	−1.75844	−	1.75844i
$583$	5.42320e14	+	5.42320e14i	0.0138116	+	0.0138116i
$584$			3.32729e16i			0.838715i
$585$			5.95775e14i			0.0148644i
$586$		−	4.89854e16i		−	1.20971i
$587$	−5.43445e15			−0.132839			−0.0664197	−	0.997792i	$-0.521158\pi$
$587$	−5.43445e15			−0.132839			−0.0664197	+	0.997792i	$0.521158\pi$
$588$	5.90570e16	−	5.90570e16i	1.42892	−	1.42892i
$589$		−	3.23800e15i		−	0.0775505i
$590$	3.52068e15	−	3.52068e15i	0.0834669	−	0.0834669i
$591$	−2.34950e16	−	2.34950e16i	−0.551379	−	0.551379i
$592$	−1.96434e16	+	1.96434e16i	−0.456338	+	0.456338i
$593$			1.49154e16i			0.343011i	0.985183	+	0.171505i	$0.0548631\pi$
$593$			1.49154e16i			0.343011i	−0.985183	+	0.171505i	$0.945137\pi$
$594$	2.07896e16	+	2.07896e16i	0.473290	+	0.473290i
$595$	−1.64343e17	+	1.64343e17i	−3.70382	+	3.70382i
$596$	−1.27903e17			−2.85368
$597$	−2.97453e16	−	2.97453e16i	−0.657010	−	0.657010i
$598$	−1.89532e16	+	1.89532e16i	−0.414453	+	0.414453i
$599$	1.86052e16	+	1.86052e16i	0.402785	+	0.402785i	0.879213	−	0.476429i	$-0.158069\pi$
$599$	1.86052e16	+	1.86052e16i	0.402785	+	0.402785i	−0.476429	+	0.879213i	$0.658069\pi$
$600$	2.35161e17			5.04032
$601$	−3.61364e15	−	3.61364e15i	−0.0766828	−	0.0766828i	0.667725	−	0.744408i	$-0.267268\pi$
$601$	−3.61364e15	−	3.61364e15i	−0.0766828	−	0.0766828i	−0.744408	+	0.667725i	$0.767268\pi$
$602$		−	8.76425e16i		−	1.84135i
$603$	−5.89111e14			−0.0122544
$604$	2.78489e16			0.573570
$605$	−7.89432e16			−1.60984
$606$	−8.68967e16	+	8.68967e16i	−1.75456	+	1.75456i
$607$	2.00208e16	−	2.00208e16i	0.400267	−	0.400267i	−0.478060	−	0.878327i	$-0.658660\pi$
$607$	2.00208e16	−	2.00208e16i	0.400267	−	0.400267i	0.878327	+	0.478060i	$0.158660\pi$
$608$		−	1.35523e15i		−	0.0268281i
$609$	3.95944e16	−	6.01184e16i	0.776122	−	1.17843i
$610$	5.27385e16			1.02364
$611$	−2.20102e16	−	2.20102e16i	−0.423036	−	0.423036i
$612$	−3.20625e15	−	3.20625e15i	−0.0610224	−	0.0610224i
$613$		−	3.85244e16i		−	0.726062i	−0.931777	−	0.363031i	$-0.881742\pi$
$613$		−	3.85244e16i		−	0.726062i	0.931777	−	0.363031i	$-0.118258\pi$
$614$			1.02718e17i			1.91706i
$615$			8.63054e16i			1.59510i
$616$	−5.69836e16			−1.04295
$617$	−1.26648e16	+	1.26648e16i	−0.229555	+	0.229555i	−0.812507	−	0.582952i	$-0.801898\pi$
$617$	−1.26648e16	+	1.26648e16i	−0.229555	+	0.229555i	0.582952	+	0.812507i	$0.301898\pi$
$618$		−	4.31784e16i		−	0.775060i
$619$	−9.67738e15	+	9.67738e15i	−0.172034	+	0.172034i	−0.787872	−	0.615839i	$-0.788817\pi$
$619$	−9.67738e15	+	9.67738e15i	−0.172034	+	0.172034i	0.615839	+	0.787872i	$0.288817\pi$
$620$	1.77464e17	+	1.77464e17i	3.12435	+	3.12435i
$621$	3.50238e16	−	3.50238e16i	0.610680	−	0.610680i
$622$			5.53773e16i			0.956290i
$623$	−3.46560e16	−	3.46560e16i	−0.592721	−	0.592721i
$624$	−2.12532e16	+	2.12532e16i	−0.360012	+	0.360012i
$625$	1.79790e17			3.01637
$626$	8.50069e16	+	8.50069e16i	1.41256	+	1.41256i
$627$	−1.16206e15	+	1.16206e15i	−0.0191259	+	0.0191259i
$628$	1.22988e17	+	1.22988e17i	2.00496	+	2.00496i
$629$	6.00347e16			0.969390
$630$	4.24265e15	+	4.24265e15i	0.0678568	+	0.0678568i
$631$		−	5.11047e16i		−	0.809626i	−0.914399	−	0.404813i	$-0.867337\pi$
$631$		−	5.11047e16i		−	0.809626i	0.914399	−	0.404813i	$-0.132663\pi$
$632$	−8.96498e16			−1.40685
$633$	−9.19104e16			−1.42870
$634$	−9.65232e16			−1.48626
$635$	8.68808e16	−	8.68808e16i	1.32520	−	1.32520i
$636$	5.05958e15	−	5.05958e15i	0.0764490	−	0.0764490i
$637$			2.42104e16i			0.362381i
$638$	−4.46869e16	+	9.19797e15i	−0.662608	+	0.136385i
$639$	1.37968e15			0.0202663
$640$	−1.39461e17	−	1.39461e17i	−2.02942	−	2.02942i
$641$	−8.65964e15	−	8.65964e15i	−0.124839	−	0.124839i	0.641927	−	0.766766i	$-0.278135\pi$
$641$	−8.65964e15	−	8.65964e15i	−0.124839	−	0.124839i	−0.766766	+	0.641927i	$0.778135\pi$
$642$			3.64105e16i			0.520015i
$643$			6.64648e15i			0.0940429i	0.998894	+	0.0470214i	$0.0149729\pi$
$643$			6.64648e15i			0.0940429i	−0.998894	+	0.0470214i	$0.985027\pi$
$644$			1.82969e17i			2.56486i
$645$	1.02788e17			1.42753
$646$	−1.25374e16	+	1.25374e16i	−0.172509	+	0.172509i
$647$		−	2.36095e16i		−	0.321856i	−0.986966	−	0.160928i	$-0.948551\pi$
$647$		−	2.36095e16i		−	0.321856i	0.986966	−	0.160928i	$-0.0514487\pi$
$648$	1.03867e17	−	1.03867e17i	1.40290	−	1.40290i
$649$	−7.19933e14	−	7.19933e14i	−0.00963438	−	0.00963438i
$650$	−9.18708e16	+	9.18708e16i	−1.21814	+	1.21814i
$651$			1.19463e17i			1.56945i
$652$	−1.47337e17	−	1.47337e17i	−1.91790	−	1.91790i
$653$	2.34675e16	−	2.34675e16i	0.302683	−	0.302683i	−0.539380	−	0.842063i	$-0.681341\pi$
$653$	2.34675e16	−	2.34675e16i	0.302683	−	0.302683i	0.842063	+	0.539380i	$0.181341\pi$
$654$	−1.80384e17			−2.30532
$655$	−2.63646e16	−	2.63646e16i	−0.333867	−	0.333867i
$656$	−6.23015e16	+	6.23015e16i	−0.781763	+	0.781763i
$657$	−5.06575e14	−	5.06575e14i	−0.00629871	−	0.00629871i
$658$	−3.13480e17			−3.86237
$659$	4.90312e16	+	4.90312e16i	0.598632	+	0.598632i	0.939949	−	0.341316i	$-0.110873\pi$
$659$	4.90312e16	+	4.90312e16i	0.598632	+	0.598632i	−0.341316	+	0.939949i	$0.610873\pi$
$660$		−	1.27377e17i		−	1.54109i
$661$	1.16763e16			0.139990			0.0699948	−	0.997547i	$-0.477702\pi$
$661$	1.16763e16			0.139990			0.0699948	+	0.997547i	$0.477702\pi$
$662$	2.28956e17			2.72022
$663$	6.49547e16			0.764767
$664$	1.68712e16	−	1.68712e16i	0.196851	−	0.196851i
$665$	1.12450e16	−	1.12450e16i	0.130025	−	0.130025i
$666$		−	1.54984e15i		−	0.0177600i
$667$	1.54956e16	+	7.52831e16i	0.175976	+	0.854954i
$668$	−8.81534e16			−0.992156
$669$	−1.22983e17	−	1.22983e17i	−1.37180	−	1.37180i
$670$	−1.26253e17	−	1.26253e17i	−1.39570	−	1.39570i
$671$		−	1.07843e16i		−	0.118157i
$672$			4.99999e16i			0.542942i
$673$			2.19691e16i			0.236440i	0.992987	+	0.118220i	$0.0377189\pi$
$673$			2.19691e16i			0.236440i	−0.992987	+	0.118220i	$0.962281\pi$
$674$	−7.15426e16			−0.763142
$675$	1.69769e17	−	1.69769e17i	1.79488	−	1.79488i
$676$			1.71600e17i			1.79819i
$677$	−6.98412e16	+	6.98412e16i	−0.725404	+	0.725404i	−0.969701	−	0.244297i	$-0.921443\pi$
$677$	−6.98412e16	+	6.98412e16i	−0.725404	+	0.725404i	0.244297	+	0.969701i	$0.421443\pi$
$678$	9.84372e16	+	9.84372e16i	1.01340	+	1.01340i
$679$	1.35227e17	−	1.35227e17i	1.37989	−	1.37989i
$680$		−	7.21040e17i		−	7.29300i
$681$	7.83383e16	+	7.83383e16i	0.785401	+	0.785401i
$682$	5.35381e16	−	5.35381e16i	0.532056	−	0.532056i
$683$	1.82115e17			1.79400			0.896998	−	0.442034i	$-0.145743\pi$
$683$	1.82115e17			1.79400			0.896998	+	0.442034i	$0.145743\pi$
$684$	2.19384e14	+	2.19384e14i	0.00214224	+	0.00214224i
$685$	−1.97865e17	+	1.97865e17i	−1.91525	+	1.91525i
$686$	−8.92704e15	−	8.92704e15i	−0.0856569	−	0.0856569i
$687$	−5.19890e14			−0.00494505
$688$	7.42000e16	+	7.42000e16i	0.699638	+	0.699638i
$689$			2.07417e15i			0.0193878i
$690$	−3.16589e17			−2.93360
$691$	−1.01400e17			−0.931475			−0.465737	−	0.884923i	$-0.654211\pi$
$691$	−1.01400e17			−0.931475			−0.465737	+	0.884923i	$0.654211\pi$
$692$	−2.70303e16			−0.246159
$693$	8.67566e14	−	8.67566e14i	0.00783255	−	0.00783255i
$694$	1.07759e17	−	1.07759e17i	0.964484	−	0.964484i
$695$			2.49246e17i			2.21167i
$696$	4.50236e16	+	2.18740e17i	0.396081	+	1.92430i
$697$	1.90408e17			1.66069
$698$	−9.13000e16	−	9.13000e16i	−0.789475	−	0.789475i
$699$	1.03785e17	+	1.03785e17i	0.889754	+	0.889754i
$700$			8.86898e17i			7.53851i
$701$			8.60657e16i			0.725307i	0.931924	+	0.362653i	$0.118129\pi$
$701$			8.60657e16i			0.725307i	−0.931924	+	0.362653i	$0.881871\pi$
$702$			7.95125e16i			0.664374i
$703$	−4.10780e15			−0.0340312
$704$	−2.12984e16	+	2.12984e16i	−0.174949	+	0.174949i
$705$		−	3.67653e17i		−	2.99436i
$706$	1.68034e17	−	1.68034e17i	1.35697	−	1.35697i
$707$	−1.71949e17	−	1.71949e17i	−1.37684	−	1.37684i
$708$	−6.71663e15	+	6.71663e15i	−0.0533276	+	0.0533276i
$709$		−	1.54862e17i		−	1.21918i	−0.792716	−	0.609591i	$-0.791334\pi$
$709$		−	1.54862e17i		−	1.21918i	0.792716	−	0.609591i	$-0.208666\pi$
$710$	2.95680e17	+	2.95680e17i	2.30819	+	2.30819i
$711$	1.36490e15	−	1.36490e15i	0.0105654	−	0.0105654i
$712$	1.52050e17			1.16710
$713$	−9.01946e16	−	9.01946e16i	−0.686505	−	0.686505i
$714$	4.62557e17	−	4.62557e17i	3.49121	−	3.49121i
$715$	2.61090e16	+	2.61090e16i	0.195413	+	0.195413i
$716$	−3.19749e17			−2.37318
$717$	6.44721e16	+	6.44721e16i	0.474522	+	0.474522i
$718$		−	1.31660e17i		−	0.960963i
$719$	4.81992e16			0.348872			0.174436	−	0.984669i	$-0.444190\pi$
$719$	4.81992e16			0.348872			0.174436	+	0.984669i	$0.444190\pi$
$720$	−7.18383e15			−0.0515657
$721$	8.54403e16			0.608207
$722$	−1.75606e17	+	1.75606e17i	−1.23970	+	1.23970i
$723$	−1.02114e17	+	1.02114e17i	−0.714917	+	0.714917i
$724$			1.43143e17i			0.993892i
$725$	7.51112e16	+	3.64916e17i	0.517222	+	2.51284i
$726$	2.22192e17			1.51743
$727$	1.47817e17	+	1.47817e17i	1.00120	+	1.00120i	0.999999	+	0.00119581i	$0.000380638\pi$
$727$	1.47817e17	+	1.47817e17i	1.00120	+	1.00120i	0.00119581	+	0.999999i	$0.499619\pi$
$728$	−1.08971e17	−	1.08971e17i	−0.732017	−	0.732017i
$729$		−	1.46868e17i		−	0.978502i
$730$		−	2.17129e17i		−	1.43476i
$731$		−	2.26772e17i		−	1.48623i
$732$	−1.00613e17			−0.654012
$733$	−1.61462e16	+	1.61462e16i	−0.104099	+	0.104099i	−0.757238	−	0.653139i	$-0.773452\pi$
$733$	−1.61462e16	+	1.61462e16i	−0.104099	+	0.104099i	0.653139	+	0.757238i	$0.273452\pi$
$734$		−	2.94770e17i		−	1.88498i
$735$	−2.02202e17	+	2.02202e17i	−1.28251	+	1.28251i
$736$	−3.77499e16	−	3.77499e16i	−0.237492	−	0.237492i
$737$	−2.58170e16	+	2.58170e16i	−0.161102	+	0.161102i
$738$		−	4.91551e15i		−	0.0304250i
$739$	−1.33570e17	−	1.33570e17i	−0.820051	−	0.820051i	0.166064	−	0.986115i	$-0.446894\pi$
$739$	−1.33570e17	−	1.33570e17i	−0.820051	−	0.820051i	−0.986115	+	0.166064i	$0.946894\pi$
$740$	2.25134e17	−	2.25134e17i	1.37104	−	1.37104i
$741$	−4.44444e15			−0.0268477
$742$	1.47706e16	+	1.47706e16i	0.0885067	+	0.0885067i
$743$	−1.62466e17	+	1.62466e17i	−0.965675	+	0.965675i	−0.999430	−	0.0337555i	$-0.989253\pi$
$743$	−1.62466e17	+	1.62466e17i	−0.965675	+	0.965675i	0.0337555	+	0.999430i	$0.489253\pi$
$744$	−2.62066e17	−	2.62066e17i	−1.54516	−	1.54516i
$745$	4.37922e17			2.56129
$746$	−7.44091e16	−	7.44091e16i	−0.431711	−	0.431711i
$747$			5.13723e14i			0.00295669i
$748$	−2.81020e17			−1.60445
$749$	−7.20482e16			−0.408068
$750$	−9.36428e17			−5.26147
$751$	3.82044e16	−	3.82044e16i	0.212948	−	0.212948i	−0.592570	−	0.805519i	$-0.701887\pi$
$751$	3.82044e16	−	3.82044e16i	0.212948	−	0.212948i	0.805519	+	0.592570i	$0.201887\pi$
$752$	2.65399e17	−	2.65399e17i	1.46755	−	1.46755i
$753$		−	3.32224e16i		−	0.182247i
$754$	−1.03045e17	−	6.78661e16i	−0.560788	−	0.369339i
$755$	−9.53503e16			−0.514802
$756$	3.83797e17	+	3.83797e17i	2.05575	+	2.05575i
$757$	7.89662e16	+	7.89662e16i	0.419630	+	0.419630i	0.885076	−	0.465446i	$-0.154106\pi$
$757$	7.89662e16	+	7.89662e16i	0.419630	+	0.419630i	−0.465446	+	0.885076i	$0.654106\pi$
$758$		−	3.23674e17i		−	1.70645i
$759$			6.47383e16i			0.338619i
$760$			4.93362e16i			0.256026i
$761$	5.98557e16			0.308175			0.154087	−	0.988057i	$-0.450756\pi$
$761$	5.98557e16			0.308175			0.154087	+	0.988057i	$0.450756\pi$
$762$	−2.44533e17	+	2.44533e17i	−1.24913	+	1.24913i
$763$		−	3.56940e17i		−	1.80904i
$764$	1.08571e16	−	1.08571e16i	0.0545953	−	0.0545953i
$765$	1.09777e16	+	1.09777e16i	0.0547701	+	0.0547701i
$766$	9.33287e16	−	9.33287e16i	0.462000	−	0.462000i
$767$		−	2.75348e15i		−	0.0135241i
$768$	2.98073e17	+	2.98073e17i	1.45263	+	1.45263i
$769$	1.22278e16	−	1.22278e16i	0.0591276	−	0.0591276i	−0.676925	−	0.736052i	$-0.736688\pi$
$769$	1.22278e16	−	1.22278e16i	0.0591276	−	0.0591276i	0.736052	+	0.676925i	$0.236688\pi$
$770$	3.71857e17			1.78415
$771$	7.20573e16	+	7.20573e16i	0.343046	+	0.343046i
$772$	3.75140e17	−	3.75140e17i	1.77210	−	1.77210i
$773$	−2.90057e16	−	2.90057e16i	−0.135959	−	0.135959i	0.635852	−	0.771811i	$-0.280649\pi$
$773$	−2.90057e16	−	2.90057e16i	−0.135959	−	0.135959i	−0.771811	+	0.635852i	$0.780649\pi$
$774$	−5.85430e15			−0.0272288
$775$	−4.37196e17	−	4.37196e17i	−2.01774	−	2.01774i
$776$			5.93295e17i			2.71707i
$777$	1.51554e17			0.688716
$778$	3.34539e17			1.50858
$779$	−1.30284e16			−0.0582996
$780$	2.43585e17	−	2.43585e17i	1.08164	−	1.08164i
$781$	6.04627e16	−	6.04627e16i	0.266429	−	0.266429i
$782$			6.98461e17i			3.05423i
$783$	1.90418e17	+	1.25410e17i	0.826298	+	0.544206i
$784$	−2.91928e17			−1.25713
$785$	−4.21093e17	−	4.21093e17i	−1.79953	−	1.79953i
$786$	7.42053e16	+	7.42053e16i	0.314702	+	0.314702i
$787$			1.56495e17i			0.658647i	0.944217	+	0.329324i	$0.106821\pi$
$787$			1.56495e17i			0.658647i	−0.944217	+	0.329324i	$0.893179\pi$
$788$			3.88768e17i			1.62380i
$789$			1.23708e17i			0.512785i
$790$	5.85026e17			2.40665
$791$	−1.94785e17	+	1.94785e17i	−0.795238	+	0.795238i
$792$			3.80636e15i			0.0154226i
$793$	2.06230e16	−	2.06230e16i	0.0829304	−	0.0829304i
$794$	−4.45413e17	−	4.45413e17i	−1.77762	−	1.77762i
$795$	−1.73232e16	+	1.73232e16i	−0.0686161	+	0.0686161i
$796$			4.92191e17i			1.93489i
$797$	1.81485e16	+	1.81485e16i	0.0708095	+	0.0708095i	0.741625	−	0.670815i	$-0.234056\pi$
$797$	1.81485e16	+	1.81485e16i	0.0708095	+	0.0708095i	−0.670815	+	0.741625i	$0.734056\pi$
$798$	−3.16498e16	+	3.16498e16i	−0.122562	+	0.122562i
$799$	−8.11119e17			−3.11748
$800$	−1.82983e17	−	1.82983e17i	−0.698026	−	0.698026i
$801$	−2.31494e15	+	2.31494e15i	−0.00876484	+	0.00876484i
$802$	−2.39731e17	−	2.39731e17i	−0.900902	−	0.900902i
$803$	−4.44000e16			−0.165611
$804$	2.40860e17	+	2.40860e17i	0.891720	+	0.891720i
$805$		−	6.26459e17i		−	2.30206i
$806$	2.04764e17			0.746866
$807$	−3.52833e17			−1.27740
$808$	7.54410e17			2.71106
$809$	−1.98770e17	+	1.98770e17i	−0.709020	+	0.709020i	−0.966329	−	0.257309i	$-0.917164\pi$
$809$	−1.98770e17	+	1.98770e17i	−0.709020	+	0.709020i	0.257309	+	0.966329i	$0.417164\pi$
$810$	−6.77799e17	+	6.77799e17i	−2.39989	+	2.39989i
$811$		−	8.81395e16i		−	0.309775i	−0.987932	−	0.154887i	$-0.950499\pi$
$811$		−	8.81395e16i		−	0.309775i	0.987932	−	0.154887i	$-0.0495014\pi$
$812$	−8.24967e17	+	1.69804e17i	−2.87806	+	0.592396i
$813$	−2.24936e17			−0.778960
$814$	−6.79197e16	−	6.79197e16i	−0.233480	−	0.233480i
$815$	5.04458e17	+	5.04458e17i	1.72139	+	1.72139i
$816$			7.83221e17i			2.65304i
$817$			1.55166e16i			0.0521752i
$818$			2.70858e17i			0.904112i
$819$	3.31812e15			0.0109948
$820$	7.14042e17	−	7.14042e17i	2.34877	−	2.34877i
$821$			2.01929e17i			0.659385i	0.944088	+	0.329692i	$0.106945\pi$
$821$			2.01929e17i			0.659385i	−0.944088	+	0.329692i	$0.893055\pi$
$822$	5.56907e17	−	5.56907e17i	1.80531	−	1.80531i
$823$	−5.97422e16	−	5.97422e16i	−0.192257	−	0.192257i	0.604414	−	0.796671i	$-0.293407\pi$
$823$	−5.97422e16	−	5.97422e16i	−0.192257	−	0.192257i	−0.796671	+	0.604414i	$0.793407\pi$
$824$	−1.87431e17	+	1.87431e17i	−0.598794	+	0.598794i
$825$			3.13803e17i			0.995252i
$826$	−1.96081e16	−	1.96081e16i	−0.0617385	−	0.0617385i
$827$	−2.00625e17	+	2.00625e17i	−0.627122	+	0.627122i	−0.947343	−	0.320221i	$-0.896243\pi$
$827$	−2.00625e17	+	2.00625e17i	−0.627122	+	0.627122i	0.320221	+	0.947343i	$0.396243\pi$
$828$	1.22219e16			0.0379277
$829$	−1.78707e17	−	1.78707e17i	−0.550572	−	0.550572i	0.376034	−	0.926606i	$-0.377288\pi$
$829$	−1.78707e17	−	1.78707e17i	−0.550572	−	0.550572i	−0.926606	+	0.376034i	$0.877288\pi$
$830$	−1.10096e17	+	1.10096e17i	−0.336747	+	0.336747i
$831$	8.03564e15	+	8.03564e15i	0.0244014	+	0.0244014i
$832$	−8.14587e16			−0.245583
$833$	4.46099e17	+	4.46099e17i	1.33525	+	1.33525i
$834$		−	7.01523e17i		−	2.08471i
$835$	3.01824e17			0.890501
$836$	1.92284e16			0.0563255
$837$	−3.78385e17			−1.10048
$838$	6.47996e17	−	6.47996e17i	1.87115	−	1.87115i
$839$	−3.15211e17	+	3.15211e17i	−0.903712	+	0.903712i	−0.995755	−	0.0920426i	$-0.970660\pi$
$839$	−3.15211e17	+	3.15211e17i	−0.903712	+	0.903712i	0.0920426	+	0.995755i	$0.470660\pi$
$840$		−	1.82022e18i		−	5.18140i
$841$	−3.25053e17	+	1.39732e17i	−0.918711	+	0.394931i
$842$	1.18028e18			3.31218
$843$	1.93758e16	+	1.93758e16i	0.0539876	+	0.0539876i
$844$	7.60414e17	+	7.60414e17i	2.10376	+	2.10376i
$845$		−	5.87530e17i		−	1.61395i
$846$			2.09397e16i			0.0571146i
$847$			4.39668e17i			1.19076i
$848$	−2.50103e16			−0.0672580
$849$	5.53964e16	−	5.53964e16i	0.147923	−	0.147923i
$850$			3.38561e18i			8.97685i
$851$	−1.14423e17	+	1.14423e17i	−0.301256	+	0.301256i
$852$	−5.64088e17	−	5.64088e17i	−1.47472	−	1.47472i
$853$	−2.29537e17	+	2.29537e17i	−0.595878	+	0.595878i	−0.939213	−	0.343335i	$-0.888443\pi$
$853$	−2.29537e17	+	2.29537e17i	−0.595878	+	0.595878i	0.343335	+	0.939213i	$0.388443\pi$
$854$		−	2.93723e17i		−	0.757165i
$855$	−7.51136e14	−	7.51136e14i	−0.00192274	−	0.00192274i
$856$	1.58052e17	−	1.58052e17i	0.401752	−	0.401752i
$857$	4.32834e17			1.09254			0.546269	−	0.837610i	$-0.316047\pi$
$857$	4.32834e17			1.09254			0.546269	+	0.837610i	$0.316047\pi$
$858$	−7.34859e16	−	7.34859e16i	−0.184196	−	0.184196i
$859$	−2.43846e17	+	2.43846e17i	−0.606954	+	0.606954i	−0.942149	−	0.335194i	$-0.891198\pi$
$859$	−2.43846e17	+	2.43846e17i	−0.606954	+	0.606954i	0.335194	+	0.942149i	$0.391198\pi$
$860$	−8.50412e17	−	8.50412e17i	−2.10203	−	2.10203i
$861$	4.80671e17			1.17986
$862$	−4.06404e17	−	4.06404e17i	−0.990637	−	0.990637i
$863$			4.72080e17i			1.14275i	0.820689	+	0.571375i	$0.193590\pi$
$863$			4.72080e17i			1.14275i	−0.820689	+	0.571375i	$0.806410\pi$
$864$	−1.58369e17			−0.380703
$865$	9.25477e16			0.220937
$866$	−6.23473e17			−1.47812
$867$	8.93436e17	−	8.93436e17i	2.10353	−	2.10353i
$868$	9.88369e17	−	9.88369e17i	2.31100	−	2.31100i
$869$		−	1.19630e17i		−	0.277793i
$870$	−2.93809e17	−	1.42743e18i	−0.677563	−	3.29184i
$871$	−9.87405e16			−0.226145
$872$	7.83019e17	+	7.83019e17i	1.78104	+	1.78104i
$873$	−9.03282e15	−	9.03282e15i	−0.0204051	−	0.0204051i
$874$		−	4.77913e16i		−	0.107221i
$875$		−	1.85298e18i		−	4.12879i
$876$			4.14230e17i			0.916678i
$877$	−5.45976e16			−0.119999			−0.0599993	−	0.998198i	$-0.519110\pi$
$877$	−5.45976e16			−0.119999			−0.0599993	+	0.998198i	$0.519110\pi$
$878$	6.71724e17	−	6.71724e17i	1.46630	−	1.46630i
$879$		−	3.19967e17i		−	0.693701i
$880$	−3.14822e17	+	3.14822e17i	−0.677905	+	0.677905i
$881$	−2.12616e17	−	2.12616e17i	−0.454716	−	0.454716i	0.442201	−	0.896916i	$-0.354198\pi$
$881$	−2.12616e17	−	2.12616e17i	−0.454716	−	0.454716i	−0.896916	+	0.442201i	$0.854198\pi$
$882$	1.15164e16	−	1.15164e16i	0.0244627	−	0.0244627i
$883$			6.09323e17i			1.28553i	0.766062	+	0.642767i	$0.222214\pi$
$883$			6.09323e17i			1.28553i	−0.766062	+	0.642767i	$0.777786\pi$
$884$	−5.37398e17	−	5.37398e17i	−1.12611	−	1.12611i
$885$	2.29967e16	−	2.29967e16i	0.0478636	−	0.0478636i
$886$	−1.48287e18			−3.06549
$887$	1.22056e17	+	1.22056e17i	0.250622	+	0.250622i	0.821225	−	0.570604i	$-0.193291\pi$
$887$	1.22056e17	+	1.22056e17i	0.250622	+	0.250622i	−0.570604	+	0.821225i	$0.693291\pi$
$888$	−3.32463e17	+	3.32463e17i	−0.678056	+	0.678056i
$889$	−4.83876e17	−	4.83876e17i	−0.980219	−	0.980219i
$890$	−9.92229e17			−1.99651
$891$	1.38601e17	+	1.38601e17i	0.277013	+	0.277013i
$892$			2.03499e18i			4.03992i
$893$	5.54997e16			0.109442
$894$	−1.23256e18			−2.41426
$895$	1.09477e18			2.13002
$896$	−7.76715e17	+	7.76715e17i	−1.50111	+	1.50111i
$897$	−1.23800e17	+	1.23800e17i	−0.237666	+	0.237666i
$898$		−	5.45961e17i		−	1.04113i
$899$	3.22962e17	−	4.90371e17i	0.611777	−	0.928895i
$900$	5.92426e16			0.111475
$901$	3.82186e16	+	3.82186e16i	0.0714375	+	0.0714375i
$902$	−2.15416e17	−	2.15416e17i	−0.399980	−	0.399980i
$903$		−	5.72471e17i		−	1.05591i
$904$		−	8.54601e17i		−	1.56586i
$905$		−	4.90100e17i		−	0.892059i
$906$	2.68371e17			0.485250
$907$	−3.44499e17	+	3.44499e17i	−0.618792	+	0.618792i	−0.945222	−	0.326430i	$-0.894154\pi$
$907$	−3.44499e17	+	3.44499e17i	−0.618792	+	0.618792i	0.326430	+	0.945222i	$0.394154\pi$
$908$		−	1.29625e18i		−	2.31299i
$909$	−1.14858e16	+	1.14858e16i	−0.0203600	+	0.0203600i
$910$	7.11107e17	+	7.11107e17i	1.25224	+	1.25224i
$911$	7.70780e17	−	7.70780e17i	1.34840	−	1.34840i	0.461008	−	0.887396i	$-0.347488\pi$
$911$	7.70780e17	−	7.70780e17i	1.34840	−	1.34840i	0.887396	−	0.461008i	$-0.152512\pi$
$912$		−	5.35909e16i		−	0.0931369i
$913$	2.25132e16	+	2.25132e16i	0.0388698	+	0.0388698i
$914$	2.46848e17	−	2.46848e17i	0.423402	−	0.423402i
$915$	3.44482e17			0.587003
$916$	4.30127e15	+	4.30127e15i	0.00728155	+	0.00728155i
$917$	−1.46836e17	+	1.46836e17i	−0.246954	+	0.246954i
$918$	1.46509e18	+	1.46509e18i	2.44799	+	2.44799i
$919$	−5.66114e17			−0.939746			−0.469873	−	0.882734i	$-0.655700\pi$
$919$	−5.66114e17			−0.939746			−0.469873	+	0.882734i	$0.655700\pi$
$920$	1.37426e18	+	1.37426e18i	2.26643	+	2.26643i
$921$			6.70942e17i			1.09933i
$922$	1.80616e18			2.94016
$923$	2.31248e17			0.373996
$924$	−7.09415e17			−1.13990
$925$	−5.54637e17	+	5.54637e17i	−0.885438	+	0.885438i
$926$	2.27923e17	−	2.27923e17i	0.361512	−	0.361512i
$927$		−	5.70720e15i		−	0.00899383i
$928$	1.35172e17	−	2.05239e17i	0.211640	−	0.321346i
$929$	9.74574e17			1.51607			0.758037	−	0.652212i	$-0.226159\pi$
$929$	9.74574e17			1.51607			0.758037	+	0.652212i	$0.226159\pi$
$930$	1.71016e18	+	1.71016e18i	2.64325	+	2.64325i
$931$	−3.05237e16	−	3.05237e16i	−0.0468748	−	0.0468748i
$932$		−	1.71731e18i		−	2.62031i
$933$			3.61719e17i			0.548379i
$934$		−	2.08809e18i		−	3.14534i
$935$	9.62167e17			1.44006
$936$	−7.27896e15	+	7.27896e15i	−0.0108247	+	0.0108247i
$937$			9.50509e16i			0.140449i	0.997531	+	0.0702245i	$0.0223716\pi$
$937$			9.50509e16i			0.140449i	−0.997531	+	0.0702245i	$0.977628\pi$
$938$	−7.03153e17	+	7.03153e17i	−1.03236	+	1.03236i
$939$	5.55256e17	+	5.55256e17i	0.810027	+	0.810027i
$940$	−3.04175e18	+	3.04175e18i	−4.40917	+	4.40917i
$941$			3.29791e17i			0.475008i	0.971387	+	0.237504i	$0.0763293\pi$
$941$			3.29791e17i			0.475008i	−0.971387	+	0.237504i	$0.923671\pi$
$942$	1.18520e18	+	1.18520e18i	1.69623	+	1.69623i
$943$	−3.62907e17	+	3.62907e17i	−0.516089	+	0.516089i
$944$	3.32013e16			0.0469163
$945$	−1.31406e18	−	1.31406e18i	−1.84512	−	1.84512i
$946$	−2.56557e17	+	2.56557e17i	−0.357962	+	0.357962i
$947$	−5.64983e16	−	5.64983e16i	−0.0783313	−	0.0783313i	0.666856	−	0.745187i	$-0.267640\pi$
$947$	−5.64983e16	−	5.64983e16i	−0.0783313	−	0.0783313i	−0.745187	+	0.666856i	$0.767640\pi$
$948$	−1.11609e18			−1.53762
$949$	−8.49067e16	−	8.49067e16i	−0.116237	−	0.116237i
$950$		−	2.31656e17i		−	0.315139i
$951$	−6.30479e17			−0.852290
$952$	−4.01577e18			−5.39446
$953$	8.14474e17			1.08723			0.543613	−	0.839336i	$-0.317056\pi$
$953$	8.14474e17			1.08723			0.543613	+	0.839336i	$0.317056\pi$
$954$	9.86642e14	−	9.86642e14i	0.00130879	−	0.00130879i
$955$	−3.71732e16	+	3.71732e16i	−0.0490015	+	0.0490015i
$956$		−	1.06681e18i		−	1.39746i
$957$	−2.91890e17	+	6.00801e16i	−0.379969	+	0.0782095i
$958$	−1.15527e18			−1.49448
$959$	1.10199e18	+	1.10199e18i	1.41667	+	1.41667i
$960$	−6.80332e17	−	6.80332e17i	−0.869148	−	0.869148i
$961$			1.86769e17i			0.237117i
$962$		−	2.59768e17i		−	0.327744i
$963$			4.81264e15i			0.00603428i
$964$	1.68967e18			2.10542
$965$	−1.28442e18	+	1.28442e18i	−1.59053	+	1.59053i
$966$			1.76322e18i			2.16992i
$967$	4.51331e17	−	4.51331e17i	0.551996	−	0.551996i	−0.375020	−	0.927017i	$-0.622364\pi$
$967$	4.51331e17	−	4.51331e17i	0.551996	−	0.551996i	0.927017	+	0.375020i	$0.122364\pi$
$968$	−9.64499e17	−	9.64499e17i	−1.17233	−	1.17233i
$969$	−8.18930e16	+	8.18930e16i	−0.0989245	+	0.0989245i
$970$		−	3.87165e18i		−	4.64800i
$971$	6.19166e17	+	6.19166e17i	0.738741	+	0.738741i	0.972334	−	0.233594i	$-0.0750485\pi$
$971$	6.19166e17	+	6.19166e17i	0.738741	+	0.738741i	−0.233594	+	0.972334i	$0.575049\pi$
$972$	5.18140e16	−	5.18140e16i	0.0614398	−	0.0614398i
$973$	1.38816e18			1.63592
$974$	1.83759e18	+	1.83759e18i	2.15226	+	2.15226i
$975$	−6.00090e17	+	6.00090e17i	−0.698536	+	0.698536i
$976$	2.48672e17	+	2.48672e17i	0.287692	+	0.287692i
$977$	−1.07074e18			−1.23117			−0.615583	−	0.788072i	$-0.711079\pi$
$977$	−1.07074e18			−1.23117			−0.615583	+	0.788072i	$0.711079\pi$
$978$	−1.41984e18	−	1.41984e18i	−1.62258	−	1.62258i
$979$			2.02898e17i			0.230452i
$980$	3.34581e18			3.77698
$981$	−2.38427e16			−0.0267511
$982$	2.10366e18			2.34589
$983$	2.50730e17	−	2.50730e17i	0.277898	−	0.277898i	−0.554371	−	0.832269i	$-0.687041\pi$
$983$	2.50730e17	−	2.50730e17i	0.277898	−	0.277898i	0.832269	+	0.554371i	$0.187041\pi$
$984$	−1.05445e18	+	1.05445e18i	−1.16159	+	1.16159i
$985$		−	1.33108e18i		−	1.45743i
$986$	−3.14920e18	+	6.48204e17i	−3.42719	+	0.705424i
$987$	−2.04762e18			−2.21486
$988$	3.67707e16	+	3.67707e16i	0.0395331	+	0.0395331i
$989$	4.32216e17	+	4.32216e17i	0.461873	+	0.461873i
$990$		−	2.48391e16i		−	0.0263830i
$991$			7.27567e17i			0.768123i	0.923308	+	0.384062i	$0.125475\pi$
$991$			7.27567e17i			0.768123i	−0.923308	+	0.384062i	$0.874525\pi$
$992$			4.07837e17i			0.427973i
$993$	1.49551e18			1.55989
$994$	1.64677e18	−	1.64677e18i	1.70732	−	1.70732i
$995$		−	1.68519e18i		−	1.73664i
$996$	2.10037e17	−	2.10037e17i	0.215150	−	0.215150i
$997$	9.78127e16	+	9.78127e16i	0.0995920	+	0.0995920i	0.755147	−	0.655555i	$-0.227565\pi$
$997$	9.78127e16	+	9.78127e16i	0.0995920	+	0.0995920i	−0.655555	+	0.755147i	$0.727565\pi$
$998$	3.71164e17	−	3.71164e17i	0.375649	−	0.375649i
$999$			4.80028e17i			0.482918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.13.c.a.12.2	✓	58
29.17	odd	4	inner	29.13.c.a.17.2	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.13.c.a.12.2	✓	58	1.1	even	1	trivial
29.13.c.a.17.2	yes	58	29.17	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-79.7284 - 79.7284i) q^{2} +(-520.777 - 520.777i) q^{3} +8617.22i q^{4} -29504.0i q^{5} +83041.4i q^{6} -164320. q^{7} +(360470. - 360470. i) q^{8} +10976.2i q^{9} +O(q^{10})\)	\(q+(-79.7284 - 79.7284i) q^{2} +(-520.777 - 520.777i) q^{3} +8617.22i q^{4} -29504.0i q^{5} +83041.4i q^{6} -164320. q^{7} +(360470. - 360470. i) q^{8} +10976.2i q^{9} +(-2.35231e6 + 2.35231e6i) q^{10} +(481016. + 481016. i) q^{11} +(4.48765e6 - 4.48765e6i) q^{12} +1.83971e6i q^{13} +(1.31010e7 + 1.31010e7i) q^{14} +(-1.53650e7 + 1.53650e7i) q^{15} -2.21832e7 q^{16} +(3.38984e7 + 3.38984e7i) q^{17} +(875113. - 875113. i) q^{18} +(-2.31945e6 - 2.31945e6i) q^{19} +2.54243e8 q^{20} +(8.55742e7 + 8.55742e7i) q^{21} -7.67013e7i q^{22} -1.29217e8 q^{23} -3.75449e8 q^{24} -6.26347e8 q^{25} +(1.46677e8 - 1.46677e8i) q^{26} +(-2.71046e8 + 2.71046e8i) q^{27} -1.41598e9i q^{28} +(-1.19919e8 - 5.82610e8i) q^{29} +2.45006e9 q^{30} +(6.98008e8 + 6.98008e8i) q^{31} +(2.92143e8 + 2.92143e8i) q^{32} -5.01004e8i q^{33} -5.40533e9i q^{34} +4.84811e9i q^{35} -9.45842e7 q^{36} +(8.85509e8 - 8.85509e8i) q^{37} +3.69852e8i q^{38} +(9.58079e8 - 9.58079e8i) q^{39} +(-1.06353e10 - 1.06353e10i) q^{40} +(2.80850e9 - 2.80850e9i) q^{41} -1.36454e10i q^{42} +(-3.34488e9 - 3.34488e9i) q^{43} +(-4.14502e9 + 4.14502e9i) q^{44} +3.23842e8 q^{45} +(1.03023e10 + 1.03023e10i) q^{46} +(-1.19640e10 + 1.19640e10i) q^{47} +(1.15525e10 + 1.15525e10i) q^{48} +1.31599e10 q^{49} +(4.99376e10 + 4.99376e10i) q^{50} -3.53070e10i q^{51} -1.58532e10 q^{52} +1.12745e9 q^{53} +4.32201e10 q^{54} +(1.41919e10 - 1.41919e10i) q^{55} +(-5.92325e10 + 5.92325e10i) q^{56} +2.41584e9i q^{57} +(-3.68895e10 + 5.60115e10i) q^{58} -1.49669e9 q^{59} +(-1.32404e11 - 1.32404e11i) q^{60} +(-1.12099e10 - 1.12099e10i) q^{61} -1.11302e11i q^{62} -1.80361e9i q^{63} +4.42780e10i q^{64} +5.42789e10 q^{65} +(-3.99443e10 + 3.99443e10i) q^{66} +5.36718e10i q^{67} +(-2.92110e11 + 2.92110e11i) q^{68} +(6.72933e10 + 6.72933e10i) q^{69} +(3.86532e11 - 3.86532e11i) q^{70} -1.25698e11i q^{71} +(3.95658e9 + 3.95658e9i) q^{72} +(-4.61522e10 + 4.61522e10i) q^{73} -1.41200e11 q^{74} +(3.26187e11 + 3.26187e11i) q^{75} +(1.99872e10 - 1.99872e10i) q^{76} +(-7.90408e10 - 7.90408e10i) q^{77} -1.52772e11 q^{78} +(-1.24351e11 - 1.24351e11i) q^{79} +6.54493e11i q^{80} +2.88142e11 q^{81} -4.47835e11 q^{82} +4.68034e10 q^{83} +(-7.37412e11 + 7.37412e11i) q^{84} +(1.00014e12 - 1.00014e12i) q^{85} +5.33364e11i q^{86} +(-2.40958e11 + 3.65861e11i) q^{87} +3.46784e11 q^{88} +(2.10905e11 + 2.10905e11i) q^{89} +(-2.58194e10 - 2.58194e10i) q^{90} -3.02302e11i q^{91} -1.11349e12i q^{92} -7.27013e11i q^{93} +1.90774e12 q^{94} +(-6.84332e10 + 6.84332e10i) q^{95} -3.04283e11i q^{96} +(-8.22947e11 + 8.22947e11i) q^{97} +(-1.04922e12 - 1.04922e12i) q^{98} +(-5.27972e9 + 5.27972e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8}+O(q^{10}) \) 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8	\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8} - 1957890 q^{10} + 4120990 q^{11} + 2920062 q^{12} - 1824520 q^{14} - 8383600 q^{15} - 133743512 q^{16} + 33971578 q^{17} - 122384158 q^{18} + 65838718 q^{19} - 59408388 q^{20} + 200896236 q^{21} + 104539676 q^{23} + 163907064 q^{24} - 3086882294 q^{25} + 607848030 q^{26} - 1190867840 q^{27} + 817714294 q^{29} + 5793833612 q^{30} - 1059975938 q^{31} + 2323254598 q^{32} + 517001400 q^{36} - 864725342 q^{37} + 18048639408 q^{39} - 22547920086 q^{40} - 17292603926 q^{41} - 3344004962 q^{43} - 53750811886 q^{44} - 16067938640 q^{45} + 43310099300 q^{46} - 15159905282 q^{47} - 4602803862 q^{48} + 32036753022 q^{49} - 16057299278 q^{50} + 81167587800 q^{52} - 69552844564 q^{53} + 38996274808 q^{54} + 3944882736 q^{55} - 156397031424 q^{56} + 107434998568 q^{58} + 82613255468 q^{59} - 147410252946 q^{60} + 128229759922 q^{61} + 125938412928 q^{65} + 364716671994 q^{66} - 141670411468 q^{68} + 529640675916 q^{69} + 518962441956 q^{70} - 180699442320 q^{72} - 428225274062 q^{73} + 307721180948 q^{74} - 617987210610 q^{75} - 455232145048 q^{76} - 963484794004 q^{77} + 688403957040 q^{78} - 183006289538 q^{79} + 1001949265154 q^{81} - 1176460419184 q^{82} + 361042835756 q^{83} - 402324805420 q^{84} + 832273178976 q^{85} - 1065344596322 q^{87} - 1836857960940 q^{88} + 1922736257242 q^{89} - 1170237151648 q^{90} - 2759662014220 q^{94} + 5518358548560 q^{95} + 1356111950818 q^{97} - 2518255928616 q^{98} + 3259343912178 q^{99}+O(q^{100}) \) 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8 - 1957890 * q^10 + 4120990 * q^11 + 2920062 * q^12 - 1824520 * q^14 - 8383600 * q^15 - 133743512 * q^16 + 33971578 * q^17 - 122384158 * q^18 + 65838718 * q^19 - 59408388 * q^20 + 200896236 * q^21 + 104539676 * q^23 + 163907064 * q^24 - 3086882294 * q^25 + 607848030 * q^26 - 1190867840 * q^27 + 817714294 * q^29 + 5793833612 * q^30 - 1059975938 * q^31 + 2323254598 * q^32 + 517001400 * q^36 - 864725342 * q^37 + 18048639408 * q^39 - 22547920086 * q^40 - 17292603926 * q^41 - 3344004962 * q^43 - 53750811886 * q^44 - 16067938640 * q^45 + 43310099300 * q^46 - 15159905282 * q^47 - 4602803862 * q^48 + 32036753022 * q^49 - 16057299278 * q^50 + 81167587800 * q^52 - 69552844564 * q^53 + 38996274808 * q^54 + 3944882736 * q^55 - 156397031424 * q^56 + 107434998568 * q^58 + 82613255468 * q^59 - 147410252946 * q^60 + 128229759922 * q^61 + 125938412928 * q^65 + 364716671994 * q^66 - 141670411468 * q^68 + 529640675916 * q^69 + 518962441956 * q^70 - 180699442320 * q^72 - 428225274062 * q^73 + 307721180948 * q^74 - 617987210610 * q^75 - 455232145048 * q^76 - 963484794004 * q^77 + 688403957040 * q^78 - 183006289538 * q^79 + 1001949265154 * q^81 - 1176460419184 * q^82 + 361042835756 * q^83 - 402324805420 * q^84 + 832273178976 * q^85 - 1065344596322 * q^87 - 1836857960940 * q^88 + 1922736257242 * q^89 - 1170237151648 * q^90 - 2759662014220 * q^94 + 5518358548560 * q^95 + 1356111950818 * q^97 - 2518255928616 * q^98 + 3259343912178 * q^99

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