LMFDB - Embedded newform 29.13.c.a.12.1

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			12.1
Character	$\chi$	$=$	29.12
Dual form			29.13.c.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-88.1500 - 88.1500i) q^{2} +(347.445 + 347.445i) q^{3} +11444.8i q^{4} +14434.6i q^{5} -61254.6i q^{6} -35450.1 q^{7} +(647800. - 647800. i) q^{8} -290005. i q^{9} +O(q^{10})$	\(q+(-88.1500 - 88.1500i) q^{2} +(347.445 + 347.445i) q^{3} +11444.8i q^{4} +14434.6i q^{5} -61254.6i q^{6} -35450.1 q^{7} +(647800. - 647800. i) q^{8} -290005. i q^{9} +(1.27241e6 - 1.27241e6i) q^{10} +(1.29325e6 + 1.29325e6i) q^{11} +(-3.97645e6 + 3.97645e6i) q^{12} -5.82852e6i q^{13} +(3.12493e6 + 3.12493e6i) q^{14} +(-5.01524e6 + 5.01524e6i) q^{15} -6.73291e7 q^{16} +(3.97007e6 + 3.97007e6i) q^{17} +(-2.55639e7 + 2.55639e7i) q^{18} +(5.27164e7 + 5.27164e7i) q^{19} -1.65202e8 q^{20} +(-1.23170e7 - 1.23170e7i) q^{21} -2.27999e8i q^{22} -3.65354e7 q^{23} +4.50150e8 q^{24} +3.57820e7 q^{25} +(-5.13784e8 + 5.13784e8i) q^{26} +(2.85407e8 - 2.85407e8i) q^{27} -4.05721e8i q^{28} +(-4.86753e8 + 3.41887e8i) q^{29} +8.84187e8 q^{30} +(5.62349e8 + 5.62349e8i) q^{31} +(3.28167e9 + 3.28167e9i) q^{32} +8.98665e8i q^{33} -6.99923e8i q^{34} -5.11709e8i q^{35} +3.31906e9 q^{36} +(-2.05003e9 + 2.05003e9i) q^{37} -9.29390e9i q^{38} +(2.02509e9 - 2.02509e9i) q^{39} +(9.35076e9 + 9.35076e9i) q^{40} +(-8.98286e8 + 8.98286e8i) q^{41} +2.17148e9i q^{42} +(-7.52420e8 - 7.52420e8i) q^{43} +(-1.48010e10 + 1.48010e10i) q^{44} +4.18611e9 q^{45} +(3.22060e9 + 3.22060e9i) q^{46} +(1.86693e9 - 1.86693e9i) q^{47} +(-2.33932e10 - 2.33932e10i) q^{48} -1.25846e10 q^{49} +(-3.15418e9 - 3.15418e9i) q^{50} +2.75876e9i q^{51} +6.67064e10 q^{52} -4.09218e10 q^{53} -5.03173e10 q^{54} +(-1.86675e10 + 1.86675e10i) q^{55} +(-2.29646e10 + 2.29646e10i) q^{56} +3.66321e10i q^{57} +(7.30446e10 + 1.27699e10i) q^{58} +5.39703e10 q^{59} +(-5.73986e10 - 5.73986e10i) q^{60} +(6.44727e10 + 6.44727e10i) q^{61} -9.91420e10i q^{62} +1.02807e10i q^{63} -3.02778e11i q^{64} +8.41325e10 q^{65} +(7.92173e10 - 7.92173e10i) q^{66} +7.43464e10i q^{67} +(-4.54368e10 + 4.54368e10i) q^{68} +(-1.26940e10 - 1.26940e10i) q^{69} +(-4.51072e10 + 4.51072e10i) q^{70} +1.34551e11i q^{71} +(-1.87865e11 - 1.87865e11i) q^{72} +(-1.55965e11 + 1.55965e11i) q^{73} +3.61421e11 q^{74} +(1.24323e10 + 1.24323e10i) q^{75} +(-6.03331e11 + 6.03331e11i) q^{76} +(-4.58458e10 - 4.58458e10i) q^{77} -3.57023e11 q^{78} +(8.42501e10 + 8.42501e10i) q^{79} -9.71870e11i q^{80} +4.42063e10 q^{81} +1.58368e11 q^{82} -2.08825e11 q^{83} +(1.40966e11 - 1.40966e11i) q^{84} +(-5.73064e10 + 5.73064e10i) q^{85} +1.32652e11i q^{86} +(-2.87907e11 - 5.03329e10i) q^{87} +1.67553e12 q^{88} +(1.63380e11 + 1.63380e11i) q^{89} +(-3.69006e11 - 3.69006e11i) q^{90} +2.06622e11i q^{91} -4.18142e11i q^{92} +3.90771e11i q^{93} -3.29140e11 q^{94} +(-7.60942e11 + 7.60942e11i) q^{95} +2.28040e12i q^{96} +(9.58473e11 - 9.58473e11i) q^{97} +(1.10933e12 + 1.10933e12i) q^{98} +(3.75048e11 - 3.75048e11i) 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 $

$2$	−88.1500	−	88.1500i	−1.37734	−	1.37734i	−0.849081	−	0.528262i	$-0.822844\pi$
$2$	−88.1500	−	88.1500i	−1.37734	−	1.37734i	−0.528262	−	0.849081i	$-0.677156\pi$
$3$	347.445	+	347.445i	0.476605	+	0.476605i	0.904044	−	0.427439i	$-0.140584\pi$
$3$	347.445	+	347.445i	0.476605	+	0.476605i	−0.427439	+	0.904044i	$0.640584\pi$
$4$			11444.8i			2.79415i
$5$			14434.6i			0.923816i	0.886928	+	0.461908i	$0.152835\pi$
$5$			14434.6i			0.923816i	−0.886928	+	0.461908i	$0.847165\pi$
$6$		−	61254.6i		−	1.31290i
$7$	−35450.1			−0.301321			−0.150661	−	0.988586i	$-0.548140\pi$
$7$	−35450.1			−0.301321			−0.150661	+	0.988586i	$0.548140\pi$
$8$	647800.	−	647800.i	2.47116	−	2.47116i
$9$		−	290005.i		−	0.545695i
$10$	1.27241e6	−	1.27241e6i	1.27241	−	1.27241i
$11$	1.29325e6	+	1.29325e6i	0.730004	+	0.730004i	0.970620	−	0.240616i	$-0.0773495\pi$
$11$	1.29325e6	+	1.29325e6i	0.730004	+	0.730004i	−0.240616	+	0.970620i	$0.577350\pi$
$12$	−3.97645e6	+	3.97645e6i	−1.33171	+	1.33171i
$13$		−	5.82852e6i		−	1.20753i	−0.797162	−	0.603765i	$-0.793667\pi$
$13$		−	5.82852e6i		−	1.20753i	0.797162	−	0.603765i	$-0.206333\pi$
$14$	3.12493e6	+	3.12493e6i	0.415023	+	0.415023i
$15$	−5.01524e6	+	5.01524e6i	−0.440296	+	0.440296i
$16$	−6.73291e7			−4.01312
$17$	3.97007e6	+	3.97007e6i	0.164477	+	0.164477i	0.784547	−	0.620070i	$-0.212896\pi$
$17$	3.97007e6	+	3.97007e6i	0.164477	+	0.164477i	−0.620070	+	0.784547i	$0.712896\pi$
$18$	−2.55639e7	+	2.55639e7i	−0.751610	+	0.751610i
$19$	5.27164e7	+	5.27164e7i	1.12053	+	1.12053i	0.991661	+	0.128871i	$0.0411353\pi$
$19$	5.27164e7	+	5.27164e7i	1.12053	+	1.12053i	0.128871	+	0.991661i	$0.458865\pi$
$20$	−1.65202e8			−2.58128
$21$	−1.23170e7	−	1.23170e7i	−0.143611	−	0.143611i
$22$		−	2.27999e8i		−	2.01093i
$23$	−3.65354e7			−0.246801			−0.123400	−	0.992357i	$-0.539380\pi$
$23$	−3.65354e7			−0.246801			−0.123400	+	0.992357i	$0.539380\pi$
$24$	4.50150e8			2.35554
$25$	3.57820e7			0.146563
$26$	−5.13784e8	+	5.13784e8i	−1.66318	+	1.66318i
$27$	2.85407e8	−	2.85407e8i	0.736686	−	0.736686i
$28$		−	4.05721e8i		−	0.841936i
$29$	−4.86753e8	+	3.41887e8i	−0.818315	+	0.574770i
$29$	−4.86753e8	+	3.41887e8i	−0.818315	+	0.574770i
$30$	8.84187e8			1.21288
$31$	5.62349e8	+	5.62349e8i	0.633630	+	0.633630i	0.948976	−	0.315347i	$-0.102121\pi$
$31$	5.62349e8	+	5.62349e8i	0.633630	+	0.633630i	−0.315347	+	0.948976i	$0.602121\pi$
$32$	3.28167e9	+	3.28167e9i	3.05629	+	3.05629i
$33$			8.98665e8i			0.695847i
$34$		−	6.99923e8i		−	0.453082i
$35$		−	5.11709e8i		−	0.278365i
$36$	3.31906e9			1.52475
$37$	−2.05003e9	+	2.05003e9i	−0.799007	+	0.799007i	−0.982939	−	0.183932i	$-0.941117\pi$
$37$	−2.05003e9	+	2.05003e9i	−0.799007	+	0.799007i	0.183932	+	0.982939i	$0.441117\pi$
$38$		−	9.29390e9i		−	3.08672i
$39$	2.02509e9	−	2.02509e9i	0.575515	−	0.575515i
$40$	9.35076e9	+	9.35076e9i	2.28290	+	2.28290i
$41$	−8.98286e8	+	8.98286e8i	−0.189109	+	0.189109i	−0.795311	−	0.606202i	$-0.792692\pi$
$41$	−8.98286e8	+	8.98286e8i	−0.189109	+	0.189109i	0.606202	+	0.795311i	$0.292692\pi$
$42$			2.17148e9i			0.395604i
$43$	−7.52420e8	−	7.52420e8i	−0.119028	−	0.119028i	0.645084	−	0.764112i	$-0.276822\pi$
$43$	−7.52420e8	−	7.52420e8i	−0.119028	−	0.119028i	−0.764112	+	0.645084i	$0.776822\pi$
$44$	−1.48010e10	+	1.48010e10i	−2.03974	+	2.03974i
$45$	4.18611e9			0.504122
$46$	3.22060e9	+	3.22060e9i	0.339930	+	0.339930i
$47$	1.86693e9	−	1.86693e9i	0.173197	−	0.173197i	−0.615185	−	0.788383i	$-0.710919\pi$
$47$	1.86693e9	−	1.86693e9i	0.173197	−	0.173197i	0.788383	+	0.615185i	$0.210919\pi$
$48$	−2.33932e10	−	2.33932e10i	−1.91268	−	1.91268i
$49$	−1.25846e10			−0.909206
$50$	−3.15418e9	−	3.15418e9i	−0.201868	−	0.201868i
$51$			2.75876e9i			0.156781i
$52$	6.67064e10			3.37402
$53$	−4.09218e10			−1.84629			−0.923144	−	0.384454i	$-0.874390\pi$
$53$	−4.09218e10			−1.84629			−0.923144	+	0.384454i	$0.874390\pi$
$54$	−5.03173e10			−2.02934
$55$	−1.86675e10	+	1.86675e10i	−0.674390	+	0.674390i
$56$	−2.29646e10	+	2.29646e10i	−0.744613	+	0.744613i
$57$			3.66321e10i			1.06810i
$58$	7.30446e10	+	1.27699e10i	1.91876	+	0.335444i
$59$	5.39703e10			1.27951			0.639754	−	0.768580i	$-0.279036\pi$
$59$	5.39703e10			1.27951			0.639754	+	0.768580i	$0.279036\pi$
$60$	−5.73986e10	−	5.73986e10i	−1.23025	−	1.23025i
$61$	6.44727e10	+	6.44727e10i	1.25140	+	1.25140i	0.955092	+	0.296310i	$0.0957560\pi$
$61$	6.44727e10	+	6.44727e10i	1.25140	+	1.25140i	0.296310	+	0.955092i	$0.404244\pi$
$62$		−	9.91420e10i		−	1.74545i
$63$			1.02807e10i			0.164429i
$64$		−	3.02778e11i		−	4.40600i
$65$	8.41325e10			1.11554
$66$	7.92173e10	−	7.92173e10i	0.958421	−	0.958421i
$67$			7.43464e10i			0.821885i	0.911661	+	0.410942i	$0.134800\pi$
$67$			7.43464e10i			0.821885i	−0.911661	+	0.410942i	$0.865200\pi$
$68$	−4.54368e10	+	4.54368e10i	−0.459572	+	0.459572i
$69$	−1.26940e10	−	1.26940e10i	−0.117627	−	0.117627i
$70$	−4.51072e10	+	4.51072e10i	−0.383405	+	0.383405i
$71$			1.34551e11i			1.05036i	0.850992	+	0.525178i	$0.176001\pi$
$71$			1.34551e11i			1.05036i	−0.850992	+	0.525178i	$0.823999\pi$
$72$	−1.87865e11	−	1.87865e11i	−1.34850	−	1.34850i
$73$	−1.55965e11	+	1.55965e11i	−1.03060	+	1.03060i	−0.0310804	+	0.999517i	$0.509895\pi$
$73$	−1.55965e11	+	1.55965e11i	−1.03060	+	1.03060i	−0.999517	+	0.0310804i	$0.990105\pi$
$74$	3.61421e11			2.20101
$75$	1.24323e10	+	1.24323e10i	0.0698527	+	0.0698527i
$76$	−6.03331e11	+	6.03331e11i	−3.13094	+	3.13094i
$77$	−4.58458e10	−	4.58458e10i	−0.219966	−	0.219966i
$78$	−3.57023e11			−1.58536
$79$	8.42501e10	+	8.42501e10i	0.346584	+	0.346584i	0.858835	−	0.512252i	$-0.171188\pi$
$79$	8.42501e10	+	8.42501e10i	0.346584	+	0.346584i	−0.512252	+	0.858835i	$0.671188\pi$
$80$		−	9.71870e11i		−	3.70739i
$81$	4.42063e10			0.156521
$82$	1.58368e11			0.520935
$83$	−2.08825e11			−0.638724			−0.319362	−	0.947633i	$-0.603469\pi$
$83$	−2.08825e11			−0.638724			−0.319362	+	0.947633i	$0.603469\pi$
$84$	1.40966e11	−	1.40966e11i	0.401271	−	0.401271i
$85$	−5.73064e10	+	5.73064e10i	−0.151946	+	0.151946i
$86$			1.32652e11i			0.327885i
$87$	−2.87907e11	−	5.03329e10i	−0.663951	−	0.116074i
$88$	1.67553e12			3.60792
$89$	1.63380e11	+	1.63380e11i	0.328746	+	0.328746i	0.852109	−	0.523364i	$-0.175323\pi$
$89$	1.63380e11	+	1.63380e11i	0.328746	+	0.328746i	−0.523364	+	0.852109i	$0.675323\pi$
$90$	−3.69006e11	−	3.69006e11i	−0.694349	−	0.694349i
$91$			2.06622e11i			0.363854i
$92$		−	4.18142e11i		−	0.689599i
$93$			3.90771e11i			0.603982i
$94$	−3.29140e11			−0.477105
$95$	−7.60942e11	+	7.60942e11i	−1.03517	+	1.03517i
$96$			2.28040e12i			2.91329i
$97$	9.58473e11	−	9.58473e11i	1.15067	−	1.15067i	0.164248	−	0.986419i	$-0.447480\pi$
$97$	9.58473e11	−	9.58473e11i	1.15067	−	1.15067i	0.986419	−	0.164248i	$-0.0525197\pi$
$98$	1.10933e12	+	1.10933e12i	1.25229	+	1.25229i
$99$	3.75048e11	−	3.75048e11i	0.398360	−	0.398360i
$100$			4.09519e11i			0.409519i
$101$	−5.13595e11	−	5.13595e11i	−0.483830	−	0.483830i	0.422523	−	0.906352i	$-0.361145\pi$
$101$	−5.13595e11	−	5.13595e11i	−0.483830	−	0.483830i	−0.906352	+	0.422523i	$0.861145\pi$
$102$	2.43185e11	−	2.43185e11i	0.215941	−	0.215941i
$103$	1.17755e11			0.0986180			0.0493090	−	0.998784i	$-0.484298\pi$
$103$	1.17755e11			0.0986180			0.0493090	+	0.998784i	$0.484298\pi$
$104$	−3.77571e12	−	3.77571e12i	−2.98400	−	2.98400i
$105$	1.77791e11	−	1.77791e11i	0.132670	−	0.132670i
$106$	3.60726e12	+	3.60726e12i	2.54297	+	2.54297i
$107$	−1.61664e12			−1.07724			−0.538618	−	0.842550i	$-0.681053\pi$
$107$	−1.61664e12			−1.07724			−0.538618	+	0.842550i	$0.681053\pi$
$108$	3.26644e12	+	3.26644e12i	2.05841	+	2.05841i
$109$			2.09064e12i			1.24658i	0.781990	+	0.623290i	$0.214205\pi$
$109$			2.09064e12i			1.24658i	−0.781990	+	0.623290i	$0.785795\pi$
$110$	3.29109e12			1.85773
$111$	−1.42455e12			−0.761621
$112$	2.38682e12			1.20924
$113$	1.77360e12	−	1.77360e12i	0.851893	−	0.851893i	−0.138473	−	0.990366i	$-0.544220\pi$
$113$	1.77360e12	−	1.77360e12i	0.851893	−	0.851893i	0.990366	+	0.138473i	$0.0442195\pi$
$114$	3.22912e12	−	3.22912e12i	1.47114	−	1.47114i
$115$		−	5.27375e11i		−	0.227999i
$116$	−3.91284e12	−	5.57081e12i	−1.60599	−	2.28649i
$117$	−1.69030e12			−0.658943
$118$	−4.75748e12	−	4.75748e12i	−1.76232	−	1.76232i
$119$	−1.40739e11	−	1.40739e11i	−0.0495603	−	0.0495603i
$120$			6.49775e12i			2.17608i
$121$			2.06547e11i			0.0658121i
$122$		−	1.13665e13i		−	3.44722i
$123$	−6.24210e11			−0.180260
$124$	−6.43599e12	+	6.43599e12i	−1.77046	+	1.77046i
$125$			4.04058e12i			1.05921i
$126$	9.06244e11	−	9.06244e11i	0.226476	−	0.226476i
$127$	1.91880e12	+	1.91880e12i	0.457307	+	0.457307i	0.897771	−	0.440464i	$-0.145186\pi$
$127$	1.91880e12	+	1.91880e12i	0.457307	+	0.457307i	−0.440464	+	0.897771i	$0.645186\pi$
$128$	−1.32482e13	+	1.32482e13i	−3.01228	+	3.01228i
$129$		−	5.22849e11i		−	0.113459i
$130$	−7.41628e12	−	7.41628e12i	−1.53648	−	1.53648i
$131$	−1.62252e12	+	1.62252e12i	−0.321042	+	0.321042i	−0.849167	−	0.528125i	$-0.822895\pi$
$131$	−1.62252e12	+	1.62252e12i	−0.321042	+	0.321042i	0.528125	+	0.849167i	$0.322895\pi$
$132$	−1.02851e13			−1.94430
$133$	−1.86880e12	−	1.86880e12i	−0.337640	−	0.337640i
$134$	6.55363e12	−	6.55363e12i	1.13202	−	1.13202i
$135$	4.11975e12	+	4.11975e12i	0.680563	+	0.680563i
$136$	5.14362e12			0.812896
$137$	−8.66006e12	−	8.66006e12i	−1.30978	−	1.30978i	−0.921574	−	0.388203i	$-0.873096\pi$
$137$	−8.66006e12	−	8.66006e12i	−1.30978	−	1.30978i	−0.388203	−	0.921574i	$-0.626904\pi$
$138$			2.23796e12i			0.324024i
$139$	2.39277e12			0.331751			0.165875	−	0.986147i	$-0.446955\pi$
$139$	2.39277e12			0.331751			0.165875	+	0.986147i	$0.446955\pi$
$140$	5.85643e12			0.777795
$141$	1.29731e12			0.165094
$142$	1.18607e13	−	1.18607e13i	1.44670	−	1.44670i
$143$	7.53771e12	−	7.53771e12i	0.881502	−	0.881502i
$144$			1.95258e13i			2.18994i
$145$	−4.93501e12	−	7.02610e12i	−0.530982	−	0.755973i
$146$	2.74966e13			2.83897
$147$	−4.37245e12	−	4.37245e12i	−0.433332	−	0.433332i
$148$	−2.34623e13	−	2.34623e13i	−2.23255	−	2.23255i
$149$		−	2.65755e11i		−	0.0242865i	−0.999926	−	0.0121432i	$-0.996135\pi$
$149$		−	2.65755e11i		−	0.0242865i	0.999926	−	0.0121432i	$-0.00386541\pi$
$150$		−	2.19181e12i		−	0.192422i
$151$			2.10174e13i			1.77304i	0.462694	+	0.886518i	$0.346883\pi$
$151$			2.10174e13i			1.77304i	−0.462694	+	0.886518i	$0.653117\pi$
$152$	6.82994e13			5.53803
$153$	1.15134e12	−	1.15134e12i	0.0897541	−	0.0897541i
$154$			8.08261e12i			0.605936i
$155$	−8.11730e12	+	8.11730e12i	−0.585358	+	0.585358i
$156$	2.31768e13	+	2.31768e13i	1.60807	+	1.60807i
$157$	7.70475e11	−	7.70475e11i	0.0514471	−	0.0514471i	−0.680915	−	0.732362i	$-0.738418\pi$
$157$	7.70475e11	−	7.70475e11i	0.0514471	−	0.0514471i	0.732362	+	0.680915i	$0.238418\pi$
$158$		−	1.48533e13i		−	0.954730i
$159$	−1.42181e13	−	1.42181e13i	−0.879951	−	0.879951i
$160$	−4.73697e13	+	4.73697e13i	−2.82345	+	2.82345i
$161$	1.29518e12			0.0743663
$162$	−3.89678e12	−	3.89678e12i	−0.215584	−	0.215584i
$163$	−1.27886e13	+	1.27886e13i	−0.681864	+	0.681864i	−0.960420	−	0.278556i	$-0.910144\pi$
$163$	−1.27886e13	+	1.27886e13i	−0.681864	+	0.681864i	0.278556	+	0.960420i	$0.410144\pi$
$164$	−1.02807e13	−	1.02807e13i	−0.528398	−	0.528398i
$165$	−1.29719e13			−0.642835
$166$	1.84079e13	+	1.84079e13i	0.879742	+	0.879742i
$167$		−	7.50644e12i		−	0.346047i	−0.984918	−	0.173023i	$-0.944646\pi$
$167$		−	7.50644e12i		−	0.346047i	0.984918	−	0.173023i	$-0.0553537\pi$
$168$	−1.59579e13			−0.709772
$169$	−1.06735e13			−0.458129
$170$	1.01031e13			0.418564
$171$	1.52880e13	−	1.52880e13i	0.611469	−	0.611469i
$172$	8.61133e12	−	8.61133e12i	0.332582	−	0.332582i
$173$			5.09174e13i			1.89928i	0.313339	+	0.949641i	$0.398552\pi$
$173$			5.09174e13i			1.89928i	−0.313339	+	0.949641i	$0.601448\pi$
$174$	2.09421e13	+	2.98158e13i	0.754615	+	1.07436i
$175$	−1.26848e12			−0.0441625
$176$	−8.70731e13	−	8.70731e13i	−2.92960	−	2.92960i
$177$	1.87517e13	+	1.87517e13i	0.609820	+	0.609820i
$178$		−	2.88040e13i		−	0.905591i
$179$		−	3.26392e13i		−	0.992251i	−0.868251	−	0.496125i	$-0.834756\pi$
$179$		−	3.26392e13i		−	0.992251i	0.868251	−	0.496125i	$-0.165244\pi$
$180$			4.79094e13i			1.40859i
$181$	−6.23745e12			−0.177393			−0.0886963	−	0.996059i	$-0.528270\pi$
$181$	−6.23745e12			−0.177393			−0.0886963	+	0.996059i	$0.528270\pi$
$182$	1.82137e13	−	1.82137e13i	0.501152	−	0.501152i
$183$			4.48014e13i			1.19285i
$184$	−2.36676e13	+	2.36676e13i	−0.609885	+	0.609885i
$185$	−2.95915e13	−	2.95915e13i	−0.738136	−	0.738136i
$186$	3.44464e13	−	3.44464e13i	0.831891	−	0.831891i
$187$			1.02686e13i			0.240137i
$188$	2.13667e13	+	2.13667e13i	0.483940	+	0.483940i
$189$	−1.01177e13	+	1.01177e13i	−0.221979	+	0.221979i
$190$	1.34154e14			2.85156
$191$	2.38961e13	+	2.38961e13i	0.492183	+	0.492183i	0.908993	−	0.416811i	$-0.136852\pi$
$191$	2.38961e13	+	2.38961e13i	0.492183	+	0.492183i	−0.416811	+	0.908993i	$0.636852\pi$
$192$	1.05199e14	−	1.05199e14i	2.09992	−	2.09992i
$193$	2.47676e13	+	2.47676e13i	0.479226	+	0.479226i	0.904884	−	0.425658i	$-0.139957\pi$
$193$	2.47676e13	+	2.47676e13i	0.479226	+	0.479226i	−0.425658	+	0.904884i	$0.639957\pi$
$194$	−1.68979e14			−3.16973
$195$	2.92314e13	+	2.92314e13i	0.531670	+	0.531670i
$196$		−	1.44028e14i		−	2.54046i
$197$	−5.22104e13			−0.893223			−0.446612	−	0.894728i	$-0.647369\pi$
$197$	−5.22104e13			−0.893223			−0.446612	+	0.894728i	$0.647369\pi$
$198$	−6.61209e13			−1.09736
$199$	1.69606e13			0.273100			0.136550	−	0.990633i	$-0.456399\pi$
$199$	1.69606e13			0.273100			0.136550	+	0.990633i	$0.456399\pi$
$200$	2.31796e13	−	2.31796e13i	0.362181	−	0.362181i
$201$	−2.58313e13	+	2.58313e13i	−0.391714	+	0.391714i
$202$			9.05468e13i			1.33280i
$203$	1.72554e13	−	1.21199e13i	0.246575	−	0.173190i
$204$	−3.15736e13			−0.438069
$205$	−1.29664e13	−	1.29664e13i	−0.174702	−	0.174702i
$206$	−1.03801e13	−	1.03801e13i	−0.135831	−	0.135831i
$207$			1.05954e13i			0.134678i
$208$			3.92429e14i			4.84597i
$209$			1.36351e14i			1.63599i
$210$	−3.13445e13			−0.365465
$211$	1.20583e13	−	1.20583e13i	0.136645	−	0.136645i	−0.635476	−	0.772121i	$-0.719196\pi$
$211$	1.20583e13	−	1.20583e13i	0.136645	−	0.136645i	0.772121	+	0.635476i	$0.219196\pi$
$212$		−	4.68344e14i		−	5.15881i
$213$	−4.67491e13	+	4.67491e13i	−0.500605	+	0.500605i
$214$	1.42507e14	+	1.42507e14i	1.48372	+	1.48372i
$215$	1.08609e13	−	1.08609e13i	0.109960	−	0.109960i
$216$		−	3.69774e14i		−	3.64094i
$217$	−1.99353e13	−	1.99353e13i	−0.190926	−	0.190926i
$218$	1.84290e14	−	1.84290e14i	1.71697	−	1.71697i
$219$	−1.08378e14			−0.982376
$220$	−2.13647e14	−	2.13647e14i	−1.88435	−	1.88435i
$221$	2.31396e13	−	2.31396e13i	0.198610	−	0.198610i
$222$	1.25574e14	+	1.25574e14i	1.04901	+	1.04901i
$223$	1.82280e14			1.48221			0.741106	−	0.671388i	$-0.234302\pi$
$223$	1.82280e14			1.48221			0.741106	+	0.671388i	$0.234302\pi$
$224$	−1.16335e14	−	1.16335e14i	−0.920925	−	0.920925i
$225$		−	1.03770e13i		−	0.0799788i
$226$	−3.12686e14			−2.34670
$227$	1.96636e14			1.43717			0.718583	−	0.695441i	$-0.244791\pi$
$227$	1.96636e14			1.43717			0.718583	+	0.695441i	$0.244791\pi$
$228$	−4.19249e14			−2.98444
$229$	−2.64613e13	+	2.64613e13i	−0.183484	+	0.183484i	−0.792872	−	0.609388i	$-0.791415\pi$
$229$	−2.64613e13	+	2.64613e13i	−0.183484	+	0.183484i	0.609388	+	0.792872i	$0.291415\pi$
$230$	−4.64881e13	+	4.64881e13i	−0.314033	+	0.314033i
$231$		−	3.18578e13i		−	0.209673i
$232$	−9.38441e13	+	5.36793e14i	−0.601837	+	3.44254i
$233$	5.38340e13			0.336450			0.168225	−	0.985749i	$-0.446196\pi$
$233$	5.38340e13			0.336450			0.168225	+	0.985749i	$0.446196\pi$
$234$	1.49000e14	+	1.49000e14i	0.907591	+	0.907591i
$235$	2.69485e13	+	2.69485e13i	0.160003	+	0.160003i
$236$			6.17682e14i			3.57514i
$237$			5.85446e13i			0.330367i
$238$			2.48123e13i			0.136523i
$239$	−2.95239e14			−1.58411			−0.792056	−	0.610449i	$-0.790989\pi$
$239$	−2.95239e14			−1.58411			−0.792056	+	0.610449i	$0.790989\pi$
$240$	3.37672e14	−	3.37672e14i	1.76696	−	1.76696i
$241$		−	2.20506e14i		−	1.12543i	−0.826651	−	0.562715i	$-0.809757\pi$
$241$		−	2.20506e14i		−	1.12543i	0.826651	−	0.562715i	$-0.190243\pi$
$242$	1.82071e13	−	1.82071e13i	0.0906459	−	0.0906459i
$243$	−1.36318e14	−	1.36318e14i	−0.662087	−	0.662087i
$244$	−7.37879e14	+	7.37879e14i	−3.49660	+	3.49660i
$245$		−	1.81654e14i		−	0.839939i
$246$	5.50241e13	+	5.50241e13i	0.248280	+	0.248280i
$247$	3.07259e14	−	3.07259e14i	1.35308	−	1.35308i
$248$	7.28579e14			3.13160
$249$	−7.25551e13	−	7.25551e13i	−0.304419	−	0.304419i
$250$	3.56177e14	−	3.56177e14i	1.45890	−	1.45890i
$251$	1.49451e14	+	1.49451e14i	0.597663	+	0.597663i	0.939690	−	0.342027i	$-0.111114\pi$
$251$	1.49451e14	+	1.49451e14i	0.597663	+	0.597663i	−0.342027	+	0.939690i	$0.611114\pi$
$252$	−1.17661e14			−0.459441
$253$	−4.72493e13	−	4.72493e13i	−0.180166	−	0.180166i
$254$		−	3.38285e14i		−	1.25974i
$255$	−3.98217e13			−0.144837
$256$	1.09547e15			3.89190
$257$	1.16939e14			0.405845			0.202923	−	0.979195i	$-0.434956\pi$
$257$	1.16939e14			0.405845			0.202923	+	0.979195i	$0.434956\pi$
$258$	−4.60892e13	+	4.60892e13i	−0.156272	+	0.156272i
$259$	7.26739e13	−	7.26739e13i	0.240758	−	0.240758i
$260$			9.62883e14i			3.11698i
$261$	9.91488e13	+	1.41161e14i	0.313649	+	0.446550i
$262$	2.86050e14			0.884371
$263$	−4.38390e14	−	4.38390e14i	−1.32473	−	1.32473i	−0.909900	−	0.414827i	$-0.863842\pi$
$263$	−4.38390e14	−	4.38390e14i	−1.32473	−	1.32473i	−0.414827	−	0.909900i	$-0.636158\pi$
$264$	5.82155e14	+	5.82155e14i	1.71955	+	1.71955i
$265$		−	5.90691e14i		−	1.70563i
$266$			3.29470e14i			0.930092i
$267$			1.13531e14i			0.313364i
$268$	−8.50882e14			−2.29647
$269$	2.23101e14	−	2.23101e14i	0.588828	−	0.588828i	−0.348486	−	0.937314i	$-0.613304\pi$
$269$	2.23101e14	−	2.23101e14i	0.588828	−	0.588828i	0.937314	+	0.348486i	$0.113304\pi$
$270$		−	7.26312e14i		−	1.87474i
$271$	7.89898e13	−	7.89898e13i	0.199414	−	0.199414i	−0.600335	−	0.799749i	$-0.704966\pi$
$271$	7.89898e13	−	7.89898e13i	0.199414	−	0.199414i	0.799749	+	0.600335i	$0.204966\pi$
$272$	−2.67301e14	−	2.67301e14i	−0.660065	−	0.660065i
$273$	−7.17897e13	+	7.17897e13i	−0.173415	+	0.173415i
$274$			1.52677e15i			3.60803i
$275$	4.62750e13	+	4.62750e13i	0.106992	+	0.106992i
$276$	1.45281e14	−	1.45281e14i	0.328666	−	0.328666i
$277$	2.44974e14			0.542301			0.271151	−	0.962537i	$-0.412596\pi$
$277$	2.44974e14			0.542301			0.271151	+	0.962537i	$0.412596\pi$
$278$	−2.10922e14	−	2.10922e14i	−0.456935	−	0.456935i
$279$	1.63084e14	−	1.63084e14i	0.345769	−	0.345769i
$280$	−3.31485e14	−	3.31485e14i	−0.687886	−	0.687886i
$281$	−4.83690e13			−0.0982492			−0.0491246	−	0.998793i	$-0.515643\pi$
$281$	−4.83690e13			−0.0982492			−0.0491246	+	0.998793i	$0.515643\pi$
$282$	−1.14358e14	−	1.14358e14i	−0.227391	−	0.227391i
$283$		−	3.98160e14i		−	0.775066i	−0.921856	−	0.387533i	$-0.873327\pi$
$283$		−	3.98160e14i		−	0.775066i	0.921856	−	0.387533i	$-0.126673\pi$
$284$	−1.53991e15			−2.93485
$285$	−5.28771e14			−0.986731
$286$	−1.32890e15			−2.42826
$287$	3.18443e13	−	3.18443e13i	0.0569824	−	0.0569824i
$288$	9.51699e14	−	9.51699e14i	1.66780	−	1.66780i
$289$		−	5.51099e14i		−	0.945895i
$290$	−1.84329e14	+	1.05437e15i	−0.309889	+	1.77258i
$291$	6.66034e14			1.09683
$292$	−1.78499e15	−	1.78499e15i	−2.87964	−	2.87964i
$293$	6.75910e14	+	6.75910e14i	1.06828	+	1.06828i	0.997492	+	0.0707836i	$0.0225500\pi$
$293$	6.75910e14	+	6.75910e14i	1.06828	+	1.06828i	0.0707836	+	0.997492i	$0.477450\pi$
$294$			7.70863e14i			1.19369i
$295$			7.79042e14i			1.18203i
$296$			2.65602e15i			3.94895i
$297$	7.38204e14			1.07557
$298$	−2.34263e13	+	2.34263e13i	−0.0334508	+	0.0334508i
$299$			2.12947e14i			0.298020i
$300$	−1.42285e14	+	1.42285e14i	−0.195179	+	0.195179i
$301$	2.66734e13	+	2.66734e13i	0.0358657	+	0.0358657i
$302$	1.85268e15	−	1.85268e15i	2.44208	−	2.44208i
$303$		−	3.56892e14i		−	0.461191i
$304$	−3.54935e15	−	3.54935e15i	−4.49684	−	4.49684i
$305$	−9.30639e14	+	9.30639e14i	−1.15607	+	1.15607i
$306$	−2.02981e14			−0.247244
$307$	1.34078e14	+	1.34078e14i	0.160151	+	0.160151i	0.782633	−	0.622483i	$-0.213876\pi$
$307$	1.34078e14	+	1.34078e14i	0.160151	+	0.160151i	−0.622483	+	0.782633i	$0.713876\pi$
$308$	5.24697e14	−	5.24697e14i	0.614617	−	0.614617i
$309$	4.09134e13	+	4.09134e13i	0.0470018	+	0.0470018i
$310$	1.43108e15			1.61248
$311$	−2.58059e14	−	2.58059e14i	−0.285204	−	0.285204i	0.549976	−	0.835180i	$-0.314637\pi$
$311$	−2.58059e14	−	2.58059e14i	−0.285204	−	0.285204i	−0.835180	+	0.549976i	$0.814637\pi$
$312$		−	2.62371e15i		−	2.84438i
$313$	1.46243e15			1.55528			0.777642	−	0.628707i	$-0.216416\pi$
$313$	1.46243e15			1.55528			0.777642	+	0.628707i	$0.216416\pi$
$314$	−1.35835e14			−0.141721
$315$	−1.48398e14			−0.151903
$316$	−9.64229e14	+	9.64229e14i	−0.968407	+	0.968407i
$317$	−1.47573e14	+	1.47573e14i	−0.145430	+	0.145430i	−0.776073	−	0.630643i	$-0.782791\pi$
$317$	−1.47573e14	+	1.47573e14i	−0.145430	+	0.145430i	0.630643	+	0.776073i	$0.282791\pi$
$318$			2.50665e15i			2.42399i
$319$	−1.07164e15	−	1.87347e14i	−1.01696	−	0.177788i
$320$	4.37049e15			4.07033
$321$	−5.61694e14	−	5.61694e14i	−0.513416	−	0.513416i
$322$	−1.14170e14	−	1.14170e14i	−0.102428	−	0.102428i
$323$			4.18575e14i			0.368603i
$324$			5.05934e14i			0.437344i
$325$		−	2.08556e14i		−	0.176979i
$326$	2.25463e15			1.87832
$327$	−7.26383e14	+	7.26383e14i	−0.594127	+	0.594127i
$328$			1.16382e15i			0.934636i
$329$	−6.61830e13	+	6.61830e13i	−0.0521880	+	0.0521880i
$330$	1.14347e15	+	1.14347e15i	0.885405	+	0.885405i
$331$	−1.32898e15	+	1.32898e15i	−1.01053	+	1.01053i	−0.0105863	+	0.999944i	$0.503370\pi$
$331$	−1.32898e15	+	1.32898e15i	−1.01053	+	1.01053i	−0.999944	+	0.0105863i	$0.996630\pi$
$332$		−	2.38996e15i		−	1.78469i
$333$	5.94519e14	+	5.94519e14i	0.436014	+	0.436014i
$334$	−6.61692e14	+	6.61692e14i	−0.476626	+	0.476626i
$335$	−1.07316e15			−0.759271
$336$	8.29290e14	+	8.29290e14i	0.576329	+	0.576329i
$337$	−1.09091e14	+	1.09091e14i	−0.0744748	+	0.0744748i	−0.743363	−	0.668888i	$-0.766770\pi$
$337$	−1.09091e14	+	1.09091e14i	−0.0744748	+	0.0744748i	0.668888	+	0.743363i	$0.266770\pi$
$338$	9.40870e14	+	9.40870e14i	0.631000	+	0.631000i
$339$	1.23246e15			0.812033
$340$	−6.55863e14	−	6.55863e14i	−0.424561	−	0.424561i
$341$			1.45451e15i			0.925105i
$342$	−2.69528e15			−1.68441
$343$	9.36800e14			0.575284
$344$	−9.74835e14			−0.588275
$345$	1.83234e14	−	1.83234e14i	0.108665	−	0.108665i
$346$	4.48837e15	−	4.48837e15i	2.61596	−	2.61596i
$347$			2.33971e15i			1.34025i	0.742249	+	0.670124i	$0.233759\pi$
$347$			2.33971e15i			1.34025i	−0.742249	+	0.670124i	$0.766241\pi$
$348$	5.76052e14	−	3.29505e15i	0.324330	−	1.85518i
$349$	3.34506e15			1.85119			0.925596	−	0.378513i	$-0.123564\pi$
$349$	3.34506e15			1.85119			0.925596	+	0.378513i	$0.123564\pi$
$350$	1.11816e14	+	1.11816e14i	0.0608270	+	0.0608270i
$351$	−1.66350e15	−	1.66350e15i	−0.889571	−	0.889571i
$352$			8.48801e15i			4.46221i
$353$		−	1.37510e15i		−	0.710700i	−0.934733	−	0.355350i	$-0.884362\pi$
$353$		−	1.37510e15i		−	0.710700i	0.934733	−	0.355350i	$-0.115638\pi$
$354$		−	3.30593e15i		−	1.67986i
$355$	−1.94219e15			−0.970336
$356$	−1.86986e15	+	1.86986e15i	−0.918565	+	0.918565i
$357$		−	9.77984e13i		−	0.0472414i
$358$	−2.87715e15	+	2.87715e15i	−1.36667	+	1.36667i
$359$	−2.27280e15	−	2.27280e15i	−1.06168	−	1.06168i	−0.997968	−	0.0637131i	$-0.979706\pi$
$359$	−2.27280e15	−	2.27280e15i	−1.06168	−	1.06168i	−0.0637131	−	0.997968i	$-0.520294\pi$
$360$	2.71176e15	−	2.71176e15i	1.24577	−	1.24577i
$361$			3.34473e15i			1.51118i
$362$	5.49831e14	+	5.49831e14i	0.244331	+	0.244331i
$363$	−7.17636e13	+	7.17636e13i	−0.0313664	+	0.0313664i
$364$	−2.36475e15			−1.01666
$365$	−2.25129e15	−	2.25129e15i	−0.952083	−	0.952083i
$366$	3.94925e15	−	3.94925e15i	1.64296	−	1.64296i
$367$	2.30159e15	+	2.30159e15i	0.941956	+	0.941956i	0.998405	−	0.0564492i	$-0.0179779\pi$
$367$	2.30159e15	+	2.30159e15i	0.941956	+	0.941956i	−0.0564492	+	0.998405i	$0.517978\pi$
$368$	2.45989e15			0.990443
$369$	2.60507e14	+	2.60507e14i	0.103196	+	0.103196i
$370$			5.21698e15i			2.03333i
$371$	1.45068e15			0.556326
$372$	−4.47231e15			−1.68762
$373$	−2.51695e15			−0.934591			−0.467296	−	0.884101i	$-0.654772\pi$
$373$	−2.51695e15			−0.934591			−0.467296	+	0.884101i	$0.654772\pi$
$374$	9.05173e14	−	9.05173e14i	0.330751	−	0.330751i
$375$	−1.40388e15	+	1.40388e15i	−0.504827	+	0.504827i
$376$		−	2.41880e15i		−	0.855998i
$377$	1.99269e15	+	2.83705e15i	0.694052	+	0.988140i
$378$	1.78375e15			0.611483
$379$	7.71915e13	+	7.71915e13i	0.0260456	+	0.0260456i	0.720010	−	0.693964i	$-0.244137\pi$
$379$	7.71915e13	+	7.71915e13i	0.0260456	+	0.0260456i	−0.693964	+	0.720010i	$0.744137\pi$
$380$	−8.70886e15	−	8.70886e15i	−2.89241	−	2.89241i
$381$			1.33336e15i			0.435910i
$382$		−	4.21288e15i		−	1.35581i
$383$		−	3.77975e15i		−	1.19749i	−0.800941	−	0.598744i	$-0.795667\pi$
$383$		−	3.77975e15i		−	1.19749i	0.800941	−	0.598744i	$-0.204333\pi$
$384$	−9.20601e15			−2.87134
$385$	6.61767e14	−	6.61767e14i	0.203208	−	0.203208i
$386$		−	4.36653e15i		−	1.32012i
$387$	−2.18205e14	+	2.18205e14i	−0.0649531	+	0.0649531i
$388$	1.09696e16	+	1.09696e16i	3.21514	+	3.21514i
$389$	−1.17366e15	+	1.17366e15i	−0.338723	+	0.338723i	−0.855887	−	0.517163i	$-0.826988\pi$
$389$	−1.17366e15	+	1.17366e15i	−0.338723	+	0.338723i	0.517163	+	0.855887i	$0.326988\pi$
$390$		−	5.15350e15i		−	1.46458i
$391$	−1.45048e14	−	1.45048e14i	−0.0405930	−	0.0405930i
$392$	−8.15229e15	+	8.15229e15i	−2.24679	+	2.24679i
$393$	−1.12747e15			−0.306021
$394$	4.60235e15	+	4.60235e15i	1.23028	+	1.23028i
$395$	−1.21612e15	+	1.21612e15i	−0.320180	+	0.320180i
$396$	4.29236e15	+	4.29236e15i	1.11308	+	1.11308i
$397$	−2.13409e15			−0.545093			−0.272546	−	0.962143i	$-0.587866\pi$
$397$	−2.13409e15			−0.545093			−0.272546	+	0.962143i	$0.587866\pi$
$398$	−1.49507e15	−	1.49507e15i	−0.376152	−	0.376152i
$399$		−	1.29861e15i		−	0.321842i
$400$	−2.40917e15			−0.588176
$401$	6.09590e15			1.46613			0.733063	−	0.680161i	$-0.238090\pi$
$401$	6.09590e15			1.46613			0.733063	+	0.680161i	$0.238090\pi$
$402$	4.55405e15			1.07905
$403$	3.27766e15	−	3.27766e15i	0.765127	−	0.765127i
$404$	5.87801e15	−	5.87801e15i	1.35189	−	1.35189i
$405$			6.38102e14i			0.144597i
$406$	−2.58944e15	−	4.52695e14i	−0.578162	−	0.101076i
$407$	−5.30240e15			−1.16656
$408$	1.78712e15	+	1.78712e15i	0.387431	+	0.387431i
$409$	−1.56037e15	−	1.56037e15i	−0.333340	−	0.333340i	0.520513	−	0.853853i	$-0.325741\pi$
$409$	−1.56037e15	−	1.56037e15i	−0.333340	−	0.333340i	−0.853853	+	0.520513i	$0.825741\pi$
$410$			2.28598e15i			0.481249i
$411$		−	6.01779e15i		−	1.24849i
$412$			1.34769e15i			0.275553i
$413$	−1.91325e15			−0.385543
$414$	9.33988e14	−	9.33988e14i	0.185498	−	0.185498i
$415$		−	3.01431e15i		−	0.590063i
$416$	1.91272e16	−	1.91272e16i	3.69056	−	3.69056i
$417$	8.31355e14	+	8.31355e14i	0.158114	+	0.158114i
$418$	1.20193e16	−	1.20193e16i	2.25332	−	2.25332i
$419$			1.16623e15i			0.215526i	0.994177	+	0.107763i	$0.0343688\pi$
$419$			1.16623e15i			0.215526i	−0.994177	+	0.107763i	$0.965631\pi$
$420$	2.03479e15	+	2.03479e15i	0.370701	+	0.370701i
$421$	4.36931e15	−	4.36931e15i	0.784730	−	0.784730i	−0.195895	−	0.980625i	$-0.562761\pi$
$421$	4.36931e15	−	4.36931e15i	0.784730	−	0.784730i	0.980625	+	0.195895i	$0.0627611\pi$
$422$	−2.12588e15			−0.376413
$423$	−5.41419e14	−	5.41419e14i	−0.0945130	−	0.0945130i
$424$	−2.65091e16	+	2.65091e16i	−4.56248	+	4.56248i
$425$	1.42057e14	+	1.42057e14i	0.0241062	+	0.0241062i
$426$	8.24186e15			1.37901
$427$	−2.28556e15	−	2.28556e15i	−0.377074	−	0.377074i
$428$		−	1.85022e16i		−	3.00996i
$429$	5.23788e15			0.840257
$430$	−1.91478e15			−0.302906
$431$	−2.66931e15			−0.416424			−0.208212	−	0.978084i	$-0.566764\pi$
$431$	−2.66931e15			−0.416424			−0.208212	+	0.978084i	$0.566764\pi$
$432$	−1.92162e16	+	1.92162e16i	−2.95641	+	2.95641i
$433$	−4.29116e15	+	4.29116e15i	−0.651099	+	0.651099i	−0.953258	−	0.302158i	$-0.902293\pi$
$433$	−4.29116e15	+	4.29116e15i	−0.651099	+	0.651099i	0.302158	+	0.953258i	$0.402293\pi$
$434$			3.51460e15i			0.525941i
$435$	7.26537e14	−	4.15583e15i	0.107232	−	0.613369i
$436$	−2.39270e16			−3.48313
$437$	−1.92602e15	−	1.92602e15i	−0.276548	−	0.276548i
$438$	9.55354e15	+	9.55354e15i	1.35307	+	1.35307i
$439$		−	6.97168e14i		−	0.0973981i	−0.998813	−	0.0486990i	$-0.984492\pi$
$439$		−	6.97168e14i		−	0.0973981i	0.998813	−	0.0486990i	$-0.0155075\pi$
$440$			2.41857e16i			3.33305i
$441$			3.64959e15i			0.496149i
$442$	−4.07951e15			−0.547110
$443$	−1.95215e15	+	1.95215e15i	−0.258280	+	0.258280i	−0.824354	−	0.566074i	$-0.808462\pi$
$443$	−1.95215e15	+	1.95215e15i	−0.258280	+	0.258280i	0.566074	+	0.824354i	$0.308462\pi$
$444$		−	1.63037e16i		−	2.12808i
$445$	−2.35834e15	+	2.35834e15i	−0.303701	+	0.303701i
$446$	−1.60680e16	−	1.60680e16i	−2.04151	−	2.04151i
$447$	9.23354e13	−	9.23354e13i	0.0115751	−	0.0115751i
$448$			1.07335e16i			1.32762i
$449$	2.01456e15	+	2.01456e15i	0.245868	+	0.245868i	0.819272	−	0.573405i	$-0.194378\pi$
$449$	2.01456e15	+	2.01456e15i	0.245868	+	0.245868i	−0.573405	+	0.819272i	$0.694378\pi$
$450$	−9.14728e14	+	9.14728e14i	−0.110158	+	0.110158i
$451$	−2.32341e15			−0.276100
$452$	2.02986e16	+	2.02986e16i	2.38032	+	2.38032i
$453$	−7.30240e15	+	7.30240e15i	−0.845038	+	0.845038i
$454$	−1.73334e16	−	1.73334e16i	−1.97947	−	1.97947i
$455$	−2.98251e15			−0.336135
$456$	2.37303e16	+	2.37303e16i	2.63945	+	2.63945i
$457$			2.11291e15i			0.231944i	0.993252	+	0.115972i	$0.0369983\pi$
$457$			2.11291e15i			0.231944i	−0.993252	+	0.115972i	$0.963002\pi$
$458$	4.66512e15			0.505440
$459$	2.26617e15			0.242335
$460$	6.03572e15			0.637063
$461$	7.90085e15	−	7.90085e15i	0.823130	−	0.823130i	−0.163426	−	0.986556i	$-0.552254\pi$
$461$	7.90085e15	−	7.90085e15i	0.823130	−	0.823130i	0.986556	+	0.163426i	$0.0522543\pi$
$462$	−2.80826e15	+	2.80826e15i	−0.288792	+	0.288792i
$463$		−	5.48742e15i		−	0.557035i	−0.960431	−	0.278517i	$-0.910157\pi$
$463$		−	5.48742e15i		−	0.557035i	0.960431	−	0.278517i	$-0.0898430\pi$
$464$	3.27726e16	−	2.30189e16i	3.28400	−	2.30663i
$465$	−5.64063e15			−0.557969
$466$	−4.74546e15	−	4.74546e15i	−0.463408	−	0.463408i
$467$	6.45215e14	+	6.45215e14i	0.0622018	+	0.0622018i	0.737523	−	0.675322i	$-0.235995\pi$
$467$	6.45215e14	+	6.45215e14i	0.0622018	+	0.0622018i	−0.675322	+	0.737523i	$0.735995\pi$
$468$		−	1.93452e16i		−	1.84119i
$469$		−	2.63559e15i		−	0.247651i
$470$		−	4.75102e15i		−	0.440757i
$471$	5.35395e14			0.0490399
$472$	3.49620e16	−	3.49620e16i	3.16187	−	3.16187i
$473$		−	1.94613e15i		−	0.173782i
$474$	5.16071e15	−	5.16071e15i	0.455029	−	0.455029i
$475$	1.88630e15	+	1.88630e15i	0.164229	+	0.164229i
$476$	1.61074e15	−	1.61074e15i	0.138479	−	0.138479i
$477$			1.18675e16i			1.00751i
$478$	2.60253e16	+	2.60253e16i	2.18187	+	2.18187i
$479$	3.50596e15	−	3.50596e15i	0.290265	−	0.290265i	−0.546920	−	0.837185i	$-0.684200\pi$
$479$	3.50596e15	−	3.50596e15i	0.290265	−	0.290265i	0.837185	+	0.546920i	$0.184200\pi$
$480$	−3.29167e16			−2.69134
$481$	1.19487e16	+	1.19487e16i	0.964825	+	0.964825i
$482$	−1.94376e16	+	1.94376e16i	−1.55010	+	1.55010i
$483$	4.50005e14	+	4.50005e14i	0.0354434	+	0.0354434i
$484$	−2.36389e15			−0.183889
$485$	1.38352e16	+	1.38352e16i	1.06301	+	1.06301i
$486$			2.40328e16i			1.82384i
$487$	1.81392e16			1.35970			0.679852	−	0.733349i	$-0.262044\pi$
$487$	1.81392e16			1.35970			0.679852	+	0.733349i	$0.262044\pi$
$488$	8.35308e16			6.18483
$489$	−8.88668e15			−0.649959
$490$	−1.60128e16	+	1.60128e16i	−1.15688	+	1.15688i
$491$	−1.04856e16	+	1.04856e16i	−0.748346	+	0.748346i	−0.974169	−	0.225822i	$-0.927493\pi$
$491$	−1.04856e16	+	1.04856e16i	−0.748346	+	0.748346i	0.225822	+	0.974169i	$0.427493\pi$
$492$		−	7.14398e15i		−	0.503674i
$493$	−3.28975e15	−	5.75127e14i	−0.229130	−	0.0400574i
$494$	−5.41697e16			−3.72730
$495$	5.41368e15	+	5.41368e15i	0.368011	+	0.368011i
$496$	−3.78624e16	−	3.78624e16i	−2.54283	−	2.54283i
$497$		−	4.76985e15i		−	0.316494i
$498$			1.27915e16i			0.838579i
$499$			4.00370e15i			0.259334i	0.991558	+	0.129667i	$0.0413908\pi$
$499$			4.00370e15i			0.259334i	−0.991558	+	0.129667i	$0.958609\pi$
$500$	−4.62438e16			−2.95960
$501$	2.60807e15	−	2.60807e15i	0.164928	−	0.164928i
$502$		−	2.63482e16i		−	1.64637i
$503$	2.55309e15	−	2.55309e15i	0.157637	−	0.157637i	−0.623882	−	0.781519i	$-0.714445\pi$
$503$	2.55309e15	−	2.55309e15i	0.157637	−	0.157637i	0.781519	+	0.623882i	$0.214445\pi$
$504$	6.65984e15	+	6.65984e15i	0.406332	+	0.406332i
$505$	7.41356e15	−	7.41356e15i	0.446970	−	0.446970i
$506$			8.33005e15i			0.496300i
$507$	−3.70846e15	−	3.70846e15i	−0.218346	−	0.218346i
$508$	−2.19604e16	+	2.19604e16i	−1.27778	+	1.27778i
$509$	−1.41238e16			−0.812166			−0.406083	−	0.913836i	$-0.633106\pi$
$509$	−1.41238e16			−0.812166			−0.406083	+	0.913836i	$0.633106\pi$
$510$	3.51028e15	+	3.51028e15i	0.199490	+	0.199490i
$511$	5.52897e15	−	5.52897e15i	0.310541	−	0.310541i
$512$	−4.23013e16	−	4.23013e16i	−2.34820	−	2.34820i
$513$	3.00913e16			1.65096
$514$	−1.03082e16	−	1.03082e16i	−0.558988	−	0.558988i
$515$			1.69975e15i			0.0911049i
$516$	5.98393e15			0.317021
$517$	4.82881e15			0.252870
$518$	−1.28124e16			−0.663212
$519$	−1.76910e16	+	1.76910e16i	−0.905208	+	0.905208i
$520$	5.45010e16	−	5.45010e16i	2.75667	−	2.75667i
$521$		−	8.31505e15i		−	0.415756i	−0.978155	−	0.207878i	$-0.933344\pi$
$521$		−	8.31505e15i		−	0.415756i	0.978155	−	0.207878i	$-0.0666557\pi$
$522$	3.70334e15	−	2.11833e16i	0.183050	−	1.04706i
$523$	−8.02423e15			−0.392097			−0.196048	−	0.980594i	$-0.562811\pi$
$523$	−8.02423e15			−0.392097			−0.196048	+	0.980594i	$0.562811\pi$
$524$	−1.85695e16	−	1.85695e16i	−0.897040	−	0.897040i
$525$	−4.40726e14	−	4.40726e14i	−0.0210481	−	0.0210481i
$526$			7.72882e16i			3.64921i
$527$			4.46512e15i			0.208435i
$528$		−	6.05062e16i		−	2.79252i
$529$	−2.05798e16			−0.939089
$530$	−5.20694e16	+	5.20694e16i	−2.34924	+	2.34924i
$531$		−	1.56517e16i		−	0.698221i
$532$	2.13882e16	−	2.13882e16i	0.943417	−	0.943417i
$533$	5.23567e15	+	5.23567e15i	0.228354	+	0.228354i
$534$	1.00078e16	−	1.00078e16i	0.431609	−	0.431609i
$535$		−	2.33356e16i		−	0.995168i
$536$	4.81616e16	+	4.81616e16i	2.03101	+	2.03101i
$537$	1.13403e16	−	1.13403e16i	0.472912	−	0.472912i
$538$	−3.93328e16			−1.62204
$539$	−1.62750e16	−	1.62750e16i	−0.663724	−	0.663724i
$540$	−4.71499e16	+	4.71499e16i	−1.90159	+	1.90159i
$541$	2.80679e16	+	2.80679e16i	1.11951	+	1.11951i	0.991814	+	0.127693i	$0.0407571\pi$
$541$	2.80679e16	+	2.80679e16i	1.11951	+	1.11951i	0.127693	+	0.991814i	$0.459243\pi$
$542$	−1.39259e16			−0.549322
$543$	−2.16717e15	−	2.16717e15i	−0.0845462	−	0.0845462i
$544$			2.60569e16i			1.00538i
$545$	−3.01776e16			−1.15161
$546$	1.26565e16			0.477703
$547$	1.85412e16			0.692172			0.346086	−	0.938203i	$-0.387511\pi$
$547$	1.85412e16			0.692172			0.346086	+	0.938203i	$0.387511\pi$
$548$	9.91130e16	−	9.91130e16i	3.65971	−	3.65971i
$549$	1.86974e16	−	1.86974e16i	0.682884	−	0.682884i
$550$		−	8.15828e15i		−	0.294729i
$551$	−4.36829e16	−	7.63681e15i	−1.56100	−	0.272899i
$552$	−1.64464e16			−0.581348
$553$	−2.98668e15	−	2.98668e15i	−0.104433	−	0.104433i
$554$	−2.15944e16	−	2.15944e16i	−0.746935	−	0.746935i
$555$		−	2.05628e16i		−	0.703598i
$556$			2.73848e16i			0.926961i
$557$			1.03639e15i			0.0347051i	0.999849	+	0.0173525i	$0.00552376\pi$
$557$			1.03639e15i			0.0347051i	−0.999849	+	0.0173525i	$0.994476\pi$
$558$	−2.87517e16			−0.952484
$559$	−4.38549e15	+	4.38549e15i	−0.143730	+	0.143730i
$560$			3.44529e16i			1.11711i
$561$	−3.56776e15	+	3.56776e15i	−0.114451	+	0.114451i
$562$	4.26372e15	+	4.26372e15i	0.135323	+	0.135323i
$563$	1.58075e16	−	1.58075e16i	0.496380	−	0.496380i	−0.413929	−	0.910309i	$-0.635844\pi$
$563$	1.58075e16	−	1.58075e16i	0.496380	−	0.496380i	0.910309	+	0.413929i	$0.135844\pi$
$564$			1.48475e16i			0.461296i
$565$	2.56013e16	+	2.56013e16i	0.786993	+	0.786993i
$566$	−3.50978e16	+	3.50978e16i	−1.06753	+	1.06753i
$567$	−1.56712e15			−0.0471632
$568$	8.71621e16	+	8.71621e16i	2.59560	+	2.59560i
$569$	3.64584e16	−	3.64584e16i	1.07430	−	1.07430i	0.0772874	−	0.997009i	$-0.475374\pi$
$569$	3.64584e16	−	3.64584e16i	1.07430	−	1.07430i	0.997009	−	0.0772874i	$-0.0246259\pi$
$570$	4.66112e16	+	4.66112e16i	1.35907	+	1.35907i
$571$	2.92830e16			0.844887			0.422443	−	0.906389i	$-0.361173\pi$
$571$	2.92830e16			0.844887			0.422443	+	0.906389i	$0.361173\pi$
$572$	8.62679e16	+	8.62679e16i	2.46305	+	2.46305i
$573$			1.66051e16i			0.469153i
$574$	−5.61416e15			−0.156969
$575$	−1.30731e15			−0.0361719
$576$	−8.78070e16			−2.40433
$577$	1.62916e16	−	1.62916e16i	0.441477	−	0.441477i	−0.451031	−	0.892508i	$-0.648944\pi$
$577$	1.62916e16	−	1.62916e16i	0.441477	−	0.441477i	0.892508	+	0.451031i	$0.148944\pi$
$578$	−4.85794e16	+	4.85794e16i	−1.30282	+	1.30282i
$579$			1.72108e16i			0.456803i
$580$	8.04125e16	−	5.64804e16i	2.11230	−	1.48364i
$581$	7.40286e15			0.192461
$582$	−5.87109e16	−	5.87109e16i	−1.51071	−	1.51071i
$583$	−5.29220e16	−	5.29220e16i	−1.34780	−	1.34780i
$584$			2.02068e17i			5.09354i
$585$		−	2.43988e16i		−	0.608743i
$586$		−	1.19163e17i		−	2.94276i
$587$	2.07809e16			0.507967			0.253983	−	0.967209i	$-0.418259\pi$
$587$	2.07809e16			0.507967			0.253983	+	0.967209i	$0.418259\pi$
$588$	5.00420e16	−	5.00420e16i	1.21079	−	1.21079i
$589$			5.92900e16i			1.42000i
$590$	6.86725e16	−	6.86725e16i	1.62806	−	1.62806i
$591$	−1.81403e16	−	1.81403e16i	−0.425715	−	0.425715i
$592$	1.38027e17	−	1.38027e17i	3.20651	−	3.20651i
$593$			1.87675e16i			0.431598i	0.976438	+	0.215799i	$0.0692355\pi$
$593$			1.87675e16i			0.431598i	−0.976438	+	0.215799i	$0.930764\pi$
$594$	−6.50727e16	−	6.50727e16i	−1.48143	−	1.48143i
$595$	2.03152e15	−	2.03152e15i	0.0457846	−	0.0457846i
$596$	3.04153e15			0.0678601
$597$	5.89286e15	+	5.89286e15i	0.130161	+	0.130161i
$598$	1.87713e16	−	1.87713e16i	0.410475	−	0.410475i
$599$	−3.97976e16	−	3.97976e16i	−0.861580	−	0.861580i	0.129941	−	0.991522i	$-0.458521\pi$
$599$	−3.97976e16	−	3.97976e16i	−0.861580	−	0.861580i	−0.991522	+	0.129941i	$0.958521\pi$
$600$	1.61073e16			0.345235
$601$	1.75880e16	+	1.75880e16i	0.373224	+	0.373224i	0.868650	−	0.495426i	$-0.164988\pi$
$601$	1.75880e16	+	1.75880e16i	0.373224	+	0.373224i	−0.495426	+	0.868650i	$0.664988\pi$
$602$		−	4.70252e15i		−	0.0987987i
$603$	2.15608e16			0.448499
$604$	−2.40541e17			−4.95413
$605$	−2.98142e15			−0.0607983
$606$	−3.14600e16	+	3.14600e16i	−0.635219	+	0.635219i
$607$	1.17879e16	−	1.17879e16i	0.235669	−	0.235669i	−0.579385	−	0.815054i	$-0.696707\pi$
$607$	1.17879e16	−	1.17879e16i	0.235669	−	0.235669i	0.815054	+	0.579385i	$0.196707\pi$
$608$			3.45995e17i			6.84934i
$609$	1.02063e16	+	1.78431e15i	0.200063	+	0.0349757i
$610$	1.64072e17			3.18460
$611$	−1.08814e16	−	1.08814e16i	−0.209141	−	0.209141i
$612$	1.31769e16	+	1.31769e16i	0.250786	+	0.250786i
$613$		−	1.32202e15i		−	0.0249159i	−0.999922	−	0.0124579i	$-0.996034\pi$
$613$		−	1.32202e15i		−	0.0249159i	0.999922	−	0.0124579i	$-0.00396558\pi$
$614$		−	2.36380e16i		−	0.441165i
$615$		−	9.01024e15i		−	0.166527i
$616$	−5.93978e16			−1.08714
$617$	−4.85172e15	+	4.85172e15i	−0.0879397	+	0.0879397i	−0.749708	−	0.661769i	$-0.769806\pi$
$617$	−4.85172e15	+	4.85172e15i	−0.0879397	+	0.0879397i	0.661769	+	0.749708i	$0.269806\pi$
$618$		−	7.21303e15i		−	0.129475i
$619$	−2.95837e16	+	2.95837e16i	−0.525907	+	0.525907i	−0.919349	−	0.393442i	$-0.871284\pi$
$619$	−2.95837e16	+	2.95837e16i	−0.525907	+	0.525907i	0.393442	+	0.919349i	$0.371284\pi$
$620$	−9.29011e16	−	9.29011e16i	−1.63558	−	1.63558i
$621$	−1.04275e16	+	1.04275e16i	−0.181815	+	0.181815i
$622$			4.54957e16i			0.785648i
$623$	−5.79186e15	−	5.79186e15i	−0.0990580	−	0.0990580i
$624$	−1.36347e17	+	1.36347e17i	−2.30961	+	2.30961i
$625$	−4.95885e16			−0.831956
$626$	−1.28913e17	−	1.28913e17i	−2.14216	−	2.14216i
$627$	−4.73744e16	+	4.73744e16i	−0.779719	+	0.779719i
$628$	8.81796e15	+	8.81796e15i	0.143751	+	0.143751i
$629$	−1.62775e16			−0.262836
$630$	1.30813e16	+	1.30813e16i	0.209222	+	0.209222i
$631$		−	1.03593e17i		−	1.64118i	−0.571518	−	0.820589i	$-0.693645\pi$
$631$		−	1.03593e17i		−	1.64118i	0.571518	−	0.820589i	$-0.306355\pi$
$632$	1.09154e17			1.71293
$633$	8.37922e15			0.130251
$634$	2.60172e16			0.400613
$635$	−2.76972e16	+	2.76972e16i	−0.422468	+	0.422468i
$636$	1.62724e17	−	1.62724e17i	2.45871	−	2.45871i
$637$			7.33494e16i			1.09789i
$638$	7.79500e16	+	1.10979e17i	1.15582	+	1.64558i
$639$	3.90204e16			0.573174
$640$	−1.91232e17	−	1.91232e17i	−2.78280	−	2.78280i
$641$	−6.14923e16	−	6.14923e16i	−0.886487	−	0.886487i	0.107697	−	0.994184i	$-0.465652\pi$
$641$	−6.14923e16	−	6.14923e16i	−0.886487	−	0.886487i	−0.994184	+	0.107697i	$0.965652\pi$
$642$			9.90266e16i			1.41430i
$643$			6.37891e15i			0.0902569i	0.998981	+	0.0451284i	$0.0143697\pi$
$643$			6.37891e15i			0.0902569i	−0.998981	+	0.0451284i	$0.985630\pi$
$644$			1.48232e16i			0.207791i
$645$	7.54714e15			0.104815
$646$	3.68974e16	−	3.68974e16i	0.507693	−	0.507693i
$647$		−	1.89781e16i		−	0.258718i	−0.991598	−	0.129359i	$-0.958708\pi$
$647$		−	1.89781e16i		−	0.258718i	0.991598	−	0.129359i	$-0.0412920\pi$
$648$	2.86368e16	−	2.86368e16i	0.386790	−	0.386790i
$649$	6.97969e16	+	6.97969e16i	0.934046	+	0.934046i
$650$	−1.83842e16	+	1.83842e16i	−0.243761	+	0.243761i
$651$		−	1.38529e16i		−	0.181993i
$652$	−1.46364e17	−	1.46364e17i	−1.90523	−	1.90523i
$653$	−2.64227e16	+	2.64227e16i	−0.340798	+	0.340798i	−0.856667	−	0.515869i	$-0.827469\pi$
$653$	−2.64227e16	+	2.64227e16i	−0.340798	+	0.340798i	0.515869	+	0.856667i	$0.327469\pi$
$654$	1.28061e17			1.63663
$655$	−2.34205e16	−	2.34205e16i	−0.296584	−	0.296584i
$656$	6.04807e16	−	6.04807e16i	0.758917	−	0.758917i
$657$	4.52305e16	+	4.52305e16i	0.562392	+	0.562392i
$658$	1.16681e16			0.143762
$659$	−7.73406e16	−	7.73406e16i	−0.944268	−	0.944268i	0.0542591	−	0.998527i	$-0.482720\pi$
$659$	−7.73406e16	−	7.73406e16i	−0.944268	−	0.944268i	−0.998527	+	0.0542591i	$0.982720\pi$
$660$		−	1.48461e17i		−	1.79618i
$661$	−5.03971e16			−0.604222			−0.302111	−	0.953273i	$-0.597691\pi$
$661$	−5.03971e16			−0.604222			−0.302111	+	0.953273i	$0.597691\pi$
$662$	2.34298e17			2.78369
$663$	1.60795e16			0.189317
$664$	−1.35277e17	+	1.35277e17i	−1.57839	+	1.57839i
$665$	2.69755e16	−	2.69755e16i	0.311917	−	0.311917i
$666$		−	1.04814e17i		−	1.20108i
$667$	1.77837e16	−	1.24910e16i	0.201961	−	0.141854i
$668$	8.59100e16			0.966907
$669$	6.33324e16	+	6.33324e16i	0.706430	+	0.706430i
$670$	9.45992e16	+	9.45992e16i	1.04578	+	1.04578i
$671$			1.66758e17i			1.82706i
$672$		−	8.08404e16i		−	0.877835i
$673$			1.69532e16i			0.182458i	0.995830	+	0.0912289i	$0.0290795\pi$
$673$			1.69532e16i			0.182458i	−0.995830	+	0.0912289i	$0.970920\pi$
$674$	1.92327e16			0.205155
$675$	1.02124e16	−	1.02124e16i	0.107971	−	0.107971i
$676$		−	1.22157e17i		−	1.28008i
$677$	−1.98405e16	+	1.98405e16i	−0.206072	+	0.206072i	−0.802596	−	0.596523i	$-0.796548\pi$
$677$	−1.98405e16	+	1.98405e16i	−0.206072	+	0.206072i	0.596523	+	0.802596i	$0.296548\pi$
$678$	−1.08641e17	−	1.08641e17i	−1.11845	−	1.11845i
$679$	−3.39780e16	+	3.39780e16i	−0.346720	+	0.346720i
$680$			7.42462e16i			0.750967i
$681$	6.83201e16	+	6.83201e16i	0.684961	+	0.684961i
$682$	1.28215e17	−	1.28215e17i	1.27419	−	1.27419i
$683$	−1.10224e17			−1.08581			−0.542905	−	0.839794i	$-0.682676\pi$
$683$	−1.10224e17			−1.08581			−0.542905	+	0.839794i	$0.682676\pi$
$684$	1.74969e17	+	1.74969e17i	1.70854	+	1.70854i
$685$	1.25005e17	−	1.25005e17i	1.20999	−	1.20999i
$686$	−8.25789e16	−	8.25789e16i	−0.792363	−	0.792363i
$687$	−1.83877e16			−0.174899
$688$	5.06597e16	+	5.06597e16i	0.477675	+	0.477675i
$689$			2.38513e17i			2.22945i
$690$	−3.23041e16			−0.299339
$691$	6.21782e16			0.571176			0.285588	−	0.958353i	$-0.407811\pi$
$691$	6.21782e16			0.571176			0.285588	+	0.958353i	$0.407811\pi$
$692$	−5.82741e17			−5.30688
$693$	−1.32955e16	+	1.32955e16i	−0.120034	+	0.120034i
$694$	2.06245e17	−	2.06245e17i	1.84598	−	1.84598i
$695$			3.45387e16i			0.306477i
$696$	−2.19112e17	+	1.53900e17i	−1.92757	+	1.35389i
$697$	−7.13251e15			−0.0622079
$698$	−2.94867e17	−	2.94867e17i	−2.54973	−	2.54973i
$699$	1.87043e16	+	1.87043e16i	0.160354	+	0.160354i
$700$		−	1.45175e16i		−	0.123397i
$701$			2.13065e17i			1.79558i	0.440428	+	0.897788i	$0.354827\pi$
$701$			2.13065e17i			1.79558i	−0.440428	+	0.897788i	$0.645173\pi$
$702$			2.93275e17i			2.45049i
$703$	−2.16141e17			−1.79063
$704$	3.91567e17	−	3.91567e17i	3.21640	−	3.21640i
$705$			1.87262e16i			0.152516i
$706$	−1.21215e17	+	1.21215e17i	−0.978878	+	0.978878i
$707$	1.82070e16	+	1.82070e16i	0.145788	+	0.145788i
$708$	−2.14610e17	+	2.14610e17i	−1.70393	+	1.70393i
$709$		−	9.92302e16i		−	0.781208i	−0.920559	−	0.390604i	$-0.872266\pi$
$709$		−	9.92302e16i		−	0.781208i	0.920559	−	0.390604i	$-0.127734\pi$
$710$	1.71204e17	+	1.71204e17i	1.33649	+	1.33649i
$711$	2.44329e16	−	2.44329e16i	0.189129	−	0.189129i
$712$	2.11676e17			1.62477
$713$	−2.05456e16	−	2.05456e16i	−0.156380	−	0.156380i
$714$	−8.62093e15	+	8.62093e15i	−0.0650676	+	0.0650676i
$715$	1.08804e17	+	1.08804e17i	0.814346	+	0.814346i
$716$	3.73551e17			2.77250
$717$	−1.02579e17	−	1.02579e17i	−0.754996	−	0.754996i
$718$			4.00694e17i			2.92460i
$719$	−2.03422e17			−1.47240			−0.736200	−	0.676765i	$-0.763382\pi$
$719$	−2.03422e17			−1.47240			−0.736200	+	0.676765i	$0.763382\pi$
$720$	−2.81847e17			−2.02311
$721$	−4.17443e15			−0.0297157
$722$	2.94838e17	−	2.94838e17i	2.08142	−	2.08142i
$723$	7.66138e16	−	7.66138e16i	0.536386	−	0.536386i
$724$		−	7.13866e16i		−	0.495662i
$725$	−1.74170e16	+	1.22334e16i	−0.119935	+	0.0842401i
$726$	1.26519e16			0.0864046
$727$	6.30842e16	+	6.30842e16i	0.427282	+	0.427282i	0.887701	−	0.460420i	$-0.152301\pi$
$727$	6.30842e16	+	6.30842e16i	0.427282	+	0.427282i	−0.460420	+	0.887701i	$0.652301\pi$
$728$	1.33849e17	+	1.33849e17i	0.899142	+	0.899142i
$729$		−	1.18219e17i		−	0.787630i
$730$			3.96903e17i			2.62269i
$731$		−	5.97431e15i		−	0.0391547i
$732$	−5.12745e17			−3.33300
$733$	2.02167e16	−	2.02167e16i	0.130343	−	0.130343i	−0.638926	−	0.769268i	$-0.720621\pi$
$733$	2.02167e16	−	2.02167e16i	0.130343	−	0.130343i	0.769268	+	0.638926i	$0.220621\pi$
$734$		−	4.05769e17i		−	2.59479i
$735$	6.31147e16	−	6.31147e16i	0.400319	−	0.400319i
$736$	−1.19897e17	−	1.19897e17i	−0.754295	−	0.754295i
$737$	−9.61482e16	+	9.61482e16i	−0.599979	+	0.599979i
$738$		−	4.59274e16i		−	0.284272i
$739$	−1.80220e17	−	1.80220e17i	−1.10646	−	1.10646i	−0.993612	−	0.112849i	$-0.964002\pi$
$739$	−1.80220e17	−	1.80220e17i	−1.10646	−	1.10646i	−0.112849	−	0.993612i	$-0.535998\pi$
$740$	3.38670e17	−	3.38670e17i	2.06246	−	2.06246i
$741$	2.13511e17			1.28977
$742$	−1.27878e17	−	1.27878e17i	−0.766252	−	0.766252i
$743$	1.80842e17	−	1.80842e17i	1.07490	−	1.07490i	0.0779380	−	0.996958i	$-0.475166\pi$
$743$	1.80842e17	−	1.80842e17i	1.07490	−	1.07490i	0.996958	−	0.0779380i	$-0.0248336\pi$
$744$	2.53141e17	+	2.53141e17i	1.49254	+	1.49254i
$745$	3.83608e15			0.0224362
$746$	2.21869e17	+	2.21869e17i	1.28725	+	1.28725i
$747$			6.05601e16i			0.348548i
$748$	−1.17522e17			−0.670980
$749$	5.73101e16			0.324594
$750$	2.47504e17			1.39064
$751$	−7.47676e16	+	7.47676e16i	−0.416748	+	0.416748i	−0.884081	−	0.467333i	$-0.845215\pi$
$751$	−7.47676e16	+	7.47676e16i	−0.416748	+	0.416748i	0.467333	+	0.884081i	$0.345215\pi$
$752$	−1.25699e17	+	1.25699e17i	−0.695063	+	0.695063i
$753$			1.03852e17i			0.569698i
$754$	7.44297e16	−	4.25741e17i	0.405059	−	2.31696i
$755$	−3.03379e17			−1.63796
$756$	−1.15796e17	−	1.15796e17i	−0.620243	−	0.620243i
$757$	1.77953e17	+	1.77953e17i	0.945652	+	0.945652i	0.998597	−	0.0529458i	$-0.0168610\pi$
$757$	1.77953e17	+	1.77953e17i	0.945652	+	0.945652i	−0.0529458	+	0.998597i	$0.516861\pi$
$758$		−	1.36089e16i		−	0.0717475i
$759$		−	3.28331e16i		−	0.171736i
$760$			9.85877e17i			5.11612i
$761$	−6.85828e16			−0.353108			−0.176554	−	0.984291i	$-0.556495\pi$
$761$	−6.85828e16			−0.353108			−0.176554	+	0.984291i	$0.556495\pi$
$762$	1.17535e17	−	1.17535e17i	0.600397	−	0.600397i
$763$		−	7.41135e16i		−	0.375621i
$764$	−2.73487e17	+	2.73487e17i	−1.37523	+	1.37523i
$765$	1.66191e16	+	1.66191e16i	0.0829163	+	0.0829163i
$766$	−3.33185e17	+	3.33185e17i	−1.64935	+	1.64935i
$767$		−	3.14567e17i		−	1.54504i
$768$	3.80616e17	+	3.80616e17i	1.85490	+	1.85490i
$769$	1.75066e17	−	1.75066e17i	0.846533	−	0.846533i	−0.143166	−	0.989699i	$-0.545728\pi$
$769$	1.75066e17	−	1.75066e17i	0.846533	−	0.846533i	0.989699	+	0.143166i	$0.0457282\pi$
$770$	−1.16669e17			−0.559774
$771$	4.06299e16	+	4.06299e16i	0.193428	+	0.193428i
$772$	−2.83461e17	+	2.83461e17i	−1.33903	+	1.33903i
$773$	−1.63376e16	−	1.63376e16i	−0.0765791	−	0.0765791i	0.667780	−	0.744359i	$-0.267245\pi$
$773$	−1.63376e16	−	1.63376e16i	−0.0765791	−	0.0765791i	−0.744359	+	0.667780i	$0.767245\pi$
$774$	3.84696e16			0.178925
$775$	2.01220e16	+	2.01220e16i	0.0928667	+	0.0928667i
$776$		−	1.24180e18i		−	5.68697i
$777$	5.05004e16			0.229493
$778$	2.06916e17			0.933077
$779$	−9.47089e16			−0.423805
$780$	−3.34549e17	+	3.34549e17i	−1.48557	+	1.48557i
$781$	−1.74008e17	+	1.74008e17i	−0.766764	+	0.766764i
$782$			2.55720e16i			0.111821i
$783$	−4.13458e16	+	2.36500e17i	−0.179416	+	1.02627i
$784$	8.47308e17			3.64876
$785$	1.11215e16	+	1.11215e16i	0.0475276	+	0.0475276i
$786$	9.93867e16	+	9.93867e16i	0.421496	+	0.421496i
$787$			1.56690e17i			0.659465i	0.944074	+	0.329733i	$0.106959\pi$
$787$			1.56690e17i			0.659465i	−0.944074	+	0.329733i	$0.893041\pi$
$788$		−	5.97540e17i		−	2.49580i
$789$		−	3.04633e17i		−	1.26274i
$790$	2.14402e17			0.881995
$791$	−6.28743e16	+	6.28743e16i	−0.256693	+	0.256693i
$792$		−	4.85912e17i		−	1.96882i
$793$	3.75780e17	−	3.75780e17i	1.51110	−	1.51110i
$794$	1.88120e17	+	1.88120e17i	0.750780	+	0.750780i
$795$	2.05233e17	−	2.05233e17i	0.812913	−	0.812913i
$796$			1.94111e17i			0.763082i
$797$	−9.74720e16	−	9.74720e16i	−0.380303	−	0.380303i	0.490908	−	0.871211i	$-0.336665\pi$
$797$	−9.74720e16	−	9.74720e16i	−0.380303	−	0.380303i	−0.871211	+	0.490908i	$0.836665\pi$
$798$	−1.14473e17	+	1.14473e17i	−0.443287	+	0.443287i
$799$	1.48237e16			0.0569739
$800$	1.17425e17	+	1.17425e17i	0.447939	+	0.447939i
$801$	4.73811e16	−	4.73811e16i	0.179395	−	0.179395i
$802$	−5.37353e17	−	5.37353e17i	−2.01936	−	2.01936i
$803$	−4.03402e17			−1.50468
$804$	−2.95635e17	−	2.95635e17i	−1.09451	−	1.09451i
$805$			1.86955e16i			0.0687008i
$806$	−5.77851e17			−2.10768
$807$	1.55031e17			0.561277
$808$	−6.65414e17			−2.39124
$809$	1.20155e17	−	1.20155e17i	0.428599	−	0.428599i	−0.459552	−	0.888151i	$-0.651990\pi$
$809$	1.20155e17	−	1.20155e17i	0.428599	−	0.428599i	0.888151	+	0.459552i	$0.151990\pi$
$810$	5.62486e16	−	5.62486e16i	0.199160	−	0.199160i
$811$		−	4.33564e17i		−	1.52380i	−0.647694	−	0.761901i	$-0.724266\pi$
$811$		−	4.33564e17i		−	1.52380i	0.647694	−	0.761901i	$-0.275734\pi$
$812$	1.38711e17	+	1.97486e17i	0.483920	+	0.688969i
$813$	5.48892e16			0.190083
$814$	4.67406e17	+	4.67406e17i	1.60675	+	1.60675i
$815$	−1.84599e17	−	1.84599e17i	−0.629917	−	0.629917i
$816$		−	1.85745e17i		−	0.629181i
$817$		−	7.93298e16i		−	0.266750i
$818$			2.75093e17i			0.918247i
$819$	5.99213e16			0.198554
$820$	1.48399e17	−	1.48399e17i	0.488143	−	0.488143i
$821$			2.56507e17i			0.837608i	0.908077	+	0.418804i	$0.137551\pi$
$821$			2.56507e17i			0.837608i	−0.908077	+	0.418804i	$0.862449\pi$
$822$	−5.30468e17	+	5.30468e17i	−1.71960	+	1.71960i
$823$	3.17768e17	+	3.17768e17i	1.02261	+	1.02261i	0.999738	+	0.0228752i	$0.00728203\pi$
$823$	3.17768e17	+	3.17768e17i	1.02261	+	1.02261i	0.0228752	+	0.999738i	$0.492718\pi$
$824$	7.62817e16	−	7.62817e16i	0.243701	−	0.243701i
$825$			3.21560e16i			0.101986i
$826$	1.68653e17	+	1.68653e17i	0.531025	+	0.531025i
$827$	4.27749e16	−	4.27749e16i	0.133708	−	0.133708i	−0.637086	−	0.770793i	$-0.719860\pi$
$827$	4.27749e16	−	4.27749e16i	0.133708	−	0.133708i	0.770793	+	0.637086i	$0.219860\pi$
$828$	−1.21263e17			−0.376311
$829$	6.47959e16	+	6.47959e16i	0.199627	+	0.199627i	0.799840	−	0.600213i	$-0.204917\pi$
$829$	6.47959e16	+	6.47959e16i	0.199627	+	0.199627i	−0.600213	+	0.799840i	$0.704917\pi$
$830$	−2.65711e17	+	2.65711e17i	−0.812720	+	0.812720i
$831$	8.51149e16	+	8.51149e16i	0.258464	+	0.258464i
$832$	−1.76475e18			−5.32037
$833$	−4.99616e16	−	4.99616e16i	−0.149543	−	0.149543i
$834$		−	1.46568e17i		−	0.435555i
$835$	1.08353e17			0.319684
$836$	−1.56051e18			−4.57119
$837$	3.20997e17			0.933572
$838$	1.02803e17	−	1.02803e17i	0.296853	−	0.296853i
$839$	1.49633e15	−	1.49633e15i	0.00428999	−	0.00428999i	−0.704959	−	0.709249i	$-0.749034\pi$
$839$	1.49633e15	−	1.49633e15i	0.00428999	−	0.00428999i	0.709249	+	0.704959i	$0.249034\pi$
$840$		−	2.30346e17i		−	0.655700i
$841$	1.20042e17	−	3.32829e17i	0.339278	−	0.940686i
$842$	−7.70309e17			−2.16169
$843$	−1.68056e16	−	1.68056e16i	−0.0468261	−	0.0468261i
$844$	1.38006e17	+	1.38006e17i	0.381806	+	0.381806i
$845$		−	1.54068e17i		−	0.423227i
$846$			9.54522e16i			0.260354i
$847$		−	7.32210e15i		−	0.0198306i
$848$	2.75523e18			7.40939
$849$	1.38339e17	−	1.38339e17i	0.369400	−	0.369400i
$850$		−	2.50446e16i		−	0.0664050i
$851$	7.48988e16	−	7.48988e16i	0.197196	−	0.197196i
$852$	−5.35035e17	−	5.35035e17i	−1.39877	−	1.39877i
$853$	−3.20561e17	+	3.20561e17i	−0.832177	+	0.832177i	−0.987814	−	0.155637i	$-0.950257\pi$
$853$	−3.20561e17	+	3.20561e17i	−0.832177	+	0.832177i	0.155637	+	0.987814i	$0.450257\pi$
$854$			4.02945e17i			1.03872i
$855$	2.20677e17	+	2.20677e17i	0.564885	+	0.564885i
$856$	−1.04726e18	+	1.04726e18i	−2.66202	+	2.66202i
$857$	1.47058e17			0.371196			0.185598	−	0.982626i	$-0.440578\pi$
$857$	1.47058e17			0.371196			0.185598	+	0.982626i	$0.440578\pi$
$858$	−4.61719e17	−	4.61719e17i	−1.15732	−	1.15732i
$859$	1.59155e17	−	1.59155e17i	0.396152	−	0.396152i	−0.480721	−	0.876873i	$-0.659625\pi$
$859$	1.59155e17	−	1.59155e17i	0.396152	−	0.396152i	0.876873	+	0.480721i	$0.159625\pi$
$860$	1.24301e17	+	1.24301e17i	0.307245	+	0.307245i
$861$	2.21283e16			0.0543162
$862$	2.35300e17	+	2.35300e17i	0.573558	+	0.573558i
$863$		−	1.16750e17i		−	0.282613i	−0.989966	−	0.141306i	$-0.954870\pi$
$863$		−	1.16750e17i		−	0.282613i	0.989966	−	0.141306i	$-0.0451303\pi$
$864$	1.87322e18			4.50305
$865$	−7.34974e17			−1.75459
$866$	7.56531e17			1.79358
$867$	1.91477e17	−	1.91477e17i	0.450818	−	0.450818i
$868$	2.28157e17	−	2.28157e17i	0.533476	−	0.533476i
$869$			2.17912e17i			0.506015i
$870$	−4.30380e17	+	3.02292e17i	−0.992515	+	0.697126i
$871$	4.33329e17			0.992450
$872$	1.35432e18	+	1.35432e18i	3.08050	+	3.08050i
$873$	−2.77962e17	−	2.77962e17i	−0.627914	−	0.627914i
$874$			3.39557e17i			0.761804i
$875$		−	1.43239e17i		−	0.319163i
$876$		−	1.24037e18i		−	2.74491i
$877$	−5.36011e17			−1.17808			−0.589042	−	0.808102i	$-0.700495\pi$
$877$	−5.36011e17			−1.17808			−0.589042	+	0.808102i	$0.700495\pi$
$878$	−6.14553e16	+	6.14553e16i	−0.134151	+	0.134151i
$879$			4.69683e17i			1.01829i
$880$	1.25687e18	−	1.25687e18i	2.70641	−	2.70641i
$881$	−2.06316e17	−	2.06316e17i	−0.441242	−	0.441242i	0.451187	−	0.892429i	$-0.351001\pi$
$881$	−2.06316e17	−	2.06316e17i	−0.441242	−	0.441242i	−0.892429	+	0.451187i	$0.851001\pi$
$882$	3.21711e17	−	3.21711e17i	0.683368	−	0.683368i
$883$		−	4.23313e17i		−	0.893095i	−0.894760	−	0.446547i	$-0.852653\pi$
$883$		−	4.23313e17i		−	0.893095i	0.894760	−	0.446547i	$-0.147347\pi$
$884$	2.64829e17	+	2.64829e17i	0.554947	+	0.554947i
$885$	−2.70674e17	+	2.70674e17i	−0.563362	+	0.563362i
$886$	3.44164e17			0.711481
$887$	4.41170e17	+	4.41170e17i	0.905867	+	0.905867i	0.995936	−	0.0900686i	$-0.0287086\pi$
$887$	4.41170e17	+	4.41170e17i	0.905867	+	0.905867i	−0.0900686	+	0.995936i	$0.528709\pi$
$888$	−9.22822e17	+	9.22822e17i	−1.88209	+	1.88209i
$889$	−6.80218e16	−	6.80218e16i	−0.137796	−	0.137796i
$890$	4.15775e17			0.836600
$891$	5.71696e16	+	5.71696e16i	0.114261	+	0.114261i
$892$			2.08617e18i			4.14152i
$893$	1.96836e17			0.388147
$894$	−1.62787e16			−0.0318857
$895$	4.71135e17			0.916658
$896$	4.69649e17	−	4.69649e17i	0.907664	−	0.907664i
$897$	−7.39875e16	+	7.39875e16i	−0.142038	+	0.142038i
$898$		−	3.55166e17i		−	0.677288i
$899$	−4.65984e17	−	8.14651e16i	−0.882700	−	0.154317i
$900$	1.18763e17			0.223473
$901$	−1.62462e17	−	1.62462e17i	−0.303671	−	0.303671i
$902$	2.04809e17	+	2.04809e17i	0.380285	+	0.380285i
$903$			1.85351e16i			0.0341875i
$904$		−	2.29788e18i		−	4.21033i
$905$		−	9.00353e16i		−	0.163878i
$906$	1.28741e18			2.32782
$907$	−5.24284e17	+	5.24284e17i	−0.941722	+	0.941722i	−0.998393	−	0.0566711i	$-0.981951\pi$
$907$	−5.24284e17	+	5.24284e17i	−0.941722	+	0.941722i	0.0566711	+	0.998393i	$0.481951\pi$
$908$			2.25046e18i			4.01566i
$909$	−1.48945e17	+	1.48945e17i	−0.264024	+	0.264024i
$910$	2.62908e17	+	2.62908e17i	0.462973	+	0.462973i
$911$	−1.11156e17	+	1.11156e17i	−0.194457	+	0.194457i	−0.797619	−	0.603162i	$-0.793907\pi$
$911$	−1.11156e17	+	1.11156e17i	−0.194457	+	0.194457i	0.603162	+	0.797619i	$0.293907\pi$
$912$		−	2.46641e18i		−	4.28643i
$913$	−2.70062e17	−	2.70062e17i	−0.466271	−	0.466271i
$914$	1.86253e17	−	1.86253e17i	0.319467	−	0.319467i
$915$	−6.46692e17			−1.10197
$916$	−3.02845e17	−	3.02845e17i	−0.512681	−	0.512681i
$917$	5.75185e16	−	5.75185e16i	0.0967368	−	0.0967368i
$918$	−1.99763e17	−	1.99763e17i	−0.333779	−	0.333779i
$919$	4.02893e17			0.668800			0.334400	−	0.942431i	$-0.391466\pi$
$919$	4.02893e17			0.668800			0.334400	+	0.942431i	$0.391466\pi$
$920$	−3.41634e17	−	3.41634e17i	−0.563422	−	0.563422i
$921$			9.31698e16i			0.152657i
$922$	−1.39292e18			−2.26747
$923$	7.84232e17			1.26834
$924$	3.64607e17			0.585859
$925$	−7.33543e16	+	7.33543e16i	−0.117105	+	0.117105i
$926$	−4.83716e17	+	4.83716e17i	−0.767228	+	0.767228i
$927$		−	3.41495e16i		−	0.0538154i
$928$	−2.71932e18	−	4.75401e17i	−4.25767	−	0.744342i
$929$	−2.79952e16			−0.0435501			−0.0217751	−	0.999763i	$-0.506932\pi$
$929$	−2.79952e16			−0.0435501			−0.0217751	+	0.999763i	$0.506932\pi$
$930$	4.97221e17	+	4.97221e17i	0.768515	+	0.768515i
$931$	−6.63414e17	−	6.63414e17i	−1.01879	−	1.01879i
$932$			6.16121e17i			0.940092i
$933$		−	1.79322e17i		−	0.271860i
$934$		−	1.13751e17i		−	0.171347i
$935$	−1.48223e17			−0.221843
$936$	−1.09497e18	+	1.09497e18i	−1.62836	+	1.62836i
$937$			7.62761e17i			1.12707i	0.826092	+	0.563535i	$0.190559\pi$
$937$			7.62761e17i			1.12707i	−0.826092	+	0.563535i	$0.809441\pi$
$938$	−2.32327e17	+	2.32327e17i	−0.341101	+	0.341101i
$939$	5.08115e17	+	5.08115e17i	0.741256	+	0.741256i
$940$	−3.08421e17	+	3.08421e17i	−0.447071	+	0.447071i
$941$			9.43698e17i			1.35924i	0.733566	+	0.679618i	$0.237855\pi$
$941$			9.43698e17i			1.35924i	−0.733566	+	0.679618i	$0.762145\pi$
$942$	−4.71951e16	−	4.71951e16i	−0.0675447	−	0.0675447i
$943$	3.28192e16	−	3.28192e16i	0.0466722	−	0.0466722i
$944$	−3.63377e18			−5.13482
$945$	−1.46046e17	−	1.46046e17i	−0.205068	−	0.205068i
$946$	−1.71551e17	+	1.71551e17i	−0.239358	+	0.239358i
$947$	7.51921e17	+	7.51921e17i	1.04249	+	1.04249i	0.999056	+	0.0434347i	$0.0138300\pi$
$947$	7.51921e17	+	7.51921e17i	1.04249	+	1.04249i	0.0434347	+	0.999056i	$0.486170\pi$
$948$	−6.70034e17			−0.923095
$949$	9.09042e17	+	9.09042e17i	1.24448	+	1.24448i
$950$		−	3.32555e17i		−	0.452399i
$951$	−1.02547e17			−0.138625
$952$	−1.82342e17			−0.244943
$953$	−1.42196e17			−0.189815			−0.0949075	−	0.995486i	$-0.530256\pi$
$953$	−1.42196e17			−0.189815			−0.0949075	+	0.995486i	$0.530256\pi$
$954$	1.04612e18	−	1.04612e18i	1.38769	−	1.38769i
$955$	−3.44931e17	+	3.44931e17i	−0.454686	+	0.454686i
$956$		−	3.37896e18i		−	4.42625i
$957$	−3.07242e17	−	4.37427e17i	−0.399952	−	0.569422i
$958$	−6.18101e17			−0.799588
$959$	3.07000e17	+	3.07000e17i	0.394663	+	0.394663i
$960$	1.51850e18	+	1.51850e18i	1.93994	+	1.93994i
$961$		−	1.55191e17i		−	0.197027i
$962$		−	2.10655e18i		−	2.65779i
$963$			4.68834e17i			0.587843i
$964$	2.52366e18			3.14462
$965$	−3.57511e17	+	3.57511e17i	−0.442717	+	0.442717i
$966$		−	7.93360e16i		−	0.0976354i
$967$	1.17139e17	−	1.17139e17i	0.143266	−	0.143266i	−0.631836	−	0.775102i	$-0.717698\pi$
$967$	1.17139e17	−	1.17139e17i	0.143266	−	0.143266i	0.775102	+	0.631836i	$0.217698\pi$
$968$	1.33801e17	+	1.33801e17i	0.162632	+	0.162632i
$969$	−1.45432e17	+	1.45432e17i	−0.175678	+	0.175678i
$970$		−	2.43915e18i		−	2.92825i
$971$	3.18436e17	+	3.18436e17i	0.379933	+	0.379933i	0.871078	−	0.491145i	$-0.163421\pi$
$971$	3.18436e17	+	3.18436e17i	0.379933	+	0.379933i	−0.491145	+	0.871078i	$0.663421\pi$
$972$	1.56014e18	−	1.56014e18i	1.84997	−	1.84997i
$973$	−8.48239e16			−0.0999634
$974$	−1.59897e18	−	1.59897e18i	−1.87278	−	1.87278i
$975$	7.24618e16	−	7.24618e16i	0.0843492	−	0.0843492i
$976$	−4.34088e18	−	4.34088e18i	−5.02203	−	5.02203i
$977$	7.69121e17			0.884357			0.442178	−	0.896927i	$-0.354206\pi$
$977$	7.69121e17			0.884357			0.442178	+	0.896927i	$0.354206\pi$
$978$	7.83360e17	+	7.83360e17i	0.895217	+	0.895217i
$979$			4.22583e17i			0.479971i
$980$	2.07900e18			2.34692
$981$	6.06296e17			0.680253
$982$	1.84860e18			2.06146
$983$	−4.36412e16	+	4.36412e16i	−0.0483700	+	0.0483700i	−0.730878	−	0.682508i	$-0.760889\pi$
$983$	−4.36412e16	+	4.36412e16i	−0.0483700	+	0.0483700i	0.682508	+	0.730878i	$0.260889\pi$
$984$	−4.04363e17	+	4.04363e17i	−0.445452	+	0.445452i
$985$		−	7.53639e17i		−	0.825174i
$986$	2.39294e17	+	3.40689e17i	0.260418	+	0.370763i
$987$	−4.59899e16			−0.0497462
$988$	3.51652e18	+	3.51652e18i	3.78070	+	3.78070i
$989$	2.74900e16	+	2.74900e16i	0.0293763	+	0.0293763i
$990$		−	9.54431e17i		−	1.01376i
$991$			1.11440e18i			1.17652i	0.808673	+	0.588258i	$0.200186\pi$
$991$			1.11440e18i			1.17652i	−0.808673	+	0.588258i	$0.799814\pi$
$992$			3.69088e18i			3.87311i
$993$	−9.23493e17			−0.963248
$994$	−4.20462e17	+	4.20462e17i	−0.435922	+	0.435922i
$995$			2.44819e17i			0.252294i
$996$	8.30381e17	−	8.30381e17i	0.850592	−	0.850592i
$997$	−9.36039e17	−	9.36039e17i	−0.953066	−	0.953066i	0.0458806	−	0.998947i	$-0.485391\pi$
$997$	−9.36039e17	−	9.36039e17i	−0.953066	−	0.953066i	−0.998947	+	0.0458806i	$0.985391\pi$
$998$	3.52926e17	−	3.52926e17i	0.357191	−	0.357191i
$999$			1.17019e18i			1.17723i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.13.c.a.12.1	✓	58
29.17	odd	4	inner	29.13.c.a.17.1	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.13.c.a.12.1	✓	58	1.1	even	1	trivial
29.13.c.a.17.1	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)

\(f(q)\)	\(=\)	\(q+(-88.1500 - 88.1500i) q^{2} +(347.445 + 347.445i) q^{3} +11444.8i q^{4} +14434.6i q^{5} -61254.6i q^{6} -35450.1 q^{7} +(647800. - 647800. i) q^{8} -290005. i q^{9} +O(q^{10})\)	\(q+(-88.1500 - 88.1500i) q^{2} +(347.445 + 347.445i) q^{3} +11444.8i q^{4} +14434.6i q^{5} -61254.6i q^{6} -35450.1 q^{7} +(647800. - 647800. i) q^{8} -290005. i q^{9} +(1.27241e6 - 1.27241e6i) q^{10} +(1.29325e6 + 1.29325e6i) q^{11} +(-3.97645e6 + 3.97645e6i) q^{12} -5.82852e6i q^{13} +(3.12493e6 + 3.12493e6i) q^{14} +(-5.01524e6 + 5.01524e6i) q^{15} -6.73291e7 q^{16} +(3.97007e6 + 3.97007e6i) q^{17} +(-2.55639e7 + 2.55639e7i) q^{18} +(5.27164e7 + 5.27164e7i) q^{19} -1.65202e8 q^{20} +(-1.23170e7 - 1.23170e7i) q^{21} -2.27999e8i q^{22} -3.65354e7 q^{23} +4.50150e8 q^{24} +3.57820e7 q^{25} +(-5.13784e8 + 5.13784e8i) q^{26} +(2.85407e8 - 2.85407e8i) q^{27} -4.05721e8i q^{28} +(-4.86753e8 + 3.41887e8i) q^{29} +8.84187e8 q^{30} +(5.62349e8 + 5.62349e8i) q^{31} +(3.28167e9 + 3.28167e9i) q^{32} +8.98665e8i q^{33} -6.99923e8i q^{34} -5.11709e8i q^{35} +3.31906e9 q^{36} +(-2.05003e9 + 2.05003e9i) q^{37} -9.29390e9i q^{38} +(2.02509e9 - 2.02509e9i) q^{39} +(9.35076e9 + 9.35076e9i) q^{40} +(-8.98286e8 + 8.98286e8i) q^{41} +2.17148e9i q^{42} +(-7.52420e8 - 7.52420e8i) q^{43} +(-1.48010e10 + 1.48010e10i) q^{44} +4.18611e9 q^{45} +(3.22060e9 + 3.22060e9i) q^{46} +(1.86693e9 - 1.86693e9i) q^{47} +(-2.33932e10 - 2.33932e10i) q^{48} -1.25846e10 q^{49} +(-3.15418e9 - 3.15418e9i) q^{50} +2.75876e9i q^{51} +6.67064e10 q^{52} -4.09218e10 q^{53} -5.03173e10 q^{54} +(-1.86675e10 + 1.86675e10i) q^{55} +(-2.29646e10 + 2.29646e10i) q^{56} +3.66321e10i q^{57} +(7.30446e10 + 1.27699e10i) q^{58} +5.39703e10 q^{59} +(-5.73986e10 - 5.73986e10i) q^{60} +(6.44727e10 + 6.44727e10i) q^{61} -9.91420e10i q^{62} +1.02807e10i q^{63} -3.02778e11i q^{64} +8.41325e10 q^{65} +(7.92173e10 - 7.92173e10i) q^{66} +7.43464e10i q^{67} +(-4.54368e10 + 4.54368e10i) q^{68} +(-1.26940e10 - 1.26940e10i) q^{69} +(-4.51072e10 + 4.51072e10i) q^{70} +1.34551e11i q^{71} +(-1.87865e11 - 1.87865e11i) q^{72} +(-1.55965e11 + 1.55965e11i) q^{73} +3.61421e11 q^{74} +(1.24323e10 + 1.24323e10i) q^{75} +(-6.03331e11 + 6.03331e11i) q^{76} +(-4.58458e10 - 4.58458e10i) q^{77} -3.57023e11 q^{78} +(8.42501e10 + 8.42501e10i) q^{79} -9.71870e11i q^{80} +4.42063e10 q^{81} +1.58368e11 q^{82} -2.08825e11 q^{83} +(1.40966e11 - 1.40966e11i) q^{84} +(-5.73064e10 + 5.73064e10i) q^{85} +1.32652e11i q^{86} +(-2.87907e11 - 5.03329e10i) q^{87} +1.67553e12 q^{88} +(1.63380e11 + 1.63380e11i) q^{89} +(-3.69006e11 - 3.69006e11i) q^{90} +2.06622e11i q^{91} -4.18142e11i q^{92} +3.90771e11i q^{93} -3.29140e11 q^{94} +(-7.60942e11 + 7.60942e11i) q^{95} +2.28040e12i q^{96} +(9.58473e11 - 9.58473e11i) q^{97} +(1.10933e12 + 1.10933e12i) q^{98} +(3.75048e11 - 3.75048e11i) 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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