LMFDB - Embedded newform 29.13.c.a.12.14

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			12.14
Character	$\chi$	$=$	29.12
Dual form			29.13.c.a.17.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.03178 - 9.03178i) q^{2} +(-704.167 - 704.167i) q^{3} -3932.85i q^{4} +8770.94i q^{5} +12719.8i q^{6} +37099.6 q^{7} +(-72514.8 + 72514.8i) q^{8} +460261. i q^{9} +O(q^{10})$	\(q+(-9.03178 - 9.03178i) q^{2} +(-704.167 - 704.167i) q^{3} -3932.85i q^{4} +8770.94i q^{5} +12719.8i q^{6} +37099.6 q^{7} +(-72514.8 + 72514.8i) q^{8} +460261. i q^{9} +(79217.2 - 79217.2i) q^{10} +(1.87931e6 + 1.87931e6i) q^{11} +(-2.76939e6 + 2.76939e6i) q^{12} +4.37215e6i q^{13} +(-335076. - 335076. i) q^{14} +(6.17620e6 - 6.17620e6i) q^{15} -1.47991e7 q^{16} +(1.85809e7 + 1.85809e7i) q^{17} +(4.15698e6 - 4.15698e6i) q^{18} +(-6.31964e7 - 6.31964e7i) q^{19} +3.44948e7 q^{20} +(-2.61243e7 - 2.61243e7i) q^{21} -3.39470e7i q^{22} +1.90764e8 q^{23} +1.02125e8 q^{24} +1.67211e8 q^{25} +(3.94883e7 - 3.94883e7i) q^{26} +(-5.01225e7 + 5.01225e7i) q^{27} -1.45907e8i q^{28} +(-3.94834e8 - 4.44883e8i) q^{29} -1.11564e8 q^{30} +(9.84626e8 + 9.84626e8i) q^{31} +(4.30683e8 + 4.30683e8i) q^{32} -2.64669e9i q^{33} -3.35637e8i q^{34} +3.25399e8i q^{35} +1.81014e9 q^{36} +(-5.39738e8 + 5.39738e8i) q^{37} +1.14155e9i q^{38} +(3.07872e9 - 3.07872e9i) q^{39} +(-6.36023e8 - 6.36023e8i) q^{40} +(5.22274e9 - 5.22274e9i) q^{41} +4.71898e8i q^{42} +(1.74684e9 + 1.74684e9i) q^{43} +(7.39104e9 - 7.39104e9i) q^{44} -4.03692e9 q^{45} +(-1.72294e9 - 1.72294e9i) q^{46} +(-2.77566e8 + 2.77566e8i) q^{47} +(1.04210e10 + 1.04210e10i) q^{48} -1.24649e10 q^{49} +(-1.51022e9 - 1.51022e9i) q^{50} -2.61681e10i q^{51} +1.71950e10 q^{52} -2.10355e10 q^{53} +9.05391e8 q^{54} +(-1.64833e10 + 1.64833e10i) q^{55} +(-2.69027e9 + 2.69027e9i) q^{56} +8.90016e10i q^{57} +(-4.52028e8 + 7.58414e9i) q^{58} +8.99219e9 q^{59} +(-2.42901e10 - 2.42901e10i) q^{60} +(6.07106e9 + 6.07106e9i) q^{61} -1.77858e10i q^{62} +1.70755e10i q^{63} +5.28374e10i q^{64} -3.83478e10 q^{65} +(-2.39043e10 + 2.39043e10i) q^{66} -6.82632e10i q^{67} +(7.30760e10 - 7.30760e10i) q^{68} +(-1.34330e11 - 1.34330e11i) q^{69} +(2.93893e9 - 2.93893e9i) q^{70} +1.65699e11i q^{71} +(-3.33758e10 - 3.33758e10i) q^{72} +(-6.29781e9 + 6.29781e9i) q^{73} +9.74958e9 q^{74} +(-1.17745e11 - 1.17745e11i) q^{75} +(-2.48542e11 + 2.48542e11i) q^{76} +(6.97216e10 + 6.97216e10i) q^{77} -5.56126e10 q^{78} +(5.01618e10 + 5.01618e10i) q^{79} -1.29802e11i q^{80} +3.15191e11 q^{81} -9.43413e10 q^{82} +4.99175e11 q^{83} +(-1.02743e11 + 1.02743e11i) q^{84} +(-1.62972e11 + 1.62972e11i) q^{85} -3.15541e10i q^{86} +(-3.52425e10 + 5.91301e11i) q^{87} -2.72555e11 q^{88} +(5.48312e11 + 5.48312e11i) q^{89} +(3.64606e10 + 3.64606e10i) q^{90} +1.62205e11i q^{91} -7.50248e11i q^{92} -1.38668e12i q^{93} +5.01382e9 q^{94} +(5.54292e11 - 5.54292e11i) q^{95} -6.06545e11i q^{96} +(9.48671e11 - 9.48671e11i) q^{97} +(1.12580e11 + 1.12580e11i) q^{98} +(-8.64971e11 + 8.64971e11i) 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 $

$2$	−9.03178	−	9.03178i	−0.141122	−	0.141122i	0.633017	−	0.774138i	$-0.281816\pi$
$2$	−9.03178	−	9.03178i	−0.141122	−	0.141122i	−0.774138	+	0.633017i	$0.781816\pi$
$3$	−704.167	−	704.167i	−0.965935	−	0.965935i	0.0335032	−	0.999439i	$-0.489334\pi$
$3$	−704.167	−	704.167i	−0.965935	−	0.965935i	−0.999439	+	0.0335032i	$0.989334\pi$
$4$		−	3932.85i		−	0.960169i
$5$			8770.94i			0.561340i	0.959804	+	0.280670i	$0.0905566\pi$
$5$			8770.94i			0.561340i	−0.959804	+	0.280670i	$0.909443\pi$
$6$			12719.8i			0.272629i
$7$	37099.6			0.315342			0.157671	−	0.987492i	$-0.449602\pi$
$7$	37099.6			0.315342			0.157671	+	0.987492i	$0.449602\pi$
$8$	−72514.8	+	72514.8i	−0.276622	+	0.276622i
$9$			460261.i			0.866062i
$10$	79217.2	−	79217.2i	0.0792172	−	0.0792172i
$11$	1.87931e6	+	1.87931e6i	1.06082	+	1.06082i	0.998027	+	0.0627926i	$0.0200007\pi$
$11$	1.87931e6	+	1.87931e6i	1.06082	+	1.06082i	0.0627926	+	0.998027i	$0.479999\pi$
$12$	−2.76939e6	+	2.76939e6i	−0.927462	+	0.927462i
$13$			4.37215e6i			0.905805i	0.891560	+	0.452902i	$0.149611\pi$
$13$			4.37215e6i			0.905805i	−0.891560	+	0.452902i	$0.850389\pi$
$14$	−335076.	−	335076.i	−0.0445015	−	0.0445015i
$15$	6.17620e6	−	6.17620e6i	0.542218	−	0.542218i
$16$	−1.47991e7			−0.882095
$17$	1.85809e7	+	1.85809e7i	0.769792	+	0.769792i	0.978070	−	0.208278i	$-0.0667858\pi$
$17$	1.85809e7	+	1.85809e7i	0.769792	+	0.769792i	−0.208278	+	0.978070i	$0.566786\pi$
$18$	4.15698e6	−	4.15698e6i	0.122220	−	0.122220i
$19$	−6.31964e7	−	6.31964e7i	−1.34329	−	1.34329i	−0.892760	−	0.450533i	$-0.851234\pi$
$19$	−6.31964e7	−	6.31964e7i	−1.34329	−	1.34329i	−0.450533	−	0.892760i	$-0.648766\pi$
$20$	3.44948e7			0.538981
$21$	−2.61243e7	−	2.61243e7i	−0.304600	−	0.304600i
$22$		−	3.39470e7i		−	0.299409i
$23$	1.90764e8			1.28864			0.644318	−	0.764758i	$-0.277141\pi$
$23$	1.90764e8			1.28864			0.644318	+	0.764758i	$0.277141\pi$
$24$	1.02125e8			0.534398
$25$	1.67211e8			0.684897
$26$	3.94883e7	−	3.94883e7i	0.127829	−	0.127829i
$27$	−5.01225e7	+	5.01225e7i	−0.129375	+	0.129375i
$28$		−	1.45907e8i		−	0.302781i
$29$	−3.94834e8	−	4.44883e8i	−0.663784	−	0.747924i
$29$	−3.94834e8	−	4.44883e8i	−0.663784	−	0.747924i
$30$	−1.11564e8			−0.153037
$31$	9.84626e8	+	9.84626e8i	1.10943	+	1.10943i	0.993225	+	0.116208i	$0.0370740\pi$
$31$	9.84626e8	+	9.84626e8i	1.10943	+	1.10943i	0.116208	+	0.993225i	$0.462926\pi$
$32$	4.30683e8	+	4.30683e8i	0.401105	+	0.401105i
$33$		−	2.64669e9i		−	2.04937i
$34$		−	3.35637e8i		−	0.217268i
$35$			3.25399e8i			0.177014i
$36$	1.81014e9			0.831567
$37$	−5.39738e8	+	5.39738e8i	−0.210364	+	0.210364i	−0.804422	−	0.594058i	$-0.797525\pi$
$37$	−5.39738e8	+	5.39738e8i	−0.210364	+	0.210364i	0.594058	+	0.804422i	$0.297525\pi$
$38$			1.14155e9i			0.379135i
$39$	3.07872e9	−	3.07872e9i	0.874949	−	0.874949i
$40$	−6.36023e8	−	6.36023e8i	−0.155279	−	0.155279i
$41$	5.22274e9	−	5.22274e9i	1.09950	−	1.09950i	0.105032	−	0.994469i	$-0.466505\pi$
$41$	5.22274e9	−	5.22274e9i	1.09950	−	1.09950i	0.994469	−	0.105032i	$-0.0334945\pi$
$42$			4.71898e8i			0.0859712i
$43$	1.74684e9	+	1.74684e9i	0.276339	+	0.276339i	0.831646	−	0.555307i	$-0.187399\pi$
$43$	1.74684e9	+	1.74684e9i	0.276339	+	0.276339i	−0.555307	+	0.831646i	$0.687399\pi$
$44$	7.39104e9	−	7.39104e9i	1.01857	−	1.01857i
$45$	−4.03692e9			−0.486156
$46$	−1.72294e9	−	1.72294e9i	−0.181854	−	0.181854i
$47$	−2.77566e8	+	2.77566e8i	−0.0257501	+	0.0257501i	−0.719865	−	0.694115i	$-0.755796\pi$
$47$	−2.77566e8	+	2.77566e8i	−0.0257501	+	0.0257501i	0.694115	+	0.719865i	$0.255796\pi$
$48$	1.04210e10	+	1.04210e10i	0.852047	+	0.852047i
$49$	−1.24649e10			−0.900560
$50$	−1.51022e9	−	1.51022e9i	−0.0966538	−	0.0966538i
$51$		−	2.61681e10i		−	1.48714i
$52$	1.71950e10			0.869726
$53$	−2.10355e10			−0.949070			−0.474535	−	0.880237i	$-0.657384\pi$
$53$	−2.10355e10			−0.949070			−0.474535	+	0.880237i	$0.657384\pi$
$54$	9.05391e8			0.0365152
$55$	−1.64833e10	+	1.64833e10i	−0.595480	+	0.595480i
$56$	−2.69027e9	+	2.69027e9i	−0.0872305	+	0.0872305i
$57$			8.90016e10i			2.59507i
$58$	−4.52028e8	+	7.58414e9i	−0.0118740	+	0.199222i
$59$	8.99219e9			0.213183			0.106592	−	0.994303i	$-0.466006\pi$
$59$	8.99219e9			0.213183			0.106592	+	0.994303i	$0.466006\pi$
$60$	−2.42901e10	−	2.42901e10i	−0.520621	−	0.520621i
$61$	6.07106e9	+	6.07106e9i	0.117838	+	0.117838i	0.763567	−	0.645729i	$-0.223446\pi$
$61$	6.07106e9	+	6.07106e9i	0.117838	+	0.117838i	−0.645729	+	0.763567i	$0.723446\pi$
$62$		−	1.77858e10i		−	0.313130i
$63$			1.70755e10i			0.273106i
$64$			5.28374e10i			0.768886i
$65$	−3.83478e10			−0.508464
$66$	−2.39043e10	+	2.39043e10i	−0.289210	+	0.289210i
$67$		−	6.82632e10i		−	0.754637i	−0.926084	−	0.377318i	$-0.876846\pi$
$67$		−	6.82632e10i		−	0.754637i	0.926084	−	0.377318i	$-0.123154\pi$
$68$	7.30760e10	−	7.30760e10i	0.739131	−	0.739131i
$69$	−1.34330e11	−	1.34330e11i	−1.24474	−	1.24474i
$70$	2.93893e9	−	2.93893e9i	0.0249805	−	0.0249805i
$71$			1.65699e11i			1.29351i	0.762696	+	0.646757i	$0.223875\pi$
$71$			1.65699e11i			1.29351i	−0.762696	+	0.646757i	$0.776125\pi$
$72$	−3.33758e10	−	3.33758e10i	−0.239572	−	0.239572i
$73$	−6.29781e9	+	6.29781e9i	−0.0416152	+	0.0416152i	−0.727608	−	0.685993i	$-0.759368\pi$
$73$	−6.29781e9	+	6.29781e9i	−0.0416152	+	0.0416152i	0.685993	+	0.727608i	$0.259368\pi$
$74$	9.74958e9			0.0593739
$75$	−1.17745e11	−	1.17745e11i	−0.661567	−	0.661567i
$76$	−2.48542e11	+	2.48542e11i	−1.28979	+	1.28979i
$77$	6.97216e10	+	6.97216e10i	0.334520	+	0.334520i
$78$	−5.56126e10			−0.246948
$79$	5.01618e10	+	5.01618e10i	0.206353	+	0.206353i	0.802715	−	0.596362i	$-0.203388\pi$
$79$	5.01618e10	+	5.01618e10i	0.206353	+	0.206353i	−0.596362	+	0.802715i	$0.703388\pi$
$80$		−	1.29802e11i		−	0.495155i
$81$	3.15191e11			1.11600
$82$	−9.43413e10			−0.310327
$83$	4.99175e11			1.52681			0.763404	−	0.645922i	$-0.223527\pi$
$83$	4.99175e11			1.52681			0.763404	+	0.645922i	$0.223527\pi$
$84$	−1.02743e11	+	1.02743e11i	−0.292467	+	0.292467i
$85$	−1.62972e11	+	1.62972e11i	−0.432115	+	0.432115i
$86$		−	3.15541e10i		−	0.0779948i
$87$	−3.52425e10	+	5.91301e11i	−0.0812740	+	1.36362i
$88$	−2.72555e11			−0.586892
$89$	5.48312e11	+	5.48312e11i	1.10328	+	1.10328i	0.994012	+	0.109273i	$0.0348522\pi$
$89$	5.48312e11	+	5.48312e11i	1.10328	+	1.10328i	0.109273	+	0.994012i	$0.465148\pi$
$90$	3.64606e10	+	3.64606e10i	0.0686070	+	0.0686070i
$91$			1.62205e11i			0.285638i
$92$		−	7.50248e11i		−	1.23731i
$93$		−	1.38668e12i		−	2.14328i
$94$	5.01382e9			0.00726778
$95$	5.54292e11	−	5.54292e11i	0.754044	−	0.754044i
$96$		−	6.06545e11i		−	0.774883i
$97$	9.48671e11	−	9.48671e11i	1.13890	−	1.13890i	0.150251	−	0.988648i	$-0.451992\pi$
$97$	9.48671e11	−	9.48671e11i	1.13890	−	1.13890i	0.988648	−	0.150251i	$-0.0480082\pi$
$98$	1.12580e11	+	1.12580e11i	0.127088	+	0.127088i
$99$	−8.64971e11	+	8.64971e11i	−0.918736	+	0.918736i
$100$		−	6.57618e11i		−	0.657618i
$101$	−7.56591e11	−	7.56591e11i	−0.712743	−	0.712743i	0.254365	−	0.967108i	$-0.418133\pi$
$101$	−7.56591e11	−	7.56591e11i	−0.712743	−	0.712743i	−0.967108	+	0.254365i	$0.918133\pi$
$102$	−2.36345e11	+	2.36345e11i	−0.209867	+	0.209867i
$103$	1.93715e12			1.62233			0.811165	−	0.584817i	$-0.198834\pi$
$103$	1.93715e12			1.62233			0.811165	+	0.584817i	$0.198834\pi$
$104$	−3.17045e11	−	3.17045e11i	−0.250566	−	0.250566i
$105$	2.29135e11	−	2.29135e11i	0.170984	−	0.170984i
$106$	1.89988e11	+	1.89988e11i	0.133934	+	0.133934i
$107$	4.15283e11			0.276721			0.138360	−	0.990382i	$-0.455817\pi$
$107$	4.15283e11			0.276721			0.138360	+	0.990382i	$0.455817\pi$
$108$	1.97125e11	+	1.97125e11i	0.124222	+	0.124222i
$109$			1.09942e12i			0.655545i	0.944757	+	0.327773i	$0.106298\pi$
$109$			1.09942e12i			0.655545i	−0.944757	+	0.327773i	$0.893702\pi$
$110$	2.97747e11			0.168070
$111$	7.60131e11			0.406397
$112$	−5.49041e11			−0.278161
$113$	−7.25248e11	+	7.25248e11i	−0.348350	+	0.348350i	−0.859495	−	0.511145i	$-0.829222\pi$
$113$	−7.25248e11	+	7.25248e11i	−0.348350	+	0.348350i	0.511145	+	0.859495i	$0.329222\pi$
$114$	8.03843e11	−	8.03843e11i	0.366220	−	0.366220i
$115$			1.67318e12i			0.723363i
$116$	−1.74966e12	+	1.55283e12i	−0.718134	+	0.637345i
$117$	−2.01233e12			−0.784483
$118$	−8.12155e10	−	8.12155e10i	−0.0300848	−	0.0300848i
$119$	6.89345e11	+	6.89345e11i	0.242747	+	0.242747i
$120$			8.95733e11i			0.299979i
$121$			3.92515e12i			1.25067i
$122$		−	1.09665e11i		−	0.0332590i
$123$	−7.35537e12			−2.12409
$124$	3.87239e12	−	3.87239e12i	1.06524	−	1.06524i
$125$			3.60794e12i			0.945800i
$126$	1.54222e11	−	1.54222e11i	0.0385411	−	0.0385411i
$127$	7.13246e11	+	7.13246e11i	0.169987	+	0.169987i	0.786974	−	0.616986i	$-0.211647\pi$
$127$	7.13246e11	+	7.13246e11i	0.169987	+	0.169987i	−0.616986	+	0.786974i	$0.711647\pi$
$128$	2.24129e12	−	2.24129e12i	0.509611	−	0.509611i
$129$		−	2.46013e12i		−	0.533851i
$130$	3.46349e11	+	3.46349e11i	0.0717553	+	0.0717553i
$131$	1.05468e12	−	1.05468e12i	0.208686	−	0.208686i	−0.595023	−	0.803709i	$-0.702857\pi$
$131$	1.05468e12	−	1.05468e12i	0.208686	−	0.208686i	0.803709	+	0.595023i	$0.202857\pi$
$132$	−1.04090e13			−1.96774
$133$	−2.34456e12	−	2.34456e12i	−0.423596	−	0.423596i
$134$	−6.16538e11	+	6.16538e11i	−0.106496	+	0.106496i
$135$	−4.39621e11	−	4.39621e11i	−0.0726233	−	0.0726233i
$136$	−2.69478e12			−0.425883
$137$	1.58648e12	+	1.58648e12i	0.239944	+	0.239944i	0.816827	−	0.576883i	$-0.195731\pi$
$137$	1.58648e12	+	1.58648e12i	0.239944	+	0.239944i	−0.576883	+	0.816827i	$0.695731\pi$
$138$			2.42648e12i			0.351319i
$139$	1.99577e12			0.276709			0.138354	−	0.990383i	$-0.455819\pi$
$139$	1.99577e12			0.276709			0.138354	+	0.990383i	$0.455819\pi$
$140$	1.27974e12			0.169963
$141$	3.90905e11			0.0497458
$142$	1.49656e12	−	1.49656e12i	0.182543	−	0.182543i
$143$	−8.21660e12	+	8.21660e12i	−0.960895	+	0.960895i
$144$		−	6.81145e12i		−	0.763949i
$145$	3.90204e12	−	3.46307e12i	0.419840	−	0.372609i
$146$	1.13761e11			0.0117456
$147$	8.77737e12	+	8.77737e12i	0.869882	+	0.869882i
$148$	2.12271e12	+	2.12271e12i	0.201985	+	0.201985i
$149$		−	1.00714e13i		−	0.920393i	−0.887817	−	0.460196i	$-0.847779\pi$
$149$		−	1.00714e13i		−	0.920393i	0.887817	−	0.460196i	$-0.152221\pi$
$150$			2.12689e12i			0.186723i
$151$			9.97004e12i			0.841076i	0.907275	+	0.420538i	$0.138159\pi$
$151$			9.97004e12i			0.841076i	−0.907275	+	0.420538i	$0.861841\pi$
$152$	9.16535e12			0.743169
$153$	−8.55207e12	+	8.55207e12i	−0.666688	+	0.666688i
$154$		−	1.25942e12i		−	0.0944161i
$155$	−8.63609e12	+	8.63609e12i	−0.622769	+	0.622769i
$156$	−1.21082e13	−	1.21082e13i	−0.840099	−	0.840099i
$157$	1.74582e13	−	1.74582e13i	1.16574	−	1.16574i	0.182544	−	0.983198i	$-0.441567\pi$
$157$	1.74582e13	−	1.74582e13i	1.16574	−	1.16574i	0.983198	−	0.182544i	$-0.0584333\pi$
$158$		−	9.06101e11i		−	0.0582417i
$159$	1.48125e13	+	1.48125e13i	0.916741	+	0.916741i
$160$	−3.77749e12	+	3.77749e12i	−0.225156	+	0.225156i
$161$	7.07729e12			0.406361
$162$	−2.84673e12	−	2.84673e12i	−0.157491	−	0.157491i
$163$	3.50556e12	−	3.50556e12i	0.186909	−	0.186909i	−0.607449	−	0.794359i	$-0.707807\pi$
$163$	3.50556e12	−	3.50556e12i	0.186909	−	0.186909i	0.794359	+	0.607449i	$0.207807\pi$
$164$	−2.05403e13	−	2.05403e13i	−1.05571	−	1.05571i
$165$	2.32140e13			1.15039
$166$	−4.50844e12	−	4.50844e12i	−0.215465	−	0.215465i
$167$		−	3.95872e12i		−	0.182497i	−0.995828	−	0.0912486i	$-0.970914\pi$
$167$		−	3.95872e12i		−	0.182497i	0.995828	−	0.0912486i	$-0.0290858\pi$
$168$	3.78880e12			0.168518
$169$	4.18243e12			0.179518
$170$	2.94385e12			0.121961
$171$	2.90868e13	−	2.90868e13i	1.16338	−	1.16338i
$172$	6.87007e12	−	6.87007e12i	0.265332	−	0.265332i
$173$			7.94023e11i			0.0296180i	0.999890	+	0.0148090i	$0.00471403\pi$
$173$			7.94023e11i			0.0296180i	−0.999890	+	0.0148090i	$0.995286\pi$
$174$	5.65880e12	−	5.02220e12i	0.203906	−	0.180967i
$175$	6.20348e12			0.215977
$176$	−2.78120e13	−	2.78120e13i	−0.935743	−	0.935743i
$177$	−6.33201e12	−	6.33201e12i	−0.205921	−	0.205921i
$178$		−	9.90446e12i		−	0.311394i
$179$			1.91199e13i			0.581257i	0.956836	+	0.290629i	$0.0938644\pi$
$179$			1.91199e13i			0.581257i	−0.956836	+	0.290629i	$0.906136\pi$
$180$			1.58766e13i			0.466792i
$181$	2.23729e13			0.636284			0.318142	−	0.948043i	$-0.396941\pi$
$181$	2.23729e13			0.636284			0.318142	+	0.948043i	$0.396941\pi$
$182$	1.46500e12	−	1.46500e12i	0.0403097	−	0.0403097i
$183$		−	8.55008e12i		−	0.227648i
$184$	−1.38332e13	+	1.38332e13i	−0.356465	+	0.356465i
$185$	−4.73400e12	−	4.73400e12i	−0.118086	−	0.118086i
$186$	−1.25242e13	+	1.25242e13i	−0.302463	+	0.302463i
$187$			6.98384e13i			1.63322i
$188$	1.09163e12	+	1.09163e12i	0.0247244	+	0.0247244i
$189$	−1.85953e12	+	1.85953e12i	−0.0407973	+	0.0407973i
$190$	−1.00125e13			−0.212824
$191$	4.89135e13	+	4.89135e13i	1.00746	+	1.00746i	0.999972	+	0.00748961i	$0.00238404\pi$
$191$	4.89135e13	+	4.89135e13i	1.00746	+	1.00746i	0.00748961	+	0.999972i	$0.497616\pi$
$192$	3.72064e13	−	3.72064e13i	0.742694	−	0.742694i
$193$	−4.47651e13	−	4.47651e13i	−0.866156	−	0.866156i	0.125889	−	0.992044i	$-0.459822\pi$
$193$	−4.47651e13	−	4.47651e13i	−0.866156	−	0.866156i	−0.992044	+	0.125889i	$0.959822\pi$
$194$	−1.71364e13			−0.321446
$195$	2.70033e13	+	2.70033e13i	0.491144	+	0.491144i
$196$			4.90226e13i			0.864690i
$197$	−1.28151e13			−0.219243			−0.109622	−	0.993973i	$-0.534964\pi$
$197$	−1.28151e13			−0.219243			−0.109622	+	0.993973i	$0.534964\pi$
$198$	1.56245e13			0.259307
$199$	−1.00431e14			−1.61715			−0.808577	−	0.588391i	$-0.799762\pi$
$199$	−1.00431e14			−1.61715			−0.808577	+	0.588391i	$0.799762\pi$
$200$	−1.21253e13	+	1.21253e13i	−0.189458	+	0.189458i
$201$	−4.80687e13	+	4.80687e13i	−0.728930	+	0.728930i
$202$			1.36667e13i			0.201167i
$203$	−1.46482e13	−	1.65050e13i	−0.209319	−	0.235852i
$204$	−1.02915e14			−1.42791
$205$	4.58084e13	+	4.58084e13i	0.617194	+	0.617194i
$206$	−1.74959e13	−	1.74959e13i	−0.228946	−	0.228946i
$207$			8.78014e13i			1.11604i
$208$		−	6.47038e13i		−	0.799005i
$209$		−	2.37531e14i		−	2.84998i
$210$	−4.13899e12			−0.0482590
$211$	−4.99008e13	+	4.99008e13i	−0.565474	+	0.565474i	−0.930857	−	0.365383i	$-0.880938\pi$
$211$	−4.99008e13	+	4.99008e13i	−0.565474	+	0.565474i	0.365383	+	0.930857i	$0.380938\pi$
$212$			8.27297e13i			0.911268i
$213$	1.16680e14	−	1.16680e14i	1.24945	−	1.24945i
$214$	−3.75074e12	−	3.75074e12i	−0.0390512	−	0.0390512i
$215$	−1.53214e13	+	1.53214e13i	−0.155120	+	0.155120i
$216$		−	7.26925e12i		−	0.0715760i
$217$	3.65293e13	+	3.65293e13i	0.349850	+	0.349850i
$218$	9.92968e12	−	9.92968e12i	0.0925116	−	0.0925116i
$219$	8.86942e12			0.0803953
$220$	6.48263e13	+	6.48263e13i	0.571762	+	0.571762i
$221$	−8.12384e13	+	8.12384e13i	−0.697281	+	0.697281i
$222$	−6.86533e12	−	6.86533e12i	−0.0573514	−	0.0573514i
$223$	−1.99657e14			−1.62351			−0.811757	−	0.583995i	$-0.801489\pi$
$223$	−1.99657e14			−1.62351			−0.811757	+	0.583995i	$0.801489\pi$
$224$	1.59782e13	+	1.59782e13i	0.126485	+	0.126485i
$225$			7.69609e13i			0.593164i
$226$	1.31006e13			0.0983195
$227$	−9.06284e13			−0.662383			−0.331192	−	0.943564i	$-0.607451\pi$
$227$	−9.06284e13			−0.662383			−0.331192	+	0.943564i	$0.607451\pi$
$228$	3.50030e14			2.49170
$229$	4.71521e13	−	4.71521e13i	0.326955	−	0.326955i	−0.524472	−	0.851427i	$-0.675737\pi$
$229$	4.71521e13	−	4.71521e13i	0.326955	−	0.326955i	0.851427	+	0.524472i	$0.175737\pi$
$230$	1.51118e13	−	1.51118e13i	0.102082	−	0.102082i
$231$		−	9.81912e13i		−	0.646250i
$232$	6.08919e13	+	3.62926e12i	0.390510	+	0.0232750i
$233$	−1.10934e14			−0.693311			−0.346656	−	0.937992i	$-0.612683\pi$
$233$	−1.10934e14			−0.693311			−0.346656	+	0.937992i	$0.612683\pi$
$234$	1.81749e13	+	1.81749e13i	0.110708	+	0.110708i
$235$	−2.43451e12	−	2.43451e12i	−0.0144546	−	0.0144546i
$236$		−	3.53650e13i		−	0.204692i
$237$		−	7.06446e13i		−	0.398647i
$238$		−	1.24520e13i		−	0.0685138i
$239$	6.76112e13			0.362770			0.181385	−	0.983412i	$-0.441942\pi$
$239$	6.76112e13			0.362770			0.181385	+	0.983412i	$0.441942\pi$
$240$	−9.14022e13	+	9.14022e13i	−0.478288	+	0.478288i
$241$			3.42471e14i			1.74792i	0.486000	+	0.873959i	$0.338456\pi$
$241$			3.42471e14i			1.74792i	−0.486000	+	0.873959i	$0.661544\pi$
$242$	3.54511e13	−	3.54511e13i	0.176497	−	0.176497i
$243$	−1.95310e14	−	1.95310e14i	−0.948607	−	0.948607i
$244$	2.38766e13	−	2.38766e13i	0.113145	−	0.113145i
$245$		−	1.09329e14i		−	0.505520i
$246$	6.64321e13	+	6.64321e13i	0.299755	+	0.299755i
$247$	2.76304e14	−	2.76304e14i	1.21676	−	1.21676i
$248$	−1.42800e14			−0.613788
$249$	−3.51502e14	−	3.51502e14i	−1.47480	−	1.47480i
$250$	3.25861e13	−	3.25861e13i	0.133473	−	0.133473i
$251$	1.88413e14	+	1.88413e14i	0.753475	+	0.753475i	0.975126	−	0.221651i	$-0.0711447\pi$
$251$	1.88413e14	+	1.88413e14i	0.753475	+	0.753475i	−0.221651	+	0.975126i	$0.571145\pi$
$252$	6.71555e13			0.262228
$253$	3.58505e14	+	3.58505e14i	1.36701	+	1.36701i
$254$		−	1.28838e13i		−	0.0479778i
$255$	2.29519e14			0.834790
$256$	1.75936e14			0.625051
$257$	−1.30523e14			−0.452988			−0.226494	−	0.974013i	$-0.572726\pi$
$257$	−1.30523e14			−0.452988			−0.226494	+	0.974013i	$0.572726\pi$
$258$	−2.22194e13	+	2.22194e13i	−0.0753379	+	0.0753379i
$259$	−2.00241e13	+	2.00241e13i	−0.0663367	+	0.0663367i
$260$			1.50816e14i			0.488212i
$261$	2.04762e14	−	1.81727e14i	0.647749	−	0.574878i
$262$	−1.90513e13			−0.0589003
$263$	−1.70799e14	−	1.70799e14i	−0.516119	−	0.516119i	0.400276	−	0.916395i	$-0.368914\pi$
$263$	−1.70799e14	−	1.70799e14i	−0.516119	−	0.516119i	−0.916395	+	0.400276i	$0.868914\pi$
$264$	1.91924e14	+	1.91924e14i	0.566900	+	0.566900i
$265$		−	1.84501e14i		−	0.532751i
$266$			4.23511e13i			0.119557i
$267$		−	7.72206e14i		−	2.13140i
$268$	−2.68469e14			−0.724579
$269$	3.34496e14	−	3.34496e14i	0.882831	−	0.882831i	−0.110990	−	0.993821i	$-0.535402\pi$
$269$	3.34496e14	−	3.34496e14i	0.882831	−	0.882831i	0.993821	+	0.110990i	$0.0354023\pi$
$270$			7.94113e12i			0.0204974i
$271$	−4.89511e13	+	4.89511e13i	−0.123579	+	0.123579i	−0.766192	−	0.642612i	$-0.777851\pi$
$271$	−4.89511e13	+	4.89511e13i	−0.123579	+	0.123579i	0.642612	+	0.766192i	$0.277851\pi$
$272$	−2.74981e14	−	2.74981e14i	−0.679029	−	0.679029i
$273$	1.14219e14	−	1.14219e14i	0.275908	−	0.275908i
$274$		−	2.86574e13i		−	0.0677226i
$275$	3.14241e14	+	3.14241e14i	0.726552	+	0.726552i
$276$	−5.28300e14	+	5.28300e14i	−1.19516	+	1.19516i
$277$	2.01340e14			0.445710			0.222855	−	0.974852i	$-0.428462\pi$
$277$	2.01340e14			0.445710			0.222855	+	0.974852i	$0.428462\pi$
$278$	−1.80254e13	−	1.80254e13i	−0.0390495	−	0.0390495i
$279$	−4.53185e14	+	4.53185e14i	−0.960838	+	0.960838i
$280$	−2.35962e13	−	2.35962e13i	−0.0489660	−	0.0489660i
$281$	8.24665e13			0.167510			0.0837548	−	0.996486i	$-0.473309\pi$
$281$	8.24665e13			0.167510			0.0837548	+	0.996486i	$0.473309\pi$
$282$	−3.53057e12	−	3.53057e12i	−0.00702021	−	0.00702021i
$283$			6.23744e14i			1.21419i	0.794628	+	0.607096i	$0.207666\pi$
$283$			6.23744e14i			1.21419i	−0.794628	+	0.607096i	$0.792334\pi$
$284$	6.51672e14			1.24199
$285$	−7.80628e14			−1.45672
$286$	1.48421e14			0.271206
$287$	1.93762e14	−	1.93762e14i	0.346718	−	0.346718i
$288$	−1.98227e14	+	1.98227e14i	−0.347382	+	0.347382i
$289$			1.07878e14i			0.185160i
$290$	−6.65200e13	−	3.96471e12i	−0.111832	−	0.00666535i
$291$	−1.33605e15			−2.20021
$292$	2.47684e13	+	2.47684e13i	0.0399577	+	0.0399577i
$293$	−4.45565e14	−	4.45565e14i	−0.704215	−	0.704215i	0.261098	−	0.965312i	$-0.415915\pi$
$293$	−4.45565e14	−	4.45565e14i	−0.704215	−	0.704215i	−0.965312	+	0.261098i	$0.915915\pi$
$294$		−	1.58551e14i		−	0.245518i
$295$			7.88700e13i			0.119668i
$296$		−	7.82780e13i		−	0.116383i
$297$	−1.88391e14			−0.274487
$298$	−9.09628e13	+	9.09628e13i	−0.129887	+	0.129887i
$299$			8.34050e14i			1.16725i
$300$	−4.63073e14	+	4.63073e14i	−0.635216	+	0.635216i
$301$	6.48071e13	+	6.48071e13i	0.0871412	+	0.0871412i
$302$	9.00472e13	−	9.00472e13i	0.118694	−	0.118694i
$303$			1.06553e15i			1.37693i
$304$	9.35249e14	+	9.35249e14i	1.18491	+	1.18491i
$305$	−5.32489e13	+	5.32489e13i	−0.0661472	+	0.0661472i
$306$	1.54481e14			0.188168
$307$	8.68452e14	+	8.68452e14i	1.03733	+	1.03733i	0.999276	+	0.0380511i	$0.0121150\pi$
$307$	8.68452e14	+	8.68452e14i	1.03733	+	1.03733i	0.0380511	+	0.999276i	$0.487885\pi$
$308$	2.74205e14	−	2.74205e14i	0.321196	−	0.321196i
$309$	−1.36408e15	−	1.36408e15i	−1.56707	−	1.56707i
$310$	1.55999e14			0.175772
$311$	−7.90867e13	−	7.90867e13i	−0.0874060	−	0.0874060i	0.662052	−	0.749458i	$-0.269686\pi$
$311$	−7.90867e13	−	7.90867e13i	−0.0874060	−	0.0874060i	−0.749458	+	0.662052i	$0.769686\pi$
$312$			4.46506e14i			0.484060i
$313$	1.55413e15			1.65281			0.826403	−	0.563078i	$-0.190383\pi$
$313$	1.55413e15			1.65281			0.826403	+	0.563078i	$0.190383\pi$
$314$	−3.15358e14			−0.329023
$315$	−1.49768e14			−0.153305
$316$	1.97279e14	−	1.97279e14i	0.198134	−	0.198134i
$317$	−7.93842e14	+	7.93842e14i	−0.782309	+	0.782309i	−0.980220	−	0.197911i	$-0.936584\pi$
$317$	−7.93842e14	+	7.93842e14i	−0.782309	+	0.782309i	0.197911	+	0.980220i	$0.436584\pi$
$318$		−	2.67567e14i		−	0.258744i
$319$	9.40566e13	−	1.57809e15i	0.0892576	−	1.49757i
$320$	−4.63434e14			−0.431606
$321$	−2.92429e14	−	2.92429e14i	−0.267294	−	0.267294i
$322$	−6.39205e13	−	6.39205e13i	−0.0573462	−	0.0573462i
$323$		−	2.34849e15i		−	2.06811i
$324$		−	1.23960e15i		−	1.07155i
$325$			7.31072e14i			0.620383i
$326$	−6.33228e13			−0.0527539
$327$	7.74172e14	−	7.74172e14i	0.633214	−	0.633214i
$328$			7.57453e14i			0.608293i
$329$	−1.02976e13	+	1.02976e13i	−0.00812007	+	0.00812007i
$330$	−2.09663e14	−	2.09663e14i	−0.162345	−	0.162345i
$331$	−1.09308e15	+	1.09308e15i	−0.831161	+	0.831161i	−0.987676	−	0.156514i	$-0.949974\pi$
$331$	−1.09308e15	+	1.09308e15i	−0.831161	+	0.831161i	0.156514	+	0.987676i	$0.449974\pi$
$332$		−	1.96318e15i		−	1.46599i
$333$	−2.48420e14	−	2.48420e14i	−0.182189	−	0.182189i
$334$	−3.57543e13	+	3.57543e13i	−0.0257543	+	0.0257543i
$335$	5.98732e14			0.423608
$336$	3.86616e14	+	3.86616e14i	0.268686	+	0.268686i
$337$	1.85787e15	−	1.85787e15i	1.26834	−	1.26834i	0.321396	−	0.946945i	$-0.395848\pi$
$337$	1.85787e15	−	1.85787e15i	1.26834	−	1.26834i	0.946945	−	0.321396i	$-0.104152\pi$
$338$	−3.77748e13	−	3.77748e13i	−0.0253339	−	0.0253339i
$339$	1.02139e15			0.672968
$340$	6.40945e14	+	6.40945e14i	0.414904	+	0.414904i
$341$			3.70083e15i			2.35382i
$342$	−5.25412e14			−0.328355
$343$	−9.75950e14			−0.599326
$344$	−2.53344e14			−0.152883
$345$	1.17820e15	−	1.17820e15i	0.698722	−	0.698722i
$346$	7.17144e12	−	7.17144e12i	0.00417974	−	0.00417974i
$347$		−	5.29733e14i		−	0.303445i	−0.988423	−	0.151723i	$-0.951518\pi$
$347$		−	5.29733e14i		−	0.303445i	0.988423	−	0.151723i	$-0.0484820\pi$
$348$	2.32550e15	+	1.38604e14i	1.30931	+	0.0780368i
$349$	−4.43939e14			−0.245681			−0.122840	−	0.992426i	$-0.539200\pi$
$349$	−4.43939e14			−0.245681			−0.122840	+	0.992426i	$0.539200\pi$
$350$	−5.60284e13	−	5.60284e13i	−0.0304790	−	0.0304790i
$351$	−2.19143e14	−	2.19143e14i	−0.117188	−	0.117188i
$352$			1.61877e15i			0.850999i
$353$			2.11466e15i			1.09293i	0.837483	+	0.546464i	$0.184026\pi$
$353$			2.11466e15i			1.09293i	−0.837483	+	0.546464i	$0.815974\pi$
$354$			1.14379e14i			0.0581199i
$355$	−1.45334e15			−0.726101
$356$	2.15643e15	−	2.15643e15i	1.05934	−	1.05934i
$357$		−	9.70828e14i		−	0.468957i
$358$	1.72687e14	−	1.72687e14i	0.0820279	−	0.0820279i
$359$	−1.63052e15	−	1.63052e15i	−0.761657	−	0.761657i	0.214965	−	0.976622i	$-0.431036\pi$
$359$	−1.63052e15	−	1.63052e15i	−0.761657	−	0.761657i	−0.976622	+	0.214965i	$0.931036\pi$
$360$	2.92737e14	−	2.92737e14i	0.134481	−	0.134481i
$361$			5.77425e15i			2.60887i
$362$	−2.02067e14	−	2.02067e14i	−0.0897934	−	0.0897934i
$363$	2.76396e15	−	2.76396e15i	1.20807	−	1.20807i
$364$	6.37928e14			0.274261
$365$	−5.52377e13	−	5.52377e13i	−0.0233603	−	0.0233603i
$366$	−7.72225e13	+	7.72225e13i	−0.0321260	+	0.0321260i
$367$	1.40086e15	+	1.40086e15i	0.573321	+	0.573321i	0.933055	−	0.359734i	$-0.117133\pi$
$367$	1.40086e15	+	1.40086e15i	0.573321	+	0.573321i	−0.359734	+	0.933055i	$0.617133\pi$
$368$	−2.82314e15			−1.13670
$369$	2.40383e15	+	2.40383e15i	0.952237	+	0.952237i
$370$			8.55130e13i			0.0333289i
$371$	−7.80411e14			−0.299281
$372$	−5.45362e15			−2.05791
$373$	1.20718e15			0.448248			0.224124	−	0.974561i	$-0.428048\pi$
$373$	1.20718e15			0.448248			0.224124	+	0.974561i	$0.428048\pi$
$374$	6.30765e14	−	6.30765e14i	0.230483	−	0.230483i
$375$	2.54059e15	−	2.54059e15i	0.913582	−	0.913582i
$376$		−	4.02553e13i		−	0.0142461i
$377$	1.94509e15	−	1.72627e15i	0.677473	−	0.601259i
$378$	3.35897e13			0.0115148
$379$	−1.51608e15	−	1.51608e15i	−0.511550	−	0.511550i	0.403451	−	0.915001i	$-0.367810\pi$
$379$	−1.51608e15	−	1.51608e15i	−0.511550	−	0.511550i	−0.915001	+	0.403451i	$0.867810\pi$
$380$	−2.17995e15	−	2.17995e15i	−0.724010	−	0.724010i
$381$		−	1.00449e15i		−	0.328394i
$382$		−	8.83552e14i		−	0.284349i
$383$		−	1.71857e15i		−	0.544469i	−0.962231	−	0.272235i	$-0.912237\pi$
$383$		−	1.71857e15i		−	0.544469i	0.962231	−	0.272235i	$-0.0877627\pi$
$384$	−3.15649e15			−0.984503
$385$	−6.11523e14	+	6.11523e14i	−0.187780	+	0.187780i
$386$			8.08618e14i			0.244466i
$387$	−8.04002e14	+	8.04002e14i	−0.239327	+	0.239327i
$388$	−3.73098e15	−	3.73098e15i	−1.09354	−	1.09354i
$389$	−3.91416e13	+	3.91416e13i	−0.0112964	+	0.0112964i	−0.712732	−	0.701436i	$-0.752543\pi$
$389$	−3.91416e13	+	3.91416e13i	−0.0112964	+	0.0112964i	0.701436	+	0.712732i	$0.252543\pi$
$390$		−	4.87775e14i		−	0.138622i
$391$	3.54458e15	+	3.54458e15i	0.991982	+	0.991982i
$392$	9.03891e14	−	9.03891e14i	0.249115	−	0.249115i
$393$	−1.48535e15			−0.403155
$394$	1.15744e14	+	1.15744e14i	0.0309399	+	0.0309399i
$395$	−4.39966e14	+	4.39966e14i	−0.115834	+	0.115834i
$396$	3.40181e15	+	3.40181e15i	0.882142	+	0.882142i
$397$	−1.00296e15			−0.256177			−0.128088	−	0.991763i	$-0.540884\pi$
$397$	−1.00296e15			−0.256177			−0.128088	+	0.991763i	$0.540884\pi$
$398$	9.07075e14	+	9.07075e14i	0.228215	+	0.228215i
$399$			3.30193e15i			0.818333i
$400$	−2.47458e15			−0.604144
$401$	−3.48344e15			−0.837803			−0.418902	−	0.908032i	$-0.637585\pi$
$401$	−3.48344e15			−0.837803			−0.418902	+	0.908032i	$0.637585\pi$
$402$	8.68292e14			0.205736
$403$	−4.30493e15	+	4.30493e15i	−1.00493	+	1.00493i
$404$	−2.97556e15	+	2.97556e15i	−0.684354	+	0.684354i
$405$			2.76452e15i			0.626454i
$406$	−1.67701e13	+	2.81369e14i	−0.00374437	+	0.0628231i
$407$	−2.02866e15			−0.446317
$408$	1.89758e15	+	1.89758e15i	0.411376	+	0.411376i
$409$	5.62500e15	+	5.62500e15i	1.20166	+	1.20166i	0.973661	+	0.228002i	$0.0732193\pi$
$409$	5.62500e15	+	5.62500e15i	1.20166	+	1.20166i	0.228002	+	0.973661i	$0.426781\pi$
$410$		−	8.27462e14i		−	0.174199i
$411$		−	2.23429e15i		−	0.463541i
$412$		−	7.61852e15i		−	1.55771i
$413$	3.33607e14			0.0672256
$414$	7.93003e14	−	7.93003e14i	0.157497	−	0.157497i
$415$			4.37823e15i			0.857058i
$416$	−1.88301e15	+	1.88301e15i	−0.363322	+	0.363322i
$417$	−1.40536e15	−	1.40536e15i	−0.267283	−	0.267283i
$418$	−2.14532e15	+	2.14532e15i	−0.402194	+	0.402194i
$419$			3.54002e15i			0.654216i	0.944987	+	0.327108i	$0.106074\pi$
$419$			3.54002e15i			0.654216i	−0.944987	+	0.327108i	$0.893926\pi$
$420$	−9.01154e14	−	9.01154e14i	−0.164174	−	0.164174i
$421$	−6.70162e14	+	6.70162e14i	−0.120361	+	0.120361i	−0.764722	−	0.644361i	$-0.777124\pi$
$421$	−6.70162e14	+	6.70162e14i	−0.120361	+	0.120361i	0.644361	+	0.764722i	$0.277124\pi$
$422$	9.01385e14			0.159601
$423$	−1.27753e14	−	1.27753e14i	−0.0223012	−	0.0223012i
$424$	1.52539e15	−	1.52539e15i	0.262534	−	0.262534i
$425$	3.10694e15	+	3.10694e15i	0.527229	+	0.527229i
$426$	−2.10766e15			−0.352649
$427$	2.25234e14	+	2.25234e14i	0.0371593	+	0.0371593i
$428$		−	1.63325e15i		−	0.265699i
$429$	1.15717e16			1.85632
$430$	2.76759e14			0.0437816
$431$	−9.51126e15			−1.48380			−0.741899	−	0.670512i	$-0.766074\pi$
$431$	−9.51126e15			−1.48380			−0.741899	+	0.670512i	$0.766074\pi$
$432$	7.41768e14	−	7.41768e14i	0.114121	−	0.114121i
$433$	3.81524e15	−	3.81524e15i	0.578888	−	0.578888i	−0.355709	−	0.934597i	$-0.615761\pi$
$433$	3.81524e15	−	3.81524e15i	0.578888	−	0.578888i	0.934597	+	0.355709i	$0.115761\pi$
$434$		−	6.59848e14i		−	0.0987429i
$435$	−5.18626e15	−	3.09110e14i	−0.765454	−	0.0456224i
$436$	4.32384e15			0.629435
$437$	−1.20556e16	−	1.20556e16i	−1.73102	−	1.73102i
$438$	−8.01066e13	−	8.01066e13i	−0.0113455	−	0.0113455i
$439$			9.60883e14i			0.134240i	0.997745	+	0.0671202i	$0.0213811\pi$
$439$			9.60883e14i			0.134240i	−0.997745	+	0.0671202i	$0.978619\pi$
$440$		−	2.39056e15i		−	0.329446i
$441$		−	5.73711e15i		−	0.779941i
$442$	1.46746e15			0.196803
$443$	9.68397e15	−	9.68397e15i	1.28124	−	1.28124i	0.341279	−	0.939962i	$-0.389140\pi$
$443$	9.68397e15	−	9.68397e15i	1.28124	−	1.28124i	0.939962	−	0.341279i	$-0.110860\pi$
$444$		−	2.98948e15i		−	0.390210i
$445$	−4.80921e15	+	4.80921e15i	−0.619318	+	0.619318i
$446$	1.80326e15	+	1.80326e15i	0.229113	+	0.229113i
$447$	−7.09196e15	+	7.09196e15i	−0.889040	+	0.889040i
$448$			1.96025e15i			0.242462i
$449$	−2.60221e15	−	2.60221e15i	−0.317588	−	0.317588i	0.530252	−	0.847840i	$-0.322097\pi$
$449$	−2.60221e15	−	2.60221e15i	−0.317588	−	0.317588i	−0.847840	+	0.530252i	$0.822097\pi$
$450$	6.95093e14	−	6.95093e14i	0.0837082	−	0.0837082i
$451$	1.96303e16			2.33274
$452$	2.85230e15	+	2.85230e15i	0.334475	+	0.334475i
$453$	7.02057e15	−	7.02057e15i	0.812425	−	0.812425i
$454$	8.18536e14	+	8.18536e14i	0.0934765	+	0.0934765i
$455$	−1.42269e15			−0.160340
$456$	−6.45394e15	−	6.45394e15i	−0.717853	−	0.717853i
$457$		−	8.92082e15i		−	0.979281i	−0.871924	−	0.489641i	$-0.837128\pi$
$457$		−	8.92082e15i		−	0.979281i	0.871924	−	0.489641i	$-0.162872\pi$
$458$	−8.51735e14			−0.0922808
$459$	−1.86264e15			−0.199184
$460$	6.58038e15			0.694551
$461$	7.12195e15	−	7.12195e15i	0.741982	−	0.741982i	−0.230977	−	0.972959i	$-0.574192\pi$
$461$	7.12195e15	−	7.12195e15i	0.741982	−	0.741982i	0.972959	+	0.230977i	$0.0741921\pi$
$462$	−8.86842e14	+	8.86842e14i	−0.0911999	+	0.0911999i
$463$			8.21245e15i			0.833656i	0.908985	+	0.416828i	$0.136858\pi$
$463$			8.21245e15i			0.833656i	−0.908985	+	0.416828i	$0.863142\pi$
$464$	5.84319e15	+	6.58386e15i	0.585520	+	0.659740i
$465$	1.21625e16			1.20311
$466$	1.00193e15	+	1.00193e15i	0.0978412	+	0.0978412i
$467$	1.29202e16	+	1.29202e16i	1.24557	+	1.24557i	0.957658	+	0.287910i	$0.0929603\pi$
$467$	1.29202e16	+	1.29202e16i	1.24557	+	1.24557i	0.287910	+	0.957658i	$0.407040\pi$
$468$			7.91419e15i			0.753237i
$469$		−	2.53254e15i		−	0.237968i
$470$			4.39759e13i			0.00407970i
$471$	−2.45870e16			−2.25206
$472$	−6.52067e14	+	6.52067e14i	−0.0589713	+	0.0589713i
$473$			6.56569e15i			0.586292i
$474$	−6.38046e14	+	6.38046e14i	−0.0562577	+	0.0562577i
$475$	−1.05671e16	−	1.05671e16i	−0.920018	−	0.920018i
$476$	2.71109e15	−	2.71109e15i	0.233079	−	0.233079i
$477$		−	9.68184e15i		−	0.821954i
$478$	−6.10649e14	−	6.10649e14i	−0.0511946	−	0.0511946i
$479$	−1.02360e16	+	1.02360e16i	−0.847458	+	0.847458i	−0.989815	−	0.142358i	$-0.954532\pi$
$479$	−1.02360e16	+	1.02360e16i	−0.847458	+	0.847458i	0.142358	+	0.989815i	$0.454532\pi$
$480$	5.31997e15			0.434973
$481$	−2.35981e15	−	2.35981e15i	−0.190549	−	0.190549i
$482$	3.09312e15	−	3.09312e15i	0.246669	−	0.246669i
$483$	−4.98359e15	−	4.98359e15i	−0.392518	−	0.392518i
$484$	1.54371e16			1.20086
$485$	8.32073e15	+	8.32073e15i	0.639310	+	0.639310i
$486$			3.52799e15i			0.267738i
$487$	−8.45561e15			−0.633827			−0.316914	−	0.948454i	$-0.602647\pi$
$487$	−8.45561e15			−0.633827			−0.316914	+	0.948454i	$0.602647\pi$
$488$	−8.80484e14			−0.0651932
$489$	−4.93699e15			−0.361085
$490$	−9.87434e14	+	9.87434e14i	−0.0713398	+	0.0713398i
$491$	1.20044e16	−	1.20044e16i	0.856744	−	0.856744i	−0.134209	−	0.990953i	$-0.542849\pi$
$491$	1.20044e16	−	1.20044e16i	0.856744	−	0.856744i	0.990953	+	0.134209i	$0.0428493\pi$
$492$			2.89276e16i			2.03949i
$493$	9.29948e14	−	1.56027e16i	0.0647705	−	1.08672i
$494$	−4.99103e15			−0.343422
$495$	−7.58661e15	−	7.58661e15i	−0.515723	−	0.515723i
$496$	−1.45716e16	−	1.45716e16i	−0.978625	−	0.978625i
$497$			6.14739e15i			0.407899i
$498$			6.34938e15i			0.416251i
$499$			2.08576e16i			1.35102i	0.737351	+	0.675510i	$0.236076\pi$
$499$			2.08576e16i			1.35102i	−0.737351	+	0.675510i	$0.763924\pi$
$500$	1.41895e16			0.908129
$501$	−2.78760e15	+	2.78760e15i	−0.176280	+	0.176280i
$502$		−	3.40341e15i		−	0.212663i
$503$	1.26401e15	−	1.26401e15i	0.0780449	−	0.0780449i	−0.667007	−	0.745052i	$-0.732425\pi$
$503$	1.26401e15	−	1.26401e15i	0.0780449	−	0.0780449i	0.745052	+	0.667007i	$0.232425\pi$
$504$	−1.23823e15	−	1.23823e15i	−0.0755471	−	0.0755471i
$505$	6.63601e15	−	6.63601e15i	0.400091	−	0.400091i
$506$		−	6.47587e15i		−	0.385829i
$507$	−2.94513e15	−	2.94513e15i	−0.173403	−	0.173403i
$508$	2.80509e15	−	2.80509e15i	0.163217	−	0.163217i
$509$	−3.01787e16			−1.73538			−0.867689	−	0.497108i	$-0.834395\pi$
$509$	−3.01787e16			−1.73538			−0.867689	+	0.497108i	$0.834395\pi$
$510$	−2.07296e15	−	2.07296e15i	−0.117807	−	0.117807i
$511$	−2.33646e14	+	2.33646e14i	−0.0131230	+	0.0131230i
$512$	−1.07694e16	−	1.07694e16i	−0.597819	−	0.597819i
$513$	6.33512e15			0.347577
$514$	1.17885e15	+	1.17885e15i	0.0639264	+	0.0639264i
$515$			1.69906e16i			0.910679i
$516$	−9.67535e15			−0.512588
$517$	−1.04326e15			−0.0546324
$518$	3.61706e14			0.0187231
$519$	5.59124e14	−	5.59124e14i	0.0286091	−	0.0286091i
$520$	2.78079e15	−	2.78079e15i	0.140652	−	0.140652i
$521$		−	3.14724e16i		−	1.57364i	−0.617185	−	0.786818i	$-0.711727\pi$
$521$		−	3.14724e16i		−	1.57364i	0.617185	−	0.786818i	$-0.288273\pi$
$522$	−3.49068e15	−	2.08051e14i	−0.172539	−	0.0102836i
$523$	−3.01254e15			−0.147205			−0.0736024	−	0.997288i	$-0.523450\pi$
$523$	−3.01254e15			−0.147205			−0.0736024	+	0.997288i	$0.523450\pi$
$524$	−4.14791e15	−	4.14791e15i	−0.200374	−	0.200374i
$525$	−4.36828e15	−	4.36828e15i	−0.208620	−	0.208620i
$526$			3.08523e15i			0.145671i
$527$			3.65905e16i			1.70807i
$528$			3.91686e16i			1.80773i
$529$	1.44764e16			0.660583
$530$	−1.66638e15	+	1.66638e15i	−0.0751827	+	0.0751827i
$531$			4.13876e15i			0.184630i
$532$	−9.22082e15	+	9.22082e15i	−0.406724	+	0.406724i
$533$	2.28346e16	+	2.28346e16i	0.995933	+	0.995933i
$534$	−6.97439e15	+	6.97439e15i	−0.300787	+	0.300787i
$535$			3.64242e15i			0.155334i
$536$	4.95010e15	+	4.95010e15i	0.208749	+	0.208749i
$537$	1.34636e16	−	1.34636e16i	0.561457	−	0.561457i
$538$	−6.04219e15			−0.249173
$539$	−2.34254e16	−	2.34254e16i	−0.955331	−	0.955331i
$540$	−1.72897e15	+	1.72897e15i	−0.0697307	+	0.0697307i
$541$	−6.86106e14	−	6.86106e14i	−0.0273658	−	0.0273658i	0.693292	−	0.720657i	$-0.256160\pi$
$541$	−6.86106e14	−	6.86106e14i	−0.0273658	−	0.0273658i	−0.720657	+	0.693292i	$0.756160\pi$
$542$	8.84230e14			0.0348795
$543$	−1.57543e16	−	1.57543e16i	−0.614609	−	0.614609i
$544$			1.60050e16i			0.617534i
$545$	−9.64290e15			−0.367984
$546$	−2.06321e15			−0.0778731
$547$	−2.46721e16			−0.921047			−0.460523	−	0.887648i	$-0.652338\pi$
$547$	−2.46721e16			−0.921047			−0.460523	+	0.887648i	$0.652338\pi$
$548$	6.23938e15	−	6.23938e15i	0.230387	−	0.230387i
$549$	−2.79427e15	+	2.79427e15i	−0.102055	+	0.102055i
$550$		−	5.67631e15i		−	0.205064i
$551$	−3.16289e15	+	5.30671e16i	−0.113025	+	1.89634i
$552$	1.94818e16			0.688645
$553$	1.86098e15	+	1.86098e15i	0.0650717	+	0.0650717i
$554$	−1.81846e15	−	1.81846e15i	−0.0628992	−	0.0628992i
$555$			6.66706e15i			0.228127i
$556$		−	7.84909e15i		−	0.265687i
$557$			5.70839e15i			0.191153i	0.995422	+	0.0955767i	$0.0304695\pi$
$557$			5.70839e15i			0.191153i	−0.995422	+	0.0955767i	$0.969530\pi$
$558$	8.18613e15			0.271190
$559$	−7.63744e15	+	7.63744e15i	−0.250309	+	0.250309i
$560$		−	4.81560e15i		−	0.156143i
$561$	4.91779e16	−	4.91779e16i	1.57759	−	1.57759i
$562$	−7.44820e14	−	7.44820e14i	−0.0236392	−	0.0236392i
$563$	1.62877e16	−	1.62877e16i	0.511458	−	0.511458i	−0.403515	−	0.914973i	$-0.632212\pi$
$563$	1.62877e16	−	1.62877e16i	0.511458	−	0.511458i	0.914973	+	0.403515i	$0.132212\pi$
$564$		−	1.53737e15i		−	0.0477644i
$565$	−6.36111e15	−	6.36111e15i	−0.195543	−	0.195543i
$566$	5.63351e15	−	5.63351e15i	0.171349	−	0.171349i
$567$	1.16935e16			0.351921
$568$	−1.20157e16	−	1.20157e16i	−0.357814	−	0.357814i
$569$	1.75909e16	−	1.75909e16i	0.518340	−	0.518340i	−0.398729	−	0.917069i	$-0.630548\pi$
$569$	1.75909e16	−	1.75909e16i	0.518340	−	0.518340i	0.917069	+	0.398729i	$0.130548\pi$
$570$	7.05046e15	+	7.05046e15i	0.205574	+	0.205574i
$571$	−3.60521e16			−1.04019			−0.520096	−	0.854108i	$-0.674104\pi$
$571$	−3.60521e16			−1.04019			−0.520096	+	0.854108i	$0.674104\pi$
$572$	3.23147e16	+	3.23147e16i	0.922622	+	0.922622i
$573$		−	6.88865e16i		−	1.94629i
$574$	−3.50003e15			−0.0978589
$575$	3.18980e16			0.882584
$576$	−2.43190e16			−0.665903
$577$	−1.30295e16	+	1.30295e16i	−0.353081	+	0.353081i	−0.861255	−	0.508174i	$-0.830321\pi$
$577$	−1.30295e16	+	1.30295e16i	−0.353081	+	0.353081i	0.508174	+	0.861255i	$0.330321\pi$
$578$	9.74331e14	−	9.74331e14i	0.0261300	−	0.0261300i
$579$			6.30443e16i			1.67330i
$580$	−1.36197e16	−	1.53462e16i	−0.357767	−	0.403117i
$581$	1.85192e16			0.481466
$582$	1.20669e16	+	1.20669e16i	0.310496	+	0.310496i
$583$	−3.95322e16	−	3.95322e16i	−1.00679	−	1.00679i
$584$		−	9.13369e14i		−	0.0230234i
$585$		−	1.76500e16i		−	0.440362i
$586$			8.04848e15i			0.198760i
$587$	3.13129e16			0.765410			0.382705	−	0.923871i	$-0.374993\pi$
$587$	3.13129e16			0.765410			0.382705	+	0.923871i	$0.374993\pi$
$588$	3.45201e16	−	3.45201e16i	0.835235	−	0.835235i
$589$		−	1.24450e17i		−	2.98059i
$590$	7.12336e14	−	7.12336e14i	0.0168878	−	0.0168878i
$591$	9.02400e15	+	9.02400e15i	0.211775	+	0.211775i
$592$	7.98763e15	−	7.98763e15i	0.185561	−	0.185561i
$593$		−	3.34117e16i		−	0.768370i	−0.923256	−	0.384185i	$-0.874482\pi$
$593$		−	3.34117e16i		−	0.768370i	0.923256	−	0.384185i	$-0.125518\pi$
$594$	1.70151e15	+	1.70151e15i	0.0387360	+	0.0387360i
$595$	−6.04620e15	+	6.04620e15i	−0.136264	+	0.136264i
$596$	−3.96094e16			−0.883733
$597$	7.07205e16	+	7.07205e16i	1.56207	+	1.56207i
$598$	7.53295e15	−	7.53295e15i	0.164724	−	0.164724i
$599$	2.14034e16	+	2.14034e16i	0.463363	+	0.463363i	0.899756	−	0.436393i	$-0.143744\pi$
$599$	2.14034e16	+	2.14034e16i	0.463363	+	0.463363i	−0.436393	+	0.899756i	$0.643744\pi$
$600$	1.70765e16			0.366008
$601$	−2.22215e16	−	2.22215e16i	−0.471549	−	0.471549i	0.430867	−	0.902416i	$-0.358208\pi$
$601$	−2.22215e16	−	2.22215e16i	−0.471549	−	0.471549i	−0.902416	+	0.430867i	$0.858208\pi$
$602$		−	1.17065e15i		−	0.0245950i
$603$	3.14189e16			0.653563
$604$	3.92107e16			0.807576
$605$	−3.44273e16			−0.702054
$606$	9.62366e15	−	9.62366e15i	0.194314	−	0.194314i
$607$	−3.86101e16	+	3.86101e16i	−0.771913	+	0.771913i	−0.978441	−	0.206528i	$-0.933784\pi$
$607$	−3.86101e16	+	3.86101e16i	−0.771913	+	0.771913i	0.206528	+	0.978441i	$0.433784\pi$
$608$		−	5.44352e16i		−	1.07760i
$609$	−1.30749e15	+	2.19370e16i	−0.0256291	+	0.430006i
$610$	9.61865e14			0.0186696
$611$	−1.21356e15	−	1.21356e15i	−0.0233245	−	0.0233245i
$612$	3.36340e16	+	3.36340e16i	0.640133	+	0.640133i
$613$			1.03075e17i			1.94264i	0.237776	+	0.971320i	$0.423582\pi$
$613$			1.03075e17i			1.94264i	−0.237776	+	0.971320i	$0.576418\pi$
$614$		−	1.56873e16i		−	0.292778i
$615$		−	6.45135e16i		−	1.19234i
$616$	−1.01117e16			−0.185072
$617$	−3.66133e16	+	3.66133e16i	−0.663633	+	0.663633i	−0.956234	−	0.292602i	$-0.905479\pi$
$617$	−3.66133e16	+	3.66133e16i	−0.663633	+	0.663633i	0.292602	+	0.956234i	$0.405479\pi$
$618$			2.46401e16i			0.442294i
$619$	1.78622e16	−	1.78622e16i	0.317535	−	0.317535i	−0.530284	−	0.847820i	$-0.677915\pi$
$619$	1.78622e16	−	1.78622e16i	0.317535	−	0.317535i	0.847820	+	0.530284i	$0.177915\pi$
$620$	3.39645e16	+	3.39645e16i	0.597964	+	0.597964i
$621$	−9.56159e15	+	9.56159e15i	−0.166717	+	0.166717i
$622$			1.42859e15i			0.0246697i
$623$	2.03422e16	+	2.03422e16i	0.347912	+	0.347912i
$624$	−4.55623e16	+	4.55623e16i	−0.771788	+	0.771788i
$625$	9.17803e15			0.153982
$626$	−1.40366e16	−	1.40366e16i	−0.233247	−	0.233247i
$627$	−1.67261e17	+	1.67261e17i	−2.75290	+	2.75290i
$628$	−6.86607e16	−	6.86607e16i	−1.11931	−	1.11931i
$629$	−2.00576e16			−0.323874
$630$	1.35267e15	+	1.35267e15i	0.0216347	+	0.0216347i
$631$		−	5.19564e16i		−	0.823120i	−0.911383	−	0.411560i	$-0.864984\pi$
$631$		−	5.19564e16i		−	0.823120i	0.911383	−	0.411560i	$-0.135016\pi$
$632$	−7.27495e15			−0.114164
$633$	7.02769e16			1.09242
$634$	1.43396e16			0.220801
$635$	−6.25583e15	+	6.25583e15i	−0.0954207	+	0.0954207i
$636$	5.82555e16	−	5.82555e16i	0.880226	−	0.880226i
$637$		−	5.44984e16i		−	0.815731i
$638$	−1.51024e16	+	1.34034e16i	−0.223935	+	0.198743i
$639$	−7.62650e16			−1.12026
$640$	1.96582e16	+	1.96582e16i	0.286065	+	0.286065i
$641$	3.54034e16	+	3.54034e16i	0.510384	+	0.510384i	0.914644	−	0.404260i	$-0.132471\pi$
$641$	3.54034e16	+	3.54034e16i	0.510384	+	0.510384i	−0.404260	+	0.914644i	$0.632471\pi$
$642$			5.28230e15i			0.0754420i
$643$		−	4.27443e16i		−	0.604801i	−0.953181	−	0.302400i	$-0.902212\pi$
$643$		−	4.27443e16i		−	0.604801i	0.953181	−	0.302400i	$-0.0977879\pi$
$644$		−	2.78339e16i		−	0.390175i
$645$	2.15777e16			0.299672
$646$	−2.12111e16	+	2.12111e16i	−0.291855	+	0.291855i
$647$			1.44101e16i			0.196445i	0.995164	+	0.0982227i	$0.0313157\pi$
$647$			1.44101e16i			0.196445i	−0.995164	+	0.0982227i	$0.968684\pi$
$648$	−2.28560e16	+	2.28560e16i	−0.308710	+	0.308710i
$649$	1.68991e16	+	1.68991e16i	0.226149	+	0.226149i
$650$	6.60288e15	−	6.60288e15i	0.0875494	−	0.0875494i
$651$		−	5.14454e16i		−	0.675866i
$652$	−1.37868e16	−	1.37868e16i	−0.179465	−	0.179465i
$653$	−4.77412e16	+	4.77412e16i	−0.615764	+	0.615764i	−0.944442	−	0.328678i	$-0.893397\pi$
$653$	−4.77412e16	+	4.77412e16i	−0.615764	+	0.615764i	0.328678	+	0.944442i	$0.393397\pi$
$654$	−1.39843e16			−0.178720
$655$	9.25055e15	+	9.25055e15i	0.117144	+	0.117144i
$656$	−7.72919e16	+	7.72919e16i	−0.969864	+	0.969864i
$657$	−2.89864e15	−	2.89864e15i	−0.0360414	−	0.0360414i
$658$	1.86011e14			0.00229183
$659$	2.08420e15	+	2.08420e15i	0.0254464	+	0.0254464i	0.719716	−	0.694269i	$-0.244272\pi$
$659$	2.08420e15	+	2.08420e15i	0.0254464	+	0.0254464i	−0.694269	+	0.719716i	$0.744272\pi$
$660$		−	9.12971e16i		−	1.10457i
$661$	−8.83707e16			−1.05950			−0.529748	−	0.848155i	$-0.677713\pi$
$661$	−8.83707e16			−1.05950			−0.529748	+	0.848155i	$0.677713\pi$
$662$	1.97450e16			0.234590
$663$	1.14411e17			1.34706
$664$	−3.61976e16	+	3.61976e16i	−0.422349	+	0.422349i
$665$	2.05640e16	−	2.05640e16i	0.237781	−	0.237781i
$666$			4.48735e15i			0.0514215i
$667$	−7.53203e16	−	8.48678e16i	−0.855376	−	0.963802i
$668$	−1.55691e16			−0.175228
$669$	1.40592e17	+	1.40592e17i	1.56821	+	1.56821i
$670$	−5.40762e15	−	5.40762e15i	−0.0597802	−	0.0597802i
$671$			2.28188e16i			0.250010i
$672$		−	2.25026e16i		−	0.244353i
$673$			1.31850e17i			1.41902i	0.704694	+	0.709511i	$0.251084\pi$
$673$			1.31850e17i			1.41902i	−0.704694	+	0.709511i	$0.748916\pi$
$674$	−3.35598e16			−0.357980
$675$	−8.38105e15	+	8.38105e15i	−0.0886086	+	0.0886086i
$676$		−	1.64489e16i		−	0.172368i
$677$	9.70756e16	−	9.70756e16i	1.00827	−	1.00827i	0.00830691	−	0.999965i	$-0.497356\pi$
$677$	9.70756e16	−	9.70756e16i	1.00827	−	1.00827i	0.999965	−	0.00830691i	$-0.00264420\pi$
$678$	−9.22499e15	−	9.22499e15i	−0.0949702	−	0.0949702i
$679$	3.51953e16	−	3.51953e16i	0.359142	−	0.359142i
$680$		−	2.36358e16i		−	0.239065i
$681$	6.38175e16	+	6.38175e16i	0.639819	+	0.639819i
$682$	3.34251e16	−	3.34251e16i	0.332174	−	0.332174i
$683$	−7.72065e16			−0.760553			−0.380277	−	0.924873i	$-0.624171\pi$
$683$	−7.72065e16			−0.760553			−0.380277	+	0.924873i	$0.624171\pi$
$684$	−1.14394e17	−	1.14394e17i	−1.11704	−	1.11704i
$685$	−1.39149e16	+	1.39149e16i	−0.134690	+	0.134690i
$686$	8.81456e15	+	8.81456e15i	0.0845778	+	0.0845778i
$687$	−6.64059e16			−0.631635
$688$	−2.58516e16	−	2.58516e16i	−0.243757	−	0.243757i
$689$		−	9.19704e16i		−	0.859672i
$690$	−2.12825e16			−0.197209
$691$	−3.72874e16			−0.342526			−0.171263	−	0.985225i	$-0.554785\pi$
$691$	−3.72874e16			−0.342526			−0.171263	+	0.985225i	$0.554785\pi$
$692$	3.12277e15			0.0284383
$693$	−3.20901e16	+	3.20901e16i	−0.289716	+	0.289716i
$694$	−4.78443e15	+	4.78443e15i	−0.0428226	+	0.0428226i
$695$			1.75048e16i			0.155328i
$696$	−4.03225e16	−	4.54337e16i	−0.354725	−	0.399689i
$697$	1.94087e17			1.69277
$698$	4.00956e15	+	4.00956e15i	0.0346708	+	0.0346708i
$699$	7.81159e16	+	7.81159e16i	0.669694	+	0.669694i
$700$		−	2.43974e16i		−	0.207374i
$701$			1.25216e17i			1.05524i	0.849481	+	0.527619i	$0.176915\pi$
$701$			1.25216e17i			1.05524i	−0.849481	+	0.527619i	$0.823085\pi$
$702$			3.95850e15i			0.0330756i
$703$	6.82189e16			0.565162
$704$	−9.92977e16	+	9.92977e16i	−0.815649	+	0.815649i
$705$			3.42860e15i			0.0279243i
$706$	1.90991e16	−	1.90991e16i	0.154236	−	0.154236i
$707$	−2.80693e16	−	2.80693e16i	−0.224758	−	0.224758i
$708$	−2.49029e16	+	2.49029e16i	−0.197720	+	0.197720i
$709$		−	6.62555e16i		−	0.521608i	−0.965392	−	0.260804i	$-0.916012\pi$
$709$		−	6.62555e16i		−	0.521608i	0.965392	−	0.260804i	$-0.0839877\pi$
$710$	1.31262e16	+	1.31262e16i	0.102468	+	0.102468i
$711$	−2.30875e16	+	2.30875e16i	−0.178715	+	0.178715i
$712$	−7.95215e16			−0.610386
$713$	1.87832e17	+	1.87832e17i	1.42966	+	1.42966i
$714$	−8.76830e15	+	8.76830e15i	−0.0661799	+	0.0661799i
$715$	−7.20673e16	−	7.20673e16i	−0.539389	−	0.539389i
$716$	7.51959e16			0.558105
$717$	−4.76095e16	−	4.76095e16i	−0.350412	−	0.350412i
$718$			2.94530e16i			0.214972i
$719$	−5.37823e16			−0.389284			−0.194642	−	0.980874i	$-0.562354\pi$
$719$	−5.37823e16			−0.389284			−0.194642	+	0.980874i	$0.562354\pi$
$720$	5.97428e16			0.428835
$721$	7.18675e16			0.511588
$722$	5.21518e16	−	5.21518e16i	0.368168	−	0.368168i
$723$	2.41156e17	−	2.41156e17i	1.68838	−	1.68838i
$724$		−	8.79894e16i		−	0.610941i
$725$	−6.60207e16	−	7.43894e16i	−0.454624	−	0.512251i
$726$	−4.99270e16			−0.340970
$727$	−9.65989e15	−	9.65989e15i	−0.0654283	−	0.0654283i	0.673635	−	0.739064i	$-0.264732\pi$
$727$	−9.65989e15	−	9.65989e15i	−0.0654283	−	0.0654283i	−0.739064	+	0.673635i	$0.764732\pi$
$728$	−1.17623e16	−	1.17623e16i	−0.0790138	−	0.0790138i
$729$			1.07556e17i			0.716588i
$730$			9.97789e14i			0.00659328i
$731$			6.49157e16i			0.425447i
$732$	−3.36262e16			−0.218581
$733$	2.03834e17	−	2.03834e17i	1.31417	−	1.31417i	0.395863	−	0.918310i	$-0.370446\pi$
$733$	2.03834e17	−	2.03834e17i	1.31417	−	1.31417i	0.918310	−	0.395863i	$-0.129554\pi$
$734$		−	2.53045e16i		−	0.161816i
$735$	−7.69858e16	+	7.69858e16i	−0.488300	+	0.488300i
$736$	8.21590e16	+	8.21590e16i	0.516878	+	0.516878i
$737$	1.28287e17	−	1.28287e17i	0.800533	−	0.800533i
$738$		−	4.34217e16i		−	0.268762i
$739$	1.56678e17	+	1.56678e17i	0.961928	+	0.961928i	0.999301	−	0.0373736i	$-0.0118991\pi$
$739$	1.56678e17	+	1.56678e17i	0.961928	+	0.961928i	−0.0373736	+	0.999301i	$0.511899\pi$
$740$	−1.86181e16	+	1.86181e16i	−0.113383	+	0.113383i
$741$	−3.89128e17			−2.35062
$742$	7.04850e15	+	7.04850e15i	0.0422351	+	0.0422351i
$743$	8.95378e16	−	8.95378e16i	0.532199	−	0.532199i	−0.389027	−	0.921226i	$-0.627189\pi$
$743$	8.95378e16	−	8.95378e16i	0.532199	−	0.532199i	0.921226	+	0.389027i	$0.127189\pi$
$744$	1.00555e17	+	1.00555e17i	0.592879	+	0.592879i
$745$	8.83358e16			0.516653
$746$	−1.09030e16	−	1.09030e16i	−0.0632575	−	0.0632575i
$747$			2.29751e17i			1.32231i
$748$	2.74664e17			1.56817
$749$	1.54068e16			0.0872615
$750$	−4.58922e16			−0.257852
$751$	−1.05375e17	+	1.05375e17i	−0.587352	+	0.587352i	−0.936913	−	0.349562i	$-0.886331\pi$
$751$	−1.05375e17	+	1.05375e17i	−0.587352	+	0.587352i	0.349562	+	0.936913i	$0.386331\pi$
$752$	4.10772e15	−	4.10772e15i	0.0227140	−	0.0227140i
$753$		−	2.65348e17i		−	1.45562i
$754$	−3.31590e16	−	1.97633e15i	−0.180457	−	0.0107555i
$755$	−8.74466e16			−0.472130
$756$	7.31325e15	+	7.31325e15i	0.0391723	+	0.0391723i
$757$	−2.54282e17	−	2.54282e17i	−1.35127	−	1.35127i	−0.884248	−	0.467017i	$-0.845329\pi$
$757$	−2.54282e17	−	2.54282e17i	−1.35127	−	1.35127i	−0.467017	−	0.884248i	$-0.654671\pi$
$758$			2.73859e16i			0.144381i
$759$		−	5.04894e17i		−	2.64089i
$760$			8.03887e16i			0.417170i
$761$	2.81203e17			1.44781			0.723906	−	0.689898i	$-0.242345\pi$
$761$	2.81203e17			1.44781			0.723906	+	0.689898i	$0.242345\pi$
$762$	−9.07231e15	+	9.07231e15i	−0.0463434	+	0.0463434i
$763$			4.07879e16i			0.206721i
$764$	1.92370e17	−	1.92370e17i	0.967334	−	0.967334i
$765$	−7.50097e16	−	7.50097e16i	−0.374239	−	0.374239i
$766$	−1.55217e16	+	1.55217e16i	−0.0768364	+	0.0768364i
$767$			3.93152e16i			0.193103i
$768$	−1.23889e17	−	1.23889e17i	−0.603759	−	0.603759i
$769$	−1.20701e17	+	1.20701e17i	−0.583650	+	0.583650i	−0.935904	−	0.352254i	$-0.885415\pi$
$769$	−1.20701e17	+	1.20701e17i	−0.583650	+	0.583650i	0.352254	+	0.935904i	$0.385415\pi$
$770$	1.10463e16			0.0529995
$771$	9.19097e16	+	9.19097e16i	0.437557	+	0.437557i
$772$	−1.76055e17	+	1.76055e17i	−0.831656	+	0.831656i
$773$	−2.46701e17	−	2.46701e17i	−1.15636	−	1.15636i	−0.985251	−	0.171113i	$-0.945264\pi$
$773$	−2.46701e17	−	2.46701e17i	−1.15636	−	1.15636i	−0.171113	−	0.985251i	$-0.554736\pi$
$774$	1.45231e16			0.0675484
$775$	1.64641e17	+	1.64641e17i	0.759848	+	0.759848i
$776$			1.37585e17i			0.630089i
$777$	2.82006e16			0.128154
$778$	7.07036e14			0.00318833
$779$	−6.60117e17			−2.95390
$780$	1.06200e17	−	1.06200e17i	0.471581	−	0.471581i
$781$	−3.11400e17	+	3.11400e17i	−1.37218	+	1.37218i
$782$		−	6.40277e16i		−	0.279980i
$783$	4.20887e16	+	2.50856e15i	0.182640	+	0.0108856i
$784$	1.84469e17			0.794379
$785$	1.53125e17	+	1.53125e17i	0.654378	+	0.654378i
$786$	1.34153e16	+	1.34153e16i	0.0568939	+	0.0568939i
$787$		−	3.94368e16i		−	0.165979i	−0.996550	−	0.0829894i	$-0.973553\pi$
$787$		−	3.94368e16i		−	0.165979i	0.996550	−	0.0829894i	$-0.0264468\pi$
$788$			5.04001e16i			0.210511i
$789$			2.40542e17i			0.997075i
$790$	7.94735e15			0.0326934
$791$	−2.69064e16	+	2.69064e16i	−0.109849	+	0.109849i
$792$		−	1.25447e17i		−	0.508285i
$793$	−2.65436e16	+	2.65436e16i	−0.106738	+	0.106738i
$794$	9.05849e15	+	9.05849e15i	0.0361520	+	0.0361520i
$795$	−1.29920e17	+	1.29920e17i	−0.514603	+	0.514603i
$796$			3.94982e17i			1.55274i
$797$	4.98166e16	+	4.98166e16i	0.194368	+	0.194368i	0.797580	−	0.603213i	$-0.206113\pi$
$797$	4.98166e16	+	4.98166e16i	0.194368	+	0.194368i	−0.603213	+	0.797580i	$0.706113\pi$
$798$	2.98223e16	−	2.98223e16i	0.115484	−	0.115484i
$799$	−1.03148e16			−0.0396444
$800$	7.20150e16	+	7.20150e16i	0.274716	+	0.274716i
$801$	−2.52367e17	+	2.52367e17i	−0.955513	+	0.955513i
$802$	3.14617e16	+	3.14617e16i	0.118232	+	0.118232i
$803$	−2.36710e16			−0.0882925
$804$	1.89047e17	+	1.89047e17i	0.699897	+	0.699897i
$805$			6.20745e16i			0.228106i
$806$	7.77623e16			0.283634
$807$	−4.71082e17			−1.70552
$808$	1.09728e17			0.394321
$809$	1.13875e17	−	1.13875e17i	0.406199	−	0.406199i	−0.474212	−	0.880411i	$-0.657267\pi$
$809$	1.13875e17	−	1.13875e17i	0.406199	−	0.406199i	0.880411	+	0.474212i	$0.157267\pi$
$810$	2.49685e16	−	2.49685e16i	0.0884062	−	0.0884062i
$811$			1.93467e17i			0.679956i	0.940433	+	0.339978i	$0.110420\pi$
$811$			1.93467e17i			0.679956i	−0.940433	+	0.339978i	$0.889580\pi$
$812$	−6.49117e16	+	5.76092e16i	−0.226458	+	0.200981i
$813$	6.89394e16			0.238740
$814$	1.83224e16	+	1.83224e16i	0.0629850	+	0.0629850i
$815$	3.07470e16	+	3.07470e16i	0.104920	+	0.104920i
$816$			3.87264e17i			1.31180i
$817$		−	2.20788e17i		−	0.742409i
$818$		−	1.01607e17i		−	0.339161i
$819$	−7.46566e16			−0.247380
$820$	1.80158e17	−	1.80158e17i	0.592611	−	0.592611i
$821$		−	1.31026e17i		−	0.427857i	−0.976849	−	0.213929i	$-0.931374\pi$
$821$		−	1.31026e17i		−	0.427857i	0.976849	−	0.213929i	$-0.0686260\pi$
$822$	−2.01796e16	+	2.01796e16i	−0.0654156	+	0.0654156i
$823$	1.41384e17	+	1.41384e17i	0.454988	+	0.454988i	0.897006	−	0.442018i	$-0.145737\pi$
$823$	1.41384e17	+	1.41384e17i	0.454988	+	0.454988i	−0.442018	+	0.897006i	$0.645737\pi$
$824$	−1.40472e17	+	1.40472e17i	−0.448773	+	0.448773i
$825$		−	4.42556e17i		−	1.40361i
$826$	−3.01307e15	−	3.01307e15i	−0.00948699	−	0.00948699i
$827$	2.81531e17	−	2.81531e17i	0.880022	−	0.880022i	−0.113515	−	0.993536i	$-0.536211\pi$
$827$	2.81531e17	−	2.81531e17i	0.880022	−	0.880022i	0.993536	+	0.113515i	$0.0362109\pi$
$828$	3.45310e17			1.07159
$829$	−2.80287e17	−	2.80287e17i	−0.863527	−	0.863527i	0.128219	−	0.991746i	$-0.459074\pi$
$829$	−2.80287e17	−	2.80287e17i	−0.863527	−	0.863527i	−0.991746	+	0.128219i	$0.959074\pi$
$830$	3.95432e16	−	3.95432e16i	0.120949	−	0.120949i
$831$	−1.41777e17	−	1.41777e17i	−0.430527	−	0.430527i
$832$	−2.31013e17			−0.696460
$833$	−2.31609e17	−	2.31609e17i	−0.693244	−	0.693244i
$834$			2.53858e16i			0.0754387i
$835$	3.47217e16			0.102443
$836$	−9.34174e17			−2.73646
$837$	−9.87039e16			−0.287066
$838$	3.19726e16	−	3.19726e16i	0.0923240	−	0.0923240i
$839$	1.60217e17	−	1.60217e17i	0.459341	−	0.459341i	−0.439098	−	0.898439i	$-0.644702\pi$
$839$	1.60217e17	−	1.60217e17i	0.459341	−	0.459341i	0.898439	+	0.439098i	$0.144702\pi$
$840$			3.32314e16i			0.0945959i
$841$	−4.20266e16	+	3.51310e17i	−0.118781	+	0.992920i
$842$	1.21055e16			0.0339711
$843$	−5.80702e16	−	5.80702e16i	−0.161804	−	0.161804i
$844$	1.96252e17	+	1.96252e17i	0.542950	+	0.542950i
$845$			3.66838e16i			0.100771i
$846$			2.30767e15i			0.00629435i
$847$			1.45622e17i			0.394390i
$848$	3.11307e17			0.837170
$849$	4.39220e17	−	4.39220e17i	1.17283	−	1.17283i
$850$		−	5.61223e16i		−	0.148807i
$851$	−1.02963e17	+	1.02963e17i	−0.271083	+	0.271083i
$852$	−4.58886e17	−	4.58886e17i	−1.19968	−	1.19968i
$853$	1.32454e17	−	1.32454e17i	0.343852	−	0.343852i	−0.513961	−	0.857813i	$-0.671822\pi$
$853$	1.32454e17	−	1.32454e17i	0.343852	−	0.343852i	0.857813	+	0.513961i	$0.171822\pi$
$854$		−	4.06853e15i		−	0.0104879i
$855$	2.55119e17	+	2.55119e17i	0.653049	+	0.653049i
$856$	−3.01142e16	+	3.01142e16i	−0.0765471	+	0.0765471i
$857$	6.30560e17			1.59163			0.795814	−	0.605541i	$-0.207043\pi$
$857$	6.30560e17			1.59163			0.795814	+	0.605541i	$0.207043\pi$
$858$	−1.04513e17	−	1.04513e17i	−0.261967	−	0.261967i
$859$	4.08706e17	−	4.08706e17i	1.01731	−	1.01731i	0.0174606	−	0.999848i	$-0.494442\pi$
$859$	4.08706e17	−	4.08706e17i	1.01731	−	1.01731i	0.999848	−	0.0174606i	$-0.00555817\pi$
$860$	6.02569e16	+	6.02569e16i	0.148942	+	0.148942i
$861$	−2.72881e17			−0.669815
$862$	8.59036e16	+	8.59036e16i	0.209396	+	0.209396i
$863$		−	3.34123e17i		−	0.808802i	−0.914582	−	0.404401i	$-0.867480\pi$
$863$		−	3.34123e17i		−	0.808802i	0.914582	−	0.404401i	$-0.132520\pi$
$864$	−4.31738e16			−0.103786
$865$	−6.96432e15			−0.0166258
$866$	−6.89168e16			−0.163387
$867$	7.59642e16	−	7.59642e16i	0.178852	−	0.178852i
$868$	1.43664e17	−	1.43664e17i	0.335916	−	0.335916i
$869$			1.88539e17i			0.437806i
$870$	4.40494e16	+	4.96330e16i	0.101584	+	0.114460i
$871$	2.98457e17			0.683553
$872$	−7.97239e16	−	7.97239e16i	−0.181338	−	0.181338i
$873$	4.36636e17	+	4.36636e17i	0.986358	+	0.986358i
$874$			2.17767e17i			0.488567i
$875$			1.33853e17i			0.298250i
$876$		−	3.48821e16i		−	0.0771931i
$877$	−5.97630e17			−1.31352			−0.656758	−	0.754102i	$-0.728073\pi$
$877$	−5.97630e17			−1.31352			−0.656758	+	0.754102i	$0.728073\pi$
$878$	8.67848e15	−	8.67848e15i	0.0189442	−	0.0189442i
$879$			6.27504e17i			1.36045i
$880$	2.43938e17	−	2.43938e17i	0.525270	−	0.525270i
$881$	−3.92447e17	−	3.92447e17i	−0.839317	−	0.839317i	0.149452	−	0.988769i	$-0.452249\pi$
$881$	−3.92447e17	−	3.92447e17i	−0.839317	−	0.839317i	−0.988769	+	0.149452i	$0.952249\pi$
$882$	−5.18163e16	+	5.18163e16i	−0.110066	+	0.110066i
$883$			1.74449e17i			0.368047i	0.982922	+	0.184023i	$0.0589122\pi$
$883$			1.74449e17i			0.368047i	−0.982922	+	0.184023i	$0.941088\pi$
$884$	3.19499e17	+	3.19499e17i	0.669508	+	0.669508i
$885$	5.55376e16	−	5.55376e16i	0.115592	−	0.115592i
$886$	−1.74927e17			−0.361622
$887$	−9.24889e16	−	9.24889e16i	−0.189910	−	0.189910i	0.605747	−	0.795657i	$-0.292874\pi$
$887$	−9.24889e16	−	9.24889e16i	−0.189910	−	0.189910i	−0.795657	+	0.605747i	$0.792874\pi$
$888$	−5.51208e16	+	5.51208e16i	−0.112418	+	0.112418i
$889$	2.64611e16	+	2.64611e16i	0.0536041	+	0.0536041i
$890$	8.68714e16			0.174798
$891$	5.92340e17	+	5.92340e17i	1.18387	+	1.18387i
$892$			7.85223e17i			1.55885i
$893$	3.50823e16			0.0691798
$894$	1.28106e17			0.250925
$895$	−1.67700e17			−0.326283
$896$	8.31511e16	−	8.31511e16i	0.160702	−	0.160702i
$897$	5.87310e17	−	5.87310e17i	1.12749	−	1.12749i
$898$			4.70051e16i			0.0896369i
$899$	4.92791e16	−	8.26807e17i	0.0933479	−	1.56620i
$900$	3.02676e17			0.569538
$901$	−3.90859e17	−	3.90859e17i	−0.730587	−	0.730587i
$902$	−1.77296e17	−	1.77296e17i	−0.329200	−	0.329200i
$903$		−	9.12700e16i		−	0.168346i
$904$		−	1.05183e17i		−	0.192723i
$905$			1.96231e17i			0.357172i
$906$	−1.26817e17			−0.229301
$907$	6.21125e17	−	6.21125e17i	1.11567	−	1.11567i	0.123299	−	0.992370i	$-0.460653\pi$
$907$	6.21125e17	−	6.21125e17i	1.11567	−	1.11567i	0.992370	−	0.123299i	$-0.0393473\pi$
$908$			3.56428e17i			0.636000i
$909$	3.48229e17	−	3.48229e17i	0.617280	−	0.617280i
$910$	1.28494e16	+	1.28494e16i	0.0226274	+	0.0226274i
$911$	−7.65901e17	+	7.65901e17i	−1.33987	+	1.33987i	−0.443687	+	0.896182i	$0.646330\pi$
$911$	−7.65901e17	+	7.65901e17i	−1.33987	+	1.33987i	−0.896182	+	0.443687i	$0.853670\pi$
$912$		−	1.31714e18i		−	2.28910i
$913$	9.38102e17	+	9.38102e17i	1.61967	+	1.61967i
$914$	−8.05709e16	+	8.05709e16i	−0.138198	+	0.138198i
$915$	7.49922e16			0.127788
$916$	−1.85442e17	−	1.85442e17i	−0.313932	−	0.313932i
$917$	3.91283e16	−	3.91283e16i	0.0658075	−	0.0658075i
$918$	1.68230e16	+	1.68230e16i	0.0281091	+	0.0281091i
$919$	−6.14056e17			−1.01933			−0.509665	−	0.860373i	$-0.670231\pi$
$919$	−6.14056e17			−1.01933			−0.509665	+	0.860373i	$0.670231\pi$
$920$	−1.21331e17	−	1.21331e17i	−0.200098	−	0.200098i
$921$		−	1.22307e18i		−	2.00398i
$922$	−1.28648e17			−0.209419
$923$	−7.24462e17			−1.17167
$924$	−3.86172e17			−0.620510
$925$	−9.02502e16	+	9.02502e16i	−0.144078	+	0.144078i
$926$	7.41731e16	−	7.41731e16i	0.117647	−	0.117647i
$927$			8.91594e17i			1.40504i
$928$	2.15551e16	−	3.61652e17i	0.0337490	−	0.566243i
$929$	−5.12816e17			−0.797751			−0.398875	−	0.917005i	$-0.630599\pi$
$929$	−5.12816e17			−0.797751			−0.398875	+	0.917005i	$0.630599\pi$
$930$	−1.09849e17	−	1.09849e17i	−0.169785	−	0.169785i
$931$	7.87737e17	+	7.87737e17i	1.20972	+	1.20972i
$932$			4.36286e17i			0.665696i
$933$			1.11380e17i			0.168857i
$934$		−	2.33384e17i		−	0.351553i
$935$	−6.12548e17			−0.916792
$936$	1.45924e17	−	1.45924e17i	0.217005	−	0.217005i
$937$			2.91649e17i			0.430946i	0.976510	+	0.215473i	$0.0691294\pi$
$937$			2.91649e17i			0.430946i	−0.976510	+	0.215473i	$0.930871\pi$
$938$	−2.28733e16	+	2.28733e16i	−0.0335825	+	0.0335825i
$939$	−1.09437e18	−	1.09437e18i	−1.59650	−	1.59650i
$940$	−9.57458e15	+	9.57458e15i	−0.0138788	+	0.0138788i
$941$			2.24473e17i			0.323316i	0.986847	+	0.161658i	$0.0516841\pi$
$941$			2.24473e17i			0.323316i	−0.986847	+	0.161658i	$0.948316\pi$
$942$	2.22065e17	+	2.22065e17i	0.317815	+	0.317815i
$943$	9.96314e17	−	9.96314e17i	1.41686	−	1.41686i
$944$	−1.33076e17			−0.188048
$945$	−1.63098e16	−	1.63098e16i	−0.0229012	−	0.0229012i
$946$	5.92999e16	−	5.92999e16i	0.0827384	−	0.0827384i
$947$	−1.75992e17	−	1.75992e17i	−0.244001	−	0.244001i	0.574502	−	0.818503i	$-0.305196\pi$
$947$	−1.75992e17	−	1.75992e17i	−0.244001	−	0.244001i	−0.818503	+	0.574502i	$0.805196\pi$
$948$	−2.77835e17			−0.382769
$949$	−2.75349e16	−	2.75349e16i	−0.0376953	−	0.0376953i
$950$			1.90880e17i			0.259669i
$951$	1.11799e18			1.51132
$952$	−9.99755e16			−0.134299
$953$	1.74661e17			0.233152			0.116576	−	0.993182i	$-0.462808\pi$
$953$	1.74661e17			0.233152			0.116576	+	0.993182i	$0.462808\pi$
$954$	−8.74442e16	+	8.74442e16i	−0.115995	+	0.115995i
$955$	−4.29017e17	+	4.29017e17i	−0.565528	+	0.565528i
$956$		−	2.65905e17i		−	0.348320i
$957$	−1.17747e18	+	1.04500e18i	−1.53277	+	1.36034i
$958$	1.84899e17			0.239189
$959$	5.88577e16	+	5.88577e16i	0.0756644	+	0.0756644i
$960$	3.26335e17	+	3.26335e17i	0.416904	+	0.416904i
$961$			1.15131e18i			1.46168i
$962$			4.26266e16i			0.0537812i
$963$			1.91139e17i			0.239657i
$964$	1.34689e18			1.67830
$965$	3.92632e17	−	3.92632e17i	0.486208	−	0.486208i
$966$			9.00214e16i			0.110786i
$967$	−1.01330e18	+	1.01330e18i	−1.23931	+	1.23931i	−0.279020	+	0.960285i	$0.590010\pi$
$967$	−1.01330e18	+	1.01330e18i	−1.23931	+	1.23931i	−0.960285	+	0.279020i	$0.909990\pi$
$968$	−2.84632e17	−	2.84632e17i	−0.345964	−	0.345964i
$969$	−1.65373e18	+	1.65373e18i	−1.99766	+	1.99766i
$970$		−	1.50302e17i		−	0.180441i
$971$	2.78447e17	+	2.78447e17i	0.332221	+	0.332221i	0.853429	−	0.521208i	$-0.174519\pi$
$971$	2.78447e17	+	2.78447e17i	0.332221	+	0.332221i	−0.521208	+	0.853429i	$0.674519\pi$
$972$	−7.68125e17	+	7.68125e17i	−0.910824	+	0.910824i
$973$	7.40425e16			0.0872577
$974$	7.63692e16	+	7.63692e16i	0.0894467	+	0.0894467i
$975$	5.14797e17	−	5.14797e17i	0.599250	−	0.599250i
$976$	−8.98462e16	−	8.98462e16i	−0.103944	−	0.103944i
$977$	−4.26282e17			−0.490151			−0.245075	−	0.969504i	$-0.578813\pi$
$977$	−4.26282e17			−0.490151			−0.245075	+	0.969504i	$0.578813\pi$
$978$	4.45898e16	+	4.45898e16i	0.0509569	+	0.0509569i
$979$			2.06089e18i			2.34077i
$980$	−4.29975e17			−0.485385
$981$	−5.06018e17			−0.567743
$982$	−2.16842e17			−0.241810
$983$	1.11043e18	−	1.11043e18i	1.23076	−	1.23076i	0.267082	−	0.963674i	$-0.413940\pi$
$983$	1.11043e18	−	1.11043e18i	1.23076	−	1.23076i	0.963674	−	0.267082i	$-0.0860595\pi$
$984$	5.33373e17	−	5.33373e17i	0.587571	−	0.587571i
$985$		−	1.12401e17i		−	0.123070i
$986$	−1.49319e17	+	1.32521e17i	−0.162500	+	0.144219i
$987$	1.45024e16			0.0156869
$988$	−1.08666e18	−	1.08666e18i	−1.16830	−	1.16830i
$989$	3.33235e17	+	3.33235e17i	0.356101	+	0.356101i
$990$			1.37041e17i			0.145559i
$991$		−	1.30389e18i		−	1.37657i	−0.725440	−	0.688285i	$-0.758364\pi$
$991$		−	1.30389e18i		−	1.37657i	0.725440	−	0.688285i	$-0.241636\pi$
$992$			8.48123e17i			0.889998i
$993$	1.53943e18			1.60570
$994$	5.55219e16	−	5.55219e16i	0.0575633	−	0.0575633i
$995$		−	8.80878e17i		−	0.907773i
$996$	−1.38241e18	+	1.38241e18i	−1.41605	+	1.41605i
$997$	−4.12854e17	−	4.12854e17i	−0.420364	−	0.420364i	0.464965	−	0.885329i	$-0.346067\pi$
$997$	−4.12854e17	−	4.12854e17i	−0.420364	−	0.420364i	−0.885329	+	0.464965i	$0.846067\pi$
$998$	1.88381e17	−	1.88381e17i	0.190658	−	0.190658i
$999$		−	5.41060e16i		−	0.0544318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.13.c.a.12.14	✓	58
29.17	odd	4	inner	29.13.c.a.17.14	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.13.c.a.12.14	✓	58	1.1	even	1	trivial
29.13.c.a.17.14	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)

\(f(q)\)	\(=\)	\(q+(-9.03178 - 9.03178i) q^{2} +(-704.167 - 704.167i) q^{3} -3932.85i q^{4} +8770.94i q^{5} +12719.8i q^{6} +37099.6 q^{7} +(-72514.8 + 72514.8i) q^{8} +460261. i q^{9} +O(q^{10})\)	\(q+(-9.03178 - 9.03178i) q^{2} +(-704.167 - 704.167i) q^{3} -3932.85i q^{4} +8770.94i q^{5} +12719.8i q^{6} +37099.6 q^{7} +(-72514.8 + 72514.8i) q^{8} +460261. i q^{9} +(79217.2 - 79217.2i) q^{10} +(1.87931e6 + 1.87931e6i) q^{11} +(-2.76939e6 + 2.76939e6i) q^{12} +4.37215e6i q^{13} +(-335076. - 335076. i) q^{14} +(6.17620e6 - 6.17620e6i) q^{15} -1.47991e7 q^{16} +(1.85809e7 + 1.85809e7i) q^{17} +(4.15698e6 - 4.15698e6i) q^{18} +(-6.31964e7 - 6.31964e7i) q^{19} +3.44948e7 q^{20} +(-2.61243e7 - 2.61243e7i) q^{21} -3.39470e7i q^{22} +1.90764e8 q^{23} +1.02125e8 q^{24} +1.67211e8 q^{25} +(3.94883e7 - 3.94883e7i) q^{26} +(-5.01225e7 + 5.01225e7i) q^{27} -1.45907e8i q^{28} +(-3.94834e8 - 4.44883e8i) q^{29} -1.11564e8 q^{30} +(9.84626e8 + 9.84626e8i) q^{31} +(4.30683e8 + 4.30683e8i) q^{32} -2.64669e9i q^{33} -3.35637e8i q^{34} +3.25399e8i q^{35} +1.81014e9 q^{36} +(-5.39738e8 + 5.39738e8i) q^{37} +1.14155e9i q^{38} +(3.07872e9 - 3.07872e9i) q^{39} +(-6.36023e8 - 6.36023e8i) q^{40} +(5.22274e9 - 5.22274e9i) q^{41} +4.71898e8i q^{42} +(1.74684e9 + 1.74684e9i) q^{43} +(7.39104e9 - 7.39104e9i) q^{44} -4.03692e9 q^{45} +(-1.72294e9 - 1.72294e9i) q^{46} +(-2.77566e8 + 2.77566e8i) q^{47} +(1.04210e10 + 1.04210e10i) q^{48} -1.24649e10 q^{49} +(-1.51022e9 - 1.51022e9i) q^{50} -2.61681e10i q^{51} +1.71950e10 q^{52} -2.10355e10 q^{53} +9.05391e8 q^{54} +(-1.64833e10 + 1.64833e10i) q^{55} +(-2.69027e9 + 2.69027e9i) q^{56} +8.90016e10i q^{57} +(-4.52028e8 + 7.58414e9i) q^{58} +8.99219e9 q^{59} +(-2.42901e10 - 2.42901e10i) q^{60} +(6.07106e9 + 6.07106e9i) q^{61} -1.77858e10i q^{62} +1.70755e10i q^{63} +5.28374e10i q^{64} -3.83478e10 q^{65} +(-2.39043e10 + 2.39043e10i) q^{66} -6.82632e10i q^{67} +(7.30760e10 - 7.30760e10i) q^{68} +(-1.34330e11 - 1.34330e11i) q^{69} +(2.93893e9 - 2.93893e9i) q^{70} +1.65699e11i q^{71} +(-3.33758e10 - 3.33758e10i) q^{72} +(-6.29781e9 + 6.29781e9i) q^{73} +9.74958e9 q^{74} +(-1.17745e11 - 1.17745e11i) q^{75} +(-2.48542e11 + 2.48542e11i) q^{76} +(6.97216e10 + 6.97216e10i) q^{77} -5.56126e10 q^{78} +(5.01618e10 + 5.01618e10i) q^{79} -1.29802e11i q^{80} +3.15191e11 q^{81} -9.43413e10 q^{82} +4.99175e11 q^{83} +(-1.02743e11 + 1.02743e11i) q^{84} +(-1.62972e11 + 1.62972e11i) q^{85} -3.15541e10i q^{86} +(-3.52425e10 + 5.91301e11i) q^{87} -2.72555e11 q^{88} +(5.48312e11 + 5.48312e11i) q^{89} +(3.64606e10 + 3.64606e10i) q^{90} +1.62205e11i q^{91} -7.50248e11i q^{92} -1.38668e12i q^{93} +5.01382e9 q^{94} +(5.54292e11 - 5.54292e11i) q^{95} -6.06545e11i q^{96} +(9.48671e11 - 9.48671e11i) q^{97} +(1.12580e11 + 1.12580e11i) q^{98} +(-8.64971e11 + 8.64971e11i) 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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