LMFDB - Embedded newform 29.13.c.a.12.4

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			12.4
Character	$\chi$	$=$	29.12
Dual form			29.13.c.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-70.5170 - 70.5170i) q^{2} +(-767.125 - 767.125i) q^{3} +5849.31i q^{4} +9904.63i q^{5} +108191. i q^{6} +71097.8 q^{7} +(123638. - 123638. i) q^{8} +645520. i q^{9} +O(q^{10})$	\(q+(-70.5170 - 70.5170i) q^{2} +(-767.125 - 767.125i) q^{3} +5849.31i q^{4} +9904.63i q^{5} +108191. i q^{6} +71097.8 q^{7} +(123638. - 123638. i) q^{8} +645520. i q^{9} +(698445. - 698445. i) q^{10} +(-139434. - 139434. i) q^{11} +(4.48715e6 - 4.48715e6i) q^{12} -6.95609e6i q^{13} +(-5.01360e6 - 5.01360e6i) q^{14} +(7.59809e6 - 7.59809e6i) q^{15} +6.52159e6 q^{16} +(1.27794e7 + 1.27794e7i) q^{17} +(4.55202e7 - 4.55202e7i) q^{18} +(-9.77674e6 - 9.77674e6i) q^{19} -5.79352e7 q^{20} +(-5.45409e7 - 5.45409e7i) q^{21} +1.96650e7i q^{22} +1.25678e8 q^{23} -1.89692e8 q^{24} +1.46039e8 q^{25} +(-4.90523e8 + 4.90523e8i) q^{26} +(8.75131e7 - 8.75131e7i) q^{27} +4.15873e8i q^{28} +(5.61762e8 + 1.95547e8i) q^{29} -1.07159e9 q^{30} +(-4.08217e8 - 4.08217e8i) q^{31} +(-9.66304e8 - 9.66304e8i) q^{32} +2.13927e8i q^{33} -1.80233e9i q^{34} +7.04197e8i q^{35} -3.77585e9 q^{36} +(-7.79180e8 + 7.79180e8i) q^{37} +1.37885e9i q^{38} +(-5.33619e9 + 5.33619e9i) q^{39} +(1.22459e9 + 1.22459e9i) q^{40} +(-2.47439e8 + 2.47439e8i) q^{41} +7.69212e9i q^{42} +(1.69200e9 + 1.69200e9i) q^{43} +(8.15593e8 - 8.15593e8i) q^{44} -6.39364e9 q^{45} +(-8.86244e9 - 8.86244e9i) q^{46} +(1.04888e10 - 1.04888e10i) q^{47} +(-5.00287e9 - 5.00287e9i) q^{48} -8.78639e9 q^{49} +(-1.02982e10 - 1.02982e10i) q^{50} -1.96068e10i q^{51} +4.06883e10 q^{52} +3.92148e10 q^{53} -1.23423e10 q^{54} +(1.38104e9 - 1.38104e9i) q^{55} +(8.79039e9 - 8.79039e9i) q^{56} +1.50000e10i q^{57} +(-2.58244e10 - 5.34032e10i) q^{58} -1.72085e10 q^{59} +(4.44435e10 + 4.44435e10i) q^{60} +(-2.60466e9 - 2.60466e9i) q^{61} +5.75726e10i q^{62} +4.58951e10i q^{63} +1.09569e11i q^{64} +6.88975e10 q^{65} +(1.50855e10 - 1.50855e10i) q^{66} +2.01604e10i q^{67} +(-7.47506e10 + 7.47506e10i) q^{68} +(-9.64107e10 - 9.64107e10i) q^{69} +(4.96579e10 - 4.96579e10i) q^{70} -9.62631e10i q^{71} +(7.98108e10 + 7.98108e10i) q^{72} +(-1.16297e11 + 1.16297e11i) q^{73} +1.09891e11 q^{74} +(-1.12030e11 - 1.12030e11i) q^{75} +(5.71871e10 - 5.71871e10i) q^{76} +(-9.91345e9 - 9.91345e9i) q^{77} +7.52585e11 q^{78} +(-2.86222e11 - 2.86222e11i) q^{79} +6.45939e10i q^{80} +2.08789e11 q^{81} +3.48974e10 q^{82} -1.02532e11 q^{83} +(3.19026e11 - 3.19026e11i) q^{84} +(-1.26575e11 + 1.26575e11i) q^{85} -2.38630e11i q^{86} +(-2.80932e11 - 5.80950e11i) q^{87} -3.44787e10 q^{88} +(-4.91053e11 - 4.91053e11i) q^{89} +(4.50861e11 + 4.50861e11i) q^{90} -4.94563e11i q^{91} +7.35129e11i q^{92} +6.26307e11i q^{93} -1.47928e12 q^{94} +(9.68350e10 - 9.68350e10i) q^{95} +1.48255e12i q^{96} +(-4.87034e11 + 4.87034e11i) q^{97} +(6.19590e11 + 6.19590e11i) q^{98} +(9.00075e10 - 9.00075e10i) 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 $

$2$	−70.5170	−	70.5170i	−1.10183	−	1.10183i	−0.994190	−	0.107639i	$-0.965671\pi$
$2$	−70.5170	−	70.5170i	−1.10183	−	1.10183i	−0.107639	−	0.994190i	$-0.534329\pi$
$3$	−767.125	−	767.125i	−1.05230	−	1.05230i	−0.998555	−	0.0537427i	$-0.982885\pi$
$3$	−767.125	−	767.125i	−1.05230	−	1.05230i	−0.0537427	−	0.998555i	$-0.517115\pi$
$4$			5849.31i			1.42805i
$5$			9904.63i			0.633896i	0.948443	+	0.316948i	$0.102658\pi$
$5$			9904.63i			0.633896i	−0.948443	+	0.316948i	$0.897342\pi$
$6$			108191.i			2.31890i
$7$	71097.8			0.604321			0.302161	−	0.953257i	$-0.402292\pi$
$7$	71097.8			0.604321			0.302161	+	0.953257i	$0.402292\pi$
$8$	123638.	−	123638.i	0.471642	−	0.471642i
$9$			645520.i			1.21466i
$10$	698445.	−	698445.i	0.698445	−	0.698445i
$11$	−139434.	−	139434.i	−0.0787069	−	0.0787069i	0.666657	−	0.745364i	$-0.267724\pi$
$11$	−139434.	−	139434.i	−0.0787069	−	0.0787069i	−0.745364	+	0.666657i	$0.767724\pi$
$12$	4.48715e6	−	4.48715e6i	1.50274	−	1.50274i
$13$		−	6.95609e6i		−	1.44114i	−0.693384	−	0.720569i	$-0.743881\pi$
$13$		−	6.95609e6i		−	1.44114i	0.693384	−	0.720569i	$-0.256119\pi$
$14$	−5.01360e6	−	5.01360e6i	−0.665858	−	0.665858i
$15$	7.59809e6	−	7.59809e6i	0.667048	−	0.667048i
$16$	6.52159e6			0.388717
$17$	1.27794e7	+	1.27794e7i	0.529440	+	0.529440i	0.920405	−	0.390965i	$-0.127859\pi$
$17$	1.27794e7	+	1.27794e7i	0.529440	+	0.529440i	−0.390965	+	0.920405i	$0.627859\pi$
$18$	4.55202e7	−	4.55202e7i	1.33835	−	1.33835i
$19$	−9.77674e6	−	9.77674e6i	−0.207813	−	0.207813i	0.595524	−	0.803337i	$-0.296944\pi$
$19$	−9.77674e6	−	9.77674e6i	−0.207813	−	0.207813i	−0.803337	+	0.595524i	$0.796944\pi$
$20$	−5.79352e7			−0.905238
$21$	−5.45409e7	−	5.45409e7i	−0.635926	−	0.635926i
$22$			1.96650e7i			0.173443i
$23$	1.25678e8			0.848970			0.424485	−	0.905435i	$-0.360455\pi$
$23$	1.25678e8			0.848970			0.424485	+	0.905435i	$0.360455\pi$
$24$	−1.89692e8			−0.992614
$25$	1.46039e8			0.598176
$26$	−4.90523e8	+	4.90523e8i	−1.58789	+	1.58789i
$27$	8.75131e7	−	8.75131e7i	0.225887	−	0.225887i
$28$			4.15873e8i			0.863003i
$29$	5.61762e8	+	1.95547e8i	0.944418	+	0.328748i
$29$	5.61762e8	+	1.95547e8i	0.944418	+	0.328748i
$30$	−1.07159e9			−1.46994
$31$	−4.08217e8	−	4.08217e8i	−0.459961	−	0.459961i	0.438681	−	0.898643i	$-0.355446\pi$
$31$	−4.08217e8	−	4.08217e8i	−0.459961	−	0.459961i	−0.898643	+	0.438681i	$0.855446\pi$
$32$	−9.66304e8	−	9.66304e8i	−0.899941	−	0.899941i
$33$			2.13927e8i			0.165646i
$34$		−	1.80233e9i		−	1.16670i
$35$			7.04197e8i			0.383077i
$36$	−3.77585e9			−1.73460
$37$	−7.79180e8	+	7.79180e8i	−0.303688	+	0.303688i	−0.842455	−	0.538767i	$-0.818890\pi$
$37$	−7.79180e8	+	7.79180e8i	−0.303688	+	0.303688i	0.538767	+	0.842455i	$0.318890\pi$
$38$			1.37885e9i			0.457948i
$39$	−5.33619e9	+	5.33619e9i	−1.51651	+	1.51651i
$40$	1.22459e9	+	1.22459e9i	0.298972	+	0.298972i
$41$	−2.47439e8	+	2.47439e8i	−0.0520913	+	0.0520913i	−0.732673	−	0.680581i	$-0.761727\pi$
$41$	−2.47439e8	+	2.47439e8i	−0.0520913	+	0.0520913i	0.680581	+	0.732673i	$0.261727\pi$
$42$			7.69212e9i			1.40136i
$43$	1.69200e9	+	1.69200e9i	0.267664	+	0.267664i	0.828158	−	0.560494i	$-0.189389\pi$
$43$	1.69200e9	+	1.69200e9i	0.267664	+	0.267664i	−0.560494	+	0.828158i	$0.689389\pi$
$44$	8.15593e8	−	8.15593e8i	0.112398	−	0.112398i
$45$	−6.39364e9			−0.769969
$46$	−8.86244e9	−	8.86244e9i	−0.935419	−	0.935419i
$47$	1.04888e10	−	1.04888e10i	0.973056	−	0.973056i	−0.0265906	−	0.999646i	$-0.508465\pi$
$47$	1.04888e10	−	1.04888e10i	0.973056	−	0.973056i	0.999646	+	0.0265906i	$0.00846505\pi$
$48$	−5.00287e9	−	5.00287e9i	−0.409046	−	0.409046i
$49$	−8.78639e9			−0.634796
$50$	−1.02982e10	−	1.02982e10i	−0.659087	−	0.659087i
$51$		−	1.96068e10i		−	1.11426i
$52$	4.06883e10			2.05802
$53$	3.92148e10			1.76927			0.884636	−	0.466282i	$-0.154407\pi$
$53$	3.92148e10			1.76927			0.884636	+	0.466282i	$0.154407\pi$
$54$	−1.23423e10			−0.497777
$55$	1.38104e9	−	1.38104e9i	0.0498920	−	0.0498920i
$56$	8.79039e9	−	8.79039e9i	0.285023	−	0.285023i
$57$			1.50000e10i			0.437362i
$58$	−2.58244e10	−	5.34032e10i	−0.678362	−	1.40281i
$59$	−1.72085e10			−0.407973			−0.203986	−	0.978974i	$-0.565390\pi$
$59$	−1.72085e10			−0.407973			−0.203986	+	0.978974i	$0.565390\pi$
$60$	4.44435e10	+	4.44435e10i	0.952579	+	0.952579i
$61$	−2.60466e9	−	2.60466e9i	−0.0505560	−	0.0505560i	0.681377	−	0.731933i	$-0.261382\pi$
$61$	−2.60466e9	−	2.60466e9i	−0.0505560	−	0.0505560i	−0.731933	+	0.681377i	$0.761382\pi$
$62$			5.75726e10i			1.01360i
$63$			4.58951e10i			0.734045i
$64$			1.09569e11i			1.59444i
$65$	6.88975e10			0.913531
$66$	1.50855e10	−	1.50855e10i	0.182514	−	0.182514i
$67$			2.01604e10i			0.222869i	0.993772	+	0.111434i	$0.0355445\pi$
$67$			2.01604e10i			0.222869i	−0.993772	+	0.111434i	$0.964455\pi$
$68$	−7.47506e10	+	7.47506e10i	−0.756069	+	0.756069i
$69$	−9.64107e10	−	9.64107e10i	−0.893369	−	0.893369i
$70$	4.96579e10	−	4.96579e10i	0.422085	−	0.422085i
$71$		−	9.62631e10i		−	0.751467i	−0.926728	−	0.375733i	$-0.877391\pi$
$71$		−	9.62631e10i		−	0.751467i	0.926728	−	0.375733i	$-0.122609\pi$
$72$	7.98108e10	+	7.98108e10i	0.572884	+	0.572884i
$73$	−1.16297e11	+	1.16297e11i	−0.768481	+	0.768481i	−0.977839	−	0.209358i	$-0.932862\pi$
$73$	−1.16297e11	+	1.16297e11i	−0.768481	+	0.768481i	0.209358	+	0.977839i	$0.432862\pi$
$74$	1.09891e11			0.669224
$75$	−1.12030e11	−	1.12030e11i	−0.629459	−	0.629459i
$76$	5.71871e10	−	5.71871e10i	0.296768	−	0.296768i
$77$	−9.91345e9	−	9.91345e9i	−0.0475642	−	0.0475642i
$78$	7.52585e11			3.34186
$79$	−2.86222e11	−	2.86222e11i	−1.17745	−	1.17745i	−0.980393	−	0.197054i	$-0.936863\pi$
$79$	−2.86222e11	−	2.86222e11i	−1.17745	−	1.17745i	−0.197054	−	0.980393i	$-0.563137\pi$
$80$			6.45939e10i			0.246406i
$81$	2.08789e11			0.739261
$82$	3.48974e10			0.114791
$83$	−1.02532e11			−0.313611			−0.156806	−	0.987629i	$-0.550120\pi$
$83$	−1.02532e11			−0.313611			−0.156806	+	0.987629i	$0.550120\pi$
$84$	3.19026e11	−	3.19026e11i	0.908136	−	0.908136i
$85$	−1.26575e11	+	1.26575e11i	−0.335610	+	0.335610i
$86$		−	2.38630e11i		−	0.589840i
$87$	−2.80932e11	−	5.80950e11i	−0.647868	−	1.33975i
$88$	−3.44787e10			−0.0742429
$89$	−4.91053e11	−	4.91053e11i	−0.988071	−	0.988071i	0.0118588	−	0.999930i	$-0.496225\pi$
$89$	−4.91053e11	−	4.91053e11i	−0.988071	−	0.988071i	−0.999930	+	0.0118588i	$0.996225\pi$
$90$	4.50861e11	+	4.50861e11i	0.848374	+	0.848374i
$91$		−	4.94563e11i		−	0.870910i
$92$			7.35129e11i			1.21237i
$93$			6.26307e11i			0.968032i
$94$	−1.47928e12			−2.14428
$95$	9.68350e10	−	9.68350e10i	0.131732	−	0.131732i
$96$			1.48255e12i			1.89401i
$97$	−4.87034e11	+	4.87034e11i	−0.584695	+	0.584695i	−0.936190	−	0.351495i	$-0.885673\pi$
$97$	−4.87034e11	+	4.87034e11i	−0.584695	+	0.584695i	0.351495	+	0.936190i	$0.385673\pi$
$98$	6.19590e11	+	6.19590e11i	0.699436	+	0.699436i
$99$	9.00075e10	−	9.00075e10i	0.0956022	−	0.0956022i
$100$			8.54227e11i			0.854227i
$101$	−7.01321e11	−	7.01321e11i	−0.660676	−	0.660676i	0.294863	−	0.955539i	$-0.404726\pi$
$101$	−7.01321e11	−	7.01321e11i	−0.660676	−	0.660676i	−0.955539	+	0.294863i	$0.904726\pi$
$102$	−1.38261e12	+	1.38261e12i	−1.22772	+	1.22772i
$103$	−2.05180e12			−1.71835			−0.859177	−	0.511678i	$-0.829024\pi$
$103$	−2.05180e12			−1.71835			−0.859177	+	0.511678i	$0.829024\pi$
$104$	−8.60037e11	−	8.60037e11i	−0.679700	−	0.679700i
$105$	5.40207e11	−	5.40207e11i	0.403111	−	0.403111i
$106$	−2.76531e12	−	2.76531e12i	−1.94943	−	1.94943i
$107$	1.62879e12			1.08533			0.542665	−	0.839949i	$-0.317415\pi$
$107$	1.62879e12			1.08533			0.542665	+	0.839949i	$0.317415\pi$
$108$	5.11891e11	+	5.11891e11i	0.322578	+	0.322578i
$109$			9.80763e11i			0.584797i	0.956297	+	0.292398i	$0.0944534\pi$
$109$			9.80763e11i			0.584797i	−0.956297	+	0.292398i	$0.905547\pi$
$110$	−1.94774e11			−0.109945
$111$	1.19546e12			0.639140
$112$	4.63670e11			0.234910
$113$	1.39240e12	−	1.39240e12i	0.668794	−	0.668794i	−0.288643	−	0.957437i	$-0.593204\pi$
$113$	1.39240e12	−	1.39240e12i	0.668794	−	0.668794i	0.957437	+	0.288643i	$0.0932041\pi$
$114$	1.05775e12	−	1.05775e12i	0.481898	−	0.481898i
$115$			1.24479e12i			0.538159i
$116$	−1.14381e12	+	3.28592e12i	−0.469470	+	1.34868i
$117$	4.49030e12			1.75049
$118$	1.21349e12	+	1.21349e12i	0.449516	+	0.449516i
$119$	9.08587e11	+	9.08587e11i	0.319952	+	0.319952i
$120$		−	1.87882e12i		−	0.629215i
$121$		−	3.09954e12i		−	0.987610i
$122$			3.67346e11i			0.111408i
$123$	3.79634e11			0.109631
$124$	2.38779e12	−	2.38779e12i	0.656849	−	0.656849i
$125$			3.86458e12i			1.01308i
$126$	3.23638e12	−	3.23638e12i	0.808792	−	0.808792i
$127$	−1.36346e12	−	1.36346e12i	−0.324953	−	0.324953i	0.525711	−	0.850663i	$-0.323799\pi$
$127$	−1.36346e12	−	1.36346e12i	−0.324953	−	0.324953i	−0.850663	+	0.525711i	$0.823799\pi$
$128$	3.76853e12	−	3.76853e12i	0.856864	−	0.856864i
$129$		−	2.59596e12i		−	0.563325i
$130$	−4.85845e12	−	4.85845e12i	−1.00656	−	1.00656i
$131$	2.72861e12	−	2.72861e12i	0.539900	−	0.539900i	−0.383599	−	0.923500i	$-0.625316\pi$
$131$	2.72861e12	−	2.72861e12i	0.539900	−	0.539900i	0.923500	+	0.383599i	$0.125316\pi$
$132$	−1.25132e12			−0.236552
$133$	−6.95104e11	−	6.95104e11i	−0.125586	−	0.125586i
$134$	1.42165e12	−	1.42165e12i	0.245563	−	0.245563i
$135$	8.66785e11	+	8.66785e11i	0.143189	+	0.143189i
$136$	3.16004e12			0.499412
$137$	3.87116e11	+	3.87116e11i	0.0585487	+	0.0585487i	0.735775	−	0.677226i	$-0.236818\pi$
$137$	3.87116e11	+	3.87116e11i	0.0585487	+	0.0585487i	−0.677226	+	0.735775i	$0.736818\pi$
$138$			1.35972e13i			1.96868i
$139$	1.27529e13			1.76815			0.884074	−	0.467347i	$-0.154790\pi$
$139$	1.27529e13			1.76815			0.884074	+	0.467347i	$0.154790\pi$
$140$	−4.11906e12			−0.547054
$141$	−1.60924e13			−2.04789
$142$	−6.78819e12	+	6.78819e12i	−0.827988	+	0.827988i
$143$	−9.69916e11	+	9.69916e11i	−0.113427	+	0.113427i
$144$			4.20982e12i			0.472159i
$145$	−1.93682e12	+	5.56404e12i	−0.208392	+	0.598663i
$146$	1.64019e13			1.69347
$147$	6.74026e12	+	6.74026e12i	0.667994	+	0.667994i
$148$	−4.55766e12	−	4.55766e12i	−0.433682	−	0.433682i
$149$			1.99539e13i			1.82352i	0.410729	+	0.911758i	$0.365274\pi$
$149$			1.99539e13i			1.82352i	−0.410729	+	0.911758i	$0.634726\pi$
$150$			1.58001e13i			1.38711i
$151$		−	2.12430e13i		−	1.79206i	−0.443990	−	0.896032i	$-0.646437\pi$
$151$		−	2.12430e13i		−	1.79206i	0.443990	−	0.896032i	$-0.353563\pi$
$152$	−2.41755e12			−0.196026
$153$	−8.24936e12	+	8.24936e12i	−0.643090	+	0.643090i
$154$			1.39813e12i			0.104815i
$155$	4.04324e12	−	4.04324e12i	0.291568	−	0.291568i
$156$	−3.12130e13	−	3.12130e13i	−2.16565	−	2.16565i
$157$	1.40503e13	−	1.40503e13i	0.938185	−	0.938185i	−0.0600127	−	0.998198i	$-0.519114\pi$
$157$	1.40503e13	−	1.40503e13i	0.938185	−	0.938185i	0.998198	+	0.0600127i	$0.0191141\pi$
$158$			4.03671e13i			2.59469i
$159$	−3.00826e13	−	3.00826e13i	−1.86180	−	1.86180i
$160$	9.57089e12	−	9.57089e12i	0.570469	−	0.570469i
$161$	8.93542e12			0.513050
$162$	−1.47232e13	−	1.47232e13i	−0.814539	−	0.814539i
$163$	1.80569e13	−	1.80569e13i	0.962758	−	0.962758i	−0.0365727	−	0.999331i	$-0.511644\pi$
$163$	1.80569e13	−	1.80569e13i	0.962758	−	0.962758i	0.999331	+	0.0365727i	$0.0116440\pi$
$164$	−1.44735e12	−	1.44735e12i	−0.0743892	−	0.0743892i
$165$	−2.11886e12			−0.105002
$166$	7.23027e12	+	7.23027e12i	0.345546	+	0.345546i
$167$		−	8.70797e12i		−	0.401438i	−0.979649	−	0.200719i	$-0.935672\pi$
$167$		−	8.70797e12i		−	0.401438i	0.979649	−	0.200719i	$-0.0643278\pi$
$168$	−1.34866e13			−0.599858
$169$	−2.50892e13			−1.07688
$170$	1.78514e13			0.739570
$171$	6.31108e12	−	6.31108e12i	0.252422	−	0.252422i
$172$	−9.89705e12	+	9.89705e12i	−0.382239	+	0.382239i
$173$			7.77195e12i			0.289904i	0.989439	+	0.144952i	$0.0463027\pi$
$173$			7.77195e12i			0.289904i	−0.989439	+	0.144952i	$0.953697\pi$
$174$	−2.11564e13	+	6.07774e13i	−0.762335	+	2.19001i
$175$	1.03830e13			0.361490
$176$	−9.09332e11	−	9.09332e11i	−0.0305947	−	0.0305947i
$177$	1.32011e13	+	1.32011e13i	0.429309	+	0.429309i
$178$			6.92552e13i			2.17737i
$179$		−	5.13782e13i		−	1.56193i	−0.624577	−	0.780963i	$-0.714729\pi$
$179$		−	5.13782e13i		−	1.56193i	0.624577	−	0.780963i	$-0.285271\pi$
$180$		−	3.73984e13i		−	1.09956i
$181$	−3.55773e13			−1.01182			−0.505908	−	0.862587i	$-0.668842\pi$
$181$	−3.55773e13			−1.01182			−0.505908	+	0.862587i	$0.668842\pi$
$182$	−3.48751e13	+	3.48751e13i	−0.959593	+	0.959593i
$183$			3.99620e12i			0.106400i
$184$	1.55386e13	−	1.55386e13i	0.400409	−	0.400409i
$185$	−7.71749e12	−	7.71749e12i	−0.192507	−	0.192507i
$186$	4.41653e13	−	4.41653e13i	1.06661	−	1.06661i
$187$		−	3.56377e12i		−	0.0833412i
$188$	6.13521e13	+	6.13521e13i	1.38958	+	1.38958i
$189$	6.22198e12	−	6.22198e12i	0.136508	−	0.136508i
$190$	−1.36570e13			−0.290292
$191$	1.74135e13	+	1.74135e13i	0.358663	+	0.358663i	0.863320	−	0.504657i	$-0.168381\pi$
$191$	1.74135e13	+	1.74135e13i	0.358663	+	0.358663i	−0.504657	+	0.863320i	$0.668381\pi$
$192$	8.40534e13	−	8.40534e13i	1.67783	−	1.67783i
$193$	−2.93006e13	−	2.93006e13i	−0.566934	−	0.566934i	0.364334	−	0.931268i	$-0.381297\pi$
$193$	−2.93006e13	−	2.93006e13i	−0.566934	−	0.566934i	−0.931268	+	0.364334i	$0.881297\pi$
$194$	6.86884e13			1.28847
$195$	−5.28530e13	−	5.28530e13i	−0.961307	−	0.961307i
$196$		−	5.13943e13i		−	0.906523i
$197$	−8.62459e13			−1.47551			−0.737753	−	0.675071i	$-0.764113\pi$
$197$	−8.62459e13			−1.47551			−0.737753	+	0.675071i	$0.764113\pi$
$198$	−1.26941e13			−0.210674
$199$	−1.17939e14			−1.89906			−0.949528	−	0.313682i	$-0.898437\pi$
$199$	−1.17939e14			−1.89906			−0.949528	+	0.313682i	$0.898437\pi$
$200$	1.80560e13	−	1.80560e13i	0.282124	−	0.282124i
$201$	1.54655e13	−	1.54655e13i	0.234524	−	0.234524i
$202$			9.89102e13i			1.45590i
$203$	3.99400e13	+	1.39030e13i	0.570732	+	0.198669i
$204$	1.14686e14			1.59122
$205$	−2.45079e12	−	2.45079e12i	−0.0330205	−	0.0330205i
$206$	1.44687e14	+	1.44687e14i	1.89333	+	1.89333i
$207$			8.11277e13i			1.03121i
$208$		−	4.53648e13i		−	0.560194i
$209$			2.72642e12i			0.0327126i
$210$	−7.61876e13			−0.888318
$211$	3.13649e13	−	3.13649e13i	0.355426	−	0.355426i	−0.506697	−	0.862124i	$-0.669134\pi$
$211$	3.13649e13	−	3.13649e13i	0.355426	−	0.355426i	0.862124	+	0.506697i	$0.169134\pi$
$212$			2.29379e14i			2.52662i
$213$	−7.38458e13	+	7.38458e13i	−0.790767	+	0.790767i
$214$	−1.14857e14	−	1.14857e14i	−1.19585	−	1.19585i
$215$	−1.67587e13	+	1.67587e13i	−0.169671	+	0.169671i
$216$		−	2.16399e13i		−	0.213075i
$217$	−2.90233e13	−	2.90233e13i	−0.277964	−	0.277964i
$218$	6.91605e13	−	6.91605e13i	0.644346	−	0.644346i
$219$	1.78429e14			1.61734
$220$	8.07814e12	+	8.07814e12i	0.0712485	+	0.0712485i
$221$	8.88947e13	−	8.88947e13i	0.762996	−	0.762996i
$222$	−8.43001e13	−	8.43001e13i	−0.704223	−	0.704223i
$223$	1.38529e14			1.12645			0.563224	−	0.826304i	$-0.309561\pi$
$223$	1.38529e14			1.12645			0.563224	+	0.826304i	$0.309561\pi$
$224$	−6.87021e13	−	6.87021e13i	−0.543853	−	0.543853i
$225$			9.42711e13i			0.726580i
$226$	−1.96375e14			−1.47379
$227$	1.60059e14			1.16984			0.584919	−	0.811091i	$-0.301126\pi$
$227$	1.60059e14			1.16984			0.584919	+	0.811091i	$0.301126\pi$
$228$	−8.77394e13			−0.624576
$229$	5.79099e13	−	5.79099e13i	0.401550	−	0.401550i	−0.477229	−	0.878779i	$-0.658359\pi$
$229$	5.79099e13	−	5.79099e13i	0.401550	−	0.401550i	0.878779	+	0.477229i	$0.158359\pi$
$230$	8.77792e13	−	8.77792e13i	0.592959	−	0.592959i
$231$			1.52097e13i			0.100103i
$232$	9.36321e13	−	4.52780e13i	0.600478	−	0.290375i
$233$	7.24409e13			0.452740			0.226370	−	0.974041i	$-0.427314\pi$
$233$	7.24409e13			0.452740			0.226370	+	0.974041i	$0.427314\pi$
$234$	−3.16643e14	−	3.16643e14i	−1.92874	−	1.92874i
$235$	1.03887e14	+	1.03887e14i	0.616816	+	0.616816i
$236$		−	1.00658e14i		−	0.582607i
$237$			4.39137e14i			2.47805i
$238$		−	1.28142e14i		−	0.705064i
$239$	6.50395e13			0.348971			0.174486	−	0.984660i	$-0.444174\pi$
$239$	6.50395e13			0.348971			0.174486	+	0.984660i	$0.444174\pi$
$240$	4.95516e13	−	4.95516e13i	0.259293	−	0.259293i
$241$		−	1.17145e14i		−	0.597889i	−0.954270	−	0.298945i	$-0.903365\pi$
$241$		−	1.17145e14i		−	0.597889i	0.954270	−	0.298945i	$-0.0966346\pi$
$242$	−2.18571e14	+	2.18571e14i	−1.08818	+	1.08818i
$243$	−2.06675e14	−	2.06675e14i	−1.00381	−	1.00381i
$244$	1.52355e13	−	1.52355e13i	0.0721966	−	0.0721966i
$245$		−	8.70260e13i		−	0.402395i
$246$	−2.67706e13	−	2.67706e13i	−0.120795	−	0.120795i
$247$	−6.80079e13	+	6.80079e13i	−0.299487	+	0.299487i
$248$	−1.00942e14			−0.433874
$249$	7.86550e13	+	7.86550e13i	0.330013	+	0.330013i
$250$	2.72519e14	−	2.72519e14i	1.11624	−	1.11624i
$251$	6.90620e13	+	6.90620e13i	0.276183	+	0.276183i	0.831583	−	0.555400i	$-0.187435\pi$
$251$	6.90620e13	+	6.90620e13i	0.276183	+	0.276183i	−0.555400	+	0.831583i	$0.687435\pi$
$252$	−2.68454e14			−1.04826
$253$	−1.75238e13	−	1.75238e13i	−0.0668198	−	0.0668198i
$254$			1.92294e14i			0.716084i
$255$	1.94198e14			0.706323
$256$	−8.26947e13			−0.293791
$257$	−2.63914e14			−0.915932			−0.457966	−	0.888970i	$-0.651422\pi$
$257$	−2.63914e14			−0.915932			−0.457966	+	0.888970i	$0.651422\pi$
$258$	−1.83059e14	+	1.83059e14i	−0.620688	+	0.620688i
$259$	−5.53980e13	+	5.53980e13i	−0.183525	+	0.183525i
$260$			4.03003e14i			1.30457i
$261$	−1.26230e14	+	3.62629e14i	−0.399317	+	1.14715i
$262$	−3.84827e14			−1.18976
$263$	−4.49701e14	−	4.49701e14i	−1.35891	−	1.35891i	−0.875269	−	0.483636i	$-0.839316\pi$
$263$	−4.49701e14	−	4.49701e14i	−1.35891	−	1.35891i	−0.483636	−	0.875269i	$-0.660684\pi$
$264$	2.64495e13	+	2.64495e13i	0.0781256	+	0.0781256i
$265$			3.88408e14i			1.12154i
$266$			9.80334e13i			0.276748i
$267$			7.53398e14i			2.07949i
$268$	−1.17924e14			−0.318269
$269$	6.81051e13	−	6.81051e13i	0.179749	−	0.179749i	−0.611497	−	0.791246i	$-0.709433\pi$
$269$	6.81051e13	−	6.81051e13i	0.179749	−	0.179749i	0.791246	+	0.611497i	$0.209433\pi$
$270$		−	1.22246e14i		−	0.315539i
$271$	−2.31906e14	+	2.31906e14i	−0.585459	+	0.585459i	−0.936398	−	0.350939i	$-0.885862\pi$
$271$	−2.31906e14	+	2.31906e14i	−0.585459	+	0.585459i	0.350939	+	0.936398i	$0.385862\pi$
$272$	8.33419e13	+	8.33419e13i	0.205802	+	0.205802i
$273$	−3.79391e14	+	3.79391e14i	−0.916456	+	0.916456i
$274$		−	5.45965e13i		−	0.129021i
$275$	−2.03628e13	−	2.03628e13i	−0.0470805	−	0.0470805i
$276$	5.63936e14	−	5.63936e14i	1.27578	−	1.27578i
$277$	8.82319e14			1.95320			0.976601	−	0.215061i	$-0.0689951\pi$
$277$	8.82319e14			1.95320			0.976601	+	0.215061i	$0.0689951\pi$
$278$	−8.99293e14	−	8.99293e14i	−1.94820	−	1.94820i
$279$	2.63513e14	−	2.63513e14i	0.558697	−	0.558697i
$280$	8.70655e13	+	8.70655e13i	0.180675	+	0.180675i
$281$	−3.28780e13			−0.0667832			−0.0333916	−	0.999442i	$-0.510631\pi$
$281$	−3.28780e13			−0.0667832			−0.0333916	+	0.999442i	$0.510631\pi$
$282$	1.13479e15	+	1.13479e15i	2.25642	+	2.25642i
$283$		−	5.17557e14i		−	1.00749i	−0.863853	−	0.503743i	$-0.831956\pi$
$283$		−	5.17557e14i		−	1.00749i	0.863853	−	0.503743i	$-0.168044\pi$
$284$	5.63073e14			1.07313
$285$	−1.48569e14			−0.277242
$286$	1.36791e14			0.249955
$287$	−1.75924e13	+	1.75924e13i	−0.0314799	+	0.0314799i
$288$	6.23769e14	−	6.23769e14i	1.09312	−	1.09312i
$289$		−	2.55996e14i		−	0.439387i
$290$	5.28939e14	−	2.55781e14i	0.889236	−	0.430011i
$291$	7.47232e14			1.23055
$292$	−6.80259e14	−	6.80259e14i	−1.09743	−	1.09743i
$293$	−8.05716e14	−	8.05716e14i	−1.27343	−	1.27343i	−0.944275	−	0.329158i	$-0.893235\pi$
$293$	−8.05716e14	−	8.05716e14i	−1.27343	−	1.27343i	−0.329158	−	0.944275i	$-0.606765\pi$
$294$		−	9.50607e14i		−	1.47203i
$295$		−	1.70444e14i		−	0.258612i
$296$			1.92672e14i			0.286464i
$297$	−2.44046e13			−0.0355577
$298$	1.40709e15	−	1.40709e15i	2.00920	−	2.00920i
$299$		−	8.74228e14i		−	1.22348i
$300$	6.55298e14	−	6.55298e14i	0.898901	−	0.898901i
$301$	1.20298e14	+	1.20298e14i	0.161755	+	0.161755i
$302$	−1.49799e15	+	1.49799e15i	−1.97455	+	1.97455i
$303$			1.07600e15i			1.39046i
$304$	−6.37598e13	−	6.37598e13i	−0.0807804	−	0.0807804i
$305$	2.57982e13	−	2.57982e13i	0.0320472	−	0.0320472i
$306$	1.16344e15			1.41715
$307$	5.77529e14	+	5.77529e14i	0.689832	+	0.689832i	0.962195	−	0.272363i	$-0.0878051\pi$
$307$	5.77529e14	+	5.77529e14i	0.689832	+	0.689832i	−0.272363	+	0.962195i	$0.587805\pi$
$308$	5.79868e13	−	5.79868e13i	0.0679243	−	0.0679243i
$309$	1.57399e15	+	1.57399e15i	1.80822	+	1.80822i
$310$	−5.70235e14			−0.642516
$311$	4.42292e14	+	4.42292e14i	0.488818	+	0.488818i	0.907933	−	0.419115i	$-0.137660\pi$
$311$	4.42292e14	+	4.42292e14i	0.488818	+	0.488818i	−0.419115	+	0.907933i	$0.637660\pi$
$312$			1.31951e15i			1.43049i
$313$	1.42996e14			0.152075			0.0760376	−	0.997105i	$-0.475773\pi$
$313$	1.42996e14			0.152075			0.0760376	+	0.997105i	$0.475773\pi$
$314$	−1.98157e15			−2.06744
$315$	−4.54574e14			−0.465308
$316$	1.67420e15	−	1.67420e15i	1.68146	−	1.68146i
$317$	−9.87053e14	+	9.87053e14i	−0.972713	+	0.972713i	−0.999637	−	0.0269244i	$-0.991429\pi$
$317$	−9.87053e14	+	9.87053e14i	−0.972713	+	0.972713i	0.0269244	+	0.999637i	$0.491429\pi$
$318$			4.24268e15i			4.10277i
$319$	−5.10628e13	−	1.05595e14i	−0.0484574	−	0.100207i
$320$	−1.08524e15			−1.01071
$321$	−1.24948e15	−	1.24948e15i	−1.14209	−	1.14209i
$322$	−6.30100e14	−	6.30100e14i	−0.565294	−	0.565294i
$323$		−	2.49882e14i		−	0.220049i
$324$			1.22127e15i			1.05570i
$325$		−	1.01586e15i		−	0.862053i
$326$	−2.54664e15			−2.12159
$327$	7.52368e14	−	7.52368e14i	0.615380	−	0.615380i
$328$			6.11858e13i			0.0491369i
$329$	7.45729e14	−	7.45729e14i	0.588038	−	0.588038i
$330$	1.49416e14	+	1.49416e14i	0.115695	+	0.115695i
$331$	−8.02416e14	+	8.02416e14i	−0.610143	+	0.610143i	−0.942983	−	0.332840i	$-0.891993\pi$
$331$	−8.02416e14	+	8.02416e14i	−0.610143	+	0.610143i	0.332840	+	0.942983i	$0.391993\pi$
$332$		−	5.99743e14i		−	0.447854i
$333$	−5.02976e14	−	5.02976e14i	−0.368878	−	0.368878i
$334$	−6.14060e14	+	6.14060e14i	−0.442316	+	0.442316i
$335$	−1.99681e14			−0.141276
$336$	−3.55693e14	−	3.55693e14i	−0.247195	−	0.247195i
$337$	3.03633e14	−	3.03633e14i	0.207286	−	0.207286i	−0.595827	−	0.803113i	$-0.703176\pi$
$337$	3.03633e14	−	3.03633e14i	0.207286	−	0.207286i	0.803113	+	0.595827i	$0.203176\pi$
$338$	1.76921e15	+	1.76921e15i	1.18653	+	1.18653i
$339$	−2.13628e15			−1.40754
$340$	−7.40377e14	−	7.40377e14i	−0.479269	−	0.479269i
$341$			1.13839e14i			0.0724043i
$342$	−8.90078e14			−0.556252
$343$	−1.60878e15			−0.987942
$344$	4.18392e14			0.252483
$345$	9.54912e14	−	9.54912e14i	0.566303	−	0.566303i
$346$	5.48055e14	−	5.48055e14i	0.319424	−	0.319424i
$347$			8.06375e14i			0.461913i	0.972964	+	0.230956i	$0.0741855\pi$
$347$			8.06375e14i			0.461913i	−0.972964	+	0.230956i	$0.925815\pi$
$348$	3.39816e15	−	1.64326e15i	1.91323	−	0.925190i
$349$	−8.25831e14			−0.457023			−0.228512	−	0.973541i	$-0.573386\pi$
$349$	−8.25831e14			−0.457023			−0.228512	+	0.973541i	$0.573386\pi$
$350$	−7.32182e14	−	7.32182e14i	−0.398300	−	0.398300i
$351$	−6.08749e14	−	6.08749e14i	−0.325533	−	0.325533i
$352$			2.69472e14i			0.141663i
$353$			2.15205e15i			1.11226i	0.831096	+	0.556128i	$0.187714\pi$
$353$			2.15205e15i			1.11226i	−0.831096	+	0.556128i	$0.812286\pi$
$354$		−	1.86180e15i		−	0.946050i
$355$	9.53451e14			0.476352
$356$	2.87232e15	−	2.87232e15i	1.41102	−	1.41102i
$357$		−	1.39400e15i		−	0.673369i
$358$	−3.62304e15	+	3.62304e15i	−1.72098	+	1.72098i
$359$	9.97978e14	+	9.97978e14i	0.466181	+	0.466181i	0.900675	−	0.434494i	$-0.143073\pi$
$359$	9.97978e14	+	9.97978e14i	0.466181	+	0.466181i	−0.434494	+	0.900675i	$0.643073\pi$
$360$	−7.90497e14	+	7.90497e14i	−0.363149	+	0.363149i
$361$		−	2.02215e15i		−	0.913628i
$362$	2.50881e15	+	2.50881e15i	1.11485	+	1.11485i
$363$	−2.37774e15	+	2.37774e15i	−1.03926	+	1.03926i
$364$	2.89285e15			1.24371
$365$	−1.15188e15	−	1.15188e15i	−0.487137	−	0.487137i
$366$	2.81800e14	−	2.81800e14i	0.117234	−	0.117234i
$367$	−9.12579e14	−	9.12579e14i	−0.373486	−	0.373486i	0.495259	−	0.868745i	$-0.335073\pi$
$367$	−9.12579e14	−	9.12579e14i	−0.373486	−	0.373486i	−0.868745	+	0.495259i	$0.835073\pi$
$368$	8.19620e14			0.330009
$369$	−1.59727e14	−	1.59727e14i	−0.0632733	−	0.0632733i
$370$			1.08843e15i			0.424219i
$371$	2.78808e15			1.06921
$372$	−3.66346e15			−1.38240
$373$	9.37176e14			0.347991			0.173996	−	0.984746i	$-0.444332\pi$
$373$	9.37176e14			0.347991			0.173996	+	0.984746i	$0.444332\pi$
$374$	−2.51306e14	+	2.51306e14i	−0.0918277	+	0.0918277i
$375$	2.96462e15	−	2.96462e15i	1.06606	−	1.06606i
$376$		−	2.59362e15i		−	0.917867i
$377$	1.36024e15	−	3.90767e15i	0.473771	−	1.36104i
$378$	−8.77512e14			−0.300817
$379$	−3.72225e15	−	3.72225e15i	−1.25594	−	1.25594i	−0.953012	−	0.302933i	$-0.902034\pi$
$379$	−3.72225e15	−	3.72225e15i	−1.25594	−	1.25594i	−0.302933	−	0.953012i	$-0.597966\pi$
$380$	5.66417e14	+	5.66417e14i	0.188120	+	0.188120i
$381$			2.09189e15i			0.683893i
$382$		−	2.45590e15i		−	0.790371i
$383$			3.47293e15i			1.10028i	0.835073	+	0.550139i	$0.185425\pi$
$383$			3.47293e15i			1.10028i	−0.835073	+	0.550139i	$0.814575\pi$
$384$	−5.78187e15			−1.80335
$385$	9.81891e13	−	9.81891e13i	0.0301508	−	0.0301508i
$386$			4.13238e15i			1.24933i
$387$	−1.09222e15	+	1.09222e15i	−0.325121	+	0.325121i
$388$	−2.84881e15	−	2.84881e15i	−0.834975	−	0.834975i
$389$	4.28706e15	−	4.28706e15i	1.23726	−	1.23726i	0.276149	−	0.961115i	$-0.410942\pi$
$389$	4.28706e15	−	4.28706e15i	1.23726	−	1.23726i	0.961115	−	0.276149i	$-0.0890582\pi$
$390$			7.45408e15i			2.11839i
$391$	1.60609e15	+	1.60609e15i	0.449478	+	0.449478i
$392$	−1.08633e15	+	1.08633e15i	−0.299396	+	0.299396i
$393$	−4.18637e15			−1.13627
$394$	6.08181e15	+	6.08181e15i	1.62576	+	1.62576i
$395$	2.83493e15	−	2.83493e15i	0.746379	−	0.746379i
$396$	5.26482e14	+	5.26482e14i	0.136525	+	0.136525i
$397$	−3.28285e14			−0.0838510			−0.0419255	−	0.999121i	$-0.513349\pi$
$397$	−3.28285e14			−0.0838510			−0.0419255	+	0.999121i	$0.513349\pi$
$398$	8.31669e15	+	8.31669e15i	2.09243	+	2.09243i
$399$			1.06646e15i			0.264307i
$400$	9.52406e14			0.232521
$401$	2.01829e15			0.485419			0.242709	−	0.970099i	$-0.421964\pi$
$401$	2.01829e15			0.485419			0.242709	+	0.970099i	$0.421964\pi$
$402$	−2.18116e15			−0.516811
$403$	−2.83960e15	+	2.83960e15i	−0.662867	+	0.662867i
$404$	4.10224e15	−	4.10224e15i	0.943481	−	0.943481i
$405$			2.06798e15i			0.468615i
$406$	−1.83606e15	−	3.79685e15i	−0.409949	−	0.847748i
$407$	2.17288e14			0.0478047
$408$	−2.42414e15	−	2.42414e15i	−0.525530	−	0.525530i
$409$	3.24722e15	+	3.24722e15i	0.693700	+	0.693700i	0.963044	−	0.269344i	$-0.0868069\pi$
$409$	3.24722e15	+	3.24722e15i	0.693700	+	0.693700i	−0.269344	+	0.963044i	$0.586807\pi$
$410$			3.45645e14i			0.0727659i
$411$		−	5.93932e14i		−	0.123221i
$412$		−	1.20016e16i		−	2.45390i
$413$	−1.22349e15			−0.246547
$414$	5.72088e15	−	5.72088e15i	1.13622	−	1.13622i
$415$		−	1.01554e15i		−	0.198797i
$416$	−6.72170e15	+	6.72170e15i	−1.29694	+	1.29694i
$417$	−9.78303e15	−	9.78303e15i	−1.86062	−	1.86062i
$418$	1.92259e14	−	1.92259e14i	0.0360437	−	0.0360437i
$419$			1.37640e15i			0.254367i	0.991879	+	0.127184i	$0.0405938\pi$
$419$			1.37640e15i			0.254367i	−0.991879	+	0.127184i	$0.959406\pi$
$420$	3.15984e15	+	3.15984e15i	0.575664	+	0.575664i
$421$	1.30703e15	−	1.30703e15i	0.234743	−	0.234743i	−0.579926	−	0.814669i	$-0.696919\pi$
$421$	1.30703e15	−	1.30703e15i	0.234743	−	0.234743i	0.814669	+	0.579926i	$0.196919\pi$
$422$	−4.42353e15			−0.783238
$423$	6.77072e15	+	6.77072e15i	1.18193	+	1.18193i
$424$	4.84844e15	−	4.84844e15i	0.834462	−	0.834462i
$425$	1.86629e15	+	1.86629e15i	0.316698	+	0.316698i
$426$	1.04148e16			1.74258
$427$	−1.85186e14	−	1.85186e14i	−0.0305520	−	0.0305520i
$428$			9.52729e15i			1.54991i
$429$	1.48809e15			0.238719
$430$	2.36354e15			0.373898
$431$	1.20632e14			0.0188192			0.00940958	−	0.999956i	$-0.497005\pi$
$431$	1.20632e14			0.0188192			0.00940958	+	0.999956i	$0.497005\pi$
$432$	5.70724e14	−	5.70724e14i	0.0878059	−	0.0878059i
$433$	−2.33826e15	+	2.33826e15i	−0.354786	+	0.354786i	−0.861887	−	0.507101i	$-0.830717\pi$
$433$	−2.33826e15	+	2.33826e15i	−0.354786	+	0.354786i	0.507101	+	0.861887i	$0.330717\pi$
$434$			4.09328e15i			0.612538i
$435$	5.75410e15	−	2.78253e15i	0.849262	−	0.410681i
$436$	−5.73678e15			−0.835121
$437$	−1.22872e15	−	1.22872e15i	−0.176427	−	0.176427i
$438$	−1.25823e16	−	1.25823e16i	−1.78203	−	1.78203i
$439$			5.04196e13i			0.00704389i	0.999994	+	0.00352195i	$0.00112107\pi$
$439$			5.04196e13i			0.00704389i	−0.999994	+	0.00352195i	$0.998879\pi$
$440$		−	3.41499e14i		−	0.0470623i
$441$		−	5.67180e15i		−	0.771061i
$442$	−1.25372e16			−1.68138
$443$	−6.19157e15	+	6.19157e15i	−0.819178	+	0.819178i	−0.985989	−	0.166811i	$-0.946653\pi$
$443$	−6.19157e15	+	6.19157e15i	−0.819178	+	0.819178i	0.166811	+	0.985989i	$0.446653\pi$
$444$			6.99259e15i			0.912726i
$445$	4.86370e15	−	4.86370e15i	0.626334	−	0.626334i
$446$	−9.76865e15	−	9.76865e15i	−1.24115	−	1.24115i
$447$	1.53071e16	−	1.53071e16i	1.91888	−	1.91888i
$448$			7.79014e15i			0.963557i
$449$	9.20879e14	+	9.20879e14i	0.112389	+	0.112389i	0.761065	−	0.648676i	$-0.224677\pi$
$449$	9.20879e14	+	9.20879e14i	0.112389	+	0.112389i	−0.648676	+	0.761065i	$0.724677\pi$
$450$	6.64772e15	−	6.64772e15i	0.800567	−	0.800567i
$451$	6.90029e13			0.00819989
$452$	8.14455e15	+	8.14455e15i	0.955073	+	0.955073i
$453$	−1.62960e16	+	1.62960e16i	−1.88578	+	1.88578i
$454$	−1.12869e16	−	1.12869e16i	−1.28896	−	1.28896i
$455$	4.89846e15			0.552066
$456$	1.85456e15	+	1.85456e15i	0.206278	+	0.206278i
$457$			3.33648e15i			0.366261i	0.983089	+	0.183131i	$0.0586231\pi$
$457$			3.33648e15i			0.366261i	−0.983089	+	0.183131i	$0.941377\pi$
$458$	−8.16726e15			−0.884879
$459$	2.23673e15			0.239187
$460$	−7.28118e15			−0.768519
$461$	−3.34159e15	+	3.34159e15i	−0.348135	+	0.348135i	−0.859414	−	0.511280i	$-0.829172\pi$
$461$	−3.34159e15	+	3.34159e15i	−0.348135	+	0.348135i	0.511280	+	0.859414i	$0.329172\pi$
$462$	1.07254e15	−	1.07254e15i	0.110297	−	0.110297i
$463$		−	3.16171e15i		−	0.320949i	−0.987040	−	0.160475i	$-0.948698\pi$
$463$		−	3.16171e15i		−	0.320949i	0.987040	−	0.160475i	$-0.0513025\pi$
$464$	3.66358e15	+	1.27528e15i	0.367111	+	0.127790i
$465$	−6.20334e15			−0.613632
$466$	−5.10832e15	−	5.10832e15i	−0.498841	−	0.498841i
$467$	1.00062e16	+	1.00062e16i	0.964649	+	0.964649i	0.999396	−	0.0347476i	$-0.0110627\pi$
$467$	1.00062e16	+	1.00062e16i	0.964649	+	0.964649i	−0.0347476	+	0.999396i	$0.511063\pi$
$468$			2.62651e16i			2.49980i
$469$			1.43336e15i			0.134684i
$470$		−	1.46517e16i		−	1.35925i
$471$	−2.15567e16			−1.97450
$472$	−2.12763e15	+	2.12763e15i	−0.192417	+	0.192417i
$473$		−	4.71846e14i		−	0.0421341i
$474$	3.09666e16	−	3.09666e16i	2.73038	−	2.73038i
$475$	−1.42778e15	−	1.42778e15i	−0.124309	−	0.124309i
$476$	−5.31460e15	+	5.31460e15i	−0.456908	+	0.456908i
$477$			2.53139e16i			2.14906i
$478$	−4.58639e15	−	4.58639e15i	−0.384507	−	0.384507i
$479$	1.78977e15	−	1.78977e15i	0.148178	−	0.148178i	−0.629125	−	0.777304i	$-0.716587\pi$
$479$	1.78977e15	−	1.78977e15i	0.148178	−	0.148178i	0.777304	+	0.629125i	$0.216587\pi$
$480$	−1.46841e16			−1.20061
$481$	5.42005e15	+	5.42005e15i	0.437656	+	0.437656i
$482$	−8.26071e15	+	8.26071e15i	−0.658772	+	0.658772i
$483$	−6.85459e15	−	6.85459e15i	−0.539881	−	0.539881i
$484$	1.81302e16			1.41036
$485$	−4.82389e15	−	4.82389e15i	−0.370636	−	0.370636i
$486$			2.91483e16i			2.21205i
$487$	2.50773e16			1.87978			0.939889	−	0.341481i	$-0.110928\pi$
$487$	2.50773e16			1.87978			0.939889	+	0.341481i	$0.110928\pi$
$488$	−6.44071e14			−0.0476886
$489$	−2.77038e16			−2.02622
$490$	−6.13681e15	+	6.13681e15i	−0.443370	+	0.443370i
$491$	8.38192e15	−	8.38192e15i	0.598212	−	0.598212i	−0.341625	−	0.939836i	$-0.610977\pi$
$491$	8.38192e15	−	8.38192e15i	0.598212	−	0.598212i	0.939836	+	0.341625i	$0.110977\pi$
$492$			2.22059e15i			0.156559i
$493$	4.68000e15	+	9.67795e15i	0.325960	+	0.674065i
$494$	9.59143e15			0.659966
$495$	8.91491e14	+	8.91491e14i	0.0606018	+	0.0606018i
$496$	−2.66223e15	−	2.66223e15i	−0.178795	−	0.178795i
$497$		−	6.84409e15i		−	0.454127i
$498$		−	1.10930e16i		−	0.727235i
$499$		−	1.81484e16i		−	1.17553i	−0.809030	−	0.587767i	$-0.800007\pi$
$499$		−	1.81484e16i		−	1.17553i	0.809030	−	0.587767i	$-0.199993\pi$
$500$	−2.26051e16			−1.44673
$501$	−6.68010e15	+	6.68010e15i	−0.422432	+	0.422432i
$502$		−	9.74009e15i		−	0.608612i
$503$	1.73555e16	−	1.73555e16i	1.07159	−	1.07159i	0.0743598	−	0.997231i	$-0.476309\pi$
$503$	1.73555e16	−	1.73555e16i	1.07159	−	1.07159i	0.997231	−	0.0743598i	$-0.0236913\pi$
$504$	5.67437e15	+	5.67437e15i	0.346206	+	0.346206i
$505$	6.94633e15	−	6.94633e15i	0.418800	−	0.418800i
$506$			2.47145e15i			0.147248i
$507$	1.92465e16	+	1.92465e16i	1.13319	+	1.13319i
$508$	7.97529e15	−	7.97529e15i	0.464050	−	0.464050i
$509$	−1.04203e16			−0.599205			−0.299602	−	0.954064i	$-0.596854\pi$
$509$	−1.04203e16			−0.599205			−0.299602	+	0.954064i	$0.596854\pi$
$510$	−1.36943e16	−	1.36943e16i	−0.778247	−	0.778247i
$511$	−8.26849e15	+	8.26849e15i	−0.464409	+	0.464409i
$512$	−9.60451e15	−	9.60451e15i	−0.533157	−	0.533157i
$513$	−1.71118e15			−0.0938842
$514$	1.86104e16	+	1.86104e16i	1.00920	+	1.00920i
$515$		−	2.03224e16i		−	1.08926i
$516$	1.51845e16			0.804458
$517$	−2.92499e15			−0.153172
$518$	7.81300e15			0.404426
$519$	5.96206e15	−	5.96206e15i	0.305065	−	0.305065i
$520$	8.51835e15	−	8.51835e15i	0.430859	−	0.430859i
$521$			1.53752e16i			0.768767i	0.923173	+	0.384384i	$0.125586\pi$
$521$			1.53752e16i			0.768767i	−0.923173	+	0.384384i	$0.874414\pi$
$522$	3.44728e16	−	1.66702e16i	1.70394	−	0.823980i
$523$	−2.49854e16			−1.22089			−0.610445	−	0.792058i	$-0.709009\pi$
$523$	−2.49854e16			−1.22089			−0.610445	+	0.792058i	$0.709009\pi$
$524$	1.59605e16	+	1.59605e16i	0.771006	+	0.771006i
$525$	−7.96509e15	−	7.96509e15i	−0.380395	−	0.380395i
$526$			6.34231e16i			2.99456i
$527$		−	1.04335e16i		−	0.487044i
$528$			1.39514e15i			0.0643895i
$529$	−6.11968e15			−0.279251
$530$	2.73894e16	−	2.73894e16i	1.23574	−	1.23574i
$531$		−	1.11084e16i		−	0.495548i
$532$	4.06588e15	−	4.06588e15i	0.179343	−	0.179343i
$533$	1.72121e15	+	1.72121e15i	0.0750707	+	0.0750707i
$534$	5.31274e16	−	5.31274e16i	2.29124	−	2.29124i
$535$			1.61326e16i			0.687987i
$536$	2.49259e15	+	2.49259e15i	0.105114	+	0.105114i
$537$	−3.94135e16	+	3.94135e16i	−1.64361	+	1.64361i
$538$	−9.60515e15			−0.396105
$539$	1.22512e15	+	1.22512e15i	0.0499628	+	0.0499628i
$540$	−5.07009e15	+	5.07009e15i	−0.204481	+	0.204481i
$541$	−1.25822e15	−	1.25822e15i	−0.0501849	−	0.0501849i	0.681569	−	0.731754i	$-0.261298\pi$
$541$	−1.25822e15	−	1.25822e15i	−0.0501849	−	0.0501849i	−0.731754	+	0.681569i	$0.761298\pi$
$542$	3.27067e16			1.29015
$543$	2.72922e16	+	2.72922e16i	1.06473	+	1.06473i
$544$		−	2.46976e16i		−	0.952930i
$545$	−9.71409e15			−0.370701
$546$	5.35071e16			2.01956
$547$	−3.06142e15			−0.114288			−0.0571438	−	0.998366i	$-0.518199\pi$
$547$	−3.06142e15			−0.114288			−0.0571438	+	0.998366i	$0.518199\pi$
$548$	−2.26436e15	+	2.26436e15i	−0.0836107	+	0.0836107i
$549$	1.68136e15	−	1.68136e15i	0.0614083	−	0.0614083i
$550$			2.87185e15i			0.103749i
$551$	−3.58038e15	−	7.40401e15i	−0.127944	−	0.264580i
$552$	−2.38401e16			−0.842699
$553$	−2.03498e16	−	2.03498e16i	−0.711556	−	0.711556i
$554$	−6.22185e16	−	6.22185e16i	−2.15209	−	2.15209i
$555$			1.18406e16i			0.405148i
$556$			7.45953e16i			2.52501i
$557$		−	3.78724e16i		−	1.26821i	−0.773247	−	0.634105i	$-0.781369\pi$
$557$		−	3.78724e16i		−	1.26821i	0.773247	−	0.634105i	$-0.218631\pi$
$558$	−3.71643e16			−1.23118
$559$	1.17697e16	−	1.17697e16i	0.385741	−	0.385741i
$560$			4.59248e15i			0.148908i
$561$	−2.73385e15	+	2.73385e15i	−0.0876997	+	0.0876997i
$562$	2.31846e15	+	2.31846e15i	0.0735836	+	0.0735836i
$563$	1.61900e16	−	1.61900e16i	0.508390	−	0.508390i	−0.405642	−	0.914032i	$-0.632952\pi$
$563$	1.61900e16	−	1.61900e16i	0.508390	−	0.508390i	0.914032	+	0.405642i	$0.132952\pi$
$564$		−	9.41294e16i		−	2.92449i
$565$	1.37912e16	+	1.37912e16i	0.423946	+	0.423946i
$566$	−3.64966e16	+	3.64966e16i	−1.11008	+	1.11008i
$567$	1.48444e16			0.446751
$568$	−1.19018e16	−	1.19018e16i	−0.354423	−	0.354423i
$569$	−3.09512e16	+	3.09512e16i	−0.912020	+	0.912020i	−0.996431	−	0.0844109i	$-0.973099\pi$
$569$	−3.09512e16	+	3.09512e16i	−0.912020	+	0.912020i	0.0844109	+	0.996431i	$0.473099\pi$
$570$	1.04766e16	+	1.04766e16i	0.305473	+	0.305473i
$571$	1.41323e16			0.407753			0.203876	−	0.978997i	$-0.434646\pi$
$571$	1.41323e16			0.407753			0.203876	+	0.978997i	$0.434646\pi$
$572$	−5.67334e15	−	5.67334e15i	−0.161980	−	0.161980i
$573$		−	2.67167e16i		−	0.754841i
$574$	2.48112e15			0.0693709
$575$	1.83539e16			0.507833
$576$	−7.07293e16			−1.93671
$577$	−4.29339e16	+	4.29339e16i	−1.16344	+	1.16344i	−0.179728	+	0.983716i	$0.557522\pi$
$577$	−4.29339e16	+	4.29339e16i	−1.16344	+	1.16344i	−0.983716	+	0.179728i	$0.942478\pi$
$578$	−1.80521e16	+	1.80521e16i	−0.484129	+	0.484129i
$579$			4.49544e16i			1.19317i
$580$	−3.25458e16	−	1.13291e16i	−0.854922	−	0.297595i
$581$	−7.28981e15			−0.189522
$582$	−5.26926e16	−	5.26926e16i	−1.35585	−	1.35585i
$583$	−5.46788e15	−	5.46788e15i	−0.139254	−	0.139254i
$584$			2.87576e16i			0.724895i
$585$			4.44748e16i			1.10963i
$586$			1.13633e17i			2.80621i
$587$	6.57942e16			1.60827			0.804135	−	0.594446i	$-0.202629\pi$
$587$	6.57942e16			1.60827			0.804135	+	0.594446i	$0.202629\pi$
$588$	−3.94259e16	+	3.94259e16i	−0.953931	+	0.953931i
$589$			7.98207e15i			0.191172i
$590$	−1.20192e16	+	1.20192e16i	−0.284947	+	0.284947i
$591$	6.61614e16	+	6.61614e16i	1.55267	+	1.55267i
$592$	−5.08149e15	+	5.08149e15i	−0.118049	+	0.118049i
$593$		−	2.69007e16i		−	0.618635i	−0.950959	−	0.309318i	$-0.899899\pi$
$593$		−	2.69007e16i		−	0.618635i	0.950959	−	0.309318i	$-0.100101\pi$
$594$	1.72094e15	+	1.72094e15i	0.0391785	+	0.0391785i
$595$	−8.99921e15	+	8.99921e15i	−0.202816	+	0.202816i
$596$	−1.16716e17			−2.60408
$597$	9.04737e16	+	9.04737e16i	1.99837	+	1.99837i
$598$	−6.16479e16	+	6.16479e16i	−1.34807	+	1.34807i
$599$	−8.75938e15	−	8.75938e15i	−0.189632	−	0.189632i	0.605905	−	0.795537i	$-0.292811\pi$
$599$	−8.75938e15	−	8.75938e15i	−0.189632	−	0.189632i	−0.795537	+	0.605905i	$0.792811\pi$
$600$	−2.77024e16			−0.593758
$601$	−1.19296e16	−	1.19296e16i	−0.253152	−	0.253152i	0.569110	−	0.822262i	$-0.307288\pi$
$601$	−1.19296e16	−	1.19296e16i	−0.253152	−	0.253152i	−0.822262	+	0.569110i	$0.807288\pi$
$602$		−	1.69661e16i		−	0.356453i
$603$	−1.30139e16			−0.270710
$604$	1.24257e17			2.55916
$605$	3.06998e16			0.626043
$606$	7.58765e16	−	7.58765e16i	1.53204	−	1.53204i
$607$	5.77611e16	−	5.77611e16i	1.15479	−	1.15479i	0.169210	−	0.985580i	$-0.445878\pi$
$607$	5.77611e16	−	5.77611e16i	1.15479	−	1.15479i	0.985580	−	0.169210i	$-0.0541215\pi$
$608$			1.88946e16i			0.374039i
$609$	−1.99737e16	−	4.13043e16i	−0.391520	−	0.809639i
$610$	−3.63843e15			−0.0706212
$611$	−7.29609e16	−	7.29609e16i	−1.40231	−	1.40231i
$612$	−4.82530e16	−	4.82530e16i	−0.918367	−	0.918367i
$613$		−	2.89910e16i		−	0.546386i	−0.961959	−	0.273193i	$-0.911920\pi$
$613$		−	2.89910e16i		−	0.546386i	0.961959	−	0.273193i	$-0.0880798\pi$
$614$		−	8.14512e16i		−	1.52015i
$615$			3.76013e15i			0.0694948i
$616$	−2.45136e15			−0.0448665
$617$	5.62782e16	−	5.62782e16i	1.02007	−	1.02007i	0.0202738	−	0.999794i	$-0.493546\pi$
$617$	5.62782e16	−	5.62782e16i	1.02007	−	1.02007i	0.999794	−	0.0202738i	$-0.00645380\pi$
$618$		−	2.21986e17i		−	3.98470i
$619$	4.54449e15	−	4.54449e15i	0.0807870	−	0.0807870i	−0.665559	−	0.746346i	$-0.731807\pi$
$619$	4.54449e15	−	4.54449e15i	0.0807870	−	0.0807870i	0.746346	+	0.665559i	$0.231807\pi$
$620$	2.36502e16	+	2.36502e16i	0.416374	+	0.416374i
$621$	1.09985e16	−	1.09985e16i	0.191771	−	0.191771i
$622$		−	6.23783e16i		−	1.07719i
$623$	−3.49128e16	−	3.49128e16i	−0.597112	−	0.597112i
$624$	−3.48004e16	+	3.48004e16i	−0.589491	+	0.589491i
$625$	−2.62323e15			−0.0440105
$626$	−1.00837e16	−	1.00837e16i	−0.167561	−	0.167561i
$627$	2.09151e15	−	2.09151e15i	0.0344234	−	0.0344234i
$628$	8.21847e16	+	8.21847e16i	1.33978	+	1.33978i
$629$	−1.99149e16			−0.321569
$630$	3.20552e16	+	3.20552e16i	0.512690	+	0.512690i
$631$		−	2.61439e16i		−	0.414185i	−0.978321	−	0.207093i	$-0.933600\pi$
$631$		−	2.61439e16i		−	0.414185i	0.978321	−	0.207093i	$-0.0664002\pi$
$632$	−7.07759e16			−1.11067
$633$	−4.81217e16			−0.748029
$634$	1.39208e17			2.14353
$635$	1.35046e16	−	1.35046e16i	0.205986	−	0.205986i
$636$	1.75963e17	−	1.75963e17i	2.65875	−	2.65875i
$637$			6.11190e16i			0.914828i
$638$	−3.84542e15	+	1.10470e16i	−0.0570191	+	0.163803i
$639$	6.21398e16			0.912777
$640$	3.73259e16	+	3.73259e16i	0.543163	+	0.543163i
$641$	3.47579e16	+	3.47579e16i	0.501078	+	0.501078i	0.911773	−	0.410695i	$-0.134714\pi$
$641$	3.47579e16	+	3.47579e16i	0.501078	+	0.501078i	−0.410695	+	0.911773i	$0.634714\pi$
$642$			1.76220e17i			2.51678i
$643$			7.61170e16i			1.07700i	0.842625	+	0.538500i	$0.181009\pi$
$643$			7.61170e16i			1.07700i	−0.842625	+	0.538500i	$0.818991\pi$
$644$			5.22660e16i			0.732663i
$645$	2.57120e16			0.357090
$646$	−1.76209e16	+	1.76209e16i	−0.242456	+	0.242456i
$647$		−	7.71275e16i		−	1.05144i	−0.850659	−	0.525719i	$-0.823796\pi$
$647$		−	7.71275e16i		−	1.05144i	0.850659	−	0.525719i	$-0.176204\pi$
$648$	2.58143e16	−	2.58143e16i	0.348666	−	0.348666i
$649$	2.39945e15	+	2.39945e15i	0.0321103	+	0.0321103i
$650$	−7.16355e16	+	7.16355e16i	−0.949835	+	0.949835i
$651$			4.45291e16i			0.585002i
$652$	1.05620e17	+	1.05620e17i	1.37487	+	1.37487i
$653$	−9.79193e16	+	9.79193e16i	−1.26296	+	1.26296i	−0.313306	+	0.949652i	$0.601437\pi$
$653$	−9.79193e16	+	9.79193e16i	−1.26296	+	1.26296i	−0.949652	+	0.313306i	$0.898563\pi$
$654$	−1.06110e17			−1.35609
$655$	2.70259e16	+	2.70259e16i	0.342241	+	0.342241i
$656$	−1.61370e15	+	1.61370e15i	−0.0202488	+	0.0202488i
$657$	−7.50723e16	−	7.50723e16i	−0.933443	−	0.933443i
$658$	−1.05173e17			−1.29583
$659$	1.96550e16	+	1.96550e16i	0.239972	+	0.239972i	0.816838	−	0.576867i	$-0.195725\pi$
$659$	1.96550e16	+	1.96550e16i	0.239972	+	0.239972i	−0.576867	+	0.816838i	$0.695725\pi$
$660$		−	1.23939e16i		−	0.149949i
$661$	−9.03075e16			−1.08272			−0.541359	−	0.840792i	$-0.682090\pi$
$661$	−9.03075e16			−1.08272			−0.541359	+	0.840792i	$0.682090\pi$
$662$	1.13168e17			1.34455
$663$	−1.36387e17			−1.60580
$664$	−1.26769e16	+	1.26769e16i	−0.147912	+	0.147912i
$665$	6.88475e15	−	6.88475e15i	0.0796083	−	0.0796083i
$666$			7.09368e16i			0.812880i
$667$	7.06011e16	+	2.45760e16i	0.801782	+	0.279097i
$668$	5.09356e16			0.573274
$669$	−1.06269e17	−	1.06269e17i	−1.18536	−	1.18536i
$670$	1.40809e16	+	1.40809e16i	0.155662	+	0.155662i
$671$			7.26358e14i			0.00795821i
$672$			1.05406e17i			1.14459i
$673$			1.17795e16i			0.126776i	0.997989	+	0.0633880i	$0.0201906\pi$
$673$			1.17795e16i			0.126776i	−0.997989	+	0.0633880i	$0.979809\pi$
$674$	−4.28226e16			−0.456787
$675$	1.27803e16	−	1.27803e16i	0.135120	−	0.135120i
$676$		−	1.46754e17i		−	1.53784i
$677$	6.30925e16	−	6.30925e16i	0.655308	−	0.655308i	−0.298958	−	0.954266i	$-0.596639\pi$
$677$	6.30925e16	−	6.30925e16i	0.655308	−	0.655308i	0.954266	+	0.298958i	$0.0966391\pi$
$678$	1.50644e17	+	1.50644e17i	1.55087	+	1.55087i
$679$	−3.46271e16	+	3.46271e16i	−0.353343	+	0.353343i
$680$			3.12990e16i			0.316575i
$681$	−1.22786e17	−	1.22786e17i	−1.23102	−	1.23102i
$682$	8.02758e15	−	8.02758e15i	0.0797771	−	0.0797771i
$683$	1.54235e17			1.51936			0.759678	−	0.650300i	$-0.225357\pi$
$683$	1.54235e17			1.51936			0.759678	+	0.650300i	$0.225357\pi$
$684$	3.69155e16	+	3.69155e16i	0.360472	+	0.360472i
$685$	−3.83424e15	+	3.83424e15i	−0.0371138	+	0.0371138i
$686$	1.13446e17	+	1.13446e17i	1.08854	+	1.08854i
$687$	−8.88482e16			−0.845100
$688$	1.10345e16	+	1.10345e16i	0.104046	+	0.104046i
$689$		−	2.72782e17i		−	2.54976i
$690$	−1.34675e17			−1.24794
$691$	4.50423e16			0.413764			0.206882	−	0.978366i	$-0.433668\pi$
$691$	4.50423e16			0.413764			0.206882	+	0.978366i	$0.433668\pi$
$692$	−4.54605e16			−0.413998
$693$	6.39934e15	−	6.39934e15i	0.0577744	−	0.0577744i
$694$	5.68632e16	−	5.68632e16i	0.508949	−	0.508949i
$695$			1.26312e17i			1.12082i
$696$	−1.06561e17	−	3.70936e16i	−0.937443	−	0.326320i
$697$	−6.32425e15			−0.0551585
$698$	5.82351e16	+	5.82351e16i	0.503561	+	0.503561i
$699$	−5.55712e16	−	5.55712e16i	−0.476417	−	0.476417i
$700$			6.07336e16i			0.516227i
$701$		−	1.20727e17i		−	1.01741i	−0.860941	−	0.508704i	$-0.830125\pi$
$701$		−	1.20727e17i		−	1.01741i	0.860941	−	0.508704i	$-0.169875\pi$
$702$			8.58544e16i			0.717364i
$703$	1.52357e16			0.126220
$704$	1.52777e16	−	1.52777e16i	0.125494	−	0.125494i
$705$		−	1.59389e17i		−	1.29815i
$706$	1.51756e17	−	1.51756e17i	1.22552	−	1.22552i
$707$	−4.98624e16	−	4.98624e16i	−0.399261	−	0.399261i
$708$	−7.72172e16	+	7.72172e16i	−0.613076	+	0.613076i
$709$			1.10326e17i			0.868558i	0.900778	+	0.434279i	$0.142997\pi$
$709$			1.10326e17i			0.868558i	−0.900778	+	0.434279i	$0.857003\pi$
$710$	−6.72345e16	−	6.72345e16i	−0.524858	−	0.524858i
$711$	1.84762e17	−	1.84762e17i	1.43020	−	1.43020i
$712$	−1.21426e17			−0.932031
$713$	−5.13039e16	−	5.13039e16i	−0.390493	−	0.390493i
$714$	−9.83007e16	+	9.83007e16i	−0.741937	+	0.741937i
$715$	−9.60666e15	−	9.60666e15i	−0.0719012	−	0.0719012i
$716$	3.00527e17			2.23051
$717$	−4.98934e16	−	4.98934e16i	−0.367222	−	0.367222i
$718$		−	1.40749e17i		−	1.02730i
$719$	7.51845e15			0.0544195			0.0272098	−	0.999630i	$-0.491338\pi$
$719$	7.51845e15			0.0544195			0.0272098	+	0.999630i	$0.491338\pi$
$720$	−4.16967e16			−0.299300
$721$	−1.45879e17			−1.03844
$722$	−1.42596e17	+	1.42596e17i	−1.00666	+	1.00666i
$723$	−8.98647e16	+	8.98647e16i	−0.629158	+	0.629158i
$724$		−	2.08103e17i		−	1.44493i
$725$	8.20391e16	+	2.85575e16i	0.564928	+	0.196649i
$726$	3.35342e17			2.29017
$727$	5.34469e16	+	5.34469e16i	0.362006	+	0.362006i	0.864551	−	0.502545i	$-0.167603\pi$
$727$	5.34469e16	+	5.34469e16i	0.362006	+	0.362006i	−0.502545	+	0.864551i	$0.667603\pi$
$728$	−6.11468e16	−	6.11468e16i	−0.410757	−	0.410757i
$729$			2.06133e17i			1.37335i
$730$			1.62455e17i			1.07348i
$731$			4.32456e16i			0.283424i
$732$	−2.33750e16			−0.151945
$733$	1.22167e17	−	1.22167e17i	0.787644	−	0.787644i	−0.193463	−	0.981108i	$-0.561972\pi$
$733$	1.22167e17	−	1.22167e17i	0.787644	−	0.787644i	0.981108	+	0.193463i	$0.0619721\pi$
$734$			1.28705e17i			0.823035i
$735$	−6.67598e16	+	6.67598e16i	−0.423439	+	0.423439i
$736$	−1.21443e17	−	1.21443e17i	−0.764023	−	0.764023i
$737$	2.81104e15	−	2.81104e15i	0.0175413	−	0.0175413i
$738$			2.25270e16i			0.139433i
$739$	−8.76268e16	−	8.76268e16i	−0.537985	−	0.537985i	0.384951	−	0.922937i	$-0.374218\pi$
$739$	−8.76268e16	−	8.76268e16i	−0.537985	−	0.537985i	−0.922937	+	0.384951i	$0.874218\pi$
$740$	4.51420e16	−	4.51420e16i	0.274910	−	0.274910i
$741$	1.04341e17			0.630298
$742$	−1.96607e17	−	1.96607e17i	−1.17808	−	1.17808i
$743$	−1.47806e17	+	1.47806e17i	−0.878538	+	0.878538i	−0.993383	−	0.114846i	$-0.963363\pi$
$743$	−1.47806e17	+	1.47806e17i	−0.878538	+	0.878538i	0.114846	+	0.993383i	$0.463363\pi$
$744$	7.74354e16	+	7.74354e16i	0.456564	+	0.456564i
$745$	−1.97636e17			−1.15592
$746$	−6.60869e16	−	6.60869e16i	−0.383427	−	0.383427i
$747$		−	6.61866e16i		−	0.380931i
$748$	2.08456e16			0.119016
$749$	1.15803e17			0.655888
$750$	−4.18112e17			−2.34923
$751$	−2.07472e17	+	2.07472e17i	−1.15643	+	1.15643i	−0.171196	+	0.985237i	$0.554763\pi$
$751$	−2.07472e17	+	2.07472e17i	−1.15643	+	1.15643i	−0.985237	+	0.171196i	$0.945237\pi$
$752$	6.84035e16	−	6.84035e16i	0.378243	−	0.378243i
$753$		−	1.05958e17i		−	0.581253i
$754$	−3.71477e17	+	1.79637e17i	−2.02164	+	0.977613i
$755$	2.10404e17			1.13598
$756$	3.63943e16	+	3.63943e16i	0.194941	+	0.194941i
$757$	2.04644e17	+	2.04644e17i	1.08748	+	1.08748i	0.995787	+	0.0916978i	$0.0292294\pi$
$757$	2.04644e17	+	2.04644e17i	1.08748	+	1.08748i	0.0916978	+	0.995787i	$0.470771\pi$
$758$			5.24964e17i			2.76767i
$759$			2.68859e16i			0.140629i
$760$		−	2.39450e16i		−	0.124260i
$761$	−1.31087e17			−0.674919			−0.337459	−	0.941340i	$-0.609568\pi$
$761$	−1.31087e17			−0.674919			−0.337459	+	0.941340i	$0.609568\pi$
$762$	1.47514e17	−	1.47514e17i	0.753533	−	0.753533i
$763$			6.97301e16i			0.353405i
$764$	−1.01857e17	+	1.01857e17i	−0.512190	+	0.512190i
$765$	−8.17068e16	−	8.17068e16i	−0.407652	−	0.407652i
$766$	2.44900e17	−	2.44900e17i	1.21232	−	1.21232i
$767$			1.19704e17i			0.587945i
$768$	6.34372e16	+	6.34372e16i	0.309155	+	0.309155i
$769$	−1.59636e17	+	1.59636e17i	−0.771919	+	0.771919i	−0.978442	−	0.206522i	$-0.933785\pi$
$769$	−1.59636e17	+	1.59636e17i	−0.771919	+	0.771919i	0.206522	+	0.978442i	$0.433785\pi$
$770$	−1.38480e16			−0.0664420
$771$	2.02455e17	+	2.02455e17i	0.963833	+	0.963833i
$772$	1.71388e17	−	1.71388e17i	0.809612	−	0.809612i
$773$	−6.45013e16	−	6.45013e16i	−0.302337	−	0.302337i	0.539591	−	0.841928i	$-0.318579\pi$
$773$	−6.45013e16	−	6.45013e16i	−0.302337	−	0.302337i	−0.841928	+	0.539591i	$0.818579\pi$
$774$	1.54041e17			0.716456
$775$	−5.96156e16	−	5.96156e16i	−0.275138	−	0.275138i
$776$			1.20432e17i			0.551533i
$777$	8.49943e16			0.386246
$778$	−6.04622e17			−2.72651
$779$	4.83830e15			0.0216505
$780$	3.09153e17	−	3.09153e17i	1.37280	−	1.37280i
$781$	−1.34224e16	+	1.34224e16i	−0.0591456	+	0.0591456i
$782$		−	2.26513e17i		−	0.990497i
$783$	6.62744e16	−	3.20486e16i	0.287591	−	0.139071i
$784$	−5.73012e16			−0.246756
$785$	1.39163e17	+	1.39163e17i	0.594712	+	0.594712i
$786$	2.95210e17	+	2.95210e17i	1.25198	+	1.25198i
$787$		−	2.94622e17i		−	1.23999i	−0.784607	−	0.619994i	$-0.787135\pi$
$787$		−	2.94622e17i		−	1.23999i	0.784607	−	0.619994i	$-0.212865\pi$
$788$		−	5.04479e17i		−	2.10710i
$789$			6.89953e17i			2.85995i
$790$	−3.99821e17			−1.64476
$791$	9.89963e16	−	9.89963e16i	0.404166	−	0.404166i
$792$		−	2.22567e16i		−	0.0901799i
$793$	−1.81183e16	+	1.81183e16i	−0.0728581	+	0.0728581i
$794$	2.31497e16	+	2.31497e16i	0.0923894	+	0.0923894i
$795$	2.97957e17	−	2.97957e17i	1.18019	−	1.18019i
$796$		−	6.89859e17i		−	2.71195i
$797$	2.96396e17	+	2.96396e17i	1.15644	+	1.15644i	0.985236	+	0.171203i	$0.0547653\pi$
$797$	2.96396e17	+	2.96396e17i	1.15644	+	1.15644i	0.171203	+	0.985236i	$0.445235\pi$
$798$	7.52039e16	−	7.52039e16i	0.291221	−	0.291221i
$799$	2.68080e17			1.03035
$800$	−1.41118e17	−	1.41118e17i	−0.538323	−	0.538323i
$801$	3.16985e17	−	3.16985e17i	1.20017	−	1.20017i
$802$	−1.42324e17	−	1.42324e17i	−0.534848	−	0.534848i
$803$	3.24316e16			0.120969
$804$	9.04625e16	+	9.04625e16i	0.334913	+	0.334913i
$805$			8.85021e16i			0.325221i
$806$	4.00480e17			1.46073
$807$	−1.04490e17			−0.378299
$808$	−1.73420e17			−0.623205
$809$	−7.16691e16	+	7.16691e16i	−0.255647	+	0.255647i	−0.823281	−	0.567634i	$-0.807859\pi$
$809$	−7.16691e16	+	7.16691e16i	−0.255647	+	0.255647i	0.567634	+	0.823281i	$0.307859\pi$
$810$	1.45828e17	−	1.45828e17i	0.516333	−	0.516333i
$811$			2.75210e17i			0.967250i	0.875275	+	0.483625i	$0.160680\pi$
$811$			2.75210e17i			0.967250i	−0.875275	+	0.483625i	$0.839320\pi$
$812$	−8.13227e16	+	2.33621e17i	−0.283711	+	0.815035i
$813$	3.55802e17			1.23215
$814$	−1.53225e16	−	1.53225e16i	−0.0526725	−	0.0526725i
$815$	1.78847e17	+	1.78847e17i	0.610289	+	0.610289i
$816$		−	1.27867e17i		−	0.433130i
$817$		−	3.30845e16i		−	0.111248i
$818$		−	4.57969e17i		−	1.52868i
$819$	3.19250e17			1.05786
$820$	1.43354e16	−	1.43354e16i	0.0471550	−	0.0471550i
$821$			5.62381e17i			1.83642i	0.396095	+	0.918210i	$0.370365\pi$
$821$			5.62381e17i			1.83642i	−0.396095	+	0.918210i	$0.629635\pi$
$822$	−4.18823e16	+	4.18823e16i	−0.135769	+	0.135769i
$823$	−1.15882e17	−	1.15882e17i	−0.372923	−	0.372923i	0.495618	−	0.868541i	$-0.334942\pi$
$823$	−1.15882e17	−	1.15882e17i	−0.372923	−	0.372923i	−0.868541	+	0.495618i	$0.834942\pi$
$824$	−2.53681e17	+	2.53681e17i	−0.810447	+	0.810447i
$825$			3.12416e16i			0.0990855i
$826$	8.62767e16	+	8.62767e16i	0.271652	+	0.271652i
$827$	6.15683e16	−	6.15683e16i	0.192453	−	0.192453i	−0.604302	−	0.796755i	$-0.706548\pi$
$827$	6.15683e16	−	6.15683e16i	0.192453	−	0.192453i	0.796755	+	0.604302i	$0.206548\pi$
$828$	−4.74541e17			−1.47262
$829$	−1.56255e16	−	1.56255e16i	−0.0481402	−	0.0481402i	0.682627	−	0.730767i	$-0.260837\pi$
$829$	−1.56255e16	−	1.56255e16i	−0.0481402	−	0.0481402i	−0.730767	+	0.682627i	$0.760837\pi$
$830$	−7.16132e16	+	7.16132e16i	−0.219040	+	0.219040i
$831$	−6.76849e17	−	6.76849e17i	−2.05535	−	2.05535i
$832$	7.62175e17			2.29781
$833$	−1.12285e17	−	1.12285e17i	−0.336086	−	0.336086i
$834$			1.37974e18i			4.10016i
$835$	8.62492e16			0.254470
$836$	−1.59477e16			−0.0467153
$837$	−7.14487e16			−0.207798
$838$	9.70599e16	−	9.70599e16i	0.280269	−	0.280269i
$839$	1.02470e17	−	1.02470e17i	0.293782	−	0.293782i	−0.544790	−	0.838573i	$-0.683391\pi$
$839$	1.02470e17	−	1.02470e17i	0.293782	−	0.293782i	0.838573	+	0.544790i	$0.183391\pi$
$840$		−	1.33580e17i		−	0.380248i
$841$	2.77338e17	+	2.19702e17i	0.783849	+	0.620951i
$842$	−1.84335e17			−0.517292
$843$	2.52215e16	+	2.52215e16i	0.0702758	+	0.0702758i
$844$	1.83463e17	+	1.83463e17i	0.507568	+	0.507568i
$845$		−	2.48499e17i		−	0.682628i
$846$		−	9.54902e17i		−	2.60457i
$847$		−	2.20371e17i		−	0.596834i
$848$	2.55743e17			0.687746
$849$	−3.97031e17	+	3.97031e17i	−1.06018	+	1.06018i
$850$		−	2.63210e17i		−	0.697894i
$851$	−9.79257e16	+	9.79257e16i	−0.257822	+	0.257822i
$852$	−4.31947e17	−	4.31947e17i	−1.12926	−	1.12926i
$853$	−1.02342e17	+	1.02342e17i	−0.265680	+	0.265680i	−0.827357	−	0.561677i	$-0.810156\pi$
$853$	−1.02342e17	+	1.02342e17i	−0.265680	+	0.265680i	0.561677	+	0.827357i	$0.310156\pi$
$854$			2.61175e16i			0.0673262i
$855$	6.25089e16	+	6.25089e16i	0.160009	+	0.160009i
$856$	2.01380e17	−	2.01380e17i	0.511887	−	0.511887i
$857$	−5.04431e17			−1.27326			−0.636630	−	0.771170i	$-0.719672\pi$
$857$	−5.04431e17			−1.27326			−0.636630	+	0.771170i	$0.719672\pi$
$858$	−1.04936e17	−	1.04936e17i	−0.263027	−	0.263027i
$859$	−2.15639e17	+	2.15639e17i	−0.536747	+	0.536747i	−0.922572	−	0.385825i	$-0.873917\pi$
$859$	−2.15639e17	+	2.15639e17i	−0.536747	+	0.536747i	0.385825	+	0.922572i	$0.373917\pi$
$860$	−9.80266e16	−	9.80266e16i	−0.242300	−	0.242300i
$861$	2.69911e16			0.0662524
$862$	−8.50664e15	−	8.50664e15i	−0.0207355	−	0.0207355i
$863$		−	3.80519e17i		−	0.921110i	−0.887631	−	0.460555i	$-0.847650\pi$
$863$		−	3.80519e17i		−	0.921110i	0.887631	−	0.460555i	$-0.152350\pi$
$864$	−1.69129e17			−0.406569
$865$	−7.69783e16			−0.183769
$866$	3.29775e17			0.781826
$867$	−1.96381e17	+	1.96381e17i	−0.462365	+	0.462365i
$868$	1.69766e17	−	1.69766e17i	0.396948	−	0.396948i
$869$			7.98183e16i			0.185346i
$870$	−6.01978e17	−	2.09546e17i	−1.38824	−	0.483241i
$871$	1.40237e17			0.321185
$872$	1.21260e17	+	1.21260e17i	0.275815	+	0.275815i
$873$	−3.14391e17	−	3.14391e17i	−0.710206	−	0.710206i
$874$			1.73291e17i			0.388784i
$875$			2.74763e17i			0.612224i
$876$			1.04369e18i			2.30965i
$877$	5.20366e16			0.114370			0.0571849	−	0.998364i	$-0.481788\pi$
$877$	5.20366e16			0.114370			0.0571849	+	0.998364i	$0.481788\pi$
$878$	3.55544e15	−	3.55544e15i	0.00776116	−	0.00776116i
$879$			1.23617e18i			2.68006i
$880$	9.00659e15	−	9.00659e15i	0.0193939	−	0.0193939i
$881$	−5.21766e17	−	5.21766e17i	−1.11589	−	1.11589i	−0.992338	−	0.123550i	$-0.960572\pi$
$881$	−5.21766e17	−	5.21766e17i	−1.11589	−	1.11589i	−0.123550	−	0.992338i	$-0.539428\pi$
$882$	−3.99958e17	+	3.99958e17i	−0.849578	+	0.849578i
$883$		−	5.57527e17i		−	1.17626i	−0.808768	−	0.588128i	$-0.799865\pi$
$883$		−	5.57527e17i		−	1.17626i	0.808768	−	0.588128i	$-0.200135\pi$
$884$	5.19972e17	+	5.19972e17i	1.08960	+	1.08960i
$885$	−1.30752e17	+	1.30752e17i	−0.272137	+	0.272137i
$886$	8.73222e17			1.80519
$887$	1.36133e17	+	1.36133e17i	0.279525	+	0.279525i	0.832919	−	0.553394i	$-0.186668\pi$
$887$	1.36133e17	+	1.36133e17i	0.279525	+	0.279525i	−0.553394	+	0.832919i	$0.686668\pi$
$888$	1.47804e17	−	1.47804e17i	0.301445	−	0.301445i
$889$	−9.69389e16	−	9.69389e16i	−0.196376	−	0.196376i
$890$	−6.85947e17			−1.38023
$891$	−2.91123e16	−	2.91123e16i	−0.0581849	−	0.0581849i
$892$			8.10298e17i			1.60863i
$893$	−2.05092e17			−0.404427
$894$	−2.15882e18			−4.22856
$895$	5.08882e17			0.990099
$896$	2.67934e17	−	2.67934e17i	0.517821	−	0.517821i
$897$	−6.70642e17	+	6.70642e17i	−1.28747	+	1.28747i
$898$		−	1.29875e17i		−	0.247667i
$899$	−1.49495e17	−	3.09147e17i	−0.283184	−	0.585607i
$900$	−5.51421e17			−1.03760
$901$	5.01141e17	+	5.01141e17i	0.936723	+	0.936723i
$902$	−4.86588e15	−	4.86588e15i	−0.00903488	−	0.00903488i
$903$		−	1.84567e17i		−	0.340429i
$904$		−	3.44306e17i		−	0.630862i
$905$		−	3.52380e17i		−	0.641386i
$906$	2.29829e18			4.15562
$907$	5.24397e17	−	5.24397e17i	0.941925	−	0.941925i	−0.0564792	−	0.998404i	$-0.517987\pi$
$907$	5.24397e17	−	5.24397e17i	0.941925	−	0.941925i	0.998404	+	0.0564792i	$0.0179875\pi$
$908$			9.36237e17i			1.67059i
$909$	4.52717e17	−	4.52717e17i	0.802497	−	0.802497i
$910$	−3.45425e17	−	3.45425e17i	−0.608283	−	0.608283i
$911$	−4.00139e17	+	4.00139e17i	−0.700005	+	0.700005i	−0.964411	−	0.264407i	$-0.914824\pi$
$911$	−4.00139e17	+	4.00139e17i	−0.700005	+	0.700005i	0.264407	+	0.964411i	$0.414824\pi$
$912$			9.78235e16i			0.170010i
$913$	1.42965e16	+	1.42965e16i	0.0246834	+	0.0246834i
$914$	2.35279e17	−	2.35279e17i	0.403557	−	0.403557i
$915$	−3.95809e16			−0.0674465
$916$	3.38733e17	+	3.38733e17i	0.573435	+	0.573435i
$917$	1.93998e17	−	1.93998e17i	0.326273	−	0.326273i
$918$	−1.57727e17	−	1.57727e17i	−0.263543	−	0.263543i
$919$	−1.02518e18			−1.70179			−0.850895	−	0.525336i	$-0.823940\pi$
$919$	−1.02518e18			−1.70179			−0.850895	+	0.525336i	$0.823940\pi$
$920$	1.53904e17	+	1.53904e17i	0.253818	+	0.253818i
$921$		−	8.86073e17i		−	1.45182i
$922$	4.71278e17			0.767169
$923$	−6.69615e17			−1.08297
$924$	−8.89663e16			−0.142953
$925$	−1.13791e17	+	1.13791e17i	−0.181659	+	0.181659i
$926$	−2.22954e17	+	2.22954e17i	−0.353631	+	0.353631i
$927$		−	1.32448e18i		−	2.08722i
$928$	−3.53875e17	−	7.31791e17i	−0.554066	−	1.14577i
$929$	−3.96020e17			−0.616060			−0.308030	−	0.951377i	$-0.599670\pi$
$929$	−3.96020e17			−0.616060			−0.308030	+	0.951377i	$0.599670\pi$
$930$	4.37441e17	+	4.37441e17i	0.676118	+	0.676118i
$931$	8.59023e16	+	8.59023e16i	0.131919	+	0.131919i
$932$			4.23729e17i			0.646536i
$933$		−	6.78587e17i		−	1.02876i
$934$		−	1.41122e18i		−	2.12576i
$935$	3.52978e16			0.0528297
$936$	5.55172e17	−	5.55172e17i	0.825605	−	0.825605i
$937$		−	4.84867e17i		−	0.716449i	−0.933635	−	0.358225i	$-0.883382\pi$
$937$		−	4.84867e17i		−	0.716449i	0.933635	−	0.358225i	$-0.116618\pi$
$938$	1.01076e17	−	1.01076e17i	0.148399	−	0.148399i
$939$	−1.09696e17	−	1.09696e17i	−0.160028	−	0.160028i
$940$	−6.07670e17	+	6.07670e17i	−0.880847	+	0.880847i
$941$			1.79797e17i			0.258967i	0.991582	+	0.129484i	$0.0413320\pi$
$941$			1.79797e17i			0.258967i	−0.991582	+	0.129484i	$0.958668\pi$
$942$	1.52012e18	+	1.52012e18i	2.17556	+	2.17556i
$943$	−3.10977e16	+	3.10977e16i	−0.0442239	+	0.0442239i
$944$	−1.12227e17			−0.158586
$945$	6.16265e16	+	6.16265e16i	0.0865319	+	0.0865319i
$946$	−3.32732e16	+	3.32732e16i	−0.0464245	+	0.0464245i
$947$	2.40586e17	+	2.40586e17i	0.333557	+	0.333557i	0.853936	−	0.520379i	$-0.174209\pi$
$947$	2.40586e17	+	2.40586e17i	0.333557	+	0.333557i	−0.520379	+	0.853936i	$0.674209\pi$
$948$	−2.56865e18			−3.53878
$949$	8.08976e17	+	8.08976e17i	1.10749	+	1.10749i
$950$			2.01366e17i			0.273933i
$951$	1.51439e18			2.04717
$952$	2.24672e17			0.301805
$953$	6.73410e17			0.898922			0.449461	−	0.893300i	$-0.351616\pi$
$953$	6.73410e17			0.898922			0.449461	+	0.893300i	$0.351616\pi$
$954$	1.78506e18	−	1.78506e18i	2.36790	−	2.36790i
$955$	−1.72475e17	+	1.72475e17i	−0.227355	+	0.227355i
$956$			3.80436e17i			0.498350i
$957$	−4.18327e16	+	1.20176e17i	−0.0544559	+	0.156439i
$958$	−2.52419e17			−0.326534
$959$	2.75231e16	+	2.75231e16i	0.0353822	+	0.0353822i
$960$	8.32518e17	+	8.32518e17i	1.06357	+	1.06357i
$961$		−	4.54380e17i		−	0.576871i
$962$		−	7.64412e17i		−	0.964444i
$963$			1.05142e18i			1.31831i
$964$	6.85216e17			0.853818
$965$	2.90212e17	−	2.90212e17i	0.359378	−	0.359378i
$966$			9.66730e17i			1.18971i
$967$	1.93045e17	−	1.93045e17i	0.236102	−	0.236102i	−0.579132	−	0.815234i	$-0.696608\pi$
$967$	1.93045e17	−	1.93045e17i	0.236102	−	0.236102i	0.815234	+	0.579132i	$0.196608\pi$
$968$	−3.83222e17	−	3.83222e17i	−0.465798	−	0.465798i
$969$	−1.91690e17	+	1.91690e17i	−0.231557	+	0.231557i
$970$			6.80334e17i			0.816754i
$971$	2.64740e17	+	2.64740e17i	0.315867	+	0.315867i	0.847177	−	0.531310i	$-0.178300\pi$
$971$	2.64740e17	+	2.64740e17i	0.315867	+	0.315867i	−0.531310	+	0.847177i	$0.678300\pi$
$972$	1.20891e18	−	1.20891e18i	1.43349	−	1.43349i
$973$	9.06699e17			1.06853
$974$	−1.76837e18	−	1.76837e18i	−2.07119	−	2.07119i
$975$	−7.79292e17	+	7.79292e17i	−0.907136	+	0.907136i
$976$	−1.69865e16	−	1.69865e16i	−0.0196520	−	0.0196520i
$977$	−2.64449e17			−0.304071			−0.152035	−	0.988375i	$-0.548583\pi$
$977$	−2.64449e17			−0.304071			−0.152035	+	0.988375i	$0.548583\pi$
$978$	1.95359e18	+	1.95359e18i	2.23254	+	2.23254i
$979$			1.36939e17i			0.155536i
$980$	5.09042e17			0.574641
$981$	−6.33102e17			−0.710330
$982$	−1.18214e18			−1.31825
$983$	4.44061e17	−	4.44061e17i	0.492177	−	0.492177i	−0.416815	−	0.908992i	$-0.636854\pi$
$983$	4.44061e17	−	4.44061e17i	0.492177	−	0.492177i	0.908992	+	0.416815i	$0.136854\pi$
$984$	4.69371e16	−	4.69371e16i	0.0517066	−	0.0517066i
$985$		−	8.54234e17i		−	0.935318i
$986$	3.52440e17	−	1.01248e18i	0.383552	−	1.10186i
$987$	−1.14413e18			−1.23758
$988$	−3.97799e17	−	3.97799e17i	−0.427683	−	0.427683i
$989$	2.12648e17	+	2.12648e17i	0.227239	+	0.227239i
$990$		−	1.25731e17i		−	0.133546i
$991$		−	8.93814e17i		−	0.943638i	−0.881695	−	0.471819i	$-0.843598\pi$
$991$		−	8.93814e17i		−	0.943638i	0.881695	−	0.471819i	$-0.156402\pi$
$992$			7.88924e17i			0.827876i
$993$	1.23111e18			1.28410
$994$	−4.82625e17	+	4.82625e17i	−0.500371	+	0.500371i
$995$		−	1.16814e18i		−	1.20380i
$996$	−4.60077e17	+	4.60077e17i	−0.471276	+	0.471276i
$997$	7.12792e17	+	7.12792e17i	0.725758	+	0.725758i	0.969772	−	0.244014i	$-0.0784643\pi$
$997$	7.12792e17	+	7.12792e17i	0.725758	+	0.725758i	−0.244014	+	0.969772i	$0.578464\pi$
$998$	−1.27977e18	+	1.27977e18i	−1.29524	+	1.29524i
$999$			1.36377e17i			0.137198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.13.c.a.12.4	✓	58
29.17	odd	4	inner	29.13.c.a.17.4	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.13.c.a.12.4	✓	58	1.1	even	1	trivial
29.13.c.a.17.4	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)

\(f(q)\)	\(=\)	\(q+(-70.5170 - 70.5170i) q^{2} +(-767.125 - 767.125i) q^{3} +5849.31i q^{4} +9904.63i q^{5} +108191. i q^{6} +71097.8 q^{7} +(123638. - 123638. i) q^{8} +645520. i q^{9} +O(q^{10})\)	\(q+(-70.5170 - 70.5170i) q^{2} +(-767.125 - 767.125i) q^{3} +5849.31i q^{4} +9904.63i q^{5} +108191. i q^{6} +71097.8 q^{7} +(123638. - 123638. i) q^{8} +645520. i q^{9} +(698445. - 698445. i) q^{10} +(-139434. - 139434. i) q^{11} +(4.48715e6 - 4.48715e6i) q^{12} -6.95609e6i q^{13} +(-5.01360e6 - 5.01360e6i) q^{14} +(7.59809e6 - 7.59809e6i) q^{15} +6.52159e6 q^{16} +(1.27794e7 + 1.27794e7i) q^{17} +(4.55202e7 - 4.55202e7i) q^{18} +(-9.77674e6 - 9.77674e6i) q^{19} -5.79352e7 q^{20} +(-5.45409e7 - 5.45409e7i) q^{21} +1.96650e7i q^{22} +1.25678e8 q^{23} -1.89692e8 q^{24} +1.46039e8 q^{25} +(-4.90523e8 + 4.90523e8i) q^{26} +(8.75131e7 - 8.75131e7i) q^{27} +4.15873e8i q^{28} +(5.61762e8 + 1.95547e8i) q^{29} -1.07159e9 q^{30} +(-4.08217e8 - 4.08217e8i) q^{31} +(-9.66304e8 - 9.66304e8i) q^{32} +2.13927e8i q^{33} -1.80233e9i q^{34} +7.04197e8i q^{35} -3.77585e9 q^{36} +(-7.79180e8 + 7.79180e8i) q^{37} +1.37885e9i q^{38} +(-5.33619e9 + 5.33619e9i) q^{39} +(1.22459e9 + 1.22459e9i) q^{40} +(-2.47439e8 + 2.47439e8i) q^{41} +7.69212e9i q^{42} +(1.69200e9 + 1.69200e9i) q^{43} +(8.15593e8 - 8.15593e8i) q^{44} -6.39364e9 q^{45} +(-8.86244e9 - 8.86244e9i) q^{46} +(1.04888e10 - 1.04888e10i) q^{47} +(-5.00287e9 - 5.00287e9i) q^{48} -8.78639e9 q^{49} +(-1.02982e10 - 1.02982e10i) q^{50} -1.96068e10i q^{51} +4.06883e10 q^{52} +3.92148e10 q^{53} -1.23423e10 q^{54} +(1.38104e9 - 1.38104e9i) q^{55} +(8.79039e9 - 8.79039e9i) q^{56} +1.50000e10i q^{57} +(-2.58244e10 - 5.34032e10i) q^{58} -1.72085e10 q^{59} +(4.44435e10 + 4.44435e10i) q^{60} +(-2.60466e9 - 2.60466e9i) q^{61} +5.75726e10i q^{62} +4.58951e10i q^{63} +1.09569e11i q^{64} +6.88975e10 q^{65} +(1.50855e10 - 1.50855e10i) q^{66} +2.01604e10i q^{67} +(-7.47506e10 + 7.47506e10i) q^{68} +(-9.64107e10 - 9.64107e10i) q^{69} +(4.96579e10 - 4.96579e10i) q^{70} -9.62631e10i q^{71} +(7.98108e10 + 7.98108e10i) q^{72} +(-1.16297e11 + 1.16297e11i) q^{73} +1.09891e11 q^{74} +(-1.12030e11 - 1.12030e11i) q^{75} +(5.71871e10 - 5.71871e10i) q^{76} +(-9.91345e9 - 9.91345e9i) q^{77} +7.52585e11 q^{78} +(-2.86222e11 - 2.86222e11i) q^{79} +6.45939e10i q^{80} +2.08789e11 q^{81} +3.48974e10 q^{82} -1.02532e11 q^{83} +(3.19026e11 - 3.19026e11i) q^{84} +(-1.26575e11 + 1.26575e11i) q^{85} -2.38630e11i q^{86} +(-2.80932e11 - 5.80950e11i) q^{87} -3.44787e10 q^{88} +(-4.91053e11 - 4.91053e11i) q^{89} +(4.50861e11 + 4.50861e11i) q^{90} -4.94563e11i q^{91} +7.35129e11i q^{92} +6.26307e11i q^{93} -1.47928e12 q^{94} +(9.68350e10 - 9.68350e10i) q^{95} +1.48255e12i q^{96} +(-4.87034e11 + 4.87034e11i) q^{97} +(6.19590e11 + 6.19590e11i) q^{98} +(9.00075e10 - 9.00075e10i) 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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