LMFDB - Embedded newform 16.9.f.a.3.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,9,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	16.f (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:	$6.51805776098$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.11
Character	$\chi$	$=$	16.3
Dual form			16.9.f.a.11.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.2604 - 12.2770i) q^{2} +(-49.7393 + 49.7393i) q^{3} +(-45.4477 - 251.934i) q^{4} +(-502.907 + 502.907i) q^{5} +(100.302 + 1120.99i) q^{6} -2327.86 q^{7} +(-3559.29 - 2026.98i) q^{8} +1613.00i q^{9} +O(q^{10})$	\(q+(10.2604 - 12.2770i) q^{2} +(-49.7393 + 49.7393i) q^{3} +(-45.4477 - 251.934i) q^{4} +(-502.907 + 502.907i) q^{5} +(100.302 + 1120.99i) q^{6} -2327.86 q^{7} +(-3559.29 - 2026.98i) q^{8} +1613.00i q^{9} +(1014.13 + 11334.2i) q^{10} +(6755.98 + 6755.98i) q^{11} +(14791.5 + 10270.5i) q^{12} +(-13562.0 - 13562.0i) q^{13} +(-23884.8 + 28579.0i) q^{14} -50028.5i q^{15} +(-61405.0 + 22899.6i) q^{16} -100431. q^{17} +(19802.8 + 16550.1i) q^{18} +(168407. - 168407. i) q^{19} +(149555. + 103843. i) q^{20} +(115786. - 115786. i) q^{21} +(152262. - 13623.7i) q^{22} -122462. q^{23} +(277857. - 76215.9i) q^{24} -115205. i q^{25} +(-305651. + 27348.3i) q^{26} +(-406569. - 406569. i) q^{27} +(105796. + 586466. i) q^{28} +(414268. + 414268. i) q^{29} +(-614198. - 513313. i) q^{30} +219722. i q^{31} +(-348904. + 988826. i) q^{32} -672076. q^{33} +(-1.03046e6 + 1.23298e6i) q^{34} +(1.17070e6 - 1.17070e6i) q^{35} +(406369. - 73307.2i) q^{36} +(-2.41114e6 + 2.41114e6i) q^{37} +(-339601. - 3.79546e6i) q^{38} +1.34913e6 q^{39} +(2.80937e6 - 770607. i) q^{40} +4.64505e6i q^{41} +(-233488. - 2.60952e6i) q^{42} +(2.08193e6 + 2.08193e6i) q^{43} +(1.39501e6 - 2.00910e6i) q^{44} +(-811189. - 811189. i) q^{45} +(-1.25652e6 + 1.50347e6i) q^{46} -3.51776e6i q^{47} +(1.91523e6 - 4.19325e6i) q^{48} -345873. q^{49} +(-1.41437e6 - 1.18205e6i) q^{50} +(4.99535e6 - 4.99535e6i) q^{51} +(-2.80035e6 + 4.03307e6i) q^{52} +(3.59377e6 - 3.59377e6i) q^{53} +(-9.16301e6 + 819866. i) q^{54} -6.79525e6 q^{55} +(8.28553e6 + 4.71853e6i) q^{56} +1.67529e7i q^{57} +(9.33652e6 - 835391. i) q^{58} +(1.18579e6 + 1.18579e6i) q^{59} +(-1.26038e7 + 2.27368e6i) q^{60} +(-1.60853e7 - 1.60853e7i) q^{61} +(2.69752e6 + 2.25444e6i) q^{62} -3.75484e6i q^{63} +(8.55989e6 + 1.44293e7i) q^{64} +1.36408e7 q^{65} +(-6.89578e6 + 8.25105e6i) q^{66} +(-172035. + 172035. i) q^{67} +(4.56434e6 + 2.53019e7i) q^{68} +(6.09119e6 - 6.09119e6i) q^{69} +(-2.36076e6 - 2.63844e7i) q^{70} -3.10311e7 q^{71} +(3.26953e6 - 5.74114e6i) q^{72} -2.46121e7i q^{73} +(4.86218e6 + 5.43409e7i) q^{74} +(5.73023e6 + 5.73023e6i) q^{75} +(-5.00812e7 - 3.47738e7i) q^{76} +(-1.57270e7 - 1.57270e7i) q^{77} +(1.38426e7 - 1.65632e7i) q^{78} +3.89023e7i q^{79} +(1.93646e7 - 4.23973e7i) q^{80} +2.98620e7 q^{81} +(5.70271e7 + 4.76602e7i) q^{82} +(4.11652e7 - 4.11652e7i) q^{83} +(-3.44326e7 - 2.39082e7i) q^{84} +(5.05073e7 - 5.05073e7i) q^{85} +(4.69213e7 - 4.19831e6i) q^{86} -4.12108e7 q^{87} +(-1.03522e7 - 3.77408e7i) q^{88} +7.46990e7i q^{89} +(-1.82821e7 + 1.63580e6i) q^{90} +(3.15703e7 + 3.15703e7i) q^{91} +(5.56563e6 + 3.08524e7i) q^{92} +(-1.09288e7 - 1.09288e7i) q^{93} +(-4.31874e7 - 3.60936e7i) q^{94} +1.69386e8i q^{95} +(-3.18293e7 - 6.65378e7i) q^{96} -8.53638e7 q^{97} +(-3.54880e6 + 4.24627e6i) q^{98} +(-1.08974e7 + 1.08974e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) $ 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	10.2604	−	12.2770i	0.641276	−	0.767310i
$2$	10.2604	−	12.2770i	0.641276	−	0.767310i
$3$	−49.7393	+	49.7393i	−0.614066	+	0.614066i	−0.944003	−	0.329937i	$-0.892972\pi$
$3$	−49.7393	+	49.7393i	−0.614066	+	0.614066i	0.329937	+	0.944003i	$0.392972\pi$
$4$	−45.4477	−	251.934i	−0.177530	−	0.984115i
$5$	−502.907	+	502.907i	−0.804651	+	0.804651i	−0.983819	−	0.179168i	$-0.942659\pi$
$5$	−502.907	+	502.907i	−0.804651	+	0.804651i	0.179168	+	0.983819i	$0.442659\pi$
$6$	100.302	+	1120.99i	0.0773932	+	0.864964i
$7$	−2327.86			−0.969537			−0.484769	−	0.874642i	$-0.661096\pi$
$7$	−2327.86			−0.969537			−0.484769	+	0.874642i	$0.661096\pi$
$8$	−3559.29	−	2026.98i	−0.868968	−	0.494869i
$9$			1613.00i			0.245847i
$10$	1014.13	+	11334.2i	0.101413	+	1.13342i
$11$	6755.98	+	6755.98i	0.461443	+	0.461443i	0.899128	−	0.437686i	$-0.144202\pi$
$11$	6755.98	+	6755.98i	0.461443	+	0.461443i	−0.437686	+	0.899128i	$0.644202\pi$
$12$	14791.5	+	10270.5i	0.713326	+	0.495296i
$13$	−13562.0	−	13562.0i	−0.474842	−	0.474842i	0.428635	−	0.903478i	$-0.358994\pi$
$13$	−13562.0	−	13562.0i	−0.474842	−	0.474842i	−0.903478	+	0.428635i	$0.858994\pi$
$14$	−23884.8	+	28579.0i	−0.621741	+	0.743936i
$15$		−	50028.5i		−	0.988217i
$16$	−61405.0	+	22899.6i	−0.936966	+	0.349420i
$17$	−100431.			−1.20246			−0.601230	−	0.799076i	$-0.705322\pi$
$17$	−100431.			−1.20246			−0.601230	+	0.799076i	$0.705322\pi$
$18$	19802.8	+	16550.1i	0.188641	+	0.157656i
$19$	168407.	−	168407.i	1.29225	−	1.29225i	0.358859	−	0.933392i	$-0.383166\pi$
$19$	168407.	−	168407.i	1.29225	−	1.29225i	0.933392	−	0.358859i	$-0.116834\pi$
$20$	149555.	+	103843.i	0.934719	+	0.649020i
$21$	115786.	−	115786.i	0.595360	−	0.595360i
$22$	152262.	−	13623.7i	0.649982	−	0.0581575i
$23$	−122462.			−0.437614			−0.218807	−	0.975768i	$-0.570217\pi$
$23$	−122462.			−0.437614			−0.218807	+	0.975768i	$0.570217\pi$
$24$	277857.	−	76215.9i	0.837485	−	0.229721i
$25$		−	115205.i		−	0.294925i
$26$	−305651.	+	27348.3i	−0.668856	+	0.0598463i
$27$	−406569.	−	406569.i	−0.765032	−	0.765032i
$28$	105796.	+	586466.i	0.172122	+	0.954137i
$29$	414268.	+	414268.i	0.585720	+	0.585720i	0.936469	−	0.350750i	$-0.114073\pi$
$29$	414268.	+	414268.i	0.585720	+	0.585720i	−0.350750	+	0.936469i	$0.614073\pi$
$30$	−614198.	−	513313.i	−0.758269	−	0.633720i
$31$			219722.i			0.237918i	0.992899	+	0.118959i	$0.0379557\pi$
$31$			219722.i			0.237918i	−0.992899	+	0.118959i	$0.962044\pi$
$32$	−348904.	+	988826.i	−0.332741	+	0.943018i
$33$	−672076.			−0.566712
$34$	−1.03046e6	+	1.23298e6i	−0.771109	+	0.922660i
$35$	1.17070e6	−	1.17070e6i	0.780139	−	0.780139i
$36$	406369.	−	73307.2i	0.241942	−	0.0436452i
$37$	−2.41114e6	+	2.41114e6i	−1.28652	+	1.28652i	−0.349632	+	0.936887i	$0.613693\pi$
$37$	−2.41114e6	+	2.41114e6i	−1.28652	+	1.28652i	−0.936887	+	0.349632i	$0.886307\pi$
$38$	−339601.	−	3.79546e6i	−0.162868	−	1.82025i
$39$	1.34913e6			0.583168
$40$	2.80937e6	−	770607.i	1.09741	−	0.301019i
$41$			4.64505e6i			1.64382i	0.569615	+	0.821912i	$0.307092\pi$
$41$			4.64505e6i			1.64382i	−0.569615	+	0.821912i	$0.692908\pi$
$42$	−233488.	−	2.60952e6i	−0.0750356	−	0.838615i
$43$	2.08193e6	+	2.08193e6i	0.608966	+	0.608966i	0.942676	−	0.333710i	$-0.108301\pi$
$43$	2.08193e6	+	2.08193e6i	0.608966	+	0.608966i	−0.333710	+	0.942676i	$0.608301\pi$
$44$	1.39501e6	−	2.00910e6i	0.372193	−	0.536033i
$45$	−811189.	−	811189.i	−0.197821	−	0.197821i
$46$	−1.25652e6	+	1.50347e6i	−0.280632	+	0.335786i
$47$		−	3.51776e6i		−	0.720899i	−0.932779	−	0.360449i	$-0.882623\pi$
$47$		−	3.51776e6i		−	0.720899i	0.932779	−	0.360449i	$-0.117377\pi$
$48$	1.91523e6	−	4.19325e6i	0.360792	−	0.789925i
$49$	−345873.			−0.0599974
$50$	−1.41437e6	−	1.18205e6i	−0.226299	−	0.189129i
$51$	4.99535e6	−	4.99535e6i	0.738389	−	0.738389i
$52$	−2.80035e6	+	4.03307e6i	−0.383001	+	0.551598i
$53$	3.59377e6	−	3.59377e6i	0.455456	−	0.455456i	−0.441705	−	0.897161i	$-0.645626\pi$
$53$	3.59377e6	−	3.59377e6i	0.455456	−	0.455456i	0.897161	+	0.441705i	$0.145626\pi$
$54$	−9.16301e6	+	819866.i	−1.07761	+	0.0964201i
$55$	−6.79525e6			−0.742600
$56$	8.28553e6	+	4.71853e6i	0.842496	+	0.479794i
$57$			1.67529e7i			1.58705i
$58$	9.33652e6	−	835391.i	0.825037	−	0.0738207i
$59$	1.18579e6	+	1.18579e6i	0.0978589	+	0.0978589i	0.754341	−	0.656482i	$-0.227956\pi$
$59$	1.18579e6	+	1.18579e6i	0.0978589	+	0.0978589i	−0.656482	+	0.754341i	$0.727956\pi$
$60$	−1.26038e7	+	2.27368e6i	−0.972519	+	0.175438i
$61$	−1.60853e7	−	1.60853e7i	−1.16175	−	1.16175i	−0.984093	−	0.177652i	$-0.943150\pi$
$61$	−1.60853e7	−	1.60853e7i	−1.16175	−	1.16175i	−0.177652	−	0.984093i	$-0.556850\pi$
$62$	2.69752e6	+	2.25444e6i	0.182557	+	0.152571i
$63$		−	3.75484e6i		−	0.238358i
$64$	8.55989e6	+	1.44293e7i	0.510209	+	0.860050i
$65$	1.36408e7			0.764164
$66$	−6.89578e6	+	8.25105e6i	−0.363419	+	0.434844i
$67$	−172035.	+	172035.i	−0.00853726	+	0.00853726i	−0.711363	−	0.702825i	$-0.751922\pi$
$67$	−172035.	+	172035.i	−0.00853726	+	0.00853726i	0.702825	+	0.711363i	$0.251922\pi$
$68$	4.56434e6	+	2.53019e7i	0.213473	+	1.18336i
$69$	6.09119e6	−	6.09119e6i	0.268724	−	0.268724i
$70$	−2.36076e6	−	2.63844e7i	−0.0983241	−	1.09889i
$71$	−3.10311e7			−1.22114			−0.610568	−	0.791964i	$-0.709059\pi$
$71$	−3.10311e7			−1.22114			−0.610568	+	0.791964i	$0.709059\pi$
$72$	3.26953e6	−	5.74114e6i	0.121662	−	0.213633i
$73$		−	2.46121e7i		−	0.866678i	−0.901231	−	0.433339i	$-0.857335\pi$
$73$		−	2.46121e7i		−	0.866678i	0.901231	−	0.433339i	$-0.142665\pi$
$74$	4.86218e6	+	5.43409e7i	0.162145	+	1.81217i
$75$	5.73023e6	+	5.73023e6i	0.181104	+	0.181104i
$76$	−5.00812e7	−	3.47738e7i	−1.50114	−	1.04231i
$77$	−1.57270e7	−	1.57270e7i	−0.447386	−	0.447386i
$78$	1.38426e7	−	1.65632e7i	0.373972	−	0.447471i
$79$			3.89023e7i			0.998773i	0.866379	+	0.499386i	$0.166441\pi$
$79$			3.89023e7i			0.998773i	−0.866379	+	0.499386i	$0.833559\pi$
$80$	1.93646e7	−	4.23973e7i	0.472770	−	1.03509i
$81$	2.98620e7			0.693712
$82$	5.70271e7	+	4.76602e7i	1.26132	+	1.05414i
$83$	4.11652e7	−	4.11652e7i	0.867396	−	0.867396i	−0.124787	−	0.992184i	$-0.539825\pi$
$83$	4.11652e7	−	4.11652e7i	0.867396	−	0.867396i	0.992184	+	0.124787i	$0.0398248\pi$
$84$	−3.44326e7	−	2.39082e7i	−0.691597	−	0.480208i
$85$	5.05073e7	−	5.05073e7i	0.967560	−	0.967560i
$86$	4.69213e7	−	4.19831e6i	0.857781	−	0.0767504i
$87$	−4.12108e7			−0.719340
$88$	−1.03522e7	−	3.77408e7i	−0.172625	−	0.629332i
$89$			7.46990e7i			1.19057i	0.803515	+	0.595285i	$0.202961\pi$
$89$			7.46990e7i			1.19057i	−0.803515	+	0.595285i	$0.797039\pi$
$90$	−1.82821e7	+	1.63580e6i	−0.278648	+	0.0249322i
$91$	3.15703e7	+	3.15703e7i	0.460377	+	0.460377i
$92$	5.56563e6	+	3.08524e7i	0.0776896	+	0.430663i
$93$	−1.09288e7	−	1.09288e7i	−0.146097	−	0.146097i
$94$	−4.31874e7	−	3.60936e7i	−0.553153	−	0.462295i
$95$			1.69386e8i			2.07962i
$96$	−3.18293e7	−	6.65378e7i	−0.374751	−	0.783400i
$97$	−8.53638e7			−0.964243			−0.482122	−	0.876104i	$-0.660134\pi$
$97$	−8.53638e7			−0.964243			−0.482122	+	0.876104i	$0.660134\pi$
$98$	−3.54880e6	+	4.24627e6i	−0.0384749	+	0.0460366i
$99$	−1.08974e7	+	1.08974e7i	−0.113444	+	0.113444i
$100$	−2.90241e7	+	5.23581e6i	−0.290241	+	0.0523581i
$101$	2.23338e7	−	2.23338e7i	0.214624	−	0.214624i	−0.591605	−	0.806228i	$-0.701505\pi$
$101$	2.23338e7	−	2.23338e7i	0.214624	−	0.214624i	0.806228	+	0.591605i	$0.201505\pi$
$102$	−1.00734e7	−	1.12582e8i	−0.0930623	−	1.04009i
$103$	−2.14749e8			−1.90802			−0.954008	−	0.299782i	$-0.903086\pi$
$103$	−2.14749e8			−1.90802			−0.954008	+	0.299782i	$0.903086\pi$
$104$	2.07811e7	+	7.57609e7i	0.177638	+	0.647607i
$105$			1.16459e8i			0.958113i
$106$	−7.24700e6	−	8.09941e7i	−0.0574030	−	0.641549i
$107$	9.51766e7	+	9.51766e7i	0.726097	+	0.726097i	0.969840	−	0.243743i	$-0.0783752\pi$
$107$	9.51766e7	+	9.51766e7i	0.726097	+	0.726097i	−0.243743	+	0.969840i	$0.578375\pi$
$108$	−8.39508e7	+	1.20906e8i	−0.617063	+	0.888696i
$109$	−3.83616e7	−	3.83616e7i	−0.271763	−	0.271763i	0.558046	−	0.829810i	$-0.311551\pi$
$109$	−3.83616e7	−	3.83616e7i	−0.271763	−	0.271763i	−0.829810	+	0.558046i	$0.811551\pi$
$110$	−6.97221e7	+	8.34251e7i	−0.476212	+	0.569805i
$111$		−	2.39857e8i		−	1.58001i
$112$	1.42942e8	−	5.33070e7i	0.908424	−	0.338776i
$113$	2.57388e8			1.57861			0.789305	−	0.614001i	$-0.210441\pi$
$113$	2.57388e8			1.57861			0.789305	+	0.614001i	$0.210441\pi$
$114$	2.05675e8	+	1.71892e8i	1.21776	+	1.01774i
$115$	6.15872e7	−	6.15872e7i	0.352127	−	0.352127i
$116$	8.55406e7	−	1.23196e8i	0.472433	−	0.680398i
$117$	2.18755e7	−	2.18755e7i	0.116738	−	0.116738i
$118$	2.67246e7	−	2.39120e6i	0.137843	−	0.0123336i
$119$	2.33788e8			1.16583
$120$	−1.01407e8	+	1.78066e8i	−0.489038	+	0.858728i
$121$		−	1.23072e8i		−	0.574142i
$122$	−3.62521e8	+	3.24368e7i	−1.63642	+	0.146420i
$123$	−2.31042e8	−	2.31042e8i	−1.00942	−	1.00942i
$124$	5.53554e7	−	9.98587e6i	0.234139	−	0.0422376i
$125$	−1.38510e8	−	1.38510e8i	−0.567339	−	0.567339i
$126$	−4.60980e7	−	3.85262e7i	−0.182894	−	0.152853i
$127$		−	1.76795e8i		−	0.679604i	−0.940497	−	0.339802i	$-0.889640\pi$
$127$		−	1.76795e8i		−	0.679604i	0.940497	−	0.339802i	$-0.110360\pi$
$128$	2.64975e8	+	4.29607e7i	0.987110	+	0.160041i
$129$	−2.07108e8			−0.747890
$130$	1.39960e8	−	1.67468e8i	0.490040	−	0.586351i
$131$	5.26025e7	−	5.26025e7i	0.178616	−	0.178616i	−0.612136	−	0.790752i	$-0.709690\pi$
$131$	5.26025e7	−	5.26025e7i	0.178616	−	0.178616i	0.790752	+	0.612136i	$0.209690\pi$
$132$	3.05443e7	+	1.69318e8i	0.100608	+	0.557710i
$133$	−3.92029e8	+	3.92029e8i	−1.25289	+	1.25289i
$134$	346917.	+	3.87723e6i	0.00107599	+	0.0120255i
$135$	4.08933e8			1.23117
$136$	3.57462e8	+	2.03571e8i	1.04490	+	0.595060i
$137$			1.26227e8i			0.358318i	0.983820	+	0.179159i	$0.0573377\pi$
$137$			1.26227e8i			0.358318i	−0.983820	+	0.179159i	$0.942662\pi$
$138$	−1.22832e7	−	1.37280e8i	−0.0338684	−	0.378521i
$139$	4.19336e7	+	4.19336e7i	0.112332	+	0.112332i	0.761038	−	0.648707i	$-0.224690\pi$
$139$	4.19336e7	+	4.19336e7i	0.112332	+	0.112332i	−0.648707	+	0.761038i	$0.724690\pi$
$140$	−3.48143e8	−	2.41732e8i	−0.906245	−	0.629249i
$141$	1.74971e8	+	1.74971e8i	0.442679	+	0.442679i
$142$	−3.18392e8	+	3.80968e8i	−0.783086	+	0.936990i
$143$		−	1.83249e8i		−	0.438225i
$144$	−3.69371e7	−	9.90464e7i	−0.0859038	−	0.230350i
$145$	−4.16677e8			−0.942599
$146$	−3.02162e8	−	2.52531e8i	−0.665011	−	0.555780i
$147$	1.72035e7	−	1.72035e7i	0.0368423	−	0.0368423i
$148$	7.17029e8	+	4.97867e8i	1.49448	+	1.03769i
$149$	−3.48110e7	+	3.48110e7i	−0.0706272	+	0.0706272i	−0.741538	−	0.670911i	$-0.765903\pi$
$149$	−3.48110e7	+	3.48110e7i	−0.0706272	+	0.0706272i	0.670911	+	0.741538i	$0.265903\pi$
$150$	1.29144e8	−	1.15553e7i	0.255100	−	0.0228252i
$151$	1.26632e8			0.243576			0.121788	−	0.992556i	$-0.461137\pi$
$151$	1.26632e8			0.243576			0.121788	+	0.992556i	$0.461137\pi$
$152$	−9.40770e8	+	2.58052e8i	−1.76242	+	0.483429i
$153$		−	1.61995e8i		−	0.295621i
$154$	−3.54445e8	+	3.17142e7i	−0.630181	+	0.0563859i
$155$	−1.10500e8	−	1.10500e8i	−0.191441	−	0.191441i
$156$	−6.13146e7	−	3.39890e8i	−0.103530	−	0.573905i
$157$	7.14122e8	+	7.14122e8i	1.17537	+	1.17537i	0.980911	+	0.194456i	$0.0622941\pi$
$157$	7.14122e8	+	7.14122e8i	1.17537	+	1.17537i	0.194456	+	0.980911i	$0.437706\pi$
$158$	4.77602e8	+	3.99154e8i	0.766369	+	0.640489i
$159$			3.57503e8i			0.559360i
$160$	−3.21821e8	−	6.72753e8i	−0.491060	−	1.02654i
$161$	2.85075e8			0.424283
$162$	3.06397e8	−	3.66615e8i	0.444861	−	0.532293i
$163$	−8.17452e8	+	8.17452e8i	−1.15801	+	1.15801i	−0.173106	+	0.984903i	$0.555380\pi$
$163$	−8.17452e8	+	8.17452e8i	−1.15801	+	1.15801i	−0.984903	+	0.173106i	$0.944620\pi$
$164$	1.17024e9	−	2.11107e8i	1.61771	−	0.291828i
$165$	3.37991e8	−	3.37991e8i	0.456005	−	0.456005i
$166$	−8.30115e7	−	9.27755e8i	−0.109322	−	1.22180i
$167$	−5.62466e8			−0.723153			−0.361577	−	0.932342i	$-0.617761\pi$
$167$	−5.62466e8			−0.723153			−0.361577	+	0.932342i	$0.617761\pi$
$168$	−6.46813e8	+	1.77420e8i	−0.811973	+	0.222723i
$169$		−	4.47877e8i		−	0.549050i
$170$	−1.01850e8	−	1.13830e9i	−0.121946	−	1.36289i
$171$	2.71641e8	+	2.71641e8i	0.317696	+	0.317696i
$172$	4.29890e8	−	6.19127e8i	0.491183	−	0.707402i
$173$	9.49095e7	+	9.49095e7i	0.105956	+	0.105956i	0.758097	−	0.652141i	$-0.226129\pi$
$173$	9.49095e7	+	9.49095e7i	0.105956	+	0.105956i	−0.652141	+	0.758097i	$0.726129\pi$
$174$	−4.22840e8	+	5.05944e8i	−0.461296	+	0.551957i
$175$			2.68182e8i			0.285941i
$176$	−5.69560e8	−	2.60142e8i	−0.593593	−	0.271119i
$177$	−1.17961e8			−0.120184
$178$	9.17077e8	+	7.66443e8i	0.913537	+	0.763484i
$179$	1.83524e7	−	1.83524e7i	0.0178765	−	0.0178765i	−0.698112	−	0.715989i	$-0.745976\pi$
$179$	1.83524e7	−	1.83524e7i	0.0178765	−	0.0178765i	0.715989	+	0.698112i	$0.245976\pi$
$180$	−1.67499e8	+	2.41232e8i	−0.159559	+	0.229798i
$181$	−1.57230e8	+	1.57230e8i	−0.146494	+	0.146494i	−0.776550	−	0.630056i	$-0.783032\pi$
$181$	−1.57230e8	+	1.57230e8i	−0.146494	+	0.146494i	0.630056	+	0.776550i	$0.283032\pi$
$182$	7.11513e8	−	6.36631e7i	0.648481	−	0.0580232i
$183$	1.60015e9			1.42678
$184$	4.35879e8	+	2.48229e8i	0.380272	+	0.216562i
$185$		−	2.42516e9i		−	2.07040i
$186$	−2.46307e8	+	2.20385e7i	−0.205791	+	0.0184133i
$187$	−6.78508e8	−	6.78508e8i	−0.554866	−	0.554866i
$188$	−8.86241e8	+	1.59874e8i	−0.709447	+	0.127981i
$189$	9.46436e8	+	9.46436e8i	0.741727	+	0.741727i
$190$	2.07955e9	+	1.73798e9i	1.59571	+	1.33361i
$191$			2.52940e8i			0.190057i	0.995475	+	0.0950286i	$0.0302942\pi$
$191$			2.52940e8i			0.190057i	−0.995475	+	0.0950286i	$0.969706\pi$
$192$	−1.14346e9	−	2.91938e8i	−0.841429	−	0.214826i
$193$	−9.67557e8			−0.697344			−0.348672	−	0.937245i	$-0.613367\pi$
$193$	−9.67557e8			−0.697344			−0.348672	+	0.937245i	$0.613367\pi$
$194$	−8.75868e8	+	1.04801e9i	−0.618346	+	0.739874i
$195$	−6.78484e8	+	6.78484e8i	−0.469247	+	0.469247i
$196$	1.57191e7	+	8.71370e7i	0.0106513	+	0.0590443i
$197$	−3.54411e8	+	3.54411e8i	−0.235311	+	0.235311i	−0.814905	−	0.579594i	$-0.803211\pi$
$197$	−3.54411e8	+	3.54411e8i	−0.235311	+	0.235311i	0.579594	+	0.814905i	$0.303211\pi$
$198$	2.19751e7	+	2.45599e8i	0.0142978	+	0.159796i
$199$	5.81825e8			0.371005			0.185503	−	0.982644i	$-0.440609\pi$
$199$	5.81825e8			0.371005			0.185503	+	0.982644i	$0.440609\pi$
$200$	−2.33519e8	+	4.10049e8i	−0.145949	+	0.256281i
$201$		−	1.71138e7i		−	0.0104849i
$202$	−4.50372e7	−	5.03346e8i	−0.0270499	−	0.302316i
$203$	−9.64358e8	−	9.64358e8i	−0.567877	−	0.567877i
$204$	−1.48552e9	−	1.03147e9i	−0.857747	−	0.595574i
$205$	−2.33603e9	−	2.33603e9i	−1.32270	−	1.32270i
$206$	−2.20341e9	+	2.63646e9i	−1.22356	+	1.46404i
$207$		−	1.97532e8i		−	0.107586i
$208$	1.14334e9	+	5.22209e8i	0.610830	+	0.278992i
$209$	2.27551e9			1.19260
$210$	1.42977e9	+	1.19492e9i	0.735170	+	0.614415i
$211$	−1.54667e9	+	1.54667e9i	−0.780313	+	0.780313i	−0.979883	−	0.199571i	$-0.936045\pi$
$211$	−1.54667e9	+	1.54667e9i	−0.780313	+	0.780313i	0.199571	+	0.979883i	$0.436045\pi$
$212$	−1.06872e9	−	7.42062e8i	−0.529078	−	0.367364i
$213$	1.54347e9	−	1.54347e9i	0.749858	−	0.749858i
$214$	2.14503e9	−	1.91928e8i	1.02277	−	0.0915130i
$215$	−2.09403e9			−0.980009
$216$	6.22989e8	+	2.27121e9i	0.286197	+	1.04338i
$217$		−	5.11483e8i		−	0.230671i
$218$	−8.64570e8	+	7.73579e7i	−0.382802	+	0.0342514i
$219$	1.22419e9	+	1.22419e9i	0.532197	+	0.532197i
$220$	3.08828e8	+	1.71195e9i	0.131834	+	0.730804i
$221$	1.36204e9	+	1.36204e9i	0.570979	+	0.570979i
$222$	−2.94472e9	−	2.46104e9i	−1.21236	−	1.01323i
$223$		−	1.69218e9i		−	0.684270i	−0.939651	−	0.342135i	$-0.888850\pi$
$223$		−	1.69218e9i		−	0.684270i	0.939651	−	0.342135i	$-0.111150\pi$
$224$	8.12199e8	−	2.30185e9i	0.322604	−	0.914292i
$225$	1.85826e8			0.0725065
$226$	2.64091e9	−	3.15995e9i	1.01233	−	1.21128i
$227$	2.12804e9	−	2.12804e9i	0.801451	−	0.801451i	−0.181871	−	0.983322i	$-0.558215\pi$
$227$	2.12804e9	−	2.12804e9i	0.801451	−	0.801451i	0.983322	+	0.181871i	$0.0582154\pi$
$228$	4.22063e9	−	7.61382e8i	1.56184	−	0.281750i
$229$	−1.46899e9	+	1.46899e9i	−0.534167	+	0.534167i	−0.921810	−	0.387643i	$-0.873289\pi$
$229$	−1.46899e9	+	1.46899e9i	−0.534167	+	0.534167i	0.387643	+	0.921810i	$0.373289\pi$
$230$	−1.24193e8	−	1.38801e9i	−0.0443800	−	0.496001i
$231$	1.56450e9			0.549448
$232$	−6.34786e8	−	2.31422e9i	−0.219117	−	0.798826i
$233$			5.41029e9i			1.83568i	0.396950	+	0.917840i	$0.370068\pi$
$233$			5.41029e9i			1.83568i	−0.396950	+	0.917840i	$0.629932\pi$
$234$	−4.41129e7	−	4.93016e8i	−0.0147130	−	0.164436i
$235$	1.76910e9	+	1.76910e9i	0.580072	+	0.580072i
$236$	2.44849e8	−	3.52632e8i	0.0789316	−	0.113677i
$237$	−1.93497e9	−	1.93497e9i	−0.613312	−	0.613312i
$238$	2.39877e9	−	2.87021e9i	0.747619	−	0.894553i
$239$		−	1.97738e9i		−	0.606036i	−0.952985	−	0.303018i	$-0.902006\pi$
$239$		−	1.97738e9i		−	0.606036i	0.952985	−	0.303018i	$-0.0979943\pi$
$240$	1.14563e9	+	3.07200e9i	0.345303	+	0.925926i
$241$	3.90770e8			0.115839			0.0579193	−	0.998321i	$-0.481553\pi$
$241$	3.90770e8			0.115839			0.0579193	+	0.998321i	$0.481553\pi$
$242$	−1.51095e9	−	1.26277e9i	−0.440545	−	0.368183i
$243$	1.18218e9	−	1.18218e9i	0.339047	−	0.339047i
$244$	−3.32140e9	+	4.78348e9i	−0.937047	+	1.34954i
$245$	1.73942e8	−	1.73942e8i	0.0482769	−	0.0482769i
$246$	−5.20707e9	+	4.65906e8i	−1.42185	+	0.127221i
$247$	−4.56787e9			−1.22723
$248$	4.45374e8	−	7.82056e8i	0.117738	−	0.206743i
$249$			4.09506e9i			1.06528i
$250$	−3.12166e9	+	2.79313e8i	−0.799146	+	0.0715040i
$251$	1.37404e9	+	1.37404e9i	0.346182	+	0.346182i	0.858685	−	0.512503i	$-0.171282\pi$
$251$	1.37404e9	+	1.37404e9i	0.346182	+	0.346182i	−0.512503	+	0.858685i	$0.671282\pi$
$252$	−9.45970e8	+	1.70649e8i	−0.234572	+	0.0423156i
$253$	−8.27353e8	−	8.27353e8i	−0.201934	−	0.201934i
$254$	−2.17051e9	−	1.81399e9i	−0.521467	−	0.435814i
$255$			5.02439e9i			1.18829i
$256$	3.24619e9	−	2.81230e9i	0.755811	−	0.654789i
$257$	−3.76030e9			−0.861965			−0.430982	−	0.902360i	$-0.641833\pi$
$257$	−3.76030e9			−0.861965			−0.430982	+	0.902360i	$0.641833\pi$
$258$	−2.12501e9	+	2.54265e9i	−0.479604	+	0.573863i
$259$	5.61280e9	−	5.61280e9i	1.24733	−	1.24733i
$260$	−6.19943e8	−	3.43658e9i	−0.135662	−	0.752026i
$261$	−6.68215e8	+	6.68215e8i	−0.143997	+	0.143997i
$262$	−1.06075e8	−	1.18552e9i	−0.0225117	−	0.251596i
$263$	−1.90346e7			−0.00397852			−0.00198926	−	0.999998i	$-0.500633\pi$
$263$	−1.90346e7			−0.00397852			−0.00198926	+	0.999998i	$0.500633\pi$
$264$	2.39211e9	+	1.36229e9i	0.492454	+	0.280448i
$265$			3.61466e9i			0.732966i
$266$	7.90544e8	+	8.83530e9i	0.157906	+	1.76480i
$267$	−3.71548e9	−	3.71548e9i	−0.731088	−	0.731088i
$268$	5.11601e7	+	3.55229e7i	0.00991727	+	0.00688603i
$269$	4.82689e9	+	4.82689e9i	0.921845	+	0.921845i	0.997160	−	0.0753144i	$-0.0239960\pi$
$269$	4.82689e9	+	4.82689e9i	0.921845	+	0.921845i	−0.0753144	+	0.997160i	$0.523996\pi$
$270$	4.19582e9	−	5.02045e9i	0.789518	−	0.944687i
$271$			5.65219e9i			1.04795i	0.851734	+	0.523974i	$0.175551\pi$
$271$			5.65219e9i			1.04795i	−0.851734	+	0.523974i	$0.824449\pi$
$272$	6.16695e9	−	2.29982e9i	1.12666	−	0.420163i
$273$	−3.14057e9			−0.565403
$274$	1.54968e9	+	1.29514e9i	0.274941	+	0.229781i
$275$	7.78324e8	−	7.78324e8i	0.136091	−	0.136091i
$276$	−1.81141e9	−	1.25775e9i	−0.312162	−	0.216749i
$277$	−8.23413e8	+	8.23413e8i	−0.139862	+	0.139862i	−0.773571	−	0.633709i	$-0.781531\pi$
$277$	−8.23413e8	+	8.23413e8i	−0.139862	+	0.139862i	0.633709	+	0.773571i	$0.281531\pi$
$278$	9.45072e8	−	8.45609e7i	0.158229	−	0.0141576i
$279$	−3.54413e8			−0.0584914
$280$	−6.53983e9	+	1.79387e9i	−1.06398	+	0.291849i
$281$		−	2.09278e9i		−	0.335659i	−0.985816	−	0.167830i	$-0.946324\pi$
$281$		−	2.09278e9i		−	0.335659i	0.985816	−	0.167830i	$-0.0536759\pi$
$282$	3.94338e9	−	3.52837e8i	0.623552	−	0.0557927i
$283$	7.06737e8	+	7.06737e8i	0.110182	+	0.110182i	0.760049	−	0.649866i	$-0.225175\pi$
$283$	7.06737e8	+	7.06737e8i	0.110182	+	0.110182i	−0.649866	+	0.760049i	$0.725175\pi$
$284$	1.41029e9	+	7.81778e9i	0.216788	+	1.20174i
$285$	−8.42516e9	−	8.42516e9i	−1.27702	−	1.27702i
$286$	−2.24974e9	−	1.88021e9i	−0.336254	−	0.281023i
$287$		−	1.08130e10i		−	1.59375i
$288$	−1.59498e9	−	5.62782e8i	−0.231838	−	0.0818032i
$289$	3.11056e9			0.445910
$290$	−4.27528e9	+	5.11552e9i	−0.604466	+	0.723266i
$291$	4.24593e9	−	4.24593e9i	0.592109	−	0.592109i
$292$	−6.20062e9	+	1.11856e9i	−0.852912	+	0.153861i
$293$	1.88718e9	−	1.88718e9i	0.256061	−	0.256061i	−0.567389	−	0.823450i	$-0.692046\pi$
$293$	1.88718e9	−	1.88718e9i	0.256061	−	0.256061i	0.823450	+	0.567389i	$0.192046\pi$
$294$	−3.46916e7	−	3.87721e8i	−0.00464339	−	0.0518956i
$295$	−1.19268e9			−0.157484
$296$	1.34693e10	−	3.69461e9i	1.75460	−	0.481285i
$297$		−	5.49355e9i		−	0.706036i
$298$	7.01981e7	+	7.84550e8i	0.00890144	+	0.0994845i
$299$	1.66083e9	+	1.66083e9i	0.207798	+	0.207798i
$300$	1.18321e9	−	1.70406e9i	0.146075	−	0.210378i
$301$	−4.84644e9	−	4.84644e9i	−0.590415	−	0.590415i
$302$	1.29929e9	−	1.55465e9i	0.156200	−	0.186898i
$303$			2.22174e9i			0.263586i
$304$	−6.48460e9	+	1.41975e10i	−0.759257	+	1.66233i
$305$	1.61789e10			1.86960
$306$	−1.98880e9	−	1.66213e9i	−0.226833	−	0.189575i
$307$	−6.73287e8	+	6.73287e8i	−0.0757961	+	0.0757961i	−0.743989	−	0.668192i	$-0.767068\pi$
$307$	−6.73287e8	+	6.73287e8i	−0.0757961	+	0.0757961i	0.668192	+	0.743989i	$0.267068\pi$
$308$	−3.24740e9	+	4.67691e9i	−0.360855	+	0.519704i
$309$	1.06815e10	−	1.06815e10i	1.17165	−	1.17165i
$310$	−2.49038e9	+	2.22828e8i	−0.269661	+	0.0241281i
$311$	−1.44709e10			−1.54688			−0.773438	−	0.633872i	$-0.781464\pi$
$311$	−1.44709e10			−1.54688			−0.773438	+	0.633872i	$0.781464\pi$
$312$	−4.80193e9	−	2.73466e9i	−0.506754	−	0.288592i
$313$		−	1.57344e9i		−	0.163936i	−0.996635	−	0.0819678i	$-0.973880\pi$
$313$		−	1.57344e9i		−	0.163936i	0.996635	−	0.0819678i	$-0.0261205\pi$
$314$	1.60944e10	−	1.44006e9i	1.65561	−	0.148136i
$315$	1.88833e9	+	1.88833e9i	0.191795	+	0.191795i
$316$	9.80079e9	−	1.76802e9i	0.982908	−	0.177312i
$317$	5.90223e9	+	5.90223e9i	0.584492	+	0.584492i	0.936134	−	0.351642i	$-0.114377\pi$
$317$	5.90223e9	+	5.90223e9i	0.584492	+	0.584492i	−0.351642	+	0.936134i	$0.614377\pi$
$318$	4.38905e9	+	3.66813e9i	0.429202	+	0.358704i
$319$			5.59758e9i			0.540552i
$320$	−1.15614e10	−	2.95174e9i	−1.10258	−	0.281500i
$321$	−9.46803e9			−0.891743
$322$	2.92499e9	−	3.49986e9i	0.272083	−	0.325557i
$323$	−1.69133e10	+	1.69133e10i	−1.55388	+	1.55388i
$324$	−1.35716e9	−	7.52325e9i	−0.123155	−	0.682693i
$325$	−1.56241e9	+	1.56241e9i	−0.140043	+	0.140043i
$326$	1.64843e9	+	1.84232e10i	0.145949	+	1.63116i
$327$	3.81616e9			0.333761
$328$	9.41544e9	−	1.65331e10i	0.813477	−	1.42843i
$329$			8.18884e9i			0.698938i
$330$	−6.81575e8	−	7.61744e9i	−0.0574722	−	0.642323i
$331$	5.84232e9	+	5.84232e9i	0.486714	+	0.486714i	0.907268	−	0.420554i	$-0.138164\pi$
$331$	5.84232e9	+	5.84232e9i	0.486714	+	0.486714i	−0.420554	+	0.907268i	$0.638164\pi$
$332$	−1.22418e10	−	8.50003e9i	−1.00761	−	0.699629i
$333$	−3.88918e9	−	3.88918e9i	−0.316287	−	0.316287i
$334$	−5.77114e9	+	6.90538e9i	−0.463741	+	0.554883i
$335$		−	1.73035e8i		−	0.0137390i
$336$	−4.45839e9	+	9.76130e9i	−0.349801	+	0.765862i
$337$	−1.58106e6			−0.000122583			−6.12913e−5	−	1.00000i	$-0.500020\pi$
$337$	−1.58106e6			−0.000122583			−6.12913e−5		1.00000i	$0.500020\pi$
$338$	−5.49857e9	−	4.59540e9i	−0.421292	−	0.352093i
$339$	−1.28023e10	+	1.28023e10i	−0.969371	+	0.969371i
$340$	−1.50199e10	−	1.04290e10i	−1.12396	−	0.780420i
$341$	−1.48444e9	+	1.48444e9i	−0.109786	+	0.109786i
$342$	6.12209e9	−	5.47777e8i	0.447502	−	0.0400405i
$343$	1.42248e10			1.02771
$344$	−3.19016e9	−	1.16302e10i	−0.227813	−	0.830530i
$345$			6.12661e9i			0.432458i
$346$	2.13901e9	−	1.91389e8i	0.149248	−	0.0133541i
$347$	−9.21998e9	−	9.21998e9i	−0.635934	−	0.635934i	0.313616	−	0.949550i	$-0.398460\pi$
$347$	−9.21998e9	−	9.21998e9i	−0.635934	−	0.635934i	−0.949550	+	0.313616i	$0.898460\pi$
$348$	1.87294e9	+	1.03824e10i	0.127704	+	0.707914i
$349$	5.91571e9	+	5.91571e9i	0.398754	+	0.398754i	0.877793	−	0.479039i	$-0.159015\pi$
$349$	5.91571e9	+	5.91571e9i	0.398754	+	0.398754i	−0.479039	+	0.877793i	$0.659015\pi$
$350$	3.29246e9	+	2.75165e9i	0.219406	+	0.183367i
$351$			1.10278e10i			0.726538i
$352$	−9.03768e9	+	4.32330e9i	−0.588689	+	0.281608i
$353$	2.97255e8			0.0191439			0.00957195	−	0.999954i	$-0.496953\pi$
$353$	2.97255e8			0.0191439			0.00957195	+	0.999954i	$0.496953\pi$
$354$	−1.21033e9	+	1.44820e9i	−0.0770708	+	0.0922181i
$355$	1.56058e10	−	1.56058e10i	0.982588	−	0.982588i
$356$	1.88192e10	−	3.39490e9i	1.17166	−	0.211362i
$357$	−1.16285e10	+	1.16285e10i	−0.715896	+	0.715896i
$358$	−3.70086e7	−	4.13616e8i	−0.00225305	−	0.0251806i
$359$	1.50049e10			0.903347			0.451674	−	0.892183i	$-0.350827\pi$
$359$	1.50049e10			0.903347			0.451674	+	0.892183i	$0.350827\pi$
$360$	1.24299e9	+	4.53153e9i	0.0740045	+	0.269795i
$361$		−	3.97386e10i		−	2.33982i
$362$	3.17061e8	+	3.54355e9i	0.0184633	+	0.206350i
$363$	6.12153e9	+	6.12153e9i	0.352561	+	0.352561i
$364$	6.51883e9	−	9.38843e9i	0.371333	−	0.534795i
$365$	1.23776e10	+	1.23776e10i	0.697373	+	0.697373i
$366$	1.64182e10	−	1.96450e10i	0.914957	−	1.09478i
$367$		−	1.21575e10i		−	0.670165i	−0.942189	−	0.335082i	$-0.891236\pi$
$367$		−	1.21575e10i		−	0.670165i	0.942189	−	0.335082i	$-0.108764\pi$
$368$	7.51981e9	−	2.80434e9i	0.410030	−	0.152911i
$369$	−7.49247e9			−0.404129
$370$	−2.97736e10	−	2.48832e10i	−1.58864	−	1.32770i
$371$	−8.36578e9	+	8.36578e9i	−0.441582	+	0.441582i
$372$	−2.25665e9	+	3.25003e9i	−0.117840	+	0.169713i
$373$	−1.35881e10	+	1.35881e10i	−0.701977	+	0.701977i	−0.964835	−	0.262858i	$-0.915335\pi$
$373$	−1.35881e10	+	1.35881e10i	−0.701977	+	0.701977i	0.262858	+	0.964835i	$0.415335\pi$
$374$	−1.52918e10	+	1.36824e9i	−0.781577	+	0.0699321i
$375$	1.37788e10			0.696766
$376$	−7.13043e9	+	1.25207e10i	−0.356750	+	0.626438i
$377$		−	1.12366e10i		−	0.556249i
$378$	2.13302e10	−	1.90853e9i	1.04479	−	0.0934829i
$379$	−1.43537e10	−	1.43537e10i	−0.695674	−	0.695674i	0.267800	−	0.963474i	$-0.413703\pi$
$379$	−1.43537e10	−	1.43537e10i	−0.695674	−	0.695674i	−0.963474	+	0.267800i	$0.913703\pi$
$380$	4.26741e10	−	7.69822e9i	2.04659	−	0.369195i
$381$	8.79368e9	+	8.79368e9i	0.417321	+	0.417321i
$382$	3.10534e9	+	2.59527e9i	0.145833	+	0.121879i
$383$		−	4.90332e9i		−	0.227874i	−0.993488	−	0.113937i	$-0.963654\pi$
$383$		−	4.90332e9i		−	0.227874i	0.993488	−	0.113937i	$-0.0363462\pi$
$384$	−1.53165e10	+	1.10429e10i	−0.704426	+	0.507875i
$385$	1.58184e10			0.719978
$386$	−9.92754e9	+	1.18787e10i	−0.447190	+	0.535079i
$387$	−3.35816e9	+	3.35816e9i	−0.149712	+	0.149712i
$388$	3.87958e9	+	2.15060e10i	0.171182	+	0.948927i
$389$	1.18771e10	−	1.18771e10i	0.518695	−	0.518695i	−0.398482	−	0.917176i	$-0.630463\pi$
$389$	1.18771e10	−	1.18771e10i	0.518695	−	0.518695i	0.917176	+	0.398482i	$0.130463\pi$
$390$	1.36819e9	+	1.52913e10i	0.0591411	+	0.660975i
$391$	1.22990e10			0.526214
$392$	1.23106e9	+	7.01079e8i	0.0521358	+	0.0296909i
$393$			5.23282e9i			0.219364i
$394$	7.14686e8	+	7.98749e9i	0.0296572	+	0.331456i
$395$	−1.95642e10	−	1.95642e10i	−0.803663	−	0.803663i
$396$	3.24068e9	+	2.25016e9i	0.131782	+	0.0915024i
$397$	1.17731e10	+	1.17731e10i	0.473946	+	0.473946i	0.903189	−	0.429243i	$-0.141220\pi$
$397$	1.17731e10	+	1.17731e10i	0.473946	+	0.473946i	−0.429243	+	0.903189i	$0.641220\pi$
$398$	5.96977e9	−	7.14304e9i	0.237917	−	0.284676i
$399$		−	3.89985e10i		−	1.53871i
$400$	2.63815e9	+	7.07418e9i	0.103053	+	0.276335i
$401$	−5.16644e10			−1.99809			−0.999043	−	0.0437359i	$-0.986074\pi$
$401$	−5.16644e10			−1.99809			−0.999043	+	0.0437359i	$0.986074\pi$
$402$	−2.10106e8	−	1.75595e8i	−0.00804515	−	0.00672370i
$403$	2.97987e9	−	2.97987e9i	0.112974	−	0.112974i
$404$	−6.64166e9	−	4.61162e9i	−0.249317	−	0.173112i
$405$	−1.50178e10	+	1.50178e10i	−0.558196	+	0.558196i
$406$	−2.17341e10	+	1.94467e9i	−0.799904	+	0.0715719i
$407$	−3.25793e10			−1.18731
$408$	−2.79054e10	+	7.65441e9i	−1.00704	+	0.276230i
$409$			3.56066e9i			0.127244i	0.997974	+	0.0636221i	$0.0202652\pi$
$409$			3.56066e9i			0.127244i	−0.997974	+	0.0636221i	$0.979735\pi$
$410$	−5.26479e10	+	4.71071e9i	−1.86314	+	0.166706i
$411$	−6.27843e9	−	6.27843e9i	−0.220031	−	0.220031i
$412$	9.75983e9	+	5.41024e10i	0.338730	+	1.87771i
$413$	−2.76036e9	−	2.76036e9i	−0.0948778	−	0.0948778i
$414$	−2.42509e9	−	2.02676e9i	−0.0825519	−	0.0689924i
$415$			4.14045e10i			1.39590i
$416$	1.81423e10	−	8.67861e9i	0.605784	−	0.289786i
$417$	−4.17149e9			−0.137958
$418$	2.33477e10	−	2.79364e10i	0.764785	−	0.915093i
$419$	1.76340e10	−	1.76340e10i	0.572132	−	0.572132i	−0.360592	−	0.932724i	$-0.617425\pi$
$419$	1.76340e10	−	1.76340e10i	0.572132	−	0.572132i	0.932724	+	0.360592i	$0.117425\pi$
$420$	2.93400e10	−	5.29280e9i	0.942894	−	0.170094i
$421$	1.80931e10	−	1.80931e10i	0.575949	−	0.575949i	−0.357835	−	0.933785i	$-0.616485\pi$
$421$	1.80931e10	−	1.80931e10i	0.575949	−	0.575949i	0.933785	+	0.357835i	$0.116485\pi$
$422$	3.11894e9	+	3.48580e10i	0.0983460	+	1.09914i
$423$	5.67414e9			0.177231
$424$	−2.00758e10	+	5.50675e9i	−0.621168	+	0.170385i
$425$			1.15701e10i			0.354636i
$426$	−3.11247e9	−	3.47857e10i	−0.0945077	−	1.05624i
$427$	3.74444e10	+	3.74444e10i	1.12636	+	1.12636i
$428$	1.96526e10	−	2.83037e10i	0.585660	−	0.843468i
$429$	9.11467e9	+	9.11467e9i	0.269099	+	0.269099i
$430$	−2.14857e10	+	2.57084e10i	−0.628456	+	0.751971i
$431$		−	4.30734e10i		−	1.24825i	−0.781326	−	0.624123i	$-0.785456\pi$
$431$		−	4.30734e10i		−	1.24825i	0.781326	−	0.624123i	$-0.214544\pi$
$432$	3.42757e10	+	1.56551e10i	0.984126	+	0.449492i
$433$	−1.19310e10			−0.339412			−0.169706	−	0.985495i	$-0.554282\pi$
$433$	−1.19310e10			−0.339412			−0.169706	+	0.985495i	$0.554282\pi$
$434$	−6.27946e9	−	5.24803e9i	−0.176996	−	0.147924i
$435$	2.07252e10	−	2.07252e10i	0.578818	−	0.578818i
$436$	−7.92113e9	+	1.14080e10i	−0.219200	+	0.315692i
$437$	−2.06236e10	+	2.06236e10i	−0.565507	+	0.565507i
$438$	2.75901e10	−	2.46864e9i	0.749646	−	0.0670750i
$439$	7.07244e10			1.90419			0.952097	−	0.305797i	$-0.0989228\pi$
$439$	7.07244e10			1.90419			0.952097	+	0.305797i	$0.0989228\pi$
$440$	2.41863e10	+	1.37739e10i	0.645295	+	0.367490i
$441$		−	5.57894e8i		−	0.0147502i
$442$	3.06967e10	−	2.74661e9i	0.804273	−	0.0719628i
$443$	−2.19698e10	−	2.19698e10i	−0.570442	−	0.570442i	0.361810	−	0.932252i	$-0.382159\pi$
$443$	−2.19698e10	−	2.19698e10i	−0.570442	−	0.570442i	−0.932252	+	0.361810i	$0.882159\pi$
$444$	−6.04281e10	+	1.09010e10i	−1.55492	+	0.280500i
$445$	−3.75666e10	−	3.75666e10i	−0.957993	−	0.957993i
$446$	−2.07749e10	−	1.73625e10i	−0.525048	−	0.438806i
$447$		−	3.46295e9i		−	0.0867395i
$448$	−1.99262e10	−	3.35893e10i	−0.494667	−	0.833851i
$449$	5.04257e10			1.24070			0.620350	−	0.784325i	$-0.286991\pi$
$449$	5.04257e10			1.24070			0.620350	+	0.784325i	$0.286991\pi$
$450$	1.90665e9	−	2.28138e9i	0.0464967	−	0.0556350i
$451$	−3.13819e10	+	3.13819e10i	−0.758530	+	0.758530i
$452$	−1.16977e10	−	6.48448e10i	−0.280251	−	1.55354i
$453$	−6.29858e9	+	6.29858e9i	−0.149572	+	0.149572i
$454$	−4.29130e9	−	4.79605e10i	−0.101010	−	1.12891i
$455$	−3.17539e10			−0.740886
$456$	3.39579e10	−	5.96286e10i	0.785384	−	1.37910i
$457$			3.77034e10i			0.864402i	0.901777	+	0.432201i	$0.142263\pi$
$457$			3.77034e10i			0.864402i	−0.901777	+	0.432201i	$0.857737\pi$
$458$	2.96228e9	+	3.31072e10i	0.0673232	+	0.752420i
$459$	4.08320e10	+	4.08320e10i	0.919920	+	0.919920i
$460$	−1.83149e10	−	1.27169e10i	−0.409046	−	0.284020i
$461$	−1.76846e9	−	1.76846e9i	−0.0391554	−	0.0391554i	0.687258	−	0.726413i	$-0.258814\pi$
$461$	−1.76846e9	−	1.76846e9i	−0.0391554	−	0.0391554i	−0.726413	+	0.687258i	$0.758814\pi$
$462$	1.60524e10	−	1.92073e10i	0.352348	−	0.421597i
$463$			3.24178e10i			0.705438i	0.935729	+	0.352719i	$0.114743\pi$
$463$			3.24178e10i			0.705438i	−0.935729	+	0.352719i	$0.885257\pi$
$464$	−3.49247e10	−	1.59516e10i	−0.753461	−	0.344137i
$465$	1.09924e10			0.235115
$466$	6.64220e10	+	5.55119e10i	1.40854	+	1.17718i
$467$	−2.98261e10	+	2.98261e10i	−0.627090	+	0.627090i	−0.947335	−	0.320245i	$-0.896235\pi$
$467$	−2.98261e10	+	2.98261e10i	−0.627090	+	0.627090i	0.320245	+	0.947335i	$0.396235\pi$
$468$	−6.50535e9	−	4.51698e9i	−0.135609	−	0.0941595i
$469$	4.00474e8	−	4.00474e8i	0.00827719	−	0.00827719i
$470$	3.98709e10	−	3.56748e9i	0.817081	−	0.0731088i
$471$	−7.10398e10			−1.44351
$472$	−1.81700e9	−	6.62416e9i	−0.0366089	−	0.133464i
$473$			2.81310e10i			0.562005i
$474$	−4.36092e10	+	3.90196e9i	−0.863903	+	0.0772982i
$475$	−1.94014e10	−	1.94014e10i	−0.381118	−	0.381118i
$476$	−1.06251e10	−	5.88991e10i	−0.206970	−	1.14731i
$477$	5.79675e9	+	5.79675e9i	0.111972	+	0.111972i
$478$	−2.42762e10	−	2.02888e10i	−0.465018	−	0.388637i
$479$			5.97108e10i			1.13426i	0.823630	+	0.567128i	$0.191945\pi$
$479$			5.97108e10i			1.13426i	−0.823630	+	0.567128i	$0.808055\pi$
$480$	4.94695e10	+	1.74551e10i	0.931906	+	0.328820i
$481$	6.53997e10			1.22179
$482$	4.00946e9	−	4.79747e9i	0.0742845	−	0.0888841i
$483$	−1.41794e10	+	1.41794e10i	−0.260538	+	0.260538i
$484$	−3.10061e10	+	5.59335e9i	−0.565022	+	0.101927i
$485$	4.29300e10	−	4.29300e10i	0.775879	−	0.775879i
$486$	−2.38393e9	−	2.66433e10i	−0.0427315	−	0.477577i
$487$	1.69894e10			0.302038			0.151019	−	0.988531i	$-0.451745\pi$
$487$	1.69894e10			0.302038			0.151019	+	0.988531i	$0.451745\pi$
$488$	2.46477e10	+	8.98571e10i	0.434607	+	1.58443i
$489$		−	8.13190e10i		−	1.42219i
$490$	−3.50762e8	−	3.92019e9i	−0.00608454	−	0.0680022i
$491$	1.65429e10	+	1.65429e10i	0.284632	+	0.284632i	0.834953	−	0.550321i	$-0.185495\pi$
$491$	1.65429e10	+	1.65429e10i	0.284632	+	0.284632i	−0.550321	+	0.834953i	$0.685495\pi$
$492$	−4.77068e10	+	6.87074e10i	−0.814180	+	1.17258i
$493$	−4.16052e10	−	4.16052e10i	−0.704304	−	0.704304i
$494$	−4.68683e10	+	5.60796e10i	−0.786993	+	0.941666i
$495$		−	1.09608e10i		−	0.182566i
$496$	−5.03155e9	−	1.34921e10i	−0.0831333	−	0.222921i
$497$	7.22361e10			1.18394
$498$	5.02748e10	+	4.20170e10i	0.817398	+	0.683136i
$499$	3.39053e9	−	3.39053e9i	0.0546847	−	0.0546847i	−0.679236	−	0.733920i	$-0.737689\pi$
$499$	3.39053e9	−	3.39053e9i	0.0546847	−	0.0546847i	0.733920	+	0.679236i	$0.237689\pi$
$500$	−2.86004e10	+	4.11904e10i	−0.457607	+	0.659046i
$501$	2.79767e10	−	2.79767e10i	0.444064	−	0.444064i
$502$	3.09673e10	−	2.77082e9i	0.487628	−	0.0436308i
$503$	−1.10760e11			−1.73026			−0.865128	−	0.501552i	$-0.832763\pi$
$503$	−1.10760e11			−1.73026			−0.865128	+	0.501552i	$0.832763\pi$
$504$	−7.61100e9	+	1.33646e10i	−0.117956	+	0.207125i
$505$			2.24637e10i			0.345394i
$506$	−1.86464e10	+	1.66840e9i	−0.284441	+	0.0254505i
$507$	2.22771e10	+	2.22771e10i	0.337153	+	0.337153i
$508$	−4.45407e10	+	8.03493e9i	−0.668809	+	0.120650i
$509$	−2.01680e10	−	2.01680e10i	−0.300463	−	0.300463i	0.540732	−	0.841195i	$-0.318147\pi$
$509$	−2.01680e10	−	2.01680e10i	−0.300463	−	0.300463i	−0.841195	+	0.540732i	$0.818147\pi$
$510$	6.16843e10	+	5.15524e10i	0.911788	+	0.762023i
$511$			5.72936e10i			0.840277i
$512$	−1.21927e9	−	6.87087e10i	−0.0177427	−	0.999843i
$513$	−1.36939e11			−1.97723
$514$	−3.85822e10	+	4.61650e10i	−0.552757	+	0.661394i
$515$	1.07999e11	−	1.07999e11i	1.53529	−	1.53529i
$516$	9.41256e9	+	5.21774e10i	0.132773	+	0.736010i
$517$	2.37659e10	−	2.37659e10i	0.332653	−	0.332653i
$518$	−1.13185e10	−	1.26498e11i	−0.157206	−	1.75697i
$519$	−9.44146e9			−0.130128
$520$	−4.85516e10	−	2.76497e10i	−0.664034	−	0.378161i
$521$			9.57418e10i			1.29942i	0.760180	+	0.649712i	$0.225111\pi$
$521$			9.57418e10i			1.29942i	−0.760180	+	0.649712i	$0.774889\pi$
$522$	1.34749e9	+	1.50598e10i	0.0181486	+	0.202833i
$523$	−3.85703e10	−	3.85703e10i	−0.515521	−	0.515521i	0.400692	−	0.916213i	$-0.368770\pi$
$523$	−3.85703e10	−	3.85703e10i	−0.515521	−	0.515521i	−0.916213	+	0.400692i	$0.868770\pi$
$524$	−1.56430e10	−	1.08617e10i	−0.207489	−	0.144069i
$525$	−1.33392e10	−	1.33392e10i	−0.175587	−	0.175587i
$526$	−1.95303e8	+	2.33687e8i	−0.00255133	+	0.00305276i
$527$		−	2.20669e10i		−	0.286087i
$528$	4.12688e10	−	1.53903e10i	0.530990	−	0.198020i
$529$	−6.33139e10			−0.808494
$530$	4.43770e10	+	3.70879e10i	0.562412	+	0.470033i
$531$	−1.91268e9	+	1.91268e9i	−0.0240583	+	0.0240583i
$532$	1.16582e11	+	8.09484e10i	1.45541	+	1.01056i
$533$	6.29960e10	−	6.29960e10i	0.780556	−	0.780556i
$534$	−8.37372e10	+	7.49243e9i	−1.02980	+	0.0921421i
$535$	−9.57298e10			−1.16851
$536$	9.61037e8	−	2.63611e8i	0.0116434	−	0.00319378i
$537$			1.82568e9i			0.0219547i
$538$	1.08785e11	−	9.73364e9i	1.29850	−	0.116184i
$539$	−2.33671e9	−	2.33671e9i	−0.0276853	−	0.0276853i
$540$	−1.85850e10	−	1.03024e11i	−0.218569	−	1.21161i
$541$	−3.41835e10	−	3.41835e10i	−0.399050	−	0.399050i	0.478848	−	0.877898i	$-0.341054\pi$
$541$	−3.41835e10	−	3.41835e10i	−0.399050	−	0.399050i	−0.877898	+	0.478848i	$0.841054\pi$
$542$	6.93917e10	+	5.79938e10i	0.804101	+	0.672024i
$543$		−	1.56410e10i		−	0.179914i
$544$	3.50406e10	−	9.93085e10i	0.400107	−	1.13394i
$545$	3.85846e10			0.437349
$546$	−3.22236e10	+	3.85567e10i	−0.362580	+	0.433840i
$547$	1.05705e11	−	1.05705e11i	1.18072	−	1.18072i	0.201160	−	0.979558i	$-0.435529\pi$
$547$	1.05705e11	−	1.05705e11i	1.18072	−	1.18072i	0.979558	−	0.201160i	$-0.0644711\pi$
$548$	3.18007e10	−	5.73671e9i	0.352626	−	0.0636122i
$549$	2.59457e10	−	2.59457e10i	0.285611	−	0.285611i
$550$	−1.56953e9	−	1.75414e10i	−0.0171521	−	0.191696i
$551$	1.39532e11			1.51379
$552$	−3.40271e10	+	9.33358e9i	−0.366495	+	0.100529i
$553$		−	9.05590e10i		−	0.968347i
$554$	1.66045e9	+	1.85576e10i	0.0176273	+	0.197007i
$555$	1.20626e11	+	1.20626e11i	1.27136	+	1.27136i
$556$	8.65869e9	−	1.24702e10i	0.0906051	−	0.130490i
$557$	6.09201e10	+	6.09201e10i	0.632907	+	0.632907i	0.948796	−	0.315889i	$-0.102303\pi$
$557$	6.09201e10	+	6.09201e10i	0.632907	+	0.632907i	−0.315889	+	0.948796i	$0.602303\pi$
$558$	−3.63642e9	+	4.35111e9i	−0.0375092	+	0.0448811i
$559$		−	5.64702e10i		−	0.578325i
$560$	−4.50782e10	+	9.86950e10i	−0.458368	+	1.00356i
$561$	6.74970e10			0.681448
$562$	−2.56930e10	−	2.14728e10i	−0.257555	−	0.215250i
$563$	−7.35205e10	+	7.35205e10i	−0.731771	+	0.731771i	−0.970970	−	0.239200i	$-0.923115\pi$
$563$	−7.35205e10	+	7.35205e10i	−0.731771	+	0.731771i	0.239200	+	0.970970i	$0.423115\pi$
$564$	3.61290e10	−	5.20330e10i	0.357058	−	0.514236i
$565$	−1.29442e11	+	1.29442e11i	−1.27023	+	1.27023i
$566$	1.59280e10	−	1.42517e9i	0.155201	−	0.0138867i
$567$	−6.95146e10			−0.672580
$568$	1.10449e11	+	6.28996e10i	1.06113	+	0.604303i
$569$			1.09284e11i			1.04258i	0.853380	+	0.521289i	$0.174549\pi$
$569$			1.09284e11i			1.04258i	−0.853380	+	0.521289i	$0.825451\pi$
$570$	−1.89881e11	+	1.69897e10i	−1.79880	+	0.160949i
$571$	−1.38807e11	−	1.38807e11i	−1.30577	−	1.30577i	−0.924437	−	0.381335i	$-0.875464\pi$
$571$	−1.38807e11	−	1.38807e11i	−1.30577	−	1.30577i	−0.381335	−	0.924437i	$-0.624536\pi$
$572$	−4.61665e10	+	8.32823e9i	−0.431264	+	0.0777980i
$573$	−1.25811e10	−	1.25811e10i	−0.116708	−	0.116708i
$574$	−1.32751e11	−	1.10946e11i	−1.22290	−	1.02203i
$575$			1.41083e10i			0.129064i
$576$	−2.32744e10	+	1.38071e10i	−0.211441	+	0.125433i
$577$	1.33017e10			0.120006			0.0600032	−	0.998198i	$-0.480889\pi$
$577$	1.33017e10			0.120006			0.0600032	+	0.998198i	$0.480889\pi$
$578$	3.19157e10	−	3.81882e10i	0.285952	−	0.342151i
$579$	4.81256e10	−	4.81256e10i	0.428215	−	0.428215i
$580$	1.89370e10	+	1.04975e11i	0.167340	+	0.927626i
$581$	−9.58267e10	+	9.58267e10i	−0.840973	+	0.840973i
$582$	−8.56212e9	−	9.56923e10i	−0.0746259	−	0.834036i
$583$	4.85588e10			0.420333
$584$	−4.98884e10	+	8.76018e10i	−0.428892	+	0.753115i
$585$			2.20026e10i			0.187867i
$586$	−3.80559e9	−	4.25322e10i	−0.0322724	−	0.360684i
$587$	6.39905e10	+	6.39905e10i	0.538968	+	0.538968i	0.923226	−	0.384258i	$-0.125543\pi$
$587$	6.39905e10	+	6.39905e10i	0.538968	+	0.538968i	−0.384258	+	0.923226i	$0.625543\pi$
$588$	−5.11599e9	−	3.55228e9i	−0.0427977	−	0.0297165i
$589$	3.70029e10	+	3.70029e10i	0.307450	+	0.307450i
$590$	−1.22374e10	+	1.46425e10i	−0.100991	+	0.120839i
$591$		−	3.52563e10i		−	0.288993i
$592$	9.28422e10	−	2.03271e11i	0.755890	−	1.65496i
$593$	−1.88978e11			−1.52825			−0.764124	−	0.645070i	$-0.776828\pi$
$593$	−1.88978e11			−1.52825			−0.764124	+	0.645070i	$0.776828\pi$
$594$	−6.74441e10	−	5.63661e10i	−0.541749	−	0.452764i
$595$	−1.17574e11	+	1.17574e11i	−0.938086	+	0.938086i
$596$	1.03521e10	+	7.18799e9i	0.0820437	+	0.0569669i
$597$	−2.89396e10	+	2.89396e10i	−0.227822	+	0.227822i
$598$	3.74308e10	−	3.34914e9i	0.292701	−	0.0261896i
$599$	1.42178e11			1.10440			0.552199	−	0.833712i	$-0.313789\pi$
$599$	1.42178e11			1.10440			0.552199	+	0.833712i	$0.313789\pi$
$600$	−8.78047e9	−	3.20106e10i	−0.0677505	−	0.246996i
$601$			1.07906e11i			0.827080i	0.910486	+	0.413540i	$0.135708\pi$
$601$			1.07906e11i			0.827080i	−0.910486	+	0.413540i	$0.864292\pi$
$602$	−1.09226e11	+	9.77308e9i	−0.831650	+	0.0744124i
$603$	−2.77493e8	−	2.77493e8i	−0.00209886	−	0.00209886i
$604$	−5.75512e9	−	3.19028e10i	−0.0432421	−	0.239707i
$605$	6.18939e10	+	6.18939e10i	0.461983	+	0.461983i
$606$	2.72762e10	+	2.27960e10i	0.202252	+	0.169031i
$607$			8.01573e10i			0.590457i	0.955427	+	0.295228i	$0.0953957\pi$
$607$			8.01573e10i			0.590457i	−0.955427	+	0.295228i	$0.904604\pi$
$608$	1.07768e11	+	2.25284e11i	0.788632	+	1.64860i
$609$	9.59330e10			0.697427
$610$	1.66002e11	−	1.98627e11i	1.19893	−	1.43456i
$611$	−4.77077e10	+	4.77077e10i	−0.342313	+	0.342313i
$612$	−4.08119e10	+	7.36229e9i	−0.290925	+	0.0524816i
$613$	−1.86107e11	+	1.86107e11i	−1.31802	+	1.31802i	−0.402676	+	0.915343i	$0.631920\pi$
$613$	−1.86107e11	+	1.86107e11i	−1.31802	+	1.31802i	−0.915343	+	0.402676i	$0.868080\pi$
$614$	1.35771e9	+	1.51741e10i	0.00955289	+	0.106765i
$615$	2.32385e11			1.62445
$616$	2.40985e10	+	8.78552e10i	0.167366	+	0.610161i
$617$		−	1.23118e11i		−	0.849533i	−0.905303	−	0.424766i	$-0.860356\pi$
$617$		−	1.23118e11i		−	0.849533i	0.905303	−	0.424766i	$-0.139644\pi$
$618$	−2.15397e10	−	2.40732e11i	−0.147667	−	1.65037i
$619$	−1.85691e11	−	1.85691e11i	−1.26482	−	1.26482i	−0.948731	−	0.316086i	$-0.897631\pi$
$619$	−1.85691e11	−	1.85691e11i	−1.26482	−	1.26482i	−0.316086	−	0.948731i	$-0.602369\pi$
$620$	−2.28167e10	+	3.28606e10i	−0.154414	+	0.222387i
$621$	4.97894e10	+	4.97894e10i	0.334789	+	0.334789i
$622$	−1.48478e11	+	1.77659e11i	−0.991974	+	1.18693i
$623$		−	1.73889e11i		−	1.15430i
$624$	−8.28431e10	+	3.08944e10i	−0.546409	+	0.203771i
$625$	1.84318e11			1.20794
$626$	−1.93171e10	−	1.61442e10i	−0.125789	−	0.105128i
$627$	−1.13183e11	+	1.13183e11i	−0.732334	+	0.732334i
$628$	1.47456e11	−	2.12366e11i	0.948034	−	1.36536i
$629$	2.42153e11	−	2.42153e11i	1.54699	−	1.54699i
$630$	4.25581e10	−	3.80791e9i	0.270159	−	0.0241727i
$631$	−1.16117e11			−0.732449			−0.366225	−	0.930526i	$-0.619350\pi$
$631$	−1.16117e11			−0.732449			−0.366225	+	0.930526i	$0.619350\pi$
$632$	7.88543e10	−	1.38465e11i	0.494262	−	0.867901i
$633$		−	1.53861e11i		−	0.958326i
$634$	1.33021e11	−	1.19021e10i	0.823308	−	0.0736660i
$635$	8.89115e10	+	8.89115e10i	0.546844	+	0.546844i
$636$	9.00670e10	−	1.62477e10i	0.550474	−	0.0993031i
$637$	4.69072e9	+	4.69072e9i	0.0284893	+	0.0284893i
$638$	6.87212e10	+	5.74335e10i	0.414771	+	0.346643i
$639$		−	5.00533e10i		−	0.300213i
$640$	−1.54863e11	+	1.11653e11i	−0.923056	+	0.665502i
$641$	−2.38504e11			−1.41275			−0.706373	−	0.707840i	$-0.749670\pi$
$641$	−2.38504e11			−1.41275			−0.706373	+	0.707840i	$0.749670\pi$
$642$	−9.71460e10	+	1.16239e11i	−0.571853	+	0.684243i
$643$	1.41841e11	−	1.41841e11i	0.829773	−	0.829773i	−0.157712	−	0.987485i	$-0.550412\pi$
$643$	1.41841e11	−	1.41841e11i	0.829773	−	0.829773i	0.987485	+	0.157712i	$0.0504119\pi$
$644$	−1.29560e10	−	7.18200e10i	−0.0753230	−	0.417544i
$645$	1.04156e11	−	1.04156e11i	0.601790	−	0.601790i
$646$	3.41064e10	+	3.81181e11i	0.195842	+	2.18877i
$647$	6.62766e10			0.378219			0.189110	−	0.981956i	$-0.439440\pi$
$647$	6.62766e10			0.378219			0.189110	+	0.981956i	$0.439440\pi$
$648$	−1.06288e11	−	6.05299e10i	−0.602814	−	0.343297i
$649$			1.60224e10i			0.0903125i
$650$	3.15067e9	+	3.52126e10i	0.0176502	+	0.197263i
$651$	2.54408e10	+	2.54408e10i	0.141647	+	0.141647i
$652$	2.43095e11	+	1.68792e11i	1.34520	+	0.934033i
$653$	−9.74275e10	−	9.74275e10i	−0.535832	−	0.535832i	0.386470	−	0.922302i	$-0.373694\pi$
$653$	−9.74275e10	−	9.74275e10i	−0.535832	−	0.535832i	−0.922302	+	0.386470i	$0.873694\pi$
$654$	3.91554e10	−	4.68508e10i	0.214033	−	0.256098i
$655$			5.29083e10i			0.287447i
$656$	−1.06370e11	−	2.85229e11i	−0.574385	−	1.54021i
$657$	3.96994e10			0.213070
$658$	1.00534e11	+	8.40209e10i	0.536302	+	0.448212i
$659$	−8.94529e10	+	8.94529e10i	−0.474300	+	0.474300i	−0.903303	−	0.429003i	$-0.858865\pi$
$659$	−8.94529e10	+	8.94529e10i	−0.474300	+	0.474300i	0.429003	+	0.903303i	$0.358865\pi$
$660$	−1.00512e11	−	6.97904e10i	−0.529716	−	0.367807i
$661$	−5.86540e10	+	5.86540e10i	−0.307250	+	0.307250i	−0.843842	−	0.536592i	$-0.819711\pi$
$661$	−5.86540e10	+	5.86540e10i	−0.307250	+	0.307250i	0.536592	+	0.843842i	$0.319711\pi$
$662$	1.31671e11	−	1.17813e10i	0.685578	−	0.0613425i
$663$	−1.35494e11			−0.701237
$664$	−2.29960e11	+	6.30777e10i	−1.18299	+	0.324492i
$665$		−	3.94308e11i		−	2.01627i
$666$	−8.76519e10	+	7.84271e9i	−0.445517	+	0.0398629i
$667$	−5.07323e10	−	5.07323e10i	−0.256319	−	0.256319i
$668$	2.55628e10	+	1.41704e11i	0.128381	+	0.711666i
$669$	8.41680e10	+	8.41680e10i	0.420187	+	0.420187i
$670$	−2.12435e9	−	1.77542e9i	−0.0105421	−	0.00881051i
$671$		−	2.17344e11i		−	1.07216i
$672$	7.40942e10	+	1.54891e11i	0.363335	+	0.759535i
$673$	−3.05454e10			−0.148897			−0.0744485	−	0.997225i	$-0.523720\pi$
$673$	−3.05454e10			−0.148897			−0.0744485	+	0.997225i	$0.523720\pi$
$674$	−1.62224e7	+	1.94106e7i	−7.86094e−5	+	9.40590e-5i
$675$	−4.68389e10	+	4.68389e10i	−0.225627	+	0.225627i
$676$	−1.12835e11	+	2.03550e10i	−0.540329	+	0.0974728i
$677$	−1.02057e11	+	1.02057e11i	−0.485832	+	0.485832i	−0.906988	−	0.421156i	$-0.861624\pi$
$677$	−1.02057e11	+	1.02057e11i	−0.485832	+	0.485832i	0.421156	+	0.906988i	$0.361624\pi$
$678$	2.58165e10	+	2.88531e11i	0.122174	+	1.36544i
$679$	1.98715e11			0.934870
$680$	−2.82147e11	+	7.73926e10i	−1.31959	+	0.361963i
$681$			2.11695e11i			0.984287i
$682$	2.99344e9	+	3.34554e10i	0.0138367	+	0.154642i
$683$	1.63851e11	+	1.63851e11i	0.752951	+	0.752951i	0.975029	−	0.222078i	$-0.0712839\pi$
$683$	1.63851e11	+	1.63851e11i	0.752951	+	0.752951i	−0.222078	+	0.975029i	$0.571284\pi$
$684$	5.60901e10	−	8.07810e10i	0.256249	−	0.369050i
$685$	−6.34802e10	−	6.34802e10i	−0.288321	−	0.288321i
$686$	1.45952e11	−	1.74637e11i	0.659044	−	0.788570i
$687$		−	1.46133e11i		−	0.656027i
$688$	−1.75516e11	−	8.01657e10i	−0.783365	−	0.357795i
$689$	−9.74771e10			−0.432539
$690$	7.52161e10	+	6.28615e10i	0.331829	+	0.277325i
$691$	−1.38117e11	+	1.38117e11i	−0.605808	+	0.605808i	−0.941848	−	0.336040i	$-0.890912\pi$
$691$	−1.38117e11	+	1.38117e11i	−0.605808	+	0.605808i	0.336040	+	0.941848i	$0.390912\pi$
$692$	1.95975e10	−	2.82243e10i	0.0854625	−	0.123083i
$693$	2.53676e10	−	2.53676e10i	0.109988	−	0.109988i
$694$	−2.07794e11	+	1.85925e10i	−0.895768	+	0.0801494i
$695$	−4.21773e10			−0.180776
$696$	1.46681e11	+	8.35337e10i	0.625083	+	0.355979i
$697$		−	4.66506e11i		−	1.97663i
$698$	1.33325e11	−	1.19293e10i	0.561679	−	0.0502566i
$699$	−2.69104e11	−	2.69104e11i	−1.12723	−	1.12723i
$700$	6.75639e10	−	1.21882e10i	0.281399	−	0.0507631i
$701$	2.38778e11	+	2.38778e11i	0.988832	+	0.988832i	0.999938	−	0.0111062i	$-0.00353530\pi$
$701$	2.38778e11	+	2.38778e11i	0.988832	+	0.988832i	−0.0111062	+	0.999938i	$0.503535\pi$
$702$	1.35387e11	+	1.13149e11i	0.557480	+	0.465912i
$703$			8.12109e11i			3.32501i
$704$	−3.96533e10	+	1.55314e11i	−0.161432	+	0.632296i
$705$	−1.75988e11			−0.712404
$706$	3.04996e9	−	3.64939e9i	0.0122765	−	0.0146893i
$707$	−5.19900e10	+	5.19900e10i	−0.208086	+	0.208086i
$708$	5.36105e9	+	2.97183e10i	0.0213362	+	0.118274i
$709$	1.01624e11	−	1.01624e11i	0.402173	−	0.402173i	−0.476825	−	0.878998i	$-0.658212\pi$
$709$	1.01624e11	−	1.01624e11i	0.402173	−	0.402173i	0.878998	+	0.476825i	$0.158212\pi$
$710$	−3.14697e10	−	3.51713e11i	−0.123840	−	1.38406i
$711$	−6.27494e10			−0.245545
$712$	1.51414e11	−	2.65876e11i	0.589176	−	1.03457i
$713$		−	2.69077e10i		−	0.104116i
$714$	2.34494e10	+	2.62075e11i	0.0902273	+	1.00840i
$715$	9.21570e10	+	9.21570e10i	0.352618	+	0.352618i
$716$	−5.45767e9	−	3.78952e9i	−0.0207661	−	0.0144189i
$717$	9.83536e10	+	9.83536e10i	0.372146	+	0.372146i
$718$	1.53956e11	−	1.84214e11i	0.579295	−	0.693148i
$719$			2.46706e11i			0.923133i	0.887106	+	0.461566i	$0.152712\pi$
$719$			2.46706e11i			0.923133i	−0.887106	+	0.461566i	$0.847288\pi$
$720$	6.83870e10	+	3.12352e10i	0.254474	+	0.116229i
$721$	4.99905e11			1.84989
$722$	−4.87869e11	−	4.07734e11i	−1.79537	−	1.50047i
$723$	−1.94366e10	+	1.94366e10i	−0.0711325	+	0.0711325i
$724$	4.67572e10	+	3.24657e10i	0.170174	+	0.118160i
$725$	4.77259e10	−	4.77259e10i	0.172744	−	0.172744i
$726$	1.37963e11	−	1.23444e10i	0.496612	−	0.0444347i
$727$	−3.92728e11			−1.40590			−0.702950	−	0.711239i	$-0.748134\pi$
$727$	−3.92728e11			−1.40590			−0.702950	+	0.711239i	$0.748134\pi$
$728$	−4.83755e10	−	1.76361e11i	−0.172226	−	0.627879i
$729$			3.13527e11i			1.11011i
$730$	2.78959e11	−	2.49600e10i	0.982311	−	0.0878928i
$731$	−2.09090e11	−	2.09090e11i	−0.732257	−	0.732257i
$732$	−7.27230e10	−	4.03131e11i	−0.253295	−	1.40411i
$733$	−2.90492e9	−	2.90492e9i	−0.0100628	−	0.0100628i	0.702057	−	0.712120i	$-0.252265\pi$
$733$	−2.90492e9	−	2.90492e9i	−0.0100628	−	0.0100628i	−0.712120	+	0.702057i	$0.752265\pi$
$734$	−1.49258e11	−	1.24741e11i	−0.514224	−	0.429761i
$735$			1.73035e10i			0.0592904i
$736$	4.27276e10	−	1.21094e11i	0.145612	−	0.412678i
$737$	−2.32453e9			−0.00787891
$738$	−7.68759e10	+	9.19848e10i	−0.259158	+	0.310092i
$739$	1.60436e11	−	1.60436e11i	0.537926	−	0.537926i	−0.384993	−	0.922919i	$-0.625796\pi$
$739$	1.60436e11	−	1.60436e11i	0.537926	−	0.537926i	0.922919	+	0.384993i	$0.125796\pi$
$740$	−6.10979e11	+	1.10218e11i	−2.03751	+	0.367557i
$741$	2.27203e11	−	2.27203e11i	0.753600	−	0.753600i
$742$	1.68700e10	+	1.88543e11i	0.0556543	+	0.622006i
$743$	3.79587e11			1.24554			0.622768	−	0.782406i	$-0.286008\pi$
$743$	3.79587e11			1.24554			0.622768	+	0.782406i	$0.286008\pi$
$744$	1.67463e10	+	6.10515e10i	0.0546548	+	0.199253i
$745$		−	3.50134e10i		−	0.113660i
$746$	2.74010e10	+	3.06240e11i	0.0884731	+	0.988795i
$747$	6.63995e10	+	6.63995e10i	0.213247	+	0.213247i
$748$	−1.40102e11	+	2.01775e11i	−0.447547	+	0.644558i
$749$	−2.21558e11	−	2.21558e11i	−0.703978	−	0.703978i
$750$	1.41377e11	−	1.69162e11i	0.446820	−	0.534636i
$751$		−	5.19575e11i		−	1.63339i	−0.577073	−	0.816693i	$-0.695805\pi$
$751$		−	5.19575e11i		−	1.63339i	0.577073	−	0.816693i	$-0.304195\pi$
$752$	8.05551e10	+	2.16008e11i	0.251896	+	0.675458i
$753$	−1.36688e11			−0.425157
$754$	−1.37951e11	−	1.15292e11i	−0.426815	−	0.356709i
$755$	−6.36839e10	+	6.36839e10i	−0.195994	+	0.195994i
$756$	1.95426e11	−	2.81452e11i	0.598266	−	0.861623i
$757$	−3.14416e11	+	3.14416e11i	−0.957461	+	0.957461i	−0.999131	−	0.0416708i	$-0.986732\pi$
$757$	−3.14416e11	+	3.14416e11i	−0.957461	+	0.957461i	0.0416708	+	0.999131i	$0.486732\pi$
$758$	−3.23494e11	+	2.89448e10i	−0.979917	+	0.0876787i
$759$	8.23040e10			0.248001
$760$	3.43344e11	−	6.02896e11i	1.02914	−	1.80712i
$761$			2.13513e11i			0.636627i	0.947985	+	0.318314i	$0.103117\pi$
$761$			2.13513e11i			0.636627i	−0.947985	+	0.318314i	$0.896883\pi$
$762$	1.98186e11	−	1.77329e10i	0.587833	−	0.0525967i
$763$	8.93004e10	+	8.93004e10i	0.263485	+	0.263485i
$764$	6.37241e10	−	1.14955e10i	0.187038	−	0.0337408i
$765$	8.14683e10	+	8.14683e10i	0.237872	+	0.237872i
$766$	−6.01979e10	−	5.03101e10i	−0.174850	−	0.146130i
$767$		−	3.21633e10i		−	0.0929350i
$768$	−2.15812e10	+	3.01345e11i	−0.0620342	+	0.866201i
$769$	4.14844e11			1.18626			0.593129	−	0.805107i	$-0.297892\pi$
$769$	4.14844e11			1.18626			0.593129	+	0.805107i	$0.297892\pi$
$770$	1.62303e11	−	1.94202e11i	0.461705	−	0.552447i
$771$	1.87035e11	−	1.87035e11i	0.529303	−	0.529303i
$772$	4.39732e10	+	2.43760e11i	0.123799	+	0.686267i
$773$	−1.35267e11	+	1.35267e11i	−0.378856	+	0.378856i	−0.870689	−	0.491833i	$-0.836327\pi$
$773$	−1.35267e11	+	1.35267e11i	−0.378856	+	0.378856i	0.491833	+	0.870689i	$0.336327\pi$
$774$	6.77188e9	+	7.56841e10i	0.0188689	+	0.210883i
$775$	2.53132e10			0.0701681
$776$	3.03834e11	+	1.73031e11i	0.837896	+	0.477174i
$777$			5.58354e11i			1.53188i
$778$	−2.39507e10	−	2.67679e11i	−0.0653732	−	0.730626i
$779$	7.82261e11	+	7.82261e11i	2.12423	+	2.12423i
$780$	2.01768e11	+	1.40097e11i	0.545098	+	0.378488i
$781$	−2.09646e11	−	2.09646e11i	−0.563484	−	0.563484i
$782$	1.26193e11	−	1.50994e11i	0.337448	−	0.403769i
$783$		−	3.36857e11i		−	0.896188i
$784$	2.12383e10	−	7.92035e9i	0.0562155	−	0.0209643i
$785$	−7.18273e11			−1.89152
$786$	6.42432e10	+	5.36909e10i	0.168320	+	0.140673i
$787$	3.21517e11	−	3.21517e11i	0.838119	−	0.838119i	−0.150493	−	0.988611i	$-0.548086\pi$
$787$	3.21517e11	−	3.21517e11i	0.838119	−	0.838119i	0.988611	+	0.150493i	$0.0480860\pi$
$788$	1.05395e11	+	7.31808e10i	0.273348	+	0.189798i
$789$	9.46769e8	−	9.46769e8i	0.00244307	−	0.00244307i
$790$	−4.40926e11	+	3.94521e10i	−1.13203	+	0.101289i
$791$	−5.99164e11			−1.53052
$792$	6.08759e10	−	1.66982e10i	0.154719	−	0.0424393i
$793$			4.36298e11i			1.10329i
$794$	2.65335e11	−	2.37410e10i	0.667594	−	0.0597334i
$795$	−1.79791e11	−	1.79791e11i	−0.450089	−	0.450089i
$796$	−2.64426e10	−	1.46581e11i	−0.0658645	−	0.365112i
$797$	−5.24819e11	−	5.24819e11i	−1.30070	−	1.30070i	−0.927921	−	0.372776i	$-0.878406\pi$
$797$	−5.24819e11	−	5.24819e11i	−1.30070	−	1.30070i	−0.372776	−	0.927921i	$-0.621594\pi$
$798$	−4.78783e11	−	4.00141e11i	−1.18067	−	0.986736i
$799$			3.53291e11i			0.866852i
$800$	1.13918e11	+	4.01955e10i	0.278120	+	0.0981336i
$801$	−1.20490e11			−0.292698
$802$	−5.30099e11	+	6.34282e11i	−1.28132	+	1.53315i
$803$	1.66279e11	−	1.66279e11i	0.399922	−	0.399922i
$804$	−4.31155e9	+	7.77784e8i	−0.0103183	+	0.00186138i
$805$	−1.43366e11	+	1.43366e11i	−0.341400	+	0.341400i
$806$	−6.00904e9	−	6.71584e10i	−0.0142385	−	0.159133i
$807$	−4.80172e11			−1.13215
$808$	−1.24763e11	+	3.42223e10i	−0.292712	+	0.0802904i
$809$			2.95853e11i			0.690688i	0.938476	+	0.345344i	$0.112238\pi$
$809$			2.95853e11i			0.690688i	−0.938476	+	0.345344i	$0.887762\pi$
$810$	3.02841e10	+	3.38462e11i	0.0703518	+	0.786267i
$811$	−3.77914e11	−	3.77914e11i	−0.873593	−	0.873593i	0.119269	−	0.992862i	$-0.461945\pi$
$811$	−3.77914e11	−	3.77914e11i	−0.873593	−	0.873593i	−0.992862	+	0.119269i	$0.961945\pi$
$812$	−1.99126e11	+	2.86782e11i	−0.458041	+	0.659672i
$813$	−2.81136e11	−	2.81136e11i	−0.643508	−	0.643508i
$814$	−3.34277e11	+	3.99975e11i	−0.761393	+	0.911035i
$815$		−	8.22205e11i		−	1.86359i
$816$	−1.92348e11	+	4.21131e11i	−0.433838	+	0.949854i
$817$	7.01226e11			1.57387
$818$	4.37141e10	+	3.65339e10i	0.0976357	+	0.0815986i
$819$	−5.09230e10	+	5.09230e10i	−0.113182	+	0.113182i
$820$	−4.82357e11	+	6.94691e11i	−1.06687	+	1.53651i
$821$	3.05547e11	−	3.05547e11i	0.672521	−	0.672521i	−0.285775	−	0.958297i	$-0.592251\pi$
$821$	3.05547e11	−	3.05547e11i	0.672521	−	0.672521i	0.958297	+	0.285775i	$0.0922511\pi$
$822$	−1.41499e11	+	1.26607e10i	−0.309932	+	0.0277314i
$823$	8.11209e11			1.76821			0.884104	−	0.467289i	$-0.154769\pi$
$823$	8.11209e11			1.76821			0.884104	+	0.467289i	$0.154769\pi$
$824$	7.64354e11	+	4.35292e11i	1.65800	+	0.944218i
$825$			7.74266e10i			0.167138i
$826$	−6.22112e10	+	5.56638e9i	−0.133644	+	0.0119578i
$827$	−1.65596e10	−	1.65596e10i	−0.0354020	−	0.0354020i	0.689184	−	0.724586i	$-0.257969\pi$
$827$	−1.65596e10	−	1.65596e10i	−0.0354020	−	0.0354020i	−0.724586	+	0.689184i	$0.757969\pi$
$828$	−4.97649e10	+	8.97737e9i	−0.105877	+	0.0190998i
$829$	−1.81809e10	−	1.81809e10i	−0.0384944	−	0.0384944i	0.687598	−	0.726092i	$-0.258665\pi$
$829$	−1.81809e10	−	1.81809e10i	−0.0384944	−	0.0384944i	−0.726092	+	0.687598i	$0.758665\pi$
$830$	5.08321e11	+	4.24827e11i	1.07109	+	0.895159i
$831$		−	8.19120e10i		−	0.171769i
$832$	7.96001e10	−	3.11778e11i	0.166119	−	0.650657i
$833$	3.47363e10			0.0721445
$834$	−4.28012e10	+	5.12133e10i	−0.0884692	+	0.105857i
$835$	2.82868e11	−	2.82868e11i	0.581886	−	0.581886i
$836$	−1.03417e11	−	5.73278e11i	−0.211722	−	1.17365i
$837$	8.93324e10	−	8.93324e10i	0.182015	−	0.182015i
$838$	−3.55599e10	−	3.97425e11i	−0.0721081	−	0.805897i
$839$	−4.19167e11			−0.845939			−0.422969	−	0.906144i	$-0.639012\pi$
$839$	−4.19167e11			−0.845939			−0.422969	+	0.906144i	$0.639012\pi$
$840$	2.36061e11	−	4.14512e11i	0.474140	−	0.832569i
$841$		−	1.57010e11i		−	0.313865i
$842$	−3.64856e10	−	4.07771e11i	−0.0725893	−	0.811275i
$843$	1.04094e11	+	1.04094e11i	0.206117	+	0.206117i
$844$	4.59951e11	+	3.19366e11i	0.906447	+	0.629389i
$845$	2.25240e11	+	2.25240e11i	0.441793	+	0.441793i
$846$	5.82191e10	−	6.96613e10i	0.113654	−	0.135991i
$847$			2.86495e11i			0.556652i
$848$	−1.38380e11	+	3.02971e11i	−0.267601	+	0.585892i
$849$	−7.03052e10			−0.135318
$850$	1.42046e11	+	1.18714e11i	0.272116	+	0.227420i
$851$	2.95274e11	−	2.95274e11i	0.562999	−	0.562999i
$852$	−4.58998e11	−	3.18704e11i	−0.871069	−	0.604824i
$853$	3.63603e11	−	3.63603e11i	0.686801	−	0.686801i	−0.274723	−	0.961523i	$-0.588586\pi$
$853$	3.63603e11	−	3.63603e11i	0.686801	−	0.686801i	0.961523	+	0.274723i	$0.0885861\pi$
$854$	8.43899e11	−	7.55084e10i	1.58657	−	0.141959i
$855$	−2.73221e11			−0.511268
$856$	−1.45840e11	−	5.31682e11i	−0.271632	−	0.990278i
$857$		−	6.39424e11i		−	1.18540i	−0.805423	−	0.592701i	$-0.798062\pi$
$857$		−	6.39424e11i		−	1.18540i	0.805423	−	0.592701i	$-0.201938\pi$
$858$	2.05421e11	−	1.83801e10i	0.379049	−	0.0339156i
$859$	−5.13739e11	−	5.13739e11i	−0.943561	−	0.943561i	0.0549295	−	0.998490i	$-0.482507\pi$
$859$	−5.13739e11	−	5.13739e11i	−0.943561	−	0.943561i	−0.998490	+	0.0549295i	$0.982507\pi$
$860$	9.51690e10	+	5.27558e11i	0.173981	+	0.964442i
$861$	5.37832e11	+	5.37832e11i	0.978666	+	0.978666i
$862$	−5.28811e11	−	4.41951e11i	−0.957792	−	0.800470i
$863$			9.18976e11i			1.65676i	0.560163	+	0.828382i	$0.310738\pi$
$863$			9.18976e11i			1.65676i	−0.560163	+	0.828382i	$0.689262\pi$
$864$	5.43880e11	−	2.60173e11i	0.975996	−	0.466882i
$865$	−9.54612e10			−0.170515
$866$	−1.22417e11	+	1.46477e11i	−0.217657	+	0.260434i
$867$	−1.54717e11	+	1.54717e11i	−0.273818	+	0.273818i
$868$	−1.28860e11	+	2.32457e10i	−0.227006	+	0.0409509i
$869$	−2.62823e11	+	2.62823e11i	−0.460876	+	0.460876i
$870$	−4.17933e10	−	4.67092e11i	−0.0729508	−	0.815315i
$871$	4.66627e9			0.00810770
$872$	5.87817e10	+	2.14298e11i	0.101666	+	0.370641i
$873$		−	1.37692e11i		−	0.237056i
$874$	4.15884e10	+	4.64801e11i	0.0712732	+	0.796566i
$875$	3.22433e11	+	3.22433e11i	0.550056	+	0.550056i
$876$	2.52778e11	−	3.64051e11i	0.429263	−	0.618225i
$877$	2.33284e11	+	2.33284e11i	0.394355	+	0.394355i	0.876236	−	0.481882i	$-0.160046\pi$
$877$	2.33284e11	+	2.33284e11i	0.394355	+	0.394355i	−0.481882	+	0.876236i	$0.660046\pi$
$878$	7.25662e11	−	8.68281e11i	1.22111	−	1.46111i
$879$			1.87734e11i			0.314477i
$880$	4.17263e11	−	1.55608e11i	0.695791	−	0.259479i
$881$	−1.82626e11			−0.303152			−0.151576	−	0.988446i	$-0.548435\pi$
$881$	−1.82626e11			−0.303152			−0.151576	+	0.988446i	$0.548435\pi$
$882$	−6.84924e9	−	5.72422e9i	−0.0113180	−	0.00945893i
$883$	−1.51009e11	+	1.51009e11i	−0.248405	+	0.248405i	−0.820316	−	0.571911i	$-0.806202\pi$
$883$	−1.51009e11	+	1.51009e11i	−0.248405	+	0.248405i	0.571911	+	0.820316i	$0.306202\pi$
$884$	2.81241e11	−	4.05044e11i	0.460543	−	0.663275i
$885$	5.93233e10	−	5.93233e10i	0.0967058	−	0.0967058i
$886$	−4.95142e11	+	4.43032e10i	−0.803517	+	0.0718952i
$887$	−1.19492e11			−0.193039			−0.0965194	−	0.995331i	$-0.530771\pi$
$887$	−1.19492e11			−0.193039			−0.0965194	+	0.995331i	$0.530771\pi$
$888$	−4.86187e11	+	8.53722e11i	−0.781900	+	1.37298i
$889$			4.11554e11i			0.658901i
$890$	−8.46654e11	+	7.57549e10i	−1.34942	+	0.120740i
$891$	2.01747e11	+	2.01747e11i	0.320108	+	0.320108i
$892$	−4.26318e11	+	7.69058e10i	−0.673401	+	0.121478i
$893$	−5.92416e11	−	5.92416e11i	−0.931582	−	0.931582i
$894$	−4.25146e10	−	3.55314e10i	−0.0665561	−	0.0556239i
$895$			1.84591e10i			0.0287686i
$896$	−6.16825e11	−	1.00006e11i	−0.957040	−	0.155166i
$897$	−1.65217e11			−0.255203
$898$	5.17389e11	−	6.19075e11i	0.795631	−	0.952001i
$899$	−9.10240e10	+	9.10240e10i	−0.139353	+	0.139353i
$900$	−8.44537e9	−	4.68159e10i	−0.0128721	−	0.0713548i
$901$	−3.60924e11	+	3.60924e11i	−0.547668	+	0.547668i
$902$	6.32830e10	+	7.07265e11i	0.0956006	+	1.06845i
$903$	4.82118e11			0.725107
$904$	−9.16120e11	−	5.21722e11i	−1.37176	−	0.781206i
$905$		−	1.58144e11i		−	0.235753i
$906$	1.27014e10	+	1.41953e11i	0.0188511	+	0.210685i
$907$	−7.26314e10	−	7.26314e10i	−0.107324	−	0.107324i	0.651406	−	0.758729i	$-0.274180\pi$
$907$	−7.26314e10	−	7.26314e10i	−0.107324	−	0.107324i	−0.758729	+	0.651406i	$0.774180\pi$
$908$	−6.32840e11	−	4.39411e11i	−0.931002	−	0.646439i
$909$	3.60245e10	+	3.60245e10i	0.0527646	+	0.0527646i
$910$	−3.25808e11	+	3.89841e11i	−0.475112	+	0.568489i
$911$			8.78140e11i			1.27494i	0.770475	+	0.637471i	$0.220019\pi$
$911$			8.78140e11i			1.27494i	−0.770475	+	0.637471i	$0.779981\pi$
$912$	−3.83635e11	−	1.02871e12i	−0.554548	−	1.48702i
$913$	5.56222e11			0.800507
$914$	4.62883e11	+	3.86853e11i	0.663265	+	0.554320i
$915$	−8.04725e11	+	8.04725e11i	−1.14806	+	1.14806i
$916$	4.36850e11	+	3.03326e11i	0.620512	+	0.430851i
$917$	−1.22451e11	+	1.22451e11i	−0.173175	+	0.173175i
$918$	9.20247e11	−	8.23396e10i	1.29579	−	0.115941i
$919$	−3.85424e11			−0.540352			−0.270176	−	0.962811i	$-0.587082\pi$
$919$	−3.85424e11			−0.540352			−0.270176	+	0.962811i	$0.587082\pi$
$920$	−3.44043e11	+	9.43704e10i	−0.480243	+	0.131730i
$921$		−	6.69777e10i		−	0.0930875i
$922$	−3.98565e10	+	3.56618e9i	−0.0551538	+	0.00493492i
$923$	4.20843e11	+	4.20843e11i	0.579847	+	0.579847i
$924$	−7.11028e10	−	3.94149e11i	−0.0975435	−	0.540721i
$925$	2.77776e11	+	2.77776e11i	0.379427	+	0.379427i
$926$	3.97992e11	+	3.32620e11i	0.541290	+	0.452381i
$927$		−	3.46390e11i		−	0.469080i
$928$	−5.54179e11	+	2.65100e11i	−0.747237	+	0.357452i
$929$	−1.29621e11			−0.174025			−0.0870125	−	0.996207i	$-0.527732\pi$
$929$	−1.29621e11			−0.174025			−0.0870125	+	0.996207i	$0.527732\pi$
$930$	1.12786e11	−	1.34953e11i	0.150773	−	0.180406i
$931$	−5.82476e10	+	5.82476e10i	−0.0775317	+	0.0775317i
$932$	1.36303e12	−	2.45885e11i	1.80652	−	0.325888i
$933$	7.19775e11	−	7.19775e11i	0.949883	−	0.949883i
$934$	6.01458e10	+	6.72203e11i	0.0790347	+	0.883310i
$935$	6.82452e11			0.892947
$936$	−1.22202e11	+	3.35199e10i	−0.159212	+	0.0436717i
$937$		−	7.30361e11i		−	0.947500i	−0.880659	−	0.473750i	$-0.842900\pi$
$937$		−	7.30361e11i		−	0.947500i	0.880659	−	0.473750i	$-0.157100\pi$
$938$	−8.07574e8	−	9.02564e9i	−0.00104321	−	0.0116591i
$939$	7.82619e10	+	7.82619e10i	0.100667	+	0.100667i
$940$	3.65295e11	−	5.26098e11i	0.467877	−	0.673837i
$941$	7.11296e11	+	7.11296e11i	0.907177	+	0.907177i	0.996044	−	0.0888663i	$-0.0283244\pi$
$941$	7.11296e11	+	7.11296e11i	0.907177	+	0.907177i	−0.0888663	+	0.996044i	$0.528324\pi$
$942$	−7.28898e11	+	8.72153e11i	−0.925685	+	1.10762i
$943$		−	5.68844e11i		−	0.719360i
$944$	−9.99677e10	−	4.56594e10i	−0.125884	−	0.0574966i
$945$	−9.51938e11			−1.19366
$946$	3.45363e11	+	2.88636e11i	0.431232	+	0.360400i
$947$	−1.58484e11	+	1.58484e11i	−0.197054	+	0.197054i	−0.798736	−	0.601682i	$-0.794498\pi$
$947$	−1.58484e11	+	1.58484e11i	−0.197054	+	0.197054i	0.601682	+	0.798736i	$0.294498\pi$
$948$	−3.99545e11	+	5.75424e11i	−0.494689	+	0.712451i
$949$	−3.33789e11	+	3.33789e11i	−0.411535	+	0.411535i
$950$	−4.37257e11	+	3.91238e10i	−0.536837	+	0.0480338i
$951$	−5.87145e11			−0.717833
$952$	−8.32121e11	−	4.73885e11i	−1.01307	−	0.576933i
$953$			3.88469e11i			0.470961i	0.971879	+	0.235481i	$0.0756664\pi$
$953$			3.88469e11i			0.470961i	−0.971879	+	0.235481i	$0.924334\pi$
$954$	1.30644e11	−	1.16894e10i	0.157723	−	0.0141123i
$955$	−1.27205e11	−	1.27205e11i	−0.152930	−	0.152930i
$956$	−4.98169e11	+	8.98674e10i	−0.596410	+	0.107590i
$957$	−2.78420e11	−	2.78420e11i	−0.331934	−	0.331934i
$958$	7.33067e11	+	6.12658e11i	0.870326	+	0.727371i
$959$		−	2.93838e11i		−	0.347403i
$960$	7.21873e11	−	4.28238e11i	0.849916	−	0.504197i
$961$	8.04613e11			0.943395
$962$	6.71028e11	−	8.02910e11i	0.783503	−	0.937490i
$963$	−1.53520e11	+	1.53520e11i	−0.178509	+	0.178509i
$964$	−1.77596e10	−	9.84481e10i	−0.0205648	−	0.113998i
$965$	4.86591e11	−	4.86591e11i	0.561118	−	0.561118i
$966$	2.85935e10	+	3.19568e11i	0.0328366	+	0.366990i
$967$	−2.41758e11			−0.276487			−0.138243	−	0.990398i	$-0.544146\pi$
$967$	−2.41758e11			−0.276487			−0.138243	+	0.990398i	$0.544146\pi$
$968$	−2.49466e11	+	4.38050e11i	−0.284125	+	0.498910i
$969$		−	1.68251e12i		−	1.90837i
$970$	−8.65703e10	−	9.67530e11i	−0.0977872	−	1.09289i
$971$	−4.60053e11	−	4.60053e11i	−0.517525	−	0.517525i	0.399297	−	0.916822i	$-0.369254\pi$
$971$	−4.60053e11	−	4.60053e11i	−0.517525	−	0.517525i	−0.916822	+	0.399297i	$0.869254\pi$
$972$	−3.51559e11	−	2.44104e11i	−0.393852	−	0.273470i
$973$	−9.76154e10	−	9.76154e10i	−0.108910	−	0.108910i
$974$	1.74318e11	−	2.08578e11i	0.193690	−	0.231757i
$975$		−	1.55426e11i		−	0.171991i
$976$	1.35607e12	+	6.19373e11i	1.49445	+	0.682579i
$977$	9.26156e11			1.01650			0.508248	−	0.861211i	$-0.330293\pi$
$977$	9.26156e11			1.01650			0.508248	+	0.861211i	$0.330293\pi$
$978$	−9.98351e11	−	8.34367e11i	−1.09126	−	0.912015i
$979$	−5.04665e11	+	5.04665e11i	−0.549380	+	0.549380i
$980$	−5.17270e10	−	3.59165e10i	−0.0560807	−	0.0389395i
$981$	6.18773e10	−	6.18773e10i	0.0668121	−	0.0668121i
$982$	3.72833e11	−	3.33594e10i	0.400929	−	0.0358734i
$983$	8.71387e11			0.933248			0.466624	−	0.884456i	$-0.345470\pi$
$983$	8.71387e11			0.933248			0.466624	+	0.884456i	$0.345470\pi$
$984$	3.54027e11	+	1.29066e12i	0.377621	+	1.37668i
$985$		−	3.56471e11i		−	0.378686i
$986$	−9.37673e11	+	8.38989e10i	−0.992073	+	0.0887664i
$987$	−4.07307e11	−	4.07307e11i	−0.429194	−	0.429194i
$988$	2.07599e11	+	1.15080e12i	0.217870	+	1.20774i
$989$	−2.54958e11	−	2.54958e11i	−0.266492	−	0.266492i
$990$	−1.34565e11	−	1.12462e11i	−0.140085	−	0.117075i
$991$		−	4.69649e11i		−	0.486944i	−0.969908	−	0.243472i	$-0.921714\pi$
$991$		−	4.69649e11i		−	0.486944i	0.969908	−	0.243472i	$-0.0782864\pi$
$992$	−2.17267e11	−	7.66620e10i	−0.224361	−	0.0791650i
$993$	−5.81186e11			−0.597748
$994$	7.41173e11	−	8.86840e11i	0.759231	−	0.908447i
$995$	−2.92604e11	+	2.92604e11i	−0.298530	+	0.298530i
$996$	1.03168e12	−	1.86111e11i	1.04836	−	0.189119i
$997$	−9.02543e10	+	9.02543e10i	−0.0913456	+	0.0913456i	−0.751303	−	0.659957i	$-0.770574\pi$
$997$	−9.02543e10	+	9.02543e10i	−0.0913456	+	0.0913456i	0.659957	+	0.751303i	$0.270574\pi$
$998$	−6.83716e9	−	7.64137e10i	−0.00689214	−	0.0770281i
$999$	1.96059e12			1.96846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.9.f.a.3.11	✓	30
4.3	odd	2		64.9.f.a.47.11		30
8.3	odd	2		128.9.f.a.95.5		30
8.5	even	2		128.9.f.b.95.11		30
16.3	odd	4		128.9.f.b.31.11		30
16.5	even	4		64.9.f.a.15.11		30
16.11	odd	4	inner	16.9.f.a.11.11	yes	30
16.13	even	4		128.9.f.a.31.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.9.f.a.3.11	✓	30	1.1	even	1	trivial
16.9.f.a.11.11	yes	30	16.11	odd	4	inner
64.9.f.a.15.11		30	16.5	even	4
64.9.f.a.47.11		30	4.3	odd	2
128.9.f.a.31.5		30	16.13	even	4
128.9.f.a.95.5		30	8.3	odd	2
128.9.f.b.31.11		30	16.3	odd	4
128.9.f.b.95.11		30	8.5	even	2

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(10.2604 - 12.2770i) q^{2} +(-49.7393 + 49.7393i) q^{3} +(-45.4477 - 251.934i) q^{4} +(-502.907 + 502.907i) q^{5} +(100.302 + 1120.99i) q^{6} -2327.86 q^{7} +(-3559.29 - 2026.98i) q^{8} +1613.00i q^{9} +O(q^{10})\)	\(q+(10.2604 - 12.2770i) q^{2} +(-49.7393 + 49.7393i) q^{3} +(-45.4477 - 251.934i) q^{4} +(-502.907 + 502.907i) q^{5} +(100.302 + 1120.99i) q^{6} -2327.86 q^{7} +(-3559.29 - 2026.98i) q^{8} +1613.00i q^{9} +(1014.13 + 11334.2i) q^{10} +(6755.98 + 6755.98i) q^{11} +(14791.5 + 10270.5i) q^{12} +(-13562.0 - 13562.0i) q^{13} +(-23884.8 + 28579.0i) q^{14} -50028.5i q^{15} +(-61405.0 + 22899.6i) q^{16} -100431. q^{17} +(19802.8 + 16550.1i) q^{18} +(168407. - 168407. i) q^{19} +(149555. + 103843. i) q^{20} +(115786. - 115786. i) q^{21} +(152262. - 13623.7i) q^{22} -122462. q^{23} +(277857. - 76215.9i) q^{24} -115205. i q^{25} +(-305651. + 27348.3i) q^{26} +(-406569. - 406569. i) q^{27} +(105796. + 586466. i) q^{28} +(414268. + 414268. i) q^{29} +(-614198. - 513313. i) q^{30} +219722. i q^{31} +(-348904. + 988826. i) q^{32} -672076. q^{33} +(-1.03046e6 + 1.23298e6i) q^{34} +(1.17070e6 - 1.17070e6i) q^{35} +(406369. - 73307.2i) q^{36} +(-2.41114e6 + 2.41114e6i) q^{37} +(-339601. - 3.79546e6i) q^{38} +1.34913e6 q^{39} +(2.80937e6 - 770607. i) q^{40} +4.64505e6i q^{41} +(-233488. - 2.60952e6i) q^{42} +(2.08193e6 + 2.08193e6i) q^{43} +(1.39501e6 - 2.00910e6i) q^{44} +(-811189. - 811189. i) q^{45} +(-1.25652e6 + 1.50347e6i) q^{46} -3.51776e6i q^{47} +(1.91523e6 - 4.19325e6i) q^{48} -345873. q^{49} +(-1.41437e6 - 1.18205e6i) q^{50} +(4.99535e6 - 4.99535e6i) q^{51} +(-2.80035e6 + 4.03307e6i) q^{52} +(3.59377e6 - 3.59377e6i) q^{53} +(-9.16301e6 + 819866. i) q^{54} -6.79525e6 q^{55} +(8.28553e6 + 4.71853e6i) q^{56} +1.67529e7i q^{57} +(9.33652e6 - 835391. i) q^{58} +(1.18579e6 + 1.18579e6i) q^{59} +(-1.26038e7 + 2.27368e6i) q^{60} +(-1.60853e7 - 1.60853e7i) q^{61} +(2.69752e6 + 2.25444e6i) q^{62} -3.75484e6i q^{63} +(8.55989e6 + 1.44293e7i) q^{64} +1.36408e7 q^{65} +(-6.89578e6 + 8.25105e6i) q^{66} +(-172035. + 172035. i) q^{67} +(4.56434e6 + 2.53019e7i) q^{68} +(6.09119e6 - 6.09119e6i) q^{69} +(-2.36076e6 - 2.63844e7i) q^{70} -3.10311e7 q^{71} +(3.26953e6 - 5.74114e6i) q^{72} -2.46121e7i q^{73} +(4.86218e6 + 5.43409e7i) q^{74} +(5.73023e6 + 5.73023e6i) q^{75} +(-5.00812e7 - 3.47738e7i) q^{76} +(-1.57270e7 - 1.57270e7i) q^{77} +(1.38426e7 - 1.65632e7i) q^{78} +3.89023e7i q^{79} +(1.93646e7 - 4.23973e7i) q^{80} +2.98620e7 q^{81} +(5.70271e7 + 4.76602e7i) q^{82} +(4.11652e7 - 4.11652e7i) q^{83} +(-3.44326e7 - 2.39082e7i) q^{84} +(5.05073e7 - 5.05073e7i) q^{85} +(4.69213e7 - 4.19831e6i) q^{86} -4.12108e7 q^{87} +(-1.03522e7 - 3.77408e7i) q^{88} +7.46990e7i q^{89} +(-1.82821e7 + 1.63580e6i) q^{90} +(3.15703e7 + 3.15703e7i) q^{91} +(5.56563e6 + 3.08524e7i) q^{92} +(-1.09288e7 - 1.09288e7i) q^{93} +(-4.31874e7 - 3.60936e7i) q^{94} +1.69386e8i q^{95} +(-3.18293e7 - 6.65378e7i) q^{96} -8.53638e7 q^{97} +(-3.54880e6 + 4.24627e6i) q^{98} +(-1.08974e7 + 1.08974e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Introduction

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