LMFDB - Embedded newform 48.7.l.a.19.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.l (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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.15
Character	$\chi$	$=$	48.19
Dual form			48.7.l.a.43.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61327 - 7.83565i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-58.7947 - 25.2820i) q^{4} +(-15.5658 + 15.5658i) q^{5} +(68.5874 + 104.153i) q^{6} +10.2991 q^{7} +(-292.952 + 419.908i) q^{8} -243.000i q^{9} +O(q^{10})$	\(q+(1.61327 - 7.83565i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-58.7947 - 25.2820i) q^{4} +(-15.5658 + 15.5658i) q^{5} +(68.5874 + 104.153i) q^{6} +10.2991 q^{7} +(-292.952 + 419.908i) q^{8} -243.000i q^{9} +(96.8564 + 147.080i) q^{10} +(1309.74 + 1309.74i) q^{11} +(926.753 - 369.401i) q^{12} +(1999.54 + 1999.54i) q^{13} +(16.6152 - 80.7003i) q^{14} -343.155i q^{15} +(2817.64 + 2972.90i) q^{16} -1800.59 q^{17} +(-1904.06 - 392.024i) q^{18} +(1703.06 - 1703.06i) q^{19} +(1308.72 - 521.653i) q^{20} +(-113.524 + 113.524i) q^{21} +(12375.6 - 8149.70i) q^{22} +5649.07 q^{23} +(-1399.40 - 7857.65i) q^{24} +15140.4i q^{25} +(18893.5 - 12441.9i) q^{26} +(2678.52 + 2678.52i) q^{27} +(-605.534 - 260.382i) q^{28} +(-11764.6 - 11764.6i) q^{29} +(-2688.84 - 553.600i) q^{30} +32237.2i q^{31} +(27840.2 - 17282.0i) q^{32} -28873.7 q^{33} +(-2904.83 + 14108.8i) q^{34} +(-160.314 + 160.314i) q^{35} +(-6143.52 + 14287.1i) q^{36} +(-49520.9 + 49520.9i) q^{37} +(-10597.1 - 16092.1i) q^{38} -44080.7 q^{39} +(-1976.17 - 11096.3i) q^{40} +87389.3i q^{41} +(706.391 + 1072.68i) q^{42} +(7129.74 + 7129.74i) q^{43} +(-43893.0 - 110119. i) q^{44} +(3782.49 + 3782.49i) q^{45} +(9113.46 - 44264.1i) q^{46} -79423.3i q^{47} +(-63827.4 - 1711.32i) q^{48} -117543. q^{49} +(118635. + 24425.5i) q^{50} +(19847.3 - 19847.3i) q^{51} +(-67010.1 - 168115. i) q^{52} +(58057.5 - 58057.5i) q^{53} +(25309.1 - 16666.7i) q^{54} -40774.3 q^{55} +(-3017.15 + 4324.69i) q^{56} +37544.8i q^{57} +(-111163. + 73203.8i) q^{58} +(9265.40 + 9265.40i) q^{59} +(-8675.63 + 20175.7i) q^{60} +(31233.4 + 31233.4i) q^{61} +(252600. + 52007.3i) q^{62} -2502.69i q^{63} +(-90501.8 - 246026. i) q^{64} -62249.0 q^{65} +(-46581.1 + 226245. i) q^{66} +(140680. - 140680. i) q^{67} +(105865. + 45522.4i) q^{68} +(-62268.0 + 62268.0i) q^{69} +(997.536 + 1514.80i) q^{70} +445186. q^{71} +(102038. + 71187.4i) q^{72} +674960. i q^{73} +(308138. + 467919. i) q^{74} +(-166888. - 166888. i) q^{75} +(-143188. + 57074.4i) q^{76} +(13489.2 + 13489.2i) q^{77} +(-71114.0 + 345401. i) q^{78} -171535. i q^{79} +(-90134.4 - 2416.66i) q^{80} -59049.0 q^{81} +(684752. + 140982. i) q^{82} +(709618. - 709618. i) q^{83} +(9544.75 - 3804.51i) q^{84} +(28027.6 - 28027.6i) q^{85} +(67368.3 - 44364.0i) q^{86} +259355. q^{87} +(-933662. + 166279. i) q^{88} -549423. i q^{89} +(35740.4 - 23536.1i) q^{90} +(20593.5 + 20593.5i) q^{91} +(-332136. - 142820. i) q^{92} +(-355342. - 355342. i) q^{93} +(-622333. - 128131. i) q^{94} +53019.2i q^{95} +(-116380. + 497368. i) q^{96} -675921. q^{97} +(-189628. + 921025. i) q^{98} +(318267. - 318267. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) $ 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.61327	−	7.83565i	0.201658	−	0.979456i
$2$	1.61327	−	7.83565i	0.201658	−	0.979456i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$4$	−58.7947	−	25.2820i	−0.918668	−	0.395031i
$5$	−15.5658	+	15.5658i	−0.124526	+	0.124526i	−0.766623	−	0.642097i	$-0.778065\pi$
$5$	−15.5658	+	15.5658i	−0.124526	+	0.124526i	0.642097	+	0.766623i	$0.278065\pi$
$6$	68.5874	+	104.153i	0.317534	+	0.482188i
$7$	10.2991			0.0300266			0.0150133	−	0.999887i	$-0.495221\pi$
$7$	10.2991			0.0300266			0.0150133	+	0.999887i	$0.495221\pi$
$8$	−292.952	+	419.908i	−0.572173	+	0.820133i
$9$		−	243.000i		−	0.333333i
$10$	96.8564	+	147.080i	0.0968564	+	0.147080i
$11$	1309.74	+	1309.74i	0.984027	+	0.984027i	0.999874	−	0.0158475i	$-0.00504461\pi$
$11$	1309.74	+	1309.74i	0.984027	+	0.984027i	−0.0158475	+	0.999874i	$0.505045\pi$
$12$	926.753	−	369.401i	0.536315	−	0.213774i
$13$	1999.54	+	1999.54i	0.910123	+	0.910123i	0.996281	−	0.0861580i	$-0.0274590\pi$
$13$	1999.54	+	1999.54i	0.910123	+	0.910123i	−0.0861580	+	0.996281i	$0.527459\pi$
$14$	16.6152	−	80.7003i	0.00605512	−	0.0294097i
$15$		−	343.155i		−	0.101675i
$16$	2817.64	+	2972.90i	0.687901	+	0.725805i
$17$	−1800.59			−0.366495			−0.183247	−	0.983067i	$-0.558661\pi$
$17$	−1800.59			−0.366495			−0.183247	+	0.983067i	$0.558661\pi$
$18$	−1904.06	−	392.024i	−0.326485	−	0.0672195i
$19$	1703.06	−	1703.06i	0.248296	−	0.248296i	−0.571975	−	0.820271i	$-0.693823\pi$
$19$	1703.06	−	1703.06i	0.248296	−	0.248296i	0.820271	+	0.571975i	$0.193823\pi$
$20$	1308.72	−	521.653i	0.163590	−	0.0652066i
$21$	−113.524	+	113.524i	−0.0122583	+	0.0122583i
$22$	12375.6	−	8149.70i	1.16225	−	0.765374i
$23$	5649.07			0.464295			0.232147	−	0.972681i	$-0.425425\pi$
$23$	5649.07			0.464295			0.232147	+	0.972681i	$0.425425\pi$
$24$	−1399.40	−	7857.65i	−0.101229	−	0.568406i
$25$			15140.4i			0.968986i
$26$	18893.5	−	12441.9i	1.07496	−	0.707892i
$27$	2678.52	+	2678.52i	0.136083	+	0.136083i
$28$	−605.534	−	260.382i	−0.0275845	−	0.0118614i
$29$	−11764.6	−	11764.6i	−0.482373	−	0.482373i	0.423516	−	0.905889i	$-0.360796\pi$
$29$	−11764.6	−	11764.6i	−0.482373	−	0.482373i	−0.905889	+	0.423516i	$0.860796\pi$
$30$	−2688.84	−	553.600i	−0.0995866	−	0.0205037i
$31$			32237.2i			1.08211i	0.840986	+	0.541057i	$0.181976\pi$
$31$			32237.2i			1.08211i	−0.840986	+	0.541057i	$0.818024\pi$
$32$	27840.2	−	17282.0i	0.849615	−	0.527404i
$33$	−28873.7			−0.803455
$34$	−2904.83	+	14108.8i	−0.0739067	+	0.358965i
$35$	−160.314	+	160.314i	−0.00373911	+	0.00373911i
$36$	−6143.52	+	14287.1i	−0.131677	+	0.306223i
$37$	−49520.9	+	49520.9i	−0.977651	+	0.977651i	−0.999756	−	0.0221048i	$-0.992963\pi$
$37$	−49520.9	+	49520.9i	−0.977651	+	0.977651i	0.0221048	+	0.999756i	$0.492963\pi$
$38$	−10597.1	−	16092.1i	−0.193124	−	0.293266i
$39$	−44080.7			−0.743113
$40$	−1976.17	−	11096.3i	−0.0308776	−	0.173379i
$41$			87389.3i			1.26796i	0.773348	+	0.633982i	$0.218580\pi$
$41$			87389.3i			1.26796i	−0.773348	+	0.633982i	$0.781420\pi$
$42$	706.391	+	1072.68i	0.00953448	+	0.0144785i
$43$	7129.74	+	7129.74i	0.0896744	+	0.0896744i	0.750521	−	0.660847i	$-0.229803\pi$
$43$	7129.74	+	7129.74i	0.0896744	+	0.0896744i	−0.660847	+	0.750521i	$0.729803\pi$
$44$	−43893.0	−	110119.i	−0.515273	−	1.29272i
$45$	3782.49	+	3782.49i	0.0415088	+	0.0415088i
$46$	9113.46	−	44264.1i	0.0936289	−	0.454756i
$47$		−	79423.3i		−	0.764987i	−0.923958	−	0.382494i	$-0.875065\pi$
$47$		−	79423.3i		−	0.764987i	0.923958	−	0.382494i	$-0.124935\pi$
$48$	−63827.4	−	1711.32i	−0.577143	−	0.0154742i
$49$	−117543.			−0.999098
$50$	118635.	+	24425.5i	0.949079	+	0.195404i
$51$	19847.3	−	19847.3i	0.149621	−	0.149621i
$52$	−67010.1	−	168115.i	−0.476574	−	1.19563i
$53$	58057.5	−	58057.5i	0.389970	−	0.389970i	−0.484707	−	0.874677i	$-0.661074\pi$
$53$	58057.5	−	58057.5i	0.389970	−	0.389970i	0.874677	+	0.484707i	$0.161074\pi$
$54$	25309.1	−	16666.7i	0.160729	−	0.105845i
$55$	−40774.3			−0.245075
$56$	−3017.15	+	4324.69i	−0.0171804	+	0.0246258i
$57$			37544.8i			0.202733i
$58$	−111163.	+	73203.8i	−0.569738	+	0.375188i
$59$	9265.40	+	9265.40i	0.0451137	+	0.0451137i	0.729304	−	0.684190i	$-0.239844\pi$
$59$	9265.40	+	9265.40i	0.0451137	+	0.0451137i	−0.684190	+	0.729304i	$0.739844\pi$
$60$	−8675.63	+	20175.7i	−0.0401650	+	0.0934059i
$61$	31233.4	+	31233.4i	0.137604	+	0.137604i	0.772553	−	0.634950i	$-0.218979\pi$
$61$	31233.4	+	31233.4i	0.137604	+	0.137604i	−0.634950	+	0.772553i	$0.718979\pi$
$62$	252600.	+	52007.3i	1.05988	+	0.218217i
$63$		−	2502.69i		−	0.0100089i
$64$	−90501.8	−	246026.i	−0.345237	−	0.938516i
$65$	−62249.0			−0.226669
$66$	−46581.1	+	226245.i	−0.162023	+	0.786948i
$67$	140680.	−	140680.i	0.467742	−	0.467742i	−0.433440	−	0.901182i	$-0.642700\pi$
$67$	140680.	−	140680.i	0.467742	−	0.467742i	0.901182	+	0.433440i	$0.142700\pi$
$68$	105865.	+	45522.4i	0.336687	+	0.144777i
$69$	−62268.0	+	62268.0i	−0.189547	+	0.189547i
$70$	997.536	+	1514.80i	0.00290827	+	0.00441631i
$71$	445186.			1.24385			0.621923	−	0.783079i	$-0.286352\pi$
$71$	445186.			1.24385			0.621923	+	0.783079i	$0.286352\pi$
$72$	102038.	+	71187.4i	0.273378	+	0.190724i
$73$			674960.i			1.73504i	0.497402	+	0.867520i	$0.334287\pi$
$73$			674960.i			1.73504i	−0.497402	+	0.867520i	$0.665713\pi$
$74$	308138.	+	467919.i	0.760414	+	1.15472i
$75$	−166888.	−	166888.i	−0.395587	−	0.395587i
$76$	−143188.	+	57074.4i	−0.326187	+	0.130017i
$77$	13489.2	+	13489.2i	0.0295470	+	0.0295470i
$78$	−71114.0	+	345401.i	−0.149855	+	0.727846i
$79$		−	171535.i		−	0.347914i	−0.984753	−	0.173957i	$-0.944345\pi$
$79$		−	171535.i		−	0.347914i	0.984753	−	0.173957i	$-0.0556553\pi$
$80$	−90134.4	−	2416.66i	−0.176044	−	0.00472004i
$81$	−59049.0			−0.111111
$82$	684752.	+	140982.i	1.24191	+	0.255695i
$83$	709618.	−	709618.i	1.24105	−	1.24105i	0.281488	−	0.959565i	$-0.409172\pi$
$83$	709618.	−	709618.i	1.24105	−	1.24105i	0.959565	−	0.281488i	$-0.0908278\pi$
$84$	9544.75	−	3804.51i	0.0161037	−	0.00641890i
$85$	28027.6	−	28027.6i	0.0456383	−	0.0456383i
$86$	67368.3	−	44364.0i	0.105916	−	0.0697485i
$87$	259355.			0.393856
$88$	−933662.	+	166279.i	−1.37007	+	0.244000i
$89$		−	549423.i		−	0.779358i	−0.920951	−	0.389679i	$-0.872586\pi$
$89$		−	549423.i		−	0.779358i	0.920951	−	0.389679i	$-0.127414\pi$
$90$	35740.4	−	23536.1i	0.0490267	−	0.0322855i
$91$	20593.5	+	20593.5i	0.0273279	+	0.0273279i
$92$	−332136.	−	142820.i	−0.426532	−	0.183411i
$93$	−355342.	−	355342.i	−0.441771	−	0.441771i
$94$	−622333.	−	128131.i	−0.749271	−	0.154266i
$95$			53019.2i			0.0618389i
$96$	−116380.	+	497368.i	−0.131542	+	0.562165i
$97$	−675921.			−0.740595			−0.370297	−	0.928913i	$-0.620744\pi$
$97$	−675921.			−0.740595			−0.370297	+	0.928913i	$0.620744\pi$
$98$	−189628.	+	921025.i	−0.201477	+	0.978573i
$99$	318267.	−	318267.i	0.328009	−	0.328009i
$100$	382780.	−	890176.i	0.382780	−	0.890176i
$101$	196185.	−	196185.i	0.190415	−	0.190415i	−0.605460	−	0.795875i	$-0.707011\pi$
$101$	196185.	−	196185.i	0.190415	−	0.190415i	0.795875	+	0.605460i	$0.207011\pi$
$102$	−123498.	−	187536.i	−0.116375	−	0.176719i
$103$	1.82223e6			1.66759			0.833797	−	0.552071i	$-0.186162\pi$
$103$	1.82223e6			1.66759			0.833797	+	0.552071i	$0.186162\pi$
$104$	−1.42539e6	+	253853.i	−1.26717	+	0.225675i
$105$		−	3534.19i		−	0.00305297i
$106$	−361256.	−	548581.i	−0.303317	−	0.460599i
$107$	−1.18982e6	−	1.18982e6i	−0.971248	−	0.971248i	0.0283501	−	0.999598i	$-0.490975\pi$
$107$	−1.18982e6	−	1.18982e6i	−0.971248	−	0.971248i	−0.999598	+	0.0283501i	$0.990975\pi$
$108$	−89764.5	−	225201.i	−0.0712579	−	0.178772i
$109$	895661.	+	895661.i	0.691615	+	0.691615i	0.962587	−	0.270972i	$-0.0873452\pi$
$109$	895661.	+	895661.i	0.691615	+	0.691615i	−0.270972	+	0.962587i	$0.587345\pi$
$110$	−65779.9	+	319493.i	−0.0494214	+	0.240040i
$111$		−	1.09171e6i		−	0.798249i
$112$	29019.3	+	30618.2i	0.0206553	+	0.0217935i
$113$	−2.27050e6			−1.57357			−0.786784	−	0.617228i	$-0.788256\pi$
$113$	−2.27050e6			−1.57357			−0.786784	+	0.617228i	$0.788256\pi$
$114$	294187.	+	60569.7i	0.198568	+	0.0408828i
$115$	−87932.4	+	87932.4i	−0.0578170	+	0.0578170i
$116$	394264.	+	989129.i	0.252588	+	0.633693i
$117$	485889.	−	485889.i	0.303374	−	0.303374i
$118$	87548.0	−	57652.8i	0.0532844	−	0.0350893i
$119$	−18544.5			−0.0110046
$120$	144093.	+	100528.i	0.0833874	+	0.0581759i
$121$			1.65928e6i			0.936618i
$122$	295122.	−	194346.i	0.162526	−	0.107028i
$123$	−963266.	−	963266.i	−0.517644	−	0.517644i
$124$	815022.	−	1.89538e6i	0.427469	−	0.994103i
$125$	−478888.	−	478888.i	−0.245191	−	0.245191i
$126$	−19610.2	−	4037.51i	−0.00980325	−	0.00201837i
$127$			3.63397e6i			1.77407i	0.461705	+	0.887034i	$0.347238\pi$
$127$			3.63397e6i			1.77407i	−0.461705	+	0.887034i	$0.652762\pi$
$128$	−2.07378e6	+	312234.i	−0.988855	+	0.148885i
$129$	−157178.			−0.0732188
$130$	−100424.	+	487761.i	−0.0457097	+	0.222012i
$131$	−1.91691e6	+	1.91691e6i	−0.852685	+	0.852685i	−0.990463	−	0.137778i	$-0.956004\pi$
$131$	−1.91691e6	+	1.91691e6i	−0.852685	+	0.852685i	0.137778	+	0.990463i	$0.456004\pi$
$132$	1.69762e6	+	729986.i	0.738108	+	0.317390i
$133$	17540.1	−	17540.1i	0.00745550	−	0.00745550i
$134$	−875362.	−	1.32927e6i	−0.363809	−	0.552457i
$135$	−83386.6			−0.0338918
$136$	527486.	−	756081.i	0.209698	−	0.300574i
$137$			16843.3i			0.00655037i	0.999995	+	0.00327519i	$0.00104253\pi$
$137$			16843.3i			0.00655037i	−0.999995	+	0.00327519i	$0.998957\pi$
$138$	387455.	+	588365.i	0.147430	+	0.223877i
$139$	−1.61360e6	−	1.61360e6i	−0.600831	−	0.600831i	0.339702	−	0.940533i	$-0.389674\pi$
$139$	−1.61360e6	−	1.61360e6i	−0.600831	−	0.600831i	−0.940533	+	0.339702i	$0.889674\pi$
$140$	13478.7	−	5372.57i	0.00491206	−	0.00195793i
$141$	875459.	+	875459.i	0.312305	+	0.312305i
$142$	718204.	−	3.48832e6i	0.250832	−	1.21829i
$143$			5.23776e6i			1.79117i
$144$	722414.	−	684687.i	0.241935	−	0.229300i
$145$	366251.			0.120136
$146$	5.28875e6	+	1.08889e6i	1.69940	+	0.349886i
$147$	1.29564e6	−	1.29564e6i	0.407880	−	0.407880i
$148$	4.16356e6	−	1.65958e6i	1.28434	−	0.511934i
$149$	3.25465e6	−	3.25465e6i	0.983889	−	0.983889i	−0.0159835	−	0.999872i	$-0.505088\pi$
$149$	3.25465e6	−	3.25465e6i	0.983889	−	0.983889i	0.999872	+	0.0159835i	$0.00508791\pi$
$150$	−1.57691e6	+	1.03844e6i	−0.467233	+	0.307687i
$151$	−534226.			−0.155165			−0.0775826	−	0.996986i	$-0.524720\pi$
$151$	−534226.			−0.155165			−0.0775826	+	0.996986i	$0.524720\pi$
$152$	216214.	+	1.21405e6i	0.0615677	+	0.345704i
$153$			437543.i			0.122165i
$154$	127458.	−	83934.8i	0.0348984	−	0.0229816i
$155$	−501799.	−	501799.i	−0.134752	−	0.134752i
$156$	2.59171e6	+	1.11445e6i	0.682674	+	0.293553i
$157$	3.24398e6	+	3.24398e6i	0.838260	+	0.838260i	0.988630	−	0.150370i	$-0.0480463\pi$
$157$	3.24398e6	+	3.24398e6i	0.838260	+	0.838260i	−0.150370	+	0.988630i	$0.548046\pi$
$158$	−1.34409e6	−	276732.i	−0.340766	−	0.0701597i
$159$			1.27990e6i			0.318409i
$160$	−164347.	+	702363.i	−0.0401238	+	0.171475i
$161$	58180.5			0.0139412
$162$	−95261.8	+	462687.i	−0.0224065	+	0.108828i
$163$	−1.38258e6	+	1.38258e6i	−0.319247	+	0.319247i	−0.848478	−	0.529231i	$-0.822480\pi$
$163$	−1.38258e6	+	1.38258e6i	−0.319247	+	0.319247i	0.529231	+	0.848478i	$0.322480\pi$
$164$	2.20938e6	−	5.13803e6i	0.500885	−	1.16484i
$165$	449443.	−	449443.i	0.100051	−	0.100051i
$166$	−4.41551e6	−	6.70512e6i	−0.965287	−	1.46582i
$167$	758120.			0.162775			0.0813877	−	0.996683i	$-0.474065\pi$
$167$	758120.			0.162775			0.0813877	+	0.996683i	$0.474065\pi$
$168$	−14412.6	−	80927.0i	−0.00303958	−	0.0170673i
$169$			3.16952e6i			0.656650i
$170$	−174398.	−	264830.i	−0.0354973	−	0.0539040i
$171$	−413845.	−	413845.i	−0.0827655	−	0.0827655i
$172$	−238937.	−	599445.i	−0.0469568	−	0.117805i
$173$	−3.74301e6	−	3.74301e6i	−0.722908	−	0.722908i	0.246289	−	0.969196i	$-0.420789\pi$
$173$	−3.74301e6	−	3.74301e6i	−0.722908	−	0.722908i	−0.969196	+	0.246289i	$0.920789\pi$
$174$	418409.	−	2.03222e6i	0.0794244	−	0.385764i
$175$			155933.i			0.0290954i
$176$	−203343.	+	7.58410e6i	−0.0372984	+	1.39112i
$177$	−204260.			−0.0368352
$178$	−4.30508e6	−	886366.i	−0.763346	−	0.157164i
$179$	−4.64678e6	+	4.64678e6i	−0.810201	+	0.810201i	−0.984664	−	0.174463i	$-0.944181\pi$
$179$	−4.64678e6	+	4.64678e6i	−0.810201	+	0.810201i	0.174463	+	0.984664i	$0.444181\pi$
$180$	−126762.	−	318019.i	−0.0217355	−	0.0545301i
$181$	6.37439e6	−	6.37439e6i	1.07499	−	1.07499i	0.0780350	−	0.996951i	$-0.475135\pi$
$181$	6.37439e6	−	6.37439e6i	1.07499	−	1.07499i	0.996951	−	0.0780350i	$-0.0248646\pi$
$182$	194587.	−	128141.i	0.0322774	−	0.0212556i
$183$	−688553.			−0.112353
$184$	−1.65491e6	+	2.37209e6i	−0.265657	+	0.380783i
$185$		−	1.54167e6i		−	0.243487i
$186$	−3.35759e6	+	2.21107e6i	−0.521782	+	0.343608i
$187$	−2.35830e6	−	2.35830e6i	−0.360640	−	0.360640i
$188$	−2.00798e6	+	4.66967e6i	−0.302194	+	0.702769i
$189$	27586.4	+	27586.4i	0.00408610	+	0.00408610i
$190$	415439.	+	85534.1i	0.0605685	+	0.0124703i
$191$			8.82548e6i			1.26660i	0.773908	+	0.633298i	$0.218299\pi$
$191$			8.82548e6i			1.26660i	−0.773908	+	0.633298i	$0.781701\pi$
$192$	3.70945e6	+	1.71430e6i	0.524090	+	0.242205i
$193$	−1.15481e7			−1.60635			−0.803175	−	0.595743i	$-0.796858\pi$
$193$	−1.15481e7			−1.60635			−0.803175	+	0.595743i	$0.796858\pi$
$194$	−1.09044e6	+	5.29628e6i	−0.149347	+	0.725380i
$195$	686152.	−	686152.i	0.0925372	−	0.0925372i
$196$	6.91091e6	+	2.97172e6i	0.917839	+	0.394675i
$197$	1.01337e7	−	1.01337e7i	1.32547	−	1.32547i	0.416195	−	0.909275i	$-0.363363\pi$
$197$	1.01337e7	−	1.01337e7i	1.32547	−	1.32547i	0.909275	−	0.416195i	$-0.136637\pi$
$198$	−1.98038e6	−	3.00728e6i	−0.255125	−	0.387416i
$199$	−1.23678e6			−0.156940			−0.0784702	−	0.996916i	$-0.525004\pi$
$199$	−1.23678e6			−0.156940			−0.0784702	+	0.996916i	$0.525004\pi$
$200$	−6.35758e6	−	4.43542e6i	−0.794698	−	0.554428i
$201$			3.10134e6i			0.381910i
$202$	−1.22074e6	−	1.85373e6i	−0.148104	−	0.224902i
$203$	−121165.	−	121165.i	−0.0144840	−	0.0144840i
$204$	−1.66870e6	+	665139.i	−0.196557	+	0.0783469i
$205$	−1.36028e6	−	1.36028e6i	−0.157895	−	0.157895i
$206$	2.93974e6	−	1.42783e7i	0.336284	−	1.63333i
$207$		−	1.37272e6i		−	0.154765i
$208$	−310437.	+	1.15784e7i	−0.0344972	+	1.28665i
$209$	4.46114e6			0.488661
$210$	−27692.7	−	5701.60i	−0.00299025	−	0.000615657i
$211$	1.18103e6	−	1.18103e6i	0.125722	−	0.125722i	−0.641446	−	0.767168i	$-0.721665\pi$
$211$	1.18103e6	−	1.18103e6i	0.125722	−	0.125722i	0.767168	+	0.641446i	$0.221665\pi$
$212$	−4.88129e6	+	1.94567e6i	−0.512303	+	0.204202i
$213$	−4.90715e6	+	4.90715e6i	−0.507798	+	0.507798i
$214$	−1.12425e7	+	7.40351e6i	−1.14715	+	0.755434i
$215$	−221960.			−0.0223337
$216$	−1.90941e6	+	340053.i	−0.189469	+	0.0337431i
$217$			332016.i			0.0324922i
$218$	8.46303e6	−	5.57314e6i	0.816876	−	0.537936i
$219$	−7.43989e6	−	7.43989e6i	−0.708327	−	0.708327i
$220$	2.39732e6	+	1.03086e6i	0.225142	+	0.0968122i
$221$	−3.60035e6	−	3.60035e6i	−0.333555	−	0.333555i
$222$	−8.55425e6	−	1.76122e6i	−0.781849	−	0.160974i
$223$		−	1.20834e7i		−	1.08962i	−0.838561	−	0.544808i	$-0.816602\pi$
$223$		−	1.20834e7i		−	1.08962i	0.838561	−	0.544808i	$-0.183398\pi$
$224$	286730.	−	177989.i	0.0255110	−	0.0158362i
$225$	3.67912e6			0.322995
$226$	−3.66292e6	+	1.77908e7i	−0.317323	+	1.54124i
$227$	1.40935e7	−	1.40935e7i	1.20488	−	1.20488i	0.232210	−	0.972666i	$-0.425404\pi$
$227$	1.40935e7	−	1.40935e7i	1.20488	−	1.20488i	0.972666	−	0.232210i	$-0.0745958\pi$
$228$	949206.	−	2.20743e6i	0.0800859	−	0.186244i
$229$	4.56390e6	−	4.56390e6i	0.380040	−	0.380040i	−0.491076	−	0.871117i	$-0.663396\pi$
$229$	4.56390e6	−	4.56390e6i	0.380040	−	0.380040i	0.871117	+	0.491076i	$0.163396\pi$
$230$	547149.	+	830865.i	0.0449699	+	0.0682884i
$231$	−297374.			−0.0241250
$232$	8.38652e6	−	1.49358e6i	0.671611	−	0.119609i
$233$		−	1.88250e7i		−	1.48822i	−0.668056	−	0.744111i	$-0.732873\pi$
$233$		−	1.88250e7i		−	1.48822i	0.668056	−	0.744111i	$-0.267127\pi$
$234$	−3.02338e6	−	4.59112e6i	−0.235964	−	0.358320i
$235$	1.23629e6	+	1.23629e6i	0.0952612	+	0.0952612i
$236$	−310509.	−	779004.i	−0.0236232	−	0.0592658i
$237$	1.89078e6	+	1.89078e6i	0.142035	+	0.142035i
$238$	−29917.2	+	145308.i	−0.00221917	+	0.0107785i
$239$			1.87271e7i			1.37176i	0.727716	+	0.685879i	$0.240582\pi$
$239$			1.87271e7i			1.37176i	−0.727716	+	0.685879i	$0.759418\pi$
$240$	1.02016e6	−	966887.i	0.0737965	−	0.0699426i
$241$	3.72390e6			0.266040			0.133020	−	0.991113i	$-0.457533\pi$
$241$	3.72390e6			0.266040			0.133020	+	0.991113i	$0.457533\pi$
$242$	1.30015e7	+	2.67686e6i	0.917376	+	0.188877i
$243$	650880.	−	650880.i	0.0453609	−	0.0453609i
$244$	−1.04672e6	−	2.62600e6i	−0.0720543	−	0.180770i
$245$	1.82965e6	−	1.82965e6i	0.124414	−	0.124414i
$246$	−9.10182e6	+	5.99381e6i	−0.611396	+	0.402622i
$247$	6.81070e6			0.451961
$248$	−1.35367e7	−	9.44398e6i	−0.887477	−	0.619156i
$249$			1.56438e7i			1.01332i
$250$	−4.52498e6	+	2.97983e6i	−0.289598	+	0.190709i
$251$	1.06030e7	+	1.06030e7i	0.670513	+	0.670513i	0.957834	−	0.287321i	$-0.0927648\pi$
$251$	1.06030e7	+	1.06030e7i	0.670513	+	0.670513i	−0.287321	+	0.957834i	$0.592765\pi$
$252$	−63272.9	+	147145.i	−0.00395382	+	0.00919483i
$253$	7.39881e6	+	7.39881e6i	0.456878	+	0.456878i
$254$	2.84745e7	+	5.86257e6i	1.73762	+	0.357756i
$255$			617880.i			0.0372635i
$256$	−899006.	+	1.67531e7i	−0.0535849	+	0.998563i
$257$	1.38806e6			0.0817730			0.0408865	−	0.999164i	$-0.486982\pi$
$257$	1.38806e6			0.0817730			0.0408865	+	0.999164i	$0.486982\pi$
$258$	−253570.	+	1.23159e6i	−0.0147652	+	0.0717146i
$259$	−510023.	+	510023.i	−0.0293555	+	0.0293555i
$260$	3.65991e6	+	1.57378e6i	0.208233	+	0.0895413i
$261$	−2.85880e6	+	2.85880e6i	−0.160791	+	0.160791i
$262$	1.19278e7	+	1.81128e7i	0.663216	+	1.00712i
$263$	7.75571e6			0.426338			0.213169	−	0.977015i	$-0.431621\pi$
$263$	7.75571e6			0.426338			0.213169	+	0.977015i	$0.431621\pi$
$264$	8.45863e6	−	1.21243e7i	0.459715	−	0.658940i
$265$			1.80742e6i			0.0971231i
$266$	−109141.	−	165735.i	−0.00579887	−	0.00880580i
$267$	6.05613e6	+	6.05613e6i	0.318171	+	0.318171i
$268$	−1.18279e7	+	4.71456e6i	−0.614473	+	0.244927i
$269$	7.01455e6	+	7.01455e6i	0.360365	+	0.360365i	0.863947	−	0.503582i	$-0.167985\pi$
$269$	7.01455e6	+	7.01455e6i	0.360365	+	0.360365i	−0.503582	+	0.863947i	$0.667985\pi$
$270$	−134525.	+	653388.i	−0.00683457	+	0.0331955i
$271$		−	3.58375e7i		−	1.80065i	−0.435216	−	0.900326i	$-0.643328\pi$
$271$		−	3.58375e7i		−	1.80065i	0.435216	−	0.900326i	$-0.356672\pi$
$272$	−5.07341e6	−	5.35296e6i	−0.252112	−	0.266003i
$273$	−453993.			−0.0223132
$274$	131978.	+	27172.8i	0.00641580	+	0.00132094i
$275$	−1.98300e7	+	1.98300e7i	−0.953509	+	0.953509i
$276$	5.23529e6	−	2.08677e6i	0.249008	−	0.0992540i
$277$	−1.43034e7	+	1.43034e7i	−0.672976	+	0.672976i	−0.958401	−	0.285425i	$-0.907865\pi$
$277$	−1.43034e7	+	1.43034e7i	−0.672976	+	0.672976i	0.285425	+	0.958401i	$0.407865\pi$
$278$	−1.52468e7	+	1.00405e7i	−0.709650	+	0.467325i
$279$	7.83365e6			0.360705
$280$	−20352.8	−	114282.i	−0.000927151	−	0.00520598i
$281$			1.53217e7i			0.690539i	0.938504	+	0.345270i	$0.112213\pi$
$281$			1.53217e7i			0.690539i	−0.938504	+	0.345270i	$0.887787\pi$
$282$	8.27214e6	−	5.44744e6i	0.368868	−	0.242910i
$283$	−2.25052e7	−	2.25052e7i	−0.992942	−	0.992942i	0.00703372	−	0.999975i	$-0.497761\pi$
$283$	−2.25052e7	−	2.25052e7i	−0.992942	−	0.992942i	−0.999975	+	0.00703372i	$0.997761\pi$
$284$	−2.61746e7	−	1.12552e7i	−1.14268	−	0.491358i
$285$	−584414.	−	584414.i	−0.0252456	−	0.0252456i
$286$	4.10412e7	+	8.44991e6i	1.75437	+	0.361205i
$287$			900033.i			0.0380726i
$288$	−4.19952e6	−	6.76516e6i	−0.175801	−	0.283205i
$289$	−2.08955e7			−0.865682
$290$	590861.	−	2.86981e6i	0.0242265	−	0.117668i
$291$	7.45047e6	−	7.45047e6i	0.302346	−	0.302346i
$292$	1.70643e7	−	3.96841e7i	0.685395	−	1.59393i
$293$	−2.66381e7	+	2.66381e7i	−1.05901	+	1.05901i	−0.0608658	+	0.998146i	$0.519386\pi$
$293$	−2.66381e7	+	2.66381e7i	−1.05901	+	1.05901i	−0.998146	+	0.0608658i	$0.980614\pi$
$294$	−8.06197e6	−	1.22424e7i	−0.317248	−	0.481753i
$295$	−288447.			−0.0112357
$296$	−6.28697e6	−	3.53015e7i	−0.242419	−	1.36119i
$297$			7.01632e6i			0.267818i
$298$	−2.02517e7	−	3.07529e7i	−0.765266	−	1.16209i
$299$	1.12956e7	+	1.12956e7i	0.422565	+	0.422565i
$300$	5.59288e6	+	1.40314e7i	0.207144	+	0.519682i
$301$	73430.1	+	73430.1i	0.00269262	+	0.00269262i
$302$	−861850.	+	4.18601e6i	−0.0312904	+	0.151977i
$303$			4.32498e6i			0.155473i
$304$	9.86166e6	+	264408.i	0.351018	+	0.00941139i
$305$	−972346.			−0.0342706
$306$	3.42843e6	+	705874.i	0.119655	+	0.0246356i
$307$	2.12747e6	−	2.12747e6i	0.0735273	−	0.0735273i	−0.669387	−	0.742914i	$-0.733443\pi$
$307$	2.12747e6	−	2.12747e6i	0.0735273	−	0.0735273i	0.742914	+	0.669387i	$0.233443\pi$
$308$	−452059.	−	1.13413e6i	−0.0154719	−	0.0388159i
$309$	−2.00858e7	+	2.00858e7i	−0.680792	+	0.680792i
$310$	−4.74145e6	+	3.12238e6i	−0.159157	+	0.104810i
$311$	−2.09965e7			−0.698018			−0.349009	−	0.937119i	$-0.613482\pi$
$311$	−2.09965e7			−0.698018			−0.349009	+	0.937119i	$0.613482\pi$
$312$	1.29135e7	−	1.85098e7i	0.425189	−	0.609451i
$313$		−	3.90976e7i		−	1.27502i	−0.770442	−	0.637511i	$-0.779964\pi$
$313$		−	3.90976e7i		−	1.27502i	0.770442	−	0.637511i	$-0.220036\pi$
$314$	3.06521e7	−	2.01853e7i	0.990081	−	0.651997i
$315$	38956.4	+	38956.4i	0.00124637	+	0.00124637i
$316$	−4.33675e6	+	1.00854e7i	−0.137437	+	0.319617i
$317$	−3.72393e7	−	3.72393e7i	−1.16902	−	1.16902i	−0.982439	−	0.186585i	$-0.940258\pi$
$317$	−3.72393e7	−	3.72393e7i	−1.16902	−	1.16902i	−0.186585	−	0.982439i	$-0.559742\pi$
$318$	1.00289e7	+	2.06482e6i	0.311868	+	0.0642099i
$319$		−	3.08171e7i		−	0.949336i
$320$	5.23833e6	+	2.42086e6i	0.159861	+	0.0738789i
$321$	2.62301e7			0.793021
$322$	93860.7	−	455882.i	0.00281136	−	0.0136548i
$323$	−3.06652e6	+	3.06652e6i	−0.0909992	+	0.0909992i
$324$	3.47177e6	+	1.49288e6i	0.102074	+	0.0438923i
$325$	−3.02739e7	+	3.02739e7i	−0.881897	+	0.881897i
$326$	8.60291e6	+	1.30638e7i	0.248309	+	0.377067i
$327$	−1.97452e7			−0.564701
$328$	−3.66955e7	−	2.56009e7i	−1.03990	−	0.725494i
$329$		−	817991.i		−	0.0229700i
$330$	−2.79661e6	−	4.24675e6i	−0.0778197	−	0.118172i
$331$	4.89023e7	+	4.89023e7i	1.34848	+	1.34848i	0.887312	+	0.461170i	$0.152570\pi$
$331$	4.89023e7	+	4.89023e7i	1.34848	+	1.34848i	0.461170	+	0.887312i	$0.347430\pi$
$332$	−5.96623e7	+	2.37812e7i	−1.63037	+	0.649860i
$333$	1.20336e7	+	1.20336e7i	0.325884	+	0.325884i
$334$	1.22305e6	−	5.94036e6i	0.0328250	−	0.159431i
$335$			4.37958e6i			0.116493i
$336$	−657366.	−	17625.1i	−0.0173296	−	0.000464638i
$337$	−2.08256e7			−0.544136			−0.272068	−	0.962278i	$-0.587708\pi$
$337$	−2.08256e7			−0.544136			−0.272068	+	0.962278i	$0.587708\pi$
$338$	2.48353e7	+	5.11329e6i	0.643159	+	0.132419i
$339$	2.50270e7	−	2.50270e7i	0.642407	−	0.642407i
$340$	−2.35647e6	+	939282.i	−0.0599549	+	0.0238979i
$341$	−4.22224e7	+	4.22224e7i	−1.06483	+	1.06483i
$342$	−3.91038e6	+	2.57510e6i	−0.0977555	+	0.0643748i
$343$	−2.42227e6			−0.0600261
$344$	−5.08251e6	+	905162.i	−0.124854	+	0.0222357i
$345$		−	1.93850e6i		−	0.0472073i
$346$	−3.53674e7	+	2.32904e7i	−0.853836	+	0.562276i
$347$	1.19435e6	+	1.19435e6i	0.0285854	+	0.0285854i	0.721255	−	0.692670i	$-0.243566\pi$
$347$	1.19435e6	+	1.19435e6i	0.0285854	+	0.0285854i	−0.692670	+	0.721255i	$0.743566\pi$
$348$	−1.52487e7	−	6.55702e6i	−0.361823	−	0.155585i
$349$	2.69344e7	+	2.69344e7i	0.633622	+	0.633622i	0.948975	−	0.315352i	$-0.102123\pi$
$349$	2.69344e7	+	2.69344e7i	0.633622	+	0.633622i	−0.315352	+	0.948975i	$0.602123\pi$
$350$	1.22184e6	+	251562.i	0.0284976	+	0.00586733i
$351$			1.07116e7i			0.247704i
$352$	5.90983e7	+	1.38285e7i	1.35502	+	0.317064i
$353$	4.91191e7			1.11667			0.558337	−	0.829615i	$-0.311440\pi$
$353$	4.91191e7			1.11667			0.558337	+	0.829615i	$0.311440\pi$
$354$	−329525.	+	1.60051e6i	−0.00742812	+	0.0360784i
$355$	−6.92968e6	+	6.92968e6i	−0.154892	+	0.154892i
$356$	−1.38905e7	+	3.23032e7i	−0.307871	+	0.715971i
$357$	204410.	−	204410.i	0.00449260	−	0.00449260i
$358$	2.89140e7	+	4.39070e7i	0.630172	+	0.956940i
$359$	3.41281e7			0.737613			0.368806	−	0.929506i	$-0.379767\pi$
$359$	3.41281e7			0.737613			0.368806	+	0.929506i	$0.379767\pi$
$360$	−2.69639e6	+	480209.i	−0.0577930	+	0.0102925i
$361$			4.12450e7i			0.876698i
$362$	−3.96639e7	−	6.02310e7i	−0.836121	−	1.26968i
$363$	−1.82897e7	−	1.82897e7i	−0.382373	−	0.382373i
$364$	−690146.	−	1.73144e6i	−0.0143099	−	0.0359007i
$365$	−1.05063e7	−	1.05063e7i	−0.216058	−	0.216058i
$366$	−1.11082e6	+	5.39526e6i	−0.0226569	+	0.110045i
$367$		−	9.40637e7i		−	1.90293i	−0.307751	−	0.951467i	$-0.599576\pi$
$367$		−	9.40637e7i		−	1.90293i	0.307751	−	0.951467i	$-0.400424\pi$
$368$	1.59171e7	+	1.67941e7i	0.319389	+	0.336987i
$369$	2.12356e7			0.422654
$370$	−1.20800e7	−	2.48712e6i	−0.238485	−	0.0491012i
$371$	597942.	−	597942.i	0.0117095	−	0.0117095i
$372$	1.19085e7	+	2.98760e7i	0.231327	+	0.580354i
$373$	6.53429e7	−	6.53429e7i	1.25913	−	1.25913i	0.307626	−	0.951507i	$-0.400465\pi$
$373$	6.53429e7	−	6.53429e7i	1.25913	−	1.25913i	0.951507	−	0.307626i	$-0.0995347\pi$
$374$	−2.22834e7	+	1.46742e7i	−0.425958	+	0.280505i
$375$	1.05573e7			0.200198
$376$	3.33505e7	+	2.32672e7i	0.627392	+	0.437705i
$377$		−	4.70476e7i		−	0.878038i
$378$	260661.	−	171653.i	0.00482616	−	0.00317816i
$379$	7.30308e7	+	7.30308e7i	1.34149	+	1.34149i	0.894575	+	0.446918i	$0.147478\pi$
$379$	7.30308e7	+	7.30308e7i	1.34149	+	1.34149i	0.446918	+	0.894575i	$0.352522\pi$
$380$	1.34043e6	−	3.11725e6i	0.0244283	−	0.0568094i
$381$	−4.00562e7	−	4.00562e7i	−0.724260	−	0.724260i
$382$	6.91534e7	+	1.42379e7i	1.24058	+	0.255420i
$383$		−	8.34668e6i		−	0.148565i	−0.997237	−	0.0742827i	$-0.976333\pi$
$383$		−	8.34668e6i		−	0.148565i	0.997237	−	0.0742827i	$-0.0236667\pi$
$384$	1.94170e7	−	2.63003e7i	0.342916	−	0.464480i
$385$	−419940.			−0.00735877
$386$	−1.86302e7	+	9.04872e7i	−0.323934	+	1.57335i
$387$	1.73253e6	−	1.73253e6i	0.0298915	−	0.0298915i
$388$	3.97406e7	+	1.70886e7i	0.680360	+	0.292558i
$389$	2.74528e7	−	2.74528e7i	0.466377	−	0.466377i	−0.434361	−	0.900739i	$-0.643026\pi$
$389$	2.74528e7	−	2.74528e7i	0.466377	−	0.466377i	0.900739	+	0.434361i	$0.143026\pi$
$390$	−4.26950e6	−	6.48339e6i	−0.0719752	−	0.109297i
$391$	−1.01716e7			−0.170161
$392$	3.44345e7	−	4.93572e7i	0.571657	−	0.819394i
$393$		−	4.22591e7i		−	0.696214i
$394$	−6.30558e7	−	9.57526e7i	−1.03095	−	1.56553i
$395$	2.67008e6	+	2.67008e6i	0.0433244	+	0.0433244i
$396$	−2.67588e7	+	1.06660e7i	−0.430905	+	0.171758i
$397$	3.93307e7	+	3.93307e7i	0.628579	+	0.628579i	0.947710	−	0.319131i	$-0.103391\pi$
$397$	3.93307e7	+	3.93307e7i	0.628579	+	0.628579i	−0.319131	+	0.947710i	$0.603391\pi$
$398$	−1.99526e6	+	9.69100e6i	−0.0316483	+	0.153716i
$399$			386678.i			0.00608739i
$400$	−4.50109e7	+	4.26603e7i	−0.703295	+	0.666566i
$401$	5.95571e7			0.923635			0.461817	−	0.886975i	$-0.347198\pi$
$401$	5.95571e7			0.923635			0.461817	+	0.886975i	$0.347198\pi$
$402$	2.43010e7	+	5.00329e6i	0.374064	+	0.0770154i
$403$	−6.44597e7	+	6.44597e7i	−0.984857	+	0.984857i
$404$	−1.64946e7	+	6.57469e6i	−0.250148	+	0.0997083i
$405$	919145.	−	919145.i	0.0138363	−	0.0138363i
$406$	−1.14488e6	+	753935.i	−0.0171073	+	0.0112656i
$407$	−1.29719e8			−1.92407
$408$	2.51973e6	+	1.41484e7i	0.0371000	+	0.208318i
$409$		−	4.56064e7i		−	0.666586i	−0.942823	−	0.333293i	$-0.891840\pi$
$409$		−	4.56064e7i		−	0.666586i	0.942823	−	0.333293i	$-0.108160\pi$
$410$	−1.28532e7	+	8.46421e6i	−0.186492	+	0.122810i
$411$	−185659.	−	185659.i	−0.00267418	−	0.00267418i
$412$	−1.07137e8	−	4.60695e7i	−1.53196	−	0.658752i
$413$	95425.5	+	95425.5i	0.00135461	+	0.00135461i
$414$	−1.07562e7	−	2.21457e6i	−0.151585	−	0.0312096i
$415$			2.20915e7i			0.309088i
$416$	9.02236e7	+	2.11116e7i	1.25326	+	0.293252i
$417$	3.55725e7			0.490576
$418$	7.19702e6	−	3.49559e7i	0.0985425	−	0.478622i
$419$	6.90997e7	−	6.90997e7i	0.939364	−	0.939364i	−0.0589000	−	0.998264i	$-0.518759\pi$
$419$	6.90997e7	−	6.90997e7i	0.939364	−	0.939364i	0.998264	+	0.0589000i	$0.0187593\pi$
$420$	−89351.4	+	207792.i	−0.00120602	+	0.00280466i
$421$	−3.73557e6	+	3.73557e6i	−0.0500623	+	0.0500623i	−0.731695	−	0.681632i	$-0.761270\pi$
$421$	−3.73557e6	+	3.73557e6i	−0.0500623	+	0.0500623i	0.681632	+	0.731695i	$0.261270\pi$
$422$	−7.34881e6	−	1.11594e7i	−0.0977866	−	0.148493i
$423$	−1.92999e7			−0.254996
$424$	7.37074e6	+	4.13869e7i	0.0966971	+	0.542957i
$425$		−	2.72616e7i		−	0.355128i
$426$	3.05342e7	+	4.63673e7i	0.394964	+	0.599767i
$427$	321677.	+	321677.i	0.00413177	+	0.00413177i
$428$	3.98741e7	+	1.00036e8i	0.508581	+	1.27593i
$429$	−5.77343e7	−	5.77343e7i	−0.731243	−	0.731243i
$430$	−358081.	+	1.73920e6i	−0.00450377	+	0.0218748i
$431$		−	5.26388e7i		−	0.657467i	−0.944423	−	0.328734i	$-0.893378\pi$
$431$		−	5.26388e7i		−	0.657467i	0.944423	−	0.328734i	$-0.106622\pi$
$432$	−415851.	+	1.55101e7i	−0.00515806	+	0.192381i
$433$	4.50617e7			0.555065			0.277532	−	0.960716i	$-0.410483\pi$
$433$	4.50617e7			0.555065			0.277532	+	0.960716i	$0.410483\pi$
$434$	2.60156e6	+	535630.i	0.0318247	+	0.00655233i
$435$	−4.03707e6	+	4.03707e6i	−0.0490455	+	0.0490455i
$436$	−3.00161e7	−	7.53043e7i	−0.362155	−	0.908574i
$437$	9.62073e6	−	9.62073e6i	0.115283	−	0.115283i
$438$	−7.02989e7	+	4.62938e7i	−0.836616	+	0.550935i
$439$	−6.13040e7			−0.724595			−0.362298	−	0.932062i	$-0.618008\pi$
$439$	−6.13040e7			−0.724595			−0.362298	+	0.932062i	$0.618008\pi$
$440$	1.19449e7	−	1.71215e7i	0.140225	−	0.200994i
$441$			2.85629e7i			0.333033i
$442$	−3.40194e7	+	2.24027e7i	−0.393967	+	0.259438i
$443$	−2.20176e7	−	2.20176e7i	−0.253255	−	0.253255i	0.569049	−	0.822304i	$-0.307312\pi$
$443$	−2.20176e7	−	2.20176e7i	−0.253255	−	0.253255i	−0.822304	+	0.569049i	$0.807312\pi$
$444$	−2.76006e7	+	6.41868e7i	−0.315333	+	0.733325i
$445$	8.55221e6	+	8.55221e6i	0.0970506	+	0.0970506i
$446$	−9.46810e7	−	1.94937e7i	−1.06723	−	0.219730i
$447$			7.17502e7i			0.803342i
$448$	−932089.	−	2.53386e6i	−0.0103663	−	0.0281804i
$449$	5.18241e7			0.572523			0.286262	−	0.958151i	$-0.407587\pi$
$449$	5.18241e7			0.572523			0.286262	+	0.958151i	$0.407587\pi$
$450$	5.93541e6	−	2.88283e7i	0.0651348	−	0.316360i
$451$	−1.14457e8	+	1.14457e8i	−1.24771	+	1.24771i
$452$	1.33493e8	+	5.74027e7i	1.44559	+	0.621609i
$453$	5.88862e6	−	5.88862e6i	0.0633459	−	0.0633459i
$454$	−8.76953e7	−	1.33169e8i	−0.937149	−	1.42310i
$455$	−641110.			−0.00680610
$456$	−1.57653e7	−	1.09988e7i	−0.166268	−	0.115998i
$457$		−	3.31182e7i		−	0.346991i	−0.984835	−	0.173495i	$-0.944494\pi$
$457$		−	3.31182e7i		−	0.346991i	0.984835	−	0.173495i	$-0.0555061\pi$
$458$	−2.83983e7	−	4.31239e7i	−0.295594	−	0.448871i
$459$	−4.82290e6	−	4.82290e6i	−0.0498736	−	0.0498736i
$460$	7.39307e6	−	2.94685e6i	0.0759541	−	0.0302751i
$461$	1.62828e7	+	1.62828e7i	0.166199	+	0.166199i	0.785306	−	0.619108i	$-0.212506\pi$
$461$	1.62828e7	+	1.62828e7i	0.166199	+	0.166199i	−0.619108	+	0.785306i	$0.712506\pi$
$462$	−479745.	+	2.33012e6i	−0.00486501	+	0.0236294i
$463$			4.56709e7i			0.460147i	0.973173	+	0.230074i	$0.0738967\pi$
$463$			4.56709e7i			0.460147i	−0.973173	+	0.230074i	$0.926103\pi$
$464$	1.82650e6	−	6.81233e7i	0.0182838	−	0.681933i
$465$	1.10624e7			0.110024
$466$	−1.47506e8	−	3.03698e7i	−1.45765	−	0.300112i
$467$	5.27710e7	−	5.27710e7i	0.518137	−	0.518137i	−0.398870	−	0.917007i	$-0.630598\pi$
$467$	5.27710e7	−	5.27710e7i	0.518137	−	0.518137i	0.917007	+	0.398870i	$0.130598\pi$
$468$	−4.08519e7	+	1.62835e7i	−0.398543	+	0.158858i
$469$	1.44888e6	−	1.44888e6i	0.0140447	−	0.0140447i
$470$	1.16816e7	−	7.69265e6i	0.112514	−	0.0740939i
$471$	−7.15148e7			−0.684437
$472$	−6.60494e6	+	1.17630e6i	−0.0628120	+	0.0111864i
$473$			1.86762e7i			0.176484i
$474$	1.78658e7	−	1.17651e7i	0.167760	−	0.110475i
$475$	2.57851e7	+	2.57851e7i	0.240596	+	0.240596i
$476$	1.09032e6	+	468841.i	0.0101096	+	0.00434715i
$477$	−1.41080e7	−	1.41080e7i	−0.129990	−	0.129990i
$478$	1.46739e8	+	3.02119e7i	1.34358	+	0.276627i
$479$			8.65283e7i			0.787320i	0.919256	+	0.393660i	$0.128791\pi$
$479$			8.65283e7i			0.787320i	−0.919256	+	0.393660i	$0.871209\pi$
$480$	−5.93039e6	−	9.55348e6i	−0.0536240	−	0.0863849i
$481$	−1.98038e8			−1.77957
$482$	6.00765e6	−	2.91792e7i	0.0536492	−	0.260575i
$483$	−641306.	+	641306.i	−0.00569147	+	0.00569147i
$484$	4.19498e7	−	9.75567e7i	0.369993	−	0.860441i
$485$	1.05213e7	−	1.05213e7i	0.0922236	−	0.0922236i
$486$	−4.05002e6	−	6.15011e6i	−0.0352816	−	0.0535764i
$487$	1.04559e8			0.905263			0.452632	−	0.891698i	$-0.350485\pi$
$487$	1.04559e8			0.905263			0.452632	+	0.891698i	$0.350485\pi$
$488$	−2.22651e7	+	3.96526e6i	−0.191586	+	0.0341202i
$489$		−	3.04795e7i		−	0.260664i
$490$	−1.13848e7	−	1.72882e7i	−0.0967690	−	0.146947i
$491$	−5.07335e7	−	5.07335e7i	−0.428598	−	0.428598i	0.459553	−	0.888151i	$-0.348010\pi$
$491$	−5.07335e7	−	5.07335e7i	−0.428598	−	0.428598i	−0.888151	+	0.459553i	$0.848010\pi$
$492$	3.22817e7	+	8.09883e7i	0.271057	+	0.680028i
$493$	2.11832e7	+	2.11832e7i	0.176787	+	0.176787i
$494$	1.09875e7	−	5.33662e7i	0.0911417	−	0.442676i
$495$			9.90816e6i			0.0816916i
$496$	−9.58380e7	+	9.08330e7i	−0.785403	+	0.744387i
$497$	4.58503e6			0.0373485
$498$	1.22579e8	+	2.52377e7i	0.992497	+	0.204344i
$499$	−1.06158e8	+	1.06158e8i	−0.854379	+	0.854379i	−0.990669	−	0.136290i	$-0.956482\pi$
$499$	−1.06158e8	+	1.06158e8i	−0.854379	+	0.854379i	0.136290	+	0.990669i	$0.456482\pi$
$500$	1.60489e7	+	4.02634e7i	0.128391	+	0.322107i
$501$	−8.35654e6	+	8.35654e6i	−0.0664528	+	0.0664528i
$502$	1.00187e8	−	6.59758e7i	0.791952	−	0.521523i
$503$	1.26794e8			0.996310			0.498155	−	0.867088i	$-0.334011\pi$
$503$	1.26794e8			0.996310			0.498155	+	0.867088i	$0.334011\pi$
$504$	1.05090e6	+	733168.i	0.00820861	+	0.00572680i
$505$			6.10755e6i			0.0474234i
$506$	6.99108e7	−	4.60382e7i	0.539626	−	0.355359i
$507$	−3.49367e7	−	3.49367e7i	−0.268076	−	0.268076i
$508$	9.18740e7	−	2.13658e8i	0.700812	−	1.62978i
$509$	241668.	+	241668.i	0.00183259	+	0.00183259i	0.708022	−	0.706190i	$-0.249588\pi$
$509$	241668.	+	241668.i	0.00183259	+	0.00183259i	−0.706190	+	0.708022i	$0.749588\pi$
$510$	4.84149e6	+	996806.i	0.0364979	+	0.00751450i
$511$			6.95150e6i			0.0520974i
$512$	1.29821e8	+	3.40715e7i	0.967243	+	0.253853i
$513$	9.12338e6			0.0675777
$514$	2.23932e6	−	1.08764e7i	0.0164902	−	0.0800931i
$515$	−2.83644e7	+	2.83644e7i	−0.207660	+	0.207660i
$516$	9.24124e6	+	3.97377e6i	0.0672638	+	0.0289237i
$517$	1.04024e8	−	1.04024e8i	0.752768	−	0.752768i
$518$	3.17355e6	+	4.81916e6i	0.0228327	+	0.0346723i
$519$	8.25162e7			0.590252
$520$	1.82360e7	−	2.61388e7i	0.129694	−	0.185899i
$521$			2.33312e8i			1.64977i	0.565301	+	0.824885i	$0.308760\pi$
$521$			2.33312e8i			1.64977i	−0.565301	+	0.824885i	$0.691240\pi$
$522$	1.77885e7	+	2.70125e7i	0.125063	+	0.189913i
$523$	1.17256e8	+	1.17256e8i	0.819652	+	0.819652i	0.986057	−	0.166405i	$-0.0532160\pi$
$523$	1.17256e8	+	1.17256e8i	0.819652	+	0.819652i	−0.166405	+	0.986057i	$0.553216\pi$
$524$	1.61168e8	−	6.42410e7i	1.12017	−	0.446497i
$525$	−1.71880e6	−	1.71880e6i	−0.0118781	−	0.0118781i
$526$	1.25120e7	−	6.07710e7i	0.0859747	−	0.417580i
$527$		−	5.80460e7i		−	0.396589i
$528$	−8.13559e7	−	8.58387e7i	−0.552697	−	0.583151i
$529$	−1.16124e8			−0.784431
$530$	1.41623e7	+	2.91586e6i	0.0951278	+	0.0195857i
$531$	2.25149e6	−	2.25149e6i	0.0150379	−	0.0150379i
$532$	−1.47471e6	+	587816.i	−0.00979428	+	0.00390397i
$533$	−1.74738e8	+	1.74738e8i	−1.15400	+	1.15400i
$534$	5.72238e7	−	3.76835e7i	0.375797	−	0.247473i
$535$	3.70410e7			0.241892
$536$	1.78601e7	+	1.00285e8i	0.115982	+	0.651240i
$537$		−	1.02440e8i		−	0.661527i
$538$	6.62799e7	−	4.36472e7i	0.425633	−	0.280291i
$539$	−1.53951e8	−	1.53951e8i	−0.983140	−	0.983140i
$540$	4.90269e6	+	2.10818e6i	0.0311353	+	0.0133883i
$541$	1.79653e8	+	1.79653e8i	1.13460	+	1.13460i	0.989403	+	0.145197i	$0.0463816\pi$
$541$	1.79653e8	+	1.79653e8i	1.13460	+	1.13460i	0.145197	+	0.989403i	$0.453618\pi$
$542$	−2.80810e8	−	5.78155e7i	−1.76366	−	0.363117i
$543$			1.40526e8i			0.877722i
$544$	−5.01287e7	+	3.11177e7i	−0.311379	+	0.193291i
$545$	−2.78834e7			−0.172249
$546$	−732412.	+	3.55733e6i	−0.00449964	+	0.0218548i
$547$	3.98185e7	−	3.98185e7i	0.243289	−	0.243289i	−0.574920	−	0.818209i	$-0.694967\pi$
$547$	3.98185e7	−	3.98185e7i	0.243289	−	0.243289i	0.818209	+	0.574920i	$0.194967\pi$
$548$	425833.	−	990298.i	0.00258760	−	0.00601761i
$549$	7.58971e6	−	7.58971e6i	0.0458679	−	0.0458679i
$550$	1.23390e8	+	1.87372e8i	0.741637	+	1.12620i
$551$	−4.00717e7			−0.239543
$552$	−7.90529e6	−	4.43884e7i	−0.0470003	−	0.263908i
$553$		−	1.76666e6i		−	0.0104467i
$554$	8.90011e7	+	1.35152e8i	0.523439	+	0.794862i
$555$	1.69933e7	+	1.69933e7i	0.0994031	+	0.0994031i
$556$	5.40763e7	+	1.35666e8i	0.314617	+	0.789311i
$557$	−3.27259e7	−	3.27259e7i	−0.189377	−	0.189377i	0.606050	−	0.795427i	$-0.292753\pi$
$557$	−3.27259e7	−	3.27259e7i	−0.189377	−	0.189377i	−0.795427	+	0.606050i	$0.792753\pi$
$558$	1.26378e7	−	6.13817e7i	0.0727391	−	0.353294i
$559$			2.85124e7i			0.163230i
$560$	−928306.	−	24889.5i	−0.00528600	−	0.000141727i
$561$	5.19897e7			0.294462
$562$	1.20056e8	+	2.47180e7i	0.676353	+	0.139253i
$563$	1.04641e8	−	1.04641e8i	0.586376	−	0.586376i	−0.350272	−	0.936648i	$-0.613911\pi$
$563$	1.04641e8	−	1.04641e8i	0.586376	−	0.586376i	0.936648	+	0.350272i	$0.113911\pi$
$564$	−2.93390e7	−	7.36058e7i	−0.163534	−	0.410274i
$565$	3.53421e7	−	3.53421e7i	0.195951	−	0.195951i
$566$	−2.12650e8	+	1.40036e8i	−1.17278	+	0.772307i
$567$	−608153.			−0.00333629
$568$	−1.30418e8	+	1.86937e8i	−0.711694	+	1.02012i
$569$			1.76056e8i			0.955684i	0.878446	+	0.477842i	$0.158581\pi$
$569$			1.76056e8i			0.955684i	−0.878446	+	0.477842i	$0.841419\pi$
$570$	−5.52208e6	+	3.63645e6i	−0.0298180	+	0.0196360i
$571$	−1.10539e8	−	1.10539e8i	−0.593754	−	0.593754i	0.344889	−	0.938643i	$-0.387917\pi$
$571$	−1.10539e8	−	1.10539e8i	−0.593754	−	0.593754i	−0.938643	+	0.344889i	$0.887917\pi$
$572$	1.32421e8	−	3.07953e8i	0.707569	−	1.64549i
$573$	−9.72807e7	−	9.72807e7i	−0.517086	−	0.517086i
$574$	7.05234e6	+	1.45199e6i	0.0372905	+	0.00767767i
$575$			8.55293e7i			0.449895i
$576$	−5.97844e7	+	2.19919e7i	−0.312839	+	0.115079i
$577$	−2.03195e8			−1.05775			−0.528877	−	0.848698i	$-0.677387\pi$
$577$	−2.03195e8			−1.05775			−0.528877	+	0.848698i	$0.677387\pi$
$578$	−3.37100e7	+	1.63729e8i	−0.174572	+	0.847897i
$579$	1.27292e8	−	1.27292e8i	0.655790	−	0.655790i
$580$	−2.15336e7	−	9.25955e6i	−0.110365	−	0.0474576i
$581$	7.30844e6	−	7.30844e6i	0.0372646	−	0.0372646i
$582$	−4.63597e7	−	7.03989e7i	−0.235164	−	0.357106i
$583$	1.52081e8			0.767482
$584$	−2.83421e8	−	1.97731e8i	−1.42296	−	0.992743i
$585$			1.51265e7i			0.0755563i
$586$	1.65753e8	+	2.51701e8i	0.823697	+	1.25081i
$587$	−2.05167e8	−	2.05167e8i	−1.01436	−	1.01436i	−0.999895	−	0.0144688i	$-0.995394\pi$
$587$	−2.05167e8	−	2.05167e8i	−1.01436	−	1.01436i	−0.0144688	−	0.999895i	$-0.504606\pi$
$588$	−1.08933e8	+	4.34205e7i	−0.535832	+	0.213581i
$589$	5.49021e7	+	5.49021e7i	0.268685	+	0.268685i
$590$	−465342.	+	2.26017e6i	−0.00226577	+	0.0110049i
$591$			2.23402e8i			1.08224i
$592$	−2.86753e8	−	7.68834e6i	−1.38211	−	0.0370568i
$593$	3.11010e7			0.149146			0.0745728	−	0.997216i	$-0.476241\pi$
$593$	3.11010e7			0.149146			0.0745728	+	0.997216i	$0.476241\pi$
$594$	5.49774e7	+	1.13192e7i	0.262316	+	0.0540078i
$595$	288660.	−	288660.i	0.00137036	−	0.00137036i
$596$	−2.73641e8	+	1.09072e8i	−1.29253	+	0.515200i
$597$	1.36327e7	−	1.36327e7i	0.0640706	−	0.0640706i
$598$	1.06731e8	−	7.02852e7i	0.499098	−	0.328670i
$599$	1.95480e8			0.909541			0.454770	−	0.890609i	$-0.349721\pi$
$599$	1.95480e8			0.909541			0.454770	+	0.890609i	$0.349721\pi$
$600$	1.18968e8	−	2.11874e7i	0.550778	−	0.0980899i
$601$		−	6.46859e7i		−	0.297979i	−0.988839	−	0.148990i	$-0.952398\pi$
$601$		−	6.46859e7i		−	0.297979i	0.988839	−	0.148990i	$-0.0476021\pi$
$602$	693835.	−	456910.i	0.00318029	−	0.00209431i
$603$	−3.41851e7	−	3.41851e7i	−0.155914	−	0.155914i
$604$	3.14097e7	+	1.35063e7i	0.142545	+	0.0612951i
$605$	−2.58280e7	−	2.58280e7i	−0.116634	−	0.116634i
$606$	3.38890e7	+	6.97734e6i	0.152279	+	0.0313525i
$607$		−	3.99248e8i		−	1.78516i	−0.450893	−	0.892578i	$-0.648894\pi$
$607$		−	3.99248e8i		−	1.78516i	0.450893	−	0.892578i	$-0.351106\pi$
$608$	1.79813e7	−	7.68459e7i	0.0800038	−	0.341909i
$609$	2.67113e6			0.0118262
$610$	−1.56865e6	+	7.61896e6i	−0.00691095	+	0.0335665i
$611$	1.58810e8	−	1.58810e8i	0.696233	−	0.696233i
$612$	1.10620e7	−	2.57252e7i	0.0482589	−	0.112229i
$613$	2.95990e8	−	2.95990e8i	1.28498	−	1.28498i	0.347177	−	0.937800i	$-0.387140\pi$
$613$	2.95990e8	−	2.95990e8i	1.28498	−	1.28498i	0.937800	−	0.347177i	$-0.112860\pi$
$614$	−1.32379e7	−	2.01023e7i	−0.0571894	−	0.0868442i
$615$	2.99880e7			0.128921
$616$	−9.61590e6	+	1.71253e6i	−0.0411385	+	0.00732649i
$617$			1.85247e8i			0.788671i	0.918967	+	0.394335i	$0.129025\pi$
$617$			1.85247e8i			0.788671i	−0.918967	+	0.394335i	$0.870975\pi$
$618$	1.24982e8	+	1.89789e8i	0.529519	+	0.804094i
$619$	−5.32171e7	−	5.32171e7i	−0.224378	−	0.224378i	0.585961	−	0.810339i	$-0.300717\pi$
$619$	−5.32171e7	−	5.32171e7i	−0.224378	−	0.224378i	−0.810339	+	0.585961i	$0.800717\pi$
$620$	1.68167e7	+	4.21896e7i	0.0705610	+	0.177023i
$621$	1.51311e7	+	1.51311e7i	0.0631825	+	0.0631825i
$622$	−3.38730e7	+	1.64521e8i	−0.140761	+	0.683677i
$623$		−	5.65858e6i		−	0.0234015i
$624$	−1.24204e8	−	1.31047e8i	−0.511188	−	0.539355i
$625$	−2.21660e8			−0.907921
$626$	−3.06355e8	−	6.30749e7i	−1.24883	−	0.257119i
$627$	−4.91739e7	+	4.91739e7i	−0.199495	+	0.199495i
$628$	−1.08715e8	−	2.72743e8i	−0.438944	−	1.10122i
$629$	8.91668e7	−	8.91668e7i	0.358304	−	0.358304i
$630$	368095.	−	242401.i	0.00147210	−	0.000969423i
$631$	9.30000e7			0.370165			0.185082	−	0.982723i	$-0.440745\pi$
$631$	9.30000e7			0.370165			0.185082	+	0.982723i	$0.440745\pi$
$632$	7.20289e7	+	5.02516e7i	0.285335	+	0.199067i
$633$			2.60362e7i			0.102652i
$634$	−3.51871e8	+	2.31717e8i	−1.38075	+	0.909264i
$635$	−5.65657e7	−	5.65657e7i	−0.220918	−	0.220918i
$636$	3.23585e7	−	7.52515e7i	0.125781	−	0.292512i
$637$	−2.35032e8	−	2.35032e8i	−0.909303	−	0.909303i
$638$	−2.41472e8	−	4.97163e7i	−0.929833	−	0.191442i
$639$		−	1.08180e8i		−	0.414615i
$640$	2.74199e7	−	3.71402e7i	0.104598	−	0.141679i
$641$	−4.74473e8			−1.80151			−0.900756	−	0.434326i	$-0.856986\pi$
$641$	−4.74473e8			−1.80151			−0.900756	+	0.434326i	$0.856986\pi$
$642$	4.23161e7	−	2.05530e8i	0.159919	−	0.776729i
$643$	1.92710e8	−	1.92710e8i	0.724890	−	0.724890i	−0.244707	−	0.969597i	$-0.578692\pi$
$643$	1.92710e8	−	1.92710e8i	0.724890	−	0.724890i	0.969597	+	0.244707i	$0.0786918\pi$
$644$	−3.42071e6	−	1.47092e6i	−0.0128073	−	0.00550720i
$645$	2.44660e6	−	2.44660e6i	0.00911768	−	0.00911768i
$646$	1.90810e7	+	2.89753e7i	0.0707790	+	0.107481i
$647$	−1.21114e8			−0.447179			−0.223589	−	0.974683i	$-0.571777\pi$
$647$	−1.21114e8			−0.447179			−0.223589	+	0.974683i	$0.571777\pi$
$648$	1.72985e7	−	2.47952e7i	0.0635747	−	0.0911259i
$649$			2.42705e7i			0.0887861i
$650$	1.88376e8	+	2.86055e8i	0.685937	+	1.04162i
$651$	−3.65971e6	−	3.65971e6i	−0.0132649	−	0.0132649i
$652$	1.16242e8	−	4.63339e7i	0.419394	−	0.167169i
$653$	2.00270e8	+	2.00270e8i	0.719244	+	0.719244i	0.968450	−	0.249207i	$-0.0801699\pi$
$653$	2.00270e8	+	2.00270e8i	0.719244	+	0.719244i	−0.249207	+	0.968450i	$0.580170\pi$
$654$	−3.18543e7	+	1.54717e8i	−0.113877	+	0.553100i
$655$		−	5.96766e7i		−	0.212364i
$656$	−2.59799e8	+	2.46232e8i	−0.920294	+	0.872233i
$657$	1.64015e8			0.578347
$658$	−6.40949e6	−	1.31964e6i	−0.0224981	−	0.00463209i
$659$	5.29275e7	−	5.29275e7i	0.184938	−	0.184938i	−0.608566	−	0.793503i	$-0.708255\pi$
$659$	5.29275e7	−	5.29275e7i	0.184938	−	0.184938i	0.793503	+	0.608566i	$0.208255\pi$
$660$	−3.77877e7	+	1.50621e7i	−0.131437	+	0.0523906i
$661$	9.26348e6	−	9.26348e6i	0.0320752	−	0.0320752i	−0.690887	−	0.722963i	$-0.742780\pi$
$661$	9.26348e6	−	9.26348e6i	0.0320752	−	0.0320752i	0.722963	+	0.690887i	$0.242780\pi$
$662$	4.62073e8	−	3.04288e8i	1.59271	−	1.04885i
$663$	7.93712e7			0.272347
$664$	9.00901e7	+	5.05858e8i	0.307732	+	1.72792i
$665$			546051.i			0.00185681i
$666$	1.13704e8	−	7.48776e7i	0.384906	−	0.253471i
$667$	−6.64590e7	−	6.64590e7i	−0.223963	−	0.223963i
$668$	−4.45735e7	−	1.91668e7i	−0.149536	−	0.0643013i
$669$	1.33191e8	+	1.33191e8i	0.444834	+	0.444834i
$670$	3.43169e7	+	7.06544e6i	0.114099	+	0.0234917i
$671$			8.18152e7i			0.270811i
$672$	−1.19861e6	+	5.12246e6i	−0.00394976	+	0.0168799i
$673$	−1.11352e8			−0.365304			−0.182652	−	0.983178i	$-0.558468\pi$
$673$	−1.11352e8			−0.365304			−0.182652	+	0.983178i	$0.558468\pi$
$674$	−3.35972e7	+	1.63182e8i	−0.109730	+	0.532957i
$675$	−4.05538e7	+	4.05538e7i	−0.131862	+	0.131862i
$676$	8.01318e7	−	1.86351e8i	0.259397	−	0.603243i
$677$	−1.72222e8	+	1.72222e8i	−0.555039	+	0.555039i	−0.927891	−	0.372852i	$-0.878380\pi$
$677$	−1.72222e8	+	1.72222e8i	−0.555039	+	0.555039i	0.372852	+	0.927891i	$0.378380\pi$
$678$	−1.55728e8	−	2.36478e8i	−0.499662	−	0.758756i
$679$	−6.96139e6			−0.0222375
$680$	3.55827e6	+	1.99798e7i	0.0113165	+	0.0635424i
$681$			3.10698e8i			0.983777i
$682$	2.62724e8	+	3.98956e8i	0.828221	+	1.25768i
$683$	2.99546e8	+	2.99546e8i	0.940160	+	0.940160i	0.998308	−	0.0581483i	$-0.0185196\pi$
$683$	2.99546e8	+	2.99546e8i	0.940160	+	0.940160i	−0.0581483	+	0.998308i	$0.518520\pi$
$684$	1.38691e7	+	3.47947e7i	0.0433390	+	0.108729i
$685$	−262180.	−	262180.i	−0.000815695	−	0.000815695i
$686$	−3.90777e6	+	1.89801e7i	−0.0121048	+	0.0587930i
$687$			1.00613e8i			0.310302i
$688$	−1.10692e6	+	4.12850e7i	−0.00339901	+	0.126773i
$689$	2.32177e8			0.709841
$690$	−1.51894e7	−	3.12733e6i	−0.0462375	−	0.00951976i
$691$	−1.31649e7	+	1.31649e7i	−0.0399008	+	0.0399008i	−0.726776	−	0.686875i	$-0.758982\pi$
$691$	−1.31649e7	+	1.31649e7i	−0.0399008	+	0.0399008i	0.686875	+	0.726776i	$0.258982\pi$
$692$	1.25439e8	+	3.14700e8i	0.378541	+	0.949683i
$693$	3.27787e6	−	3.27787e6i	0.00984900	−	0.00984900i
$694$	1.12853e7	−	7.43172e6i	0.0337626	−	0.0222337i
$695$	5.02341e7			0.149639
$696$	−7.59788e7	+	1.08905e8i	−0.225354	+	0.323014i
$697$		−	1.57352e8i		−	0.464702i
$698$	2.54501e8	−	1.67596e8i	0.748380	−	0.492830i
$699$	2.07503e8	+	2.07503e8i	0.607564	+	0.607564i
$700$	3.94230e6	−	9.16804e6i	0.0114936	−	0.0267290i
$701$	5.88418e7	+	5.88418e7i	0.170817	+	0.170817i	0.787338	−	0.616521i	$-0.211458\pi$
$701$	5.88418e7	+	5.88418e7i	0.170817	+	0.170817i	−0.616521	+	0.787338i	$0.711458\pi$
$702$	8.39324e7	+	1.72807e7i	0.242615	+	0.0499517i
$703$			1.68675e8i			0.485494i
$704$	2.03697e8	−	4.40764e8i	0.583802	−	1.26325i
$705$	−2.72545e7			−0.0777804
$706$	7.92422e7	−	3.84880e8i	0.225187	−	1.09373i
$707$	2.02053e6	−	2.02053e6i	0.00571752	−	0.00571752i
$708$	1.20094e7	+	5.16409e6i	0.0338393	+	0.0145510i
$709$	1.03453e8	−	1.03453e8i	0.290272	−	0.290272i	−0.546915	−	0.837188i	$-0.684198\pi$
$709$	1.03453e8	−	1.03453e8i	0.290272	−	0.290272i	0.837188	+	0.546915i	$0.184198\pi$
$710$	4.31191e7	+	6.54779e7i	0.120474	+	0.182945i
$711$	−4.16830e7			−0.115971
$712$	2.30707e8	+	1.60955e8i	0.639177	+	0.445927i
$713$			1.82111e8i			0.502419i
$714$	−1.27192e6	−	1.93146e6i	−0.00349434	−	0.00530628i
$715$	−8.15299e7	−	8.15299e7i	−0.223048	−	0.223048i
$716$	3.90686e8	−	1.55726e8i	1.06436	−	0.424251i
$717$	−2.06424e8	−	2.06424e8i	−0.560018	−	0.560018i
$718$	5.50577e7	−	2.67416e8i	0.148746	−	0.722459i
$719$			2.43205e8i			0.654314i	0.944970	+	0.327157i	$0.106091\pi$
$719$			2.43205e8i			0.654314i	−0.944970	+	0.327157i	$0.893909\pi$
$720$	−587248.	+	2.19027e7i	−0.00157335	+	0.0586812i
$721$	1.87673e7			0.0500722
$722$	3.23181e8	+	6.65393e7i	0.858687	+	0.176794i
$723$	−4.10475e7	+	4.10475e7i	−0.108610	+	0.108610i
$724$	−5.35938e8	+	2.13623e8i	−1.41221	+	0.562902i
$725$	1.78121e8	−	1.78121e8i	0.467413	−	0.467413i
$726$	−1.72818e8	+	1.13806e8i	−0.451626	+	0.297409i
$727$	4.48848e7			0.116814			0.0584071	−	0.998293i	$-0.481398\pi$
$727$	4.48848e7			0.116814			0.0584071	+	0.998293i	$0.481398\pi$
$728$	−1.46803e7	+	2.61447e6i	−0.0380488	+	0.00677625i
$729$			1.43489e7i			0.0370370i
$730$	−9.92731e7	+	6.53742e7i	−0.255190	+	0.168050i
$731$	−1.28377e7	−	1.28377e7i	−0.0328652	−	0.0328652i
$732$	4.04833e7	+	1.74080e7i	0.103215	+	0.0443829i
$733$	−2.55826e8	−	2.55826e8i	−0.649579	−	0.649579i	0.303312	−	0.952891i	$-0.401908\pi$
$733$	−2.55826e8	−	2.55826e8i	−0.649579	−	0.649579i	−0.952891	+	0.303312i	$0.901908\pi$
$734$	−7.37050e8	−	1.51750e8i	−1.86384	−	0.383743i
$735$			4.03354e7i			0.101584i
$736$	1.57271e8	−	9.76271e7i	0.394471	−	0.244871i
$737$	3.68507e8			0.920542
$738$	3.42587e7	−	1.66395e8i	0.0852318	−	0.413971i
$739$	−2.81372e8	+	2.81372e8i	−0.697184	+	0.697184i	−0.963802	−	0.266619i	$-0.914094\pi$
$739$	−2.81372e8	+	2.81372e8i	−0.697184	+	0.697184i	0.266619	+	0.963802i	$0.414094\pi$
$740$	−3.89764e7	+	9.06419e7i	−0.0961849	+	0.223683i
$741$	−7.50723e7	+	7.50723e7i	−0.184512	+	0.184512i
$742$	−3.72062e6	−	5.64990e6i	−0.00910760	−	0.0138302i
$743$	−1.35968e8			−0.331489			−0.165744	−	0.986169i	$-0.553003\pi$
$743$	−1.35968e8			−0.331489			−0.165744	+	0.986169i	$0.553003\pi$
$744$	2.53309e8	−	4.51127e7i	0.615080	−	0.109542i
$745$			1.01323e8i			0.245040i
$746$	−4.06588e8	−	6.17419e8i	−0.979351	−	1.48718i
$747$	−1.72437e8	−	1.72437e8i	−0.413684	−	0.413684i
$748$	7.90331e7	+	1.98278e8i	0.188845	+	0.473773i
$749$	−1.22541e7	−	1.22541e7i	−0.0291633	−	0.0291633i
$750$	1.70317e7	−	8.27232e7i	0.0403715	−	0.196085i
$751$		−	3.87723e7i		−	0.0915382i	−0.998952	−	0.0457691i	$-0.985426\pi$
$751$		−	3.87723e7i		−	0.0915382i	0.998952	−	0.0457691i	$-0.0145738\pi$
$752$	2.36117e8	−	2.23786e8i	0.555231	−	0.526235i
$753$	−2.33747e8			−0.547471
$754$	−3.68648e8	−	7.59003e7i	−0.859999	−	0.177064i
$755$	8.31566e6	−	8.31566e6i	0.0193222	−	0.0193222i
$756$	−924496.	−	2.31937e6i	−0.00213963	−	0.00536791i
$757$	−4.20208e8	+	4.20208e8i	−0.968672	+	0.968672i	−0.999524	−	0.0308517i	$-0.990178\pi$
$757$	−4.20208e8	+	4.20208e8i	−0.968672	+	0.968672i	0.0308517	+	0.999524i	$0.490178\pi$
$758$	6.90062e8	−	4.54425e8i	1.58446	−	1.04341i
$759$	−1.63110e8			−0.373040
$760$	−2.22632e7	−	1.55321e7i	−0.0507162	−	0.0353825i
$761$		−	5.17271e8i		−	1.17372i	−0.809689	−	0.586860i	$-0.800364\pi$
$761$		−	5.17271e8i		−	1.17372i	0.809689	−	0.586860i	$-0.199636\pi$
$762$	−3.78487e8	+	2.49245e8i	−0.855434	+	0.563328i
$763$	9.22453e6	+	9.22453e6i	0.0207669	+	0.0207669i
$764$	2.23126e8	−	5.18892e8i	0.500345	−	1.16358i
$765$	−6.81071e6	−	6.81071e6i	−0.0152128	−	0.0152128i
$766$	−6.54017e7	−	1.34654e7i	−0.145513	−	0.0299595i
$767$			3.70531e7i			0.0821180i
$768$	−1.74755e8	−	1.94574e8i	−0.385786	−	0.429538i
$769$	5.94158e8			1.30654			0.653270	−	0.757125i	$-0.273397\pi$
$769$	5.94158e8			1.30654			0.653270	+	0.757125i	$0.273397\pi$
$770$	−677475.	+	3.29050e6i	−0.00148396	+	0.00720759i
$771$	−1.53002e7	+	1.53002e7i	−0.0333837	+	0.0333837i
$772$	6.78970e8	+	2.91960e8i	1.47570	+	0.634558i
$773$	2.95585e8	−	2.95585e8i	0.639948	−	0.639948i	−0.310595	−	0.950542i	$-0.600528\pi$
$773$	2.95585e8	−	2.95585e8i	0.639948	−	0.639948i	0.950542	+	0.310595i	$0.100528\pi$
$774$	−1.07804e7	−	1.63705e7i	−0.0232495	−	0.0353052i
$775$	−4.88085e8			−1.04855
$776$	1.98013e8	−	2.83825e8i	0.423748	−	0.607386i
$777$		−	1.12437e7i		−	0.0239687i
$778$	−1.70822e8	−	2.59399e8i	−0.362747	−	0.550845i
$779$	1.48830e8	+	1.48830e8i	0.314831	+	0.314831i
$780$	−5.76894e7	+	2.29948e7i	−0.121566	+	0.0484559i
$781$	5.83078e8	+	5.83078e8i	1.22398	+	1.22398i
$782$	−1.64096e7	+	7.97014e7i	−0.0343145	+	0.166666i
$783$		−	6.30233e7i		−	0.131285i
$784$	−3.31194e8	−	3.49443e8i	−0.687281	−	0.725150i
$785$	−1.00990e8			−0.208771
$786$	−3.31128e8	−	6.81753e7i	−0.681911	−	0.140398i
$787$	−1.97521e8	+	1.97521e8i	−0.405218	+	0.405218i	−0.880067	−	0.474849i	$-0.842503\pi$
$787$	−1.97521e8	+	1.97521e8i	−0.405218	+	0.405218i	0.474849	+	0.880067i	$0.342503\pi$
$788$	−8.52010e8	+	3.39609e8i	−1.74127	+	0.694065i
$789$	−8.54889e7	+	8.54889e7i	−0.174052	+	0.174052i
$790$	2.52294e7	−	1.66143e7i	0.0511711	−	0.0336976i
$791$	−2.33841e7			−0.0472489
$792$	4.04058e7	+	2.26880e8i	0.0813333	+	0.456689i
$793$			1.24905e8i			0.250472i
$794$	3.71632e8	−	2.44730e8i	0.742424	−	0.488907i
$795$	−1.99227e7	−	1.99227e7i	−0.0396503	−	0.0396503i
$796$	7.27164e7	+	3.12684e7i	0.144176	+	0.0619963i
$797$	−4.31312e8	−	4.31312e8i	−0.851954	−	0.851954i	0.138419	−	0.990374i	$-0.455798\pi$
$797$	−4.31312e8	−	4.31312e8i	−0.851954	−	0.851954i	−0.990374	+	0.138419i	$0.955798\pi$
$798$	3.02987e6	+	623815.i	0.00596233	+	0.00122757i
$799$			1.43009e8i			0.280364i
$800$	2.61656e8	+	4.21512e8i	0.511047	+	0.823265i
$801$	−1.33510e8			−0.259786
$802$	9.60815e7	−	4.66668e8i	0.186259	−	0.904660i
$803$	−8.84022e8	+	8.84022e8i	−1.70733	+	1.70733i
$804$	7.84080e7	−	1.82342e8i	0.150866	−	0.350848i
$805$	−905627.	+	905627.i	−0.00173605	+	0.00173605i
$806$	4.01093e8	+	6.09074e8i	0.766019	+	1.16323i
$807$	−1.54639e8			−0.294237
$808$	2.49068e7	+	1.39852e8i	0.0472154	+	0.265116i
$809$		−	5.32321e8i		−	1.00538i	−0.864468	−	0.502688i	$-0.832345\pi$
$809$		−	5.32321e8i		−	1.00538i	0.864468	−	0.502688i	$-0.167655\pi$
$810$	−5.71927e6	−	8.68493e6i	−0.0107618	−	0.0163422i
$811$	9.63456e7	+	9.63456e7i	0.180622	+	0.180622i	0.791627	−	0.611005i	$-0.209235\pi$
$811$	9.63456e7	+	9.63456e7i	0.180622	+	0.180622i	−0.611005	+	0.791627i	$0.709235\pi$
$812$	4.06057e6	+	1.01872e7i	0.00758437	+	0.0190276i
$813$	3.95026e8	+	3.95026e8i	0.735113	+	0.735113i
$814$	−2.09272e8	+	1.01643e9i	−0.388005	+	1.88454i
$815$		−	4.30418e7i		−	0.0795093i
$816$	1.14927e8	+	3.08138e6i	0.211520	+	0.00567121i
$817$	2.42848e7			0.0445316
$818$	−3.57356e8	−	7.35754e7i	−0.652892	−	0.134423i
$819$	5.00423e6	−	5.00423e6i	0.00910931	−	0.00910931i
$820$	4.55869e7	+	1.14368e8i	0.0826796	+	0.207426i
$821$	−2.51953e8	+	2.51953e8i	−0.455293	+	0.455293i	−0.897107	−	0.441814i	$-0.854335\pi$
$821$	−2.51953e8	+	2.51953e8i	−0.455293	+	0.455293i	0.441814	+	0.897107i	$0.354335\pi$
$822$	−1.75428e6	+	1.15524e6i	−0.00315851	+	0.00207997i
$823$	−8.42435e8			−1.51125			−0.755626	−	0.655004i	$-0.772667\pi$
$823$	−8.42435e8			−1.51125			−0.755626	+	0.655004i	$0.772667\pi$
$824$	−5.33825e8	+	7.65167e8i	−0.954152	+	1.36765i
$825$		−	4.37160e8i		−	0.778537i
$826$	901668.	−	593774.i	0.00159995	−	0.00105361i
$827$	1.58922e8	+	1.58922e8i	0.280975	+	0.280975i	0.833498	−	0.552523i	$-0.186335\pi$
$827$	1.58922e8	+	1.58922e8i	0.280975	+	0.280975i	−0.552523	+	0.833498i	$0.686335\pi$
$828$	−3.47052e7	+	8.07090e7i	−0.0611369	+	0.142177i
$829$	−1.73710e8	−	1.73710e8i	−0.304902	−	0.304902i	0.538026	−	0.842928i	$-0.319170\pi$
$829$	−1.73710e8	−	1.73710e8i	−0.304902	−	0.304902i	−0.842928	+	0.538026i	$0.819170\pi$
$830$	1.73102e8	+	3.56396e7i	0.302738	+	0.0623302i
$831$		−	3.15324e8i		−	0.549483i
$832$	3.10978e8	−	6.72902e8i	0.539957	−	1.16837i
$833$	2.11646e8			0.366164
$834$	5.73880e7	−	2.78734e8i	0.0989289	−	0.480498i
$835$	−1.18008e7	+	1.18008e7i	−0.0202698	+	0.0202698i
$836$	−2.62292e8	−	1.12787e8i	−0.448917	−	0.193036i
$837$	−8.63480e7	+	8.63480e7i	−0.147257	+	0.147257i
$838$	−4.29964e8	−	6.52917e8i	−0.730635	−	1.10950i
$839$	1.40758e8			0.238335			0.119168	−	0.992874i	$-0.461977\pi$
$839$	1.40758e8			0.238335			0.119168	+	0.992874i	$0.461977\pi$
$840$	1.48404e6	+	1.03535e6i	0.00250384	+	0.00174683i
$841$		−	3.18012e8i		−	0.534633i
$842$	2.32441e7	+	3.52971e7i	0.0389383	+	0.0591293i
$843$	−1.68887e8	−	1.68887e8i	−0.281911	−	0.281911i
$844$	−9.92970e7	+	3.95795e7i	−0.165161	+	0.0658329i
$845$	−4.93362e7	−	4.93362e7i	−0.0817702	−	0.0817702i
$846$	−3.11358e7	+	1.51227e8i	−0.0514221	+	0.249757i
$847$			1.70891e7i			0.0281235i
$848$	3.36184e8	+	9.01368e6i	0.551302	+	0.0147814i
$849$	4.96136e8			0.810733
$850$	−2.13613e8	−	4.39803e7i	−0.347832	−	0.0716146i
$851$	−2.79747e8	+	2.79747e8i	−0.453918	+	0.453918i
$852$	4.12577e8	−	1.64452e8i	0.667093	−	0.265901i
$853$	−2.21132e8	+	2.21132e8i	−0.356291	+	0.356291i	−0.862444	−	0.506153i	$-0.831067\pi$
$853$	−2.21132e8	+	2.21132e8i	−0.356291	+	0.356291i	0.506153	+	0.862444i	$0.331067\pi$
$854$	3.03950e6	−	2.00159e6i	0.00488009	−	0.00321368i
$855$	1.28837e7			0.0206130
$856$	8.48176e8	−	1.51055e8i	1.35227	−	0.240831i
$857$		−	1.00862e9i		−	1.60245i	−0.598365	−	0.801224i	$-0.704183\pi$
$857$		−	1.00862e9i		−	1.60245i	0.598365	−	0.801224i	$-0.295817\pi$
$858$	−5.45526e8	+	3.59244e8i	−0.863682	+	0.568759i
$859$	6.56398e8	+	6.56398e8i	1.03559	+	1.03559i	0.999343	+	0.0362465i	$0.0115402\pi$
$859$	6.56398e8	+	6.56398e8i	1.03559	+	1.03559i	0.0362465	+	0.999343i	$0.488460\pi$
$860$	1.30501e7	+	5.61160e6i	0.0205172	+	0.00882249i
$861$	−9.92080e6	−	9.92080e6i	−0.0155431	−	0.0155431i
$862$	−4.12459e8	−	8.49205e7i	−0.643960	−	0.132584i
$863$		−	1.27673e8i		−	0.198641i	−0.995056	−	0.0993204i	$-0.968333\pi$
$863$		−	1.27673e8i		−	0.198641i	0.995056	−	0.0993204i	$-0.0316669\pi$
$864$	1.20860e8	+	2.82803e7i	0.187388	+	0.0438473i
$865$	1.16526e8			0.180042
$866$	7.26965e7	−	3.53087e8i	0.111933	−	0.543661i
$867$	2.30324e8	−	2.30324e8i	0.353413	−	0.353413i
$868$	8.39401e6	−	1.95208e7i	0.0128354	−	0.0298495i
$869$	2.24666e8	−	2.24666e8i	0.342356	−	0.342356i
$870$	2.51202e7	+	3.81460e7i	0.0381474	+	0.0579283i
$871$	5.62589e8			0.851407
$872$	−6.38482e8	+	1.13709e8i	−0.962939	+	0.171493i
$873$			1.64249e8i			0.246865i
$874$	−5.98639e7	−	9.09055e7i	−0.0896665	−	0.136162i
$875$	−4.93213e6	−	4.93213e6i	−0.00736225	−	0.00736225i
$876$	2.49331e8	+	6.25521e8i	0.370906	+	0.930529i
$877$	2.52901e8	+	2.52901e8i	0.374931	+	0.374931i	0.869269	−	0.494339i	$-0.164590\pi$
$877$	2.52901e8	+	2.52901e8i	0.374931	+	0.374931i	−0.494339	+	0.869269i	$0.664590\pi$
$878$	−9.88998e7	+	4.80357e8i	−0.146121	+	0.709709i
$879$		−	5.87248e8i		−	0.864679i
$880$	−1.14887e8	−	1.21218e8i	−0.168587	−	0.177876i
$881$	1.24837e9			1.82564			0.912819	−	0.408365i	$-0.133901\pi$
$881$	1.24837e9			1.82564			0.912819	+	0.408365i	$0.133901\pi$
$882$	2.23809e8	+	4.60797e7i	0.326191	+	0.0671589i
$883$	9.14023e8	−	9.14023e8i	1.32762	−	1.32762i	0.420185	−	0.907438i	$-0.361965\pi$
$883$	9.14023e8	−	9.14023e8i	1.32762	−	1.32762i	0.907438	−	0.420185i	$-0.138035\pi$
$884$	1.20658e8	+	3.02706e8i	0.174662	+	0.438191i
$885$	3.17946e6	−	3.17946e6i	0.00458695	−	0.00458695i
$886$	−2.08042e8	+	1.37002e8i	−0.299123	+	0.196981i
$887$	−2.29976e8			−0.329542			−0.164771	−	0.986332i	$-0.552689\pi$
$887$	−2.29976e8			−0.329542			−0.164771	+	0.986332i	$0.552689\pi$
$888$	4.58418e8	+	3.19819e8i	0.654670	+	0.456736i
$889$			3.74267e7i			0.0532692i
$890$	8.08091e7	−	5.32151e7i	0.114628	−	0.0754857i
$891$	−7.73388e7	−	7.73388e7i	−0.109336	−	0.109336i
$892$	−3.05492e8	+	7.10439e8i	−0.430432	+	1.00100i
$893$	−1.35263e8	−	1.35263e8i	−0.189944	−	0.189944i
$894$	5.62209e8	+	1.15752e8i	0.786838	+	0.162001i
$895$		−	1.44662e8i		−	0.201783i
$896$	−2.13581e7	+	3.21574e6i	−0.0296920	+	0.00447050i
$897$	−2.49015e8			−0.345023
$898$	8.36062e7	−	4.06076e8i	0.115454	−	0.560761i
$899$	3.79258e8	−	3.79258e8i	0.521982	−	0.521982i
$900$	−2.16313e8	−	9.30155e7i	−0.296725	−	0.127593i
$901$	−1.04538e8	+	1.04538e8i	−0.142922	+	0.142922i
$902$	7.12196e8	+	1.08150e9i	0.970466	+	1.47369i
$903$	−1.61880e6			−0.00219851
$904$	6.65148e8	−	9.53400e8i	0.900353	−	1.29054i
$905$			1.98445e8i			0.267728i
$906$	−3.66412e7	−	5.56410e7i	−0.0492703	−	0.0748188i
$907$	−4.51748e8	−	4.51748e8i	−0.605444	−	0.605444i	0.336308	−	0.941752i	$-0.390822\pi$
$907$	−4.51748e8	−	4.51748e8i	−0.605444	−	0.605444i	−0.941752	+	0.336308i	$0.890822\pi$
$908$	−1.18494e9	+	4.72313e8i	−1.58284	+	0.630917i
$909$	−4.76729e7	−	4.76729e7i	−0.0634717	−	0.0634717i
$910$	−1.03428e6	+	5.02351e6i	−0.00137251	+	0.00666627i
$911$		−	5.67087e8i		−	0.750058i	−0.927013	−	0.375029i	$-0.877633\pi$
$911$		−	5.67087e8i		−	0.750058i	0.927013	−	0.375029i	$-0.122367\pi$
$912$	−1.11617e8	+	1.05788e8i	−0.147145	+	0.139460i
$913$	1.85883e9			2.44246
$914$	−2.59502e8	−	5.34285e7i	−0.339862	−	0.0699736i
$915$	1.07179e7	−	1.07179e7i	0.0139909	−	0.0139909i
$916$	−3.83718e8	+	1.52949e8i	−0.499259	+	0.199003i
$917$	−1.97425e7	+	1.97425e7i	−0.0256032	+	0.0256032i
$918$	−4.55712e7	+	3.00099e7i	−0.0589064	+	0.0387915i
$919$	8.38744e8			1.08065			0.540323	−	0.841458i	$-0.318302\pi$
$919$	8.38744e8			1.08065			0.540323	+	0.841458i	$0.318302\pi$
$920$	−1.11635e7	−	6.26835e7i	−0.0143363	−	0.0804989i
$921$			4.69010e7i			0.0600348i
$922$	1.53855e8	−	1.01318e8i	0.196300	−	0.129269i
$923$	8.90168e8	+	8.90168e8i	1.13205	+	1.13205i
$924$	1.74841e7	+	7.51822e6i	0.0221629	+	0.00953013i
$925$	−7.49768e8	−	7.49768e8i	−0.947330	−	0.947330i
$926$	3.57861e8	+	7.36794e7i	0.450694	+	0.0927926i
$927$		−	4.42801e8i		−	0.555865i
$928$	−5.30844e8	−	1.24213e8i	−0.664237	−	0.155426i
$929$	−1.36976e9			−1.70842			−0.854212	−	0.519924i	$-0.825960\pi$
$929$	−1.36976e9			−1.70842			−0.854212	+	0.519924i	$0.825960\pi$
$930$	1.78465e7	−	8.66807e7i	0.0221873	−	0.107764i
$931$	−2.00183e8	+	2.00183e8i	−0.248072	+	0.248072i
$932$	−4.75934e8	+	1.10681e9i	−0.587894	+	1.36718i
$933$	2.31439e8	−	2.31439e8i	0.284964	−	0.284964i
$934$	−3.28361e8	−	4.98629e8i	−0.403006	−	0.611979i
$935$	7.34177e7			0.0898186
$936$	6.16864e7	+	3.46371e8i	0.0752249	+	0.422390i
$937$			6.89998e8i			0.838743i	0.907815	+	0.419371i	$0.137749\pi$
$937$			6.89998e8i			0.838743i	−0.907815	+	0.419371i	$0.862251\pi$
$938$	−9.01546e6	−	1.36903e7i	−0.0109239	−	0.0165884i
$939$	4.30962e8	+	4.30962e8i	0.520525	+	0.520525i
$940$	−4.14314e7	−	1.03943e8i	−0.0498822	−	0.125144i
$941$	−1.06002e8	−	1.06002e8i	−0.127218	−	0.127218i	0.640631	−	0.767849i	$-0.278673\pi$
$941$	−1.06002e8	−	1.06002e8i	−0.127218	−	0.127218i	−0.767849	+	0.640631i	$0.778673\pi$
$942$	−1.15373e8	+	5.60365e8i	−0.138022	+	0.670376i
$943$			4.93668e8i			0.588708i
$944$	−1.43849e6	+	5.36516e7i	−0.00170998	+	0.0637774i
$945$	−858809.			−0.00101766
$946$	1.46340e8	+	3.01297e7i	0.172858	+	0.0355895i
$947$	−1.85082e8	+	1.85082e8i	−0.217928	+	0.217928i	−0.807625	−	0.589696i	$-0.799247\pi$
$947$	−1.85082e8	+	1.85082e8i	−0.217928	+	0.217928i	0.589696	+	0.807625i	$0.299247\pi$
$948$	−6.33652e7	−	1.58971e8i	−0.0743748	−	0.186591i
$949$	−1.34961e9	+	1.34961e9i	−1.57910	+	1.57910i
$950$	2.43641e8	−	1.60445e8i	0.284171	−	0.187135i
$951$	8.20955e8			0.954504
$952$	5.43265e6	−	7.78698e6i	0.00629652	−	0.00902523i
$953$		−	7.03272e8i		−	0.812540i	−0.913753	−	0.406270i	$-0.866829\pi$
$953$		−	7.03272e8i		−	0.812540i	0.913753	−	0.406270i	$-0.133171\pi$
$954$	−1.33305e8	+	8.77852e7i	−0.153533	+	0.101106i
$955$	−1.37376e8	−	1.37376e8i	−0.157725	−	0.157725i
$956$	4.73459e8	−	1.10106e9i	0.541887	−	1.26019i
$957$	3.39688e8	+	3.39688e8i	0.387565	+	0.387565i
$958$	6.78005e8	+	1.39593e8i	0.771145	+	0.158770i
$959$			173471.i			0.000196685i
$960$	−8.44250e7	+	3.10561e7i	−0.0954240	+	0.0351021i
$961$	−1.51736e8			−0.170970
$962$	−3.19489e8	+	1.55176e9i	−0.358865	+	1.74301i
$963$	−2.89126e8	+	2.89126e8i	−0.323749	+	0.323749i
$964$	−2.18946e8	−	9.41477e7i	−0.244403	−	0.105094i
$965$	1.79756e8	−	1.79756e8i	0.200033	−	0.200033i
$966$	3.99045e6	+	6.05965e6i	0.00442681	+	0.00672227i
$967$	−5.58827e8			−0.618013			−0.309007	−	0.951060i	$-0.599997\pi$
$967$	−5.58827e8			−0.618013			−0.309007	+	0.951060i	$0.599997\pi$
$968$	−6.96744e8	−	4.86089e8i	−0.768152	−	0.535907i
$969$		−	6.76026e7i		−	0.0743006i
$970$	−6.54672e7	−	9.94144e7i	−0.0717313	−	0.108927i
$971$	2.38035e8	+	2.38035e8i	0.260006	+	0.260006i	0.825056	−	0.565051i	$-0.191143\pi$
$971$	2.38035e8	+	2.38035e8i	0.260006	+	0.260006i	−0.565051	+	0.825056i	$0.691143\pi$
$972$	−5.47238e7	+	2.18128e7i	−0.0595906	+	0.0237526i
$973$	−1.66187e7	−	1.66187e7i	−0.0180409	−	0.0180409i
$974$	1.68682e8	−	8.19288e8i	0.182554	−	0.886666i
$975$		−	6.67400e8i		−	0.720066i
$976$	−4.84912e6	+	1.80858e8i	−0.00521571	+	0.194531i
$977$	−9.76599e8			−1.04721			−0.523603	−	0.851962i	$-0.675413\pi$
$977$	−9.76599e8			−1.04721			−0.523603	+	0.851962i	$0.675413\pi$
$978$	−2.38826e8	−	4.91715e7i	−0.255309	−	0.0525651i
$979$	7.19601e8	−	7.19601e8i	0.766909	−	0.766909i
$980$	−1.53831e8	+	6.13166e7i	−0.163443	+	0.0651478i
$981$	2.17646e8	−	2.17646e8i	0.230538	−	0.230538i
$982$	−4.79376e8	+	3.15683e8i	−0.506223	+	0.333362i
$983$	−1.57271e9			−1.65573			−0.827863	−	0.560930i	$-0.810444\pi$
$983$	−1.57271e9			−1.65573			−0.827863	+	0.560930i	$0.810444\pi$
$984$	6.86675e8	−	1.22292e8i	0.720718	−	0.128355i
$985$			3.15479e8i			0.330112i
$986$	2.00158e8	−	1.31810e8i	0.208806	−	0.137505i
$987$	9.01647e6	+	9.01647e6i	0.00937745	+	0.00937745i
$988$	−4.00433e8	−	1.72188e8i	−0.415202	−	0.178539i
$989$	4.02764e7	+	4.02764e7i	0.0416353	+	0.0416353i
$990$	7.76368e7	+	1.59845e7i	0.0800133	+	0.0164738i
$991$		−	9.47817e8i		−	0.973875i	−0.873437	−	0.486938i	$-0.838114\pi$
$991$		−	9.47817e8i		−	0.973875i	0.873437	−	0.486938i	$-0.161886\pi$
$992$	5.57123e8	+	8.97491e8i	0.570711	+	0.919380i
$993$	−1.07807e9			−1.10103
$994$	7.39687e6	−	3.59266e7i	0.00753163	−	0.0365812i
$995$	1.92515e7	−	1.92515e7i	0.0195432	−	0.0195432i
$996$	3.95507e8	−	9.19774e8i	0.400291	−	0.930900i
$997$	−5.42772e8	+	5.42772e8i	−0.547686	+	0.547686i	−0.925771	−	0.378085i	$-0.876583\pi$
$997$	−5.42772e8	+	5.42772e8i	−0.547686	+	0.547686i	0.378085	+	0.925771i	$0.376583\pi$
$998$	6.60554e8	+	1.00308e9i	0.664533	+	1.00912i
$999$	−2.65285e8			−0.266083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.l.a.19.15	✓	48
4.3	odd	2		192.7.l.a.175.21		48
8.3	odd	2		384.7.l.a.223.4		48
8.5	even	2		384.7.l.b.223.21		48
16.3	odd	4		384.7.l.b.31.21		48
16.5	even	4		192.7.l.a.79.21		48
16.11	odd	4	inner	48.7.l.a.43.15	yes	48
16.13	even	4		384.7.l.a.31.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.15	✓	48	1.1	even	1	trivial
48.7.l.a.43.15	yes	48	16.11	odd	4	inner
192.7.l.a.79.21		48	16.5	even	4
192.7.l.a.175.21		48	4.3	odd	2
384.7.l.a.31.4		48	16.13	even	4
384.7.l.a.223.4		48	8.3	odd	2
384.7.l.b.31.21		48	16.3	odd	4
384.7.l.b.223.21		48	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61327 - 7.83565i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-58.7947 - 25.2820i) q^{4} +(-15.5658 + 15.5658i) q^{5} +(68.5874 + 104.153i) q^{6} +10.2991 q^{7} +(-292.952 + 419.908i) q^{8} -243.000i q^{9} +O(q^{10})\)	\(q+(1.61327 - 7.83565i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-58.7947 - 25.2820i) q^{4} +(-15.5658 + 15.5658i) q^{5} +(68.5874 + 104.153i) q^{6} +10.2991 q^{7} +(-292.952 + 419.908i) q^{8} -243.000i q^{9} +(96.8564 + 147.080i) q^{10} +(1309.74 + 1309.74i) q^{11} +(926.753 - 369.401i) q^{12} +(1999.54 + 1999.54i) q^{13} +(16.6152 - 80.7003i) q^{14} -343.155i q^{15} +(2817.64 + 2972.90i) q^{16} -1800.59 q^{17} +(-1904.06 - 392.024i) q^{18} +(1703.06 - 1703.06i) q^{19} +(1308.72 - 521.653i) q^{20} +(-113.524 + 113.524i) q^{21} +(12375.6 - 8149.70i) q^{22} +5649.07 q^{23} +(-1399.40 - 7857.65i) q^{24} +15140.4i q^{25} +(18893.5 - 12441.9i) q^{26} +(2678.52 + 2678.52i) q^{27} +(-605.534 - 260.382i) q^{28} +(-11764.6 - 11764.6i) q^{29} +(-2688.84 - 553.600i) q^{30} +32237.2i q^{31} +(27840.2 - 17282.0i) q^{32} -28873.7 q^{33} +(-2904.83 + 14108.8i) q^{34} +(-160.314 + 160.314i) q^{35} +(-6143.52 + 14287.1i) q^{36} +(-49520.9 + 49520.9i) q^{37} +(-10597.1 - 16092.1i) q^{38} -44080.7 q^{39} +(-1976.17 - 11096.3i) q^{40} +87389.3i q^{41} +(706.391 + 1072.68i) q^{42} +(7129.74 + 7129.74i) q^{43} +(-43893.0 - 110119. i) q^{44} +(3782.49 + 3782.49i) q^{45} +(9113.46 - 44264.1i) q^{46} -79423.3i q^{47} +(-63827.4 - 1711.32i) q^{48} -117543. q^{49} +(118635. + 24425.5i) q^{50} +(19847.3 - 19847.3i) q^{51} +(-67010.1 - 168115. i) q^{52} +(58057.5 - 58057.5i) q^{53} +(25309.1 - 16666.7i) q^{54} -40774.3 q^{55} +(-3017.15 + 4324.69i) q^{56} +37544.8i q^{57} +(-111163. + 73203.8i) q^{58} +(9265.40 + 9265.40i) q^{59} +(-8675.63 + 20175.7i) q^{60} +(31233.4 + 31233.4i) q^{61} +(252600. + 52007.3i) q^{62} -2502.69i q^{63} +(-90501.8 - 246026. i) q^{64} -62249.0 q^{65} +(-46581.1 + 226245. i) q^{66} +(140680. - 140680. i) q^{67} +(105865. + 45522.4i) q^{68} +(-62268.0 + 62268.0i) q^{69} +(997.536 + 1514.80i) q^{70} +445186. q^{71} +(102038. + 71187.4i) q^{72} +674960. i q^{73} +(308138. + 467919. i) q^{74} +(-166888. - 166888. i) q^{75} +(-143188. + 57074.4i) q^{76} +(13489.2 + 13489.2i) q^{77} +(-71114.0 + 345401. i) q^{78} -171535. i q^{79} +(-90134.4 - 2416.66i) q^{80} -59049.0 q^{81} +(684752. + 140982. i) q^{82} +(709618. - 709618. i) q^{83} +(9544.75 - 3804.51i) q^{84} +(28027.6 - 28027.6i) q^{85} +(67368.3 - 44364.0i) q^{86} +259355. q^{87} +(-933662. + 166279. i) q^{88} -549423. i q^{89} +(35740.4 - 23536.1i) q^{90} +(20593.5 + 20593.5i) q^{91} +(-332136. - 142820. i) q^{92} +(-355342. - 355342. i) q^{93} +(-622333. - 128131. i) q^{94} +53019.2i q^{95} +(-116380. + 497368. i) q^{96} -675921. q^{97} +(-189628. + 921025. i) q^{98} +(318267. - 318267. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \) 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Introduction

L-functions

Modular forms

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