LMFDB - Embedded newform 11.6.c.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,6,Mod(3,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("11.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	11.c (of order $5$, degree $4$, 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:	$1.76422201794$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 86 x^{14} - 146 x^{13} + 7205 x^{12} - 23732 x^{11} + 774165 x^{10} + \cdots + 393784336 $ x^16 - 5x^15 + 86x^14 - 146x^13 + 7205x^12 - 23732x^11 + 774165x^10 - 1228996x^9 + 44649817x^8 - 92720004x^7 + 943915592x^6 - 1892495035x^5 + 8611100939x^4 - 17760110698x^3 + 18348896492x^2 - 4224271656*x + 393784336
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.1
Root			$2.73971 - 8.43195i$ of defining polynomial
Character	$\chi$	$=$	11.4
Dual form			11.6.c.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.36363 - 4.62345i) q^{2} +(-5.98507 + 18.4202i) q^{3} +(9.23097 + 28.4100i) q^{4} +(-59.3249 + 43.1020i) q^{5} +(123.251 - 89.5474i) q^{6} +(-51.6143 - 158.852i) q^{7} +(-5.17243 + 15.9191i) q^{8} +(-106.890 - 77.6601i) q^{9} +O(q^{10})$	\(q+(-6.36363 - 4.62345i) q^{2} +(-5.98507 + 18.4202i) q^{3} +(9.23097 + 28.4100i) q^{4} +(-59.3249 + 43.1020i) q^{5} +(123.251 - 89.5474i) q^{6} +(-51.6143 - 158.852i) q^{7} +(-5.17243 + 15.9191i) q^{8} +(-106.890 - 77.6601i) q^{9} +576.801 q^{10} +(3.42402 + 401.297i) q^{11} -578.565 q^{12} +(-139.478 - 101.337i) q^{13} +(-405.991 + 1249.51i) q^{14} +(-438.883 - 1350.74i) q^{15} +(879.860 - 639.256i) q^{16} +(365.505 - 265.555i) q^{17} +(321.151 + 988.400i) q^{18} +(-764.308 + 2352.30i) q^{19} +(-1772.15 - 1287.55i) q^{20} +3235.00 q^{21} +(1833.59 - 2569.54i) q^{22} -2589.01 q^{23} +(-262.275 - 190.554i) q^{24} +(695.975 - 2141.99i) q^{25} +(419.062 + 1289.74i) q^{26} +(-1737.34 + 1262.25i) q^{27} +(4036.54 - 2932.72i) q^{28} +(-709.309 - 2183.03i) q^{29} +(-3452.20 + 10624.8i) q^{30} +(3782.18 + 2747.92i) q^{31} -8019.04 q^{32} +(-7412.45 - 2338.72i) q^{33} -3553.72 q^{34} +(9908.87 + 7199.21i) q^{35} +(1219.63 - 3753.62i) q^{36} +(951.875 + 2929.57i) q^{37} +(15739.5 - 11435.4i) q^{38} +(2701.43 - 1962.70i) q^{39} +(-379.292 - 1167.34i) q^{40} +(2213.70 - 6813.06i) q^{41} +(-20586.3 - 14956.9i) q^{42} +398.961 q^{43} +(-11369.2 + 3801.64i) q^{44} +9688.54 q^{45} +(16475.5 + 11970.2i) q^{46} +(415.282 - 1278.11i) q^{47} +(6509.16 + 20033.1i) q^{48} +(-8972.88 + 6519.18i) q^{49} +(-14332.3 + 10413.0i) q^{50} +(2703.99 + 8322.03i) q^{51} +(1591.46 - 4898.02i) q^{52} +(-8163.81 - 5931.36i) q^{53} +16891.7 q^{54} +(-17499.8 - 23659.3i) q^{55} +2795.76 q^{56} +(-38755.2 - 28157.3i) q^{57} +(-5579.34 + 17171.4i) q^{58} +(12277.9 + 37787.5i) q^{59} +(34323.3 - 24937.3i) q^{60} +(13623.8 - 9898.29i) q^{61} +(-11363.6 - 34973.4i) q^{62} +(-6819.44 + 20988.1i) q^{63} +(22874.7 + 16619.4i) q^{64} +12642.4 q^{65} +(36357.1 + 49153.8i) q^{66} -28904.6 q^{67} +(10918.4 + 7932.67i) q^{68} +(15495.4 - 47690.0i) q^{69} +(-29771.2 - 91626.2i) q^{70} +(-49150.0 + 35709.6i) q^{71} +(1789.16 - 1299.90i) q^{72} +(11036.1 + 33965.7i) q^{73} +(7487.33 - 23043.6i) q^{74} +(35290.4 + 25639.9i) q^{75} -73884.0 q^{76} +(63570.2 - 21256.6i) q^{77} -26265.4 q^{78} +(10128.2 + 7358.60i) q^{79} +(-24644.3 + 75847.5i) q^{80} +(-22774.1 - 70091.3i) q^{81} +(-45586.9 + 33120.9i) q^{82} +(12273.1 - 8916.96i) q^{83} +(29862.2 + 91906.3i) q^{84} +(-10237.6 + 31508.0i) q^{85} +(-2538.84 - 1844.57i) q^{86} +44457.0 q^{87} +(-6405.99 - 2021.17i) q^{88} +101481. q^{89} +(-61654.3 - 44794.5i) q^{90} +(-8898.54 + 27386.9i) q^{91} +(-23899.1 - 73553.8i) q^{92} +(-73253.7 + 53221.9i) q^{93} +(-8551.95 + 6213.36i) q^{94} +(-56046.3 - 172493. i) q^{95} +(47994.5 - 147712. i) q^{96} +(108448. + 78792.3i) q^{97} +87241.2 q^{98} +(30798.8 - 43160.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 24 q^{3} - 73 q^{4} - 10 q^{5} + 121 q^{6} + 196 q^{7} + 527 q^{8} - 530 q^{9}+O(q^{10}) $ 16 * q - q^2 - 24 * q^3 - 73 * q^4 - 10 * q^5 + 121 * q^6 + 196 * q^7 + 527 * q^8 - 530 * q^9	\( 16 q - q^{2} - 24 q^{3} - 73 q^{4} - 10 q^{5} + 121 q^{6} + 196 q^{7} + 527 q^{8} - 530 q^{9} - 672 q^{10} - 692 q^{11} - 1562 q^{12} + 1162 q^{13} + 560 q^{14} + 1796 q^{15} + 6399 q^{16} - 22 q^{17} + 834 q^{18} - 3236 q^{19} - 5514 q^{20} - 7772 q^{21} - 13059 q^{22} - 10848 q^{23} + 13233 q^{24} + 15686 q^{25} + 16216 q^{26} + 22500 q^{27} + 8838 q^{28} + 13070 q^{29} - 22830 q^{30} - 14764 q^{31} - 58812 q^{32} - 48544 q^{33} - 26966 q^{34} + 43368 q^{35} + 63696 q^{36} + 4638 q^{37} + 68144 q^{38} + 20300 q^{39} + 52284 q^{40} - 14806 q^{41} - 69922 q^{42} - 24376 q^{43} - 104960 q^{44} - 97480 q^{45} + 50452 q^{46} + 40364 q^{47} + 30236 q^{48} + 32246 q^{49} + 10839 q^{50} + 75564 q^{51} - 80654 q^{52} - 11654 q^{53} + 43796 q^{54} + 7052 q^{55} + 70632 q^{56} - 40020 q^{57} + 10276 q^{58} + 70804 q^{59} + 46116 q^{60} - 31446 q^{61} - 153388 q^{62} - 7064 q^{63} + 17695 q^{64} - 41284 q^{65} + 48006 q^{66} - 64200 q^{67} - 94114 q^{68} - 62412 q^{69} - 103768 q^{70} - 184380 q^{71} - 14729 q^{72} - 1750 q^{73} + 306048 q^{74} + 246596 q^{75} + 174806 q^{76} + 384646 q^{77} + 360916 q^{78} + 24324 q^{79} - 386444 q^{80} - 259412 q^{81} - 316255 q^{82} - 46028 q^{83} - 271956 q^{84} + 63914 q^{85} + 22931 q^{86} - 47592 q^{87} + 211871 q^{88} + 148364 q^{89} - 347186 q^{90} - 258448 q^{91} - 58658 q^{92} - 387478 q^{93} - 55370 q^{94} - 4716 q^{95} + 328396 q^{96} + 484296 q^{97} + 743692 q^{98} + 724964 q^{99}+O(q^{100}) \) 16 * q - q^2 - 24 * q^3 - 73 * q^4 - 10 * q^5 + 121 * q^6 + 196 * q^7 + 527 * q^8 - 530 * q^9 - 672 * q^10 - 692 * q^11 - 1562 * q^12 + 1162 * q^13 + 560 * q^14 + 1796 * q^15 + 6399 * q^16 - 22 * q^17 + 834 * q^18 - 3236 * q^19 - 5514 * q^20 - 7772 * q^21 - 13059 * q^22 - 10848 * q^23 + 13233 * q^24 + 15686 * q^25 + 16216 * q^26 + 22500 * q^27 + 8838 * q^28 + 13070 * q^29 - 22830 * q^30 - 14764 * q^31 - 58812 * q^32 - 48544 * q^33 - 26966 * q^34 + 43368 * q^35 + 63696 * q^36 + 4638 * q^37 + 68144 * q^38 + 20300 * q^39 + 52284 * q^40 - 14806 * q^41 - 69922 * q^42 - 24376 * q^43 - 104960 * q^44 - 97480 * q^45 + 50452 * q^46 + 40364 * q^47 + 30236 * q^48 + 32246 * q^49 + 10839 * q^50 + 75564 * q^51 - 80654 * q^52 - 11654 * q^53 + 43796 * q^54 + 7052 * q^55 + 70632 * q^56 - 40020 * q^57 + 10276 * q^58 + 70804 * q^59 + 46116 * q^60 - 31446 * q^61 - 153388 * q^62 - 7064 * q^63 + 17695 * q^64 - 41284 * q^65 + 48006 * q^66 - 64200 * q^67 - 94114 * q^68 - 62412 * q^69 - 103768 * q^70 - 184380 * q^71 - 14729 * q^72 - 1750 * q^73 + 306048 * q^74 + 246596 * q^75 + 174806 * q^76 + 384646 * q^77 + 360916 * q^78 + 24324 * q^79 - 386444 * q^80 - 259412 * q^81 - 316255 * q^82 - 46028 * q^83 - 271956 * q^84 + 63914 * q^85 + 22931 * q^86 - 47592 * q^87 + 211871 * q^88 + 148364 * q^89 - 347186 * q^90 - 258448 * q^91 - 58658 * q^92 - 387478 * q^93 - 55370 * q^94 - 4716 * q^95 + 328396 * q^96 + 484296 * q^97 + 743692 * q^98 + 724964 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−6.36363	−	4.62345i	−1.12494	−	0.817318i	−0.139991	−	0.990153i	$-0.544707\pi$
$2$	−6.36363	−	4.62345i	−1.12494	−	0.817318i	−0.984951	+	0.172835i	$0.944707\pi$
$3$	−5.98507	+	18.4202i	−0.383943	+	1.18165i	0.553302	+	0.832981i	$0.313368\pi$
$3$	−5.98507	+	18.4202i	−0.383943	+	1.18165i	−0.937244	+	0.348673i	$0.886632\pi$
$4$	9.23097	+	28.4100i	0.288468	+	0.887812i
$5$	−59.3249	+	43.1020i	−1.06124	+	0.771033i	−0.974317	−	0.225183i	$-0.927702\pi$
$5$	−59.3249	+	43.1020i	−1.06124	+	0.771033i	−0.0869187	+	0.996215i	$0.527702\pi$
$6$	123.251	−	89.5474i	1.39770	−	1.01549i
$7$	−51.6143	−	158.852i	−0.398130	−	1.22532i	−0.926497	−	0.376301i	$-0.877196\pi$
$7$	−51.6143	−	158.852i	−0.398130	−	1.22532i	0.528368	−	0.849016i	$-0.322804\pi$
$8$	−5.17243	+	15.9191i	−0.0285739	+	0.0879414i
$9$	−106.890	−	77.6601i	−0.439876	−	0.319589i
$10$	576.801			1.82401
$11$	3.42402	+	401.297i	0.00853208	+	0.999964i
$11$	3.42402	+	401.297i	0.00853208	+	0.999964i
$12$	−578.565			−1.15984
$13$	−139.478	−	101.337i	−0.228901	−	0.166307i	0.467423	−	0.884034i	$-0.345183\pi$
$13$	−139.478	−	101.337i	−0.228901	−	0.166307i	−0.696324	+	0.717727i	$0.745183\pi$
$14$	−405.991	+	1249.51i	−0.553601	+	1.70381i
$15$	−438.883	−	1350.74i	−0.503640	−	1.55004i
$16$	879.860	−	639.256i	0.859238	−	0.624273i
$17$	365.505	−	265.555i	0.306741	−	0.222860i	−0.423756	−	0.905776i	$-0.639289\pi$
$17$	365.505	−	265.555i	0.306741	−	0.222860i	0.730497	+	0.682916i	$0.239289\pi$
$18$	321.151	+	988.400i	0.233629	+	0.719038i
$19$	−764.308	+	2352.30i	−0.485718	+	1.49489i	0.345220	+	0.938522i	$0.387804\pi$
$19$	−764.308	+	2352.30i	−0.485718	+	1.49489i	−0.830938	+	0.556364i	$0.812196\pi$
$20$	−1772.15	−	1287.55i	−0.990664	−	0.719760i
$21$	3235.00			1.60076
$22$	1833.59	−	2569.54i	0.807690	−	1.13187i
$23$	−2589.01			−1.02050			−0.510251	−	0.860025i	$-0.670448\pi$
$23$	−2589.01			−1.02050			−0.510251	+	0.860025i	$0.670448\pi$
$24$	−262.275	−	190.554i	−0.0929455	−	0.0675289i
$25$	695.975	−	2141.99i	0.222712	−	0.685437i
$26$	419.062	+	1289.74i	0.121575	+	0.374170i
$27$	−1737.34	+	1262.25i	−0.458644	+	0.333224i
$28$	4036.54	−	2932.72i	0.973004	−	0.706929i
$29$	−709.309	−	2183.03i	−0.156618	−	0.482019i	0.841704	−	0.539940i	$-0.181553\pi$
$29$	−709.309	−	2183.03i	−0.156618	−	0.482019i	−0.998321	+	0.0579204i	$0.981553\pi$
$30$	−3452.20	+	10624.8i	−0.700313	+	2.15534i
$31$	3782.18	+	2747.92i	0.706868	+	0.513570i	0.882162	−	0.470947i	$-0.156088\pi$
$31$	3782.18	+	2747.92i	0.706868	+	0.513570i	−0.175294	+	0.984516i	$0.556088\pi$
$32$	−8019.04			−1.38435
$33$	−7412.45	−	2338.72i	−1.18489	−	0.373847i
$34$	−3553.72			−0.527213
$35$	9908.87	+	7199.21i	1.36727	+	0.993379i
$36$	1219.63	−	3753.62i	0.156845	−	0.482719i
$37$	951.875	+	2929.57i	0.114308	+	0.351803i	0.991802	−	0.127784i	$-0.0407865\pi$
$37$	951.875	+	2929.57i	0.114308	+	0.351803i	−0.877494	+	0.479587i	$0.840786\pi$
$38$	15739.5	−	11435.4i	1.76820	−	1.28467i
$39$	2701.43	−	1962.70i	0.284402	−	0.206630i
$40$	−379.292	−	1167.34i	−0.0374821	−	0.115358i
$41$	2213.70	−	6813.06i	0.205664	−	0.632969i	−0.794021	−	0.607890i	$-0.792016\pi$
$41$	2213.70	−	6813.06i	0.205664	−	0.632969i	0.999685	−	0.0250791i	$-0.00798376\pi$
$42$	−20586.3	−	14956.9i	−1.80076	−	1.30833i
$43$	398.961			0.0329048			0.0164524	−	0.999865i	$-0.494763\pi$
$43$	398.961			0.0329048			0.0164524	+	0.999865i	$0.494763\pi$
$44$	−11369.2	+	3801.64i	−0.885319	+	0.296032i
$45$	9688.54			0.713226
$46$	16475.5	+	11970.2i	1.14801	+	0.834075i
$47$	415.282	−	1278.11i	0.0274219	−	0.0843960i	−0.936409	−	0.350911i	$-0.885872\pi$
$47$	415.282	−	1278.11i	0.0274219	−	0.0843960i	0.963831	+	0.266515i	$0.0858721\pi$
$48$	6509.16	+	20033.1i	0.407776	+	1.25501i
$49$	−8972.88	+	6519.18i	−0.533878	+	0.387885i
$50$	−14332.3	+	10413.0i	−0.810758	+	0.589050i
$51$	2703.99	+	8322.03i	0.145573	+	0.448027i
$52$	1591.46	−	4898.02i	0.0816184	−	0.251196i
$53$	−8163.81	−	5931.36i	−0.399212	−	0.290044i	0.370008	−	0.929029i	$-0.379355\pi$
$53$	−8163.81	−	5931.36i	−0.399212	−	0.290044i	−0.769220	+	0.638984i	$0.779355\pi$
$54$	16891.7			0.788298
$55$	−17499.8	−	23659.3i	−0.780059	−	1.05462i
$56$	2795.76			0.119132
$57$	−38755.2	−	28157.3i	−1.57995	−	1.14790i
$58$	−5579.34	+	17171.4i	−0.217777	+	0.670250i
$59$	12277.9	+	37787.5i	0.459192	+	1.41325i	0.866142	+	0.499798i	$0.166593\pi$
$59$	12277.9	+	37787.5i	0.459192	+	1.41325i	−0.406949	+	0.913451i	$0.633407\pi$
$60$	34323.3	−	24937.3i	1.23086	−	0.894276i
$61$	13623.8	−	9898.29i	0.468786	−	0.340593i	−0.328182	−	0.944615i	$-0.606436\pi$
$61$	13623.8	−	9898.29i	0.468786	−	0.340593i	0.796968	+	0.604022i	$0.206436\pi$
$62$	−11363.6	−	34973.4i	−0.375435	−	1.15547i
$63$	−6819.44	+	20988.1i	−0.216470	+	0.666226i
$64$	22874.7	+	16619.4i	0.698080	+	0.507185i
$65$	12642.4			0.371146
$66$	36357.1	+	49153.8i	1.02738	+	1.38898i
$67$	−28904.6			−0.786648			−0.393324	−	0.919400i	$-0.628675\pi$
$67$	−28904.6			−0.786648			−0.393324	+	0.919400i	$0.628675\pi$
$68$	10918.4	+	7932.67i	0.286343	+	0.208040i
$69$	15495.4	−	47690.0i	0.391815	−	1.20588i
$70$	−29771.2	−	91626.2i	−0.726191	−	2.23499i
$71$	−49150.0	+	35709.6i	−1.15712	+	0.840696i	−0.989411	−	0.145141i	$-0.953636\pi$
$71$	−49150.0	+	35709.6i	−1.15712	+	0.840696i	−0.167708	+	0.985837i	$0.553636\pi$
$72$	1789.16	−	1299.90i	0.0406741	−	0.0295514i
$73$	11036.1	+	33965.7i	0.242387	+	0.745992i	0.996055	+	0.0887361i	$0.0282828\pi$
$73$	11036.1	+	33965.7i	0.242387	+	0.745992i	−0.753668	+	0.657256i	$0.771717\pi$
$74$	7487.33	−	23043.6i	0.158945	−	0.489183i
$75$	35290.4	+	25639.9i	0.724441	+	0.526337i
$76$	−73884.0			−1.46729
$77$	63570.2	−	21256.6i	1.22188	−	0.408570i
$78$	−26265.4			−0.488818
$79$	10128.2	+	7358.60i	0.182586	+	0.132656i	0.675324	−	0.737521i	$-0.264004\pi$
$79$	10128.2	+	7358.60i	0.182586	+	0.132656i	−0.492738	+	0.870178i	$0.664004\pi$
$80$	−24644.3	+	75847.5i	−0.430519	+	1.32500i
$81$	−22774.1	−	70091.3i	−0.385681	−	1.18700i
$82$	−45586.9	+	33120.9i	−0.748697	+	0.543960i
$83$	12273.1	−	8916.96i	0.195551	−	0.142076i	−0.485701	−	0.874125i	$-0.661436\pi$
$83$	12273.1	−	8916.96i	0.195551	−	0.142076i	0.681252	+	0.732049i	$0.261436\pi$
$84$	29862.2	+	91906.3i	0.461767	+	1.42117i
$85$	−10237.6	+	31508.0i	−0.153692	+	0.473014i
$86$	−2538.84	−	1844.57i	−0.0370159	−	0.0268937i
$87$	44457.0			0.629712
$88$	−6405.99	−	2021.17i	−0.0881820	−	0.0278225i
$89$	101481.			1.35803			0.679016	−	0.734123i	$-0.262406\pi$
$89$	101481.			1.35803			0.679016	+	0.734123i	$0.262406\pi$
$90$	−61654.3	−	44794.5i	−0.802337	−	0.582932i
$91$	−8898.54	+	27386.9i	−0.112646	+	0.346688i
$92$	−23899.1	−	73553.8i	−0.294382	−	0.906015i
$93$	−73253.7	+	53221.9i	−0.878258	+	0.638092i
$94$	−8551.95	+	6213.36i	−0.0998264	+	0.0725282i
$95$	−56046.3	−	172493.i	−0.637145	−	1.96093i
$96$	47994.5	−	147712.i	0.531513	−	1.63583i
$97$	108448.	+	78792.3i	1.17029	+	0.850266i	0.991044	−	0.133539i	$-0.0426340\pi$
$97$	108448.	+	78792.3i	1.17029	+	0.850266i	0.179247	+	0.983804i	$0.442634\pi$
$98$	87241.2			0.917606
$99$	30798.8	−	43160.5i	0.315824	−	0.442587i
$100$	67278.5			0.672785
$101$	−4121.09	−	2994.15i	−0.0401984	−	0.0292058i	0.567505	−	0.823370i	$-0.307909\pi$
$101$	−4121.09	−	2994.15i	−0.0401984	−	0.0292058i	−0.607703	+	0.794164i	$0.707909\pi$
$102$	21269.3	−	65460.1i	0.202419	−	0.622983i
$103$	20815.6	+	64063.8i	0.193328	+	0.595004i	0.999992	+	0.00399289i	$0.00127098\pi$
$103$	20815.6	+	64063.8i	0.193328	+	0.595004i	−0.806664	+	0.591011i	$0.798729\pi$
$104$	2334.63	−	1696.21i	0.0211658	−	0.0153779i
$105$	−191916.	+	139435.i	−1.69878	+	1.23424i
$106$	24528.2	+	75489.9i	0.212031	+	0.652566i
$107$	−10913.8	+	33589.1i	−0.0921542	+	0.283622i	−0.986502	−	0.163752i	$-0.947640\pi$
$107$	−10913.8	+	33589.1i	−0.0921542	+	0.283622i	0.894347	+	0.447373i	$0.147640\pi$
$108$	−51897.9	−	37706.0i	−0.428145	−	0.311065i
$109$	−141350.			−1.13954			−0.569770	−	0.821804i	$-0.692968\pi$
$109$	−141350.			−1.13954			−0.569770	+	0.821804i	$0.692968\pi$
$110$	1974.98	+	231469.i	0.0155626	+	1.82394i
$111$	−59660.2			−0.459597
$112$	−146961.	−	106773.i	−1.10702	−	0.804298i
$113$	18325.9	−	56401.5i	0.135011	−	0.415522i	−0.860580	−	0.509315i	$-0.829899\pi$
$113$	18325.9	−	56401.5i	0.135011	−	0.415522i	0.995592	+	0.0937924i	$0.0298990\pi$
$114$	116440.	+	358366.i	0.839151	+	2.58264i
$115$	153593.	−	111592.i	1.08299	−	0.786841i
$116$	55472.2	−	40302.9i	0.382764	−	0.278094i
$117$	7039.00	+	21663.8i	0.0475386	+	0.146309i
$118$	96576.6	−	297232.i	0.638509	−	1.96513i
$119$	−61049.3	−	44354.9i	−0.395197	−	0.287127i
$120$	23772.7			0.150704
$121$	−161028.	+	2748.10i	−0.999854	+	0.0170635i
$122$	−132461.			−0.805729
$123$	112248.	+	81553.3i	0.668987	+	0.486047i
$124$	−43155.1	+	132818.i	−0.252045	+	0.775714i
$125$	−19777.2	−	60868.0i	−0.113211	−	0.348429i
$126$	140434.	−	102031.i	0.788034	−	0.572540i
$127$	219427.	−	159423.i	1.20720	−	0.877085i	0.212230	−	0.977220i	$-0.431928\pi$
$127$	219427.	−	159423.i	1.20720	−	0.877085i	0.994974	+	0.100135i	$0.0319275\pi$
$128$	10569.7	+	32530.2i	0.0570214	+	0.175494i
$129$	−2387.81	+	7348.92i	−0.0126335	+	0.0388821i
$130$	−80451.3	−	58451.3i	−0.417518	−	0.303344i
$131$	−359242.			−1.82898			−0.914490	−	0.404609i	$-0.867408\pi$
$131$	−359242.			−1.82898			−0.914490	+	0.404609i	$0.867408\pi$
$132$	−1981.02	−	232176.i	−0.00989586	−	1.15980i
$133$	413117.			2.02509
$134$	183938.	+	133639.i	0.884933	+	0.642941i
$135$	48661.9	−	149766.i	0.229802	−	0.707259i
$136$	2336.85	+	7192.07i	0.0108339	+	0.0333432i
$137$	−212722.	+	154552.i	−0.968303	+	0.703513i	−0.955064	−	0.296399i	$-0.904214\pi$
$137$	−212722.	+	154552.i	−0.968303	+	0.703513i	−0.0132389	+	0.999912i	$0.504214\pi$
$138$	−319099.	+	231839.i	−1.42636	+	1.03631i
$139$	−11066.7	−	34059.8i	−0.0485826	−	0.149522i	0.923822	−	0.382822i	$-0.125048\pi$
$139$	−11066.7	−	34059.8i	−0.0485826	−	0.149522i	−0.972405	+	0.233300i	$0.925048\pi$
$140$	−113061.	+	347966.i	−0.487521	+	1.50044i
$141$	21057.4	+	15299.1i	0.0891984	+	0.0648065i
$142$	477874.			1.98881
$143$	40188.6	−	56319.2i	0.164348	−	0.230312i
$144$	−143693.			−0.577469
$145$	136173.	+	98935.2i	0.537861	+	0.390779i
$146$	86808.9	−	267170.i	0.337041	−	1.03730i
$147$	−66381.0	−	204300.i	−0.253367	−	0.779784i
$148$	−74442.3	+	54085.5i	−0.279361	+	0.202968i
$149$	92117.0	−	66926.9i	0.339918	−	0.246965i	−0.404709	−	0.914445i	$-0.632627\pi$
$149$	92117.0	−	66926.9i	0.339918	−	0.246965i	0.744627	+	0.667481i	$0.232627\pi$
$150$	−106030.	−	326326.i	−0.384769	−	1.18420i
$151$	−130182.	+	400658.i	−0.464631	+	1.42999i	0.394816	+	0.918760i	$0.370808\pi$
$151$	−130182.	+	400658.i	−0.464631	+	1.42999i	−0.859446	+	0.511226i	$0.829192\pi$
$152$	−33493.1	−	24334.2i	−0.117584	−	0.0854294i
$153$	−59691.9			−0.206152
$154$	−502816.	−	158645.i	−1.70847	−	0.539044i
$155$	−342818.			−1.14613
$156$	80697.2	+	58630.0i	0.265489	+	0.192889i
$157$	−151673.	+	466803.i	−0.491089	+	1.51142i	0.331874	+	0.943324i	$0.392319\pi$
$157$	−151673.	+	466803.i	−0.491089	+	1.51142i	−0.822964	+	0.568094i	$0.807681\pi$
$158$	−30430.3	−	93654.8i	−0.0969758	−	0.298461i
$159$	158118.	−	114879.i	0.496006	−	0.360370i
$160$	475728.	−	345637.i	1.46913	−	1.06738i
$161$	133630.	+	411270.i	0.406292	+	1.25044i
$162$	−179138.	+	551330.i	−0.536290	+	1.65053i
$163$	53272.2	+	38704.5i	0.157048	+	0.114102i	0.663534	−	0.748146i	$-0.269056\pi$
$163$	53272.2	+	38704.5i	0.157048	+	0.114102i	−0.506486	+	0.862248i	$0.669056\pi$
$164$	213993.			0.621285
$165$	540546.	−	180747.i	1.54569	−	0.516847i
$166$	−119329.			−0.336105
$167$	117235.	+	85175.9i	0.325285	+	0.236334i	0.738427	−	0.674333i	$-0.235569\pi$
$167$	117235.	+	85175.9i	0.325285	+	0.236334i	−0.413142	+	0.910667i	$0.635569\pi$
$168$	−16732.8	+	51498.3i	−0.0457399	+	0.140773i
$169$	−105551.	−	324852.i	−0.284279	−	0.874921i
$170$	210824.	−	153172.i	0.559496	−	0.406498i
$171$	264376.	−	192081.i	0.691405	−	0.502335i
$172$	3682.79	+	11334.5i	0.00949197	+	0.0292133i
$173$	65248.8	−	200815.i	0.165751	−	0.510130i	−0.833339	−	0.552762i	$-0.813574\pi$
$173$	65248.8	−	200815.i	0.165751	−	0.510130i	0.999091	+	0.0426312i	$0.0135740\pi$
$174$	−282908.	−	205545.i	−0.708389	−	0.514675i
$175$	−376183.			−0.928546
$176$	259544.	+	350896.i	0.631581	+	0.853881i
$177$	−769537.			−1.84627
$178$	−645788.	−	469193.i	−1.52771	−	1.10994i
$179$	224974.	−	692398.i	0.524807	−	1.61519i	−0.239890	−	0.970800i	$-0.577111\pi$
$179$	224974.	−	692398.i	0.524807	−	1.61519i	0.764697	−	0.644390i	$-0.222889\pi$
$180$	89434.6	+	275251.i	0.205743	+	0.633211i
$181$	507999.	−	369083.i	1.15257	−	0.837389i	0.163747	−	0.986502i	$-0.447642\pi$
$181$	507999.	−	369083.i	1.15257	−	0.837389i	0.988820	+	0.149113i	$0.0476418\pi$
$182$	183249.	−	133138.i	0.410075	−	0.297937i
$183$	100788.	+	310195.i	0.222476	+	0.684711i
$184$	13391.5	−	41214.7i	0.0291597	−	0.0897445i
$185$	−182740.	−	132769.i	−0.392559	−	0.285211i
$186$	712228.			1.50951
$187$	107818.	+	145767.i	0.225469	+	0.304828i
$188$	40144.4			0.0828382
$189$	290183.	+	210830.i	0.590905	+	0.429318i
$190$	−440854.	+	1.35681e6i	−0.885952	+	2.72668i
$191$	189676.	+	583762.i	0.376208	+	1.15785i	0.942660	+	0.333755i	$0.108316\pi$
$191$	189676.	+	583762.i	0.376208	+	1.15785i	−0.566452	+	0.824095i	$0.691684\pi$
$192$	−443039.	+	321887.i	−0.867339	+	0.630159i
$193$	−671346.	+	487761.i	−1.29734	+	0.942571i	−0.999926	−	0.0121784i	$-0.996123\pi$
$193$	−671346.	+	487761.i	−1.29734	+	0.942571i	−0.297412	+	0.954749i	$0.596123\pi$
$194$	−325833.	−	1.00281e6i	−0.621571	−	1.91300i
$195$	−75665.4	+	232874.i	−0.142499	+	0.438566i
$196$	−268038.	−	194741.i	−0.498375	−	0.362091i
$197$	577890.			1.06091			0.530456	−	0.847712i	$-0.322021\pi$
$197$	577890.			1.06091			0.530456	+	0.847712i	$0.322021\pi$
$198$	−395542.	+	132261.i	−0.717018	+	0.239756i
$199$	79423.0			0.142172			0.0710859	−	0.997470i	$-0.477354\pi$
$199$	79423.0			0.142172			0.0710859	+	0.997470i	$0.477354\pi$
$200$	30498.7	+	22158.6i	0.0539145	+	0.0391712i
$201$	172996.	−	532428.i	0.302028	−	0.929545i
$202$	12381.8	+	38107.3i	0.0213504	+	0.0657097i
$203$	−310169.	+	225351.i	−0.528273	+	0.383812i
$204$	−211468.	+	153641.i	−0.355770	+	0.258482i
$205$	162329.	+	499598.i	0.269782	+	0.830303i
$206$	163733.	−	503918.i	0.268824	−	0.827355i
$207$	276739.	+	201063.i	0.448895	+	0.326141i
$208$	−187502.			−0.300502
$209$	−946587.	−	298660.i	−1.49898	−	0.472946i
$210$	1.86595e6			2.91979
$211$	−448445.	−	325815.i	−0.693431	−	0.503807i	0.184355	−	0.982860i	$-0.440980\pi$
$211$	−448445.	−	325815.i	−0.693431	−	0.503807i	−0.877786	+	0.479052i	$0.840980\pi$
$212$	93149.9	−	286686.i	0.142345	−	0.438094i
$213$	−363610.	−	1.11908e6i	−0.549144	−	1.69009i
$214$	224749.	−	163289.i	0.335477	−	0.243738i
$215$	−23668.3	+	17196.0i	−0.0349197	+	0.0253707i
$216$	−11107.6	−	34185.8i	−0.0161990	−	0.0498553i
$217$	241298.	−	742640.i	0.347861	−	1.07060i
$218$	899499.	+	653524.i	1.28192	+	0.931366i
$219$	−691706.			−0.974566
$220$	510620.	−	715569.i	0.711281	−	0.996769i
$221$	−77890.6			−0.107276
$222$	379655.	+	275836.i	0.517019	+	0.375637i
$223$	2530.09	−	7786.81i	0.00340701	−	0.0104857i	−0.949339	−	0.314255i	$-0.898245\pi$
$223$	2530.09	−	7786.81i	0.00340701	−	0.0104857i	0.952746	+	0.303769i	$0.0982453\pi$
$224$	413897.	+	1.27384e6i	0.551153	+	1.69627i
$225$	−240740.	+	174908.i	−0.317024	+	0.230331i
$226$	−377389.	+	274189.i	−0.491493	+	0.357091i
$227$	−73503.2	−	226220.i	−0.0946764	−	0.291384i	0.892493	−	0.451062i	$-0.148955\pi$
$227$	−73503.2	−	226220.i	−0.0946764	−	0.291384i	−0.987169	+	0.159678i	$0.948955\pi$
$228$	442201.	−	1.36096e6i	0.563356	−	1.73383i
$229$	294453.	+	213933.i	0.371046	+	0.269581i	0.757644	−	0.652668i	$-0.226350\pi$
$229$	294453.	+	213933.i	0.371046	+	0.269581i	−0.386599	+	0.922248i	$0.626350\pi$
$230$	−1.49334e6			−1.86140
$231$	11076.7	+	1.29820e6i	0.0136578	+	1.60070i
$232$	38420.7			0.0468646
$233$	421693.	+	306378.i	0.508870	+	0.369716i	0.812395	−	0.583108i	$-0.198163\pi$
$233$	421693.	+	306378.i	0.508870	+	0.369716i	−0.303525	+	0.952824i	$0.598163\pi$
$234$	55367.9	−	170405.i	0.0661026	−	0.203443i
$235$	30452.4	+	93722.9i	0.0359710	+	0.110707i
$236$	−960207.	+	697631.i	−1.12224	+	0.815353i
$237$	−196165.	+	142522.i	−0.226856	+	0.164821i
$238$	183423.	+	564516.i	0.209899	+	0.646003i
$239$	55398.7	−	170500.i	0.0627342	−	0.193076i	−0.914777	−	0.403959i	$-0.867634\pi$
$239$	55398.7	−	170500.i	0.0627342	−	0.193076i	0.977511	+	0.210883i	$0.0676339\pi$
$240$	−1.24962e6	−	907905.i	−1.40040	−	1.01745i
$241$	−1.07705e6			−1.19452			−0.597261	−	0.802047i	$-0.703744\pi$
$241$	−1.07705e6			−1.19452			−0.597261	+	0.802047i	$0.703744\pi$
$242$	1.03743e6	+	727014.i	1.13872	+	0.798003i
$243$	905562.			0.983791
$244$	406971.	+	295682.i	0.437612	+	0.317944i
$245$	251325.	−	773499.i	0.267498	−	0.823274i
$246$	−337250.	−	1.03795e6i	−0.355316	−	1.09355i
$247$	344979.	−	250642.i	0.359791	−	0.261403i
$248$	−63307.4	+	45995.5i	−0.0653620	+	0.0474883i
$249$	90796.1	+	279442.i	0.0928045	+	0.285623i
$250$	−155565.	+	478780.i	−0.157421	+	0.484491i
$251$	1.18626e6	+	861869.i	1.18849	+	0.863490i	0.993104	−	0.117236i	$-0.0374035\pi$
$251$	1.18626e6	+	861869.i	1.18849	+	0.863490i	0.195388	+	0.980726i	$0.437404\pi$
$252$	−659222.			−0.653928
$253$	−8864.83	−	1.03896e6i	−0.00870701	−	1.02047i
$254$	−2.13343e6			−2.07489
$255$	−519110.	−	377156.i	−0.499930	−	0.363220i
$256$	362735.	−	1.11638e6i	0.345931	−	1.06467i
$257$	312287.	+	961122.i	0.294932	+	0.907707i	0.983244	+	0.182293i	$0.0583518\pi$
$257$	312287.	+	961122.i	0.294932	+	0.907707i	−0.688312	+	0.725414i	$0.741648\pi$
$258$	49172.5	−	35725.9i	0.0459910	−	0.0334144i
$259$	416239.	−	302415.i	0.385561	−	0.280126i
$260$	116701.	+	359169.i	0.107064	+	0.329508i
$261$	−93716.3	+	288429.i	−0.0851557	+	0.262082i
$262$	2.28608e6	+	1.66094e6i	2.05749	+	1.49486i
$263$	692197.			0.617078			0.308539	−	0.951212i	$-0.400160\pi$
$263$	692197.			0.617078			0.308539	+	0.951212i	$0.400160\pi$
$264$	75570.6	−	105903.i	0.0667334	−	0.0935183i
$265$	739971.			0.647291
$266$	−2.62892e6	−	1.91002e6i	−2.27811	−	1.65514i
$267$	−607372.	+	1.86930e6i	−0.521407	+	1.60472i
$268$	−266818.	−	821180.i	−0.226923	−	0.698396i
$269$	107297.	−	77955.6i	0.0904077	−	0.0656851i	−0.541663	−	0.840596i	$-0.682205\pi$
$269$	107297.	−	77955.6i	0.0904077	−	0.0656851i	0.632071	+	0.774911i	$0.282205\pi$
$270$	−1.00210e6	+	728069.i	−0.836569	+	0.607803i
$271$	−357645.	−	1.10072e6i	−0.295821	−	0.910443i	−0.982944	−	0.183903i	$-0.941127\pi$
$271$	−357645.	−	1.10072e6i	−0.295821	−	0.910443i	0.687123	−	0.726541i	$-0.258873\pi$
$272$	151836.	−	467302.i	0.124438	−	0.382980i
$273$	−451213.	−	327825.i	−0.366416	−	0.266217i
$274$	2.06825e6			1.66428
$275$	861958.	+	271958.i	0.687312	+	0.216856i
$276$	1.49791e6			1.18362
$277$	−198498.	−	144217.i	−0.155438	−	0.112932i	0.507348	−	0.861741i	$-0.330626\pi$
$277$	−198498.	−	144217.i	−0.155438	−	0.112932i	−0.662786	+	0.748809i	$0.730626\pi$
$278$	−87049.3	+	267910.i	−0.0675543	+	0.207911i
$279$	−190874.	−	587450.i	−0.146803	−	0.451814i
$280$	−165858.	+	120503.i	−0.126427	+	0.0918548i
$281$	1.05704e6	−	767987.i	0.798596	−	0.580214i	−0.111906	−	0.993719i	$-0.535696\pi$
$281$	1.05704e6	−	767987.i	0.798596	−	0.580214i	0.910502	+	0.413505i	$0.135696\pi$
$282$	−63267.0	−	194716.i	−0.0473755	−	0.145807i
$283$	61415.5	−	189017.i	0.0455839	−	0.140293i	−0.925674	−	0.378322i	$-0.876501\pi$
$283$	61415.5	−	189017.i	0.0455839	−	0.140293i	0.971258	+	0.238029i	$0.0765013\pi$
$284$	−1.46821e6	−	1.06672e6i	−1.08017	−	0.784791i
$285$	3.51279e6			2.56177
$286$	−516135.	+	172585.i	−0.373119	+	0.124763i
$287$	−1.19653e6			−0.857469
$288$	857155.	+	622760.i	0.608945	+	0.442425i
$289$	−375685.	+	1.15624e6i	−0.264594	+	0.814336i
$290$	−409130.	−	1.25917e6i	−0.285671	−	0.879206i
$291$	−2.10044e6	+	1.52606e6i	−1.45404	+	1.05642i
$292$	−863092.	+	627073.i	−0.592380	+	0.430389i
$293$	−127927.	−	393718.i	−0.0870547	−	0.267927i	0.898047	−	0.439899i	$-0.144986\pi$
$293$	−127927.	−	393718.i	−0.0870547	−	0.267927i	−0.985102	+	0.171973i	$0.944986\pi$
$294$	−522145.	+	1.60700e6i	−0.352308	+	1.08429i
$295$	−2.35711e6	−	1.71254e6i	−1.57697	−	1.14574i
$296$	−51559.6			−0.0342043
$297$	−512487.	−	692868.i	−0.337125	−	0.455784i
$298$	−895631.			−0.584236
$299$	361111.	+	262363.i	0.233595	+	0.169716i
$300$	−402666.	+	1.23928e6i	−0.258311	+	0.794999i
$301$	−20592.1	−	63375.8i	−0.0131004	−	0.0403188i
$302$	2.68085e6	−	1.94775e6i	1.69143	−	1.22890i
$303$	79817.7	−	57990.9i	0.0499450	−	0.0362872i
$304$	831235.	+	2.55828e6i	0.515870	+	1.58768i
$305$	−381595.	+	1.17443e6i	−0.234884	+	0.722898i
$306$	379857.	+	275982.i	0.231908	+	0.168491i
$307$	−766604.			−0.464221			−0.232111	−	0.972689i	$-0.574563\pi$
$307$	−766604.			−0.464221			−0.232111	+	0.972689i	$0.574563\pi$
$308$	1.19071e6	+	1.60981e6i	0.715205	+	0.966937i
$309$	−1.30465e6			−0.777315
$310$	2.18157e6	+	1.58500e6i	1.28933	+	0.936754i
$311$	−463251.	+	1.42574e6i	−0.271591	+	0.835872i	0.718510	+	0.695517i	$0.244824\pi$
$311$	−463251.	+	1.42574e6i	−0.271591	+	0.835872i	−0.990101	+	0.140355i	$0.955176\pi$
$312$	17271.5	+	53156.3i	0.0100449	+	0.0309149i
$313$	−772853.	+	561510.i	−0.445898	+	0.323964i	−0.787974	−	0.615708i	$-0.788870\pi$
$313$	−772853.	+	561510.i	−0.445898	+	0.323964i	0.342076	+	0.939672i	$0.388870\pi$
$314$	3.12343e6	−	2.26931e6i	1.78775	−	1.29888i
$315$	−500067.	−	1.53905e6i	−0.283956	−	0.873928i
$316$	−115564.	+	355670.i	−0.0651037	+	0.200369i
$317$	−663718.	−	482219.i	−0.370967	−	0.269523i	0.386645	−	0.922229i	$-0.373634\pi$
$317$	−663718.	−	482219.i	−0.370967	−	0.269523i	−0.757612	+	0.652705i	$0.773634\pi$
$318$	−1.53734e6			−0.852515
$319$	873614.	−	292118.i	0.480666	−	0.160725i
$320$	−2.07337e6			−1.13188
$321$	−553397.	−	402067.i	−0.299761	−	0.217789i
$322$	1.05112e6	−	3.23500e6i	0.564951	−	1.73874i
$323$	345306.	+	1.06274e6i	0.184161	+	0.566789i
$324$	1.78107e6	−	1.29402e6i	0.942579	−	0.684824i
$325$	−314136.	+	228233.i	−0.164972	+	0.119859i
$326$	−160056.	−	492603.i	−0.0834121	−	0.256716i
$327$	845990.	−	2.60369e6i	0.437518	−	1.34654i
$328$	97007.5	+	70480.1i	0.0497875	+	0.0361728i
$329$	−224464.			−0.114329
$330$	−4.27551e6	−	1.34898e6i	−2.16124	−	0.681898i
$331$	3.51843e6			1.76514			0.882570	−	0.470181i	$-0.155811\pi$
$331$	3.51843e6			1.76514			0.882570	+	0.470181i	$0.155811\pi$
$332$	366624.	+	266368.i	0.182547	+	0.132628i
$333$	125765.	−	387064.i	0.0621511	−	0.191281i
$334$	−352231.	−	1.08406e6i	−0.172767	−	0.531723i
$335$	1.71476e6	−	1.24585e6i	0.834819	−	0.606531i
$336$	2.84635e6	−	2.06799e6i	1.37543	−	0.999311i
$337$	−137605.	−	423506.i	−0.0660025	−	0.203135i	0.912616	−	0.408817i	$-0.134059\pi$
$337$	−137605.	−	423506.i	−0.0660025	−	0.203135i	−0.978619	+	0.205682i	$0.934059\pi$
$338$	−830250.	+	2.55525e6i	−0.395291	+	1.21658i
$339$	929242.	+	675134.i	0.439167	+	0.319073i
$340$	−989645.			−0.464283
$341$	−1.08978e6	+	1.52719e6i	−0.507520	+	0.711224i
$342$	−2.57047e6			−1.18836
$343$	−772378.	−	561166.i	−0.354482	−	0.257547i
$344$	−2063.60	+	6351.09i	−0.000940218	+	0.00289369i
$345$	1.13627e6	+	3.49709e6i	0.513966	+	1.58183i
$346$	−1.34368e6	+	976239.i	−0.603399	+	0.438395i
$347$	−2.01515e6	+	1.46409e6i	−0.898429	+	0.652747i	−0.938062	−	0.346467i	$-0.887381\pi$
$347$	−2.01515e6	+	1.46409e6i	−0.898429	+	0.652747i	0.0396330	+	0.999214i	$0.487381\pi$
$348$	410381.	+	1.26302e6i	0.181652	+	0.559066i
$349$	−1.38913e6	+	4.27529e6i	−0.610490	+	1.87889i	−0.157097	+	0.987583i	$0.550214\pi$
$349$	−1.38913e6	+	4.27529e6i	−0.610490	+	1.87889i	−0.453393	+	0.891311i	$0.649786\pi$
$350$	2.39389e6	+	1.73926e6i	1.04456	+	0.758917i
$351$	370234.			0.160402
$352$	−27457.4	−	3.21802e6i	−0.0118114	−	1.38430i
$353$	1.74717e6			0.746273			0.373136	−	0.927776i	$-0.378282\pi$
$353$	1.74717e6			0.746273			0.373136	+	0.927776i	$0.378282\pi$
$354$	4.89705e6	+	3.55791e6i	2.07695	+	1.50899i
$355$	1.37666e6	−	4.23693e6i	0.579771	−	1.78435i
$356$	936769.	+	2.88308e6i	0.391749	+	1.20568i
$357$	1.18241e6	−	859070.i	0.491018	−	0.356745i
$358$	−4.63292e6	+	3.36601e6i	−1.91050	+	1.38806i
$359$	−1.34744e6	−	4.14699e6i	−0.551788	−	1.69823i	−0.704277	−	0.709925i	$-0.748729\pi$
$359$	−1.34744e6	−	4.14699e6i	−0.551788	−	1.69823i	0.152489	−	0.988305i	$-0.451271\pi$
$360$	−50113.3	+	154233.i	−0.0203796	+	0.0627221i
$361$	−2.94593e6	−	2.14034e6i	−1.18975	−	0.864401i
$362$	−4.93915e6			−1.98098
$363$	913141.	−	2.98260e6i	0.363723	−	1.18803i
$364$	−860204.			−0.340289
$365$	−2.11871e6	−	1.53933e6i	−0.832414	−	0.604784i
$366$	792790.	−	2.43996e6i	0.309354	−	0.952093i
$367$	1.00020e6	+	3.07829e6i	0.387633	+	1.19301i	0.934552	+	0.355825i	$0.115800\pi$
$367$	1.00020e6	+	3.07829e6i	0.387633	+	1.19301i	−0.546920	+	0.837185i	$0.684200\pi$
$368$	−2.27797e6	+	1.65504e6i	−0.876855	+	0.637073i
$369$	−765725.	+	556332.i	−0.292757	+	0.212700i
$370$	549043.	+	1.68978e6i	0.208498	+	0.641691i
$371$	−520841.	+	1.60298e6i	−0.196458	+	0.604636i
$372$	−2.18824e6	−	1.58985e6i	−0.819855	−	0.595659i
$373$	3.81558e6			1.42000			0.710000	−	0.704202i	$-0.248695\pi$
$373$	3.81558e6			1.42000			0.710000	+	0.704202i	$0.248695\pi$
$374$	−12168.0	−	1.42610e6i	−0.00449822	−	0.527193i
$375$	1.23957e6			0.455188
$376$	18198.3	+	13221.8i	0.00663835	+	0.00482305i
$377$	−122288.	+	376365.i	−0.0443130	+	0.136381i
$378$	−871855.	−	2.68329e6i	−0.313845	−	0.965914i
$379$	2.38365e6	−	1.73182e6i	0.852402	−	0.619307i	−0.0734051	−	0.997302i	$-0.523387\pi$
$379$	2.38365e6	−	1.73182e6i	0.852402	−	0.619307i	0.925807	+	0.377996i	$0.123387\pi$
$380$	4.38316e6	−	3.18455e6i	1.55714	−	1.13133i
$381$	1.62331e6	+	4.99604e6i	0.572914	+	1.76325i
$382$	1.49197e6	−	4.59180e6i	0.523119	−	1.60999i
$383$	1.02625e6	+	745611.i	0.357482	+	0.259726i	0.752001	−	0.659162i	$-0.229089\pi$
$383$	1.02625e6	+	745611.i	0.357482	+	0.259726i	−0.394519	+	0.918888i	$0.629089\pi$
$384$	−662472.			−0.229266
$385$	−2.85509e6	+	4.00105e6i	−0.981677	+	1.37569i
$386$	6.52733e6			2.22981
$387$	−42644.9	−	30983.3i	−0.0144740	−	0.0105160i
$388$	−1.23741e6	+	3.80835e6i	−0.417285	+	1.28427i
$389$	−72527.5	−	223217.i	−0.0243012	−	0.0747916i	0.938170	−	0.346174i	$-0.112519\pi$
$389$	−72527.5	−	223217.i	−0.0243012	−	0.0747916i	−0.962472	+	0.271382i	$0.912519\pi$
$390$	1.55819e6	−	1.13209e6i	0.518751	−	0.376894i
$391$	−946297.	+	687525.i	−0.313030	+	0.227429i
$392$	−57367.9	−	176560.i	−0.0188562	−	0.0580333i
$393$	2.15009e6	−	6.61729e6i	0.702223	−	2.16122i
$394$	−3.67748e6	−	2.67184e6i	−1.19346	−	0.867102i
$395$	−918027.			−0.296048
$396$	1.51049e6	+	476580.i	0.484039	+	0.152721i
$397$	−5.42749e6			−1.72831			−0.864157	−	0.503222i	$-0.832148\pi$
$397$	−5.42749e6			−1.72831			−0.864157	+	0.503222i	$0.832148\pi$
$398$	−505419.	−	367208.i	−0.159935	−	0.116200i
$399$	−2.47253e6	+	7.60968e6i	−0.777518	+	2.39295i
$400$	−756919.	−	2.32956e6i	−0.236537	−	0.727987i
$401$	121481.	−	88260.9i	0.0377265	−	0.0274099i	−0.568762	−	0.822502i	$-0.692578\pi$
$401$	121481.	−	88260.9i	0.0377265	−	0.0274099i	0.606489	+	0.795092i	$0.292578\pi$
$402$	−3.56254e6	+	2.58833e6i	−1.09950	+	0.798832i
$403$	−249067.	−	766550.i	−0.0763930	−	0.235114i
$404$	47022.0	−	144719.i	0.0143334	−	0.0441135i
$405$	4.37215e6	+	3.17655e6i	1.32452	+	0.962317i
$406$	3.01570e6			0.907972
$407$	−1.17237e6	+	392015.i	−0.350815	+	0.117305i
$408$	−146465.			−0.0435597
$409$	2.27528e6	+	1.65309e6i	0.672553	+	0.488638i	0.870879	−	0.491498i	$-0.163550\pi$
$409$	2.27528e6	+	1.65309e6i	0.672553	+	0.488638i	−0.198326	+	0.980136i	$0.563550\pi$
$410$	1.27686e6	−	3.92978e6i	0.375132	−	1.15454i
$411$	−1.57371e6	−	4.84338e6i	−0.459536	−	1.41431i
$412$	−1.62790e6	+	1.18274e6i	−0.472483	+	0.343279i
$413$	5.36892e6	−	3.90075e6i	1.54886	−	1.12531i
$414$	−831463.	−	2.55898e6i	−0.238420	−	0.733780i
$415$	−343763.	+	1.05799e6i	−0.0979804	+	0.301553i
$416$	1.11848e6	+	812625.i	0.316881	+	0.230227i
$417$	693621.			0.195336
$418$	4.64289e6	+	6.27705e6i	1.29971	+	1.75718i
$419$	−4.50355e6			−1.25320			−0.626599	−	0.779342i	$-0.715554\pi$
$419$	−4.50355e6			−1.25320			−0.626599	+	0.779342i	$0.715554\pi$
$420$	−5.73292e6	−	4.16521e6i	−1.58581	−	1.15216i
$421$	847872.	−	2.60948e6i	0.233144	−	0.717545i	−0.764218	−	0.644958i	$-0.776875\pi$
$421$	847872.	−	2.60948e6i	0.233144	−	0.717545i	0.997362	−	0.0725863i	$-0.0231253\pi$
$422$	1.34735e6	+	4.14673e6i	0.368299	+	1.13351i
$423$	−143647.	+	104366.i	−0.0390343	+	0.0283601i
$424$	136649.	−	99281.0i	0.0369139	−	0.0268195i
$425$	−314434.	−	967728.i	−0.0844417	−	0.259885i
$426$	−2.86011e6	+	8.80251e6i	−0.763587	+	2.35008i
$427$	−2.27555e6	−	1.65328e6i	−0.603972	−	0.438811i
$428$	−1.05501e6			−0.278386
$429$	796877.	+	1.07736e6i	0.209049	+	0.282628i
$430$	230121.			0.0600185
$431$	−557991.	−	405404.i	−0.144688	−	0.105122i	0.513086	−	0.858337i	$-0.328502\pi$
$431$	−557991.	−	405404.i	−0.144688	−	0.105122i	−0.657775	+	0.753215i	$0.728502\pi$
$432$	−721715.	+	2.22121e6i	−0.186061	+	0.572638i
$433$	−1.02133e6	−	3.14332e6i	−0.261785	−	0.805691i	−0.992417	−	0.122919i	$-0.960774\pi$
$433$	−1.02133e6	−	3.14332e6i	−0.261785	−	0.805691i	0.730632	−	0.682772i	$-0.239226\pi$
$434$	−4.96909e6	+	3.61026e6i	−1.26635	+	0.920055i
$435$	−2.63741e6	+	1.91619e6i	−0.668273	+	0.485529i
$436$	−1.30480e6	−	4.01575e6i	−0.328721	−	1.01170i
$437$	1.97880e6	−	6.09012e6i	0.495677	−	1.52554i
$438$	4.40176e6	+	3.19807e6i	1.09633	+	0.796530i
$439$	7.13877e6			1.76792			0.883959	−	0.467564i	$-0.154868\pi$
$439$	7.13877e6			1.76792			0.883959	+	0.467564i	$0.154868\pi$
$440$	467151.	−	156206.i	0.115034	−	0.0384649i
$441$	1.46539e6			0.358804
$442$	495667.	+	360123.i	0.120680	+	0.0876789i
$443$	−1.75678e6	+	5.40683e6i	−0.425314	+	1.30898i	0.477380	+	0.878697i	$0.341586\pi$
$443$	−1.75678e6	+	5.40683e6i	−0.425314	+	1.30898i	−0.902694	+	0.430284i	$0.858414\pi$
$444$	−550721.	−	1.69494e6i	−0.132579	−	0.408036i
$445$	−6.02035e6	+	4.37404e6i	−1.44119	+	1.04709i
$446$	−52102.4	+	37854.6i	−0.0124028	+	0.00901119i
$447$	681477.	+	2.09737e6i	0.161318	+	0.496485i
$448$	1.45938e6	−	4.49150e6i	0.343536	−	1.05729i
$449$	2.86753e6	+	2.08339e6i	0.671263	+	0.487701i	0.870448	−	0.492261i	$-0.163829\pi$
$449$	2.86753e6	+	2.08339e6i	0.671263	+	0.487701i	−0.199185	+	0.979962i	$0.563829\pi$
$450$	2.34066e6			0.544887
$451$	2.74164e6	+	865022.i	0.634701	+	0.200256i
$452$	1.77153e6			0.407852
$453$	−6.60104e6	−	4.79594e6i	−1.51136	−	1.09806i
$454$	−578167.	+	1.77942e6i	−0.131648	+	0.405171i
$455$	−652526.	−	2.00827e6i	−0.147764	−	0.454772i
$456$	648698.	−	471307.i	0.146093	−	0.106143i
$457$	1.66201e6	−	1.20752e6i	0.372258	−	0.270461i	−0.385889	−	0.922545i	$-0.626105\pi$
$457$	1.66201e6	−	1.20752e6i	0.372258	−	0.270461i	0.758147	+	0.652084i	$0.226105\pi$
$458$	−884684.	−	2.72278e6i	−0.197072	−	0.606525i
$459$	−299810.	+	922719.i	−0.0664223	+	0.204427i
$460$	4.58813e6	+	3.33347e6i	1.01098	+	0.734517i
$461$	−5.77944e6			−1.26658			−0.633291	−	0.773914i	$-0.718296\pi$
$461$	−5.77944e6			−1.26658			−0.633291	+	0.773914i	$0.718296\pi$
$462$	5.93165e6	−	8.31245e6i	1.29292	−	1.81186i
$463$	4.74214e6			1.02807			0.514034	−	0.857770i	$-0.328150\pi$
$463$	4.74214e6			1.02807			0.514034	+	0.857770i	$0.328150\pi$
$464$	−2.01961e6	−	1.46733e6i	−0.435484	−	0.316397i
$465$	2.05179e6	−	6.31477e6i	0.440049	−	1.35433i
$466$	−1.26698e6	−	3.89935e6i	−0.270274	−	0.831817i
$467$	3.14959e6	−	2.28831e6i	0.668286	−	0.485538i	−0.201165	−	0.979557i	$-0.564473\pi$
$467$	3.14959e6	−	2.28831e6i	0.668286	−	0.485538i	0.869451	+	0.494019i	$0.164473\pi$
$468$	−550492.	+	399956.i	−0.116181	+	0.0844107i
$469$	1.49189e6	+	4.59157e6i	0.313188	+	0.963893i
$470$	239535.	−	737213.i	0.0500178	−	0.153939i
$471$	−7.69081e6	−	5.58770e6i	−1.59742	−	1.16059i
$472$	−665050.			−0.137404
$473$	1366.05	+	160102.i	0.000280746	+	0.0329036i
$474$	1.90726e6			0.389910
$475$	4.50666e6	+	3.27428e6i	0.916475	+	0.665858i
$476$	696579.	−	2.14385e6i	0.140914	−	0.433687i
$477$	412000.	+	1.26801e6i	0.0829089	+	0.255167i
$478$	−1.14083e6	+	828863.i	−0.228377	+	0.165925i
$479$	−826321.	+	600358.i	−0.164555	+	0.119556i	−0.667015	−	0.745044i	$-0.732428\pi$
$479$	−826321.	+	600358.i	−0.164555	+	0.119556i	0.502460	+	0.864600i	$0.332428\pi$
$480$	3.51942e6	+	1.08317e7i	0.697217	+	2.14581i
$481$	164108.	−	505072.i	0.0323420	−	0.0995383i
$482$	6.85396e6	+	4.97969e6i	1.34377	+	0.976304i
$483$	−8.37545e6			−1.63358
$484$	−1.56451e6	−	4.54942e6i	−0.303575	−	0.882761i
$485$	−9.82979e6			−1.89754
$486$	−5.76266e6	−	4.18682e6i	−1.10671	−	0.804069i
$487$	−211456.	+	650796.i	−0.0404016	+	0.124343i	−0.969223	−	0.246184i	$-0.920823\pi$
$487$	−211456.	+	650796.i	−0.0404016	+	0.124343i	0.928821	+	0.370528i	$0.120823\pi$
$488$	87103.6	+	268077.i	0.0165572	+	0.0509578i
$489$	−1.03178e6	+	749633.i	−0.195126	+	0.141768i
$490$	−5.17557e6	+	3.76027e6i	−0.973796	+	0.707504i
$491$	2.94765e6	+	9.07194e6i	0.551789	+	1.69823i	0.704277	+	0.709925i	$0.251271\pi$
$491$	2.94765e6	+	9.07194e6i	0.551789	+	1.69823i	−0.152489	+	0.988305i	$0.548729\pi$
$492$	−1.28077e6	+	3.94179e6i	−0.238538	+	0.734144i
$493$	−838971.	−	609548.i	−0.155464	−	0.112951i
$494$	−3.35415e6			−0.618393
$495$	33173.8	+	3.88798e6i	0.00608530	+	0.713200i
$496$	5.08441e6			0.927976
$497$	8.20939e6	+	5.96447e6i	1.49080	+	1.08313i
$498$	714191.	−	2.19805e6i	0.129045	−	0.397160i
$499$	−610897.	−	1.88015e6i	−0.109829	−	0.338019i	0.881005	−	0.473108i	$-0.156868\pi$
$499$	−610897.	−	1.88015e6i	−0.109829	−	0.338019i	−0.990833	+	0.135089i	$0.956868\pi$
$500$	1.54670e6	−	1.12374e6i	0.276681	−	0.201021i
$501$	−2.27061e6	+	1.64969e6i	−0.404155	+	0.293636i
$502$	−3.56412e6	−	1.09692e7i	−0.631238	−	1.94275i
$503$	−292873.	+	901371.i	−0.0516130	+	0.158849i	−0.973541	−	0.228513i	$-0.926614\pi$
$503$	−292873.	+	901371.i	−0.0516130	+	0.158849i	0.921928	+	0.387362i	$0.126614\pi$
$504$	−298838.	−	217119.i	−0.0524035	−	0.0380733i
$505$	373537.			0.0651786
$506$	−4.74717e6	+	6.65256e6i	−0.824250	+	1.15508i
$507$	6.61555e6			1.14300
$508$	6.55473e6	+	4.76229e6i	1.12693	+	0.818759i
$509$	783457.	−	2.41123e6i	0.134036	−	0.412520i	−0.861403	−	0.507922i	$-0.830414\pi$
$509$	783457.	−	2.41123e6i	0.134036	−	0.412520i	0.995439	+	0.0954024i	$0.0304138\pi$
$510$	1.55967e6	+	4.80016e6i	0.265525	+	0.817203i
$511$	4.82591e6	−	3.50623e6i	0.817575	−	0.594003i
$512$	−6.58436e6	+	4.78381e6i	−1.11004	+	0.806491i
$513$	−1.64133e6	−	5.05149e6i	−0.275361	−	0.847473i
$514$	2.45642e6	−	7.56007e6i	0.410104	−	1.26217i
$515$	−3.99616e6	−	2.90338e6i	−0.663934	−	0.482376i
$516$	−230825.			−0.0381643
$517$	514322.	+	162275.i	0.0846269	+	0.0267009i
$518$	−4.04699e6			−0.662685
$519$	3.30853e6	+	2.40379e6i	0.539158	+	0.391722i
$520$	−65391.7	+	201255.i	−0.0106051	+	0.0326391i
$521$	−786163.	−	2.41956e6i	−0.126887	−	0.390519i	0.867353	−	0.497694i	$-0.165820\pi$
$521$	−786163.	−	2.41956e6i	−0.126887	−	0.390519i	−0.994240	+	0.107174i	$0.965820\pi$
$522$	1.92991e6	−	1.40216e6i	0.310000	−	0.225228i
$523$	1.47657e6	−	1.07279e6i	0.236048	−	0.171499i	−0.463473	−	0.886111i	$-0.653397\pi$
$523$	1.47657e6	−	1.07279e6i	0.236048	−	0.171499i	0.699521	+	0.714612i	$0.253397\pi$
$524$	−3.31615e6	−	1.02061e7i	−0.527601	−	1.62379i
$525$	2.25148e6	−	6.92934e6i	0.356508	−	1.09722i
$526$	−4.40488e6	−	3.20034e6i	−0.694177	−	0.504349i
$527$	2.11213e6			0.331279
$528$	−8.01696e6	+	2.68070e6i	−1.25148	+	0.418469i
$529$	266634.			0.0414263
$530$	−4.70890e6	−	3.42121e6i	−0.728165	−	0.529043i
$531$	1.62220e6	−	4.99261e6i	0.249671	−	0.768408i
$532$	3.81347e6	+	1.17367e7i	0.584173	+	1.79790i
$533$	−999177.	+	725945.i	−0.152344	+	0.110684i
$534$	1.25077e7	−	9.08737e6i	1.89812	−	1.37907i
$535$	−800302.	−	2.46308e6i	−0.120884	−	0.372043i
$536$	149507.	−	460136.i	0.0224776	−	0.0691789i
$537$	1.14076e7	+	8.28811e6i	1.70710	+	1.24028i
$538$	−1.04322e6			−0.155389
$539$	−2.64685e6	−	3.57847e6i	−0.392426	−	0.530549i
$540$	4.70404e6			0.694203
$541$	−6.07892e6	−	4.41659e6i	−0.892962	−	0.648775i	0.0436864	−	0.999045i	$-0.486090\pi$
$541$	−6.07892e6	−	4.41659e6i	−0.892962	−	0.648775i	−0.936649	+	0.350270i	$0.886090\pi$
$542$	−2.81319e6	+	8.65812e6i	−0.411340	+	1.26598i
$543$	3.75815e6	+	1.15664e7i	0.546984	+	1.68344i
$544$	−2.93100e6	+	2.12950e6i	−0.424638	+	0.308517i
$545$	8.38557e6	−	6.09247e6i	1.20932	−	0.878623i
$546$	1.35567e6	+	4.17231e6i	0.194613	+	0.598957i
$547$	−3.62875e6	+	1.11681e7i	−0.518548	+	1.59593i	0.258184	+	0.966096i	$0.416876\pi$
$547$	−3.62875e6	+	1.11681e7i	−0.518548	+	1.59593i	−0.776732	+	0.629831i	$0.783124\pi$
$548$	−6.35444e6	−	4.61677e6i	−0.903912	−	0.656731i
$549$	−2.22495e6			−0.315058
$550$	−4.22779e6	−	5.71586e6i	−0.595946	−	0.805703i
$551$	5.67726e6			0.796636
$552$	679032.	+	493346.i	0.0948512	+	0.0689134i
$553$	646169.	−	1.98870e6i	0.0898531	−	0.276540i
$554$	596386.	+	1.83549e6i	0.0825569	+	0.254084i
$555$	3.53933e6	−	2.57147e6i	0.487740	−	0.354364i
$556$	865482.	−	628809.i	0.118733	−	0.0862645i
$557$	1.16401e6	+	3.58245e6i	0.158971	+	0.489263i	0.998542	−	0.0539880i	$-0.0171933\pi$
$557$	1.16401e6	+	3.58245e6i	0.158971	+	0.489263i	−0.839570	+	0.543251i	$0.817193\pi$
$558$	−1.50139e6	+	4.62081e6i	−0.204131	+	0.628250i
$559$	−55646.4	−	40429.5i	−0.00753195	−	0.00547228i
$560$	1.33206e7			1.79495
$561$	−3.33035e6	+	1.11360e6i	−0.446768	+	0.149390i
$562$	−1.02774e7			−1.37259
$563$	5.45786e6	+	3.96536e6i	0.725690	+	0.527245i	0.888197	−	0.459463i	$-0.151958\pi$
$563$	5.45786e6	+	3.96536e6i	0.725690	+	0.527245i	−0.162507	+	0.986707i	$0.551958\pi$
$564$	−240267.	+	739467.i	−0.0318051	+	0.0978860i
$565$	1.34383e6	+	4.13589e6i	0.177102	+	0.545065i
$566$	−1.26474e6	+	918886.i	−0.165943	+	0.120565i
$567$	−9.95871e6	+	7.23542e6i	−1.30090	+	0.945162i
$568$	−314239.	−	967129.i	−0.0408686	−	0.125781i
$569$	2.14422e6	−	6.59922e6i	0.277644	−	0.854500i	−0.710864	−	0.703330i	$-0.751696\pi$
$569$	2.14422e6	−	6.59922e6i	0.277644	−	0.854500i	0.988508	−	0.151170i	$-0.0483042\pi$
$570$	−2.23541e7	−	1.62412e7i	−2.88184	−	2.09378i
$571$	−9.40986e6			−1.20779			−0.603897	−	0.797062i	$-0.706386\pi$
$571$	−9.40986e6			−1.20779			−0.603897	+	0.797062i	$0.706386\pi$
$572$	1.97101e6	+	621878.i	0.251883	+	0.0794722i
$573$	−1.18882e7			−1.51262
$574$	7.61426e6	+	5.53208e6i	0.964602	+	0.700824i
$575$	−1.80189e6	+	5.54564e6i	−0.227278	+	0.699491i
$576$	−1.15441e6	−	3.55290e6i	−0.144978	−	0.446197i
$577$	3.04535e6	−	2.21258e6i	0.380801	−	0.276668i	−0.380875	−	0.924627i	$-0.624377\pi$
$577$	3.04535e6	−	2.21258e6i	0.380801	−	0.276668i	0.761675	+	0.647959i	$0.224377\pi$
$578$	7.73654e6	−	5.62093e6i	0.963224	−	0.699823i
$579$	−4.96659e6	−	1.52856e7i	−0.615689	−	1.89490i
$580$	−1.55374e6	+	4.78193e6i	−0.191783	+	0.590246i
$581$	−2.04995e6	−	1.48937e6i	−0.251943	−	0.183047i
$582$	2.04221e7			2.49915
$583$	2.35228e6	−	3.29642e6i	0.286628	−	0.401672i
$584$	−597787.			−0.0725295
$585$	−1.35134e6	−	981807.i	−0.163258	−	0.118614i
$586$	−1.00626e6	+	3.09694e6i	−0.121050	+	0.372553i
$587$	−3.22700e6	−	9.93168e6i	−0.386548	−	1.18967i	−0.935351	−	0.353721i	$-0.884916\pi$
$587$	−3.22700e6	−	9.93168e6i	−0.386548	−	1.18967i	0.548803	−	0.835952i	$-0.315084\pi$
$588$	5.19139e6	−	3.77177e6i	0.619214	−	0.449885i
$589$	−9.35467e6	+	6.79656e6i	−1.11107	+	0.807237i
$590$	7.08192e6	+	2.17959e7i	0.837570	+	2.57777i
$591$	−3.45871e6	+	1.06448e7i	−0.407329	+	1.25363i
$592$	2.71026e6	+	1.96912e6i	0.317839	+	0.230923i
$593$	6.86016e6			0.801120			0.400560	−	0.916271i	$-0.368816\pi$
$593$	6.86016e6			0.801120			0.400560	+	0.916271i	$0.368816\pi$
$594$	57837.7	+	6.77861e6i	0.00672582	+	0.788269i
$595$	5.53353e6			0.640781
$596$	2.75172e6	+	1.99924e6i	0.317314	+	0.230542i
$597$	−475352.	+	1.46298e6i	−0.0545858	+	0.167998i
$598$	−1.08496e6	−	3.33916e6i	−0.124068	−	0.381842i
$599$	2.45587e6	−	1.78429e6i	0.279665	−	0.203189i	−0.439106	−	0.898435i	$-0.644705\pi$
$599$	2.45587e6	−	1.78429e6i	0.279665	−	0.203189i	0.718771	+	0.695247i	$0.244705\pi$
$600$	−590701.	+	429170.i	−0.0669869	+	0.0486688i
$601$	3.98521e6	+	1.22652e7i	0.450054	+	1.38512i	0.876844	+	0.480774i	$0.159644\pi$
$601$	3.98521e6	+	1.22652e7i	0.450054	+	1.38512i	−0.426790	+	0.904351i	$0.640356\pi$
$602$	−161975.	+	498507.i	−0.0182161	+	0.0560634i
$603$	3.08962e6	+	2.24474e6i	0.346028	+	0.251404i
$604$	−1.25844e7			−1.40359
$605$	9.43449e6	−	7.10364e6i	1.04792	−	0.789029i
$606$	−776048.			−0.0858434
$607$	−1.43107e7	−	1.03973e7i	−1.57648	−	1.14538i	−0.920592	−	0.390525i	$-0.872293\pi$
$607$	−1.43107e7	−	1.03973e7i	−1.57648	−	1.14538i	−0.655890	−	0.754856i	$-0.727707\pi$
$608$	6.12901e6	−	1.88632e7i	0.672406	−	2.06945i
$609$	−2.29462e6	−	7.06210e6i	−0.250707	−	0.771597i
$610$	7.85824e6	−	5.70935e6i	0.855068	−	0.621244i
$611$	−187442.	+	136185.i	−0.0203125	+	0.0147579i
$612$	−551014.	−	1.69585e6i	−0.0594681	−	0.183024i
$613$	−5.45654e6	+	1.67935e7i	−0.586497	+	1.80505i	0.00667637	+	0.999978i	$0.497875\pi$
$613$	−5.45654e6	+	1.67935e7i	−0.586497	+	1.80505i	−0.593173	+	0.805075i	$0.702125\pi$
$614$	4.87838e6	+	3.54435e6i	0.522221	+	0.379416i
$615$	−1.01742e7			−1.08471
$616$	9572.73	+	1.12193e6i	0.00101645	+	0.119128i
$617$	−1.06278e7			−1.12390			−0.561951	−	0.827170i	$-0.689949\pi$
$617$	−1.06278e7			−1.12390			−0.561951	+	0.827170i	$0.689949\pi$
$618$	8.30230e6	+	6.03197e6i	0.874434	+	0.635314i
$619$	−559306.	+	1.72137e6i	−0.0586709	+	0.180571i	−0.976097	−	0.217336i	$-0.930263\pi$
$619$	−559306.	+	1.72137e6i	−0.0586709	+	0.180571i	0.917426	+	0.397907i	$0.130263\pi$
$620$	−3.16454e6	−	9.73946e6i	−0.330622	−	1.01755i
$621$	4.49799e6	−	3.26798e6i	0.468047	−	0.340056i
$622$	9.53980e6	−	6.93107e6i	0.988697	−	0.718330i
$623$	−5.23787e6	−	1.61205e7i	−0.540673	−	1.66402i
$624$	1.12221e6	−	3.45381e6i	0.115375	−	0.355089i
$625$	9.49083e6	+	6.89549e6i	0.971861	+	0.706099i
$626$	7.51426e6			0.766391
$627$	1.11668e7	−	1.56488e7i	1.13438	−	1.58969i
$628$	−1.46620e7			−1.48352
$629$	1.12588e6	+	817997.i	0.113466	+	0.0824376i
$630$	−3.93346e6	+	1.21060e7i	−0.394842	+	1.21520i
$631$	−4.66477e6	−	1.43567e7i	−0.466398	−	1.43542i	−0.857216	−	0.514957i	$-0.827808\pi$
$631$	−4.66477e6	−	1.43567e7i	−0.466398	−	1.43542i	0.390818	−	0.920468i	$-0.372192\pi$
$632$	−169530.	+	123171.i	−0.0168831	+	0.0122663i
$633$	8.68554e6	−	6.31041e6i	0.861564	−	0.625963i
$634$	1.99414e6	+	6.13733e6i	0.197030	+	0.606396i
$635$	−6.14601e6	+	1.89155e7i	−0.604866	+	1.86159i
$636$	4.72329e6	+	3.43167e6i	0.463022	+	0.336406i
$637$	1.91216e6			0.186713
$638$	−6.90995e6	−	2.18018e6i	−0.672084	−	0.212051i
$639$	8.02686e6			0.777666
$640$	−2.02916e6	−	1.47427e6i	−0.195825	−	0.142275i
$641$	259308.	−	798067.i	0.0249270	−	0.0767175i	−0.937819	−	0.347124i	$-0.887158\pi$
$641$	259308.	−	798067.i	0.0249270	−	0.0767175i	0.962746	+	0.270407i	$0.0871582\pi$
$642$	1.66268e6	+	5.11721e6i	0.159210	+	0.489999i
$643$	−9.95423e6	+	7.23217e6i	−0.949467	+	0.689828i	−0.950681	−	0.310171i	$-0.899614\pi$
$643$	−9.95423e6	+	7.23217e6i	−0.949467	+	0.689828i	0.00121342	+	0.999999i	$0.499614\pi$
$644$	−1.04507e7	+	7.59285e6i	−0.992953	+	0.721423i
$645$	−175097.	−	538893.i	−0.0165722	−	0.0510039i
$646$	2.71613e6	−	8.35940e6i	0.256077	−	0.788123i
$647$	−5.92951e6	−	4.30804e6i	−0.556876	−	0.404594i	0.273439	−	0.961889i	$-0.411839\pi$
$647$	−5.92951e6	−	4.30804e6i	−0.556876	−	0.404594i	−0.830314	+	0.557296i	$0.811839\pi$
$648$	1.23359e6			0.115407
$649$	−1.51220e7	+	5.05648e6i	−1.40928	+	0.471234i
$650$	3.05427e6			0.283547
$651$	1.22354e7	+	8.88951e6i	1.13153	+	0.822101i
$652$	−607842.	+	1.87074e6i	−0.0559979	+	0.172344i
$653$	5.51856e6	+	1.69844e7i	0.506457	+	1.55871i	0.798307	+	0.602250i	$0.205729\pi$
$653$	5.51856e6	+	1.69844e7i	0.506457	+	1.55871i	−0.291851	+	0.956464i	$0.594271\pi$
$654$	−1.74216e7	+	1.26575e7i	−1.59273	+	1.15719i
$655$	2.13120e7	−	1.54841e7i	1.94098	−	1.41020i
$656$	−2.40754e6	−	7.40965e6i	−0.218431	−	0.672262i
$657$	1.45813e6	−	4.48766e6i	0.131790	−	0.405608i
$658$	1.42841e6	+	1.03780e6i	0.128614	+	0.0934434i
$659$	2.63581e6			0.236429			0.118215	−	0.992988i	$-0.462283\pi$
$659$	2.63581e6			0.236429			0.118215	+	0.992988i	$0.462283\pi$
$660$	1.01248e7	+	1.36884e7i	0.904745	+	1.22319i
$661$	1.63578e7			1.45620			0.728100	−	0.685471i	$-0.240403\pi$
$661$	1.63578e7			1.45620			0.728100	+	0.685471i	$0.240403\pi$
$662$	−2.23900e7	−	1.62673e7i	−1.98568	−	1.44268i
$663$	466181.	−	1.43476e6i	0.0411880	−	0.126764i
$664$	78467.9	+	241499.i	0.00690672	+	0.0212567i
$665$	−2.45081e7	+	1.78062e7i	−2.14909	+	1.56141i
$666$	−2.58989e6	+	1.88167e6i	−0.226254	+	0.164383i
$667$	1.83641e6	+	5.65189e6i	0.159829	+	0.491902i
$668$	−1.33766e6	+	4.11689e6i	−0.115986	+	0.356967i
$669$	128291.	+	93209.2i	0.0110824	+	0.00805181i
$670$	−1.66722e7			−1.43485
$671$	4.01880e6	+	5.43331e6i	0.344580	+	0.465863i
$672$	−2.59416e7			−2.21602
$673$	3.30858e6	+	2.40383e6i	0.281582	+	0.204581i	0.719607	−	0.694382i	$-0.244322\pi$
$673$	3.30858e6	+	2.40383e6i	0.281582	+	0.204581i	−0.438025	+	0.898963i	$0.644322\pi$
$674$	−1.08239e6	+	3.33124e6i	−0.0917768	+	0.282460i
$675$	1.49459e6	+	4.59986e6i	0.126259	+	0.388585i
$676$	8.25471e6	−	5.99740e6i	0.694760	−	0.504773i
$677$	−9.89407e6	+	7.18846e6i	−0.829666	+	0.602788i	−0.919465	−	0.393172i	$-0.871378\pi$
$677$	−9.89407e6	+	7.18846e6i	−0.829666	+	0.602788i	0.0897989	+	0.995960i	$0.471378\pi$
$678$	−2.79190e6	−	8.59260e6i	−0.233253	−	0.717877i
$679$	6.91887e6	−	2.12941e7i	0.575918	−	1.77249i
$680$	−448626.	−	325946.i	−0.0372059	−	0.0270317i
$681$	4.60692e6			0.380665
$682$	1.39958e7	−	4.67991e6i	1.15223	−	0.385280i
$683$	1.91987e7			1.57478			0.787391	−	0.616454i	$-0.211431\pi$
$683$	1.91987e7			1.57478			0.787391	+	0.616454i	$0.211431\pi$
$684$	7.89746e6	+	5.73784e6i	0.645427	+	0.468930i
$685$	5.95822e6	−	1.83375e7i	0.485166	−	1.49319i
$686$	2.32061e6	+	7.14210e6i	0.188275	+	0.579450i
$687$	−5.70300e6	+	4.14347e6i	−0.461011	+	0.334944i
$688$	351030.	−	255038.i	0.0282730	−	0.0205416i
$689$	537610.	+	1.65459e6i	0.0431439	+	0.132783i
$690$	8.93778e6	−	2.75076e7i	0.714672	−	2.19953i
$691$	5.35884e6	+	3.89342e6i	0.426948	+	0.310196i	0.780428	−	0.625246i	$-0.215001\pi$
$691$	5.35884e6	+	3.89342e6i	0.426948	+	0.310196i	−0.353479	+	0.935442i	$0.615001\pi$
$692$	6.30747e6			0.500714
$693$	−8.44581e6	−	2.66476e6i	−0.668049	−	0.210778i
$694$	1.95928e7			1.54418
$695$	2.12458e6	+	1.54359e6i	0.166844	+	0.121219i
$696$	−229951.	+	707715.i	−0.0179933	+	0.0553778i
$697$	−1.00012e6	−	3.07807e6i	−0.0779780	−	0.239992i
$698$	2.86065e7	−	2.07838e7i	2.22242	−	1.61468i
$699$	−8.16740e6	+	5.93396e6i	−0.632253	+	0.459359i
$700$	−3.47253e6	−	1.06873e7i	−0.267856	−	0.824375i
$701$	992573.	−	3.05482e6i	0.0762899	−	0.234796i	−0.905638	−	0.424052i	$-0.860607\pi$
$701$	992573.	−	3.05482e6i	0.0762899	−	0.234796i	0.981928	+	0.189256i	$0.0606074\pi$
$702$	−2.35603e6	−	1.71176e6i	−0.180442	−	0.131099i
$703$	−7.61874e6			−0.581427
$704$	−6.59100e6	+	9.23644e6i	−0.501210	+	0.702382i
$705$	−1.90865e6			−0.144628
$706$	−1.11183e7	−	8.07794e6i	−0.839513	−	0.609942i
$707$	−262920.	+	809185.i	−0.0197822	+	0.0608835i
$708$	−7.10357e6	−	2.18625e7i	−0.532590	−	1.63914i
$709$	591691.	−	429889.i	0.0442058	−	0.0321174i	−0.565463	−	0.824774i	$-0.691302\pi$
$709$	591691.	−	429889.i	0.0442058	−	0.0321174i	0.609669	+	0.792656i	$0.291302\pi$
$710$	−2.83498e7	+	2.05973e7i	−2.11059	+	1.53343i
$711$	−511138.	−	1.57312e6i	−0.0379196	−	0.116705i
$712$	−524904.	+	1.61549e6i	−0.0388043	+	0.119427i
$713$	−9.79211e6	−	7.11439e6i	−0.721361	−	0.524099i
$714$	−1.14963e7			−0.843940
$715$	43287.7	+	5.07334e6i	0.00316665	+	0.371133i
$716$	2.17478e7			1.58538
$717$	2.80906e6	+	2.04090e6i	0.204063	+	0.148260i
$718$	−1.05988e7	+	3.26197e7i	−0.767264	+	2.36140i
$719$	1.15550e6	+	3.55626e6i	0.0833579	+	0.256549i	0.984045	−	0.177919i	$-0.0569364\pi$
$719$	1.15550e6	+	3.55626e6i	0.0833579	+	0.256549i	−0.900687	+	0.434468i	$0.856936\pi$
$720$	8.52456e6	−	6.19345e6i	0.612831	−	0.445248i
$721$	9.10230e6	−	6.61321e6i	0.652098	−	0.473777i
$722$	8.85103e6	+	2.72407e7i	0.631904	+	1.94480i
$723$	6.44624e6	−	1.98395e7i	0.458628	−	1.41151i
$724$	1.51750e7	+	1.10253e7i	1.07592	+	0.781704i
$725$	−5.16969e6			−0.365275
$726$	−1.96008e7	+	1.47583e7i	−1.38017	+	1.03919i
$727$	−1.55643e7			−1.09218			−0.546088	−	0.837728i	$-0.683884\pi$
$727$	−1.55643e7			−1.09218			−0.546088	+	0.837728i	$0.683884\pi$
$728$	−389947.	−	283313.i	−0.0272695	−	0.0198125i
$729$	114240.	−	351595.i	0.00796160	−	0.0245033i
$730$	6.36566e6	+	1.95915e7i	0.442116	+	1.36069i
$731$	145822.	−	105946.i	0.0100932	−	0.00733316i
$732$	−7.88226e6	+	5.72680e6i	−0.543717	+	0.395034i
$733$	5.76528e6	+	1.77437e7i	0.396334	+	1.21979i	0.927918	+	0.372784i	$0.121597\pi$
$733$	5.76528e6	+	1.77437e7i	0.396334	+	1.21979i	−0.531585	+	0.847005i	$0.678403\pi$
$734$	7.86742e6	−	2.42134e7i	0.539005	−	1.65889i
$735$	1.27438e7	+	9.25889e6i	0.870121	+	0.632180i
$736$	2.07614e7			1.41274
$737$	−98970.1	−	1.15993e7i	−0.00671174	−	0.786619i
$738$	7.44496e6			0.503178
$739$	−1.76021e7	−	1.27887e7i	−1.18564	−	0.861419i	−0.192845	−	0.981229i	$-0.561771\pi$
$739$	−1.76021e7	−	1.27887e7i	−1.18564	−	0.861419i	−0.992797	+	0.119810i	$0.961771\pi$
$740$	2.08508e6	−	6.41723e6i	0.139973	−	0.430793i
$741$	2.55214e6	+	7.85468e6i	0.170749	+	0.525512i
$742$	1.07257e7	−	7.79271e6i	0.715184	−	0.519612i
$743$	−2.16453e7	+	1.57262e7i	−1.43844	+	1.04509i	−0.450075	+	0.892991i	$0.648603\pi$
$743$	−2.16453e7	+	1.57262e7i	−1.43844	+	1.04509i	−0.988366	+	0.152097i	$0.951397\pi$
$744$	−468345.	−	1.44142e6i	−0.0310194	−	0.0954680i
$745$	−2.58014e6	+	7.94086e6i	−0.170315	+	0.524175i
$746$	−2.42809e7	−	1.76411e7i	−1.59742	−	1.16059i
$747$	−2.00437e6			−0.131424
$748$	−3.14597e6	+	4.40868e6i	−0.205589	+	0.288107i
$749$	5.89902e6			0.384216
$750$	−7.88813e6	−	5.73106e6i	−0.512060	−	0.372034i
$751$	387453.	−	1.19246e6i	0.0250680	−	0.0771513i	−0.937740	−	0.347338i	$-0.887086\pi$
$751$	387453.	−	1.19246e6i	0.0250680	−	0.0771513i	0.962808	+	0.270187i	$0.0870855\pi$
$752$	−451646.	−	1.39002e6i	−0.0291242	−	0.0896351i
$753$	−2.29756e7	+	1.66928e7i	−1.47666	+	1.07285i
$754$	2.51830e6	−	1.82965e6i	0.161317	−	0.117203i
$755$	−9.54617e6	−	2.93801e7i	−0.609483	−	1.87580i
$756$	−3.31102e6	+	1.01903e7i	−0.210696	+	0.648457i
$757$	−893821.	−	649399.i	−0.0566906	−	0.0411881i	0.559079	−	0.829114i	$-0.311155\pi$
$757$	−893821.	−	649399.i	−0.0566906	−	0.0411881i	−0.615770	+	0.787926i	$0.711155\pi$
$758$	−2.31757e7			−1.46507
$759$	1.91909e7	+	6.05497e6i	1.20918	+	0.381512i
$760$	3.03583e6			0.190653
$761$	1.64027e7	+	1.19173e7i	1.02672	+	0.745959i	0.967650	−	0.252295i	$-0.0811853\pi$
$761$	1.64027e7	+	1.19173e7i	1.02672	+	0.745959i	0.0590736	+	0.998254i	$0.481185\pi$
$762$	1.27688e7	−	3.92982e7i	0.796638	−	2.45180i
$763$	7.29568e6	+	2.24538e7i	0.453685	+	1.39630i
$764$	−1.48338e7	+	1.07774e7i	−0.919429	+	0.668004i
$765$	3.54121e6	−	2.57284e6i	0.218775	−	0.158950i
$766$	−3.08335e6	−	9.48959e6i	−0.189868	−	0.584353i
$767$	2.11677e6	−	6.51475e6i	0.129923	−	0.399861i
$768$	1.83930e7	+	1.33633e7i	1.12525	+	0.817542i
$769$	1.22086e7			0.744475			0.372237	−	0.928138i	$-0.378591\pi$
$769$	1.22086e7			0.744475			0.372237	+	0.928138i	$0.378591\pi$
$770$	3.66674e7	−	1.22608e7i	2.22871	−	0.745233i
$771$	−1.95731e7			−1.18583
$772$	−2.00545e7	−	1.45704e7i	−1.21107	−	0.879891i
$773$	3.44879e6	−	1.06143e7i	0.207596	−	0.638914i	−0.792001	−	0.610520i	$-0.790961\pi$
$773$	3.44879e6	−	1.06143e7i	0.207596	−	0.638914i	0.999597	−	0.0283941i	$-0.00903935\pi$
$774$	128127.	+	394333.i	0.00768753	+	0.0236598i
$775$	8.51832e6	−	6.18892e6i	0.509448	−	0.370135i
$776$	−1.81524e6	+	1.31885e6i	−0.108213	+	0.0786216i
$777$	3.07931e6	+	9.47716e6i	0.182979	+	0.563152i
$778$	−570492.	+	1.75579e6i	−0.0337910	+	0.103998i
$779$	1.43344e7	+	1.04145e7i	0.846322	+	0.614889i
$780$	−7.31442e6			−0.430471
$781$	−1.44984e7	−	1.96015e7i	−0.850538	−	1.14990i
$782$	9.20062e6			0.538022
$783$	3.98784e6	+	2.89734e6i	0.232452	+	0.168886i
$784$	−3.72746e6	+	1.14719e7i	−0.216582	+	0.666571i
$785$	−1.11221e7	−	3.42304e7i	−0.644191	−	1.98262i
$786$	−4.42771e7	+	3.21692e7i	−2.55636	+	1.85731i
$787$	9.60832e6	−	6.98086e6i	0.552982	−	0.401765i	−0.275902	−	0.961186i	$-0.588976\pi$
$787$	9.60832e6	−	6.98086e6i	0.552982	−	0.401765i	0.828884	+	0.559421i	$0.188976\pi$
$788$	5.33448e6	+	1.64178e7i	0.306039	+	0.941891i
$789$	−4.14285e6	+	1.27504e7i	−0.236923	+	0.729173i
$790$	5.84198e6	+	4.24445e6i	0.333037	+	0.241966i
$791$	−9.90538e6			−0.562898
$792$	527772.	+	713533.i	0.0298974	+	0.0404205i
$793$	−2.90329e6			−0.163949
$794$	3.45385e7	+	2.50937e7i	1.94425	+	1.41258i
$795$	−4.42878e6	+	1.36304e7i	−0.248523	+	0.764874i
$796$	733151.	+	2.25641e6i	0.0410120	+	0.126222i
$797$	2.40104e7	−	1.74446e7i	1.33892	−	0.972781i	0.339436	−	0.940629i	$-0.389764\pi$
$797$	2.40104e7	−	1.74446e7i	1.33892	−	0.972781i	0.999483	−	0.0321520i	$-0.0102361\pi$
$798$	5.09172e7	−	3.69935e7i	2.83046	−	2.05645i
$799$	−187620.	−	577434.i	−0.0103971	−	0.0319989i
$800$	−5.58105e6	+	1.71767e7i	−0.308312	+	0.948888i
$801$	−1.08473e7	−	7.88104e6i	−0.597367	−	0.434012i
$802$	−1.18113e6			−0.0648427
$803$	−1.35926e7	+	4.54507e6i	−0.743896	+	0.248743i
$804$	1.67232e7			0.912387
$805$	−2.56542e7	−	1.86388e7i	−1.39530	−	1.01375i
$806$	−1.95913e6	+	6.02959e6i	−0.106225	+	0.326926i
$807$	793776.	+	2.44299e6i	0.0429056	+	0.132050i
$808$	68980.1	−	50117.0i	0.00371703	−	0.00270058i
$809$	1.42224e7	−	1.03332e7i	0.764017	−	0.555091i	−0.136123	−	0.990692i	$-0.543464\pi$
$809$	1.42224e7	−	1.03332e7i	0.764017	−	0.555091i	0.900140	+	0.435601i	$0.143464\pi$
$810$	−1.31361e7	−	4.04288e7i	−0.703484	−	2.16510i
$811$	−1.68232e6	+	5.17766e6i	−0.0898168	+	0.276428i	−0.985868	−	0.167522i	$-0.946423\pi$
$811$	−1.68232e6	+	5.17766e6i	−0.0898168	+	0.276428i	0.896051	+	0.443950i	$0.146423\pi$
$812$	−9.26537e6	−	6.73169e6i	−0.493143	−	0.358289i
$813$	2.24159e7			1.18941
$814$	9.27298e6	+	2.92574e6i	0.490522	+	0.154766i
$815$	−4.82861e6			−0.254641
$816$	7.69904e6	+	5.59368e6i	0.404772	+	0.294084i
$817$	−304929.	+	938474.i	−0.0159824	+	0.0491889i
$818$	−6.83607e6	−	2.10393e7i	−0.357210	−	1.09938i
$819$	3.07803e6	−	2.23632e6i	0.160348	−	0.116500i
$820$	−1.26951e7	+	9.22355e6i	−0.659329	+	0.479031i
$821$	4.69029e6	+	1.44352e7i	0.242852	+	0.747422i	0.995982	+	0.0895502i	$0.0285430\pi$
$821$	4.69029e6	+	1.44352e7i	0.242852	+	0.747422i	−0.753130	+	0.657871i	$0.771457\pi$
$822$	−1.23786e7	+	3.80974e7i	−0.638987	+	1.96660i
$823$	27134.1	+	19714.1i	0.00139642	+	0.00101456i	0.588483	−	0.808509i	$-0.299725\pi$
$823$	27134.1	+	19714.1i	0.00139642	+	0.00101456i	−0.587087	+	0.809524i	$0.699725\pi$
$824$	−1.12750e6			−0.0578496
$825$	−1.01684e7	+	1.42497e7i	−0.520137	+	0.728905i
$826$	−5.22008e7			−2.66211
$827$	−3.18016e6	−	2.31052e6i	−0.161691	−	0.117475i	0.503998	−	0.863705i	$-0.331862\pi$
$827$	−3.18016e6	−	2.31052e6i	−0.161691	−	0.117475i	−0.665688	+	0.746230i	$0.731862\pi$
$828$	−3.15762e6	+	9.71817e6i	−0.160061	+	0.492616i
$829$	−9.59666e6	−	2.95355e7i	−0.484991	−	1.49265i	−0.831993	−	0.554785i	$-0.812800\pi$
$829$	−9.59666e6	−	2.95355e7i	−0.484991	−	1.49265i	0.347002	−	0.937864i	$-0.387200\pi$
$830$	7.07916e6	−	5.14331e6i	0.356686	−	0.259148i
$831$	3.84453e6	−	2.79321e6i	0.193126	−	0.140314i
$832$	−1.50636e6	−	4.63610e6i	−0.0754433	−	0.232191i
$833$	−1.54843e6	+	4.76559e6i	−0.0773179	+	0.237960i
$834$	−4.41395e6	−	3.20692e6i	−0.219742	−	0.159652i
$835$	−1.06262e7			−0.527425
$836$	−252981.	−	2.96494e7i	−0.0125191	−	1.46724i
$837$	−1.00395e7			−0.495335
$838$	2.86589e7	+	2.08219e7i	1.40977	+	1.02426i
$839$	−5.45493e6	+	1.67885e7i	−0.267537	+	0.823394i	0.723561	+	0.690260i	$0.242504\pi$
$839$	−5.45493e6	+	1.67885e7i	−0.267537	+	0.823394i	−0.991098	+	0.133134i	$0.957496\pi$
$840$	−1.22701e6	−	3.77634e6i	−0.0599997	−	0.184660i
$841$	1.23314e7	−	8.95927e6i	0.601203	−	0.436800i
$842$	−1.74603e7	+	1.26857e7i	−0.848736	+	0.616643i
$843$	7.81996e6	+	2.40674e7i	0.378997	+	1.16643i
$844$	5.11681e6	−	1.57479e7i	0.247254	−	0.760969i
$845$	2.02636e7	+	1.47223e7i	0.976279	+	0.709308i
$846$	1.39665e6			0.0670905
$847$	8.74786e6	+	2.54378e7i	0.418980	+	1.21835i
$848$	−1.09747e7			−0.524085
$849$	3.11415e6	+	2.26257e6i	0.148276	+	0.107729i
$850$	−2.47330e6	+	7.61203e6i	−0.117417	+	0.361371i
$851$	−2.46441e6	−	7.58469e6i	−0.116651	−	0.359016i
$852$	2.84365e7	−	2.06603e7i	1.34207	−	0.975074i
$853$	−2.20539e7	+	1.60231e7i	−1.03780	+	0.754003i	−0.969854	−	0.243686i	$-0.921643\pi$
$853$	−2.20539e7	+	1.60231e7i	−1.03780	+	0.754003i	−0.0679421	+	0.997689i	$0.521643\pi$
$854$	6.83689e6	+	2.10418e7i	0.320785	+	0.987274i
$855$	−7.40502e6	+	2.27903e7i	−0.346427	+	1.06619i
$856$	−478258.	−	347475.i	−0.0223089	−	0.0162083i
$857$	2.11835e7			0.985248			0.492624	−	0.870242i	$-0.336038\pi$
$857$	2.11835e7			0.985248			0.492624	+	0.870242i	$0.336038\pi$
$858$	−89933.2	−	1.05402e7i	−0.00417063	−	0.488800i
$859$	−651618.			−0.0301308			−0.0150654	−	0.999887i	$-0.504796\pi$
$859$	−651618.			−0.0301308			−0.0150654	+	0.999887i	$0.504796\pi$
$860$	−707020.	−	513680.i	−0.0325976	−	0.0236835i
$861$	7.16131e6	−	2.20402e7i	0.329219	−	1.01323i
$862$	1.67648e6	+	5.15968e6i	0.0768477	+	0.236513i
$863$	−7.41391e6	+	5.38652e6i	−0.338860	+	0.246196i	−0.744181	−	0.667978i	$-0.767160\pi$
$863$	−7.41391e6	+	5.38652e6i	−0.338860	+	0.246196i	0.405321	+	0.914175i	$0.367160\pi$
$864$	1.39318e7	−	1.01220e7i	0.634926	−	0.461301i
$865$	4.78466e6	+	1.47257e7i	0.217426	+	0.669168i
$866$	−8.03362e6	+	2.47250e7i	−0.364013	+	1.12032i
$867$	−1.90496e7	−	1.38404e7i	−0.860674	−	0.625317i
$868$	2.33258e7			1.05084
$869$	−2.91830e6	+	4.08963e6i	−0.131094	+	0.183711i
$870$	2.56429e7			1.14860
$871$	4.03157e6	+	2.92911e6i	0.180065	+	0.130825i
$872$	731123.	−	2.25016e6i	0.0325611	−	0.100213i
$873$	−5.47302e6	−	1.68442e7i	−0.243048	−	0.748024i
$874$	−4.07497e7	+	2.96064e7i	−1.80445	+	1.31101i
$875$	−8.64823e6	+	6.28331e6i	−0.381863	+	0.277439i
$876$	−6.38512e6	−	1.96514e7i	−0.281131	−	0.865232i
$877$	7.43000e6	−	2.28672e7i	0.326204	−	1.00395i	−0.644690	−	0.764444i	$-0.723014\pi$
$877$	7.43000e6	−	2.28672e7i	0.326204	−	1.00395i	0.970894	−	0.239509i	$-0.0769865\pi$
$878$	−4.54285e7	−	3.30057e7i	−1.98881	−	1.44495i
$879$	8.01799e6			0.350021
$880$	−3.05218e7	−	9.63000e6i	−1.32863	−	0.419198i
$881$	−4.64205e6			−0.201498			−0.100749	−	0.994912i	$-0.532124\pi$
$881$	−4.64205e6			−0.201498			−0.100749	+	0.994912i	$0.532124\pi$
$882$	−9.32521e6	−	6.77516e6i	−0.403633	−	0.293257i
$883$	642034.	−	1.97598e6i	0.0277112	−	0.0852864i	−0.936244	−	0.351349i	$-0.885723\pi$
$883$	642034.	−	1.97598e6i	0.0277112	−	0.0852864i	0.963956	+	0.266063i	$0.0857229\pi$
$884$	−719005.	−	2.21287e6i	−0.0309458	−	0.0952413i
$885$	4.56527e7	−	3.31686e7i	1.95933	−	1.42354i
$886$	3.61777e7	−	2.62846e7i	1.54831	−	1.12491i
$887$	−5.21179e6	−	1.60402e7i	−0.222422	−	0.684545i	−0.998543	−	0.0539606i	$-0.982815\pi$
$887$	−5.21179e6	−	1.60402e7i	−0.222422	−	0.684545i	0.776121	−	0.630584i	$-0.217185\pi$
$888$	308588.	−	949736.i	0.0131325	−	0.0404176i
$889$	−3.66503e7	−	2.66280e7i	−1.55533	−	1.13001i
$890$	5.85344e7			2.47706
$891$	2.80495e7	−	9.37915e6i	1.18367	−	0.395794i
$892$	244578.			0.0102921
$893$	2.68908e6	+	1.95373e6i	0.112843	+	0.0819853i
$894$	5.36042e6	−	1.64977e7i	0.224313	−	0.690365i
$895$	1.64972e7	+	5.07733e7i	0.688420	+	2.11874i
$896$	4.62195e6	−	3.35805e6i	0.192334	−	0.139739i
$897$	−6.99403e6	+	5.08146e6i	−0.290233	+	0.210867i
$898$	−8.61550e6	−	2.65158e7i	−0.356525	−	1.09727i
$899$	3.31605e6	−	1.02057e7i	0.136843	−	0.421158i
$900$	−7.19139e6	−	5.22485e6i	−0.295942	−	0.215015i
$901$	−4.55902e6			−0.187094
$902$	−1.34474e7	−	1.81805e7i	−0.550328	−	0.744028i
$903$	1.29064e6			0.0526726
$904$	803070.	+	583465.i	0.0326838	+	0.0237462i
$905$	−1.42287e7	+	4.37916e7i	−0.577491	+	1.77733i
$906$	1.98328e7	+	6.10391e7i	0.802720	+	2.47052i
$907$	1.91896e7	−	1.39421e7i	0.774548	−	0.562742i	−0.128790	−	0.991672i	$-0.541109\pi$
$907$	1.91896e7	−	1.39421e7i	0.774548	−	0.562742i	0.903338	+	0.428930i	$0.141109\pi$
$908$	5.74839e6	−	4.17645e6i	0.231383	−	0.168110i
$909$	207977.	+	640088.i	0.00834846	+	0.0256939i
$910$	−5.13269e6	+	1.57968e7i	−0.205467	+	0.632362i
$911$	2.08554e7	+	1.51523e7i	0.832574	+	0.604900i	0.920286	−	0.391245i	$-0.127956\pi$
$911$	2.08554e7	+	1.51523e7i	0.832574	+	0.604900i	−0.0877125	+	0.996146i	$0.527956\pi$
$912$	−5.20989e7			−2.07416
$913$	3.62037e6	+	4.89464e6i	0.143739	+	0.194332i
$914$	−1.61594e7			−0.639822
$915$	−1.93493e7	−	1.40581e7i	−0.764034	−	0.555103i
$916$	−3.35974e6	+	1.03402e7i	−0.132302	+	0.407184i
$917$	1.85420e7	+	5.70664e7i	0.728171	+	2.24108i
$918$	6.17402e6	−	4.48569e6i	0.241803	−	0.175680i
$919$	2.81835e7	−	2.04765e7i	1.10080	−	0.799775i	0.119606	−	0.992821i	$-0.461837\pi$
$919$	2.81835e7	−	2.04765e7i	1.10080	−	0.799775i	0.981190	+	0.193046i	$0.0618367\pi$
$920$	981990.	+	3.02226e6i	0.0382505	+	0.117723i
$921$	4.58818e6	−	1.41210e7i	0.178234	−	0.548549i
$922$	3.67782e7	+	2.67209e7i	1.42483	+	1.03520i
$923$	1.04741e7			0.404679
$924$	−3.67795e7	+	1.22983e7i	−1.41718	+	0.473876i
$925$	6.93759e6			0.266596
$926$	−3.01772e7	−	2.19250e7i	−1.15652	−	0.840258i
$927$	2.75022e6	−	8.46432e6i	0.105116	−	0.323514i
$928$	5.68798e6	+	1.75058e7i	0.216814	+	0.667286i
$929$	−2.22970e7	+	1.61997e7i	−0.847630	+	0.615840i	−0.924492	−	0.381202i	$-0.875510\pi$
$929$	−2.22970e7	+	1.61997e7i	−0.847630	+	0.615840i	0.0768613	+	0.997042i	$0.475510\pi$
$930$	−4.22528e7	+	3.06985e7i	−1.60195	+	1.16388i
$931$	−8.47701e6	−	2.60895e7i	−0.320530	−	0.986489i
$932$	−4.81156e6	+	1.48085e7i	−0.181446	+	0.558432i
$933$	−2.34898e7	−	1.70663e7i	−0.883435	−	0.641853i
$934$	−3.06227e7			−1.14862
$935$	−1.26791e7	−	4.00042e6i	−0.474308	−	0.149650i
$936$	−381277.			−0.0142250
$937$	1.71930e7	+	1.24915e7i	0.639740	+	0.464799i	0.859761	−	0.510697i	$-0.170612\pi$
$937$	1.71930e7	+	1.24915e7i	0.639740	+	0.464799i	−0.220021	+	0.975495i	$0.570612\pi$
$938$	1.17350e7	−	3.61167e7i	0.435489	−	1.34030i
$939$	−5.71753e6	−	1.75967e7i	−0.211614	−	0.651281i
$940$	−2.38156e6	+	1.73031e6i	−0.0879108	+	0.0638709i
$941$	−7.68824e6	+	5.58583e6i	−0.283043	+	0.205643i	−0.720244	−	0.693721i	$-0.755970\pi$
$941$	−7.68824e6	+	5.58583e6i	−0.283043	+	0.205643i	0.437200	+	0.899364i	$0.355970\pi$
$942$	2.31070e7	+	7.11161e7i	0.848431	+	2.61120i
$943$	−5.73128e6	+	1.76391e7i	−0.209881	+	0.645947i
$944$	3.49588e7	+	2.53990e7i	1.27681	+	0.927656i
$945$	−2.63023e7			−0.958107
$946$	731529.	−	1.02514e6i	0.0265769	−	0.0372441i
$947$	2.28091e7			0.826483			0.413241	−	0.910621i	$-0.364397\pi$
$947$	2.28091e7			0.826483			0.413241	+	0.910621i	$0.364397\pi$
$948$	−5.85984e6	−	4.25742e6i	−0.211770	−	0.153860i
$949$	1.90268e6	−	5.85585e6i	0.0685805	−	0.211069i
$950$	−1.35403e7	−	4.16726e7i	−0.486763	−	1.49810i
$951$	1.28550e7	−	9.33967e6i	0.460913	−	0.334873i
$952$	1.02186e6	−	742427.i	0.0365427	−	0.0265498i
$953$	−7.87271e6	−	2.42297e7i	−0.280797	−	0.864203i	−0.987627	−	0.156820i	$-0.949876\pi$
$953$	−7.87271e6	−	2.42297e7i	−0.280797	−	0.864203i	0.706831	−	0.707383i	$-0.250124\pi$
$954$	3.24074e6	−	9.97398e6i	0.115285	−	0.354811i
$955$	−3.64138e7	−	2.64562e7i	−1.29199	−	0.938682i
$956$	5.35527e6			0.189512
$957$	152222.	+	1.78405e7i	0.00537275	+	0.629689i
$958$	8.03412e6			0.282830
$959$	3.55304e7	+	2.58143e7i	1.24754	+	0.906389i
$960$	1.24093e7	−	3.81918e7i	0.434578	−	1.33749i
$961$	−2.09303e6	−	6.44169e6i	−0.0731085	−	0.225005i
$962$	−3.37949e6	+	2.45534e6i	−0.117737	+	0.0855411i
$963$	3.77511e6	−	2.74278e6i	0.131179	−	0.0953070i
$964$	−9.94223e6	−	3.05990e7i	−0.344581	−	1.06051i
$965$	1.88040e7	−	5.78727e7i	0.650027	−	2.00058i
$966$	5.32983e7	+	3.87234e7i	1.83768	+	1.33515i
$967$	−5.21847e7			−1.79464			−0.897319	−	0.441384i	$-0.854488\pi$
$967$	−5.21847e7			−1.79464			−0.897319	+	0.441384i	$0.854488\pi$
$968$	789156.	−	2.57763e6i	0.0270691	−	0.0884162i
$969$	−2.16426e7			−0.740456
$970$	6.25531e7	+	4.54475e7i	2.13462	+	1.55089i
$971$	−2.43016e6	+	7.47927e6i	−0.0827156	+	0.254572i	−0.983858	−	0.178951i	$-0.942730\pi$
$971$	−2.43016e6	+	7.47927e6i	−0.0827156	+	0.254572i	0.901142	+	0.433523i	$0.142730\pi$
$972$	8.35921e6	+	2.57270e7i	0.283792	+	0.873421i
$973$	−4.83928e6	+	3.51594e6i	−0.163870	+	0.119058i
$974$	4.35455e6	−	3.16377e6i	0.147077	−	0.106858i
$975$	−2.32397e6	−	7.15243e6i	−0.0782922	−	0.240959i
$976$	5.65952e6	−	1.74182e7i	0.190176	−	0.585301i
$977$	−2.35608e7	−	1.71179e7i	−0.789686	−	0.573740i	0.118184	−	0.992992i	$-0.462293\pi$
$977$	−2.35608e7	−	1.71179e7i	−0.789686	−	0.573740i	−0.907870	+	0.419251i	$0.862293\pi$
$978$	1.00318e7			0.335375
$979$	347474.	+	4.07241e7i	0.0115868	+	1.35798i
$980$	2.42951e7			0.808077
$981$	1.51089e7	+	1.09773e7i	0.501257	+	0.364184i
$982$	2.31859e7	−	7.13588e7i	0.767264	−	2.36140i
$983$	−1.34998e7	−	4.15482e7i	−0.445599	−	1.37141i	−0.881825	−	0.471576i	$-0.843685\pi$
$983$	−1.34998e7	−	4.15482e7i	−0.445599	−	1.37141i	0.436226	−	0.899837i	$-0.356315\pi$
$984$	−1.87885e6	+	1.36507e6i	−0.0618592	+	0.0449434i
$985$	−3.42832e7	+	2.49082e7i	−1.12588	+	0.817998i
$986$	2.52069e6	+	7.75787e6i	0.0825708	+	0.254127i
$987$	1.34344e6	−	4.13467e6i	0.0438959	−	0.135098i
$988$	1.03052e7	+	7.48718e6i	0.335865	+	0.244020i
$989$	−1.03291e6			−0.0335794
$990$	1.77648e7	−	2.48951e7i	0.576065	−	0.807282i
$991$	−9.05087e6			−0.292756			−0.146378	−	0.989229i	$-0.546762\pi$
$991$	−9.05087e6			−0.292756			−0.146378	+	0.989229i	$0.546762\pi$
$992$	−3.03295e7	−	2.20357e7i	−0.978556	−	0.710963i
$993$	−2.10581e7	+	6.48101e7i	−0.677712	+	2.08578i
$994$	−2.46651e7	−	7.59114e7i	−0.791803	−	2.43692i
$995$	−4.71176e6	+	3.42329e6i	−0.150878	+	0.109619i
$996$	−7.10080e6	+	5.15903e6i	−0.226808	+	0.164786i
$997$	1.46475e6	+	4.50803e6i	0.0466686	+	0.143631i	0.971675	−	0.236319i	$-0.0759411\pi$
$997$	1.46475e6	+	4.50803e6i	0.0466686	+	0.143631i	−0.925007	+	0.379950i	$0.875941\pi$
$998$	−4.80524e6	+	1.47890e7i	−0.152717	+	0.470016i
$999$	−5.35159e6	−	3.88815e6i	−0.169656	−	0.123262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.6.c.a.4.1	yes	16
3.2	odd	2		99.6.f.a.37.4		16
11.3	even	5	inner	11.6.c.a.3.1	✓	16
11.5	even	5		121.6.a.g.1.7		8
11.6	odd	10		121.6.a.i.1.2		8
33.5	odd	10		1089.6.a.bg.1.2		8
33.14	odd	10		99.6.f.a.91.4		16
33.17	even	10		1089.6.a.bb.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.6.c.a.3.1	✓	16	11.3	even	5	inner
11.6.c.a.4.1	yes	16	1.1	even	1	trivial
99.6.f.a.37.4		16	3.2	odd	2
99.6.f.a.91.4		16	33.14	odd	10
121.6.a.g.1.7		8	11.5	even	5
121.6.a.i.1.2		8	11.6	odd	10
1089.6.a.bb.1.7		8	33.17	even	10
1089.6.a.bg.1.2		8	33.5	odd	10

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.36363 - 4.62345i) q^{2} +(-5.98507 + 18.4202i) q^{3} +(9.23097 + 28.4100i) q^{4} +(-59.3249 + 43.1020i) q^{5} +(123.251 - 89.5474i) q^{6} +(-51.6143 - 158.852i) q^{7} +(-5.17243 + 15.9191i) q^{8} +(-106.890 - 77.6601i) q^{9} +O(q^{10})\)	\(q+(-6.36363 - 4.62345i) q^{2} +(-5.98507 + 18.4202i) q^{3} +(9.23097 + 28.4100i) q^{4} +(-59.3249 + 43.1020i) q^{5} +(123.251 - 89.5474i) q^{6} +(-51.6143 - 158.852i) q^{7} +(-5.17243 + 15.9191i) q^{8} +(-106.890 - 77.6601i) q^{9} +576.801 q^{10} +(3.42402 + 401.297i) q^{11} -578.565 q^{12} +(-139.478 - 101.337i) q^{13} +(-405.991 + 1249.51i) q^{14} +(-438.883 - 1350.74i) q^{15} +(879.860 - 639.256i) q^{16} +(365.505 - 265.555i) q^{17} +(321.151 + 988.400i) q^{18} +(-764.308 + 2352.30i) q^{19} +(-1772.15 - 1287.55i) q^{20} +3235.00 q^{21} +(1833.59 - 2569.54i) q^{22} -2589.01 q^{23} +(-262.275 - 190.554i) q^{24} +(695.975 - 2141.99i) q^{25} +(419.062 + 1289.74i) q^{26} +(-1737.34 + 1262.25i) q^{27} +(4036.54 - 2932.72i) q^{28} +(-709.309 - 2183.03i) q^{29} +(-3452.20 + 10624.8i) q^{30} +(3782.18 + 2747.92i) q^{31} -8019.04 q^{32} +(-7412.45 - 2338.72i) q^{33} -3553.72 q^{34} +(9908.87 + 7199.21i) q^{35} +(1219.63 - 3753.62i) q^{36} +(951.875 + 2929.57i) q^{37} +(15739.5 - 11435.4i) q^{38} +(2701.43 - 1962.70i) q^{39} +(-379.292 - 1167.34i) q^{40} +(2213.70 - 6813.06i) q^{41} +(-20586.3 - 14956.9i) q^{42} +398.961 q^{43} +(-11369.2 + 3801.64i) q^{44} +9688.54 q^{45} +(16475.5 + 11970.2i) q^{46} +(415.282 - 1278.11i) q^{47} +(6509.16 + 20033.1i) q^{48} +(-8972.88 + 6519.18i) q^{49} +(-14332.3 + 10413.0i) q^{50} +(2703.99 + 8322.03i) q^{51} +(1591.46 - 4898.02i) q^{52} +(-8163.81 - 5931.36i) q^{53} +16891.7 q^{54} +(-17499.8 - 23659.3i) q^{55} +2795.76 q^{56} +(-38755.2 - 28157.3i) q^{57} +(-5579.34 + 17171.4i) q^{58} +(12277.9 + 37787.5i) q^{59} +(34323.3 - 24937.3i) q^{60} +(13623.8 - 9898.29i) q^{61} +(-11363.6 - 34973.4i) q^{62} +(-6819.44 + 20988.1i) q^{63} +(22874.7 + 16619.4i) q^{64} +12642.4 q^{65} +(36357.1 + 49153.8i) q^{66} -28904.6 q^{67} +(10918.4 + 7932.67i) q^{68} +(15495.4 - 47690.0i) q^{69} +(-29771.2 - 91626.2i) q^{70} +(-49150.0 + 35709.6i) q^{71} +(1789.16 - 1299.90i) q^{72} +(11036.1 + 33965.7i) q^{73} +(7487.33 - 23043.6i) q^{74} +(35290.4 + 25639.9i) q^{75} -73884.0 q^{76} +(63570.2 - 21256.6i) q^{77} -26265.4 q^{78} +(10128.2 + 7358.60i) q^{79} +(-24644.3 + 75847.5i) q^{80} +(-22774.1 - 70091.3i) q^{81} +(-45586.9 + 33120.9i) q^{82} +(12273.1 - 8916.96i) q^{83} +(29862.2 + 91906.3i) q^{84} +(-10237.6 + 31508.0i) q^{85} +(-2538.84 - 1844.57i) q^{86} +44457.0 q^{87} +(-6405.99 - 2021.17i) q^{88} +101481. q^{89} +(-61654.3 - 44794.5i) q^{90} +(-8898.54 + 27386.9i) q^{91} +(-23899.1 - 73553.8i) q^{92} +(-73253.7 + 53221.9i) q^{93} +(-8551.95 + 6213.36i) q^{94} +(-56046.3 - 172493. i) q^{95} +(47994.5 - 147712. i) q^{96} +(108448. + 78792.3i) q^{97} +87241.2 q^{98} +(30798.8 - 43160.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 24 q^{3} - 73 q^{4} - 10 q^{5} + 121 q^{6} + 196 q^{7} + 527 q^{8} - 530 q^{9}+O(q^{10}) \) 16 * q - q^2 - 24 * q^3 - 73 * q^4 - 10 * q^5 + 121 * q^6 + 196 * q^7 + 527 * q^8 - 530 * q^9	\( 16 q - q^{2} - 24 q^{3} - 73 q^{4} - 10 q^{5} + 121 q^{6} + 196 q^{7} + 527 q^{8} - 530 q^{9} - 672 q^{10} - 692 q^{11} - 1562 q^{12} + 1162 q^{13} + 560 q^{14} + 1796 q^{15} + 6399 q^{16} - 22 q^{17} + 834 q^{18} - 3236 q^{19} - 5514 q^{20} - 7772 q^{21} - 13059 q^{22} - 10848 q^{23} + 13233 q^{24} + 15686 q^{25} + 16216 q^{26} + 22500 q^{27} + 8838 q^{28} + 13070 q^{29} - 22830 q^{30} - 14764 q^{31} - 58812 q^{32} - 48544 q^{33} - 26966 q^{34} + 43368 q^{35} + 63696 q^{36} + 4638 q^{37} + 68144 q^{38} + 20300 q^{39} + 52284 q^{40} - 14806 q^{41} - 69922 q^{42} - 24376 q^{43} - 104960 q^{44} - 97480 q^{45} + 50452 q^{46} + 40364 q^{47} + 30236 q^{48} + 32246 q^{49} + 10839 q^{50} + 75564 q^{51} - 80654 q^{52} - 11654 q^{53} + 43796 q^{54} + 7052 q^{55} + 70632 q^{56} - 40020 q^{57} + 10276 q^{58} + 70804 q^{59} + 46116 q^{60} - 31446 q^{61} - 153388 q^{62} - 7064 q^{63} + 17695 q^{64} - 41284 q^{65} + 48006 q^{66} - 64200 q^{67} - 94114 q^{68} - 62412 q^{69} - 103768 q^{70} - 184380 q^{71} - 14729 q^{72} - 1750 q^{73} + 306048 q^{74} + 246596 q^{75} + 174806 q^{76} + 384646 q^{77} + 360916 q^{78} + 24324 q^{79} - 386444 q^{80} - 259412 q^{81} - 316255 q^{82} - 46028 q^{83} - 271956 q^{84} + 63914 q^{85} + 22931 q^{86} - 47592 q^{87} + 211871 q^{88} + 148364 q^{89} - 347186 q^{90} - 258448 q^{91} - 58658 q^{92} - 387478 q^{93} - 55370 q^{94} - 4716 q^{95} + 328396 q^{96} + 484296 q^{97} + 743692 q^{98} + 724964 q^{99}+O(q^{100}) \) 16 * q - q^2 - 24 * q^3 - 73 * q^4 - 10 * q^5 + 121 * q^6 + 196 * q^7 + 527 * q^8 - 530 * q^9 - 672 * q^10 - 692 * q^11 - 1562 * q^12 + 1162 * q^13 + 560 * q^14 + 1796 * q^15 + 6399 * q^16 - 22 * q^17 + 834 * q^18 - 3236 * q^19 - 5514 * q^20 - 7772 * q^21 - 13059 * q^22 - 10848 * q^23 + 13233 * q^24 + 15686 * q^25 + 16216 * q^26 + 22500 * q^27 + 8838 * q^28 + 13070 * q^29 - 22830 * q^30 - 14764 * q^31 - 58812 * q^32 - 48544 * q^33 - 26966 * q^34 + 43368 * q^35 + 63696 * q^36 + 4638 * q^37 + 68144 * q^38 + 20300 * q^39 + 52284 * q^40 - 14806 * q^41 - 69922 * q^42 - 24376 * q^43 - 104960 * q^44 - 97480 * q^45 + 50452 * q^46 + 40364 * q^47 + 30236 * q^48 + 32246 * q^49 + 10839 * q^50 + 75564 * q^51 - 80654 * q^52 - 11654 * q^53 + 43796 * q^54 + 7052 * q^55 + 70632 * q^56 - 40020 * q^57 + 10276 * q^58 + 70804 * q^59 + 46116 * q^60 - 31446 * q^61 - 153388 * q^62 - 7064 * q^63 + 17695 * q^64 - 41284 * q^65 + 48006 * q^66 - 64200 * q^67 - 94114 * q^68 - 62412 * q^69 - 103768 * q^70 - 184380 * q^71 - 14729 * q^72 - 1750 * q^73 + 306048 * q^74 + 246596 * q^75 + 174806 * q^76 + 384646 * q^77 + 360916 * q^78 + 24324 * q^79 - 386444 * q^80 - 259412 * q^81 - 316255 * q^82 - 46028 * q^83 - 271956 * q^84 + 63914 * q^85 + 22931 * q^86 - 47592 * q^87 + 211871 * q^88 + 148364 * q^89 - 347186 * q^90 - 258448 * q^91 - 58658 * q^92 - 387478 * q^93 - 55370 * q^94 - 4716 * q^95 + 328396 * q^96 + 484296 * q^97 + 743692 * q^98 + 724964 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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