LMFDB - Embedded newform 16.6.e.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,6,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	16.e (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:	$2.56614111701$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} + \cdots + 68719476736 $ x^18 - 5x^16 - 30x^15 - 42x^14 - 344x^13 + 2904x^12 + 5344x^11 + 16576x^10 - 297472x^9 + 265216x^8 + 1368064x^7 + 11894784x^6 - 22544384x^5 - 44040192x^4 - 503316480x^3 - 1342177280*x^2 + 68719476736
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Root			$0.592893 - 3.95582i$ of defining polynomial
Character	$\chi$	$=$	16.13
Dual form			16.6.e.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.36292 - 4.54871i) q^{2} +(16.8936 + 16.8936i) q^{3} +(-9.38150 + 30.5939i) q^{4} +(66.0049 - 66.0049i) q^{5} +(20.0322 - 133.656i) q^{6} +75.3048i q^{7} +(170.712 - 60.2112i) q^{8} +327.790i q^{9} +O(q^{10})$	\(q+(-3.36292 - 4.54871i) q^{2} +(16.8936 + 16.8936i) q^{3} +(-9.38150 + 30.5939i) q^{4} +(66.0049 - 66.0049i) q^{5} +(20.0322 - 133.656i) q^{6} +75.3048i q^{7} +(170.712 - 60.2112i) q^{8} +327.790i q^{9} +(-522.206 - 78.2676i) q^{10} +(-79.0644 + 79.0644i) q^{11} +(-675.330 + 358.355i) q^{12} +(-238.441 - 238.441i) q^{13} +(342.540 - 253.244i) q^{14} +2230.13 q^{15} +(-847.975 - 574.034i) q^{16} -1753.52 q^{17} +(1491.02 - 1102.33i) q^{18} +(-311.614 - 311.614i) q^{19} +(1400.12 + 2638.57i) q^{20} +(-1272.17 + 1272.17i) q^{21} +(625.528 + 93.7534i) q^{22} -1305.23i q^{23} +(3901.14 + 1866.76i) q^{24} -5588.28i q^{25} +(-282.740 + 1886.46i) q^{26} +(-1432.42 + 1432.42i) q^{27} +(-2303.87 - 706.472i) q^{28} +(2586.71 + 2586.71i) q^{29} +(-7499.74 - 10144.2i) q^{30} -2374.34 q^{31} +(240.562 + 5787.62i) q^{32} -2671.37 q^{33} +(5896.95 + 7976.25i) q^{34} +(4970.48 + 4970.48i) q^{35} +(-10028.4 - 3075.17i) q^{36} +(-1940.89 + 1940.89i) q^{37} +(-369.508 + 2465.38i) q^{38} -8056.28i q^{39} +(7293.59 - 15242.1i) q^{40} -3919.59i q^{41} +(10065.0 + 1508.52i) q^{42} +(-8827.10 + 8827.10i) q^{43} +(-1677.15 - 3160.63i) q^{44} +(21635.8 + 21635.8i) q^{45} +(-5937.10 + 4389.38i) q^{46} +23247.6 q^{47} +(-4627.86 - 24022.9i) q^{48} +11136.2 q^{49} +(-25419.5 + 18793.0i) q^{50} +(-29623.3 - 29623.3i) q^{51} +(9531.79 - 5057.91i) q^{52} +(7573.22 - 7573.22i) q^{53} +(11332.8 + 1698.54i) q^{54} +10437.3i q^{55} +(4534.20 + 12855.4i) q^{56} -10528.6i q^{57} +(3067.29 - 20465.1i) q^{58} +(-33005.3 + 33005.3i) q^{59} +(-20921.9 + 68228.3i) q^{60} +(-26526.1 - 26526.1i) q^{61} +(7984.72 + 10800.2i) q^{62} -24684.2 q^{63} +(25517.2 - 20557.6i) q^{64} -31476.6 q^{65} +(8983.61 + 12151.3i) q^{66} +(16271.7 + 16271.7i) q^{67} +(16450.7 - 53647.0i) q^{68} +(22050.0 - 22050.0i) q^{69} +(5893.93 - 39324.6i) q^{70} -33614.3i q^{71} +(19736.7 + 55957.8i) q^{72} +56226.7i q^{73} +(15355.6 + 2301.49i) q^{74} +(94406.5 - 94406.5i) q^{75} +(12456.9 - 6610.09i) q^{76} +(-5953.93 - 5953.93i) q^{77} +(-36645.7 + 27092.7i) q^{78} +1296.61 q^{79} +(-93859.5 + 18081.4i) q^{80} +31255.5 q^{81} +(-17829.1 + 13181.3i) q^{82} +(78743.5 + 78743.5i) q^{83} +(-26985.8 - 50855.6i) q^{84} +(-115741. + 115741. i) q^{85} +(69836.8 + 10467.1i) q^{86} +87398.0i q^{87} +(-8736.68 + 18257.8i) q^{88} -86929.2i q^{89} +(25655.4 - 171174. i) q^{90} +(17955.8 - 17955.8i) q^{91} +(39932.0 + 12245.0i) q^{92} +(-40111.3 - 40111.3i) q^{93} +(-78180.0 - 105747. i) q^{94} -41136.1 q^{95} +(-93710.1 + 101838. i) q^{96} -8397.09 q^{97} +(-37450.1 - 50655.3i) q^{98} +(-25916.5 - 25916.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.36292	−	4.54871i	−0.594486	−	0.804106i
$2$	−3.36292	−	4.54871i	−0.594486	−	0.804106i
$3$	16.8936	+	16.8936i	1.08373	+	1.08373i	0.996158	+	0.0875694i	$0.0279100\pi$
$3$	16.8936	+	16.8936i	1.08373	+	1.08373i	0.0875694	+	0.996158i	$0.472090\pi$
$4$	−9.38150	+	30.5939i	−0.293172	+	0.956060i
$5$	66.0049	−	66.0049i	1.18073	−	1.18073i	0.201176	−	0.979555i	$-0.435524\pi$
$5$	66.0049	−	66.0049i	1.18073	−	1.18073i	0.979555	−	0.201176i	$-0.0644762\pi$
$6$	20.0322	−	133.656i	0.227170	−	1.51569i
$7$			75.3048i			0.580868i	0.956895	+	0.290434i	$0.0937997\pi$
$7$			75.3048i			0.580868i	−0.956895	+	0.290434i	$0.906200\pi$
$8$	170.712	−	60.2112i	0.943060	−	0.332623i
$9$			327.790i			1.34893i
$10$	−522.206	−	78.2676i	−1.65136	−	0.247504i
$11$	−79.0644	+	79.0644i	−0.197015	+	0.197015i	−0.798719	−	0.601704i	$-0.794489\pi$
$11$	−79.0644	+	79.0644i	−0.197015	+	0.197015i	0.601704	+	0.798719i	$0.294489\pi$
$12$	−675.330	+	358.355i	−1.35383	+	0.718390i
$13$	−238.441	−	238.441i	−0.391312	−	0.391312i	0.483843	−	0.875155i	$-0.339241\pi$
$13$	−238.441	−	238.441i	−0.391312	−	0.391312i	−0.875155	+	0.483843i	$0.839241\pi$
$14$	342.540	−	253.244i	0.467079	−	0.345318i
$15$	2230.13			2.55918
$16$	−847.975	−	574.034i	−0.828100	−	0.560580i
$17$	−1753.52			−1.47160			−0.735798	−	0.677201i	$-0.763193\pi$
$17$	−1753.52			−1.47160			−0.735798	+	0.677201i	$0.763193\pi$
$18$	1491.02	−	1102.33i	1.08468	−	0.801922i
$19$	−311.614	−	311.614i	−0.198031	−	0.198031i	0.601124	−	0.799156i	$-0.294720\pi$
$19$	−311.614	−	311.614i	−0.198031	−	0.198031i	−0.799156	+	0.601124i	$0.794720\pi$
$20$	1400.12	+	2638.57i	0.782692	+	1.47501i
$21$	−1272.17	+	1272.17i	−0.629503	+	0.629503i
$22$	625.528	+	93.7534i	0.275543	+	0.0412981i
$23$		−	1305.23i		−	0.514478i	−0.966348	−	0.257239i	$-0.917187\pi$
$23$		−	1305.23i		−	0.514478i	0.966348	−	0.257239i	$-0.0828127\pi$
$24$	3901.14	+	1866.76i	1.38249	+	0.661547i
$25$		−	5588.28i		−	1.78825i
$26$	−282.740	+	1886.46i	−0.0820265	+	0.547286i
$27$	−1432.42	+	1432.42i	−0.378147	+	0.378147i
$28$	−2303.87	−	706.472i	−0.555345	−	0.170294i
$29$	2586.71	+	2586.71i	0.571154	+	0.571154i	0.932451	−	0.361297i	$-0.117666\pi$
$29$	2586.71	+	2586.71i	0.571154	+	0.571154i	−0.361297	+	0.932451i	$0.617666\pi$
$30$	−7499.74	−	10144.2i	−1.52140	−	2.05785i
$31$	−2374.34			−0.443750			−0.221875	−	0.975075i	$-0.571218\pi$
$31$	−2374.34			−0.443750			−0.221875	+	0.975075i	$0.571218\pi$
$32$	240.562	+	5787.62i	0.0415290	+	0.999137i
$33$	−2671.37			−0.427021
$34$	5896.95	+	7976.25i	0.874843	+	1.18332i
$35$	4970.48	+	4970.48i	0.685849	+	0.685849i
$36$	−10028.4	−	3075.17i	−1.28966	−	0.395469i
$37$	−1940.89	+	1940.89i	−0.233076	+	0.233076i	−0.813975	−	0.580899i	$-0.802701\pi$
$37$	−1940.89	+	1940.89i	−0.233076	+	0.233076i	0.580899	+	0.813975i	$0.302701\pi$
$38$	−369.508	+	2465.38i	−0.0415112	+	0.276965i
$39$		−	8056.28i		−	0.848151i
$40$	7293.59	−	15242.1i	0.720761	−	1.50624i
$41$		−	3919.59i		−	0.364150i	−0.983285	−	0.182075i	$-0.941719\pi$
$41$		−	3919.59i		−	0.364150i	0.983285	−	0.182075i	$-0.0582814\pi$
$42$	10065.0	+	1508.52i	0.880418	+	0.131956i
$43$	−8827.10	+	8827.10i	−0.728026	+	0.728026i	−0.970226	−	0.242200i	$-0.922131\pi$
$43$	−8827.10	+	8827.10i	−0.728026	+	0.728026i	0.242200	+	0.970226i	$0.422131\pi$
$44$	−1677.15	−	3160.63i	−0.130599	−	0.246117i
$45$	21635.8	+	21635.8i	1.59273	+	1.59273i
$46$	−5937.10	+	4389.38i	−0.413694	+	0.305850i
$47$	23247.6			1.53509			0.767546	−	0.640994i	$-0.221478\pi$
$47$	23247.6			1.53509			0.767546	+	0.640994i	$0.221478\pi$
$48$	−4627.86	−	24022.9i	−0.289920	−	1.50495i
$49$	11136.2			0.662592
$50$	−25419.5	+	18793.0i	−1.43794	+	1.06309i
$51$	−29623.3	−	29623.3i	−1.59481	−	1.59481i
$52$	9531.79	−	5057.91i	0.488839	−	0.259396i
$53$	7573.22	−	7573.22i	0.370332	−	0.370332i	−0.497266	−	0.867598i	$-0.665663\pi$
$53$	7573.22	−	7573.22i	0.370332	−	0.370332i	0.867598	+	0.497266i	$0.165663\pi$
$54$	11332.8	+	1698.54i	0.528874	+	0.0792670i
$55$			10437.3i			0.465243i
$56$	4534.20	+	12855.4i	0.193210	+	0.547793i
$57$		−	10528.6i		−	0.429224i
$58$	3067.29	−	20465.1i	0.119725	−	0.798811i
$59$	−33005.3	+	33005.3i	−1.23439	+	1.23439i	−0.272134	+	0.962259i	$0.587729\pi$
$59$	−33005.3	+	33005.3i	−1.23439	+	1.23439i	−0.962259	+	0.272134i	$0.912271\pi$
$60$	−20921.9	+	68228.3i	−0.750280	+	2.44673i
$61$	−26526.1	−	26526.1i	−0.912743	−	0.912743i	0.0837445	−	0.996487i	$-0.473312\pi$
$61$	−26526.1	−	26526.1i	−0.912743	−	0.912743i	−0.996487	+	0.0837445i	$0.973312\pi$
$62$	7984.72	+	10800.2i	0.263803	+	0.356822i
$63$	−24684.2			−0.783552
$64$	25517.2	−	20557.6i	0.778724	−	0.627367i
$65$	−31476.6			−0.924068
$66$	8983.61	+	12151.3i	0.253858	+	0.343370i
$67$	16271.7	+	16271.7i	0.442839	+	0.442839i	0.892965	−	0.450126i	$-0.148621\pi$
$67$	16271.7	+	16271.7i	0.442839	+	0.442839i	−0.450126	+	0.892965i	$0.648621\pi$
$68$	16450.7	−	53647.0i	0.431430	−	1.40693i
$69$	22050.0	−	22050.0i	0.557554	−	0.557554i
$70$	5893.93	−	39324.6i	0.143767	−	0.959223i
$71$		−	33614.3i		−	0.791367i	−0.918387	−	0.395684i	$-0.870508\pi$
$71$		−	33614.3i		−	0.791367i	0.918387	−	0.395684i	$-0.129492\pi$
$72$	19736.7	+	55957.8i	0.448686	+	1.27212i
$73$			56226.7i			1.23491i	0.786606	+	0.617455i	$0.211836\pi$
$73$			56226.7i			1.23491i	−0.786606	+	0.617455i	$0.788164\pi$
$74$	15355.6	+	2301.49i	0.325978	+	0.0488572i
$75$	94406.5	−	94406.5i	1.93798	−	1.93798i
$76$	12456.9	−	6610.09i	0.247387	−	0.131272i
$77$	−5953.93	−	5953.93i	−0.114440	−	0.114440i
$78$	−36645.7	+	27092.7i	−0.682003	+	0.504214i
$79$	1296.61			0.0233745			0.0116873	−	0.999932i	$-0.496280\pi$
$79$	1296.61			0.0233745			0.0116873	+	0.999932i	$0.496280\pi$
$80$	−93859.5	+	18081.4i	−1.63966	+	0.315870i
$81$	31255.5			0.529314
$82$	−17829.1	+	13181.3i	−0.292815	+	0.216482i
$83$	78743.5	+	78743.5i	1.25464	+	1.25464i	0.953616	+	0.301025i	$0.0973288\pi$
$83$	78743.5	+	78743.5i	1.25464	+	1.25464i	0.301025	+	0.953616i	$0.402671\pi$
$84$	−26985.8	−	50855.6i	−0.417290	−	0.786395i
$85$	−115741.	+	115741.i	−1.73756	+	1.73756i
$86$	69836.8	+	10467.1i	1.01821	+	0.152608i
$87$			87398.0i			1.23795i
$88$	−8736.68	+	18257.8i	−0.120265	+	0.251329i
$89$		−	86929.2i		−	1.16330i	−0.813440	−	0.581649i	$-0.802408\pi$
$89$		−	86929.2i		−	1.16330i	0.813440	−	0.581649i	$-0.197592\pi$
$90$	25655.4	−	171174.i	0.333866	−	2.22757i
$91$	17955.8	−	17955.8i	0.227301	−	0.227301i
$92$	39932.0	+	12245.0i	0.491871	+	0.150830i
$93$	−40111.3	−	40111.3i	−0.480905	−	0.480905i
$94$	−78180.0	−	105747.i	−0.912591	−	1.23438i
$95$	−41136.1			−0.467643
$96$	−93710.1	+	101838.i	−1.03779	+	1.12780i
$97$	−8397.09			−0.0906149			−0.0453074	−	0.998973i	$-0.514427\pi$
$97$	−8397.09			−0.0906149			−0.0453074	+	0.998973i	$0.514427\pi$
$98$	−37450.1	−	50655.3i	−0.393902	−	0.532794i
$99$	−25916.5	−	25916.5i	−0.265760	−	0.265760i
$100$	170967.	+	52426.5i	1.70967	+	0.524265i
$101$	117321.	−	117321.i	1.14438	−	1.14438i	0.156741	−	0.987640i	$-0.449901\pi$
$101$	117321.	−	117321.i	1.14438	−	1.14438i	0.987640	−	0.156741i	$-0.0500988\pi$
$102$	−35126.9	+	234369.i	−0.334303	+	2.23049i
$103$			43905.5i			0.407780i	0.978994	+	0.203890i	$0.0653584\pi$
$103$			43905.5i			0.407780i	−0.978994	+	0.203890i	$0.934642\pi$
$104$	−55061.6	−	26348.0i	−0.499190	−	0.238871i
$105$			167939.i			1.48655i
$106$	−59916.5	−	8980.22i	−0.517943	−	0.0776287i
$107$	−22314.1	+	22314.1i	−0.188417	+	0.188417i	−0.795011	−	0.606595i	$-0.792535\pi$
$107$	−22314.1	+	22314.1i	−0.188417	+	0.188417i	0.606595	+	0.795011i	$0.292535\pi$
$108$	−30385.1	−	57261.6i	−0.250669	−	0.472394i
$109$	−28711.3	−	28711.3i	−0.231466	−	0.231466i	0.581839	−	0.813304i	$-0.302334\pi$
$109$	−28711.3	−	28711.3i	−0.231466	−	0.231466i	−0.813304	+	0.581839i	$0.802334\pi$
$110$	47476.1	−	35099.7i	0.374105	−	0.276581i
$111$	−65577.6			−0.505182
$112$	43227.5	−	63856.6i	0.325623	−	0.481017i
$113$	184108.			1.35636			0.678182	−	0.734894i	$-0.262768\pi$
$113$	184108.			1.35636			0.678182	+	0.734894i	$0.262768\pi$
$114$	−47891.6	+	35406.9i	−0.345141	+	0.255168i
$115$	−86151.4	−	86151.4i	−0.607460	−	0.607460i
$116$	−103405.	+	54870.4i	−0.713504	+	0.378611i
$117$	78158.8	−	78158.8i	0.527853	−	0.527853i
$118$	261126.	+	39137.2i	1.72641	+	0.258753i
$119$		−	132048.i		−	0.854803i
$120$	380709.	−	134279.i	2.41346	−	0.851243i
$121$			148549.i			0.922370i
$122$	−31454.2	+	209865.i	−0.191329	+	1.27655i
$123$	66216.1	−	66216.1i	0.394640	−	0.394640i
$124$	22274.9	−	72640.3i	0.130095	−	0.424252i
$125$	−162589.	−	162589.i	−0.930712	−	0.930712i
$126$	83011.0	+	112281.i	0.465811	+	0.630058i
$127$	−52049.7			−0.286358			−0.143179	−	0.989697i	$-0.545732\pi$
$127$	−52049.7			−0.286358			−0.143179	+	0.989697i	$0.545732\pi$
$128$	−179323.	−	46936.9i	−0.967410	−	0.253215i
$129$	−298244.			−1.57796
$130$	105853.	+	143178.i	0.549346	+	0.743048i
$131$	−102008.	−	102008.i	−0.519347	−	0.519347i	0.398026	−	0.917374i	$-0.369695\pi$
$131$	−102008.	−	102008.i	−0.519347	−	0.519347i	−0.917374	+	0.398026i	$0.869695\pi$
$132$	25061.5	−	81727.7i	0.125191	−	0.408258i
$133$	23466.1	−	23466.1i	0.115030	−	0.115030i
$134$	19294.8	−	128736.i	0.0928277	−	0.619351i
$135$			189093.i			0.892980i
$136$	−299347.	+	105582.i	−1.38780	+	0.489487i
$137$		−	77586.5i		−	0.353171i	−0.984285	−	0.176585i	$-0.943495\pi$
$137$		−	77586.5i		−	0.353171i	0.984285	−	0.176585i	$-0.0565052\pi$
$138$	−174452.	−	26146.6i	−0.779790	−	0.116874i
$139$	−180111.	+	180111.i	−0.790686	+	0.790686i	−0.981606	−	0.190920i	$-0.938853\pi$
$139$	−180111.	+	180111.i	−0.790686	+	0.790686i	0.190920	+	0.981606i	$0.438853\pi$
$140$	−198697.	+	105436.i	−0.856784	+	0.454641i
$141$	392737.	+	392737.i	1.66362	+	1.66362i
$142$	−152902.	+	113042.i	−0.636343	+	0.470457i
$143$	37704.4			0.154189
$144$	188163.	−	277958.i	0.756184	−	1.11705i
$145$	341471.			1.34876
$146$	255759.	−	189086.i	0.992998	−	0.734137i
$147$	188131.	+	188131.i	0.718070	+	0.718070i
$148$	−41171.0	−	77588.0i	−0.154503	−	0.291166i
$149$	−168813.	+	168813.i	−0.622931	+	0.622931i	−0.946280	−	0.323349i	$-0.895191\pi$
$149$	−168813.	+	168813.i	−0.622931	+	0.622931i	0.323349	+	0.946280i	$0.395191\pi$
$150$	−746909.	−	111946.i	−2.71044	−	0.406238i
$151$		−	413701.i		−	1.47653i	−0.674508	−	0.738267i	$-0.735644\pi$
$151$		−	413701.i		−	1.47653i	0.674508	−	0.738267i	$-0.264356\pi$
$152$	−71959.0	−	34433.6i	−0.252625	−	0.120885i
$153$		−	574787.i		−	1.98508i
$154$	−7060.08	+	47105.3i	−0.0239888	+	0.160054i
$155$	−156718.	+	156718.i	−0.523950	+	0.523950i
$156$	246473.	+	75580.1i	0.810883	+	0.248654i
$157$	246324.	+	246324.i	0.797549	+	0.797549i	0.982708	−	0.185159i	$-0.0592802\pi$
$157$	246324.	+	246324.i	0.797549	+	0.797549i	−0.185159	+	0.982708i	$0.559280\pi$
$158$	−4360.41	−	5897.91i	−0.0138958	−	0.0187956i
$159$	255879.			0.802677
$160$	397889.	+	366133.i	1.22875	+	1.13068i
$161$	98289.9			0.298844
$162$	−105110.	−	142172.i	−0.314670	−	0.425625i
$163$	−97384.7	−	97384.7i	−0.287092	−	0.287092i	0.548837	−	0.835929i	$-0.315071\pi$
$163$	−97384.7	−	97384.7i	−0.287092	−	0.287092i	−0.835929	+	0.548837i	$0.815071\pi$
$164$	119915.	+	36771.6i	0.348149	+	0.106759i
$165$	−176323.	+	176323.i	−0.504197	+	0.504197i
$166$	93373.0	−	622990.i	0.262997	−	1.75473i
$167$			506877.i			1.40641i	0.710987	+	0.703205i	$0.248248\pi$
$167$			506877.i			1.40641i	−0.710987	+	0.703205i	$0.751752\pi$
$168$	−140576.	+	293774.i	−0.384272	+	0.803046i
$169$		−	257585.i		−	0.693750i
$170$	915699.	+	137244.i	2.43013	+	0.364226i
$171$	102144.	−	102144.i	0.267131	−	0.267131i
$172$	−187244.	−	352867.i	−0.482600	−	0.909474i
$173$	−217173.	−	217173.i	−0.551683	−	0.551683i	0.375243	−	0.926926i	$-0.377559\pi$
$173$	−217173.	−	217173.i	−0.551683	−	0.551683i	−0.926926	+	0.375243i	$0.877559\pi$
$174$	397548.	−	293913.i	0.995443	−	0.735945i
$175$	420825.			1.03874
$176$	112430.	−	21659.0i	0.273591	−	0.0527056i
$177$	−1.11516e6			−2.67549
$178$	−395416.	+	292336.i	−0.935414	+	0.691564i
$179$	477273.	+	477273.i	1.11336	+	1.11336i	0.992693	+	0.120663i	$0.0385022\pi$
$179$	477273.	+	477273.i	1.11336	+	1.11336i	0.120663	+	0.992693i	$0.461498\pi$
$180$	−864899.	+	458947.i	−1.98968	+	1.05580i
$181$	−133200.	+	133200.i	−0.302209	+	0.302209i	−0.841878	−	0.539668i	$-0.818550\pi$
$181$	−133200.	+	133200.i	−0.302209	+	0.302209i	0.539668	+	0.841878i	$0.318550\pi$
$182$	−142059.	−	21291.7i	−0.317901	−	0.0476466i
$183$		−	896244.i		−	1.97833i
$184$	−78589.4	−	222818.i	−0.171127	−	0.485183i
$185$			256217.i			0.550400i
$186$	−47563.4	+	317345.i	−0.100807	+	0.672589i
$187$	138641.	−	138641.i	0.289926	−	0.289926i
$188$	−218098.	+	711236.i	−0.450046	+	1.46764i
$189$	−107868.	−	107868.i	−0.219654	−	0.219654i
$190$	138338.	+	187116.i	0.278007	+	0.376034i
$191$	−172800.			−0.342736			−0.171368	−	0.985207i	$-0.554819\pi$
$191$	−172800.			−0.342736			−0.171368	+	0.985207i	$0.554819\pi$
$192$	778371.	+	83786.5i	1.52382	+	0.164029i
$193$	−94073.9			−0.181792			−0.0908962	−	0.995860i	$-0.528973\pi$
$193$	−94073.9			−0.181792			−0.0908962	+	0.995860i	$0.528973\pi$
$194$	28238.8	+	38195.9i	0.0538693	+	0.0728640i
$195$	−531754.	−	531754.i	−1.00144	−	1.00144i
$196$	−104474.	+	340699.i	−0.194253	+	0.633478i
$197$	270855.	−	270855.i	0.497245	−	0.497245i	−0.413334	−	0.910579i	$-0.635636\pi$
$197$	270855.	−	270855.i	0.497245	−	0.497245i	0.910579	+	0.413334i	$0.135636\pi$
$198$	−30731.5	+	205042.i	−0.0557084	+	0.371689i
$199$		−	2631.83i		−	0.00471113i	−0.999997	−	0.00235556i	$-0.999250\pi$
$199$		−	2631.83i		−	0.00471113i	0.999997	−	0.00235556i	$-0.000749800\pi$
$200$	−336477.	−	953987.i	−0.594814	−	1.68643i
$201$			549777.i			0.959834i
$202$	−928197.	−	139117.i	−1.60052	−	0.239884i
$203$	−194792.	+	194792.i	−0.331765	+	0.331765i
$204$	1.18421e6	−	628382.i	1.99229	−	1.05718i
$205$	−258712.	−	258712.i	−0.429963	−	0.429963i
$206$	199713.	−	147651.i	0.327898	−	0.242419i
$207$	427841.			0.693995
$208$	65318.9	+	339066.i	0.104684	+	0.543407i
$209$	49275.2			0.0780302
$210$	763906.	−	564766.i	1.19534	−	0.883732i
$211$	−404834.	−	404834.i	−0.625994	−	0.625994i	0.321063	−	0.947058i	$-0.395960\pi$
$211$	−404834.	−	404834.i	−0.625994	−	0.625994i	−0.947058	+	0.321063i	$0.895960\pi$
$212$	160646.	+	302743.i	0.245488	+	0.462630i
$213$	567868.	−	567868.i	0.857627	−	0.857627i
$214$	176541.	+	26459.7i	0.263518	+	0.0394958i
$215$			1.16526e6i			1.71921i
$216$	−158284.	+	330779.i	−0.230835	+	0.482396i
$217$		−	178799.i		−	0.257760i
$218$	−34045.4	+	227153.i	−0.0485197	+	0.323726i
$219$	−949874.	+	949874.i	−1.33831	+	1.33831i
$220$	−319317.	−	97917.2i	−0.444800	−	0.136396i
$221$	418112.	+	418112.i	0.575853	+	0.575853i
$222$	220532.	+	298293.i	0.300324	+	0.406220i
$223$	136925.			0.184382			0.0921912	−	0.995741i	$-0.470613\pi$
$223$	136925.			0.184382			0.0921912	+	0.995741i	$0.470613\pi$
$224$	−435836.	+	18115.5i	−0.580367	+	0.0241229i
$225$	1.83179e6			2.41223
$226$	−619141.	−	837453.i	−0.806340	−	1.09066i
$227$	54021.3	+	54021.3i	0.0695826	+	0.0695826i	0.741042	−	0.671459i	$-0.234332\pi$
$227$	54021.3	+	54021.3i	0.0695826	+	0.0695826i	−0.671459	+	0.741042i	$0.734332\pi$
$228$	322111.	+	98774.1i	0.410364	+	0.125836i
$229$	−694896.	+	694896.i	−0.875651	+	0.875651i	−0.993081	−	0.117430i	$-0.962534\pi$
$229$	−694896.	+	694896.i	−0.875651	+	0.875651i	0.117430	+	0.993081i	$0.462534\pi$
$230$	−102157.	+	681598.i	−0.127335	+	0.849588i
$231$		−	201167.i		−	0.248043i
$232$	597332.	+	285834.i	0.728611	+	0.348653i
$233$		−	848123.i		−	1.02346i	−0.859147	−	0.511728i	$-0.829006\pi$
$233$		−	848123.i		−	1.02346i	0.859147	−	0.511728i	$-0.170994\pi$
$234$	−618363.	−	92679.6i	−0.738251	−	0.110648i
$235$	1.53446e6	−	1.53446e6i	1.81253	−	1.81253i
$236$	−700122.	−	1.31940e6i	−0.818264	−	1.54204i
$237$	21904.5	+	21904.5i	0.0253316	+	0.0253316i
$238$	−600650.	+	444069.i	−0.687352	+	0.508169i
$239$	−865467.			−0.980066			−0.490033	−	0.871704i	$-0.663015\pi$
$239$	−865467.			−0.980066			−0.490033	+	0.871704i	$0.663015\pi$
$240$	−1.89109e6	−	1.28017e6i	−2.11926	−	1.43463i
$241$	447447.			0.496249			0.248124	−	0.968728i	$-0.420186\pi$
$241$	447447.			0.496249			0.248124	+	0.968728i	$0.420186\pi$
$242$	675705.	−	499558.i	0.741683	−	0.548337i
$243$	876097.	+	876097.i	0.951780	+	0.951780i
$244$	1.06039e6	−	562682.i	1.14023	−	0.605046i
$245$	735042.	−	735042.i	0.782343	−	0.782343i
$246$	−523877.	−	78518.1i	−0.551940	−	0.0827241i
$247$			148603.i			0.154984i
$248$	−405328.	+	142962.i	−0.418483	+	0.147602i
$249$			2.66053e6i			2.71938i
$250$	−192795.	+	1.28634e6i	−0.195095	+	1.30169i
$251$	−111369.	+	111369.i	−0.111578	+	0.111578i	−0.760692	−	0.649113i	$-0.775140\pi$
$251$	−111369.	+	111369.i	−0.111578	+	0.111578i	0.649113	+	0.760692i	$0.275140\pi$
$252$	231575.	−	755186.i	0.229715	−	0.749122i
$253$	103197.	+	103197.i	0.101360	+	0.101360i
$254$	175039.	+	236759.i	0.170236	+	0.230262i
$255$	−3.91057e6			−3.76608
$256$	389547.	+	973532.i	0.371501	+	0.928433i
$257$	−1.33325e6			−1.25916			−0.629578	−	0.776937i	$-0.716772\pi$
$257$	−1.33325e6			−1.25916			−0.629578	+	0.776937i	$0.716772\pi$
$258$	1.00297e6	+	1.35662e6i	0.938079	+	1.26885i
$259$	−146159.	−	146159.i	−0.135386	−	0.135386i
$260$	295298.	−	962991.i	0.270911	−	0.883464i
$261$	−847900.	+	847900.i	−0.770448	+	0.770448i
$262$	−120960.	+	807053.i	−0.108865	+	0.726355i
$263$		−	595491.i		−	0.530867i	−0.964129	−	0.265433i	$-0.914485\pi$
$263$		−	595491.i		−	0.530867i	0.964129	−	0.265433i	$-0.0855150\pi$
$264$	−456035.	+	160847.i	−0.402706	+	0.142037i
$265$		−	999738.i		−	0.874524i
$266$	−185655.	−	27825.7i	−0.160880	−	0.0241125i
$267$	1.46855e6	−	1.46855e6i	1.26070	−	1.26070i
$268$	−650468.	+	345162.i	−0.553209	+	0.293553i
$269$	−1.23361e6	−	1.23361e6i	−1.03943	−	1.03943i	−0.999190	−	0.0402435i	$-0.987187\pi$
$269$	−1.23361e6	−	1.23361e6i	−1.03943	−	1.03943i	−0.0402435	−	0.999190i	$-0.512813\pi$
$270$	860131.	−	635906.i	0.718051	−	0.530865i
$271$	1.40067e6			1.15855			0.579274	−	0.815133i	$-0.303336\pi$
$271$	1.40067e6			1.15855			0.579274	+	0.815133i	$0.303336\pi$
$272$	1.48694e6	+	1.00658e6i	1.21863	+	0.824947i
$273$	606677.			0.492664
$274$	−352918.	+	260917.i	−0.283987	+	0.209955i
$275$	441834.	+	441834.i	0.352312	+	0.352312i
$276$	467735.	+	881460.i	0.369596	+	0.696514i
$277$	287168.	−	287168.i	0.224873	−	0.224873i	−0.585674	−	0.810547i	$-0.699170\pi$
$277$	287168.	−	287168.i	0.224873	−	0.224873i	0.810547	+	0.585674i	$0.199170\pi$
$278$	1.42497e6	+	213574.i	1.10585	+	0.165743i
$279$		−	778286.i		−	0.598589i
$280$	1.14780e6	+	549242.i	0.874926	+	0.418667i
$281$		−	281626.i		−	0.212768i	−0.994325	−	0.106384i	$-0.966073\pi$
$281$		−	281626.i		−	0.212768i	0.994325	−	0.106384i	$-0.0339273\pi$
$282$	465702.	−	3.10719e6i	0.348727	−	2.32673i
$283$	−633674.	+	633674.i	−0.470327	+	0.470327i	−0.902020	−	0.431693i	$-0.857916\pi$
$283$	−633674.	+	633674.i	−0.470327	+	0.470327i	0.431693	+	0.902020i	$0.357916\pi$
$284$	1.02839e6	+	315353.i	0.756594	+	0.232007i
$285$	−694939.	−	694939.i	−0.506798	−	0.506798i
$286$	−126797.	−	171506.i	−0.0916630	−	0.123984i
$287$	295164.			0.211523
$288$	−1.89713e6	+	78853.8i	−1.34777	+	0.0560198i
$289$	1.65498e6			1.16559
$290$	−1.14834e6	−	1.55325e6i	−0.801818	−	1.08454i
$291$	−141857.	−	141857.i	−0.0982019	−	0.0982019i
$292$	−1.72019e6	−	527491.i	−1.18065	−	0.362041i
$293$	1.05194e6	−	1.05194e6i	0.715852	−	0.715852i	−0.251901	−	0.967753i	$-0.581056\pi$
$293$	1.05194e6	−	1.05194e6i	0.715852	−	0.715852i	0.967753	+	0.251901i	$0.0810556\pi$
$294$	223083.	−	1.48842e6i	0.150521	−	1.00429i
$295$			4.35702e6i			2.91497i
$296$	−214470.	+	448198.i	−0.142278	+	0.297331i
$297$		−	226507.i		−	0.149001i
$298$	1.33558e6	+	200176.i	0.871226	+	0.130578i
$299$	−311220.	+	311220.i	−0.201321	+	0.201321i
$300$	2.00259e6	+	3.77394e6i	1.28466	+	2.42098i
$301$	−664723.	−	664723.i	−0.422887	−	0.422887i
$302$	−1.88180e6	+	1.39124e6i	−1.18729	+	0.877780i
$303$	3.96394e6			2.48039
$304$	85364.0	+	443118.i	0.0529774	+	0.275002i
$305$	−3.50170e6			−2.15541
$306$	−2.61454e6	+	1.93296e6i	−1.59622	+	1.18010i
$307$	−1.86364e6	−	1.86364e6i	−1.12854	−	1.12854i	−0.990415	−	0.138123i	$-0.955893\pi$
$307$	−1.86364e6	−	1.86364e6i	−1.12854	−	1.12854i	−0.138123	−	0.990415i	$-0.544107\pi$
$308$	238011.	−	126297.i	0.142962	−	0.0758607i
$309$	−741724.	+	741724.i	−0.441922	+	0.441922i
$310$	1.23989e6	+	185834.i	0.732792	+	0.109830i
$311$		−	3.33859e6i		−	1.95732i	−0.205476	−	0.978662i	$-0.565874\pi$
$311$		−	3.33859e6i		−	1.95732i	0.205476	−	0.978662i	$-0.434126\pi$
$312$	−485079.	−	1.37530e6i	−0.282115	−	0.799857i
$313$			695457.i			0.401245i	0.979669	+	0.200622i	$0.0642964\pi$
$313$			695457.i			0.401245i	−0.979669	+	0.200622i	$0.935704\pi$
$314$	292087.	−	1.94882e6i	0.167182	−	1.11545i
$315$	−1.62928e6	+	1.62928e6i	−0.925164	+	0.925164i
$316$	−12164.2	+	39668.5i	−0.00685275	+	0.0223474i
$317$	2.37405e6	+	2.37405e6i	1.32691	+	1.32691i	0.908049	+	0.418864i	$0.137572\pi$
$317$	2.37405e6	+	2.37405e6i	1.32691	+	1.32691i	0.418864	+	0.908049i	$0.362428\pi$
$318$	−860500.	−	1.16392e6i	−0.477181	−	0.645437i
$319$	−409034.			−0.225052
$320$	327361.	−	3.04116e6i	0.178711	−	1.66021i
$321$	−753932.			−0.408385
$322$	−330541.	−	447092.i	−0.177659	−	0.240302i
$323$	546422.	+	546422.i	0.291422	+	0.291422i
$324$	−293223.	+	956228.i	−0.155180	+	0.506056i
$325$	−1.33248e6	+	1.33248e6i	−0.699764	+	0.699764i
$326$	−115477.	+	770472.i	−0.0601801	+	0.401525i
$327$		−	970077.i		−	0.501691i
$328$	−236003.	−	669121.i	−0.121125	−	0.343415i
$329$			1.75066e6i			0.891686i
$330$	1.39501e6	+	209082.i	0.705166	+	0.105689i
$331$	999148.	−	999148.i	0.501256	−	0.501256i	−0.410572	−	0.911828i	$-0.634671\pi$
$331$	999148.	−	999148.i	0.501256	−	0.501256i	0.911828	+	0.410572i	$0.134671\pi$
$332$	−3.14780e6	+	1.67034e6i	−1.56734	+	0.831686i
$333$	−636207.	−	636207.i	−0.314404	−	0.314404i
$334$	2.30564e6	−	1.70459e6i	1.13090	−	0.836091i
$335$	2.14802e6			1.04575
$336$	1.80904e6	−	348500.i	0.874178	−	0.168405i
$337$	229530.			0.110094			0.0550471	−	0.998484i	$-0.482469\pi$
$337$	229530.			0.110094			0.0550471	+	0.998484i	$0.482469\pi$
$338$	−1.17168e6	+	866237.i	−0.557848	+	0.412425i
$339$	3.11025e6	+	3.11025e6i	1.46993	+	1.46993i
$340$	−2.45514e6	−	4.62679e6i	−1.15181	−	2.17061i
$341$	187726.	−	187726.i	0.0874254	−	0.0874254i
$342$	−808128.	−	121121.i	−0.373607	−	0.0559957i
$343$			2.10426e6i			0.965747i
$344$	−975402.	+	2.03838e6i	−0.444414	+	0.928731i
$345$		−	2.91082e6i		−	1.31664i
$346$	−257520.	+	1.71819e6i	−0.115643	+	0.771580i
$347$	1.21960e6	−	1.21960e6i	0.543742	−	0.543742i	−0.380882	−	0.924624i	$-0.624379\pi$
$347$	1.21960e6	−	1.21960e6i	0.543742	−	0.543742i	0.924624	+	0.380882i	$0.124379\pi$
$348$	−2.67385e6	−	819925.i	−1.18355	−	0.362932i
$349$	230382.	+	230382.i	0.101248	+	0.101248i	0.755916	−	0.654668i	$-0.227192\pi$
$349$	230382.	+	230382.i	0.101248	+	0.101248i	−0.654668	+	0.755916i	$0.727192\pi$
$350$	−1.41520e6	−	1.91421e6i	−0.617516	−	0.835255i
$351$	683096.			0.295947
$352$	−476614.	−	438575.i	−0.205027	−	0.188663i
$353$	624189.			0.266612			0.133306	−	0.991075i	$-0.457441\pi$
$353$	624189.			0.266612			0.133306	+	0.991075i	$0.457441\pi$
$354$	3.75020e6	+	5.07254e6i	1.59054	+	2.15138i
$355$	−2.21871e6	−	2.21871e6i	−0.934392	−	0.934392i
$356$	2.65950e6	+	815527.i	1.11218	+	0.341046i
$357$	2.23078e6	−	2.23078e6i	0.926374	−	0.926374i
$358$	565944.	−	3.77601e6i	0.233381	−	1.55713i
$359$		−	1.12736e6i		−	0.461664i	−0.972994	−	0.230832i	$-0.925855\pi$
$359$		−	1.12736e6i		−	0.461664i	0.972994	−	0.230832i	$-0.0741448\pi$
$360$	4.99620e6	+	2.39077e6i	2.03181	+	0.972258i
$361$		−	2.28189e6i		−	0.921567i
$362$	1.05383e6	+	157947.i	0.422668	+	0.0633489i
$363$	−2.50953e6	+	2.50953e6i	−0.999598	+	0.999598i
$364$	380885.	+	717790.i	0.150675	+	0.283951i
$365$	3.71123e6	+	3.71123e6i	1.45810	+	1.45810i
$366$	−4.07675e6	+	3.01400e6i	−1.59079	+	1.17609i
$367$	−4.39717e6			−1.70415			−0.852075	−	0.523419i	$-0.824656\pi$
$367$	−4.39717e6			−1.70415			−0.852075	+	0.523419i	$0.824656\pi$
$368$	−749244.	+	1.10680e6i	−0.288406	+	0.426039i
$369$	1.28480e6			0.491214
$370$	1.16546e6	−	861638.i	0.442580	−	0.327205i
$371$	570300.	+	570300.i	0.215114	+	0.215114i
$372$	1.60346e6	−	850856.i	0.600761	−	0.318786i
$373$	−2.02742e6	+	2.02742e6i	−0.754522	+	0.754522i	−0.975320	−	0.220798i	$-0.929134\pi$
$373$	−2.02742e6	+	2.02742e6i	−0.754522	+	0.754522i	0.220798	+	0.975320i	$0.429134\pi$
$374$	−1.09688e6	−	164398.i	−0.405488	−	0.0607741i
$375$		−	5.49343e6i		−	2.01728i
$376$	3.96865e6	−	1.39977e6i	1.44768	−	0.510607i
$377$		−	1.23356e6i		−	0.446999i
$378$	−127909.	+	853413.i	−0.0460437	+	0.307206i
$379$	−3.25545e6	+	3.25545e6i	−1.16416	+	1.16416i	−0.180606	+	0.983556i	$0.557806\pi$
$379$	−3.25545e6	+	3.25545e6i	−1.16416	+	1.16416i	−0.983556	+	0.180606i	$0.942194\pi$
$380$	385919.	−	1.25852e6i	0.137100	−	0.447095i
$381$	−879309.	−	879309.i	−0.310334	−	0.310334i
$382$	581112.	+	786016.i	0.203752	+	0.275596i
$383$	−5.13780e6			−1.78970			−0.894851	−	0.446365i	$-0.852718\pi$
$383$	−5.13780e6			−1.78970			−0.894851	+	0.446365i	$0.852718\pi$
$384$	−2.23648e6	−	3.82235e6i	−0.773993	−	1.32283i
$385$	−785976.			−0.270245
$386$	316363.	+	427915.i	0.108073	+	0.146180i
$387$	−2.89344e6	−	2.89344e6i	−0.982058	−	0.982058i
$388$	78777.3	−	256900.i	0.0265657	−	0.0866333i
$389$	−1.12949e6	+	1.12949e6i	−0.378449	+	0.378449i	−0.870542	−	0.492093i	$-0.836232\pi$
$389$	−1.12949e6	+	1.12949e6i	−0.378449	+	0.378449i	0.492093	+	0.870542i	$0.336232\pi$
$390$	−630546.	+	4.20704e6i	−0.209921	+	1.40060i
$391$			2.28874e6i			0.757103i
$392$	1.90108e6	−	670524.i	0.624864	−	0.220394i
$393$		−	3.44659e6i		−	1.12566i
$394$	−2.14290e6	−	321176.i	−0.695443	−	0.104232i
$395$	85582.7	−	85582.7i	0.0275990	−	0.0275990i
$396$	1.03602e6	−	549752.i	0.331995	−	0.176169i
$397$	2.72721e6	+	2.72721e6i	0.868446	+	0.868446i	0.992300	−	0.123855i	$-0.0395256\pi$
$397$	2.72721e6	+	2.72721e6i	0.868446	+	0.868446i	−0.123855	+	0.992300i	$0.539526\pi$
$398$	−11971.4	+	8850.63i	−0.00378824	+	0.00280070i
$399$	792855.			0.249322
$400$	−3.20786e6	+	4.73872e6i	−1.00246	+	1.48085i
$401$	2.99586e6			0.930380			0.465190	−	0.885211i	$-0.345986\pi$
$401$	2.99586e6			0.930380			0.465190	+	0.885211i	$0.345986\pi$
$402$	2.50077e6	−	1.84886e6i	0.771808	−	0.570608i
$403$	566141.	+	566141.i	0.173645	+	0.173645i
$404$	2.48865e6	+	4.68994e6i	0.758596	+	1.42960i
$405$	2.06301e6	−	2.06301e6i	0.624978	−	0.624978i
$406$	1.54112e6	+	230981.i	0.464004	+	0.0695444i
$407$		−	306911.i		−	0.0918389i
$408$	−6.84072e6	−	3.27340e6i	−2.03447	−	0.973530i
$409$		−	1.92517e6i		−	0.569064i	−0.958667	−	0.284532i	$-0.908162\pi$
$409$		−	1.92517e6i		−	0.569064i	0.958667	−	0.284532i	$-0.0918382\pi$
$410$	−306777.	+	2.04683e6i	−0.0901287	+	0.601343i
$411$	1.31072e6	−	1.31072e6i	0.382741	−	0.382741i
$412$	−1.34324e6	−	411899.i	−0.389862	−	0.119550i
$413$	−2.48546e6	−	2.48546e6i	−0.717020	−	0.717020i
$414$	−1.43880e6	−	1.94612e6i	−0.412571	−	0.558046i
$415$	1.03949e7			2.96279
$416$	1.32265e6	−	1.43737e6i	0.374724	−	0.407225i
$417$	−6.08547e6			−1.71378
$418$	−165709.	−	224138.i	−0.0463879	−	0.0627445i
$419$	−3.34923e6	−	3.34923e6i	−0.931986	−	0.931986i	0.0658442	−	0.997830i	$-0.479026\pi$
$419$	−3.34923e6	−	3.34923e6i	−0.931986	−	0.931986i	−0.997830	+	0.0658442i	$0.979026\pi$
$420$	−5.13792e6	−	1.57552e6i	−1.42123	−	0.435814i
$421$	−1.64448e6	+	1.64448e6i	−0.452193	+	0.452193i	−0.896082	−	0.443889i	$-0.853598\pi$
$421$	−1.64448e6	+	1.64448e6i	−0.452193	+	0.452193i	0.443889	+	0.896082i	$0.353598\pi$
$422$	−480046.	+	3.20289e6i	−0.131221	+	0.875511i
$423$			7.62035e6i			2.07073i
$424$	836847.	−	1.74883e6i	0.226064	−	0.472426i
$425$			9.79917e6i			2.63158i
$426$	−4.49276e6	−	673370.i	−1.19947	−	0.179775i
$427$	1.99754e6	−	1.99754e6i	0.530183	−	0.530183i
$428$	−473335.	−	892015.i	−0.124899	−	0.235376i
$429$	636965.	+	636965.i	0.167098	+	0.167098i
$430$	5.30044e6	−	3.91869e6i	1.38242	−	1.02204i
$431$	2.16064e6			0.560260			0.280130	−	0.959962i	$-0.409622\pi$
$431$	2.16064e6			0.560260			0.280130	+	0.959962i	$0.409622\pi$
$432$	2.03691e6	−	392399.i	0.525126	−	0.101162i
$433$	4.71014e6			1.20730			0.603648	−	0.797251i	$-0.293713\pi$
$433$	4.71014e6			1.20730			0.603648	+	0.797251i	$0.293713\pi$
$434$	−813305.	+	601288.i	−0.207267	+	0.153235i
$435$	5.76869e6	+	5.76869e6i	1.46169	+	1.46169i
$436$	1.14775e6	−	609036.i	0.289154	−	0.153436i
$437$	−406728.	+	406728.i	−0.101883	+	0.101883i
$438$	7.51505e6	+	1.12635e6i	1.87174	+	0.280535i
$439$		−	5.09905e6i		−	1.26278i	−0.775466	−	0.631390i	$-0.782485\pi$
$439$		−	5.09905e6i		−	1.26278i	0.775466	−	0.631390i	$-0.217515\pi$
$440$	628441.	+	1.78177e6i	0.154751	+	0.438752i
$441$			3.65034e6i			0.893792i
$442$	495791.	−	3.30794e6i	0.120710	−	0.805383i
$443$	1.11742e6	−	1.11742e6i	0.270526	−	0.270526i	−0.558786	−	0.829312i	$-0.688733\pi$
$443$	1.11742e6	−	1.11742e6i	0.270526	−	0.270526i	0.829312	+	0.558786i	$0.188733\pi$
$444$	615216.	−	2.00627e6i	0.148105	−	0.482984i
$445$	−5.73775e6	−	5.73775e6i	−1.37354	−	1.37354i
$446$	−460467.	−	622830.i	−0.109613	−	0.148263i
$447$	−5.70373e6			−1.35017
$448$	1.54808e6	+	1.92157e6i	0.364418	+	0.452336i
$449$	1.16537e6			0.272801			0.136401	−	0.990654i	$-0.456447\pi$
$449$	1.16537e6			0.272801			0.136401	+	0.990654i	$0.456447\pi$
$450$	−6.16016e6	−	8.33226e6i	−1.43404	−	1.93969i
$451$	309900.	+	309900.i	0.0717430	+	0.0717430i
$452$	−1.72721e6	+	5.63258e6i	−0.397648	+	1.29677i
$453$	6.98891e6	−	6.98891e6i	1.60016	−	1.60016i
$454$	64057.7	−	427397.i	0.0145858	−	0.0973176i
$455$		−	2.37034e6i		−	0.536762i
$456$	−633940.	−	1.79736e6i	−0.142770	−	0.404784i
$457$			6.32020e6i			1.41560i	0.706413	+	0.707800i	$0.250312\pi$
$457$			6.32020e6i			1.41560i	−0.706413	+	0.707800i	$0.749688\pi$
$458$	5.49776e6	+	823998.i	1.22468	+	0.183553i
$459$	2.51178e6	−	2.51178e6i	0.556480	−	0.556480i
$460$	3.44394e6	−	1.82748e6i	0.758858	−	0.402678i
$461$	−3.35574e6	−	3.35574e6i	−0.735420	−	0.735420i	0.236268	−	0.971688i	$-0.424076\pi$
$461$	−3.35574e6	−	3.35574e6i	−0.735420	−	0.735420i	−0.971688	+	0.236268i	$0.924076\pi$
$462$	−915050.	+	676509.i	−0.199453	+	0.147458i
$463$	−2.89894e6			−0.628472			−0.314236	−	0.949345i	$-0.601748\pi$
$463$	−2.89894e6			−0.628472			−0.314236	+	0.949345i	$0.601748\pi$
$464$	−708607.	−	3.67833e6i	−0.152795	−	0.793150i
$465$	−5.29508e6			−1.13564
$466$	−3.85787e6	+	2.85217e6i	−0.822967	+	0.608431i
$467$	806983.	+	806983.i	0.171227	+	0.171227i	0.787518	−	0.616291i	$-0.211366\pi$
$467$	806983.	+	806983.i	0.171227	+	0.171227i	−0.616291	+	0.787518i	$0.711366\pi$
$468$	1.65794e6	+	3.12443e6i	0.349907	+	0.659411i
$469$	−1.22534e6	+	1.22534e6i	−0.257231	+	0.257231i
$470$	−1.21401e7	−	1.81954e6i	−2.53499	−	0.379941i
$471$			8.32262e6i			1.72865i
$472$	−3.64711e6	+	7.62169e6i	−0.753519	+	1.57469i
$473$		−	1.39582e6i		−	0.286864i
$474$	25974.1	−	173300.i	0.00530999	−	0.0354286i
$475$	−1.74139e6	+	1.74139e6i	−0.354129	+	0.354129i
$476$	4.03988e6	+	1.23881e6i	0.817243	+	0.250604i
$477$	2.48243e6	+	2.48243e6i	0.499552	+	0.499552i
$478$	2.91050e6	+	3.93676e6i	0.582636	+	0.788077i
$479$	−981579.			−0.195473			−0.0977365	−	0.995212i	$-0.531160\pi$
$479$	−981579.			−0.195473			−0.0977365	+	0.995212i	$0.531160\pi$
$480$	536483.	+	1.29071e7i	0.106280	+	2.55697i
$481$	925579.			0.182411
$482$	−1.50473e6	−	2.03531e6i	−0.295013	−	0.399036i
$483$	1.66047e6	+	1.66047e6i	0.323865	+	0.323865i
$484$	−4.54468e6	−	1.39361e6i	−0.881841	−	0.270413i
$485$	−554249.	+	554249.i	−0.106992	+	0.106992i
$486$	1.03886e6	−	6.93136e6i	0.199512	−	1.33115i
$487$			3.17956e6i			0.607498i	0.952752	+	0.303749i	$0.0982384\pi$
$487$			3.17956e6i			0.607498i	−0.952752	+	0.303749i	$0.901762\pi$
$488$	−6.12549e6	−	2.93115e6i	−1.16437	−	0.557172i
$489$		−	3.29036e6i		−	0.622260i
$490$	−5.81538e6	−	871603.i	−1.09418	−	0.163994i
$491$	4.44230e6	−	4.44230e6i	0.831579	−	0.831579i	−0.156153	−	0.987733i	$-0.549909\pi$
$491$	4.44230e6	−	4.44230e6i	0.831579	−	0.831579i	0.987733	+	0.156153i	$0.0499094\pi$
$492$	1.40460e6	+	2.64702e6i	0.261602	+	0.492997i
$493$	−4.53585e6	−	4.53585e6i	−0.840507	−	0.840507i
$494$	675954.	−	499742.i	0.124623	−	0.0921358i
$495$	−3.42124e6			−0.627581
$496$	2.01338e6	+	1.36295e6i	0.367470	+	0.248757i
$497$	2.53132e6			0.459680
$498$	1.21020e7	−	8.94716e6i	2.18667	−	1.61663i
$499$	−1.09055e6	−	1.09055e6i	−0.196062	−	0.196062i	0.602247	−	0.798309i	$-0.294272\pi$
$499$	−1.09055e6	−	1.09055e6i	−0.196062	−	0.196062i	−0.798309	+	0.602247i	$0.794272\pi$
$500$	6.49955e6	−	3.44890e6i	1.16268	−	0.616958i
$501$	−8.56301e6	+	8.56301e6i	−1.52416	+	1.52416i
$502$	881108.	+	132059.i	0.156052	+	0.0233889i
$503$		−	3.29704e6i		−	0.581037i	−0.956869	−	0.290518i	$-0.906172\pi$
$503$		−	3.29704e6i		−	0.581037i	0.956869	−	0.290518i	$-0.0938278\pi$
$504$	−4.21389e6	+	1.48627e6i	−0.738936	+	0.260627i
$505$		−	1.54874e7i		−	2.70241i
$506$	122370.	−	816456.i	0.0212470	−	0.141761i
$507$	4.35154e6	−	4.35154e6i	0.751836	−	0.751836i
$508$	488304.	−	1.59240e6i	0.0839520	−	0.273775i
$509$	−2.37340e6	−	2.37340e6i	−0.406047	−	0.406047i	0.474311	−	0.880357i	$-0.342697\pi$
$509$	−2.37340e6	−	2.37340e6i	−0.406047	−	0.406047i	−0.880357	+	0.474311i	$0.842697\pi$
$510$	1.31509e7	+	1.77880e7i	2.23888	+	3.02833i
$511$	−4.23414e6			−0.717320
$512$	3.11830e6	−	5.04585e6i	0.525706	−	0.850666i
$513$	892725.			0.149770
$514$	4.48363e6	+	6.06458e6i	0.748552	+	1.01250i
$515$	2.89798e6	+	2.89798e6i	0.481478	+	0.481478i
$516$	2.79798e6	−	9.12445e6i	0.462615	−	1.50863i
$517$	−1.83806e6	+	1.83806e6i	−0.302436	+	0.302436i
$518$	−173313.	+	1.15635e6i	−0.0283796	+	0.189350i
$519$		−	7.33768e6i		−	1.19575i
$520$	−5.37343e6	+	1.89524e6i	−0.871452	+	0.307367i
$521$			1.72575e6i			0.278538i	0.990255	+	0.139269i	$0.0444753\pi$
$521$			1.72575e6i			0.278538i	−0.990255	+	0.139269i	$0.955525\pi$
$522$	6.70827e6	+	1.00543e6i	1.07754	+	0.161501i
$523$	−2.09172e6	+	2.09172e6i	−0.334387	+	0.334387i	−0.854250	−	0.519863i	$-0.825983\pi$
$523$	−2.09172e6	+	2.09172e6i	−0.334387	+	0.334387i	0.519863	+	0.854250i	$0.325983\pi$
$524$	4.07783e6	−	2.16385e6i	0.648785	−	0.344269i
$525$	7.10926e6	+	7.10926e6i	1.12571	+	1.12571i
$526$	−2.70871e6	+	2.00259e6i	−0.426873	+	0.315593i
$527$	4.16345e6			0.653021
$528$	2.26526e6	+	1.53346e6i	0.353616	+	0.239379i
$529$	4.73272e6			0.735313
$530$	−4.54752e6	+	3.36204e6i	−0.703210	+	0.519893i
$531$	−1.08188e7	−	1.08188e7i	−1.66511	−	1.66511i
$532$	497772.	+	938066.i	0.0762520	+	0.143699i
$533$	−934591.	+	934591.i	−0.142496	+	0.142496i
$534$	−1.16186e7	−	1.74139e6i	−1.76320	−	0.264267i
$535$			2.94568e6i			0.444939i
$536$	3.75752e6	+	1.79804e6i	0.564922	+	0.270325i
$537$			1.61258e7i			2.41315i
$538$	−1.46280e6	+	9.75986e6i	−0.217885	+	1.45374i
$539$	−880475.	+	880475.i	−0.130541	+	0.130541i
$540$	−5.78511e6	−	1.77398e6i	−0.853743	−	0.261797i
$541$	5.03628e6	+	5.03628e6i	0.739804	+	0.739804i	0.972540	−	0.232736i	$-0.0747679\pi$
$541$	5.03628e6	+	5.03628e6i	0.739804	+	0.739804i	−0.232736	+	0.972540i	$0.574768\pi$
$542$	−4.71036e6	−	6.37126e6i	−0.688741	−	0.931595i
$543$	−4.50047e6			−0.655025
$544$	−421830.	−	1.01487e7i	−0.0611139	−	1.47033i
$545$	−3.79017e6			−0.546597
$546$	−2.04021e6	−	2.75960e6i	−0.292882	−	0.396154i
$547$	7.99064e6	+	7.99064e6i	1.14186	+	1.14186i	0.988110	+	0.153751i	$0.0491355\pi$
$547$	7.99064e6	+	7.99064e6i	1.14186	+	1.14186i	0.153751	+	0.988110i	$0.450864\pi$
$548$	2.37367e6	+	727878.i	0.337652	+	0.103540i
$549$	8.69499e6	−	8.69499e6i	1.23123	−	1.23123i
$550$	523921.	−	3.49563e6i	0.0738514	−	0.492741i
$551$		−	1.61211e6i		−	0.226213i
$552$	2.43655e6	−	5.09187e6i	0.340351	−	0.711262i
$553$			97641.2i			0.0135775i
$554$	−2.27197e6	−	340520.i	−0.314505	−	0.0471376i
$555$	−4.32844e6	+	4.32844e6i	−0.596484	+	0.596484i
$556$	−3.82060e6	−	7.20002e6i	−0.524136	−	0.987750i
$557$	−235720.	−	235720.i	−0.0321928	−	0.0321928i	0.690827	−	0.723020i	$-0.257247\pi$
$557$	−235720.	−	235720.i	−0.0321928	−	0.0321928i	−0.723020	+	0.690827i	$0.757247\pi$
$558$	−3.54020e6	+	2.61732e6i	−0.481329	+	0.355853i
$559$	4.20949e6			0.569771
$560$	−1.36162e6	−	7.06807e6i	−0.183479	−	0.952425i
$561$	4.68430e6			0.628402
$562$	−1.28103e6	+	947086.i	−0.171088	+	0.126488i
$563$	1.27572e6	+	1.27572e6i	0.169623	+	0.169623i	0.786814	−	0.617190i	$-0.211729\pi$
$563$	1.27572e6	+	1.27572e6i	0.169623	+	0.169623i	−0.617190	+	0.786814i	$0.711729\pi$
$564$	−1.56998e7	+	8.33091e6i	−2.07825	+	1.10279i
$565$	1.21520e7	−	1.21520e7i	1.60150	−	1.60150i
$566$	5.01340e6	+	751402.i	0.657796	+	0.0985897i
$567$			2.35369e6i			0.307462i
$568$	−2.02396e6	−	5.73836e6i	−0.263227	−	0.746307i
$569$			759484.i			0.0983418i	0.998790	+	0.0491709i	$0.0156579\pi$
$569$			759484.i			0.0983418i	−0.998790	+	0.0491709i	$0.984342\pi$
$570$	−824049.	+	5.49810e6i	−0.106235	+	0.708803i
$571$	−2.88567e6	+	2.88567e6i	−0.370387	+	0.370387i	−0.867618	−	0.497231i	$-0.834350\pi$
$571$	−2.88567e6	+	2.88567e6i	−0.370387	+	0.370387i	0.497231	+	0.867618i	$0.334350\pi$
$572$	−353724.	+	1.15353e6i	−0.0452038	+	0.147413i
$573$	−2.91922e6	−	2.91922e6i	−0.371433	−	0.371433i
$574$	−992613.	−	1.34261e6i	−0.125748	−	0.170087i
$575$	−7.29398e6			−0.920015
$576$	6.73858e6	+	8.36430e6i	0.846276	+	1.05045i
$577$	4.77807e6			0.597466			0.298733	−	0.954337i	$-0.403436\pi$
$577$	4.77807e6			0.597466			0.298733	+	0.954337i	$0.403436\pi$
$578$	−5.56555e6	−	7.52800e6i	−0.692929	−	0.937260i
$579$	−1.58925e6	−	1.58925e6i	−0.197013	−	0.197013i
$580$	−3.20351e6	+	1.04469e7i	−0.395418	+	1.28949i
$581$	−5.92977e6	+	5.92977e6i	−0.728781	+	0.728781i
$582$	−168213.	+	1.12232e6i	−0.0205850	+	0.137344i
$583$			1.19754e6i			0.145922i
$584$	3.38548e6	+	9.59857e6i	0.410760	+	1.16459i
$585$		−	1.03177e7i		−	1.24651i
$586$	−8.32259e6	−	1.24738e6i	−1.00119	−	0.150057i
$587$	−1.02170e7	+	1.02170e7i	−1.22385	+	1.22385i	−0.257593	+	0.966253i	$0.582929\pi$
$587$	−1.02170e7	+	1.02170e7i	−1.22385	+	1.22385i	−0.966253	+	0.257593i	$0.917071\pi$
$588$	−7.52061e6	+	3.99071e6i	−0.897035	+	0.476000i
$589$	739878.	+	739878.i	0.0878764	+	0.0878764i
$590$	1.98188e7	−	1.46523e7i	2.34395	−	1.73291i
$591$	9.15144e6			1.07776
$592$	2.75997e6	−	531691.i	0.323668	−	0.0623526i
$593$	−8.25323e6			−0.963801			−0.481900	−	0.876226i	$-0.660053\pi$
$593$	−8.25323e6			−0.963801			−0.481900	+	0.876226i	$0.660053\pi$
$594$	−1.03031e6	+	761725.i	−0.119813	+	0.0885792i
$595$	−8.71584e6	−	8.71584e6i	−1.00929	−	1.00929i
$596$	−3.58093e6	−	6.74836e6i	−0.412933	−	0.778185i
$597$	44461.2	−	44461.2i	0.00510558	−	0.00510558i
$598$	2.46226e6	+	369040.i	0.281566	+	0.0422008i
$599$			5.68979e6i			0.647932i	0.946069	+	0.323966i	$0.105016\pi$
$599$			5.68979e6i			0.647932i	−0.946069	+	0.323966i	$0.894984\pi$
$600$	1.04320e7	−	2.18007e7i	1.18301	−	2.47224i
$601$			9.93569e6i			1.12205i	0.827799	+	0.561025i	$0.189593\pi$
$601$			9.93569e6i			1.12205i	−0.827799	+	0.561025i	$0.810407\pi$
$602$	−788220.	+	5.25905e6i	−0.0886454	+	0.591447i
$603$	−5.33371e6	+	5.33371e6i	−0.597360	+	0.597360i
$604$	1.26567e7	+	3.88113e6i	1.41166	+	0.432879i
$605$	9.80493e6	+	9.80493e6i	1.08907	+	1.08907i
$606$	−1.33304e7	−	1.80308e7i	−1.47456	−	1.99450i
$607$	1.50377e7			1.65657			0.828284	−	0.560308i	$-0.189317\pi$
$607$	1.50377e7			1.65657			0.828284	+	0.560308i	$0.189317\pi$
$608$	1.72854e6	−	1.87847e6i	0.189636	−	0.206084i
$609$	−6.58149e6			−0.719086
$610$	1.17759e7	+	1.59282e7i	1.28136	+	1.73318i
$611$	−5.54320e6	−	5.54320e6i	−0.600700	−	0.600700i
$612$	1.75850e7	+	5.39237e6i	1.89786	+	0.581970i
$613$	−4.51772e6	+	4.51772e6i	−0.485588	+	0.485588i	−0.906911	−	0.421323i	$-0.861566\pi$
$613$	−4.51772e6	+	4.51772e6i	−0.485588	+	0.485588i	0.421323	+	0.906911i	$0.361566\pi$
$614$	−2.20988e6	+	1.47444e7i	−0.236563	+	1.57836i
$615$		−	8.74117e6i		−	0.931927i
$616$	−1.37490e6	−	657914.i	−0.145989	−	0.0698582i
$617$		−	1.08325e7i		−	1.14556i	−0.819710	−	0.572778i	$-0.805866\pi$
$617$		−	1.08325e7i		−	1.14556i	0.819710	−	0.572778i	$-0.194134\pi$
$618$	5.86824e6	+	879525.i	0.618069	+	0.0926355i
$619$	1.10140e7	−	1.10140e7i	1.15536	−	1.15536i	0.169898	−	0.985462i	$-0.445656\pi$
$619$	1.10140e7	−	1.10140e7i	1.15536	−	1.15536i	0.985462	−	0.169898i	$-0.0543438\pi$
$620$	−3.32437e6	−	6.26487e6i	−0.347320	−	0.654535i
$621$	1.86963e6	+	1.86963e6i	0.194548	+	0.194548i
$622$	−1.51863e7	+	1.12274e7i	−1.57390	+	1.16360i
$623$	6.54619e6			0.675722
$624$	−4.62458e6	+	6.83153e6i	−0.475456	+	0.702354i
$625$	−3.99991e6			−0.409590
$626$	3.16343e6	−	2.33877e6i	0.322643	−	0.238534i
$627$	832438.	+	832438.i	0.0845635	+	0.0845635i
$628$	−9.84690e6	+	5.22512e6i	−0.996324	+	0.528686i
$629$	3.40340e6	−	3.40340e6i	0.342994	−	0.342994i
$630$	1.28902e7	+	1.93197e6i	1.29393	+	0.193932i
$631$		−	7.66760e6i		−	0.766630i	−0.923618	−	0.383315i	$-0.874782\pi$
$631$		−	7.66760e6i		−	0.766630i	0.923618	−	0.383315i	$-0.125218\pi$
$632$	221347.	−	78070.7i	0.0220436	−	0.00777491i
$633$		−	1.36782e7i		−	1.35682i
$634$	2.81512e6	−	1.87826e7i	0.278147	−	1.85581i
$635$	−3.43553e6	+	3.43553e6i	−0.338111	+	0.338111i
$636$	−2.40052e6	+	7.82832e6i	−0.235322	+	0.767407i
$637$	−2.65533e6	−	2.65533e6i	−0.259280	−	0.259280i
$638$	1.37555e6	+	1.86057e6i	0.133790	+	0.180965i
$639$	1.10184e7			1.06750
$640$	−1.49342e7	+	8.73812e6i	−1.44123	+	0.843272i
$641$	3.59134e6			0.345232			0.172616	−	0.984989i	$-0.444778\pi$
$641$	3.59134e6			0.345232			0.172616	+	0.984989i	$0.444778\pi$
$642$	2.53542e6	+	3.42942e6i	0.242779	+	0.328385i
$643$	4.29588e6	+	4.29588e6i	0.409755	+	0.409755i	0.881653	−	0.471898i	$-0.156431\pi$
$643$	4.29588e6	+	4.29588e6i	0.409755	+	0.409755i	−0.471898	+	0.881653i	$0.656431\pi$
$644$	−922107.	+	3.00707e6i	−0.0876126	+	0.285712i
$645$	−1.96855e7	+	1.96855e7i	−1.86315	+	1.86315i
$646$	647940.	−	4.32309e6i	0.0610876	−	0.407580i
$647$		−	1.76944e7i		−	1.66178i	−0.556435	−	0.830891i	$-0.687831\pi$
$647$		−	1.76944e7i		−	1.66178i	0.556435	−	0.830891i	$-0.312169\pi$
$648$	5.33569e6	−	1.88193e6i	0.499175	−	0.176062i
$649$		−	5.21909e6i		−	0.486388i
$650$	1.05421e7	+	1.58003e6i	0.978684	+	0.146684i
$651$	3.02057e6	−	3.02057e6i	0.279342	−	0.279342i
$652$	3.89299e6	−	2.06576e6i	0.358645	−	0.190310i
$653$	−5.96181e6	−	5.96181e6i	−0.547136	−	0.547136i	0.378475	−	0.925611i	$-0.376448\pi$
$653$	−5.96181e6	−	5.96181e6i	−0.547136	−	0.547136i	−0.925611	+	0.378475i	$0.876448\pi$
$654$	−4.41260e6	+	3.26229e6i	−0.403413	+	0.298249i
$655$	−1.34661e7			−1.22642
$656$	−2.24997e6	+	3.32371e6i	−0.204135	+	0.301553i
$657$	−1.84306e7			−1.66581
$658$	7.96324e6	−	5.88733e6i	0.717010	−	0.530095i
$659$	1.12893e7	+	1.12893e7i	1.01264	+	1.01264i	0.999919	+	0.0127190i	$0.00404870\pi$
$659$	1.12893e7	+	1.12893e7i	1.01264	+	1.01264i	0.0127190	+	0.999919i	$0.495951\pi$
$660$	−3.74025e6	−	7.04860e6i	−0.334226	−	0.629859i
$661$	−6.36806e6	+	6.36806e6i	−0.566896	+	0.566896i	−0.931258	−	0.364362i	$-0.881287\pi$
$661$	−6.36806e6	+	6.36806e6i	−0.566896	+	0.566896i	0.364362	+	0.931258i	$0.381287\pi$
$662$	−7.90489e6	−	1.18478e6i	−0.701053	−	0.105073i
$663$			1.41269e7i			1.24814i
$664$	1.81837e7	+	8.70122e6i	1.60052	+	0.765879i
$665$		−	3.09775e6i		−	0.271639i
$666$	−754405.	+	5.03343e6i	−0.0659051	+	0.439722i
$667$	3.37625e6	−	3.37625e6i	0.293846	−	0.293846i
$668$	−1.55074e7	−	4.75527e6i	−1.34461	−	0.412320i
$669$	2.31316e6	+	2.31316e6i	0.199820	+	0.199820i
$670$	−7.22364e6	−	9.77073e6i	−0.621683	−	0.840892i
$671$	4.19453e6			0.359648
$672$	−7.66889e6	−	7.05682e6i	−0.655103	−	0.602817i
$673$	−7.19306e6			−0.612176			−0.306088	−	0.952003i	$-0.599020\pi$
$673$	−7.19306e6			−0.612176			−0.306088	+	0.952003i	$0.599020\pi$
$674$	−771891.	−	1.04406e6i	−0.0654495	−	0.0885274i
$675$	8.00477e6	+	8.00477e6i	0.676222	+	0.676222i
$676$	7.88052e6	+	2.41653e6i	0.663266	+	0.203388i
$677$	8.05533e6	−	8.05533e6i	0.675479	−	0.675479i	−0.283495	−	0.958974i	$-0.591494\pi$
$677$	8.05533e6	−	8.05533e6i	0.675479	−	0.675479i	0.958974	+	0.283495i	$0.0914939\pi$
$678$	3.68810e6	−	2.46072e7i	0.308126	−	2.05583i
$679$		−	632341.i		−	0.0526353i
$680$	−1.27895e7	+	2.67273e7i	−1.06067	+	2.21657i
$681$			1.82523e6i			0.150817i
$682$	−1.48522e6	−	222602.i	−0.122272	−	0.0183261i
$683$	−9.66998e6	+	9.66998e6i	−0.793184	+	0.793184i	−0.982010	−	0.188827i	$-0.939532\pi$
$683$	−9.66998e6	+	9.66998e6i	−0.793184	+	0.793184i	0.188827	+	0.982010i	$0.439532\pi$
$684$	2.16673e6	+	4.08326e6i	0.177078	+	0.333708i
$685$	−5.12109e6	−	5.12109e6i	−0.417000	−	0.417000i
$686$	9.57165e6	−	7.07645e6i	0.776563	−	0.574123i
$687$	−2.34787e7			−1.89794
$688$	1.25522e7	−	2.41811e6i	1.01100	−	0.194762i
$689$	−3.61154e6			−0.289830
$690$	−1.32405e7	+	9.78887e6i	−1.05872	+	0.782726i
$691$	−1.02355e7	−	1.02355e7i	−0.815482	−	0.815482i	0.169968	−	0.985450i	$-0.445634\pi$
$691$	−1.02355e7	−	1.02355e7i	−0.815482	−	0.815482i	−0.985450	+	0.169968i	$0.945634\pi$
$692$	8.68157e6	−	4.60676e6i	0.689180	−	0.365704i
$693$	1.95164e6	−	1.95164e6i	0.154371	−	0.154371i
$694$	−9.64901e6	−	1.44618e6i	−0.760473	−	0.113979i
$695$			2.37764e7i			1.86717i
$696$	5.26234e6	+	1.49199e7i	0.411771	+	1.16746i
$697$			6.87307e6i			0.535882i
$698$	273184.	−	1.82270e6i	0.0212235	−	0.141604i
$699$	1.43279e7	−	1.43279e7i	1.10915	−	1.10915i
$700$	−3.94797e6	+	1.28747e7i	−0.304529	+	0.993096i
$701$	9.12363e6	+	9.12363e6i	0.701250	+	0.701250i	0.964679	−	0.263429i	$-0.0848535\pi$
$701$	9.12363e6	+	9.12363e6i	0.701250	+	0.701250i	−0.263429	+	0.964679i	$0.584854\pi$
$702$	−2.29720e6	−	3.10721e6i	−0.175937	−	0.237973i
$703$	1.20962e6			0.0923126
$704$	−392131.	+	3.64287e6i	−0.0298195	+	0.277021i
$705$	5.18452e7			3.92858
$706$	−2.09910e6	−	2.83926e6i	−0.158497	−	0.214384i
$707$	8.83480e6	+	8.83480e6i	0.664734	+	0.664734i
$708$	1.04619e7	−	3.41171e7i	0.784379	−	2.55793i
$709$	7.51883e6	−	7.51883e6i	0.561739	−	0.561739i	−0.368062	−	0.929801i	$-0.619979\pi$
$709$	7.51883e6	−	7.51883e6i	0.561739	−	0.561739i	0.929801	+	0.368062i	$0.119979\pi$
$710$	−2.63091e6	+	1.75536e7i	−0.195867	+	1.30683i
$711$			425017.i			0.0315306i
$712$	−5.23412e6	−	1.48399e7i	−0.386940	−	1.09706i
$713$			3.09905e6i			0.228300i
$714$	−1.76491e7	−	2.64523e6i	−1.29562	−	0.194186i
$715$	2.48867e6	−	2.48867e6i	0.182055	−	0.182055i
$716$	−1.90792e7	+	1.01241e7i	−1.39084	+	0.738031i
$717$	−1.46209e7	−	1.46209e7i	−1.06213	−	1.06213i
$718$	−5.12803e6	+	3.79122e6i	−0.371227	+	0.274453i
$719$	−1.44353e7			−1.04137			−0.520684	−	0.853749i	$-0.674323\pi$
$719$	−1.44353e7			−1.04137			−0.520684	+	0.853749i	$0.674323\pi$
$720$	−5.92693e6	−	3.07662e7i	−0.426087	−	2.21179i
$721$	−3.30629e6			−0.236866
$722$	−1.03797e7	+	7.67383e6i	−0.741038	+	0.547859i
$723$	7.55902e6	+	7.55902e6i	0.537798	+	0.537798i
$724$	−2.82549e6	−	5.32473e6i	−0.200331	−	0.377530i
$725$	1.44553e7	−	1.44553e7i	1.02137	−	1.02137i
$726$	1.98545e7	+	2.97576e6i	1.39803	+	0.209535i
$727$		−	2.53963e7i		−	1.78211i	−0.453895	−	0.891055i	$-0.649966\pi$
$727$		−	2.53963e7i		−	1.78211i	0.453895	−	0.891055i	$-0.350034\pi$
$728$	1.98413e6	−	4.14641e6i	0.138753	−	0.289964i
$729$			2.20059e7i			1.53363i
$730$	4.40073e6	−	2.93619e7i	0.305645	−	2.03928i
$731$	1.54785e7	−	1.54785e7i	1.07136	−	1.07136i
$732$	2.74196e7	+	8.40812e6i	1.89140	+	0.579991i
$733$	1.92504e7	+	1.92504e7i	1.32336	+	1.32336i	0.911034	+	0.412331i	$0.135285\pi$
$733$	1.92504e7	+	1.92504e7i	1.32336	+	1.32336i	0.412331	+	0.911034i	$0.364715\pi$
$734$	1.47873e7	+	2.00014e7i	1.01309	+	1.37032i
$735$	2.48351e7			1.69569
$736$	7.55416e6	−	313988.i	0.514034	−	0.0213658i
$737$	−2.57302e6			−0.174492
$738$	−4.32069e6	−	5.84420e6i	−0.292020	−	0.394988i
$739$	−1.61617e6	−	1.61617e6i	−0.108862	−	0.108862i	0.650578	−	0.759440i	$-0.274527\pi$
$739$	−1.61617e6	−	1.61617e6i	−0.108862	−	0.108862i	−0.759440	+	0.650578i	$0.774527\pi$
$740$	−7.83868e6	−	2.40370e6i	−0.526215	−	0.161362i
$741$	−2.51045e6	+	2.51045e6i	−0.167960	+	0.167960i
$742$	676253.	−	4.51200e6i	0.0450920	−	0.300857i
$743$			1.59119e7i			1.05743i	0.848801	+	0.528713i	$0.177325\pi$
$743$			1.59119e7i			1.05743i	−0.848801	+	0.528713i	$0.822675\pi$
$744$	−9.26262e6	−	4.43233e6i	−0.613482	−	0.293562i
$745$			2.22849e7i			1.47103i
$746$	1.60402e7	+	2.40409e6i	1.05527	+	0.158162i
$747$	−2.58114e7	+	2.58114e7i	−1.69243	+	1.69243i
$748$	2.94091e6	+	5.54223e6i	0.192189	+	0.362185i
$749$	−1.68036e6	−	1.68036e6i	−0.109445	−	0.109445i
$750$	−2.49880e7	+	1.84740e7i	−1.62210	+	1.19924i
$751$	−1.27040e7			−0.821942			−0.410971	−	0.911649i	$-0.634810\pi$
$751$	−1.27040e7			−0.821942			−0.410971	+	0.911649i	$0.634810\pi$
$752$	−1.97134e7	−	1.33449e7i	−1.27121	−	0.860541i
$753$	−3.76285e6			−0.241841
$754$	−5.61110e6	+	4.14836e6i	−0.359434	+	0.265735i
$755$	−2.73062e7	−	2.73062e7i	−1.74339	−	1.74339i
$756$	4.31207e6	−	2.28814e6i	0.274398	−	0.145606i
$757$	−216825.	+	216825.i	−0.0137521	+	0.0137521i	−0.713949	−	0.700197i	$-0.753095\pi$
$757$	−216825.	+	216825.i	−0.0137521	+	0.0137521i	0.700197	+	0.713949i	$0.253095\pi$
$758$	2.57559e7	+	3.86027e6i	1.62819	+	0.244031i
$759$			3.48675e6i			0.219693i
$760$	−7.02243e6	+	2.47686e6i	−0.441015	+	0.155549i
$761$		−	7.64453e6i		−	0.478508i	−0.970957	−	0.239254i	$-0.923097\pi$
$761$		−	7.64453e6i		−	0.478508i	0.970957	−	0.239254i	$-0.0769029\pi$
$762$	−1.04267e6	+	6.95677e6i	−0.0650520	+	0.434030i
$763$	2.16210e6	−	2.16210e6i	0.134451	−	0.134451i
$764$	1.62112e6	−	5.28662e6i	0.100481	−	0.327676i
$765$	−3.79387e7	−	3.79387e7i	−2.34385	−	2.34385i
$766$	1.72780e7	+	2.33704e7i	1.06395	+	1.43911i
$767$	1.57397e7			0.966066
$768$	−9.86565e6	+	2.30274e7i	−0.603563	+	1.40877i
$769$	−3.02295e7			−1.84338			−0.921690	−	0.387927i	$-0.873191\pi$
$769$	−3.02295e7			−1.84338			−0.921690	+	0.387927i	$0.873191\pi$
$770$	2.64318e6	+	3.57518e6i	0.160657	+	0.217306i
$771$	−2.25235e7	−	2.25235e7i	−1.36458	−	1.36458i
$772$	882554.	−	2.87809e6i	0.0532964	−	0.173804i
$773$	−1.02682e7	+	1.02682e7i	−0.618081	+	0.618081i	−0.945039	−	0.326958i	$-0.893977\pi$
$773$	−1.02682e7	+	1.02682e7i	−0.618081	+	0.618081i	0.326958	+	0.945039i	$0.393977\pi$
$774$	−3.43100e6	+	2.28918e7i	−0.205858	+	1.37350i
$775$			1.32685e7i			0.793537i
$776$	−1.43348e6	+	505599.i	−0.0854553	+	0.0301406i
$777$		−	4.93830e6i		−	0.293444i
$778$	8.93609e6	+	1.33933e6i	0.529296	+	0.0793302i
$779$	−1.22140e6	+	1.22140e6i	−0.0721131	+	0.0721131i
$780$	2.12571e7	−	1.12798e7i	1.25103	−	0.663841i
$781$	2.65769e6	+	2.65769e6i	0.155911	+	0.155911i
$782$	1.04108e7	−	7.69686e6i	0.608791	−	0.450087i
$783$	−7.41052e6			−0.431961
$784$	−9.44321e6	−	6.39255e6i	−0.548693	−	0.371436i
$785$	3.25171e7			1.88338
$786$	−1.56775e7	+	1.15906e7i	−0.905152	+	0.669191i
$787$	1.42655e7	+	1.42655e7i	0.821016	+	0.821016i	0.986254	−	0.165238i	$-0.0528392\pi$
$787$	1.42655e7	+	1.42655e7i	0.821016	+	0.821016i	−0.165238	+	0.986254i	$0.552839\pi$
$788$	5.74548e6	+	1.08275e7i	0.329618	+	0.621174i
$789$	1.00600e7	−	1.00600e7i	0.575315	−	0.575315i
$790$	−677099.	−	101483.i	−0.0385998	−	0.00578529i
$791$			1.38642e7i			0.787869i
$792$	−5.98473e6	−	2.86380e6i	−0.339025	−	0.162229i
$793$			1.26498e7i			0.714334i
$794$	3.23389e6	−	2.15767e7i	0.182043	−	1.21460i
$795$	1.68892e7	−	1.68892e7i	0.947746	−	0.947746i
$796$	80517.9	+	24690.5i	0.00450412	+	0.00138117i
$797$	−8.39957e6	−	8.39957e6i	−0.468394	−	0.468394i	0.433000	−	0.901394i	$-0.357455\pi$
$797$	−8.39957e6	−	8.39957e6i	−0.468394	−	0.468394i	−0.901394	+	0.433000i	$0.857455\pi$
$798$	−2.66631e6	−	3.60646e6i	−0.148219	−	0.200482i
$799$	−4.07652e7			−2.25903
$800$	3.23429e7	−	1.34433e6i	1.78671	−	0.0742643i
$801$	2.84946e7			1.56921
$802$	−1.00748e7	−	1.36273e7i	−0.553098	−	0.748124i
$803$	−4.44553e6	−	4.44553e6i	−0.243296	−	0.243296i
$804$	−1.68198e7	−	5.15773e6i	−0.917659	−	0.281397i
$805$	6.48761e6	−	6.48761e6i	0.352854	−	0.352854i
$806$	671322.	−	4.47910e6i	0.0363993	−	0.242858i
$807$		−	4.16803e7i		−	2.25293i
$808$	1.29640e7	−	2.70920e7i	0.698572	−	1.45987i
$809$		−	2.07256e7i		−	1.11336i	−0.830728	−	0.556679i	$-0.812075\pi$
$809$		−	2.07256e7i		−	1.11336i	0.830728	−	0.556679i	$-0.187925\pi$
$810$	−1.63218e7	−	2.44629e6i	−0.874089	−	0.131007i
$811$	−1.00207e7	+	1.00207e7i	−0.534990	+	0.534990i	−0.922053	−	0.387063i	$-0.873490\pi$
$811$	−1.00207e7	+	1.00207e7i	−0.534990	+	0.534990i	0.387063	+	0.922053i	$0.373490\pi$
$812$	−4.13200e6	−	7.78689e6i	−0.219923	−	0.414451i
$813$	2.36625e7	+	2.36625e7i	1.25555	+	1.25555i
$814$	−1.39605e6	+	1.03212e6i	−0.0738482	+	0.0545970i
$815$	−1.28557e7			−0.677958
$816$	8.11505e6	+	4.21246e7i	0.426644	+	2.21468i
$817$	5.50131e6			0.288344
$818$	−8.75704e6	+	6.47420e6i	−0.457587	+	0.338301i
$819$	5.88573e6	+	5.88573e6i	0.306613	+	0.306613i
$820$	1.03421e7	−	5.48790e6i	0.537124	−	0.285018i
$821$	−9.59469e6	+	9.59469e6i	−0.496790	+	0.496790i	−0.910437	−	0.413647i	$-0.864255\pi$
$821$	−9.59469e6	+	9.59469e6i	−0.496790	+	0.496790i	0.413647	+	0.910437i	$0.364255\pi$
$822$	−1.03699e7	−	1.55423e6i	−0.535299	−	0.0802299i
$823$			2.70409e6i			0.139162i	0.997576	+	0.0695812i	$0.0221663\pi$
$823$			2.70409e6i			0.139162i	−0.997576	+	0.0695812i	$0.977834\pi$
$824$	2.64360e6	+	7.49519e6i	0.135637	+	0.384561i
$825$			1.49284e7i			0.763621i
$826$	−2.94722e6	+	1.96640e7i	−0.150301	+	1.00282i
$827$	1.66844e7	−	1.66844e7i	0.848296	−	0.848296i	−0.141624	−	0.989921i	$-0.545232\pi$
$827$	1.66844e7	−	1.66844e7i	0.848296	−	0.848296i	0.989921	+	0.141624i	$0.0452324\pi$
$828$	−4.01379e6	+	1.30893e7i	−0.203460	+	0.663501i
$829$	1.17600e7	+	1.17600e7i	0.594323	+	0.594323i	0.938796	−	0.344473i	$-0.111942\pi$
$829$	1.17600e7	+	1.17600e7i	0.594323	+	0.594323i	−0.344473	+	0.938796i	$0.611942\pi$
$830$	−3.49573e7	−	4.72834e7i	−1.76134	−	2.38239i
$831$	9.70263e6			0.487401
$832$	−1.09861e7	−	1.18258e6i	−0.550220	−	0.0592275i
$833$	−1.95275e7			−0.975068
$834$	2.04650e7	+	2.76810e7i	1.01882	+	1.37806i
$835$	3.34564e7	+	3.34564e7i	1.66059	+	1.66059i
$836$	−462275.	+	1.50752e6i	−0.0228763	+	0.0746015i
$837$	3.40105e6	−	3.40105e6i	0.167803	−	0.167803i
$838$	−3.97146e6	+	2.64978e7i	−0.195362	+	1.30347i
$839$			3.04420e7i			1.49303i	0.665370	+	0.746514i	$0.268274\pi$
$839$			3.04420e7i			1.49303i	−0.665370	+	0.746514i	$0.731726\pi$
$840$	1.01118e7	+	2.86692e7i	0.494460	+	1.40190i
$841$		−	7.12899e6i		−	0.347566i
$842$	1.30105e7	+	1.95000e6i	0.632433	+	0.0947883i
$843$	4.75769e6	−	4.75769e6i	0.230583	−	0.230583i
$844$	1.61834e7	−	8.58750e6i	0.782012	−	0.414964i
$845$	−1.70018e7	−	1.70018e7i	−0.819132	−	0.819132i
$846$	3.46628e7	−	2.56267e7i	1.66509	−	1.23102i
$847$	−1.11864e7			−0.535776
$848$	−1.07692e7	+	2.07462e6i	−0.514272	+	0.0990714i
$849$	−2.14101e7			−1.01941
$850$	4.45736e7	−	3.29538e7i	2.11607	−	1.56444i
$851$	2.53331e6	+	2.53331e6i	0.119912	+	0.119912i
$852$	1.20458e7	+	2.27008e7i	0.568510	+	1.07137i
$853$	1.72267e7	−	1.72267e7i	0.810645	−	0.810645i	−0.174086	−	0.984731i	$-0.555697\pi$
$853$	1.72267e7	−	1.72267e7i	0.810645	−	0.810645i	0.984731	+	0.174086i	$0.0556969\pi$
$854$	−1.58038e7	−	2.36866e6i	−0.741510	−	0.111137i
$855$		−	1.34840e7i		−	0.630819i
$856$	−2.46572e6	+	5.15284e6i	−0.115017	+	0.240360i
$857$		−	2.12352e7i		−	0.987654i	−0.869560	−	0.493827i	$-0.835598\pi$
$857$		−	2.12352e7i		−	0.987654i	0.869560	−	0.493827i	$-0.164402\pi$
$858$	755304.	−	5.03943e6i	0.0350271	−	0.233703i
$859$	−1.09233e7	+	1.09233e7i	−0.505094	+	0.505094i	−0.913017	−	0.407923i	$-0.866253\pi$
$859$	−1.09233e7	+	1.09233e7i	−0.505094	+	0.505094i	0.407923	+	0.913017i	$0.366253\pi$
$860$	−3.56500e7	−	1.09319e7i	−1.64366	−	0.504023i
$861$	4.98639e6	+	4.98639e6i	0.229234	+	0.229234i
$862$	−7.26607e6	−	9.82813e6i	−0.333067	−	0.450508i
$863$	−1.69966e6			−0.0776846			−0.0388423	−	0.999245i	$-0.512367\pi$
$863$	−1.69966e6			−0.0776846			−0.0388423	+	0.999245i	$0.512367\pi$
$864$	−8.63489e6	−	7.94572e6i	−0.393525	−	0.362117i
$865$	−2.86689e7			−1.30278
$866$	−1.58398e7	−	2.14251e7i	−0.717721	−	0.970794i
$867$	2.79586e7	+	2.79586e7i	1.26319	+	1.26319i
$868$	5.47017e6	+	1.67741e6i	0.246434	+	0.0755681i
$869$	−102516.	+	102516.i	−0.00460513	+	0.00460513i
$870$	6.84044e6	−	4.56398e7i	0.306398	−	2.04430i
$871$		−	7.75969e6i		−	0.346577i
$872$	−6.63011e6	−	3.17262e6i	−0.295277	−	0.141295i
$873$		−	2.75249e6i		−	0.122233i
$874$	3.21788e6	+	482292.i	0.142492	+	0.0213566i
$875$	1.22437e7	−	1.22437e7i	0.540621	−	0.540621i
$876$	−2.01491e7	−	3.79716e7i	−0.887147	−	1.67185i
$877$	−2.03805e6	−	2.03805e6i	−0.0894779	−	0.0894779i	0.660951	−	0.750429i	$-0.270153\pi$
$877$	−2.03805e6	−	2.03805e6i	−0.0894779	−	0.0894779i	−0.750429	+	0.660951i	$0.770153\pi$
$878$	−2.31941e7	+	1.71477e7i	−1.01541	+	0.750705i
$879$	3.55423e7			1.55158
$880$	5.99134e6	−	8.85054e6i	0.260806	−	0.385268i
$881$	2.77415e7			1.20418			0.602089	−	0.798429i	$-0.294335\pi$
$881$	2.77415e7			1.20418			0.602089	+	0.798429i	$0.294335\pi$
$882$	1.66043e7	−	1.22758e7i	0.718703	−	0.531347i
$883$	−5.23951e6	−	5.23951e6i	−0.226146	−	0.226146i	0.584935	−	0.811080i	$-0.301120\pi$
$883$	−5.23951e6	−	5.23951e6i	−0.226146	−	0.226146i	−0.811080	+	0.584935i	$0.801120\pi$
$884$	−1.67142e7	+	8.86915e6i	−0.719374	+	0.381726i
$885$	−7.36059e7	+	7.36059e7i	−3.15904	+	3.15904i
$886$	−8.84065e6	−	1.32503e6i	−0.378355	−	0.0567075i
$887$			8.76481e6i			0.374053i	0.982355	+	0.187027i	$0.0598850\pi$
$887$			8.76481e6i			0.374053i	−0.982355	+	0.187027i	$0.940115\pi$
$888$	−1.11949e7	+	3.94851e6i	−0.476417	+	0.168035i
$889$		−	3.91959e6i		−	0.166336i
$890$	−6.80375e6	+	4.53950e7i	−0.287921	+	1.92102i
$891$	−2.47120e6	+	2.47120e6i	−0.104283	+	0.104283i
$892$	−1.28456e6	+	4.18906e6i	−0.0540557	+	0.176281i
$893$	−7.24430e6	−	7.24430e6i	−0.303996	−	0.303996i
$894$	1.91812e7	+	2.59446e7i	0.802661	+	1.08568i
$895$	6.30047e7			2.62915
$896$	3.53457e6	−	1.35039e7i	0.147084	−	0.561938i
$897$	−1.05153e7			−0.436355
$898$	−3.91904e6	−	5.30091e6i	−0.162177	−	0.219361i
$899$	−6.14173e6	−	6.14173e6i	−0.253450	−	0.253450i
$900$	−1.71849e7	+	5.60415e7i	−0.707198	+	2.30623i
$901$	−1.32798e7	+	1.32798e7i	−0.544978	+	0.544978i
$902$	367475.	−	2.45181e6i	0.0150387	−	0.100339i
$903$		−	2.24592e7i		−	0.916590i
$904$	3.14294e7	−	1.10854e7i	1.27913	−	0.451158i
$905$			1.75837e7i			0.713656i
$906$	−5.52937e7	−	8.28735e6i	−2.23797	−	0.335425i
$907$	−2.35663e7	+	2.35663e7i	−0.951205	+	0.951205i	−0.998864	−	0.0476588i	$-0.984824\pi$
$907$	−2.35663e7	+	2.35663e7i	−0.951205	+	0.951205i	0.0476588	+	0.998864i	$0.484824\pi$
$908$	−2.15952e6	+	1.14592e6i	−0.0869247	+	0.0461254i
$909$	3.84565e7	+	3.84565e7i	1.54369	+	1.54369i
$910$	−1.07820e7	+	7.97126e6i	−0.431613	+	0.319098i
$911$	3.54883e7			1.41674			0.708368	−	0.705843i	$-0.249432\pi$
$911$	3.54883e7			1.41674			0.708368	+	0.705843i	$0.249432\pi$
$912$	−6.04377e6	+	8.92799e6i	−0.240614	+	0.355440i
$913$	−1.24516e7			−0.494366
$914$	2.87488e7	−	2.12544e7i	1.13829	−	0.841555i
$915$	−5.91565e7	−	5.91565e7i	−2.33587	−	2.33587i
$916$	−1.47404e7	−	2.77788e7i	−0.580459	−	1.09389i
$917$	7.68173e6	−	7.68173e6i	0.301672	−	0.301672i
$918$	−1.98723e7	−	2.97843e6i	−0.778288	−	0.116649i
$919$		−	9.42181e6i		−	0.367998i	−0.982926	−	0.183999i	$-0.941096\pi$
$919$		−	9.42181e6i		−	0.367998i	0.982926	−	0.183999i	$-0.0589043\pi$
$920$	−1.98944e7	−	9.51980e6i	−0.774926	−	0.370816i
$921$		−	6.29673e7i		−	2.44606i
$922$	−3.97919e6	+	2.65494e7i	−0.154158	+	1.02855i
$923$	−8.01503e6	+	8.01503e6i	−0.309671	+	0.309671i
$924$	6.15449e6	+	1.88725e6i	0.237144	+	0.0727192i
$925$	1.08463e7	+	1.08463e7i	0.416798	+	0.416798i
$926$	9.74890e6	+	1.31864e7i	0.373618	+	0.505358i
$927$	−1.43918e7			−0.550067
$928$	−1.43486e7	+	1.55932e7i	−0.546942	+	0.594381i
$929$	−7.56247e6			−0.287491			−0.143745	−	0.989615i	$-0.545915\pi$
$929$	−7.56247e6			−0.287491			−0.143745	+	0.989615i	$0.545915\pi$
$930$	1.78069e7	+	2.40858e7i	0.675121	+	0.913173i
$931$	−3.47020e6	−	3.47020e6i	−0.131214	−	0.131214i
$932$	2.59474e7	+	7.95667e6i	0.978485	+	0.300049i
$933$	5.64010e7	−	5.64010e7i	2.12121	−	2.12121i
$934$	956909.	−	6.38455e6i	0.0358925	−	0.239477i
$935$		−	1.83020e7i		−	0.684650i
$936$	8.63661e6	−	1.80487e7i	0.322221	−	0.673373i
$937$			3.14171e7i			1.16901i	0.811392	+	0.584503i	$0.198710\pi$
$937$			3.14171e7i			1.16901i	−0.811392	+	0.584503i	$0.801290\pi$
$938$	9.69442e6	+	1.45299e6i	0.359762	+	0.0539206i
$939$	−1.17488e7	+	1.17488e7i	−0.434840	+	0.434840i
$940$	3.25495e7	+	6.13406e7i	1.20150	+	2.26427i
$941$	−1.53398e7	−	1.53398e7i	−0.564735	−	0.564735i	0.365914	−	0.930649i	$-0.380756\pi$
$941$	−1.53398e7	−	1.53398e7i	−0.564735	−	0.564735i	−0.930649	+	0.365914i	$0.880756\pi$
$942$	3.78572e7	−	2.79883e7i	1.39002	−	1.02766i
$943$	−5.11595e6			−0.187347
$944$	4.69338e7	−	9.04151e6i	1.71418	−	0.330226i
$945$	−1.42396e7			−0.518704
$946$	−6.34917e6	+	4.69403e6i	−0.230669	+	0.170537i
$947$	9.15072e6	+	9.15072e6i	0.331574	+	0.331574i	0.853184	−	0.521610i	$-0.174668\pi$
$947$	9.15072e6	+	9.15072e6i	0.331574	+	0.331574i	−0.521610	+	0.853184i	$0.674668\pi$
$948$	−875642.	+	464647.i	−0.0316450	+	0.0167920i
$949$	1.34068e7	−	1.34068e7i	0.483235	−	0.483235i
$950$	1.37772e7	+	2.06492e6i	0.495283	+	0.0742324i
$951$			8.02129e7i			2.87603i
$952$	−7.95080e6	−	2.25423e7i	−0.284327	−	0.806130i
$953$		−	6.82130e6i		−	0.243296i	−0.992573	−	0.121648i	$-0.961182\pi$
$953$		−	6.82130e6i		−	0.243296i	0.992573	−	0.121648i	$-0.0388179\pi$
$954$	2.94363e6	−	1.96401e7i	0.104716	−	0.698670i
$955$	−1.14056e7	+	1.14056e7i	−0.404679	+	0.404679i
$956$	8.11938e6	−	2.64780e7i	0.287328	−	0.937002i
$957$	−6.91007e6	−	6.91007e6i	−0.243895	−	0.243895i
$958$	3.30098e6	+	4.46492e6i	0.116206	+	0.157181i
$959$	5.84264e6			0.205146
$960$	5.69066e7	−	4.58460e7i	1.99290	−	1.60555i
$961$	−2.29917e7			−0.803086
$962$	−3.11265e6	−	4.21019e6i	−0.108441	−	0.146678i
$963$	−7.31434e6	−	7.31434e6i	−0.254161	−	0.254161i
$964$	−4.19773e6	+	1.36892e7i	−0.145486	+	0.474443i
$965$	−6.20933e6	+	6.20933e6i	−0.214648	+	0.214648i
$966$	1.96897e6	−	1.31371e7i	0.0678884	−	0.452955i
$967$		−	5.59643e7i		−	1.92462i	−0.271956	−	0.962310i	$-0.587671\pi$
$967$		−	5.59643e7i		−	1.92462i	0.271956	−	0.962310i	$-0.412329\pi$
$968$	8.94430e6	+	2.53590e7i	0.306802	+	0.869850i
$969$			1.84621e7i			0.631644i
$970$	4.38501e6	+	657221.i	0.149638	+	0.0224276i
$971$	−1.61009e7	+	1.61009e7i	−0.548027	+	0.548027i	−0.925870	−	0.377843i	$-0.876666\pi$
$971$	−1.61009e7	+	1.61009e7i	−0.548027	+	0.548027i	0.377843	+	0.925870i	$0.376666\pi$
$972$	−3.50224e7	+	1.85841e7i	−1.18899	+	0.630923i
$973$	−1.35632e7	−	1.35632e7i	−0.459284	−	0.459284i
$974$	1.44629e7	−	1.06926e7i	0.488493	−	0.361149i
$975$	−4.50208e7			−1.51671
$976$	7.26658e6	+	3.77203e7i	0.244178	+	1.26751i
$977$	3.10217e7			1.03975			0.519876	−	0.854242i	$-0.325978\pi$
$977$	3.10217e7			1.03975			0.519876	+	0.854242i	$0.325978\pi$
$978$	−1.49669e7	+	1.10652e7i	−0.500363	+	0.369925i
$979$	6.87300e6	+	6.87300e6i	0.229187	+	0.229187i
$980$	1.55920e7	+	2.93836e7i	0.518606	+	0.977328i
$981$	9.41129e6	−	9.41129e6i	0.312231	−	0.312231i
$982$	−3.51458e7	−	5.26761e6i	−1.16304	−	0.174315i
$983$		−	3.14963e7i		−	1.03962i	−0.854281	−	0.519812i	$-0.826002\pi$
$983$		−	3.14963e7i		−	1.03962i	0.854281	−	0.519812i	$-0.173998\pi$
$984$	7.31693e6	−	1.52908e7i	0.240903	−	0.503435i
$985$		−	3.57554e7i		−	1.17423i
$986$	−5.37855e6	+	3.58860e7i	−0.176187	+	1.17553i
$987$	−2.95750e7	+	2.95750e7i	−0.966345	+	0.966345i
$988$	−4.54636e6	−	1.39412e6i	−0.148174	−	0.0454369i
$989$	1.15214e7	+	1.15214e7i	0.374553	+	0.374553i
$990$	1.15054e7	+	1.55622e7i	0.373089	+	0.504642i
$991$	−1.75561e7			−0.567863			−0.283932	−	0.958845i	$-0.591639\pi$
$991$	−1.75561e7			−0.567863			−0.283932	+	0.958845i	$0.591639\pi$
$992$	−571175.	−	1.37418e7i	−0.0184285	−	0.443367i
$993$	3.37585e7			1.08645
$994$	−8.51263e6	−	1.15142e7i	−0.273274	−	0.369631i
$995$	−173713.	−	173713.i	−0.00556257	−	0.00556257i
$996$	−8.13960e7	−	2.49598e7i	−2.59989	−	0.797246i
$997$	3.27974e7	−	3.27974e7i	1.04497	−	1.04497i	0.0460254	−	0.998940i	$-0.485344\pi$
$997$	3.27974e7	−	3.27974e7i	1.04497	−	1.04497i	0.998940	−	0.0460254i	$-0.0146555\pi$
$998$	−1.29316e6	+	8.62801e6i	−0.0410984	+	0.274211i
$999$		−	5.56035e6i		−	0.176274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.6.e.a.13.3	yes	18
3.2	odd	2		144.6.k.a.109.7		18
4.3	odd	2		64.6.e.a.17.1		18
8.3	odd	2		128.6.e.a.33.9		18
8.5	even	2		128.6.e.b.33.1		18
12.11	even	2		576.6.k.a.145.1		18
16.3	odd	4		128.6.e.a.97.9		18
16.5	even	4	inner	16.6.e.a.5.3	✓	18
16.11	odd	4		64.6.e.a.49.1		18
16.13	even	4		128.6.e.b.97.1		18
32.5	even	8		1024.6.a.k.1.2		18
32.11	odd	8		1024.6.a.l.1.2		18
32.21	even	8		1024.6.a.k.1.17		18
32.27	odd	8		1024.6.a.l.1.17		18
48.5	odd	4		144.6.k.a.37.7		18
48.11	even	4		576.6.k.a.433.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.3	✓	18	16.5	even	4	inner
16.6.e.a.13.3	yes	18	1.1	even	1	trivial
64.6.e.a.17.1		18	4.3	odd	2
64.6.e.a.49.1		18	16.11	odd	4
128.6.e.a.33.9		18	8.3	odd	2
128.6.e.a.97.9		18	16.3	odd	4
128.6.e.b.33.1		18	8.5	even	2
128.6.e.b.97.1		18	16.13	even	4
144.6.k.a.37.7		18	48.5	odd	4
144.6.k.a.109.7		18	3.2	odd	2
576.6.k.a.145.1		18	12.11	even	2
576.6.k.a.433.1		18	48.11	even	4
1024.6.a.k.1.2		18	32.5	even	8
1024.6.a.k.1.17		18	32.21	even	8
1024.6.a.l.1.2		18	32.11	odd	8
1024.6.a.l.1.17		18	32.27	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.36292 - 4.54871i) q^{2} +(16.8936 + 16.8936i) q^{3} +(-9.38150 + 30.5939i) q^{4} +(66.0049 - 66.0049i) q^{5} +(20.0322 - 133.656i) q^{6} +75.3048i q^{7} +(170.712 - 60.2112i) q^{8} +327.790i q^{9} +O(q^{10})\)	\(q+(-3.36292 - 4.54871i) q^{2} +(16.8936 + 16.8936i) q^{3} +(-9.38150 + 30.5939i) q^{4} +(66.0049 - 66.0049i) q^{5} +(20.0322 - 133.656i) q^{6} +75.3048i q^{7} +(170.712 - 60.2112i) q^{8} +327.790i q^{9} +(-522.206 - 78.2676i) q^{10} +(-79.0644 + 79.0644i) q^{11} +(-675.330 + 358.355i) q^{12} +(-238.441 - 238.441i) q^{13} +(342.540 - 253.244i) q^{14} +2230.13 q^{15} +(-847.975 - 574.034i) q^{16} -1753.52 q^{17} +(1491.02 - 1102.33i) q^{18} +(-311.614 - 311.614i) q^{19} +(1400.12 + 2638.57i) q^{20} +(-1272.17 + 1272.17i) q^{21} +(625.528 + 93.7534i) q^{22} -1305.23i q^{23} +(3901.14 + 1866.76i) q^{24} -5588.28i q^{25} +(-282.740 + 1886.46i) q^{26} +(-1432.42 + 1432.42i) q^{27} +(-2303.87 - 706.472i) q^{28} +(2586.71 + 2586.71i) q^{29} +(-7499.74 - 10144.2i) q^{30} -2374.34 q^{31} +(240.562 + 5787.62i) q^{32} -2671.37 q^{33} +(5896.95 + 7976.25i) q^{34} +(4970.48 + 4970.48i) q^{35} +(-10028.4 - 3075.17i) q^{36} +(-1940.89 + 1940.89i) q^{37} +(-369.508 + 2465.38i) q^{38} -8056.28i q^{39} +(7293.59 - 15242.1i) q^{40} -3919.59i q^{41} +(10065.0 + 1508.52i) q^{42} +(-8827.10 + 8827.10i) q^{43} +(-1677.15 - 3160.63i) q^{44} +(21635.8 + 21635.8i) q^{45} +(-5937.10 + 4389.38i) q^{46} +23247.6 q^{47} +(-4627.86 - 24022.9i) q^{48} +11136.2 q^{49} +(-25419.5 + 18793.0i) q^{50} +(-29623.3 - 29623.3i) q^{51} +(9531.79 - 5057.91i) q^{52} +(7573.22 - 7573.22i) q^{53} +(11332.8 + 1698.54i) q^{54} +10437.3i q^{55} +(4534.20 + 12855.4i) q^{56} -10528.6i q^{57} +(3067.29 - 20465.1i) q^{58} +(-33005.3 + 33005.3i) q^{59} +(-20921.9 + 68228.3i) q^{60} +(-26526.1 - 26526.1i) q^{61} +(7984.72 + 10800.2i) q^{62} -24684.2 q^{63} +(25517.2 - 20557.6i) q^{64} -31476.6 q^{65} +(8983.61 + 12151.3i) q^{66} +(16271.7 + 16271.7i) q^{67} +(16450.7 - 53647.0i) q^{68} +(22050.0 - 22050.0i) q^{69} +(5893.93 - 39324.6i) q^{70} -33614.3i q^{71} +(19736.7 + 55957.8i) q^{72} +56226.7i q^{73} +(15355.6 + 2301.49i) q^{74} +(94406.5 - 94406.5i) q^{75} +(12456.9 - 6610.09i) q^{76} +(-5953.93 - 5953.93i) q^{77} +(-36645.7 + 27092.7i) q^{78} +1296.61 q^{79} +(-93859.5 + 18081.4i) q^{80} +31255.5 q^{81} +(-17829.1 + 13181.3i) q^{82} +(78743.5 + 78743.5i) q^{83} +(-26985.8 - 50855.6i) q^{84} +(-115741. + 115741. i) q^{85} +(69836.8 + 10467.1i) q^{86} +87398.0i q^{87} +(-8736.68 + 18257.8i) q^{88} -86929.2i q^{89} +(25655.4 - 171174. i) q^{90} +(17955.8 - 17955.8i) q^{91} +(39932.0 + 12245.0i) q^{92} +(-40111.3 - 40111.3i) q^{93} +(-78180.0 - 105747. i) q^{94} -41136.1 q^{95} +(-93710.1 + 101838. i) q^{96} -8397.09 q^{97} +(-37450.1 - 50655.3i) q^{98} +(-25916.5 - 25916.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Introduction

L-functions

Modular forms

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