LMFDB - Embedded newform 11.6.c.a.9.2

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			9.2
Root			$1.13051 - 0.821361i$ of defining polynomial
Character	$\chi$	$=$	11.9
Dual form			11.6.c.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.740832 + 2.28005i) q^{2} +(-21.7558 + 15.8065i) q^{3} +(21.2388 + 15.4309i) q^{4} +(-5.23817 - 16.1214i) q^{5} +(-19.9222 - 61.3143i) q^{6} +(87.7560 + 63.7585i) q^{7} +(-112.982 + 82.0864i) q^{8} +(148.378 - 456.662i) q^{9} +O(q^{10})$	\(q+(-0.740832 + 2.28005i) q^{2} +(-21.7558 + 15.8065i) q^{3} +(21.2388 + 15.4309i) q^{4} +(-5.23817 - 16.1214i) q^{5} +(-19.9222 - 61.3143i) q^{6} +(87.7560 + 63.7585i) q^{7} +(-112.982 + 82.0864i) q^{8} +(148.378 - 456.662i) q^{9} +40.6382 q^{10} +(391.188 + 89.5726i) q^{11} -705.975 q^{12} +(-235.008 + 723.279i) q^{13} +(-210.385 + 152.854i) q^{14} +(368.785 + 267.938i) q^{15} +(156.140 + 480.548i) q^{16} +(-490.945 - 1510.97i) q^{17} +(931.287 + 676.620i) q^{18} +(950.832 - 690.820i) q^{19} +(137.515 - 423.229i) q^{20} -2917.01 q^{21} +(-494.034 + 825.568i) q^{22} +1155.24 q^{23} +(1160.52 - 3571.71i) q^{24} +(2295.72 - 1667.94i) q^{25} +(-1475.01 - 1071.66i) q^{26} +(1970.82 + 6065.56i) q^{27} +(879.981 + 2708.30i) q^{28} +(-1971.40 - 1432.31i) q^{29} +(-884.118 + 642.350i) q^{30} +(-577.146 + 1776.27i) q^{31} -5680.26 q^{32} +(-9926.44 + 4234.59i) q^{33} +3808.80 q^{34} +(568.197 - 1748.73i) q^{35} +(10198.1 - 7409.33i) q^{36} +(10260.8 + 7454.93i) q^{37} +(870.695 + 2679.72i) q^{38} +(-6319.75 - 19450.2i) q^{39} +(1915.17 + 1391.45i) q^{40} +(-2414.80 + 1754.46i) q^{41} +(2161.01 - 6650.91i) q^{42} -3678.37 q^{43} +(6926.16 + 7938.77i) q^{44} -8139.28 q^{45} +(-855.836 + 2633.99i) q^{46} +(-680.826 + 494.649i) q^{47} +(-10992.8 - 7986.70i) q^{48} +(-1557.67 - 4794.02i) q^{49} +(2102.23 + 6470.00i) q^{50} +(34564.2 + 25112.4i) q^{51} +(-16152.1 + 11735.2i) q^{52} +(5513.39 - 16968.5i) q^{53} -15289.8 q^{54} +(-605.069 - 6775.70i) q^{55} -15148.6 q^{56} +(-9766.67 + 30058.7i) q^{57} +(4726.21 - 3433.79i) q^{58} +(8582.37 + 6235.45i) q^{59} +(3698.02 + 11381.3i) q^{60} +(-10344.5 - 31837.2i) q^{61} +(-3622.42 - 2631.84i) q^{62} +(42137.2 - 30614.4i) q^{63} +(-788.346 + 2426.28i) q^{64} +12891.3 q^{65} +(-2301.24 - 25769.9i) q^{66} +4490.08 q^{67} +(12888.6 - 39666.9i) q^{68} +(-25133.1 + 18260.3i) q^{69} +(3566.25 + 2591.03i) q^{70} +(-3717.16 - 11440.2i) q^{71} +(20721.6 + 63774.5i) q^{72} +(-64776.3 - 47062.8i) q^{73} +(-24599.1 + 17872.3i) q^{74} +(-23580.9 + 72574.6i) q^{75} +30854.4 q^{76} +(28618.1 + 32802.1i) q^{77} +49029.2 q^{78} +(8053.94 - 24787.5i) q^{79} +(6929.24 - 5034.39i) q^{80} +(-44356.5 - 32226.9i) q^{81} +(-2211.28 - 6805.62i) q^{82} +(21298.8 + 65550.9i) q^{83} +(-61953.6 - 45011.9i) q^{84} +(-21787.4 + 15829.5i) q^{85} +(2725.05 - 8386.85i) q^{86} +65529.4 q^{87} +(-51549.9 + 21991.1i) q^{88} +15665.5 q^{89} +(6029.84 - 18557.9i) q^{90} +(-66738.5 + 48488.4i) q^{91} +(24535.8 + 17826.3i) q^{92} +(-15520.4 - 47767.0i) q^{93} +(-623.445 - 1918.77i) q^{94} +(-16117.6 - 11710.1i) q^{95} +(123579. - 89785.3i) q^{96} +(22330.9 - 68727.4i) q^{97} +12084.6 q^{98} +(98948.2 - 165350. i) 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 $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.740832	+	2.28005i	−0.130962	+	0.403059i	−0.994940	−	0.100470i	$-0.967965\pi$
$2$	−0.740832	+	2.28005i	−0.130962	+	0.403059i	0.863978	+	0.503529i	$0.167965\pi$
$3$	−21.7558	+	15.8065i	−1.39564	+	1.01399i	−0.400417	+	0.916333i	$0.631135\pi$
$3$	−21.7558	+	15.8065i	−1.39564	+	1.01399i	−0.995220	+	0.0976567i	$0.968865\pi$
$4$	21.2388	+	15.4309i	0.663711	+	0.482215i
$5$	−5.23817	−	16.1214i	−0.0937033	−	0.288389i	0.893210	−	0.449639i	$-0.148447\pi$
$5$	−5.23817	−	16.1214i	−0.0937033	−	0.288389i	−0.986914	+	0.161250i	$0.948447\pi$
$6$	−19.9222	−	61.3143i	−0.225923	−	0.695318i
$7$	87.7560	+	63.7585i	0.676911	+	0.491805i	0.872332	−	0.488915i	$-0.162607\pi$
$7$	87.7560	+	63.7585i	0.676911	+	0.491805i	−0.195420	+	0.980720i	$0.562607\pi$
$8$	−112.982	+	82.0864i	−0.624144	+	0.453467i
$9$	148.378	−	456.662i	0.610611	−	1.87927i
$10$	40.6382			0.128509
$11$	391.188	+	89.5726i	0.974773	+	0.223200i
$11$	391.188	+	89.5726i	0.974773	+	0.223200i
$12$	−705.975			−1.41526
$13$	−235.008	+	723.279i	−0.385677	+	1.18699i	0.550311	+	0.834960i	$0.314509\pi$
$13$	−235.008	+	723.279i	−0.385677	+	1.18699i	−0.935988	+	0.352032i	$0.885491\pi$
$14$	−210.385	+	152.854i	−0.286876	+	0.208428i
$15$	368.785	+	267.938i	0.423199	+	0.307472i
$16$	156.140	+	480.548i	0.152480	+	0.469285i
$17$	−490.945	−	1510.97i	−0.412013	−	1.26805i	−0.914895	−	0.403691i	$-0.867727\pi$
$17$	−490.945	−	1510.97i	−0.412013	−	1.26805i	0.502882	−	0.864355i	$-0.332273\pi$
$18$	931.287	+	676.620i	0.677489	+	0.492225i
$19$	950.832	−	690.820i	0.604254	−	0.439017i	−0.243132	−	0.969993i	$-0.578175\pi$
$19$	950.832	−	690.820i	0.604254	−	0.439017i	0.847386	+	0.530977i	$0.178175\pi$
$20$	137.515	−	423.229i	0.0768734	−	0.236592i
$21$	−2917.01			−1.44341
$22$	−494.034	+	825.568i	−0.217621	+	0.363660i
$23$	1155.24			0.455356			0.227678	−	0.973736i	$-0.426887\pi$
$23$	1155.24			0.455356			0.227678	+	0.973736i	$0.426887\pi$
$24$	1160.52	−	3571.71i	0.411268	−	1.26575i
$25$	2295.72	−	1667.94i	0.734629	−	0.533739i
$26$	−1475.01	−	1071.66i	−0.427919	−	0.310901i
$27$	1970.82	+	6065.56i	0.520280	+	1.60126i
$28$	879.981	+	2708.30i	0.212118	+	0.652833i
$29$	−1971.40	−	1432.31i	−0.435292	−	0.316258i	0.348469	−	0.937320i	$-0.386702\pi$
$29$	−1971.40	−	1432.31i	−0.435292	−	0.316258i	−0.783761	+	0.621062i	$0.786702\pi$
$30$	−884.118	+	642.350i	−0.179352	+	0.130307i
$31$	−577.146	+	1776.27i	−0.107865	+	0.331975i	−0.990392	−	0.138287i	$-0.955840\pi$
$31$	−577.146	+	1776.27i	−0.107865	+	0.331975i	0.882527	+	0.470262i	$0.155840\pi$
$32$	−5680.26			−0.980604
$33$	−9926.44	+	4234.59i	−1.58675	+	0.676904i
$34$	3808.80			0.565055
$35$	568.197	−	1748.73i	0.0784023	−	0.241298i
$36$	10198.1	−	7409.33i	1.31148	−	0.952845i
$37$	10260.8	+	7454.93i	1.23219	+	0.895240i	0.997053	−	0.0767219i	$-0.0244454\pi$
$37$	10260.8	+	7454.93i	1.23219	+	0.895240i	0.235139	+	0.971962i	$0.424445\pi$
$38$	870.695	+	2679.72i	0.0978153	+	0.301045i
$39$	−6319.75	−	19450.2i	−0.665332	−	2.04768i
$40$	1915.17	+	1391.45i	0.189259	+	0.137505i
$41$	−2414.80	+	1754.46i	−0.224348	+	0.162998i	−0.694282	−	0.719703i	$-0.744278\pi$
$41$	−2414.80	+	1754.46i	−0.224348	+	0.162998i	0.469934	+	0.882702i	$0.344278\pi$
$42$	2161.01	−	6650.91i	0.189031	−	0.581779i
$43$	−3678.37			−0.303378			−0.151689	−	0.988428i	$-0.548471\pi$
$43$	−3678.37			−0.303378			−0.151689	+	0.988428i	$0.548471\pi$
$44$	6926.16	+	7938.77i	0.539338	+	0.618190i
$45$	−8139.28			−0.599176
$46$	−855.836	+	2633.99i	−0.0596343	+	0.183535i
$47$	−680.826	+	494.649i	−0.0449564	+	0.0326627i	−0.610037	−	0.792373i	$-0.708845\pi$
$47$	−680.826	+	494.649i	−0.0449564	+	0.0326627i	0.565080	+	0.825036i	$0.308845\pi$
$48$	−10992.8	−	7986.70i	−0.688657	−	0.500339i
$49$	−1557.67	−	4794.02i	−0.0926800	−	0.285240i
$50$	2102.23	+	6470.00i	0.118920	+	0.365998i
$51$	34564.2	+	25112.4i	1.86081	+	1.35195i
$52$	−16152.1	+	11735.2i	−0.828362	+	0.601840i
$53$	5513.39	−	16968.5i	0.269606	−	0.829761i	−0.720991	−	0.692945i	$-0.756313\pi$
$53$	5513.39	−	16968.5i	0.269606	−	0.829761i	0.990596	−	0.136816i	$-0.0436869\pi$
$54$	−15289.8			−0.713538
$55$	−605.069	−	6775.70i	−0.0269711	−	0.302028i
$56$	−15148.6			−0.645508
$57$	−9766.67	+	30058.7i	−0.398162	+	1.22542i
$58$	4726.21	−	3433.79i	0.184477	−	0.134031i
$59$	8582.37	+	6235.45i	0.320979	+	0.233205i	0.736593	−	0.676336i	$-0.236433\pi$
$59$	8582.37	+	6235.45i	0.320979	+	0.233205i	−0.415614	+	0.909541i	$0.636433\pi$
$60$	3698.02	+	11381.3i	0.132615	+	0.408146i
$61$	−10344.5	−	31837.2i	−0.355948	−	1.09550i	−0.955458	−	0.295128i	$-0.904638\pi$
$61$	−10344.5	−	31837.2i	−0.355948	−	1.09550i	0.599510	−	0.800367i	$-0.295362\pi$
$62$	−3622.42	−	2631.84i	−0.119679	−	0.0869521i
$63$	42137.2	−	30614.4i	1.33756	−	0.971796i
$64$	−788.346	+	2426.28i	−0.0240584	+	0.0740441i
$65$	12891.3			0.378454
$66$	−2301.24	−	25769.9i	−0.0650284	−	0.728203i
$67$	4490.08			0.122199			0.0610994	−	0.998132i	$-0.480539\pi$
$67$	4490.08			0.122199			0.0610994	+	0.998132i	$0.480539\pi$
$68$	12888.6	−	39666.9i	0.338012	−	1.04029i
$69$	−25133.1	+	18260.3i	−0.635512	+	0.461726i
$70$	3566.25	+	2591.03i	0.0869895	+	0.0632015i
$71$	−3717.16	−	11440.2i	−0.0875115	−	0.269333i	0.897718	−	0.440570i	$-0.145224\pi$
$71$	−3717.16	−	11440.2i	−0.0875115	−	0.269333i	−0.985230	+	0.171237i	$0.945224\pi$
$72$	20721.6	+	63774.5i	0.471077	+	1.44983i
$73$	−64776.3	−	47062.8i	−1.42269	−	1.03364i	−0.991321	−	0.131465i	$-0.958032\pi$
$73$	−64776.3	−	47062.8i	−1.42269	−	1.03364i	−0.431366	−	0.902177i	$-0.641968\pi$
$74$	−24599.1	+	17872.3i	−0.522205	+	0.379404i
$75$	−23580.9	+	72574.6i	−0.484069	+	1.48981i
$76$	30854.4			0.612751
$77$	28618.1	+	32802.1i	0.550064	+	0.630484i
$78$	49029.2			0.912470
$79$	8053.94	−	24787.5i	0.145191	−	0.446853i	−0.851844	−	0.523795i	$-0.824516\pi$
$79$	8053.94	−	24787.5i	0.145191	−	0.446853i	0.997036	+	0.0769422i	$0.0245157\pi$
$80$	6929.24	−	5034.39i	0.121049	−	0.0879472i
$81$	−44356.5	−	32226.9i	−0.751181	−	0.545765i
$82$	−2211.28	−	6805.62i	−0.0363169	−	0.111772i
$83$	21298.8	+	65550.9i	0.339359	+	1.04444i	0.964535	+	0.263955i	$0.0850272\pi$
$83$	21298.8	+	65550.9i	0.339359	+	1.04444i	−0.625176	+	0.780484i	$0.714973\pi$
$84$	−61953.6	−	45011.9i	−0.958006	−	0.696032i
$85$	−21787.4	+	15829.5i	−0.327083	+	0.237640i
$86$	2725.05	−	8386.85i	0.0397309	−	0.122279i
$87$	65529.4			0.928192
$88$	−51549.9	+	21991.1i	−0.709613	+	0.302719i
$89$	15665.5			0.209638			0.104819	−	0.994491i	$-0.466574\pi$
$89$	15665.5			0.209638			0.104819	+	0.994491i	$0.466574\pi$
$90$	6029.84	−	18557.9i	0.0784692	−	0.241503i
$91$	−66738.5	+	48488.4i	−0.844837	+	0.613810i
$92$	24535.8	+	17826.3i	0.302225	+	0.219579i
$93$	−15520.4	−	47767.0i	−0.186079	−	0.572691i
$94$	−623.445	−	1918.77i	−0.00727744	−	0.0223977i
$95$	−16117.6	−	11710.1i	−0.183228	−	0.133123i
$96$	123579.	−	89785.3i	1.36857	−	0.994322i
$97$	22330.9	−	68727.4i	0.240978	−	0.741653i	−0.755294	−	0.655386i	$-0.772506\pi$
$97$	22330.9	−	68727.4i	0.240978	−	0.741653i	0.996272	−	0.0862671i	$-0.0274938\pi$
$98$	12084.6			0.127106
$99$	98948.2	−	165350.i	1.01466	−	1.69557i
$100$	74495.8			0.744958
$101$	−41960.5	+	129141.i	−0.409295	+	1.25968i	0.507960	+	0.861381i	$0.330400\pi$
$101$	−41960.5	+	129141.i	−0.409295	+	1.25968i	−0.917255	+	0.398301i	$0.869600\pi$
$102$	−82863.6	+	60203.9i	−0.788612	+	0.572960i
$103$	10646.7	+	7735.26i	0.0988828	+	0.0718426i	0.636128	−	0.771584i	$-0.280535\pi$
$103$	10646.7	+	7735.26i	0.0988828	+	0.0718426i	−0.537245	+	0.843426i	$0.680535\pi$
$104$	−32819.7	−	101009.i	−0.297544	−	0.915746i
$105$	15279.8	+	47026.3i	0.135252	+	0.416263i
$106$	34604.4	+	25141.6i	0.299135	+	0.217334i
$107$	−134899.	+	98009.9i	−1.13907	+	0.827581i	−0.986989	−	0.160787i	$-0.948597\pi$
$107$	−134899.	+	98009.9i	−1.13907	+	0.827581i	−0.152078	+	0.988368i	$0.548597\pi$
$108$	−51739.0	+	159236.i	−0.426834	+	1.31366i
$109$	87920.6			0.708801			0.354400	−	0.935094i	$-0.384685\pi$
$109$	87920.6			0.708801			0.354400	+	0.935094i	$0.384685\pi$
$110$	15897.2	+	3640.07i	0.125267	+	0.0286833i
$111$	−341070.			−2.62746
$112$	−16936.8	+	52126.2i	−0.127581	+	0.392655i
$113$	85996.8	−	62480.3i	0.633558	−	0.460307i	−0.224073	−	0.974572i	$-0.571936\pi$
$113$	85996.8	−	62480.3i	0.633558	−	0.460307i	0.857631	+	0.514266i	$0.171936\pi$
$114$	−61299.8	−	44536.9i	−0.441771	−	0.320965i
$115$	−6051.33	−	18624.1i	−0.0426684	−	0.131320i
$116$	−19768.4	−	60840.9i	−0.136404	−	0.419808i
$117$	295424.	+	214638.i	1.99517	+	1.44958i
$118$	−20575.2	+	14948.8i	−0.136031	+	0.0988327i
$119$	53254.0	−	163899.i	0.344735	−	1.06098i
$120$	−63660.2			−0.403566
$121$	145004.	+	70079.4i	0.900364	+	0.435138i
$122$	80253.9			0.488165
$123$	24804.1	−	76339.3i	0.147830	−	0.454973i
$124$	−39667.3	+	28820.0i	−0.231675	+	0.168321i
$125$	−81770.2	−	59409.5i	−0.468080	−	0.340080i
$126$	38585.8	+	118755.i	0.216522	+	0.666385i
$127$	−33544.7	−	103240.i	−0.184550	−	0.567988i	0.815390	−	0.578912i	$-0.196523\pi$
$127$	−33544.7	−	103240.i	−0.184550	−	0.567988i	−0.999940	+	0.0109245i	$0.996523\pi$
$128$	−152002.	−	110436.i	−0.820019	−	0.595778i
$129$	80025.9	−	58142.2i	0.423405	−	0.307622i
$130$	−9550.29	+	29392.8i	−0.0495631	+	0.152539i
$131$	18507.3			0.0942245			0.0471123	−	0.998890i	$-0.484998\pi$
$131$	18507.3			0.0942245			0.0471123	+	0.998890i	$0.484998\pi$
$132$	−276169.	−	63236.1i	−1.37956	−	0.315886i
$133$	127487.			0.624937
$134$	−3326.39	+	10237.6i	−0.0160034	+	0.0492533i
$135$	87462.0	−	63544.9i	0.413033	−	0.300086i
$136$	179499.	+	130413.i	0.832173	+	0.604609i
$137$	−52275.5	−	160887.i	−0.237956	−	0.732354i	−0.996716	−	0.0809826i	$-0.974194\pi$
$137$	−52275.5	−	160887.i	−0.237956	−	0.732354i	0.758759	−	0.651371i	$-0.225806\pi$
$138$	−23014.9	−	70832.5i	−0.102875	−	0.316617i
$139$	−86561.2	−	62890.4i	−0.380002	−	0.276088i	0.381344	−	0.924433i	$-0.375461\pi$
$139$	−86561.2	−	62890.4i	−0.380002	−	0.276088i	−0.761346	+	0.648345i	$0.775461\pi$
$140$	39052.2	−	28373.1i	0.168394	−	0.122345i
$141$	6993.25	−	21523.0i	0.0296232	−	0.0911707i
$142$	28838.1			0.120018
$143$	−156718.	+	261888.i	−0.640883	+	1.07096i
$144$	242616.			0.975019
$145$	−12764.3	+	39284.5i	−0.0504171	+	0.155168i
$146$	155294.	−	112827.i	0.602937	−	0.438059i
$147$	109665.	+	79676.6i	0.418578	+	0.304115i
$148$	102891.	+	316667.i	0.386122	+	1.18836i
$149$	36849.5	+	113411.i	0.135977	+	0.418495i	0.995741	−	0.0921977i	$-0.0293892\pi$
$149$	36849.5	+	113411.i	0.135977	+	0.418495i	−0.859764	+	0.510692i	$0.829389\pi$
$150$	−148004.	−	107531.i	−0.537088	−	0.390217i
$151$	−311508.	+	226324.i	−1.11180	+	0.807771i	−0.982946	−	0.183893i	$-0.941130\pi$
$151$	−311508.	+	226324.i	−1.11180	+	0.807771i	−0.128855	+	0.991664i	$0.541130\pi$
$152$	−50720.2	+	156101.i	−0.178062	+	0.548019i
$153$	−762850.			−2.63458
$154$	−95991.4	+	40949.7i	−0.326160	+	0.139139i
$155$	31659.3			0.105845
$156$	165910.	−	510617.i	0.545833	−	1.67990i
$157$	196631.	−	142861.i	0.636653	−	0.462556i	−0.222046	−	0.975036i	$-0.571273\pi$
$157$	196631.	−	142861.i	0.636653	−	0.462556i	0.858699	+	0.512481i	$0.171273\pi$
$158$	50550.0	+	36726.7i	0.161094	+	0.117041i
$159$	148264.	+	456311.i	0.465097	+	1.43142i
$160$	29754.2	+	91574.0i	0.0918858	+	0.282795i
$161$	101379.	+	73656.1i	0.308236	+	0.223946i
$162$	106340.	−	77260.2i	0.318352	−	0.231296i
$163$	111070.	−	341838.i	0.327436	−	1.00775i	−0.642892	−	0.765956i	$-0.722266\pi$
$163$	111070.	−	341838.i	0.327436	−	1.00775i	0.970329	−	0.241789i	$-0.0777342\pi$
$164$	−78360.2			−0.227502
$165$	120264.	+	137847.i	0.343895	+	0.394174i
$166$	−165238.			−0.465414
$167$	−4902.97	+	15089.8i	−0.0136041	+	0.0418690i	−0.957628	−	0.288008i	$-0.907007\pi$
$167$	−4902.97	+	15089.8i	−0.0136041	+	0.0418690i	0.944024	+	0.329877i	$0.107007\pi$
$168$	329570.	−	239446.i	0.900895	−	0.654539i
$169$	−167521.	−	121711.i	−0.451184	−	0.327804i
$170$	−19951.2	−	61403.3i	−0.0529475	−	0.162956i
$171$	−174388.	−	536712.i	−0.456065	−	1.40362i
$172$	−78124.0	−	56760.4i	−0.201355	−	0.146293i
$173$	501933.	−	364676.i	1.27506	−	0.926385i	0.275668	−	0.961253i	$-0.411101\pi$
$173$	501933.	−	364676.i	1.27506	−	0.926385i	0.999392	+	0.0348675i	$0.0111009\pi$
$174$	−48546.3	+	149410.i	−0.121558	+	0.374116i
$175$	307808.			0.759774
$176$	18035.9	+	201970.i	0.0438891	+	0.491480i
$177$	−285277.			−0.684438
$178$	−11605.5	+	35718.1i	−0.0274546	+	0.0844964i
$179$	−635377.	+	461629.i	−1.48217	+	1.07686i	−0.505325	+	0.862929i	$0.668628\pi$
$179$	−635377.	+	461629.i	−1.48217	+	1.07686i	−0.976848	+	0.213933i	$0.931372\pi$
$180$	−172868.	−	125596.i	−0.397680	−	0.288931i
$181$	47219.2	+	145326.i	0.107133	+	0.329721i	0.990225	−	0.139478i	$-0.0445426\pi$
$181$	47219.2	+	145326.i	0.107133	+	0.329721i	−0.883092	+	0.469199i	$0.844543\pi$
$182$	−61113.7	−	188089.i	−0.136760	−	0.420905i
$183$	728290.	+	529134.i	1.60759	+	1.16799i
$184$	−130521.	+	94829.1i	−0.284208	+	0.206489i
$185$	66436.2	−	204470.i	0.142717	−	0.439237i
$186$	120409.			0.255197
$187$	−56709.8	−	635050.i	−0.118592	−	1.32802i
$188$	−22092.8			−0.0455885
$189$	−213779.	+	657946.i	−0.435323	+	1.33979i
$190$	38640.1	−	28073.7i	0.0776524	−	0.0564177i
$191$	473118.	+	343740.i	0.938396	+	0.681784i	0.948034	−	0.318169i	$-0.103068\pi$
$191$	473118.	+	343740.i	0.938396	+	0.681784i	−0.00963816	+	0.999954i	$0.503068\pi$
$192$	−21199.9	−	65246.7i	−0.0415032	−	0.127734i
$193$	−167918.	−	516799.i	−0.324492	−	0.998685i	−0.971669	−	0.236345i	$-0.924051\pi$
$193$	−167918.	−	516799.i	−0.324492	−	0.998685i	0.647177	−	0.762340i	$-0.275949\pi$
$194$	140158.	+	101831.i	0.267371	+	0.194256i
$195$	−280461.	+	203767.i	−0.528185	+	0.383749i
$196$	40892.9	−	125855.i	0.0760340	−	0.234008i
$197$	−589261.			−1.08179			−0.540894	−	0.841091i	$-0.681914\pi$
$197$	−589261.			−1.08179			−0.540894	+	0.841091i	$0.681914\pi$
$198$	303701.	+	348103.i	0.550533	+	0.631022i
$199$	−471872.			−0.844679			−0.422339	−	0.906438i	$-0.638791\pi$
$199$	−471872.			−0.844679			−0.422339	+	0.906438i	$0.638791\pi$
$200$	−122460.	+	376894.i	−0.216481	+	0.666261i
$201$	−97685.4	+	70972.6i	−0.170545	+	0.123908i
$202$	−263362.	−	191344.i	−0.454124	−	0.329940i
$203$	−81680.7	−	251387.i	−0.139117	−	0.428157i
$204$	346595.	+	1.06671e6i	0.583106	+	1.79462i
$205$	40933.5	+	29739.9i	0.0680290	+	0.0494260i
$206$	−25524.2	+	18544.4i	−0.0419067	+	0.0304470i
$207$	171412.	−	527552.i	0.278045	−	0.855736i
$208$	−384264.			−0.615846
$209$	433832.	−	185072.i	0.686999	−	0.293072i
$210$	−118542.			−0.185491
$211$	118101.	−	363478.i	0.182620	−	0.562047i	−0.817279	−	0.576242i	$-0.804519\pi$
$211$	118101.	−	363478.i	0.182620	−	0.562047i	0.999899	+	0.0141953i	$0.00451865\pi$
$212$	378936.	−	275313.i	0.579063	−	0.420714i
$213$	261700.	+	190136.i	0.395235	+	0.287155i
$214$	−123530.	−	380185.i	−0.184390	−	0.567493i
$215$	19267.9	+	59300.6i	0.0284275	+	0.0874909i
$216$	−720567.	−	523523.i	−1.05085	−	0.763486i
$217$	−163901.	+	119081.i	−0.236282	+	0.171669i
$218$	−65134.4	+	200463.i	−0.0928259	+	0.285689i
$219$	2.15316e6			3.03366
$220$	91704.0	−	153244.i	0.127741	−	0.213465i
$221$	1.20823e6			1.66406
$222$	252675.	−	777655.i	0.344097	−	1.05902i
$223$	−223526.	+	162401.i	−0.300999	+	0.218689i	−0.728025	−	0.685551i	$-0.759561\pi$
$223$	−223526.	+	162401.i	−0.300999	+	0.218689i	0.427026	+	0.904240i	$0.359561\pi$
$224$	−498477.	−	362165.i	−0.663782	−	0.482266i
$225$	−421048.	−	1.29585e6i	−0.554466	−	1.70647i
$226$	78748.9	+	242364.i	0.102559	+	0.315644i
$227$	−604572.	−	439247.i	−0.778723	−	0.565776i	0.125872	−	0.992046i	$-0.459827\pi$
$227$	−604572.	−	439247.i	−0.778723	−	0.565776i	−0.904596	+	0.426271i	$0.859827\pi$
$228$	−671264.	+	487702.i	−0.855178	+	0.621323i
$229$	−442109.	+	1.36067e6i	−0.557110	+	1.71461i	0.133196	+	0.991090i	$0.457476\pi$
$229$	−442109.	+	1.36067e6i	−0.557110	+	1.71461i	−0.690306	+	0.723518i	$0.742524\pi$
$230$	46946.8			0.0585175
$231$	−1.14110e6	−	261284.i	−1.40699	−	0.322168i
$232$	340307.			0.415098
$233$	−360276.	+	1.10882e6i	−0.434756	+	1.33804i	0.458580	+	0.888653i	$0.348358\pi$
$233$	−360276.	+	1.10882e6i	−0.434756	+	1.33804i	−0.893336	+	0.449389i	$0.851642\pi$
$234$	−708244.	+	514569.i	−0.845558	+	0.614334i
$235$	11540.7	+	8384.84i	0.0136321	+	0.00990433i
$236$	86060.4	+	264867.i	0.100583	+	0.309562i
$237$	216584.	+	666577.i	0.250470	+	0.770867i
$238$	334245.	+	242843.i	0.382492	+	0.277897i
$239$	1.32889e6	−	965492.i	1.50485	−	1.09334i	0.536449	−	0.843932i	$-0.319765\pi$
$239$	1.32889e6	−	965492.i	1.50485	−	1.09334i	0.968399	−	0.249404i	$-0.0802348\pi$
$240$	−71175.2	+	219055.i	−0.0797628	+	0.245485i
$241$	99150.6			0.109965			0.0549823	−	0.998487i	$-0.482490\pi$
$241$	99150.6			0.109965			0.0549823	+	0.998487i	$0.482490\pi$
$242$	−267208.	+	278700.i	−0.293300	+	0.305913i
$243$	−75373.8			−0.0818850
$244$	271571.	−	835808.i	0.292017	−	0.898736i
$245$	−69127.2	+	50223.8i	−0.0735756	+	0.0534558i
$246$	155681.	+	113109.i	0.164021	+	0.119168i
$247$	276203.	+	850065.i	0.288062	+	0.886563i
$248$	−80600.6	−	248063.i	−0.0832164	−	0.256114i
$249$	−1.49950e6	−	1.08945e6i	−1.53267	−	1.11355i
$250$	196035.	−	142427.i	0.198373	−	0.144126i
$251$	−453091.	+	1.39447e6i	−0.453943	+	1.39709i	0.418429	+	0.908249i	$0.362581\pi$
$251$	−453091.	+	1.39447e6i	−0.453943	+	1.39709i	−0.872372	+	0.488842i	$0.837419\pi$
$252$	1.36735e6			1.35637
$253$	451914.	+	103478.i	0.443869	+	0.101635i
$254$	260243.			0.253102
$255$	223794.	−	688767.i	0.215525	−	0.663319i
$256$	298361.	−	216772.i	0.284539	−	0.206730i
$257$	−1.02040e6	−	741365.i	−0.963691	−	0.700163i	−0.00968624	−	0.999953i	$-0.503083\pi$
$257$	−1.02040e6	−	741365.i	−0.963691	−	0.700163i	−0.954005	+	0.299790i	$0.903083\pi$
$258$	73281.3	+	225536.i	0.0685399	+	0.210944i
$259$	425135.	+	1.30843e6i	0.393801	+	1.21200i
$260$	273795.	+	198924.i	0.251184	+	0.182496i
$261$	−946595.	+	687741.i	−0.860127	+	0.624919i
$262$	−13710.8	+	42197.4i	−0.0123398	+	0.0379780i
$263$	−1.74296e6			−1.55381			−0.776906	−	0.629617i	$-0.783212\pi$
$263$	−1.74296e6			−1.55381			−0.776906	+	0.629617i	$0.783212\pi$
$264$	773909.	−	1.29326e6i	0.683408	−	1.14203i
$265$	−302436.			−0.264557
$266$	−94446.4	+	290676.i	−0.0818429	+	0.251887i
$267$	−340816.	+	247618.i	−0.292578	+	0.212571i
$268$	95363.7	+	69285.8i	0.0811047	+	0.0589260i
$269$	−702997.	−	2.16360e6i	−0.592343	−	1.82304i	−0.567533	−	0.823351i	$-0.692102\pi$
$269$	−702997.	−	2.16360e6i	−0.592343	−	1.82304i	−0.0248100	−	0.999692i	$-0.507898\pi$
$270$	80090.6	+	246494.i	0.0668609	+	0.205777i
$271$	847258.	+	615569.i	0.700798	+	0.509159i	0.880192	−	0.474618i	$-0.157414\pi$
$271$	847258.	+	615569.i	0.700798	+	0.509159i	−0.179394	+	0.983777i	$0.557414\pi$
$272$	649440.	−	471846.i	0.532252	−	0.386703i
$273$	685518.	−	2.10981e6i	0.556689	−	1.71331i
$274$	405558.			0.326345
$275$	1.04746e6	−	446842.i	0.835227	−	0.356306i
$276$	−815568.			−0.644448
$277$	101283.	−	311718.i	0.0793118	−	0.244097i	−0.903537	−	0.428510i	$-0.859039\pi$
$277$	101283.	−	311718.i	0.0793118	−	0.244097i	0.982849	+	0.184414i	$0.0590386\pi$
$278$	207520.	−	150772.i	0.161045	−	0.117006i
$279$	725520.	+	527121.i	0.558006	+	0.405415i
$280$	79350.8	+	244217.i	0.0604862	+	0.186157i
$281$	164233.	+	505456.i	0.124078	+	0.381872i	0.993732	−	0.111789i	$-0.0356582\pi$
$281$	164233.	+	505456.i	0.124078	+	0.381872i	−0.869654	+	0.493661i	$0.835658\pi$
$282$	43892.6	+	31889.9i	0.0328677	+	0.0238798i
$283$	407872.	−	296336.i	0.302732	−	0.219947i	−0.426040	−	0.904704i	$-0.640092\pi$
$283$	407872.	−	296336.i	0.302732	−	0.219947i	0.728771	+	0.684757i	$0.240092\pi$
$284$	97584.9	−	300336.i	0.0717938	−	0.220959i
$285$	535749.			0.390705
$286$	−481014.	−	551339.i	−0.347730	−	0.398569i
$287$	−323775.			−0.232027
$288$	−842829.	+	2.59396e6i	−0.598767	+	1.84282i
$289$	−893328.	+	649041.i	−0.629168	+	0.457117i
$290$	−80114.4	−	58206.5i	−0.0559391	−	0.0406421i
$291$	600515.	+	1.84820e6i	0.415711	+	1.27943i
$292$	−649550.	−	1.99911e6i	−0.445816	−	1.37208i
$293$	1.01310e6	+	736058.i	0.689417	+	0.500891i	0.876469	−	0.481459i	$-0.159893\pi$
$293$	1.01310e6	+	736058.i	0.689417	+	0.500891i	−0.187051	+	0.982350i	$0.559893\pi$
$294$	−262910.	+	191015.i	−0.177394	+	0.128884i
$295$	55568.6	−	171022.i	0.0371770	−	0.114419i
$296$	−1.77124e6			−1.17503
$297$	227652.	+	2.54930e6i	0.149755	+	1.67699i
$298$	−285882.			−0.186486
$299$	−271489.	+	835558.i	−0.175620	+	0.540504i
$300$	−1.62072e6	+	1.17752e6i	−1.03969	+	0.755380i
$301$	−322799.	−	234527.i	−0.205360	−	0.149203i
$302$	−285254.	−	877921.i	−0.179976	−	0.553909i
$303$	−1.12839e6	−	3.47282e6i	−0.706076	−	2.17308i
$304$	480435.	+	349056.i	0.298161	+	0.216627i
$305$	−459075.	+	333538.i	−0.282575	+	0.205303i
$306$	565144.	−	1.73933e6i	0.345029	−	1.06189i
$307$	1.14803e6			0.695193			0.347597	−	0.937644i	$-0.386998\pi$
$307$	1.14803e6			0.695193			0.347597	+	0.937644i	$0.386998\pi$
$308$	101648.	+	1.13828e6i	0.0610550	+	0.683709i
$309$	−353895.			−0.210852
$310$	−23454.2	+	72184.6i	−0.0138617	+	0.0426619i
$311$	1.80363e6	−	1.31041e6i	1.05742	−	0.768259i	0.0838083	−	0.996482i	$-0.473292\pi$
$311$	1.80363e6	−	1.31041e6i	1.05742	−	0.768259i	0.973609	+	0.228223i	$0.0732917\pi$
$312$	2.31061e6	+	1.67876e6i	1.34382	+	0.976342i
$313$	813427.	+	2.50347e6i	0.469308	+	1.44438i	0.853483	+	0.521121i	$0.174486\pi$
$313$	813427.	+	2.50347e6i	0.469308	+	1.44438i	−0.384175	+	0.923260i	$0.625514\pi$
$314$	180059.	+	554164.i	0.103060	+	0.317186i
$315$	−714271.	−	518948.i	−0.405589	−	0.294678i
$316$	553548.	−	402176.i	0.311844	−	0.226568i
$317$	60450.2	−	186046.i	0.0337870	−	0.103986i	−0.932741	−	0.360548i	$-0.882590\pi$
$317$	60450.2	−	186046.i	0.0337870	−	0.103986i	0.966528	+	0.256562i	$0.0825898\pi$
$318$	−1.15025e6			−0.637858
$319$	−642893.	−	736885.i	−0.353722	−	0.405437i
$320$	43244.6			0.0236079
$321$	1.38564e6	−	4.26457e6i	0.750566	−	2.31001i
$322$	−243044.	+	176582.i	−0.130631	+	0.0949088i
$323$	−1.51062e6	−	1.09753e6i	−0.805654	−	0.585342i
$324$	−444789.	−	1.36892e6i	−0.235392	−	0.724461i
$325$	666872.	+	2.05242e6i	0.350214	+	1.07785i
$326$	697122.	+	506489.i	0.363299	+	0.263952i
$327$	−1.91279e6	+	1.38972e6i	−0.989229	+	0.718717i
$328$	128813.	−	396445.i	0.0661110	−	0.203469i
$329$	−91284.7			−0.0464952
$330$	−403393.	+	172086.i	−0.203912	+	0.0869885i
$331$	−400604.			−0.200977			−0.100488	−	0.994938i	$-0.532041\pi$
$331$	−400604.			−0.200977			−0.100488	+	0.994938i	$0.532041\pi$
$332$	−559147.	+	1.72088e6i	−0.278407	+	0.856850i
$333$	4.92687e6	−	3.57958e6i	2.43478	−	1.76897i
$334$	−30773.2	−	22358.0i	−0.0150941	−	0.0109665i
$335$	−23519.8	−	72386.5i	−0.0114504	−	0.0352408i
$336$	−455460.	−	1.40176e6i	−0.220091	−	0.677370i
$337$	−1.24797e6	−	906700.i	−0.598588	−	0.434900i	0.246790	−	0.969069i	$-0.420624\pi$
$337$	−1.24797e6	−	906700.i	−0.598588	−	0.434900i	−0.845377	+	0.534170i	$0.820624\pi$
$338$	401613.	−	291789.i	0.191212	−	0.138924i
$339$	−883334.	+	2.71862e6i	−0.417470	+	1.28484i
$340$	−707001.			−0.331682
$341$	−384878.	+	643159.i	−0.179241	+	0.299525i
$342$	1.35292e6			0.625470
$343$	732332.	−	2.25389e6i	0.336103	−	1.03442i
$344$	415590.	−	301944.i	0.189352	−	0.137572i
$345$	426034.	+	309531.i	0.192706	+	0.140009i
$346$	459630.	+	1.41459e6i	0.206404	+	0.635246i
$347$	289001.	+	889453.i	0.128847	+	0.396551i	0.994582	−	0.103951i	$-0.0331486\pi$
$347$	289001.	+	889453.i	0.128847	+	0.396551i	−0.865735	+	0.500503i	$0.833149\pi$
$348$	1.39176e6	+	1.01117e6i	0.616052	+	0.447588i
$349$	194305.	−	141171.i	0.0853927	−	0.0620415i	−0.544270	−	0.838910i	$-0.683193\pi$
$349$	194305.	−	141171.i	0.0853927	−	0.0620415i	0.629662	+	0.776869i	$0.283193\pi$
$350$	−228034.	+	701816.i	−0.0995015	+	0.306234i
$351$	−4.85025e6			−2.10134
$352$	−2.22205e6	−	508796.i	−0.955866	−	0.218870i
$353$	2.84230e6			1.21404			0.607021	−	0.794686i	$-0.292365\pi$
$353$	2.84230e6			1.21404			0.607021	+	0.794686i	$0.292365\pi$
$354$	211343.	−	650446.i	0.0896353	−	0.275869i
$355$	−164962.	+	119852.i	−0.0694725	+	0.0504747i
$356$	332716.	+	241732.i	0.139139	+	0.101090i
$357$	1.43209e6	+	4.40752e6i	0.594703	+	1.83031i
$358$	−581827.	−	1.79068e6i	−0.239931	−	0.738431i
$359$	−1.15981e6	−	842654.i	−0.474955	−	0.345075i	0.324414	−	0.945915i	$-0.394833\pi$
$359$	−1.15981e6	−	842654.i	−0.474955	−	0.345075i	−0.799369	+	0.600840i	$0.794833\pi$
$360$	919593.	−	668124.i	0.373972	−	0.271707i
$361$	−338307.	+	1.04120e6i	−0.136629	+	0.420501i
$362$	−366331.			−0.146927
$363$	−4.26241e6	+	767383.i	−1.69781	+	0.305665i
$364$	−2.16566e6			−0.856716
$365$	−419410.	+	1.29081e6i	−0.164781	+	0.507143i
$366$	−1.74599e6	+	1.26854e6i	−0.681301	+	0.494994i
$367$	1.43203e6	+	1.04043e6i	0.554991	+	0.403225i	0.829622	−	0.558325i	$-0.188556\pi$
$367$	1.43203e6	+	1.04043e6i	0.554991	+	0.403225i	−0.274631	+	0.961550i	$0.588556\pi$
$368$	180378.	+	555147.i	0.0694327	+	0.213692i
$369$	442889.	+	1.36307e6i	0.169328	+	0.521138i
$370$	416982.	+	302955.i	0.158348	+	0.115047i
$371$	1.56572e6	−	1.13756e6i	0.590580	−	0.429081i
$372$	407451.	−	1.25400e6i	0.152657	−	0.469831i
$373$	−302614.			−0.112620			−0.0563101	−	0.998413i	$-0.517934\pi$
$373$	−302614.			−0.112620			−0.0563101	+	0.998413i	$0.517934\pi$
$374$	1.48996e6	+	341164.i	0.550801	+	0.126120i
$375$	2.71804e6			0.998108
$376$	36317.3	−	111773.i	0.0132478	−	0.0407725i
$377$	1.49925e6	−	1.08927e6i	0.543278	−	0.394714i
$378$	−1.34177e6	−	974854.i	−0.483002	−	0.350922i
$379$	−1.63960e6	−	5.04616e6i	−0.586326	−	1.80453i	−0.593880	−	0.804554i	$-0.702405\pi$
$379$	−1.63960e6	−	5.04616e6i	−0.586326	−	1.80453i	0.00755403	−	0.999971i	$-0.497595\pi$
$380$	−161621.	−	497418.i	−0.0574167	−	0.176711i
$381$	2.36166e6	+	1.71585e6i	0.833499	+	0.605572i
$382$	−1.13425e6	+	824077.i	−0.397694	+	0.288941i
$383$	−67038.9	+	206325.i	−0.0233523	+	0.0718710i	−0.962054	−	0.272861i	$-0.912030\pi$
$383$	−67038.9	+	206325.i	−0.0233523	+	0.0718710i	0.938701	+	0.344732i	$0.112030\pi$
$384$	5.05253e6			1.74856
$385$	378910.	−	633187.i	0.130282	−	0.217711i
$386$	1.30273e6			0.445025
$387$	−545790.	+	1.67977e6i	−0.185246	+	0.570128i
$388$	1.53480e6	−	1.11510e6i	0.517575	−	0.376040i
$389$	−4.21187e6	−	3.06010e6i	−1.41124	−	1.02533i	−0.993141	−	0.116924i	$-0.962697\pi$
$389$	−4.21187e6	−	3.06010e6i	−1.41124	−	1.02533i	−0.418098	−	0.908402i	$-0.637303\pi$
$390$	−256823.	−	790421.i	−0.0855014	−	0.263146i
$391$	−567158.	−	1.74553e6i	−0.187613	−	0.577412i
$392$	569513.	+	413776.i	0.187193	+	0.136003i
$393$	−402641.	+	292536.i	−0.131503	+	0.0955427i
$394$	436543.	−	1.34354e6i	0.141673	−	0.436024i
$395$	−441798.			−0.142472
$396$	4.65303e6	−	1.98497e6i	1.49107	−	0.636086i
$397$	−5.30077e6			−1.68796			−0.843982	−	0.536372i	$-0.819794\pi$
$397$	−5.30077e6			−1.68796			−0.843982	+	0.536372i	$0.819794\pi$
$398$	349578.	−	1.07589e6i	0.110621	−	0.340455i
$399$	−2.77358e6	+	2.01513e6i	−0.872186	+	0.633680i
$400$	1.15998e6	+	842772.i	0.362492	+	0.263366i
$401$	−506119.	−	1.55767e6i	−0.157178	−	0.483744i	0.841197	−	0.540729i	$-0.181851\pi$
$401$	−506119.	−	1.55767e6i	−0.157178	−	0.483744i	−0.998375	+	0.0569847i	$0.981851\pi$
$402$	−89452.3	−	275306.i	−0.0276075	−	0.0849670i
$403$	−1.14911e6	−	834875.i	−0.352450	−	0.256070i
$404$	−2.88395e6	+	2.09531e6i	−0.879091	+	0.638697i
$405$	−287197.	+	883901.i	−0.0870045	+	0.267772i
$406$	633687.			0.190792
$407$	3.34615e6	+	3.83537e6i	1.00129	+	1.14768i
$408$	−5.96652e6			−1.77448
$409$	−68816.1	+	211794.i	−0.0203414	+	0.0626045i	−0.960712	−	0.277547i	$-0.910478\pi$
$409$	−68816.1	+	211794.i	−0.0203414	+	0.0626045i	0.940371	+	0.340152i	$0.110478\pi$
$410$	−98133.3	+	71298.0i	−0.0288308	+	0.0209468i
$411$	3.68037e6	+	2.67395e6i	1.07470	+	0.780815i
$412$	106760.	+	328575.i	0.0309861	+	0.0953655i
$413$	355591.	+	1.09440e6i	0.102583	+	0.315718i
$414$	1.07586e6	+	781655.i	0.308499	+	0.224137i
$415$	945207.	−	686733.i	0.269406	−	0.195735i
$416$	1.33490e6	−	4.10842e6i	0.378196	−	1.16397i
$417$	2.87729e6			0.810295
$418$	100575.	+	1.12626e6i	0.0281547	+	0.315282i
$419$	4.18290e6			1.16397			0.581985	−	0.813199i	$-0.302276\pi$
$419$	4.18290e6			1.16397			0.581985	+	0.813199i	$0.302276\pi$
$420$	−401133.	+	1.23456e6i	−0.110960	+	0.341499i
$421$	−2.83755e6	+	2.06160e6i	−0.780257	+	0.566890i	−0.905056	−	0.425292i	$-0.860171\pi$
$421$	−2.83755e6	+	2.06160e6i	−0.780257	+	0.566890i	0.124799	+	0.992182i	$0.460171\pi$
$422$	741254.	+	538553.i	0.202622	+	0.147213i
$423$	124868.	+	384303.i	0.0339311	+	0.104429i
$424$	769965.	+	2.36971e6i	0.207997	+	0.640148i
$425$	−3.64728e6	−	2.64990e6i	−0.979482	−	0.711636i
$426$	−627396.	+	455830.i	−0.167501	+	0.121697i
$427$	1.12210e6	−	3.45346e6i	0.297825	−	0.916610i
$428$	−4.37747e6			−1.15508
$429$	−730003.	−	8.17475e6i	−0.191506	−	2.14453i
$430$	−149482.			−0.0389869
$431$	−2.18000e6	+	6.70935e6i	−0.565279	+	1.73975i	0.101841	+	0.994801i	$0.467527\pi$
$431$	−2.18000e6	+	6.70935e6i	−0.565279	+	1.73975i	−0.667120	+	0.744950i	$0.732473\pi$
$432$	−2.60707e6	+	1.89415e6i	−0.672115	+	0.488320i
$433$	3.66796e6	+	2.66493e6i	0.940168	+	0.683072i	0.948461	−	0.316894i	$-0.102640\pi$
$433$	3.66796e6	+	2.66493e6i	0.940168	+	0.683072i	−0.00829328	+	0.999966i	$0.502640\pi$
$434$	−150087.	−	461920.i	−0.0382488	−	0.117718i
$435$	−343254.	−	1.05643e6i	−0.0869746	−	0.267680i
$436$	1.86732e6	+	1.35669e6i	0.470439	+	0.341794i
$437$	1.09844e6	−	798060.i	0.275151	−	0.199909i
$438$	−1.59513e6	+	4.90931e6i	−0.397293	+	1.22274i
$439$	6.63709e6			1.64368			0.821839	−	0.569720i	$-0.192948\pi$
$439$	6.63709e6			1.64368			0.821839	+	0.569720i	$0.192948\pi$
$440$	624555.	+	715866.i	0.153794	+	0.176279i
$441$	−2.42037e6			−0.592633
$442$	−895097.	+	2.75483e6i	−0.217929	+	0.670716i
$443$	−4.65278e6	+	3.38044e6i	−1.12643	+	0.818397i	−0.985171	−	0.171576i	$-0.945114\pi$
$443$	−4.65278e6	+	3.38044e6i	−1.12643	+	0.818397i	−0.141256	+	0.989973i	$0.545114\pi$
$444$	−7.24390e6	−	5.26300e6i	−1.74387	−	1.26700i
$445$	−82058.7	−	252551.i	−0.0196438	−	0.0604572i
$446$	−204687.	−	629961.i	−0.0487251	−	0.149960i
$447$	−2.59433e6	−	1.88489e6i	−0.614124	−	0.446187i
$448$	−223878.	+	162657.i	−0.0527007	+	0.0382893i
$449$	−466105.	+	1.43452e6i	−0.109111	+	0.335808i	−0.990673	−	0.136259i	$-0.956492\pi$
$449$	−466105.	+	1.43452e6i	−0.109111	+	0.335808i	0.881562	+	0.472067i	$0.156492\pi$
$450$	3.26653e6			0.760423
$451$	−1.10179e6	+	470021.i	−0.255069	+	0.108812i
$452$	2.79059e6			0.642466
$453$	3.19972e6	−	9.84773e6i	0.732599	−	2.25471i
$454$	1.44939e6	−	1.05304e6i	0.330024	−	0.239777i
$455$	1.13129e6	+	821930.i	0.256180	+	0.186126i
$456$	−1.36395e6	−	4.19781e6i	−0.307176	−	0.945390i
$457$	1.42806e6	+	4.39513e6i	0.319858	+	0.984421i	0.973709	+	0.227798i	$0.0731525\pi$
$457$	1.42806e6	+	4.39513e6i	0.319858	+	0.984421i	−0.653851	+	0.756624i	$0.726848\pi$
$458$	−2.77487e6	−	2.01606e6i	−0.618128	−	0.449096i
$459$	8.19734e6	−	5.95571e6i	1.81611	−	1.31948i
$460$	158863.	−	488929.i	0.0350048	−	0.107734i
$461$	1.72062e6			0.377079			0.188540	−	0.982066i	$-0.439625\pi$
$461$	1.72062e6			0.377079			0.188540	+	0.982066i	$0.439625\pi$
$462$	1.44110e6	−	2.40819e6i	0.314115	−	0.524910i
$463$	8.23965e6			1.78631			0.893154	−	0.449752i	$-0.148488\pi$
$463$	8.23965e6			1.78631			0.893154	+	0.449752i	$0.148488\pi$
$464$	380479.	−	1.17099e6i	0.0820420	−	0.252499i
$465$	−688773.	+	500423.i	−0.147722	+	0.107326i
$466$	−2.26125e6	−	1.64289e6i	−0.482373	−	0.350465i
$467$	−1.29051e6	−	3.97177e6i	−0.273822	−	0.842736i	−0.989529	−	0.144336i	$-0.953895\pi$
$467$	−1.29051e6	−	3.97177e6i	−0.273822	−	0.842736i	0.715707	−	0.698401i	$-0.246105\pi$
$468$	2.96239e6	+	9.11729e6i	0.625212	+	1.92420i
$469$	394031.	+	286281.i	0.0827177	+	0.0600980i
$470$	−27667.6	+	20101.7i	−0.00577732	+	0.00419747i
$471$	−2.01974e6	+	6.21611e6i	−0.419510	+	1.29112i
$472$	−1.48150e6			−0.306088
$473$	−1.43893e6	−	329481.i	−0.295725	−	0.0677139i
$474$	−1.68028e6			−0.343507
$475$	1.03060e6	−	3.17185e6i	0.209583	−	0.645029i
$476$	3.66015e6	−	2.65926e6i	0.740427	−	0.537951i
$477$	−6.93078e6	−	5.03551e6i	−1.39472	−	1.01332i
$478$	1.21689e6	+	3.74519e6i	0.243602	+	0.749728i
$479$	71643.7	+	220497.i	0.0142672	+	0.0439100i	0.957937	−	0.286980i	$-0.0926512\pi$
$479$	71643.7	+	220497.i	0.0142672	+	0.0439100i	−0.943669	+	0.330890i	$0.892651\pi$
$480$	−2.09480e6	−	1.52196e6i	−0.414991	−	0.301508i
$481$	−7.80337e6	+	5.66948e6i	−1.53787	+	1.11733i
$482$	−73453.9	+	226068.i	−0.0144012	+	0.0443222i
$483$	−3.36983e6			−0.657265
$484$	1.99833e6	+	3.72594e6i	0.387752	+	0.722974i
$485$	−1.22496e6			−0.236465
$486$	55839.3	−	171856.i	0.0107238	−	0.0330045i
$487$	−1.51431e6	+	1.10021e6i	−0.289328	+	0.210209i	−0.722976	−	0.690873i	$-0.757226\pi$
$487$	−1.51431e6	+	1.10021e6i	−0.289328	+	0.210209i	0.433648	+	0.901083i	$0.357226\pi$
$488$	3.78215e6	+	2.74789e6i	0.718934	+	0.522336i
$489$	2.98685e6	+	9.19259e6i	0.564861	+	1.73846i
$490$	−63301.1	−	194821.i	−0.0119102	−	0.0366560i
$491$	−3.02814e6	−	2.20007e6i	−0.566856	−	0.411845i	0.267106	−	0.963667i	$-0.413933\pi$
$491$	−3.02814e6	−	2.20007e6i	−0.566856	−	0.411845i	−0.833962	+	0.551822i	$0.813933\pi$
$492$	1.70479e6	−	1.23860e6i	0.317511	−	0.230685i
$493$	−1.19633e6	+	3.68193e6i	−0.221684	+	0.682273i
$494$	−2.14281e6			−0.395062
$495$	−3.18398e6	−	729056.i	−0.584061	−	0.133736i
$496$	−943700.			−0.172238
$497$	403209.	−	1.24095e6i	0.0732216	−	0.225353i
$498$	3.59489e6	−	2.61184e6i	0.649549	−	0.471925i
$499$	1.63631e6	+	1.18885e6i	0.294181	+	0.213735i	0.725079	−	0.688666i	$-0.241803\pi$
$499$	1.63631e6	+	1.18885e6i	0.294181	+	0.213735i	−0.430898	+	0.902401i	$0.641803\pi$
$500$	−819958.	−	2.52357e6i	−0.146678	−	0.451430i
$501$	−131849.	−	405790.i	−0.0234684	−	0.0722283i
$502$	−2.84379e6	−	2.06614e6i	−0.503661	−	0.365931i
$503$	2.67787e6	−	1.94558e6i	0.471920	−	0.342870i	−0.326269	−	0.945277i	$-0.605791\pi$
$503$	2.67787e6	−	1.94558e6i	0.471920	−	0.342870i	0.798189	+	0.602407i	$0.205791\pi$
$504$	−2.24772e6	+	6.91778e6i	−0.394154	+	1.21308i
$505$	2.30173e6			0.401631
$506$	−570726.	+	953726.i	−0.0990949	+	0.165595i
$507$	5.56841e6			0.962080
$508$	880635.	−	2.71031e6i	0.151404	−	0.465973i
$509$	−451018.	+	327684.i	−0.0771612	+	0.0560609i	−0.625697	−	0.780066i	$-0.715185\pi$
$509$	−451018.	+	327684.i	−0.0771612	+	0.0560609i	0.548536	+	0.836127i	$0.315185\pi$
$510$	1.40463e6	+	1.02052e6i	0.239131	+	0.173739i
$511$	−2.68386e6	−	8.26008e6i	−0.454682	−	1.39937i
$512$	−1.58469e6	−	4.87717e6i	−0.267159	−	0.822230i
$513$	6.06413e6	+	4.40585e6i	1.01736	+	0.739155i
$514$	2.44629e6	−	1.77733e6i	0.408414	−	0.296730i
$515$	68934.4	−	212158.i	0.0114530	−	0.0352486i
$516$	2.59684e6			0.429359
$517$	−310638.	+	132517.i	−0.0511126	+	0.0218045i
$518$	−3.29824e6			−0.540079
$519$	−5.15571e6	+	1.58676e7i	−0.840176	+	2.58580i
$520$	−1.45649e6	+	1.05820e6i	−0.236210	+	0.171617i
$521$	4.10970e6	+	2.98587e6i	0.663310	+	0.481923i	0.867779	−	0.496950i	$-0.165547\pi$
$521$	4.10970e6	+	2.98587e6i	0.663310	+	0.481923i	−0.204469	+	0.978873i	$0.565547\pi$
$522$	−866815.	−	2.66778e6i	−0.139235	−	0.428523i
$523$	−1.57868e6	−	4.85869e6i	−0.252372	−	0.776721i	−0.994336	−	0.106281i	$-0.966106\pi$
$523$	−1.57868e6	−	4.85869e6i	−0.252372	−	0.776721i	0.741964	−	0.670439i	$-0.233894\pi$
$524$	393071.	+	285583.i	0.0625379	+	0.0454364i
$525$	−6.69662e6	+	4.86538e6i	−1.06037	+	0.770403i
$526$	1.29124e6	−	3.97403e6i	0.203490	−	0.626278i
$527$	2.96725e6			0.465401
$528$	−3.58484e6	−	4.10895e6i	−0.559609	−	0.641425i
$529$	−5.10177e6			−0.792651
$530$	224054.	−	689568.i	0.0346468	−	0.106632i
$531$	4.12093e6	−	2.99403e6i	0.634248	−	0.460808i
$532$	2.70766e6	+	1.96723e6i	0.414778	+	0.301354i
$533$	−701464.	−	2.15889e6i	−0.106952	−	0.329163i
$534$	−312092.	−	960520.i	−0.0473619	−	0.145765i
$535$	2.28668e6	+	1.66137e6i	0.345400	+	0.250947i
$536$	−507299.	+	368574.i	−0.0762697	+	0.0554132i
$537$	6.52641e6	−	2.00862e7i	0.976649	−	3.00582i
$538$	5.45392e6			0.812368
$539$	−179929.	−	2.01489e6i	−0.0266765	−	0.298730i
$540$	2.83814e6			0.418841
$541$	1.43995e6	−	4.43171e6i	0.211522	−	0.650996i	−0.787861	−	0.615853i	$-0.788811\pi$
$541$	1.43995e6	−	4.43171e6i	0.211522	−	0.650996i	0.999382	−	0.0351429i	$-0.0111886\pi$
$542$	−2.03120e6	+	1.47576e6i	−0.296999	+	0.215782i
$543$	−3.32439e6	−	2.41531e6i	−0.483852	−	0.351539i
$544$	2.78870e6	+	8.58273e6i	0.404021	+	1.24345i
$545$	−460543.	−	1.41741e6i	−0.0664170	−	0.204410i
$546$	4.30261e6	+	3.12603e6i	0.617661	+	0.448757i
$547$	−2.48694e6	+	1.80686e6i	−0.355383	+	0.258201i	−0.751124	−	0.660162i	$-0.770488\pi$
$547$	−2.48694e6	+	1.80686e6i	−0.355383	+	0.258201i	0.395741	+	0.918362i	$0.370488\pi$
$548$	1.37237e6	−	4.22371e6i	0.195217	−	0.600817i
$549$	−1.60737e7			−2.27607
$550$	242832.	+	2.71929e6i	0.0342293	+	0.383308i
$551$	−2.86394e6			−0.401870
$552$	1.34068e6	−	4.12617e6i	0.187273	−	0.576368i
$553$	2.28719e6	−	1.66174e6i	0.318046	−	0.231074i
$554$	635697.	+	461861.i	0.0879986	+	0.0639347i
$555$	1.78658e6	+	5.49853e6i	0.246201	+	0.757730i
$556$	−867999.	−	2.67143e6i	−0.119078	−	0.366485i
$557$	7.09906e6	+	5.15777e6i	0.969533	+	0.704407i	0.955345	−	0.295492i	$-0.0954837\pi$
$557$	7.09906e6	+	5.15777e6i	0.969533	+	0.704407i	0.0141880	+	0.999899i	$0.495484\pi$
$558$	−1.73935e6	+	1.26371e6i	−0.236484	+	0.171816i
$559$	864444.	−	2.66049e6i	0.117006	−	0.360107i
$560$	929068.			0.125192
$561$	1.12717e7	+	1.29197e7i	1.51211	+	1.73318i
$562$	−1.27413e6			−0.170166
$563$	−2.85883e6	+	8.79857e6i	−0.380117	+	1.16988i	0.559844	+	0.828598i	$0.310861\pi$
$563$	−2.85883e6	+	8.79857e6i	−0.380117	+	1.16988i	−0.939961	+	0.341282i	$0.889139\pi$
$564$	480647.	−	349210.i	0.0636250	−	0.0462263i
$565$	−1.45774e6	−	1.05911e6i	−0.192114	−	0.139579i
$566$	373496.	+	1.14950e6i	0.0490055	+	0.150823i
$567$	−1.83781e6	−	5.65621e6i	−0.240073	−	0.738870i
$568$	1.35906e6	+	987415.i	0.176753	+	0.128419i
$569$	−5.45694e6	+	3.96470e6i	−0.706592	+	0.513369i	−0.882073	−	0.471114i	$-0.843852\pi$
$569$	−5.45694e6	+	3.96470e6i	−0.706592	+	0.513369i	0.175480	+	0.984483i	$0.443852\pi$
$570$	−396900.	+	1.22153e6i	−0.0511675	+	0.157477i
$571$	−1.23578e7			−1.58618			−0.793088	−	0.609108i	$-0.791528\pi$
$571$	−1.23578e7			−1.58618			−0.793088	+	0.609108i	$0.791528\pi$
$572$	−7.36965e6	+	3.14387e6i	−0.941796	+	0.401767i
$573$	−1.57264e7			−2.00098
$574$	239863.	−	738222.i	0.0303867	−	0.0935206i
$575$	2.65209e6	−	1.92686e6i	0.334518	−	0.243041i
$576$	991015.	+	720015.i	0.124458	+	0.0904243i
$577$	−1.29850e6	−	3.99638e6i	−0.162369	−	0.499721i	0.836464	−	0.548022i	$-0.184619\pi$
$577$	−1.29850e6	−	3.99638e6i	−0.162369	−	0.499721i	−0.998833	+	0.0483017i	$0.984619\pi$
$578$	−818038.	−	2.51766e6i	−0.101848	−	0.313457i
$579$	1.18220e7	+	8.58919e6i	1.46553	+	1.06477i
$580$	−877293.	+	637391.i	−0.108287	+	0.0786748i
$581$	−2.31033e6	+	7.11046e6i	−0.283944	+	0.873891i
$582$	−4.65885e6			−0.570127
$583$	3.67668e6	−	6.14400e6i	0.448006	−	0.748652i
$584$	1.11818e7			1.35668
$585$	1.91279e6	−	5.88697e6i	0.231088	−	0.711217i
$586$	−2.42878e6	+	1.76461e6i	−0.292176	+	0.212278i
$587$	1.33275e6	+	968298.i	0.159644	+	0.115988i	0.664739	−	0.747075i	$-0.268543\pi$
$587$	1.33275e6	+	968298.i	0.159644	+	0.115988i	−0.505095	+	0.863064i	$0.668543\pi$
$588$	1.09968e6	+	3.38446e6i	0.131166	+	0.403689i
$589$	678316.	+	2.08764e6i	0.0805645	+	0.247952i
$590$	348772.	+	253398.i	0.0412488	+	0.0299690i
$591$	1.28199e7	−	9.31417e6i	1.50978	−	1.09692i
$592$	−1.98033e6	+	6.09484e6i	−0.232238	+	0.714756i
$593$	1.09231e7			1.27558			0.637791	−	0.770209i	$-0.279848\pi$
$593$	1.09231e7			1.27558			0.637791	+	0.770209i	$0.279848\pi$
$594$	−5.98118e6	−	1.36955e6i	−0.695538	−	0.159262i
$595$	−2.92124e6			−0.338279
$596$	−967393.	+	2.97733e6i	−0.111555	+	0.343330i
$597$	1.02660e7	−	7.45866e6i	1.17887	−	0.856496i
$598$	−1.70398e6	−	1.23802e6i	−0.194855	−	0.141571i
$599$	2.78573e6	+	8.57360e6i	0.317228	+	0.976329i	0.974827	+	0.222961i	$0.0715721\pi$
$599$	2.78573e6	+	8.57360e6i	0.317228	+	0.976329i	−0.657599	+	0.753368i	$0.728428\pi$
$600$	−3.29316e6	−	1.01353e7i	−0.373452	−	1.14937i
$601$	−1.00450e7	−	7.29814e6i	−1.13440	−	0.824188i	−0.148068	−	0.988977i	$-0.547306\pi$
$601$	−1.00450e7	−	7.29814e6i	−1.13440	−	0.824188i	−0.986329	+	0.164789i	$0.947306\pi$
$602$	773873.	−	562251.i	0.0870319	−	0.0632323i
$603$	666231.	−	2.05045e6i	0.0746159	−	0.229644i
$604$	−1.01084e7			−1.12743
$605$	370222.	−	2.70477e6i	0.0411220	−	0.300429i
$606$	8.75414e6			0.968349
$607$	−290653.	+	894539.i	−0.0320187	+	0.0985434i	−0.965789	−	0.259330i	$-0.916498\pi$
$607$	−290653.	+	894539.i	−0.0320187	+	0.0985434i	0.933770	+	0.357874i	$0.116498\pi$
$608$	−5.40098e6	+	3.92404e6i	−0.592534	+	0.430501i
$609$	5.75060e6	+	4.17805e6i	0.628304	+	0.456489i
$610$	−420384.	−	1.29381e6i	−0.0457426	−	0.140781i
$611$	−197770.	−	608674.i	−0.0214317	−	0.0659601i
$612$	−1.62020e7	−	1.17714e7i	−1.74860	−	1.27043i
$613$	4.65646e6	−	3.38312e6i	0.500501	−	0.363635i	−0.308707	−	0.951157i	$-0.599896\pi$
$613$	4.65646e6	−	3.38312e6i	0.500501	−	0.363635i	0.809208	+	0.587522i	$0.199896\pi$
$614$	−850494.	+	2.61755e6i	−0.0910438	+	0.280204i
$615$	−1.36063e6			−0.145061
$616$	−5.92593e6	−	1.35690e6i	−0.629224	−	0.144077i
$617$	2.05597e6			0.217423			0.108711	−	0.994073i	$-0.465328\pi$
$617$	2.05597e6			0.217423			0.108711	+	0.994073i	$0.465328\pi$
$618$	262177.	−	806897.i	0.0276136	−	0.0849859i
$619$	4.67936e6	−	3.39976e6i	0.490863	−	0.356633i	−0.314653	−	0.949207i	$-0.601888\pi$
$619$	4.67936e6	−	3.39976e6i	0.490863	−	0.356633i	0.805516	+	0.592574i	$0.201888\pi$
$620$	672403.	+	488530.i	0.0702507	+	0.0510401i
$621$	2.27676e6	+	7.00715e6i	0.236913	+	0.729143i
$622$	1.65162e6	+	5.08316e6i	0.171172	+	0.526814i
$623$	1.37474e6	+	998810.i	0.141906	+	0.103101i
$624$	8.35999e6	−	6.07389e6i	0.859497	−	0.624461i
$625$	2.21083e6	−	6.80422e6i	0.226389	−	0.696753i
$626$	−6.31065e6			−0.643633
$627$	−6.51304e6	+	1.08838e7i	−0.661629	+	1.10563i
$628$	6.38067e6			0.645605
$629$	6.22670e6	−	1.91638e7i	0.627526	−	1.93133i
$630$	1.71238e6	−	1.24412e6i	0.171889	−	0.124885i
$631$	−7.47497e6	−	5.43088e6i	−0.747370	−	0.542996i	0.147640	−	0.989041i	$-0.452832\pi$
$631$	−7.47497e6	−	5.43088e6i	−0.747370	−	0.542996i	−0.895011	+	0.446045i	$0.852832\pi$
$632$	1.12476e6	+	3.46166e6i	0.112013	+	0.344740i
$633$	3.17594e6	+	9.77454e6i	0.315038	+	0.969588i
$634$	379411.	+	275658.i	0.0374875	+	0.0272363i
$635$	−1.48866e6	+	1.08158e6i	−0.146508	+	0.106445i
$636$	−3.89232e6	+	1.19793e7i	−0.381562	+	1.17433i
$637$	3.83348e6			0.374321
$638$	2.15641e6	−	919918.i	0.209739	−	0.0894741i
$639$	−5.77587e6			−0.559584
$640$	−984171.	+	3.02897e6i	−0.0949775	+	0.292311i
$641$	3.57156e6	−	2.59489e6i	0.343331	−	0.249445i	−0.402735	−	0.915317i	$-0.631940\pi$
$641$	3.57156e6	−	2.59489e6i	0.343331	−	0.249445i	0.746066	+	0.665872i	$0.231940\pi$
$642$	8.69690e6	+	6.31867e6i	0.832773	+	0.605045i
$643$	2.60125e6	+	8.00583e6i	0.248116	+	0.763623i	0.995108	+	0.0987902i	$0.0314973\pi$
$643$	2.60125e6	+	8.00583e6i	0.248116	+	0.763623i	−0.746992	+	0.664833i	$0.768503\pi$
$644$	1.01659e6	+	3.12873e6i	0.0965894	+	0.297272i
$645$	−1.35653e6	−	985574.i	−0.128389	−	0.0932803i
$646$	3.62153e6	−	2.63120e6i	0.341437	−	0.248069i
$647$	776542.	−	2.38995e6i	0.0729296	−	0.224454i	−0.907947	−	0.419085i	$-0.862351\pi$
$647$	776542.	−	2.38995e6i	0.0729296	−	0.224454i	0.980877	+	0.194631i	$0.0623509\pi$
$648$	7.65689e6			0.716332
$649$	2.79879e6	+	3.20798e6i	0.260831	+	0.298964i
$650$	−5.17365e6			−0.480302
$651$	1.68354e6	−	5.18140e6i	0.155694	−	0.479175i
$652$	7.63384e6	−	5.54631e6i	0.703273	−	0.510958i
$653$	−1.23650e7	−	8.98370e6i	−1.13478	−	0.824465i	−0.148395	−	0.988928i	$-0.547411\pi$
$653$	−1.23650e7	−	8.98370e6i	−1.13478	−	0.824465i	−0.986383	+	0.164463i	$0.947411\pi$
$654$	−1.75157e6	−	5.39079e6i	−0.160134	−	0.492842i
$655$	−96944.2	−	298364.i	−0.00882914	−	0.0271733i
$656$	−1.22015e6	−	886489.i	−0.110701	−	0.0804292i
$657$	−3.11032e7	+	2.25978e7i	−2.81120	+	2.04245i
$658$	67626.6	−	208133.i	0.00608910	−	0.0187403i
$659$	−8.88451e6			−0.796929			−0.398465	−	0.917184i	$-0.630457\pi$
$659$	−8.88451e6			−0.796929			−0.398465	+	0.917184i	$0.630457\pi$
$660$	427164.	+	4.78348e6i	0.0381711	+	0.427449i
$661$	1.12365e7			1.00030			0.500148	−	0.865940i	$-0.333279\pi$
$661$	1.12365e7			1.00030			0.500148	+	0.865940i	$0.333279\pi$
$662$	296780.	−	913396.i	0.0263203	−	0.0810055i
$663$	−2.62861e7	+	1.90980e7i	−2.32243	+	1.68734i
$664$	−7.78721e6	−	5.65774e6i	−0.685428	−	0.497993i
$665$	−667798.	−	2.05527e6i	−0.0585587	−	0.180225i
$666$	4.51163e6	+	1.38854e7i	0.394137	+	1.21303i
$667$	−2.27744e6	−	1.65465e6i	−0.198213	−	0.144010i
$668$	−336982.	+	244832.i	−0.0292190	+	0.0212288i
$669$	2.29599e6	−	7.06633e6i	0.198338	−	0.610420i
$670$	182469.			0.0157037
$671$	−1.19491e6	−	1.33809e7i	−0.102454	−	1.14731i
$672$	1.65694e7			1.41541
$673$	−6.28105e6	+	1.93311e7i	−0.534558	+	1.64520i	0.210044	+	0.977692i	$0.432639\pi$
$673$	−6.28105e6	+	1.93311e7i	−0.534558	+	1.64520i	−0.744602	+	0.667509i	$0.767361\pi$
$674$	2.99185e6	−	2.17371e6i	0.253682	−	0.184311i
$675$	1.46414e7	+	1.06376e7i	1.23687	+	0.898637i
$676$	−1.67984e6	−	5.17000e6i	−0.141384	−	0.435135i
$677$	1.49636e6	+	4.60532e6i	0.125477	+	0.386178i	0.993988	−	0.109492i	$-0.0349224\pi$
$677$	1.49636e6	+	4.60532e6i	0.125477	+	0.386178i	−0.868511	+	0.495670i	$0.834922\pi$
$678$	−5.54418e6	−	4.02809e6i	−0.463194	−	0.336530i
$679$	6.34162e6	−	4.60746e6i	0.527869	−	0.383519i
$680$	1.16221e6	−	3.57690e6i	0.0963853	−	0.296643i
$681$	2.00959e7			1.66051
$682$	−1.18130e6	−	1.35401e6i	−0.0972525	−	0.111471i
$683$	−1.78470e7			−1.46391			−0.731953	−	0.681355i	$-0.761391\pi$
$683$	−1.78470e7			−1.46391			−0.731953	+	0.681355i	$0.761391\pi$
$684$	4.57813e6	−	1.40900e7i	0.374152	−	1.15152i
$685$	−2.31991e6	+	1.68551e6i	−0.188905	+	0.137248i
$686$	4.59643e6	+	3.33950e6i	0.372916	+	0.270939i
$687$	−1.18891e7	−	3.65908e7i	−0.961071	−	2.95787i
$688$	−574339.	−	1.76763e6i	−0.0462591	−	0.142371i
$689$	1.09772e7	+	7.97543e6i	0.880938	+	0.640039i
$690$	−1.02137e6	+	742066.i	−0.0816692	+	0.0593362i
$691$	−4.81723e6	+	1.48259e7i	−0.383798	+	1.18121i	0.553551	+	0.832815i	$0.313272\pi$
$691$	−4.81723e6	+	1.48259e7i	−0.383798	+	1.18121i	−0.937349	+	0.348393i	$0.886728\pi$
$692$	1.62877e7			1.29299
$693$	1.92258e7	−	8.20165e6i	1.52072	−	0.648737i
$694$	−2.24210e6			−0.176708
$695$	−560461.	+	1.72492e6i	−0.0440132	+	0.135459i
$696$	−7.40365e6	+	5.37907e6i	−0.579326	+	0.420905i
$697$	3.83647e6	+	2.78736e6i	0.299123	+	0.217326i
$698$	177929.	+	547609.i	0.0138232	+	0.0425434i
$699$	−9.68843e6	−	2.98179e7i	−0.749999	−	2.30826i
$700$	6.53746e6	+	4.74974e6i	0.504271	+	0.366374i
$701$	1.76866e7	−	1.28501e7i	1.35941	−	0.987668i	0.360926	−	0.932594i	$-0.382461\pi$
$701$	1.76866e7	−	1.28501e7i	1.35941	−	0.987668i	0.998482	−	0.0550736i	$-0.0175394\pi$
$702$	3.59322e6	−	1.10588e7i	0.275195	−	0.846964i
$703$	1.49063e7			1.13758
$704$	−525719.	+	878516.i	−0.0399781	+	0.0668064i
$705$	−383614.			−0.0290684
$706$	−2.10567e6	+	6.48058e6i	−0.158993	+	0.489330i
$707$	−1.19161e7	+	8.65757e6i	−0.896574	+	0.651399i
$708$	−6.05894e6	−	4.40208e6i	−0.454269	−	0.330046i
$709$	898044.	+	2.76390e6i	0.0670938	+	0.206493i	0.978983	−	0.203944i	$-0.0653760\pi$
$709$	898044.	+	2.76390e6i	0.0670938	+	0.206493i	−0.911889	+	0.410437i	$0.865376\pi$
$710$	−151059.	−	464911.i	−0.0112461	−	0.0346118i
$711$	−1.01245e7	−	7.35586e6i	−0.751101	−	0.545707i
$712$	−1.76992e6	+	1.28593e6i	−0.130844	+	0.0950639i
$713$	−666740.	+	2.05201e6i	−0.0491171	+	0.151167i
$714$	−1.11103e7			−0.815605
$715$	5.04292e6	+	1.15471e6i	0.368907	+	0.0844709i
$716$	−2.06180e7			−1.50301
$717$	−1.36499e7	+	4.20102e7i	−0.991591	+	3.05180i
$718$	2.78052e6	−	2.02017e6i	0.201287	−	0.146243i
$719$	−2.65661e6	−	1.93014e6i	−0.191648	−	0.139241i	0.487823	−	0.872942i	$-0.337791\pi$
$719$	−2.65661e6	−	1.93014e6i	−0.191648	−	0.139241i	−0.679472	+	0.733702i	$0.737791\pi$
$720$	−1.27086e6	−	3.91132e6i	−0.0913624	−	0.281185i
$721$	441121.	+	1.35763e6i	0.0316024	+	0.0972621i
$722$	−2.12336e6	−	1.54271e6i	−0.151594	−	0.110139i
$723$	−2.15710e6	+	1.56723e6i	−0.153471	+	0.111503i
$724$	−1.23963e6	+	3.81518e6i	−0.0878909	+	0.270501i
$725$	−6.91478e6			−0.488578
$726$	1.40806e6	−	1.02870e7i	0.0991468	−	0.724347i
$727$	6.00745e6			0.421555			0.210778	−	0.977534i	$-0.432400\pi$
$727$	6.00745e6			0.421555			0.210778	+	0.977534i	$0.432400\pi$
$728$	3.56003e6	−	1.09566e7i	0.248957	−	0.766212i
$729$	1.24185e7	−	9.02253e6i	0.865463	−	0.628796i
$730$	−2.63240e6	−	1.91255e6i	−0.182829	−	0.132833i
$731$	1.80588e6	+	5.55792e6i	0.124996	+	0.384697i
$732$	7.30299e6	+	2.24763e7i	0.503759	+	1.55041i
$733$	1.53860e7	+	1.11785e7i	1.05770	+	0.768468i	0.973662	−	0.227995i	$-0.0732169\pi$
$733$	1.53860e7	+	1.11785e7i	1.05770	+	0.768468i	0.0840424	+	0.996462i	$0.473217\pi$
$734$	−3.43312e6	+	2.49431e6i	−0.235206	+	0.170887i
$735$	710054.	−	2.18532e6i	0.0484812	−	0.149210i
$736$	−6.56205e6			−0.446524
$737$	1.75646e6	+	402188.i	0.119116	+	0.0272747i
$738$	−3.43597e6			−0.232225
$739$	−2.34675e6	+	7.22256e6i	−0.158072	+	0.486497i	−0.998459	−	0.0554902i	$-0.982328\pi$
$739$	−2.34675e6	+	7.22256e6i	−0.158072	+	0.486497i	0.840387	+	0.541987i	$0.182328\pi$
$740$	4.56616e6	−	3.31751e6i	0.306530	−	0.222707i
$741$	−1.94456e7	−	1.41281e7i	−1.30100	−	0.945229i
$742$	1.43376e6	+	4.41265e6i	0.0956017	+	0.294232i
$743$	3.99067e6	+	1.22820e7i	0.265200	+	0.816202i	0.991647	+	0.128980i	$0.0411702\pi$
$743$	3.99067e6	+	1.22820e7i	0.265200	+	0.816202i	−0.726447	+	0.687222i	$0.758830\pi$
$744$	5.67455e6	+	4.12280e6i	0.375837	+	0.273061i
$745$	1.63533e6	−	1.18813e6i	0.107948	−	0.0784286i
$746$	224186.	−	689973.i	0.0147490	−	0.0453926i
$747$	3.30949e7			2.17000
$748$	8.59492e6	−	1.43628e7i	0.561679	−	0.938607i
$749$	−1.80872e7			−1.17806
$750$	−2.01361e6	+	6.19725e6i	−0.130714	+	0.402296i
$751$	−1.10221e7	+	8.00799e6i	−0.713120	+	0.518112i	−0.884179	−	0.467149i	$-0.845281\pi$
$751$	−1.10221e7	+	8.00799e6i	−0.713120	+	0.518112i	0.171059	+	0.985261i	$0.445281\pi$
$752$	−344007.	−	249936.i	−0.0221831	−	0.0161170i
$753$	−1.21844e7	−	3.74997e7i	−0.783097	−	2.41013i
$754$	1.37289e6	+	4.22534e6i	0.0879445	+	0.270665i
$755$	5.28040e6	+	3.83643e6i	0.337132	+	0.244940i
$756$	−1.46931e7	+	1.06751e7i	−0.934993	+	0.679312i
$757$	−4.16778e6	+	1.28271e7i	−0.264341	+	0.813559i	0.727503	+	0.686105i	$0.240681\pi$
$757$	−4.16778e6	+	1.28271e7i	−0.264341	+	0.813559i	−0.991844	+	0.127455i	$0.959319\pi$
$758$	1.27201e7			0.804117
$759$	−1.14674e7	+	4.89196e6i	−0.722537	+	0.308232i
$760$	2.78225e6			0.174728
$761$	7.13655e6	−	2.19640e7i	0.446711	−	1.37483i	−0.433886	−	0.900968i	$-0.642858\pi$
$761$	7.13655e6	−	2.19640e7i	0.446711	−	1.37483i	0.880597	−	0.473867i	$-0.157142\pi$
$762$	−5.66181e6	+	4.11354e6i	−0.353238	+	0.256642i
$763$	7.71556e6	+	5.60568e6i	0.479796	+	0.348592i
$764$	4.74423e6	+	1.46012e7i	0.294058	+	0.905016i
$765$	3.99594e6	+	1.22982e7i	0.246868	+	0.759783i
$766$	−420765.	−	305704.i	−0.0259100	−	0.0188247i
$767$	−6.52689e6	+	4.74207e6i	−0.400607	+	0.291058i
$768$	−3.06468e6	+	9.43211e6i	−0.187492	+	0.577040i
$769$	−2.58924e7			−1.57890			−0.789452	−	0.613812i	$-0.789635\pi$
$769$	−2.58924e7			−1.57890			−0.789452	+	0.613812i	$0.789635\pi$
$770$	1.16299e6	+	1.33302e6i	0.0706884	+	0.0810232i
$771$	3.39181e7			2.05492
$772$	4.40828e6	−	1.35673e7i	0.266211	−	0.819313i
$773$	−8.62449e6	+	6.26606e6i	−0.519140	+	0.377177i	−0.816280	−	0.577657i	$-0.803967\pi$
$773$	−8.62449e6	+	6.26606e6i	−0.519140	+	0.377177i	0.297140	+	0.954834i	$0.403967\pi$
$774$	−3.42561e6	−	2.48885e6i	−0.205535	−	0.149330i
$775$	1.63774e6	+	5.04046e6i	0.0979472	+	0.301450i
$776$	3.11859e6	+	9.59803e6i	0.185911	+	0.572174i
$777$	−2.99309e7	−	2.17461e7i	−1.77856	−	1.29220i
$778$	1.00975e7	−	7.33623e6i	0.598085	−	0.434534i
$779$	−1.08406e6	+	3.33639e6i	−0.0640042	+	0.196985i
$780$	−9.10094e6			−0.535612
$781$	−429374.	−	4.80824e6i	−0.0251889	−	0.282071i
$782$	4.40006e6			0.257301
$783$	4.80247e6	−	1.47805e7i	0.279937	−	0.861557i
$784$	2.06055e6	−	1.49707e6i	0.119727	−	0.0869867i
$785$	−3.33311e6	−	2.42164e6i	−0.193052	−	0.140261i
$786$	−368706.	−	1.13476e6i	−0.0212874	−	0.0655160i
$787$	−9.49492e6	−	2.92224e7i	−0.546455	−	1.68182i	−0.717504	−	0.696554i	$-0.754716\pi$
$787$	−9.49492e6	−	2.92224e7i	−0.546455	−	1.68182i	0.171049	−	0.985263i	$-0.445284\pi$
$788$	−1.25152e7	−	9.09280e6i	−0.717994	−	0.521653i
$789$	3.79196e7	−	2.75502e7i	2.16856	−	1.57555i
$790$	327298.	−	1.00732e6i	0.0186585	−	0.0574248i
$791$	1.15304e7			0.655243
$792$	2.39358e6	+	2.68039e7i	0.135592	+	1.51840i
$793$	2.54582e7			1.43762
$794$	3.92698e6	−	1.20860e7i	0.221059	−	0.680349i
$795$	6.57975e6	−	4.78047e6i	0.369225	−	0.268258i
$796$	−1.00220e7	−	7.28139e6i	−0.560623	−	0.407316i
$797$	7.68754e6	+	2.36598e7i	0.428688	+	1.31937i	0.899418	+	0.437089i	$0.143991\pi$
$797$	7.68754e6	+	2.36598e7i	0.428688	+	1.31937i	−0.470730	+	0.882277i	$0.656009\pi$
$798$	−2.53982e6	−	7.81677e6i	−0.141187	−	0.434530i
$799$	1.08165e6	+	785865.i	0.0599405	+	0.0435493i
$800$	−1.30403e7	+	9.47431e6i	−0.720380	+	0.523387i
$801$	2.32442e6	−	7.15384e6i	0.128007	−	0.393965i
$802$	3.92652e6			0.215562
$803$	−2.11242e7	−	2.42126e7i	−1.15609	−	1.32511i
$804$	−3.16988e6			−0.172943
$805$	656402.	−	2.02020e6i	0.0357010	−	0.109876i
$806$	2.75485e6	−	2.00152e6i	0.149369	−	0.108523i
$807$	4.94934e7	+	3.59590e7i	2.67524	+	1.94368i
$808$	−5.85993e6	−	1.80350e7i	−0.315765	−	0.971825i
$809$	861570.	+	2.65164e6i	0.0462827	+	0.142444i	0.971527	−	0.236927i	$-0.0761404\pi$
$809$	861570.	+	2.65164e6i	0.0462827	+	0.142444i	−0.925245	+	0.379371i	$0.876140\pi$
$810$	−1.80257e6	−	1.30964e6i	−0.0965339	−	0.0701360i
$811$	−7.08673e6	+	5.14881e6i	−0.378350	+	0.274887i	−0.760665	−	0.649145i	$-0.775127\pi$
$811$	−7.08673e6	+	5.14881e6i	−0.378350	+	0.274887i	0.382315	+	0.924032i	$0.375127\pi$
$812$	2.14433e6	−	6.59956e6i	0.114130	−	0.351257i
$813$	−2.81628e7			−1.49434
$814$	−1.12238e7	+	4.78802e6i	−0.593714	+	0.253277i
$815$	−6.09272e6			−0.321305
$816$	−6.67086e6	+	2.05308e7i	−0.350717	+	1.07940i
$817$	−3.49751e6	+	2.54109e6i	−0.183317	+	0.133188i
$818$	−431920.	−	313808.i	−0.0225694	−	0.0163976i
$819$	1.22402e7	+	3.76716e7i	0.637646	+	1.96247i
$820$	410464.	+	1.26328e6i	0.0213177	+	0.0656091i
$821$	−244362.	−	177539.i	−0.0126525	−	0.00919255i	0.581441	−	0.813589i	$-0.302489\pi$
$821$	−244362.	−	177539.i	−0.0126525	−	0.00919255i	−0.594094	+	0.804396i	$0.702489\pi$
$822$	−8.82326e6	+	6.41047e6i	−0.455459	+	0.330910i
$823$	−1.26090e6	+	3.88064e6i	−0.0648903	+	0.199712i	−0.978245	−	0.207453i	$-0.933483\pi$
$823$	−1.26090e6	+	3.88064e6i	−0.0648903	+	0.199712i	0.913355	+	0.407165i	$0.133483\pi$
$824$	−1.83784e6			−0.0942954
$825$	−1.57253e7	+	2.62781e7i	−0.804383	+	1.34418i
$826$	−2.75871e6			−0.140688
$827$	6.72400e6	−	2.06943e7i	0.341872	−	1.05218i	−0.621364	−	0.783522i	$-0.713421\pi$
$827$	6.72400e6	−	2.06943e7i	0.341872	−	1.05218i	0.963237	−	0.268653i	$-0.0865786\pi$
$828$	1.17812e7	−	8.55952e6i	0.597190	−	0.433884i
$829$	−1.27231e7	−	9.24390e6i	−0.642995	−	0.467163i	0.217883	−	0.975975i	$-0.430085\pi$
$829$	−1.27231e7	−	9.24390e6i	−0.642995	−	0.467163i	−0.860878	+	0.508812i	$0.830085\pi$
$830$	865544.	+	2.66387e6i	0.0436108	+	0.134220i
$831$	2.72368e6	+	8.38261e6i	0.136821	+	0.421092i
$832$	−1.56961e6	−	1.14039e6i	−0.0786110	−	0.0571142i
$833$	−6.47892e6	+	4.70721e6i	−0.323512	+	0.235045i
$834$	−2.13159e6	+	6.56035e6i	−0.106118	+	0.326597i
$835$	268952.			0.0133493
$836$	1.20699e7	+	2.76371e6i	0.597293	+	0.136766i
$837$	−1.19115e7			−0.587698
$838$	−3.09882e6	+	9.53720e6i	−0.152436	+	0.469149i
$839$	1.68375e7	−	1.22332e7i	0.825798	−	0.599977i	−0.0925695	−	0.995706i	$-0.529508\pi$
$839$	1.68375e7	−	1.22332e7i	0.825798	−	0.599977i	0.918367	+	0.395729i	$0.129508\pi$
$840$	−5.58656e6	−	4.05888e6i	−0.273179	−	0.198476i
$841$	−4.50337e6	−	1.38599e7i	−0.219557	−	0.675727i
$842$	−2.59840e6	−	7.99704e6i	−0.126306	−	0.388731i
$843$	−1.15625e7	−	8.40067e6i	−0.560382	−	0.407141i
$844$	8.11711e6	−	5.89742e6i	0.392234	−	0.284975i
$845$	−1.08466e6	+	3.33823e6i	−0.0522578	+	0.160833i
$846$	−968734.			−0.0465349
$847$	8.25686e6	+	1.53952e7i	0.395464	+	0.737353i
$848$	9.01502e6			0.430504
$849$	−4.18954e6	+	1.28941e7i	−0.199479	+	0.613933i
$850$	8.74392e6	−	6.35283e6i	0.415106	−	0.301592i
$851$	1.18537e7	+	8.61221e6i	0.561086	+	0.407653i
$852$	2.62422e6	+	8.07653e6i	0.123852	+	0.381176i
$853$	5.36684e6	+	1.65174e7i	0.252549	+	0.777266i	0.994303	+	0.106594i	$0.0339944\pi$
$853$	5.36684e6	+	1.65174e7i	0.252549	+	0.777266i	−0.741753	+	0.670673i	$0.766006\pi$
$854$	7.04276e6	+	5.11687e6i	0.330444	+	0.240082i
$855$	−7.73909e6	+	5.62277e6i	−0.362055	+	0.263048i
$856$	7.19591e6	−	2.21467e7i	0.335662	−	1.03306i
$857$	1.63786e6			0.0761771			0.0380885	−	0.999274i	$-0.487873\pi$
$857$	1.63786e6			0.0761771			0.0380885	+	0.999274i	$0.487873\pi$
$858$	1.91796e7	+	4.39168e6i	0.889450	+	0.203663i
$859$	−3.11764e7			−1.44160			−0.720798	−	0.693146i	$-0.756224\pi$
$859$	−3.11764e7			−1.44160			−0.720798	+	0.693146i	$0.756224\pi$
$860$	−505832.	+	1.55679e6i	−0.0233217	+	0.0717768i
$861$	7.04399e6	−	5.11776e6i	0.323825	−	0.235273i
$862$	−1.36826e7	−	9.94100e6i	−0.627193	−	0.455682i
$863$	7.05395e6	+	2.17098e7i	0.322407	+	0.992268i	0.972597	+	0.232496i	$0.0746894\pi$
$863$	7.05395e6	+	2.17098e7i	0.322407	+	0.992268i	−0.650190	+	0.759772i	$0.725311\pi$
$864$	−1.11948e7	−	3.44540e7i	−0.510189	−	1.57020i
$865$	−8.50831e6	−	6.18165e6i	−0.386637	−	0.280908i
$866$	−8.79352e6	+	6.38886e6i	−0.398444	+	0.289487i
$867$	9.17601e6	−	2.82409e7i	0.414578	−	1.27594i
$868$	−5.31856e6			−0.239604
$869$	5.37088e6	−	8.97514e6i	0.241266	−	0.403173i
$870$	2.66300e6			0.119281
$871$	−1.05520e6	+	3.24758e6i	−0.0471292	+	0.145049i
$872$	−9.93346e6	+	7.21708e6i	−0.442394	+	0.321418i
$873$	−2.80718e7	−	2.03953e7i	−1.24662	−	0.905722i
$874$	1.00586e6	+	3.09571e6i	0.0445408	+	0.137083i
$875$	−3.38797e6	−	1.04271e7i	−0.149596	−	0.460408i
$876$	4.57305e7	+	3.32252e7i	2.01347	+	1.46287i
$877$	−546517.	+	397068.i	−0.0239941	+	0.0174327i	−0.599718	−	0.800212i	$-0.704720\pi$
$877$	−546517.	+	397068.i	−0.0239941	+	0.0174327i	0.575724	+	0.817644i	$0.304720\pi$
$878$	−4.91697e6	+	1.51329e7i	−0.215259	+	0.662499i
$879$	−3.36753e7			−1.47007
$880$	3.16158e6	−	1.34872e6i	0.137625	−	0.0587104i
$881$	−9.27469e6			−0.402587			−0.201293	−	0.979531i	$-0.564514\pi$
$881$	−9.27469e6			−0.402587			−0.201293	+	0.979531i	$0.564514\pi$
$882$	1.79309e6	−	5.51856e6i	0.0776123	−	0.238866i
$883$	−1.84879e6	+	1.34323e6i	−0.0797970	+	0.0579759i	−0.626969	−	0.779045i	$-0.715705\pi$
$883$	−1.84879e6	+	1.34323e6i	−0.0797970	+	0.0579759i	0.547171	+	0.837021i	$0.315705\pi$
$884$	2.56614e7	+	1.86441e7i	1.10446	+	0.802435i
$885$	1.49433e6	+	4.59908e6i	0.0641341	+	0.197384i
$886$	−4.26064e6	−	1.31129e7i	−0.182343	−	0.561196i
$887$	2.55525e7	+	1.85650e7i	1.09050	+	0.792292i	0.979483	−	0.201527i	$-0.0645903\pi$
$887$	2.55525e7	+	1.85650e7i	1.09050	+	0.792292i	0.111013	+	0.993819i	$0.464590\pi$
$888$	3.85348e7	−	2.79972e7i	1.63991	−	1.19147i
$889$	3.63868e6	−	1.11987e7i	0.154415	−	0.475240i
$890$	636619.			0.0269404
$891$	−1.44651e7	−	1.65799e7i	−0.610417	−	0.699661i
$892$	−7.25340e6			−0.305231
$893$	−305638.	+	940657.i	−0.0128256	+	0.0394732i
$894$	6.21960e6	−	4.51880e6i	0.260267	−	0.189095i
$895$	1.07703e7	+	7.82510e6i	0.449440	+	0.326537i
$896$	−6.29785e6	−	1.93828e7i	−0.262073	−	0.806578i
$897$	−7.30080e6	−	2.24696e7i	−0.302963	−	0.932424i
$898$	−2.92547e6	−	2.12548e6i	−0.121061	−	0.0879562i
$899$	3.68196e6	−	2.67510e6i	0.151943	−	0.110393i
$900$	1.10536e7	−	3.40194e7i	0.454880	−	1.39998i
$901$	−2.83457e7			−1.16326
$902$	−255428.	−	2.86034e6i	−0.0104533	−	0.117058i
$903$	1.07298e7			0.437898
$904$	−4.58732e6	+	1.41183e7i	−0.186697	+	0.574595i
$905$	2.09552e6	−	1.52248e6i	0.0850492	−	0.0617919i
$906$	2.00828e7	+	1.45910e7i	0.812839	+	0.590562i
$907$	−3.14863e6	−	9.69047e6i	−0.127087	−	0.391135i	0.867188	−	0.497981i	$-0.165925\pi$
$907$	−3.14863e6	−	9.69047e6i	−0.127087	−	0.391135i	−0.994276	+	0.106846i	$0.965925\pi$
$908$	−6.06239e6	−	1.86581e7i	−0.244022	−	0.751024i
$909$	5.27477e7	+	3.83235e7i	2.11736	+	1.53835i
$910$	−2.71213e6	+	1.97048e6i	−0.108569	+	0.0788803i
$911$	1.73632e6	−	5.34386e6i	0.0693162	−	0.213333i	−0.910398	−	0.413734i	$-0.864224\pi$
$911$	1.73632e6	−	5.34386e6i	0.0693162	−	0.213333i	0.979714	+	0.200401i	$0.0642244\pi$
$912$	−1.59696e7			−0.635781
$913$	2.46025e6	+	2.75505e7i	0.0976793	+	1.09384i
$914$	−1.10791e7			−0.438669
$915$	4.71549e6	−	1.45128e7i	0.186197	−	0.573057i
$916$	−3.03862e7	+	2.20769e7i	−1.19657	+	0.869358i
$917$	1.62412e6	+	1.17999e6i	0.0637816	+	0.0463401i
$918$	7.50646e6	+	2.31025e7i	0.293987	+	0.904799i
$919$	−3.37651e6	−	1.03918e7i	−0.131880	−	0.405886i	0.863211	−	0.504843i	$-0.168449\pi$
$919$	−3.37651e6	−	1.03918e7i	−0.131880	−	0.405886i	−0.995092	+	0.0989568i	$0.968449\pi$
$920$	2.21247e6	+	1.60746e6i	0.0861804	+	0.0626137i
$921$	−2.49762e7	+	1.81463e7i	−0.970237	+	0.704919i
$922$	−1.27469e6	+	3.92309e6i	−0.0493830	+	0.151985i
$923$	9.14804e6			0.353447
$924$	−2.02036e7	−	2.31575e7i	−0.778484	−	0.892300i
$925$	3.59903e7			1.38303
$926$	−6.10419e6	+	1.87868e7i	−0.233938	+	0.719987i
$927$	5.11214e6	−	3.71418e6i	0.195390	−	0.141959i
$928$	1.11981e7	+	8.13589e6i	0.426849	+	0.310124i
$929$	97916.3	+	301355.i	0.00372234	+	0.0114562i	0.952900	−	0.303283i	$-0.0980828\pi$
$929$	97916.3	+	301355.i	0.00372234	+	0.0114562i	−0.949178	+	0.314739i	$0.898083\pi$
$930$	−630723.	−	1.94117e6i	−0.0239128	−	0.0735962i
$931$	−4.79289e6	−	3.48224e6i	−0.181227	−	0.131669i
$932$	−2.47618e7	+	1.79905e7i	−0.933776	+	0.678428i
$933$	−1.85264e7	+	5.70183e7i	−0.696764	+	2.14442i
$934$	1.00119e7			0.375533
$935$	−9.94086e6	+	4.24074e6i	−0.371873	+	0.158640i
$936$	−5.09965e7			−1.90261
$937$	−543953.	+	1.67412e6i	−0.0202401	+	0.0622926i	−0.960666	−	0.277705i	$-0.910426\pi$
$937$	−543953.	+	1.67412e6i	−0.0202401	+	0.0622926i	0.940426	+	0.339998i	$0.110426\pi$
$938$	−944644.	+	686324.i	−0.0350559	+	0.0254696i
$939$	−5.72680e7	−	4.16076e7i	−2.11957	−	1.53996i
$940$	115726.	+	356167.i	0.00427179	+	0.0131472i
$941$	2.24112e6	+	6.89746e6i	0.0825071	+	0.253931i	0.983797	−	0.179286i	$-0.0573786\pi$
$941$	2.24112e6	+	6.89746e6i	0.0825071	+	0.253931i	−0.901290	+	0.433216i	$0.857379\pi$
$942$	−1.26767e7	−	9.21019e6i	−0.465458	−	0.338175i
$943$	−2.78967e6	+	2.02681e6i	−0.102158	+	0.0742222i
$944$	−1.65639e6	+	5.09784e6i	−0.0604968	+	0.186190i
$945$	1.17268e7			0.427171
$946$	1.81724e6	−	3.03674e6i	0.0660213	−	0.110327i
$947$	−4.74711e6			−0.172010			−0.0860051	−	0.996295i	$-0.527410\pi$
$947$	−4.74711e6			−0.172010			−0.0860051	+	0.996295i	$0.527410\pi$
$948$	−5.68588e6	+	1.74994e7i	−0.205484	+	0.632414i
$949$	4.92624e7	−	3.57913e7i	1.77562	−	1.29006i
$950$	6.46847e6	+	4.69962e6i	0.232537	+	0.168948i
$951$	1.62561e6	+	5.00310e6i	0.0582860	+	0.179386i
$952$	7.43712e6	+	2.28891e7i	0.265958	+	0.818534i
$953$	−2.75409e7	−	2.00096e7i	−0.982304	−	0.713685i	−0.0240813	−	0.999710i	$-0.507666\pi$
$953$	−2.75409e7	−	2.00096e7i	−0.982304	−	0.713685i	−0.958222	+	0.286025i	$0.907666\pi$
$954$	1.66157e7	−	1.20720e7i	0.591083	−	0.429447i
$955$	3.06331e6	−	9.42791e6i	0.108688	−	0.334508i
$956$	4.31223e7			1.52601
$957$	2.56343e7	+	5.86964e6i	0.904776	+	0.207172i
$958$	−555818.			−0.0195668
$959$	5.67045e6	−	1.74519e7i	0.199100	−	0.612767i
$960$	−940822.	+	683547.i	−0.0329480	+	0.0239381i
$961$	2.03394e7	+	1.47775e7i	0.710444	+	0.516168i
$962$	−7.14569e6	−	2.19922e7i	−0.248947	−	0.766180i
$963$	2.47413e7	+	7.61458e7i	0.859719	+	2.64594i
$964$	2.10584e6	+	1.52998e6i	0.0729847	+	0.0530265i
$965$	−7.45196e6	+	5.41416e6i	−0.257604	+	0.187160i
$966$	2.49648e6	−	7.68337e6i	0.0860766	−	0.264916i
$967$	94717.5			0.00325735			0.00162867	−	0.999999i	$-0.499482\pi$
$967$	94717.5			0.00325735			0.00162867	+	0.999999i	$0.499482\pi$
$968$	−2.21355e7	+	3.98517e6i	−0.759278	+	0.136697i
$969$	5.02129e7			1.71793
$970$	907488.	−	2.79296e6i	0.0309679	−	0.0953093i
$971$	3.92497e6	−	2.85165e6i	0.133594	−	0.0970619i	−0.518981	−	0.854786i	$-0.673689\pi$
$971$	3.92497e6	−	2.85165e6i	0.133594	−	0.0970619i	0.652575	+	0.757724i	$0.273689\pi$
$972$	−1.60085e6	−	1.16308e6i	−0.0543480	−	0.0394862i
$973$	−3.58647e6	−	1.10380e7i	−0.121446	−	0.373774i
$974$	−1.38668e6	−	4.26776e6i	−0.0468358	−	0.144146i
$975$	−4.69500e7	−	3.41112e7i	−1.58170	−	1.14917i
$976$	1.36841e7	−	9.94210e6i	0.459825	−	0.334082i
$977$	1.33207e7	−	4.09970e7i	0.446470	−	1.37409i	−0.434394	−	0.900723i	$-0.643037\pi$
$977$	1.33207e7	−	4.09970e7i	0.446470	−	1.37409i	0.880864	−	0.473370i	$-0.156963\pi$
$978$	−2.31723e7			−0.774679
$979$	6.12816e6	+	1.40320e6i	0.204349	+	0.0467911i
$980$	−2.24317e6			−0.0746101
$981$	1.30455e7	−	4.01500e7i	0.432802	−	1.33203i
$982$	7.25962e6	−	5.27442e6i	0.240234	−	0.174540i
$983$	−1.27766e7	−	9.28277e6i	−0.421728	−	0.306403i	0.356605	−	0.934255i	$-0.383934\pi$
$983$	−1.27766e7	−	9.28277e6i	−0.421728	−	0.306403i	−0.778333	+	0.627852i	$0.783934\pi$
$984$	3.46399e6	+	1.06611e7i	0.114048	+	0.351005i
$985$	3.08665e6	+	9.49973e6i	0.101367	+	0.311976i
$986$	−7.50869e6	−	5.45538e6i	−0.245964	−	0.178703i
$987$	1.98597e6	−	1.44289e6i	0.0648904	−	0.0471457i
$988$	−7.25103e6	+	2.23164e7i	−0.236324	+	0.727330i
$989$	−4.24938e6			−0.138145
$990$	4.02108e6	−	6.71952e6i	0.130393	−	0.217897i
$991$	1.01892e7			0.329577			0.164789	−	0.986329i	$-0.447306\pi$
$991$	1.01892e7			0.329577			0.164789	+	0.986329i	$0.447306\pi$
$992$	3.27834e6	−	1.00897e7i	0.105773	−	0.325536i
$993$	8.71548e6	−	6.33216e6i	0.280490	−	0.203788i
$994$	2.53071e6	+	1.83867e6i	0.0812414	+	0.0590253i
$995$	2.47175e6	+	7.60726e6i	0.0791492	+	0.243596i
$996$	−1.50364e7	−	4.62773e7i	−0.480281	−	1.47815i
$997$	−4.66782e7	−	3.39137e7i	−1.48722	−	1.08053i	−0.975139	−	0.221595i	$-0.928874\pi$
$997$	−4.66782e7	−	3.39137e7i	−1.48722	−	1.08053i	−0.512084	−	0.858935i	$-0.671126\pi$
$998$	−3.92286e6	+	2.85013e6i	−0.124674	+	0.0905812i
$999$	−2.49961e7	+	7.69300e7i	−0.792425	+	2.43883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.6.c.a.9.2	yes	16
3.2	odd	2		99.6.f.a.64.3		16
11.4	even	5		121.6.a.g.1.4		8
11.5	even	5	inner	11.6.c.a.5.2	✓	16
11.7	odd	10		121.6.a.i.1.5		8
33.5	odd	10		99.6.f.a.82.3		16
33.26	odd	10		1089.6.a.bg.1.5		8
33.29	even	10		1089.6.a.bb.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.6.c.a.5.2	✓	16	11.5	even	5	inner
11.6.c.a.9.2	yes	16	1.1	even	1	trivial
99.6.f.a.64.3		16	3.2	odd	2
99.6.f.a.82.3		16	33.5	odd	10
121.6.a.g.1.4		8	11.4	even	5
121.6.a.i.1.5		8	11.7	odd	10
1089.6.a.bb.1.4		8	33.29	even	10
1089.6.a.bg.1.5		8	33.26	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)

\(f(q)\)	\(=\)	\(q+(-0.740832 + 2.28005i) q^{2} +(-21.7558 + 15.8065i) q^{3} +(21.2388 + 15.4309i) q^{4} +(-5.23817 - 16.1214i) q^{5} +(-19.9222 - 61.3143i) q^{6} +(87.7560 + 63.7585i) q^{7} +(-112.982 + 82.0864i) q^{8} +(148.378 - 456.662i) q^{9} +O(q^{10})\)	\(q+(-0.740832 + 2.28005i) q^{2} +(-21.7558 + 15.8065i) q^{3} +(21.2388 + 15.4309i) q^{4} +(-5.23817 - 16.1214i) q^{5} +(-19.9222 - 61.3143i) q^{6} +(87.7560 + 63.7585i) q^{7} +(-112.982 + 82.0864i) q^{8} +(148.378 - 456.662i) q^{9} +40.6382 q^{10} +(391.188 + 89.5726i) q^{11} -705.975 q^{12} +(-235.008 + 723.279i) q^{13} +(-210.385 + 152.854i) q^{14} +(368.785 + 267.938i) q^{15} +(156.140 + 480.548i) q^{16} +(-490.945 - 1510.97i) q^{17} +(931.287 + 676.620i) q^{18} +(950.832 - 690.820i) q^{19} +(137.515 - 423.229i) q^{20} -2917.01 q^{21} +(-494.034 + 825.568i) q^{22} +1155.24 q^{23} +(1160.52 - 3571.71i) q^{24} +(2295.72 - 1667.94i) q^{25} +(-1475.01 - 1071.66i) q^{26} +(1970.82 + 6065.56i) q^{27} +(879.981 + 2708.30i) q^{28} +(-1971.40 - 1432.31i) q^{29} +(-884.118 + 642.350i) q^{30} +(-577.146 + 1776.27i) q^{31} -5680.26 q^{32} +(-9926.44 + 4234.59i) q^{33} +3808.80 q^{34} +(568.197 - 1748.73i) q^{35} +(10198.1 - 7409.33i) q^{36} +(10260.8 + 7454.93i) q^{37} +(870.695 + 2679.72i) q^{38} +(-6319.75 - 19450.2i) q^{39} +(1915.17 + 1391.45i) q^{40} +(-2414.80 + 1754.46i) q^{41} +(2161.01 - 6650.91i) q^{42} -3678.37 q^{43} +(6926.16 + 7938.77i) q^{44} -8139.28 q^{45} +(-855.836 + 2633.99i) q^{46} +(-680.826 + 494.649i) q^{47} +(-10992.8 - 7986.70i) q^{48} +(-1557.67 - 4794.02i) q^{49} +(2102.23 + 6470.00i) q^{50} +(34564.2 + 25112.4i) q^{51} +(-16152.1 + 11735.2i) q^{52} +(5513.39 - 16968.5i) q^{53} -15289.8 q^{54} +(-605.069 - 6775.70i) q^{55} -15148.6 q^{56} +(-9766.67 + 30058.7i) q^{57} +(4726.21 - 3433.79i) q^{58} +(8582.37 + 6235.45i) q^{59} +(3698.02 + 11381.3i) q^{60} +(-10344.5 - 31837.2i) q^{61} +(-3622.42 - 2631.84i) q^{62} +(42137.2 - 30614.4i) q^{63} +(-788.346 + 2426.28i) q^{64} +12891.3 q^{65} +(-2301.24 - 25769.9i) q^{66} +4490.08 q^{67} +(12888.6 - 39666.9i) q^{68} +(-25133.1 + 18260.3i) q^{69} +(3566.25 + 2591.03i) q^{70} +(-3717.16 - 11440.2i) q^{71} +(20721.6 + 63774.5i) q^{72} +(-64776.3 - 47062.8i) q^{73} +(-24599.1 + 17872.3i) q^{74} +(-23580.9 + 72574.6i) q^{75} +30854.4 q^{76} +(28618.1 + 32802.1i) q^{77} +49029.2 q^{78} +(8053.94 - 24787.5i) q^{79} +(6929.24 - 5034.39i) q^{80} +(-44356.5 - 32226.9i) q^{81} +(-2211.28 - 6805.62i) q^{82} +(21298.8 + 65550.9i) q^{83} +(-61953.6 - 45011.9i) q^{84} +(-21787.4 + 15829.5i) q^{85} +(2725.05 - 8386.85i) q^{86} +65529.4 q^{87} +(-51549.9 + 21991.1i) q^{88} +15665.5 q^{89} +(6029.84 - 18557.9i) q^{90} +(-66738.5 + 48488.4i) q^{91} +(24535.8 + 17826.3i) q^{92} +(-15520.4 - 47767.0i) q^{93} +(-623.445 - 1918.77i) q^{94} +(-16117.6 - 11710.1i) q^{95} +(123579. - 89785.3i) q^{96} +(22330.9 - 68727.4i) q^{97} +12084.6 q^{98} +(98948.2 - 165350. i) 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

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Database

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