LMFDB - Embedded newform 69.6.e.b.13.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0664835671$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.9
Character	$\chi$	$=$	69.13
Dual form			69.6.e.b.16.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.18515 + 5.98398i) q^{2} +(7.57128 + 4.86577i) q^{3} +(-4.36819 + 30.3814i) q^{4} +(-11.2004 + 24.5255i) q^{5} +(10.1416 + 70.5362i) q^{6} +(164.984 + 48.4438i) q^{7} +(8.70029 - 5.59133i) q^{8} +(33.6486 + 73.6802i) q^{9} +O(q^{10})$	\(q+(5.18515 + 5.98398i) q^{2} +(7.57128 + 4.86577i) q^{3} +(-4.36819 + 30.3814i) q^{4} +(-11.2004 + 24.5255i) q^{5} +(10.1416 + 70.5362i) q^{6} +(164.984 + 48.4438i) q^{7} +(8.70029 - 5.59133i) q^{8} +(33.6486 + 73.6802i) q^{9} +(-204.836 + 60.1453i) q^{10} +(-392.935 + 453.471i) q^{11} +(-180.902 + 208.772i) q^{12} +(-562.128 + 165.056i) q^{13} +(565.582 + 1238.45i) q^{14} +(-204.137 + 131.191i) q^{15} +(1020.99 + 299.789i) q^{16} +(-301.061 - 2093.92i) q^{17} +(-266.428 + 583.396i) q^{18} +(5.19479 - 36.1306i) q^{19} +(-696.194 - 447.417i) q^{20} +(1013.43 + 1169.56i) q^{21} -4750.99 q^{22} +(2536.35 - 57.2233i) q^{23} +93.0784 q^{24} +(1570.39 + 1812.33i) q^{25} +(-3902.41 - 2507.93i) q^{26} +(-103.748 + 721.580i) q^{27} +(-2192.47 + 4800.85i) q^{28} +(-906.241 - 6303.04i) q^{29} +(-1843.52 - 541.307i) q^{30} +(-1155.34 + 742.490i) q^{31} +(3362.56 + 7362.99i) q^{32} +(-5181.51 + 1521.43i) q^{33} +(10969.0 - 12658.9i) q^{34} +(-3036.00 + 3503.73i) q^{35} +(-2385.49 + 700.444i) q^{36} +(2734.59 + 5987.93i) q^{37} +(243.141 - 156.257i) q^{38} +(-5059.15 - 1485.50i) q^{39} +(39.6834 + 276.004i) q^{40} +(8542.88 - 18706.3i) q^{41} +(-1743.84 + 12128.7i) q^{42} +(7531.07 + 4839.92i) q^{43} +(-12060.7 - 13918.8i) q^{44} -2183.92 q^{45} +(13493.8 + 14880.8i) q^{46} +10219.9 q^{47} +(6271.48 + 7237.68i) q^{48} +(10734.1 + 6898.39i) q^{49} +(-2702.22 + 18794.4i) q^{50} +(7909.13 - 17318.6i) q^{51} +(-2559.15 - 17799.3i) q^{52} +(3811.35 + 1119.11i) q^{53} +(-4855.87 + 3120.68i) q^{54} +(-6720.57 - 14716.0i) q^{55} +(1706.28 - 501.008i) q^{56} +(215.134 - 248.278i) q^{57} +(33018.3 - 38105.2i) q^{58} +(-38765.2 + 11382.5i) q^{59} +(-3094.05 - 6775.03i) q^{60} +(31567.3 - 20287.0i) q^{61} +(-10433.6 - 3063.59i) q^{62} +(1982.15 + 13786.1i) q^{63} +(-12479.3 + 27325.9i) q^{64} +(2248.00 - 15635.2i) q^{65} +(-35971.1 - 23117.2i) q^{66} +(-23430.2 - 27039.8i) q^{67} +64931.5 q^{68} +(19481.9 + 11908.0i) q^{69} -36708.4 q^{70} +(-19175.0 - 22129.2i) q^{71} +(704.723 + 452.898i) q^{72} +(9239.18 - 64259.9i) q^{73} +(-21652.4 + 47412.1i) q^{74} +(3071.50 + 21362.8i) q^{75} +(1075.01 + 315.650i) q^{76} +(-86796.0 + 55780.4i) q^{77} +(-17343.3 - 37976.4i) q^{78} +(3133.16 - 919.980i) q^{79} +(-18788.0 + 21682.5i) q^{80} +(-4296.54 + 4958.47i) q^{81} +(156234. - 45874.5i) q^{82} +(38050.7 + 83319.3i) q^{83} +(-39959.7 + 25680.5i) q^{84} +(54726.5 + 16069.2i) q^{85} +(10087.7 + 70161.5i) q^{86} +(23807.7 - 52131.7i) q^{87} +(-883.138 + 6142.36i) q^{88} +(-78303.6 - 50322.7i) q^{89} +(-11324.0 - 13068.5i) q^{90} -100738. q^{91} +(-9340.73 + 77307.9i) q^{92} -12360.2 q^{93} +(52991.5 + 61155.4i) q^{94} +(827.936 + 532.082i) q^{95} +(-10367.7 + 72108.7i) q^{96} +(-18957.9 + 41511.9i) q^{97} +(14378.1 + 100002. i) q^{98} +(-46633.6 - 13692.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9}+O(q^{10}) $ 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9} - 38 q^{10} + 404 q^{11} - 1332 q^{12} - 2850 q^{13} - 724 q^{14} + 639 q^{15} - 5556 q^{16} - 2519 q^{17} + 972 q^{18} + 1117 q^{19} - 22411 q^{20} - 702 q^{21} + 32798 q^{22} + 12040 q^{23} - 756 q^{24} - 5928 q^{25} - 788 q^{26} - 7290 q^{27} - 54024 q^{28} + 13774 q^{29} - 342 q^{30} + 12501 q^{31} + 37412 q^{32} - 4185 q^{33} + 9441 q^{34} + 28894 q^{35} - 21789 q^{36} - 38902 q^{37} - 15042 q^{38} - 25650 q^{39} - 133835 q^{40} - 19456 q^{41} + 85950 q^{42} - 8126 q^{43} + 120643 q^{44} + 40500 q^{45} + 90500 q^{46} + 60846 q^{47} + 62955 q^{48} - 25762 q^{49} - 110197 q^{50} - 51084 q^{51} + 91725 q^{52} - 83896 q^{53} - 31347 q^{54} + 190331 q^{55} - 358140 q^{56} - 40437 q^{57} + 150977 q^{58} + 248368 q^{59} + 122625 q^{60} - 81516 q^{61} + 82657 q^{62} - 6318 q^{63} - 298028 q^{64} - 25475 q^{65} - 6669 q^{66} + 51337 q^{67} + 491228 q^{68} + 17082 q^{69} + 395832 q^{70} - 206653 q^{71} - 149364 q^{72} - 121007 q^{73} + 716844 q^{74} - 59490 q^{75} + 171145 q^{76} + 71982 q^{77} + 11916 q^{78} - 661118 q^{79} - 1386592 q^{80} - 65610 q^{81} - 136394 q^{82} - 368400 q^{83} + 165204 q^{84} + 45505 q^{85} - 99668 q^{86} + 50112 q^{87} - 474416 q^{88} + 328408 q^{89} - 3078 q^{90} + 1042320 q^{91} + 1554071 q^{92} + 160722 q^{93} - 299081 q^{94} - 434011 q^{95} + 412740 q^{96} - 88136 q^{97} + 515807 q^{98} - 37665 q^{99}+O(q^{100}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9 - 38 * q^10 + 404 * q^11 - 1332 * q^12 - 2850 * q^13 - 724 * q^14 + 639 * q^15 - 5556 * q^16 - 2519 * q^17 + 972 * q^18 + 1117 * q^19 - 22411 * q^20 - 702 * q^21 + 32798 * q^22 + 12040 * q^23 - 756 * q^24 - 5928 * q^25 - 788 * q^26 - 7290 * q^27 - 54024 * q^28 + 13774 * q^29 - 342 * q^30 + 12501 * q^31 + 37412 * q^32 - 4185 * q^33 + 9441 * q^34 + 28894 * q^35 - 21789 * q^36 - 38902 * q^37 - 15042 * q^38 - 25650 * q^39 - 133835 * q^40 - 19456 * q^41 + 85950 * q^42 - 8126 * q^43 + 120643 * q^44 + 40500 * q^45 + 90500 * q^46 + 60846 * q^47 + 62955 * q^48 - 25762 * q^49 - 110197 * q^50 - 51084 * q^51 + 91725 * q^52 - 83896 * q^53 - 31347 * q^54 + 190331 * q^55 - 358140 * q^56 - 40437 * q^57 + 150977 * q^58 + 248368 * q^59 + 122625 * q^60 - 81516 * q^61 + 82657 * q^62 - 6318 * q^63 - 298028 * q^64 - 25475 * q^65 - 6669 * q^66 + 51337 * q^67 + 491228 * q^68 + 17082 * q^69 + 395832 * q^70 - 206653 * q^71 - 149364 * q^72 - 121007 * q^73 + 716844 * q^74 - 59490 * q^75 + 171145 * q^76 + 71982 * q^77 + 11916 * q^78 - 661118 * q^79 - 1386592 * q^80 - 65610 * q^81 - 136394 * q^82 - 368400 * q^83 + 165204 * q^84 + 45505 * q^85 - 99668 * q^86 + 50112 * q^87 - 474416 * q^88 + 328408 * q^89 - 3078 * q^90 + 1042320 * q^91 + 1554071 * q^92 + 160722 * q^93 - 299081 * q^94 - 434011 * q^95 + 412740 * q^96 - 88136 * q^97 + 515807 * q^98 - 37665 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	5.18515	+	5.98398i	0.916614	+	1.05783i	0.998128	+	0.0611566i	$0.0194789\pi$
$2$	5.18515	+	5.98398i	0.916614	+	1.05783i	−0.0815143	+	0.996672i	$0.525976\pi$
$3$	7.57128	+	4.86577i	0.485698	+	0.312139i
$3$	7.57128	+	4.86577i	0.485698	+	0.312139i
$4$	−4.36819	+	30.3814i	−0.136506	+	0.949420i
$5$	−11.2004	+	24.5255i	−0.200359	+	0.438725i	−0.982965	−	0.183792i	$-0.941163\pi$
$5$	−11.2004	+	24.5255i	−0.200359	+	0.438725i	0.782606	+	0.622517i	$0.213890\pi$
$6$	10.1416	+	70.5362i	0.115008	+	0.799896i
$7$	164.984	+	48.4438i	1.27262	+	0.373674i	0.847176	−	0.531312i	$-0.178301\pi$
$7$	164.984	+	48.4438i	1.27262	+	0.373674i	0.425441	+	0.904986i	$0.360119\pi$
$8$	8.70029	−	5.59133i	0.0480627	−	0.0308881i
$9$	33.6486	+	73.6802i	0.138472	+	0.303211i
$10$	−204.836	+	60.1453i	−0.647748	+	0.190196i
$11$	−392.935	+	453.471i	−0.979127	+	1.12997i	0.0123802	+	0.999923i	$0.496059\pi$
$11$	−392.935	+	453.471i	−0.979127	+	1.12997i	−0.991507	+	0.130050i	$0.958486\pi$
$12$	−180.902	+	208.772i	−0.362652	+	0.418522i
$13$	−562.128	+	165.056i	−0.922523	+	0.270877i	−0.708303	−	0.705908i	$-0.750539\pi$
$13$	−562.128	+	165.056i	−0.922523	+	0.270877i	−0.214220	+	0.976786i	$0.568721\pi$
$14$	565.582	+	1238.45i	0.771215	+	1.68873i
$15$	−204.137	+	131.191i	−0.234257	+	0.150548i
$16$	1020.99	+	299.789i	0.997058	+	0.292763i
$17$	−301.061	−	2093.92i	−0.252657	−	1.75727i	−0.582121	−	0.813102i	$-0.697777\pi$
$17$	−301.061	−	2093.92i	−0.252657	−	1.75727i	0.329463	−	0.944168i	$-0.393132\pi$
$18$	−266.428	+	583.396i	−0.193820	+	0.424406i
$19$	5.19479	−	36.1306i	0.00330129	−	0.0229610i	−0.988104	−	0.153786i	$-0.950853\pi$
$19$	5.19479	−	36.1306i	0.00330129	−	0.0229610i	0.991406	+	0.130825i	$0.0417625\pi$
$20$	−696.194	−	447.417i	−0.389184	−	0.250113i
$21$	1013.43	+	1169.56i	0.501469	+	0.578726i
$22$	−4750.99			−2.09280
$23$	2536.35	−	57.2233i	0.999746	−	0.0225555i
$23$	2536.35	−	57.2233i	0.999746	−	0.0225555i
$24$	93.0784			0.0329853
$25$	1570.39	+	1812.33i	0.502525	+	0.579944i
$26$	−3902.41	−	2507.93i	−1.13214	−	0.727581i
$27$	−103.748	+	721.580i	−0.0273885	+	0.190491i
$28$	−2192.47	+	4800.85i	−0.528493	+	1.15724i
$29$	−906.241	−	6303.04i	−0.200101	−	1.39173i	−0.803980	−	0.594656i	$-0.797288\pi$
$29$	−906.241	−	6303.04i	−0.200101	−	1.39173i	0.603880	−	0.797075i	$-0.293621\pi$
$30$	−1843.52	−	541.307i	−0.373978	−	0.109810i
$31$	−1155.34	+	742.490i	−0.215926	+	0.138767i	−0.644133	−	0.764914i	$-0.722782\pi$
$31$	−1155.34	+	742.490i	−0.215926	+	0.138767i	0.428207	+	0.903681i	$0.359145\pi$
$32$	3362.56	+	7362.99i	0.580491	+	1.27110i
$33$	−5181.51	+	1521.43i	−0.828269	+	0.243202i
$34$	10969.0	−	12658.9i	1.62730	−	1.87801i
$35$	−3036.00	+	3503.73i	−0.418921	+	0.483460i
$36$	−2385.49	+	700.444i	−0.306776	+	0.0900777i
$37$	2734.59	+	5987.93i	0.328389	+	0.719072i	0.999757	−	0.0220526i	$-0.00702014\pi$
$37$	2734.59	+	5987.93i	0.328389	+	0.719072i	−0.671368	+	0.741124i	$0.734293\pi$
$38$	243.141	−	156.257i	0.0273148	−	0.0175542i
$39$	−5059.15	−	1485.50i	−0.532619	−	0.156391i
$40$	39.6834	+	276.004i	0.00392156	+	0.0272750i
$41$	8542.88	−	18706.3i	0.793679	−	1.73791i	0.127870	−	0.991791i	$-0.459186\pi$
$41$	8542.88	−	18706.3i	0.793679	−	1.73791i	0.665808	−	0.746123i	$-0.268087\pi$
$42$	−1743.84	+	12128.7i	−0.152540	+	1.06094i
$43$	7531.07	+	4839.92i	0.621134	+	0.399179i	0.813018	−	0.582239i	$-0.197823\pi$
$43$	7531.07	+	4839.92i	0.621134	+	0.399179i	−0.191884	+	0.981418i	$0.561460\pi$
$44$	−12060.7	−	13918.8i	−0.939162	−	1.08385i
$45$	−2183.92			−0.160770
$46$	13493.8	+	14880.8i	0.940241	+	1.03688i
$47$	10219.9			0.674839			0.337419	−	0.941354i	$-0.390446\pi$
$47$	10219.9			0.674839			0.337419	+	0.941354i	$0.390446\pi$
$48$	6271.48	+	7237.68i	0.392886	+	0.453415i
$49$	10734.1	+	6898.39i	0.638669	+	0.410447i
$50$	−2702.22	+	18794.4i	−0.152861	+	1.06317i
$51$	7909.13	−	17318.6i	0.425798	−	0.932367i
$52$	−2559.15	−	17799.3i	−0.131246	−	0.912837i
$53$	3811.35	+	1119.11i	0.186376	+	0.0547248i	0.373588	−	0.927595i	$-0.378127\pi$
$53$	3811.35	+	1119.11i	0.186376	+	0.0547248i	−0.187213	+	0.982319i	$0.559945\pi$
$54$	−4855.87	+	3120.68i	−0.226612	+	0.145635i
$55$	−6720.57	−	14716.0i	−0.299571	−	0.655968i
$56$	1706.28	−	501.008i	0.0727075	−	0.0213489i
$57$	215.134	−	248.278i	0.00877046	−	0.0101216i
$58$	33018.3	−	38105.2i	1.28880	−	1.48735i
$59$	−38765.2	+	11382.5i	−1.44981	+	0.425703i	−0.909479	−	0.415749i	$-0.863520\pi$
$59$	−38765.2	+	11382.5i	−1.44981	+	0.425703i	−0.540332	+	0.841452i	$0.681701\pi$
$60$	−3094.05	−	6775.03i	−0.110956	−	0.242959i
$61$	31567.3	−	20287.0i	1.08621	−	0.698062i	0.130223	−	0.991485i	$-0.458431\pi$
$61$	31567.3	−	20287.0i	1.08621	−	0.698062i	0.955983	+	0.293423i	$0.0947943\pi$
$62$	−10433.6	−	3063.59i	−0.344712	−	0.101217i
$63$	1982.15	+	13786.1i	0.0629194	+	0.437614i
$64$	−12479.3	+	27325.9i	−0.380839	+	0.833921i
$65$	2248.00	−	15635.2i	0.0659952	−	0.459007i
$66$	−35971.1	−	23117.2i	−1.01647	−	0.653245i
$67$	−23430.2	−	27039.8i	−0.637659	−	0.735897i	0.341300	−	0.939954i	$-0.389133\pi$
$67$	−23430.2	−	27039.8i	−0.637659	−	0.735897i	−0.978959	+	0.204057i	$0.934587\pi$
$68$	64931.5			1.70288
$69$	19481.9	+	11908.0i	0.492615	+	0.301105i
$70$	−36708.4			−0.895407
$71$	−19175.0	−	22129.2i	−0.451430	−	0.520978i	0.483724	−	0.875221i	$-0.339284\pi$
$71$	−19175.0	−	22129.2i	−0.451430	−	0.520978i	−0.935153	+	0.354243i	$0.884739\pi$
$72$	704.723	+	452.898i	0.0160209	+	0.0102960i
$73$	9239.18	−	64259.9i	0.202921	−	1.41134i	−0.592639	−	0.805468i	$-0.701914\pi$
$73$	9239.18	−	64259.9i	0.202921	−	1.41134i	0.795559	−	0.605876i	$-0.207177\pi$
$74$	−21652.4	+	47412.1i	−0.459649	+	1.00649i
$75$	3071.50	+	21362.8i	0.0630519	+	0.438535i
$76$	1075.01	+	315.650i	0.0213490	+	0.00626863i
$77$	−86796.0	+	55780.4i	−1.66830	+	1.07215i
$78$	−17343.3	−	37976.4i	−0.322771	−	0.706770i
$79$	3133.16	−	919.980i	0.0564827	−	0.0165848i	−0.253369	−	0.967370i	$-0.581539\pi$
$79$	3133.16	−	919.980i	0.0564827	−	0.0165848i	0.309852	+	0.950785i	$0.399721\pi$
$80$	−18788.0	+	21682.5i	−0.328212	+	0.378777i
$81$	−4296.54	+	4958.47i	−0.0727623	+	0.0839722i
$82$	156234.	−	45874.5i	2.56591	−	0.753420i
$83$	38050.7	+	83319.3i	0.606271	+	1.32755i	0.925095	+	0.379735i	$0.123985\pi$
$83$	38050.7	+	83319.3i	0.606271	+	1.32755i	−0.318824	+	0.947814i	$0.603288\pi$
$84$	−39959.7	+	25680.5i	−0.617908	+	0.397105i
$85$	54726.5	+	16069.2i	0.821581	+	0.241238i
$86$	10087.7	+	70161.5i	0.147077	+	1.02295i
$87$	23807.7	−	52131.7i	0.337225	−	0.738420i
$88$	−883.138	+	6142.36i	−0.0121569	+	0.0845529i
$89$	−78303.6	−	50322.7i	−1.04787	−	0.673424i	−0.100947	−	0.994892i	$-0.532187\pi$
$89$	−78303.6	−	50322.7i	−1.04787	−	0.673424i	−0.946920	+	0.321468i	$0.895824\pi$
$90$	−11324.0	−	13068.5i	−0.147364	−	0.170067i
$91$	−100738.			−1.27524
$92$	−9340.73	+	77307.9i	−0.115057	+	0.952257i
$93$	−12360.2			−0.148189
$94$	52991.5	+	61155.4i	0.618567	+	0.713864i
$95$	827.936	+	532.082i	0.00941213	+	0.00604881i
$96$	−10367.7	+	72108.7i	−0.114816	+	0.798564i
$97$	−18957.9	+	41511.9i	−0.204579	+	0.447964i	−0.983914	−	0.178642i	$-0.942830\pi$
$97$	−18957.9	+	41511.9i	−0.204579	+	0.447964i	0.779336	+	0.626607i	$0.215557\pi$
$98$	14378.1	+	100002.i	0.151229	+	1.05182i
$99$	−46633.6	−	13692.9i	−0.478201	−	0.140413i
$100$	−61920.8	+	39794.1i	−0.619208	+	0.397941i
$101$	−40291.4	−	88226.0i	−0.393015	−	0.860583i	−0.997931	−	0.0642939i	$-0.979521\pi$
$101$	−40291.4	−	88226.0i	−0.393015	−	0.860583i	0.604916	−	0.796289i	$-0.293207\pi$
$102$	144644.	−	42471.4i	1.37658	−	0.404199i
$103$	−70467.7	+	81324.1i	−0.654481	+	0.755312i	−0.981865	−	0.189580i	$-0.939287\pi$
$103$	−70467.7	+	81324.1i	−0.654481	+	0.755312i	0.327384	+	0.944891i	$0.393833\pi$
$104$	−3967.79	+	4579.08i	−0.0359721	+	0.0415140i
$105$	−40034.8	+	11755.3i	−0.354376	+	0.104054i
$106$	13065.7	+	28609.8i	0.112945	+	0.247315i
$107$	−58529.5	+	37614.6i	−0.494215	+	0.317612i	−0.763898	−	0.645337i	$-0.776717\pi$
$107$	−58529.5	+	37614.6i	−0.494215	+	0.317612i	0.269684	+	0.962949i	$0.413081\pi$
$108$	−21469.4	−	6304.00i	−0.177117	−	0.0520064i
$109$	19595.0	+	136286.i	0.157972	+	1.09872i	0.902364	+	0.430975i	$0.141830\pi$
$109$	19595.0	+	136286.i	0.157972	+	1.09872i	−0.744392	+	0.667743i	$0.767260\pi$
$110$	53213.1	−	116520.i	0.419311	−	0.918164i
$111$	−8431.47	+	58642.2i	−0.0649525	+	0.451755i
$112$	153924.	+	98921.0i	1.15948	+	0.745150i
$113$	−72528.0	−	83701.8i	−0.534330	−	0.616650i	0.422830	−	0.906209i	$-0.361037\pi$
$113$	−72528.0	−	83701.8i	−0.534330	−	0.616650i	−0.957160	+	0.289559i	$0.906491\pi$
$114$	2601.20			0.0187461
$115$	−27004.7	+	62846.1i	−0.190412	+	0.443133i
$116$	195454.			1.34865
$117$	−31076.2	−	35863.8i	−0.209876	−	0.242210i
$118$	−269116.	−	172950.i	−1.77924	−	1.14345i
$119$	51767.3	−	360049.i	0.335110	−	2.33074i
$120$	−1042.52	+	2282.79i	−0.00660891	+	0.0144715i
$121$	−28318.3	−	196958.i	−0.175834	−	1.22295i
$122$	285078.	+	83706.5i	1.73406	+	0.509166i
$123$	155701.	−	100063.i	0.927959	−	0.596363i
$124$	−17511.2	−	38344.1i	−0.102273	−	0.223947i
$125$	−142880.	+	41953.5i	−0.817895	+	0.240156i
$126$	−72218.3	+	83344.4i	−0.405248	+	0.467681i
$127$	7389.48	−	8527.92i	0.0406541	−	0.0469174i	−0.735058	−	0.678004i	$-0.762845\pi$
$127$	7389.48	−	8527.92i	0.0406541	−	0.0469174i	0.775712	+	0.631086i	$0.217391\pi$
$128$	20305.6	−	5962.27i	0.109545	−	0.0321652i
$129$	33469.9	+	73288.8i	0.177084	+	0.387760i
$130$	105217.	−	67618.7i	0.546043	−	0.350920i
$131$	728.751	+	213.980i	0.00371023	+	0.00108942i	0.283587	−	0.958946i	$-0.408475\pi$
$131$	728.751	+	213.980i	0.00371023	+	0.00108942i	−0.279877	+	0.960036i	$0.590294\pi$
$132$	−23589.3	−	164068.i	−0.117837	−	0.819573i
$133$	2607.36	−	5709.33i	0.0127812	−	0.0279870i
$134$	40317.1	−	280411.i	0.193967	−	1.34907i
$135$	−16535.1	−	10626.5i	−0.0780858	−	0.0501827i
$136$	−14327.1	−	16534.4i	−0.0664221	−	0.0766552i
$137$	−238827.			−1.08713			−0.543566	−	0.839366i	$-0.682926\pi$
$137$	−238827.			−1.08713			−0.543566	+	0.839366i	$0.682926\pi$
$138$	29758.9	+	178324.i	0.133021	+	0.797099i
$139$	5923.27			0.0260031			0.0130015	−	0.999915i	$-0.495861\pi$
$139$	5923.27			0.0260031			0.0130015	+	0.999915i	$0.495861\pi$
$140$	−93186.6	−	107543.i	−0.401821	−	0.463727i
$141$	77377.4	+	49727.4i	0.327768	+	0.210644i
$142$	32995.1	−	229486.i	0.137318	−	0.955071i
$143$	146032.	−	319765.i	0.597183	−	1.30765i
$144$	12266.3	+	85314.1i	0.0492955	+	0.342858i
$145$	164736.	+	48370.7i	0.650680	+	0.191057i
$146$	432437.	−	277910.i	1.67896	−	1.07900i
$147$	47705.0	+	104459.i	0.182083	+	0.398707i
$148$	−193867.	+	56924.5i	−0.727528	+	0.213621i
$149$	−85269.8	+	98406.6i	−0.314651	+	0.363127i	−0.890941	−	0.454118i	$-0.849954\pi$
$149$	−85269.8	+	98406.6i	−0.314651	+	0.363127i	0.576290	+	0.817245i	$0.304500\pi$
$150$	−111908.	+	129149.i	−0.406101	+	0.468666i
$151$	125744.	−	36921.8i	0.448792	−	0.131777i	−0.0495234	−	0.998773i	$-0.515770\pi$
$151$	125744.	−	36921.8i	0.448792	−	0.131777i	0.498316	+	0.866996i	$0.333952\pi$
$152$	−156.822	−	343.392i	−0.000550551	−	0.00120554i
$153$	144150.	−	92639.9i	0.497837	−	0.319941i
$154$	−783840.	−	230156.i	−2.66333	−	0.782025i
$155$	−5269.67	−	36651.4i	−0.0176179	−	0.122535i
$156$	67231.0	−	147215.i	0.221186	−	0.484330i
$157$	−58943.0	+	409957.i	−0.190846	+	1.32736i	0.638929	+	0.769265i	$0.279378\pi$
$157$	−58943.0	+	409957.i	−0.190846	+	1.32736i	−0.829775	+	0.558097i	$0.811532\pi$
$158$	21751.1	+	13978.6i	0.0693167	+	0.0445471i
$159$	23411.4	+	27018.3i	0.0734405	+	0.0847548i
$160$	−218243.			−0.673969
$161$	421230.	+	113429.i	1.28072	+	0.344874i
$162$	−51949.6			−0.155523
$163$	167374.	+	193159.i	0.493421	+	0.569439i	0.946777	−	0.321891i	$-0.104319\pi$
$163$	167374.	+	193159.i	0.493421	+	0.569439i	−0.453355	+	0.891330i	$0.649773\pi$
$164$	531007.	+	341258.i	1.54167	+	0.990770i
$165$	20721.3	−	144120.i	0.0592525	−	0.412110i
$166$	−301283.	+	659718.i	−0.848603	+	1.85818i
$167$	44229.5	+	307623.i	0.122721	+	0.853547i	0.954451	+	0.298366i	$0.0964417\pi$
$167$	44229.5	+	307623.i	0.122721	+	0.853547i	−0.831730	+	0.555180i	$0.812649\pi$
$168$	15356.5	+	4509.07i	0.0419777	+	0.0123258i
$169$	−23606.7	+	15171.1i	−0.0635798	+	0.0408603i
$170$	187608.	+	410804.i	0.497884	+	1.09021i
$171$	2836.90	−	832.990i	0.00741916	−	0.00217846i
$172$	−179941.	+	207663.i	−0.463776	+	0.535227i
$173$	−75391.3	+	87006.2i	−0.191516	+	0.221022i	−0.843384	−	0.537311i	$-0.819440\pi$
$173$	−75391.3	+	87006.2i	−0.191516	+	0.221022i	0.651868	+	0.758333i	$0.273986\pi$
$174$	435402.	−	127846.i	1.09023	−	0.320120i
$175$	171294.	+	375081.i	0.422811	+	0.925828i
$176$	−537128.	+	345191.i	−1.30706	+	0.839997i
$177$	−348886.	−	102442.i	−0.837049	−	0.245780i
$178$	−104886.	−	729498.i	−0.248123	−	1.72573i
$179$	−47839.5	+	104754.i	−0.111597	+	0.244364i	−0.957188	−	0.289468i	$-0.906522\pi$
$179$	−47839.5	+	104754.i	−0.111597	+	0.244364i	0.845590	+	0.533833i	$0.179249\pi$
$180$	9539.78	−	66350.6i	0.0219461	−	0.152638i
$181$	−74654.4	−	47977.5i	−0.169379	−	0.108853i	0.453205	−	0.891406i	$-0.350281\pi$
$181$	−74654.4	−	47977.5i	−0.169379	−	0.108853i	−0.622584	+	0.782553i	$0.713917\pi$
$182$	−522343.	−	602816.i	−1.16890	−	1.34898i
$183$	337717.			0.745461
$184$	21747.0	−	14679.4i	0.0473538	−	0.0319643i
$185$	−177485.			−0.381271
$186$	−64089.3	−	73963.0i	−0.135832	−	0.156759i
$187$	1.06783e6	+	686254.i	2.23305	+	1.43510i
$188$	−44642.3	+	310494.i	−0.0921195	+	0.640705i
$189$	−52072.8	+	114023.i	−0.106037	+	0.232188i
$190$	1109.00	+	7713.28i	0.00222868	+	0.0155008i
$191$	−375873.	−	110366.i	−0.745518	−	0.218904i	−0.113156	−	0.993577i	$-0.536096\pi$
$191$	−375873.	−	110366.i	−0.745518	−	0.218904i	−0.632362	+	0.774673i	$0.717914\pi$
$192$	−227446.	+	146171.i	−0.445272	+	0.286159i
$193$	−237557.	−	520177.i	−0.459065	−	1.00521i	−0.987700	−	0.156363i	$-0.950023\pi$
$193$	−237557.	−	520177.i	−0.459065	−	1.00521i	0.528634	−	0.848850i	$-0.322704\pi$
$194$	−346706.	+	101802.i	−0.661389	+	0.194201i
$195$	93097.3	−	107440.i	0.175328	−	0.202339i
$196$	−256472.	+	295984.i	−0.476869	+	0.550336i
$197$	650592.	−	191031.i	1.19438	−	0.350702i	0.376680	−	0.926344i	$-0.377066\pi$
$197$	650592.	−	191031.i	1.19438	−	0.350702i	0.817702	+	0.575641i	$0.195248\pi$
$198$	−159864.	−	350054.i	−0.289793	−	0.634559i
$199$	−619180.	+	397923.i	−1.10837	+	0.712306i	−0.960937	−	0.276767i	$-0.910737\pi$
$199$	−619180.	+	397923.i	−1.10837	+	0.712306i	−0.147432	+	0.989072i	$0.547101\pi$
$200$	23796.2	+	6987.18i	0.0420661	+	0.0123517i
$201$	−45826.7	−	318732.i	−0.0800072	−	0.556462i
$202$	319025.	−	698568.i	0.550107	−	1.20457i
$203$	155828.	−	1.08381e6i	0.265402	−	1.84591i
$204$	491615.	+	315942.i	0.827084	+	0.531534i
$205$	363097.	+	419037.i	0.603446	+	0.696414i
$206$	−852028.			−1.39890
$207$	89560.9	+	184953.i	0.145276	+	0.300010i
$208$	−623408.			−0.999112
$209$	14343.0	+	16552.7i	0.0227129	+	0.0262121i
$210$	−277930.	−	178615.i	−0.434897	−	0.279491i
$211$	146174.	−	1.01667e6i	0.226030	−	1.57207i	−0.488562	−	0.872529i	$-0.662479\pi$
$211$	146174.	−	1.01667e6i	0.226030	−	1.57207i	0.714592	−	0.699541i	$-0.246612\pi$
$212$	−50648.9	+	110906.i	−0.0773982	+	0.169478i
$213$	−37504.2	−	260847.i	−0.0566410	−	0.393947i
$214$	−528570.	−	155202.i	−0.788983	−	0.231666i
$215$	−203052.	+	130494.i	−0.299580	+	0.192528i
$216$	3131.96	+	6858.04i	0.00456754	+	0.0100015i
$217$	−226582.	+	66530.3i	−0.326644	+	0.0959114i
$218$	−713933.	+	823922.i	−1.01746	+	1.17421i
$219$	382626.	−	441574.i	0.539094	−	0.622148i
$220$	476450.	−	139898.i	0.663682	−	0.194875i
$221$	514849.	+	1.12736e6i	0.709087	+	1.55268i
$222$	−394632.	+	253615.i	−0.537416	+	0.345376i
$223$	−153485.	−	45067.1i	−0.206682	−	0.0606873i	0.176753	−	0.984255i	$-0.443441\pi$
$223$	−153485.	−	45067.1i	−0.206682	−	0.0606873i	−0.383435	+	0.923568i	$0.625259\pi$
$224$	198079.	+	1.37767e6i	0.263766	+	1.83454i
$225$	−80691.1	+	176689.i	−0.106260	+	0.232677i
$226$	124801.	−	868013.i	0.162536	−	1.13046i
$227$	178821.	+	114921.i	0.230332	+	0.148025i	0.650717	−	0.759321i	$-0.274469\pi$
$227$	178821.	+	114921.i	0.230332	+	0.148025i	−0.420385	+	0.907346i	$0.638105\pi$
$228$	6603.30	+	7620.61i	0.00841247	+	0.00970851i
$229$	886512.			1.11711			0.558555	−	0.829467i	$-0.311356\pi$
$229$	886512.			1.11711			0.558555	+	0.829467i	$0.311356\pi$
$230$	−516094.	+	164271.i	−0.643293	+	0.204758i
$231$	−928572.			−1.14495
$232$	−43127.0	−	49771.2i	−0.0526053	−	0.0607097i
$233$	672473.	+	432172.i	0.811493	+	0.521515i	0.879348	−	0.476180i	$-0.157979\pi$
$233$	672473.	+	432172.i	0.811493	+	0.521515i	−0.0678544	+	0.997695i	$0.521615\pi$
$234$	53473.8	−	371919.i	0.0638413	−	0.444026i
$235$	−114467.	+	250647.i	−0.135210	+	0.296069i
$236$	−176482.	−	1.22746e6i	−0.206263	−	1.43459i
$237$	28198.5	+	8279.82i	0.0326103	+	0.00957524i
$238$	2.42295e6	−	1.55714e6i	2.77270	−	1.78190i
$239$	103522.	+	226682.i	0.117230	+	0.256698i	0.959147	−	0.282910i	$-0.0912997\pi$
$239$	103522.	+	226682.i	0.117230	+	0.256698i	−0.841916	+	0.539608i	$0.818572\pi$
$240$	−247751.	+	72746.2i	−0.277643	+	0.0815234i
$241$	−145507.	+	167924.i	−0.161376	+	0.186238i	−0.830679	−	0.556752i	$-0.812048\pi$
$241$	−145507.	+	167924.i	−0.161376	+	0.186238i	0.669303	+	0.742990i	$0.266593\pi$
$242$	1.03176e6	−	1.19071e6i	1.13250	−	1.30698i
$243$	−56657.1	+	16636.0i	−0.0615515	+	0.0180732i
$244$	478457.	+	1.04768e6i	0.514480	+	1.12655i
$245$	−289413.	+	185994.i	−0.308037	+	0.197963i
$246$	1.40611e6	+	412871.i	1.48143	+	0.434987i
$247$	3043.42	+	21167.4i	0.00317409	+	0.0220763i
$248$	−5900.25	+	12919.7i	−0.00609174	+	0.0133390i
$249$	−117320.	+	815980.i	−0.119915	+	0.834029i
$250$	−991906.	−	637459.i	−1.00374	−	0.645063i
$251$	378286.	+	436565.i	0.378997	+	0.437386i	0.912915	−	0.408151i	$-0.133826\pi$
$251$	378286.	+	436565.i	0.378997	+	0.437386i	−0.533917	+	0.845537i	$0.679281\pi$
$252$	−427501.			−0.424069
$253$	−970672.	+	1.17265e6i	−0.953391	+	1.15177i
$254$	89346.5			0.0868947
$255$	336161.	+	387951.i	0.323740	+	0.373616i
$256$	949663.	+	610311.i	0.905669	+	0.582038i
$257$	87879.9	−	611218.i	0.0829959	−	0.577249i	−0.905308	−	0.424755i	$-0.860360\pi$
$257$	87879.9	−	611218.i	0.0829959	−	0.577249i	0.988304	−	0.152494i	$-0.0487306\pi$
$258$	−265013.	+	580297.i	−0.247866	+	0.542751i
$259$	161088.	+	1.12039e6i	0.149215	+	1.03781i
$260$	465199.	+	136595.i	0.426781	+	0.125314i
$261$	433916.	−	278861.i	0.394279	−	0.253388i
$262$	2498.23	+	5470.35i	0.00224843	+	0.00492337i
$263$	551963.	−	162071.i	0.492063	−	0.144483i	−0.0262817	−	0.999655i	$-0.508367\pi$
$263$	551963.	−	162071.i	0.492063	−	0.144483i	0.518345	+	0.855172i	$0.326549\pi$
$264$	−36573.8	+	42208.4i	−0.0322969	+	0.0372726i
$265$	−70135.5	+	80940.6i	−0.0613512	+	0.0708030i
$266$	47684.1	−	14001.3i	0.0413208	−	0.0121329i
$267$	−348000.	−	762014.i	−0.298745	−	0.654161i
$268$	923856.	−	593727.i	0.785719	−	0.504951i
$269$	−2.14922e6	−	631068.i	−1.81093	−	0.531736i	−0.812256	−	0.583301i	$-0.801761\pi$
$269$	−2.14922e6	−	631068.i	−1.81093	−	0.531736i	−0.998670	+	0.0515658i	$0.983579\pi$
$270$	−22148.4	−	154045.i	−0.0184898	−	0.128600i
$271$	987983.	−	2.16338e6i	0.817196	−	1.78941i	0.244484	−	0.969653i	$-0.421381\pi$
$271$	987983.	−	2.16338e6i	0.817196	−	1.78941i	0.572712	−	0.819757i	$-0.305891\pi$
$272$	320356.	−	2.22813e6i	0.262549	−	1.82607i
$273$	−762718.	−	490169.i	−0.619380	−	0.398052i
$274$	−1.23835e6	−	1.42914e6i	−0.996480	−	1.15000i
$275$	−1.43890e6			−1.14736
$276$	−446883.	+	539870.i	−0.353119	+	0.426596i
$277$	−991566.			−0.776466			−0.388233	−	0.921561i	$-0.626914\pi$
$277$	−991566.			−0.776466			−0.388233	+	0.921561i	$0.626914\pi$
$278$	30713.1	+	35444.8i	0.0238348	+	0.0275068i
$279$	−93582.3	−	60141.7i	−0.0719752	−	0.0462557i
$280$	−6823.54	+	47458.8i	−0.00520133	+	0.0361761i
$281$	−817770.	+	1.79067e6i	−0.617825	+	1.35285i	0.299265	+	0.954170i	$0.403258\pi$
$281$	−817770.	+	1.79067e6i	−0.617825	+	1.35285i	−0.917091	+	0.398679i	$0.869469\pi$
$282$	103645.	+	720869.i	0.0776117	+	0.539801i
$283$	765599.	+	224800.i	0.568245	+	0.166852i	0.553220	−	0.833035i	$-0.313399\pi$
$283$	765599.	+	224800.i	0.568245	+	0.166852i	0.0150250	+	0.999887i	$0.495217\pi$
$284$	756076.	−	485900.i	0.556249	−	0.357480i
$285$	3679.55	+	8057.09i	0.00268338	+	0.00587579i
$286$	2.67067e6	−	784179.i	1.93066	−	0.566892i
$287$	2.31565e6	−	2.67240e6i	1.65946	−	1.91512i
$288$	−429361.	+	495509.i	−0.305029	+	0.352022i
$289$	−2.93154e6	+	860777.i	−2.06467	+	0.606242i
$290$	564729.	+	1.23658e6i	0.394317	+	0.863433i
$291$	−345523.	+	222054.i	−0.239191	+	0.153718i
$292$	1.91195e6	+	561399.i	1.31226	+	0.385314i
$293$	−357613.	−	2.48725e6i	−0.243357	−	1.69258i	−0.635036	−	0.772483i	$-0.719015\pi$
$293$	−357613.	−	2.48725e6i	−0.243357	−	1.69258i	0.391679	−	0.920102i	$-0.371894\pi$
$294$	−377725.	+	827103.i	−0.254864	+	0.558073i
$295$	155025.	−	1.07822e6i	0.103716	−	0.721362i
$296$	57272.3	+	36806.6i	0.0379940	+	0.0244173i
$297$	−286450.	−	330581.i	−0.188433	−	0.217463i
$298$	−1.03100e6			−0.672540
$299$	−1.41631e6	+	450806.i	−0.916178	+	0.291616i
$300$	−662449.			−0.424961
$301$	1.00804e6	+	1.16334e6i	0.641303	+	0.740103i
$302$	872942.	+	561006.i	0.550767	+	0.353956i
$303$	124229.	−	864032.i	0.0777350	−	0.540659i
$304$	16135.4	−	35331.5i	0.0100137	−	0.0219270i
$305$	143983.	+	1.00143e6i	0.0886262	+	0.616409i
$306$	1.30180e6	+	382242.i	0.794767	+	0.233365i
$307$	−17857.7	+	11476.4i	−0.0108138	+	0.00694962i	−0.546037	−	0.837761i	$-0.683864\pi$
$307$	−17857.7	+	11476.4i	−0.0108138	+	0.00694962i	0.535223	+	0.844711i	$0.320228\pi$
$308$	−1.31555e6	−	2.88065e6i	−0.790187	−	1.73027i
$309$	−929235.	+	272848.i	−0.553643	+	0.162564i
$310$	191997.	−	221577.i	0.113473	−	0.130954i
$311$	1.31481e6	−	1.51737e6i	0.770837	−	0.889593i	−0.225575	−	0.974226i	$-0.572426\pi$
$311$	1.31481e6	−	1.51737e6i	0.770837	−	0.889593i	0.996412	+	0.0846325i	$0.0269716\pi$
$312$	−52322.0	+	15363.1i	−0.0304297	+	0.00893497i
$313$	524259.	+	1.14797e6i	0.302472	+	0.662321i	0.998445	−	0.0557467i	$-0.0177539\pi$
$313$	524259.	+	1.14797e6i	0.302472	+	0.662321i	−0.695973	+	0.718068i	$0.745027\pi$
$314$	−2.75881e6	+	1.77298e6i	−1.57905	+	1.01480i
$315$	−360313.	−	105797.i	−0.204599	−	0.0600757i
$316$	14264.0	+	99208.6i	0.00803572	+	0.0558897i
$317$	−757864.	+	1.65949e6i	−0.423587	+	0.927527i	0.570737	+	0.821133i	$0.306658\pi$
$317$	−757864.	+	1.65949e6i	−0.423587	+	0.927527i	−0.994324	+	0.106394i	$0.966070\pi$
$318$	−40284.9	+	280187.i	−0.0223395	+	0.155375i
$319$	3.21434e6	+	2.06573e6i	1.76854	+	1.13657i
$320$	−530408.	−	612123.i	−0.289558	−	0.334167i
$321$	−626168.			−0.339178
$322$	1.50538e6	+	3.10878e6i	0.809109	+	1.67090i
$323$	−77218.6			−0.0411828
$324$	−131877.	−	152195.i	−0.0697923	−	0.0805447i
$325$	−1.18190e6	−	759558.i	−0.620684	−	0.398889i
$326$	−288005.	+	2.00312e6i	−0.150092	+	1.04391i
$327$	−514779.	+	1.12721e6i	−0.266226	+	0.582955i
$328$	−30267.7	−	210516.i	−0.0155344	−	0.108044i
$329$	1.68612e6	+	495089.i	0.858812	+	0.252170i
$330$	969853.	−	623286.i	0.490254	−	0.315067i
$331$	−1.41539e6	−	3.09927e6i	−0.710079	−	1.55486i	−0.827307	−	0.561750i	$-0.810128\pi$
$331$	−1.41539e6	−	3.09927e6i	−0.710079	−	1.55486i	0.117228	−	0.993105i	$-0.462599\pi$
$332$	−2.69757e6	+	792079.i	−1.34316	+	0.394387i
$333$	−349176.	+	402971.i	−0.172558	+	0.199142i
$334$	−1.61147e6	+	1.85974e6i	−0.790418	+	0.912191i
$335$	925593.	−	271779.i	0.450617	−	0.132313i
$336$	684076.	+	1.49792e6i	0.330565	+	0.723835i
$337$	−1.48804e6	+	956302.i	−0.713737	+	0.458691i	−0.846453	−	0.532463i	$-0.821267\pi$
$337$	−1.48804e6	+	956302.i	−0.713737	+	0.458691i	0.132716	+	0.991154i	$0.457630\pi$
$338$	−213188.	−	62597.7i	−0.101501	−	0.0298035i
$339$	−141857.	−	986634.i	−0.0670425	−	0.466291i
$340$	−727260.	+	1.59248e6i	−0.341187	+	0.747095i
$341$	117275.	−	815662.i	0.0546157	−	0.379861i
$342$	19694.4	+	12656.8i	0.00910494	+	0.00585139i
$343$	−455744.	−	525956.i	−0.209163	−	0.241387i
$344$	92584.0			0.0421833
$345$	−510255.	+	344427.i	−0.230802	+	0.155794i
$346$	−911559.			−0.409350
$347$	41637.5	+	48052.2i	0.0185635	+	0.0214235i	0.764955	−	0.644083i	$-0.222761\pi$
$347$	41637.5	+	48052.2i	0.0185635	+	0.0214235i	−0.746392	+	0.665507i	$0.768216\pi$
$348$	1.47984e6	+	951034.i	0.655037	+	0.420967i
$349$	−61749.5	+	429477.i	−0.0271375	+	0.188745i	−0.998881	−	0.0472938i	$-0.984940\pi$
$349$	−61749.5	+	429477.i	−0.0271375	+	0.188745i	0.971744	+	0.236039i	$0.0758494\pi$
$350$	−1.35630e6	+	2.96987e6i	−0.591812	+	1.29589i
$351$	−60781.5	−	422745.i	−0.0263332	−	0.183151i
$352$	−4.66017e6	−	1.36835e6i	−2.00468	−	0.588628i
$353$	−630947.	+	405485.i	−0.269498	+	0.173196i	−0.668409	−	0.743794i	$-0.733025\pi$
$353$	−630947.	+	405485.i	−0.269498	+	0.173196i	0.398911	+	0.916990i	$0.369388\pi$
$354$	−1.19602e6	−	2.61891e6i	−0.507258	−	1.11074i
$355$	757497.	−	222421.i	0.319014	−	0.0936710i
$356$	1.87092e6	−	2.15916e6i	0.782402	−	0.902940i
$357$	2.14386e6	−	2.47415e6i	0.890279	−	1.02744i
$358$	−874901.	+	256894.i	−0.360787	+	0.105937i
$359$	603982.	+	1.32254e6i	0.247336	+	0.541591i	0.992058	−	0.125785i	$-0.0401449\pi$
$359$	603982.	+	1.32254e6i	0.247336	+	0.541591i	−0.744721	+	0.667376i	$0.767418\pi$
$360$	−19000.7	+	12211.0i	−0.00772706	+	0.00496588i
$361$	2.37452e6	+	697222.i	0.958977	+	0.281581i
$362$	−99998.0	−	695502.i	−0.0401070	−	0.278950i
$363$	743946.	−	1.62901e6i	0.296329	−	0.648871i
$364$	440044.	−	3.06057e6i	0.174078	−	1.21074i
$365$	1.47252e6	+	946333.i	0.578535	+	0.371802i
$366$	1.75111e6	+	2.02089e6i	0.683299	+	0.788570i
$367$	2.06720e6			0.801157			0.400579	−	0.916262i	$-0.368809\pi$
$367$	2.06720e6			0.801157			0.400579	+	0.916262i	$0.368809\pi$
$368$	2.60674e6	+	701945.i	1.00341	+	0.270199i
$369$	1.66574e6			0.636856
$370$	−920289.	−	1.06207e6i	−0.349478	−	0.403319i
$371$	574599.	+	369272.i	0.216735	+	0.139287i
$372$	53991.5	−	375519.i	0.0202287	−	0.140694i
$373$	−1.99475e6	+	4.36790e6i	−0.742364	+	1.62555i	0.0372620	+	0.999306i	$0.488136\pi$
$373$	−1.99475e6	+	4.36790e6i	−0.742364	+	1.62555i	−0.779626	+	0.626245i	$0.784591\pi$
$374$	1.43034e6	+	9.94822e6i	0.528761	+	3.67762i
$375$	−1.28592e6	−	377581.i	−0.472212	−	0.138654i
$376$	88915.7	−	57142.6i	0.0324346	−	0.0208445i
$377$	1.54978e6	+	3.39354e6i	0.561586	+	1.22970i
$378$	−952320.	+	279626.i	−0.342810	+	0.100658i
$379$	−1.84028e6	+	2.12380e6i	−0.658092	+	0.759478i	−0.982464	−	0.186451i	$-0.940301\pi$
$379$	−1.84028e6	+	2.12380e6i	−0.658092	+	0.759478i	0.324373	+	0.945929i	$0.394847\pi$
$380$	−19782.0	+	22829.6i	−0.00702767	+	0.00811036i
$381$	97442.7	−	28611.8i	0.0343904	−	0.0100979i
$382$	−1.28853e6	−	2.82149e6i	−0.451789	−	0.989281i
$383$	1.89125e6	−	1.21543e6i	0.658799	−	0.423384i	−0.168073	−	0.985775i	$-0.553754\pi$
$383$	1.89125e6	−	1.21543e6i	0.658799	−	0.423384i	0.826872	+	0.562390i	$0.190118\pi$
$384$	182751.	+	53660.4i	0.0632457	+	0.0185706i
$385$	−395891.	−	2.75348e6i	−0.136120	−	0.946738i
$386$	1.88096e6	−	4.11874e6i	0.642558	−	1.40700i
$387$	−103196.	+	717747.i	−0.0350257	+	0.243609i
$388$	−1.17838e6	−	757299.i	−0.397380	−	0.255381i
$389$	−3.13774e6	−	3.62115e6i	−1.05134	−	1.21331i	−0.976366	−	0.216125i	$-0.930658\pi$
$389$	−3.13774e6	−	3.62115e6i	−1.05134	−	1.21331i	−0.0749743	−	0.997185i	$-0.523887\pi$
$390$	1.12564e6			0.374748
$391$	−883417.	−	5.29370e6i	−0.292229	−	1.75112i
$392$	131961.			0.0433741
$393$	4476.40	+	5166.04i	0.00146200	+	0.00168724i
$394$	4.51655e6	+	2.90261e6i	1.46577	+	0.941993i
$395$	−12529.8	+	87146.5i	−0.00404064	+	0.0281033i
$396$	619713.	−	1.35698e6i	0.198588	−	0.434847i
$397$	−649167.	−	4.51505e6i	−0.206719	−	1.43776i	−0.783769	−	0.621052i	$-0.786705\pi$
$397$	−649167.	−	4.51505e6i	−0.206719	−	1.43776i	0.577050	−	0.816709i	$-0.304204\pi$
$398$	−5.59171e6	−	1.64187e6i	−1.76944	−	0.519556i
$399$	47521.3	−	30540.1i	0.0149436	−	0.00960369i
$400$	1.06003e6	+	2.32115e6i	0.331260	+	0.725359i
$401$	3.19953e6	−	939467.i	0.993631	−	0.291757i	0.255791	−	0.966732i	$-0.417664\pi$
$401$	3.19953e6	−	939467.i	0.993631	−	0.291757i	0.737840	+	0.674976i	$0.235846\pi$
$402$	1.66967e6	−	1.92690e6i	0.515306	−	0.594695i
$403$	526895.	−	608069.i	0.161608	−	0.186505i
$404$	2.85643e6	−	838724.i	0.870704	−	0.255662i
$405$	−73485.9	−	160912.i	−0.0222621	−	0.0487472i
$406$	7.29347e6	−	4.68723e6i	2.19593	−	1.41124i
$407$	−3.78987e6	−	1.11281e6i	−1.13407	−	0.332992i
$408$	−28022.3	−	194899.i	−0.00833399	−	0.0579642i
$409$	−2.18285e6	+	4.77977e6i	−0.645231	+	1.41286i	0.250437	+	0.968133i	$0.419426\pi$
$409$	−2.18285e6	+	4.77977e6i	−0.645231	+	1.41286i	−0.895667	+	0.444725i	$0.853301\pi$
$410$	−624794.	+	4.34554e6i	−0.183560	+	1.27668i
$411$	−1.80823e6	−	1.16208e6i	−0.528018	−	0.339336i
$412$	−2.16293e6	−	2.49615e6i	−0.627767	−	0.724482i
$413$	−6.94706e6			−2.00413
$414$	−642370.	+	1.49494e6i	−0.184198	+	0.428670i
$415$	−2.46963e6			−0.703901
$416$	−3.10550e6	−	3.58393e6i	−0.879827	−	1.01538i
$417$	44846.8	+	28821.3i	0.0126296	+	0.00811658i
$418$	−24680.4	+	171656.i	−0.00690895	+	0.0480528i
$419$	1.02613e6	−	2.24692e6i	0.285541	−	0.625248i	−0.711452	−	0.702734i	$-0.751962\pi$
$419$	1.02613e6	−	2.24692e6i	0.285541	−	0.625248i	0.996993	+	0.0774865i	$0.0246895\pi$
$420$	−182262.	−	1.26766e6i	−0.0504166	−	0.350655i
$421$	−3.02222e6	−	887402.i	−0.831037	−	0.244014i	−0.161574	−	0.986861i	$-0.551657\pi$
$421$	−3.02222e6	−	887402.i	−0.831037	−	0.244014i	−0.669462	+	0.742846i	$0.733475\pi$
$422$	6.84165e6	−	4.39686e6i	1.87016	−	1.20188i
$423$	343884.	+	753001.i	0.0934461	+	0.204618i
$424$	39417.2	−	11573.9i	0.0106481	−	0.00312655i
$425$	3.32209e6	−	3.83390e6i	0.892153	−	1.02960i
$426$	1.36644e6	−	1.57696e6i	0.364810	−	0.421013i
$427$	6.19089e6	−	1.81781e6i	1.64317	−	0.482479i
$428$	−887118.	−	1.94252e6i	−0.234084	−	0.512573i
$429$	2.66155e6	−	1.71048e6i	0.698219	−	0.448718i
$430$	−1.83373e6	−	538432.i	−0.478261	−	0.140430i
$431$	700103.	+	4.86932e6i	0.181539	+	1.26263i	0.853127	+	0.521704i	$0.174703\pi$
$431$	700103.	+	4.86932e6i	0.181539	+	1.26263i	−0.671588	+	0.740925i	$0.734388\pi$
$432$	−322247.	+	705622.i	−0.0830767	+	0.181913i
$433$	173060.	−	1.20366e6i	0.0443585	−	0.308520i	−0.955548	−	0.294836i	$-0.904735\pi$
$433$	173060.	−	1.20366e6i	0.0443585	−	0.308520i	0.999906	−	0.0136842i	$-0.00435595\pi$
$434$	−1.57298e6	−	1.01089e6i	−0.400865	−	0.257620i
$435$	1.01190e6	+	1.16779e6i	0.256397	+	0.295898i
$436$	−4.22617e6			−1.06471
$437$	11108.3	−	91937.0i	0.00278256	−	0.0230296i
$438$	4.62635e6			1.15227
$439$	−3.84728e6	−	4.44000e6i	−0.952780	−	1.09957i	−0.994941	−	0.100456i	$-0.967970\pi$
$439$	−3.84728e6	−	4.44000e6i	−0.952780	−	1.09957i	0.0421613	−	0.999111i	$-0.486576\pi$
$440$	−140753.	−	90456.4i	−0.0346598	−	0.0222745i
$441$	−147087.	+	1.02301e6i	−0.0360145	+	0.250486i
$442$	−4.07655e6	+	8.92639e6i	−0.992514	+	2.17330i
$443$	426280.	+	2.96485e6i	0.103202	+	0.717782i	0.974067	+	0.226261i	$0.0726501\pi$
$443$	426280.	+	2.96485e6i	0.103202	+	0.717782i	−0.870865	+	0.491522i	$0.836441\pi$
$444$	−1.74480e6	−	512320.i	−0.420038	−	0.123334i
$445$	2.11122e6	−	1.35680e6i	0.505398	−	0.324800i
$446$	−526160.	−	1.15213e6i	−0.125251	−	0.274261i
$447$	−1.12442e6	+	330161.i	−0.266172	+	0.0781550i
$448$	−3.38267e6	+	3.90380e6i	−0.796277	+	0.918952i
$449$	−1.77374e6	+	2.04701e6i	−0.415216	+	0.479185i	−0.924374	−	0.381488i	$-0.875412\pi$
$449$	−1.77374e6	+	2.04701e6i	−0.415216	+	0.479185i	0.509157	+	0.860673i	$0.329957\pi$
$450$	−1.47570e6	+	433304.i	−0.343531	+	0.100870i
$451$	5.12597e6	+	1.12243e7i	1.18668	+	2.59847i
$452$	2.85980e6	−	1.83788e6i	0.658399	−	0.423127i
$453$	1.13170e6	+	332296.i	0.259110	+	0.0760817i
$454$	239527.	+	1.66595e6i	0.0545400	+	0.379334i
$455$	1.12831e6	−	2.47066e6i	0.255506	−	0.559479i
$456$	483.523	−	3362.98i	0.000108894	−	0.000757377i
$457$	2.64089e6	+	1.69719e6i	0.591506	+	0.380138i	0.801882	−	0.597483i	$-0.203832\pi$
$457$	2.64089e6	+	1.69719e6i	0.591506	+	0.380138i	−0.210376	+	0.977621i	$0.567469\pi$
$458$	4.59670e6	+	5.30487e6i	1.02396	+	1.18171i
$459$	1.54217e6			0.341665
$460$	−1.79139e6	−	1.09497e6i	−0.394727	−	0.241272i
$461$	4.83403e6			1.05939			0.529696	−	0.848188i	$-0.322306\pi$
$461$	4.83403e6			1.05939			0.529696	+	0.848188i	$0.322306\pi$
$462$	−4.81479e6	−	5.55656e6i	−1.04947	−	1.21116i
$463$	355861.	+	228698.i	0.0771486	+	0.0495804i	0.578646	−	0.815578i	$-0.303581\pi$
$463$	355861.	+	228698.i	0.0771486	+	0.0495804i	−0.501498	+	0.865159i	$0.667217\pi$
$464$	964323.	−	6.70701e6i	0.207935	−	1.44622i
$465$	138439.	−	303139.i	0.0296911	−	0.0650144i
$466$	900763.	+	6.26494e6i	0.192152	+	1.33645i
$467$	1.37015e6	+	402313.i	0.290721	+	0.0853635i	0.423841	−	0.905736i	$-0.360681\pi$
$467$	1.37015e6	+	402313.i	0.290721	+	0.0853635i	−0.133120	+	0.991100i	$0.542500\pi$
$468$	1.22534e6	−	787479.i	0.258608	−	0.166197i
$469$	−2.55570e6	−	5.59620e6i	−0.536510	−	1.17479i
$470$	−2.09339e6	+	614676.i	−0.437126	+	0.128352i
$471$	−2.44103e6	+	2.81710e6i	−0.507015	+	0.585127i
$472$	−273625.	+	315780.i	−0.0565328	+	0.0652423i
$473$	−5.15399e6	+	1.51335e6i	−1.05923	+	0.311018i
$474$	96667.0	+	211671.i	0.0197621	+	0.0432729i
$475$	73638.2	−	47324.4i	0.0149751	−	0.00962390i
$476$	1.07127e7	+	3.14553e6i	2.16711	+	0.636321i
$477$	45790.1	+	318477.i	0.00921459	+	0.0640889i
$478$	−819684.	+	1.79486e6i	−0.164088	+	0.359303i
$479$	−258558.	+	1.79831e6i	−0.0514895	+	0.358118i	0.947746	+	0.319026i	$0.103356\pi$
$479$	−258558.	+	1.79831e6i	−0.0514895	+	0.358118i	−0.999236	+	0.0390920i	$0.987553\pi$
$480$	−1.65238e6	−	1.06192e6i	−0.327346	−	0.210372i
$481$	−2.52554e6	−	2.91462e6i	−0.497726	−	0.574407i
$482$	−1.75933e6			−0.344928
$483$	2.63733e6	+	2.90841e6i	0.514395	+	0.567268i
$484$	6.10756e6			1.18510
$485$	−805764.	−	929902.i	−0.155544	−	0.179508i
$486$	−393325.	−	252775.i	−0.0755373	−	0.0485449i
$487$	−1.11636e6	+	7.76445e6i	−0.213295	+	1.48350i	0.548754	+	0.835984i	$0.315102\pi$
$487$	−1.11636e6	+	7.76445e6i	−0.213295	+	1.48350i	−0.762050	+	0.647519i	$0.775807\pi$
$488$	161212.	−	353006.i	0.0306443	−	0.0671016i
$489$	327364.	+	2.27687e6i	0.0619097	+	0.430591i
$490$	−2.61364e6	−	767433.i	−0.491762	−	0.144394i
$491$	−715195.	+	459628.i	−0.133882	+	0.0860405i	−0.605867	−	0.795566i	$-0.707174\pi$
$491$	−715195.	+	459628.i	−0.133882	+	0.0860405i	0.471986	+	0.881606i	$0.343537\pi$
$492$	2.35992e6	+	5.16751e6i	0.439527	+	0.962430i
$493$	−1.29253e7	+	3.79520e6i	−2.39509	+	0.703262i
$494$	−110885.	+	127968.i	−0.0204435	+	0.0235931i
$495$	858139.	−	990346.i	0.157415	−	0.181666i
$496$	−1.40217e6	+	411716.i	−0.255916	+	0.0751438i
$497$	−2.09156e6	−	4.57988e6i	−0.379821	−	0.831693i
$498$	−5.49113e6	+	3.52894e6i	−0.992175	+	0.637632i
$499$	5.79614e6	+	1.70190e6i	1.04205	+	0.305973i	0.757600	−	0.652719i	$-0.226372\pi$
$499$	5.79614e6	+	1.70190e6i	1.04205	+	0.305973i	0.284447	+	0.958692i	$0.408190\pi$
$500$	−650478.	−	4.52417e6i	−0.116361	−	0.809309i
$501$	−1.16195e6	+	2.54431e6i	−0.206820	+	0.452872i
$502$	−650930.	+	4.52731e6i	−0.115285	+	0.801828i
$503$	−588740.	−	378360.i	−0.103754	−	0.0666784i	0.487735	−	0.872992i	$-0.337823\pi$
$503$	−588740.	−	378360.i	−0.103754	−	0.0666784i	−0.591489	+	0.806313i	$0.701460\pi$
$504$	94328.2	+	108861.i	0.0165411	+	0.0190895i
$505$	2.61507e6			0.456304
$506$	−1.20502e7	+	271868.i	−2.09227	+	0.0472042i
$507$	−252552.			−0.0436347
$508$	226812.	+	261755.i	0.0389948	+	0.0450023i
$509$	−5.11307e6	−	3.28597e6i	−0.874757	−	0.562172i	0.0244471	−	0.999701i	$-0.492217\pi$
$509$	−5.11307e6	−	3.28597e6i	−0.874757	−	0.562172i	−0.899204	+	0.437529i	$0.855854\pi$
$510$	−578444.	+	4.02316e6i	−0.0984772	+	0.684924i
$511$	4.63731e6	−	1.01543e7i	0.785623	−	1.72027i
$512$	1.17568e6	+	8.17701e6i	0.198204	+	1.37854i
$513$	25532.1	+	7496.91i	0.00428345	+	0.00125773i
$514$	4.11319e6	−	2.64339e6i	0.686706	−	0.441319i
$515$	−1.20525e6	−	2.63912e6i	−0.200243	−	0.438471i
$516$	−2.37282e6	+	696723.i	−0.392320	+	0.115196i
$517$	−4.01574e6	+	4.63441e6i	−0.660753	+	0.762550i
$518$	−5.86912e6	+	6.77333e6i	−0.961056	+	1.10912i
$519$	−994161.	+	291912.i	−0.162009	+	0.0475700i
$520$	−67863.2	−	148600.i	−0.0110059	−	0.0240996i
$521$	8.53391e6	−	5.48441e6i	1.37738	−	0.885188i	0.378202	−	0.925723i	$-0.376542\pi$
$521$	8.53391e6	−	5.48441e6i	1.37738	−	0.885188i	0.999178	+	0.0405346i	$0.0129061\pi$
$522$	3.91862e6	+	1.15061e6i	0.629443	+	0.184821i
$523$	−219385.	−	1.52586e6i	−0.0350713	−	0.243927i	0.964743	−	0.263194i	$-0.0847758\pi$
$523$	−219385.	−	1.52586e6i	−0.0350713	−	0.243927i	−0.999814	+	0.0192671i	$0.993867\pi$
$524$	−9684.35	+	21205.8i	−0.00154079	+	0.00337385i
$525$	−528144.	+	3.67332e6i	−0.0836284	+	0.581649i
$526$	3.83184e6	+	2.46257e6i	0.603870	+	0.388083i
$527$	1.90254e6	+	2.19565e6i	0.298406	+	0.344379i
$528$	−5.74636e6			−0.897033
$529$	6.42979e6	−	290277.i	0.998982	−	0.0450996i
$530$	−848010.			−0.131133
$531$	−2.14306e6	−	2.47322e6i	−0.329836	−	0.380650i
$532$	162068.	+	104155.i	0.0248267	+	0.0159551i
$533$	−1.71461e6	+	1.19254e7i	−0.261425	+	1.81825i
$534$	2.75545e6	−	6.03358e6i	0.418156	−	0.915635i
$535$	−266962.	−	1.85676e6i	−0.0403242	−	0.280461i
$536$	−355038.	−	104249.i	−0.0533781	−	0.0156732i
$537$	−871915.	+	560346.i	−0.130478	+	0.0838533i
$538$	−7.36774e6	−	1.61331e7i	−1.09743	−	2.40305i
$539$	−7.34603e6	+	2.15699e6i	−1.08913	+	0.319798i
$540$	395075.	−	455941.i	0.0583036	−	0.0672859i
$541$	−1.04226e6	+	1.20283e6i	−0.153103	+	0.176690i	−0.827120	−	0.562026i	$-0.810022\pi$
$541$	−1.04226e6	+	1.20283e6i	−0.153103	+	0.176690i	0.674017	+	0.738716i	$0.264568\pi$
$542$	1.80685e7	−	5.30538e6i	2.64194	−	0.775744i
$543$	−331783.	−	726502.i	−0.0482896	−	0.105740i
$544$	1.44052e7	−	9.25766e6i	2.08700	−	1.34123i
$545$	−3.56196e6	−	1.04589e6i	−0.513687	−	0.150832i
$546$	−1.02164e6	−	7.10569e6i	−0.146662	−	1.02006i
$547$	617565.	−	1.35228e6i	0.0882500	−	0.193241i	−0.860361	−	0.509685i	$-0.829762\pi$
$547$	617565.	−	1.35228e6i	0.0882500	−	0.193241i	0.948611	+	0.316445i	$0.102489\pi$
$548$	1.04324e6	−	7.25591e6i	0.148400	−	1.03214i
$549$	2.55695e6	+	1.64325e6i	0.362069	+	0.232687i
$550$	−7.46091e6	−	8.61035e6i	−1.05168	−	1.21371i
$551$	−232440.			−0.0326161
$552$	236079.	−	5326.26i	0.0329770	−	0.000744003i
$553$	561490.			0.0780781
$554$	−5.14142e6	−	5.93352e6i	−0.711719	−	0.821368i
$555$	−1.34379e6	−	863603.i	−0.185182	−	0.119009i
$556$	−25874.0	+	179958.i	−0.00354958	+	0.0246878i
$557$	3.16564e6	−	6.93178e6i	0.432338	−	0.946688i	−0.560604	−	0.828084i	$-0.689431\pi$
$557$	3.16564e6	−	6.93178e6i	0.432338	−	0.946688i	0.992942	−	0.118604i	$-0.0378418\pi$
$558$	−125351.	−	871838.i	−0.0170429	−	0.118536i
$559$	−5.03228e6	−	1.47761e6i	−0.681139	−	0.200000i
$560$	−4.15010e6	+	2.66711e6i	−0.559228	+	0.359394i
$561$	4.74570e6	+	1.03916e7i	0.636640	+	1.39405i
$562$	−1.49556e7	+	4.39136e6i	−1.99739	+	0.586486i
$563$	−537178.	+	619937.i	−0.0714245	+	0.0824283i	−0.790337	−	0.612672i	$-0.790095\pi$
$563$	−537178.	+	619937.i	−0.0714245	+	0.0824283i	0.718913	+	0.695100i	$0.244640\pi$
$564$	−1.84879e6	+	2.13362e6i	−0.244731	+	0.282435i
$565$	2.86517e6	−	841290.i	0.377598	−	0.110873i
$566$	2.62455e6	+	5.74696e6i	0.344360	+	0.754044i
$567$	−949070.	+	609930.i	−0.123977	+	0.0796750i
$568$	−290560.	−	85316.0i	−0.0377889	−	0.0110958i
$569$	−1.63400e6	−	1.13647e7i	−0.211578	−	1.47156i	−0.767887	−	0.640585i	$-0.778692\pi$
$569$	−1.63400e6	−	1.13647e7i	−0.211578	−	1.47156i	0.556309	−	0.830975i	$-0.312217\pi$
$570$	−29134.5	+	63795.6i	−0.00375595	+	0.00822438i
$571$	−184357.	+	1.28223e6i	−0.0236630	+	0.164580i	−0.998226	−	0.0595322i	$-0.981039\pi$
$571$	−184357.	+	1.28223e6i	−0.0236630	+	0.164580i	0.974563	+	0.224112i	$0.0719482\pi$
$572$	9.07703e6	+	5.83345e6i	1.15999	+	0.745479i
$573$	−2.30883e6	−	2.66453e6i	−0.293768	−	0.339027i
$574$	2.79986e7			3.54696
$575$	4.08676e6	+	4.50683e6i	0.515478	+	0.568462i
$576$	−2.43329e6			−0.305589
$577$	6.47244e6	+	7.46960e6i	0.809336	+	0.934023i	0.998854	−	0.0478540i	$-0.0152382\pi$
$577$	6.47244e6	+	7.46960e6i	0.809336	+	0.934023i	−0.189519	+	0.981877i	$0.560693\pi$
$578$	−2.03513e7	−	1.30790e7i	−2.53381	−	1.62838i
$579$	732451.	−	5.09431e6i	0.0907992	−	0.631522i
$580$	−2.18917e6	+	4.79361e6i	−0.270215	+	0.591688i
$581$	2.24146e6	+	1.55897e7i	0.275480	+	1.91601i
$582$	−3.12035e6	−	916219.i	−0.381853	−	0.112122i
$583$	−2.00510e6	+	1.28860e6i	−0.244323	+	0.157017i
$584$	−278915.	−	610739.i	−0.0338407	−	0.0741009i
$585$	1.22764e6	−	360469.i	0.148314	−	0.0435490i
$586$	1.30294e7	−	1.50367e7i	1.56740	−	1.80888i
$587$	3.68573e6	−	4.25356e6i	0.441497	−	0.509515i	−0.490768	−	0.871290i	$-0.663284\pi$
$587$	3.68573e6	−	4.25356e6i	0.441497	−	0.509515i	0.932265	+	0.361775i	$0.117829\pi$
$588$	−3.38201e6	+	993047.i	−0.403396	+	0.118448i
$589$	20824.8	+	45600.0i	0.00247340	+	0.00541598i
$590$	7.25590e6	−	4.66308e6i	0.858146	−	0.551497i
$591$	5.85533e6	+	1.71928e6i	0.689577	+	0.202478i
$592$	996873.	+	6.93340e6i	0.116906	+	0.813097i
$593$	−4.23840e6	+	9.28080e6i	−0.494955	+	1.08380i	0.483122	+	0.875553i	$0.339503\pi$
$593$	−4.23840e6	+	9.28080e6i	−0.494955	+	1.08380i	−0.978076	+	0.208246i	$0.933224\pi$
$594$	492904.	−	3.42822e6i	0.0573187	−	0.398660i
$595$	8.25057e6	+	5.30232e6i	0.955414	+	0.614007i
$596$	−2.61726e6	−	3.02048e6i	−0.301808	−	0.348305i
$597$	−6.62419e6			−0.760671
$598$	−1.00414e7	−	6.13767e6i	−1.14826	−	0.701860i
$599$	−5.95801e6			−0.678475			−0.339238	−	0.940701i	$-0.610169\pi$
$599$	−5.95801e6			−0.678475			−0.339238	+	0.940701i	$0.610169\pi$
$600$	146169.	+	168689.i	0.0165759	+	0.0191297i
$601$	5.17889e6	+	3.32827e6i	0.584858	+	0.375865i	0.799355	−	0.600859i	$-0.205175\pi$
$601$	5.17889e6	+	3.32827e6i	0.584858	+	0.375865i	−0.214497	+	0.976725i	$0.568811\pi$
$602$	−1.73458e6	+	1.20642e7i	−0.195075	+	1.35678i
$603$	1.20391e6	−	2.63619e6i	0.134834	−	0.295246i
$604$	572463.	+	3.98157e6i	0.0638491	+	0.444081i
$605$	5.14767e6	+	1.51149e6i	0.571771	+	0.167887i
$606$	5.81450e6	−	3.73675e6i	0.643178	−	0.413345i
$607$	−3.30513e6	−	7.23722e6i	−0.364096	−	0.797260i	−0.999682	−	0.0252291i	$-0.991968\pi$
$607$	−3.30513e6	−	7.23722e6i	−0.364096	−	0.797260i	0.635585	−	0.772031i	$-0.280759\pi$
$608$	283497.	−	83242.1i	0.0311021	−	0.00913239i
$609$	6.45336e6	−	7.44758e6i	0.705087	−	0.813714i
$610$	−5.24594e6	+	6.05414e6i	−0.570819	+	0.658760i
$611$	−5.74487e6	+	1.68685e6i	−0.622554	+	0.182798i
$612$	2.18486e6	+	4.78417e6i	0.235800	+	0.516330i
$613$	1.49084e7	−	9.58106e6i	1.60243	−	1.02982i	0.636418	−	0.771345i	$-0.280416\pi$
$613$	1.49084e7	−	9.58106e6i	1.60243	−	1.02982i	0.966017	−	0.258478i	$-0.0832208\pi$
$614$	−161270.	−	47353.0i	−0.0172636	−	0.00506905i
$615$	710177.	+	4.93939e6i	0.0757145	+	0.526606i
$616$	−443263.	+	970611.i	−0.0470663	+	0.103061i
$617$	−2.20650e6	+	1.53465e7i	−0.233341	+	1.62292i	0.450145	+	0.892955i	$0.351372\pi$
$617$	−2.20650e6	+	1.53465e7i	−0.233341	+	1.62292i	−0.683486	+	0.729964i	$0.739537\pi$
$618$	−6.45094e6	−	4.14577e6i	−0.679442	−	0.436651i
$619$	−182282.	−	210365.i	−0.0191213	−	0.0220672i	0.746108	−	0.665825i	$-0.231920\pi$
$619$	−182282.	−	210365.i	−0.0191213	−	0.0220672i	−0.765230	+	0.643757i	$0.777375\pi$
$620$	1.13654e6			0.118742
$621$	−221849.	+	1.83612e6i	−0.0230849	+	0.191061i
$622$	1.58974e7			1.64760
$623$	−1.04810e7	−	1.20958e7i	−1.08189	−	1.24857i
$624$	−4.72000e6	−	3.03336e6i	−0.485266	−	0.311862i
$625$	−495104.	+	3.44352e6i	−0.0506987	+	0.352617i
$626$	−4.15106e6	+	9.08954e6i	−0.423373	+	0.927057i
$627$	28053.2	+	195114.i	0.00284980	+	0.0198208i
$628$	−1.21976e7	−	3.58154e6i	−1.23417	−	0.362386i
$629$	1.17150e7	−	7.52877e6i	1.18063	−	0.758747i
$630$	−1.23519e6	−	2.70468e6i	−0.123988	−	0.271497i
$631$	1.37442e7	−	4.03567e6i	1.37419	−	0.403499i	0.490447	−	0.871471i	$-0.336834\pi$
$631$	1.37442e7	−	4.03567e6i	1.37419	−	0.403499i	0.883743	+	0.467973i	$0.155015\pi$
$632$	22115.5	−	25522.6i	0.00220244	−	0.00254175i
$633$	6.05359e6	−	6.98621e6i	0.600487	−	0.692999i
$634$	−1.38600e7	+	4.06966e6i	−1.36943	+	0.402101i
$635$	126386.	+	276747.i	0.0124384	+	0.0272363i
$636$	−923119.	+	593252.i	−0.0904930	+	0.0581563i
$637$	−7.17256e6	−	2.10605e6i	−0.700367	−	0.205646i
$638$	4.30554e6	+	2.99457e7i	0.418771	+	2.91261i
$639$	985268.	−	2.15744e6i	0.0954557	−	0.209019i
$640$	−81203.9	+	564785.i	−0.00783658	+	0.0545046i
$641$	20721.0	+	13316.6i	0.00199189	+	0.00128011i	0.541636	−	0.840613i	$-0.317805\pi$
$641$	20721.0	+	13316.6i	0.00199189	+	0.00128011i	−0.539644	+	0.841893i	$0.681441\pi$
$642$	−3.24677e6	−	3.74698e6i	−0.310895	−	0.358793i
$643$	6.15266e6			0.586862			0.293431	−	0.955980i	$-0.405203\pi$
$643$	6.15266e6			0.586862			0.293431	+	0.955980i	$0.405203\pi$
$644$	−5.28616e6	+	1.23021e7i	−0.502257	+	1.16887i
$645$	−2.17232e6			−0.205601
$646$	−400390.	−	462075.i	−0.0377487	−	0.0435643i
$647$	−1.61022e6	−	1.03482e6i	−0.151225	−	0.0971863i	0.462840	−	0.886442i	$-0.346830\pi$
$647$	−1.61022e6	−	1.03482e6i	−0.151225	−	0.0971863i	−0.614065	+	0.789255i	$0.710467\pi$
$648$	−9656.66	+	67163.5i	−0.000903419	+	0.00628342i
$649$	1.00706e7	−	2.20515e7i	0.938517	−	2.05507i
$650$	−1.58312e6	−	1.10109e7i	−0.146971	−	1.02221i
$651$	−2.03923e6	−	598773.i	−0.188588	−	0.0553745i
$652$	−6.59958e6	+	4.24129e6i	−0.607991	+	0.390732i
$653$	200189.	+	438352.i	0.0183720	+	0.0402291i	0.918596	−	0.395199i	$-0.129324\pi$
$653$	200189.	+	438352.i	0.0183720	+	0.0402291i	−0.900224	+	0.435428i	$0.856597\pi$
$654$	−9.41440e6	+	2.76432e6i	−0.860693	+	0.252722i
$655$	−13410.3	+	15476.3i	−0.00122133	+	0.00140950i
$656$	1.43301e7	−	1.65378e7i	1.30014	−	1.50044i
$657$	5.04557e6	−	1.48151e6i	0.456033	−	0.133903i
$658$	5.78017e6	+	1.26568e7i	0.520446	+	1.13962i
$659$	−1.17008e7	+	7.51963e6i	−1.04954	+	0.674502i	−0.947329	−	0.320261i	$-0.896229\pi$
$659$	−1.17008e7	+	7.51963e6i	−1.04954	+	0.674502i	−0.102215	+	0.994762i	$0.532593\pi$
$660$	4.28805e6	+	1.25908e6i	0.383177	+	0.112511i
$661$	732517.	+	5.09477e6i	0.0652100	+	0.453545i	0.996099	+	0.0882432i	$0.0281253\pi$
$661$	732517.	+	5.09477e6i	0.0652100	+	0.453545i	−0.930889	+	0.365302i	$0.880966\pi$
$662$	1.12070e7	−	2.45399e7i	0.993903	−	2.17634i
$663$	−1.58741e6	+	1.10407e7i	−0.140251	+	0.975469i
$664$	796918.	+	512148.i	0.0701444	+	0.0450791i
$665$	110820.	+	127894.i	0.00971775	+	0.0112149i
$666$	−4.22190e6			−0.368827
$667$	−2.65922e6	−	1.59349e7i	−0.231441	−	1.38686i
$668$	−9.53922e6			−0.827126
$669$	−942788.	−	1.08804e6i	−0.0814421	−	0.0939892i
$670$	6.42566e6	+	4.12952e6i	0.553007	+	0.355396i
$671$	−3.20429e6	+	2.22863e7i	−0.274742	+	1.91088i
$672$	−5.20372e6	+	1.13946e7i	−0.444520	+	0.973362i
$673$	−11955.2	−	83150.6i	−0.00101747	−	0.00707665i	0.989306	−	0.145852i	$-0.0465924\pi$
$673$	−11955.2	−	83150.6i	−0.00101747	−	0.00707665i	−0.990324	+	0.138776i	$0.955683\pi$
$674$	−1.34382e7	−	3.94581e6i	−1.13944	−	0.334569i
$675$	−1.47066e6	+	945137.i	−0.124238	+	0.0798427i
$676$	−357802.	−	783477.i	−0.0301145	−	0.0659416i
$677$	6.05783e6	−	1.77874e6i	0.507979	−	0.149156i	−0.0176930	−	0.999843i	$-0.505632\pi$
$677$	6.05783e6	−	1.77874e6i	0.507979	−	0.149156i	0.525672	+	0.850687i	$0.323814\pi$
$678$	5.16846e6	−	5.96472e6i	0.431804	−	0.498328i
$679$	−5.13875e6	+	5.93043e6i	−0.427743	+	0.493642i
$680$	565984.	−	166188.i	0.0469388	−	0.0137825i
$681$	794725.	+	1.74020e6i	0.0656673	+	0.143791i
$682$	5.48900e6	−	3.52756e6i	0.451889	−	0.290412i
$683$	2.00332e7	+	5.88227e6i	1.64323	+	0.482496i	0.967123	−	0.254309i	$-0.0818479\pi$
$683$	2.00332e7	+	5.88227e6i	1.64323	+	0.482496i	0.676106	+	0.736804i	$0.263666\pi$
$684$	12915.3	+	89827.9i	0.00105551	+	0.00734127i
$685$	2.67496e6	−	5.85735e6i	0.217817	−	0.476952i
$686$	784213.	−	5.45432e6i	0.0636244	−	0.442518i
$687$	6.71203e6	+	4.31356e6i	0.542578	+	0.348694i
$688$	6.23817e6	+	7.19923e6i	0.502442	+	0.579849i
$689$	−2.32718e6			−0.186759
$690$	−4.70680e6	−	1.26745e6i	−0.376359	−	0.101347i
$691$	−2.00656e7			−1.59866			−0.799331	−	0.600892i	$-0.794812\pi$
$691$	−2.00656e7			−1.59866			−0.799331	+	0.600892i	$0.794812\pi$
$692$	−2.31405e6	−	2.67056e6i	−0.183699	−	0.212000i
$693$	−7.03048e6	−	4.51821e6i	−0.556099	−	0.357383i
$694$	−71647.0	+	498316.i	−0.00564676	+	0.0392741i
$695$	−66343.1	+	145271.i	−0.00520995	+	0.0114082i
$696$	−84351.5	−	586678.i	−0.00660039	−	0.0459067i
$697$	−4.17415e7	−	1.22564e7i	−3.25451	−	0.955611i
$698$	−2.89016e6	+	1.85740e6i	−0.224535	+	0.144300i
$699$	2.98863e6	+	6.54419e6i	0.231355	+	0.506598i
$700$	−1.21437e7	+	3.56573e6i	−0.936715	+	0.275044i
$701$	−1.58383e6	+	1.82784e6i	−0.121734	+	0.140489i	−0.813345	−	0.581781i	$-0.802356\pi$
$701$	−1.58383e6	+	1.82784e6i	−0.121734	+	0.140489i	0.691611	+	0.722270i	$0.256901\pi$
$702$	2.21454e6	−	2.55571e6i	0.169605	−	0.195735i
$703$	230553.	−	67696.4i	0.0175947	−	0.00516627i
$704$	−7.48795e6	−	1.63963e7i	−0.569418	−	1.24685i
$705$	−2.08625e6	+	1.34075e6i	−0.158086	+	0.101596i
$706$	−5.69797e6	−	1.67308e6i	−0.430238	−	0.126329i
$707$	−2.37346e6	−	1.65078e7i	−0.178580	−	1.24205i
$708$	4.63635e6	−	1.01522e7i	0.347610	−	0.761160i
$709$	988247.	−	6.87341e6i	0.0738329	−	0.513519i	−0.919023	−	0.394203i	$-0.871021\pi$
$709$	988247.	−	6.87341e6i	0.0738329	−	0.513519i	0.992856	−	0.119316i	$-0.0380702\pi$
$710$	5.25870e6	+	3.37956e6i	0.391501	+	0.251602i
$711$	173211.	+	199896.i	0.0128499	+	0.0148296i
$712$	−962634.			−0.0711642
$713$	−2.88785e6	+	1.94933e6i	−0.212741	+	0.143602i
$714$	2.59215e7			1.90289
$715$	6.20678e6	+	7.16301e6i	0.454048	+	0.523999i
$716$	−2.97360e6	−	1.91102e6i	−0.216771	−	0.139310i
$717$	−319186.	+	2.21999e6i	−0.0231871	+	0.161270i
$718$	−4.78230e6	+	1.04718e7i	−0.346199	+	0.758069i
$719$	−218098.	−	1.51691e6i	−0.0157337	−	0.109430i	0.980441	−	0.196812i	$-0.0630589\pi$
$719$	−218098.	−	1.51691e6i	−0.0157337	−	0.109430i	−0.996175	+	0.0873823i	$0.972150\pi$
$720$	−2.22976e6	−	654716.i	−0.160297	−	0.0470675i
$721$	−1.55657e7	+	1.00035e7i	−1.11514	+	0.716660i
$722$	8.14008e6	+	1.78243e7i	0.581147	+	1.27253i
$723$	−1.91875e6	+	563396.i	−0.136513	+	0.0400837i
$724$	1.78373e6	−	2.05853e6i	0.126469	−	0.145953i
$725$	1.00000e7	−	1.15406e7i	0.706571	−	0.815427i
$726$	1.36055e7	−	3.99492e6i	0.958014	−	0.281298i
$727$	−5.33673e6	−	1.16858e7i	−0.374489	−	0.820017i	−0.999232	−	0.0391865i	$-0.987523\pi$
$727$	−5.33673e6	−	1.16858e7i	−0.374489	−	0.820017i	0.624743	−	0.780831i	$-0.285204\pi$
$728$	−876452.	+	563262.i	−0.0612914	+	0.0393896i
$729$	−509914.	−	149724.i	−0.0355368	−	0.0104345i
$730$	1.97241e6	+	1.37184e7i	0.136991	+	0.952790i
$731$	7.86712e6	−	1.72266e7i	0.544531	−	1.19236i
$732$	−1.47521e6	+	1.02603e7i	−0.101760	+	0.707755i
$733$	−3.53959e6	−	2.27476e6i	−0.243329	−	0.156378i	0.413293	−	0.910598i	$-0.364379\pi$
$733$	−3.53959e6	−	2.27476e6i	−0.243329	−	0.156378i	−0.656621	+	0.754220i	$0.728015\pi$
$734$	1.07188e7	+	1.23701e7i	0.734352	+	0.847487i
$735$	−3.09623e6			−0.211405
$736$	8.94997e6	+	1.84827e7i	0.609014	+	1.25768i
$737$	2.14683e7			1.45589
$738$	8.63711e6	+	9.96776e6i	0.583751	+	0.673685i
$739$	7.90920e6	+	5.08294e6i	0.532748	+	0.342376i	0.779197	−	0.626780i	$-0.215627\pi$
$739$	7.90920e6	+	5.08294e6i	0.532748	+	0.342376i	−0.246449	+	0.969156i	$0.579264\pi$
$740$	775290.	−	5.39226e6i	0.0520457	−	0.361986i
$741$	−79953.3	+	175073.i	−0.00534922	+	0.0117132i
$742$	769663.	+	5.35312e6i	0.0513205	+	0.356942i
$743$	−1.57691e7	−	4.63021e6i	−1.04793	−	0.307701i	−0.287951	−	0.957645i	$-0.592974\pi$
$743$	−1.57691e7	−	4.63021e6i	−1.04793	−	0.307701i	−0.759982	+	0.649944i	$0.774792\pi$
$744$	−107537.	+	69109.8i	−0.00712238	+	0.00457728i
$745$	−1.45841e6	−	3.19348e6i	−0.0962697	−	0.210801i
$746$	−3.64805e7	+	1.07117e7i	−2.40002	+	0.704708i
$747$	−4.85863e6	+	5.60716e6i	−0.318575	+	0.367656i
$748$	−2.55139e7	+	2.94446e7i	−1.66733	+	1.92420i
$749$	−1.14787e7	+	3.37044e6i	−0.747629	+	0.219524i
$750$	−4.40827e6	−	9.65276e6i	−0.286164	−	0.626612i
$751$	−7.41211e6	+	4.76347e6i	−0.479559	+	0.308194i	−0.757994	−	0.652261i	$-0.773821\pi$
$751$	−7.41211e6	+	4.76347e6i	−0.479559	+	0.308194i	0.278435	+	0.960455i	$0.410184\pi$
$752$	1.04343e7	+	3.06380e6i	0.672854	+	0.197568i
$753$	739885.	+	5.14601e6i	0.0475529	+	0.330737i
$754$	−1.22711e7	+	2.68699e7i	−0.786056	+	1.72122i
$755$	−502861.	+	3.49748e6i	−0.0321056	+	0.223299i
$756$	−3.23673e6	−	2.08012e6i	−0.205969	−	0.132368i
$757$	−1.11246e7	−	1.28384e7i	−0.705576	−	0.814278i	0.283919	−	0.958848i	$-0.408365\pi$
$757$	−1.11246e7	−	1.28384e7i	−0.705576	−	0.814278i	−0.989494	+	0.144571i	$0.953820\pi$
$758$	−2.22509e7			−1.40661
$759$	−1.30551e7	+	4.15538e6i	−0.822573	+	0.261822i
$760$	10178.3			0.000639208
$761$	1.48136e7	+	1.70958e7i	0.927255	+	1.07011i	0.997363	+	0.0725704i	$0.0231202\pi$
$761$	1.48136e7	+	1.70958e7i	0.927255	+	1.07011i	−0.0701078	+	0.997539i	$0.522334\pi$
$762$	676468.	+	434739.i	0.0422046	+	0.0271232i
$763$	−3.36936e6	+	2.34344e7i	−0.209525	+	1.45728i
$764$	4.99498e6	−	1.09375e7i	0.309599	−	0.677928i
$765$	657493.	+	4.57297e6i	0.0406198	+	0.282517i
$766$	1.70796e7	+	5.01502e6i	1.05173	+	0.308816i
$767$	1.99122e7	−	1.27968e7i	1.22217	−	0.785441i
$768$	4.22053e6	+	9.24168e6i	0.258205	+	0.565390i
$769$	2.12322e7	−	6.23433e6i	1.29473	−	0.380166i	0.439418	−	0.898283i	$-0.355185\pi$
$769$	2.12322e7	−	6.23433e6i	1.29473	−	0.380166i	0.855310	+	0.518116i	$0.173367\pi$
$770$	1.44240e7	−	1.66462e7i	0.876717	−	1.01179i
$771$	3.63941e6	−	4.20010e6i	0.220493	−	0.254462i
$772$	1.68414e7	−	4.94509e6i	1.01703	−	0.298628i
$773$	3.23707e6	+	7.08819e6i	0.194851	+	0.426665i	0.981688	−	0.190497i	$-0.0610099\pi$
$773$	3.23707e6	+	7.08819e6i	0.194851	+	0.426665i	−0.786837	+	0.617161i	$0.788283\pi$
$774$	−4.83008e6	+	3.10410e6i	−0.289802	+	0.186244i
$775$	−3.15996e6	−	927848.i	−0.188985	−	0.0554910i
$776$	67168.2	+	467165.i	0.00400414	+	0.0278494i
$777$	−4.23191e6	+	9.26659e6i	−0.251469	+	0.550640i
$778$	5.39922e6	−	3.75524e7i	0.319802	−	2.22428i
$779$	−631491.	−	405834.i	−0.0372841	−	0.0239610i
$780$	2.85751e6	+	3.29775e6i	0.168171	+	0.194080i
$781$	1.75695e7			1.03070
$782$	2.70967e7	−	3.27350e7i	1.58453	−	1.91423i
$783$	4.64217e6			0.270593
$784$	8.89133e6	+	1.02611e7i	0.516626	+	0.596218i
$785$	−9.39422e6	−	6.03730e6i	−0.544110	−	0.349678i
$786$	−7702.69	+	53573.4i	−0.000444719	+	0.00309309i
$787$	−1.04301e7	+	2.28387e7i	−0.600275	+	1.31442i	0.328756	+	0.944415i	$0.393371\pi$
$787$	−1.04301e7	+	2.28387e7i	−0.600275	+	1.31442i	−0.929030	+	0.370003i	$0.879357\pi$
$788$	2.96189e6	+	2.06004e7i	0.169923	+	1.18184i
$789$	4.96767e6	+	1.45864e6i	0.284093	+	0.0834171i
$790$	−586452.	+	376890.i	−0.0334322	+	0.0214856i
$791$	−7.91116e6	−	1.73230e7i	−0.449572	−	0.984425i
$792$	−482287.	+	141612.i	−0.0273207	+	0.00802209i
$793$	−1.43964e7	+	1.66143e7i	−0.812961	+	0.938207i
$794$	2.36520e7	−	2.72958e7i	1.33142	−	1.53654i
$795$	−924854.	+	271562.i	−0.0518985	+	0.0152388i
$796$	−9.38477e6	−	2.05498e7i	−0.524978	−	1.14954i
$797$	1.32041e7	−	8.48576e6i	0.736314	−	0.473200i	−0.117963	−	0.993018i	$-0.537636\pi$
$797$	1.32041e7	−	8.48576e6i	0.736314	−	0.473200i	0.854277	+	0.519818i	$0.174000\pi$
$798$	429157.	+	126012.i	0.0238566	+	0.00700493i
$799$	−3.07680e6	−	2.13996e7i	−0.170503	−	1.18587i
$800$	−8.06360e6	+	1.76568e7i	−0.445455	+	0.975411i
$801$	1.07298e6	−	7.46271e6i	0.0590893	−	0.410975i
$802$	2.22118e7	+	1.42747e7i	1.21940	+	0.783664i
$803$	2.55096e7	+	2.94397e7i	1.39610	+	1.61118i
$804$	9.88371e6			0.539237
$805$	−7.49986e6	+	9.06042e6i	−0.407909	+	0.492786i
$806$	6.37071e6			0.345422
$807$	−1.32017e7	−	1.52356e7i	−0.713587	−	0.823524i
$808$	−843848.	−	542308.i	−0.0454711	−	0.0292225i
$809$	2.63734e6	−	1.83431e7i	0.141675	−	0.985374i	−0.787653	−	0.616119i	$-0.788704\pi$
$809$	2.63734e6	−	1.83431e7i	0.141675	−	0.985374i	0.929328	−	0.369255i	$-0.120387\pi$
$810$	581857.	−	1.27409e6i	0.0311605	−	0.0682319i
$811$	−196645.	−	1.36770e6i	−0.0104986	−	0.0730193i	0.983899	−	0.178728i	$-0.0571981\pi$
$811$	−196645.	−	1.36770e6i	−0.0104986	−	0.0730193i	−0.994397	+	0.105708i	$0.966289\pi$
$812$	3.22469e7	+	9.46854e6i	1.71632	+	0.503956i
$813$	1.80068e7	−	1.15723e7i	0.955455	−	0.614034i
$814$	−1.29920e7	−	2.84486e7i	−0.687253	−	1.50487i
$815$	−6.61198e6	+	1.94145e6i	−0.348689	+	0.102384i
$816$	1.32670e7	−	1.53110e7i	0.697508	−	0.804967i
$817$	213991.	−	246959.i	0.0112161	−	0.0129441i
$818$	−3.99204e7	+	1.17217e7i	−2.08599	+	0.612502i
$819$	−3.38971e6	−	7.42242e6i	−0.176584	−	0.386666i
$820$	−1.43170e7	+	9.20098e6i	−0.743563	+	0.477859i
$821$	−2.23868e7	−	6.57336e6i	−1.15914	−	0.340353i	−0.355039	−	0.934851i	$-0.615533\pi$
$821$	−2.23868e7	−	6.57336e6i	−1.15914	−	0.340353i	−0.804097	+	0.594498i	$0.797351\pi$
$822$	−2.42208e6	−	1.68459e7i	−0.125029	−	0.869593i
$823$	−4.66658e6	+	1.02184e7i	−0.240159	+	0.525875i	−0.990880	−	0.134744i	$-0.956979\pi$
$823$	−4.66658e6	+	1.02184e7i	−0.240159	+	0.525875i	0.750721	+	0.660619i	$0.229706\pi$
$824$	−158379.	+	1.10155e6i	−0.00812606	+	0.0565180i
$825$	−1.08943e7	−	7.00135e6i	−0.557269	−	0.358135i
$826$	−3.60215e7	−	4.15711e7i	−1.83701	−	2.12003i
$827$	−2.03022e7			−1.03224			−0.516118	−	0.856517i	$-0.672623\pi$
$827$	−2.03022e7			−1.03224			−0.516118	+	0.856517i	$0.672623\pi$
$828$	−6.01036e6	+	1.91308e6i	−0.304667	+	0.0969743i
$829$	1.52653e7			0.771468			0.385734	−	0.922610i	$-0.373948\pi$
$829$	1.52653e7			0.771468			0.385734	+	0.922610i	$0.373948\pi$
$830$	−1.28054e7	−	1.47782e7i	−0.645205	−	0.744607i
$831$	−7.50743e6	−	4.82473e6i	−0.377128	−	0.242365i
$832$	2.50468e6	−	1.74205e7i	0.125442	−	0.872472i
$833$	1.12131e7	−	2.45532e7i	0.559903	−	1.22602i
$834$	60071.3	+	417805.i	0.00299056	+	0.0207998i
$835$	−8.03999e6	−	2.36075e6i	−0.399061	−	0.117175i
$836$	−565546.	+	363454.i	−0.0279867	+	0.0179860i
$837$	−415902.	−	910699.i	−0.0205200	−	0.0449326i
$838$	1.87662e7	−	5.51025e6i	0.923136	−	0.271057i
$839$	−2.04457e7	+	2.35956e7i	−1.00276	+	1.15725i	−0.0152197	+	0.999884i	$0.504845\pi$
$839$	−2.04457e7	+	2.35956e7i	−1.00276	+	1.15725i	−0.987541	+	0.157363i	$0.949701\pi$
$840$	−282586.	+	326122.i	−0.0138182	+	0.0159471i
$841$	−1.92268e7	+	5.64550e6i	−0.937382	+	0.275240i
$842$	−1.03604e7	−	2.26862e7i	−0.503614	−	1.10276i
$843$	−1.49045e7	+	9.57857e6i	−0.722353	+	0.464228i
$844$	3.02492e7	+	8.88198e6i	1.46170	+	0.429194i
$845$	−107674.	−	748890.i	−0.00518764	−	0.0360808i
$846$	−2.72285e6	+	5.96222e6i	−0.130797	+	0.286406i
$847$	4.86931e6	−	3.38668e7i	0.233217	−	1.62206i
$848$	3.55584e6	+	2.28520e6i	0.169806	+	0.109128i
$849$	4.70274e6	+	5.42725e6i	0.223914	+	0.258411i
$850$	4.01675e7			1.90690
$851$	7.27854e6	+	1.50310e7i	0.344525	+	0.711482i
$852$	8.08874e6			0.381752
$853$	−1.27417e7	−	1.47047e7i	−0.599592	−	0.691966i	0.372106	−	0.928190i	$-0.378636\pi$
$853$	−1.27417e7	−	1.47047e7i	−0.599592	−	0.691966i	−0.971699	+	0.236224i	$0.924090\pi$
$854$	4.29784e7	+	2.76205e7i	2.01653	+	1.29595i
$855$	−11345.0	+	78906.3i	−0.000530750	+	0.00369145i
$856$	−298908.	+	654516.i	−0.0139429	+	0.0305306i
$857$	−5.24934e6	−	3.65100e7i	−0.244148	−	1.69808i	−0.630870	−	0.775888i	$-0.717302\pi$
$857$	−5.24934e6	−	3.65100e7i	−0.244148	−	1.69808i	0.386723	−	0.922196i	$-0.373607\pi$
$858$	2.40360e7	+	7.05761e6i	1.11466	+	0.327295i
$859$	6.15839e6	−	3.95775e6i	0.284763	−	0.183006i	−0.390460	−	0.920620i	$-0.627684\pi$
$859$	6.15839e6	−	3.95775e6i	0.284763	−	0.183006i	0.675223	+	0.737614i	$0.264047\pi$
$860$	−3.07762e6	−	6.73905e6i	−0.141896	−	0.310708i
$861$	3.05357e7	−	8.96608e6i	1.40378	−	0.412188i
$862$	−2.55078e7	+	2.94376e7i	−1.16924	+	1.34938i
$863$	−6.38975e6	+	7.37417e6i	−0.292050	+	0.337043i	−0.882746	−	0.469851i	$-0.844308\pi$
$863$	−6.38975e6	+	7.37417e6i	−0.292050	+	0.337043i	0.590696	+	0.806894i	$0.298853\pi$
$864$	−5.66184e6	+	1.66247e6i	−0.258032	+	0.0757650i
$865$	−1.28946e6	−	2.82351e6i	−0.0585958	−	0.128307i
$866$	8.10002e6	−	5.20556e6i	0.367021	−	0.235870i
$867$	−2.63838e7	−	7.74700e6i	−1.19204	−	0.350014i
$868$	−1.03154e6	−	7.17449e6i	−0.0464713	−	0.323215i
$869$	−813945.	+	1.78229e6i	−0.0365633	+	0.0800625i
$870$	−1.74121e6	+	1.21104e7i	−0.0779924	+	0.542449i
$871$	1.76338e7	+	1.13326e7i	0.787592	+	0.506155i
$872$	932506.	+	1.07617e6i	0.0415298	+	0.0479280i
$873$	−3.69651e6			−0.164156
$874$	607748.	−	410235.i	0.0269119	−	0.0181658i
$875$	−2.56054e7			−1.13061
$876$	1.17443e7	+	1.35536e7i	0.517090	+	0.596753i
$877$	9.87325e6	+	6.34515e6i	0.433472	+	0.278576i	0.739126	−	0.673567i	$-0.235239\pi$
$877$	9.87325e6	+	6.34515e6i	0.433472	+	0.278576i	−0.305654	+	0.952143i	$0.598875\pi$
$878$	6.62015e6	−	4.60441e7i	0.289822	−	2.01576i
$879$	9.39480e6	−	2.05717e7i	0.410124	−	0.898046i
$880$	−2.44992e6	−	1.70396e7i	−0.106646	−	0.741742i
$881$	2.35571e7	+	6.91700e6i	1.02255	+	0.300246i	0.749676	−	0.661805i	$-0.230209\pi$
$881$	2.35571e7	+	6.91700e6i	1.02255	+	0.300246i	0.272869	+	0.962051i	$0.412027\pi$
$882$	−6.88435e6	+	4.42431e6i	−0.297983	+	0.191502i
$883$	5.90242e6	+	1.29245e7i	0.254759	+	0.557843i	0.993193	−	0.116482i	$-0.0371618\pi$
$883$	5.90242e6	+	1.29245e7i	0.254759	+	0.557843i	−0.738434	+	0.674325i	$0.764435\pi$
$884$	−3.64998e7	+	1.07173e7i	−1.57094	+	0.461270i
$885$	6.42012e6	−	7.40921e6i	0.275540	−	0.317990i
$886$	−1.55313e7	+	1.79240e7i	−0.664695	+	0.767099i
$887$	−1.54316e7	+	4.53112e6i	−0.658569	+	0.193373i	−0.593907	−	0.804534i	$-0.702415\pi$
$887$	−1.54316e7	+	4.53112e6i	−0.658569	+	0.193373i	−0.0646623	+	0.997907i	$0.520597\pi$
$888$	254532.	+	557347.i	0.0108320	+	0.0237188i
$889$	1.63227e6	−	1.04900e6i	0.0692690	−	0.0445165i
$890$	1.90661e7	+	5.59830e6i	0.806837	+	0.236909i
$891$	−560263.	−	3.89672e6i	−0.0236427	−	0.164439i
$892$	2.03965e6	−	4.46622e6i	0.0858310	−	0.187944i
$893$	53090.0	−	369249.i	0.00222784	−	0.0154950i
$894$	−7.80599e6	−	5.01661e6i	−0.326651	−	0.209926i
$895$	−2.03332e6	−	2.34658e6i	−0.0848493	−	0.0979213i
$896$	3.63895e6			0.151428
$897$	−1.29168e7	−	3.47825e6i	−0.536011	−	0.144338i
$898$	−2.14464e7			−0.887489
$899$	5.72696e6	+	6.60926e6i	0.236333	+	0.272743i
$900$	−5.01559e6	−	3.22332e6i	−0.206403	−	0.132647i
$901$	1.19589e6	−	8.31760e6i	0.0490771	−	0.341339i
$902$	−4.05872e7	+	8.88735e7i	−1.66101	+	3.63711i
$903$	1.97162e6	+	1.37129e7i	0.0804644	+	0.559642i
$904$	−1.09902e6	−	322701.i	−0.0447285	−	0.0131335i
$905$	2.01283e6	−	1.29357e6i	0.0816932	−	0.0525011i
$906$	3.87957e6	+	8.49506e6i	0.157023	+	0.343832i
$907$	2.89129e7	−	8.48959e6i	1.16701	−	0.342664i	0.359855	−	0.933008i	$-0.382826\pi$
$907$	2.89129e7	−	8.48959e6i	1.16701	−	0.342664i	0.807152	+	0.590344i	$0.201008\pi$
$908$	−4.27260e6	+	4.93084e6i	−0.171980	+	0.198475i
$909$	5.14475e6	−	5.93736e6i	0.206517	−	0.238333i
$910$	2.06348e7	−	6.05893e6i	0.826033	−	0.242545i
$911$	1.35141e7	+	2.95918e7i	0.539501	+	1.18134i	0.961515	+	0.274752i	$0.0885959\pi$
$911$	1.35141e7	+	2.95918e7i	0.539501	+	1.18134i	−0.422014	+	0.906589i	$0.638677\pi$
$912$	294080.	−	188994.i	0.0117079	−	0.00752421i
$913$	−5.27344e7	−	1.54842e7i	−2.09371	−	0.614769i
$914$	3.53741e6	+	2.46032e7i	0.140062	+	0.974152i
$915$	−3.78257e6	+	8.28266e6i	−0.149360	+	0.327052i
$916$	−3.87245e6	+	2.69335e7i	−0.152492	+	1.06061i
$917$	109866.	+	70606.9i	0.00431461	+	0.00277283i
$918$	7.99637e6	+	9.22831e6i	0.313174	+	0.361423i
$919$	−1.62808e7			−0.635899			−0.317950	−	0.948108i	$-0.602994\pi$
$919$	−1.62808e7			−0.635899			−0.317950	+	0.948108i	$0.602994\pi$
$920$	116445.	+	697772.i	0.00453576	+	0.0271796i
$921$	−191047.			−0.00742150
$922$	2.50652e7	+	2.89267e7i	0.971053	+	1.12066i
$923$	1.44314e7	+	9.27448e6i	0.557575	+	0.358332i
$924$	4.05618e6	−	2.82113e7i	0.156292	−	1.08704i
$925$	−6.55770e6	+	1.43594e7i	−0.251998	+	0.551799i
$926$	476668.	+	3.31530e6i	0.0182679	+	0.127056i
$927$	−8.36312e6	−	2.45563e6i	−0.319646	−	0.0938565i
$928$	4.33619e7	−	2.78670e7i	1.65287	−	1.06224i
$929$	1.87115e7	+	4.09726e7i	0.711329	+	1.55759i	0.825671	+	0.564152i	$0.190797\pi$
$929$	1.87115e7	+	4.09726e7i	0.711329	+	1.55759i	−0.114342	+	0.993441i	$0.536476\pi$
$930$	2.53180e6	−	743405.i	0.0959893	−	0.0281850i
$931$	305004.	−	351994.i	0.0115327	−	0.0133095i
$932$	−1.60675e7	+	1.85429e7i	−0.605910	+	0.699258i
$933$	1.73380e7	−	5.09089e6i	0.652071	−	0.191465i
$934$	4.69701e6	+	1.02850e7i	0.176179	+	0.385779i
$935$	−2.87909e7	+	1.85028e7i	−1.07703	+	0.692162i
$936$	−470898.	−	138268.i	−0.0175686	−	0.00515861i
$937$	−127504.	−	886811.i	−0.00474433	−	0.0329976i	0.987312	−	0.158794i	$-0.0507605\pi$
$937$	−127504.	−	886811.i	−0.00474433	−	0.0329976i	−0.992056	+	0.125796i	$0.959851\pi$
$938$	2.02359e7	−	4.43104e7i	0.750957	−	1.64437i
$939$	−1.61643e6	+	1.12425e7i	−0.0598264	+	0.416101i
$940$	−7.11500e6	−	4.57253e6i	−0.262637	−	0.168786i
$941$	3.22745e7	+	3.72468e7i	1.18819	+	1.37124i	0.912025	+	0.410134i	$0.134518\pi$
$941$	3.22745e7	+	3.72468e7i	1.18819	+	1.37124i	0.276165	+	0.961110i	$0.410937\pi$
$942$	−2.95146e7			−1.08370
$943$	2.05973e7	−	4.79346e7i	0.754277	−	1.75537i
$944$	−4.29911e7			−1.57018
$945$	−2.21324e6	−	2.55422e6i	−0.0806213	−	0.0930420i
$946$	−3.57800e7	−	2.29944e7i	−1.29991	−	0.835401i
$947$	−4.63536e6	+	3.22396e7i	−0.167961	+	1.16819i	0.715130	+	0.698992i	$0.246367\pi$
$947$	−4.63536e6	+	3.22396e7i	−0.167961	+	1.16819i	−0.883091	+	0.469202i	$0.844542\pi$
$948$	−374729.	+	820542.i	−0.0135424	+	0.0296538i
$949$	5.41286e6	+	3.76473e7i	0.195102	+	1.35696i
$950$	665014.	+	195266.i	0.0239068	+	0.00701967i
$951$	−1.38127e7	+	8.87688e6i	−0.495253	+	0.318280i
$952$	−1.56277e6	−	3.42198e6i	−0.0558858	−	0.122373i
$953$	6.35749e6	−	1.86673e6i	0.226753	−	0.0665807i	−0.166382	−	0.986061i	$-0.553209\pi$
$953$	6.35749e6	−	1.86673e6i	0.226753	−	0.0665807i	0.393135	+	0.919481i	$0.371390\pi$
$954$	−1.66833e6	+	1.92536e6i	−0.0593488	+	0.0684922i
$955$	6.91673e6	−	7.98233e6i	0.245410	−	0.283218i
$956$	−7.33914e6	+	2.15496e6i	−0.259717	+	0.0762598i
$957$	1.42853e7	+	3.12805e7i	0.504209	+	1.10406i
$958$	−1.21017e7	+	7.77730e6i	−0.426023	+	0.273789i
$959$	−3.94028e7	−	1.15697e7i	−1.38350	−	0.406233i
$960$	−1.03742e6	−	7.21540e6i	−0.0363309	−	0.252687i
$961$	−1.11095e7	+	2.43263e7i	−0.388047	+	0.849705i
$962$	4.34577e6	−	3.02255e7i	0.151401	−	1.05302i
$963$	−4.74089e6	−	3.04679e6i	−0.164738	−	0.105871i
$964$	−4.46616e6	−	5.15422e6i	−0.154790	−	0.178637i
$965$	1.54183e7			0.532990
$966$	−3.72894e6	+	3.08623e7i	−0.128571	+	1.06411i
$967$	3.00866e6			0.103468			0.0517340	−	0.998661i	$-0.483525\pi$
$967$	3.00866e6			0.103468			0.0517340	+	0.998661i	$0.483525\pi$
$968$	−1.34763e6	−	1.55525e6i	−0.0462257	−	0.0533473i
$969$	−584644.	−	375728.i	−0.0200024	−	0.0128548i
$970$	1.38651e6	−	9.64336e6i	0.0473143	−	0.329078i
$971$	1.32400e7	−	2.89915e7i	0.450649	−	0.986784i	−0.538871	−	0.842388i	$-0.681149\pi$
$971$	1.32400e7	−	2.89915e7i	0.450649	−	0.986784i	0.989520	−	0.144396i	$-0.0461238\pi$
$972$	−257937.	−	1.79399e6i	−0.00875686	−	0.0609053i
$973$	977248.	+	286946.i	0.0330920	+	0.00971668i
$974$	−5.22508e7	+	3.35796e7i	−1.76480	+	1.13417i
$975$	−5.25263e6	−	1.15017e7i	−0.176956	−	0.387480i
$976$	3.83116e7	−	1.12493e7i	1.28738	−	0.378008i
$977$	−1.72879e7	+	1.99513e7i	−0.579438	+	0.668707i	−0.967484	−	0.252933i	$-0.918605\pi$
$977$	−1.72879e7	+	1.99513e7i	−0.579438	+	0.668707i	0.388046	+	0.921640i	$0.373150\pi$
$978$	−1.19273e7	+	1.37648e7i	−0.398745	+	0.460176i
$979$	5.35881e7	−	1.57349e7i	1.78695	−	0.524695i
$980$	−4.38656e6	−	9.60523e6i	−0.145901	−	0.319479i
$981$	−9.38227e6	+	6.02962e6i	−0.311269	+	0.200040i
$982$	−6.45880e6	−	1.89648e6i	−0.213734	−	0.0627579i
$983$	−6.32596e6	−	4.39980e7i	−0.208806	−	1.45228i	−0.777062	−	0.629425i	$-0.783291\pi$
$983$	−6.32596e6	−	4.39980e7i	−0.208806	−	1.45228i	0.568256	−	0.822852i	$-0.307618\pi$
$984$	795158.	−	1.74115e6i	0.0261798	−	0.0573257i
$985$	−2.60177e6	+	1.80957e7i	−0.0854434	+	0.594272i
$986$	−8.97299e7	−	5.76659e7i	−2.93931	−	1.88898i
$987$	1.03571e7	+	1.19527e7i	0.338411	+	0.390547i
$988$	−656391.			−0.0213929
$989$	1.93784e7	+	1.18448e7i	0.629980	+	0.385067i
$990$	1.03758e7			0.336460
$991$	3.69091e7	+	4.25954e7i	1.19385	+	1.37778i	0.907715	+	0.419587i	$0.137825\pi$
$991$	3.69091e7	+	4.25954e7i	1.19385	+	1.37778i	0.286135	+	0.958189i	$0.407629\pi$
$992$	−9.35183e6	−	6.01006e6i	−0.301729	−	0.193910i
$993$	4.36402e6	−	3.03524e7i	0.140447	−	0.976833i
$994$	1.65609e7	−	3.62632e7i	0.531639	−	1.16413i
$995$	−2.82418e6	−	1.96426e7i	−0.0904346	−	0.628986i
$996$	−2.42781e7	−	7.12871e6i	−0.775474	−	0.227700i
$997$	7.55939e6	−	4.85812e6i	0.240851	−	0.154786i	−0.414647	−	0.909982i	$-0.636095\pi$
$997$	7.55939e6	−	4.85812e6i	0.240851	−	0.154786i	0.655498	+	0.755197i	$0.272459\pi$
$998$	1.98697e7	+	4.35086e7i	0.631488	+	1.38277i
$999$	−4.60448e6	+	1.35200e6i	−0.145971	+	0.0428609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.b.13.9	✓	100
23.16	even	11	inner	69.6.e.b.16.9	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.b.13.9	✓	100	1.1	even	1	trivial
69.6.e.b.16.9	yes	100	23.16	even	11	inner

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(5.18515 + 5.98398i) q^{2} +(7.57128 + 4.86577i) q^{3} +(-4.36819 + 30.3814i) q^{4} +(-11.2004 + 24.5255i) q^{5} +(10.1416 + 70.5362i) q^{6} +(164.984 + 48.4438i) q^{7} +(8.70029 - 5.59133i) q^{8} +(33.6486 + 73.6802i) q^{9} +O(q^{10})\)	\(q+(5.18515 + 5.98398i) q^{2} +(7.57128 + 4.86577i) q^{3} +(-4.36819 + 30.3814i) q^{4} +(-11.2004 + 24.5255i) q^{5} +(10.1416 + 70.5362i) q^{6} +(164.984 + 48.4438i) q^{7} +(8.70029 - 5.59133i) q^{8} +(33.6486 + 73.6802i) q^{9} +(-204.836 + 60.1453i) q^{10} +(-392.935 + 453.471i) q^{11} +(-180.902 + 208.772i) q^{12} +(-562.128 + 165.056i) q^{13} +(565.582 + 1238.45i) q^{14} +(-204.137 + 131.191i) q^{15} +(1020.99 + 299.789i) q^{16} +(-301.061 - 2093.92i) q^{17} +(-266.428 + 583.396i) q^{18} +(5.19479 - 36.1306i) q^{19} +(-696.194 - 447.417i) q^{20} +(1013.43 + 1169.56i) q^{21} -4750.99 q^{22} +(2536.35 - 57.2233i) q^{23} +93.0784 q^{24} +(1570.39 + 1812.33i) q^{25} +(-3902.41 - 2507.93i) q^{26} +(-103.748 + 721.580i) q^{27} +(-2192.47 + 4800.85i) q^{28} +(-906.241 - 6303.04i) q^{29} +(-1843.52 - 541.307i) q^{30} +(-1155.34 + 742.490i) q^{31} +(3362.56 + 7362.99i) q^{32} +(-5181.51 + 1521.43i) q^{33} +(10969.0 - 12658.9i) q^{34} +(-3036.00 + 3503.73i) q^{35} +(-2385.49 + 700.444i) q^{36} +(2734.59 + 5987.93i) q^{37} +(243.141 - 156.257i) q^{38} +(-5059.15 - 1485.50i) q^{39} +(39.6834 + 276.004i) q^{40} +(8542.88 - 18706.3i) q^{41} +(-1743.84 + 12128.7i) q^{42} +(7531.07 + 4839.92i) q^{43} +(-12060.7 - 13918.8i) q^{44} -2183.92 q^{45} +(13493.8 + 14880.8i) q^{46} +10219.9 q^{47} +(6271.48 + 7237.68i) q^{48} +(10734.1 + 6898.39i) q^{49} +(-2702.22 + 18794.4i) q^{50} +(7909.13 - 17318.6i) q^{51} +(-2559.15 - 17799.3i) q^{52} +(3811.35 + 1119.11i) q^{53} +(-4855.87 + 3120.68i) q^{54} +(-6720.57 - 14716.0i) q^{55} +(1706.28 - 501.008i) q^{56} +(215.134 - 248.278i) q^{57} +(33018.3 - 38105.2i) q^{58} +(-38765.2 + 11382.5i) q^{59} +(-3094.05 - 6775.03i) q^{60} +(31567.3 - 20287.0i) q^{61} +(-10433.6 - 3063.59i) q^{62} +(1982.15 + 13786.1i) q^{63} +(-12479.3 + 27325.9i) q^{64} +(2248.00 - 15635.2i) q^{65} +(-35971.1 - 23117.2i) q^{66} +(-23430.2 - 27039.8i) q^{67} +64931.5 q^{68} +(19481.9 + 11908.0i) q^{69} -36708.4 q^{70} +(-19175.0 - 22129.2i) q^{71} +(704.723 + 452.898i) q^{72} +(9239.18 - 64259.9i) q^{73} +(-21652.4 + 47412.1i) q^{74} +(3071.50 + 21362.8i) q^{75} +(1075.01 + 315.650i) q^{76} +(-86796.0 + 55780.4i) q^{77} +(-17343.3 - 37976.4i) q^{78} +(3133.16 - 919.980i) q^{79} +(-18788.0 + 21682.5i) q^{80} +(-4296.54 + 4958.47i) q^{81} +(156234. - 45874.5i) q^{82} +(38050.7 + 83319.3i) q^{83} +(-39959.7 + 25680.5i) q^{84} +(54726.5 + 16069.2i) q^{85} +(10087.7 + 70161.5i) q^{86} +(23807.7 - 52131.7i) q^{87} +(-883.138 + 6142.36i) q^{88} +(-78303.6 - 50322.7i) q^{89} +(-11324.0 - 13068.5i) q^{90} -100738. q^{91} +(-9340.73 + 77307.9i) q^{92} -12360.2 q^{93} +(52991.5 + 61155.4i) q^{94} +(827.936 + 532.082i) q^{95} +(-10367.7 + 72108.7i) q^{96} +(-18957.9 + 41511.9i) q^{97} +(14378.1 + 100002. i) q^{98} +(-46633.6 - 13692.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9}+O(q^{10}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9} - 38 q^{10} + 404 q^{11} - 1332 q^{12} - 2850 q^{13} - 724 q^{14} + 639 q^{15} - 5556 q^{16} - 2519 q^{17} + 972 q^{18} + 1117 q^{19} - 22411 q^{20} - 702 q^{21} + 32798 q^{22} + 12040 q^{23} - 756 q^{24} - 5928 q^{25} - 788 q^{26} - 7290 q^{27} - 54024 q^{28} + 13774 q^{29} - 342 q^{30} + 12501 q^{31} + 37412 q^{32} - 4185 q^{33} + 9441 q^{34} + 28894 q^{35} - 21789 q^{36} - 38902 q^{37} - 15042 q^{38} - 25650 q^{39} - 133835 q^{40} - 19456 q^{41} + 85950 q^{42} - 8126 q^{43} + 120643 q^{44} + 40500 q^{45} + 90500 q^{46} + 60846 q^{47} + 62955 q^{48} - 25762 q^{49} - 110197 q^{50} - 51084 q^{51} + 91725 q^{52} - 83896 q^{53} - 31347 q^{54} + 190331 q^{55} - 358140 q^{56} - 40437 q^{57} + 150977 q^{58} + 248368 q^{59} + 122625 q^{60} - 81516 q^{61} + 82657 q^{62} - 6318 q^{63} - 298028 q^{64} - 25475 q^{65} - 6669 q^{66} + 51337 q^{67} + 491228 q^{68} + 17082 q^{69} + 395832 q^{70} - 206653 q^{71} - 149364 q^{72} - 121007 q^{73} + 716844 q^{74} - 59490 q^{75} + 171145 q^{76} + 71982 q^{77} + 11916 q^{78} - 661118 q^{79} - 1386592 q^{80} - 65610 q^{81} - 136394 q^{82} - 368400 q^{83} + 165204 q^{84} + 45505 q^{85} - 99668 q^{86} + 50112 q^{87} - 474416 q^{88} + 328408 q^{89} - 3078 q^{90} + 1042320 q^{91} + 1554071 q^{92} + 160722 q^{93} - 299081 q^{94} - 434011 q^{95} + 412740 q^{96} - 88136 q^{97} + 515807 q^{98} - 37665 q^{99}+O(q^{100}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9 - 38 * q^10 + 404 * q^11 - 1332 * q^12 - 2850 * q^13 - 724 * q^14 + 639 * q^15 - 5556 * q^16 - 2519 * q^17 + 972 * q^18 + 1117 * q^19 - 22411 * q^20 - 702 * q^21 + 32798 * q^22 + 12040 * q^23 - 756 * q^24 - 5928 * q^25 - 788 * q^26 - 7290 * q^27 - 54024 * q^28 + 13774 * q^29 - 342 * q^30 + 12501 * q^31 + 37412 * q^32 - 4185 * q^33 + 9441 * q^34 + 28894 * q^35 - 21789 * q^36 - 38902 * q^37 - 15042 * q^38 - 25650 * q^39 - 133835 * q^40 - 19456 * q^41 + 85950 * q^42 - 8126 * q^43 + 120643 * q^44 + 40500 * q^45 + 90500 * q^46 + 60846 * q^47 + 62955 * q^48 - 25762 * q^49 - 110197 * q^50 - 51084 * q^51 + 91725 * q^52 - 83896 * q^53 - 31347 * q^54 + 190331 * q^55 - 358140 * q^56 - 40437 * q^57 + 150977 * q^58 + 248368 * q^59 + 122625 * q^60 - 81516 * q^61 + 82657 * q^62 - 6318 * q^63 - 298028 * q^64 - 25475 * q^65 - 6669 * q^66 + 51337 * q^67 + 491228 * q^68 + 17082 * q^69 + 395832 * q^70 - 206653 * q^71 - 149364 * q^72 - 121007 * q^73 + 716844 * q^74 - 59490 * q^75 + 171145 * q^76 + 71982 * q^77 + 11916 * q^78 - 661118 * q^79 - 1386592 * q^80 - 65610 * q^81 - 136394 * q^82 - 368400 * q^83 + 165204 * q^84 + 45505 * q^85 - 99668 * q^86 + 50112 * q^87 - 474416 * q^88 + 328408 * q^89 - 3078 * q^90 + 1042320 * q^91 + 1554071 * q^92 + 160722 * q^93 - 299081 * q^94 - 434011 * q^95 + 412740 * q^96 - 88136 * q^97 + 515807 * q^98 - 37665 * q^99

Introduction

L-functions

Modular forms

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Database

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