LMFDB - Embedded newform 138.4.e.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,4,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	138.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:	$8.14226358079$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	138.49
Dual form			138.4.e.c.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.284630 + 1.97964i) q^{2} +(1.24625 - 2.72890i) q^{3} +(-3.83797 + 1.12693i) q^{4} +(-2.69854 + 3.11428i) q^{5} +(5.75696 + 1.69040i) q^{6} +(22.2299 - 14.2863i) q^{7} +(-3.32332 - 7.27706i) q^{8} +(-5.89375 - 6.80175i) q^{9} +O(q^{10})$	\(q+(0.284630 + 1.97964i) q^{2} +(1.24625 - 2.72890i) q^{3} +(-3.83797 + 1.12693i) q^{4} +(-2.69854 + 3.11428i) q^{5} +(5.75696 + 1.69040i) q^{6} +(22.2299 - 14.2863i) q^{7} +(-3.32332 - 7.27706i) q^{8} +(-5.89375 - 6.80175i) q^{9} +(-6.93325 - 4.45573i) q^{10} +(3.56117 - 24.7685i) q^{11} +(-1.70778 + 11.8779i) q^{12} +(43.8490 + 28.1800i) q^{13} +(34.6090 + 39.9409i) q^{14} +(5.13551 + 11.2452i) q^{15} +(13.4601 - 8.65025i) q^{16} +(12.3201 + 3.61752i) q^{17} +(11.7875 - 13.6035i) q^{18} +(108.272 - 31.7916i) q^{19} +(6.84735 - 14.9936i) q^{20} +(-11.2819 - 78.4672i) q^{21} +50.0463 q^{22} +(63.9328 - 89.8866i) q^{23} -24.0000 q^{24} +(15.3727 + 106.920i) q^{25} +(-43.3057 + 94.8262i) q^{26} +(-25.9063 + 7.60678i) q^{27} +(-69.2180 + 79.8818i) q^{28} +(-34.9666 - 10.2671i) q^{29} +(-20.7998 + 13.3672i) q^{30} +(-54.8096 - 120.016i) q^{31} +(20.9555 + 24.1840i) q^{32} +(-63.1525 - 40.5856i) q^{33} +(-3.65472 + 25.4191i) q^{34} +(-15.4967 + 107.782i) q^{35} +(30.2851 + 19.4631i) q^{36} +(91.2802 + 105.343i) q^{37} +(93.7535 + 205.292i) q^{38} +(131.547 - 84.5401i) q^{39} +(31.6309 + 9.28768i) q^{40} +(-114.432 + 132.061i) q^{41} +(152.126 - 44.6682i) q^{42} +(52.4991 - 114.957i) q^{43} +(14.2447 + 99.0738i) q^{44} +37.0871 q^{45} +(196.141 + 100.980i) q^{46} -304.231 q^{47} +(-6.83111 - 47.5114i) q^{48} +(147.582 - 323.160i) q^{49} +(-207.287 + 60.8650i) q^{50} +(25.2257 - 29.1120i) q^{51} +(-200.048 - 58.7394i) q^{52} +(-510.494 + 328.075i) q^{53} +(-22.4324 - 49.1201i) q^{54} +(67.5260 + 77.9292i) q^{55} +(-177.839 - 114.290i) q^{56} +(48.1778 - 335.084i) q^{57} +(10.3727 - 72.1436i) q^{58} +(-279.360 - 179.534i) q^{59} +(-32.3825 - 37.3714i) q^{60} +(-345.892 - 757.399i) q^{61} +(221.989 - 142.664i) q^{62} +(-228.189 - 67.0023i) q^{63} +(-41.9111 + 48.3680i) q^{64} +(-206.089 + 60.5132i) q^{65} +(62.3700 - 136.571i) q^{66} +(-15.7755 - 109.721i) q^{67} -51.3610 q^{68} +(-165.615 - 286.487i) q^{69} -217.781 q^{70} +(135.007 + 938.991i) q^{71} +(-29.9099 + 65.4935i) q^{72} +(147.933 - 43.4371i) q^{73} +(-182.560 + 210.686i) q^{74} +(310.931 + 91.2975i) q^{75} +(-379.719 + 244.031i) q^{76} +(-274.685 - 601.475i) q^{77} +(204.801 + 236.353i) q^{78} +(-290.607 - 186.762i) q^{79} +(-9.38319 + 65.2615i) q^{80} +(-11.5275 + 80.1755i) q^{81} +(-294.005 - 188.946i) q^{82} +(552.940 + 638.127i) q^{83} +(131.727 + 288.441i) q^{84} +(-44.5124 + 28.6064i) q^{85} +(242.516 + 71.2092i) q^{86} +(-71.5948 + 82.6248i) q^{87} +(-192.076 + 56.3987i) q^{88} +(493.722 - 1081.10i) q^{89} +(10.5561 + 73.4192i) q^{90} +1377.35 q^{91} +(-144.076 + 417.030i) q^{92} -395.818 q^{93} +(-86.5931 - 602.269i) q^{94} +(-193.169 + 422.982i) q^{95} +(92.1113 - 27.0463i) q^{96} +(-743.252 + 857.758i) q^{97} +(681.748 + 200.179i) q^{98} +(-189.457 + 121.757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} - 9 q^{3} - 12 q^{4} - 4 q^{5} + 18 q^{6} + 4 q^{7} + 24 q^{8} - 27 q^{9}+O(q^{10}) $ 30 * q + 6 * q^2 - 9 * q^3 - 12 * q^4 - 4 * q^5 + 18 * q^6 + 4 * q^7 + 24 * q^8 - 27 * q^9	\( 30 q + 6 q^{2} - 9 q^{3} - 12 q^{4} - 4 q^{5} + 18 q^{6} + 4 q^{7} + 24 q^{8} - 27 q^{9} - 36 q^{10} - 5 q^{11} - 36 q^{12} - 59 q^{13} + 36 q^{14} + 120 q^{15} - 48 q^{16} - 291 q^{17} + 54 q^{18} + 319 q^{19} + 160 q^{20} + 45 q^{21} + 384 q^{22} + 472 q^{23} - 720 q^{24} + 321 q^{25} + 250 q^{26} - 81 q^{27} - 72 q^{28} + 753 q^{29} - 108 q^{30} - 345 q^{31} + 96 q^{32} - 609 q^{33} + 164 q^{34} - 646 q^{35} - 108 q^{36} - 349 q^{37} + 242 q^{38} - 177 q^{39} - 56 q^{40} - 548 q^{41} - 24 q^{42} + 1800 q^{43} - 20 q^{44} - 1026 q^{45} + 46 q^{46} + 2666 q^{47} - 144 q^{48} - 1685 q^{49} + 414 q^{50} + 51 q^{51} - 280 q^{52} + 769 q^{53} + 162 q^{54} - 4188 q^{55} - 32 q^{56} - 1518 q^{57} - 1264 q^{58} + 2649 q^{59} - 48 q^{60} + 876 q^{61} + 8 q^{62} + 36 q^{63} - 192 q^{64} + 906 q^{65} - 300 q^{66} - 451 q^{67} - 1648 q^{68} + 459 q^{69} + 1512 q^{70} - 2161 q^{71} + 216 q^{72} - 1838 q^{73} + 698 q^{74} - 621 q^{75} + 264 q^{76} + 7182 q^{77} - 1098 q^{78} - 4324 q^{79} - 64 q^{80} - 243 q^{81} + 3736 q^{82} + 191 q^{83} - 84 q^{84} - 2734 q^{85} + 1086 q^{86} - 1074 q^{87} + 392 q^{88} + 4073 q^{89} + 72 q^{90} - 1970 q^{91} - 4624 q^{92} + 1506 q^{93} - 954 q^{94} + 2153 q^{95} + 288 q^{96} - 157 q^{97} - 2988 q^{98} - 1827 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 - 9 * q^3 - 12 * q^4 - 4 * q^5 + 18 * q^6 + 4 * q^7 + 24 * q^8 - 27 * q^9 - 36 * q^10 - 5 * q^11 - 36 * q^12 - 59 * q^13 + 36 * q^14 + 120 * q^15 - 48 * q^16 - 291 * q^17 + 54 * q^18 + 319 * q^19 + 160 * q^20 + 45 * q^21 + 384 * q^22 + 472 * q^23 - 720 * q^24 + 321 * q^25 + 250 * q^26 - 81 * q^27 - 72 * q^28 + 753 * q^29 - 108 * q^30 - 345 * q^31 + 96 * q^32 - 609 * q^33 + 164 * q^34 - 646 * q^35 - 108 * q^36 - 349 * q^37 + 242 * q^38 - 177 * q^39 - 56 * q^40 - 548 * q^41 - 24 * q^42 + 1800 * q^43 - 20 * q^44 - 1026 * q^45 + 46 * q^46 + 2666 * q^47 - 144 * q^48 - 1685 * q^49 + 414 * q^50 + 51 * q^51 - 280 * q^52 + 769 * q^53 + 162 * q^54 - 4188 * q^55 - 32 * q^56 - 1518 * q^57 - 1264 * q^58 + 2649 * q^59 - 48 * q^60 + 876 * q^61 + 8 * q^62 + 36 * q^63 - 192 * q^64 + 906 * q^65 - 300 * q^66 - 451 * q^67 - 1648 * q^68 + 459 * q^69 + 1512 * q^70 - 2161 * q^71 + 216 * q^72 - 1838 * q^73 + 698 * q^74 - 621 * q^75 + 264 * q^76 + 7182 * q^77 - 1098 * q^78 - 4324 * q^79 - 64 * q^80 - 243 * q^81 + 3736 * q^82 + 191 * q^83 - 84 * q^84 - 2734 * q^85 + 1086 * q^86 - 1074 * q^87 + 392 * q^88 + 4073 * q^89 + 72 * q^90 - 1970 * q^91 - 4624 * q^92 + 1506 * q^93 - 954 * q^94 + 2153 * q^95 + 288 * q^96 - 157 * q^97 - 2988 * q^98 - 1827 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.284630	+	1.97964i	0.100632	+	0.699909i
$2$	0.284630	+	1.97964i	0.100632	+	0.699909i
$3$	1.24625	−	2.72890i	0.239840	−	0.525176i
$3$	1.24625	−	2.72890i	0.239840	−	0.525176i
$4$	−3.83797	+	1.12693i	−0.479746	+	0.140866i
$5$	−2.69854	+	3.11428i	−0.241365	+	0.278550i	−0.863488	−	0.504370i	$-0.831725\pi$
$5$	−2.69854	+	3.11428i	−0.241365	+	0.278550i	0.622123	+	0.782920i	$0.286270\pi$
$6$	5.75696	+	1.69040i	0.391711	+	0.115017i
$7$	22.2299	−	14.2863i	1.20030	−	0.771386i	0.221292	−	0.975208i	$-0.428973\pi$
$7$	22.2299	−	14.2863i	1.20030	−	0.771386i	0.979008	+	0.203821i	$0.0653361\pi$
$8$	−3.32332	−	7.27706i	−0.146871	−	0.321603i
$9$	−5.89375	−	6.80175i	−0.218287	−	0.251917i
$10$	−6.93325	−	4.45573i	−0.219249	−	0.140903i
$11$	3.56117	−	24.7685i	0.0976120	−	0.678906i	−0.880989	−	0.473137i	$-0.843121\pi$
$11$	3.56117	−	24.7685i	0.0976120	−	0.678906i	0.978601	−	0.205769i	$-0.0659695\pi$
$12$	−1.70778	+	11.8779i	−0.0410828	+	0.285737i
$13$	43.8490	+	28.1800i	0.935502	+	0.601210i	0.917116	−	0.398621i	$-0.130511\pi$
$13$	43.8490	+	28.1800i	0.935502	+	0.601210i	0.0183857	+	0.999831i	$0.494147\pi$
$14$	34.6090	+	39.9409i	0.660689	+	0.762476i
$15$	5.13551	+	11.2452i	0.0883989	+	0.193567i
$16$	13.4601	−	8.65025i	0.210313	−	0.135160i
$17$	12.3201	+	3.61752i	0.175769	+	0.0516104i	0.368433	−	0.929654i	$-0.379895\pi$
$17$	12.3201	+	3.61752i	0.175769	+	0.0516104i	−0.192664	+	0.981265i	$0.561713\pi$
$18$	11.7875	−	13.6035i	0.154352	−	0.178132i
$19$	108.272	−	31.7916i	1.30733	−	0.383868i	0.447428	−	0.894320i	$-0.352340\pi$
$19$	108.272	−	31.7916i	1.30733	−	0.383868i	0.859906	+	0.510452i	$0.170522\pi$
$20$	6.84735	−	14.9936i	0.0765557	−	0.167634i
$21$	−11.2819	−	78.4672i	−0.117234	−	0.815379i
$22$	50.0463			0.484996
$23$	63.9328	−	89.8866i	0.579604	−	0.814898i
$23$	63.9328	−	89.8866i	0.579604	−	0.814898i
$24$	−24.0000			−0.204124
$25$	15.3727	+	106.920i	0.122982	+	0.855357i
$26$	−43.3057	+	94.8262i	−0.326652	+	0.715267i
$27$	−25.9063	+	7.60678i	−0.184655	+	0.0542195i
$28$	−69.2180	+	79.8818i	−0.467178	+	0.539152i
$29$	−34.9666	−	10.2671i	−0.223901	−	0.0657433i	0.167858	−	0.985811i	$-0.446315\pi$
$29$	−34.9666	−	10.2671i	−0.223901	−	0.0657433i	−0.391759	+	0.920068i	$0.628133\pi$
$30$	−20.7998	+	13.3672i	−0.126583	+	0.0813502i
$31$	−54.8096	−	120.016i	−0.317551	−	0.695340i	0.681793	−	0.731545i	$-0.261200\pi$
$31$	−54.8096	−	120.016i	−0.317551	−	0.695340i	−0.999344	+	0.0362048i	$0.988473\pi$
$32$	20.9555	+	24.1840i	0.115764	+	0.133599i
$33$	−63.1525	−	40.5856i	−0.333134	−	0.214092i
$34$	−3.65472	+	25.4191i	−0.0184347	+	0.128216i
$35$	−15.4967	+	107.782i	−0.0748408	+	0.520529i
$36$	30.2851	+	19.4631i	0.140209	+	0.0901068i
$37$	91.2802	+	105.343i	0.405578	+	0.468062i	0.921390	−	0.388640i	$-0.127055\pi$
$37$	91.2802	+	105.343i	0.405578	+	0.468062i	−0.515812	+	0.856702i	$0.672510\pi$
$38$	93.7535	+	205.292i	0.400232	+	0.876387i
$39$	131.547	−	84.5401i	0.540112	−	0.347109i
$40$	31.6309	+	9.28768i	0.125032	+	0.0367128i
$41$	−114.432	+	132.061i	−0.435884	+	0.503037i	−0.930610	−	0.366012i	$-0.880723\pi$
$41$	−114.432	+	132.061i	−0.435884	+	0.503037i	0.494726	+	0.869049i	$0.335268\pi$
$42$	152.126	−	44.6682i	0.558894	−	0.164106i
$43$	52.4991	−	114.957i	0.186187	−	0.407692i	−0.793404	−	0.608696i	$-0.791693\pi$
$43$	52.4991	−	114.957i	0.186187	−	0.407692i	0.979591	+	0.201004i	$0.0644203\pi$
$44$	14.2447	+	99.0738i	0.0488060	+	0.339453i
$45$	37.0871			0.122858
$46$	196.141	+	100.980i	0.628681	+	0.323666i
$47$	−304.231			−0.944184			−0.472092	−	0.881549i	$-0.656501\pi$
$47$	−304.231			−0.944184			−0.472092	+	0.881549i	$0.656501\pi$
$48$	−6.83111	−	47.5114i	−0.0205414	−	0.142868i
$49$	147.582	−	323.160i	0.430269	−	0.942159i
$50$	−207.287	+	60.8650i	−0.586297	+	0.172152i
$51$	25.2257	−	29.1120i	0.0692610	−	0.0799314i
$52$	−200.048	−	58.7394i	−0.533494	−	0.156648i
$53$	−510.494	+	328.075i	−1.32305	+	0.850274i	−0.995519	−	0.0945655i	$-0.969854\pi$
$53$	−510.494	+	328.075i	−1.32305	+	0.850274i	−0.327534	+	0.944840i	$0.606217\pi$
$54$	−22.4324	−	49.1201i	−0.0565308	−	0.123785i
$55$	67.5260	+	77.9292i	0.165549	+	0.191054i
$56$	−177.839	−	114.290i	−0.424370	−	0.272726i
$57$	48.1778	−	335.084i	0.111953	−	0.778648i
$58$	10.3727	−	72.1436i	0.0234828	−	0.163326i
$59$	−279.360	−	179.534i	−0.616434	−	0.396158i	0.194831	−	0.980837i	$-0.437584\pi$
$59$	−279.360	−	179.534i	−0.616434	−	0.396158i	−0.811265	+	0.584679i	$0.801221\pi$
$60$	−32.3825	−	37.3714i	−0.0696761	−	0.0804105i
$61$	−345.892	−	757.399i	−0.726016	−	1.58975i	−0.805277	−	0.592899i	$-0.797983\pi$
$61$	−345.892	−	757.399i	−0.726016	−	1.58975i	0.0792606	−	0.996854i	$-0.474744\pi$
$62$	221.989	−	142.664i	0.454719	−	0.292230i
$63$	−228.189	−	67.0023i	−0.456335	−	0.133992i
$64$	−41.9111	+	48.3680i	−0.0818576	+	0.0944687i
$65$	−206.089	+	60.5132i	−0.393264	+	0.115473i
$66$	62.3700	−	136.571i	0.116321	−	0.254708i
$67$	−15.7755	−	109.721i	−0.0287653	−	0.200067i	0.970371	−	0.241620i	$-0.0776787\pi$
$67$	−15.7755	−	109.721i	−0.0287653	−	0.200067i	−0.999136	+	0.0415525i	$0.986770\pi$
$68$	−51.3610			−0.0915947
$69$	−165.615	−	286.487i	−0.288953	−	0.499840i
$70$	−217.781			−0.371855
$71$	135.007	+	938.991i	0.225667	+	1.56955i	0.716056	+	0.698043i	$0.245945\pi$
$71$	135.007	+	938.991i	0.225667	+	1.56955i	−0.490389	+	0.871503i	$0.663145\pi$
$72$	−29.9099	+	65.4935i	−0.0489571	+	0.107201i
$73$	147.933	−	43.4371i	0.237182	−	0.0696428i	−0.160982	−	0.986957i	$-0.551466\pi$
$73$	147.933	−	43.4371i	0.237182	−	0.0696428i	0.398163	+	0.917315i	$0.369648\pi$
$74$	−182.560	+	210.686i	−0.286787	+	0.330970i
$75$	310.931	+	91.2975i	0.478709	+	0.140562i
$76$	−379.719	+	244.031i	−0.573115	+	0.368319i
$77$	−274.685	−	601.475i	−0.406535	−	0.890188i
$78$	204.801	+	236.353i	0.297297	+	0.343099i
$79$	−290.607	−	186.762i	−0.413872	−	0.265979i	0.317093	−	0.948394i	$-0.397293\pi$
$79$	−290.607	−	186.762i	−0.413872	−	0.265979i	−0.730965	+	0.682415i	$0.760930\pi$
$80$	−9.38319	+	65.2615i	−0.0131134	+	0.0912057i
$81$	−11.5275	+	80.1755i	−0.0158128	+	0.109980i
$82$	−294.005	−	188.946i	−0.395944	−	0.254458i
$83$	552.940	+	638.127i	0.731242	+	0.843898i	0.992611	−	0.121341i	$-0.0387193\pi$
$83$	552.940	+	638.127i	0.731242	+	0.843898i	−0.261369	+	0.965239i	$0.584174\pi$
$84$	131.727	+	288.441i	0.171102	+	0.374661i
$85$	−44.5124	+	28.6064i	−0.0568005	+	0.0365035i
$86$	242.516	+	71.2092i	0.304084	+	0.0892871i
$87$	−71.5948	+	82.6248i	−0.0882272	+	0.101820i
$88$	−192.076	+	56.3987i	−0.232675	+	0.0683196i
$89$	493.722	−	1081.10i	0.588027	−	1.28760i	−0.348600	−	0.937272i	$-0.613343\pi$
$89$	493.722	−	1081.10i	0.588027	−	1.28760i	0.936627	−	0.350328i	$-0.113930\pi$
$90$	10.5561	+	73.4192i	0.0123634	+	0.0859896i
$91$	1377.35			1.58665
$92$	−144.076	+	417.030i	−0.163272	+	0.472591i
$93$	−395.818			−0.441338
$94$	−86.5931	−	602.269i	−0.0950149	−	0.660843i
$95$	−193.169	+	422.982i	−0.208618	+	0.456810i
$96$	92.1113	−	27.0463i	0.0979278	−	0.0287542i
$97$	−743.252	+	857.758i	−0.777998	+	0.897857i	−0.996963	−	0.0778754i	$-0.975186\pi$
$97$	−743.252	+	857.758i	−0.777998	+	0.897857i	0.218965	+	0.975733i	$0.429732\pi$
$98$	681.748	+	200.179i	0.702724	+	0.206339i
$99$	−189.457	+	121.757i	−0.192335	+	0.123606i
$100$	−179.491	−	393.031i	−0.179491	−	0.393031i
$101$	272.570	+	314.562i	0.268532	+	0.309902i	0.873960	−	0.485998i	$-0.161544\pi$
$101$	272.570	+	314.562i	0.268532	+	0.309902i	−0.605429	+	0.795900i	$0.706998\pi$
$102$	64.8114	+	41.6518i	0.0629146	+	0.0404328i
$103$	−230.347	+	1602.10i	−0.220357	+	1.53262i	0.516332	+	0.856388i	$0.327297\pi$
$103$	−230.347	+	1602.10i	−0.220357	+	1.53262i	−0.736690	+	0.676231i	$0.763612\pi$
$104$	59.3435	−	412.743i	0.0559529	−	0.389161i
$105$	274.814	+	176.612i	0.255420	+	0.164148i
$106$	−794.773	−	917.216i	−0.728256	−	0.840452i
$107$	−171.578	−	375.702i	−0.155019	−	0.339444i	0.816149	−	0.577842i	$-0.196105\pi$
$107$	−171.578	−	375.702i	−0.155019	−	0.339444i	−0.971168	+	0.238398i	$0.923378\pi$
$108$	90.8554	−	58.3892i	0.0809497	−	0.0520232i
$109$	1283.25	+	376.797i	1.12764	+	0.331106i	0.791781	−	0.610805i	$-0.209154\pi$
$109$	1283.25	+	376.797i	1.12764	+	0.331106i	0.335863	+	0.941911i	$0.390972\pi$
$110$	−135.052	+	155.858i	−0.117061	+	0.135096i
$111$	401.228	−	117.811i	0.343089	−	0.100740i
$112$	175.635	−	384.588i	0.148179	−	0.324466i
$113$	306.491	+	2131.69i	0.255152	+	1.77462i	0.566239	+	0.824241i	$0.308398\pi$
$113$	306.491	+	2131.69i	0.255152	+	1.77462i	−0.311086	+	0.950382i	$0.600693\pi$
$114$	677.059			0.556249
$115$	107.407	+	441.668i	0.0870937	+	0.358137i
$116$	145.771			0.116677
$117$	−66.7614	−	464.336i	−0.0527529	−	0.366905i
$118$	275.899	−	604.134i	0.215242	−	0.471314i
$119$	325.556	−	95.5918i	0.250787	−	0.0736377i
$120$	64.7650	−	74.7428i	0.0492684	−	0.0568588i
$121$	676.291	+	198.577i	0.508107	+	0.149194i
$122$	1400.93	−	900.321i	1.03962	−	0.668125i
$123$	217.772	+	476.853i	0.159641	+	0.349564i
$124$	345.607	+	398.852i	0.250294	+	0.288855i
$125$	−807.790	−	519.135i	−0.578008	−	0.371463i
$126$	67.6913	−	470.803i	0.0478605	−	0.332877i
$127$	43.7551	−	304.323i	0.0305719	−	0.212632i	−0.968809	−	0.247808i	$-0.920290\pi$
$127$	43.7551	−	304.323i	0.0305719	−	0.212632i	0.999381	+	0.0351753i	$0.0111990\pi$
$128$	−107.680	−	69.2020i	−0.0743570	−	0.0477863i
$129$	−248.279	−	286.529i	−0.169455	−	0.195562i
$130$	−178.454	−	390.759i	−0.120395	−	0.263629i
$131$	−1225.58	+	787.634i	−0.817402	+	0.525312i	−0.881252	−	0.472647i	$-0.843299\pi$
$131$	−1225.58	+	787.634i	−0.817402	+	0.525312i	0.0638497	+	0.997960i	$0.479662\pi$
$132$	288.114	+	84.5980i	0.189978	+	0.0557827i
$133$	1952.70	−	2253.53i	1.27308	−	1.46922i
$134$	212.718	−	62.4595i	0.137134	−	0.0402663i
$135$	46.2196	−	101.207i	0.0294663	−	0.0645222i
$136$	−14.6189	−	101.676i	−0.00921733	−	0.0641080i
$137$	117.173			0.0730715			0.0365358	−	0.999332i	$-0.488368\pi$
$137$	117.173			0.0730715			0.0365358	+	0.999332i	$0.488368\pi$
$138$	520.002	−	409.402i	0.320765	−	0.252541i
$139$	−1165.13			−0.710972			−0.355486	−	0.934682i	$-0.615685\pi$
$139$	−1165.13			−0.710972			−0.355486	+	0.934682i	$0.615685\pi$
$140$	−61.9870	−	431.129i	−0.0374204	−	0.260265i
$141$	−379.146	+	830.214i	−0.226453	+	0.495863i
$142$	−1820.44	+	534.530i	−1.07583	+	0.315892i
$143$	854.129	−	985.718i	0.499482	−	0.576433i
$144$	−138.167	−	40.5695i	−0.0799577	−	0.0234777i
$145$	126.333	−	81.1896i	0.0723546	−	0.0464995i
$146$	128.096	+	280.491i	0.0726116	+	0.158997i
$147$	−697.947	−	805.474i	−0.391604	−	0.451935i
$148$	−469.045	−	301.437i	−0.260509	−	0.167419i
$149$	236.016	−	1641.53i	0.129767	−	0.902546i	−0.816081	−	0.577937i	$-0.803858\pi$
$149$	236.016	−	1641.53i	0.129767	−	0.902546i	0.945848	−	0.324610i	$-0.105233\pi$
$150$	−92.2363	+	641.518i	−0.0502071	+	0.349198i
$151$	3036.84	+	1951.66i	1.63665	+	1.05181i	0.943684	+	0.330847i	$0.107334\pi$
$151$	3036.84	+	1951.66i	1.63665	+	1.05181i	0.692970	+	0.720967i	$0.256302\pi$
$152$	−591.173	−	682.250i	−0.315463	−	0.364064i
$153$	−48.0063	−	105.119i	−0.0253665	−	0.0555450i
$154$	1112.52	−	714.975i	0.582141	−	0.374119i
$155$	521.670	+	153.176i	0.270333	+	0.0793769i
$156$	−409.603	+	472.707i	−0.210221	+	0.242608i
$157$	−2724.38	+	799.950i	−1.38490	+	0.406643i	−0.887471	−	0.460863i	$-0.847540\pi$
$157$	−2724.38	+	799.950i	−1.38490	+	0.406643i	−0.497427	+	0.867506i	$0.665722\pi$
$158$	287.007	−	628.457i	0.144513	−	0.316439i
$159$	259.081	+	1801.95i	0.129223	+	0.898765i
$160$	−131.865			−0.0651554
$161$	137.072	−	2911.53i	0.0670983	−	1.42522i
$162$	−162.000			−0.0785674
$163$	21.5502	+	149.885i	0.0103555	+	0.0720238i	0.994344	−	0.106209i	$-0.0338712\pi$
$163$	21.5502	+	149.885i	0.0103555	+	0.0720238i	−0.983988	+	0.178233i	$0.942962\pi$
$164$	290.362	−	635.804i	0.138253	−	0.302732i
$165$	296.815	−	87.1527i	0.140042	−	0.0411202i
$166$	−1105.88	+	1276.25i	−0.517066	+	0.596726i
$167$	425.938	+	125.067i	0.197365	+	0.0579517i	0.378921	−	0.925429i	$-0.376295\pi$
$167$	425.938	+	125.067i	0.197365	+	0.0579517i	−0.181556	+	0.983381i	$0.558113\pi$
$168$	−533.517	+	342.871i	−0.245010	+	0.157459i
$169$	215.953	+	472.871i	0.0982944	+	0.215235i
$170$	−69.2999	−	79.9764i	−0.0312651	−	0.0360818i
$171$	−854.368	−	549.069i	−0.382077	−	0.245546i
$172$	−71.9415	+	500.364i	−0.0318924	+	0.221816i
$173$	123.288	−	857.486i	0.0541815	−	0.376841i	−0.944632	−	0.328133i	$-0.893581\pi$
$173$	123.288	−	857.486i	0.0541815	−	0.376841i	0.998813	−	0.0487077i	$-0.0155103\pi$
$174$	−183.946	−	118.215i	−0.0801430	−	0.0515048i
$175$	1869.22	+	2157.19i	0.807426	+	0.931819i
$176$	−166.320	−	364.190i	−0.0712320	−	0.155976i
$177$	−838.081	+	538.602i	−0.355898	+	0.228722i
$178$	2280.72	+	669.680i	0.960377	+	0.281992i
$179$	187.608	−	216.512i	0.0783380	−	0.0904069i	−0.715227	−	0.698892i	$-0.753677\pi$
$179$	187.608	−	216.512i	0.0783380	−	0.0904069i	0.793565	+	0.608485i	$0.208222\pi$
$180$	−142.339	+	41.7946i	−0.0589408	+	0.0173066i
$181$	−805.031	+	1762.77i	−0.330594	+	0.723899i	−0.999816	−	0.0191626i	$-0.993900\pi$
$181$	−805.031	+	1762.77i	−0.330594	+	0.723899i	0.669223	+	0.743062i	$0.266627\pi$
$182$	392.033	+	2726.65i	0.159667	+	1.11051i
$183$	−2497.93			−1.00903
$184$	−866.579	−	166.520i	−0.347201	−	0.0667176i
$185$	−574.392			−0.228271
$186$	−112.662	−	783.578i	−0.0444126	−	0.308896i
$187$	133.474	−	292.268i	0.0521958	−	0.114293i
$188$	1167.63	−	342.847i	0.452969	−	0.133004i
$189$	−467.222	+	539.202i	−0.179817	+	0.207520i
$190$	−892.334	−	262.013i	−0.340720	−	0.100044i
$191$	−1369.51	+	880.128i	−0.518817	+	0.333423i	−0.773704	−	0.633548i	$-0.781598\pi$
$191$	−1369.51	+	880.128i	−0.518817	+	0.333423i	0.254887	+	0.966971i	$0.417962\pi$
$192$	79.7597	+	174.649i	0.0299800	+	0.0656470i
$193$	−2887.16	−	3331.96i	−1.07680	−	1.24269i	−0.968616	−	0.248563i	$-0.920042\pi$
$193$	−2887.16	−	3331.96i	−1.07680	−	1.24269i	−0.108185	−	0.994131i	$-0.534504\pi$
$194$	−1909.61	−	1227.23i	−0.706710	−	0.454175i
$195$	−91.7032	+	637.810i	−0.0336769	+	0.234228i
$196$	−202.238	+	1406.60i	−0.0737019	+	0.512608i
$197$	−468.009	−	300.771i	−0.169260	−	0.108777i	0.453268	−	0.891374i	$-0.350258\pi$
$197$	−468.009	−	300.771i	−0.169260	−	0.108777i	−0.622528	+	0.782597i	$0.713894\pi$
$198$	−294.960	−	340.402i	−0.105868	−	0.122178i
$199$	1514.25	+	3315.74i	0.539407	+	1.18114i	0.961556	+	0.274610i	$0.0885488\pi$
$199$	1514.25	+	3315.74i	0.539407	+	1.18114i	−0.422149	+	0.906527i	$0.638724\pi$
$200$	726.972	−	467.196i	0.257023	−	0.165179i
$201$	−319.076	−	93.6893i	−0.111970	−	0.0328773i
$202$	−545.139	+	629.124i	−0.189880	+	0.219134i
$203$	−923.981	+	271.305i	−0.319462	+	0.0938025i
$204$	−64.0084	+	140.159i	−0.0219681	+	0.0481033i
$205$	−102.477	−	712.746i	−0.0349138	−	0.242831i
$206$	−3237.15			−1.09487
$207$	−988.189	+	94.9145i	−0.331806	+	0.0318696i
$208$	833.974			0.278008
$209$	−401.853	−	2794.95i	−0.132999	−	0.925028i
$210$	−271.409	+	594.302i	−0.0891856	+	0.195289i
$211$	−4424.96	+	1299.29i	−1.44373	+	0.423917i	−0.907463	−	0.420132i	$-0.861984\pi$
$211$	−4424.96	+	1299.29i	−1.44373	+	0.423917i	−0.536266	+	0.844049i	$0.680166\pi$
$212$	1589.55	−	1834.43i	0.514955	−	0.594289i
$213$	2730.66	+	801.795i	0.878412	+	0.257925i
$214$	694.920	−	446.598i	0.221980	−	0.142658i
$215$	216.338	+	473.713i	0.0686237	+	0.150265i
$216$	141.450	+	163.242i	0.0445576	+	0.0514222i
$217$	−2932.99	−	1884.92i	−0.917533	−	0.589662i
$218$	−380.671	+	2647.63i	−0.118267	+	0.822568i
$219$	65.8256	−	457.827i	0.0203109	−	0.141265i
$220$	−346.984	−	222.993i	−0.106335	−	0.0683372i
$221$	438.284	+	505.806i	0.133403	+	0.153956i
$222$	347.425	+	760.755i	0.105034	+	0.229993i
$223$	3470.58	−	2230.40i	1.04218	−	0.669771i	0.0966580	−	0.995318i	$-0.469185\pi$
$223$	3470.58	−	2230.40i	1.04218	−	0.669771i	0.945526	+	0.325547i	$0.105548\pi$
$224$	811.338	+	238.230i	0.242008	+	0.0710600i
$225$	636.637	−	734.719i	0.188633	−	0.217694i
$226$	−4132.75	+	1213.48i	−1.21640	+	0.357167i
$227$	526.438	−	1152.74i	0.153925	−	0.337048i	−0.816922	−	0.576748i	$-0.804322\pi$
$227$	526.438	−	1152.74i	0.153925	−	0.337048i	0.970847	+	0.239699i	$0.0770489\pi$
$228$	192.711	+	1340.34i	0.0559764	+	0.389324i
$229$	−2337.38			−0.674490			−0.337245	−	0.941417i	$-0.609495\pi$
$229$	−2337.38			−0.674490			−0.337245	+	0.941417i	$0.609495\pi$
$230$	−843.773	+	338.340i	−0.241899	+	0.0969976i
$231$	−1983.69			−0.565009
$232$	41.4908	+	288.575i	0.0117414	+	0.0816631i
$233$	2241.29	−	4907.74i	0.630179	−	1.37990i	−0.277700	−	0.960668i	$-0.589572\pi$
$233$	2241.29	−	4907.74i	0.630179	−	1.37990i	0.907879	−	0.419232i	$-0.137701\pi$
$234$	900.217	−	264.327i	0.251491	−	0.0738446i
$235$	820.980	−	947.461i	0.227893	−	0.263002i
$236$	1274.50	+	374.227i	0.351537	+	0.103221i
$237$	−871.822	+	560.286i	−0.238949	+	0.153563i
$238$	281.901	+	617.276i	0.0767769	+	0.168118i
$239$	−4561.12	−	5263.81i	−1.23445	−	1.42463i	−0.869737	−	0.493515i	$-0.835712\pi$
$239$	−4561.12	−	5263.81i	−1.23445	−	1.42463i	−0.364715	−	0.931119i	$-0.618834\pi$
$240$	166.398	+	106.938i	0.0447540	+	0.0287616i
$241$	−218.516	+	1519.81i	−0.0584060	+	0.406223i	0.939555	+	0.342398i	$0.111239\pi$
$241$	−218.516	+	1519.81i	−0.0584060	+	0.406223i	−0.997961	+	0.0638249i	$0.979670\pi$
$242$	−200.619	+	1395.33i	−0.0532904	+	0.370643i
$243$	204.425	+	131.376i	0.0539664	+	0.0346821i
$244$	2181.06	+	2517.08i	0.572246	+	0.660407i
$245$	608.156	+	1331.68i	0.158586	+	0.347256i
$246$	−882.015	+	566.837i	−0.228598	+	0.146911i
$247$	5643.52	+	1657.09i	1.45380	+	0.426874i
$248$	−691.215	+	797.705i	−0.176985	+	0.204251i
$249$	2430.48	−	713.654i	0.618577	−	0.181630i
$250$	797.782	−	1746.90i	0.201825	−	0.441934i
$251$	264.719	+	1841.16i	0.0665694	+	0.463000i	0.995654	+	0.0931323i	$0.0296880\pi$
$251$	264.719	+	1841.16i	0.0665694	+	0.463000i	−0.929084	+	0.369868i	$0.879403\pi$
$252$	951.289			0.237800
$253$	−1998.68	−	1903.62i	−0.496663	−	0.473041i
$254$	614.905			0.151900
$255$	22.5905	+	157.120i	0.00554773	+	0.0385853i
$256$	106.346	−	232.866i	0.0259634	−	0.0568520i
$257$	5130.43	−	1506.43i	1.24524	−	0.365636i	0.408260	−	0.912866i	$-0.366136\pi$
$257$	5130.43	−	1506.43i	1.24524	−	0.365636i	0.836982	+	0.547230i	$0.184318\pi$
$258$	496.558	−	573.058i	0.119823	−	0.138283i
$259$	3534.11	+	1037.71i	0.847872	+	0.248958i
$260$	722.770	−	464.496i	0.172401	−	0.110795i
$261$	136.250	+	298.345i	0.0323128	+	0.0707552i
$262$	−1908.07	−	2202.03i	−0.449928	−	0.519244i
$263$	−1128.50	−	725.244i	−0.264587	−	0.170040i	0.401620	−	0.915806i	$-0.368447\pi$
$263$	−1128.50	−	725.244i	−0.264587	−	0.170040i	−0.666208	+	0.745766i	$0.732084\pi$
$264$	−85.4680	+	594.443i	−0.0199250	+	0.138581i
$265$	355.872	−	2475.15i	0.0824946	−	0.573763i
$266$	5016.98	+	3224.22i	1.15643	+	0.743194i
$267$	−2334.91	−	2694.63i	−0.535184	−	0.617636i
$268$	184.193	+	403.327i	0.0419828	+	0.0919296i
$269$	−2198.27	+	1412.74i	−0.498256	+	0.320210i	−0.765518	−	0.643414i	$-0.777517\pi$
$269$	−2198.27	+	1412.74i	−0.498256	+	0.320210i	0.267262	+	0.963624i	$0.413881\pi$
$270$	213.509	+	62.6918i	0.0481249	+	0.0141308i
$271$	−160.503	+	185.231i	−0.0359775	+	0.0415202i	−0.773453	−	0.633854i	$-0.781472\pi$
$271$	−160.503	+	185.231i	−0.0359775	+	0.0415202i	0.737476	+	0.675374i	$0.236018\pi$
$272$	197.122	−	57.8803i	0.0439422	−	0.0129026i
$273$	1716.51	−	3758.63i	0.380542	−	0.833270i
$274$	33.3510	+	231.961i	0.00735332	+	0.0511434i
$275$	2702.98			0.592712
$276$	958.477	+	912.891i	0.209035	+	0.199093i
$277$	−1295.80			−0.281073			−0.140537	−	0.990075i	$-0.544883\pi$
$277$	−1295.80			−0.281073			−0.140537	+	0.990075i	$0.544883\pi$
$278$	−331.631	−	2306.54i	−0.0715464	−	0.497616i
$279$	−493.286	+	1080.15i	−0.105850	+	0.231780i
$280$	835.838	−	245.424i	0.178396	−	0.0523818i
$281$	−1556.81	+	1796.66i	−0.330504	+	0.381422i	−0.896543	−	0.442957i	$-0.853930\pi$
$281$	−1556.81	+	1796.66i	−0.330504	+	0.381422i	0.566039	+	0.824378i	$0.308475\pi$
$282$	−1751.44	−	514.270i	−0.369847	−	0.108597i
$283$	33.4460	−	21.4945i	0.00702530	−	0.00451488i	−0.537123	−	0.843504i	$-0.680489\pi$
$283$	33.4460	−	21.4945i	0.00702530	−	0.00451488i	0.544149	+	0.838989i	$0.316853\pi$
$284$	−1576.33	−	3451.68i	−0.329359	−	0.721195i
$285$	913.537	+	1054.28i	0.189871	+	0.219123i
$286$	2194.48	+	1410.31i	0.453714	+	0.291585i
$287$	−657.140	+	4570.51i	−0.135156	+	0.940030i
$288$	40.9867	−	285.069i	0.00838598	−	0.0583258i
$289$	−3994.38	−	2567.03i	−0.813022	−	0.522498i
$290$	196.685	+	226.986i	0.0398266	+	0.0459624i
$291$	1414.46	+	3097.23i	0.284938	+	0.623928i
$292$	−518.812	+	333.420i	−0.103977	+	0.0668218i
$293$	8574.97	+	2517.84i	1.70975	+	0.502026i	0.982801	−	0.184670i	$-0.0591215\pi$
$293$	8574.97	+	2517.84i	1.70975	+	0.502026i	0.726945	+	0.686696i	$0.240940\pi$
$294$	1395.89	−	1610.95i	0.276905	−	0.319566i
$295$	1312.99	−	385.527i	0.259136	−	0.0760890i
$296$	463.234	−	1014.34i	0.0909625	−	0.199180i
$297$	96.1515	+	668.748i	0.0187854	+	0.130656i
$298$	3316.82			0.644759
$299$	5336.39	−	2139.81i	1.03215	−	0.413874i
$300$	−1296.23			−0.249459
$301$	−475.258	−	3305.49i	−0.0910081	−	0.632975i
$302$	−2999.22	+	6567.37i	−0.571475	+	1.25136i
$303$	1198.10	−	351.793i	0.227158	−	0.0666995i
$304$	1182.35	−	1364.50i	0.223066	−	0.257432i
$305$	3292.16	+	966.665i	0.618061	+	0.181479i
$306$	194.434	−	124.955i	0.0363238	−	0.0233439i
$307$	−3042.47	−	6662.08i	−0.565613	−	1.23852i	−0.949101	−	0.314973i	$-0.898005\pi$
$307$	−3042.47	−	6662.08i	−0.565613	−	1.23852i	0.383488	−	0.923546i	$-0.374723\pi$
$308$	1732.05	+	1998.90i	0.320431	+	0.369798i
$309$	4084.90	+	2625.21i	0.752045	+	0.483310i
$310$	−154.751	+	1076.32i	−0.0283525	+	0.197196i
$311$	−849.104	+	5905.65i	−0.154818	+	1.07678i	0.753183	+	0.657811i	$0.228518\pi$
$311$	−849.104	+	5905.65i	−0.154818	+	1.07678i	−0.908000	+	0.418969i	$0.862392\pi$
$312$	−1052.38	−	676.321i	−0.190958	−	0.122722i
$313$	3173.58	+	3662.51i	0.573103	+	0.661397i	0.966107	−	0.258140i	$-0.0831096\pi$
$313$	3173.58	+	3662.51i	0.573103	+	0.661397i	−0.393004	+	0.919537i	$0.628564\pi$
$314$	−2359.05	−	5165.61i	−0.423978	−	0.928382i
$315$	824.441	−	529.836i	0.147467	−	0.0947711i
$316$	1325.81	+	389.293i	0.236021	+	0.0693021i
$317$	−4309.88	+	4973.87i	−0.763619	+	0.881263i	−0.995814	−	0.0914065i	$-0.970864\pi$
$317$	−4309.88	+	4973.87i	−0.763619	+	0.881263i	0.232195	+	0.972669i	$0.425409\pi$
$318$	−3493.47	+	1025.78i	−0.616050	+	0.180889i
$319$	−378.822	+	829.505i	−0.0664889	+	0.145590i
$320$	−37.5328	−	261.046i	−0.00655670	−	0.0456029i
$321$	−1239.08			−0.215448
$322$	5802.80	−	557.353i	1.00428	−	0.0964598i
$323$	1448.94			0.249600
$324$	−46.1100	−	320.702i	−0.00790638	−	0.0549901i
$325$	−2338.92	+	5121.52i	−0.399200	+	0.874126i
$326$	−290.585	+	85.3233i	−0.0493681	+	0.0144958i
$327$	2627.48	−	3032.28i	0.444343	−	0.512799i
$328$	1341.31	+	393.844i	0.225797	+	0.0663001i
$329$	−6763.01	+	4346.33i	−1.13330	+	0.728330i
$330$	257.013	+	562.781i	0.0428731	+	0.0938790i
$331$	−6289.17	−	7258.09i	−1.04436	−	1.20526i	−0.978246	−	0.207448i	$-0.933484\pi$
$331$	−6289.17	−	7258.09i	−1.04436	−	1.20526i	−0.0661171	−	0.997812i	$-0.521061\pi$
$332$	−2841.29	−	1825.99i	−0.469688	−	0.301850i
$333$	178.534	−	1241.73i	0.0293802	−	0.204344i
$334$	−126.353	+	878.802i	−0.0206997	+	0.143970i
$335$	384.272	+	246.957i	0.0626717	+	0.0402767i
$336$	−830.616	−	958.582i	−0.134863	−	0.155640i
$337$	−2321.91	−	5084.28i	−0.375320	−	0.821835i	−0.999187	−	0.0403053i	$-0.987167\pi$
$337$	−2321.91	−	5084.28i	−0.375320	−	0.821835i	0.623868	−	0.781530i	$-0.285560\pi$
$338$	−874.649	+	562.103i	−0.140753	+	0.0904566i
$339$	6199.12	+	1820.23i	0.993186	+	0.291626i
$340$	138.600	−	159.953i	0.0221077	−	0.0255137i
$341$	−3167.80	+	930.151i	−0.503068	+	0.147714i
$342$	843.782	−	1847.62i	0.133411	−	0.292129i
$343$	−46.1239	−	320.799i	−0.00726081	−	0.0505000i
$344$	−1011.02			−0.158461
$345$	1339.12	+	257.323i	0.208973	+	0.0401560i
$346$	1732.61			0.269207
$347$	−1201.48	−	8356.49i	−0.185876	−	1.29280i	−0.842549	−	0.538620i	$-0.818946\pi$
$347$	−1201.48	−	8356.49i	−0.185876	−	1.29280i	0.656673	−	0.754176i	$-0.271963\pi$
$348$	181.666	−	397.794i	0.0279837	−	0.0612758i
$349$	−912.841	+	268.034i	−0.140009	+	0.0411104i	−0.350986	−	0.936381i	$-0.614154\pi$
$349$	−912.841	+	268.034i	−0.140009	+	0.0411104i	0.210977	+	0.977491i	$0.432335\pi$
$350$	−3738.43	+	4314.38i	−0.570936	+	0.658896i
$351$	−1350.32	−	396.491i	−0.205342	−	0.0602938i
$352$	673.626	−	432.913i	0.102001	−	0.0655521i
$353$	2383.49	+	5219.12i	0.359378	+	0.786929i	0.999821	+	0.0189227i	$0.00602363\pi$
$353$	2383.49	+	5219.12i	0.359378	+	0.786929i	−0.640443	+	0.768006i	$0.721249\pi$
$354$	−1304.78	−	1505.80i	−0.195899	−	0.226080i
$355$	−3288.61	−	2113.46i	−0.491665	−	0.315974i
$356$	−676.566	+	4705.62i	−0.100725	+	0.700555i
$357$	144.862	−	1007.54i	0.0214760	−	0.149369i
$358$	482.014	+	309.772i	0.0711599	+	0.0457317i
$359$	−454.921	−	525.007i	−0.0668797	−	0.0771833i	0.721324	−	0.692598i	$-0.243534\pi$
$359$	−454.921	−	525.007i	−0.0668797	−	0.0771833i	−0.788203	+	0.615415i	$0.788989\pi$
$360$	−123.252	−	269.885i	−0.0180443	−	0.0395116i
$361$	4942.02	−	3176.04i	0.720516	−	0.463048i
$362$	−3718.79	−	1091.94i	−0.539932	−	0.158538i
$363$	1384.72	−	1598.05i	0.200217	−	0.231063i
$364$	−5286.21	+	1552.17i	−0.761189	+	0.223505i
$365$	−263.928	+	577.922i	−0.0378483	+	0.0828762i
$366$	−710.985	−	4945.01i	−0.101540	−	0.706229i
$367$	10997.7			1.56424			0.782119	−	0.623128i	$-0.214139\pi$
$367$	10997.7			1.56424			0.782119	+	0.623128i	$0.214139\pi$
$368$	82.9966	−	1762.91i	0.0117568	−	0.249723i
$369$	1572.68			0.221871
$370$	−163.489	−	1137.09i	−0.0229713	−	0.159769i
$371$	−6661.26	+	14586.1i	−0.932170	+	2.04117i
$372$	1519.14	−	446.059i	0.211730	−	0.0621696i
$373$	−7154.95	+	8257.25i	−0.993215	+	1.14623i	−0.00396543	+	0.999992i	$0.501262\pi$
$373$	−7154.95	+	8257.25i	−0.993215	+	1.14623i	−0.989249	+	0.146239i	$0.953283\pi$
$374$	616.577	+	181.043i	0.0852472	+	0.0250308i
$375$	−2423.37	+	1557.41i	−0.333713	+	0.214464i
$376$	1011.06	+	2213.91i	0.138674	+	0.303653i
$377$	−1243.92	−	1435.56i	−0.169934	−	0.196115i
$378$	−1200.41	−	771.459i	−0.163340	−	0.104972i
$379$	−914.422	+	6359.94i	−0.123933	+	0.861975i	0.829098	+	0.559103i	$0.188854\pi$
$379$	−914.422	+	6359.94i	−0.123933	+	0.861975i	−0.953031	+	0.302872i	$0.902055\pi$
$380$	264.707	−	1841.08i	0.0357347	−	0.248541i
$381$	−775.937	−	498.664i	−0.104337	−	0.0670534i
$382$	−2132.14	−	2460.62i	−0.285575	−	0.329572i
$383$	−720.605	−	1577.91i	−0.0961389	−	0.210515i	0.855452	−	0.517882i	$-0.173279\pi$
$383$	−720.605	−	1577.91i	−0.0961389	−	0.210515i	−0.951591	+	0.307367i	$0.900552\pi$
$384$	−323.041	+	207.606i	−0.0429300	+	0.0275895i
$385$	2614.41	+	767.661i	0.346085	+	0.101620i
$386$	5774.32	−	6663.92i	0.761413	−	0.878717i
$387$	−1091.32	+	320.442i	−0.143347	+	0.0420903i
$388$	1885.95	−	4129.64i	0.246764	−	0.540337i
$389$	757.360	+	5267.55i	0.0987138	+	0.686569i	0.977744	+	0.209803i	$0.0672822\pi$
$389$	757.360	+	5267.55i	0.0987138	+	0.686569i	−0.879030	+	0.476767i	$0.841809\pi$
$390$	−1288.74			−0.167327
$391$	1112.83	−	876.137i	0.143934	−	0.113320i
$392$	−2842.12			−0.366196
$393$	621.995	+	4326.07i	0.0798359	+	0.555271i
$394$	462.210	−	1012.10i	0.0591010	−	0.129413i
$395$	1365.85	−	401.049i	0.173983	−	0.0510859i
$396$	589.921	−	680.805i	0.0748602	−	0.0863932i
$397$	4543.17	+	1333.99i	0.574345	+	0.168643i	0.555991	−	0.831189i	$-0.312339\pi$
$397$	4543.17	+	1333.99i	0.574345	+	0.168643i	0.0183546	+	0.999832i	$0.494157\pi$
$398$	−6132.97	+	3941.42i	−0.772407	+	0.496396i
$399$	−3716.11	−	8137.15i	−0.466262	−	1.02097i
$400$	1131.80	+	1306.17i	0.141475	+	0.163271i
$401$	−1555.76	−	999.829i	−0.193744	−	0.124511i	0.440173	−	0.897913i	$-0.354917\pi$
$401$	−1555.76	−	999.829i	−0.193744	−	0.124511i	−0.633916	+	0.773402i	$0.718554\pi$
$402$	94.6527	−	658.324i	0.0117434	−	0.0816772i
$403$	978.717	−	6807.12i	0.120976	−	0.841407i
$404$	−1400.60	−	900.113i	−0.172482	−	0.110847i
$405$	−218.582	−	252.257i	−0.0268183	−	0.0309500i
$406$	−800.080	−	1751.93i	−0.0978012	−	0.214155i
$407$	2934.25	−	1885.73i	0.357359	−	0.229661i
$408$	−295.683	−	86.8204i	−0.0358787	−	0.0105349i
$409$	−8658.42	+	9992.35i	−1.04678	+	1.20804i	−0.0691694	+	0.997605i	$0.522035\pi$
$409$	−8658.42	+	9992.35i	−1.04678	+	1.20804i	−0.977607	+	0.210439i	$0.932511\pi$
$410$	1381.81	−	405.737i	0.166446	−	0.0488730i
$411$	146.027	−	319.754i	0.0175255	−	0.0383754i
$412$	−921.390	−	6408.41i	−0.110179	−	0.766310i
$413$	−8775.02			−1.04550
$414$	−469.165	−	1929.25i	−0.0556961	−	0.229027i
$415$	−3479.44			−0.411564
$416$	237.374	+	1650.97i	0.0279765	+	0.194581i
$417$	−1452.04	+	3179.52i	−0.170520	+	0.373386i
$418$	5418.63	−	1591.05i	0.634052	−	0.186174i
$419$	−3622.97	+	4181.13i	−0.422419	+	0.487498i	−0.926572	−	0.376117i	$-0.877259\pi$
$419$	−3622.97	+	4181.13i	−0.422419	+	0.487498i	0.504153	+	0.863614i	$0.331805\pi$
$420$	−1253.76	−	368.136i	−0.145660	−	0.0427696i
$421$	−5682.70	+	3652.05i	−0.657857	+	0.422779i	−0.826530	−	0.562893i	$-0.809688\pi$
$421$	−5682.70	+	3652.05i	−0.657857	+	0.422779i	0.168673	+	0.985672i	$0.446052\pi$
$422$	−3831.60	−	8390.03i	−0.441989	−	0.967820i
$423$	1793.06	+	2069.30i	0.206103	+	0.237855i
$424$	4083.95	+	2624.60i	0.467770	+	0.300617i
$425$	−197.390	+	1372.87i	−0.0225289	+	0.156692i
$426$	−810.040	+	5633.95i	−0.0921280	+	0.640765i
$427$	−18509.5	−	11895.4i	−2.09775	−	1.34814i
$428$	1081.90	+	1248.58i	0.122186	+	0.141010i
$429$	−1625.47	−	3559.28i	−0.182933	−	0.400568i
$430$	−876.207	+	563.104i	−0.0982661	+	0.0631518i
$431$	9195.93	+	2700.17i	1.02773	+	0.301769i	0.751788	−	0.659405i	$-0.229192\pi$
$431$	9195.93	+	2700.17i	1.02773	+	0.301769i	0.275943	+	0.961174i	$0.411010\pi$
$432$	−282.900	+	326.484i	−0.0315070	+	0.0363610i
$433$	4690.28	−	1377.19i	0.520555	−	0.152849i	−0.0108911	−	0.999941i	$-0.503467\pi$
$433$	4690.28	−	1377.19i	0.520555	−	0.152849i	0.531447	+	0.847092i	$0.321649\pi$
$434$	2896.65	−	6342.79i	0.320377	−	0.701529i
$435$	−64.1155	−	445.933i	−0.00706690	−	0.0491514i
$436$	−5349.71			−0.587625
$437$	4064.50	−	11764.8i	0.444924	−	1.28784i
$438$	925.070			0.100917
$439$	−641.613	−	4462.51i	−0.0697551	−	0.485158i	−0.994514	−	0.104604i	$-0.966643\pi$
$439$	−641.613	−	4462.51i	−0.0697551	−	0.485158i	0.924759	−	0.380554i	$-0.124267\pi$
$440$	342.685	−	750.374i	0.0371292	−	0.0813016i
$441$	−3067.87	+	900.807i	−0.331267	+	0.0972689i
$442$	−876.567	+	1011.61i	−0.0943304	+	0.108863i
$443$	−14216.1	−	4174.22i	−1.52467	−	0.447682i	−0.591253	−	0.806486i	$-0.701366\pi$
$443$	−14216.1	−	4174.22i	−1.52467	−	0.447682i	−0.933413	+	0.358804i	$0.883185\pi$
$444$	−1407.14	+	904.311i	−0.150405	+	0.0966593i
$445$	2034.52	+	4454.98i	0.216732	+	0.474576i
$446$	5403.23	+	6235.66i	0.573656	+	0.662034i
$447$	−4185.43	−	2689.81i	−0.442873	−	0.284617i
$448$	−240.680	+	1673.97i	−0.0253818	+	0.176535i
$449$	−591.885	+	4116.65i	−0.0622111	+	0.432688i	0.934784	+	0.355218i	$0.115593\pi$
$449$	−591.885	+	4116.65i	−0.0622111	+	0.432688i	−0.996995	+	0.0774700i	$0.975316\pi$
$450$	1635.69	+	1051.19i	0.171349	+	0.110119i
$451$	2863.44	+	3304.59i	0.298967	+	0.345027i
$452$	−3578.57	−	7835.97i	−0.372393	−	0.815427i
$453$	9110.53	−	5854.98i	0.944923	−	0.607265i
$454$	2431.85	+	714.056i	0.251393	+	0.0738156i
$455$	−3716.82	+	4289.44i	−0.382961	+	0.441961i
$456$	−2598.53	+	762.999i	−0.266859	+	0.0783568i
$457$	3867.76	−	8469.21i	0.395900	−	0.866899i	−0.601770	−	0.798669i	$-0.705538\pi$
$457$	3867.76	−	8469.21i	0.395900	−	0.866899i	0.997670	−	0.0682297i	$-0.0217351\pi$
$458$	−665.287	−	4627.17i	−0.0678752	−	0.472082i
$459$	−346.687			−0.0352548
$460$	−909.954	−	1574.07i	−0.0922323	−	0.159546i
$461$	17828.4			1.80119			0.900596	−	0.434658i	$-0.143131\pi$
$461$	17828.4			1.80119			0.900596	+	0.434658i	$0.143131\pi$
$462$	−564.617	−	3926.99i	−0.0568579	−	0.395455i
$463$	−6791.54	+	14871.4i	−0.681705	+	1.49273i	0.179120	+	0.983827i	$0.442675\pi$
$463$	−6791.54	+	14871.4i	−0.681705	+	1.49273i	−0.860826	+	0.508900i	$0.830052\pi$
$464$	−559.465	+	164.274i	−0.0559752	+	0.0164358i
$465$	1068.13	−	1232.69i	0.106523	−	0.122935i
$466$	10353.5	+	3040.06i	1.02922	+	0.302207i
$467$	1640.33	−	1054.18i	0.162538	−	0.104457i	−0.456843	−	0.889547i	$-0.651020\pi$
$467$	1640.33	−	1054.18i	0.162538	−	0.104457i	0.619381	+	0.785090i	$0.287383\pi$
$468$	779.502	+	1706.87i	0.0769925	+	0.168590i
$469$	−1918.19	−	2213.70i	−0.188856	−	0.217952i
$470$	2109.31	+	1355.57i	0.207011	+	0.133038i
$471$	−1212.26	+	8431.48i	−0.118595	+	0.824845i
$472$	−378.075	+	2629.57i	−0.0368693	+	0.256432i
$473$	−2660.35	−	1709.70i	−0.258611	−	0.166199i
$474$	−1357.31	−	1566.42i	−0.131526	−	0.151789i
$475$	5063.59	+	11087.7i	0.489123	+	1.07103i
$476$	−1141.75	+	733.757i	−0.109941	+	0.0706549i
$477$	5240.20	+	1538.66i	0.503003	+	0.147695i
$478$	9122.23	−	10527.6i	0.872890	−	1.00737i
$479$	2922.73	−	858.190i	0.278795	−	0.0818616i	−0.139346	−	0.990244i	$-0.544500\pi$
$479$	2922.73	−	858.190i	0.278795	−	0.0818616i	0.418141	+	0.908382i	$0.362682\pi$
$480$	−164.336	+	359.846i	−0.0156269	+	0.0342181i
$481$	1033.98	+	7191.47i	0.0980151	+	0.681710i
$482$	−3070.88			−0.290197
$483$	−7774.43	−	4002.54i	−0.732400	−	0.377063i
$484$	−2819.37			−0.264779
$485$	−665.606	−	4629.39i	−0.0623168	−	0.433423i
$486$	−201.892	+	442.081i	−0.0188436	+	0.0412617i
$487$	19059.4	−	5596.34i	1.77343	−	0.520727i	0.779088	−	0.626914i	$-0.215682\pi$
$487$	19059.4	−	5596.34i	1.77343	−	0.520727i	0.994346	+	0.106187i	$0.0338643\pi$
$488$	−4362.12	+	5034.16i	−0.404639	+	0.466979i
$489$	435.877	+	127.985i	0.0403089	+	0.0118357i
$490$	−2463.14	+	1582.97i	−0.227089	+	0.145941i
$491$	−6418.01	−	14053.5i	−0.589900	−	1.29170i	−0.935503	−	0.353320i	$-0.885053\pi$
$491$	−6418.01	−	14053.5i	−0.589900	−	1.29170i	0.345603	−	0.938381i	$-0.387674\pi$
$492$	−1373.18	−	1584.74i	−0.125829	−	0.145214i
$493$	−393.651	−	252.984i	−0.0359618	−	0.0231112i
$494$	−1674.13	+	11643.8i	−0.152475	+	1.06049i
$495$	132.073	−	918.590i	0.0119924	−	0.0834092i
$496$	−1775.91	−	1141.31i	−0.160768	−	0.103319i
$497$	16415.9	+	18944.9i	1.48159	+	1.70985i
$498$	2104.57	+	4608.36i	0.189373	+	0.414670i
$499$	12609.8	−	8103.84i	1.13125	−	0.727010i	0.165429	−	0.986222i	$-0.447099\pi$
$499$	12609.8	−	8103.84i	1.13125	−	0.727010i	0.965820	+	0.259212i	$0.0834629\pi$
$500$	3685.31	+	1082.10i	0.329624	+	0.0967863i
$501$	872.116	−	1006.48i	0.0777710	−	0.0897525i
$502$	−3569.49	+	1048.10i	−0.317359	+	0.0931851i
$503$	−5848.62	+	12806.7i	−0.518444	+	1.13523i	0.451582	+	0.892230i	$0.350860\pi$
$503$	−5848.62	+	12806.7i	−0.518444	+	1.13523i	−0.970025	+	0.243003i	$0.921867\pi$
$504$	270.765	+	1883.21i	0.0239302	+	0.166438i
$505$	−1715.18			−0.151137
$506$	3199.60	−	4498.49i	0.281106	−	0.395222i
$507$	1559.55			0.136611
$508$	175.020	+	1217.29i	0.0152860	+	0.106316i
$509$	3611.92	−	7909.01i	0.314530	−	0.688724i	−0.684664	−	0.728858i	$-0.740051\pi$
$509$	3611.92	−	7909.01i	0.314530	−	0.688724i	0.999194	+	0.0401341i	$0.0127785\pi$
$510$	−304.612	+	89.4421i	−0.0264479	+	0.00776581i
$511$	2667.98	−	3079.01i	0.230968	−	0.266551i
$512$	491.260	+	144.247i	0.0424040	+	0.0124509i
$513$	−2563.10	+	1647.21i	−0.220592	+	0.141766i
$514$	4442.46	+	9727.64i	0.381223	+	0.834762i
$515$	−4367.80	−	5040.71i	−0.373725	−	0.431301i
$516$	1275.79	+	819.897i	0.108844	+	0.0699495i
$517$	−1083.42	+	7535.33i	−0.0921637	+	0.641012i
$518$	−1048.38	+	7291.63i	−0.0889249	+	0.618486i
$519$	−2186.34	−	1405.08i	−0.184913	−	0.118836i
$520$	1125.26	+	1298.62i	0.0948958	+	0.109516i
$521$	3532.63	+	7735.37i	0.297058	+	0.650466i	0.998031	−	0.0627217i	$-0.0199780\pi$
$521$	3532.63	+	7735.37i	0.297058	+	0.650466i	−0.700973	+	0.713188i	$0.747251\pi$
$522$	−551.837	+	354.644i	−0.0462706	+	0.0297363i
$523$	−2896.37	−	850.451i	−0.242160	−	0.0711045i	0.158401	−	0.987375i	$-0.449366\pi$
$523$	−2896.37	−	850.451i	−0.242160	−	0.0711045i	−0.400560	+	0.916270i	$0.631184\pi$
$524$	3816.14	−	4404.06i	0.318147	−	0.367161i
$525$	8216.25	−	2412.51i	0.683022	−	0.200553i
$526$	1114.52	−	2440.46i	0.0923866	−	0.202298i
$527$	−241.100	−	1676.89i	−0.0199288	−	0.138608i
$528$	−1201.11			−0.0989994
$529$	−3992.21	−	11493.4i	−0.328118	−	0.944637i
$530$	5001.20			0.409883
$531$	425.334	+	2958.27i	0.0347607	+	0.241766i
$532$	−4954.82	+	10849.5i	−0.403794	+	0.884186i
$533$	−8739.21	+	2566.06i	−0.710201	+	0.208534i
$534$	4669.82	−	5389.26i	0.378432	−	0.436734i
$535$	1633.05	+	479.508i	0.131968	+	0.0387494i
$536$	−746.017	+	479.436i	−0.0601176	+	0.0386352i
$537$	−357.031	−	781.790i	−0.0286910	−	0.0628244i
$538$	−3422.42	−	3949.68i	−0.274258	−	0.316511i
$539$	−7478.62	−	4806.22i	−0.597638	−	0.384079i
$540$	−63.3365	+	440.515i	−0.00504735	+	0.0351051i
$541$	−2172.13	+	15107.5i	−0.172620	+	1.20060i	0.700703	+	0.713453i	$0.252870\pi$
$541$	−2172.13	+	15107.5i	−0.172620	+	1.20060i	−0.873322	+	0.487143i	$0.838039\pi$
$542$	−412.375	−	265.017i	−0.0326809	−	0.0210027i
$543$	3807.16	+	4393.69i	0.300885	+	0.347240i
$544$	170.689	+	373.757i	0.0134526	+	0.0294572i
$545$	−4636.36	+	2979.61i	−0.364403	+	0.234188i
$546$	7929.32	+	2328.26i	0.621508	+	0.182491i
$547$	11479.9	−	13248.5i	0.897337	−	1.03558i	−0.101831	−	0.994802i	$-0.532470\pi$
$547$	11479.9	−	13248.5i	0.897337	−	1.03558i	0.999168	−	0.0407808i	$-0.0129845\pi$
$548$	−449.708	+	132.046i	−0.0350558	+	0.0102933i
$549$	−3113.03	+	6816.59i	−0.242005	+	0.529918i
$550$	769.348	+	5350.93i	0.0596456	+	0.414845i
$551$	−4112.32			−0.317950
$552$	−1534.39	+	2157.28i	−0.118311	+	0.166340i
$553$	−9128.30			−0.701944
$554$	−368.824	−	2565.23i	−0.0282849	−	0.196726i
$555$	−715.833	+	1567.46i	−0.0547485	+	0.119882i
$556$	4471.74	−	1313.02i	0.341086	−	0.100152i
$557$	14308.3	−	16512.6i	1.08844	−	1.25613i	0.123868	−	0.992299i	$-0.460470\pi$
$557$	14308.3	−	16512.6i	1.08844	−	1.25613i	0.964570	−	0.263826i	$-0.0849846\pi$
$558$	−2278.71	−	669.089i	−0.172877	−	0.0507613i
$559$	5541.52	−	3561.32i	0.419287	−	0.269459i
$560$	723.757	+	1584.81i	0.0546148	+	0.119590i
$561$	−631.227	−	728.475i	−0.0475052	−	0.0548240i
$562$	−3999.85	−	2570.55i	−0.300220	−	0.192940i
$563$	3224.02	−	22423.6i	0.241343	−	1.67858i	−0.404055	−	0.914735i	$-0.632400\pi$
$563$	3224.02	−	22423.6i	0.241343	−	1.67858i	0.645399	−	0.763846i	$-0.276691\pi$
$564$	519.559	−	3613.61i	0.0387897	−	0.269788i
$565$	−7465.76	−	4797.95i	−0.555906	−	0.357259i
$566$	52.0711	+	60.0932i	0.00386698	+	0.00446273i
$567$	889.155	+	1946.98i	0.0658571	+	0.144207i
$568$	6384.42	−	4103.02i	0.471628	−	0.303097i
$569$	4800.36	+	1409.51i	0.353676	+	0.103849i	0.453744	−	0.891132i	$-0.350088\pi$
$569$	4800.36	+	1409.51i	0.353676	+	0.103849i	−0.100068	+	0.994981i	$0.531906\pi$
$570$	−1827.07	+	2108.55i	−0.134259	+	0.154943i
$571$	7365.81	−	2162.80i	0.539842	−	0.158512i	−0.000433949	−	1.00000i	$-0.500138\pi$
$571$	7365.81	−	2162.80i	0.539842	−	0.158512i	0.540276	+	0.841488i	$0.318320\pi$
$572$	−2167.29	+	4745.70i	−0.158425	+	0.346902i
$573$	695.038	+	4834.09i	0.0506730	+	0.352438i
$574$	−9235.02			−0.671537
$575$	10593.5	+	5453.86i	0.768309	+	0.395551i
$576$	576.000			0.0416667
$577$	336.012	+	2337.02i	0.0242433	+	0.168616i	0.998346	−	0.0574898i	$-0.0183097\pi$
$577$	336.012	+	2337.02i	0.0242433	+	0.168616i	−0.974103	+	0.226106i	$0.927401\pi$
$578$	3944.89	−	8638.10i	0.283885	−	0.621622i
$579$	−12690.7	+	3726.32i	−0.910893	+	0.267462i
$580$	−393.369	+	453.972i	−0.0281617	+	0.0325003i
$581$	21408.3	+	6286.03i	1.52868	+	0.448862i
$582$	−5728.82	+	3681.69i	−0.408019	+	0.262218i
$583$	6307.95	+	13812.5i	0.448111	+	0.981226i
$584$	−807.723	−	932.162i	−0.0572325	−	0.0660499i
$585$	1626.23	+	1045.12i	0.114934	+	0.0738636i
$586$	−2543.73	+	17692.0i	−0.179318	+	1.24719i
$587$	2751.27	−	19135.5i	0.193453	−	1.34549i	−0.629330	−	0.777138i	$-0.716670\pi$
$587$	2751.27	−	19135.5i	0.193453	−	1.34549i	0.822783	−	0.568356i	$-0.192420\pi$
$588$	3586.41	+	2304.85i	0.251533	+	0.161650i
$589$	−9749.86	−	11251.9i	−0.682065	−	0.787145i
$590$	1136.92	+	2489.51i	0.0793327	+	0.173714i
$591$	−1404.03	+	902.313i	−0.0977224	+	0.0628024i
$592$	2139.88	+	628.326i	0.148562	+	0.0436217i
$593$	11955.5	−	13797.4i	0.827918	−	0.955468i	−0.171642	−	0.985159i	$-0.554907\pi$
$593$	11955.5	−	13797.4i	0.827918	−	0.955468i	0.999559	+	0.0296917i	$0.00945255\pi$
$594$	−1296.52	+	380.691i	−0.0895567	+	0.0262962i
$595$	−580.826	+	1271.83i	−0.0400194	+	0.0876303i
$596$	944.066	+	6566.12i	0.0648833	+	0.451273i
$597$	10935.4			0.749676
$598$	5754.96	+	9955.10i	0.393541	+	0.680760i
$599$	24800.6			1.69169			0.845846	−	0.533427i	$-0.179096\pi$
$599$	24800.6			1.69169			0.845846	+	0.533427i	$0.179096\pi$
$600$	−368.945	−	2566.07i	−0.0251035	−	0.174599i
$601$	−7306.93	+	16000.0i	−0.495934	+	1.08594i	0.481836	+	0.876261i	$0.339970\pi$
$601$	−7306.93	+	16000.0i	−0.495934	+	1.08594i	−0.977770	+	0.209682i	$0.932757\pi$
$602$	6408.42	−	1881.68i	0.433867	−	0.127395i
$603$	−653.316	+	753.966i	−0.0441212	+	0.0509186i
$604$	−13854.7	−	4068.11i	−0.933344	−	0.274055i
$605$	−2443.42	+	1570.29i	−0.164197	+	0.105523i
$606$	1037.44	+	2271.67i	0.0695429	+	0.152278i
$607$	−9957.54	−	11491.6i	−0.665839	−	0.768419i	0.317880	−	0.948131i	$-0.397029\pi$
$607$	−9957.54	−	11491.6i	−0.665839	−	0.768419i	−0.983719	+	0.179712i	$0.942483\pi$
$608$	3037.75	+	1952.24i	0.202627	+	0.130220i
$609$	−411.143	+	2859.56i	−0.0273569	+	0.190271i
$610$	−976.606	+	6792.44i	−0.0648223	+	0.450849i
$611$	−13340.2	−	8573.24i	−0.883285	−	0.567653i
$612$	302.709	+	349.345i	0.0199939	+	0.0230742i
$613$	−9983.11	−	21860.0i	−0.657772	−	1.44032i	−0.884584	−	0.466381i	$-0.845558\pi$
$613$	−9983.11	−	21860.0i	−0.657772	−	1.44032i	0.226812	−	0.973939i	$-0.427170\pi$
$614$	12322.6	−	7919.24i	0.809932	−	0.520512i
$615$	−2072.72	−	608.606i	−0.135903	−	0.0399047i
$616$	−3464.11	+	3997.79i	−0.226579	+	0.261486i
$617$	8431.25	−	2475.64i	0.550129	−	0.161532i	0.00515677	−	0.999987i	$-0.498359\pi$
$617$	8431.25	−	2475.64i	0.550129	−	0.161532i	0.544972	+	0.838454i	$0.316540\pi$
$618$	−4034.29	+	8833.85i	−0.262594	+	0.575000i
$619$	1123.06	+	7811.03i	0.0729232	+	0.507192i	0.993246	+	0.116031i	$0.0370172\pi$
$619$	1123.06	+	7811.03i	0.0729232	+	0.507192i	−0.920322	+	0.391161i	$0.872074\pi$
$620$	−2174.78			−0.140873
$621$	−972.514	+	2814.95i	−0.0628432	+	0.181900i
$622$	−11932.8			−0.769228
$623$	−4469.51	−	31086.2i	−0.287427	−	1.99910i
$624$	1039.34	−	2275.83i	0.0666775	−	0.146003i
$625$	−9158.86	+	2689.28i	−0.586167	+	0.172114i
$626$	−6347.16	+	7325.01i	−0.405245	+	0.467678i
$627$	−8127.94	−	2386.58i	−0.517701	−	0.152011i
$628$	9554.60	−	6140.37i	0.607118	−	0.390171i
$629$	743.504	+	1628.05i	0.0471311	+	0.103203i
$630$	1283.55	+	1481.29i	0.0811710	+	0.0936764i
$631$	−16144.1	−	10375.2i	−1.01852	−	0.654564i	−0.0789369	−	0.996880i	$-0.525153\pi$
$631$	−16144.1	−	10375.2i	−1.01852	−	0.654564i	−0.939585	+	0.342315i	$0.888789\pi$
$632$	−393.296	+	2735.44i	−0.0247539	+	0.172167i
$633$	−1968.97	+	13694.5i	−0.123633	+	0.859884i
$634$	−11073.2	−	7116.32i	−0.693648	−	0.445781i
$635$	829.674	+	957.495i	0.0518498	+	0.0598378i
$636$	−3025.01	−	6623.86i	−0.188600	−	0.412976i
$637$	15578.0	−	10011.4i	0.968953	−	0.622708i
$638$	−1749.95	−	513.831i	−0.108591	−	0.0318852i
$639$	5591.09	−	6452.46i	0.346135	−	0.399461i
$640$	506.095	−	148.603i	0.0312581	−	0.00917820i
$641$	−4189.60	+	9173.95i	−0.258158	+	0.565287i	−0.993685	−	0.112208i	$-0.964208\pi$
$641$	−4189.60	+	9173.95i	−0.258158	+	0.565287i	0.735527	+	0.677496i	$0.236935\pi$
$642$	−352.679	−	2452.94i	−0.0216809	−	0.150794i
$643$	−13881.4			−0.851366			−0.425683	−	0.904872i	$-0.639966\pi$
$643$	−13881.4			−0.851366			−0.425683	+	0.904872i	$0.639966\pi$
$644$	2755.01	+	11328.8i	0.168575	+	0.693197i
$645$	1562.32			0.0953743
$646$	412.410	+	2868.37i	0.0251177	+	0.174698i
$647$	−5933.97	+	12993.6i	−0.360570	+	0.789537i	0.639220	+	0.769024i	$0.279257\pi$
$647$	−5933.97	+	12993.6i	−0.360570	+	0.789537i	−0.999790	+	0.0205133i	$0.993470\pi$
$648$	621.751	−	182.563i	0.0376924	−	0.0110675i
$649$	−5441.63	+	6279.97i	−0.329126	+	0.379831i
$650$	−10804.5	−	3172.49i	−0.651981	−	0.191439i
$651$	−8798.98	+	5654.76i	−0.529738	+	0.340442i
$652$	−251.619	−	550.968i	−0.0151137	−	0.0330944i
$653$	−19295.7	−	22268.4i	−1.15635	−	1.33450i	−0.933046	−	0.359757i	$-0.882860\pi$
$653$	−19295.7	−	22268.4i	−1.15635	−	1.33450i	−0.223309	−	0.974748i	$-0.571686\pi$
$654$	6750.69	+	4338.40i	0.403628	+	0.259396i
$655$	854.370	−	5942.28i	0.0509664	−	0.354479i
$656$	−397.894	+	2767.42i	−0.0236817	+	0.164710i
$657$	−1167.33	−	750.196i	−0.0693178	−	0.0445478i
$658$	−10529.1	−	12151.3i	−0.623812	−	0.719917i
$659$	−10200.0	−	22334.9i	−0.602936	−	1.32025i	−0.927302	−	0.374315i	$-0.877878\pi$
$659$	−10200.0	−	22334.9i	−0.602936	−	1.32025i	0.324366	−	0.945932i	$-0.394849\pi$
$660$	−1040.95	+	668.979i	−0.0613924	+	0.0394545i
$661$	−19132.5	−	5617.80i	−1.12582	−	0.330571i	−0.334757	−	0.942305i	$-0.608654\pi$
$661$	−19132.5	−	5617.80i	−1.12582	−	0.330571i	−0.791063	+	0.611734i	$0.790472\pi$
$662$	12578.3	−	14516.2i	0.738476	−	0.852247i
$663$	1926.50	−	565.672i	0.112849	−	0.0331356i
$664$	2806.09	−	6144.48i	0.164002	−	0.359115i
$665$	1748.70	+	12162.5i	0.101973	+	0.709235i
$666$	2509.00			0.145979
$667$	−3158.38	+	2486.62i	−0.183348	+	0.144351i
$668$	−1775.68			−0.102849
$669$	−1761.35	−	12250.5i	−0.101790	−	0.707968i
$670$	−379.511	+	831.013i	−0.0218833	+	0.0479176i
$671$	−19991.4	+	5870.00i	−1.15016	+	0.337718i
$672$	1661.23	−	1917.16i	0.0953622	−	0.110054i
$673$	29406.4	+	8634.48i	1.68430	+	0.494554i	0.977157	−	0.212520i	$-0.0681670\pi$
$673$	29406.4	+	8634.48i	1.68430	+	0.494554i	0.707140	+	0.707074i	$0.249985\pi$
$674$	9404.17	−	6043.70i	0.537441	−	0.345392i
$675$	−1211.56	−	2652.96i	−0.0690861	−	0.151278i
$676$	−1361.71	−	1571.50i	−0.0774757	−	0.0894117i
$677$	10406.4	+	6687.81i	0.590770	+	0.379665i	0.801603	−	0.597857i	$-0.203981\pi$
$677$	10406.4	+	6687.81i	0.590770	+	0.379665i	−0.210832	+	0.977522i	$0.567617\pi$
$678$	−1838.94	+	12790.1i	−0.104165	+	0.724487i
$679$	−4268.22	+	29686.2i	−0.241236	+	1.67784i
$680$	356.099	+	228.851i	0.0200820	+	0.0129059i
$681$	−2489.63	−	2873.19i	−0.140092	−	0.161675i
$682$	−2743.02	−	6006.37i	−0.154011	−	0.337237i
$683$	−20805.9	+	13371.1i	−1.16561	+	0.749095i	−0.972688	−	0.232118i	$-0.925434\pi$
$683$	−20805.9	+	13371.1i	−1.16561	+	0.749095i	−0.192927	+	0.981213i	$0.561798\pi$
$684$	3897.80	+	1144.50i	0.217889	+	0.0639780i
$685$	−316.197	+	364.911i	−0.0176369	+	0.0203541i
$686$	621.939	−	182.618i	0.0346148	−	0.0101638i
$687$	−2912.95	+	6378.46i	−0.161770	+	0.354226i
$688$	−287.766	−	2001.46i	−0.0159462	−	0.110908i
$689$	−31629.8			−1.74891
$690$	−128.254	+	2724.22i	−0.00707617	+	0.150303i
$691$	26456.6			1.45652			0.728260	−	0.685301i	$-0.240330\pi$
$691$	26456.6			1.45652			0.728260	+	0.685301i	$0.240330\pi$
$692$	493.151	+	3429.94i	0.0270907	+	0.188420i
$693$	−2472.16	+	5413.28i	−0.135512	+	0.296729i
$694$	16200.9	−	4757.01i	0.886135	−	0.260193i
$695$	3144.16	−	3628.55i	0.171604	−	0.198041i
$696$	839.198	+	246.411i	0.0457036	+	0.0134198i
$697$	−1887.55	+	1213.05i	−0.102577	+	0.0659221i
$698$	−790.434	−	1730.81i	−0.0428630	−	0.0938568i
$699$	−10599.5	−	12232.5i	−0.573549	−	0.661910i
$700$	−9605.00	−	6172.76i	−0.518622	−	0.333298i
$701$	−2822.32	+	19629.7i	−0.152065	+	1.05764i	0.760686	+	0.649120i	$0.224863\pi$
$701$	−2822.32	+	19629.7i	−0.152065	+	1.05764i	−0.912751	+	0.408516i	$0.866046\pi$
$702$	400.568	−	2786.01i	0.0215363	−	0.149788i
$703$	13232.1	+	8503.78i	0.709900	+	0.456225i
$704$	1048.75	+	1210.32i	0.0561451	+	0.0647949i
$705$	−1562.38	−	3421.14i	−0.0834648	−	0.182762i
$706$	−9653.58	+	6203.98i	−0.514614	+	0.330722i
$707$	10553.1	+	3098.67i	0.561373	+	0.164834i
$708$	2609.56	−	3011.60i	0.138522	−	0.159863i
$709$	−19688.0	+	5780.92i	−1.04287	+	0.306216i	−0.757935	−	0.652330i	$-0.773792\pi$
$709$	−19688.0	+	5780.92i	−1.04287	+	0.306216i	−0.284939	+	0.958546i	$0.591974\pi$
$710$	3247.86	−	7111.82i	0.171676	−	0.375918i
$711$	442.458	+	3077.37i	0.0233382	+	0.162321i
$712$	−9508.02			−0.500461
$713$	−14292.0	−	2746.32i	−0.750685	−	0.144250i
$714$	2035.80			0.106706
$715$	764.901	+	5320.00i	0.0400079	+	0.278261i
$716$	−476.042	+	1042.39i	−0.0248471	+	0.0544076i
$717$	−20048.7	+	5886.82i	−1.04426	+	0.306621i
$718$	909.842	−	1050.01i	0.0472911	−	0.0545768i
$719$	23560.5	+	6917.98i	1.22205	+	0.358828i	0.828246	−	0.560365i	$-0.189339\pi$
$719$	23560.5	+	6917.98i	1.22205	+	0.358828i	0.393809	+	0.919192i	$0.371157\pi$
$720$	499.194	−	320.813i	0.0258387	−	0.0166055i
$721$	17767.5	+	38905.3i	0.917746	+	2.00958i
$722$	7694.08	+	8879.44i	0.396598	+	0.457699i
$723$	3875.08	+	2490.36i	0.199330	+	0.128102i
$724$	1103.17	−	7672.68i	0.0566282	−	0.393858i
$725$	560.224	−	3896.45i	0.0286982	−	0.199600i
$726$	3557.70	+	2286.40i	0.181872	+	0.116882i
$727$	10497.0	+	12114.2i	0.535505	+	0.618006i	0.957444	−	0.288619i	$-0.0931959\pi$
$727$	10497.0	+	12114.2i	0.535505	+	0.618006i	−0.421939	+	0.906624i	$0.638650\pi$
$728$	−4577.36	−	10023.0i	−0.233033	−	0.510272i
$729$	613.274	−	394.127i	0.0311575	−	0.0200237i
$730$	−1219.20	−	357.990i	−0.0618146	−	0.0181504i
$731$	1062.65	−	1226.37i	0.0537670	−	0.0620504i
$732$	9586.98	−	2814.99i	0.484078	−	0.142138i
$733$	4273.97	−	9358.70i	0.215365	−	0.471584i	−0.770857	−	0.637008i	$-0.780172\pi$
$733$	4273.97	−	9358.70i	0.215365	−	0.471584i	0.986223	+	0.165424i	$0.0528991\pi$
$734$	3130.27	+	21771.5i	0.157412	+	1.09483i
$735$	4391.91			0.220406
$736$	3513.56	−	337.474i	0.175967	−	0.0169014i
$737$	−2773.79			−0.138635
$738$	447.631	+	3113.34i	0.0223273	+	0.155290i
$739$	−2397.54	+	5249.87i	−0.119343	+	0.261326i	−0.959870	−	0.280444i	$-0.909518\pi$
$739$	−2397.54	+	5249.87i	−0.119343	+	0.261326i	0.840527	+	0.541770i	$0.182246\pi$
$740$	2204.50	−	647.299i	0.109512	−	0.0321557i
$741$	11555.2	−	13335.4i	0.572863	−	0.661120i
$742$	−30771.3	−	9035.27i	−1.52244	−	0.447028i
$743$	−30504.8	+	19604.2i	−1.50621	+	0.967981i	−0.512176	+	0.858880i	$0.671161\pi$
$743$	−30504.8	+	19604.2i	−1.50621	+	0.967981i	−0.994031	+	0.109100i	$0.965203\pi$
$744$	1315.43	+	2880.39i	0.0648199	+	0.141936i
$745$	4475.29	+	5164.76i	0.220083	+	0.253990i
$746$	−18382.9	−	11814.0i	−0.902207	−	0.579813i
$747$	1081.49	−	7521.92i	0.0529714	−	0.368424i
$748$	−182.905	+	1272.13i	−0.00894074	+	0.0621842i
$749$	−9181.53	−	5900.61i	−0.447912	−	0.287855i
$750$	−3772.87	−	4354.13i	−0.183688	−	0.211987i
$751$	7667.04	+	16788.5i	0.372536	+	0.815740i	0.999332	+	0.0365561i	$0.0116388\pi$
$751$	7667.04	+	16788.5i	0.372536	+	0.815740i	−0.626796	+	0.779184i	$0.715634\pi$
$752$	−4094.96	+	2631.67i	−0.198574	+	0.127616i
$753$	5354.24	+	1572.15i	0.259123	+	0.0760853i
$754$	2487.84	−	2871.12i	0.120162	−	0.138674i
$755$	−14273.1	+	4190.95i	−0.688014	+	0.202019i
$756$	1185.54	−	2595.97i	0.0570339	−	0.124887i
$757$	−2733.22	−	19010.0i	−0.131229	−	0.912719i	−0.943955	−	0.330073i	$-0.892927\pi$
$757$	−2733.22	−	19010.0i	−0.131229	−	0.912719i	0.812726	−	0.582646i	$-0.197983\pi$
$758$	−12850.7			−0.615776
$759$	−7685.61	+	3081.81i	−0.367550	+	0.147382i
$760$	3720.02			0.177552
$761$	−1127.71	−	7843.37i	−0.0537179	−	0.373616i	−0.998893	−	0.0470507i	$-0.985018\pi$
$761$	−1127.71	−	7843.37i	−0.0537179	−	0.373616i	0.945175	−	0.326565i	$-0.105891\pi$
$762$	766.322	−	1678.01i	0.0364317	−	0.0797742i
$763$	33909.5	−	9956.74i	1.60892	−	0.472422i
$764$	4264.28	−	4921.24i	0.201932	−	0.233042i
$765$	456.918	+	134.163i	0.0215946	+	0.00634076i
$766$	2918.58	−	1875.66i	0.137667	−	0.0884730i
$767$	−7190.40	−	15744.8i	−0.338501	−	0.741213i
$768$	−502.933	−	580.416i	−0.0236303	−	0.0272708i
$769$	−14952.4	−	9609.34i	−0.701168	−	0.450613i	0.140872	−	0.990028i	$-0.455009\pi$
$769$	−14952.4	−	9609.34i	−0.701168	−	0.450613i	−0.842040	+	0.539414i	$0.818646\pi$
$770$	−775.555	+	5394.10i	−0.0362975	+	0.252455i
$771$	2282.88	−	15877.8i	0.106635	−	0.741666i
$772$	14835.7	+	9534.35i	0.691645	+	0.444493i
$773$	23589.5	+	27223.8i	1.09762	+	1.26672i	0.961137	+	0.276072i	$0.0890330\pi$
$773$	23589.5	+	27223.8i	1.09762	+	1.26672i	0.136478	+	0.990643i	$0.456422\pi$
$774$	−944.983	−	2069.22i	−0.0438846	−	0.0960940i
$775$	11989.5	−	7705.19i	0.555711	−	0.357134i
$776$	8712.02	+	2558.08i	0.403020	+	0.118337i
$777$	7236.16	−	8350.97i	0.334100	−	0.385572i
$778$	−10212.3	+	2998.60i	−0.470603	+	0.138181i
$779$	−8191.35	+	17936.6i	−0.376746	+	0.824960i
$780$	−366.813	−	2551.24i	−0.0168385	−	0.117114i
$781$	23738.1			1.08760
$782$	2051.18	+	1953.62i	0.0937981	+	0.0893369i
$783$	983.954			0.0449089
$784$	−808.952	−	5626.38i	−0.0368509	−	0.256304i
$785$	4860.58	−	10643.2i	0.220996	−	0.483913i
$786$	−8387.04	+	2462.66i	−0.380605	+	0.111756i
$787$	−473.308	+	546.227i	−0.0214379	+	0.0247406i	−0.766367	−	0.642403i	$-0.777938\pi$
$787$	−473.308	+	546.227i	−0.0214379	+	0.0247406i	0.744929	+	0.667143i	$0.232483\pi$
$788$	2135.15	+	626.938i	0.0965250	+	0.0283423i
$789$	−3385.51	+	2175.73i	−0.152759	+	0.0981726i
$790$	1182.69	+	2589.74i	0.0532637	+	0.116631i
$791$	37267.1	+	43008.6i	1.67518	+	1.93326i
$792$	1515.66	+	974.055i	0.0680007	+	0.0437014i
$793$	6176.49	−	42958.4i	0.276587	−	1.92371i
$794$	−1347.71	+	9373.55i	−0.0602374	+	0.418961i
$795$	−6310.91	−	4055.78i	−0.281541	−	0.180935i
$796$	−9548.23	−	11019.2i	−0.425161	−	0.490662i
$797$	−3496.18	−	7655.57i	−0.155384	−	0.340244i	0.815890	−	0.578207i	$-0.196247\pi$
$797$	−3496.18	−	7655.57i	−0.155384	−	0.340244i	−0.971274	+	0.237963i	$0.923520\pi$
$798$	15050.9	−	9672.65i	0.667666	−	0.429083i
$799$	−3748.16	−	1100.56i	−0.165958	−	0.0487297i
$800$	−2263.60	+	2612.33i	−0.100038	+	0.115450i
$801$	−10263.2	+	3013.56i	−0.452726	+	0.132932i
$802$	1536.49	−	3364.44i	0.0676500	−	0.148133i
$803$	−549.055	−	3818.76i	−0.0241292	−	0.167822i
$804$	1330.19			0.0583484
$805$	8697.43	+	8283.77i	0.380800	+	0.362689i
$806$	13754.2			0.601083
$807$	1115.64	+	7759.48i	0.0486649	+	0.338472i
$808$	1383.25	−	3028.89i	0.0602259	−	0.131876i
$809$	5599.87	−	1644.27i	0.243363	−	0.0714579i	−0.157776	−	0.987475i	$-0.550432\pi$
$809$	5599.87	−	1644.27i	0.243363	−	0.0714579i	0.401139	+	0.916017i	$0.368614\pi$
$810$	437.164	−	504.514i	0.0189634	−	0.0218850i
$811$	28513.8	+	8372.40i	1.23459	+	0.362509i	0.832981	−	0.553302i	$-0.186632\pi$
$811$	28513.8	+	8372.40i	1.23459	+	0.362509i	0.401611	+	0.915810i	$0.368451\pi$
$812$	3240.47	−	2082.52i	0.140047	−	0.0900028i
$813$	305.449	+	668.840i	0.0131766	+	0.0288527i
$814$	4568.24	+	5272.03i	0.196704	+	0.227008i
$815$	−524.938	−	337.357i	−0.0225617	−	0.0144995i
$816$	87.7132	−	610.059i	0.00376296	−	0.0261720i
$817$	2029.53	−	14115.7i	0.0869084	−	0.604461i
$818$	−22245.7	−	14296.5i	−0.950861	−	0.611081i
$819$	−8117.72	−	9368.35i	−0.346345	−	0.399703i
$820$	1196.52	+	2620.01i	0.0509565	+	0.111579i
$821$	17012.5	−	10933.3i	0.723192	−	0.464767i	−0.126554	−	0.991960i	$-0.540392\pi$
$821$	17012.5	−	10933.3i	0.723192	−	0.464767i	0.849746	+	0.527192i	$0.176755\pi$
$822$	674.562	+	198.069i	0.0286229	+	0.00840446i
$823$	−11565.2	+	13347.0i	−0.489840	+	0.565306i	−0.945823	−	0.324683i	$-0.894742\pi$
$823$	−11565.2	+	13347.0i	−0.489840	+	0.565306i	0.455983	+	0.889989i	$0.349288\pi$
$824$	12424.1	−	3648.05i	0.525260	−	0.154230i
$825$	3368.57	−	7376.15i	0.142156	−	0.311278i
$826$	−2497.63	−	17371.4i	−0.105210	−	0.731753i
$827$	13291.6			0.558882			0.279441	−	0.960163i	$-0.409851\pi$
$827$	13291.6			0.558882			0.279441	+	0.960163i	$0.409851\pi$
$828$	3685.68	−	1477.90i	0.154694	−	0.0620297i
$829$	11461.1			0.480170			0.240085	−	0.970752i	$-0.422825\pi$
$829$	11461.1			0.480170			0.240085	+	0.970752i	$0.422825\pi$
$830$	−990.353	−	6888.05i	−0.0414164	−	0.288058i
$831$	−1614.89	+	3536.12i	−0.0674126	+	0.147613i
$832$	−3200.77	+	939.831i	−0.133373	+	0.0391620i
$833$	2987.27	−	3447.50i	0.124253	−	0.143396i
$834$	−6707.61	−	1969.53i	−0.278496	−	0.0817738i
$835$	−1538.90	+	988.993i	−0.0637796	+	0.0409886i
$836$	4692.02	+	10274.1i	0.194111	+	0.425044i
$837$	2332.85	+	2692.25i	0.0963382	+	0.111180i
$838$	−9308.34	−	5982.11i	−0.383713	−	0.246597i
$839$	1967.25	−	13682.5i	0.0809498	−	0.563018i	−0.908471	−	0.417947i	$-0.862750\pi$
$839$	1967.25	−	13682.5i	0.0809498	−	0.563018i	0.989421	−	0.145071i	$-0.0463412\pi$
$840$	371.922	−	2586.77i	0.0152768	−	0.106253i
$841$	−19400.1	−	12467.7i	−0.795444	−	0.511201i
$842$	−8847.22	−	10210.2i	−0.362108	−	0.417895i
$843$	2962.72	+	6487.45i	0.121046	+	0.265053i
$844$	15518.7	−	9973.24i	0.632908	−	0.406745i
$845$	−2055.41	−	603.523i	−0.0836785	−	0.0245702i
$846$	−3586.12	+	4138.60i	−0.145737	+	0.168189i
$847$	17870.8	−	5247.33i	0.724967	−	0.212870i
$848$	−4033.35	+	8831.81i	−0.163332	+	0.357648i
$849$	−16.9742	−	118.058i	−0.000686163	−	0.00477237i
$850$	−2773.99			−0.111938
$851$	15304.7	−	1470.00i	0.616497	−	0.0592139i
$852$	−11383.8			−0.457748
$853$	5640.50	+	39230.6i	0.226409	+	1.57471i	0.713053	+	0.701110i	$0.247312\pi$
$853$	5640.50	+	39230.6i	0.226409	+	1.57471i	−0.486643	+	0.873601i	$0.661779\pi$
$854$	18280.2	−	40028.1i	0.732477	−	1.60390i
$855$	4015.50	−	1179.06i	0.160617	−	0.0471613i
$856$	−2163.80	+	2497.16i	−0.0863986	+	0.0997093i
$857$	−11167.7	−	3279.13i	−0.445135	−	0.130703i	0.0514806	−	0.998674i	$-0.483606\pi$
$857$	−11167.7	−	3279.13i	−0.445135	−	0.130703i	−0.496616	+	0.867971i	$0.665424\pi$
$858$	6583.44	−	4230.92i	0.261952	−	0.168346i
$859$	3608.80	+	7902.16i	0.143342	+	0.313875i	0.967663	−	0.252248i	$-0.0811700\pi$
$859$	3608.80	+	7902.16i	0.143342	+	0.313875i	−0.824321	+	0.566123i	$0.808443\pi$
$860$	−1364.14	−	1574.30i	−0.0540892	−	0.0624223i
$861$	11653.5	+	7489.24i	0.461266	+	0.296438i
$862$	−2727.93	+	18973.2i	−0.107789	+	0.749686i
$863$	−761.130	+	5293.78i	−0.0300222	+	0.208809i	−0.999311	−	0.0371164i	$-0.988183\pi$
$863$	−761.130	+	5293.78i	−0.0300222	+	0.208809i	0.969289	+	0.245926i	$0.0790919\pi$
$864$	−726.843	−	467.114i	−0.0286200	−	0.0183930i
$865$	2337.76	+	2697.91i	0.0918914	+	0.106048i
$866$	4061.34	+	8893.09i	0.159365	+	0.348960i
$867$	−11983.1	+	7701.10i	−0.469399	+	0.301664i
$868$	13380.9	+	3928.99i	0.523247	+	0.153639i
$869$	−5660.71	+	6532.81i	−0.220974	+	0.255018i
$870$	864.539	−	253.851i	0.0336904	−	0.00989238i
$871$	2400.19	−	5255.69i	0.0933726	−	0.204457i
$872$	−1522.68	−	10590.5i	−0.0591337	−	0.411284i
$873$	10214.8			0.396012
$874$	24446.9	+	4697.67i	0.946142	+	0.181809i
$875$	−25373.6			−0.980324
$876$	263.302	+	1831.31i	0.0101554	+	0.0706326i
$877$	−9374.44	+	20527.2i	−0.360949	+	0.790368i	0.638830	+	0.769348i	$0.279419\pi$
$877$	−9374.44	+	20527.2i	−0.360949	+	0.790368i	−0.999779	+	0.0210203i	$0.993309\pi$
$878$	8651.56	−	2540.33i	0.332547	−	0.0976446i
$879$	17557.4	−	20262.4i	0.673718	−	0.777512i
$880$	1583.01	+	464.814i	0.0606401	+	0.0178055i
$881$	−17766.9	+	11418.1i	−0.679437	+	0.436647i	−0.834316	−	0.551286i	$-0.814137\pi$
$881$	−17766.9	+	11418.1i	−0.679437	+	0.436647i	0.154880	+	0.987933i	$0.450501\pi$
$882$	−2656.48	−	5816.89i	−0.101415	−	0.222069i
$883$	−15794.6	−	18227.9i	−0.601959	−	0.694698i	0.370218	−	0.928945i	$-0.379283\pi$
$883$	−15794.6	−	18227.9i	−0.601959	−	0.694698i	−0.972177	+	0.234247i	$0.924738\pi$
$884$	−2252.13	−	1447.36i	−0.0856870	−	0.0550677i
$885$	584.238	−	4063.46i	0.0221909	−	0.154341i
$886$	4217.14	−	29330.9i	0.159907	−	1.11218i
$887$	24500.8	+	15745.7i	0.927460	+	0.596043i	0.914813	−	0.403877i	$-0.132338\pi$
$887$	24500.8	+	15745.7i	0.927460	+	0.596043i	0.0126473	+	0.999920i	$0.495974\pi$
$888$	−2190.73	−	2528.23i	−0.0827882	−	0.0955427i
$889$	−3374.97	−	7390.16i	−0.127326	−	0.278805i
$890$	−8240.19	+	5295.65i	−0.310350	+	0.199450i
$891$	1944.77	+	571.037i	0.0731227	+	0.0214708i
$892$	−10806.5	+	12471.3i	−0.405636	+	0.468129i
$893$	−32939.8	+	9671.99i	−1.23436	+	0.362442i
$894$	4133.57	−	9051.26i	0.154639	−	0.338612i
$895$	168.009	+	1168.53i	0.00627479	+	0.0436421i
$896$	−3382.36			−0.126112
$897$	811.137	−	17229.2i	0.0301929	−	0.641322i
$898$	−8317.97			−0.309103
$899$	684.283	+	4759.29i	0.0253861	+	0.176564i
$900$	−1615.42	+	3537.27i	−0.0598303	+	0.131010i
$901$	−7476.17	+	2195.20i	−0.276434	+	0.0811685i
$902$	−5726.89	+	6609.18i	−0.211402	+	0.243971i
$903$	−9612.64	−	2822.52i	−0.354251	−	0.104017i
$904$	14493.9	−	9314.63i	0.533250	−	0.342699i
$905$	−3317.36	−	7264.01i	−0.121848	−	0.266811i
$906$	14183.9	+	16369.1i	0.520120	+	0.600250i
$907$	−15666.1	−	10068.0i	−0.573521	−	0.368579i	0.221501	−	0.975160i	$-0.428904\pi$
$907$	−15666.1	−	10068.0i	−0.573521	−	0.368579i	−0.795022	+	0.606581i	$0.792541\pi$
$908$	−721.399	+	5017.44i	−0.0263661	+	0.183381i
$909$	533.115	−	3707.90i	0.0194525	−	0.135295i
$910$	−9549.49	−	6137.08i	−0.347871	−	0.223563i
$911$	25299.1	+	29196.7i	0.920083	+	1.06183i	0.997894	+	0.0648641i	$0.0206614\pi$
$911$	25299.1	+	29196.7i	0.920083	+	1.06183i	−0.0778112	+	0.996968i	$0.524793\pi$
$912$	−2250.08	−	4927.00i	−0.0816971	−	0.178892i
$913$	17774.5	−	11423.0i	0.644306	−	0.414070i
$914$	17866.9	+	5246.19i	0.646591	+	0.189856i
$915$	6740.77	−	7779.26i	0.243544	−	0.281065i
$916$	8970.79	−	2634.06i	0.323584	−	0.0950129i
$917$	−15992.2	+	35018.0i	−0.575909	+	1.26107i
$918$	−98.6774	−	686.316i	−0.00354775	−	0.0246752i
$919$	15028.1			0.539426			0.269713	−	0.962941i	$-0.413071\pi$
$919$	15028.1			0.539426			0.269713	+	0.962941i	$0.413071\pi$
$920$	2857.09	−	2249.41i	0.102386	−	0.0806096i
$921$	−21971.8			−0.786097
$922$	5074.48	+	35293.8i	0.181257	+	1.26067i
$923$	−20540.9	+	44978.3i	−0.732516	+	1.60399i
$924$	7613.34	−	2235.48i	0.271061	−	0.0795907i
$925$	−9860.01	+	11379.1i	−0.350481	+	0.404477i
$926$	−31373.1	−	9211.98i	−1.11337	−	0.326916i
$927$	12254.7	−	7875.62i	0.434193	−	0.279039i
$928$	−484.444	−	1060.78i	−0.0171365	−	0.0375236i
$929$	9656.69	+	11144.4i	0.341040	+	0.393581i	0.900198	−	0.435480i	$-0.143421\pi$
$929$	9656.69	+	11144.4i	0.341040	+	0.393581i	−0.559159	+	0.829061i	$0.688876\pi$
$930$	2744.31	+	1763.66i	0.0967627	+	0.0621856i
$931$	5705.29	−	39681.2i	0.200842	−	1.39688i
$932$	−3071.33	+	21361.5i	−0.107945	+	0.750773i
$933$	15057.7	+	9677.01i	0.528368	+	0.339562i
$934$	2553.78	+	2947.22i	0.0894670	+	0.103250i
$935$	550.019	+	1204.37i	0.0192380	+	0.0421254i
$936$	−3157.13	+	2028.96i	−0.110250	+	0.0708533i
$937$	−5551.75	−	1630.14i	−0.193562	−	0.0568350i	0.183515	−	0.983017i	$-0.441253\pi$
$937$	−5551.75	−	1630.14i	−0.193562	−	0.0568350i	−0.377077	+	0.926182i	$0.623071\pi$
$938$	3836.37	−	4427.41i	0.133542	−	0.154115i
$939$	13949.7	−	4095.99i	0.484803	−	0.142351i
$940$	−2083.17	+	4561.52i	−0.0722826	+	0.158277i
$941$	−10.7215	−	74.5699i	−0.000371426	−	0.00258332i	0.989635	−	0.143606i	$-0.0458699\pi$
$941$	−10.7215	−	74.5699i	−0.000371426	−	0.00258332i	−0.990006	+	0.141023i	$0.954961\pi$
$942$	−17036.4			−0.589251
$943$	4554.61	+	18728.9i	0.157284	+	0.646763i
$944$	−5313.22			−0.183189
$945$	−418.412	−	2910.12i	−0.0144031	−	0.100176i
$946$	2627.38	−	5753.17i	0.0902998	−	0.197729i
$947$	7244.98	−	2127.32i	0.248606	−	0.0729974i	−0.155055	−	0.987906i	$-0.549556\pi$
$947$	7244.98	−	2127.32i	0.248606	−	0.0729974i	0.403661	+	0.914908i	$0.367737\pi$
$948$	2714.63	−	3132.84i	0.0930031	−	0.107331i
$949$	7710.77	+	2264.09i	0.263754	+	0.0774451i
$950$	−20508.5	+	13180.0i	−0.700402	+	0.450121i
$951$	8202.00	+	17959.9i	0.279672	+	0.612396i
$952$	−1777.55	−	2051.41i	−0.0605156	−	0.0698387i
$953$	11403.0	+	7328.23i	0.387595	+	0.249092i	0.719897	−	0.694081i	$-0.244189\pi$
$953$	11403.0	+	7328.23i	0.387595	+	0.249092i	−0.332302	+	0.943173i	$0.607825\pi$
$954$	−1554.49	+	10811.7i	−0.0527550	+	0.366919i
$955$	954.701	−	6640.09i	0.0323491	−	0.224993i
$956$	23437.4	+	15062.3i	0.792907	+	0.509570i
$957$	1791.53	+	2067.53i	0.0605139	+	0.0698368i
$958$	2530.80	+	5541.69i	0.0853513	+	0.186893i
$959$	2604.75	−	1673.97i	0.0877078	−	0.0563664i
$960$	−759.142	−	222.904i	−0.0255221	−	0.00749397i
$961$	8109.16	−	9358.46i	0.272202	−	0.314137i
$962$	−13942.2	+	4093.81i	−0.467272	+	0.137203i
$963$	−1544.20	+	3381.32i	−0.0516730	+	0.113148i
$964$	−874.063	−	6079.24i	−0.0292030	−	0.203111i
$965$	18167.8			0.606054
$966$	5710.76	−	16529.8i	0.190208	−	0.550558i
$967$	−17919.5			−0.595916			−0.297958	−	0.954579i	$-0.596306\pi$
$967$	−17919.5			−0.595916			−0.297958	+	0.954579i	$0.596306\pi$
$968$	−802.476	−	5581.34i	−0.0266452	−	0.185321i
$969$	1805.73	−	3953.99i	0.0598641	−	0.131084i
$970$	8975.09	−	2635.33i	0.297085	−	0.0872322i
$971$	5842.91	−	6743.08i	0.193108	−	0.222858i	−0.650936	−	0.759133i	$-0.725623\pi$
$971$	5842.91	−	6743.08i	0.193108	−	0.222858i	0.844044	+	0.536274i	$0.180169\pi$
$972$	−932.627	−	273.844i	−0.0307758	−	0.00903658i
$973$	−25900.7	+	16645.4i	−0.853380	+	0.548434i
$974$	16503.6	+	36137.9i	0.542926	+	1.18884i
$975$	11061.2	+	12765.3i	0.363326	+	0.419301i
$976$	−11207.4	−	7202.57i	−0.367562	−	0.236218i
$977$	5422.57	−	37714.8i	0.177567	−	1.23501i	−0.684802	−	0.728729i	$-0.740111\pi$
$977$	5422.57	−	37714.8i	0.177567	−	1.23501i	0.862369	−	0.506280i	$-0.168980\pi$
$978$	−129.301	+	899.309i	−0.00422760	+	0.0294036i
$979$	−25018.9	−	16078.7i	−0.816761	−	0.524900i
$980$	−3834.79	−	4425.58i	−0.124998	−	0.144255i
$981$	−5000.28	−	10949.1i	−0.162739	−	0.356348i
$982$	25994.1	−	16705.4i	0.844711	−	0.542863i
$983$	−56510.1	−	16592.9i	−1.83356	−	0.538383i	−0.833660	−	0.552278i	$-0.813759\pi$
$983$	−56510.1	−	16592.9i	−1.83356	−	0.538383i	−0.999903	+	0.0138948i	$0.995577\pi$
$984$	2746.36	−	3169.47i	0.0889744	−	0.102682i
$985$	2199.63	−	645.869i	0.0711533	−	0.0208925i
$986$	388.774	−	851.296i	0.0125569	−	0.0274957i
$987$	3432.30	+	23872.1i	0.110690	+	0.769867i
$988$	−23527.1			−0.757587
$989$	−6976.68	−	12068.5i	−0.224313	−	0.388023i
$990$	1856.07			0.0595857
$991$	616.766	+	4289.70i	0.0197702	+	0.137504i	0.997316	−	0.0732189i	$-0.0233272\pi$
$991$	616.766	+	4289.70i	0.0197702	+	0.137504i	−0.977546	+	0.210723i	$0.932418\pi$
$992$	1753.91	−	3840.52i	0.0561357	−	0.122920i
$993$	−27644.4	+	8117.14i	−0.883454	+	0.259405i
$994$	−32831.7	+	37889.8i	−1.04765	+	1.20905i
$995$	−14412.4	−	4231.86i	−0.459200	−	0.134833i
$996$	−8523.88	+	5477.97i	−0.271174	+	0.174273i
$997$	−14486.2	−	31720.3i	−0.460163	−	1.00762i	−0.987450	−	0.157929i	$-0.949518\pi$
$997$	−14486.2	−	31720.3i	−0.460163	−	1.00762i	0.527288	−	0.849687i	$-0.323209\pi$
$998$	19631.8	+	22656.4i	0.622681	+	0.718612i
$999$	−3166.06	−	2034.70i	−0.100270	−	0.0644395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.4.e.c.49.2	yes	30
23.8	even	11	inner	138.4.e.c.31.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.4.e.c.31.2	✓	30	23.8	even	11	inner
138.4.e.c.49.2	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.284630 + 1.97964i) q^{2} +(1.24625 - 2.72890i) q^{3} +(-3.83797 + 1.12693i) q^{4} +(-2.69854 + 3.11428i) q^{5} +(5.75696 + 1.69040i) q^{6} +(22.2299 - 14.2863i) q^{7} +(-3.32332 - 7.27706i) q^{8} +(-5.89375 - 6.80175i) q^{9} +O(q^{10})\)	\(q+(0.284630 + 1.97964i) q^{2} +(1.24625 - 2.72890i) q^{3} +(-3.83797 + 1.12693i) q^{4} +(-2.69854 + 3.11428i) q^{5} +(5.75696 + 1.69040i) q^{6} +(22.2299 - 14.2863i) q^{7} +(-3.32332 - 7.27706i) q^{8} +(-5.89375 - 6.80175i) q^{9} +(-6.93325 - 4.45573i) q^{10} +(3.56117 - 24.7685i) q^{11} +(-1.70778 + 11.8779i) q^{12} +(43.8490 + 28.1800i) q^{13} +(34.6090 + 39.9409i) q^{14} +(5.13551 + 11.2452i) q^{15} +(13.4601 - 8.65025i) q^{16} +(12.3201 + 3.61752i) q^{17} +(11.7875 - 13.6035i) q^{18} +(108.272 - 31.7916i) q^{19} +(6.84735 - 14.9936i) q^{20} +(-11.2819 - 78.4672i) q^{21} +50.0463 q^{22} +(63.9328 - 89.8866i) q^{23} -24.0000 q^{24} +(15.3727 + 106.920i) q^{25} +(-43.3057 + 94.8262i) q^{26} +(-25.9063 + 7.60678i) q^{27} +(-69.2180 + 79.8818i) q^{28} +(-34.9666 - 10.2671i) q^{29} +(-20.7998 + 13.3672i) q^{30} +(-54.8096 - 120.016i) q^{31} +(20.9555 + 24.1840i) q^{32} +(-63.1525 - 40.5856i) q^{33} +(-3.65472 + 25.4191i) q^{34} +(-15.4967 + 107.782i) q^{35} +(30.2851 + 19.4631i) q^{36} +(91.2802 + 105.343i) q^{37} +(93.7535 + 205.292i) q^{38} +(131.547 - 84.5401i) q^{39} +(31.6309 + 9.28768i) q^{40} +(-114.432 + 132.061i) q^{41} +(152.126 - 44.6682i) q^{42} +(52.4991 - 114.957i) q^{43} +(14.2447 + 99.0738i) q^{44} +37.0871 q^{45} +(196.141 + 100.980i) q^{46} -304.231 q^{47} +(-6.83111 - 47.5114i) q^{48} +(147.582 - 323.160i) q^{49} +(-207.287 + 60.8650i) q^{50} +(25.2257 - 29.1120i) q^{51} +(-200.048 - 58.7394i) q^{52} +(-510.494 + 328.075i) q^{53} +(-22.4324 - 49.1201i) q^{54} +(67.5260 + 77.9292i) q^{55} +(-177.839 - 114.290i) q^{56} +(48.1778 - 335.084i) q^{57} +(10.3727 - 72.1436i) q^{58} +(-279.360 - 179.534i) q^{59} +(-32.3825 - 37.3714i) q^{60} +(-345.892 - 757.399i) q^{61} +(221.989 - 142.664i) q^{62} +(-228.189 - 67.0023i) q^{63} +(-41.9111 + 48.3680i) q^{64} +(-206.089 + 60.5132i) q^{65} +(62.3700 - 136.571i) q^{66} +(-15.7755 - 109.721i) q^{67} -51.3610 q^{68} +(-165.615 - 286.487i) q^{69} -217.781 q^{70} +(135.007 + 938.991i) q^{71} +(-29.9099 + 65.4935i) q^{72} +(147.933 - 43.4371i) q^{73} +(-182.560 + 210.686i) q^{74} +(310.931 + 91.2975i) q^{75} +(-379.719 + 244.031i) q^{76} +(-274.685 - 601.475i) q^{77} +(204.801 + 236.353i) q^{78} +(-290.607 - 186.762i) q^{79} +(-9.38319 + 65.2615i) q^{80} +(-11.5275 + 80.1755i) q^{81} +(-294.005 - 188.946i) q^{82} +(552.940 + 638.127i) q^{83} +(131.727 + 288.441i) q^{84} +(-44.5124 + 28.6064i) q^{85} +(242.516 + 71.2092i) q^{86} +(-71.5948 + 82.6248i) q^{87} +(-192.076 + 56.3987i) q^{88} +(493.722 - 1081.10i) q^{89} +(10.5561 + 73.4192i) q^{90} +1377.35 q^{91} +(-144.076 + 417.030i) q^{92} -395.818 q^{93} +(-86.5931 - 602.269i) q^{94} +(-193.169 + 422.982i) q^{95} +(92.1113 - 27.0463i) q^{96} +(-743.252 + 857.758i) q^{97} +(681.748 + 200.179i) q^{98} +(-189.457 + 121.757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} - 9 q^{3} - 12 q^{4} - 4 q^{5} + 18 q^{6} + 4 q^{7} + 24 q^{8} - 27 q^{9}+O(q^{10}) \) 30 * q + 6 * q^2 - 9 * q^3 - 12 * q^4 - 4 * q^5 + 18 * q^6 + 4 * q^7 + 24 * q^8 - 27 * q^9	\( 30 q + 6 q^{2} - 9 q^{3} - 12 q^{4} - 4 q^{5} + 18 q^{6} + 4 q^{7} + 24 q^{8} - 27 q^{9} - 36 q^{10} - 5 q^{11} - 36 q^{12} - 59 q^{13} + 36 q^{14} + 120 q^{15} - 48 q^{16} - 291 q^{17} + 54 q^{18} + 319 q^{19} + 160 q^{20} + 45 q^{21} + 384 q^{22} + 472 q^{23} - 720 q^{24} + 321 q^{25} + 250 q^{26} - 81 q^{27} - 72 q^{28} + 753 q^{29} - 108 q^{30} - 345 q^{31} + 96 q^{32} - 609 q^{33} + 164 q^{34} - 646 q^{35} - 108 q^{36} - 349 q^{37} + 242 q^{38} - 177 q^{39} - 56 q^{40} - 548 q^{41} - 24 q^{42} + 1800 q^{43} - 20 q^{44} - 1026 q^{45} + 46 q^{46} + 2666 q^{47} - 144 q^{48} - 1685 q^{49} + 414 q^{50} + 51 q^{51} - 280 q^{52} + 769 q^{53} + 162 q^{54} - 4188 q^{55} - 32 q^{56} - 1518 q^{57} - 1264 q^{58} + 2649 q^{59} - 48 q^{60} + 876 q^{61} + 8 q^{62} + 36 q^{63} - 192 q^{64} + 906 q^{65} - 300 q^{66} - 451 q^{67} - 1648 q^{68} + 459 q^{69} + 1512 q^{70} - 2161 q^{71} + 216 q^{72} - 1838 q^{73} + 698 q^{74} - 621 q^{75} + 264 q^{76} + 7182 q^{77} - 1098 q^{78} - 4324 q^{79} - 64 q^{80} - 243 q^{81} + 3736 q^{82} + 191 q^{83} - 84 q^{84} - 2734 q^{85} + 1086 q^{86} - 1074 q^{87} + 392 q^{88} + 4073 q^{89} + 72 q^{90} - 1970 q^{91} - 4624 q^{92} + 1506 q^{93} - 954 q^{94} + 2153 q^{95} + 288 q^{96} - 157 q^{97} - 2988 q^{98} - 1827 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 - 9 * q^3 - 12 * q^4 - 4 * q^5 + 18 * q^6 + 4 * q^7 + 24 * q^8 - 27 * q^9 - 36 * q^10 - 5 * q^11 - 36 * q^12 - 59 * q^13 + 36 * q^14 + 120 * q^15 - 48 * q^16 - 291 * q^17 + 54 * q^18 + 319 * q^19 + 160 * q^20 + 45 * q^21 + 384 * q^22 + 472 * q^23 - 720 * q^24 + 321 * q^25 + 250 * q^26 - 81 * q^27 - 72 * q^28 + 753 * q^29 - 108 * q^30 - 345 * q^31 + 96 * q^32 - 609 * q^33 + 164 * q^34 - 646 * q^35 - 108 * q^36 - 349 * q^37 + 242 * q^38 - 177 * q^39 - 56 * q^40 - 548 * q^41 - 24 * q^42 + 1800 * q^43 - 20 * q^44 - 1026 * q^45 + 46 * q^46 + 2666 * q^47 - 144 * q^48 - 1685 * q^49 + 414 * q^50 + 51 * q^51 - 280 * q^52 + 769 * q^53 + 162 * q^54 - 4188 * q^55 - 32 * q^56 - 1518 * q^57 - 1264 * q^58 + 2649 * q^59 - 48 * q^60 + 876 * q^61 + 8 * q^62 + 36 * q^63 - 192 * q^64 + 906 * q^65 - 300 * q^66 - 451 * q^67 - 1648 * q^68 + 459 * q^69 + 1512 * q^70 - 2161 * q^71 + 216 * q^72 - 1838 * q^73 + 698 * q^74 - 621 * q^75 + 264 * q^76 + 7182 * q^77 - 1098 * q^78 - 4324 * q^79 - 64 * q^80 - 243 * q^81 + 3736 * q^82 + 191 * q^83 - 84 * q^84 - 2734 * q^85 + 1086 * q^86 - 1074 * q^87 + 392 * q^88 + 4073 * q^89 + 72 * q^90 - 1970 * q^91 - 4624 * q^92 + 1506 * q^93 - 954 * q^94 + 2153 * q^95 + 288 * q^96 - 157 * q^97 - 2988 * q^98 - 1827 * q^99

Introduction

L-functions

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