LMFDB - Embedded newform 177.4.e.a.133.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, 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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			133.2
Character	$\chi$	$=$	177.133
Dual form			177.4.e.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.95061 + 0.538411i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(16.4057 - 3.61116i) q^{4} +(10.7888 - 8.20142i) q^{5} +(10.8459 + 10.2738i) q^{6} +(11.1308 + 27.9361i) q^{7} +(-41.5207 + 13.9900i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})$	\(q+(-4.95061 + 0.538411i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(16.4057 - 3.61116i) q^{4} +(10.7888 - 8.20142i) q^{5} +(10.8459 + 10.2738i) q^{6} +(11.1308 + 27.9361i) q^{7} +(-41.5207 + 13.9900i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(-48.9953 + 46.4108i) q^{10} +(22.1794 + 10.2613i) q^{11} +(-40.1193 - 30.4979i) q^{12} +(-3.00494 - 18.3293i) q^{13} +(-70.1451 - 132.308i) q^{14} +(-39.7060 - 8.73994i) q^{15} +(76.0539 - 35.1863i) q^{16} +(35.3205 - 88.6477i) q^{17} +(2.42641 - 44.7525i) q^{18} +(-89.9954 + 132.733i) q^{19} +(147.381 - 173.510i) q^{20} +(42.2578 - 79.7067i) q^{21} +(-115.326 - 38.8579i) q^{22} +(10.2146 + 188.397i) q^{23} +(112.628 + 67.7658i) q^{24} +(15.6935 - 56.5230i) q^{25} +(24.7450 + 89.1235i) q^{26} +(23.1351 - 13.9200i) q^{27} +(283.489 + 418.115i) q^{28} +(-204.072 - 22.1941i) q^{29} +(201.274 + 21.8899i) q^{30} +(38.9665 + 57.4712i) q^{31} +(-57.2279 + 34.4329i) q^{32} +(-19.6136 - 70.6419i) q^{33} +(-127.129 + 457.877i) q^{34} +(349.203 + 210.108i) q^{35} +(8.18502 + 150.964i) q^{36} +(384.432 + 129.530i) q^{37} +(374.067 - 705.565i) q^{38} +(-36.0737 + 42.4693i) q^{39} +(-333.221 + 491.464i) q^{40} +(-1.15380 + 21.2805i) q^{41} +(-166.287 + 417.348i) q^{42} +(105.084 - 48.6172i) q^{43} +(400.923 + 88.2498i) q^{44} +(57.1315 + 107.762i) q^{45} +(-152.003 - 927.179i) q^{46} +(-42.6787 - 32.4435i) q^{47} +(-228.162 - 105.559i) q^{48} +(-407.515 + 386.019i) q^{49} +(-47.2599 + 288.273i) q^{50} +(-271.290 + 91.4082i) q^{51} +(-115.488 - 289.854i) q^{52} +(105.019 + 99.4794i) q^{53} +(-107.038 + 81.3684i) q^{54} +(323.446 - 71.1958i) q^{55} +(-852.982 - 1004.21i) q^{56} +(478.278 - 52.0159i) q^{57} +1022.23 q^{58} +(434.478 + 128.871i) q^{59} -682.964 q^{60} +(156.585 - 17.0296i) q^{61} +(-223.851 - 263.538i) q^{62} +(-264.320 + 58.1811i) q^{63} +(-268.921 + 204.428i) q^{64} +(-182.746 - 173.107i) q^{65} +(135.134 + 339.160i) q^{66} +(405.101 - 136.494i) q^{67} +(259.335 - 1581.87i) q^{68} +(410.929 - 389.252i) q^{69} +(-1841.89 - 852.150i) q^{70} +(11.4962 + 8.73921i) q^{71} +(-63.7952 - 389.134i) q^{72} +(397.204 + 749.207i) q^{73} +(-1972.91 - 434.270i) q^{74} +(-159.718 + 73.8936i) q^{75} +(-997.113 + 2502.56i) q^{76} +(-39.7866 + 733.822i) q^{77} +(155.721 - 229.671i) q^{78} +(442.726 - 521.217i) q^{79} +(531.952 - 1003.37i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(-5.74567 - 105.973i) q^{82} +(-1041.44 - 626.612i) q^{83} +(405.434 - 1460.24i) q^{84} +(-345.972 - 1246.08i) q^{85} +(-494.056 + 297.263i) q^{86} +(345.593 + 509.712i) q^{87} +(-1064.46 - 115.767i) q^{88} +(142.103 + 15.4547i) q^{89} +(-340.856 - 502.725i) q^{90} +(478.603 - 287.966i) q^{91} +(847.908 + 3053.89i) q^{92} +(55.7281 - 200.715i) q^{93} +(228.753 + 137.636i) q^{94} +(117.661 + 2170.12i) q^{95} +(189.876 + 63.9766i) q^{96} +(589.244 - 1111.43i) q^{97} +(1809.61 - 2130.44i) q^{98} +(-123.429 + 182.044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{28}{29}\right)$	$1$

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 $

$2$	−4.95061	+	0.538411i	−1.75030	+	0.190357i	−0.926443	−	0.376435i	$-0.877150\pi$
$2$	−4.95061	+	0.538411i	−1.75030	+	0.190357i	−0.823861	+	0.566792i	$0.808184\pi$
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$4$	16.4057	−	3.61116i	2.05071	−	0.451395i
$5$	10.7888	−	8.20142i	0.964978	−	0.733557i	0.00112729	−	0.999999i	$-0.499641\pi$
$5$	10.7888	−	8.20142i	0.964978	−	0.733557i	0.963851	+	0.266442i	$0.0858481\pi$
$6$	10.8459	+	10.2738i	0.737972	+	0.699045i
$7$	11.1308	+	27.9361i	0.601004	+	1.50841i	0.842881	+	0.538100i	$0.180858\pi$
$7$	11.1308	+	27.9361i	0.601004	+	1.50841i	−0.241876	+	0.970307i	$0.577763\pi$
$8$	−41.5207	+	13.9900i	−1.83497	+	0.618275i
$9$	−1.45604	+	8.88144i	−0.0539273	+	0.328942i
$10$	−48.9953	+	46.4108i	−1.54937	+	1.46764i
$11$	22.1794	+	10.2613i	0.607940	+	0.281263i	0.699608	−	0.714527i	$-0.253358\pi$
$11$	22.1794	+	10.2613i	0.607940	+	0.281263i	−0.0916683	+	0.995790i	$0.529220\pi$
$12$	−40.1193	−	30.4979i	−0.965120	−	0.733665i
$13$	−3.00494	−	18.3293i	−0.0641093	−	0.391050i	−0.999317	−	0.0369502i	$-0.988236\pi$
$13$	−3.00494	−	18.3293i	−0.0641093	−	0.391050i	0.935208	−	0.354099i	$-0.115213\pi$
$14$	−70.1451	−	132.308i	−1.33908	−	2.52577i
$15$	−39.7060	−	8.73994i	−0.683469	−	0.150443i
$16$	76.0539	−	35.1863i	1.18834	−	0.549786i
$17$	35.3205	−	88.6477i	0.503910	−	1.26472i	−0.428573	−	0.903507i	$-0.640984\pi$
$17$	35.3205	−	88.6477i	0.503910	−	1.26472i	0.932484	−	0.361213i	$-0.117637\pi$
$18$	2.42641	−	44.7525i	0.0317728	−	0.586014i
$19$	−89.9954	+	132.733i	−1.08665	+	1.60269i	−0.336165	+	0.941803i	$0.609130\pi$
$19$	−89.9954	+	132.733i	−1.08665	+	1.60269i	−0.750486	+	0.660886i	$0.770180\pi$
$20$	147.381	−	173.510i	1.64776	−	1.93990i
$21$	42.2578	−	79.7067i	0.439115	−	0.828258i
$22$	−115.326	−	38.8579i	−1.11762	−	0.376570i
$23$	10.2146	+	188.397i	0.0926038	+	1.70798i	0.563770	+	0.825932i	$0.309351\pi$
$23$	10.2146	+	188.397i	0.0926038	+	1.70798i	−0.471166	+	0.882045i	$0.656167\pi$
$24$	112.628	+	67.7658i	0.957918	+	0.576360i
$25$	15.6935	−	56.5230i	0.125548	−	0.452184i
$26$	24.7450	+	89.1235i	0.186650	+	0.672252i
$27$	23.1351	−	13.9200i	0.164902	−	0.0992184i
$28$	283.489	+	418.115i	1.91337	+	2.82201i
$29$	−204.072	−	22.1941i	−1.30673	−	0.142116i	−0.571876	−	0.820340i	$-0.693784\pi$
$29$	−204.072	−	22.1941i	−1.30673	−	0.142116i	−0.734855	+	0.678225i	$0.762750\pi$
$30$	201.274	+	21.8899i	1.22492	+	0.133218i
$31$	38.9665	+	57.4712i	0.225761	+	0.332972i	0.923653	−	0.383231i	$-0.125189\pi$
$31$	38.9665	+	57.4712i	0.225761	+	0.332972i	−0.697892	+	0.716203i	$0.745878\pi$
$32$	−57.2279	+	34.4329i	−0.316142	+	0.190217i
$33$	−19.6136	−	70.6419i	−0.103463	−	0.372642i
$34$	−127.129	+	457.877i	−0.641248	+	2.30957i
$35$	349.203	+	210.108i	1.68646	+	1.01471i
$36$	8.18502	+	150.964i	0.0378936	+	0.698907i
$37$	384.432	+	129.530i	1.70811	+	0.575530i	0.992421	−	0.122886i	$-0.0392149\pi$
$37$	384.432	+	129.530i	1.70811	+	0.575530i	0.715692	+	0.698416i	$0.246111\pi$
$38$	374.067	−	705.565i	1.59689	−	3.01205i
$39$	−36.0737	+	42.4693i	−0.148113	+	0.174372i
$40$	−333.221	+	491.464i	−1.31717	+	1.94268i
$41$	−1.15380	+	21.2805i	−0.00439494	+	0.0810599i	−0.999908	−	0.0135643i	$-0.995682\pi$
$41$	−1.15380	+	21.2805i	−0.00439494	+	0.0810599i	0.995513	+	0.0946243i	$0.0301650\pi$
$42$	−166.287	+	417.348i	−0.610919	+	1.53329i
$43$	105.084	−	48.6172i	0.372680	−	0.172420i	−0.224604	−	0.974450i	$-0.572109\pi$
$43$	105.084	−	48.6172i	0.372680	−	0.172420i	0.597283	+	0.802030i	$0.296247\pi$
$44$	400.923	+	88.2498i	1.37367	+	0.302367i
$45$	57.1315	+	107.762i	0.189259	+	0.356981i
$46$	−152.003	−	927.179i	−0.487210	−	2.97185i
$47$	−42.6787	−	32.4435i	−0.132454	−	0.100689i	0.536850	−	0.843678i	$-0.319614\pi$
$47$	−42.6787	−	32.4435i	−0.132454	−	0.100689i	−0.669303	+	0.742989i	$0.733407\pi$
$48$	−228.162	−	105.559i	−0.686090	−	0.317419i
$49$	−407.515	+	386.019i	−1.18809	+	1.12542i
$50$	−47.2599	+	288.273i	−0.133671	+	0.815358i
$51$	−271.290	+	91.4082i	−0.744866	+	0.250975i
$52$	−115.488	−	289.854i	−0.307987	−	0.772990i
$53$	105.019	+	99.4794i	0.272179	+	0.257822i	0.811599	−	0.584216i	$-0.198598\pi$
$53$	105.019	+	99.4794i	0.272179	+	0.257822i	−0.539420	+	0.842037i	$0.681356\pi$
$54$	−107.038	+	81.3684i	−0.269742	+	0.205053i
$55$	323.446	−	71.1958i	0.792971	−	0.174546i
$56$	−852.982	−	1004.21i	−2.03544	−	2.39630i
$57$	478.278	−	52.0159i	1.11139	−	0.120871i
$58$	1022.23			2.31423
$59$	434.478	+	128.871i	0.958716	+	0.284367i
$59$	434.478	+	128.871i	0.958716	+	0.284367i
$60$	−682.964			−1.46950
$61$	156.585	−	17.0296i	0.328666	−	0.0357446i	0.0577013	−	0.998334i	$-0.481623\pi$
$61$	156.585	−	17.0296i	0.328666	−	0.0357446i	0.270965	+	0.962589i	$0.412657\pi$
$62$	−223.851	−	263.538i	−0.458534	−	0.539828i
$63$	−264.320	+	58.1811i	−0.528589	+	0.116351i
$64$	−268.921	+	204.428i	−0.525236	+	0.399274i
$65$	−182.746	−	173.107i	−0.348721	−	0.330327i
$66$	135.134	+	339.160i	0.252028	+	0.632541i
$67$	405.101	−	136.494i	0.738671	−	0.248887i	0.0752826	−	0.997162i	$-0.476014\pi$
$67$	405.101	−	136.494i	0.738671	−	0.248887i	0.663389	+	0.748275i	$0.269118\pi$
$68$	259.335	−	1581.87i	0.462485	−	2.82103i
$69$	410.929	−	389.252i	0.716956	−	0.679137i
$70$	−1841.89	−	852.150i	−3.14497	−	1.45502i
$71$	11.4962	+	8.73921i	0.0192162	+	0.0146078i	0.614738	−	0.788731i	$-0.289262\pi$
$71$	11.4962	+	8.73921i	0.0192162	+	0.0146078i	−0.595522	+	0.803339i	$0.703055\pi$
$72$	−63.7952	−	389.134i	−0.104421	−	0.636942i
$73$	397.204	+	749.207i	0.636839	+	1.20121i	0.966393	+	0.257069i	$0.0827567\pi$
$73$	397.204	+	749.207i	0.636839	+	1.20121i	−0.329554	+	0.944137i	$0.606898\pi$
$74$	−1972.91	−	434.270i	−3.09927	−	0.682202i
$75$	−159.718	+	73.8936i	−0.245902	+	0.113767i
$76$	−997.113	+	2502.56i	−1.50496	+	3.77716i
$77$	−39.7866	+	733.822i	−0.0588845	+	1.08606i
$78$	155.721	−	229.671i	0.226050	−	0.333399i
$79$	442.726	−	521.217i	0.630513	−	0.742297i	−0.350431	−	0.936589i	$-0.613965\pi$
$79$	442.726	−	521.217i	0.630513	−	0.742297i	0.980944	+	0.194291i	$0.0622407\pi$
$80$	531.952	−	1003.37i	0.743425	−	1.40225i
$81$	−76.7599	−	25.8634i	−0.105295	−	0.0354779i
$82$	−5.74567	−	105.973i	−0.00773784	−	0.142716i
$83$	−1041.44	−	626.612i	−1.37726	−	0.828670i	−0.381836	−	0.924230i	$-0.624708\pi$
$83$	−1041.44	−	626.612i	−1.37726	−	0.828670i	−0.995424	+	0.0955603i	$0.969536\pi$
$84$	405.434	−	1460.24i	0.526624	−	1.89673i
$85$	−345.972	−	1246.08i	−0.441482	−	1.59007i
$86$	−494.056	+	297.263i	−0.619481	+	0.372730i
$87$	345.593	+	509.712i	0.425879	+	0.628125i
$88$	−1064.46	−	115.767i	−1.28945	−	0.140236i
$89$	142.103	+	15.4547i	0.169246	+	0.0184066i	0.192350	−	0.981326i	$-0.438389\pi$
$89$	142.103	+	15.4547i	0.169246	+	0.0184066i	−0.0231034	+	0.999733i	$0.507355\pi$
$90$	−340.856	−	502.725i	−0.399215	−	0.588798i
$91$	478.603	−	287.966i	0.551332	−	0.331726i
$92$	847.908	+	3053.89i	0.960875	+	3.46076i
$93$	55.7281	−	200.715i	0.0621370	−	0.223797i
$94$	228.753	+	137.636i	0.251001	+	0.151022i
$95$	117.661	+	2170.12i	0.127071	+	2.34368i
$96$	189.876	+	63.9766i	0.201866	+	0.0680165i
$97$	589.244	−	1111.43i	0.616790	−	1.16339i	−0.356605	−	0.934255i	$-0.616066\pi$
$97$	589.244	−	1111.43i	0.616790	−	1.16339i	0.973395	−	0.229134i	$-0.0735895\pi$
$98$	1809.61	−	2130.44i	1.86529	−	2.19599i
$99$	−123.429	+	182.044i	−0.125304	+	0.184809i
$100$	53.3492	−	983.969i	0.0533492	−	0.983969i
$101$	−535.746	+	1344.62i	−0.527809	+	1.32470i	0.387471	+	0.921882i	$0.373349\pi$
$101$	−535.746	+	1344.62i	−0.527809	+	1.32470i	−0.915280	+	0.402819i	$0.868030\pi$
$102$	1293.83	−	598.591i	1.25597	−	0.581072i
$103$	514.109	+	113.164i	0.491812	+	0.108256i	0.453950	−	0.891027i	$-0.350014\pi$
$103$	514.109	+	113.164i	0.491812	+	0.108256i	0.0378617	+	0.999283i	$0.487945\pi$
$104$	381.194	+	719.008i	0.359415	+	0.677929i
$105$	−197.798	−	1206.51i	−0.183839	−	1.12137i
$106$	−573.469	−	435.940i	−0.525474	−	0.399455i
$107$	−157.334	−	72.7905i	−0.142150	−	0.0657656i	0.347524	−	0.937671i	$-0.387022\pi$
$107$	−157.334	−	72.7905i	−0.142150	−	0.0657656i	−0.489675	+	0.871905i	$0.662884\pi$
$108$	329.280	−	311.911i	0.293380	−	0.277904i
$109$	−49.4707	+	301.758i	−0.0434718	+	0.265166i	−0.999615	−	0.0277320i	$-0.991172\pi$
$109$	−49.4707	+	301.758i	−0.0434718	+	0.265166i	0.956144	+	0.292898i	$0.0946198\pi$
$110$	−1562.92	+	526.609i	−1.35471	+	0.456457i
$111$	−450.459	−	1130.57i	−0.385186	−	0.966744i
$112$	1829.50	+	1733.00i	1.54350	+	1.46208i
$113$	728.345	−	553.673i	0.606344	−	0.460931i	−0.256400	−	0.966571i	$-0.582537\pi$
$113$	728.345	−	553.673i	0.606344	−	0.460931i	0.862745	+	0.505640i	$0.168743\pi$
$114$	−2339.76	+	515.020i	−1.92227	+	0.423124i
$115$	1655.33	+	1948.80i	1.34226	+	1.58023i
$116$	−3428.08	+	372.826i	−2.74387	+	0.298414i
$117$	167.166			0.132090
$118$	−2220.32	−	404.064i	−1.73217	−	0.315230i
$119$	2869.61			2.21056
$120$	1770.89	−	192.596i	1.34716	−	0.146513i
$121$	−475.039	−	559.260i	−0.356904	−	0.420180i
$122$	−766.020	+	168.614i	−0.568461	+	0.125128i
$123$	50.8985	−	38.6920i	0.0373119	−	0.0283637i
$124$	846.809	+	802.140i	0.613271	+	0.580922i
$125$	332.767	+	835.182i	0.238109	+	0.597608i
$126$	1277.22	−	430.344i	0.903044	−	0.304271i
$127$	−98.3083	+	599.654i	−0.0686886	+	0.418982i	0.929990	+	0.367586i	$0.119815\pi$
$127$	−98.3083	+	599.654i	−0.0686886	+	0.418982i	−0.998678	+	0.0513965i	$0.983633\pi$
$128$	1609.16	−	1524.27i	1.11118	−	1.05256i
$129$	−315.253	−	145.852i	−0.215167	−	0.0995467i
$130$	997.908	+	758.590i	0.673249	+	0.511790i
$131$	102.833	+	627.253i	0.0685844	+	0.418346i	0.998695	+	0.0510672i	$0.0162623\pi$
$131$	102.833	+	627.253i	0.0685844	+	0.418346i	−0.930111	+	0.367279i	$0.880289\pi$
$132$	−576.874	−	1088.10i	−0.380382	−	0.717477i
$133$	−4709.77	−	1036.70i	−3.07059	−	0.675888i
$134$	−1932.01	+	893.842i	−1.24552	+	0.576240i
$135$	135.437	−	339.920i	0.0863447	−	0.216709i
$136$	−226.354	+	4174.85i	−0.142718	+	2.63228i
$137$	264.250	−	389.740i	0.164791	−	0.243049i	−0.736323	−	0.676630i	$-0.763440\pi$
$137$	264.250	−	389.740i	0.164791	−	0.243049i	0.901115	+	0.433581i	$0.142750\pi$
$138$	−1824.77	+	2148.28i	−1.12561	+	1.32517i
$139$	−714.621	+	1347.92i	−0.436067	+	0.822510i	−0.999995	−	0.00331460i	$-0.998945\pi$
$139$	−714.621	+	1347.92i	−0.436067	+	0.822510i	0.563927	+	0.825824i	$0.309290\pi$
$140$	6487.64	+	2185.94i	3.91647	+	1.31961i
$141$	8.70719	+	160.595i	0.00520055	+	0.0959186i
$142$	−61.6186	−	37.0747i	−0.0364149	−	0.0219101i
$143$	121.435	−	437.368i	0.0710132	−	0.255766i
$144$	201.767	+	726.701i	0.116764	+	0.420544i
$145$	−2383.71	+	1434.23i	−1.36522	+	0.821424i
$146$	−2369.78	−	3495.17i	−1.34332	−	1.98125i
$147$	1674.09	+	182.068i	0.939294	+	0.102154i
$148$	6774.61	+	736.783i	3.76263	+	0.409211i
$149$	563.451	+	831.027i	0.309796	+	0.456916i	0.950433	−	0.310928i	$-0.100640\pi$
$149$	563.451	+	831.027i	0.309796	+	0.456916i	−0.640637	+	0.767844i	$0.721330\pi$
$150$	750.918	−	451.812i	0.408748	−	0.245935i
$151$	−649.242	−	2338.36i	−0.349898	−	1.26022i	−0.903915	−	0.427712i	$-0.859320\pi$
$151$	−649.242	−	2338.36i	−0.349898	−	1.26022i	0.554017	−	0.832505i	$-0.313094\pi$
$152$	1879.74	−	6770.21i	1.00307	−	3.61274i
$153$	735.891	+	442.771i	0.388845	+	0.233960i
$154$	−198.130	−	3654.28i	−0.103674	−	1.91215i
$155$	891.747	+	300.464i	0.462109	+	0.155702i
$156$	−438.450	+	827.004i	−0.225026	+	0.424444i
$157$	717.406	−	844.596i	0.364683	−	0.429338i	−0.548964	−	0.835846i	$-0.684978\pi$
$157$	717.406	−	844.596i	0.364683	−	0.429338i	0.913647	+	0.406508i	$0.133254\pi$
$158$	−1911.13	+	2818.71i	−0.962288	+	1.41927i
$159$	23.4944	−	433.329i	0.0117184	−	0.216134i
$160$	−335.021	+	840.839i	−0.165536	+	0.415463i
$161$	−5149.38	+	2382.36i	−2.52067	+	1.16619i
$162$	393.933	+	86.7113i	0.191051	+	0.0420536i
$163$	1369.82	+	2583.75i	0.658237	+	1.24157i	0.957785	+	0.287485i	$0.0928192\pi$
$163$	1369.82	+	2583.75i	0.658237	+	1.24157i	−0.299548	+	0.954081i	$0.596836\pi$
$164$	57.9185	+	353.287i	0.0275773	+	0.168214i
$165$	−790.971	−	601.281i	−0.373194	−	0.283695i
$166$	5493.12	+	2541.39i	2.56837	+	1.18825i
$167$	−0.300434	+	0.284587i	−0.000139211	+	0.000131868i	−0.687769	−	0.725930i	$-0.741410\pi$
$167$	−0.300434	+	0.284587i	−0.000139211	+	0.000131868i	0.687630	+	0.726061i	$0.258651\pi$
$168$	−639.481	+	3900.66i	−0.293673	+	1.79133i
$169$	1755.06	−	591.348i	0.798843	−	0.269162i
$170$	2383.68	+	5982.57i	1.07541	+	2.69907i
$171$	−1047.83	−	992.553i	−0.468592	−	0.443874i
$172$	1548.41	−	1177.07i	0.686427	−	0.521809i
$173$	146.757	−	32.3036i	0.0644955	−	0.0141965i	−0.182605	−	0.983186i	$-0.558453\pi$
$173$	146.757	−	32.3036i	0.0644955	−	0.0141965i	0.247101	+	0.968990i	$0.420522\pi$
$174$	−1985.33	−	2337.31i	−0.864986	−	1.01834i
$175$	1753.71	−	190.728i	0.757533	−	0.0823866i
$176$	2047.89			0.877075
$177$	−549.162	−	1243.72i	−0.233207	−	0.528155i
$178$	−711.819			−0.299736
$179$	275.156	−	29.9250i	0.114894	−	0.0124955i	−0.0504912	−	0.998725i	$-0.516079\pi$
$179$	275.156	−	29.9250i	0.114894	−	0.0124955i	0.165386	+	0.986229i	$0.447113\pi$
$180$	1326.42	+	1561.59i	0.549255	+	0.646633i
$181$	−2747.12	+	604.686i	−1.12813	+	0.248320i	−0.739554	−	0.673097i	$-0.764964\pi$
$181$	−2747.12	+	604.686i	−1.12813	+	0.248320i	−0.388576	+	0.921417i	$0.627033\pi$
$182$	−2214.33	+	1683.29i	−0.901853	+	0.685570i
$183$	−343.050	−	324.955i	−0.138574	−	0.131264i
$184$	−3059.78	−	7679.47i	−1.22592	−	3.07684i
$185$	5209.88	−	1755.41i	2.07048	−	0.697625i
$186$	−167.821	+	1023.66i	−0.0661572	+	0.403541i
$187$	1693.03	−	1603.72i	0.662066	−	0.627142i
$188$	−817.331	−	378.138i	−0.317074	−	0.146694i
$189$	646.381	+	491.366i	0.248769	+	0.189109i
$190$	−1750.91	−	10680.1i	−0.668549	−	4.07797i
$191$	−1295.95	−	2444.43i	−0.490952	−	0.926034i	−0.997945	−	0.0640837i	$-0.979588\pi$
$191$	−1295.95	−	2444.43i	−0.490952	−	0.926034i	0.506992	−	0.861951i	$-0.330757\pi$
$192$	989.709	+	217.851i	0.372011	+	0.0818858i
$193$	−818.545	+	378.699i	−0.305286	+	0.141240i	−0.566551	−	0.824027i	$-0.691722\pi$
$193$	−818.545	+	378.699i	−0.305286	+	0.141240i	0.261265	+	0.965267i	$0.415860\pi$
$194$	−2318.71	+	5819.52i	−0.858111	+	2.15370i
$195$	−40.8833	+	754.047i	−0.0150139	+	0.276915i
$196$	−5291.58	+	7804.50i	−1.92842	+	2.84420i
$197$	1059.86	−	1247.77i	0.383310	−	0.451267i	−0.536343	−	0.844000i	$-0.680194\pi$
$197$	1059.86	−	1247.77i	0.383310	−	0.451267i	0.919653	+	0.392733i	$0.128470\pi$
$198$	513.034	−	967.685i	0.184140	−	0.347325i
$199$	−4272.63	−	1439.62i	−1.52200	−	0.512822i	−0.570720	−	0.821145i	$-0.693336\pi$
$199$	−4272.63	−	1439.62i	−1.52200	−	0.512822i	−0.951282	+	0.308322i	$0.900232\pi$
$200$	139.148	+	2566.43i	0.0491961	+	0.907369i
$201$	−1098.86	−	661.164i	−0.385611	−	0.232015i
$202$	1928.31	−	6945.14i	0.671660	−	2.41910i
$203$	−1651.46	−	5948.01i	−0.570983	−	2.05649i
$204$	−4120.60	+	2479.28i	−1.41421	+	0.850904i
$205$	162.082	+	239.054i	0.0552211	+	0.0814450i
$206$	−2606.08	−	283.428i	−0.881428	−	0.0958611i
$207$	−1688.11	−	183.593i	−0.566819	−	0.0616453i
$208$	−873.479	−	1288.29i	−0.291177	−	0.429454i
$209$	−3358.06	+	2020.48i	−1.11140	+	0.668705i
$210$	1628.82	+	5866.47i	0.535234	+	1.92774i
$211$	907.831	−	3269.71i	0.296198	−	1.06681i	−0.654341	−	0.756200i	$-0.727054\pi$
$211$	907.831	−	3269.71i	0.296198	−	1.06681i	0.950538	−	0.310607i	$-0.100532\pi$
$212$	2082.14	+	1252.78i	0.674539	+	0.405856i
$213$	−2.34543	−	43.2589i	−0.000754489	−	0.0139157i
$214$	818.091	+	275.647i	0.261325	+	0.0880506i
$215$	735.003	−	1386.36i	0.233148	−	0.439763i
$216$	−765.848	+	901.626i	−0.241247	+	0.284018i
$217$	−1171.80	+	1728.27i	−0.366575	+	0.540657i
$218$	82.4402	−	1520.52i	0.0256126	−	0.472397i
$219$	941.617	−	2363.28i	0.290541	−	0.729204i
$220$	5049.24	−	2336.03i	1.54736	−	0.715886i
$221$	−1730.99	−	381.020i	−0.526874	−	0.115974i
$222$	2838.75	+	5354.46i	0.858219	+	1.61877i
$223$	−613.163	−	3740.13i	−0.184128	−	1.12313i	−0.903527	−	0.428532i	$-0.859031\pi$
$223$	−613.163	−	3740.13i	−0.184128	−	1.12313i	0.719399	−	0.694597i	$-0.244417\pi$
$224$	−1598.91	−	1215.46i	−0.476927	−	0.362550i
$225$	479.155	+	221.681i	0.141972	+	0.0656832i
$226$	−3307.64	+	3133.17i	−0.973545	+	0.922191i
$227$	−124.149	+	757.278i	−0.0362999	+	0.221420i	−0.998747	−	0.0500508i	$-0.984062\pi$
$227$	−124.149	+	757.278i	−0.0362999	+	0.221420i	0.962447	+	0.271471i	$0.0875100\pi$
$228$	7658.63	−	2580.49i	2.22458	−	0.749550i
$229$	2403.06	+	6031.24i	0.693445	+	1.74042i	0.671892	+	0.740649i	$0.265482\pi$
$229$	2403.06	+	6031.24i	0.693445	+	1.74042i	0.0215529	+	0.999768i	$0.493139\pi$
$230$	−9244.12	−	8756.50i	−2.65017	−	2.51037i
$231$	1755.14	−	1334.23i	0.499914	−	0.380024i
$232$	8783.70	−	1933.44i	2.48568	−	0.547140i
$233$	−2264.49	−	2665.96i	−0.636701	−	0.749583i	0.345293	−	0.938495i	$-0.387780\pi$
$233$	−2264.49	−	2665.96i	−0.636701	−	0.749583i	−0.981994	+	0.188912i	$0.939504\pi$
$234$	−827.575	+	90.0042i	−0.231198	+	0.0251443i
$235$	−726.534			−0.201676
$236$	7593.27	+	545.253i	2.09441	+	0.150394i
$237$	−2051.60			−0.562302
$238$	−14206.3	+	1545.03i	−3.86916	+	0.420796i
$239$	−799.457	−	941.194i	−0.216371	−	0.254731i	0.643259	−	0.765648i	$-0.277582\pi$
$239$	−799.457	−	941.194i	−0.216371	−	0.254731i	−0.859630	+	0.510917i	$0.829306\pi$
$240$	−3327.32	+	732.399i	−0.894907	+	0.196984i
$241$	2660.47	−	2022.44i	0.711103	−	0.540566i	−0.185912	−	0.982566i	$-0.559524\pi$
$241$	2660.47	−	2022.44i	0.711103	−	0.540566i	0.897015	+	0.442000i	$0.145731\pi$
$242$	2652.85	+	2512.91i	0.704675	+	0.667504i
$243$	89.9436	+	225.741i	0.0237444	+	0.0595939i
$244$	2507.38	−	844.834i	0.657863	−	0.221660i
$245$	−1230.69	+	7506.88i	−0.320922	+	1.95754i
$246$	−231.146	+	218.953i	−0.0599079	+	0.0567477i
$247$	2703.35	+	1250.70i	0.696396	+	0.322187i
$248$	−2421.94	−	1841.11i	−0.620133	−	0.471413i
$249$	589.897	+	3598.21i	0.150133	+	0.915773i
$250$	−2097.07	−	3955.49i	−0.530521	−	1.00067i
$251$	4254.55	+	936.497i	1.06990	+	0.235503i	0.714802	−	0.699327i	$-0.246517\pi$
$251$	4254.55	+	936.497i	1.06990	+	0.235503i	0.355097	+	0.934829i	$0.384448\pi$
$252$	−4126.23	+	1909.00i	−1.03146	+	0.477205i
$253$	−1706.64	+	4283.34i	−0.424093	+	1.06439i
$254$	163.825	−	3021.58i	0.0404698	−	0.746421i
$255$	−2177.21	+	3211.15i	−0.534675	+	0.788587i
$256$	−5396.12	+	6352.80i	−1.31741	+	1.55098i
$257$	2621.06	−	4943.85i	0.636176	−	1.19996i	−0.330464	−	0.943819i	$-0.607205\pi$
$257$	2621.06	−	4943.85i	0.636176	−	1.19996i	0.966640	−	0.256137i	$-0.0824499\pi$
$258$	1639.22	+	552.319i	0.395557	+	0.133279i
$259$	660.450	+	12181.3i	0.158449	+	2.92243i
$260$	−3623.19	−	2180.00i	−0.864234	−	0.519992i
$261$	494.252	−	1780.14i	0.117216	−	0.422175i
$262$	−846.805	−	3049.92i	−0.199679	−	0.719177i
$263$	−6923.03	+	4165.45i	−1.62316	+	0.976625i	−0.646214	+	0.763156i	$0.723649\pi$
$263$	−6923.03	+	4165.45i	−1.62316	+	0.976625i	−0.976950	+	0.213469i	$0.931524\pi$
$264$	1802.65	+	2658.71i	0.420248	+	0.619819i
$265$	1948.90	+	211.956i	0.451774	+	0.0491333i
$266$	23874.4	+	2596.49i	5.50313	+	0.598501i
$267$	−240.650	−	354.933i	−0.0551594	−	0.0813540i
$268$	6153.05	−	3702.17i	1.40245	−	0.843828i
$269$	704.061	+	2535.80i	0.159581	+	0.574759i	0.999487	+	0.0320272i	$0.0101963\pi$
$269$	704.061	+	2535.80i	0.159581	+	0.574759i	−0.839906	+	0.542732i	$0.817390\pi$
$270$	−487.477	+	1755.73i	−0.109877	+	0.395743i
$271$	2132.32	+	1282.97i	0.477967	+	0.287583i	0.734079	−	0.679064i	$-0.237614\pi$
$271$	2132.32	+	1282.97i	0.477967	+	0.287583i	−0.256112	+	0.966647i	$0.582442\pi$
$272$	−432.923	−	7984.80i	−0.0965068	−	1.77996i
$273$	−1587.95	−	535.044i	−0.352041	−	0.118617i
$274$	−1098.36	+	2071.72i	−0.242169	+	0.456779i
$275$	928.071	−	1092.61i	0.203508	−	0.239589i
$276$	5335.90	−	7869.87i	1.16371	−	1.71634i
$277$	46.8803	−	864.656i	0.0101688	−	0.187553i	−0.989036	−	0.147676i	$-0.952821\pi$
$277$	46.8803	−	864.656i	0.0101688	−	0.187553i	0.999205	−	0.0398768i	$-0.0126966\pi$
$278$	2812.07	−	7057.77i	0.606679	−	1.52265i
$279$	−567.164	+	262.398i	−0.121703	+	0.0563059i
$280$	−17438.6	−	3838.52i	−3.72198	−	0.819269i
$281$	−1324.14	−	2497.60i	−0.281110	−	0.530229i	0.702243	−	0.711937i	$-0.252182\pi$
$281$	−1324.14	−	2497.60i	−0.281110	−	0.530229i	−0.983352	+	0.181709i	$0.941837\pi$
$282$	−129.572	−	790.353i	−0.0273613	−	0.166897i
$283$	3905.63	+	2968.99i	0.820374	+	0.623632i	0.928845	−	0.370467i	$-0.120802\pi$
$283$	3905.63	+	2968.99i	0.820374	+	0.623632i	−0.108471	+	0.994100i	$0.534596\pi$
$284$	220.162	+	101.858i	0.0460007	+	0.0212822i
$285$	4733.44	−	4483.75i	0.983805	−	0.931910i
$286$	−365.692	+	2230.62i	−0.0756077	+	0.461187i
$287$	−607.337	+	204.636i	−0.124913	+	0.0420880i
$288$	−222.487	−	558.401i	−0.0455215	−	0.114250i
$289$	−3044.07	−	2883.49i	−0.619595	−	0.586911i
$290$	11028.6	−	8383.73i	2.23318	−	1.69762i
$291$	−3685.68	+	811.279i	−0.742468	+	0.163430i
$292$	9221.90	+	10856.9i	1.84819	+	2.17586i
$293$	−5425.23	+	590.030i	−1.08173	+	0.117645i	−0.631580	−	0.775311i	$-0.717593\pi$
$293$	−5425.23	+	590.030i	−1.08173	+	0.117645i	−0.450145	+	0.892955i	$0.648628\pi$
$294$	−8385.77			−1.66350
$295$	5744.42	−	2172.97i	1.13374	−	0.428865i
$296$	−17774.0			−3.49018
$297$	655.960	−	71.3400i	0.128157	−	0.0139379i
$298$	−3236.86	−	3810.72i	−0.629215	−	0.740769i
$299$	3422.50	−	753.349i	0.661967	−	0.145710i
$300$	−2353.44	+	1789.04i	−0.452920	+	0.344301i
$301$	2527.84	+	2394.50i	0.484062	+	0.458528i
$302$	4473.14	+	11226.7i	0.852318	+	2.13916i
$303$	4114.96	−	1386.49i	0.780192	−	0.262877i
$304$	−2174.11	+	13261.5i	−0.410177	+	2.50197i
$305$	1549.69	−	1467.95i	0.290935	−	0.275588i
$306$	−3881.50	−	1795.77i	−0.725133	−	0.335482i
$307$	−1204.54	−	915.668i	−0.223931	−	0.170228i	0.487193	−	0.873294i	$-0.338021\pi$
$307$	−1204.54	−	915.668i	−0.223931	−	0.170228i	−0.711124	+	0.703066i	$0.751814\pi$
$308$	1997.22	+	12182.5i	0.369488	+	2.25377i
$309$	−739.733	−	1395.29i	−0.136188	−	0.256877i
$310$	−4576.46	−	1007.36i	−0.838469	−	0.184561i
$311$	−1584.10	+	732.881i	−0.288829	+	0.133627i	−0.558954	−	0.829199i	$-0.688797\pi$
$311$	−1584.10	+	732.881i	−0.288829	+	0.133627i	0.270125	+	0.962825i	$0.412935\pi$
$312$	903.663	−	2268.02i	0.163974	−	0.411543i
$313$	64.9804	−	1198.49i	0.0117345	−	0.216431i	−0.986785	−	0.162035i	$-0.948194\pi$
$313$	64.9804	−	1198.49i	0.0117345	−	0.216431i	0.998519	−	0.0543954i	$-0.0173231\pi$
$314$	−3096.86	+	4567.52i	−0.556579	+	0.820893i
$315$	−2374.52	+	2795.50i	−0.424727	+	0.500027i
$316$	5381.01	−	10149.7i	0.957928	−	1.80684i
$317$	−3807.03	−	1282.74i	−0.674524	−	0.227274i	−0.0388661	−	0.999244i	$-0.512375\pi$
$317$	−3807.03	−	1282.74i	−0.674524	−	0.227274i	−0.635658	+	0.771971i	$0.719271\pi$
$318$	116.998	+	2157.89i	0.0206318	+	0.380530i
$319$	−4298.45	−	2586.29i	−0.754442	−	0.453933i
$320$	−1224.73	+	4411.06i	−0.213951	+	0.770581i
$321$	139.133	+	501.113i	0.0241921	+	0.0871321i
$322$	24209.9	−	14566.6i	4.18995	−	2.52101i
$323$	8587.82	+	12666.1i	1.47938	+	2.18192i
$324$	−1352.69	−	147.114i	−0.231943	−	0.0252254i
$325$	−1083.19	−	117.804i	−0.184875	−	0.0201064i
$326$	−8172.56	−	12053.6i	−1.38846	−	2.04782i
$327$	786.045	−	472.947i	0.132931	−	0.0799818i
$328$	−249.807	−	899.724i	−0.0420527	−	0.151460i
$329$	431.299	−	1553.40i	0.0722744	−	0.260309i
$330$	4239.52	+	2550.84i	0.707207	+	0.425512i
$331$	152.597	+	2814.49i	0.0253399	+	0.467367i	0.983474	+	0.181048i	$0.0579489\pi$
$331$	152.597	+	2814.49i	0.0253399	+	0.467367i	−0.958134	+	0.286319i	$0.907568\pi$
$332$	−19348.3	−	6519.19i	−3.19841	−	1.07767i
$333$	−1710.16	+	3225.71i	−0.281430	+	0.530834i
$334$	1.33411	−	1.57063i	0.000218560	−	0.000257309i
$335$	3251.10	−	4795.02i	0.530229	−	0.782029i
$336$	409.289	−	7548.90i	0.0664541	−	1.22567i
$337$	1053.38	−	2643.80i	0.170272	−	0.427349i	−0.818933	−	0.573889i	$-0.805434\pi$
$337$	1053.38	−	2643.80i	0.170272	−	0.427349i	0.989205	+	0.146539i	$0.0468135\pi$
$338$	−8370.22	+	3872.48i	−1.34698	+	0.623180i
$339$	−2680.53	−	590.029i	−0.429458	−	0.0945309i
$340$	−10175.7	−	19193.4i	−1.62310	−	3.06149i
$341$	274.524	+	1674.52i	0.0435962	+	0.265925i
$342$	5721.78	+	4349.58i	0.904673	+	0.687715i
$343$	−5958.48	−	2756.68i	−0.937981	−	0.433956i
$344$	−3683.03	+	3488.75i	−0.577254	+	0.546804i
$345$	1241.00	−	7569.76i	0.193661	−	1.18128i
$346$	−709.143	+	238.938i	−0.110184	+	0.0371254i
$347$	−4656.15	−	11686.1i	−0.720332	−	1.80790i	−0.574348	−	0.818611i	$-0.694744\pi$
$347$	−4656.15	−	11686.1i	−0.720332	−	1.80790i	−0.145984	−	0.989287i	$-0.546635\pi$
$348$	7510.34	+	7114.17i	1.15689	+	1.09586i
$349$	−1615.80	+	1228.30i	−0.247828	+	0.188394i	−0.721712	−	0.692193i	$-0.756645\pi$
$349$	−1615.80	+	1228.30i	−0.247828	+	0.188394i	0.473884	+	0.880587i	$0.342852\pi$
$350$	−8579.25	+	1888.44i	−1.31023	+	0.288403i
$351$	−324.663	−	382.223i	−0.0493711	−	0.0581241i
$352$	−1622.61	+	176.469i	−0.245696	+	0.0267211i
$353$	4016.22			0.605558			0.302779	−	0.953061i	$-0.402086\pi$
$353$	4016.22			0.605558			0.302779	+	0.953061i	$0.402086\pi$
$354$	3388.32	+	5861.48i	0.508721	+	0.880040i
$355$	195.704			0.0292589
$356$	2387.11	−	259.614i	0.355383	−	0.0386503i
$357$	−5573.25	−	6561.33i	−0.826240	−	0.972725i
$358$	−1346.07	+	296.293i	−0.198721	+	0.0437419i
$359$	7032.86	−	5346.24i	1.03393	−	0.785972i	0.0567491	−	0.998388i	$-0.481926\pi$
$359$	7032.86	−	5346.24i	1.03393	−	0.785972i	0.977179	+	0.212417i	$0.0681334\pi$
$360$	−3879.72	−	3675.07i	−0.567998	−	0.538036i
$361$	−6980.17	−	17518.9i	−1.01767	−	2.55415i
$362$	13274.3	−	4472.64i	1.92730	−	0.649383i
$363$	−356.137	+	2172.34i	−0.0514941	+	0.314100i
$364$	6811.91	−	6452.58i	0.980882	−	0.929141i
$365$	10429.9	+	4825.39i	1.49569	+	0.691979i
$366$	1873.27	+	1424.02i	0.267533	+	0.203374i
$367$	1750.44	+	10677.2i	0.248971	+	1.51865i	0.754763	+	0.655998i	$0.227752\pi$
$367$	1750.44	+	10677.2i	0.248971	+	1.51865i	−0.505792	+	0.862656i	$0.668800\pi$
$368$	7405.85	+	13968.9i	1.04907	+	1.97875i
$369$	−187.322	−	41.2326i	−0.0264270	−	0.00581703i
$370$	−24846.9	+	11495.4i	−3.49117	+	1.61518i
$371$	−1610.12	+	4041.10i	−0.225319	+	0.565509i
$372$	189.445	−	3494.10i	0.0264039	−	0.486991i
$373$	−1800.01	+	2654.81i	−0.249868	+	0.368528i	−0.931852	−	0.362840i	$-0.881807\pi$
$373$	−1800.01	+	2654.81i	−0.249868	+	0.368528i	0.681983	+	0.731368i	$0.261118\pi$
$374$	−7518.05	+	8850.93i	−1.03944	+	1.22372i
$375$	1263.35	−	2382.92i	0.173970	−	0.328143i
$376$	2225.93	+	750.005i	0.305303	+	0.102868i
$377$	206.420	+	3807.20i	0.0281994	+	0.520107i
$378$	−3464.53	−	2084.54i	−0.471419	−	0.283643i
$379$	52.7532	−	190.000i	0.00714974	−	0.0257510i	−0.959889	−	0.280380i	$-0.909540\pi$
$379$	52.7532	−	190.000i	0.00714974	−	0.0257510i	0.967039	+	0.254629i	$0.0819533\pi$
$380$	9766.95	+	35177.4i	1.31851	+	4.74885i
$381$	1562.03	−	939.843i	0.210040	−	0.126377i
$382$	7731.86	+	11403.6i	1.03559	+	1.52739i
$383$	−11525.5	−	1253.47i	−1.53766	−	0.167230i	−0.700286	−	0.713863i	$-0.746944\pi$
$383$	−11525.5	−	1253.47i	−1.53766	−	0.167230i	−0.837373	+	0.546632i	$0.815910\pi$
$384$	−6610.47	−	718.932i	−0.878488	−	0.0955413i
$385$	5589.13	+	8243.35i	0.739866	+	1.09122i
$386$	3848.40	−	2315.50i	0.507457	−	0.305327i
$387$	278.784	+	1004.09i	0.0366186	+	0.131888i
$388$	5653.38	−	20361.6i	0.739708	−	2.66419i
$389$	−11855.2	−	7133.06i	−1.54520	−	0.929719i	−0.995541	−	0.0943326i	$-0.969928\pi$
$389$	−11855.2	−	7133.06i	−1.54520	−	0.929719i	−0.549664	−	0.835386i	$-0.685244\pi$
$390$	−203.590	−	3755.00i	−0.0264339	−	0.487544i
$391$	17061.7	+	5748.77i	2.20678	+	0.743549i
$392$	11519.9	−	21728.9i	1.48430	−	2.79968i
$393$	1234.49	−	1453.35i	0.158452	−	0.186544i
$394$	−4575.15	+	6747.84i	−0.585007	+	0.862821i
$395$	501.752	−	9254.27i	0.0639137	−	1.17882i
$396$	−1367.54	+	3432.28i	−0.173540	+	0.435551i
$397$	8693.07	−	4021.84i	1.09897	−	0.508439i	0.215302	−	0.976547i	$-0.430926\pi$
$397$	8693.07	−	4021.84i	1.09897	−	0.508439i	0.883671	+	0.468108i	$0.155064\pi$
$398$	21927.2	+	4826.54i	2.76159	+	0.607871i
$399$	6776.72	+	12782.2i	0.850276	+	1.60379i
$400$	−795.280	−	4850.99i	−0.0994100	−	0.606374i
$401$	9032.58	+	6866.39i	1.12485	+	0.855090i	0.990726	−	0.135874i	$-0.0433842\pi$
$401$	9032.58	+	6866.39i	1.12485	+	0.855090i	0.134126	+	0.990964i	$0.457177\pi$
$402$	5796.02	+	2681.52i	0.719103	+	0.332692i
$403$	936.318	−	886.928i	0.115735	−	0.109630i
$404$	−3933.63	+	23994.1i	−0.484419	+	2.95482i
$405$	−1040.26	+	350.505i	−0.127632	+	0.0430043i
$406$	11378.2	+	28557.1i	1.39086	+	3.49080i
$407$	7197.32	+	6817.66i	0.876555	+	0.830317i
$408$	9985.35	−	7590.67i	1.21164	−	0.921064i
$409$	−11584.7	+	2550.00i	−1.40056	+	0.308287i	−0.850120	−	0.526588i	$-0.823471\pi$
$409$	−11584.7	+	2550.00i	−1.40056	+	0.308287i	−0.550440	+	0.834875i	$0.685540\pi$
$410$	−931.115	−	1096.19i	−0.112157	−	0.132042i
$411$	−1404.35	+	152.732i	−0.168544	+	0.0183302i
$412$	8842.95			1.05743
$413$	1235.90	+	13572.1i	0.147251	+	1.61704i
$414$	8456.01			1.00384
$415$	−16374.9	+	1780.88i	−1.93690	+	0.210651i
$416$	803.098	+	945.481i	0.0946518	+	0.111433i
$417$	4469.90	−	983.900i	0.524921	−	0.115544i
$418$	15536.6	−	11810.6i	1.81799	−	1.38200i
$419$	−943.957	−	894.163i	−0.110060	−	0.104255i	0.630691	−	0.776034i	$-0.282772\pi$
$419$	−943.957	−	894.163i	−0.110060	−	0.104255i	−0.740751	+	0.671779i	$0.765530\pi$
$420$	−7601.91	−	19079.3i	−0.883179	−	2.21661i
$421$	−8099.99	+	2729.20i	−0.937694	+	0.315946i	−0.746332	−	0.665574i	$-0.768187\pi$
$421$	−8099.99	+	2729.20i	−0.937694	+	0.315946i	−0.191362	+	0.981520i	$0.561290\pi$
$422$	−2733.87	+	16675.9i	−0.315362	+	1.92362i
$423$	350.287	−	331.809i	0.0402637	−	0.0381398i
$424$	−5752.18	−	2661.24i	−0.658846	−	0.304814i
$425$	−4456.33	−	3387.62i	−0.508621	−	0.386643i
$426$	34.9024	+	212.895i	0.00396954	+	0.0242131i
$427$	2218.65	+	4184.81i	0.251447	+	0.474279i
$428$	−2844.03	−	626.018i	−0.321195	−	0.0707003i
$429$	−1235.88	+	571.780i	−0.139088	+	0.0643492i
$430$	−2892.28	+	7259.07i	−0.324367	+	0.814101i
$431$	51.8169	−	955.706i	0.00579102	−	0.106809i	−0.994209	−	0.107466i	$-0.965726\pi$
$431$	51.8169	−	955.706i	0.00579102	−	0.106809i	1.00000		0.000656839i	$0.000209078\pi$
$432$	1269.73	−	1872.71i	0.141411	−	0.208566i
$433$	4512.55	−	5312.59i	0.500830	−	0.589623i	−0.452420	−	0.891805i	$-0.649439\pi$
$433$	4512.55	−	5312.59i	0.500830	−	0.589623i	0.953250	+	0.302182i	$0.0977151\pi$
$434$	4870.58	−	9186.89i	0.538699	−	1.01609i
$435$	7908.89	+	2664.82i	0.871730	+	0.293720i
$436$	278.096	+	5129.18i	0.0305468	+	0.563402i
$437$	−25925.8	−	15599.0i	−2.83798	−	1.70756i
$438$	−3389.16	+	12206.6i	−0.369727	+	1.33164i
$439$	−3313.45	−	11934.0i	−0.360233	−	1.29744i	−0.892569	−	0.450910i	$-0.851099\pi$
$439$	−3313.45	−	11934.0i	−0.360233	−	1.29744i	0.532336	−	0.846533i	$-0.321314\pi$
$440$	−12433.7	+	7481.09i	−1.34716	+	0.810562i
$441$	−2835.04	−	4181.38i	−0.306127	−	0.451504i
$442$	8774.60	+	954.295i	0.944265	+	0.102695i
$443$	−233.242	−	25.3666i	−0.0250150	−	0.00272055i	0.0956029	−	0.995420i	$-0.469522\pi$
$443$	−233.242	−	25.3666i	−0.0250150	−	0.00272055i	−0.120618	+	0.992699i	$0.538488\pi$
$444$	−11472.7	−	16921.0i	−1.22629	−	1.80864i
$445$	1659.87	−	998.712i	0.176821	−	0.106390i
$446$	5049.26	+	18185.8i	0.536075	+	1.93077i
$447$	805.822	−	2902.31i	0.0852664	−	0.307102i
$448$	−8704.22	−	5237.15i	−0.917936	−	0.552304i
$449$	−987.022	−	18204.6i	−0.103743	−	1.91342i	−0.337833	−	0.941206i	$-0.609694\pi$
$449$	−987.022	−	18204.6i	−0.103743	−	1.91342i	0.234091	−	0.972215i	$-0.424789\pi$
$450$	−2491.46	−	839.472i	−0.260997	−	0.0879402i
$451$	−243.956	+	460.149i	−0.0254710	+	0.0480434i
$452$	9949.57	−	11713.5i	1.03537	−	1.21894i
$453$	−4085.69	+	6025.94i	−0.423758	+	0.624997i
$454$	206.888	−	3815.83i	0.0213871	−	0.394462i
$455$	2801.82	−	7032.03i	0.288684	−	0.724542i
$456$	−19130.8	+	8850.83i	−1.96465	+	0.908943i
$457$	2176.22	+	479.023i	0.222756	+	0.0490322i	0.324946	−	0.945733i	$-0.394654\pi$
$457$	2176.22	+	479.023i	0.222756	+	0.0490322i	−0.102190	+	0.994765i	$0.532585\pi$
$458$	−15143.9	−	28564.5i	−1.54504	−	2.91426i
$459$	−416.828	−	2542.54i	−0.0423875	−	0.258552i
$460$	34194.1	+	25993.7i	3.46589	+	2.63470i
$461$	−9886.20	−	4573.85i	−0.998799	−	0.462094i	−0.148794	−	0.988868i	$-0.547539\pi$
$461$	−9886.20	−	4573.85i	−0.998799	−	0.462094i	−0.850005	+	0.526774i	$0.823401\pi$
$462$	−7970.67	+	7550.22i	−0.802660	+	0.760320i
$463$	2200.79	−	13424.2i	0.220906	−	1.34747i	−0.610594	−	0.791943i	$-0.709069\pi$
$463$	2200.79	−	13424.2i	0.220906	−	1.34747i	0.831500	−	0.555524i	$-0.187482\pi$
$464$	−16301.4	+	5492.58i	−1.63098	+	0.549540i
$465$	−1044.91	−	2622.52i	−0.104207	−	0.261540i
$466$	12646.0	+	11978.9i	1.25711	+	1.19080i
$467$	−7752.33	+	5893.17i	−0.768170	+	0.583947i	−0.914167	−	0.405338i	$-0.867154\pi$
$467$	−7752.33	+	5893.17i	−0.768170	+	0.583947i	0.145997	+	0.989285i	$0.453361\pi$
$468$	2742.47	−	603.664i	0.270878	−	0.0596247i
$469$	8322.21	+	9797.66i	0.819368	+	0.964635i
$470$	3596.79	−	391.174i	0.352994	−	0.0383905i
$471$	−3324.47			−0.325231
$472$	−19842.7	+	727.492i	−1.93503	+	0.0709439i
$473$	2829.58			0.275062
$474$	10156.7	−	1104.60i	0.984200	−	0.107038i
$475$	6090.14	+	7169.86i	0.588283	+	0.692581i
$476$	47077.9	−	10362.6i	4.53322	−	0.997837i
$477$	−1036.43	+	787.875i	−0.0994863	+	0.0756275i
$478$	4464.55	+	4229.04i	0.427204	+	0.404669i
$479$	2400.27	+	6024.22i	0.228958	+	0.574642i	0.997907	−	0.0646686i	$-0.0205990\pi$
$479$	2400.27	+	6024.22i	0.228958	+	0.574642i	−0.768948	+	0.639311i	$0.779220\pi$
$480$	2573.23	−	867.022i	0.244690	−	0.0824457i
$481$	1219.01	−	7435.61i	0.115555	−	0.704854i
$482$	−12082.0	+	11444.7i	−1.14175	+	1.08152i
$483$	15448.1	+	7147.07i	1.45531	+	0.673298i
$484$	−9812.91	−	7459.58i	−0.921573	−	0.700562i
$485$	−2758.09	−	16823.6i	−0.258224	−	1.57510i
$486$	−566.817	−	1069.13i	−0.0529040	−	0.0997875i
$487$	−8350.39	−	1838.06i	−0.776986	−	0.171028i	−0.191263	−	0.981539i	$-0.561258\pi$
$487$	−8350.39	−	1838.06i	−0.776986	−	0.171028i	−0.585723	+	0.810511i	$0.699189\pi$
$488$	−6263.27	+	2897.70i	−0.580993	+	0.268796i
$489$	3247.31	−	8150.14i	0.300304	−	0.753705i
$490$	2050.88	−	37826.2i	0.189080	−	3.48738i
$491$	−2749.33	+	4054.95i	−0.252699	+	0.372703i	−0.932788	−	0.360427i	$-0.882631\pi$
$491$	−2749.33	+	4054.95i	−0.252699	+	0.372703i	0.680088	+	0.733130i	$0.261941\pi$
$492$	695.300	−	818.570i	0.0637125	−	0.0750081i
$493$	−9175.38	+	17306.6i	−0.838211	+	1.58103i
$494$	−14056.6	−	4736.22i	−1.28023	−	0.431361i
$495$	161.372	+	2976.33i	0.0146528	+	0.270255i
$496$	4985.75	+	2999.83i	0.451345	+	0.271565i
$497$	−116.178	+	418.434i	−0.0104855	+	0.0377652i
$498$	−4857.66	−	17495.7i	−0.437103	−	1.57430i
$499$	−11298.6	+	6798.13i	−1.01361	+	0.609872i	−0.922511	−	0.385970i	$-0.873867\pi$
$499$	−11298.6	+	6798.13i	−1.01361	+	0.609872i	−0.0911033	+	0.995841i	$0.529039\pi$
$500$	8475.24	+	12500.0i	0.758048	+	1.11804i
$501$	1.23419	+	0.134227i	0.000110059	+	1.19697e-5i
$502$	−21566.8	−	2345.53i	−1.91748	−	0.208538i
$503$	8619.77	+	12713.2i	0.764089	+	1.12695i	0.988317	+	0.152410i	$0.0487034\pi$
$503$	8619.77	+	12713.2i	0.764089	+	1.12695i	−0.224229	+	0.974537i	$0.571986\pi$
$504$	10160.8	−	6113.54i	0.898010	−	0.540315i
$505$	5247.75	+	18900.7i	0.462420	+	1.66549i
$506$	6142.71	−	22124.0i	0.539677	−	1.94374i
$507$	−4760.71	−	2864.43i	−0.417023	−	0.250914i
$508$	552.634	+	10192.7i	0.0482661	+	0.890215i
$509$	−20161.7	−	6793.25i	−1.75570	−	0.591563i	−0.757571	−	0.652753i	$-0.773614\pi$
$509$	−20161.7	−	6793.25i	−1.75570	−	0.591563i	−0.998126	+	0.0611899i	$0.980510\pi$
$510$	9049.60	−	17069.4i	0.785731	−	1.48205i
$511$	−16508.7	+	19435.6i	−1.42916	+	1.68254i
$512$	13342.8	−	19679.1i	1.15170	−	1.69863i
$513$	−234.415	+	4323.54i	−0.0201748	+	0.372103i
$514$	−10314.0	+	25886.2i	−0.885082	+	2.22139i
$515$	6474.71	−	2995.52i	0.554000	−	0.256308i
$516$	−5698.63	−	1254.36i	−0.486179	−	0.107016i
$517$	−613.676	−	1157.52i	−0.0522040	−	0.0984671i
$518$	−9828.17	−	59949.2i	−0.833639	−	5.08497i
$519$	−358.887	−	272.819i	−0.0303534	−	0.0230740i
$520$	10009.5	+	4630.89i	0.844127	+	0.390535i
$521$	9554.35	−	9050.36i	0.803423	−	0.761043i	−0.171118	−	0.985251i	$-0.554738\pi$
$521$	9554.35	−	9050.36i	0.803423	−	0.761043i	0.974541	+	0.224208i	$0.0719793\pi$
$522$	−1488.40	+	9078.86i	−0.124800	+	0.761247i
$523$	−7205.79	+	2427.91i	−0.602461	+	0.202993i	−0.603971	−	0.797006i	$-0.706416\pi$
$523$	−7205.79	+	2427.91i	−0.602461	+	0.202993i	0.00151026	+	0.999999i	$0.499519\pi$
$524$	3952.15	+	9919.15i	0.329486	+	0.826947i
$525$	−3842.08	−	3639.42i	−0.319395	−	0.302547i
$526$	32030.5	−	24348.9i	2.65512	−	2.01837i
$527$	6471.01	−	1424.38i	0.534880	−	0.117736i
$528$	−3977.32	−	4682.46i	−0.327823	−	0.385943i
$529$	−23293.4	+	2533.31i	−1.91447	+	0.208211i
$530$	−9762.36			−0.800094
$531$	−1777.18	+	3671.15i	−0.145241	+	0.300027i
$532$	−81010.5			−6.60198
$533$	393.525	−	42.7984i	0.0319802	−	0.00347806i
$534$	1382.47	+	1627.56i	0.112032	+	0.131894i
$535$	−2294.43	+	505.042i	−0.185415	+	0.0408129i
$536$	−14910.5	+	11334.7i	−1.20156	+	0.913404i
$537$	−602.819	−	571.020i	−0.0484424	−	0.0458870i
$538$	−4850.83	−	12174.7i	−0.388725	−	0.975626i
$539$	−12999.5	+	4380.04i	−1.03883	+	0.350021i
$540$	994.422	−	6065.70i	0.0792465	−	0.483382i
$541$	2906.20	−	2752.90i	0.230956	−	0.218773i	−0.563466	−	0.826139i	$-0.690532\pi$
$541$	2906.20	−	2752.90i	0.230956	−	0.218773i	0.794422	+	0.607366i	$0.207774\pi$
$542$	−11247.0	−	5203.44i	−0.891332	−	0.412374i
$543$	6717.94	+	5106.85i	0.530929	+	0.403602i
$544$	1031.08	+	6289.31i	0.0812632	+	0.495683i
$545$	1941.11	+	3661.33i	0.152565	+	0.287769i
$546$	8149.40	+	1793.82i	0.638759	+	0.140601i
$547$	4103.47	−	1898.47i	0.320753	−	0.148396i	−0.252905	−	0.967491i	$-0.581386\pi$
$547$	4103.47	−	1898.47i	0.320753	−	0.148396i	0.573658	+	0.819095i	$0.305524\pi$
$548$	2927.78	−	7348.18i	0.228228	−	0.572808i
$549$	−76.7458	+	1415.49i	−0.00596618	+	0.110040i
$550$	−4006.24	+	5908.77i	−0.310594	+	0.458092i
$551$	21311.4	−	25089.8i	1.64773	−	1.93985i
$552$	−11616.4	+	21910.9i	−0.895703	+	1.68947i
$553$	19488.6	+	6566.48i	1.49863	+	0.504946i
$554$	233.455	+	4305.82i	0.0179035	+	0.330210i
$555$	−14132.1	−	8503.03i	−1.08086	−	0.650331i
$556$	−6856.28	+	24694.1i	−0.522969	+	1.88357i
$557$	818.893	+	2949.39i	0.0622938	+	0.224362i	0.988144	−	0.153528i	$-0.0490636\pi$
$557$	818.893	+	2949.39i	0.0622938	+	0.224362i	−0.925851	+	0.377890i	$0.876650\pi$
$558$	2666.53	−	1604.40i	0.202300	−	0.121720i
$559$	−1206.89	−	1780.04i	−0.0913170	−	0.134683i
$560$	33951.2	+	3692.41i	2.56196	+	0.278630i
$561$	−6955.01	−	756.403i	−0.523424	−	0.0569258i
$562$	7900.05	+	11651.7i	0.592960	+	0.874550i
$563$	7406.02	−	4456.06i	0.554399	−	0.333571i	−0.210631	−	0.977566i	$-0.567552\pi$
$563$	7406.02	−	4456.06i	0.554399	−	0.333571i	0.765030	+	0.643995i	$0.222724\pi$
$564$	722.780	+	2603.22i	0.0539620	+	0.194353i
$565$	3317.05	−	11946.9i	0.246990	−	0.889577i
$566$	−20933.8	−	12595.4i	−1.55462	−	0.935382i
$567$	−131.873	−	2432.25i	−0.00976744	−	0.180150i
$568$	−599.593	−	202.026i	−0.0442929	−	0.0149240i
$569$	−1122.67	+	2117.57i	−0.0827146	+	0.156016i	−0.921419	−	0.388571i	$-0.872969\pi$
$569$	−1122.67	+	2117.57i	−0.0827146	+	0.156016i	0.838704	+	0.544587i	$0.183314\pi$
$570$	−21019.3	+	24745.8i	−1.54456	+	1.81840i
$571$	7512.02	−	11079.4i	0.550557	−	0.812011i	−0.445990	−	0.895038i	$-0.647148\pi$
$571$	7512.02	−	11079.4i	0.550557	−	0.812011i	0.996547	+	0.0830267i	$0.0264587\pi$
$572$	412.810	−	7613.84i	0.0301756	−	0.556557i
$573$	−3072.20	+	7710.65i	−0.223984	+	0.562159i
$574$	2896.51	−	1340.07i	0.210624	−	0.0974448i
$575$	10809.1	+	2379.25i	0.783946	+	0.172560i
$576$	−1424.06	−	2686.06i	−0.103013	−	0.194304i
$577$	1335.24	+	8144.59i	0.0963373	+	0.587632i	0.990240	+	0.139371i	$0.0445081\pi$
$577$	1335.24	+	8144.59i	0.0963373	+	0.587632i	−0.893903	+	0.448261i	$0.852044\pi$
$578$	16622.5	+	12636.1i	1.19620	+	0.909329i
$579$	2455.63	+	1136.10i	0.176257	+	0.0815451i
$580$	−33927.1	+	32137.5i	−2.42887	+	2.30075i
$581$	5913.11	−	36068.3i	0.422232	−	2.57550i
$582$	17809.5	−	6000.73i	1.26844	−	0.427386i
$583$	1308.47	+	3284.02i	0.0929528	+	0.233294i
$584$	−26973.6	−	25550.7i	−1.91126	−	1.81044i
$585$	1803.52	−	1371.00i	0.127464	−	0.0968956i
$586$	26540.5	−	5842.01i	1.87095	−	0.411828i
$587$	7666.43	+	9025.62i	0.539059	+	0.634629i	0.962496	−	0.271297i	$-0.0874524\pi$
$587$	7666.43	+	9025.62i	0.539059	+	0.634629i	−0.423437	+	0.905925i	$0.639177\pi$
$588$	28122.0	−	3058.45i	1.97233	−	0.214504i
$589$	−11135.2			−0.778974
$590$	−27268.4	+	13850.4i	−1.90275	+	0.966460i
$591$	−4911.42			−0.341843
$592$	33795.2	−	3675.45i	2.34624	−	0.255169i
$593$	7661.58	+	9019.91i	0.530562	+	0.624626i	0.960516	−	0.278225i	$-0.0897461\pi$
$593$	7661.58	+	9019.91i	0.530562	+	0.624626i	−0.429954	+	0.902851i	$0.641470\pi$
$594$	−3208.99	+	706.352i	−0.221661	+	0.0487912i
$595$	30959.7	−	23534.9i	2.13315	−	1.62158i
$596$	12244.8	+	11598.8i	0.841551	+	0.797160i
$597$	5006.46	+	12565.3i	0.343217	+	0.861410i
$598$	−16537.8	+	5572.24i	−1.13091	+	0.381047i
$599$	780.058	−	4758.14i	0.0532092	−	0.324562i	−0.946787	−	0.321860i	$-0.895692\pi$
$599$	780.058	−	4758.14i	0.0532092	−	0.324562i	0.999996	−	0.00270137i	$-0.000859875\pi$
$600$	5597.85	−	5302.57i	0.380886	−	0.360794i
$601$	−3898.52	−	1803.65i	−0.264599	−	0.122417i	0.283104	−	0.959089i	$-0.408636\pi$
$601$	−3898.52	−	1803.65i	−0.264599	−	0.122417i	−0.547703	+	0.836673i	$0.684498\pi$
$602$	−13803.6	−	10493.2i	−0.934539	−	0.710418i
$603$	622.425	+	3796.62i	0.0420350	+	0.256402i
$604$	−19095.4	−	36017.8i	−1.28639	−	2.42640i
$605$	−9711.82	−	2137.73i	−0.652631	−	0.143655i
$606$	−19625.1	+	9079.52i	−1.31553	+	0.608631i
$607$	−10014.0	+	25133.4i	−0.669617	+	1.68061i	0.0612764	+	0.998121i	$0.480483\pi$
$607$	−10014.0	+	25133.4i	−0.669617	+	1.68061i	−0.730894	+	0.682491i	$0.760896\pi$
$608$	579.858	−	10694.8i	0.0386782	−	0.713377i
$609$	−10392.6	+	15328.0i	−0.691513	+	1.01991i
$610$	−6881.56	+	8101.60i	−0.456764	+	0.537744i
$611$	−466.421	+	879.764i	−0.0308828	+	0.0582511i
$612$	13671.7	+	4606.53i	0.903016	+	0.304262i
$613$	−575.433	−	10613.2i	−0.0379144	−	0.699290i	−0.954274	−	0.298933i	$-0.903369\pi$
$613$	−575.433	−	10613.2i	−0.0379144	−	0.699290i	0.916360	−	0.400356i	$-0.131114\pi$
$614$	6456.22	+	3884.58i	0.424351	+	0.255324i
$615$	231.803	−	834.879i	0.0151987	−	0.0547408i
$616$	−8614.16	−	31025.4i	−0.563433	−	2.02930i
$617$	−5621.45	+	3382.32i	−0.366793	+	0.220692i	−0.687003	−	0.726655i	$-0.741074\pi$
$617$	−5621.45	+	3382.32i	−0.366793	+	0.220692i	0.320210	+	0.947347i	$0.396246\pi$
$618$	4413.37	+	6509.23i	0.287268	+	0.423689i
$619$	22246.8	+	2419.48i	1.44455	+	0.157104i	0.796565	−	0.604553i	$-0.206648\pi$
$619$	22246.8	+	2419.48i	1.44455	+	0.157104i	0.647981	+	0.761657i	$0.275614\pi$
$620$	15714.7	+	1709.08i	1.01793	+	0.110707i
$621$	2858.79	+	4216.40i	0.184733	+	0.272461i
$622$	7447.65	−	4481.10i	0.480102	−	0.288868i
$623$	1149.97	+	4141.83i	0.0739531	+	0.266355i
$624$	−1249.21	+	4499.25i	−0.0801418	+	0.288645i
$625$	16722.9	+	10061.8i	1.07026	+	0.643956i
$626$	323.589	+	5968.26i	0.0206601	+	0.381053i
$627$	11141.7	+	3754.07i	0.709658	+	0.239112i
$628$	8719.56	−	16446.8i	0.554058	−	1.04506i
$629$	25060.9	−	29503.9i	1.58862	−	1.87027i
$630$	10250.2	−	15117.9i	0.648217	−	0.956049i
$631$	849.451	−	15667.2i	0.0535913	−	0.988433i	−0.840856	−	0.541259i	$-0.817948\pi$
$631$	849.451	−	15667.2i	0.0535913	−	0.988433i	0.894447	−	0.447174i	$-0.147570\pi$
$632$	−11090.5	+	27835.0i	−0.698031	+	1.75193i
$633$	−9239.31	+	4274.56i	−0.580141	+	0.268402i
$634$	19537.8	+	4300.58i	1.22389	+	0.269397i
$635$	3857.39	+	7275.81i	0.241064	+	0.454696i
$636$	−1179.38	−	7193.90i	−0.0735306	−	0.448517i
$637$	8300.03	+	6309.52i	0.516263	+	0.392453i
$638$	22672.4	+	10489.4i	1.40691	+	0.650907i
$639$	−94.3557	+	89.3785i	−0.00584140	+	0.00553327i
$640$	4859.63	−	29642.4i	0.300147	−	1.83081i
$641$	−3773.47	+	1271.43i	−0.232517	+	0.0783440i	−0.433148	−	0.901323i	$-0.642597\pi$
$641$	−3773.47	+	1271.43i	−0.232517	+	0.0783440i	0.200631	+	0.979667i	$0.435701\pi$
$642$	−958.599	−	2405.90i	−0.0589297	−	0.147903i
$643$	442.295	+	418.965i	0.0271266	+	0.0256957i	0.701143	−	0.713021i	$-0.252674\pi$
$643$	442.295	+	418.965i	0.0271266	+	0.0256957i	−0.674016	+	0.738717i	$0.735432\pi$
$644$	−75875.9	+	57679.3i	−4.64275	+	3.52932i
$645$	−4597.39	+	1011.96i	−0.280654	+	0.0617767i
$646$	−49334.5	−	58081.1i	−3.00471	−	3.53741i
$647$	805.531	−	87.6068i	0.0489470	−	0.00532331i	−0.0836128	−	0.996498i	$-0.526646\pi$
$647$	805.531	−	87.6068i	0.0489470	−	0.00532331i	0.132560	+	0.991175i	$0.457680\pi$
$648$	3548.95			0.215148
$649$	8314.07	+	7316.59i	0.502860	+	0.442529i
$650$	5425.86			0.327415
$651$	6227.48	−	677.279i	0.374922	−	0.0407752i
$652$	31803.2	+	37441.6i	1.91029	+	2.24896i
$653$	22421.9	−	4935.43i	1.34370	−	0.295771i	0.515830	−	0.856691i	$-0.327484\pi$
$653$	22421.9	−	4935.43i	1.34370	−	0.295771i	0.827870	+	0.560920i	$0.189553\pi$
$654$	−3636.76	+	2764.59i	−0.217444	+	0.165297i
$655$	6253.81	+	5923.92i	0.373063	+	0.353384i
$656$	661.031	+	1659.06i	0.0393429	+	0.0987432i
$657$	−7232.38	+	2436.87i	−0.429470	+	0.144705i
$658$	−1298.82	+	7922.48i	−0.0769505	+	0.469377i
$659$	5646.20	−	5348.37i	0.333755	−	0.316150i	−0.502408	−	0.864631i	$-0.667552\pi$
$659$	5646.20	−	5348.37i	0.333755	−	0.316150i	0.836163	+	0.548481i	$0.184794\pi$
$660$	−15147.7	−	7008.09i	−0.893371	−	0.413317i
$661$	17061.1	+	12969.5i	1.00394	+	0.763172i	0.971678	−	0.236308i	$-0.0759373\pi$
$661$	17061.1	+	12969.5i	1.00394	+	0.763172i	0.0322571	+	0.999480i	$0.489730\pi$
$662$	−2270.80	−	13851.3i	−0.133319	−	0.813210i
$663$	2490.66	+	4697.89i	0.145896	+	0.275190i
$664$	52007.5	+	11447.7i	3.03958	+	0.669062i
$665$	−59315.1	+	27442.1i	−3.45886	+	1.60024i
$666$	6729.58	−	16890.0i	0.391540	−	0.982692i
$667$	2096.80	−	38673.2i	0.121722	−	2.24503i
$668$	−3.90114	+	5.75375i	−0.000225957	+	0.000333262i
$669$	−7360.90	+	8665.92i	−0.425394	+	0.500813i
$670$	−13513.2	+	25488.7i	−0.779197	+	1.46972i
$671$	3647.70	+	1229.05i	0.209863	+	0.0707110i
$672$	326.205	+	6016.50i	0.0187256	+	0.345374i
$673$	−27995.6	−	16844.4i	−1.60349	−	0.964789i	−0.983656	−	0.180057i	$-0.942372\pi$
$673$	−27995.6	−	16844.4i	−1.60349	−	0.964789i	−0.619835	−	0.784732i	$-0.712801\pi$
$674$	−3791.44	+	13655.5i	−0.216678	+	0.780404i
$675$	−423.725	−	1526.12i	−0.0241618	−	0.0870228i
$676$	26657.4	−	16039.3i	1.51670	−	0.912566i
$677$	19746.3	+	29123.6i	1.12099	+	1.65334i	0.601535	+	0.798846i	$0.294556\pi$
$677$	19746.3	+	29123.6i	1.12099	+	1.65334i	0.519459	+	0.854496i	$0.326134\pi$
$678$	13587.9	+	1477.77i	0.769677	+	0.0837074i
$679$	37607.8	+	4090.09i	2.12556	+	0.231168i
$680$	31797.6	+	46898.0i	1.79321	+	2.64479i
$681$	1972.62	−	1186.89i	0.111000	−	0.0667865i
$682$	−2260.64	−	8142.10i	−0.126927	−	0.457151i
$683$	−5532.21	+	19925.2i	−0.309933	+	1.11628i	0.630469	+	0.776214i	$0.282862\pi$
$683$	−5532.21	+	19925.2i	−0.309933	+	1.11628i	−0.940402	+	0.340064i	$0.889551\pi$
$684$	−20774.5	−	12499.6i	−1.16131	−	0.698736i
$685$	−345.482	−	6372.04i	−0.0192704	−	0.355421i
$686$	30982.3	+	10439.2i	1.72436	+	0.581004i
$687$	9123.21	−	17208.2i	0.506655	−	0.955653i
$688$	6281.42	−	7395.06i	0.348077	−	0.409788i
$689$	1507.82	−	2223.86i	0.0833718	−	0.122964i
$690$	−2068.06	+	38143.1i	−0.114101	+	2.10447i
$691$	429.243	−	1077.32i	0.0236312	−	0.0593098i	−0.916688	−	0.399604i	$-0.869147\pi$
$691$	429.243	−	1077.32i	0.0236312	−	0.0593098i	0.940319	+	0.340295i	$0.110527\pi$
$692$	2290.99	−	1059.93i	0.125853	−	0.0582259i
$693$	−6459.46	−	1421.83i	−0.354076	−	0.0779380i
$694$	29342.7	+	55346.2i	1.60495	+	3.02725i
$695$	3344.95	+	20403.3i	0.182563	+	1.11358i
$696$	−21480.1	−	16328.8i	−1.16983	−	0.889282i
$697$	1845.72	+	853.919i	0.100303	+	0.0464053i
$698$	7337.88	−	6950.81i	0.397912	−	0.376923i
$699$	−1697.69	+	10355.4i	−0.0918633	+	0.560341i
$700$	28082.1	−	9461.95i	1.51629	−	0.510897i
$701$	4238.98	+	10639.0i	0.228394	+	0.573226i	0.997855	−	0.0654686i	$-0.0208542\pi$
$701$	4238.98	+	10639.0i	0.228394	+	0.573226i	−0.769461	+	0.638694i	$0.779475\pi$
$702$	1813.07	+	1717.44i	0.0974788	+	0.0923368i
$703$	−51790.0	+	39369.8i	−2.77852	+	2.11217i
$704$	−8062.19	+	1774.62i	−0.431613	+	0.0950051i
$705$	1411.05	+	1661.21i	0.0753802	+	0.0887444i
$706$	−19882.7	+	2162.38i	−1.05991	+	0.115272i
$707$	−43526.7			−2.31540
$708$	−13500.6	−	18420.9i	−0.716645	−	0.977824i
$709$	17389.1			0.921100			0.460550	−	0.887634i	$-0.347652\pi$
$709$	17389.1			0.921100			0.460550	+	0.887634i	$0.347652\pi$
$710$	−968.855	+	105.369i	−0.0512120	+	0.00556964i
$711$	3984.53	+	4690.95i	0.210171	+	0.247432i
$712$	−6116.44	+	1346.33i	−0.321943	+	0.0708650i
$713$	−10429.4	+	7928.21i	−0.547803	+	0.416429i
$714$	31123.7	+	29481.9i	1.63134	+	1.54528i
$715$	−2276.91	−	5714.61i	−0.119093	−	0.298901i
$716$	4406.04	−	1484.57i	0.229974	−	0.0774874i
$717$	−599.354	+	3655.90i	−0.0312180	+	0.190421i
$718$	−31938.5	+	30253.7i	−1.66007	+	1.57251i
$719$	24343.2	+	11262.4i	1.26265	+	0.584166i	0.932980	−	0.359928i	$-0.117199\pi$
$719$	24343.2	+	11262.4i	1.26265	+	0.584166i	0.329675	+	0.944095i	$0.393061\pi$
$720$	8136.80	+	6185.44i	0.421168	+	0.320163i
$721$	2561.06	+	15621.8i	0.132287	+	0.806915i
$722$	43988.5	+	82971.1i	2.26743	+	4.27682i
$723$	−9791.32	−	2155.23i	−0.503656	−	0.110863i
$724$	−42884.6	+	19840.5i	−2.20137	+	1.01846i
$725$	−4457.09	+	11186.4i	−0.228320	+	0.573040i
$726$	593.484	−	10946.2i	0.0303392	−	0.559573i
$727$	21570.0	−	31813.4i	1.10040	−	1.62296i	0.387206	−	0.921993i	$-0.373440\pi$
$727$	21570.0	−	31813.4i	1.10040	−	1.62296i	0.713191	−	0.700970i	$-0.247249\pi$
$728$	−15843.3	+	18652.2i	−0.806583	+	0.949582i
$729$	341.470	−	644.080i	0.0173485	−	0.0327227i
$730$	−54232.4	−	18273.0i	−2.74963	−	0.926459i
$731$	−598.175	−	11032.7i	−0.0302658	−	0.558219i
$732$	−6801.43	−	4092.28i	−0.343426	−	0.206633i
$733$	9614.50	−	34628.3i	0.484474	−	1.74492i	−0.166717	−	0.986005i	$-0.553317\pi$
$733$	9614.50	−	34628.3i	0.484474	−	1.74492i	0.651192	−	0.758913i	$-0.274269\pi$
$734$	−14414.5	−	51916.2i	−0.724861	−	2.61071i
$735$	19554.6	−	11765.6i	0.981335	−	0.590450i
$736$	−7071.60	−	10429.8i	−0.354161	−	0.522349i
$737$	10385.5	+	1129.49i	0.519071	+	0.0564523i
$738$	949.556	+	103.270i	0.0473626	+	0.00515100i
$739$	−16590.7	−	24469.5i	−0.825845	−	1.21803i	−0.973431	−	0.228981i	$-0.926461\pi$
$739$	−16590.7	−	24469.5i	−0.825845	−	1.21803i	0.147586	−	0.989049i	$-0.452850\pi$
$740$	79132.5	−	47612.4i	3.93104	−	2.36523i
$741$	−2390.62	−	8610.22i	−0.118518	−	0.426861i
$742$	5795.31	−	20872.8i	0.286729	−	1.03270i
$743$	13218.3	+	7953.16i	0.652666	+	0.392696i	0.803033	−	0.595934i	$-0.203218\pi$
$743$	13218.3	+	7953.16i	0.652666	+	0.392696i	−0.150367	+	0.988630i	$0.548046\pi$
$744$	494.117	+	9113.45i	0.0243484	+	0.449080i
$745$	12894.6	+	4344.68i	0.634121	+	0.213660i
$746$	7481.75	−	14112.1i	0.367193	−	0.692600i
$747$	7081.59	−	8337.09i	0.346856	−	0.408351i
$748$	21983.9	−	32423.9i	1.07462	−	1.58494i
$749$	282.235	−	5205.51i	0.0137685	−	0.253946i
$750$	−4971.34	+	12477.1i	−0.242037	+	0.607467i
$751$	−5713.21	+	2643.21i	−0.277600	+	0.128432i	−0.553750	−	0.832683i	$-0.686804\pi$
$751$	−5713.21	+	2643.21i	−0.277600	+	0.128432i	0.276149	+	0.961115i	$0.410942\pi$
$752$	−4387.45	−	965.751i	−0.212758	−	0.0468315i
$753$	−6121.72	−	11546.8i	−0.296265	−	0.558816i
$754$	−3071.74	−	18736.8i	−0.148364	−	0.904978i
$755$	−26182.4	−	19903.3i	−1.26209	−	0.959412i
$756$	12378.7	+	5727.00i	0.595515	+	0.275514i
$757$	−7837.40	+	7423.98i	−0.376295	+	0.356445i	−0.852352	−	0.522969i	$-0.824824\pi$
$757$	−7837.40	+	7423.98i	−0.376295	+	0.356445i	0.476057	+	0.879415i	$0.342066\pi$
$758$	−158.862	+	969.018i	−0.00761232	+	0.0464331i
$759$	13108.4	−	4416.73i	0.626882	−	0.211221i
$760$	−35245.3	−	88458.9i	−1.68221	−	4.22203i
$761$	1616.27	+	1531.02i	0.0769907	+	0.0729294i	0.725227	−	0.688509i	$-0.241735\pi$
$761$	1616.27	+	1531.02i	0.0769907	+	0.0729294i	−0.648237	+	0.761439i	$0.724493\pi$
$762$	−7226.98	+	5493.81i	−0.343577	+	0.261181i
$763$	−8980.58	+	1976.77i	−0.426106	+	0.0937930i
$764$	−30088.2	−	35422.6i	−1.42481	−	1.67741i
$765$	11570.7	−	1258.39i	0.546850	−	0.0594736i
$766$	57732.9			2.72320
$767$	1056.55	−	8350.95i	0.0497389	−	0.393136i
$768$	25005.7			1.17489
$769$	8510.90	−	925.616i	0.399104	−	0.0434052i	0.0936335	−	0.995607i	$-0.470152\pi$
$769$	8510.90	−	925.616i	0.399104	−	0.0434052i	0.305470	+	0.952202i	$0.401186\pi$
$770$	−32107.9	−	37800.3i	−1.50271	−	1.76913i
$771$	−16394.6	+	3608.71i	−0.765805	+	0.168566i
$772$	−12061.2	+	9168.71i	−0.562297	+	0.427447i
$773$	−28018.6	−	26540.6i	−1.30370	−	1.23493i	−0.954617	−	0.297836i	$-0.903735\pi$
$773$	−28018.6	−	26540.6i	−1.30370	−	1.23493i	−0.349081	−	0.937093i	$-0.613506\pi$
$774$	−1920.76	−	4820.75i	−0.0891995	−	0.223874i
$775$	3859.97	−	1300.57i	0.178909	−	0.0602813i
$776$	−8916.94	+	54390.9i	−0.412499	+	2.51613i
$777$	26569.6	−	25168.1i	1.22674	−	1.16203i
$778$	62531.2	+	28930.0i	2.88156	+	1.33315i
$779$	−2720.80	−	2068.30i	−0.125138	−	0.0951276i
$780$	2052.27	+	12518.3i	0.0942090	+	0.574649i
$781$	165.304	+	311.796i	0.00757368	+	0.0142855i
$782$	−87561.2	−	19273.7i	−4.00407	−	0.881362i
$783$	−5030.17	+	2327.21i	−0.229583	+	0.106217i
$784$	−17410.5	+	43697.2i	−0.793119	+	1.99058i
$785$	813.055	−	14995.9i	0.0369671	−	0.681818i
$786$	−5328.96	+	7859.63i	−0.241829	+	0.356671i
$787$	−1925.04	+	2266.33i	−0.0871923	+	0.102651i	−0.804028	−	0.594591i	$-0.797314\pi$
$787$	−1925.04	+	2266.33i	−0.0871923	+	0.102651i	0.716836	+	0.697242i	$0.245590\pi$
$788$	12881.9	−	24297.8i	0.582357	−	1.09844i
$789$	22969.9	+	7739.45i	1.03644	+	0.349216i
$790$	2498.63	+	46084.4i	0.112528	+	2.07546i
$791$	23574.5	+	14184.3i	1.05969	+	0.637593i
$792$	2578.07	−	9285.37i	0.115666	−	0.416592i
$793$	−782.670	−	2818.92i	−0.0350485	−	0.126233i
$794$	−40870.6	+	24591.0i	−1.82675	+	1.09912i
$795$	−3300.44	−	4867.79i	−0.147238	−	0.217160i
$796$	−75293.9	−	8188.71i	−3.35267	−	0.364624i
$797$	−41.8387	−	4.55023i	−0.00185947	−	0.000202230i	0.107189	−	0.994239i	$-0.465815\pi$
$797$	−41.8387	−	4.55023i	−0.00185947	−	0.000202230i	−0.109049	+	0.994036i	$0.534780\pi$
$798$	−40431.0	−	59631.2i	−1.79354	−	2.64527i
$799$	−4383.48	+	2637.45i	−0.194088	+	0.116779i
$800$	1048.14	+	3775.06i	0.0463217	+	0.166836i
$801$	−344.168	+	1239.58i	−0.0151817	+	0.0546796i
$802$	−48413.7	−	29129.6i	−2.13161	−	1.28254i
$803$	1121.93	+	20692.8i	0.0493051	+	0.909380i
$804$	−20415.2	−	6878.67i	−0.895506	−	0.301731i
$805$	−36016.8	+	67934.9i	−1.57693	+	2.97440i
$806$	−4157.81	+	4894.95i	−0.181703	+	0.213917i
$807$	4430.67	−	6534.74i	0.193267	−	0.285048i
$808$	3433.36	−	63324.7i	0.149487	−	2.75712i
$809$	−417.649	+	1048.22i	−0.0181505	+	0.0455543i	−0.937773	−	0.347250i	$-0.887116\pi$
$809$	−417.649	+	1048.22i	−0.0181505	+	0.0455543i	0.919622	+	0.392804i	$0.128495\pi$
$810$	4961.22	−	2295.30i	0.215209	−	0.0995664i
$811$	−4267.76	−	939.406i	−0.184786	−	0.0406745i	0.121613	−	0.992578i	$-0.461193\pi$
$811$	−4267.76	−	939.406i	−0.184786	−	0.0406745i	−0.306399	+	0.951903i	$0.599124\pi$
$812$	−48572.4	−	91617.3i	−2.09921	−	3.95953i
$813$	−1207.80	−	7367.26i	−0.0521026	−	0.317812i
$814$	−39301.8	−	29876.4i	−1.69229	−	1.28645i
$815$	35969.2	+	16641.1i	1.54594	+	0.715230i
$816$	−17416.3	+	16497.6i	−0.747174	+	0.707760i
$817$	−3003.99	+	18323.5i	−0.128637	+	0.784650i
$818$	55978.6	−	18861.4i	2.39272	−	0.806202i
$819$	1860.69	+	4669.97i	0.0793866	+	0.199245i
$820$	3522.33	+	3336.53i	0.150006	+	0.142093i
$821$	23541.9	−	17896.1i	1.00075	−	0.760754i	0.0296869	−	0.999559i	$-0.490549\pi$
$821$	23541.9	−	17896.1i	1.00075	−	0.760754i	0.971067	+	0.238806i	$0.0767559\pi$
$822$	6870.15	−	1512.23i	0.291513	−	0.0641670i
$823$	−27008.1	−	31796.4i	−1.14391	−	1.34672i	−0.928996	−	0.370089i	$-0.879327\pi$
$823$	−27008.1	−	31796.4i	−1.14391	−	1.34672i	−0.214918	−	0.976632i	$-0.568949\pi$
$824$	−22929.3	+	2493.71i	−0.969394	+	0.105428i
$825$	−4300.70			−0.181492
$826$	−13425.8	−	66524.5i	−0.565549	−	2.80228i
$827$	7329.62			0.308193			0.154097	−	0.988056i	$-0.450753\pi$
$827$	7329.62			0.308193			0.154097	+	0.988056i	$0.450753\pi$
$828$	−28357.5	+	3084.07i	−1.19021	+	0.129443i
$829$	16016.1	+	18855.7i	0.671005	+	0.789969i	0.987330	−	0.158683i	$-0.0507246\pi$
$829$	16016.1	+	18855.7i	0.671005	+	0.789969i	−0.316324	+	0.948651i	$0.602449\pi$
$830$	80107.1	−	17632.9i	3.35007	−	0.737406i
$831$	−2068.07	+	1572.11i	−0.0863306	+	0.0656268i
$832$	4555.13	+	4314.84i	0.189808	+	0.179796i
$833$	19826.1	+	49759.7i	0.824649	+	2.06971i
$834$	−21599.0	+	7277.54i	−0.896776	+	0.302159i
$835$	−0.907308	+	5.53433i	−3.76032e−5	+	0.000229369i
$836$	−47794.9	+	45273.7i	−1.97730	+	1.87300i
$837$	1701.49	+	787.194i	0.0702654	+	0.0325083i
$838$	5154.59	+	3918.42i	0.212485	+	0.161527i
$839$	4564.66	+	27843.2i	0.187830	+	1.14571i	0.897446	+	0.441125i	$0.145420\pi$
$839$	4564.66	+	27843.2i	0.187830	+	1.14571i	−0.709615	+	0.704589i	$0.751131\pi$
$840$	25091.7	+	47328.1i	1.03065	+	1.94402i
$841$	17333.9	+	3815.49i	0.710728	+	0.156443i
$842$	38630.4	−	17872.3i	1.58111	−	0.731498i
$843$	−3139.03	+	7878.37i	−0.128249	+	0.321881i
$844$	3086.12	−	56920.1i	0.125863	−	2.32141i
$845$	14085.1	−	20773.9i	0.573421	−	0.845733i
$846$	−1555.48	+	1831.26i	−0.0632135	+	0.0744207i
$847$	10336.0	−	19495.7i	0.419302	−	0.790887i
$848$	11487.4	+	3870.56i	0.465188	+	0.156740i
$849$	−796.817	−	14696.4i	−0.0322105	−	0.594087i
$850$	23885.5	+	14371.4i	0.963841	+	0.579924i
$851$	−20476.3	+	73748.8i	−0.824815	+	2.97071i
$852$	−194.693	−	701.221i	−0.00782873	−	0.0281965i
$853$	−16907.0	+	10172.6i	−0.678645	+	0.408327i	−0.812728	−	0.582643i	$-0.802019\pi$
$853$	−16907.0	+	10172.6i	−0.678645	+	0.408327i	0.134083	+	0.990970i	$0.457191\pi$
$854$	−13236.8	−	19522.8i	−0.530391	−	0.782268i
$855$	−19445.1	−	2114.78i	−0.777788	−	0.0845896i
$856$	7550.96	+	821.217i	0.301503	+	0.0327904i
$857$	7268.37	+	10720.0i	0.289712	+	0.427293i	0.944496	−	0.328523i	$-0.106551\pi$
$857$	7268.37	+	10720.0i	0.289712	+	0.427293i	−0.654784	+	0.755816i	$0.727241\pi$
$858$	5810.51	−	3496.07i	0.231198	−	0.139107i
$859$	−1673.43	−	6027.16i	−0.0664689	−	0.239399i	0.922852	−	0.385156i	$-0.125852\pi$
$859$	−1673.43	−	6027.16i	−0.0664689	−	0.239399i	−0.989321	+	0.145756i	$0.953438\pi$
$860$	7051.83	−	25398.4i	0.279611	−	1.00707i
$861$	1647.44	+	991.233i	0.0652087	+	0.0392347i
$862$	258.038	+	4759.23i	0.0101958	+	0.188051i
$863$	−32691.3	−	11015.0i	−1.28948	−	0.434478i	−0.410732	−	0.911756i	$-0.634727\pi$
$863$	−32691.3	−	11015.0i	−1.28948	−	0.434478i	−0.878752	+	0.477278i	$0.841623\pi$
$864$	−844.671	+	1593.22i	−0.0332596	+	0.0627343i
$865$	1318.39	−	1552.13i	0.0518228	−	0.0610105i
$866$	−19479.5	+	28730.1i	−0.764366	+	1.12736i
$867$	−681.006	+	12560.4i	−0.0266761	+	0.492012i
$868$	−12983.0	+	32584.9i	−0.507687	+	1.27420i
$869$	15167.7	−	7017.34i	0.592095	−	0.273932i
$870$	−40588.6	−	8934.23i	−1.58170	−	0.348159i
$871$	−3719.16	−	7015.08i	−0.144683	−	0.272901i
$872$	−2167.52	−	13221.3i	−0.0841760	−	0.513451i
$873$	9013.15	+	6851.62i	0.349426	+	0.265627i
$874$	136747.	+	63266.0i	5.29238	+	2.44852i
$875$	−19627.8	+	18592.4i	−0.758331	+	0.718330i
$876$	6913.67	−	42171.5i	0.266657	−	1.62653i
$877$	6488.63	−	2186.27i	0.249835	−	0.0841793i	−0.191598	−	0.981474i	$-0.561367\pi$
$877$	6488.63	−	2186.27i	0.249835	−	0.0841793i	0.441433	+	0.897294i	$0.354470\pi$
$878$	22829.0	+	57296.4i	0.877495	+	2.20235i
$879$	11885.8	+	11258.8i	0.456083	+	0.432024i
$880$	22094.2	−	16795.6i	0.846358	−	0.643385i
$881$	16766.7	−	3690.63i	0.641185	−	0.141136i	0.117535	−	0.993069i	$-0.462501\pi$
$881$	16766.7	−	3690.63i	0.641185	−	0.141136i	0.523651	+	0.851933i	$0.324570\pi$
$882$	16286.5	+	19173.9i	0.621763	+	0.731996i
$883$	12373.2	−	1345.67i	0.471564	−	0.0512857i	0.130748	−	0.991416i	$-0.458262\pi$
$883$	12373.2	−	1345.67i	0.471564	−	0.0512857i	0.340816	+	0.940130i	$0.389297\pi$
$884$	−29774.0			−1.13281
$885$	−16125.0	−	8914.28i	−0.612472	−	0.338588i
$886$	1168.35			0.0443018
$887$	34067.1	−	3705.03i	1.28959	−	0.140251i	0.562500	−	0.826797i	$-0.309840\pi$
$887$	34067.1	−	3705.03i	1.28959	−	0.140251i	0.727086	+	0.686546i	$0.240874\pi$
$888$	34519.9	+	40640.0i	1.30452	+	1.53580i
$889$	−17846.2	+	3928.26i	−0.673278	+	0.148200i
$890$	−7679.66	+	5837.93i	−0.289239	+	0.219874i
$891$	−1437.10	−	1361.29i	−0.0540343	−	0.0511840i
$892$	−23565.6	−	59145.1i	−0.884566	−	2.22009i
$893$	8147.22	−	2745.12i	0.305304	−	0.102869i
$894$	−2426.67	+	14802.1i	−0.0907831	+	0.553753i
$895$	2723.17	−	2579.52i	0.101704	−	0.0963395i
$896$	60493.4	+	27987.2i	2.25552	+	1.04351i
$897$	−8369.55	−	6362.37i	−0.311540	−	0.236826i
$898$	14687.9	+	89592.2i	0.545814	+	3.32932i
$899$	−6676.43	−	12593.1i	−0.247688	−	0.467189i
$900$	8661.38	+	1906.51i	0.320792	+	0.0706116i
$901$	12527.9	−	5796.05i	0.463226	−	0.214311i
$902$	959.980	−	2409.37i	0.0354366	−	0.0889392i
$903$	565.519	−	10430.4i	0.0208409	−	0.384387i
$904$	−22495.5	+	33178.4i	−0.827644	+	1.22068i
$905$	−24678.8	+	29054.1i	−0.906464	+	1.06717i
$906$	16982.2	−	32031.9i	0.622733	−	1.17460i
$907$	−15054.2	−	5072.35i	−0.551120	−	0.185694i	0.0299442	−	0.999552i	$-0.490467\pi$
$907$	−15054.2	−	5072.35i	−0.551120	−	0.185694i	−0.581065	+	0.813858i	$0.697364\pi$
$908$	697.898	+	12872.0i	0.0255072	+	0.470453i
$909$	−11162.1	−	6716.01i	−0.407287	−	0.245056i
$910$	−10084.6	+	36321.3i	−0.367363	+	1.32312i
$911$	1077.12	+	3879.43i	0.0391729	+	0.141088i	0.980551	−	0.196266i	$-0.0628817\pi$
$911$	1077.12	+	3879.43i	0.0391729	+	0.141088i	−0.941378	+	0.337354i	$0.890468\pi$
$912$	34544.7	−	20784.8i	1.25426	−	0.754665i
$913$	−16668.6	−	24584.4i	−0.604217	−	0.891154i
$914$	−11031.5	−	1199.75i	−0.399224	−	0.0434182i
$915$	−6366.19	−	692.364i	−0.230011	−	0.0250151i
$916$	61203.6	+	90268.6i	2.20767	+	3.25607i
$917$	−16378.4	+	9854.55i	−0.589817	+	0.354881i
$918$	3432.48	+	12362.7i	0.123408	+	0.444476i
$919$	−1617.65	+	5826.23i	−0.0580644	+	0.209129i	−0.986892	−	0.161384i	$-0.948404\pi$
$919$	−1617.65	+	5826.23i	−0.0580644	+	0.209129i	0.928827	+	0.370513i	$0.120818\pi$
$920$	−95993.9	−	57757.6i	−3.44003	−	2.06980i
$921$	245.747	+	4532.54i	0.00879223	+	0.162163i
$922$	51405.3	+	17320.5i	1.83617	+	0.618676i
$923$	125.638	−	236.979i	0.00448043	−	0.00845099i
$924$	23976.2	−	28227.0i	0.853636	−	1.00498i
$925$	13354.5	−	19696.4i	0.474696	−	0.700124i
$926$	−3667.50	+	67643.1i	−0.130153	+	2.40053i
$927$	−1753.62	+	4401.26i	−0.0621321	+	0.155940i
$928$	12442.8	−	5756.65i	0.440146	−	0.203633i
$929$	−16235.4	−	3573.68i	−0.573375	−	0.126209i	−0.0811879	−	0.996699i	$-0.525871\pi$
$929$	−16235.4	−	3573.68i	−0.573375	−	0.126209i	−0.492187	+	0.870489i	$0.663802\pi$
$930$	6584.91	+	12420.5i	0.232180	+	0.437939i
$931$	−14563.1	−	88830.7i	−0.512658	−	3.12708i
$932$	−46777.6	−	35559.4i	−1.64405	−	1.24977i
$933$	4752.29	+	2198.64i	0.166756	+	0.0771493i
$934$	35205.8	−	33348.7i	1.23337	−	1.16831i
$935$	5112.92	−	31187.4i	0.178834	−	1.09084i
$936$	−6940.86	+	2338.65i	−0.242382	+	0.0816679i
$937$	4514.76	+	11331.2i	0.157408	+	0.395063i	0.986437	−	0.164142i	$-0.0524856\pi$
$937$	4514.76	+	11331.2i	0.157408	+	0.395063i	−0.829029	+	0.559205i	$0.811106\pi$
$938$	−46475.1	−	44023.6i	−1.61777	−	1.53243i
$939$	−2866.54	+	2179.09i	−0.0996230	+	0.0757315i
$940$	−11919.3	+	2623.63i	−0.413579	+	0.0910356i
$941$	−1479.93	−	1742.30i	−0.0512691	−	0.0603586i	0.735930	−	0.677058i	$-0.236745\pi$
$941$	−1479.93	−	1742.30i	−0.0512691	−	0.0603586i	−0.787199	+	0.616699i	$0.788469\pi$
$942$	16458.2	−	1789.93i	0.569253	−	0.0619100i
$943$	−4020.97			−0.138855
$944$	37578.3	−	5486.49i	1.29562	−	0.189163i
$945$	11003.6			0.378779
$946$	−14008.2	+	1523.48i	−0.481442	+	0.0523600i
$947$	−11923.0	−	14036.8i	−0.409129	−	0.481664i	0.518547	−	0.855049i	$-0.326473\pi$
$947$	−11923.0	−	14036.8i	−0.409129	−	0.481664i	−0.927677	+	0.373385i	$0.878197\pi$
$948$	−33657.8	+	7408.65i	−1.15312	+	0.253820i
$949$	12538.9	−	9531.82i	0.428904	−	0.326044i
$950$	−34010.2	−	32216.2i	−1.16151	−	1.10024i
$951$	4460.89	+	11196.0i	0.152108	+	0.381762i
$952$	−119148.	+	40145.8i	−4.05633	+	1.36674i
$953$	6164.43	−	37601.4i	0.209534	−	1.27810i	−0.647192	−	0.762327i	$-0.724057\pi$
$953$	6164.43	−	37601.4i	0.209534	−	1.27810i	0.856726	−	0.515772i	$-0.172495\pi$
$954$	4706.77	−	4458.49i	0.159735	−	0.151309i
$955$	−34029.5	−	15743.7i	−1.15306	−	0.533461i
$956$	−16514.4	−	12553.9i	−0.558697	−	0.424711i
$957$	2434.75	+	14851.3i	0.0822407	+	0.501646i
$958$	−15126.3	−	28531.2i	−0.510134	−	0.962215i
$959$	13829.1	+	3044.02i	0.465657	+	0.102499i
$960$	12464.4	−	5766.67i	0.419050	−	0.193873i
$961$	9242.23	−	23196.2i	0.310236	−	0.778633i
$962$	−2031.41	+	37467.1i	−0.0680824	+	1.25571i
$963$	875.569	−	1291.37i	0.0292989	−	0.0432126i
$964$	36343.4	−	42786.8i	1.21426	−	1.42953i
$965$	−5725.23	+	10798.9i	−0.190986	+	0.360238i
$966$	−80325.7	−	27064.9i	−2.67540	−	0.901447i
$967$	−73.8301	−	1361.72i	−0.00245524	−	0.0452842i	0.997049	−	0.0767671i	$-0.0244598\pi$
$967$	−73.8301	−	1361.72i	−0.00245524	−	0.0452842i	−0.999504	+	0.0314829i	$0.989977\pi$
$968$	27548.0	+	16575.1i	0.914696	+	0.550355i
$969$	12281.9	−	44235.5i	0.407175	−	1.46651i
$970$	22712.3	+	81802.2i	0.751801	+	2.70774i
$971$	−21698.8	+	13055.7i	−0.717144	+	0.431491i	−0.826813	−	0.562477i	$-0.809849\pi$
$971$	−21698.8	+	13055.7i	−0.717144	+	0.431491i	0.109669	+	0.993968i	$0.465021\pi$
$972$	2290.77	+	3378.64i	0.0755931	+	0.111492i
$973$	−45609.8	−	4960.37i	−1.50276	−	0.163435i
$974$	42329.1	+	4603.57i	1.39252	+	0.151445i
$975$	1834.37	+	2705.49i	0.0602530	+	0.0888666i
$976$	11309.7	−	6804.80i	0.370916	−	0.223173i
$977$	6077.79	+	21890.2i	0.199023	+	0.716817i	0.993923	+	0.110077i	$0.0351096\pi$
$977$	6077.79	+	21890.2i	0.199023	+	0.716817i	−0.794900	+	0.606741i	$0.792477\pi$
$978$	−11688.0	+	42096.5i	−0.382150	+	1.37638i
$979$	2993.18	+	1800.94i	0.0977145	+	0.0587929i
$980$	6918.24	+	127599.i	0.225505	+	4.15920i
$981$	−2608.01	−	878.741i	−0.0848801	−	0.0285994i
$982$	11427.6	−	21554.7i	0.371354	−	0.700447i
$983$	−18865.4	+	22210.0i	−0.612117	+	0.720640i	−0.977669	−	0.210151i	$-0.932605\pi$
$983$	−18865.4	+	22210.0i	−0.612117	+	0.720640i	0.365552	+	0.930791i	$0.380880\pi$
$984$	−1572.04	+	2318.59i	−0.0509297	+	0.0751157i
$985$	1201.17	−	22154.3i	0.0388553	−	0.716643i
$986$	36105.6	−	90618.3i	1.16616	−	2.92685i
$987$	−4389.47	+	2030.79i	−0.141559	+	0.0654920i
$988$	48866.6	+	10756.4i	1.57354	+	0.346362i
$989$	10232.7	+	19301.0i	0.329001	+	0.620561i
$990$	−2401.38	−	14647.7i	−0.0770917	−	0.470238i
$991$	10916.0	+	8298.15i	0.349908	+	0.265993i	0.765333	−	0.643634i	$-0.222574\pi$
$991$	10916.0	+	8298.15i	0.349908	+	0.265993i	−0.415425	+	0.909627i	$0.636367\pi$
$992$	−4208.87	−	1947.23i	−0.134709	−	0.0623232i
$993$	6138.92	−	5815.10i	0.196186	−	0.185837i
$994$	349.860	−	2134.05i	0.0111639	−	0.0680966i
$995$	−57903.3	+	19509.9i	−1.84488	+	0.621614i
$996$	22671.4	+	56900.8i	0.721255	+	1.81021i
$997$	−5684.61	−	5384.75i	−0.180575	−	0.171050i	0.592073	−	0.805884i	$-0.298310\pi$
$997$	−5684.61	−	5384.75i	−0.180575	−	0.171050i	−0.772648	+	0.634834i	$0.781068\pi$
$998$	52274.6	−	39738.1i	1.65804	−	1.26041i
$999$	10696.9	−	2354.57i	0.338775	−	0.0745700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.a.133.2	yes	420
59.4	even	29	inner	177.4.e.a.4.2	✓	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.a.4.2	✓	420	59.4	even	29	inner
177.4.e.a.133.2	yes	420	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.95061 + 0.538411i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(16.4057 - 3.61116i) q^{4} +(10.7888 - 8.20142i) q^{5} +(10.8459 + 10.2738i) q^{6} +(11.1308 + 27.9361i) q^{7} +(-41.5207 + 13.9900i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})\)	\(q+(-4.95061 + 0.538411i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(16.4057 - 3.61116i) q^{4} +(10.7888 - 8.20142i) q^{5} +(10.8459 + 10.2738i) q^{6} +(11.1308 + 27.9361i) q^{7} +(-41.5207 + 13.9900i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(-48.9953 + 46.4108i) q^{10} +(22.1794 + 10.2613i) q^{11} +(-40.1193 - 30.4979i) q^{12} +(-3.00494 - 18.3293i) q^{13} +(-70.1451 - 132.308i) q^{14} +(-39.7060 - 8.73994i) q^{15} +(76.0539 - 35.1863i) q^{16} +(35.3205 - 88.6477i) q^{17} +(2.42641 - 44.7525i) q^{18} +(-89.9954 + 132.733i) q^{19} +(147.381 - 173.510i) q^{20} +(42.2578 - 79.7067i) q^{21} +(-115.326 - 38.8579i) q^{22} +(10.2146 + 188.397i) q^{23} +(112.628 + 67.7658i) q^{24} +(15.6935 - 56.5230i) q^{25} +(24.7450 + 89.1235i) q^{26} +(23.1351 - 13.9200i) q^{27} +(283.489 + 418.115i) q^{28} +(-204.072 - 22.1941i) q^{29} +(201.274 + 21.8899i) q^{30} +(38.9665 + 57.4712i) q^{31} +(-57.2279 + 34.4329i) q^{32} +(-19.6136 - 70.6419i) q^{33} +(-127.129 + 457.877i) q^{34} +(349.203 + 210.108i) q^{35} +(8.18502 + 150.964i) q^{36} +(384.432 + 129.530i) q^{37} +(374.067 - 705.565i) q^{38} +(-36.0737 + 42.4693i) q^{39} +(-333.221 + 491.464i) q^{40} +(-1.15380 + 21.2805i) q^{41} +(-166.287 + 417.348i) q^{42} +(105.084 - 48.6172i) q^{43} +(400.923 + 88.2498i) q^{44} +(57.1315 + 107.762i) q^{45} +(-152.003 - 927.179i) q^{46} +(-42.6787 - 32.4435i) q^{47} +(-228.162 - 105.559i) q^{48} +(-407.515 + 386.019i) q^{49} +(-47.2599 + 288.273i) q^{50} +(-271.290 + 91.4082i) q^{51} +(-115.488 - 289.854i) q^{52} +(105.019 + 99.4794i) q^{53} +(-107.038 + 81.3684i) q^{54} +(323.446 - 71.1958i) q^{55} +(-852.982 - 1004.21i) q^{56} +(478.278 - 52.0159i) q^{57} +1022.23 q^{58} +(434.478 + 128.871i) q^{59} -682.964 q^{60} +(156.585 - 17.0296i) q^{61} +(-223.851 - 263.538i) q^{62} +(-264.320 + 58.1811i) q^{63} +(-268.921 + 204.428i) q^{64} +(-182.746 - 173.107i) q^{65} +(135.134 + 339.160i) q^{66} +(405.101 - 136.494i) q^{67} +(259.335 - 1581.87i) q^{68} +(410.929 - 389.252i) q^{69} +(-1841.89 - 852.150i) q^{70} +(11.4962 + 8.73921i) q^{71} +(-63.7952 - 389.134i) q^{72} +(397.204 + 749.207i) q^{73} +(-1972.91 - 434.270i) q^{74} +(-159.718 + 73.8936i) q^{75} +(-997.113 + 2502.56i) q^{76} +(-39.7866 + 733.822i) q^{77} +(155.721 - 229.671i) q^{78} +(442.726 - 521.217i) q^{79} +(531.952 - 1003.37i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(-5.74567 - 105.973i) q^{82} +(-1041.44 - 626.612i) q^{83} +(405.434 - 1460.24i) q^{84} +(-345.972 - 1246.08i) q^{85} +(-494.056 + 297.263i) q^{86} +(345.593 + 509.712i) q^{87} +(-1064.46 - 115.767i) q^{88} +(142.103 + 15.4547i) q^{89} +(-340.856 - 502.725i) q^{90} +(478.603 - 287.966i) q^{91} +(847.908 + 3053.89i) q^{92} +(55.7281 - 200.715i) q^{93} +(228.753 + 137.636i) q^{94} +(117.661 + 2170.12i) q^{95} +(189.876 + 63.9766i) q^{96} +(589.244 - 1111.43i) q^{97} +(1809.61 - 2130.44i) q^{98} +(-123.429 + 182.044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more