LMFDB - Embedded newform 177.4.e.b.4.15

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			4.15
Character	$\chi$	$=$	177.4
Dual form			177.4.e.b.133.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.20320 + 0.565882i) q^{2} +(1.94216 - 2.28649i) q^{3} +(18.9401 + 4.16902i) q^{4} +(3.73106 + 2.83628i) q^{5} +(11.3993 - 10.7980i) q^{6} +(-7.57844 + 19.0204i) q^{7} +(56.5105 + 19.0406i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})$	\(q+(5.20320 + 0.565882i) q^{2} +(1.94216 - 2.28649i) q^{3} +(18.9401 + 4.16902i) q^{4} +(3.73106 + 2.83628i) q^{5} +(11.3993 - 10.7980i) q^{6} +(-7.57844 + 19.0204i) q^{7} +(56.5105 + 19.0406i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(17.8084 + 16.8690i) q^{10} +(-14.1232 + 6.53410i) q^{11} +(46.3170 - 35.2093i) q^{12} +(4.31969 - 26.3490i) q^{13} +(-50.1954 + 94.6786i) q^{14} +(13.7314 - 3.02251i) q^{15} +(142.452 + 65.9055i) q^{16} +(-36.5050 - 91.6206i) q^{17} +(-2.55021 - 47.0358i) q^{18} +(-4.84610 - 7.14746i) q^{19} +(58.8420 + 69.2742i) q^{20} +(28.7715 + 54.2687i) q^{21} +(-77.1835 + 26.0062i) q^{22} +(3.37594 - 62.2656i) q^{23} +(153.289 - 92.2306i) q^{24} +(-27.5647 - 99.2791i) q^{25} +(37.3866 - 134.654i) q^{26} +(-23.1351 - 13.9200i) q^{27} +(-222.833 + 328.654i) q^{28} +(-13.6444 + 1.48392i) q^{29} +(73.1577 - 7.95637i) q^{30} +(-145.027 + 213.899i) q^{31} +(295.143 + 177.582i) q^{32} +(-12.4894 + 44.9829i) q^{33} +(-138.096 - 497.377i) q^{34} +(-82.2228 + 49.4718i) q^{35} +(9.44948 - 174.285i) q^{36} +(177.830 - 59.9178i) q^{37} +(-21.1706 - 39.9320i) q^{38} +(-51.8570 - 61.0508i) q^{39} +(156.840 + 231.321i) q^{40} +(9.20035 + 169.691i) q^{41} +(118.994 + 298.652i) q^{42} +(202.638 + 93.7502i) q^{43} +(-294.736 + 64.8763i) q^{44} +(19.7577 - 37.2669i) q^{45} +(52.8007 - 322.070i) q^{46} +(-137.959 + 104.874i) q^{47} +(427.357 - 197.716i) q^{48} +(-55.3281 - 52.4095i) q^{49} +(-87.2444 - 532.167i) q^{50} +(-280.388 - 94.4736i) q^{51} +(191.665 - 481.042i) q^{52} +(-94.5857 + 89.5963i) q^{53} +(-112.500 - 85.5200i) q^{54} +(-71.2272 - 15.6783i) q^{55} +(-790.422 + 930.557i) q^{56} +(-25.7545 - 2.80097i) q^{57} -71.8342 q^{58} +(-124.893 + 435.638i) q^{59} +272.675 q^{60} +(-871.011 - 94.7281i) q^{61} +(-875.648 + 1030.89i) q^{62} +(179.963 + 39.6129i) q^{63} +(435.565 + 331.108i) q^{64} +(90.8500 - 86.0577i) q^{65} +(-90.4399 + 226.987i) q^{66} +(1024.15 + 345.075i) q^{67} +(-309.438 - 1887.49i) q^{68} +(-135.813 - 128.649i) q^{69} +(-455.817 + 210.883i) q^{70} +(-134.633 + 102.346i) q^{71} +(86.8266 - 529.619i) q^{72} +(44.8165 - 84.5328i) q^{73} +(959.190 - 211.134i) q^{74} +(-280.535 - 129.789i) q^{75} +(-61.9875 - 155.577i) q^{76} +(-17.2495 - 318.148i) q^{77} +(-235.275 - 347.004i) q^{78} +(-454.597 - 535.193i) q^{79} +(344.572 + 649.931i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-48.1535 + 888.140i) q^{82} +(1045.41 - 629.004i) q^{83} +(318.686 + 1147.80i) q^{84} +(123.659 - 445.380i) q^{85} +(1001.31 + 602.470i) q^{86} +(-23.1066 + 34.0797i) q^{87} +(-922.525 + 100.331i) q^{88} +(1304.36 - 141.857i) q^{89} +(123.892 - 182.727i) q^{90} +(468.432 + 281.846i) q^{91} +(323.528 - 1165.24i) q^{92} +(207.412 + 747.030i) q^{93} +(-777.176 + 467.611i) q^{94} +(2.19110 - 40.4125i) q^{95} +(979.254 - 329.949i) q^{96} +(-82.2340 - 155.110i) q^{97} +(-258.225 - 304.006i) q^{98} +(78.5962 + 115.921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	5.20320	+	0.565882i	1.83961	+	0.200069i	0.960826	−	0.277154i	$-0.0893911\pi$
$2$	5.20320	+	0.565882i	1.83961	+	0.200069i	0.878782	+	0.477223i	$0.158357\pi$
$3$	1.94216	−	2.28649i	0.373769	−	0.440034i
$3$	1.94216	−	2.28649i	0.373769	−	0.440034i
$4$	18.9401	+	4.16902i	2.36751	+	0.521128i
$5$	3.73106	+	2.83628i	0.333716	+	0.253684i	0.758590	−	0.651568i	$-0.225889\pi$
$5$	3.73106	+	2.83628i	0.333716	+	0.253684i	−0.424874	+	0.905252i	$0.639682\pi$
$6$	11.3993	−	10.7980i	0.775625	−	0.734711i
$7$	−7.57844	+	19.0204i	−0.409197	+	1.02701i	0.569554	+	0.821954i	$0.307116\pi$
$7$	−7.57844	+	19.0204i	−0.409197	+	1.02701i	−0.978751	+	0.205053i	$0.934263\pi$
$8$	56.5105	+	19.0406i	2.49744	+	0.841484i
$9$	−1.45604	−	8.88144i	−0.0539273	−	0.328942i
$10$	17.8084	+	16.8690i	0.563152	+	0.533446i
$11$	−14.1232	+	6.53410i	−0.387120	+	0.179101i	−0.603789	−	0.797145i	$-0.706343\pi$
$11$	−14.1232	+	6.53410i	−0.387120	+	0.179101i	0.216669	+	0.976245i	$0.430481\pi$
$12$	46.3170	−	35.2093i	1.11421	−	0.847004i
$13$	4.31969	−	26.3490i	0.0921590	−	0.562145i	−0.899872	−	0.436154i	$-0.856340\pi$
$13$	4.31969	−	26.3490i	0.0921590	−	0.562145i	0.992031	−	0.125992i	$-0.0402113\pi$
$14$	−50.1954	+	94.6786i	−0.958235	+	1.80742i
$15$	13.7314	−	3.02251i	0.236362	−	0.0520273i
$16$	142.452	+	65.9055i	2.22582	+	1.02977i
$17$	−36.5050	−	91.6206i	−0.520809	−	1.30713i	−0.920593	−	0.390523i	$-0.872294\pi$
$17$	−36.5050	−	91.6206i	−0.520809	−	1.30713i	0.399784	−	0.916609i	$-0.369085\pi$
$18$	−2.55021	−	47.0358i	−0.0333939	−	0.615914i
$19$	−4.84610	−	7.14746i	−0.0585143	−	0.0863021i	0.797306	−	0.603575i	$-0.206258\pi$
$19$	−4.84610	−	7.14746i	−0.0585143	−	0.0863021i	−0.855821	+	0.517273i	$0.826947\pi$
$20$	58.8420	+	69.2742i	0.657874	+	0.774509i
$21$	28.7715	+	54.2687i	0.298974	+	0.563924i
$22$	−77.1835	+	26.0062i	−0.747981	+	0.252024i
$23$	3.37594	−	62.2656i	0.0306058	−	0.564491i	−0.942511	−	0.334176i	$-0.891542\pi$
$23$	3.37594	−	62.2656i	0.0306058	−	0.564491i	0.973116	−	0.230314i	$-0.0739754\pi$
$24$	153.289	−	92.2306i	1.30375	−	0.784438i
$25$	−27.5647	−	99.2791i	−0.220518	−	0.794233i
$26$	37.3866	−	134.654i	0.282005	−	1.01569i
$27$	−23.1351	−	13.9200i	−0.164902	−	0.0992184i
$28$	−222.833	+	328.654i	−1.50398	+	2.21820i
$29$	−13.6444	+	1.48392i	−0.0873690	+	0.00950195i	−0.151699	−	0.988427i	$-0.548474\pi$
$29$	−13.6444	+	1.48392i	−0.0873690	+	0.00950195i	0.0643301	+	0.997929i	$0.479509\pi$
$30$	73.1577	−	7.95637i	0.445223	−	0.0484210i
$31$	−145.027	+	213.899i	−0.840248	+	1.23927i	0.128620	+	0.991694i	$0.458945\pi$
$31$	−145.027	+	213.899i	−0.840248	+	1.23927i	−0.968868	+	0.247579i	$0.920365\pi$
$32$	295.143	+	177.582i	1.63045	+	0.981010i
$33$	−12.4894	+	44.9829i	−0.0658827	+	0.237288i
$34$	−138.096	−	497.377i	−0.696567	−	2.50881i
$35$	−82.2228	+	49.4718i	−0.397091	+	0.238922i
$36$	9.44948	−	174.285i	0.0437476	−	0.806877i
$37$	177.830	−	59.9178i	0.790136	−	0.266228i	0.104837	−	0.994489i	$-0.466568\pi$
$37$	177.830	−	59.9178i	0.790136	−	0.266228i	0.685299	+	0.728262i	$0.259671\pi$
$38$	−21.1706	−	39.9320i	−0.0903769	−	0.170469i
$39$	−51.8570	−	61.0508i	−0.212917	−	0.250665i
$40$	156.840	+	231.321i	0.619963	+	0.914377i
$41$	9.20035	+	169.691i	0.0350452	+	0.646371i	0.962308	+	0.271961i	$0.0876721\pi$
$41$	9.20035	+	169.691i	0.0350452	+	0.646371i	−0.927263	+	0.374410i	$0.877845\pi$
$42$	118.994	+	298.652i	0.437170	+	1.09721i
$43$	202.638	+	93.7502i	0.718650	+	0.332483i	0.744903	−	0.667172i	$-0.232496\pi$
$43$	202.638	+	93.7502i	0.718650	+	0.332483i	−0.0262531	+	0.999655i	$0.508358\pi$
$44$	−294.736	+	64.8763i	−1.00984	+	0.222283i
$45$	19.7577	−	37.2669i	0.0654511	−	0.123454i
$46$	52.8007	−	322.070i	0.169240	−	1.03232i
$47$	−137.959	+	104.874i	−0.428158	+	0.325477i	−0.796962	−	0.604030i	$-0.793561\pi$
$47$	−137.959	+	104.874i	−0.428158	+	0.325477i	0.368803	+	0.929507i	$0.379768\pi$
$48$	427.357	−	197.716i	1.28508	−	0.594540i
$49$	−55.3281	−	52.4095i	−0.161306	−	0.152797i
$50$	−87.2444	−	532.167i	−0.246764	−	1.50520i
$51$	−280.388	−	94.4736i	−0.769845	−	0.259391i
$52$	191.665	−	481.042i	0.511137	−	1.28286i
$53$	−94.5857	+	89.5963i	−0.245139	+	0.232208i	−0.800397	−	0.599470i	$-0.795378\pi$
$53$	−94.5857	+	89.5963i	−0.245139	+	0.232208i	0.555258	+	0.831678i	$0.312619\pi$
$54$	−112.500	−	85.5200i	−0.283505	−	0.215515i
$55$	−71.2272	−	15.6783i	−0.174623	−	0.0384374i
$56$	−790.422	+	930.557i	−1.88615	+	2.22055i
$57$	−25.7545	−	2.80097i	−0.0598467	−	0.00650872i
$58$	−71.8342			−0.162626
$59$	−124.893	+	435.638i	−0.275588	+	0.961276i
$59$	−124.893	+	435.638i	−0.275588	+	0.961276i
$60$	272.675			0.586703
$61$	−871.011	−	94.7281i	−1.82822	−	0.198831i	−0.871610	−	0.490199i	$-0.836924\pi$
$61$	−871.011	−	94.7281i	−1.82822	−	0.198831i	−0.956611	+	0.291368i	$0.905890\pi$
$62$	−875.648	+	1030.89i	−1.79367	+	2.11167i
$63$	179.963	+	39.6129i	0.359893	+	0.0792184i
$64$	435.565	+	331.108i	0.850714	+	0.646696i
$65$	90.8500	−	86.0577i	0.173362	−	0.164218i
$66$	−90.4399	+	226.987i	−0.168673	+	0.423336i
$67$	1024.15	+	345.075i	1.86745	+	0.629218i	0.988266	+	0.152742i	$0.0488103\pi$
$67$	1024.15	+	345.075i	1.86745	+	0.629218i	0.879187	+	0.476476i	$0.158086\pi$
$68$	−309.438	−	1887.49i	−0.551837	−	3.36606i
$69$	−135.813	−	128.649i	−0.236956	−	0.224456i
$70$	−455.817	+	210.883i	−0.778293	+	0.360077i
$71$	−134.633	+	102.346i	−0.225043	+	0.171073i	−0.711620	−	0.702564i	$-0.752038\pi$
$71$	−134.633	+	102.346i	−0.225043	+	0.171073i	0.486577	+	0.873637i	$0.338245\pi$
$72$	86.8266	−	529.619i	0.142120	−	0.866891i
$73$	44.8165	−	84.5328i	0.0718544	−	0.135532i	−0.844982	−	0.534794i	$-0.820389\pi$
$73$	44.8165	−	84.5328i	0.0718544	−	0.135532i	0.916837	+	0.399263i	$0.130734\pi$
$74$	959.190	−	211.134i	1.50680	−	0.331673i
$75$	−280.535	−	129.789i	−0.431912	−	0.199824i
$76$	−61.9875	−	155.577i	−0.0935586	−	0.234814i
$77$	−17.2495	−	318.148i	−0.0255294	−	0.470862i
$78$	−235.275	−	347.004i	−0.341534	−	0.503724i
$79$	−454.597	−	535.193i	−0.647420	−	0.762201i	0.336331	−	0.941744i	$-0.390814\pi$
$79$	−454.597	−	535.193i	−0.647420	−	0.762201i	−0.983750	+	0.179543i	$0.942538\pi$
$80$	344.572	+	649.931i	0.481554	+	0.908307i
$81$	−76.7599	+	25.8634i	−0.105295	+	0.0354779i
$82$	−48.1535	+	888.140i	−0.0648496	+	1.19608i
$83$	1045.41	−	629.004i	1.38252	−	0.831833i	0.386613	−	0.922242i	$-0.373645\pi$
$83$	1045.41	−	629.004i	1.38252	−	0.831833i	0.995905	+	0.0904086i	$0.0288173\pi$
$84$	318.686	+	1147.80i	0.413946	+	1.49090i
$85$	123.659	−	445.380i	0.157797	−	0.568332i
$86$	1001.31	+	602.470i	1.25552	+	0.755418i
$87$	−23.1066	+	34.0797i	−0.0284746	+	0.0419969i
$88$	−922.525	+	100.331i	−1.11752	+	0.121537i
$89$	1304.36	−	141.857i	1.55350	−	0.168953i	0.709271	−	0.704936i	$-0.249024\pi$
$89$	1304.36	−	141.857i	1.55350	−	0.168953i	0.844229	+	0.535982i	$0.180059\pi$
$90$	123.892	−	182.727i	0.145104	−	0.214012i
$91$	468.432	+	281.846i	0.539616	+	0.324676i
$92$	323.528	−	1165.24i	0.366631	−	1.32049i
$93$	207.412	+	747.030i	0.231265	+	0.832940i
$94$	−777.176	+	467.611i	−0.852761	+	0.513089i
$95$	2.19110	−	40.4125i	0.00236634	−	0.0436445i
$96$	979.254	−	329.949i	1.04109	−	0.350784i
$97$	−82.2340	−	155.110i	−0.0860783	−	0.162361i	0.836735	−	0.547607i	$-0.184461\pi$
$97$	−82.2340	−	155.110i	−0.0860783	−	0.162361i	−0.922814	+	0.385246i	$0.874116\pi$
$98$	−258.225	−	304.006i	−0.266170	−	0.313360i
$99$	78.5962	+	115.921i	0.0797901	+	0.117682i
$100$	−108.180	−	1995.27i	−0.108180	−	1.99527i
$101$	85.0792	+	213.533i	0.0838188	+	0.210369i	0.964912	−	0.262573i	$-0.0845711\pi$
$101$	85.0792	+	213.533i	0.0838188	+	0.210369i	−0.881093	+	0.472943i	$0.843192\pi$
$102$	−1405.45	−	650.231i	−1.36432	−	0.631200i
$103$	−1575.18	+	346.723i	−1.50686	+	0.331686i	−0.890211	−	0.455549i	$-0.849443\pi$
$103$	−1575.18	+	346.723i	−1.50686	+	0.331686i	−0.616653	+	0.787235i	$0.711512\pi$
$104$	745.809	−	1406.74i	0.703198	−	1.32637i
$105$	−46.5731	+	284.084i	−0.0432864	+	0.264035i
$106$	−542.849	+	412.663i	−0.497416	+	0.378126i
$107$	1135.38	−	525.282i	1.02581	−	0.474588i	0.166495	−	0.986042i	$-0.446755\pi$
$107$	1135.38	−	525.282i	1.02581	−	0.474588i	0.859310	+	0.511454i	$0.170893\pi$
$108$	−380.149	−	360.096i	−0.338702	−	0.320836i
$109$	293.401	+	1789.67i	0.257823	+	1.57265i	0.725166	+	0.688574i	$0.241763\pi$
$109$	293.401	+	1789.67i	0.257823	+	1.57265i	−0.467343	+	0.884076i	$0.654789\pi$
$110$	−361.737	−	121.883i	−0.313548	−	0.105647i
$111$	208.372	−	522.975i	0.178179	−	0.447195i
$112$	−2333.12	+	2210.05i	−1.96838	+	1.86455i
$113$	−1325.90	−	1007.93i	−1.10381	−	0.839095i	−0.115768	−	0.993276i	$-0.536933\pi$
$113$	−1325.90	−	1007.93i	−1.10381	−	0.839095i	−0.988043	+	0.154181i	$0.950726\pi$
$114$	−132.420	−	29.1480i	−0.108792	−	0.0239470i
$115$	189.198	−	222.742i	0.153416	−	0.180615i
$116$	−264.612	−	28.7783i	−0.211799	−	0.0230345i
$117$	−240.306			−0.189883
$118$	−896.362	+	2196.04i	−0.699295	+	1.71323i
$119$	2019.31			1.55555
$120$	833.520	+	90.6508i	0.634080	+	0.0689604i
$121$	−704.900	+	829.872i	−0.529602	+	0.623495i
$122$	−4478.44	−	985.778i	−3.32343	−	0.731542i
$123$	405.864	+	308.529i	0.297524	+	0.226172i
$124$	−3638.58	+	3446.65i	−2.63511	+	2.49611i
$125$	395.579	−	992.828i	0.283053	−	0.710410i
$126$	913.969	+	307.952i	0.646213	+	0.217734i
$127$	228.863	+	1396.01i	0.159908	+	0.975397i	0.937845	+	0.347055i	$0.112818\pi$
$127$	228.863	+	1396.01i	0.159908	+	0.975397i	−0.777937	+	0.628343i	$0.783734\pi$
$128$	78.4191	+	74.2825i	0.0541510	+	0.0512946i
$129$	607.913	−	281.251i	0.414913	−	0.191959i
$130$	521.409	−	396.365i	0.351774	−	0.267411i
$131$	357.509	−	2180.71i	0.238440	−	1.45442i	−0.547856	−	0.836572i	$-0.684556\pi$
$131$	357.509	−	2180.71i	0.238440	−	1.45442i	0.786297	−	0.617849i	$-0.211996\pi$
$132$	−424.085	+	799.910i	−0.279635	+	0.527448i
$133$	172.674	−	38.0084i	0.112577	−	0.0247800i
$134$	5133.56	+	2375.04i	3.30949	+	1.53114i
$135$	−46.8377	−	117.554i	−0.0298604	−	0.0749439i
$136$	−318.403	−	5872.60i	−0.200756	−	3.70273i
$137$	1063.86	+	1569.08i	0.663443	+	0.978505i	0.999330	+	0.0366026i	$0.0116536\pi$
$137$	1063.86	+	1569.08i	0.663443	+	0.978505i	−0.335887	+	0.941902i	$0.609036\pi$
$138$	−633.861	−	746.239i	−0.390999	−	0.460320i
$139$	−211.876	−	399.641i	−0.129289	−	0.243864i	0.810413	−	0.585858i	$-0.199243\pi$
$139$	−211.876	−	399.641i	−0.129289	−	0.243864i	−0.939702	+	0.341994i	$0.888898\pi$
$140$	−1763.56	+	594.211i	−1.06463	+	0.358714i
$141$	−28.1461	+	519.124i	−0.0168108	+	0.310058i
$142$	−758.439	+	456.338i	−0.448217	+	0.269683i
$143$	111.159	+	400.358i	0.0650040	+	0.234123i
$144$	377.919	−	1361.14i	0.218703	−	0.787698i
$145$	−55.1169	−	33.1627i	−0.0315669	−	0.0189932i
$146$	281.024	−	414.480i	0.159300	−	0.234949i
$147$	−227.290	+	24.7192i	−0.127527	+	0.0138694i
$148$	3617.91	−	393.471i	2.00939	−	0.218535i
$149$	−516.124	+	761.226i	−0.283775	+	0.418537i	−0.942685	−	0.333685i	$-0.891708\pi$
$149$	−516.124	+	761.226i	−0.283775	+	0.418537i	0.658909	+	0.752222i	$0.271018\pi$
$150$	−1386.24	−	834.070i	−0.754571	−	0.454010i
$151$	523.962	−	1887.14i	0.282380	−	1.01704i	−0.677244	−	0.735758i	$-0.736826\pi$
$151$	523.962	−	1887.14i	0.282380	−	1.01704i	0.959625	−	0.281284i	$-0.0907602\pi$
$152$	−137.764	−	496.179i	−0.0735138	−	0.264773i
$153$	−760.570	+	457.620i	−0.401885	+	0.241806i
$154$	90.2818	−	1665.15i	0.0472410	−	0.871309i
$155$	−1147.78	+	386.733i	−0.594788	+	0.200408i
$156$	−727.653	−	1372.50i	−0.373454	−	0.704410i
$157$	−277.751	−	326.993i	−0.141191	−	0.166222i	0.687022	−	0.726637i	$-0.258918\pi$
$157$	−277.751	−	326.993i	−0.141191	−	0.166222i	−0.828212	+	0.560414i	$0.810642\pi$
$158$	−2062.50	−	3041.96i	−1.03851	−	1.53168i
$159$	21.1603	+	390.279i	0.0105542	+	0.194661i
$160$	597.526	+	1499.68i	0.295241	+	0.740999i
$161$	1158.74	+	536.088i	0.567212	+	0.262420i
$162$	−414.033	+	91.1355i	−0.200799	+	0.0441992i
$163$	−895.225	+	1688.57i	−0.430181	+	0.811407i	−0.999946	−	0.0104008i	$-0.996689\pi$
$163$	−895.225	+	1688.57i	−0.430181	+	0.811407i	0.569765	+	0.821807i	$0.307034\pi$
$164$	−533.189	+	3252.31i	−0.253872	+	1.54855i
$165$	−174.183	+	132.410i	−0.0821824	+	0.0624735i
$166$	5795.43	−	2681.25i	2.70972	−	1.25365i
$167$	1966.28	+	1862.56i	0.911112	+	0.863051i	0.991015	−	0.133752i	$-0.0427025\pi$
$167$	1966.28	+	1862.56i	0.911112	+	0.863051i	−0.0799031	+	0.996803i	$0.525461\pi$
$168$	592.580	+	3614.58i	0.272134	+	1.65995i
$169$	1406.39	+	473.867i	0.640139	+	0.215688i
$170$	895.455	−	2247.42i	0.403990	−	1.01394i
$171$	−56.4236	+	53.4473i	−0.0252329	+	0.0239019i
$172$	3447.13	+	2620.44i	1.52814	+	1.16167i
$173$	3602.58	+	792.988i	1.58323	+	0.348496i	0.917513	−	0.397706i	$-0.130194\pi$
$173$	3602.58	+	792.988i	1.58323	+	0.348496i	0.665720	+	0.746202i	$0.268125\pi$
$174$	−139.513	+	164.248i	−0.0607844	+	0.0715609i
$175$	2097.23	+	228.088i	0.905918	+	0.0985245i
$176$	−2442.52			−1.04609
$177$	753.519	+	1131.64i	0.319989	+	0.480563i
$178$	6867.10			2.89163
$179$	3199.80	+	347.999i	1.33611	+	0.145311i	0.748124	−	0.663559i	$-0.230955\pi$
$179$	3199.80	+	347.999i	1.33611	+	0.145311i	0.587988	+	0.808870i	$0.299920\pi$
$180$	529.578	−	623.468i	0.219291	−	0.258170i
$181$	−3705.78	−	815.704i	−1.52182	−	0.334977i	−0.626149	−	0.779703i	$-0.715370\pi$
$181$	−3705.78	−	815.704i	−1.52182	−	0.334977i	−0.895667	+	0.444726i	$0.853301\pi$
$182$	2277.85	+	1731.58i	0.927724	+	0.705238i
$183$	−1908.24	+	1807.58i	−0.770824	+	0.730164i
$184$	1376.35	−	3454.38i	0.551446	−	1.38402i
$185$	833.437	+	280.818i	0.331219	+	0.111601i
$186$	656.474	+	4004.31i	0.258790	+	1.57855i
$187$	1114.23	+	1055.45i	0.435724	+	0.412739i
$188$	−3050.18	+	1411.16i	−1.18328	+	0.547445i
$189$	440.092	−	334.549i	0.169376	−	0.128756i
$190$	34.2694	−	209.034i	0.0130851	−	0.0798154i
$191$	1067.22	−	2012.99i	0.404301	−	0.762592i	−0.594848	−	0.803838i	$-0.702788\pi$
$191$	1067.22	−	2012.99i	0.404301	−	0.762592i	0.999149	+	0.0412460i	$0.0131327\pi$
$192$	1603.01	−	352.850i	0.602539	−	0.132629i
$193$	−211.477	−	97.8397i	−0.0788728	−	0.0364905i	0.380056	−	0.924963i	$-0.375905\pi$
$193$	−211.477	−	97.8397i	−0.0788728	−	0.0364905i	−0.458929	+	0.888473i	$0.651767\pi$
$194$	−340.106	−	853.601i	−0.125867	−	0.315902i
$195$	−20.3246	−	374.865i	−0.00746397	−	0.137665i
$196$	−829.421	−	1223.30i	−0.302267	−	0.445811i
$197$	186.486	+	219.548i	0.0674446	+	0.0794019i	0.794850	−	0.606806i	$-0.207550\pi$
$197$	186.486	+	219.548i	0.0674446	+	0.0794019i	−0.727405	+	0.686208i	$0.759274\pi$
$198$	343.354	+	647.635i	0.123238	+	0.232451i
$199$	−1099.03	+	370.306i	−0.391498	+	0.131911i	−0.508164	−	0.861260i	$-0.669676\pi$
$199$	−1099.03	+	370.306i	−0.391498	+	0.131911i	0.116667	+	0.993171i	$0.462779\pi$
$200$	332.639	−	6135.16i	0.117606	−	2.16911i
$201$	2778.06	−	1671.51i	0.974873	−	0.586562i
$202$	321.850	+	1159.20i	0.112105	+	0.403767i
$203$	75.1784	−	270.768i	0.0259926	−	0.0936168i
$204$	−4916.70	−	2958.28i	−1.68744	−	1.01530i
$205$	−446.962	+	659.220i	−0.152279	+	0.224595i
$206$	−8392.17	+	912.703i	−2.83840	+	0.308694i
$207$	−557.924	+	60.6779i	−0.187335	+	0.0203739i
$208$	2351.89	−	3468.78i	0.784011	−	1.15633i
$209$	115.145	+	69.2803i	0.0381088	+	0.0229293i
$210$	−403.087	+	1451.79i	−0.132455	+	0.477061i
$211$	1144.42	+	4121.84i	0.373390	+	1.34483i	0.876830	+	0.480800i	$0.159654\pi$
$211$	1144.42	+	4121.84i	0.373390	+	1.34483i	−0.503440	+	0.864030i	$0.667932\pi$
$212$	−2164.99	+	1302.63i	−0.701378	+	0.422005i
$213$	−27.4675	+	506.609i	−0.00883589	+	0.162968i
$214$	6204.84	−	2090.66i	1.98203	−	0.667824i
$215$	490.152	+	924.524i	0.155479	+	0.293265i
$216$	−1042.33	−	1227.13i	−0.328342	−	0.386554i
$217$	−2969.38	−	4379.51i	−0.928916	−	1.37005i
$218$	513.883	+	9478.01i	0.159654	+	2.94464i
$219$	−106.242	−	266.648i	−0.0327817	−	0.0822759i
$220$	−1283.68	−	593.896i	−0.393391	−	0.182002i
$221$	−2571.80	+	566.095i	−0.782795	+	0.172306i
$222$	1380.14	−	2603.23i	0.417249	−	0.787015i
$223$	215.800	−	1316.32i	0.0648029	−	0.395280i	−0.934431	−	0.356144i	$-0.884091\pi$
$223$	215.800	−	1316.32i	0.0648029	−	0.395280i	0.999234	−	0.0391358i	$-0.0124605\pi$
$224$	−5614.41	+	4267.96i	−1.67468	+	1.27306i
$225$	−841.606	+	389.368i	−0.249365	+	0.115368i
$226$	−6328.57	−	5994.74i	−1.86270	−	1.76444i
$227$	−896.023	−	5465.50i	−0.261987	−	1.59805i	−0.710117	−	0.704084i	$-0.751358\pi$
$227$	−896.023	−	5465.50i	−0.261987	−	1.59805i	0.448129	−	0.893969i	$-0.352090\pi$
$228$	−476.114	−	160.421i	−0.138296	−	0.0465972i
$229$	−718.385	+	1803.01i	−0.207302	+	0.520290i	−0.995460	−	0.0951841i	$-0.969656\pi$
$229$	−718.385	+	1803.01i	−0.207302	+	0.520290i	0.788157	+	0.615474i	$0.211035\pi$
$230$	1110.48	−	1051.90i	0.318361	−	0.301568i
$231$	−760.943	−	578.454i	−0.216738	−	0.164760i
$232$	−799.307	−	175.941i	−0.226194	−	0.0497891i
$233$	−757.034	+	891.249i	−0.212854	+	0.250591i	−0.858219	−	0.513283i	$-0.828429\pi$
$233$	−757.034	+	891.249i	−0.212854	+	0.250591i	0.645366	+	0.763874i	$0.276705\pi$
$234$	−1250.36	−	135.985i	−0.349311	−	0.0379898i
$235$	−812.186			−0.225452
$236$	−4181.67	+	7730.34i	−1.15340	+	2.13221i
$237$	−2106.61			−0.577380
$238$	10506.9	+	1142.69i	2.86160	+	0.311218i
$239$	2433.90	−	2865.40i	0.658727	−	0.775513i	−0.326789	−	0.945097i	$-0.605967\pi$
$239$	2433.90	−	2865.40i	0.658727	−	0.775513i	0.985516	+	0.169584i	$0.0542425\pi$
$240$	2155.27	+	474.411i	0.579676	+	0.127596i
$241$	−3601.57	−	2737.85i	−0.962646	−	0.731785i	0.000712629	−	1.00000i	$-0.499773\pi$
$241$	−3601.57	−	2737.85i	−0.962646	−	0.731785i	−0.963359	+	0.268215i	$0.913566\pi$
$242$	−4137.34	+	3919.10i	−1.09900	+	1.04103i
$243$	−89.9436	+	225.741i	−0.0237444	+	0.0595939i
$244$	−16102.1	−	5425.42i	−4.22471	−	1.42347i
$245$	−57.7843	−	352.469i	−0.0150682	−	0.0919119i
$246$	1937.20	+	1835.01i	0.502078	+	0.475593i
$247$	−209.262	+	96.8148i	−0.0539069	+	0.0249400i
$248$	−12268.4	+	9326.16i	−3.14129	+	2.38795i
$249$	592.149	−	3611.95i	0.150706	−	0.919269i
$250$	2620.10	−	4942.03i	0.662838	−	1.25025i
$251$	−2479.47	+	545.773i	−0.623518	+	0.137247i	−0.515482	−	0.856900i	$-0.672387\pi$
$251$	−2479.47	+	545.773i	−0.623518	+	0.137247i	−0.108036	+	0.994147i	$0.534456\pi$
$252$	3243.37	+	1500.54i	0.810767	+	0.375101i
$253$	359.171	+	901.451i	0.0892525	+	0.224007i
$254$	400.848	+	7393.20i	0.0990214	+	1.82634i
$255$	−778.189	−	1147.74i	−0.191106	−	0.281861i
$256$	−2467.63	−	2905.12i	−0.602450	−	0.709259i
$257$	−869.231	−	1639.54i	−0.210977	−	0.397945i	0.755327	−	0.655348i	$-0.227478\pi$
$257$	−869.231	−	1639.54i	−0.210977	−	0.397945i	−0.966304	+	0.257403i	$0.917133\pi$
$258$	3322.25	−	1119.40i	0.801682	−	0.270118i
$259$	−208.008	+	3836.48i	−0.0499035	+	0.920415i
$260$	2079.48	−	1251.18i	0.496015	−	0.298443i
$261$	33.0461	+	119.021i	0.00783717	+	0.0282269i
$262$	3094.21	−	11144.3i	0.729622	−	2.62786i
$263$	−843.827	−	507.714i	−0.197842	−	0.119038i	0.413185	−	0.910647i	$-0.364416\pi$
$263$	−843.827	−	507.714i	−0.197842	−	0.119038i	−0.611028	+	0.791609i	$0.709244\pi$
$264$	−1562.29	+	2304.20i	−0.364212	+	0.537173i
$265$	−607.025	+	66.0179i	−0.140714	+	0.0153036i
$266$	919.963	−	100.052i	0.212055	−	0.0230623i
$267$	2208.91	−	3257.90i	0.506304	−	0.746743i
$268$	17958.8	+	10805.4i	4.09331	+	2.46286i
$269$	101.744	−	366.447i	0.0230610	−	0.0830583i	−0.951124	−	0.308809i	$-0.900070\pi$
$269$	101.744	−	366.447i	0.0230610	−	0.0830583i	0.974185	+	0.225751i	$0.0724834\pi$
$270$	−177.184	−	638.160i	−0.0399374	−	0.143842i
$271$	1749.58	−	1052.69i	0.392175	−	0.235964i	−0.305785	−	0.952100i	$-0.598919\pi$
$271$	1749.58	−	1052.69i	0.392175	−	0.235964i	0.697960	+	0.716137i	$0.254091\pi$
$272$	838.078	−	15457.4i	0.186823	−	3.44575i
$273$	1554.21	−	523.674i	0.344560	−	0.116096i
$274$	4647.56	+	8766.23i	1.02471	+	1.93280i
$275$	1038.00	+	1222.03i	0.227614	+	0.267968i
$276$	−2035.97	−	3002.82i	−0.444024	−	0.654887i
$277$	1.53859	+	28.3777i	0.000333737	+	0.00615541i	0.998696	−	0.0510609i	$-0.0162603\pi$
$277$	1.53859	+	28.3777i	0.000333737	+	0.00615541i	−0.998362	+	0.0572164i	$0.981778\pi$
$278$	−876.285	−	2199.31i	−0.189051	−	0.474481i
$279$	2110.90	+	976.606i	0.452962	+	0.209562i
$280$	−5588.43	+	1230.11i	−1.19276	+	0.262546i
$281$	1342.48	−	2532.18i	0.285002	−	0.537570i	−0.699133	−	0.714991i	$-0.746431\pi$
$281$	1342.48	−	2532.18i	0.285002	−	0.537570i	0.984135	+	0.177421i	$0.0567754\pi$
$282$	−440.212	+	2685.18i	−0.0929584	+	0.567021i
$283$	−7432.87	+	5650.32i	−1.56127	+	1.18684i	−0.661947	+	0.749551i	$0.730270\pi$
$283$	−7432.87	+	5650.32i	−1.56127	+	1.18684i	−0.899319	+	0.437293i	$0.855937\pi$
$284$	−2976.65	+	1377.14i	−0.621942	+	0.287741i
$285$	−88.1471	−	83.4973i	−0.0183206	−	0.0173542i
$286$	351.826	+	2146.04i	0.0727409	+	0.443700i
$287$	−3297.31	−	1110.99i	−0.678168	−	0.228501i
$288$	1147.44	−	2879.86i	0.234770	−	0.589228i
$289$	−3494.90	+	3310.54i	−0.711357	+	0.673833i
$290$	−268.018	−	203.742i	−0.0542708	−	0.0412556i
$291$	−514.368	−	113.221i	−0.103618	−	0.0228080i
$292$	1201.25	−	1414.22i	0.240745	−	0.283427i
$293$	−5688.23	−	618.632i	−1.13416	−	0.123348i	−0.478279	−	0.878208i	$-0.658739\pi$
$293$	−5688.23	−	618.632i	−1.13416	−	0.123348i	−0.655885	+	0.754860i	$0.727705\pi$
$294$	−1196.62			−0.237375
$295$	−1701.57	+	1271.16i	−0.335829	+	0.250881i
$296$	11190.1			2.19734
$297$	417.698	+	45.4273i	0.0816070	+	0.00887529i
$298$	−3116.26	+	3668.74i	−0.605772	+	0.713170i
$299$	−1626.05	−	357.921i	−0.314505	−	0.0692278i
$300$	−4772.26	−	3627.78i	−0.918423	−	0.698167i
$301$	−3318.85	+	3143.78i	−0.635532	+	0.602008i
$302$	3794.17	−	9522.66i	0.722948	−	1.81446i
$303$	653.477	+	220.182i	0.123899	+	0.0417463i
$304$	−219.281	−	1337.56i	−0.0413705	−	0.252349i
$305$	−2981.12	−	2823.86i	−0.559666	−	0.530144i
$306$	−4216.35	+	1950.69i	−0.787689	+	0.364424i
$307$	3996.11	−	3037.76i	0.742899	−	0.564737i	−0.163811	−	0.986492i	$-0.552379\pi$
$307$	3996.11	−	3037.76i	0.742899	−	0.564737i	0.906710	+	0.421755i	$0.138586\pi$
$308$	999.662	−	6097.67i	0.184938	−	1.12807i
$309$	−2266.47	+	4275.02i	−0.417265	+	0.787046i
$310$	−6190.99	+	1362.74i	−1.13427	+	0.249672i
$311$	1834.15	+	848.568i	0.334422	+	0.154720i	0.579912	−	0.814679i	$-0.303087\pi$
$311$	1834.15	+	848.568i	0.334422	+	0.154720i	−0.245490	+	0.969399i	$0.578949\pi$
$312$	−1768.02	−	4437.40i	−0.320816	−	0.805187i
$313$	−268.963	−	4960.73i	−0.0485708	−	0.895836i	−0.916719	−	0.399532i	$-0.869173\pi$
$313$	−268.963	−	4960.73i	−0.0485708	−	0.895836i	0.868148	−	0.496305i	$-0.165310\pi$
$314$	−1260.15	−	1858.59i	−0.226479	−	0.334032i
$315$	559.101	+	658.224i	0.100006	+	0.117736i
$316$	−6378.87	−	12031.8i	−1.13557	−	2.14191i
$317$	−766.157	+	258.148i	−0.135747	+	0.0457383i	−0.386355	−	0.922350i	$-0.626266\pi$
$317$	−766.157	+	258.148i	−0.135747	+	0.0457383i	0.250608	+	0.968089i	$0.419369\pi$
$318$	−110.751	+	2042.67i	−0.0195301	+	0.360212i
$319$	183.007	−	110.112i	0.0321205	−	0.0193262i
$320$	686.006	+	2470.77i	0.119840	+	0.431626i
$321$	1004.04	−	3616.21i	0.174579	−	0.628776i
$322$	5725.77	+	3445.08i	0.990946	+	0.596232i
$323$	−477.948	+	704.920i	−0.0823335	+	0.121433i
$324$	−1561.66	+	169.841i	−0.267775	+	0.0291223i
$325$	−2734.97	+	297.446i	−0.466797	+	0.0507672i
$326$	−5613.56	+	8279.39i	−0.953701	+	1.40660i
$327$	4661.88	+	2804.96i	0.788386	+	0.474356i
$328$	−2711.10	+	9764.48i	−0.456388	+	1.64376i
$329$	−949.233	−	3418.83i	−0.159067	−	0.572906i
$330$	−981.235	+	590.390i	−0.163682	+	0.0984845i
$331$	−104.442	+	1926.31i	−0.0173433	+	0.319878i	0.976969	+	0.213379i	$0.0684469\pi$
$331$	−104.442	+	1926.31i	−0.0173433	+	0.319878i	−0.994313	+	0.106499i	$0.966036\pi$
$332$	22422.5	−	7555.03i	3.70661	−	1.24890i
$333$	−791.083	−	1492.14i	−0.130183	−	0.245552i
$334$	9176.97	+	10804.0i	1.50342	+	1.76996i
$335$	2842.42	+	4192.26i	0.463576	+	0.683724i
$336$	521.955	+	9626.90i	0.0847470	+	1.56307i
$337$	−3217.55	−	8075.45i	−0.520093	−	1.30534i	−0.921123	−	0.389270i	$-0.872727\pi$
$337$	−3217.55	−	8075.45i	−0.520093	−	1.30534i	0.401030	−	0.916065i	$-0.368652\pi$
$338$	7049.55	+	3261.47i	1.13445	+	0.524854i
$339$	−4879.73	+	1074.11i	−0.781800	+	0.172087i
$340$	4198.91	−	7919.99i	0.669759	−	1.26330i
$341$	650.615	−	3968.58i	0.103322	−	0.630236i
$342$	−323.828	+	246.168i	−0.0512006	+	0.0389217i
$343$	−4957.56	+	2293.61i	−0.780417	+	0.361060i
$344$	9666.11	+	9156.22i	1.51500	+	1.43509i
$345$	−141.842	−	865.199i	−0.0221349	−	0.135017i
$346$	18296.2	+	6164.71i	2.84280	+	0.957852i
$347$	−1527.72	+	3834.29i	−0.236347	+	0.593186i	−0.998532	−	0.0541736i	$-0.982748\pi$
$347$	−1527.72	+	3834.29i	−0.236347	+	0.593186i	0.762185	+	0.647360i	$0.224127\pi$
$348$	−579.721	+	549.140i	−0.0892997	+	0.0845891i
$349$	−7485.25	−	5690.14i	−1.14807	−	0.872740i	−0.154729	−	0.987957i	$-0.549451\pi$
$349$	−7485.25	−	5690.14i	−1.14807	−	0.872740i	−0.993340	+	0.115217i	$0.963244\pi$
$350$	10783.2	+	2373.57i	1.64682	+	0.362493i
$351$	−466.713	+	549.457i	−0.0709724	+	0.0835551i
$352$	−5328.72	−	579.533i	−0.806880	−	0.0877534i
$353$	−1744.18			−0.262985			−0.131492	−	0.991317i	$-0.541977\pi$
$353$	−1744.18			−0.262985			−0.131492	+	0.991317i	$0.541977\pi$
$354$	3280.33	+	6314.57i	0.492508	+	0.948067i
$355$	−792.605			−0.118499
$356$	25296.0	+	2751.11i	3.76597	+	0.409574i
$357$	3921.83	−	4617.13i	0.581415	−	0.684495i
$358$	16452.2	+	3621.41i	2.42885	+	0.534630i
$359$	2056.79	+	1563.53i	0.302377	+	0.229861i	0.745349	−	0.666674i	$-0.232283\pi$
$359$	2056.79	+	1563.53i	0.302377	+	0.229861i	−0.442972	+	0.896535i	$0.646076\pi$
$360$	1826.10	−	1729.77i	0.267344	−	0.253242i
$361$	2511.18	−	6302.58i	0.366114	−	0.918877i
$362$	−18820.3	−	6341.31i	−2.73253	−	0.920695i
$363$	528.464	+	3223.49i	0.0764109	+	0.466086i
$364$	7697.12	+	7291.10i	1.10835	+	1.04988i
$365$	406.971	−	188.285i	0.0583612	−	0.0270008i
$366$	−10951.8	+	8325.34i	−1.56410	+	1.18900i
$367$	−143.570	+	875.736i	−0.0204204	+	0.124559i	−0.995069	−	0.0991802i	$-0.968378\pi$
$367$	−143.570	+	875.736i	−0.0204204	+	0.124559i	0.974649	+	0.223739i	$0.0718263\pi$
$368$	4584.56	−	8647.39i	0.649420	−	1.22494i
$369$	1493.70	−	328.788i	0.210729	−	0.0463849i
$370$	4177.63	+	1932.78i	0.586985	+	0.271568i
$371$	−987.350	−	2478.06i	−0.138169	−	0.346778i
$372$	814.008	+	15013.5i	0.113453	+	2.09251i
$373$	5405.63	+	7972.71i	0.750383	+	1.10673i	0.990703	+	0.136039i	$0.0434372\pi$
$373$	5405.63	+	7972.71i	0.750383	+	1.10673i	−0.240320	+	0.970694i	$0.577252\pi$
$374$	5200.28	+	6122.24i	0.718984	+	0.846453i
$375$	−1501.81	−	2832.72i	−0.206808	−	0.390082i
$376$	−9793.02	+	3299.65i	−1.34318	+	0.452571i
$377$	−19.8399	+	365.926i	−0.00271037	+	0.0499898i
$378$	2479.20	−	1491.69i	0.337345	−	0.202974i
$379$	−1753.70	−	6316.25i	−0.237682	−	0.856053i	−0.982103	−	0.188343i	$-0.939688\pi$
$379$	−1753.70	−	6316.25i	−0.237682	−	0.856053i	0.744421	−	0.667710i	$-0.232725\pi$
$380$	209.980	−	756.280i	0.0283467	−	0.102096i
$381$	3636.44	+	2187.97i	0.488977	+	0.294208i
$382$	6692.08	−	9870.08i	0.896326	−	1.32198i
$383$	−11749.1	+	1277.79i	−1.56750	+	0.170476i	−0.850264	−	0.526357i	$-0.823558\pi$
$383$	−11749.1	+	1277.79i	−1.56750	+	0.170476i	−0.717234	+	0.696833i	$0.754592\pi$
$384$	322.148	−	35.0357i	0.0428113	−	0.00465601i
$385$	837.998	−	1235.96i	0.110931	−	0.163611i
$386$	−1044.99	−	628.751i	−0.137794	−	0.0829082i
$387$	537.588	−	1936.22i	0.0706128	−	0.254324i
$388$	−910.861	−	3280.63i	−0.119180	−	0.429249i
$389$	5703.90	−	3431.92i	0.743442	−	0.447314i	−0.0927930	−	0.995685i	$-0.529579\pi$
$389$	5703.90	−	3431.92i	0.743442	−	0.447314i	0.836235	+	0.548371i	$0.184752\pi$
$390$	106.376	−	1962.00i	0.0138117	−	0.254743i
$391$	−5828.05	+	1963.70i	−0.753804	+	0.253986i
$392$	−2128.71	−	4015.17i	−0.274276	−	0.517339i
$393$	−4291.82	−	5052.72i	−0.550874	−	0.648539i
$394$	846.085	+	1247.88i	0.108186	+	0.159562i
$395$	−178.173	−	3286.20i	−0.0226958	−	0.418599i
$396$	1005.34	+	2523.22i	0.127577	+	0.320193i
$397$	−5520.95	−	2554.26i	−0.697955	−	0.322909i	0.0386295	−	0.999254i	$-0.487701\pi$
$397$	−5520.95	−	2554.26i	−0.697955	−	0.322909i	−0.736585	+	0.676345i	$0.763563\pi$
$398$	−5928.01	+	1304.85i	−0.746593	+	0.164338i
$399$	248.454	−	468.634i	0.0311736	−	0.0587996i
$400$	2616.38	−	15959.2i	0.327047	−	1.99490i
$401$	175.771	−	133.618i	0.0218892	−	0.0166398i	−0.594172	−	0.804338i	$-0.702520\pi$
$401$	175.771	−	133.618i	0.0218892	−	0.0166398i	0.616062	+	0.787698i	$0.288727\pi$
$402$	15400.7	−	7125.12i	1.91074	−	0.884001i
$403$	5009.55	+	4745.30i	0.619215	+	0.586552i
$404$	721.183	+	4399.02i	0.0888124	+	0.541732i
$405$	−359.752	−	121.214i	−0.0441388	−	0.0148721i
$406$	544.391	−	1366.32i	0.0665460	−	0.167018i
$407$	−2120.02	+	2008.19i	−0.258196	+	0.244576i
$408$	−14046.0	−	10677.5i	−1.70437	−	1.29563i
$409$	13861.9	+	3051.23i	1.67586	+	0.368884i	0.948353	−	0.317217i	$-0.102748\pi$
$409$	13861.9	+	3051.23i	1.67586	+	0.368884i	0.727506	+	0.686102i	$0.240679\pi$
$410$	−2698.67	+	3177.12i	−0.325068	+	0.382700i
$411$	5653.85	+	614.894i	0.678550	+	0.0737967i
$412$	−31279.5			−3.74036
$413$	−7339.54	−	5676.98i	−0.874468	−	0.676382i
$414$	−2937.32			−0.348700
$415$	5684.53	+	618.230i	0.672391	+	0.0731270i
$416$	5954.03	−	7009.62i	0.701731	−	0.826142i
$417$	−1325.27	−	291.714i	−0.155633	−	0.0342574i
$418$	559.917	+	425.638i	0.0655178	+	0.0498053i
$419$	−4905.22	+	4646.47i	−0.571923	+	0.541754i	−0.918066	−	0.396427i	$-0.870250\pi$
$419$	−4905.22	+	4646.47i	−0.571923	+	0.541754i	0.346143	+	0.938182i	$0.387491\pi$
$420$	−2066.45	+	5186.40i	−0.240077	+	0.602548i
$421$	−10596.6	−	3570.40i	−1.22671	−	0.413327i	−0.369956	−	0.929049i	$-0.620627\pi$
$421$	−10596.6	−	3570.40i	−1.22671	−	0.413327i	−0.856756	+	0.515722i	$0.827524\pi$
$422$	3622.19	+	22094.4i	0.417832	+	2.54866i
$423$	1132.31	+	1072.58i	0.130153	+	0.123287i
$424$	−7051.06	+	3262.17i	−0.807617	+	0.373643i
$425$	−8089.76	+	6149.67i	−0.923320	+	0.701890i
$426$	−429.600	+	2620.44i	−0.0488595	+	0.298030i
$427$	8402.67	−	15849.1i	0.952304	−	1.79624i
$428$	23694.1	−	5215.46i	2.67592	−	0.589015i
$429$	1131.30	+	523.396i	0.127319	+	0.0589039i
$430$	2027.18	+	5087.85i	0.227348	+	0.570600i
$431$	876.227	+	16161.0i	0.0979266	+	1.80615i	0.475021	+	0.879974i	$0.342440\pi$
$431$	876.227	+	16161.0i	0.0979266	+	1.80615i	−0.377095	+	0.926175i	$0.623077\pi$
$432$	−2378.25	−	3507.66i	−0.264870	−	0.390654i
$433$	−5776.56	−	6800.69i	−0.641117	−	0.754782i	0.341610	−	0.939842i	$-0.389028\pi$
$433$	−5776.56	−	6800.69i	−0.641117	−	0.754782i	−0.982727	+	0.185060i	$0.940752\pi$
$434$	−12972.0	−	24467.8i	−1.43474	−	2.70620i
$435$	−182.872	+	61.6167i	−0.0201564	+	0.00679148i
$436$	−1904.13	+	35119.6i	−0.209154	+	3.85762i
$437$	−461.401	+	277.616i	−0.0505076	+	0.0303894i
$438$	−401.909	−	1447.54i	−0.0438446	−	0.157914i
$439$	1400.73	−	5044.97i	0.152285	−	0.548481i	−0.847557	−	0.530705i	$-0.821927\pi$
$439$	1400.73	−	5044.97i	0.152285	−	0.548481i	0.999842	−	0.0177768i	$-0.00565881\pi$
$440$	−3726.56	−	2242.20i	−0.403765	−	0.242938i
$441$	−384.912	+	567.703i	−0.0415627	+	0.0613004i
$442$	−13701.9	+	1490.17i	−1.47451	+	0.160363i
$443$	13755.9	−	1496.04i	1.47531	−	0.160449i	0.665172	−	0.746690i	$-0.268358\pi$
$443$	13755.9	−	1496.04i	1.47531	−	0.160449i	0.810137	+	0.586241i	$0.199393\pi$
$444$	6126.88	−	9036.48i	0.654885	−	0.965884i
$445$	5268.98	+	3170.24i	0.561289	+	0.337716i
$446$	1867.73	−	6726.96i	0.198295	−	0.714195i
$447$	738.138	+	2658.53i	0.0781045	+	0.281307i
$448$	−9598.73	+	5775.36i	−1.01227	+	0.609063i
$449$	140.867	−	2598.14i	0.0148061	−	0.273082i	−0.981751	−	0.190171i	$-0.939096\pi$
$449$	140.867	−	2598.14i	0.0148061	−	0.273082i	0.996557	−	0.0829104i	$-0.0264215\pi$
$450$	−4599.38	+	1549.71i	−0.481815	+	0.162342i
$451$	−1238.71	−	2336.46i	−0.129332	−	0.243946i
$452$	−20910.7	−	24617.9i	−2.17601	−	2.56179i
$453$	−3297.30	−	4863.16i	−0.341989	−	0.504395i
$454$	−1569.36	−	28945.1i	−0.162233	−	2.99221i
$455$	948.354	+	2380.19i	0.0977133	+	0.245242i
$456$	−1402.07	−	648.665i	−0.143986	−	0.0666152i
$457$	−8890.41	+	1956.93i	−0.910013	+	0.200309i	−0.645221	−	0.763996i	$-0.723235\pi$
$457$	−8890.41	+	1956.93i	−0.910013	+	0.200309i	−0.264793	+	0.964305i	$0.585304\pi$
$458$	−4758.19	+	8974.90i	−0.485449	+	0.915654i
$459$	−430.806	+	2627.80i	−0.0438090	+	0.267223i
$460$	4512.05	−	3429.97i	0.457338	−	0.347659i
$461$	10065.9	−	4656.97i	1.01695	−	0.470491i	0.160673	−	0.987008i	$-0.448633\pi$
$461$	10065.9	−	4656.97i	1.01695	−	0.470491i	0.856277	+	0.516516i	$0.172771\pi$
$462$	−3632.00	−	3440.41i	−0.365749	−	0.346456i
$463$	1800.73	+	10984.0i	0.180749	+	1.10252i	0.908872	+	0.417076i	$0.136945\pi$
$463$	1800.73	+	10984.0i	0.180749	+	1.10252i	−0.728122	+	0.685447i	$0.759607\pi$
$464$	−2041.47	−	687.853i	−0.204252	−	0.0688206i
$465$	−1344.92	+	3375.49i	−0.134127	+	0.336634i
$466$	−4443.34	+	4208.95i	−0.441703	+	0.418403i
$467$	5355.17	+	4070.89i	0.530637	+	0.403380i	0.835895	−	0.548890i	$-0.184949\pi$
$467$	5355.17	+	4070.89i	0.530637	+	0.403380i	−0.305257	+	0.952270i	$0.598742\pi$
$468$	−4551.42	−	1001.84i	−0.449550	−	0.0989534i
$469$	−14324.9	+	16864.6i	−1.41037	+	1.66041i
$470$	−4225.96	−	459.601i	−0.414743	−	0.0451060i
$471$	−1287.10			−0.125916
$472$	−15352.6	+	22240.1i	−1.49716	+	2.16882i
$473$	−3474.47			−0.337752
$474$	−10961.1	−	1192.09i	−1.06215	−	0.115516i
$475$	−576.012	+	678.134i	−0.0556405	+	0.0655051i
$476$	38246.0	+	8418.57i	3.68277	+	0.810640i
$477$	933.465	+	709.601i	0.0896025	+	0.0681141i
$478$	14285.5	−	13532.0i	1.36696	−	1.29485i
$479$	−6482.31	+	16269.4i	−0.618339	+	1.55191i	0.201602	+	0.979467i	$0.435385\pi$
$479$	−6482.31	+	16269.4i	−0.618339	+	1.55191i	−0.819942	+	0.572447i	$0.805994\pi$
$480$	4589.48	+	1546.38i	0.436417	+	0.147046i
$481$	−810.603	−	4944.46i	−0.0768405	−	0.468707i
$482$	−17190.4	−	16283.6i	−1.62448	−	1.53879i
$483$	3476.21	−	1608.26i	0.327480	−	0.151508i
$484$	−16810.6	+	12779.1i	−1.57876	+	1.20014i
$485$	133.114	−	811.962i	0.0124627	−	0.0760192i
$486$	−595.737	+	1123.68i	−0.0556033	+	0.104879i
$487$	11881.2	−	2615.26i	1.10552	−	0.243344i	0.375538	−	0.926807i	$-0.377458\pi$
$487$	11881.2	−	2615.26i	1.10552	−	0.243344i	0.729985	+	0.683463i	$0.239527\pi$
$488$	−47417.6	−	21937.7i	−4.39855	−	2.03499i
$489$	2122.23	+	5326.40i	0.196259	+	0.492573i
$490$	−101.208	−	1866.66i	−0.00933080	−	0.172096i
$491$	8401.41	+	12391.2i	0.772200	+	1.13891i	0.986758	+	0.162199i	$0.0518586\pi$
$491$	8401.41	+	12391.2i	0.772200	+	1.13891i	−0.214558	+	0.976711i	$0.568831\pi$
$492$	6400.82	+	7535.63i	0.586527	+	0.690513i
$493$	634.046	+	1195.94i	0.0579229	+	0.109254i
$494$	−1143.62	+	385.329i	−0.104157	+	0.0350947i
$495$	−35.5363	+	655.428i	−0.00322674	+	0.0595137i
$496$	−34756.6	+	20912.4i	−3.14641	+	1.89313i
$497$	−926.348	−	3336.41i	−0.0836064	−	0.301123i
$498$	5125.00	−	18458.6i	0.461158	−	1.66094i
$499$	2759.49	+	1660.33i	0.247559	+	0.148951i	0.633926	−	0.773394i	$-0.281443\pi$
$499$	2759.49	+	1660.33i	0.247559	+	0.148951i	−0.386367	+	0.922345i	$0.626270\pi$
$500$	11631.4	−	17155.1i	1.04035	−	1.53439i
$501$	8077.56	−	878.488i	0.720317	−	0.0783392i
$502$	−13210.0	+	1436.68i	−1.17449	+	0.127733i
$503$	9370.44	−	13820.4i	0.830631	−	1.22509i	−0.141334	−	0.989962i	$-0.545139\pi$
$503$	9370.44	−	13820.4i	0.830631	−	1.22509i	0.971965	−	0.235127i	$-0.0755504\pi$
$504$	9415.57	+	5665.16i	0.832149	+	0.500687i
$505$	−288.203	+	1038.01i	−0.0253957	+	0.0914672i
$506$	1358.72	+	4893.68i	0.119373	+	0.429942i
$507$	3814.91	−	2295.36i	0.334174	−	0.201066i
$508$	−1485.29	+	27394.6i	−0.129723	+	2.39259i
$509$	−12608.1	+	4248.17i	−1.09793	+	0.369935i	−0.809234	−	0.587487i	$-0.800117\pi$
$509$	−12608.1	+	4248.17i	−1.09793	+	0.369935i	−0.288694	+	0.957422i	$0.593221\pi$
$510$	−3399.59	−	6412.30i	−0.295169	−	0.556748i
$511$	1268.21	+	1493.06i	0.109789	+	0.129254i
$512$	−11680.6	−	17227.6i	−1.00823	−	1.48703i
$513$	12.6229	+	232.815i	0.00108638	+	0.0200371i
$514$	−3594.99	−	9022.75i	−0.308499	−	0.774274i
$515$	−6860.49	−	3174.00i	−0.587008	−	0.271579i
$516$	12686.5	−	2792.50i	1.08235	−	0.238242i
$517$	1263.17	−	2382.60i	0.107455	−	0.202682i
$518$	−3253.30	+	19844.3i	−0.275950	+	1.68322i
$519$	8809.95	−	6697.15i	0.745113	−	0.566420i
$520$	6772.57	−	3133.33i	0.571148	−	0.264241i
$521$	414.066	+	392.224i	0.0348187	+	0.0329820i	0.704911	−	0.709296i	$-0.250987\pi$
$521$	414.066	+	392.224i	0.0348187	+	0.0329820i	−0.670092	+	0.742278i	$0.733746\pi$
$522$	104.593	+	637.991i	0.00876997	+	0.0534945i
$523$	16039.3	+	5404.27i	1.34101	+	0.451840i	0.896147	−	0.443758i	$-0.146355\pi$
$523$	16039.3	+	5404.27i	1.34101	+	0.451840i	0.444865	+	0.895597i	$0.353252\pi$
$524$	15862.7	−	39812.3i	1.32245	−	3.31910i
$525$	4594.67	−	4352.31i	0.381958	−	0.361810i
$526$	−4103.29	−	3119.24i	−0.340137	−	0.258565i
$527$	24891.8	+	5479.10i	2.05750	+	0.452891i
$528$	−4743.76	+	5584.79i	−0.390996	+	0.460316i
$529$	8230.06	+	895.073i	0.676425	+	0.0735657i
$530$	−3195.83			−0.261921
$531$	4050.94	+	474.923i	0.331066	+	0.0388133i
$532$	3428.91			0.279440
$533$	4510.91	+	490.591i	0.366584	+	0.0398684i
$534$	13337.0	−	15701.5i	1.08080	−	1.27242i
$535$	5726.01	+	1260.39i	0.462723	+	0.101853i
$536$	51304.6	+	39000.7i	4.13437	+	3.14287i
$537$	7010.21	−	6640.42i	0.563339	−	0.533623i
$538$	736.757	−	1849.12i	0.0590406	−	0.148181i
$539$	1123.86	+	378.673i	0.0898110	+	0.0302608i
$540$	−397.025	−	2421.75i	−0.0316393	−	0.192991i
$541$	9721.23	+	9208.44i	0.772548	+	0.731796i	0.968553	−	0.248807i	$-0.0800384\pi$
$541$	9721.23	+	9208.44i	0.772548	+	0.731796i	−0.196005	+	0.980603i	$0.562797\pi$
$542$	9699.10	−	4487.28i	0.768657	−	0.355618i
$543$	−9062.32	+	6888.99i	−0.716208	+	0.544447i
$544$	5495.95	−	33523.8i	0.433156	−	2.64214i
$545$	−3981.29	+	7509.51i	−0.312917	+	0.590224i
$546$	8383.19	−	1845.28i	0.657083	−	0.144635i
$547$	1502.36	+	695.064i	0.117433	+	0.0543305i	0.477726	−	0.878509i	$-0.341461\pi$
$547$	1502.36	+	695.064i	0.117433	+	0.0543305i	−0.360293	+	0.932839i	$0.617323\pi$
$548$	13608.1	+	34153.7i	1.06078	+	2.66236i
$549$	426.903	+	7873.76i	0.0331872	+	0.612102i
$550$	4709.41	+	6945.86i	0.365109	+	0.538495i
$551$	76.7283	+	90.3316i	0.00593237	+	0.00698413i
$552$	−5225.31	−	9855.97i	−0.402905	−	0.759960i
$553$	13624.7	−	4590.71i	1.04771	−	0.353014i
$554$	−8.05280	+	148.525i	−0.000617565	+	0.0113903i
$555$	2260.75	−	1360.25i	0.172907	−	0.104035i
$556$	−2346.84	−	8452.55i	−0.179007	−	0.644727i
$557$	3214.62	−	11578.0i	0.244538	−	0.880747i	−0.734761	−	0.678326i	$-0.762706\pi$
$557$	3214.62	−	11578.0i	0.244538	−	0.880747i	0.979299	−	0.202420i	$-0.0648807\pi$
$558$	10430.8	+	6275.99i	0.791345	+	0.476136i
$559$	3345.55	−	4934.32i	0.253134	−	0.373345i
$560$	−14973.3	+	1628.44i	−1.12989	+	0.122883i
$561$	4577.28	−	497.809i	0.344479	−	0.0374644i
$562$	8418.09	−	12415.8i	0.631843	−	0.931898i
$563$	−8685.11	−	5225.66i	−0.650149	−	0.391182i	0.151937	−	0.988390i	$-0.451449\pi$
$563$	−8685.11	−	5225.66i	−0.650149	−	0.391182i	−0.802086	+	0.597209i	$0.796276\pi$
$564$	−2697.33	+	9714.90i	−0.201379	+	0.725303i
$565$	−2088.27	−	7521.26i	−0.155494	−	0.560039i
$566$	−41872.1	+	25193.6i	−3.10957	+	1.87097i
$567$	89.7863	−	1656.01i	0.00665022	−	0.122656i
$568$	−9556.92	+	3220.10i	−0.705985	+	0.237874i
$569$	−7275.66	−	13723.4i	−0.536049	−	1.01109i	−0.992604	−	0.121400i	$-0.961262\pi$
$569$	−7275.66	−	13723.4i	−0.536049	−	1.01109i	0.456555	−	0.889695i	$-0.349083\pi$
$570$	−411.397	−	484.334i	−0.0302307	−	0.0355904i
$571$	10099.6	+	14895.8i	0.740202	+	1.09172i	0.992281	+	0.124010i	$0.0395754\pi$
$571$	10099.6	+	14895.8i	0.740202	+	1.09172i	−0.252079	+	0.967707i	$0.581114\pi$
$572$	436.254	+	8046.23i	0.0318893	+	0.588164i
$573$	−2529.97	−	6349.74i	−0.184452	−	0.462939i
$574$	−16527.9	−	7646.61i	−1.20185	−	0.556034i
$575$	−6274.73	+	1381.17i	−0.455086	+	0.100172i
$576$	2306.52	−	4350.55i	0.166849	−	0.314710i
$577$	−1633.72	+	9965.24i	−0.117873	+	0.718992i	0.860079	+	0.510161i	$0.170414\pi$
$577$	−1633.72	+	9965.24i	−0.117873	+	0.718992i	−0.977952	+	0.208831i	$0.933034\pi$
$578$	−20058.0	+	15247.7i	−1.44343	+	1.09727i
$579$	−634.431	+	293.519i	−0.0455373	+	0.0210678i
$580$	−905.661	−	857.888i	−0.0648371	−	0.0614170i
$581$	4041.34	+	24651.1i	0.288577	+	1.76024i
$582$	−2612.29	−	880.182i	−0.186053	−	0.0626885i
$583$	750.424	−	1883.42i	0.0533094	−	0.133797i
$584$	4142.16	−	3923.66i	0.293500	−	0.278018i
$585$	−896.597	−	681.575i	−0.0633671	−	0.0481704i
$586$	−29246.9	−	6437.73i	−2.06174	−	0.453823i
$587$	−7372.19	+	8679.21i	−0.518369	+	0.610271i	−0.957599	−	0.288103i	$-0.906975\pi$
$587$	−7372.19	+	8679.21i	−0.518369	+	0.610271i	0.439230	+	0.898375i	$0.355251\pi$
$588$	−4407.94	−	479.392i	−0.309150	−	0.0336221i
$589$	2231.65			0.156118
$590$	−9572.95	+	5651.21i	−0.667987	+	0.394334i
$591$	864.180			0.0601482
$592$	29281.2	+	3184.52i	2.03285	+	0.221086i
$593$	−3939.63	+	4638.09i	−0.272818	+	0.321186i	−0.881460	−	0.472259i	$-0.843439\pi$
$593$	−3939.63	+	4638.09i	−0.272818	+	0.321186i	0.608642	+	0.793445i	$0.291715\pi$
$594$	2147.66	+	472.735i	0.148349	+	0.0326541i
$595$	7534.18	+	5727.33i	0.519111	+	0.394618i
$596$	−12949.0	+	12265.9i	−0.889952	+	0.843008i
$597$	−1287.79	+	3232.10i	−0.0882842	+	0.221577i
$598$	−8258.13	−	2782.49i	−0.564716	−	0.190275i
$599$	−2562.57	−	15631.0i	−0.174798	−	1.06622i	−0.917833	−	0.396967i	$-0.870063\pi$
$599$	−2562.57	−	15631.0i	−0.174798	−	1.06622i	0.743035	−	0.669252i	$-0.233385\pi$
$600$	−13381.9	−	12676.0i	−0.910525	−	0.862495i
$601$	−13087.0	+	6054.69i	−0.888236	+	0.410942i	−0.810299	−	0.586017i	$-0.800695\pi$
$601$	−13087.0	+	6054.69i	−0.888236	+	0.410942i	−0.0779368	+	0.996958i	$0.524833\pi$
$602$	−19047.6	+	14479.6i	−1.28957	+	0.980308i
$603$	1573.57	−	9598.33i	0.106270	−	0.648216i
$604$	17791.4	−	33558.2i	1.19855	−	2.26070i
$605$	−4983.77	+	1097.01i	−0.334908	+	0.0737187i
$606$	3275.57	+	1515.44i	0.219573	+	0.101585i
$607$	1039.43	+	2608.78i	0.0695045	+	0.174443i	0.959625	−	0.281282i	$-0.0907595\pi$
$607$	1039.43	+	2608.78i	0.0695045	+	0.174443i	−0.890121	+	0.455725i	$0.849380\pi$
$608$	−161.034	−	2970.10i	−0.0107415	−	0.198115i
$609$	−473.099	−	697.770i	−0.0314794	−	0.0464287i
$610$	−13913.4	−	16380.1i	−0.923501	−	1.08723i
$611$	2167.38	+	4088.11i	0.143507	+	0.270683i
$612$	−16313.1	+	5496.51i	−1.07748	+	0.363045i
$613$	589.911	−	10880.3i	0.0388683	−	0.716884i	−0.912547	−	0.408973i	$-0.865887\pi$
$613$	589.911	−	10880.3i	0.0388683	−	0.716884i	0.951415	−	0.307912i	$-0.0996301\pi$
$614$	22511.6	−	13544.8i	1.47963	−	0.890264i
$615$	639.226	+	2302.28i	0.0419123	+	0.150955i
$616$	5082.96	−	18307.2i	0.332465	−	1.19743i
$617$	1943.29	+	1169.24i	0.126797	+	0.0762913i	0.577539	−	0.816363i	$-0.304013\pi$
$617$	1943.29	+	1169.24i	0.126797	+	0.0762913i	−0.450742	+	0.892654i	$0.648841\pi$
$618$	−14212.0	+	20961.2i	−0.925068	+	1.36437i
$619$	9596.64	−	1043.70i	0.623136	−	0.0677702i	0.208896	−	0.977938i	$-0.433013\pi$
$619$	9596.64	−	1043.70i	0.623136	−	0.0677702i	0.414240	+	0.910168i	$0.364047\pi$
$620$	−23351.4	+	2539.62i	−1.51260	+	0.164506i
$621$	−944.838	+	1393.53i	−0.0610548	+	0.0900491i
$622$	9063.25	+	5453.18i	0.584250	+	0.351531i
$623$	−7186.80	+	25884.5i	−0.462172	+	1.66459i
$624$	−3363.57	−	12114.5i	−0.215786	−	0.777192i
$625$	−6743.89	+	4057.67i	−0.431609	+	0.259691i
$626$	1407.72	−	25963.8i	0.0898782	−	1.65771i
$627$	382.038	−	128.724i	0.0243335	−	0.00819893i
$628$	−3897.37	−	7351.23i	−0.247647	−	0.467111i
$629$	−11981.4	−	14105.6i	−0.759505	−	0.894158i
$630$	2536.63	+	3741.26i	0.160416	+	0.236596i
$631$	−960.238	−	17710.5i	−0.0605808	−	1.11735i	−0.857909	−	0.513801i	$-0.828237\pi$
$631$	−960.238	−	17710.5i	−0.0605808	−	1.11735i	0.797329	−	0.603545i	$-0.206246\pi$
$632$	−15499.1	−	38899.8i	−0.975509	−	2.44834i
$633$	11647.2	+	5388.56i	0.731333	+	0.338351i
$634$	−4132.54	+	909.642i	−0.258871	+	0.0569819i
$635$	−3105.56	+	5857.70i	−0.194079	+	0.366072i
$636$	−1226.31	+	7480.13i	−0.0764563	+	0.466363i
$637$	−1619.94	+	1231.44i	−0.100760	+	0.0765959i
$638$	1014.53	−	469.372i	0.0629556	−	0.0291264i
$639$	1105.01	+	1046.72i	0.0684091	+	0.0648005i
$640$	81.9004	+	499.571i	0.00505844	+	0.0308551i
$641$	−6149.28	−	2071.93i	−0.378911	−	0.127670i	0.123400	−	0.992357i	$-0.460620\pi$
$641$	−6149.28	−	2071.93i	−0.378911	−	0.127670i	−0.502311	+	0.864687i	$0.667517\pi$
$642$	7270.54	−	18247.7i	0.446955	−	1.12177i
$643$	−1327.53	+	1257.50i	−0.0814195	+	0.0771246i	−0.727327	−	0.686291i	$-0.759238\pi$
$643$	−1327.53	+	1257.50i	−0.0814195	+	0.0771246i	0.645908	+	0.763416i	$0.276479\pi$
$644$	19711.6	+	14984.3i	1.20613	+	0.916873i
$645$	3065.86	+	674.848i	0.187160	+	0.0411971i
$646$	−2885.76	+	3397.38i	−0.175756	+	0.206916i
$647$	−5729.19	−	623.087i	−0.348126	−	0.0378610i	−0.0676142	−	0.997712i	$-0.521539\pi$
$647$	−5729.19	−	623.087i	−0.348126	−	0.0378610i	−0.280512	+	0.959851i	$0.590504\pi$
$648$	−4830.20			−0.292821
$649$	−1082.61	−	6968.69i	−0.0654797	−	0.421487i
$650$	−14398.9			−0.868880
$651$	−15780.7	−	1716.25i	−0.950068	−	0.103326i
$652$	−23995.3	+	28249.5i	−1.44130	+	1.69683i
$653$	25637.3	+	5643.19i	1.53639	+	0.338185i	0.900936	−	0.433952i	$-0.142881\pi$
$653$	25637.3	+	5643.19i	1.53639	+	0.338185i	0.635456	+	0.772137i	$0.280812\pi$
$654$	22669.4	+	17232.8i	1.35542	+	1.03036i
$655$	7518.97	−	7122.35i	0.448535	−	0.424875i
$656$	−9872.92	+	24779.2i	−0.587611	+	1.47479i
$657$	−816.027	−	274.952i	−0.0484570	−	0.0163271i
$658$	−3004.39	−	18326.0i	−0.177999	−	1.08575i
$659$	−14693.3	−	13918.2i	−0.868543	−	0.822727i	0.116828	−	0.993152i	$-0.462727\pi$
$659$	−14693.3	−	13918.2i	−0.868543	−	0.822727i	−0.985371	+	0.170425i	$0.945486\pi$
$660$	−3851.05	+	1781.69i	−0.227124	+	0.105079i
$661$	−639.907	+	486.445i	−0.0376543	+	0.0286241i	−0.623832	−	0.781558i	$-0.714425\pi$
$661$	−639.907	+	486.445i	−0.0376543	+	0.0286241i	0.586178	+	0.810182i	$0.300632\pi$
$662$	−1633.50	+	9963.88i	−0.0959027	+	0.584981i
$663$	−3700.47	+	6979.82i	−0.216764	+	0.408860i
$664$	71053.5	−	15640.1i	4.15272	−	0.914084i
$665$	752.058	+	347.939i	0.0438550	+	0.0202895i
$666$	−3271.79	−	8211.57i	−0.190359	−	0.477765i
$667$	46.3344	+	854.587i	0.00268977	+	0.0496098i
$668$	29476.5	+	43474.6i	1.70731	+	2.51809i
$669$	−2590.63	−	3049.93i	−0.149716	−	0.176259i
$670$	12417.4	+	23421.6i	0.716006	+	1.35053i
$671$	12920.5	−	4353.41i	0.743351	−	0.250464i
$672$	−1145.44	+	21126.3i	−0.0657532	+	1.21275i
$673$	−26125.7	+	15719.3i	−1.49639	+	0.900348i	−0.496921	+	0.867796i	$0.665536\pi$
$673$	−26125.7	+	15719.3i	−1.49639	+	0.900348i	−0.999470	+	0.0325523i	$0.989636\pi$
$674$	−12171.8	−	43838.9i	−0.695610	−	2.50536i
$675$	−744.247	+	2680.54i	−0.0424386	+	0.152850i
$676$	24661.5	+	14838.3i	1.40313	+	0.844238i
$677$	9426.53	−	13903.1i	0.535142	−	0.789275i	−0.459980	−	0.887929i	$-0.652143\pi$
$677$	9426.53	−	13903.1i	0.535142	−	0.789275i	0.995122	+	0.0986540i	$0.0314537\pi$
$678$	−25998.0	+	2827.45i	−1.47264	+	0.160159i
$679$	3573.46	−	388.637i	0.201969	−	0.0219654i
$680$	15468.3	−	22814.1i	0.872330	−	1.28659i
$681$	−14237.0	−	8566.13i	−0.801121	−	0.482019i
$682$	5631.02	−	20281.1i	0.316163	−	1.13872i
$683$	−3569.20	−	12855.1i	−0.199959	−	0.720186i	−0.993714	−	0.111949i	$-0.964291\pi$
$683$	−3569.20	−	12855.1i	−0.199959	−	0.720186i	0.793755	−	0.608237i	$-0.208123\pi$
$684$	−1291.49	+	777.064i	−0.0721950	+	0.0434383i
$685$	−481.010	+	8871.71i	−0.0268299	+	0.494848i
$686$	−27093.1	+	9128.72i	−1.50790	+	0.508070i
$687$	2727.34	+	5144.31i	0.151462	+	0.285688i
$688$	22687.6	+	26709.9i	1.25720	+	1.48009i
$689$	1952.19	+	2879.26i	0.107943	+	0.159203i
$690$	−248.433	−	4582.07i	−0.0137068	−	0.252806i
$691$	−10742.6	−	26961.8i	−0.591413	−	1.48433i	−0.854442	−	0.519547i	$-0.826101\pi$
$691$	−10742.6	−	26961.8i	−0.591413	−	1.48433i	0.263029	−	0.964788i	$-0.415279\pi$
$692$	64927.2	+	30038.5i	3.56671	+	1.65013i
$693$	−2800.50	+	616.437i	−0.153510	+	0.0337900i
$694$	−10118.8	+	19086.1i	−0.553464	+	1.04394i
$695$	342.970	−	2092.03i	0.0187188	−	0.114180i
$696$	−1954.67	+	1485.90i	−0.106453	+	0.0809237i
$697$	15211.3	−	7037.49i	0.826640	−	0.382445i
$698$	−35727.3	−	33842.7i	−1.93739	−	1.83519i
$699$	567.549	+	3461.89i	0.0307105	+	0.187326i
$700$	38770.8	+	13063.4i	2.09343	+	0.705357i
$701$	2898.84	−	7275.53i	0.156188	−	0.392001i	−0.829971	−	0.557807i	$-0.811643\pi$
$701$	2898.84	−	7275.53i	0.156188	−	0.392001i	0.986159	+	0.165805i	$0.0530223\pi$
$702$	−2739.33	+	2594.83i	−0.147278	+	0.139509i
$703$	−1290.04	−	980.663i	−0.0692102	−	0.0526123i
$704$	−8315.09	−	1830.29i	−0.445152	−	0.0979853i
$705$	−1577.39	+	1857.05i	−0.0842668	+	0.0992065i
$706$	−9075.33	−	987.002i	−0.483788	−	0.0526152i
$707$	−4706.26			−0.250349
$708$	9553.85	+	24574.9i	0.507141	+	1.30449i
$709$	−1624.73			−0.0860620			−0.0430310	−	0.999074i	$-0.513701\pi$
$709$	−1624.73			−0.0860620			−0.0430310	+	0.999074i	$0.513701\pi$
$710$	−4124.08	−	448.521i	−0.217992	−	0.0237080i
$711$	−4091.37	+	4816.74i	−0.215807	+	0.254067i
$712$	76410.9	+	16819.3i	4.02194	+	0.885296i
$713$	12829.0	+	9752.34i	0.673842	+	0.512241i
$714$	23018.8	−	21804.6i	1.20652	−	1.14288i
$715$	−720.786	+	1809.04i	−0.0377005	+	0.0946212i
$716$	59153.6	+	19931.2i	3.08753	+	1.04031i
$717$	−1824.69	−	11130.1i	−0.0950411	−	0.579725i
$718$	9817.11	+	9299.26i	0.510267	+	0.483350i
$719$	−22647.1	+	10477.7i	−1.17468	+	0.543464i	−0.907446	−	0.420168i	$-0.861971\pi$
$719$	−22647.1	+	10477.7i	−1.17468	+	0.543464i	−0.267232	+	0.963632i	$0.586109\pi$
$720$	5270.62	−	4006.62i	0.272811	−	0.207386i
$721$	5342.57	−	32588.2i	0.275961	−	1.68329i
$722$	16632.7	−	31372.5i	0.857345	−	1.61712i
$723$	−13254.9	+	2917.62i	−0.681818	+	0.150079i
$724$	−66787.1	−	30899.0i	−3.42835	−	1.58612i
$725$	523.426	+	1313.70i	0.0268132	+	0.0672960i
$726$	925.589	+	17071.5i	0.0473166	+	0.872703i
$727$	11161.9	+	16462.5i	0.569423	+	0.839836i	0.997970	−	0.0636837i	$-0.0202849\pi$
$727$	11161.9	+	16462.5i	0.569423	+	0.839836i	−0.428548	+	0.903519i	$0.640975\pi$
$728$	21104.8	+	24846.5i	1.07445	+	1.26494i
$729$	341.470	+	644.080i	0.0173485	+	0.0327227i
$730$	2224.10	−	749.386i	0.112764	−	0.0379946i
$731$	1192.16	−	21988.1i	0.0603197	−	1.11253i
$732$	−43678.0	+	26280.2i	−2.20544	+	1.32697i
$733$	6115.75	+	22026.9i	0.308172	+	1.10994i	0.941766	+	0.336270i	$0.109166\pi$
$733$	6115.75	+	22026.9i	0.308172	+	1.10994i	−0.633593	+	0.773666i	$0.718421\pi$
$734$	−1242.58	+	4475.38i	−0.0624858	+	0.225054i
$735$	−918.141	−	552.427i	−0.0460764	−	0.0277233i
$736$	12053.6	−	17777.8i	0.603672	−	0.890350i
$737$	−16719.0	+	1818.30i	−0.835621	+	0.0908793i
$738$	7958.07	−	865.492i	0.396938	−	0.0431697i
$739$	−10784.7	+	15906.3i	−0.536838	+	0.791777i	−0.995290	−	0.0969422i	$-0.969094\pi$
$739$	−10784.7	+	15906.3i	−0.536838	+	0.791777i	0.458452	+	0.888719i	$0.348404\pi$
$740$	14614.6	+	8793.32i	0.726006	+	0.436823i
$741$	−185.054	+	666.504i	−0.00917426	+	0.0330427i
$742$	−3735.09	−	13452.6i	−0.184797	−	0.665579i
$743$	23795.2	−	14317.1i	1.17492	−	0.706923i	0.212143	−	0.977239i	$-0.431956\pi$
$743$	23795.2	−	14317.1i	1.17492	−	0.706923i	0.962772	+	0.270316i	$0.0871280\pi$
$744$	−2502.96	+	46164.3i	−0.123337	+	2.27482i
$745$	−4084.74	+	1376.31i	−0.200877	+	0.0676833i
$746$	23615.0	+	44542.5i	1.15899	+	2.18608i
$747$	−7108.62	−	8368.92i	−0.348181	−	0.409910i
$748$	16703.3	+	24635.6i	0.816489	+	1.20423i
$749$	1386.70	+	25576.2i	0.0676488	+	1.24771i
$750$	−6211.24	−	15589.0i	−0.302403	−	0.758974i
$751$	−22785.0	−	10541.5i	−1.10711	−	0.512202i	−0.220808	−	0.975317i	$-0.570869\pi$
$751$	−22785.0	−	10541.5i	−1.10711	−	0.512202i	−0.886298	+	0.463115i	$0.846732\pi$
$752$	−26564.4	+	5847.26i	−1.28817	+	0.283548i
$753$	−3567.63	+	6729.26i	−0.172658	+	0.325668i
$754$	−310.302	+	1892.76i	−0.0149874	+	0.0914193i
$755$	7307.39	−	5554.93i	0.352242	−	0.267768i
$756$	9730.12	−	4501.63i	0.468096	−	0.216564i
$757$	−29205.4	−	27664.8i	−1.40223	−	1.32826i	−0.879609	−	0.475697i	$-0.842196\pi$
$757$	−29205.4	−	27664.8i	−1.40223	−	1.32826i	−0.522620	−	0.852566i	$-0.675045\pi$
$758$	−5550.59	−	33857.1i	−0.265971	−	1.62235i
$759$	2758.72	+	929.522i	0.131931	+	0.0444526i
$760$	893.298	−	2242.01i	0.0426360	−	0.107008i
$761$	19531.7	−	18501.4i	0.930384	−	0.881306i	−0.0627811	−	0.998027i	$-0.519997\pi$
$761$	19531.7	−	18501.4i	0.930384	−	0.881306i	0.993165	+	0.116721i	$0.0372384\pi$
$762$	17683.0	+	13442.2i	0.840664	+	0.639056i
$763$	−36263.7	−	7982.25i	−1.72062	−	0.378738i
$764$	28605.5	−	33677.0i	1.35459	−	1.59475i
$765$	−4135.67	−	449.781i	−0.195458	−	0.0212573i
$766$	−61856.0			−2.91769
$767$	10939.1	+	5172.62i	0.514979	+	0.243511i
$768$	−11435.1			−0.537275
$769$	20432.4	+	2222.15i	0.958140	+	0.104204i	0.573807	−	0.818991i	$-0.305466\pi$
$769$	20432.4	+	2222.15i	0.958140	+	0.104204i	0.384333	+	0.923195i	$0.374432\pi$
$770$	5059.68	−	5956.71i	0.236803	−	0.278786i
$771$	−5436.98	−	1196.77i	−0.253966	−	0.0559022i
$772$	−3597.50	−	2734.75i	−0.167716	−	0.127494i
$773$	−1230.91	+	1165.98i	−0.0572738	+	0.0542526i	−0.715801	−	0.698304i	$-0.753938\pi$
$773$	−1230.91	+	1165.98i	−0.0572738	+	0.0542526i	0.658527	+	0.752557i	$0.271180\pi$
$774$	3892.85	−	9770.31i	0.180782	−	0.453730i
$775$	25233.4	+	8502.12i	1.16956	+	0.394071i
$776$	−1693.70	−	10331.1i	−0.0783509	−	0.477920i
$777$	8368.08	+	7926.67i	0.386362	+	0.365982i
$778$	31620.5	−	14629.2i	1.45714	−	0.674143i
$779$	1168.27	−	888.096i	0.0537325	−	0.0408464i
$780$	1177.87	−	7184.70i	0.0540700	−	0.329812i
$781$	1232.72	−	2325.16i	0.0564792	−	0.106531i
$782$	−31435.7	+	6919.52i	−1.43752	+	0.316422i
$783$	336.321	+	155.599i	0.0153501	+	0.00710172i
$784$	−4427.54	−	11112.3i	−0.201692	−	0.506208i
$785$	−108.860	−	2007.81i	−0.00494954	−	0.0912889i
$786$	−19471.9	−	28718.9i	−0.883639	−	1.30327i
$787$	12756.6	+	15018.2i	0.577793	+	0.680231i	0.970961	−	0.239236i	$-0.0768969\pi$
$787$	12756.6	+	15018.2i	0.577793	+	0.680231i	−0.393168	+	0.919467i	$0.628621\pi$
$788$	2616.76	+	4935.72i	0.118297	+	0.223132i
$789$	−2799.73	+	943.337i	−0.126328	+	0.0425649i
$790$	932.533	−	17199.6i	0.0419975	−	0.774599i
$791$	29219.5	−	17580.8i	1.31343	−	0.790266i
$792$	2234.31	+	8047.26i	0.100243	+	0.361044i
$793$	−6258.49	+	22541.0i	−0.280259	+	1.00940i
$794$	−27281.2	−	16414.5i	−1.21936	−	0.733665i
$795$	−1027.99	+	1516.17i	−0.0458604	+	0.0676391i
$796$	−22359.5	+	2431.74i	−0.995616	+	0.108280i
$797$	−24811.2	+	2698.38i	−1.10271	+	0.119926i	−0.641320	−	0.767273i	$-0.721613\pi$
$797$	−24811.2	+	2698.38i	−1.10271	+	0.119926i	−0.461385	+	0.887200i	$0.652647\pi$
$798$	1557.95	−	2297.80i	0.0691112	−	0.101931i
$799$	14644.8	+	8811.49i	0.648431	+	0.390148i
$800$	9494.63	−	34196.6i	0.419607	−	1.51129i
$801$	−3159.09	−	11378.0i	−0.139352	−	0.501901i
$802$	990.182	−	595.773i	0.0435967	−	0.0262313i
$803$	−80.6072	+	1486.71i	−0.00354242	+	0.0653362i
$804$	59585.3	−	20076.6i	2.61369	−	0.880656i
$805$	2802.82	+	5286.67i	0.122716	+	0.231467i
$806$	23380.4	+	27525.6i	1.02176	+	1.20291i
$807$	−640.274	−	944.334i	−0.0279290	−	0.0411922i
$808$	742.077	+	13686.8i	0.0323096	+	0.595916i
$809$	11904.7	+	29878.6i	0.517365	+	1.29849i	0.923122	+	0.384507i	$0.125629\pi$
$809$	11904.7	+	29878.6i	0.517365	+	1.29849i	−0.405757	+	0.913981i	$0.632992\pi$
$810$	−1803.27	−	834.279i	−0.0782226	−	0.0361896i
$811$	−20871.4	+	4594.14i	−0.903692	+	0.198918i	−0.642424	−	0.766349i	$-0.722071\pi$
$811$	−20871.4	+	4594.14i	−0.903692	+	0.198918i	−0.261267	+	0.965267i	$0.584140\pi$
$812$	2552.72	−	4814.95i	0.110324	−	0.208093i
$813$	991.006	−	6044.87i	0.0427504	−	0.260766i
$814$	−12167.3	+	9249.34i	−0.523911	+	0.398267i
$815$	−8129.40	+	3761.06i	−0.349399	+	0.161649i
$816$	−33715.5	−	31937.1i	−1.44642	−	1.37012i
$817$	−311.927	−	1902.67i	−0.0133573	−	0.0814760i
$818$	70399.5	+	23720.3i	3.00912	+	1.01389i
$819$	1821.15	−	4570.73i	0.0776996	−	0.195011i
$820$	−11213.8	+	10622.3i	−0.477565	+	0.452373i
$821$	−28916.1	−	21981.4i	−1.22921	−	0.934419i	−0.229959	−	0.973200i	$-0.573859\pi$
$821$	−28916.1	−	21981.4i	−1.22921	−	0.934419i	−0.999248	+	0.0387816i	$0.987652\pi$
$822$	29070.2	+	6398.82i	1.23350	+	0.271514i
$823$	−12783.2	+	15049.6i	−0.541427	+	0.637417i	−0.963040	−	0.269359i	$-0.913188\pi$
$823$	−12783.2	+	15049.6i	−0.541427	+	0.637417i	0.421613	+	0.906776i	$0.361464\pi$
$824$	−95616.0	−	10398.9i	−4.04240	−	0.439638i
$825$	4810.13			0.202990
$826$	−34976.6	−	33691.7i	−1.47335	−	1.41923i
$827$	−34585.8			−1.45425			−0.727125	−	0.686505i	$-0.759144\pi$
$827$	−34585.8			−1.45425			−0.727125	+	0.686505i	$0.759144\pi$
$828$	−10820.1	−	1176.76i	−0.454135	−	0.0493902i
$829$	9941.03	−	11703.5i	0.416485	−	0.490324i	−0.513413	−	0.858142i	$-0.671619\pi$
$829$	9941.03	−	11703.5i	0.416485	−	0.490324i	0.929898	+	0.367817i	$0.119895\pi$
$830$	29227.9	+	6433.54i	1.22231	+	0.269050i
$831$	67.8733	+	51.5960i	0.00283333	+	0.00215384i
$832$	10605.9	−	10046.4i	0.441938	−	0.418626i
$833$	−2782.04	+	6982.40i	−0.115717	+	0.290427i
$834$	−6730.57	−	2267.79i	−0.279449	−	0.0941574i
$835$	2053.58	+	12526.3i	0.0851101	+	0.519149i
$836$	1892.02	+	1792.22i	0.0782738	+	0.0741448i
$837$	6332.70	−	2929.82i	0.261517	−	0.120991i
$838$	−28152.2	+	21400.7i	−1.16050	+	0.882191i
$839$	−1424.05	+	8686.30i	−0.0585978	+	0.357431i	0.941210	+	0.337822i	$0.109690\pi$
$839$	−1424.05	+	8686.30i	−0.0585978	+	0.357431i	−0.999808	+	0.0196085i	$0.993758\pi$
$840$	−8041.00	+	15166.9i	−0.330287	+	0.622987i
$841$	−23634.8	+	5202.42i	−0.969077	+	0.213310i
$842$	−53115.6	−	24573.9i	−2.17397	−	1.00579i
$843$	−3182.49	−	7987.45i	−0.130025	−	0.326338i
$844$	4491.41	+	82839.1i	0.183176	+	3.37848i
$845$	3903.29	+	5756.92i	0.158908	+	0.234372i
$846$	5284.66	+	6221.58i	0.214764	+	0.252840i
$847$	−10442.5	−	19696.6i	−0.423623	−	0.799037i
$848$	−19378.8	+	6529.49i	−0.784755	+	0.264415i
$849$	−1516.43	+	27969.0i	−0.0613002	+	1.13062i
$850$	−45572.6	+	27420.1i	−1.83897	+	1.10647i
$851$	−3130.48	−	11275.0i	−0.126100	−	0.454172i
$852$	−2632.30	+	9480.69i	−0.105846	+	0.381224i
$853$	20989.2	+	12628.8i	0.842503	+	0.506917i	0.870200	−	0.492699i	$-0.163990\pi$
$853$	20989.2	+	12628.8i	0.842503	+	0.506917i	−0.0276967	+	0.999616i	$0.508817\pi$
$854$	52689.5	−	77711.2i	2.11124	−	3.11384i
$855$	−362.111	+	39.3820i	−0.0144841	+	0.00157525i
$856$	74162.5	−	8065.66i	2.96124	−	0.322054i
$857$	24447.7	−	36057.7i	0.974467	−	1.43723i	0.0765501	−	0.997066i	$-0.475609\pi$
$857$	24447.7	−	36057.7i	0.974467	−	1.43723i	0.897917	−	0.440165i	$-0.145080\pi$
$858$	5590.20	+	3363.51i	0.222432	+	0.133833i
$859$	12964.5	−	46693.8i	0.514950	−	1.85468i	−0.00418591	−	0.999991i	$-0.501332\pi$
$859$	12964.5	−	46693.8i	0.514950	−	1.85468i	0.519136	−	0.854692i	$-0.326254\pi$
$860$	5429.14	+	19554.0i	0.215270	+	0.775333i
$861$	−8944.18	+	5381.53i	−0.354026	+	0.213011i
$862$	−4586.06	+	84585.0i	−0.181209	+	3.34220i
$863$	−10992.2	+	3703.70i	−0.433578	+	0.146090i	−0.527623	−	0.849478i	$-0.676917\pi$
$863$	−10992.2	+	3703.70i	−0.433578	+	0.146090i	0.0940451	+	0.995568i	$0.470020\pi$
$864$	−4356.25	−	8216.76i	−0.171531	−	0.323542i
$865$	11192.3	+	13176.6i	0.439942	+	0.517940i
$866$	−26208.2	−	38654.2i	−1.02840	−	1.51677i
$867$	781.864	+	14420.6i	0.0306269	+	0.564879i
$868$	−37982.0	−	95327.6i	−1.48525	−	3.72768i
$869$	9917.39	+	4588.27i	0.387140	+	0.179110i
$870$	−986.386	+	217.120i	−0.0384386	+	0.00846098i
$871$	13516.4	−	25494.6i	0.525815	−	0.991792i
$872$	−17496.1	+	106721.i	−0.679464	+	4.14455i
$873$	−1257.86	+	956.202i	−0.0487654	+	0.0370705i
$874$	−2557.86	+	1183.39i	−0.0989941	+	0.0457996i
$875$	15886.2	+	15048.2i	0.613772	+	0.581395i
$876$	−900.575	−	5493.27i	−0.0347347	−	0.211872i
$877$	−26728.8	−	9005.97i	−1.02915	−	0.346762i	−0.246448	−	0.969156i	$-0.579263\pi$
$877$	−26728.8	−	9005.97i	−1.02915	−	0.346762i	−0.782704	+	0.622394i	$0.786160\pi$
$878$	10143.1	−	25457.3i	0.389879	−	0.978523i
$879$	−12461.9	+	11804.6i	−0.478192	+	0.452968i
$880$	−9113.19	−	6927.67i	−0.349097	−	0.265377i
$881$	10611.7	+	2335.81i	0.405809	+	0.0893253i	0.413184	−	0.910648i	$-0.364417\pi$
$881$	10611.7	+	2335.81i	0.405809	+	0.0893253i	−0.00737521	+	0.999973i	$0.502348\pi$
$882$	−2324.03	+	2736.06i	−0.0887234	+	0.104453i
$883$	5136.60	+	558.639i	0.195765	+	0.0212907i	0.205476	−	0.978662i	$-0.434126\pi$
$883$	5136.60	+	558.639i	0.195765	+	0.0212907i	−0.00971129	+	0.999953i	$0.503091\pi$
$884$	−51070.1			−1.94307
$885$	−398.234	+	6359.42i	−0.0151260	+	0.241548i
$886$	72421.2			2.74609
$887$	−498.089	−	54.1704i	−0.0188548	−	0.00205058i	0.0986868	−	0.995119i	$-0.468536\pi$
$887$	−498.089	−	54.1704i	−0.0188548	−	0.00205058i	−0.117542	+	0.993068i	$0.537501\pi$
$888$	21733.0	−	25586.1i	0.821297	−	0.966906i
$889$	−28287.1	−	6226.46i	−1.06717	−	0.234903i
$890$	25621.6	+	19477.0i	0.964985	+	0.733562i
$891$	915.104	−	866.833i	0.0344076	−	0.0325926i
$892$	9575.04	−	24031.6i	0.359413	−	0.902058i
$893$	1418.15	+	477.829i	0.0531427	+	0.0179059i
$894$	2336.26	+	14250.6i	0.0874008	+	0.533121i
$895$	10951.6	+	10373.9i	0.409019	+	0.387443i
$896$	−2007.18	+	928.620i	−0.0748384	+	0.0346239i
$897$	−3976.43	+	3022.81i	−0.148015	+	0.112518i
$898$	2203.20	−	13438.9i	0.0818726	−	0.499401i
$899$	1661.40	−	3133.74i	0.0616361	−	0.116258i
$900$	−17563.4	+	3865.99i	−0.650495	+	0.143185i
$901$	11661.7	+	5395.28i	0.431196	+	0.199493i
$902$	−5123.11	−	12858.0i	−0.189114	−	0.474641i
$903$	742.479	+	13694.2i	0.0273623	+	0.504668i
$904$	−55736.0	−	82204.5i	−2.05061	−	3.02443i
$905$	−11512.9	−	13554.1i	−0.422876	−	0.497848i
$906$	−14404.5	−	27169.8i	−0.528211	−	0.996311i
$907$	37699.8	−	12702.5i	1.38015	−	0.465028i	0.471238	−	0.882006i	$-0.343807\pi$
$907$	37699.8	−	12702.5i	1.38015	−	0.465028i	0.908916	+	0.416978i	$0.136911\pi$
$908$	5815.06	−	107253.i	0.212533	−	3.91993i
$909$	1772.60	−	1066.54i	0.0646792	−	0.0389162i
$910$	3587.57	+	12921.3i	0.130689	+	0.470698i
$911$	2310.93	−	8323.23i	0.0840446	−	0.302701i	−0.909567	−	0.415558i	$-0.863586\pi$
$911$	2310.93	−	8323.23i	0.0840446	−	0.302701i	0.993611	+	0.112857i	$0.0360001\pi$
$912$	−3484.18	−	2096.36i	−0.126505	−	0.0761157i
$913$	−10654.6	+	15714.4i	−0.386218	+	0.569629i
$914$	−47366.0	+	5151.36i	−1.71414	+	0.186424i
$915$	−12246.5	+	1331.89i	−0.442468	+	0.0481212i
$916$	−21123.1	+	31154.2i	−0.761928	+	1.12376i
$917$	38768.6	+	23326.3i	1.39613	+	0.840025i
$918$	−3728.60	+	13429.2i	−0.134054	+	0.482820i
$919$	−711.939	−	2564.17i	−0.0255546	−	0.0920395i	0.949673	−	0.313243i	$-0.101415\pi$
$919$	−711.939	−	2564.17i	−0.0255546	−	0.0920395i	−0.975228	+	0.221203i	$0.929002\pi$
$920$	14932.8	−	8984.79i	0.535132	−	0.321978i
$921$	815.275	−	15036.9i	0.0291685	−	0.537982i
$922$	55010.0	−	18535.0i	1.96492	−	0.662059i
$923$	2115.13	+	3989.55i	0.0754282	+	0.142273i
$924$	−12000.7	−	14128.4i	−0.427267	−	0.503018i
$925$	−10850.4	−	16003.2i	−0.385686	−	0.568844i
$926$	3153.93	+	58170.7i	0.111927	+	2.06437i
$927$	5372.92	+	13485.0i	0.190367	+	0.477784i
$928$	−4290.57	−	1985.03i	−0.151772	−	0.0702174i
$929$	34349.2	−	7560.84i	1.21309	−	0.267022i	0.438061	−	0.898945i	$-0.355665\pi$
$929$	34349.2	−	7560.84i	1.21309	−	0.267022i	0.775031	+	0.631924i	$0.217734\pi$
$930$	−8908.00	+	16802.3i	−0.314091	+	0.592439i
$931$	−106.470	+	649.437i	−0.00374802	+	0.0228619i
$932$	−18053.9	+	13724.2i	−0.634523	+	0.482352i
$933$	5502.45	−	2545.70i	0.193078	−	0.0893276i
$934$	25560.4	+	24212.1i	0.895461	+	0.848226i
$935$	1163.69	+	7098.21i	0.0407025	+	0.248274i
$936$	−13579.8	−	4575.58i	−0.474221	−	0.159784i
$937$	−10920.9	+	27409.4i	−0.380758	+	0.955631i	0.606295	+	0.795240i	$0.292655\pi$
$937$	−10920.9	+	27409.4i	−0.380758	+	0.955631i	−0.987053	+	0.160392i	$0.948724\pi$
$938$	−84078.7	+	79643.6i	−2.92672	+	2.77234i
$939$	−11865.0	−	9019.54i	−0.412353	−	0.313463i
$940$	−15382.9	−	3386.02i	−0.533759	−	0.117489i
$941$	17088.6	−	20118.3i	0.592000	−	0.696957i	−0.381830	−	0.924233i	$-0.624706\pi$
$941$	17088.6	−	20118.3i	0.592000	−	0.696957i	0.973830	+	0.227276i	$0.0729819\pi$
$942$	−6697.04	−	728.347i	−0.231636	−	0.0251920i
$943$	10596.9			0.365943
$944$	−46502.2	+	53826.6i	−1.60330	+	1.85583i
$945$	2590.88			0.0891867
$946$	−18078.4	−	1966.14i	−0.621330	−	0.0675738i
$947$	−30260.6	+	35625.5i	−1.03837	+	1.22246i	−0.0638967	+	0.997957i	$0.520353\pi$
$947$	−30260.6	+	35625.5i	−1.03837	+	1.22246i	−0.974473	+	0.224506i	$0.927923\pi$
$948$	−39899.4	−	8782.51i	−1.36695	−	0.300889i
$949$	−2033.76	−	1546.02i	−0.0695665	−	0.0528831i
$950$	−3380.85	+	3202.51i	−0.115462	+	0.109372i
$951$	−897.745	+	2253.17i	−0.0306113	+	0.0768287i
$952$	114113.	+	38449.0i	3.88488	+	1.30897i
$953$	−1671.77	−	10197.4i	−0.0568248	−	0.346616i	−0.999901	−	0.0140403i	$-0.995531\pi$
$953$	−1671.77	−	10197.4i	−0.0568248	−	0.346616i	0.943077	−	0.332575i	$-0.107918\pi$
$954$	4455.45	+	4220.43i	0.151206	+	0.143230i
$955$	9691.27	−	4483.66i	0.328379	−	0.151924i
$956$	58044.1	−	44124.0i	1.96368	−	1.49275i
$957$	103.660	−	632.297i	0.00350141	−	0.0213576i
$958$	−42935.3	+	80984.6i	−1.44799	+	2.73120i
$959$	−37906.9	+	8343.94i	−1.27641	+	0.280959i
$960$	6981.71	+	3230.08i	0.234723	+	0.108594i
$961$	−13693.2	−	34367.4i	−0.459643	−	1.15362i
$962$	−1419.75	−	26185.7i	−0.0475826	−	0.877610i
$963$	−6318.41	−	9318.96i	−0.211431	−	0.311837i
$964$	−56799.9	−	66870.0i	−1.89772	−	2.23417i
$965$	−511.533	−	964.854i	−0.0170641	−	0.0321863i
$966$	18997.5	−	6400.99i	0.632747	−	0.213197i
$967$	853.120	−	15734.9i	0.0283707	−	0.523267i	−0.949462	−	0.313881i	$-0.898371\pi$
$967$	853.120	−	15734.9i	0.0283707	−	0.523267i	0.977833	−	0.209386i	$-0.0671466\pi$
$968$	−55635.5	+	33474.8i	−1.84731	+	1.11149i
$969$	683.540	+	2461.89i	0.0226609	+	0.0816173i
$970$	1152.10	−	4149.47i	0.0381356	−	0.137352i
$971$	−48120.7	−	28953.3i	−1.59039	−	0.956904i	−0.987234	−	0.159280i	$-0.949083\pi$
$971$	−48120.7	−	28953.3i	−1.59039	−	0.956904i	−0.603154	−	0.797625i	$-0.706090\pi$
$972$	−2644.66	+	3900.58i	−0.0872711	+	0.128715i
$973$	9207.05	−	1001.33i	0.303355	−	0.0329918i
$974$	63300.3	−	6884.33i	2.08242	−	0.226476i
$975$	−4631.65	+	6831.17i	−0.152135	+	0.224382i
$976$	−117834.	−	70898.6i	−3.86454	−	2.32521i
$977$	7486.29	−	26963.2i	0.245146	−	0.882936i	−0.733893	−	0.679265i	$-0.762299\pi$
$977$	7486.29	−	26963.2i	0.245146	−	0.882936i	0.979039	−	0.203671i	$-0.0652873\pi$
$978$	8028.27	+	28915.2i	0.262491	+	0.945406i
$979$	−17494.8	+	10526.3i	−0.571131	+	0.343638i
$980$	375.012	−	6916.69i	0.0122238	−	0.225455i
$981$	15467.6	−	5211.64i	0.503407	−	0.169618i
$982$	36702.3	+	69227.8i	1.19268	+	2.24964i
$983$	34777.5	+	40943.2i	1.12841	+	1.32847i	0.937949	+	0.346774i	$0.112723\pi$
$983$	34777.5	+	40943.2i	1.12841	+	1.32847i	0.190463	+	0.981694i	$0.439001\pi$
$984$	17061.0	+	25163.1i	0.552728	+	0.815212i
$985$	73.0904	+	1348.07i	0.00236432	+	0.0436073i
$986$	2622.31	+	6581.49i	0.0846970	+	0.212573i
$987$	−9660.66	−	4469.50i	−0.311552	−	0.144140i
$988$	−4367.06	+	961.262i	−0.140622	+	0.0309533i
$989$	6521.51	−	12300.9i	0.209678	−	0.395495i
$990$	−555.797	+	3390.21i	−0.0178428	+	0.108836i
$991$	19967.8	−	15179.1i	0.640058	−	0.486560i	−0.234092	−	0.972214i	$-0.575212\pi$
$991$	19967.8	−	15179.1i	0.640058	−	0.486560i	0.874151	+	0.485655i	$0.161419\pi$
$992$	−80788.5	+	37376.8i	−2.58572	+	1.19628i
$993$	4201.65	+	3980.01i	0.134275	+	0.127192i
$994$	−2931.96	−	17884.2i	−0.0935575	−	0.570676i
$995$	−5150.83	−	1735.52i	−0.164113	−	0.0552960i
$996$	26273.6	−	65941.9i	0.835856	−	2.09784i
$997$	−14215.7	+	13465.9i	−0.451572	+	0.427751i	−0.879382	−	0.476117i	$-0.842044\pi$
$997$	−14215.7	+	13465.9i	−0.451572	+	0.427751i	0.427810	+	0.903869i	$0.359285\pi$
$998$	13418.6	+	10200.6i	0.425610	+	0.323541i
$999$	−4948.17	−	1089.17i	−0.156710	−	0.0344945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.b.4.15	✓	420
59.15	even	29	inner	177.4.e.b.133.15	yes	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.b.4.15	✓	420	1.1	even	1	trivial
177.4.e.b.133.15	yes	420	59.15	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(5.20320 + 0.565882i) q^{2} +(1.94216 - 2.28649i) q^{3} +(18.9401 + 4.16902i) q^{4} +(3.73106 + 2.83628i) q^{5} +(11.3993 - 10.7980i) q^{6} +(-7.57844 + 19.0204i) q^{7} +(56.5105 + 19.0406i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})\)	\(q+(5.20320 + 0.565882i) q^{2} +(1.94216 - 2.28649i) q^{3} +(18.9401 + 4.16902i) q^{4} +(3.73106 + 2.83628i) q^{5} +(11.3993 - 10.7980i) q^{6} +(-7.57844 + 19.0204i) q^{7} +(56.5105 + 19.0406i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(17.8084 + 16.8690i) q^{10} +(-14.1232 + 6.53410i) q^{11} +(46.3170 - 35.2093i) q^{12} +(4.31969 - 26.3490i) q^{13} +(-50.1954 + 94.6786i) q^{14} +(13.7314 - 3.02251i) q^{15} +(142.452 + 65.9055i) q^{16} +(-36.5050 - 91.6206i) q^{17} +(-2.55021 - 47.0358i) q^{18} +(-4.84610 - 7.14746i) q^{19} +(58.8420 + 69.2742i) q^{20} +(28.7715 + 54.2687i) q^{21} +(-77.1835 + 26.0062i) q^{22} +(3.37594 - 62.2656i) q^{23} +(153.289 - 92.2306i) q^{24} +(-27.5647 - 99.2791i) q^{25} +(37.3866 - 134.654i) q^{26} +(-23.1351 - 13.9200i) q^{27} +(-222.833 + 328.654i) q^{28} +(-13.6444 + 1.48392i) q^{29} +(73.1577 - 7.95637i) q^{30} +(-145.027 + 213.899i) q^{31} +(295.143 + 177.582i) q^{32} +(-12.4894 + 44.9829i) q^{33} +(-138.096 - 497.377i) q^{34} +(-82.2228 + 49.4718i) q^{35} +(9.44948 - 174.285i) q^{36} +(177.830 - 59.9178i) q^{37} +(-21.1706 - 39.9320i) q^{38} +(-51.8570 - 61.0508i) q^{39} +(156.840 + 231.321i) q^{40} +(9.20035 + 169.691i) q^{41} +(118.994 + 298.652i) q^{42} +(202.638 + 93.7502i) q^{43} +(-294.736 + 64.8763i) q^{44} +(19.7577 - 37.2669i) q^{45} +(52.8007 - 322.070i) q^{46} +(-137.959 + 104.874i) q^{47} +(427.357 - 197.716i) q^{48} +(-55.3281 - 52.4095i) q^{49} +(-87.2444 - 532.167i) q^{50} +(-280.388 - 94.4736i) q^{51} +(191.665 - 481.042i) q^{52} +(-94.5857 + 89.5963i) q^{53} +(-112.500 - 85.5200i) q^{54} +(-71.2272 - 15.6783i) q^{55} +(-790.422 + 930.557i) q^{56} +(-25.7545 - 2.80097i) q^{57} -71.8342 q^{58} +(-124.893 + 435.638i) q^{59} +272.675 q^{60} +(-871.011 - 94.7281i) q^{61} +(-875.648 + 1030.89i) q^{62} +(179.963 + 39.6129i) q^{63} +(435.565 + 331.108i) q^{64} +(90.8500 - 86.0577i) q^{65} +(-90.4399 + 226.987i) q^{66} +(1024.15 + 345.075i) q^{67} +(-309.438 - 1887.49i) q^{68} +(-135.813 - 128.649i) q^{69} +(-455.817 + 210.883i) q^{70} +(-134.633 + 102.346i) q^{71} +(86.8266 - 529.619i) q^{72} +(44.8165 - 84.5328i) q^{73} +(959.190 - 211.134i) q^{74} +(-280.535 - 129.789i) q^{75} +(-61.9875 - 155.577i) q^{76} +(-17.2495 - 318.148i) q^{77} +(-235.275 - 347.004i) q^{78} +(-454.597 - 535.193i) q^{79} +(344.572 + 649.931i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-48.1535 + 888.140i) q^{82} +(1045.41 - 629.004i) q^{83} +(318.686 + 1147.80i) q^{84} +(123.659 - 445.380i) q^{85} +(1001.31 + 602.470i) q^{86} +(-23.1066 + 34.0797i) q^{87} +(-922.525 + 100.331i) q^{88} +(1304.36 - 141.857i) q^{89} +(123.892 - 182.727i) q^{90} +(468.432 + 281.846i) q^{91} +(323.528 - 1165.24i) q^{92} +(207.412 + 747.030i) q^{93} +(-777.176 + 467.611i) q^{94} +(2.19110 - 40.4125i) q^{95} +(979.254 - 329.949i) q^{96} +(-82.2340 - 155.110i) q^{97} +(-258.225 - 304.006i) q^{98} +(78.5962 + 115.921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Introduction

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