LMFDB - Embedded newform 128.3.l.a.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(3,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("128.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.l (of order $32$, degree $16$, 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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$31$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			43.3
Character	$\chi$	$=$	128.43
Dual form			128.3.l.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90117 - 0.620914i) q^{2} +(0.779996 + 0.640126i) q^{3} +(3.22893 + 2.36093i) q^{4} +(0.179045 - 0.0543127i) q^{5} +(-1.08545 - 1.70130i) q^{6} +(-2.44195 + 12.2765i) q^{7} +(-4.67283 - 6.49343i) q^{8} +(-1.55718 - 7.82847i) q^{9} +O(q^{10})$	\(q+(-1.90117 - 0.620914i) q^{2} +(0.779996 + 0.640126i) q^{3} +(3.22893 + 2.36093i) q^{4} +(0.179045 - 0.0543127i) q^{5} +(-1.08545 - 1.70130i) q^{6} +(-2.44195 + 12.2765i) q^{7} +(-4.67283 - 6.49343i) q^{8} +(-1.55718 - 7.82847i) q^{9} +(-0.374119 - 0.00791361i) q^{10} +(-0.360362 + 3.65882i) q^{11} +(1.00726 + 3.90844i) q^{12} +(-4.42408 + 14.5842i) q^{13} +(12.2652 - 21.8236i) q^{14} +(0.174421 + 0.0722477i) q^{15} +(4.85200 + 15.2466i) q^{16} +(5.83214 + 14.0800i) q^{17} +(-1.90034 + 15.8502i) q^{18} +(1.99470 + 3.73182i) q^{19} +(0.706353 + 0.247341i) q^{20} +(-9.76323 + 8.01248i) q^{21} +(2.95693 - 6.73230i) q^{22} +(28.6157 + 19.1204i) q^{23} +(0.511831 - 8.05606i) q^{24} +(-20.7576 + 13.8698i) q^{25} +(17.4665 - 24.9802i) q^{26} +(8.07753 - 15.1120i) q^{27} +(-36.8689 + 33.8747i) q^{28} +(0.216869 + 2.20191i) q^{29} +(-0.286746 - 0.245656i) q^{30} +(7.33155 - 7.33155i) q^{31} +(0.242322 - 31.9991i) q^{32} +(-2.62319 + 2.62319i) q^{33} +(-2.34543 - 30.3899i) q^{34} +(0.229552 + 2.33068i) q^{35} +(13.4545 - 28.9540i) q^{36} +(28.2321 - 52.8185i) q^{37} +(-1.47513 - 8.33338i) q^{38} +(-12.7865 + 8.54369i) q^{39} +(-1.18932 - 0.908823i) q^{40} +(-46.7256 - 31.2210i) q^{41} +(23.5367 - 9.17099i) q^{42} +(-25.1836 + 20.6676i) q^{43} +(-9.80181 + 10.9633i) q^{44} +(-0.703991 - 1.31707i) q^{45} +(-42.5313 - 54.1191i) q^{46} +(5.14627 + 12.4242i) q^{47} +(-5.97520 + 14.9982i) q^{48} +(-99.4795 - 41.2058i) q^{49} +(48.0758 - 13.4802i) q^{50} +(-4.46395 + 14.7157i) q^{51} +(-48.7175 + 36.6466i) q^{52} +(4.27149 - 43.3692i) q^{53} +(-24.7401 + 23.7151i) q^{54} +(0.134199 + 0.674666i) q^{55} +(91.1275 - 41.5094i) q^{56} +(-0.832978 + 4.18766i) q^{57} +(0.954890 - 4.32087i) q^{58} +(96.9754 - 29.4172i) q^{59} +(0.392623 + 0.645080i) q^{60} +(57.4420 + 47.1415i) q^{61} +(-18.4908 + 9.38630i) q^{62} +99.9089 q^{63} +(-20.3294 + 60.6854i) q^{64} +2.85152i q^{65} +(6.61592 - 3.35837i) q^{66} +(32.5831 - 39.7026i) q^{67} +(-14.4104 + 59.2327i) q^{68} +(10.0807 + 33.2315i) q^{69} +(1.01073 - 4.57356i) q^{70} +(-62.5563 - 12.4432i) q^{71} +(-43.5573 + 46.6926i) q^{72} +(36.4386 - 7.24810i) q^{73} +(-86.4699 + 82.8875i) q^{74} +(-25.0693 - 2.46911i) q^{75} +(-2.36983 + 16.7591i) q^{76} +(-44.0376 - 13.3587i) q^{77} +(29.6143 - 8.30371i) q^{78} +(-36.5862 + 88.3269i) q^{79} +(1.69681 + 2.46630i) q^{80} +(-50.3943 + 20.8740i) q^{81} +(69.4479 + 88.3692i) q^{82} +(111.195 - 59.4350i) q^{83} +(-50.4417 + 2.82141i) q^{84} +(1.80894 + 2.20420i) q^{85} +(60.7112 - 23.6559i) q^{86} +(-1.24034 + 1.85630i) q^{87} +(25.4422 - 14.7570i) q^{88} +(24.9043 + 37.2719i) q^{89} +(0.520620 + 2.94111i) q^{90} +(-168.240 - 89.9263i) q^{91} +(47.2562 + 129.298i) q^{92} +(10.4117 - 1.02546i) q^{93} +(-2.06960 - 26.8160i) q^{94} +(0.559826 + 0.559826i) q^{95} +(20.6725 - 24.8041i) q^{96} +(-34.9278 - 34.9278i) q^{97} +(163.543 + 140.108i) q^{98} +(29.2041 - 2.87636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{29}{32}\right)$	$-1$

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 $

$2$	−1.90117	−	0.620914i	−0.950587	−	0.310457i
$2$	−1.90117	−	0.620914i	−0.950587	−	0.310457i
$3$	0.779996	+	0.640126i	0.259999	+	0.213375i	0.755357	−	0.655313i	$-0.227463\pi$
$3$	0.779996	+	0.640126i	0.259999	+	0.213375i	−0.495359	+	0.868689i	$0.664963\pi$
$4$	3.22893	+	2.36093i	0.807233	+	0.590233i
$5$	0.179045	−	0.0543127i	0.0358090	−	0.0108625i	−0.272329	−	0.962204i	$-0.587794\pi$
$5$	0.179045	−	0.0543127i	0.0358090	−	0.0108625i	0.308138	+	0.951342i	$0.400294\pi$
$6$	−1.08545	−	1.70130i	−0.180908	−	0.283551i
$7$	−2.44195	+	12.2765i	−0.348850	+	1.75379i	0.264889	+	0.964279i	$0.414665\pi$
$7$	−2.44195	+	12.2765i	−0.348850	+	1.75379i	−0.613739	+	0.789509i	$0.710335\pi$
$8$	−4.67283	−	6.49343i	−0.584103	−	0.811679i
$9$	−1.55718	−	7.82847i	−0.173020	−	0.869831i
$10$	−0.374119	−	0.00791361i	−0.0374119	−	0.000791361i
$11$	−0.360362	+	3.65882i	−0.0327602	+	0.332620i	0.964810	+	0.262949i	$0.0846950\pi$
$11$	−0.360362	+	3.65882i	−0.0327602	+	0.332620i	−0.997570	+	0.0696713i	$0.977805\pi$
$12$	1.00726	+	3.90844i	0.0839383	+	0.325704i
$13$	−4.42408	+	14.5842i	−0.340314	+	1.12187i	0.605143	+	0.796117i	$0.293116\pi$
$13$	−4.42408	+	14.5842i	−0.340314	+	1.12187i	−0.945457	+	0.325748i	$0.894384\pi$
$14$	12.2652	−	21.8236i	0.876088	−	1.55883i
$15$	0.174421	+	0.0722477i	0.0116281	+	0.00481652i
$16$	4.85200	+	15.2466i	0.303250	+	0.952911i
$17$	5.83214	+	14.0800i	0.343067	+	0.828237i	0.997402	+	0.0720325i	$0.0229485\pi$
$17$	5.83214	+	14.0800i	0.343067	+	0.828237i	−0.654335	+	0.756205i	$0.727051\pi$
$18$	−1.90034	+	15.8502i	−0.105574	+	0.880565i
$19$	1.99470	+	3.73182i	0.104984	+	0.196411i	0.928928	−	0.370259i	$-0.120731\pi$
$19$	1.99470	+	3.73182i	0.104984	+	0.196411i	−0.823944	+	0.566671i	$0.808231\pi$
$20$	0.706353	+	0.247341i	0.0353176	+	0.0123671i
$21$	−9.76323	+	8.01248i	−0.464916	+	0.381547i
$22$	2.95693	−	6.73230i	0.134406	−	0.306014i
$23$	28.6157	+	19.1204i	1.24416	+	0.831322i	0.990705	−	0.136025i	$-0.0434328\pi$
$23$	28.6157	+	19.1204i	1.24416	+	0.831322i	0.253456	+	0.967347i	$0.418433\pi$
$24$	0.511831	−	8.05606i	0.0213263	−	0.335669i
$25$	−20.7576	+	13.8698i	−0.830305	+	0.554792i
$26$	17.4665	−	24.9802i	0.671789	−	0.960778i
$27$	8.07753	−	15.1120i	0.299168	−	0.559704i
$28$	−36.8689	+	33.8747i	−1.31675	+	1.20981i
$29$	0.216869	+	2.20191i	0.00747825	+	0.0759279i	0.998199	−	0.0599818i	$-0.0191043\pi$
$29$	0.216869	+	2.20191i	0.00747825	+	0.0759279i	−0.990721	+	0.135910i	$0.956604\pi$
$30$	−0.286746	−	0.245656i	−0.00955820	−	0.00818854i
$31$	7.33155	−	7.33155i	0.236502	−	0.236502i	−0.578898	−	0.815400i	$-0.696517\pi$
$31$	7.33155	−	7.33155i	0.236502	−	0.236502i	0.815400	+	0.578898i	$0.196517\pi$
$32$	0.242322	−	31.9991i	0.00757255	−	0.999971i
$33$	−2.62319	+	2.62319i	−0.0794906	+	0.0794906i
$34$	−2.34543	−	30.3899i	−0.0689832	−	0.893819i
$35$	0.229552	+	2.33068i	0.00655862	+	0.0665908i
$36$	13.4545	−	28.9540i	0.373735	−	0.804278i
$37$	28.2321	−	52.8185i	0.763029	−	1.42753i	−0.136488	−	0.990642i	$-0.543582\pi$
$37$	28.2321	−	52.8185i	0.763029	−	1.42753i	0.899517	−	0.436885i	$-0.143918\pi$
$38$	−1.47513	−	8.33338i	−0.0388193	−	0.219299i
$39$	−12.7865	+	8.54369i	−0.327860	+	0.219069i
$40$	−1.18932	−	0.908823i	−0.0297331	−	0.0227206i
$41$	−46.7256	−	31.2210i	−1.13965	−	0.761488i	−0.165235	−	0.986254i	$-0.552838\pi$
$41$	−46.7256	−	31.2210i	−1.13965	−	0.761488i	−0.974413	+	0.224766i	$0.927838\pi$
$42$	23.5367	−	9.17099i	0.560397	−	0.218357i
$43$	−25.1836	+	20.6676i	−0.585664	+	0.480642i	−0.879944	−	0.475077i	$-0.842420\pi$
$43$	−25.1836	+	20.6676i	−0.585664	+	0.480642i	0.294280	+	0.955719i	$0.404920\pi$
$44$	−9.80181	+	10.9633i	−0.222769	+	0.249166i
$45$	−0.703991	−	1.31707i	−0.0156442	−	0.0292683i
$46$	−42.5313	−	54.1191i	−0.924594	−	1.17650i
$47$	5.14627	+	12.4242i	0.109495	+	0.264345i	0.969124	−	0.246575i	$-0.0793051\pi$
$47$	5.14627	+	12.4242i	0.109495	+	0.264345i	−0.859629	+	0.510919i	$0.829305\pi$
$48$	−5.97520	+	14.9982i	−0.124483	+	0.312462i
$49$	−99.4795	−	41.2058i	−2.03019	−	0.840934i
$50$	48.0758	−	13.4802i	0.961517	−	0.269604i
$51$	−4.46395	+	14.7157i	−0.0875285	+	0.288543i
$52$	−48.7175	+	36.6466i	−0.936875	+	0.704742i
$53$	4.27149	−	43.3692i	0.0805942	−	0.818286i	−0.866893	−	0.498494i	$-0.833887\pi$
$53$	4.27149	−	43.3692i	0.0805942	−	0.818286i	0.947488	−	0.319793i	$-0.103613\pi$
$54$	−24.7401	+	23.7151i	−0.458149	+	0.439168i
$55$	0.134199	+	0.674666i	0.00243999	+	0.0122667i
$56$	91.1275	−	41.5094i	1.62728	−	0.741239i
$57$	−0.832978	+	4.18766i	−0.0146137	+	0.0734678i
$58$	0.954890	−	4.32087i	0.0164636	−	0.0744978i
$59$	96.9754	−	29.4172i	1.64365	−	0.498596i	0.673112	−	0.739540i	$-0.264957\pi$
$59$	96.9754	−	29.4172i	1.64365	−	0.498596i	0.970539	+	0.240944i	$0.0774570\pi$
$60$	0.392623	+	0.645080i	0.00654372	+	0.0107513i
$61$	57.4420	+	47.1415i	0.941673	+	0.772811i	0.973972	−	0.226667i	$-0.0727831\pi$
$61$	57.4420	+	47.1415i	0.941673	+	0.772811i	−0.0322995	+	0.999478i	$0.510283\pi$
$62$	−18.4908	+	9.38630i	−0.298239	+	0.151392i
$63$	99.9089			1.58586
$64$	−20.3294	+	60.6854i	−0.317647	+	0.948209i
$65$			2.85152i			0.0438695i
$66$	6.61592	−	3.35837i	0.100241	−	0.0508843i
$67$	32.5831	−	39.7026i	0.486315	−	0.592576i	−0.470816	−	0.882231i	$-0.656041\pi$
$67$	32.5831	−	39.7026i	0.486315	−	0.592576i	0.957131	+	0.289655i	$0.0935405\pi$
$68$	−14.4104	+	59.2327i	−0.211918	+	0.871070i
$69$	10.0807	+	33.2315i	0.146097	+	0.481616i
$70$	1.01073	−	4.57356i	0.0144390	−	0.0653365i
$71$	−62.5563	−	12.4432i	−0.881074	−	0.175257i	−0.266234	−	0.963908i	$-0.585779\pi$
$71$	−62.5563	−	12.4432i	−0.881074	−	0.175257i	−0.614840	+	0.788652i	$0.710779\pi$
$72$	−43.5573	+	46.6926i	−0.604962	+	0.648508i
$73$	36.4386	−	7.24810i	0.499159	−	0.0992890i	0.0609116	−	0.998143i	$-0.480599\pi$
$73$	36.4386	−	7.24810i	0.499159	−	0.0992890i	0.438248	+	0.898854i	$0.355599\pi$
$74$	−86.4699	+	82.8875i	−1.16851	+	1.12010i
$75$	−25.0693	−	2.46911i	−0.334257	−	0.0329215i
$76$	−2.36983	+	16.7591i	−0.0311819	+	0.220515i
$77$	−44.0376	−	13.3587i	−0.571917	−	0.173489i
$78$	29.6143	−	8.30371i	0.379671	−	0.106458i
$79$	−36.5862	+	88.3269i	−0.463116	+	1.11806i	0.503995	+	0.863707i	$0.331863\pi$
$79$	−36.5862	+	88.3269i	−0.463116	+	1.11806i	−0.967111	+	0.254355i	$0.918137\pi$
$80$	1.69681	+	2.46630i	0.0212101	+	0.0308287i
$81$	−50.3943	+	20.8740i	−0.622152	+	0.257704i
$82$	69.4479	+	88.3692i	0.846925	+	1.07767i
$83$	111.195	−	59.4350i	1.33970	−	0.716084i	0.363221	−	0.931703i	$-0.381677\pi$
$83$	111.195	−	59.4350i	1.33970	−	0.716084i	0.976478	+	0.215619i	$0.0691770\pi$
$84$	−50.4417	+	2.82141i	−0.600497	+	0.0335882i
$85$	1.80894	+	2.20420i	0.0212816	+	0.0259318i
$86$	60.7112	−	23.6559i	0.705944	−	0.275069i
$87$	−1.24034	+	1.85630i	−0.0142568	+	0.0213368i
$88$	25.4422	−	14.7570i	0.289116	−	0.167694i
$89$	24.9043	+	37.2719i	0.279824	+	0.418786i	0.944583	−	0.328271i	$-0.106466\pi$
$89$	24.9043	+	37.2719i	0.279824	+	0.418786i	−0.664760	+	0.747057i	$0.731466\pi$
$90$	0.520620	+	2.94111i	0.00578467	+	0.0326790i
$91$	−168.240	−	89.9263i	−1.84879	−	0.988201i
$92$	47.2562	+	129.298i	0.513654	+	1.40542i
$93$	10.4117	−	1.02546i	0.111954	−	0.0110265i
$94$	−2.06960	−	26.8160i	−0.0220170	−	0.285276i
$95$	0.559826	+	0.559826i	0.00589290	+	0.00589290i
$96$	20.6725	−	24.8041i	0.215338	−	0.258376i
$97$	−34.9278	−	34.9278i	−0.360080	−	0.360080i	0.503762	−	0.863842i	$-0.331949\pi$
$97$	−34.9278	−	34.9278i	−0.360080	−	0.360080i	−0.863842	+	0.503762i	$0.831949\pi$
$98$	163.543	+	140.108i	1.66880	+	1.42967i
$99$	29.2041	−	2.87636i	0.294991	−	0.0290541i
$100$	−99.7707	−	4.22271i	−0.997707	−	0.0422271i
$101$	−80.9960	−	43.2933i	−0.801941	−	0.428646i	0.0188871	−	0.999822i	$-0.493988\pi$
$101$	−80.9960	−	43.2933i	−0.801941	−	0.428646i	−0.820828	+	0.571175i	$0.806488\pi$
$102$	17.6239	−	25.2053i	0.172784	−	0.247111i
$103$	87.6953	+	131.245i	0.851411	+	1.27423i	0.959960	+	0.280136i	$0.0903794\pi$
$103$	87.6953	+	131.245i	0.851411	+	1.27423i	−0.108549	+	0.994091i	$0.534621\pi$
$104$	115.375	−	39.4222i	1.10937	−	0.379059i
$105$	−1.31288	+	1.96486i	−0.0125036	+	0.0187130i
$106$	−35.0494	+	79.8002i	−0.330655	+	0.752832i
$107$	−87.1884	−	106.239i	−0.814845	−	0.992892i	−0.999948	−	0.0101728i	$-0.996762\pi$
$107$	−87.1884	−	106.239i	−0.814845	−	0.992892i	0.185103	−	0.982719i	$-0.440738\pi$
$108$	61.7602	−	29.7251i	0.571854	−	0.275232i
$109$	118.891	−	63.5487i	1.09075	−	0.583016i	0.174917	−	0.984583i	$-0.444034\pi$
$109$	118.891	−	63.5487i	1.09075	−	0.583016i	0.915829	+	0.401567i	$0.131534\pi$
$110$	0.163773	−	1.36598i	0.00148885	−	0.0124180i
$111$	55.8314	−	23.1261i	0.502986	−	0.208344i
$112$	−199.023	+	22.3342i	−1.77699	+	0.199413i
$113$	20.8142	−	50.2500i	0.184197	−	0.444690i	−0.804627	−	0.593781i	$-0.797635\pi$
$113$	20.8142	−	50.2500i	0.184197	−	0.444690i	0.988824	+	0.149091i	$0.0476346\pi$
$114$	4.18382	−	7.44427i	0.0367001	−	0.0653006i
$115$	6.16198	+	1.86922i	0.0535824	+	0.0162541i
$116$	−4.49830	+	7.62183i	−0.0387785	+	0.0657054i
$117$	121.062	+	11.9235i	1.03471	+	0.101910i
$118$	−202.633	−	4.28622i	−1.71723	−	0.0363239i
$119$	−187.095	+	37.2156i	−1.57223	+	0.312736i
$120$	−0.345905	−	1.47020i	−0.00288254	−	0.0122516i
$121$	105.418	+	20.9689i	0.871222	+	0.173297i
$122$	−79.9366	−	125.291i	−0.655218	−	1.02697i
$123$	−16.4604	−	54.2626i	−0.133824	−	0.441159i
$124$	40.9824	−	6.36378i	0.330503	−	0.0513208i
$125$	−5.93064	+	7.22651i	−0.0474451	+	0.0578121i
$126$	−189.944	−	62.0349i	−1.50749	−	0.492340i
$127$			28.4528i			0.224038i	0.993706	+	0.112019i	$0.0357317\pi$
$127$			28.4528i			0.224038i	−0.993706	+	0.112019i	$0.964268\pi$
$128$	76.3301	−	102.751i	0.596329	−	0.802740i
$129$	−32.8730			−0.254829
$130$	1.77055	−	5.42124i	0.0136196	−	0.0417018i
$131$	0.389433	+	0.319599i	0.00297277	+	0.00243969i	0.635878	−	0.771789i	$-0.280638\pi$
$131$	0.389433	+	0.319599i	0.00297277	+	0.00243969i	−0.632906	+	0.774229i	$0.718138\pi$
$132$	−14.6633	+	2.27693i	−0.111085	+	0.0172494i
$133$	−50.6847	+	15.3750i	−0.381088	+	0.115602i
$134$	−86.5981	+	55.2503i	−0.646254	+	0.412316i
$135$	0.625468	−	3.14444i	0.00463310	−	0.0232921i
$136$	64.1752	−	103.664i	0.471876	−	0.762236i
$137$	5.31134	+	26.7019i	0.0387689	+	0.194905i	0.995316	−	0.0966726i	$-0.0308200\pi$
$137$	5.31134	+	26.7019i	0.0387689	+	0.194905i	−0.956547	+	0.291577i	$0.905820\pi$
$138$	1.46880	−	69.4382i	0.0106435	−	0.503175i
$139$	−3.02375	+	30.7006i	−0.0217536	+	0.220868i	0.978162	+	0.207846i	$0.0666452\pi$
$139$	−3.02375	+	30.7006i	−0.0217536	+	0.220868i	−0.999915	+	0.0130220i	$0.995855\pi$
$140$	−4.76136	+	8.06755i	−0.0340097	+	0.0576254i
$141$	−3.93899	+	12.9851i	−0.0279361	+	0.0920929i
$142$	111.204	+	62.4988i	0.783129	+	0.440132i
$143$	−51.7669	−	21.4425i	−0.362006	−	0.149948i
$144$	111.802	−	61.7254i	0.776403	−	0.428649i
$145$	0.158421	+	0.382462i	0.00109256	+	0.00263767i
$146$	−73.7767	−	8.84537i	−0.505320	−	0.0605847i
$147$	−51.2168	−	95.8198i	−0.348413	−	0.651836i
$148$	215.860	−	103.893i	1.45852	−	0.701982i
$149$	166.599	−	136.725i	1.11812	−	0.917615i	0.120937	−	0.992660i	$-0.461410\pi$
$149$	166.599	−	136.725i	1.11812	−	0.917615i	0.997180	+	0.0750449i	$0.0239100\pi$
$150$	46.1280	+	20.2601i	0.307520	+	0.135067i
$151$	−5.44391	−	3.63751i	−0.0360524	−	0.0240894i	0.537413	−	0.843319i	$-0.319401\pi$
$151$	−5.44391	−	3.63751i	−0.0360524	−	0.0240894i	−0.573466	+	0.819229i	$0.694401\pi$
$152$	14.9114	−	30.3906i	0.0981016	−	0.199938i
$153$	101.143	−	67.5819i	0.661068	−	0.441712i
$154$	75.4286	+	52.7407i	0.489796	+	0.342472i
$155$	0.914481	−	1.71087i	0.00589988	−	0.0110379i
$156$	−61.4579	−	2.60116i	−0.393961	−	0.0166741i
$157$	16.8862	+	171.448i	0.107555	+	1.09203i	0.885801	+	0.464066i	$0.153610\pi$
$157$	16.8862	+	171.448i	0.107555	+	1.09203i	−0.778246	+	0.627960i	$0.783890\pi$
$158$	124.400	−	145.208i	0.787343	−	0.919038i
$159$	31.0935	−	31.0935i	0.195557	−	0.195557i
$160$	−1.69457	−	5.74244i	−0.0105911	−	0.0358902i
$161$	−304.610	+	304.610i	−1.89199	+	1.89199i
$162$	108.769	−	8.39460i	0.671416	−	0.0518185i
$163$	23.4436	+	238.027i	0.143826	+	1.46029i	0.748139	+	0.663542i	$0.230948\pi$
$163$	23.4436	+	238.027i	0.143826	+	1.46029i	−0.604313	+	0.796747i	$0.706552\pi$
$164$	−77.1629	−	211.126i	−0.470506	−	1.28736i
$165$	−0.327196	+	0.612142i	−0.00198301	+	0.00370995i
$166$	−248.305	+	43.9537i	−1.49581	+	0.264781i
$167$	−163.315	+	109.124i	−0.977936	+	0.653436i	−0.938316	−	0.345779i	$-0.887615\pi$
$167$	−163.315	+	109.124i	−0.977936	+	0.653436i	−0.0396201	+	0.999215i	$0.512615\pi$
$168$	97.6504	+	25.9560i	0.581252	+	0.154500i
$169$	−52.6094	−	35.1525i	−0.311298	−	0.208003i
$170$	−2.07049	−	5.31377i	−0.0121794	−	0.0312574i
$171$	26.1083	−	21.4266i	0.152680	−	0.125302i
$172$	−130.111	+	7.27762i	−0.756458	+	0.0423118i
$173$	115.663	+	216.391i	0.668574	+	1.25081i	0.956100	+	0.293042i	$0.0946674\pi$
$173$	115.663	+	216.391i	0.668574	+	1.25081i	−0.287525	+	0.957773i	$0.592833\pi$
$174$	3.51072	−	2.75901i	0.0201765	−	0.0158564i
$175$	−119.584	−	288.701i	−0.683336	−	1.64972i
$176$	−57.5330	+	12.2583i	−0.326892	+	0.0696494i
$177$	94.4712	+	39.1313i	0.533736	+	0.221081i
$178$	−24.2048	−	86.3239i	−0.135982	−	0.484966i
$179$	−14.0354	+	46.2687i	−0.0784103	+	0.258484i	−0.987378	−	0.158383i	$-0.949372\pi$
$179$	−14.0354	+	46.2687i	−0.0784103	+	0.258484i	0.908967	+	0.416867i	$0.136872\pi$
$180$	0.836385	−	5.91482i	0.00464659	−	0.0328601i
$181$	16.7722	−	170.291i	0.0926641	−	0.940835i	−0.830651	−	0.556793i	$-0.812032\pi$
$181$	16.7722	−	170.291i	0.0926641	−	0.940835i	0.923316	−	0.384042i	$-0.125468\pi$
$182$	264.018	+	275.428i	1.45065	+	1.51334i
$183$	14.6281	+	73.5403i	0.0799349	+	0.401860i
$184$	−9.55916	−	275.161i	−0.0519520	−	1.49544i
$185$	2.18610	−	10.9902i	0.0118167	−	0.0594068i
$186$	−20.4312	−	4.51519i	−0.109845	−	0.0242752i
$187$	−53.6180	+	16.2648i	−0.286727	+	0.0869778i
$188$	−12.7157	+	52.2669i	−0.0676369	+	0.278015i
$189$	165.798	+	136.067i	0.877236	+	0.719929i
$190$	−0.716723	−	1.41193i	−0.00377223	−	0.00743121i
$191$	2.11553			0.0110761			0.00553803	−	0.999985i	$-0.498237\pi$
$191$	2.11553			0.0110761			0.00553803	+	0.999985i	$0.498237\pi$
$192$	−54.7032	+	34.3210i	−0.284912	+	0.178755i
$193$		−	5.67407i		−	0.0293993i	−0.999892	−	0.0146997i	$-0.995321\pi$
$193$		−	5.67407i		−	0.0293993i	0.999892	−	0.0146997i	$-0.00467921\pi$
$194$	44.7167	+	88.0910i	0.230498	+	0.454077i
$195$	−1.82533	+	2.22418i	−0.00936069	+	0.0114060i
$196$	−223.929	−	367.915i	−1.14249	−	1.87712i
$197$	43.2311	+	142.514i	0.219447	+	0.723420i	0.995670	+	0.0929611i	$0.0296332\pi$
$197$	43.2311	+	142.514i	0.219447	+	0.723420i	−0.776223	+	0.630459i	$0.782867\pi$
$198$	−57.3081	−	12.6648i	−0.289435	−	0.0639637i
$199$	164.311	+	32.6835i	0.825685	+	0.164239i	0.589807	−	0.807544i	$-0.299204\pi$
$199$	164.311	+	32.6835i	0.825685	+	0.164239i	0.235877	+	0.971783i	$0.424204\pi$
$200$	187.060	+	69.9771i	0.935298	+	0.349886i
$201$	50.8294	−	10.1106i	0.252883	−	0.0503015i
$202$	127.106	+	132.600i	0.629239	+	0.656434i
$203$	−27.5613	−	2.71456i	−0.135770	−	0.0133722i
$204$	−49.1565	+	36.9768i	−0.240963	+	0.181259i
$205$	−10.0617	−	3.05218i	−0.0490813	−	0.0148887i
$206$	−85.2321	−	303.972i	−0.413748	−	1.47559i
$207$	105.124	−	253.791i	0.507844	−	1.22604i
$208$	−243.825	+	3.31059i	−1.17224	+	0.0159163i
$209$	−14.3729	+	5.95344i	−0.0687697	+	0.0284853i
$210$	3.71602	−	2.92036i	0.0176953	−	0.0139065i
$211$	−131.917	+	70.5111i	−0.625199	+	0.334176i	−0.753390	−	0.657574i	$-0.771583\pi$
$211$	−131.917	+	70.5111i	−0.625199	+	0.334176i	0.128191	+	0.991749i	$0.459083\pi$
$212$	116.184	−	129.951i	0.548038	−	0.612978i
$213$	−40.8284	−	49.7496i	−0.191683	−	0.233566i
$214$	99.7949	+	256.116i	0.466331	+	1.19681i
$215$	−3.38648	+	5.06822i	−0.0157511	+	0.0235731i
$216$	−135.874	+	18.1648i	−0.629045	+	0.0840965i
$217$	72.1026	+	107.909i	0.332270	+	0.497277i
$218$	−265.491	+	46.9960i	−1.21785	+	0.215578i
$219$	33.0617	+	17.6718i	0.150967	+	0.0806934i
$220$	−1.15952	+	2.49529i	−0.00527055	+	0.0113422i
$221$	−231.149	+	22.7661i	−1.04592	+	0.103014i
$222$	−120.505	+	9.30031i	−0.542814	+	0.0418933i
$223$	63.4345	+	63.4345i	0.284460	+	0.284460i	0.834885	−	0.550425i	$-0.185534\pi$
$223$	63.4345	+	63.4345i	0.284460	+	0.284460i	−0.550425	+	0.834885i	$0.685534\pi$
$224$	392.245	+	81.1150i	1.75110	+	0.362121i
$225$	140.903	+	140.903i	0.626235	+	0.626235i
$226$	−70.7724	+	82.6102i	−0.313152	+	0.365532i
$227$	−25.3446	+	2.49623i	−0.111650	+	0.0109966i	−0.153688	−	0.988119i	$-0.549115\pi$
$227$	−25.3446	+	2.49623i	−0.111650	+	0.0109966i	0.0420377	+	0.999116i	$0.486615\pi$
$228$	−12.5764	+	11.5551i	−0.0551597	+	0.0506802i
$229$	−250.219	−	133.745i	−1.09266	−	0.584038i	−0.176276	−	0.984341i	$-0.556405\pi$
$229$	−250.219	−	133.745i	−1.09266	−	0.584038i	−0.916383	+	0.400303i	$0.868905\pi$
$230$	−10.5544	−	7.37977i	−0.0458886	−	0.0320859i
$231$	−25.7979	−	38.6093i	−0.111679	−	0.167140i
$232$	13.2846	−	11.6974i	0.0572610	−	0.0504197i
$233$	23.6295	−	35.3640i	0.101414	−	0.151777i	−0.777292	−	0.629140i	$-0.783407\pi$
$233$	23.6295	−	35.3640i	0.101414	−	0.151777i	0.878706	+	0.477363i	$0.158407\pi$
$234$	−222.756	−	97.8375i	−0.951947	−	0.418109i
$235$	1.59621	+	1.94498i	0.00679237	+	0.00827652i
$236$	382.579	+	133.966i	1.62110	+	0.567654i
$237$	−85.0775	+	45.4749i	−0.358977	+	0.191877i
$238$	378.809	+	45.4168i	1.59163	+	0.190827i
$239$	−254.459	+	105.400i	−1.06468	+	0.441006i	−0.845111	−	0.534590i	$-0.820466\pi$
$239$	−254.459	+	105.400i	−1.06468	+	0.441006i	−0.219572	+	0.975596i	$0.570466\pi$
$240$	−0.255238	+	3.00988i	−0.00106349	+	0.0125411i
$241$	136.120	−	328.624i	0.564815	−	1.36358i	−0.341061	−	0.940041i	$-0.610786\pi$
$241$	136.120	−	328.624i	0.564815	−	1.36358i	0.905876	−	0.423543i	$-0.139214\pi$
$242$	−187.398	−	105.321i	−0.774372	−	0.435211i
$243$	−200.247	−	60.7442i	−0.824060	−	0.249976i
$244$	74.1786	+	287.833i	0.304011	+	1.17964i
$245$	−20.0493	−	1.97468i	−0.0818339	−	0.00805994i
$246$	−2.39835	+	113.383i	−0.00974939	+	0.460907i
$247$	−63.2505	+	12.5813i	−0.256075	+	0.0509364i
$248$	−81.8660	−	13.3479i	−0.330105	−	0.0538221i
$249$	124.778	+	24.8198i	0.501115	+	0.0996779i
$250$	15.7622	−	10.0564i	0.0630489	−	0.0402257i
$251$	−51.6275	−	170.193i	−0.205687	−	0.678060i	−0.997714	−	0.0675739i	$-0.978474\pi$
$251$	−51.6275	−	170.193i	−0.205687	−	0.678060i	0.792027	−	0.610486i	$-0.209026\pi$
$252$	322.599	+	235.878i	1.28015	+	0.936025i
$253$	−80.2702	+	97.8095i	−0.317273	+	0.386599i
$254$	17.6667	−	54.0937i	0.0695541	−	0.212967i
$255$			2.87722i			0.0112832i
$256$	−208.916	+	147.953i	−0.816079	+	0.577940i
$257$	−136.948			−0.532870			−0.266435	−	0.963853i	$-0.585846\pi$
$257$	−136.948			−0.532870			−0.266435	+	0.963853i	$0.585846\pi$
$258$	62.4973	+	20.4113i	0.242237	+	0.0791135i
$259$	579.486	+	475.572i	2.23740	+	1.83618i
$260$	−6.73225	+	9.20736i	−0.0258933	+	0.0354129i
$261$	16.8999	−	5.12652i	0.0647505	−	0.0196419i
$262$	−0.541937	−	0.849419i	−0.00206846	−	0.00324206i
$263$	−81.0656	+	407.544i	−0.308234	+	1.54960i	0.447236	+	0.894416i	$0.352408\pi$
$263$	−81.0656	+	407.544i	−0.308234	+	1.54960i	−0.755470	+	0.655183i	$0.772592\pi$
$264$	29.2912	+	4.77580i	0.110952	+	0.0180901i
$265$	−1.59071	−	7.99703i	−0.00600267	−	0.0301775i
$266$	105.907	+	2.24021i	0.398147	+	0.00842185i
$267$	−4.43348	+	45.0139i	−0.0166048	+	0.168591i
$268$	198.944	−	51.2705i	0.742328	−	0.191308i
$269$	−6.91271	+	22.7882i	−0.0256978	+	0.0847144i	−0.968851	−	0.247643i	$-0.920344\pi$
$269$	−6.91271	+	22.7882i	−0.0256978	+	0.0847144i	0.943154	+	0.332357i	$0.107844\pi$
$270$	−3.14155	+	5.58977i	−0.0116354	+	0.0207028i
$271$	219.775	+	91.0336i	0.810977	+	0.335918i	0.749344	−	0.662181i	$-0.230369\pi$
$271$	219.775	+	91.0336i	0.810977	+	0.335918i	0.0616330	+	0.998099i	$0.480369\pi$
$272$	−186.375	+	157.236i	−0.685201	+	0.578075i
$273$	−73.6626	−	177.837i	−0.269826	−	0.651419i
$274$	6.48181	−	54.0629i	0.0236562	−	0.197310i
$275$	−43.2669	−	80.9466i	−0.157334	−	0.294351i
$276$	−45.9076	+	131.102i	−0.166332	+	0.475008i
$277$	198.881	−	163.217i	0.717982	−	0.589233i	−0.202842	−	0.979212i	$-0.565018\pi$
$277$	198.881	−	163.217i	0.717982	−	0.589233i	0.920824	+	0.389979i	$0.127518\pi$
$278$	24.8111	−	56.4897i	0.0892486	−	0.203200i
$279$	−68.8114	−	45.9783i	−0.246636	−	0.164797i
$280$	14.0614	−	12.3814i	0.0502194	−	0.0442194i
$281$	405.955	−	271.251i	1.44468	−	0.965304i	0.447194	−	0.894437i	$-0.352423\pi$
$281$	405.955	−	271.251i	1.44468	−	0.965304i	0.997486	−	0.0708675i	$-0.0225768\pi$
$282$	15.5513	−	22.2412i	0.0551466	−	0.0788694i
$283$	179.652	−	336.105i	0.634812	−	1.18765i	−0.334635	−	0.942348i	$-0.608613\pi$
$283$	179.652	−	336.105i	0.634812	−	1.18765i	0.969447	−	0.245302i	$-0.0788871\pi$
$284$	−172.612	−	187.869i	−0.607790	−	0.661512i
$285$	0.0783028	+	0.795022i	0.000274747	+	0.00278955i
$286$	85.1039	+	72.9088i	0.297566	+	0.254926i
$287$	497.387	−	497.387i	1.73305	−	1.73305i
$288$	−250.881	+	47.9313i	−0.871116	+	0.166428i
$289$	40.1205	−	40.1205i	0.138825	−	0.138825i
$290$	−0.0637099	−	0.825493i	−0.000219689	−	0.00284653i
$291$	−4.88535	−	49.6018i	−0.0167881	−	0.170453i
$292$	134.770	+	62.6256i	0.461541	+	0.214471i
$293$	−155.056	+	290.090i	−0.529202	+	0.990067i	0.465281	+	0.885163i	$0.345953\pi$
$293$	−155.056	+	290.090i	−0.529202	+	0.990067i	−0.994482	+	0.104904i	$0.966547\pi$
$294$	37.8761	+	213.971i	0.128830	+	0.727794i
$295$	15.7652	−	10.5340i	0.0534415	−	0.0357085i
$296$	−474.897	+	63.4886i	−1.60438	+	0.214488i
$297$	52.3813	+	35.0000i	0.176368	+	0.117845i
$298$	−401.629	+	156.494i	−1.34775	+	0.525146i
$299$	−405.455	+	332.748i	−1.35604	+	1.11287i
$300$	−75.1177	−	67.1595i	−0.250392	−	0.223865i
$301$	−192.229	−	359.636i	−0.638635	−	1.19480i
$302$	8.09125	+	10.2957i	0.0267922	+	0.0340918i
$303$	−35.4634	−	85.6163i	−0.117041	−	0.282562i
$304$	−47.2192	+	48.5191i	−0.155326	+	0.159602i
$305$	12.8451	+	5.32061i	0.0421150	+	0.0174446i
$306$	−234.254	+	65.6836i	−0.765536	+	0.214652i
$307$	8.75738	−	28.8692i	0.0285257	−	0.0940365i	−0.941522	−	0.336952i	$-0.890604\pi$
$307$	8.75738	−	28.8692i	0.0285257	−	0.0940365i	0.970047	+	0.242916i	$0.0781039\pi$
$308$	−110.655	−	147.104i	−0.359271	−	0.477610i
$309$	−15.6116	+	158.507i	−0.0505229	+	0.512968i
$310$	−2.80090	+	2.68486i	−0.00903515	+	0.00866083i
$311$	−112.679	−	566.474i	−0.362311	−	1.82146i	−0.545176	−	0.838322i	$-0.683537\pi$
$311$	−112.679	−	566.474i	−0.362311	−	1.82146i	0.182865	−	0.983138i	$-0.441463\pi$
$312$	115.227	+	43.1053i	0.369318	+	0.138158i
$313$	−51.1265	+	257.030i	−0.163343	+	0.821183i	0.809033	+	0.587763i	$0.199991\pi$
$313$	−51.1265	+	257.030i	−0.163343	+	0.821183i	−0.972376	+	0.233419i	$0.925009\pi$
$314$	74.3510	−	336.438i	0.236787	−	1.07146i
$315$	17.8882	−	5.42632i	0.0567879	−	0.0172264i
$316$	−326.668	+	198.824i	−1.03376	+	0.629190i
$317$	−279.950	−	229.749i	−0.883123	−	0.724760i	0.0791454	−	0.996863i	$-0.474781\pi$
$317$	−279.950	−	229.749i	−0.883123	−	0.724760i	−0.962268	+	0.272103i	$0.912281\pi$
$318$	−78.4206	+	39.8078i	−0.246606	+	0.125182i
$319$	−8.13454			−0.0255001
$320$	−0.343885	+	11.9696i	−0.00107464	+	0.0374049i
$321$		−	138.678i		−	0.432019i
$322$	768.253	−	389.980i	2.38588	−	1.21112i
$323$	−40.9108	+	49.8499i	−0.126659	+	0.154334i
$324$	−212.002	−	51.5768i	−0.654327	−	0.159188i
$325$	−110.447	−	364.096i	−0.339838	−	1.12029i
$326$	103.224	−	467.087i	0.316638	−	1.43278i
$327$	133.414	+	26.5377i	0.407994	+	0.0811550i
$328$	15.6088	+	449.300i	0.0475878	+	1.36982i
$329$	−165.093	+	32.8390i	−0.501802	+	0.0998146i
$330$	1.00214	−	0.960627i	0.00303680	−	0.00291099i
$331$	−68.8846	−	6.78454i	−0.208111	−	0.0204971i	−0.00657541	−	0.999978i	$-0.502093\pi$
$331$	−68.8846	−	6.78454i	−0.208111	−	0.0204971i	−0.201535	+	0.979481i	$0.564593\pi$
$332$	499.363	+	70.6124i	1.50411	+	0.212688i
$333$	−457.451	−	138.766i	−1.37373	−	0.416715i
$334$	378.248	−	106.059i	1.13248	−	0.317541i
$335$	3.67748	−	8.87823i	0.0109776	−	0.0265022i
$336$	−169.534	−	109.979i	−0.504566	−	0.327320i
$337$	−134.964	+	55.9038i	−0.400486	+	0.165887i	−0.573830	−	0.818975i	$-0.694543\pi$
$337$	−134.964	+	55.9038i	−0.400486	+	0.165887i	0.173344	+	0.984861i	$0.444543\pi$
$338$	78.1930	+	99.4969i	0.231340	+	0.294369i
$339$	48.4014	−	25.8711i	0.142777	−	0.0763159i
$340$	0.636977	+	11.3880i	0.00187346	+	0.0334941i
$341$	24.1828	+	29.4669i	0.0709174	+	0.0864131i
$342$	−62.9406	+	24.5246i	−0.184037	+	0.0717094i
$343$	408.037	−	610.670i	1.18961	−	1.78038i
$344$	251.882	+	66.9516i	0.732216	+	0.194627i
$345$	3.60979	+	5.40243i	0.0104632	+	0.0156592i
$346$	−85.5361	−	483.214i	−0.247214	−	1.39657i
$347$	158.866	+	84.9158i	0.457828	+	0.244714i	0.684154	−	0.729337i	$-0.260172\pi$
$347$	158.866	+	84.9158i	0.457828	+	0.244714i	−0.226326	+	0.974052i	$0.572672\pi$
$348$	−8.38759	+	3.06551i	−0.0241023	+	0.00880895i
$349$	658.144	−	64.8215i	1.88580	−	0.185735i	0.911547	−	0.411196i	$-0.134889\pi$
$349$	658.144	−	64.8215i	1.88580	−	0.185735i	0.974252	+	0.225461i	$0.0723887\pi$
$350$	48.0913	+	623.122i	0.137404	+	1.78035i
$351$	184.661	+	184.661i	0.526101	+	0.526101i
$352$	116.992	+	12.4179i	0.332362	+	0.0352781i
$353$	−47.8607	−	47.8607i	−0.135583	−	0.135583i	0.636058	−	0.771641i	$-0.280564\pi$
$353$	−47.8607	−	47.8607i	−0.135583	−	0.135583i	−0.771641	+	0.636058i	$0.780564\pi$
$354$	−155.309	−	133.054i	−0.438726	−	0.375858i
$355$	−11.8762	+	1.16971i	−0.0334541	+	0.00329494i
$356$	−7.58221	+	179.146i	−0.0212983	+	0.503219i
$357$	−169.756	−	90.7367i	−0.475508	−	0.254164i
$358$	55.4127	−	79.2500i	0.154784	−	0.221369i
$359$	−256.281	−	383.552i	−0.713875	−	1.06839i	−0.994101	−	0.108455i	$-0.965410\pi$
$359$	−256.281	−	383.552i	−0.713875	−	1.06839i	0.280226	−	0.959934i	$-0.409590\pi$
$360$	−5.26271	+	10.7258i	−0.0146186	+	0.0297938i
$361$	190.613	−	285.273i	0.528014	−	0.790229i
$362$	−137.623	+	313.339i	−0.380174	+	0.865577i
$363$	68.8028	+	83.8365i	0.189539	+	0.230954i
$364$	−330.926	−	687.570i	−0.909138	−	1.88893i
$365$	6.13049	−	3.27682i	0.0167959	−	0.00897758i
$366$	17.8517	−	148.896i	0.0487751	−	0.406819i
$367$	−565.788	+	234.357i	−1.54166	+	0.638575i	−0.981784	−	0.190003i	$-0.939150\pi$
$367$	−565.788	+	234.357i	−1.54166	+	0.638575i	−0.559873	+	0.828578i	$0.689150\pi$
$368$	−152.677	+	529.064i	−0.414884	+	1.43767i
$369$	−171.653	+	414.407i	−0.465184	+	1.12305i
$370$	−10.9802	+	19.5370i	−0.0296761	+	0.0528027i
$371$	521.991	+	158.344i	1.40699	+	0.426804i
$372$	36.0397	+	21.2702i	0.0968810	+	0.0571779i
$373$	−571.109	−	56.2493i	−1.53112	−	0.150802i	−0.702935	−	0.711254i	$-0.748128\pi$
$373$	−571.109	−	56.2493i	−1.53112	−	0.150802i	−0.828187	+	0.560451i	$0.810628\pi$
$374$	112.036	+	2.36986i	0.299562	+	0.00633653i
$375$	−9.25176	+	1.84029i	−0.0246714	+	0.00490744i
$376$	56.6281	−	91.4731i	0.150607	−	0.243280i
$377$	−33.0726	−	6.57856i	−0.0877258	−	0.0174497i
$378$	−230.725	−	361.633i	−0.610383	−	0.956700i
$379$	174.074	+	573.846i	0.459299	+	1.51410i	0.814975	+	0.579496i	$0.196750\pi$
$379$	174.074	+	573.846i	0.459299	+	1.51410i	−0.355677	+	0.934609i	$0.615750\pi$
$380$	0.485928	+	3.12935i	0.00127876	+	0.00823513i
$381$	−18.2134	+	22.1931i	−0.0478042	+	0.0582495i
$382$	−4.02199	−	1.31356i	−0.0105288	−	0.00343864i
$383$		−	183.117i		−	0.478113i	−0.971006	−	0.239056i	$-0.923162\pi$
$383$		−	183.117i		−	0.478113i	0.971006	−	0.239056i	$-0.0768381\pi$
$384$	125.311	−	31.2843i	0.326330	−	0.0814695i
$385$	−8.61025			−0.0223643
$386$	−3.52311	+	10.7874i	−0.00912722	+	0.0279466i
$387$	201.011	+	164.966i	0.519409	+	0.426268i
$388$	−30.3173	−	195.242i	−0.0781373	−	0.503200i
$389$	−201.855	+	61.2321i	−0.518908	+	0.157409i	−0.538865	−	0.842392i	$-0.681147\pi$
$389$	−201.855	+	61.2321i	−0.518908	+	0.157409i	0.0199576	+	0.999801i	$0.493647\pi$
$390$	4.85130	−	3.09517i	0.0124392	−	0.00793634i
$391$	−102.325	+	514.423i	−0.261701	+	1.31566i
$392$	197.284	+	838.511i	0.503275	+	2.13906i
$393$	0.0991723	+	0.498573i	0.000252347	+	0.00126863i
$394$	6.29896	−	297.786i	0.0159872	−	0.755803i
$395$	−1.75330	+	17.8016i	−0.00443874	+	0.0450673i
$396$	101.089	+	59.6614i	0.255275	+	0.150660i
$397$	153.114	−	504.748i	0.385677	−	1.27141i	−0.522436	−	0.852679i	$-0.674976\pi$
$397$	153.114	−	504.748i	0.385677	−	1.27141i	0.908112	−	0.418727i	$-0.137524\pi$
$398$	−292.091	−	164.160i	−0.733896	−	0.412463i
$399$	−49.3758	−	20.4521i	−0.123749	−	0.0512585i
$400$	−312.183	−	249.187i	−0.780458	−	0.622967i
$401$	−276.911	−	668.521i	−0.690550	−	1.66714i	−0.743669	−	0.668548i	$-0.766916\pi$
$401$	−276.911	−	668.521i	−0.690550	−	1.66714i	0.0531191	−	0.998588i	$-0.483084\pi$
$402$	−102.913	−	12.3387i	−0.256003	−	0.0306932i
$403$	74.4898	+	139.361i	0.184838	+	0.345808i
$404$	−159.318	−	331.017i	−0.394352	−	0.819350i
$405$	−7.88913	+	6.47444i	−0.0194793	+	0.0159863i
$406$	50.7134	+	22.2741i	0.124910	+	0.0548622i
$407$	183.080	+	122.330i	0.449827	+	0.300565i
$408$	116.415	−	39.7774i	0.285330	−	0.0974937i
$409$	444.176	−	296.789i	1.08600	−	0.725645i	0.122266	−	0.992497i	$-0.460984\pi$
$409$	444.176	−	296.789i	1.08600	−	0.725645i	0.963737	+	0.266853i	$0.0859837\pi$
$410$	17.2339	+	12.0502i	0.0420338	+	0.0293906i
$411$	−12.9498	+	24.2273i	−0.0315080	+	0.0589473i
$412$	−26.6992	+	630.825i	−0.0648038	+	1.53113i
$413$	124.331	+	1262.36i	0.301044	+	3.05655i
$414$	−357.441	+	417.229i	−0.863385	+	1.00780i
$415$	16.6808	−	16.6808i	0.0401948	−	0.0401948i
$416$	465.610	+	145.101i	1.11926	+	0.348800i
$417$	−22.0108	+	22.0108i	−0.0527836	+	0.0527836i
$418$	31.0219	−	2.39421i	0.0742151	−	0.00572777i
$419$	−12.6258	−	128.192i	−0.0301331	−	0.305947i	−0.998424	−	0.0561210i	$-0.982127\pi$
$419$	−12.6258	−	128.192i	−0.0301331	−	0.305947i	0.968291	−	0.249826i	$-0.0803733\pi$
$420$	−8.87810	+	3.24479i	−0.0211383	+	0.00772568i
$421$	−14.6415	+	27.3924i	−0.0347780	+	0.0650651i	−0.898710	−	0.438543i	$-0.855495\pi$
$421$	−14.6415	+	27.3924i	−0.0347780	+	0.0650651i	0.863932	+	0.503608i	$0.167995\pi$
$422$	294.578	−	52.1448i	0.698053	−	0.123566i
$423$	89.2489	−	59.6342i	0.210990	−	0.140979i
$424$	−301.575	+	174.920i	−0.711261	+	0.412547i
$425$	−316.349	−	211.377i	−0.744350	−	0.497359i
$426$	46.7318	+	119.934i	0.109699	+	0.281534i
$427$	−719.003	+	590.071i	−1.68385	+	1.38190i
$428$	−30.7014	−	548.886i	−0.0717323	−	1.28244i
$429$	−26.6520	−	49.8625i	−0.0621260	−	0.116229i
$430$	9.58521	−	7.53286i	0.0222912	−	0.0175183i
$431$	104.739	+	252.862i	0.243014	+	0.586688i	0.997579	−	0.0695373i	$-0.0221523\pi$
$431$	104.739	+	252.862i	0.243014	+	0.586688i	−0.754565	+	0.656225i	$0.772152\pi$
$432$	269.598	+	49.8313i	0.624070	+	0.115350i
$433$	707.681	+	293.131i	1.63437	+	0.676977i	0.995711	−	0.0925159i	$-0.0294909\pi$
$433$	707.681	+	293.131i	1.63437	+	0.676977i	0.638656	+	0.769493i	$0.279491\pi$
$434$	−70.0773	−	249.924i	−0.161469	−	0.575861i
$435$	−0.121256	+	0.399728i	−0.000278750	+	0.000918916i
$436$	533.926	+	75.4999i	1.22460	+	0.173165i
$437$	−14.2742	+	144.928i	−0.0326640	+	0.331643i
$438$	−51.8834	−	54.1257i	−0.118455	−	0.123575i
$439$	61.0221	+	306.779i	0.139003	+	0.698813i	0.985937	+	0.167116i	$0.0534454\pi$
$439$	61.0221	+	306.779i	0.139003	+	0.698813i	−0.846935	+	0.531697i	$0.821555\pi$
$440$	3.75381	−	4.02401i	0.00853138	−	0.00914548i
$441$	−167.671	+	842.938i	−0.380206	+	1.91142i
$442$	453.590	+	100.241i	1.02622	+	0.226789i
$443$	763.237	−	231.525i	1.72288	−	0.522631i	0.735031	−	0.678034i	$-0.237168\pi$
$443$	763.237	−	231.525i	1.72288	−	0.522631i	0.987851	+	0.155403i	$0.0496677\pi$
$444$	234.875	+	57.1415i	0.528998	+	0.128697i
$445$	6.48333	+	5.32073i	0.0145693	+	0.0119567i
$446$	−81.2127	−	159.987i	−0.182091	−	0.358716i
$447$	217.468			0.486506
$448$	−695.362	−	397.765i	−1.55215	−	0.887867i
$449$			462.217i			1.02944i	0.857359	+	0.514718i	$0.172104\pi$
$449$			462.217i			1.02944i	−0.857359	+	0.514718i	$0.827896\pi$
$450$	−180.392	−	355.369i	−0.400872	−	0.789710i
$451$	131.070	−	159.710i	0.290621	−	0.354123i
$452$	185.845	−	113.113i	0.411161	−	0.250250i
$453$	−1.91777	−	6.32203i	−0.00423348	−	0.0139559i
$454$	49.7345	+	10.9911i	0.109547	+	0.0242094i
$455$	−35.0067	−	6.96327i	−0.0769379	−	0.0153039i
$456$	31.0847	−	14.1593i	0.0681682	−	0.0310512i
$457$	−275.239	+	54.7484i	−0.602273	+	0.119800i	−0.486804	−	0.873511i	$-0.661837\pi$
$457$	−275.239	+	54.7484i	−0.602273	+	0.119800i	−0.115470	+	0.993311i	$0.536837\pi$
$458$	392.666	+	409.637i	0.857349	+	0.894403i
$459$	259.887	+	25.5966i	0.566202	+	0.0557660i
$460$	15.4835	+	20.5836i	0.0336598	+	0.0447469i
$461$	−584.436	−	177.287i	−1.26776	−	0.384570i	−0.416413	−	0.909176i	$-0.636713\pi$
$461$	−584.436	−	177.287i	−1.26776	−	0.384570i	−0.851345	+	0.524606i	$0.824213\pi$
$462$	25.0733	+	89.4214i	0.0542712	+	0.193553i
$463$	−72.8050	+	175.767i	−0.157246	+	0.379626i	−0.982794	−	0.184707i	$-0.940867\pi$
$463$	−72.8050	+	175.767i	−0.157246	+	0.379626i	0.825547	+	0.564333i	$0.190867\pi$
$464$	−32.5193	+	13.9902i	−0.0700848	+	0.0301512i
$465$	1.80847	−	0.749092i	0.00388918	−	0.00161095i
$466$	−66.8818	+	52.5613i	−0.143523	+	0.112792i
$467$	−156.436	+	83.6169i	−0.334981	+	0.179051i	−0.630308	−	0.776345i	$-0.717071\pi$
$467$	−156.436	+	83.6169i	−0.334981	+	0.179051i	0.295327	+	0.955396i	$0.404571\pi$
$468$	362.749	+	324.318i	0.775104	+	0.692988i
$469$	407.843	+	496.959i	0.869602	+	1.05961i
$470$	−1.82700	−	4.68886i	−0.00388723	−	0.00997630i
$471$	−96.5773	+	144.538i	−0.205047	+	0.306875i
$472$	−644.168	−	492.242i	−1.36476	−	1.04289i
$473$	−66.5439	−	99.5900i	−0.140685	−	0.210550i
$474$	189.983	−	33.6299i	0.400808	−	0.0709491i
$475$	−93.1648	−	49.7976i	−0.196136	−	0.104837i
$476$	−691.982	−	321.553i	−1.45374	−	0.675532i
$477$	−346.166	+	34.0944i	−0.725715	+	0.0714767i
$478$	549.216	−	42.3874i	1.14899	−	0.0886766i
$479$	−168.895	−	168.895i	−0.352599	−	0.352599i	0.508476	−	0.861076i	$-0.330209\pi$
$479$	−168.895	−	168.895i	−0.352599	−	0.352599i	−0.861076	+	0.508476i	$0.830209\pi$
$480$	2.35413	−	5.56382i	0.00490443	−	0.0115913i
$481$	645.417	+	645.417i	1.34182	+	1.34182i
$482$	−462.836	+	540.252i	−0.960241	+	1.12086i
$483$	−432.584	+	42.6058i	−0.895618	+	0.0882107i
$484$	290.881	+	316.592i	0.600994	+	0.654115i
$485$	−8.15067	−	4.35662i	−0.0168055	−	0.00898273i
$486$	342.987	+	239.821i	0.705735	+	0.493459i
$487$	−58.1228	−	86.9870i	−0.119349	−	0.178618i	0.766985	−	0.641665i	$-0.221756\pi$
$487$	−58.1228	−	86.9870i	−0.119349	−	0.178618i	−0.886334	+	0.463047i	$0.846756\pi$
$488$	37.6933	−	593.280i	0.0772403	−	1.21574i
$489$	−134.081	+	200.667i	−0.274195	+	0.410362i
$490$	36.8911	+	16.2031i	0.0752880	+	0.0330676i
$491$	100.977	+	123.041i	0.205656	+	0.250593i	0.865616	−	0.500708i	$-0.166927\pi$
$491$	100.977	+	123.041i	0.205656	+	0.250593i	−0.659960	+	0.751301i	$0.729427\pi$
$492$	74.9608	−	214.072i	0.152359	−	0.435105i
$493$	−29.7381	+	15.8954i	−0.0603208	+	0.0322421i
$494$	128.062	+	15.3539i	0.259235	+	0.0310807i
$495$	5.07263	−	2.10115i	0.0102477	−	0.00424475i
$496$	147.354	+	76.2084i	0.297084	+	0.153646i
$497$	305.519	−	737.587i	0.614726	−	1.48408i
$498$	−221.813	−	124.663i	−0.445408	−	0.250327i
$499$	−924.845	−	280.549i	−1.85340	−	0.562222i	−0.999099	−	0.0424371i	$-0.986488\pi$
$499$	−924.845	−	280.549i	−1.85340	−	0.562222i	−0.854297	−	0.519785i	$-0.826012\pi$
$500$	−36.2109	+	9.33206i	−0.0724219	+	0.0186641i
$501$	−197.238	−	19.4263i	−0.393689	−	0.0387750i
$502$	−7.52236	+	355.623i	−0.0149848	+	0.708412i
$503$	289.663	−	57.6176i	0.575871	−	0.114548i	0.101442	−	0.994841i	$-0.467654\pi$
$503$	289.663	−	57.6176i	0.575871	−	0.114548i	0.474429	+	0.880294i	$0.342654\pi$
$504$	−466.857	−	648.752i	−0.926304	−	1.28721i
$505$	−16.8533	−	3.35233i	−0.0333729	−	0.00663828i
$506$	213.339	−	136.112i	0.421618	−	0.268996i
$507$	−18.5331	−	61.0954i	−0.0365544	−	0.120504i
$508$	−67.1751	+	91.8721i	−0.132234	+	0.180851i
$509$	74.8281	−	91.1783i	0.147010	−	0.179132i	−0.694299	−	0.719687i	$-0.744285\pi$
$509$	74.8281	−	91.1783i	0.147010	−	0.179132i	0.841309	+	0.540554i	$0.181785\pi$
$510$	1.78651	−	5.47009i	0.00350295	−	0.0107257i
$511$			465.039i			0.910056i
$512$	489.052	−	151.565i	0.955180	−	0.296025i
$513$	72.5075			0.141340
$514$	260.361	+	85.0327i	0.506540	+	0.165433i
$515$	22.8297	+	18.7359i	0.0443295	+	0.0363803i
$516$	−106.145	−	77.6109i	−0.205707	−	0.150409i
$517$	−47.3125	+	14.3521i	−0.0915135	+	0.0277603i
$518$	−806.414	−	1263.96i	−1.55678	−	2.44007i
$519$	−48.3006	+	242.823i	−0.0930647	+	0.467868i
$520$	18.5162	−	13.3247i	0.0356080	−	0.0256243i
$521$	9.89649	+	49.7530i	0.0189952	+	0.0954952i	0.989120	−	0.147111i	$-0.0469976\pi$
$521$	9.89649	+	49.7530i	0.0189952	+	0.0954952i	−0.970125	+	0.242607i	$0.921998\pi$
$522$	−35.3128	−	0.746958i	−0.0676490	−	0.00143095i
$523$	57.0683	−	579.424i	0.109117	−	1.10788i	−0.772206	−	0.635372i	$-0.780847\pi$
$523$	57.0683	−	579.424i	0.109117	−	1.10788i	0.881324	−	0.472513i	$-0.156653\pi$
$524$	0.502900	+	1.95139i	0.000959733	+	0.00372403i
$525$	91.5301	−	301.734i	0.174343	−	0.574732i
$526$	407.170	−	724.478i	0.774088	−	1.37734i
$527$	145.987	+	60.4698i	0.277015	+	0.114744i
$528$	−52.7224	−	27.2670i	−0.0998530	−	0.0516420i
$529$	250.829	+	605.556i	0.474158	+	1.14472i
$530$	−1.94125	+	16.1914i	−0.00366274	+	0.0305499i
$531$	−381.300	−	713.362i	−0.718079	−	1.34343i
$532$	−199.957	−	70.0182i	−0.375858	−	0.131613i
$533$	662.053	−	543.333i	1.24213	−	1.01939i
$534$	36.3786	−	82.8265i	0.0681247	−	0.155106i
$535$	−21.3808	−	14.2862i	−0.0399641	−	0.0267032i
$536$	−410.062	−	26.0527i	−0.765040	−	0.0486058i
$537$	−40.5654	+	27.1049i	−0.0755408	+	0.0504747i
$538$	27.2918	−	39.0321i	0.0507282	−	0.0725503i
$539$	186.613	−	349.129i	0.346221	−	0.647734i
$540$	9.44340	−	8.67649i	0.0174878	−	0.0160676i
$541$	−19.9483	−	202.539i	−0.0368731	−	0.374378i	−0.995858	−	0.0909216i	$-0.971019\pi$
$541$	−19.9483	−	202.539i	−0.0368731	−	0.374378i	0.958985	−	0.283457i	$-0.0914813\pi$
$542$	−361.306	−	309.532i	−0.666616	−	0.571092i
$543$	122.090	−	122.090i	0.224844	−	0.224844i
$544$	451.961	−	183.211i	0.830811	−	0.336785i
$545$	17.8354	−	17.8354i	0.0327255	−	0.0327255i
$546$	29.6238	+	383.838i	0.0542561	+	0.703000i
$547$	−32.6071	−	331.066i	−0.0596109	−	0.605239i	−0.977863	−	0.209244i	$-0.932900\pi$
$547$	−32.6071	−	331.066i	−0.0596109	−	0.605239i	0.918253	−	0.395995i	$-0.129600\pi$
$548$	−45.8915	+	98.7584i	−0.0837436	+	0.180216i
$549$	279.598	−	523.091i	0.509286	−	0.952807i
$550$	31.9970	+	180.759i	0.0581763	+	0.328652i
$551$	−7.78454	+	5.20146i	−0.0141280	+	0.00944004i
$552$	168.681	−	220.743i	0.305582	−	0.399897i
$553$	−995.004	−	664.841i	−1.79928	−	1.20224i
$554$	−479.452	+	186.817i	−0.865436	+	0.337215i
$555$	8.74030	−	7.17298i	0.0157483	−	0.0129243i
$556$	−82.2455	+	91.9913i	−0.147924	+	0.165452i
$557$	215.208	+	402.626i	0.386370	+	0.722847i	0.997646	−	0.0685699i	$-0.0218436\pi$
$557$	215.208	+	402.626i	0.386370	+	0.722847i	−0.611276	+	0.791417i	$0.709344\pi$
$558$	102.274	+	130.139i	0.183287	+	0.233224i
$559$	−190.007	−	458.718i	−0.339906	−	0.820606i
$560$	−34.4211	+	14.8083i	−0.0614662	+	0.0264434i
$561$	−52.2334	−	21.6358i	−0.0931077	−	0.0385665i
$562$	−940.215	+	263.631i	−1.67298	+	0.469095i
$563$	−150.349	+	495.635i	−0.267050	+	0.880347i	0.716170	+	0.697926i	$0.245893\pi$
$563$	−150.349	+	495.635i	−0.267050	+	0.880347i	−0.983221	+	0.182421i	$0.941607\pi$
$564$	−43.3757	+	32.6283i	−0.0769072	+	0.0578516i
$565$	0.997471	−	10.1275i	0.00176544	−	0.0179248i
$566$	−550.242	+	527.446i	−0.972159	+	0.931883i
$567$	−133.200	−	669.640i	−0.234920	−	1.18102i
$568$	211.515	+	464.350i	0.372386	+	0.817518i
$569$	−22.2019	+	111.617i	−0.0390192	+	0.196163i	−0.995378	−	0.0960309i	$-0.969385\pi$
$569$	−22.2019	+	111.617i	−0.0390192	+	0.196163i	0.956359	+	0.292194i	$0.0943852\pi$
$570$	0.344773	−	1.56009i	0.000604865	−	0.00273701i
$571$	−289.448	+	87.8030i	−0.506914	+	0.153771i	−0.533374	−	0.845879i	$-0.679076\pi$
$571$	−289.448	+	87.8030i	−0.506914	+	0.153771i	0.0264606	+	0.999650i	$0.491576\pi$
$572$	−116.527	−	191.455i	−0.203719	−	0.334711i
$573$	1.65010	+	1.35420i	0.00287976	+	0.00236336i
$574$	−1254.45	+	636.785i	−2.18546	+	1.10938i
$575$	−859.191			−1.49424
$576$	506.731	+	64.6499i	0.879741	+	0.112239i
$577$		−	764.316i		−	1.32464i	−0.749222	−	0.662319i	$-0.769573\pi$
$577$		−	764.316i		−	1.32464i	0.749222	−	0.662319i	$-0.230427\pi$
$578$	−101.187	+	51.3646i	−0.175065	+	0.0888662i
$579$	3.63212	−	4.42575i	0.00627309	−	0.00764379i
$580$	−0.391437	+	1.60897i	−0.000674891	+	0.00277408i
$581$	458.121	+	1510.22i	0.788505	+	2.59935i
$582$	−21.5105	+	97.3350i	−0.0369597	+	0.167242i
$583$	157.141	+	31.2572i	0.269538	+	0.0536145i
$584$	−217.336	−	202.743i	−0.372151	−	0.347162i
$585$	22.3231	−	4.44033i	0.0381591	−	0.00759031i
$586$	474.909	−	455.234i	0.810426	−	0.776851i
$587$	410.569	+	40.4375i	0.699437	+	0.0688885i	0.441484	−	0.897269i	$-0.354452\pi$
$587$	410.569	+	40.4375i	0.699437	+	0.0688885i	0.257953	+	0.966158i	$0.416952\pi$
$588$	60.8487	−	430.315i	0.103484	−	0.731828i
$589$	41.9843	+	12.7358i	0.0712806	+	0.0216227i
$590$	−36.5132	+	10.2381i	−0.0618868	+	0.0173527i
$591$	−57.5067	+	138.834i	−0.0973041	+	0.234913i
$592$	942.283	+	174.167i	1.59169	+	0.294202i
$593$	887.889	−	367.775i	1.49728	−	0.620195i	0.524395	−	0.851475i	$-0.324291\pi$
$593$	887.889	−	367.775i	1.49728	−	0.620195i	0.972887	+	0.231280i	$0.0742914\pi$
$594$	−77.8539	−	99.0654i	−0.131067	−	0.166777i
$595$	−31.4772	+	16.8249i	−0.0529029	+	0.0282772i
$596$	860.736	−	48.1444i	1.44419	−	0.0807793i
$597$	107.241	+	130.673i	0.179632	+	0.218883i
$598$	977.449	−	380.860i	1.63453	−	0.636890i
$599$	237.979	−	356.161i	0.397294	−	0.594593i	−0.577856	−	0.816139i	$-0.696110\pi$
$599$	237.979	−	356.161i	0.397294	−	0.594593i	0.975150	+	0.221546i	$0.0711104\pi$
$600$	101.112	+	174.324i	0.168519	+	0.290539i
$601$	−133.832	−	200.294i	−0.222683	−	0.333269i	0.703259	−	0.710933i	$-0.251727\pi$
$601$	−133.832	−	200.294i	−0.222683	−	0.333269i	−0.925942	+	0.377665i	$0.876727\pi$
$602$	142.159	+	803.088i	0.236144	+	1.33403i
$603$	−361.549	−	193.252i	−0.599583	−	0.320484i
$604$	−8.99011	−	24.5980i	−0.0148843	−	0.0407251i
$605$	20.0134	−	1.97115i	0.0330800	−	0.00325810i
$606$	14.2618	+	184.791i	0.0235344	+	0.304936i
$607$	136.312	+	136.312i	0.224566	+	0.224566i	0.810418	−	0.585852i	$-0.199240\pi$
$607$	136.312	+	136.312i	0.224566	+	0.224566i	−0.585852	+	0.810418i	$0.699240\pi$
$608$	119.898	−	62.9242i	0.197201	−	0.103494i
$609$	−19.7601	−	19.7601i	−0.0324468	−	0.0324468i
$610$	−21.1171	−	18.0911i	−0.0346182	−	0.0296576i
$611$	−203.965	+	20.0888i	−0.333822	+	0.0328786i
$612$	486.142	+	20.5756i	0.794349	+	0.0336202i
$613$	−305.695	−	163.397i	−0.498687	−	0.266554i	0.202821	−	0.979216i	$-0.434989\pi$
$613$	−305.695	−	163.397i	−0.498687	−	0.266554i	−0.701507	+	0.712662i	$0.747489\pi$
$614$	−34.5746	+	49.4478i	−0.0563104	+	0.0805339i
$615$	−5.89429	−	8.82143i	−0.00958421	−	0.0143438i
$616$	119.036	+	348.378i	0.193241	+	0.565548i
$617$	−376.255	+	563.105i	−0.609814	+	0.912651i	−0.999967	−	0.00809923i	$-0.997422\pi$
$617$	−376.255	+	563.105i	−0.609814	+	0.912651i	0.390154	+	0.920750i	$0.372422\pi$
$618$	128.100	−	291.656i	0.207281	−	0.471935i
$619$	327.054	+	398.516i	0.528358	+	0.643806i	0.966976	−	0.254868i	$-0.0820319\pi$
$619$	327.054	+	398.516i	0.528358	+	0.643806i	−0.438618	+	0.898674i	$0.644532\pi$
$620$	6.99206	−	3.36527i	0.0112775	−	0.00542785i
$621$	520.092	−	277.995i	0.837507	−	0.447657i
$622$	−137.510	+	1146.93i	−0.221077	+	1.84394i
$623$	−518.385	+	214.722i	−0.832078	+	0.344658i
$624$	−192.302	−	153.497i	−0.308177	−	0.245989i
$625$	238.173	−	575.000i	0.381077	−	0.920000i
$626$	256.794	−	456.914i	0.410214	−	0.729895i
$627$	−15.0217	−	4.55679i	−0.0239581	−	0.00726762i
$628$	−350.253	+	593.461i	−0.557728	+	0.945002i
$629$	908.340	+	89.4636i	1.44410	+	0.142232i
$630$	−37.3779	−	0.790640i	−0.0593299	−	0.00125498i
$631$	−744.582	+	148.107i	−1.18000	+	0.234717i	−0.745845	−	0.666119i	$-0.767954\pi$
$631$	−744.582	+	148.107i	−1.18000	+	0.234717i	−0.434158	+	0.900837i	$0.642954\pi$
$632$	744.506	−	175.166i	1.17802	−	0.277162i
$633$	−148.031	−	29.4451i	−0.233856	−	0.0465168i
$634$	389.579	+	610.618i	0.614479	+	0.963120i
$635$	1.54535	+	5.09433i	0.00243362	+	0.00802257i
$636$	173.808	−	26.9891i	0.273284	−	0.0424357i
$637$	1041.06	−	1268.54i	1.63432	−	1.99142i
$638$	15.4652	+	5.05085i	0.0242401	+	0.00791670i
$639$			509.097i			0.796708i
$640$	8.08585	−	22.5427i	0.0126341	−	0.0352230i
$641$	−671.813			−1.04807			−0.524035	−	0.851697i	$-0.675574\pi$
$641$	−671.813			−1.04807			−0.524035	+	0.851697i	$0.675574\pi$
$642$	−86.1071	+	263.651i	−0.134123	+	0.410672i
$643$	54.2415	+	44.5148i	0.0843569	+	0.0692299i	0.675627	−	0.737244i	$-0.263873\pi$
$643$	54.2415	+	44.5148i	0.0843569	+	0.0692299i	−0.591270	+	0.806474i	$0.701373\pi$
$644$	−1702.73	+	264.401i	−2.64399	+	0.410561i
$645$	−5.88574	+	1.78542i	−0.00912518	+	0.00276809i
$646$	108.731	−	69.3713i	0.168314	−	0.107386i
$647$	31.8136	−	159.938i	0.0491710	−	0.247199i	−0.948381	−	0.317135i	$-0.897279\pi$
$647$	31.8136	−	159.938i	0.0491710	−	0.247199i	0.997552	+	0.0699353i	$0.0222793\pi$
$648$	371.028	+	229.692i	0.572574	+	0.354462i
$649$	72.6859	+	365.417i	0.111997	+	0.563046i
$650$	−16.0927	+	760.788i	−0.0247579	+	1.17044i
$651$	−12.8358	+	130.324i	−0.0197170	+	0.200190i
$652$	−486.268	+	823.922i	−0.745810	+	1.26368i
$653$	−28.1186	+	92.6945i	−0.0430606	+	0.141952i	−0.975835	−	0.218509i	$-0.929881\pi$
$653$	−28.1186	+	92.6945i	−0.0430606	+	0.141952i	0.932774	+	0.360461i	$0.117381\pi$
$654$	−237.166	−	133.291i	−0.362639	−	0.203810i
$655$	0.0870844	+	0.0360715i	0.000132953	+	5.50710e-5i
$656$	249.301	−	863.889i	0.380033	−	1.31690i
$657$	−113.483	−	273.972i	−0.172729	−	0.417005i
$658$	334.260	+	40.0758i	0.507995	+	0.0609054i
$659$	−557.165	−	1042.38i	−0.845471	−	1.58176i	−0.812980	−	0.582292i	$-0.802156\pi$
$659$	−557.165	−	1042.38i	−0.845471	−	1.58176i	−0.0324909	−	0.999472i	$-0.510344\pi$
$660$	−2.50172	+	1.20407i	−0.00379048	+	0.00182435i
$661$	380.705	−	312.437i	0.575954	−	0.472673i	−0.300750	−	0.953703i	$-0.597237\pi$
$661$	380.705	−	312.437i	0.575954	−	0.472673i	0.876704	+	0.481030i	$0.159737\pi$
$662$	126.749	+	55.6700i	0.191464	+	0.0840937i
$663$	−194.868	−	130.207i	−0.293919	−	0.196390i
$664$	−905.532	−	444.308i	−1.36375	−	0.669139i
$665$	−8.23978	+	5.50564i	−0.0123906	+	0.00827916i
$666$	783.532	+	547.856i	1.17647	+	0.822607i
$667$	−35.8955	+	67.1558i	−0.0538164	+	0.100683i
$668$	−784.968	−	33.2231i	−1.17510	−	0.0497352i
$669$	8.87257	+	90.0848i	0.0132624	+	0.134656i
$670$	−12.5042	+	14.5957i	−0.0186629	+	0.0217846i
$671$	−193.182	+	193.182i	−0.287902	+	0.287902i
$672$	254.026	+	314.356i	0.378015	+	0.467792i
$673$	−937.826	+	937.826i	−1.39350	+	1.39350i	−0.576171	+	0.817329i	$0.695454\pi$
$673$	−937.826	+	937.826i	−1.39350	+	1.39350i	−0.817329	+	0.576171i	$0.804546\pi$
$674$	291.301	−	22.4820i	0.432198	−	0.0333561i
$675$	41.9301	+	425.723i	0.0621186	+	0.630701i
$676$	−86.8795	−	237.712i	−0.128520	−	0.351645i
$677$	−69.3070	+	129.664i	−0.102374	+	0.191528i	−0.927893	−	0.372845i	$-0.878382\pi$
$677$	−69.3070	+	129.664i	−0.102374	+	0.191528i	0.825520	+	0.564373i	$0.190882\pi$
$678$	−108.083	+	19.1323i	−0.159415	+	0.0282188i
$679$	514.083	−	343.500i	0.757118	−	0.505890i
$680$	5.85996	−	22.0461i	0.00861759	−	0.0324207i
$681$	−21.3666	−	14.2767i	−0.0313753	−	0.0209643i
$682$	−27.6794	−	71.0371i	−0.0405856	−	0.104160i
$683$	437.107	−	358.725i	0.639981	−	0.525219i	−0.257496	−	0.966279i	$-0.582897\pi$
$683$	437.107	−	358.725i	0.639981	−	0.525219i	0.897478	+	0.441060i	$0.145397\pi$
$684$	134.889	−	7.54487i	0.197206	−	0.0110305i
$685$	2.40122	+	4.49237i	0.00350544	+	0.00655821i
$686$	−1154.92	+	907.635i	−1.68356	+	1.32308i
$687$	−109.556	−	264.492i	−0.159471	−	0.384996i
$688$	−437.301	−	283.684i	−0.635612	−	0.412331i
$689$	613.609	+	254.165i	0.890580	+	0.368890i
$690$	−3.50839	−	12.5123i	−0.00508463	−	0.0181338i
$691$	165.930	−	546.997i	0.240130	−	0.791602i	−0.751185	−	0.660092i	$-0.770517\pi$
$691$	165.930	−	546.997i	0.240130	−	0.791602i	0.991315	−	0.131510i	$-0.0419826\pi$
$692$	−137.415	+	971.785i	−0.198577	+	1.40431i
$693$	−36.0034	+	365.549i	−0.0519530	+	0.527488i
$694$	−249.307	−	260.082i	−0.359232	−	0.374758i
$695$	1.12605	+	5.66102i	0.00162021	+	0.00814535i
$696$	17.8497	−	0.620104i	0.0256461	−	0.000890954i
$697$	167.083	−	839.983i	0.239717	−	1.20514i
$698$	−1291.50	−	285.414i	−1.85028	−	0.408902i
$699$	41.0683	−	12.4579i	0.0587530	−	0.0178225i
$700$	295.475	−	1214.52i	0.422107	−	1.73503i
$701$	617.590	+	506.843i	0.881013	+	0.723029i	0.961815	−	0.273701i	$-0.0882479\pi$
$701$	617.590	+	506.843i	0.881013	+	0.723029i	−0.0808014	+	0.996730i	$0.525748\pi$
$702$	−236.415	−	465.733i	−0.336773	−	0.663437i
$703$	253.424			0.360489
$704$	−214.711	−	96.2503i	−0.304987	−	0.136719i
$705$			2.53885i			0.00360121i
$706$	61.2742	+	120.709i	0.0867906	+	0.170976i
$707$	729.279	−	888.629i	1.03151	−	1.25690i
$708$	212.655	+	349.392i	0.300360	+	0.493492i
$709$	304.610	+	1004.16i	0.429633	+	1.41631i	0.858440	+	0.512913i	$0.171434\pi$
$709$	304.610	+	1004.16i	0.429633	+	1.41631i	−0.428808	+	0.903396i	$0.641066\pi$
$710$	23.3050	+	5.15030i	0.0328240	+	0.00725394i
$711$	748.436	+	148.873i	1.05265	+	0.209386i
$712$	125.649	−	335.880i	0.176474	−	0.471741i
$713$	349.980	−	69.6153i	0.490855	−	0.0976372i
$714$	266.397	+	277.911i	0.373105	+	0.389230i
$715$	−10.4332	−	1.02758i	−0.0145919	−	0.00143718i
$716$	−154.557	+	116.262i	−0.215861	+	0.162377i
$717$	−265.947	−	80.6741i	−0.370916	−	0.112516i
$718$	249.082	+	888.327i	0.346911	+	1.23722i
$719$	−281.899	+	680.565i	−0.392071	+	0.946544i	0.597417	+	0.801931i	$0.296194\pi$
$719$	−281.899	+	680.565i	−0.392071	+	0.946544i	−0.989488	+	0.144613i	$0.953806\pi$
$720$	16.6651	−	17.1239i	0.0231460	−	0.0237832i
$721$	−1825.38	+	756.098i	−2.53174	+	1.04868i
$722$	−539.519	+	423.999i	−0.747256	+	0.587256i
$723$	316.534	−	169.191i	0.437807	−	0.234013i
$724$	456.202	−	510.260i	0.630113	−	0.704779i
$725$	−35.0417	−	42.6985i	−0.0483334	−	0.0588945i
$726$	−78.7509	−	202.108i	−0.108472	−	0.278386i
$727$	416.189	−	622.870i	0.572474	−	0.856768i	−0.426384	−	0.904542i	$-0.640213\pi$
$727$	416.189	−	622.870i	0.572474	−	0.856768i	0.998858	+	0.0477743i	$0.0152128\pi$
$728$	202.227	+	1512.67i	0.277785	+	2.07784i
$729$	155.432	+	232.620i	0.213212	+	0.319094i
$730$	−13.6898	+	2.42329i	−0.0187531	+	0.00331958i
$731$	−437.875	−	234.049i	−0.599008	−	0.320176i
$732$	−126.391	+	271.993i	−0.172665	+	0.371575i
$733$	−1350.34	+	132.997i	−1.84222	+	0.181442i	−0.958216	−	0.286045i	$-0.907659\pi$
$733$	−1350.34	+	132.997i	−1.84222	+	0.181442i	−0.884000	+	0.467487i	$0.845159\pi$
$734$	1221.18	−	94.2480i	1.66373	−	0.128403i
$735$	−14.3743	−	14.3743i	−0.0195569	−	0.0195569i
$736$	618.770	−	911.043i	0.840720	−	1.23783i
$737$	133.523	+	133.523i	0.181171	+	0.181171i
$738$	583.653	−	681.278i	0.790858	−	0.923141i
$739$	−777.834	+	76.6100i	−1.05255	+	0.103667i	−0.609465	−	0.792813i	$-0.708616\pi$
$739$	−777.834	+	76.6100i	−1.05255	+	0.103667i	−0.443084	+	0.896480i	$0.646116\pi$
$740$	33.0060	−	30.3255i	0.0446027	−	0.0409805i
$741$	−57.3888	−	30.6749i	−0.0774477	−	0.0413967i
$742$	−894.079	−	625.152i	−1.20496	−	0.842523i
$743$	−14.2804	−	21.3722i	−0.0192200	−	0.0287647i	0.821735	−	0.569869i	$-0.193006\pi$
$743$	−14.2804	−	21.3722i	−0.0192200	−	0.0287647i	−0.840955	+	0.541105i	$0.818006\pi$
$744$	−55.3109	−	62.8159i	−0.0743426	−	0.0844300i
$745$	22.4029	−	33.5283i	0.0300710	−	0.0450045i
$746$	1050.85	+	461.549i	1.40865	+	0.618699i
$747$	−638.436	−	777.936i	−0.854666	−	1.04141i
$748$	−211.529	−	74.0704i	−0.282793	−	0.0990246i
$749$	1517.16	−	810.939i	2.02558	−	1.08270i
$750$	18.7319	+	2.24584i	0.0249758	+	0.00299445i
$751$	484.081	−	200.513i	0.644581	−	0.266994i	−0.0363528	−	0.999339i	$-0.511574\pi$
$751$	484.081	−	200.513i	0.644581	−	0.266994i	0.680934	+	0.732345i	$0.261574\pi$
$752$	−164.457	+	138.745i	−0.218693	+	0.184502i
$753$	68.6758	−	165.798i	0.0912029	−	0.220183i
$754$	58.7921	+	33.0422i	0.0779737	+	0.0438226i
$755$	−1.17227	−	0.355604i	−0.00155267	−	0.000470998i
$756$	214.105	+	830.787i	0.283208	+	1.09892i
$757$	−564.216	−	55.5704i	−0.745331	−	0.0734087i	−0.281780	−	0.959479i	$-0.590925\pi$
$757$	−564.216	−	55.5704i	−0.745331	−	0.0734087i	−0.463551	+	0.886070i	$0.653425\pi$
$758$	25.3634	−	1199.07i	0.0334610	−	1.58188i
$759$	−125.221	+	24.9080i	−0.164981	+	0.0328168i
$760$	1.01922	−	6.25116i	0.00134108	−	0.00822521i
$761$	−758.853	−	150.945i	−0.997178	−	0.198351i	−0.330588	−	0.943775i	$-0.607247\pi$
$761$	−758.853	−	150.945i	−0.997178	−	0.198351i	−0.666591	+	0.745424i	$0.732247\pi$
$762$	48.4068	−	30.8840i	0.0635260	−	0.0405301i
$763$	489.830	+	1614.75i	0.641979	+	2.11632i
$764$	6.83089	+	4.99462i	0.00894096	+	0.00653745i
$765$	14.4387	−	17.5936i	0.0188741	−	0.0229981i
$766$	−113.700	+	348.138i	−0.148433	+	0.454488i
$767$			1544.46i			2.01363i
$768$	−257.662	−	18.3303i	−0.335498	−	0.0238676i
$769$	1076.10			1.39935			0.699677	−	0.714459i	$-0.253327\pi$
$769$	1076.10			1.39935			0.699677	+	0.714459i	$0.253327\pi$
$770$	16.3696	+	5.34623i	0.0212592	+	0.00694315i
$771$	−106.819	−	87.6638i	−0.138546	−	0.113701i
$772$	13.3961	−	18.3212i	0.0173524	−	0.0237321i
$773$	−387.588	+	117.573i	−0.501407	+	0.152100i	−0.530849	−	0.847466i	$-0.678127\pi$
$773$	−387.588	+	117.573i	−0.501407	+	0.152100i	0.0294421	+	0.999566i	$0.490627\pi$
$774$	−279.728	−	438.439i	−0.361406	−	0.566459i
$775$	−50.4985	+	253.873i	−0.0651593	+	0.327578i
$776$	−63.5898	+	390.013i	−0.0819456	+	0.502594i
$777$	147.571	+	741.888i	0.189924	+	0.954811i
$778$	421.782	+	8.92179i	0.542136	+	0.0114676i
$779$	23.3078	−	236.648i	0.0299201	−	0.303784i
$780$	−11.1450	+	2.87222i	−0.0142885	+	0.00368233i
$781$	68.0704	−	224.398i	0.0871581	−	0.287322i
$782$	513.950	−	914.473i	0.657225	−	1.16940i
$783$	35.0270	+	14.5087i	0.0447344	+	0.0185296i
$784$	145.573	−	1716.65i	0.185679	−	2.18961i
$785$	12.3352	+	29.7798i	0.0157136	+	0.0379360i
$786$	0.121027	−	1.00945i	0.000153978	−	0.00128429i
$787$	−556.949	−	1041.98i	−0.707686	−	1.32399i	−0.936552	−	0.350530i	$-0.886002\pi$
$787$	−556.949	−	1041.98i	−0.707686	−	1.32399i	0.228865	−	0.973458i	$-0.426498\pi$
$788$	−196.875	+	562.233i	−0.249842	+	0.713493i
$789$	−324.111	+	265.991i	−0.410787	+	0.337124i
$790$	14.3866	−	32.7553i	0.0182109	−	0.0414624i
$791$	566.068	+	378.234i	0.715635	+	0.478172i
$792$	−155.143	−	176.194i	−0.195888	−	0.222468i
$793$	−941.651	+	629.191i	−1.18745	+	0.793431i
$794$	−604.501	+	864.544i	−0.761336	+	1.08885i
$795$	3.87836	−	7.25591i	0.00487845	−	0.00912693i
$796$	453.386	+	493.461i	0.569581	+	0.619925i
$797$	−143.116	−	1453.08i	−0.179569	−	1.82319i	−0.489015	−	0.872276i	$-0.662644\pi$
$797$	−143.116	−	1453.08i	−0.179569	−	1.82319i	0.309446	−	0.950917i	$-0.399856\pi$
$798$	81.1730	+	69.5412i	0.101721	+	0.0871444i
$799$	−144.919	+	144.919i	−0.181376	+	0.181376i
$800$	438.791	+	667.586i	0.548489	+	0.834483i
$801$	253.002	−	253.002i	0.315858	−	0.315858i
$802$	111.361	+	1442.91i	0.138854	+	1.79914i
$803$	13.3884	+	135.934i	0.0166729	+	0.169283i
$804$	187.995	+	87.3584i	0.233825	+	0.108655i
$805$	−37.9947	+	71.0831i	−0.0471984	+	0.0883020i
$806$	−55.0872	−	311.201i	−0.0683463	−	0.386105i
$807$	−19.9792	+	13.3497i	−0.0247574	+	0.0165423i
$808$	97.3584	+	728.245i	0.120493	+	0.901293i
$809$	−33.2138	−	22.1928i	−0.0410554	−	0.0274323i	0.534873	−	0.844932i	$-0.320359\pi$
$809$	−33.2138	−	22.1928i	−0.0410554	−	0.0274323i	−0.575929	+	0.817500i	$0.695359\pi$
$810$	19.0187	−	7.41057i	0.0234799	−	0.00914885i
$811$	−260.681	+	213.935i	−0.321431	+	0.263792i	−0.781246	−	0.624223i	$-0.785416\pi$
$811$	−260.681	+	213.935i	−0.321431	+	0.263792i	0.459815	+	0.888015i	$0.347916\pi$
$812$	−82.5848	−	73.8356i	−0.101705	−	0.0909305i
$813$	113.150	+	211.689i	0.139176	+	0.260381i
$814$	−272.110	−	346.247i	−0.334288	−	0.425365i
$815$	17.1254	+	41.3443i	0.0210127	+	0.0507292i
$816$	−246.023	+	3.34042i	−0.301499	+	0.00409365i
$817$	−127.361	−	52.7548i	−0.155889	−	0.0645714i
$818$	−1028.74	+	288.452i	−1.25762	+	0.352631i
$819$	−442.005	+	1457.10i	−0.539689	+	1.77912i
$820$	−25.2825	−	33.6102i	−0.0308323	−	0.0409881i
$821$	−79.2818	+	804.962i	−0.0965674	+	0.980465i	0.817779	+	0.575532i	$0.195205\pi$
$821$	−79.2818	+	804.962i	−0.0965674	+	0.980465i	−0.914346	+	0.404933i	$0.867295\pi$
$822$	39.6629	−	38.0197i	0.0482517	−	0.0462527i
$823$	193.222	+	971.392i	0.234778	+	1.18031i	0.900753	+	0.434332i	$0.143016\pi$
$823$	193.222	+	971.392i	0.234778	+	1.18031i	−0.665975	+	0.745974i	$0.731984\pi$
$824$	442.448	−	1182.73i	0.536951	−	1.43535i
$825$	18.0681	−	90.8343i	0.0219007	−	0.110102i
$826$	547.439	−	2477.16i	0.662759	−	2.99898i
$827$	1004.77	−	304.795i	1.21496	−	0.368555i	0.383189	−	0.923670i	$-0.374826\pi$
$827$	1004.77	−	304.795i	1.21496	−	0.368555i	0.831774	+	0.555115i	$0.187326\pi$
$828$	938.622	−	571.284i	1.13360	−	0.689957i
$829$	−933.639	−	766.218i	−1.12622	−	0.924267i	−0.128500	−	0.991710i	$-0.541016\pi$
$829$	−933.639	−	766.218i	−1.12622	−	0.924267i	−0.997723	+	0.0674423i	$0.978516\pi$
$830$	−42.0705	+	21.3558i	−0.0506874	+	0.0257299i
$831$	259.606			0.312402
$832$	−795.112	−	564.966i	−0.955663	−	0.679045i
$833$		−	1640.99i		−	1.96998i
$834$	55.5131	−	28.1795i	0.0665625	−	0.0337884i
$835$	−23.3140	+	28.4082i	−0.0279209	+	0.0340218i
$836$	−60.4647	−	14.7101i	−0.0723262	−	0.0175959i
$837$	−51.5736	−	170.015i	−0.0616172	−	0.203125i
$838$	−55.5922	+	251.554i	−0.0663391	+	0.300184i
$839$	−410.049	−	81.5639i	−0.488736	−	0.0972156i	−0.0554299	−	0.998463i	$-0.517653\pi$
$839$	−410.049	−	81.5639i	−0.488736	−	0.0972156i	−0.433306	+	0.901247i	$0.642653\pi$
$840$	18.8936	−	0.656368i	0.0224923	−	0.000781390i
$841$	820.039	−	163.116i	0.975076	−	0.193955i
$842$	44.8445	−	42.9866i	0.0532594	−	0.0510530i
$843$	490.278	+	48.2882i	0.581587	+	0.0572814i
$844$	−592.423	−	83.7715i	−0.701922	−	0.0992554i
$845$	−11.3287	−	3.43651i	−0.0134067	−	0.00406688i
$846$	−206.705	+	57.9591i	−0.244333	+	0.0685096i
$847$	−514.851	+	1242.96i	−0.607852	+	1.46748i
$848$	681.957	−	145.301i	0.804194	−	0.171346i
$849$	355.277	−	147.161i	0.418466	−	0.173334i
$850$	470.187	+	598.291i	0.553161	+	0.703872i
$851$	1817.79	−	971.630i	2.13607	−	1.14175i
$852$	−14.3768	−	257.031i	−0.0168742	−	0.301680i
$853$	−17.9938	−	21.9255i	−0.0210947	−	0.0257039i	0.762356	−	0.647158i	$-0.224042\pi$
$853$	−17.9938	−	21.9255i	−0.0210947	−	0.0257039i	−0.783451	+	0.621454i	$0.786542\pi$
$854$	1733.33	−	675.388i	2.02967	−	0.790853i
$855$	3.51083	−	5.25433i	0.00410624	−	0.00614542i
$856$	−282.442	+	1062.59i	−0.329956	+	1.24134i
$857$	−282.392	−	422.629i	−0.329512	−	0.493149i	0.629311	−	0.777153i	$-0.283337\pi$
$857$	−282.392	−	422.629i	−0.329512	−	0.493149i	−0.958823	+	0.284004i	$0.908337\pi$
$858$	19.7099	+	111.346i	0.0229719	+	0.129774i
$859$	−470.403	−	251.436i	−0.547618	−	0.292708i	0.174293	−	0.984694i	$-0.444236\pi$
$859$	−470.403	−	251.436i	−0.547618	−	0.292708i	−0.721911	+	0.691986i	$0.756736\pi$
$860$	−22.9004	+	8.36969i	−0.0266284	+	0.00973220i
$861$	706.350	−	69.5694i	0.820384	−	0.0808007i
$862$	−42.1214	−	545.769i	−0.0488647	−	0.633143i
$863$	−192.746	−	192.746i	−0.223345	−	0.223345i	0.586561	−	0.809905i	$-0.300482\pi$
$863$	−192.746	−	192.746i	−0.223345	−	0.223345i	−0.809905	+	0.586561i	$0.800482\pi$
$864$	−481.613	−	262.136i	−0.557422	−	0.303398i
$865$	32.4617	+	32.4617i	0.0375280	+	0.0375280i
$866$	−1163.42	−	996.702i	−1.34344	−	1.15093i
$867$	56.9760	−	5.61164i	0.0657162	−	0.00647248i
$868$	−21.9519	+	518.661i	−0.0252902	+	0.597535i
$869$	−309.988	−	165.692i	−0.356718	−	0.190670i
$870$	0.478726	−	0.684664i	0.000550260	−	0.000786970i
$871$	434.882	+	650.848i	0.499291	+	0.747242i
$872$	−968.208	−	475.061i	−1.11033	−	0.544794i
$873$	−219.042	+	327.820i	−0.250908	+	0.375510i
$874$	117.126	−	266.671i	0.134011	−	0.305115i
$875$	−74.2340	−	90.4544i	−0.0848388	−	0.103376i
$876$	65.0319	+	135.118i	0.0742374	+	0.154244i
$877$	−744.557	+	397.974i	−0.848982	+	0.453790i	−0.837690	−	0.546146i	$-0.816094\pi$
$877$	−744.557	+	397.974i	−0.848982	+	0.453790i	−0.0112919	+	0.999936i	$0.503594\pi$
$878$	74.4696	−	621.130i	0.0848173	−	0.707437i
$879$	−306.637	+	127.013i	−0.348848	+	0.144497i
$880$	−9.63521	+	5.31956i	−0.0109491	+	0.00604495i
$881$	−207.599	+	501.187i	−0.235640	+	0.568884i	−0.996823	−	0.0796527i	$-0.974619\pi$
$881$	−207.599	+	501.187i	−0.235640	+	0.568884i	0.761183	+	0.648537i	$0.224619\pi$
$882$	842.163	−	1498.46i	0.954834	−	1.69894i
$883$	299.517	+	90.8576i	0.339204	+	0.102896i	0.455291	−	0.890343i	$-0.349535\pi$
$883$	299.517	+	90.8576i	0.339204	+	0.102896i	−0.116087	+	0.993239i	$0.537035\pi$
$884$	−800.112	−	472.216i	−0.905104	−	0.534181i
$885$	19.0399	+	1.87527i	0.0215140	+	0.00211895i
$886$	−1594.80	−	33.7343i	−1.80000	−	0.0380748i
$887$	−1134.95	+	225.756i	−1.27954	+	0.254517i	−0.787641	−	0.616134i	$-0.788698\pi$
$887$	−1134.95	+	225.756i	−1.27954	+	0.254517i	−0.491901	+	0.870651i	$0.663698\pi$
$888$	−411.059	−	254.473i	−0.462904	−	0.286569i
$889$	−349.301	−	69.4803i	−0.392914	−	0.0781555i
$890$	−9.02223	−	14.1412i	−0.0101373	−	0.0158890i
$891$	−58.2141	−	191.906i	−0.0653356	−	0.215383i
$892$	55.0611	+	354.590i	0.0617277	+	0.397523i
$893$	−36.0996	+	43.9875i	−0.0404251	+	0.0492581i
$894$	−413.445	−	135.029i	−0.462466	−	0.151039i
$895$			9.04648i			0.0101078i
$896$	1075.03	+	1187.98i	1.19981	+	1.32587i
$897$	−529.254			−0.590027
$898$	286.997	−	878.756i	0.319596	−	0.978570i
$899$	17.7334	+	14.5534i	0.0197257	+	0.0161885i
$900$	122.304	+	787.628i	0.135893	+	0.875142i
$901$	635.551	−	192.792i	0.705384	−	0.213976i
$902$	−348.353	+	222.252i	−0.386201	+	0.246400i
$903$	80.2742	−	403.565i	0.0888972	−	0.446916i
$904$	−423.556	+	99.6537i	−0.468536	+	0.110236i
$905$	−6.24599	−	31.4007i	−0.00690165	−	0.0346969i
$906$	−0.279428	+	13.2101i	−0.000308419	+	0.0145806i
$907$	−49.9342	+	506.991i	−0.0550543	+	0.558975i	0.927606	+	0.373560i	$0.121863\pi$
$907$	−49.9342	+	506.991i	−0.0550543	+	0.558975i	−0.982660	+	0.185415i	$0.940637\pi$
$908$	−87.7294	−	51.7768i	−0.0966183	−	0.0570229i
$909$	−212.795	+	701.491i	−0.234098	+	0.771717i
$910$	62.2303	+	34.9746i	0.0683850	+	0.0384336i
$911$	819.603	+	339.490i	0.899673	+	0.372657i	0.784095	−	0.620641i	$-0.213128\pi$
$911$	819.603	+	339.490i	0.899673	+	0.372657i	0.115579	+	0.993298i	$0.463128\pi$
$912$	−67.8892	+	7.61846i	−0.0744399	+	0.00835358i
$913$	177.391	+	428.261i	0.194295	+	0.469070i
$914$	557.271	+	66.8134i	0.609706	+	0.0731000i
$915$	6.61326	+	12.3725i	0.00722761	+	0.0135219i
$916$	−492.177	−	1022.60i	−0.537311	−	1.11638i
$917$	−4.87454	+	4.00043i	−0.00531575	+	0.00436252i
$918$	−478.197	−	210.031i	−0.520911	−	0.228792i
$919$	914.325	+	610.932i	0.994913	+	0.664780i	0.942625	−	0.333853i	$-0.108349\pi$
$919$	914.325	+	610.932i	0.994913	+	0.664780i	0.0522876	+	0.998632i	$0.483349\pi$
$920$	−16.6562	−	48.7469i	−0.0181046	−	0.0529858i
$921$	25.3107	−	16.9120i	0.0274817	−	0.0183627i
$922$	1001.04	+	699.938i	1.08572	+	0.759152i
$923$	458.229	−	857.286i	0.496456	−	0.928804i
$924$	7.85427	−	185.574i	0.00850029	−	0.200838i
$925$	146.551	+	1487.96i	0.158434	+	1.60861i
$926$	247.551	−	288.958i	0.267334	−	0.312050i
$927$	890.893	−	890.893i	0.961050	−	0.961050i
$928$	70.5116	−	6.40604i	0.0759824	−	0.00690306i
$929$	281.911	−	281.911i	0.303457	−	0.303457i	−0.538908	−	0.842365i	$-0.681163\pi$
$929$	281.911	−	281.911i	0.303457	−	0.303457i	0.842365	+	0.538908i	$0.181163\pi$
$930$	−3.90334	+	0.301252i	−0.00419714	+	0.000323926i
$931$	−44.6592	−	453.433i	−0.0479691	−	0.487038i
$932$	159.790	−	58.4004i	0.171448	−	0.0626613i
$933$	274.726	−	513.976i	0.294454	−	0.550886i
$934$	349.332	−	61.8369i	0.374017	−	0.0662066i
$935$	−8.71665	+	5.82428i	−0.00932262	+	0.00622917i
$936$	−488.275	−	841.821i	−0.521661	−	0.899382i
$937$	−1391.21	−	929.575i	−1.48475	−	0.992076i	−0.992582	−	0.121574i	$-0.961206\pi$
$937$	−1391.21	−	929.575i	−1.48475	−	0.992076i	−0.492165	−	0.870502i	$-0.663794\pi$
$938$	−466.813	−	1198.04i	−0.497668	−	1.27723i
$939$	−204.410	+	167.755i	−0.217689	+	0.178653i
$940$	0.562067	+	10.0488i	0.000597944	+	0.0106902i
$941$	−223.869	−	418.829i	−0.237905	−	0.445089i	0.734428	−	0.678686i	$-0.237450\pi$
$941$	−223.869	−	418.829i	−0.237905	−	0.445089i	−0.972334	+	0.233597i	$0.924950\pi$
$942$	273.356	−	214.826i	0.290187	−	0.228053i
$943$	−740.126	−	1786.82i	−0.784864	−	1.89483i
$944$	919.036	+	1335.81i	0.973555	+	1.41505i
$945$	37.0754	+	15.3571i	0.0392332	+	0.0162509i
$946$	64.6748	+	230.656i	0.0683666	+	0.243822i
$947$	−505.044	+	1664.91i	−0.533310	+	1.75809i	0.111523	+	0.993762i	$0.464427\pi$
$947$	−505.044	+	1664.91i	−0.533310	+	1.75809i	−0.644832	+	0.764324i	$0.723073\pi$
$948$	−382.072	−	54.0270i	−0.403030	−	0.0569905i
$949$	−55.4995	+	563.496i	−0.0584821	+	0.593779i
$950$	146.203	+	152.521i	0.153897	+	0.160549i
$951$	−71.2915	−	358.407i	−0.0749648	−	0.376874i
$952$	1115.92	+	1040.99i	1.17219	+	1.09348i
$953$	−215.565	+	1083.72i	−0.226196	+	1.13716i	0.686061	+	0.727544i	$0.259338\pi$
$953$	−215.565	+	1083.72i	−0.226196	+	1.13716i	−0.912257	+	0.409619i	$0.865662\pi$
$954$	679.292	+	150.120i	0.712046	+	0.157358i
$955$	0.378774	−	0.114900i	0.000396622	−	0.000120314i
$956$	−1070.48	−	260.430i	−1.11974	−	0.272417i
$957$	−6.34491	−	5.20714i	−0.00663000	−	0.00544110i
$958$	216.230	+	425.969i	0.225710	+	0.444644i
$959$	−340.777			−0.355346
$960$	−7.93026	+	9.11608i	−0.00826069	+	0.00949592i
$961$			853.497i			0.888134i
$962$	−826.302	−	1627.80i	−0.858942	−	1.69210i
$963$	−695.925	+	847.987i	−0.722663	+	0.880568i
$964$	1215.38	−	739.733i	1.26077	−	0.767358i
$965$	−0.308174	−	1.01591i	−0.000319351	−	0.00105276i
$966$	848.872	+	187.596i	0.878749	+	0.194199i
$967$	136.335	+	27.1186i	0.140987	+	0.0280441i	0.265079	−	0.964227i	$-0.414602\pi$
$967$	136.335	+	27.1186i	0.140987	+	0.0280441i	−0.124092	+	0.992271i	$0.539602\pi$
$968$	−356.439	−	782.508i	−0.368222	−	0.808376i
$969$	−63.8205	+	12.6947i	−0.0658622	+	0.0131008i
$970$	12.7908	+	13.3436i	0.0131863	+	0.0137563i
$971$	1709.96	+	168.417i	1.76103	+	0.173447i	0.926194	−	0.377048i	$-0.123061\pi$
$971$	1709.96	+	168.417i	1.76103	+	0.173447i	0.834839	+	0.550495i	$0.185561\pi$
$972$	−503.170	−	668.908i	−0.517664	−	0.688176i
$973$	−369.512	−	112.090i	−0.379766	−	0.115201i
$974$	56.4903	+	201.467i	0.0579982	+	0.206845i
$975$	146.919	−	354.693i	0.150686	−	0.363788i
$976$	−440.037	+	1104.52i	−0.450858	+	1.13169i
$977$	−1119.19	+	463.582i	−1.14553	+	0.474495i	−0.873033	−	0.487661i	$-0.837850\pi$
$977$	−1119.19	+	463.582i	−1.14553	+	0.474495i	−0.272500	+	0.962156i	$0.587850\pi$
$978$	379.509	−	298.250i	0.388046	−	0.304959i
$979$	−145.346	+	77.6890i	−0.148464	+	0.0793555i
$980$	−60.0757	−	53.7112i	−0.0613018	−	0.0548073i
$981$	−682.625	−	831.781i	−0.695846	−	0.847891i
$982$	−115.577	−	296.621i	−0.117696	−	0.302058i
$983$	221.623	−	331.683i	0.225456	−	0.337419i	−0.701446	−	0.712723i	$-0.747462\pi$
$983$	221.623	−	331.683i	0.225456	−	0.337419i	0.926902	+	0.375304i	$0.122462\pi$
$984$	−275.434	+	360.444i	−0.279912	+	0.366305i
$985$	15.4806	+	23.1684i	0.0157164	+	0.0235212i
$986$	66.4071	−	11.7550i	0.0673500	−	0.0119219i
$987$	−149.793	−	80.0660i	−0.151766	−	0.0811205i
$988$	−233.935	−	108.706i	−0.236776	−	0.110026i
$989$	−1115.82	+	109.899i	−1.12823	+	0.111121i
$990$	−10.9486	+	0.844991i	−0.0110592	+	0.000853526i
$991$	−941.611	−	941.611i	−0.950163	−	0.950163i	0.0486532	−	0.998816i	$-0.484507\pi$
$991$	−941.611	−	941.611i	−0.950163	−	0.950163i	−0.998816	+	0.0486532i	$0.984507\pi$
$992$	−232.826	−	236.380i	−0.234704	−	0.238286i
$993$	−49.3868	−	49.3868i	−0.0497349	−	0.0497349i
$994$	−1038.82	+	1212.58i	−1.04509	+	1.21990i
$995$	31.1942	−	3.07236i	0.0313510	−	0.00308780i
$996$	344.300	+	374.733i	0.345683	+	0.376238i
$997$	186.418	+	99.6422i	0.186978	+	0.0999421i	0.562230	−	0.826981i	$-0.309944\pi$
$997$	186.418	+	99.6422i	0.186978	+	0.0999421i	−0.375251	+	0.926923i	$0.622444\pi$
$998$	1584.10	+	1107.62i	1.58727	+	1.10984i
$999$	−570.148	−	853.286i	−0.570718	−	0.854140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.l.a.43.3	yes	496
128.3	odd	32	inner	128.3.l.a.3.3	✓	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.3.l.a.3.3	✓	496	128.3	odd	32	inner
128.3.l.a.43.3	yes	496	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.l (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90117 - 0.620914i) q^{2} +(0.779996 + 0.640126i) q^{3} +(3.22893 + 2.36093i) q^{4} +(0.179045 - 0.0543127i) q^{5} +(-1.08545 - 1.70130i) q^{6} +(-2.44195 + 12.2765i) q^{7} +(-4.67283 - 6.49343i) q^{8} +(-1.55718 - 7.82847i) q^{9} +O(q^{10})\)	\(q+(-1.90117 - 0.620914i) q^{2} +(0.779996 + 0.640126i) q^{3} +(3.22893 + 2.36093i) q^{4} +(0.179045 - 0.0543127i) q^{5} +(-1.08545 - 1.70130i) q^{6} +(-2.44195 + 12.2765i) q^{7} +(-4.67283 - 6.49343i) q^{8} +(-1.55718 - 7.82847i) q^{9} +(-0.374119 - 0.00791361i) q^{10} +(-0.360362 + 3.65882i) q^{11} +(1.00726 + 3.90844i) q^{12} +(-4.42408 + 14.5842i) q^{13} +(12.2652 - 21.8236i) q^{14} +(0.174421 + 0.0722477i) q^{15} +(4.85200 + 15.2466i) q^{16} +(5.83214 + 14.0800i) q^{17} +(-1.90034 + 15.8502i) q^{18} +(1.99470 + 3.73182i) q^{19} +(0.706353 + 0.247341i) q^{20} +(-9.76323 + 8.01248i) q^{21} +(2.95693 - 6.73230i) q^{22} +(28.6157 + 19.1204i) q^{23} +(0.511831 - 8.05606i) q^{24} +(-20.7576 + 13.8698i) q^{25} +(17.4665 - 24.9802i) q^{26} +(8.07753 - 15.1120i) q^{27} +(-36.8689 + 33.8747i) q^{28} +(0.216869 + 2.20191i) q^{29} +(-0.286746 - 0.245656i) q^{30} +(7.33155 - 7.33155i) q^{31} +(0.242322 - 31.9991i) q^{32} +(-2.62319 + 2.62319i) q^{33} +(-2.34543 - 30.3899i) q^{34} +(0.229552 + 2.33068i) q^{35} +(13.4545 - 28.9540i) q^{36} +(28.2321 - 52.8185i) q^{37} +(-1.47513 - 8.33338i) q^{38} +(-12.7865 + 8.54369i) q^{39} +(-1.18932 - 0.908823i) q^{40} +(-46.7256 - 31.2210i) q^{41} +(23.5367 - 9.17099i) q^{42} +(-25.1836 + 20.6676i) q^{43} +(-9.80181 + 10.9633i) q^{44} +(-0.703991 - 1.31707i) q^{45} +(-42.5313 - 54.1191i) q^{46} +(5.14627 + 12.4242i) q^{47} +(-5.97520 + 14.9982i) q^{48} +(-99.4795 - 41.2058i) q^{49} +(48.0758 - 13.4802i) q^{50} +(-4.46395 + 14.7157i) q^{51} +(-48.7175 + 36.6466i) q^{52} +(4.27149 - 43.3692i) q^{53} +(-24.7401 + 23.7151i) q^{54} +(0.134199 + 0.674666i) q^{55} +(91.1275 - 41.5094i) q^{56} +(-0.832978 + 4.18766i) q^{57} +(0.954890 - 4.32087i) q^{58} +(96.9754 - 29.4172i) q^{59} +(0.392623 + 0.645080i) q^{60} +(57.4420 + 47.1415i) q^{61} +(-18.4908 + 9.38630i) q^{62} +99.9089 q^{63} +(-20.3294 + 60.6854i) q^{64} +2.85152i q^{65} +(6.61592 - 3.35837i) q^{66} +(32.5831 - 39.7026i) q^{67} +(-14.4104 + 59.2327i) q^{68} +(10.0807 + 33.2315i) q^{69} +(1.01073 - 4.57356i) q^{70} +(-62.5563 - 12.4432i) q^{71} +(-43.5573 + 46.6926i) q^{72} +(36.4386 - 7.24810i) q^{73} +(-86.4699 + 82.8875i) q^{74} +(-25.0693 - 2.46911i) q^{75} +(-2.36983 + 16.7591i) q^{76} +(-44.0376 - 13.3587i) q^{77} +(29.6143 - 8.30371i) q^{78} +(-36.5862 + 88.3269i) q^{79} +(1.69681 + 2.46630i) q^{80} +(-50.3943 + 20.8740i) q^{81} +(69.4479 + 88.3692i) q^{82} +(111.195 - 59.4350i) q^{83} +(-50.4417 + 2.82141i) q^{84} +(1.80894 + 2.20420i) q^{85} +(60.7112 - 23.6559i) q^{86} +(-1.24034 + 1.85630i) q^{87} +(25.4422 - 14.7570i) q^{88} +(24.9043 + 37.2719i) q^{89} +(0.520620 + 2.94111i) q^{90} +(-168.240 - 89.9263i) q^{91} +(47.2562 + 129.298i) q^{92} +(10.4117 - 1.02546i) q^{93} +(-2.06960 - 26.8160i) q^{94} +(0.559826 + 0.559826i) q^{95} +(20.6725 - 24.8041i) q^{96} +(-34.9278 - 34.9278i) q^{97} +(163.543 + 140.108i) q^{98} +(29.2041 - 2.87636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more