LMFDB - Embedded newform 135.3.r.a.103.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(7,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([32, 9]))

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

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

chi := DirichletCharacter("135.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.r (of order $36$, degree $12$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			103.16
Character	$\chi$	$=$	135.103
Dual form			135.3.r.a.97.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0483933 + 0.553138i) q^{2} +(-2.99964 + 0.0467854i) q^{3} +(3.63561 + 0.641056i) q^{4} +(-3.45350 - 3.61571i) q^{5} +(0.119284 - 1.66148i) q^{6} +(-4.63063 - 3.24240i) q^{7} +(-1.10537 + 4.12530i) q^{8} +(8.99562 - 0.280678i) q^{9} +O(q^{10})$	\(q+(-0.0483933 + 0.553138i) q^{2} +(-2.99964 + 0.0467854i) q^{3} +(3.63561 + 0.641056i) q^{4} +(-3.45350 - 3.61571i) q^{5} +(0.119284 - 1.66148i) q^{6} +(-4.63063 - 3.24240i) q^{7} +(-1.10537 + 4.12530i) q^{8} +(8.99562 - 0.280678i) q^{9} +(2.16711 - 1.73528i) q^{10} +(-11.8731 - 4.32147i) q^{11} +(-10.9355 - 1.75284i) q^{12} +(-2.19784 - 25.1215i) q^{13} +(2.01759 - 2.40447i) q^{14} +(10.5284 + 10.6842i) q^{15} +(11.6479 + 4.23948i) q^{16} +(-2.82813 - 10.5547i) q^{17} +(-0.280074 + 4.98941i) q^{18} +(9.55360 - 5.51578i) q^{19} +(-10.2377 - 15.3592i) q^{20} +(14.0419 + 9.50938i) q^{21} +(2.96495 - 6.35836i) q^{22} +(-6.26507 + 4.38685i) q^{23} +(3.12270 - 12.4261i) q^{24} +(-1.14673 + 24.9737i) q^{25} +14.0020 q^{26} +(-26.9705 + 1.26280i) q^{27} +(-14.7566 - 14.7566i) q^{28} +(-26.5603 - 31.6533i) q^{29} +(-6.41937 + 5.30661i) q^{30} +(-3.50453 + 19.8752i) q^{31} +(-10.1284 + 21.7204i) q^{32} +(35.8173 + 12.4073i) q^{33} +(5.97509 - 1.05357i) q^{34} +(4.26827 + 27.9406i) q^{35} +(32.8845 + 4.74626i) q^{36} +(9.11942 + 34.0341i) q^{37} +(2.58866 + 5.55139i) q^{38} +(7.76805 + 75.2524i) q^{39} +(18.7333 - 10.2500i) q^{40} +(33.5861 + 28.1821i) q^{41} +(-5.93954 + 7.30692i) q^{42} +(5.66037 + 12.1387i) q^{43} +(-40.3958 - 23.3225i) q^{44} +(-32.0812 - 31.5562i) q^{45} +(-2.12335 - 3.67775i) q^{46} +(16.1600 + 11.3154i) q^{47} +(-35.1377 - 12.1719i) q^{48} +(-5.82943 - 16.0162i) q^{49} +(-13.7584 - 1.84286i) q^{50} +(8.97717 + 31.5280i) q^{51} +(8.11377 - 92.7408i) q^{52} +(-8.21767 - 8.21767i) q^{53} +(0.606689 - 14.9795i) q^{54} +(25.3787 + 57.8540i) q^{55} +(18.4944 - 15.5187i) q^{56} +(-28.3993 + 16.9923i) q^{57} +(18.7940 - 13.1597i) q^{58} +(-4.71616 - 12.9575i) q^{59} +(31.4279 + 45.5930i) q^{60} +(-8.07405 - 45.7902i) q^{61} +(-10.8241 - 2.90032i) q^{62} +(-42.5655 - 27.8677i) q^{63} +(31.4147 + 18.1373i) q^{64} +(-83.2417 + 94.7036i) q^{65} +(-8.59630 + 19.2115i) q^{66} +(64.0900 - 5.60715i) q^{67} +(-3.51581 - 40.1859i) q^{68} +(18.5877 - 13.4521i) q^{69} +(-15.6616 + 1.00881i) q^{70} +(-7.89558 + 13.6755i) q^{71} +(-8.78561 + 37.4199i) q^{72} +(18.5472 - 69.2192i) q^{73} +(-19.2669 + 3.39728i) q^{74} +(2.27137 - 74.9656i) q^{75} +(38.2691 - 13.9288i) q^{76} +(40.9682 + 58.5086i) q^{77} +(-42.0009 + 0.655090i) q^{78} +(-81.2686 - 96.8521i) q^{79} +(-24.8971 - 56.7563i) q^{80} +(80.8424 - 5.04976i) q^{81} +(-17.2139 + 17.2139i) q^{82} +(6.12603 + 0.535958i) q^{83} +(44.9548 + 43.5740i) q^{84} +(-28.3959 + 46.6764i) q^{85} +(-6.98830 + 2.54353i) q^{86} +(81.1521 + 93.7058i) q^{87} +(30.9516 - 44.2035i) q^{88} +(149.362 - 86.2341i) q^{89} +(19.0075 - 16.2182i) q^{90} +(-71.2765 + 123.454i) q^{91} +(-25.5896 + 11.9326i) q^{92} +(9.58244 - 59.7822i) q^{93} +(-7.04100 + 8.39113i) q^{94} +(-52.9368 - 15.4944i) q^{95} +(29.3653 - 65.6273i) q^{96} +(-156.113 + 72.7967i) q^{97} +(9.14129 - 2.44940i) q^{98} +(-108.019 - 35.5418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8}+O(q^{10}) $ 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8	$ 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8} - 6 q^{10} - 60 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 6 q^{17} - 54 q^{18} - 300 q^{20} - 24 q^{21} - 12 q^{22} - 156 q^{23} + 6 q^{25} - 48 q^{26} + 180 q^{27} - 24 q^{28} + 276 q^{30} - 24 q^{31} + 72 q^{32} - 78 q^{33} + 156 q^{35} - 312 q^{36} - 6 q^{37} - 252 q^{38} - 108 q^{40} - 384 q^{41} - 528 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 210 q^{47} + 444 q^{48} + 276 q^{50} - 144 q^{51} - 60 q^{52} + 516 q^{53} - 24 q^{55} + 912 q^{56} + 168 q^{57} - 12 q^{58} + 864 q^{60} - 312 q^{61} - 6 q^{62} - 54 q^{63} + 420 q^{65} + 1224 q^{66} - 480 q^{67} - 540 q^{68} - 12 q^{70} - 12 q^{71} - 1548 q^{72} - 6 q^{73} - 852 q^{75} - 216 q^{76} - 876 q^{77} - 1362 q^{78} - 1644 q^{80} - 204 q^{81} - 24 q^{82} - 372 q^{83} - 12 q^{85} + 516 q^{86} + 540 q^{87} + 348 q^{88} - 384 q^{90} - 12 q^{91} + 2082 q^{92} - 1404 q^{93} + 198 q^{95} + 924 q^{96} + 600 q^{97} - 1032 q^{98}+O(q^{100}) $ 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8 - 6 * q^10 - 60 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 6 * q^17 - 54 * q^18 - 300 * q^20 - 24 * q^21 - 12 * q^22 - 156 * q^23 + 6 * q^25 - 48 * q^26 + 180 * q^27 - 24 * q^28 + 276 * q^30 - 24 * q^31 + 72 * q^32 - 78 * q^33 + 156 * q^35 - 312 * q^36 - 6 * q^37 - 252 * q^38 - 108 * q^40 - 384 * q^41 - 528 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 210 * q^47 + 444 * q^48 + 276 * q^50 - 144 * q^51 - 60 * q^52 + 516 * q^53 - 24 * q^55 + 912 * q^56 + 168 * q^57 - 12 * q^58 + 864 * q^60 - 312 * q^61 - 6 * q^62 - 54 * q^63 + 420 * q^65 + 1224 * q^66 - 480 * q^67 - 540 * q^68 - 12 * q^70 - 12 * q^71 - 1548 * q^72 - 6 * q^73 - 852 * q^75 - 216 * q^76 - 876 * q^77 - 1362 * q^78 - 1644 * q^80 - 204 * q^81 - 24 * q^82 - 372 * q^83 - 12 * q^85 + 516 * q^86 + 540 * q^87 + 348 * q^88 - 384 * q^90 - 12 * q^91 + 2082 * q^92 - 1404 * q^93 + 198 * q^95 + 924 * q^96 + 600 * q^97 - 1032 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0483933	+	0.553138i	−0.0241967	+	0.276569i	0.974452	+	0.224597i	$0.0721064\pi$
$2$	−0.0483933	+	0.553138i	−0.0241967	+	0.276569i	−0.998649	+	0.0519726i	$0.983449\pi$
$3$	−2.99964	+	0.0467854i	−0.999878	+	0.0155951i
$3$	−2.99964	+	0.0467854i	−0.999878	+	0.0155951i
$4$	3.63561	+	0.641056i	0.908903	+	0.160264i
$5$	−3.45350	−	3.61571i	−0.690699	−	0.723142i
$5$	−3.45350	−	3.61571i	−0.690699	−	0.723142i
$6$	0.119284	−	1.66148i	0.0198806	−	0.276913i
$7$	−4.63063	−	3.24240i	−0.661519	−	0.463200i	0.193980	−	0.981005i	$-0.437860\pi$
$7$	−4.63063	−	3.24240i	−0.661519	−	0.463200i	−0.855499	+	0.517805i	$0.826749\pi$
$8$	−1.10537	+	4.12530i	−0.138171	+	0.515662i
$9$	8.99562	−	0.280678i	0.999514	−	0.0311865i
$10$	2.16711	−	1.73528i	0.216711	−	0.173528i
$11$	−11.8731	−	4.32147i	−1.07938	−	0.392861i	−0.259701	−	0.965689i	$-0.583624\pi$
$11$	−11.8731	−	4.32147i	−1.07938	−	0.392861i	−0.819676	+	0.572828i	$0.805846\pi$
$12$	−10.9355	−	1.75284i	−0.911292	−	0.146070i
$13$	−2.19784	−	25.1215i	−0.169065	−	1.93242i	−0.327106	−	0.944988i	$-0.606073\pi$
$13$	−2.19784	−	25.1215i	−0.169065	−	1.93242i	0.158041	−	0.987433i	$-0.449482\pi$
$14$	2.01759	−	2.40447i	0.144113	−	0.171748i
$15$	10.5284	+	10.6842i	0.701893	+	0.712283i
$16$	11.6479	+	4.23948i	0.727992	+	0.264967i
$17$	−2.82813	−	10.5547i	−0.166361	−	0.620866i	−0.997863	−	0.0653447i	$-0.979185\pi$
$17$	−2.82813	−	10.5547i	−0.166361	−	0.620866i	0.831502	−	0.555522i	$-0.187481\pi$
$18$	−0.280074	+	4.98941i	−0.0155597	+	0.277189i
$19$	9.55360	−	5.51578i	0.502821	−	0.290304i	−0.227057	−	0.973882i	$-0.572910\pi$
$19$	9.55360	−	5.51578i	0.502821	−	0.290304i	0.729878	+	0.683578i	$0.239577\pi$
$20$	−10.2377	−	15.3592i	−0.511885	−	0.767960i
$21$	14.0419	+	9.50938i	0.668662	+	0.452827i
$22$	2.96495	−	6.35836i	0.134771	−	0.289016i
$23$	−6.26507	+	4.38685i	−0.272394	+	0.190733i	−0.701790	−	0.712384i	$-0.747616\pi$
$23$	−6.26507	+	4.38685i	−0.272394	+	0.190733i	0.429396	+	0.903117i	$0.358727\pi$
$24$	3.12270	−	12.4261i	0.130113	−	0.517755i
$25$	−1.14673	+	24.9737i	−0.0458692	+	0.998947i
$26$	14.0020			0.538539
$27$	−26.9705	+	1.26280i	−0.998906	+	0.0467703i
$28$	−14.7566	−	14.7566i	−0.527022	−	0.527022i
$29$	−26.5603	−	31.6533i	−0.915872	−	1.09149i	−0.995509	−	0.0946697i	$-0.969821\pi$
$29$	−26.5603	−	31.6533i	−0.915872	−	1.09149i	0.0796368	−	0.996824i	$-0.474624\pi$
$30$	−6.41937	+	5.30661i	−0.213979	+	0.176887i
$31$	−3.50453	+	19.8752i	−0.113049	+	0.641134i	0.874648	+	0.484758i	$0.161092\pi$
$31$	−3.50453	+	19.8752i	−0.113049	+	0.641134i	−0.987698	+	0.156376i	$0.950019\pi$
$32$	−10.1284	+	21.7204i	−0.316513	+	0.678764i
$33$	35.8173	+	12.4073i	1.08537	+	0.375980i
$34$	5.97509	−	1.05357i	0.175738	−	0.0309873i
$35$	4.26827	+	27.9406i	0.121951	+	0.798304i
$36$	32.8845	+	4.74626i	0.913459	+	0.131841i
$37$	9.11942	+	34.0341i	0.246471	+	0.919841i	0.972638	+	0.232324i	$0.0746329\pi$
$37$	9.11942	+	34.0341i	0.246471	+	0.919841i	−0.726168	+	0.687518i	$0.758700\pi$
$38$	2.58866	+	5.55139i	0.0681225	+	0.146089i
$39$	7.76805	+	75.2524i	0.199181	+	1.92955i
$40$	18.7333	−	10.2500i	0.468332	−	0.256250i
$41$	33.5861	+	28.1821i	0.819172	+	0.687367i	0.952778	−	0.303667i	$-0.0982112\pi$
$41$	33.5861	+	28.1821i	0.819172	+	0.687367i	−0.133606	+	0.991035i	$0.542656\pi$
$42$	−5.93954	+	7.30692i	−0.141418	+	0.173974i
$43$	5.66037	+	12.1387i	0.131636	+	0.282295i	0.961067	−	0.276314i	$-0.0891130\pi$
$43$	5.66037	+	12.1387i	0.131636	+	0.282295i	−0.829431	+	0.558609i	$0.811335\pi$
$44$	−40.3958	−	23.3225i	−0.918087	−	0.530058i
$45$	−32.0812	−	31.5562i	−0.712916	−	0.701250i
$46$	−2.12335	−	3.67775i	−0.0461597	−	0.0799510i
$47$	16.1600	+	11.3154i	0.343830	+	0.240752i	0.732718	−	0.680533i	$-0.238252\pi$
$47$	16.1600	+	11.3154i	0.343830	+	0.240752i	−0.388888	+	0.921285i	$0.627141\pi$
$48$	−35.1377	−	12.1719i	−0.732035	−	0.253582i
$49$	−5.82943	−	16.0162i	−0.118968	−	0.326862i
$50$	−13.7584	−	1.84286i	−0.275168	−	0.0368572i
$51$	8.97717	+	31.5280i	0.176023	+	0.618196i
$52$	8.11377	−	92.7408i	0.156034	−	1.78348i
$53$	−8.21767	−	8.21767i	−0.155050	−	0.155050i	0.625319	−	0.780369i	$-0.284969\pi$
$53$	−8.21767	−	8.21767i	−0.155050	−	0.155050i	−0.780369	+	0.625319i	$0.784969\pi$
$54$	0.606689	−	14.9795i	0.0112350	−	0.277398i
$55$	25.3787	+	57.8540i	0.461430	+	1.05189i
$56$	18.4944	−	15.5187i	0.330258	−	0.277119i
$57$	−28.3993	+	16.9923i	−0.498233	+	0.298110i
$58$	18.7940	−	13.1597i	0.324035	−	0.226891i
$59$	−4.71616	−	12.9575i	−0.0799348	−	0.219619i	0.893287	−	0.449486i	$-0.148393\pi$
$59$	−4.71616	−	12.9575i	−0.0799348	−	0.219619i	−0.973222	+	0.229867i	$0.926171\pi$
$60$	31.4279	+	45.5930i	0.523799	+	0.759884i
$61$	−8.07405	−	45.7902i	−0.132361	−	0.750659i	−0.976661	−	0.214787i	$-0.931094\pi$
$61$	−8.07405	−	45.7902i	−0.132361	−	0.750659i	0.844299	−	0.535872i	$-0.180017\pi$
$62$	−10.8241	−	2.90032i	−0.174583	−	0.0467793i
$63$	−42.5655	−	27.8677i	−0.675642	−	0.442345i
$64$	31.4147	+	18.1373i	0.490854	+	0.283395i
$65$	−83.2417	+	94.7036i	−1.28064	+	1.45698i
$66$	−8.59630	+	19.2115i	−0.130247	+	0.291083i
$67$	64.0900	−	5.60715i	0.956567	−	0.0836888i	0.401830	−	0.915714i	$-0.368374\pi$
$67$	64.0900	−	5.60715i	0.956567	−	0.0836888i	0.554737	+	0.832026i	$0.312819\pi$
$68$	−3.51581	−	40.1859i	−0.0517031	−	0.590969i
$69$	18.5877	−	13.4521i	0.269387	−	0.194957i
$70$	−15.6616	+	1.00881i	−0.223737	+	0.0144115i
$71$	−7.89558	+	13.6755i	−0.111205	+	0.192613i	−0.916257	−	0.400592i	$-0.868804\pi$
$71$	−7.89558	+	13.6755i	−0.111205	+	0.192613i	0.805051	+	0.593205i	$0.202138\pi$
$72$	−8.78561	+	37.4199i	−0.122022	+	0.519721i
$73$	18.5472	−	69.2192i	0.254072	−	0.948209i	−0.714533	−	0.699602i	$-0.753361\pi$
$73$	18.5472	−	69.2192i	0.254072	−	0.948209i	0.968604	−	0.248607i	$-0.0799727\pi$
$74$	−19.2669	+	3.39728i	−0.260364	+	0.0459091i
$75$	2.27137	−	74.9656i	0.0302849	−	0.999541i
$76$	38.2691	−	13.9288i	0.503541	−	0.183274i
$77$	40.9682	+	58.5086i	0.532054	+	0.759852i
$78$	−42.0009	+	0.655090i	−0.538473	+	0.00839859i
$79$	−81.2686	−	96.8521i	−1.02872	−	1.22598i	−0.973781	−	0.227486i	$-0.926949\pi$
$79$	−81.2686	−	96.8521i	−1.02872	−	1.22598i	−0.0549346	−	0.998490i	$-0.517495\pi$
$80$	−24.8971	−	56.7563i	−0.311214	−	0.709454i
$81$	80.8424	−	5.04976i	0.998055	−	0.0623427i
$82$	−17.2139	+	17.2139i	−0.209926	+	0.209926i
$83$	6.12603	+	0.535958i	0.0738076	+	0.00645732i	0.124000	−	0.992282i	$-0.460428\pi$
$83$	6.12603	+	0.535958i	0.0738076	+	0.00645732i	−0.0501921	+	0.998740i	$0.515983\pi$
$84$	44.9548	+	43.5740i	0.535177	+	0.518739i
$85$	−28.3959	+	46.6764i	−0.334069	+	0.549134i
$86$	−6.98830	+	2.54353i	−0.0812593	+	0.0295760i
$87$	81.1521	+	93.7058i	0.932783	+	1.07708i
$88$	30.9516	−	44.2035i	0.351723	−	0.502312i
$89$	149.362	−	86.2341i	1.67822	−	0.968923i	0.715429	−	0.698685i	$-0.246231\pi$
$89$	149.362	−	86.2341i	1.67822	−	0.968923i	0.962794	−	0.270238i	$-0.0871023\pi$
$90$	19.0075	−	16.2182i	0.211194	−	0.180203i
$91$	−71.2765	+	123.454i	−0.783258	+	1.35664i
$92$	−25.5896	+	11.9326i	−0.278148	+	0.129702i
$93$	9.58244	−	59.7822i	0.103037	−	0.642820i
$94$	−7.04100	+	8.39113i	−0.0749042	+	0.0892674i
$95$	−52.9368	−	15.4944i	−0.557229	−	0.163099i
$96$	29.3653	−	65.6273i	0.305889	−	0.683617i
$97$	−156.113	+	72.7967i	−1.60941	+	0.750481i	−0.999130	−	0.0417034i	$-0.986722\pi$
$97$	−156.113	+	72.7967i	−1.60941	+	0.750481i	−0.610282	+	0.792184i	$0.708944\pi$
$98$	9.14129	−	2.44940i	0.0932785	−	0.0249939i
$99$	−108.019	−	35.5418i	−1.09110	−	0.359008i
$100$	−20.1786	+	90.0595i	−0.201786	+	0.900595i
$101$	−17.7092	−	100.434i	−0.175339	−	0.994397i	−0.937752	−	0.347306i	$-0.887096\pi$
$101$	−17.7092	−	100.434i	−0.175339	−	0.994397i	0.762413	−	0.647091i	$-0.224015\pi$
$102$	−17.8738	+	3.43987i	−0.175233	+	0.0337242i
$103$	38.6374	+	18.0169i	0.375120	+	0.174922i	0.601029	−	0.799227i	$-0.294757\pi$
$103$	38.6374	+	18.0169i	0.375120	+	0.174922i	−0.225909	+	0.974148i	$0.572535\pi$
$104$	106.063	+	18.7018i	1.01984	+	0.179825i
$105$	−14.1105	−	83.6120i	−0.134386	−	0.796305i
$106$	4.94319	−	4.14783i	0.0466338	−	0.0391304i
$107$	110.011	−	110.011i	1.02814	−	1.02814i	0.0285462	−	0.999592i	$-0.490912\pi$
$107$	110.011	−	110.011i	1.02814	−	1.02814i	0.999592	−	0.0285462i	$-0.00908778\pi$
$108$	−98.8636	−	12.6985i	−0.915404	−	0.117579i
$109$		−	0.861341i		−	0.00790221i	−0.999992	−	0.00395111i	$-0.998742\pi$
$109$		−	0.861341i		−	0.00790221i	0.999992	−	0.00395111i	$-0.00125768\pi$
$110$	−33.2295	+	11.2382i	−0.302086	+	0.102165i
$111$	−28.9472	−	101.663i	−0.260786	−	0.915886i
$112$	−40.1909	−	57.3985i	−0.358847	−	0.512487i
$113$	168.885	+	78.7526i	1.49456	+	0.696925i	0.986404	−	0.164339i	$-0.0525491\pi$
$113$	168.885	+	78.7526i	1.49456	+	0.696925i	0.508157	+	0.861264i	$0.330327\pi$
$114$	−8.02475	−	16.5310i	−0.0703925	−	0.145009i
$115$	37.4980	+	7.50272i	0.326069	+	0.0652410i
$116$	−76.2713	−	132.106i	−0.657511	−	1.13884i
$117$	−26.8220	−	225.366i	−0.229248	−	1.92621i
$118$	7.39554	−	1.98163i	0.0626741	−	0.0167935i
$119$	−21.1266	+	58.0450i	−0.177535	+	0.487773i
$120$	−55.7135	+	31.6227i	−0.464279	+	0.263523i
$121$	29.6051	+	24.8416i	0.244670	+	0.205303i
$122$	25.7191	−	2.25013i	0.210812	−	0.0184437i
$123$	−102.064	−	82.9645i	−0.829792	−	0.674508i
$124$	−25.4822	+	70.0118i	−0.205502	+	0.564611i
$125$	94.2579	−	82.1003i	0.754063	−	0.656802i
$126$	17.4746	−	22.1960i	0.138687	−	0.176159i
$127$	−195.891	−	52.4887i	−1.54245	−	0.413297i	−0.615391	−	0.788222i	$-0.711002\pi$
$127$	−195.891	−	52.4887i	−1.54245	−	0.413297i	−0.927055	+	0.374925i	$0.877669\pi$
$128$	−66.5377	+	95.0257i	−0.519826	+	0.742388i
$129$	−17.5469	−	36.1468i	−0.136023	−	0.280208i
$130$	−48.3559	−	50.6272i	−0.371968	−	0.389440i
$131$	−41.6790	+	236.373i	−0.318160	+	1.80438i	0.235764	+	0.971810i	$0.424241\pi$
$131$	−41.6790	+	236.373i	−0.318160	+	1.80438i	−0.553924	+	0.832567i	$0.686870\pi$
$132$	122.264	+	68.0692i	0.926242	+	0.515676i
$133$	−62.1236	−	5.43511i	−0.467094	−	0.0408655i
$134$			35.7220i			0.266582i
$135$	97.7083	+	93.1563i	0.723765	+	0.690047i
$136$	46.6675			0.343144
$137$	2.05837	−	23.5273i	0.0150246	−	0.171732i	−0.984975	−	0.172697i	$-0.944752\pi$
$137$	2.05837	−	23.5273i	0.0150246	−	0.171732i	1.00000		0.000965490i	$0.000307325\pi$
$138$	6.54133	+	10.9326i	0.0474010	+	0.0792214i
$139$	108.437	+	19.1203i	0.780121	+	0.137556i	0.549507	−	0.835489i	$-0.314816\pi$
$139$	108.437	+	19.1203i	0.780121	+	0.137556i	0.230614	+	0.973045i	$0.425927\pi$
$140$	−2.39374	+	104.317i	−0.0170981	+	0.745125i
$141$	−49.0035	−	33.1859i	−0.347543	−	0.235361i
$142$	−7.18238	−	5.02916i	−0.0505801	−	0.0354166i
$143$	−82.4664	+	307.769i	−0.576688	+	2.15223i
$144$	105.970	+	34.8674i	0.735901	+	0.242135i
$145$	−22.7234	+	205.349i	−0.156713	+	1.41620i
$146$	37.3903	+	13.6089i	0.256098	+	0.0932119i
$147$	18.2355	+	47.7701i	0.124051	+	0.324966i
$148$	11.3369	+	129.581i	0.0766004	+	0.875547i
$149$	113.649	−	135.442i	0.762746	−	0.909005i	−0.235272	−	0.971929i	$-0.575598\pi$
$149$	113.649	−	135.442i	0.762746	−	0.909005i	0.998018	+	0.0629242i	$0.0200426\pi$
$150$	41.3564	+	4.88422i	0.275710	+	0.0325614i
$151$	122.539	+	44.6004i	0.811514	+	0.295367i	0.714249	−	0.699891i	$-0.246768\pi$
$151$	122.539	+	44.6004i	0.811514	+	0.295367i	0.0972650	+	0.995259i	$0.468991\pi$
$152$	12.1940	+	45.5085i	0.0802234	+	0.299398i
$153$	−28.4033	−	94.1525i	−0.185642	−	0.615376i
$154$	−34.3460	+	19.8297i	−0.223026	+	0.128764i
$155$	83.9657	−	55.9675i	0.541714	−	0.361080i
$156$	−19.9994	+	278.568i	−0.128201	+	1.78569i
$157$	47.8753	−	102.669i	0.304938	−	0.653942i	−0.692802	−	0.721127i	$-0.743624\pi$
$157$	47.8753	−	102.669i	0.304938	−	0.653942i	0.997740	+	0.0671856i	$0.0214020\pi$
$158$	57.5055	−	40.2658i	0.363959	−	0.254847i
$159$	25.0345	+	24.2655i	0.157450	+	0.152613i
$160$	113.513	−	38.3901i	0.709458	−	0.239938i
$161$	43.2352			0.268541
$162$	−1.11902	+	44.9614i	−0.00690754	+	0.277540i
$163$	146.282	+	146.282i	0.897433	+	0.897433i	0.995208	−	0.0977755i	$-0.0311727\pi$
$163$	146.282	+	146.282i	0.897433	+	0.897433i	−0.0977755	+	0.995208i	$0.531173\pi$
$164$	104.040	+	123.990i	0.634388	+	0.756034i
$165$	−78.8335	−	172.354i	−0.477779	−	1.04457i
$166$	−0.592918	+	3.36260i	−0.00357179	+	0.0202567i
$167$	−24.6610	+	52.8858i	−0.147671	+	0.316681i	−0.966204	−	0.257778i	$-0.917010\pi$
$167$	−24.6610	+	52.8858i	−0.147671	+	0.316681i	0.818533	+	0.574459i	$0.194788\pi$
$168$	−54.7505	+	47.4156i	−0.325896	+	0.282236i
$169$	−459.825	+	81.0795i	−2.72086	+	0.479761i
$170$	−24.4443	−	17.9657i	−0.143790	−	0.105681i
$171$	84.3925	−	52.2993i	0.493523	−	0.305844i
$172$	12.7973	+	47.7602i	0.0744029	+	0.277675i
$173$	−64.9773	−	139.344i	−0.375591	−	0.805458i	−0.999709	−	0.0241275i	$-0.992319\pi$
$173$	−64.9773	−	139.344i	−0.375591	−	0.805458i	0.624118	−	0.781330i	$-0.285459\pi$
$174$	−55.7595	+	40.3536i	−0.320457	+	0.231917i
$175$	86.2848	−	111.926i	0.493056	−	0.639576i
$176$	−119.976	−	100.672i	−0.681682	−	0.571999i
$177$	14.7530	+	38.6472i	0.0833501	+	0.218346i
$178$	40.4713	+	86.7909i	0.227367	+	0.487590i
$179$	−112.249	−	64.8068i	−0.627088	−	0.362049i	0.152536	−	0.988298i	$-0.451256\pi$
$179$	−112.249	−	64.8068i	−0.627088	−	0.362049i	−0.779623	+	0.626249i	$0.784589\pi$
$180$	−96.4054	−	135.292i	−0.535586	−	0.751623i
$181$	−59.3027	−	102.715i	−0.327639	−	0.567488i	0.654404	−	0.756145i	$-0.272920\pi$
$181$	−59.3027	−	102.715i	−0.327639	−	0.567488i	−0.982043	+	0.188658i	$0.939586\pi$
$182$	−64.8381	−	45.4001i	−0.356253	−	0.249451i
$183$	26.3615	+	136.976i	0.144052	+	0.748504i
$184$	−11.1718	−	30.6944i	−0.0607166	−	0.166817i
$185$	91.5637	−	150.510i	0.494939	−	0.813567i
$186$	32.6041	+	8.19348i	0.175291	+	0.0440509i
$187$	−12.0331	+	137.539i	−0.0643484	+	0.735505i
$188$	51.4977	+	51.4977i	0.273924	+	0.273924i
$189$	128.985	+	81.6015i	0.682459	+	0.431754i
$190$	11.1323	−	28.5315i	0.0585911	−	0.150166i
$191$	−24.5764	+	20.6221i	−0.128672	+	0.107969i	−0.704853	−	0.709354i	$-0.748987\pi$
$191$	−24.5764	+	20.6221i	−0.128672	+	0.107969i	0.576180	+	0.817323i	$0.304543\pi$
$192$	−95.0811	−	52.9354i	−0.495214	−	0.275705i
$193$	68.2248	−	47.7715i	0.353496	−	0.247521i	−0.383317	−	0.923617i	$-0.625218\pi$
$193$	68.2248	−	47.7715i	0.353496	−	0.247521i	0.736814	+	0.676096i	$0.236330\pi$
$194$	−32.7118	−	89.8749i	−0.168618	−	0.463273i
$195$	245.264	−	287.971i	1.25776	−	1.47677i
$196$	−10.9262	−	61.9657i	−0.0557461	−	0.316152i
$197$	82.3714	+	22.0713i	0.418129	+	0.112037i	0.461748	−	0.887011i	$-0.347222\pi$
$197$	82.3714	+	22.0713i	0.418129	+	0.112037i	−0.0436196	+	0.999048i	$0.513889\pi$
$198$	24.8869	−	58.0296i	0.125692	−	0.293079i
$199$	−44.1683	−	25.5006i	−0.221951	−	0.128144i	0.384902	−	0.922957i	$-0.374235\pi$
$199$	−44.1683	−	25.5006i	−0.221951	−	0.128144i	−0.606853	+	0.794814i	$0.707569\pi$
$200$	−101.756	−	32.3358i	−0.508782	−	0.161679i
$201$	−191.984	+	19.8179i	−0.955146	+	0.0985964i
$202$	56.4110	−	4.93532i	0.279262	−	0.0244323i
$203$	20.3581	+	232.694i	0.100286	+	1.14628i
$204$	12.4263	+	120.378i	0.0609130	+	0.590090i
$205$	−14.0912	−	218.764i	−0.0687375	−	1.06714i
$206$	−11.8356	+	20.4999i	−0.0574546	+	0.0995142i
$207$	−55.1269	+	41.2209i	−0.266314	+	0.199135i
$208$	80.9017	−	301.929i	0.388950	−	1.45158i
$209$	−137.268	+	24.2040i	−0.656783	+	0.115809i
$210$	46.9319	−	3.75878i	0.223485	−	0.0178990i
$211$	−204.965	+	74.6012i	−0.971399	+	0.353560i	−0.778490	−	0.627657i	$-0.784014\pi$
$211$	−204.965	+	74.6012i	−0.971399	+	0.353560i	−0.192908	+	0.981217i	$0.561792\pi$
$212$	−24.6083	−	35.1442i	−0.116077	−	0.165775i
$213$	23.0440	−	41.3911i	0.108188	−	0.194324i
$214$	55.5274	+	66.1750i	0.259474	+	0.309229i
$215$	24.3420	−	62.3872i	0.113218	−	0.290173i
$216$	24.6029	−	112.657i	0.113902	−	0.521560i
$217$	80.6715	−	80.6715i	0.371758	−	0.371758i
$218$	0.476441	+	0.0416832i	0.00218551	+	0.000191207i
$219$	−52.3965	+	208.500i	−0.239253	+	0.952056i
$220$	55.1793	+	226.604i	0.250815	+	1.03002i
$221$	−258.934	+	94.2444i	−1.17165	+	0.426445i
$222$	57.6347	−	11.0920i	0.259616	−	0.0499639i
$223$	85.2030	−	121.683i	0.382076	−	0.545662i	−0.581343	−	0.813658i	$-0.697473\pi$
$223$	85.2030	−	121.683i	0.382076	−	0.545662i	0.963420	+	0.267997i	$0.0863616\pi$
$224$	117.327	−	67.7390i	0.523783	−	0.302406i
$225$	−3.30597	+	224.976i	−0.0146932	+	0.999892i
$226$	−51.7340	+	89.6059i	−0.228911	+	0.396486i
$227$	269.320	−	125.586i	1.18643	−	0.553242i	0.273705	−	0.961814i	$-0.411751\pi$
$227$	269.320	−	125.586i	1.18643	−	0.553242i	0.912726	+	0.408572i	$0.133973\pi$
$228$	−114.142	+	43.5718i	−0.500622	+	0.191104i
$229$	−73.2719	+	87.3221i	−0.319965	+	0.381319i	−0.901921	−	0.431901i	$-0.857843\pi$
$229$	−73.2719	+	87.3221i	−0.319965	+	0.381319i	0.581956	+	0.813220i	$0.302287\pi$
$230$	−5.96469	+	20.3785i	−0.0259335	+	0.0886022i
$231$	−125.627	−	173.588i	−0.543840	−	0.751463i
$232$	159.938	−	74.5805i	0.689389	−	0.321468i
$233$	281.921	−	75.5405i	1.20996	−	0.324208i	0.403215	−	0.915105i	$-0.367893\pi$
$233$	281.921	−	75.5405i	1.20996	−	0.324208i	0.806747	+	0.590897i	$0.201226\pi$
$234$	125.957	−	3.93006i	0.538277	−	0.0167951i
$235$	−14.8955	−	97.5075i	−0.0633849	−	0.414925i
$236$	−8.83960	−	50.1319i	−0.0374559	−	0.212423i
$237$	248.307	+	286.719i	1.04771	+	1.20978i
$238$	−31.0845	−	14.4949i	−0.130607	−	0.0609031i
$239$	−241.965	−	42.6650i	−1.01241	−	0.178515i	−0.357251	−	0.934008i	$-0.616286\pi$
$239$	−241.965	−	42.6650i	−1.01241	−	0.178515i	−0.655156	+	0.755494i	$0.727397\pi$
$240$	77.3377	+	169.084i	0.322241	+	0.704515i
$241$	−114.577	+	96.1412i	−0.475422	+	0.398926i	−0.848768	−	0.528766i	$-0.822655\pi$
$241$	−114.577	+	96.1412i	−0.475422	+	0.398926i	0.373346	+	0.927692i	$0.378210\pi$
$242$	−15.1735	+	15.1735i	−0.0627006	+	0.0627006i
$243$	−242.262	+	18.9297i	−0.996961	+	0.0778999i
$244$		−	171.651i		−	0.703489i
$245$	−37.7781	+	76.3895i	−0.154196	+	0.311794i
$246$	50.8301	−	52.4408i	0.206626	−	0.213174i
$247$	−159.562	−	227.878i	−0.645999	−	0.922582i
$248$	−78.1172	−	36.4267i	−0.314989	−	0.146882i
$249$	−18.4009	−	1.32107i	−0.0738993	−	0.00530550i
$250$	40.8514	+	56.1107i	0.163405	+	0.224443i
$251$	−139.937	−	242.379i	−0.557520	−	0.965653i	−0.997703	−	0.0677446i	$-0.978420\pi$
$251$	−139.937	−	242.379i	−0.557520	−	0.965653i	0.440183	−	0.897908i	$-0.354914\pi$
$252$	−136.887	−	128.603i	−0.543201	−	0.510329i
$253$	93.3438	−	25.0114i	0.368948	−	0.0988592i
$254$	38.5133	−	105.815i	0.151627	−	0.416593i
$255$	82.9936	−	141.341i	0.325465	−	0.554277i
$256$	61.8093	+	51.8641i	0.241442	+	0.202594i
$257$	118.966	−	10.4081i	0.462901	−	0.0404986i	0.146680	−	0.989184i	$-0.453141\pi$
$257$	118.966	−	10.4081i	0.462901	−	0.0404986i	0.316222	+	0.948685i	$0.397586\pi$
$258$	20.8434	−	7.95662i	0.0807882	−	0.0308396i
$259$	68.1237	−	187.168i	0.263026	−	0.722657i
$260$	−363.345	+	290.943i	−1.39748	+	1.11901i
$261$	−247.811	−	277.286i	−0.949466	−	1.06240i
$262$	−128.730	−	34.4932i	−0.491337	−	0.131653i
$263$	−65.7689	+	93.9277i	−0.250072	+	0.357139i	−0.924488	−	0.381212i	$-0.875507\pi$
$263$	−65.7689	+	93.9277i	−0.250072	+	0.357139i	0.674416	+	0.738352i	$0.264396\pi$
$264$	−90.7754	+	134.042i	−0.343846	+	0.507736i
$265$	−1.33303	+	58.0924i	−0.00503029	+	0.219217i
$266$	6.01273	−	34.0999i	0.0226043	−	0.128195i
$267$	−443.997	+	265.659i	−1.66291	+	0.994977i
$268$	236.601	+	20.6999i	0.882839	+	0.0772384i
$269$			96.3036i			0.358006i	0.983849	+	0.179003i	$0.0572872\pi$
$269$			96.3036i			0.358006i	−0.983849	+	0.179003i	$0.942713\pi$
$270$	−56.2568	+	49.5380i	−0.208358	+	0.183474i
$271$	207.682			0.766354			0.383177	−	0.923675i	$-0.374830\pi$
$271$	207.682			0.766354			0.383177	+	0.923675i	$0.374830\pi$
$272$	11.8048	−	134.930i	0.0434001	−	0.496066i
$273$	208.028	−	373.653i	0.762006	−	1.36869i
$274$	12.9142	+	2.27712i	0.0471322	+	0.00831067i
$275$	121.538	−	291.561i	0.441958	−	1.06022i
$276$	76.2011	−	36.9907i	0.276091	−	0.134024i
$277$	272.342	+	190.696i	0.983183	+	0.688432i	0.950400	−	0.311030i	$-0.100674\pi$
$277$	272.342	+	190.696i	0.983183	+	0.688432i	0.0327831	+	0.999462i	$0.489563\pi$
$278$	−15.8238	+	59.0553i	−0.0569202	+	0.212429i
$279$	−25.9469	+	179.773i	−0.0929996	+	0.644348i
$280$	−119.982	−	13.2769i	−0.428505	−	0.0474173i
$281$	172.361	+	62.7342i	0.613384	+	0.223254i	0.629983	−	0.776609i	$-0.283062\pi$
$281$	172.361	+	62.7342i	0.613384	+	0.223254i	−0.0165993	+	0.999862i	$0.505284\pi$
$282$	20.7278	−	25.4998i	0.0735030	−	0.0904247i
$283$	−38.0598	−	435.025i	−0.134487	−	1.53719i	−0.701013	−	0.713149i	$-0.747268\pi$
$283$	−38.0598	−	435.025i	−0.134487	−	1.53719i	0.566526	−	0.824044i	$-0.308287\pi$
$284$	−37.4721	+	44.6575i	−0.131944	+	0.157245i
$285$	159.516	+	44.0008i	0.559705	+	0.154389i
$286$	−166.248	−	60.5093i	−0.581286	−	0.211571i
$287$	−64.1471	−	239.400i	−0.223509	−	0.834147i
$288$	−85.0149	+	198.232i	−0.295191	+	0.688305i
$289$	146.877	−	84.7997i	0.508226	−	0.293425i
$290$	−112.487	−	22.5067i	−0.387885	−	0.0776093i
$291$	464.876	−	225.667i	1.59751	−	0.775489i
$292$	111.804	−	239.764i	0.382890	−	0.821111i
$293$	−364.964	+	255.550i	−1.24561	+	0.872185i	−0.995381	−	0.0960017i	$-0.969395\pi$
$293$	−364.964	+	255.550i	−1.24561	+	0.872185i	−0.250228	+	0.968187i	$0.580506\pi$
$294$	−27.3059	+	7.77499i	−0.0928773	+	0.0264455i
$295$	−30.5635	+	61.8010i	−0.103605	+	0.209495i
$296$	−150.481			−0.508383
$297$	325.681	+	101.559i	1.09657	+	0.341948i
$298$	69.4182	+	69.4182i	0.232947	+	0.232947i
$299$	123.974	+	147.746i	0.414628	+	0.494134i
$300$	56.3150	−	271.090i	0.187717	−	0.903632i
$301$	13.1475	−	74.5630i	0.0436793	−	0.247718i
$302$	−30.6003	+	65.6225i	−0.101325	+	0.217293i
$303$	57.8201	+	300.437i	0.190825	+	0.991542i
$304$	134.663	−	23.7447i	0.442971	−	0.0781077i
$305$	−137.680	+	187.330i	−0.451411	+	0.614196i
$306$	53.4539	−	11.1546i	0.174686	−	0.0364529i
$307$	72.5844	+	270.889i	0.236431	+	0.882373i	0.977499	+	0.210942i	$0.0676532\pi$
$307$	72.5844	+	270.889i	0.236431	+	0.882373i	−0.741067	+	0.671431i	$0.765680\pi$
$308$	111.437	+	238.978i	0.361809	+	0.775901i
$309$	−116.741	−	52.2365i	−0.377803	−	0.169050i
$310$	26.8944	+	49.1531i	0.0867560	+	0.158558i
$311$	−70.6694	−	59.2987i	−0.227233	−	0.190671i	0.522062	−	0.852908i	$-0.325163\pi$
$311$	−70.6694	−	59.2987i	−0.227233	−	0.190671i	−0.749295	+	0.662237i	$0.769607\pi$
$312$	−319.025	−	51.1363i	−1.02252	−	0.163898i
$313$	−138.795	−	297.647i	−0.443435	−	0.950950i	−0.993286	−	0.115687i	$-0.963093\pi$
$313$	−138.795	−	297.647i	−0.443435	−	0.950950i	0.549850	−	0.835263i	$-0.314685\pi$
$314$	54.4732	+	31.4501i	0.173482	+	0.100160i
$315$	46.2381	+	250.145i	0.146788	+	0.794112i
$316$	−233.373	−	404.214i	−0.738523	−	1.27916i
$317$	274.596	+	192.274i	0.866232	+	0.606542i	0.919960	−	0.392013i	$-0.128221\pi$
$317$	274.596	+	192.274i	0.866232	+	0.606542i	−0.0537274	+	0.998556i	$0.517110\pi$
$318$	−14.6337	+	12.6732i	−0.0460179	+	0.0398529i
$319$	178.565	+	490.604i	0.559766	+	1.53794i
$320$	−42.9113	−	176.223i	−0.134098	−	0.550698i
$321$	−324.845	+	335.139i	−1.01198	+	1.04405i
$322$	−2.09229	+	23.9150i	−0.00649781	+	0.0742703i
$323$	−85.2363	−	85.2363i	−0.263890	−	0.263890i
$324$	297.149	+	33.4656i	0.917126	+	0.103289i
$325$	629.896	−	26.0807i	1.93814	−	0.0802484i
$326$	−87.9930	+	73.8349i	−0.269917	+	0.226487i
$327$	0.0402982	+	2.58371i	0.000123236	+	0.00790125i
$328$	−153.384	+	107.401i	−0.467636	+	0.327442i
$329$	−38.1421	−	104.794i	−0.115933	−	0.318524i
$330$	99.1505	−	35.2651i	0.300456	−	0.106864i
$331$	69.8452	+	396.112i	0.211013	+	1.19671i	0.887693	+	0.460435i	$0.152307\pi$
$331$	69.8452	+	396.112i	0.211013	+	1.19671i	−0.676681	+	0.736277i	$0.736582\pi$
$332$	21.9283	+	5.87566i	0.0660490	+	0.0176978i
$333$	91.5875	+	303.599i	0.275038	+	0.911707i
$334$	−28.0597	−	16.2003i	−0.0840111	−	0.0485038i
$335$	−241.608	−	212.367i	−0.721219	−	0.633930i
$336$	123.243	+	170.294i	0.366796	+	0.506828i
$337$	−315.597	+	27.6112i	−0.936489	+	0.0819322i	−0.545173	−	0.838324i	$-0.683536\pi$
$337$	−315.597	+	27.6112i	−0.936489	+	0.0819322i	−0.391317	+	0.920256i	$0.627980\pi$
$338$	−22.5957	−	258.271i	−0.0668513	−	0.764114i
$339$	−510.279	−	228.328i	−1.50525	−	0.673533i
$340$	−133.159	+	151.494i	−0.391643	+	0.445570i
$341$	127.500	−	220.836i	0.373900	−	0.647613i
$342$	24.8447	+	49.2116i	0.0726454	+	0.143894i
$343$	−96.6286	+	360.623i	−0.281716	+	1.05138i
$344$	−56.3325	+	9.93295i	−0.163757	+	0.0288748i
$345$	−112.831	−	20.7511i	−0.327047	−	0.0601480i
$346$	80.2211	−	29.1981i	0.231853	−	0.0843875i
$347$	−97.1591	−	138.758i	−0.279997	−	0.399878i	0.654378	−	0.756167i	$-0.272930\pi$
$347$	−97.1591	−	138.758i	−0.279997	−	0.399878i	−0.934375	+	0.356290i	$0.884042\pi$
$348$	234.967	+	392.701i	0.675192	+	1.12845i
$349$	−91.9403	−	109.570i	−0.263439	−	0.313955i	0.618068	−	0.786124i	$-0.287915\pi$
$349$	−91.9403	−	109.570i	−0.263439	−	0.313955i	−0.881508	+	0.472170i	$0.843471\pi$
$350$	57.7348	+	53.1439i	0.164957	+	0.151840i
$351$	91.0001	+	674.762i	0.259260	+	1.92240i
$352$	214.120	−	214.120i	0.608297	−	0.608297i
$353$	−25.6087	−	2.24047i	−0.0725459	−	0.00634694i	0.0508250	−	0.998708i	$-0.483815\pi$
$353$	−25.6087	−	2.24047i	−0.0725459	−	0.00634694i	−0.123371	+	0.992361i	$0.539370\pi$
$354$	−22.0912	+	6.29017i	−0.0624045	+	0.0177688i
$355$	76.7142	−	18.6803i	0.216096	−	0.0526206i
$356$	598.303	−	217.764i	1.68063	−	0.611697i
$357$	60.6565	−	175.102i	0.169906	−	0.490482i
$358$	41.2792	−	58.9528i	0.115305	−	0.164673i
$359$	199.276	−	115.052i	0.555086	−	0.320479i	−0.196085	−	0.980587i	$-0.562823\pi$
$359$	199.276	−	115.052i	0.555086	−	0.320479i	0.751171	+	0.660108i	$0.229490\pi$
$360$	165.641	−	97.4632i	0.460113	−	0.270731i
$361$	−119.652	+	207.244i	−0.331447	+	0.574083i
$362$	59.6856	−	27.8319i	0.164877	−	0.0768836i
$363$	−89.9667	−	73.1307i	−0.247842	−	0.201462i
$364$	−338.275	+	403.140i	−0.929326	+	1.10753i
$365$	−314.330	+	171.987i	−0.861177	+	0.471197i
$366$	−77.0425	+	7.95283i	−0.210499	+	0.0217291i
$367$	144.698	−	67.4737i	0.394272	−	0.183852i	−0.215363	−	0.976534i	$-0.569094\pi$
$367$	144.698	−	67.4737i	0.394272	−	0.183852i	0.609636	+	0.792682i	$0.291316\pi$
$368$	−91.5727	+	24.5368i	−0.248839	+	0.0666762i
$369$	310.038	+	244.088i	0.840210	+	0.661486i
$370$	78.8217	+	57.9311i	0.213032	+	0.156570i
$371$	11.4080	+	64.6980i	0.0307493	+	0.174388i
$372$	73.1618	−	211.202i	0.196671	−	0.567747i
$373$	11.9173	+	5.55713i	0.0319499	+	0.0148985i	0.438528	−	0.898718i	$-0.355500\pi$
$373$	11.9173	+	5.55713i	0.0319499	+	0.0148985i	−0.406578	+	0.913616i	$0.633278\pi$
$374$	−75.4960	−	13.3120i	−0.201861	−	0.0355936i
$375$	−278.898	+	250.681i	−0.743728	+	0.668482i
$376$	−64.5420	+	54.1572i	−0.171654	+	0.144035i
$377$	−736.802	+	736.802i	−1.95438	+	1.95438i
$378$	−51.3789	+	67.3974i	−0.135923	+	0.178300i
$379$		−	596.696i		−	1.57440i	−0.616700	−	0.787198i	$-0.711531\pi$
$379$		−	596.696i		−	1.57440i	0.616700	−	0.787198i	$-0.288469\pi$
$380$	−182.525	−	90.2669i	−0.480328	−	0.237545i
$381$	590.056	+	148.282i	1.54870	+	0.389192i
$382$	−10.2175	−	14.5921i	−0.0267475	−	0.0381993i
$383$	170.672	+	79.5859i	0.445620	+	0.207796i	0.632458	−	0.774595i	$-0.282046\pi$
$383$	170.672	+	79.5859i	0.445620	+	0.207796i	−0.186838	+	0.982391i	$0.559824\pi$
$384$	195.143	−	288.155i	0.508185	−	0.750405i
$385$	70.0668	−	350.189i	0.181992	−	0.909581i
$386$	23.1226	+	40.0496i	0.0599032	+	0.103755i
$387$	54.3256	+	107.606i	0.140376	+	0.278053i
$388$	−614.233	+	164.583i	−1.58307	+	0.424183i
$389$	3.84137	−	10.5541i	0.00987499	−	0.0271313i	−0.934657	−	0.355550i	$-0.884294\pi$
$389$	3.84137	−	10.5541i	0.00987499	−	0.0271313i	0.944532	+	0.328419i	$0.106516\pi$
$390$	147.419	+	149.601i	0.377996	+	0.383592i
$391$	64.0205	+	53.7195i	0.163735	+	0.137390i
$392$	72.5154	−	6.34427i	0.184988	−	0.0161844i
$393$	113.963	−	710.984i	0.289982	−	1.80912i
$394$	−16.1947	+	44.4947i	−0.0411034	+	0.112931i
$395$	−69.5285	+	628.322i	−0.176022	+	1.59069i
$396$	−369.932	−	198.463i	−0.934171	−	0.501168i
$397$	−329.039	−	88.1658i	−0.828814	−	0.222080i	−0.180618	−	0.983553i	$-0.557810\pi$
$397$	−329.039	−	88.1658i	−0.828814	−	0.222080i	−0.648196	+	0.761473i	$0.724476\pi$
$398$	16.2428	−	23.1971i	0.0408111	−	0.0582842i
$399$	186.602	+	13.3969i	0.467675	+	0.0335761i
$400$	−119.232	+	286.029i	−0.298081	+	0.715072i
$401$	6.83659	−	38.7722i	0.0170488	−	0.0966888i	−0.975096	−	0.221783i	$-0.928812\pi$
$401$	6.83659	−	38.7722i	0.0170488	−	0.0966888i	0.992145	+	0.125094i	$0.0399234\pi$
$402$	−1.67127	−	107.153i	−0.00415738	−	0.266550i
$403$	506.996	+	44.3564i	1.25805	+	0.110065i
$404$		−	376.492i		−	0.931911i
$405$	−297.448	−	274.864i	−0.734438	−	0.678675i
$406$	−129.697			−0.319451
$407$	38.8014	−	443.501i	0.0953350	−	1.08968i
$408$	−139.986	+	2.18336i	−0.343102	+	0.00535138i
$409$	−17.4627	−	3.07914i	−0.0426960	−	0.00752846i	0.152259	−	0.988341i	$-0.451345\pi$
$409$	−17.4627	−	3.07914i	−0.0426960	−	0.00752846i	−0.194955	+	0.980812i	$0.562456\pi$
$410$	121.689	+	2.79235i	0.296802	+	0.00681061i
$411$	−5.07362	+	70.6695i	−0.0123446	+	0.171945i
$412$	128.921	+	90.2712i	0.312914	+	0.219105i
$413$	−20.1748	+	75.2932i	−0.0488493	+	0.182308i
$414$	−20.1331	−	32.4876i	−0.0486307	−	0.0784726i
$415$	−19.2183	−	24.0009i	−0.0463093	−	0.0578334i
$416$	567.910	+	206.702i	1.36517	+	0.496881i
$417$	−326.165	−	52.2808i	−0.782171	−	0.125374i
$418$	−6.74531	−	77.0993i	−0.0161371	−	0.184448i
$419$	−262.389	+	312.703i	−0.626227	+	0.746308i	−0.982128	−	0.188215i	$-0.939730\pi$
$419$	−262.389	+	312.703i	−0.626227	+	0.746308i	0.355901	+	0.934524i	$0.384174\pi$
$420$	2.29980	−	313.026i	0.00547572	−	0.745301i
$421$	435.394	+	158.470i	1.03419	+	0.376414i	0.802675	−	0.596417i	$-0.203410\pi$
$421$	435.394	+	158.470i	1.03419	+	0.376414i	0.231515	+	0.972831i	$0.425632\pi$
$422$	−31.3458	−	116.984i	−0.0742792	−	0.277214i
$423$	148.545	+	97.2529i	0.351171	+	0.229912i
$424$	42.9839	−	24.8168i	0.101377	−	0.0585301i
$425$	266.834	−	58.5254i	0.627844	−	0.137707i
$426$	21.7798	+	14.7496i	0.0511263	+	0.0346235i
$427$	−111.082	+	238.217i	−0.260146	+	0.557885i
$428$	470.480	−	329.433i	1.09925	−	0.769704i
$429$	232.970	−	927.052i	0.543054	−	2.16096i
$430$	33.3308	+	16.4836i	0.0775134	+	0.0383339i
$431$	16.0036			0.0371314			0.0185657	−	0.999828i	$-0.494090\pi$
$431$	16.0036			0.0371314			0.0185657	+	0.999828i	$0.494090\pi$
$432$	−319.502	−	99.6317i	−0.739588	−	0.230629i
$433$	196.129	+	196.129i	0.452954	+	0.452954i	0.896334	−	0.443380i	$-0.146221\pi$
$433$	196.129	+	196.129i	0.452954	+	0.452954i	−0.443380	+	0.896334i	$0.646221\pi$
$434$	40.7185	+	48.5264i	0.0938215	+	0.111812i
$435$	58.5546	−	617.035i	0.134608	−	1.41847i
$436$	0.552168	−	3.13150i	0.00126644	−	0.00718234i
$437$	−35.6571	+	76.4670i	−0.0815953	+	0.174982i
$438$	−112.794	−	39.0725i	−0.257520	−	0.0892067i
$439$	−130.608	+	23.0298i	−0.297513	+	0.0524596i	−0.320412	−	0.947278i	$-0.603821\pi$
$439$	−130.608	+	23.0298i	−0.297513	+	0.0524596i	0.0228991	+	0.999738i	$0.492710\pi$
$440$	−266.718	+	40.7444i	−0.606177	+	0.0926010i
$441$	−56.9347	−	142.440i	−0.129104	−	0.322992i
$442$	−39.5995	−	147.787i	−0.0895916	−	0.334361i
$443$	−286.508	−	614.418i	−0.646745	−	1.38695i	−0.906885	−	0.421378i	$-0.861547\pi$
$443$	−286.508	−	614.418i	−0.646745	−	1.38695i	0.260140	−	0.965571i	$-0.416231\pi$
$444$	−40.0689	−	388.165i	−0.0902454	−	0.874246i
$445$	−827.618	−	242.240i	−1.85982	−	0.544360i
$446$	63.1840	+	53.0177i	0.141668	+	0.118874i
$447$	−334.569	+	411.593i	−0.748477	+	0.920790i
$448$	−86.6614	−	185.846i	−0.193441	−	0.414835i
$449$	743.794	+	429.430i	1.65656	+	0.956414i	0.974286	+	0.225315i	$0.0723410\pi$
$449$	743.794	+	429.430i	1.65656	+	0.956414i	0.682271	+	0.731099i	$0.260992\pi$
$450$	−124.283	−	12.7160i	−0.276184	−	0.0282577i
$451$	−276.984	−	479.751i	−0.614156	−	1.06375i
$452$	563.517	+	394.579i	1.24672	+	0.872962i
$453$	−369.658	−	128.052i	−0.816022	−	0.282675i
$454$	56.4331	+	155.049i	0.124302	+	0.341517i
$455$	692.529	−	168.634i	1.52204	−	0.370625i
$456$	−38.7065	−	135.938i	−0.0848828	−	0.298110i
$457$	−39.0258	+	446.067i	−0.0853955	+	0.976076i	0.825762	+	0.564018i	$0.190745\pi$
$457$	−39.0258	+	446.067i	−0.0853955	+	0.976076i	−0.911158	+	0.412057i	$0.864810\pi$
$458$	−44.7553	−	44.7553i	−0.0977190	−	0.0977190i
$459$	89.6044	+	281.094i	0.195217	+	0.612406i
$460$	131.518	+	51.3153i	0.285910	+	0.111555i
$461$	−101.671	+	85.3119i	−0.220544	+	0.185058i	−0.746365	−	0.665537i	$-0.768203\pi$
$461$	−101.671	+	85.3119i	−0.220544	+	0.185058i	0.525821	+	0.850595i	$0.323758\pi$
$462$	102.098	−	61.0886i	0.220991	−	0.132226i
$463$	−316.659	+	221.727i	−0.683929	+	0.478892i	−0.863170	−	0.504913i	$-0.831525\pi$
$463$	−316.659	+	221.727i	−0.683929	+	0.478892i	0.179241	+	0.983805i	$0.442636\pi$
$464$	−175.177	−	481.295i	−0.377537	−	1.03727i
$465$	−249.248	+	171.810i	−0.536017	+	0.369485i
$466$	28.1413	+	159.597i	0.0603890	+	0.342483i
$467$	−259.907	−	69.6419i	−0.556546	−	0.149126i	−0.0304270	−	0.999537i	$-0.509687\pi$
$467$	−259.907	−	69.6419i	−0.556546	−	0.149126i	−0.526119	+	0.850411i	$0.676353\pi$
$468$	46.9581	−	836.539i	0.100338	−	1.78748i
$469$	−314.958	−	181.841i	−0.671551	−	0.387720i
$470$	54.6560	−	3.52054i	0.116289	−	0.00749050i
$471$	−138.805	+	310.209i	−0.294703	+	0.658618i
$472$	58.6668	−	5.13268i	0.124294	−	0.0108743i
$473$	−14.7493	−	168.586i	−0.0311825	−	0.356418i
$474$	−170.612	+	123.473i	−0.359940	+	0.260492i
$475$	126.794	+	244.914i	0.266934	+	0.515608i
$476$	−114.018	+	197.486i	−0.239534	+	0.414886i
$477$	−76.2296	−	71.6165i	−0.159810	−	0.150139i
$478$	35.3091	−	131.776i	0.0738685	−	0.275681i
$479$	409.526	−	72.2105i	0.854960	−	0.150753i	0.271045	−	0.962567i	$-0.412631\pi$
$479$	409.526	−	72.2105i	0.854960	−	0.150753i	0.583916	+	0.811814i	$0.301520\pi$
$480$	−338.702	+	120.467i	−0.705630	+	0.250973i
$481$	834.944	−	303.895i	1.73585	−	0.631798i
$482$	−47.6346	−	68.0293i	−0.0988270	−	0.141140i
$483$	−129.690	+	2.02278i	−0.268509	+	0.00418794i
$484$	91.7077	+	109.293i	0.189479	+	0.225812i
$485$	802.347	+	313.056i	1.65432	+	0.645477i
$486$	1.25312	−	134.920i	0.00257843	−	0.277614i
$487$	−83.6043	+	83.6043i	−0.171672	+	0.171672i	−0.787714	−	0.616042i	$-0.788735\pi$
$487$	−83.6043	+	83.6043i	−0.171672	+	0.171672i	0.616042	+	0.787714i	$0.288735\pi$
$488$	197.823	+	17.3073i	0.405375	+	0.0354657i
$489$	−445.635	−	431.948i	−0.911319	−	0.883328i
$490$	−40.4257	−	24.5933i	−0.0825015	−	0.0501903i
$491$	−398.644	+	145.095i	−0.811903	+	0.295508i	−0.714410	−	0.699728i	$-0.753305\pi$
$491$	−398.644	+	145.095i	−0.811903	+	0.295508i	−0.0974931	+	0.995236i	$0.531082\pi$
$492$	−317.882	−	367.056i	−0.646101	−	0.746048i
$493$	−258.976	+	369.856i	−0.525307	+	0.750215i
$494$	133.770	−	77.2319i	0.270789	−	0.156340i
$495$	244.535	+	513.310i	0.494011	+	1.03699i
$496$	−125.081	+	216.646i	−0.252179	+	0.436786i
$497$	80.9031	−	37.7258i	0.162783	−	0.0759070i
$498$	1.62122	−	10.1143i	0.00325545	−	0.0203099i
$499$	416.679	−	496.579i	0.835029	−	0.995148i	−0.164932	−	0.986305i	$-0.552741\pi$
$499$	416.679	−	496.579i	0.835029	−	0.995148i	0.999961	−	0.00884344i	$-0.00281499\pi$
$500$	395.316	−	238.060i	0.790632	−	0.476120i
$501$	71.4998	−	159.792i	0.142714	−	0.318946i
$502$	140.841	−	65.6753i	0.280560	−	0.130827i
$503$	−76.1615	+	20.4074i	−0.151414	+	0.0405714i	−0.333730	−	0.942669i	$-0.608307\pi$
$503$	−76.1615	+	20.4074i	−0.151414	+	0.0405714i	0.182316	+	0.983240i	$0.441641\pi$
$504$	162.013	−	144.791i	0.321455	−	0.287284i
$505$	−301.982	+	410.880i	−0.597984	+	0.813624i
$506$	9.31754	+	52.8424i	0.0184141	+	0.104432i
$507$	1375.51	−	264.722i	2.71304	−	0.522134i
$508$	−678.534	−	316.406i	−1.33570	−	0.622846i
$509$	−690.077	−	121.679i	−1.35575	−	0.239055i	−0.551912	−	0.833903i	$-0.686101\pi$
$509$	−690.077	−	121.679i	−1.35575	−	0.239055i	−0.803839	+	0.594847i	$0.797213\pi$
$510$	74.1646	+	52.7469i	0.145421	+	0.103425i
$511$	−310.322	+	260.391i	−0.607284	+	0.509572i
$512$	−359.791	+	359.791i	−0.702716	+	0.702716i
$513$	−250.700	+	160.827i	−0.488693	+	0.313503i
$514$			66.3082i			0.129004i
$515$	−68.2902	−	201.923i	−0.132602	−	0.392084i
$516$	−40.6217	−	142.664i	−0.0787243	−	0.276481i
$517$	−142.971	−	204.184i	−0.276540	−	0.394940i
$518$	100.233	+	46.7395i	0.193500	+	0.0902307i
$519$	201.427	+	414.942i	0.388107	+	0.799502i
$520$	−298.668	−	448.080i	−0.574361	−	0.861692i
$521$	36.4514	+	63.1356i	0.0699642	+	0.121182i	0.898885	−	0.438184i	$-0.144378\pi$
$521$	36.4514	+	63.1356i	0.0699642	+	0.121182i	−0.828921	+	0.559366i	$0.811045\pi$
$522$	165.370	−	123.655i	0.316801	−	0.236887i
$523$	173.438	−	46.4724i	0.331620	−	0.0888574i	−0.0891670	−	0.996017i	$-0.528420\pi$
$523$	173.438	−	46.4724i	0.331620	−	0.0888574i	0.420787	+	0.907159i	$0.361754\pi$
$524$	−303.057	+	832.643i	−0.578354	+	1.58901i
$525$	−253.586	+	339.773i	−0.483022	+	0.647187i
$526$	−48.7722	−	40.9248i	−0.0927229	−	0.0778037i
$527$	219.688	−	19.2202i	0.416866	−	0.0364710i
$528$	364.594	+	296.366i	0.690520	+	0.561299i
$529$	−160.922	+	442.130i	−0.304200	+	0.835784i
$530$	−32.0686	−	3.54863i	−0.0605068	−	0.00669553i
$531$	−46.0617	−	115.237i	−0.0867451	−	0.217019i
$532$	−222.373	−	59.5846i	−0.417994	−	0.112001i
$533$	634.158	−	905.671i	1.18979	−	1.69919i
$534$	−125.460	−	258.448i	−0.234943	−	0.483984i
$535$	−777.689	−	17.8454i	−1.45363	−	0.0333559i
$536$	−47.7120	+	270.588i	−0.0890150	+	0.504829i
$537$	339.737	+	189.145i	0.632657	+	0.352226i
$538$	−53.2692	−	4.66045i	−0.0990134	−	0.00866255i
$539$			215.355i			0.399545i
$540$	295.511	+	401.317i	0.547242	+	0.743179i
$541$	927.278			1.71401			0.857004	−	0.515310i	$-0.172323\pi$
$541$	927.278			1.71401			0.857004	+	0.515310i	$0.172323\pi$
$542$	−10.0504	+	114.877i	−0.0185432	+	0.211950i
$543$	182.692	+	305.334i	0.336449	+	0.562309i
$544$	257.898	+	45.4743i	0.474077	+	0.0835925i
$545$	−3.11436	+	2.97464i	−0.00571442	+	0.00545805i
$546$	196.615	+	133.150i	0.360100	+	0.243865i
$547$	39.9056	+	27.9422i	0.0729535	+	0.0510826i	0.609484	−	0.792798i	$-0.291377\pi$
$547$	39.9056	+	27.9422i	0.0729535	+	0.0510826i	−0.536531	+	0.843881i	$0.680265\pi$
$548$	22.5657	−	84.2164i	0.0411783	−	0.153680i
$549$	−85.4834	−	409.645i	−0.155708	−	0.746166i
$550$	155.392	+	81.3371i	0.282530	+	0.147886i
$551$	−428.339	−	155.903i	−0.777385	−	0.282945i
$552$	34.9475	+	91.5493i	0.0633107	+	0.165850i
$553$	62.2912	+	711.992i	0.112642	+	1.28751i
$554$	−118.661	+	141.414i	−0.214189	+	0.255260i
$555$	−267.616	+	455.759i	−0.482191	+	0.821187i
$556$	381.977	+	139.028i	0.687009	+	0.250051i
$557$	−63.5260	−	237.082i	−0.114050	−	0.425642i	0.885164	−	0.465280i	$-0.154046\pi$
$557$	−63.5260	−	237.082i	−0.114050	−	0.425642i	−0.999214	+	0.0396380i	$0.987380\pi$
$558$	−98.1838	−	23.0520i	−0.175957	−	0.0413119i
$559$	292.501	−	168.876i	0.523258	−	0.302103i
$560$	−68.7374	+	343.544i	−0.122745	+	0.613472i
$561$	29.6602	−	413.131i	0.0528702	−	0.736419i
$562$	−43.0418	+	92.3035i	−0.0765869	+	0.164241i
$563$	−204.088	+	142.904i	−0.362500	+	0.253826i	−0.740610	−	0.671935i	$-0.765463\pi$
$563$	−204.088	+	142.904i	−0.362500	+	0.253826i	0.378109	+	0.925761i	$0.376574\pi$
$564$	−156.884	−	152.065i	−0.278163	−	0.269619i
$565$	−298.499	−	882.612i	−0.528316	−	1.56215i
$566$	242.471			0.428394
$567$	−390.725	−	238.740i	−0.689109	−	0.421058i
$568$	−47.6882	−	47.6882i	−0.0839581	−	0.0839581i
$569$	371.948	+	443.270i	0.653686	+	0.779033i	0.986465	−	0.163972i	$-0.0524306\pi$
$569$	371.948	+	443.270i	0.653686	+	0.779033i	−0.332779	+	0.943005i	$0.607986\pi$
$570$	−32.0580	+	86.1051i	−0.0562421	+	0.151062i
$571$	140.087	−	794.475i	0.245337	−	1.39138i	−0.574372	−	0.818595i	$-0.694754\pi$
$571$	140.087	−	794.475i	0.245337	−	1.39138i	0.819709	−	0.572781i	$-0.194135\pi$
$572$	−497.113	+	1066.06i	−0.869078	+	1.86374i
$573$	72.7555	−	63.0085i	0.126973	−	0.109963i
$574$	135.526	−	23.8968i	0.236108	−	0.0416321i
$575$	−102.371	−	161.492i	−0.178037	−	0.280856i
$576$	287.685	+	154.339i	0.499454	+	0.267949i
$577$	16.5513	+	61.7702i	0.0286850	+	0.107054i	0.978784	−	0.204894i	$-0.0656851\pi$
$577$	16.5513	+	61.7702i	0.0286850	+	0.107054i	−0.950099	+	0.311948i	$0.899018\pi$
$578$	39.7981	+	85.3473i	0.0688548	+	0.147660i
$579$	−202.414	+	146.489i	−0.349593	+	0.253004i
$580$	−214.254	+	732.002i	−0.369403	+	1.26207i
$581$	−26.6296	−	22.3449i	−0.0458340	−	0.0384593i
$582$	102.328	+	268.062i	0.175822	+	0.460587i
$583$	62.0571	+	133.082i	0.106445	+	0.228271i
$584$	265.049	+	153.026i	0.453850	+	0.262031i
$585$	−722.230	+	875.282i	−1.23458	+	1.49621i
$586$	−123.693	−	214.242i	−0.211080	−	0.365601i
$587$	−757.468	−	530.385i	−1.29040	−	0.903551i	−0.291806	−	0.956477i	$-0.594256\pi$
$587$	−757.468	−	530.385i	−1.29040	−	0.903551i	−0.998598	+	0.0529261i	$0.983145\pi$
$588$	35.6738	+	185.363i	0.0606697	+	0.315244i
$589$	76.1461	+	209.210i	0.129280	+	0.355195i
$590$	−32.7055	−	19.8966i	−0.0554330	−	0.0337230i
$591$	−248.117	−	62.3522i	−0.419825	−	0.105503i
$592$	−38.0652	+	435.087i	−0.0642992	+	0.734944i
$593$	−417.422	−	417.422i	−0.703916	−	0.703916i	0.261333	−	0.965249i	$-0.415838\pi$
$593$	−417.422	−	417.422i	−0.703916	−	0.703916i	−0.965249	+	0.261333i	$0.915838\pi$
$594$	−71.9368	+	175.232i	−0.121106	+	0.295003i
$595$	282.835	−	124.070i	0.475352	−	0.208521i
$596$	500.010	−	419.558i	0.838943	−	0.703957i
$597$	133.682	+	74.4260i	0.223923	+	0.124667i
$598$	−87.7236	+	61.4247i	−0.146695	+	0.102717i
$599$	−378.957	−	1041.18i	−0.632649	−	1.73819i	−0.673672	−	0.739031i	$-0.735284\pi$
$599$	−378.957	−	1041.18i	−0.632649	−	1.73819i	0.0410227	−	0.999158i	$-0.486938\pi$
$600$	306.745	+	92.2348i	0.511241	+	0.153725i
$601$	105.574	+	598.741i	0.175664	+	0.996241i	0.937374	+	0.348323i	$0.113249\pi$
$601$	105.574	+	598.741i	0.175664	+	0.996241i	−0.761710	+	0.647918i	$0.775640\pi$
$602$	40.6074	+	10.8807i	0.0674541	+	0.0180743i
$603$	574.956	−	68.4285i	0.953492	−	0.113480i
$604$	416.911	+	240.704i	0.690251	+	0.398516i
$605$	−12.4209	−	192.834i	−0.0205305	−	0.318734i
$606$	−168.981	+	17.4434i	−0.278847	+	0.0287844i
$607$	324.038	−	28.3497i	0.533836	−	0.0467046i	0.182949	−	0.983122i	$-0.441436\pi$
$607$	324.038	−	28.3497i	0.533836	−	0.0467046i	0.350887	+	0.936418i	$0.385880\pi$
$608$	23.0423	+	263.375i	0.0378985	+	0.433182i
$609$	−71.9535	−	697.044i	−0.118150	−	1.14457i
$610$	−96.9565	−	85.2219i	−0.158945	−	0.139708i
$611$	248.741	−	430.832i	0.407105	−	0.705127i
$612$	−42.9062	−	360.510i	−0.0701082	−	0.589069i
$613$	−36.6630	+	136.828i	−0.0598091	+	0.223211i	−0.989361	−	0.145480i	$-0.953527\pi$
$613$	−36.6630	+	136.828i	−0.0598091	+	0.223211i	0.929552	+	0.368691i	$0.120194\pi$
$614$	−153.351	+	27.0400i	−0.249758	+	0.0440391i
$615$	52.5034	+	655.553i	0.0853713	+	1.06594i
$616$	−286.651	+	104.332i	−0.465342	+	0.169371i
$617$	−192.324	−	274.667i	−0.311708	−	0.445165i	0.632478	−	0.774579i	$-0.282038\pi$
$617$	−192.324	−	274.667i	−0.311708	−	0.445165i	−0.944186	+	0.329413i	$0.893149\pi$
$618$	34.5435	−	62.0461i	0.0558956	−	0.100398i
$619$	−328.814	−	391.866i	−0.531203	−	0.633063i	0.431989	−	0.901879i	$-0.357812\pi$
$619$	−328.814	−	391.866i	−0.531203	−	0.633063i	−0.963191	+	0.268816i	$0.913368\pi$
$620$	341.145	−	149.649i	0.550234	−	0.241370i
$621$	163.432	−	126.227i	0.263176	−	0.203264i
$622$	36.2203	−	36.2203i	0.0582320	−	0.0582320i
$623$	−971.245	−	84.9729i	−1.55898	−	0.136393i
$624$	−228.550	+	909.463i	−0.366265	+	1.45747i
$625$	−622.370	−	57.2761i	−0.995792	−	0.0916418i
$626$	171.357	−	62.3688i	0.273733	−	0.0996307i
$627$	410.620	−	79.0252i	0.654897	−	0.126037i
$628$	239.872	−	342.573i	0.381962	−	0.545499i
$629$	333.430	−	192.506i	0.530095	−	0.306051i
$630$	−140.603	+	13.4707i	−0.223179	+	0.0213821i
$631$	360.741	−	624.822i	0.571698	−	0.990209i	−0.424694	−	0.905337i	$-0.639618\pi$
$631$	360.741	−	624.822i	0.571698	−	0.990209i	0.996392	−	0.0848725i	$-0.0270483\pi$
$632$	489.376	−	228.200i	0.774329	−	0.361075i
$633$	611.330	−	233.366i	0.965767	−	0.368666i
$634$	−119.643	+	142.585i	−0.188711	+	0.224897i
$635$	486.724	+	889.554i	0.766494	+	1.40087i
$636$	75.4600	+	104.269i	0.118648	+	0.163944i
$637$	−389.539	+	181.645i	−0.611521	+	0.285157i
$638$	−280.013	+	75.0293i	−0.438892	+	0.117601i
$639$	−67.1872	+	125.236i	−0.105144	+	0.195988i
$640$	573.373	−	87.5897i	0.895895	−	0.136859i
$641$	198.618	+	1126.42i	0.309856	+	1.75728i	0.599716	+	0.800213i	$0.295280\pi$
$641$	198.618	+	1126.42i	0.309856	+	1.75728i	−0.289860	+	0.957069i	$0.593609\pi$
$642$	−169.658	−	195.903i	−0.264265	−	0.305145i
$643$	38.9147	+	18.1462i	0.0605205	+	0.0282212i	0.452643	−	0.891692i	$-0.350481\pi$
$643$	38.9147	+	18.1462i	0.0605205	+	0.0282212i	−0.392122	+	0.919913i	$0.628259\pi$
$644$	157.186	+	27.7162i	0.244078	+	0.0430375i
$645$	−70.0982	+	188.278i	−0.108679	+	0.291903i
$646$	51.2724	−	43.0226i	0.0793690	−	0.0665985i
$647$	523.524	−	523.524i	0.809156	−	0.809156i	−0.175350	−	0.984506i	$-0.556106\pi$
$647$	523.524	−	523.524i	0.809156	−	0.809156i	0.984506	+	0.175350i	$0.0561057\pi$
$648$	−68.5291	+	339.081i	−0.105755	+	0.523273i
$649$			174.227i			0.268455i
$650$	−16.0565	+	349.682i	−0.0247023	+	0.537972i
$651$	−238.211	+	245.759i	−0.365915	+	0.377510i
$652$	438.048	+	625.598i	0.671853	+	0.959506i
$653$	197.957	+	92.3090i	0.303150	+	0.141361i	0.568241	−	0.822862i	$-0.307624\pi$
$653$	197.957	+	92.3090i	0.303150	+	0.141361i	−0.265091	+	0.964223i	$0.585402\pi$
$654$	−1.43110	−	0.102744i	−0.00218822	−	0.000157101i
$655$	998.596	−	665.616i	1.52457	−	1.01621i
$656$	271.729	+	470.648i	0.414221	+	0.717452i
$657$	147.416	−	627.876i	0.224377	−	0.955671i
$658$	59.8117	−	16.0265i	0.0908992	−	0.0243564i
$659$	−379.078	+	1041.51i	−0.575231	+	1.58044i	0.220890	+	0.975299i	$0.429104\pi$
$659$	−379.078	+	1041.51i	−0.575231	+	1.58044i	−0.796122	+	0.605137i	$0.793118\pi$
$660$	−176.119	−	677.148i	−0.266848	−	1.02598i
$661$	27.4026	+	22.9935i	0.0414563	+	0.0347859i	0.663280	−	0.748371i	$-0.269164\pi$
$661$	27.4026	+	22.9935i	0.0414563	+	0.0347859i	−0.621824	+	0.783157i	$0.713608\pi$
$662$	−222.485	+	19.4649i	−0.336080	+	0.0294031i
$663$	772.299	−	294.813i	1.16486	−	0.444665i
$664$	−8.98252	+	24.6793i	−0.0135279	+	0.0371676i
$665$	194.892	+	243.391i	0.293070	+	0.366001i
$666$	−172.364	+	35.9684i	−0.258805	+	0.0540066i
$667$	305.260	+	81.7943i	0.457662	+	0.122630i
$668$	−123.561	+	176.463i	−0.184971	+	0.264166i
$669$	−249.885	+	368.990i	−0.373520	+	0.551554i
$670$	129.160	−	123.366i	0.192777	−	0.184128i
$671$	−102.017	+	578.566i	−0.152037	+	0.862244i
$672$	−348.770	+	208.681i	−0.519003	+	0.310538i
$673$	−664.260	−	58.1152i	−0.987013	−	0.0863525i	−0.417797	−	0.908540i	$-0.637198\pi$
$673$	−664.260	−	58.1152i	−0.987013	−	0.0863525i	−0.569216	+	0.822188i	$0.692753\pi$
$674$		−	175.905i		−	0.260987i
$675$	−0.608884	−	675.000i	−0.000902051	−	1.00000i
$676$	−1723.72			−2.54988
$677$	42.0143	−	480.226i	0.0620596	−	0.709344i	−0.899890	−	0.436117i	$-0.856353\pi$
$677$	42.0143	−	480.226i	0.0620596	−	0.709344i	0.961950	−	0.273227i	$-0.0880911\pi$
$678$	150.991	−	271.205i	0.222700	−	0.400008i
$679$	958.937	+	169.087i	1.41228	+	0.249023i
$680$	−161.166	−	168.736i	−0.237009	−	0.248142i
$681$	−801.986	+	389.312i	−1.17766	+	0.571677i
$682$	115.983	+	81.2120i	0.170063	+	0.119079i
$683$	−55.2218	+	206.091i	−0.0808519	+	0.301743i	−0.994496	−	0.104771i	$-0.966589\pi$
$683$	−55.2218	+	206.091i	−0.0808519	+	0.301743i	0.913645	+	0.406514i	$0.133256\pi$
$684$	340.345	−	136.040i	0.497580	−	0.198888i
$685$	−92.1763	+	73.8088i	−0.134564	+	0.107750i
$686$	−194.798	−	70.9007i	−0.283962	−	0.103354i
$687$	215.704	−	265.362i	0.313979	−	0.386263i
$688$	14.4695	+	165.387i	0.0210312	+	0.240388i
$689$	−188.379	+	224.501i	−0.273409	+	0.325836i
$690$	16.9385	−	61.4071i	0.0245485	−	0.0889958i
$691$	−879.621	−	320.156i	−1.27297	−	0.463322i	−0.384867	−	0.922972i	$-0.625753\pi$
$691$	−879.621	−	320.156i	−1.27297	−	0.463322i	−0.888100	+	0.459650i	$0.847975\pi$
$692$	−146.905	−	548.255i	−0.212290	−	0.792276i
$693$	384.956	+	514.823i	0.555493	+	0.742890i
$694$	81.4540	−	47.0275i	0.117369	−	0.0677629i
$695$	−305.352	−	458.108i	−0.439356	−	0.659148i
$696$	−476.267	+	231.197i	−0.684292	+	0.332180i
$697$	202.468	−	434.194i	0.290485	−	0.622947i
$698$	65.0568	−	45.5532i	0.0932045	−	0.0652625i
$699$	−842.126	+	239.784i	−1.20476	+	0.343038i
$700$	385.449	−	351.605i	0.550641	−	0.502293i
$701$	76.9287			0.109741			0.0548707	−	0.998493i	$-0.482525\pi$
$701$	76.9287			0.109741			0.0548707	+	0.998493i	$0.482525\pi$
$702$	−377.640	+	17.6817i	−0.537949	+	0.0251876i
$703$	274.848	+	274.848i	0.390964	+	0.390964i
$704$	−294.611	−	351.104i	−0.418482	−	0.498727i
$705$	49.2429	+	291.790i	0.0698480	+	0.413886i
$706$	2.47858	−	14.0567i	0.00351074	−	0.0199104i
$707$	−243.643	+	522.494i	−0.344615	+	0.739029i
$708$	28.8610	+	149.964i	0.0407641	+	0.211813i
$709$	119.471	−	21.0660i	0.168507	−	0.0297123i	−0.0887582	−	0.996053i	$-0.528290\pi$
$709$	119.471	−	21.0660i	0.168507	−	0.0297123i	0.257265	+	0.966341i	$0.417179\pi$
$710$	6.62034	+	43.3376i	0.00932443	+	0.0610388i
$711$	−758.246	−	848.435i	−1.06645	−	1.19330i
$712$	190.641	+	711.483i	0.267755	+	0.999274i
$713$	−65.2333	−	139.893i	−0.0914913	−	0.196204i
$714$	93.9203	+	42.0252i	0.131541	+	0.0588589i
$715$	1397.60	−	764.703i	1.95469	−	1.06952i
$716$	−366.548	−	307.570i	−0.511938	−	0.429567i
$717$	727.803	+	116.659i	1.01507	+	0.162704i
$718$	53.9960	+	115.795i	0.0752034	+	0.161274i
$719$	−1127.50	−	650.961i	−1.56815	−	0.905370i	−0.996385	−	0.0849512i	$-0.972927\pi$
$719$	−1127.50	−	650.961i	−1.56815	−	0.905370i	−0.571762	−	0.820419i	$-0.693740\pi$
$720$	−239.896	−	503.571i	−0.333188	−	0.699404i
$721$	−120.497	−	208.708i	−0.167125	−	0.289470i
$722$	−108.844	−	76.2136i	−0.150754	−	0.105559i
$723$	339.190	−	293.749i	0.469142	−	0.406292i
$724$	−149.755	−	411.449i	−0.206844	−	0.568300i
$725$	820.957	−	627.010i	1.13236	−	0.864842i
$726$	44.8052	−	46.2250i	0.0617151	−	0.0636708i
$727$	58.7636	−	671.671i	0.0808303	−	0.923895i	−0.842199	−	0.539166i	$-0.818740\pi$
$727$	58.7636	−	671.671i	0.0808303	−	0.923895i	0.923030	−	0.384729i	$-0.125705\pi$
$728$	−430.500	−	430.500i	−0.591346	−	0.591346i
$729$	725.811	−	68.1164i	0.995625	−	0.0934382i
$730$	−79.9211	−	182.191i	−0.109481	−	0.249576i
$731$	112.112	−	94.0734i	0.153368	−	0.128691i
$732$	8.03078	+	514.891i	0.0109710	+	0.703403i
$733$	−24.3409	+	17.0437i	−0.0332072	+	0.0232519i	−0.590062	−	0.807358i	$-0.700897\pi$
$733$	−24.3409	+	17.0437i	−0.0332072	+	0.0232519i	0.556855	+	0.830610i	$0.312008\pi$
$734$	30.3199	+	83.3033i	0.0413078	+	0.113492i
$735$	109.747	−	230.908i	0.149315	−	0.314160i
$736$	−31.8291	−	180.512i	−0.0432461	−	0.245261i
$737$	−785.181	−	210.389i	−1.06537	−	0.285466i
$738$	−150.018	+	159.681i	−0.203277	+	0.216371i
$739$	491.983	+	284.047i	0.665742	+	0.384366i	0.794461	−	0.607315i	$-0.207753\pi$
$739$	491.983	+	284.047i	0.665742	+	0.384366i	−0.128719	+	0.991681i	$0.541087\pi$
$740$	429.375	−	488.498i	0.580237	−	0.660132i
$741$	489.288	+	676.085i	0.660308	+	0.912395i
$742$	−36.3390	+	3.17925i	−0.0489744	+	0.00428470i
$743$	−105.445	−	1205.24i	−0.141918	−	1.62212i	−0.649389	−	0.760456i	$-0.724975\pi$
$743$	−105.445	−	1205.24i	−0.141918	−	1.62212i	0.507472	−	0.861669i	$-0.330580\pi$
$744$	236.027	+	105.612i	0.317241	+	0.141952i
$745$	−882.205	+	56.8252i	−1.18417	+	0.0762754i
$746$	−3.65058	+	6.32299i	−0.00489354	+	0.00847586i
$747$	55.2579	+	3.10183i	0.0739730	+	0.00415238i
$748$	−131.918	+	492.326i	−0.176361	+	0.658190i
$749$	−866.119	+	152.720i	−1.15637	+	0.203899i
$750$	−125.164	−	166.401i	−0.166886	−	0.221867i
$751$	886.218	−	322.557i	1.18005	−	0.429503i	0.323831	−	0.946115i	$-0.395029\pi$
$751$	886.218	−	322.557i	1.18005	−	0.429503i	0.856220	+	0.516611i	$0.172807\pi$
$752$	140.258	+	200.310i	0.186514	+	0.266369i
$753$	431.101	+	720.501i	0.572512	+	0.956841i
$754$	−371.897	−	443.210i	−0.493233	−	0.587812i
$755$	−261.925	−	597.092i	−0.346920	−	0.790850i
$756$	416.627	+	379.358i	0.551094	+	0.501796i
$757$	−736.156	+	736.156i	−0.972465	+	0.972465i	−0.999631	−	0.0271663i	$-0.991352\pi$
$757$	−736.156	+	736.156i	−0.972465	+	0.972465i	0.0271663	+	0.999631i	$0.491352\pi$
$758$	330.055	+	28.8761i	0.435429	+	0.0380951i
$759$	−278.827	+	79.3922i	−0.367361	+	0.104601i
$760$	122.434	−	201.253i	0.161097	−	0.264807i
$761$	−321.216	+	116.913i	−0.422097	+	0.153631i	−0.544331	−	0.838871i	$-0.683216\pi$
$761$	−321.216	+	116.913i	−0.422097	+	0.153631i	0.122234	+	0.992501i	$0.460994\pi$
$762$	−110.575	+	319.207i	−0.145112	+	0.418907i
$763$	−2.79281	+	3.98855i	−0.00366031	+	0.00522746i
$764$	−102.570	+	59.2190i	−0.134254	+	0.0775118i
$765$	−242.338	+	427.853i	−0.316781	+	0.559286i
$766$	−52.2814	+	90.5541i	−0.0682525	+	0.118217i
$767$	−315.147	+	146.955i	−0.410882	+	0.191598i
$768$	−187.832	−	152.682i	−0.244573	−	0.198804i
$769$	648.770	−	773.174i	0.843655	−	1.00543i	−0.156189	−	0.987727i	$-0.549921\pi$
$769$	648.770	−	773.174i	0.843655	−	1.00543i	0.999843	−	0.0177011i	$-0.00563473\pi$
$770$	190.312	+	55.7035i	0.247158	+	0.0723421i
$771$	−356.367	+	36.7865i	−0.462214	+	0.0477127i
$772$	278.663	−	129.943i	0.360962	−	0.168320i
$773$	237.800	−	63.7182i	0.307632	−	0.0824298i	−0.101700	−	0.994815i	$-0.532428\pi$
$773$	237.800	−	63.7182i	0.307632	−	0.0824298i	0.409333	+	0.912385i	$0.365762\pi$
$774$	−62.1502	+	24.8421i	−0.0802974	+	0.0320958i
$775$	−492.337	−	110.312i	−0.635274	−	0.142339i
$776$	−127.745	−	724.480i	−0.164620	−	0.933608i
$777$	−195.589	+	564.624i	−0.251724	+	0.726671i
$778$	5.65197	+	2.63556i	0.00726474	+	0.00338761i
$779$	476.314	+	83.9870i	0.611443	+	0.107814i
$780$	1076.29	−	889.722i	1.37986	−	1.14067i
$781$	152.844	−	128.251i	0.195703	−	0.164214i
$782$	−32.8125	+	32.8125i	−0.0419597	+	0.0419597i
$783$	756.315	+	820.164i	0.965919	+	1.04746i
$784$		−	211.268i		−	0.269475i
$785$	−536.558	+	181.463i	−0.683513	+	0.231164i
$786$	387.758	+	97.4442i	0.493330	+	0.123975i
$787$	15.3545	+	21.9284i	0.0195101	+	0.0278633i	0.828789	−	0.559562i	$-0.189031\pi$
$787$	15.3545	+	21.9284i	0.0195101	+	0.0278633i	−0.809279	+	0.587425i	$0.800142\pi$
$788$	285.321	+	133.048i	0.362083	+	0.168842i
$789$	192.888	−	284.826i	0.244472	−	0.360996i
$790$	−344.184	−	68.8655i	−0.435676	−	0.0871715i
$791$	−526.698	−	912.268i	−0.665864	−	1.15331i
$792$	266.022	−	406.325i	0.335886	−	0.513037i
$793$	−1132.57	+	303.472i	−1.42821	+	0.382688i
$794$	64.6912	−	177.738i	0.0814750	−	0.223851i
$795$	1.28072	−	174.318i	0.00161096	−	0.219268i
$796$	−144.231	−	121.025i	−0.181195	−	0.152041i
$797$	407.355	−	35.6390i	0.511111	−	0.0447164i	0.171316	−	0.985216i	$-0.445198\pi$
$797$	407.355	−	35.6390i	0.511111	−	0.0447164i	0.339795	+	0.940500i	$0.389642\pi$
$798$	−16.4406	+	102.569i	−0.0206023	+	0.128532i
$799$	73.7279	−	202.566i	0.0922752	−	0.253524i
$800$	−530.825	−	277.851i	−0.663531	−	0.347314i
$801$	1319.40	−	817.652i	1.64719	−	1.02079i
$802$	21.1156	+	5.65790i	0.0263286	+	0.00705473i
$803$	−519.343	+	741.699i	−0.646754	+	0.923660i
$804$	−710.684	−	51.0226i	−0.883936	−	0.0634610i
$805$	−149.312	−	156.326i	−0.185481	−	0.194194i
$806$	−49.0704	+	278.292i	−0.0608814	+	0.345276i
$807$	−4.50561	−	288.876i	−0.00558316	−	0.357962i
$808$	433.896	+	37.9610i	0.537000	+	0.0469814i
$809$			505.724i			0.625122i	0.949898	+	0.312561i	$0.101187\pi$
$809$			505.724i			0.625122i	−0.949898	+	0.312561i	$0.898813\pi$
$810$	166.432	−	151.228i	0.205472	−	0.186701i
$811$	−591.520			−0.729371			−0.364686	−	0.931131i	$-0.618824\pi$
$811$	−591.520			−0.729371			−0.364686	+	0.931131i	$0.618824\pi$
$812$	−75.1558	+	859.035i	−0.0925564	+	1.05793i
$813$	−622.970	+	9.71649i	−0.766261	+	0.0119514i
$814$	243.440	+	42.9250i	0.299066	+	0.0527335i
$815$	23.7290	−	1034.09i	0.0291154	−	1.26883i
$816$	−29.0974	+	405.293i	−0.0356586	+	0.496682i
$817$	121.031	+	84.7470i	0.148141	+	0.103729i
$818$	2.54827	−	9.51026i	0.00311524	−	0.0116262i
$819$	−606.525	+	1130.56i	−0.740568	+	1.38041i
$820$	89.0100	−	804.374i	0.108549	−	0.980944i
$821$	457.522	+	166.524i	0.557274	+	0.202831i	0.605276	−	0.796016i	$-0.293063\pi$
$821$	457.522	+	166.524i	0.557274	+	0.202831i	−0.0480013	+	0.998847i	$0.515285\pi$
$822$	−38.8445	−	6.22635i	−0.0472561	−	0.00757463i
$823$	−54.8682	−	627.147i	−0.0666686	−	0.762025i	−0.953787	−	0.300484i	$-0.902852\pi$
$823$	−54.8682	−	627.147i	−0.0666686	−	0.762025i	0.887118	−	0.461542i	$-0.152704\pi$
$824$	−117.034	+	139.475i	−0.142031	+	0.169266i
$825$	−350.930	+	880.262i	−0.425370	+	1.06698i
$826$	−40.6712	−	14.8031i	−0.0492388	−	0.0179215i
$827$	−133.996	−	500.081i	−0.162027	−	0.604693i	−0.998401	−	0.0565332i	$-0.981995\pi$
$827$	−133.996	−	500.081i	−0.162027	−	0.604693i	0.836374	−	0.548160i	$-0.184671\pi$
$828$	−226.845	+	114.524i	−0.273967	+	0.138314i
$829$	1302.96	−	752.263i	1.57172	−	0.907434i	0.575764	−	0.817616i	$-0.304705\pi$
$829$	1302.96	−	752.263i	1.57172	−	0.907434i	0.995958	−	0.0898184i	$-0.0286287\pi$
$830$	14.2058	−	9.46892i	0.0171155	−	0.0114083i
$831$	−825.848	−	559.276i	−0.993800	−	0.673016i
$832$	386.590	−	829.045i	0.464652	−	0.996449i
$833$	−152.560	+	106.824i	−0.183146	+	0.128240i
$834$	44.7027	−	177.885i	0.0536004	−	0.213291i
$835$	276.386	−	93.4736i	0.331002	−	0.111944i
$836$	−514.568			−0.615512
$837$	69.4204	−	540.468i	0.0829396	−	0.645720i
$838$	−160.270	−	160.270i	−0.191253	−	0.191253i
$839$	189.988	+	226.418i	0.226445	+	0.269867i	0.867290	−	0.497804i	$-0.165860\pi$
$839$	189.988	+	226.418i	0.226445	+	0.269867i	−0.640844	+	0.767671i	$0.721416\pi$
$840$	360.522	+	34.2123i	0.429193	+	0.0407290i
$841$	−150.446	+	853.219i	−0.178889	+	1.01453i
$842$	−108.726	+	233.164i	−0.129129	+	0.276917i
$843$	−519.955	−	180.116i	−0.616791	−	0.213661i
$844$	−792.997	+	139.827i	−0.939570	+	0.165671i
$845$	1881.16	+	1382.59i	2.22623	+	1.63620i
$846$	−60.9829	+	77.4597i	−0.0720838	+	0.0915599i
$847$	−56.5437	−	211.024i	−0.0667576	−	0.249143i
$848$	−60.8797	−	130.557i	−0.0717921	−	0.153959i
$849$	134.518	+	1303.14i	0.158443	+	1.53491i
$850$	19.4597	+	150.428i	0.0228938	+	0.176974i
$851$	−206.436	−	173.221i	−0.242581	−	0.203550i
$852$	110.313	−	135.709i	0.129476	−	0.159283i
$853$	219.072	+	469.802i	0.256826	+	0.550764i	0.991870	−	0.127255i	$-0.0406165\pi$
$853$	219.072	+	469.802i	0.256826	+	0.550764i	−0.735044	+	0.678019i	$0.762839\pi$
$854$	−126.391	−	72.9720i	−0.147999	−	0.0854473i
$855$	−480.548	−	124.523i	−0.562045	−	0.145641i
$856$	332.225	+	575.430i	0.388113	+	0.672232i
$857$	−447.034	−	313.017i	−0.521627	−	0.365247i	0.282913	−	0.959146i	$-0.408699\pi$
$857$	−447.034	−	313.017i	−0.521627	−	0.365247i	−0.804540	+	0.593899i	$0.797588\pi$
$858$	501.514	+	173.728i	0.584515	+	0.202480i
$859$	509.798	+	1400.66i	0.593479	+	1.63057i	0.764001	+	0.645215i	$0.223232\pi$
$859$	509.798	+	1400.66i	0.593479	+	1.63057i	−0.170522	+	0.985354i	$0.554546\pi$
$860$	128.492	−	211.211i	0.149409	−	0.245594i
$861$	203.618	+	715.112i	0.236490	+	0.830560i
$862$	−0.774468	+	8.85221i	−0.000898455	+	0.0102694i
$863$	692.322	+	692.322i	0.802227	+	0.802227i	0.983443	−	0.181216i	$-0.0580034\pi$
$863$	692.322	+	692.322i	0.802227	+	0.802227i	−0.181216	+	0.983443i	$0.558003\pi$
$864$	245.739	−	598.600i	0.284420	−	0.692825i
$865$	−279.430	+	716.164i	−0.323040	+	0.827935i
$866$	−117.978	+	98.9952i	−0.136233	+	0.114313i
$867$	−436.611	+	261.240i	−0.503589	+	0.301315i
$868$	345.005	−	241.575i	0.397471	−	0.278312i
$869$	546.370	+	1501.14i	0.628734	+	1.72743i
$870$	338.472	+	62.2492i	0.389048	+	0.0715508i
$871$	−281.720	−	1597.71i	−0.323444	−	1.83434i
$872$	3.55329	+	0.952101i	0.00407487	+	0.00109186i
$873$	−1383.90	+	698.669i	−1.58522	+	0.800308i
$874$	−40.5713	−	23.4238i	−0.0464202	−	0.0268007i
$875$	−702.675	+	74.5542i	−0.803058	+	0.0852048i
$876$	−324.154	+	724.437i	−0.370038	+	0.826982i
$877$	808.302	−	70.7173i	0.921668	−	0.0806355i	0.383564	−	0.923514i	$-0.374697\pi$
$877$	808.302	−	70.7173i	0.921668	−	0.0806355i	0.538103	+	0.842879i	$0.319141\pi$
$878$	−6.41808	−	73.3590i	−0.00730988	−	0.0835524i
$879$	1082.80	−	783.633i	1.23186	−	0.891505i
$880$	50.3365	+	781.469i	0.0572006	+	0.888033i
$881$	−494.898	+	857.189i	−0.561746	+	0.972972i	0.435599	+	0.900141i	$0.356537\pi$
$881$	−494.898	+	857.189i	−0.561746	+	0.972972i	−0.997344	+	0.0728311i	$0.976797\pi$
$882$	81.5441	−	24.5996i	0.0924536	−	0.0278908i
$883$	−315.152	+	1176.16i	−0.356911	+	1.33201i	0.521152	+	0.853464i	$0.325502\pi$
$883$	−315.152	+	1176.16i	−0.356911	+	1.33201i	−0.878063	+	0.478545i	$0.841164\pi$
$884$	−1001.80	+	176.644i	−1.13326	+	0.199824i
$885$	88.7878	−	186.810i	0.100325	−	0.211085i
$886$	353.723	−	128.745i	0.399236	−	0.145310i
$887$	667.653	+	953.507i	0.752709	+	1.07498i	0.994509	+	0.104654i	$0.0333734\pi$
$887$	667.653	+	953.507i	0.752709	+	1.07498i	−0.241800	+	0.970326i	$0.577738\pi$
$888$	451.389	−	7.04033i	0.508321	−	0.00792830i
$889$	736.908	+	878.212i	0.828917	+	0.987865i
$890$	174.044	−	446.065i	0.195555	−	0.501196i
$891$	−981.676	−	289.402i	−1.10177	−	0.324806i
$892$	387.770	−	387.770i	0.434720	−	0.434720i
$893$	216.799	+	18.9675i	0.242776	+	0.0212402i
$894$	−211.477	−	204.981i	−0.236551	−	0.229286i
$895$	153.328	+	629.669i	0.171316	+	0.703540i
$896$	616.223	−	224.287i	0.687749	−	0.250320i
$897$	−378.788	−	437.384i	−0.422284	−	0.487608i
$898$	−273.529	+	390.640i	−0.304598	+	0.435011i
$899$	722.196	−	416.960i	0.803333	−	0.463804i
$900$	−156.241	+	815.805i	−0.173601	+	0.906450i
$901$	−63.4946	+	109.976i	−0.0704713	+	0.122060i
$902$	278.773	−	129.994i	0.309061	−	0.144117i
$903$	−35.9491	+	224.277i	−0.0398108	+	0.248369i
$904$	−511.559	+	609.652i	−0.565884	+	0.674394i
$905$	−166.587	+	569.148i	−0.184074	+	0.628893i
$906$	88.7194	−	198.275i	0.0979243	−	0.218847i
$907$	657.631	−	306.658i	0.725061	−	0.338102i	−0.0248039	−	0.999692i	$-0.507896\pi$
$907$	657.631	−	306.658i	0.725061	−	0.338102i	0.749865	+	0.661591i	$0.230118\pi$
$908$	1059.65	−	283.932i	1.16702	−	0.312701i
$909$	−187.495	−	898.497i	−0.206266	−	0.988445i
$910$	59.7644	+	391.225i	0.0656752	+	0.429918i
$911$	−38.5666	−	218.722i	−0.0423343	−	0.240090i	0.956297	−	0.292398i	$-0.0944532\pi$
$911$	−38.5666	−	218.722i	−0.0423343	−	0.240090i	−0.998631	+	0.0523083i	$0.983342\pi$
$912$	−402.829	+	77.5258i	−0.441699	+	0.0850064i
$913$	−70.4191	−	32.8370i	−0.0771293	−	0.0359660i
$914$	−244.848	−	43.1733i	−0.267886	−	0.0472356i
$915$	404.227	−	568.362i	0.441778	−	0.621161i
$916$	−322.366	+	270.498i	−0.351928	+	0.295303i
$917$	959.418	−	959.418i	1.04626	−	1.04626i
$918$	−159.820	+	35.9606i	−0.174096	+	0.0391727i
$919$		−	90.9186i		−	0.0989321i	−0.998776	−	0.0494660i	$-0.984248\pi$
$919$		−	90.9186i		−	0.0989321i	0.998776	−	0.0494660i	$-0.0157520\pi$
$920$	−72.4001	+	146.397i	−0.0786958	+	0.159127i
$921$	−230.400	−	809.171i	−0.250163	−	0.878579i
$922$	−42.2691	−	60.3666i	−0.0458450	−	0.0654735i
$923$	360.903	+	168.292i	0.391011	+	0.182331i
$924$	−345.451	−	711.632i	−0.373865	−	0.770164i
$925$	−860.415	+	188.718i	−0.930179	+	0.204019i
$926$	−107.322	−	185.886i	−0.115898	−	0.200741i
$927$	352.624	+	151.229i	0.380393	+	0.163138i
$928$	956.538	−	256.303i	1.03075	−	0.276189i
$929$	−9.34113	+	25.6645i	−0.0100550	+	0.0276260i	−0.944619	−	0.328170i	$-0.893568\pi$
$929$	−9.34113	+	25.6645i	−0.0100550	+	0.0276260i	0.934564	+	0.355796i	$0.115790\pi$
$930$	−82.9729	−	146.183i	−0.0892182	−	0.157186i
$931$	−144.034	−	120.859i	−0.154709	−	0.129816i
$932$	1073.38	−	93.9086i	1.15170	−	0.100760i
$933$	214.757	+	174.568i	0.230179	+	0.187104i
$934$	51.0994	−	140.394i	0.0547102	−	0.150315i
$935$	538.859	−	431.484i	0.576320	−	0.461480i
$936$	959.352	+	138.464i	1.02495	+	0.147932i
$937$	−373.482	−	100.074i	−0.398593	−	0.106803i	0.0539533	−	0.998543i	$-0.482818\pi$
$937$	−373.482	−	100.074i	−0.398593	−	0.106803i	−0.452547	+	0.891741i	$0.649484\pi$
$938$	115.825	−	165.415i	0.123481	−	0.176349i
$939$	430.261	+	886.340i	0.458212	+	0.943919i
$940$	8.35369	−	364.048i	0.00888690	−	0.387285i
$941$	−193.373	+	1096.67i	−0.205498	+	1.16543i	0.691157	+	0.722704i	$0.257101\pi$
$941$	−193.373	+	1096.67i	−0.205498	+	1.16543i	−0.896655	+	0.442730i	$0.854010\pi$
$942$	−164.871	−	91.7904i	−0.175023	−	0.0974420i
$943$	−334.050	−	29.2255i	−0.354241	−	0.0309921i
$944$		−	170.922i		−	0.181061i
$945$	−150.401	−	748.182i	−0.159154	−	0.791727i
$946$	93.9649			0.0993287
$947$	−83.2032	+	951.017i	−0.0878598	+	1.00424i	0.816465	+	0.577396i	$0.195931\pi$
$947$	−83.2032	+	951.017i	−0.0878598	+	1.00424i	−0.904324	+	0.426846i	$0.859625\pi$
$948$	718.946	+	1201.58i	0.758382	+	1.26749i
$949$	−1779.65	−	313.801i	−1.87529	−	0.330665i
$950$	−141.607	+	58.2824i	−0.149060	+	0.0613498i
$951$	−832.682	−	563.904i	−0.875586	−	0.592959i
$952$	−216.100	−	151.315i	−0.226996	−	0.158944i
$953$	−104.047	+	388.307i	−0.109178	+	0.407458i	−0.998786	−	0.0492678i	$-0.984311\pi$
$953$	−104.047	+	388.307i	−0.109178	+	0.407458i	0.889608	+	0.456726i	$0.150978\pi$
$954$	43.3028	−	38.6997i	0.0453908	−	0.0405658i
$955$	159.438	+	17.6430i	0.166951	+	0.0184744i
$956$	−852.340	−	310.227i	−0.891570	−	0.324505i
$957$	−558.584	−	1463.28i	−0.583682	−	1.52903i
$958$	20.1241	+	230.019i	0.0210063	+	0.240103i
$959$	−85.8164	+	102.272i	−0.0894852	+	0.106644i
$960$	136.963	+	526.598i	0.142670	+	0.548540i
$961$	520.304	+	189.375i	0.541419	+	0.197061i
$962$	127.690	+	476.546i	0.132734	+	0.495370i
$963$	958.738	−	1020.49i	0.995575	−	1.05970i
$964$	−478.188	+	276.082i	−0.496045	+	0.286392i
$965$	−408.342	−	81.7024i	−0.423152	−	0.0846657i
$966$	5.15724	−	71.8342i	0.00533876	−	0.0743626i
$967$	123.735	−	265.350i	0.127957	−	0.274405i	−0.831884	−	0.554950i	$-0.812737\pi$
$967$	123.735	−	265.350i	0.127957	−	0.274405i	0.959841	+	0.280545i	$0.0905151\pi$
$968$	−135.204	+	94.6707i	−0.139673	+	0.0978003i
$969$	259.666	+	251.690i	0.267973	+	0.259742i
$970$	−211.992	+	428.659i	−0.218548	+	0.441917i
$971$	1113.16			1.14641			0.573203	−	0.819413i	$-0.305701\pi$
$971$	1113.16			1.14641			0.573203	+	0.819413i	$0.305701\pi$
$972$	−892.904	−	86.4824i	−0.918625	−	0.0889736i
$973$	−440.135	−	440.135i	−0.452348	−	0.452348i
$974$	−42.1989	−	50.2907i	−0.0433253	−	0.0516331i
$975$	−1888.24	+	107.703i	−1.93665	+	0.110464i
$976$	100.081	−	567.588i	0.102542	−	0.581545i
$977$	−411.740	+	882.980i	−0.421433	+	0.903767i	0.574901	+	0.818223i	$0.305041\pi$
$977$	−411.740	+	882.980i	−0.421433	+	0.903767i	−0.996334	+	0.0855439i	$0.972737\pi$
$978$	260.493	−	225.595i	0.266352	−	0.230669i
$979$	−2146.05	+	378.407i	−2.19209	+	0.386524i
$980$	−186.316	+	253.504i	−0.190119	+	0.258678i
$981$	−0.241760	−	7.74830i	−0.000246442	−	0.00789837i
$982$	−60.9657	−	227.527i	−0.0620832	−	0.231698i
$983$	65.0823	+	139.569i	0.0662078	+	0.141983i	0.936627	−	0.350328i	$-0.113930\pi$
$983$	65.0823	+	139.569i	0.0662078	+	0.141983i	−0.870419	+	0.492311i	$0.836152\pi$
$984$	455.073	−	329.340i	0.462472	−	0.334695i
$985$	−204.666	−	374.054i	−0.207782	−	0.379751i
$986$	−192.049	−	161.148i	−0.194776	−	0.163436i
$987$	119.315	+	312.561i	0.120887	+	0.316678i
$988$	−434.022	−	930.763i	−0.439293	−	0.942068i
$989$	−88.7132	−	51.2186i	−0.0896999	−	0.0517883i
$990$	−295.765	+	110.421i	−0.298753	+	0.111536i
$991$	561.098	+	971.850i	0.566193	+	0.980676i	0.996938	+	0.0782016i	$0.0249178\pi$
$991$	561.098	+	971.850i	0.566193	+	0.980676i	−0.430744	+	0.902474i	$0.641749\pi$
$992$	−396.202	−	277.424i	−0.399397	−	0.279661i
$993$	−228.042	−	1184.92i	−0.229650	−	1.19328i
$994$	16.9524	+	46.5763i	0.0170547	+	0.0468575i
$995$	60.3323	+	247.766i	0.0606355	+	0.249011i
$996$	−66.0517	−	16.5989i	−0.0663170	−	0.0166656i
$997$	−18.0948	+	206.824i	−0.0181492	+	0.207447i	0.981706	+	0.190405i	$0.0609802\pi$
$997$	−18.0948	+	206.824i	−0.0181492	+	0.207447i	−0.999855	+	0.0170412i	$0.994575\pi$
$998$	254.512	+	254.512i	0.255022	+	0.255022i
$999$	−288.933	−	906.400i	−0.289222	−	0.907307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.r.a.103.16	yes	408
3.2	odd	2		405.3.s.a.118.19		408
5.2	odd	4	inner	135.3.r.a.22.16	✓	408
15.2	even	4		405.3.s.a.37.19		408
27.11	odd	18		405.3.s.a.208.19		408
27.16	even	9	inner	135.3.r.a.43.16	yes	408
135.92	even	36		405.3.s.a.127.19		408
135.97	odd	36	inner	135.3.r.a.97.16	yes	408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.16	✓	408	5.2	odd	4	inner
135.3.r.a.43.16	yes	408	27.16	even	9	inner
135.3.r.a.97.16	yes	408	135.97	odd	36	inner
135.3.r.a.103.16	yes	408	1.1	even	1	trivial
405.3.s.a.37.19		408	15.2	even	4
405.3.s.a.118.19		408	3.2	odd	2
405.3.s.a.127.19		408	135.92	even	36
405.3.s.a.208.19		408	27.11	odd	18

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0483933 + 0.553138i) q^{2} +(-2.99964 + 0.0467854i) q^{3} +(3.63561 + 0.641056i) q^{4} +(-3.45350 - 3.61571i) q^{5} +(0.119284 - 1.66148i) q^{6} +(-4.63063 - 3.24240i) q^{7} +(-1.10537 + 4.12530i) q^{8} +(8.99562 - 0.280678i) q^{9} +O(q^{10})\)	\(q+(-0.0483933 + 0.553138i) q^{2} +(-2.99964 + 0.0467854i) q^{3} +(3.63561 + 0.641056i) q^{4} +(-3.45350 - 3.61571i) q^{5} +(0.119284 - 1.66148i) q^{6} +(-4.63063 - 3.24240i) q^{7} +(-1.10537 + 4.12530i) q^{8} +(8.99562 - 0.280678i) q^{9} +(2.16711 - 1.73528i) q^{10} +(-11.8731 - 4.32147i) q^{11} +(-10.9355 - 1.75284i) q^{12} +(-2.19784 - 25.1215i) q^{13} +(2.01759 - 2.40447i) q^{14} +(10.5284 + 10.6842i) q^{15} +(11.6479 + 4.23948i) q^{16} +(-2.82813 - 10.5547i) q^{17} +(-0.280074 + 4.98941i) q^{18} +(9.55360 - 5.51578i) q^{19} +(-10.2377 - 15.3592i) q^{20} +(14.0419 + 9.50938i) q^{21} +(2.96495 - 6.35836i) q^{22} +(-6.26507 + 4.38685i) q^{23} +(3.12270 - 12.4261i) q^{24} +(-1.14673 + 24.9737i) q^{25} +14.0020 q^{26} +(-26.9705 + 1.26280i) q^{27} +(-14.7566 - 14.7566i) q^{28} +(-26.5603 - 31.6533i) q^{29} +(-6.41937 + 5.30661i) q^{30} +(-3.50453 + 19.8752i) q^{31} +(-10.1284 + 21.7204i) q^{32} +(35.8173 + 12.4073i) q^{33} +(5.97509 - 1.05357i) q^{34} +(4.26827 + 27.9406i) q^{35} +(32.8845 + 4.74626i) q^{36} +(9.11942 + 34.0341i) q^{37} +(2.58866 + 5.55139i) q^{38} +(7.76805 + 75.2524i) q^{39} +(18.7333 - 10.2500i) q^{40} +(33.5861 + 28.1821i) q^{41} +(-5.93954 + 7.30692i) q^{42} +(5.66037 + 12.1387i) q^{43} +(-40.3958 - 23.3225i) q^{44} +(-32.0812 - 31.5562i) q^{45} +(-2.12335 - 3.67775i) q^{46} +(16.1600 + 11.3154i) q^{47} +(-35.1377 - 12.1719i) q^{48} +(-5.82943 - 16.0162i) q^{49} +(-13.7584 - 1.84286i) q^{50} +(8.97717 + 31.5280i) q^{51} +(8.11377 - 92.7408i) q^{52} +(-8.21767 - 8.21767i) q^{53} +(0.606689 - 14.9795i) q^{54} +(25.3787 + 57.8540i) q^{55} +(18.4944 - 15.5187i) q^{56} +(-28.3993 + 16.9923i) q^{57} +(18.7940 - 13.1597i) q^{58} +(-4.71616 - 12.9575i) q^{59} +(31.4279 + 45.5930i) q^{60} +(-8.07405 - 45.7902i) q^{61} +(-10.8241 - 2.90032i) q^{62} +(-42.5655 - 27.8677i) q^{63} +(31.4147 + 18.1373i) q^{64} +(-83.2417 + 94.7036i) q^{65} +(-8.59630 + 19.2115i) q^{66} +(64.0900 - 5.60715i) q^{67} +(-3.51581 - 40.1859i) q^{68} +(18.5877 - 13.4521i) q^{69} +(-15.6616 + 1.00881i) q^{70} +(-7.89558 + 13.6755i) q^{71} +(-8.78561 + 37.4199i) q^{72} +(18.5472 - 69.2192i) q^{73} +(-19.2669 + 3.39728i) q^{74} +(2.27137 - 74.9656i) q^{75} +(38.2691 - 13.9288i) q^{76} +(40.9682 + 58.5086i) q^{77} +(-42.0009 + 0.655090i) q^{78} +(-81.2686 - 96.8521i) q^{79} +(-24.8971 - 56.7563i) q^{80} +(80.8424 - 5.04976i) q^{81} +(-17.2139 + 17.2139i) q^{82} +(6.12603 + 0.535958i) q^{83} +(44.9548 + 43.5740i) q^{84} +(-28.3959 + 46.6764i) q^{85} +(-6.98830 + 2.54353i) q^{86} +(81.1521 + 93.7058i) q^{87} +(30.9516 - 44.2035i) q^{88} +(149.362 - 86.2341i) q^{89} +(19.0075 - 16.2182i) q^{90} +(-71.2765 + 123.454i) q^{91} +(-25.5896 + 11.9326i) q^{92} +(9.58244 - 59.7822i) q^{93} +(-7.04100 + 8.39113i) q^{94} +(-52.9368 - 15.4944i) q^{95} +(29.3653 - 65.6273i) q^{96} +(-156.113 + 72.7967i) q^{97} +(9.14129 - 2.44940i) q^{98} +(-108.019 - 35.5418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8}+O(q^{10}) \) 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8	\( 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8} - 6 q^{10} - 60 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 6 q^{17} - 54 q^{18} - 300 q^{20} - 24 q^{21} - 12 q^{22} - 156 q^{23} + 6 q^{25} - 48 q^{26} + 180 q^{27} - 24 q^{28} + 276 q^{30} - 24 q^{31} + 72 q^{32} - 78 q^{33} + 156 q^{35} - 312 q^{36} - 6 q^{37} - 252 q^{38} - 108 q^{40} - 384 q^{41} - 528 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 210 q^{47} + 444 q^{48} + 276 q^{50} - 144 q^{51} - 60 q^{52} + 516 q^{53} - 24 q^{55} + 912 q^{56} + 168 q^{57} - 12 q^{58} + 864 q^{60} - 312 q^{61} - 6 q^{62} - 54 q^{63} + 420 q^{65} + 1224 q^{66} - 480 q^{67} - 540 q^{68} - 12 q^{70} - 12 q^{71} - 1548 q^{72} - 6 q^{73} - 852 q^{75} - 216 q^{76} - 876 q^{77} - 1362 q^{78} - 1644 q^{80} - 204 q^{81} - 24 q^{82} - 372 q^{83} - 12 q^{85} + 516 q^{86} + 540 q^{87} + 348 q^{88} - 384 q^{90} - 12 q^{91} + 2082 q^{92} - 1404 q^{93} + 198 q^{95} + 924 q^{96} + 600 q^{97} - 1032 q^{98}+O(q^{100}) \) 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8 - 6 * q^10 - 60 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 6 * q^17 - 54 * q^18 - 300 * q^20 - 24 * q^21 - 12 * q^22 - 156 * q^23 + 6 * q^25 - 48 * q^26 + 180 * q^27 - 24 * q^28 + 276 * q^30 - 24 * q^31 + 72 * q^32 - 78 * q^33 + 156 * q^35 - 312 * q^36 - 6 * q^37 - 252 * q^38 - 108 * q^40 - 384 * q^41 - 528 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 210 * q^47 + 444 * q^48 + 276 * q^50 - 144 * q^51 - 60 * q^52 + 516 * q^53 - 24 * q^55 + 912 * q^56 + 168 * q^57 - 12 * q^58 + 864 * q^60 - 312 * q^61 - 6 * q^62 - 54 * q^63 + 420 * q^65 + 1224 * q^66 - 480 * q^67 - 540 * q^68 - 12 * q^70 - 12 * q^71 - 1548 * q^72 - 6 * q^73 - 852 * q^75 - 216 * q^76 - 876 * q^77 - 1362 * q^78 - 1644 * q^80 - 204 * q^81 - 24 * q^82 - 372 * q^83 - 12 * q^85 + 516 * q^86 + 540 * q^87 + 348 * q^88 - 384 * q^90 - 12 * q^91 + 2082 * q^92 - 1404 * q^93 + 198 * q^95 + 924 * q^96 + 600 * q^97 - 1032 * q^98

Introduction

L-functions

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